Finite Group Databasebeta

← #29888879

Subgroups — #29888879

Order 15616.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454114C211yesmaximal, characteristic, complemented
2#21454105C211yesmaximal, characteristic, complemented
3#21453656C211yesmaximal, characteristic, complemented
4#21453201C211yesmaximal, characteristic, complemented
5#21453154C211yesmaximal, characteristic, complemented
6#21453067C211yesmaximal, characteristic, complemented
7#21452875C211yesmaximal, characteristic, complemented
8#21452820C211yesmaximal, characteristic, complemented
9#21452738C211yesmaximal, characteristic, complemented
10#21452630C211yesmaximal, characteristic, complemented
11#21452589C211yesmaximal, characteristic, complemented
12#21452556C211yesmaximal, characteristic, complemented
13#21452493C211yesmaximal, characteristic, complemented
14#21452427C211yesmaximal, characteristic, complemented
15#21452414C211yesmaximal, characteristic, complemented
16#21452303C211yesmaximal, characteristic, complemented
17#21452228C211yesmaximal, characteristic, complemented
18#21452067C211yesmaximal, characteristic, complemented
19#21451630C211yesmaximal, characteristic, complemented
20#21451597C211yesmaximal, characteristic, complemented
21#21451001C211yesmaximal, characteristic, complemented
22#21450831C211yesmaximal, characteristic, complemented
23#21450065C211yesmaximal, characteristic, complemented
24#21450065C211yesmaximal, characteristic, complemented
25#21449945C211yesmaximal, characteristic, complemented
26#21449945C211yesmaximal, characteristic, complemented
27#21449471C211yesmaximal, characteristic, complemented
28#21449176C211yesmaximal, characteristic
29#21448453C211yesmaximal, characteristic, complemented
30C2×#16839640C211yesmaximal, characteristic, complemented
31C61×#2329C211yesmaximal, characteristic, complemented
32C23×D244C2211yescharacteristic
33C23×C4×D61C2211yescharacteristic
34C2×#14519771C2211yescharacteristic, complemented
35C2×#14519771C2211yescharacteristic, complemented
36C2×#14519766C2211yescharacteristic
37C2×#14519766C2211yescharacteristic
38C2×#14519765C2211yescharacteristic, complemented
39C2×#14519765C2211yescharacteristic, complemented
40C2×#14519762C2211yescharacteristic, complemented
41C2×#14519762C2211yescharacteristic, complemented
42C2×#14519755C2211yescharacteristic, complemented
43C2×#14519755C2211yescharacteristic, complemented
44C2×#14519754C2211yescharacteristic
45C2×#14519754C2211yescharacteristic
46C2×#14519752C2211yescharacteristic
47C2×#14519752C2211yescharacteristic
48C2×#14519747C2211yescharacteristic
49C2×#14519747C2211yescharacteristic
50C2×C4×C22⋊D61C2211yescharacteristic
51C22×#11758198C2211yescharacteristic
52C22×#11758198C2211yescharacteristic
53C22×#11758198C2211yescharacteristic
54#16839700C2211yescharacteristic, complemented
55#16839697C2211yescharacteristic, complemented
56#16839697C2211yescharacteristic, complemented
57#16839697C2211yescharacteristic, complemented
58#16839695C2211yescharacteristic, complemented
59#16839695C2211yescharacteristic, complemented
60#16839691C2211yescharacteristic, complemented
61#16839691C2211yescharacteristic, complemented
62#16839691C2211yescharacteristic, complemented
63#16839691C2211yescharacteristic, complemented
64#16839691C2211yescharacteristic, complemented
65#16839691C2211yescharacteristic, complemented
66#16839691C2211yescharacteristic, complemented
67#16839691C2211yescharacteristic, complemented
68#16839689C2211yescharacteristic, complemented
69#16839689C2211yescharacteristic, complemented
70#16839688C2211yescharacteristic, complemented
71#16839688C2211yescharacteristic, complemented
72#16839686C2211yescharacteristic, complemented
73#16839686C2211yescharacteristic, complemented
74#16839686C2211yescharacteristic, complemented
75#16839686C2211yescharacteristic, complemented
76#16839684C2211yescharacteristic, complemented
77#16839684C2211yescharacteristic, complemented
78#16839682C2211yescharacteristic, complemented
79#16839682C2211yescharacteristic, complemented
80#16839681C2211yescharacteristic, complemented
81#16839680C2211yescharacteristic
82#16839680C2211yescharacteristic
83#16839680C2211yescharacteristic, complemented
84#16839680C2211yescharacteristic, complemented
85#16839680C2211yescharacteristic, complemented
86#16839680C2211yescharacteristic, complemented
87#16839680C2211yescharacteristic, complemented
88#16839680C2211yescharacteristic, complemented
89#16839679C2211yescharacteristic
90#16839679C2211yescharacteristic
91#16839679C2211yescharacteristic
92#16839679C2211yescharacteristic
93#16839679C2211yescharacteristic, complemented
94#16839679C2211yescharacteristic, complemented
95#16839675C2211yescharacteristic, complemented
96#16839675C2211yescharacteristic, complemented
97#16839675C2211yescharacteristic, complemented
98#16839675C2211yescharacteristic, complemented
99#16839673C2211yescharacteristic, complemented
100#16839672C2211yescharacteristic
101#16839672C2211yescharacteristic
102#16839666C2211yescharacteristic, complemented
103#16839666C2211yescharacteristic, complemented
104#16839664C2211yescharacteristic, complemented
105#16839664C2211yescharacteristic, complemented
106#16839663C2211yescharacteristic
107#16839663C2211yescharacteristic
108#16839663C2211yescharacteristic
109#16839663C2211yescharacteristic
110#16839659C2211yescharacteristic, complemented
111#16839659C2211yescharacteristic, complemented
112#16839653C2211yescharacteristic, complemented
113#16839653C2211yescharacteristic, complemented
114#16839653C2211yescharacteristic, complemented
115#16839653C2211yescharacteristic, complemented
116#16839653C2211yescharacteristic, complemented
117#16839653C2211yescharacteristic, complemented
118#16839653C2211yescharacteristic, complemented
119#16839653C2211yescharacteristic, complemented
120#16839653C2211yescharacteristic, complemented
121#16839653C2211yescharacteristic, complemented
122#16839651C2211yescharacteristic, complemented
123#16839651C2211yescharacteristic, complemented
124#16839644C2211yescharacteristic, complemented
125#16839644C2211yescharacteristic, complemented
126#16839643C2211yescharacteristic, complemented
127#16839643C2211yescharacteristic, complemented
128#16839641C2211yescharacteristic
129#16839641C2211yescharacteristic
130#16839640C2211yescharacteristic
131#16839640C2211yescharacteristic
132#16839640C2211yescharacteristic
133#16839640C2211yescharacteristic
134#16839640C2211yescharacteristic
135#16839640C2211yescharacteristic
136#16839640C2211yescharacteristic
137#16839640C2211yescharacteristic
138#16839640C2211yescharacteristic, complemented
139#16839640C2211yescharacteristic, complemented
140#16839639C2211yescharacteristic
141#16839639C2211yescharacteristic
142#16839636C2211yescharacteristic, complemented
143#16839636C2211yescharacteristic, complemented
144#16839635C2211yescharacteristic
145#16839635C2211yescharacteristic
146#16839634C2211yescharacteristic
147#16839634C2211yescharacteristic
148#16839633C2211yescharacteristic, complemented
149#16839633C2211yescharacteristic, complemented
150#16839633C2211yescharacteristic, complemented
151#16839633C2211yescharacteristic, complemented
152#16839633C2211yescharacteristic, complemented
153#16839633C2211yescharacteristic, complemented
154#16839629C2211yescharacteristic, complemented
155#16839626C2211yescharacteristic, complemented
156#16839624C2211yescharacteristic, complemented
157#16839624C2211yescharacteristic, complemented
158#16839624C2211yescharacteristic, complemented
159#16839621C2211yescharacteristic, complemented
160#16839621C2211yescharacteristic, complemented
161#16839621C2211yescharacteristic, complemented
162#16839620C2211yescharacteristic
163#16839620C2211yescharacteristic
164#16839617C2211yescharacteristic
165#16839617C2211yescharacteristic
166#16839617C2211yescharacteristic
167#16839617C2211yescharacteristic
168#16839617C2211yescharacteristic
169#16839617C2211yescharacteristic
170C4×C22⋊Dic61C2211yescharacteristic
171C2×#14519684C2211yescharacteristic
172C2×C22⋊Q8×C61C2211yescharacteristic
173C61×#391C2211yescharacteristic, complemented
174C61×#391C2211yescharacteristic, complemented
175C61×#389C2211yescharacteristic, complemented
176C61×#389C2211yescharacteristic, complemented
177C61×#387C2211yescharacteristic, complemented
178C61×#387C2211yescharacteristic, complemented
179C61×#387C2211yescharacteristic, complemented
180C61×#387C2211yescharacteristic, complemented
181C61×#385C2211yescharacteristic
182C61×#385C2211yescharacteristic
183C61×#380C2211yescharacteristic
184C4×C22⋊C4×C61C2211yescharacteristic
185C4×C22⋊C4×C61C2211yescharacteristic
186C2×#95×C61C2211yescharacteristic
187C24×D61C2311yescharacteristic
188C24×D61C2311yescharacteristic
189C22×Dic122C2311yescharacteristic
190C22×Dic122C2311yescharacteristic
191C22×D244—24no—
192C22×D244—42no—
193C22×D244—42no—
194C22×D244C2311yescharacteristic
195C22×D244C2311yescharacteristic
196C22×D244C2311yescharacteristic
197C22×D244C2311yescharacteristic
198C22×D244C2311yescharacteristic
199C22×D244C2311yescharacteristic
200C22×D244C2311yescharacteristic
201C22×D244C2311yescharacteristic
202C22×C22⋊D61C2311yescharacteristic
203C23×Dic61C2311yescharacteristic
204C23×Dic61C2311yescharacteristic
205C22×C4×D61—42no—
206C22×C4×D61—42no—
207C22×C4×D61—42no—
208C22×C4×D61C2311yescharacteristic
209C22×C4×D61C2311yescharacteristic
210C22×C4×D61C2311yescharacteristic
211C22×C4×D61C2311yescharacteristic
212C22×C4×D61C2311yescharacteristic
213#14519771—42no—
214#14519771—42no—
215#14519766—42no—
216#14519766—42no—
217#14519765—42no—
218#14519765—42no—
219#14519762—42no—
220#14519762—42no—
221#14519755—42no—
222#14519755—42no—
223#14519754—42no—
224#14519754—42no—
225#14519752—42no—
226#14519752—42no—
227#14519747—42no—
228#14519747—42no—
229C4×C22⋊D61—24no—
230C2×C4⋊Dic61C2311yescharacteristic
231C2×C4⋊Dic61C2311yescharacteristic
232C2×#11758196C2311yescharacteristic
233C2×#11758196C2311yescharacteristic
234C2×#11758196C2311yescharacteristic
235C2×#11758196C2311yescharacteristic
236C2×#11758196C2311yescharacteristic
237C2×#11758196C2311yescharacteristic
238C2×#11758196C2311yescharacteristic
239C2×#11758196C2311yescharacteristic
240C2×#11758196C2311yescharacteristic
241C2×#11758196C2311yescharacteristic
242C2×#11758196C2311yescharacteristic
243C2×#11758196C2311yescharacteristic
244C2×#11758196C2311yescharacteristic
245C2×#11758196C2311yescharacteristic
246C2×#11758196C2311yescharacteristic
247C2×#11758196C2311yescharacteristic
248C2×#11758196C2311yescharacteristic
249C2×C22⋊Dic61C2311yescharacteristic
250C2×C22⋊Dic61C2311yescharacteristic
251C2×C22⋊Dic61C2311yescharacteristic
252C2×#11758198—42no—
253C2×#11758198—42no—
254C2×#11758198—42no—
255C2×#11758198C2311yescharacteristic
256C2×#11758198C2311yescharacteristic
257C2×#11758198C2311yescharacteristic
258C2×#11758198C2311yescharacteristic
259C2×#11758198C2311yescharacteristic
260C2×#11758198C2311yescharacteristic
261C2×#11758198C2311yescharacteristic
262C2×#11758198C2311yescharacteristic
263C2×#11758198C2311yescharacteristic
264C2×#11758198C2311yescharacteristic
265C2×#11758198C2311yescharacteristic
266C2×#11758198C2311yescharacteristic
267C2×#11758198C2311yescharacteristic
268C2×#11758198C2311yescharacteristic
269C2×#11758198C2311yescharacteristic
270C2×#11758198C2311yescharacteristic
271C2×#11758198C2311yescharacteristic
272C2×#11758198C2311yescharacteristic
273C2×#11758198C2311yescharacteristic
274C2×#11758198C2311yescharacteristic
275C2×#11758198C2311yescharacteristic
276C2×#11758198C2311yescharacteristic
277C2×#11758198C2311yescharacteristic
278C2×#11758198C2311yescharacteristic
279C2×#11758198C2311yescharacteristic
280C2×#11758198C2311yescharacteristic
281C2×#11758198C2311yescharacteristic
282C2×#11758198C2311yescharacteristic
283C2×#11758198C2311yescharacteristic
284C2×#11758198C2311yescharacteristic
285C2×#11758198C2311yescharacteristic
286C2×#11758198C2311yescharacteristic
287C2×#11758198C2311yescharacteristic
288C2×#11758198C2311yescharacteristic
289C2×#11758198C2311yescharacteristic
290C2×#11758198C2311yescharacteristic
291C2×#11758198C2311yescharacteristic
292C2×#11758198C2311yescharacteristic
293C2×#11758198C2311yescharacteristic
294C2×#11758198C2311yescharacteristic
295C2×#11758198C2311yescharacteristic
296C2×#11758198C2311yescharacteristic
297C2×#11758198C2311yescharacteristic
298C2×#11758198C2311yescharacteristic
299C2×#11758198C2311yescharacteristic
300C2×#11758198C2311yescharacteristic
301C2×#11758198C2311yescharacteristic
302C2×#11758198C2311yescharacteristic
303C2×#11758198C2311yescharacteristic
304C2×C4×Dic61C2311yescharacteristic
305C2×C4×Dic61C2311yescharacteristic
306C2×C4×Dic61C2311yescharacteristic
307#14519684C2311yescharacteristic
308#14519684C2311yescharacteristic
309#14519684C2311yescharacteristic
310#14519684C2311yescharacteristic
311#14519684C2311yescharacteristic
312#14519684C2311yescharacteristic
313#14519684C2311yescharacteristic
314#14519684C2311yescharacteristic
315#14519684C2311yescharacteristic
316#14519684C2311yescharacteristic
317#14519684C2311yescharacteristic
318#14519684C2311yescharacteristic
319#14519684C2311yescharacteristic
320#14519684C2311yescharacteristic
321#14519684C2311yescharacteristic
322#14519684C2311yescharacteristic
323#14519684C2311yescharacteristic
324#14519684C2311yescharacteristic
325#14519684C2311yescharacteristic
326#14519684C2311yescharacteristic
327#14519684C2311yescharacteristic
328#14519684C2311yescharacteristic
329#14519684C2311yescharacteristic
330#14519684C2311yescharacteristic
331#14519684C2311yescharacteristic
332#14519684C2311yescharacteristic
333C22×Q8×C61C2311yescharacteristic
334C23×C4×C61C2311yescharacteristic
335C23×C4×C61C2311yescharacteristic
336C23×C4×C61C2311yescharacteristic
337C22⋊Q8×C61—24no—
338C2×C4⋊C4×C61C2311yescharacteristic
339C2×C4⋊C4×C61C2311yescharacteristic
340C2×C4⋊C4×C61C2311yescharacteristic
341C2×C4⋊C4×C61C2311yescharacteristic
342C2×C4⋊C4×C61C2311yescharacteristic
343C2×C4⋊C4×C61C2311yescharacteristic
344C2×C4⋊C4×C61C2311yescharacteristic
345C2×C4⋊C4×C61C2311yescharacteristic
346C2×C4⋊C4×C61C2311yescharacteristic
347C2×C22⋊C4×C61C2311yescharacteristic
348C2×C22⋊C4×C61C2311yescharacteristic
349C2×C22⋊C4×C61C2311yescharacteristic
350C2×C22⋊C4×C61C2311yescharacteristic
351C2×C42×C61C2311yescharacteristic
352C2×C42×C61C2311yescharacteristic
353C2×C42×C61C2311yescharacteristic
354C2×C42×C61C2311yescharacteristic
355#95×C61C2311yescharacteristic
356#95×C61C2311yescharacteristic
357#95×C61C2311yescharacteristic
358#95×C61C2311yescharacteristic
359#95×C61C2311yescharacteristic
360#95×C61C2311yescharacteristic
361#95×C61C2311yescharacteristic
362#95×C61C2311yescharacteristic
363#95×C61C2311yescharacteristic
364#95×C61C2311yescharacteristic
365#95×C61C2311yescharacteristic
366#95×C61C2311yescharacteristic
367#95×C61C2311yescharacteristic
368#95×C61C2311yescharacteristic
369C24×C61C2411yescharacteristic
370C23×D61—22no—
371C23×D61—22no—
372C23×D61—22no—
373C23×D61—22no—
374C23×D61—22no—
375C23×D61—22no—
376C23×D61—22no—
377C23×D61—22no—
378C23×D61—41no—
379C23×D61—41no—
380C23×D61—41no—
381C23×D61—41no—
382C23×D61—41no—
383C23×D61—41no—
384C23×D61C2411yescharacteristic
385C23×D61C2411yescharacteristic
386C23×D61C2411yescharacteristic
387C23×D61C2411yescharacteristic
388C23×D61C2411yescharacteristic
389C2×Q8×C61—22no—
390C2×Q8×C61—41no—
391C2×Q8×C61—41no—
392C22×C4×C61—22no—
393C22×C4×C61—22no—
394C22×C4×C61—41no—
395C22×C4×C61—41no—
396C22×C4×C61—41no—
397C22×C4×C61—41no—
398C22×C4×C61—41no—
399C22×C4×C61—41no—
400C22×C4×C61#4114yes—
401C22×C4×C61C2411yescharacteristic
402C22×C4×C61C2411yescharacteristic
403C22×C4×C61C2411yescharacteristic
404C22×C4×C61C2411yescharacteristic
405C22×C4×C61C2411yescharacteristic
406C22×C4×C61C2411yescharacteristic
407C22×C4×C61C2411yescharacteristic
408C22×C4×C61C2411yescharacteristic
409C22×C4×C61C2411yescharacteristic
410C22×C4×C61C2411yescharacteristic
411C22×C4×C61C2411yescharacteristic
412C22×C4×C61C2411yescharacteristic
413C22×C4×C61C2411yescharacteristic
414C22×C4×C61C2411yescharacteristic
415C2×C22⋊D61—22no—
416C2×C22⋊D61—22no—
417C2×C22⋊D61—22no—
418C22×Dic61—22no—
419C22×Dic61—22no—
420C22×Dic61—22no—
421C22×Dic61—41no—
422C22×Dic61—41no—
423C22×Dic61—41no—
424C22×Dic61C2411yescharacteristic
425C22×Dic61C2411yescharacteristic
426C22×Dic61C2411yescharacteristic
427C22×Dic61C2411yescharacteristic
428C22×Dic61C2411yescharacteristic
429C22×Dic61C2411yescharacteristic
430C22×Dic61C2411yescharacteristic
431C22×Dic61C2411yescharacteristic
432C22×Dic61C2411yescharacteristic
433C22×Dic61C2411yescharacteristic
434C22×Dic61C2411yescharacteristic
435C2×D244—22no—
436C2×D244—22no—
437C2×D244—22no—
438C2×D244—22no—
439C2×D244—22no—
440C2×D244—22no—
441C2×D244—22no—
442C2×D244—22no—
443C2×D244—22no—
444C2×D244—22no—
445C2×D244—41no—
446C2×D244—41no—
447C2×D244—41no—
448C2×D244—41no—
449C2×D244—416no—
450C2×D244—41no—
451C2×D244—41no—
452C2×D244—41no—
453C2×D244—41no—
454C2×D244—41no—
455C2×D244—41no—
456C2×D244—41no—
457C2×D244—41no—
458C2×D244—41no—
459C2×D244—41no—
460C2×C4×D61—22no—
461C2×C4×D61—22no—
462C2×C4×D61—22no—
463C2×C4×D61—22no—
464C2×C4×D61—22no—
465C2×C4×D61—41no—
466C2×C4×D61—41no—
467C2×C4×D61—41no—
468C2×C4×D61—41no—
469C2×C4×D61—41no—
470C2×C4×D61—41no—
471C2×C4×D61—41no—
472C2×C4×D61—41no—
473C2×C4×D61—416no—
474C2×C4×D61—41no—
475C2×C4×D61—41no—
476C2×Dic122—22no—
477C2×Dic122—41no—
478C2×Dic122—41no—
479C2×Dic122—41no—
480C2×Dic122—41no—
481C2×Dic122—41no—
482C4⋊C4×C61—22no—
483C4⋊C4×C61—22no—
484C4⋊C4×C61—22no—
485C4⋊C4×C61—41no—
486C4⋊C4×C61—41no—
487C4⋊C4×C61—41no—
488C4⋊C4×C61—41no—
489C4⋊C4×C61—41no—
490C4⋊C4×C61—41no—
491C22⋊C4×C61—22no—
492C22⋊C4×C61—22no—
493C22⋊C4×C61—22no—
494C22⋊C4×C61—22no—
495C42×C61—41no—
496C42×C61—41no—
497C42×C61—41no—
498C42×C61—41no—
499C22⋊Dic61—22no—
500C22⋊Dic61—22no—
501C22⋊Dic61—22no—
502#11758198—22no—
503#11758198—22no—
504#11758198—22no—
505#11758198—22no—
506#11758198—22no—
507#11758198—22no—
508#11758198—22no—
509#11758198—22no—
510#11758198—22no—
511#11758198—22no—
512#11758198—22no—
513#11758198—22no—
514#11758198—41no—
515#11758198—41no—
516#11758198—41no—
517#11758198—41no—
518#11758198—41no—
519#11758198—41no—
520#11758198—41no—
521#11758198—41no—
522#11758198—41no—
523#11758198—41no—
524#11758198—41no—
525#11758198—41no—
526#11758198—41no—
527#11758198—41no—
528#11758198—41no—
529#11758198—41no—
530#11758198—41no—
531#11758198—41no—
532#11758198—41no—
533#11758198—41no—
534#11758198—41no—
535#11758198—41no—
536#11758198—41no—
537#11758198—41no—
538#11758198—41no—
539#11758198—41no—
540#11758198—41no—
541#11758198—41no—
542#11758198—41no—
543#11758198—41no—
544#11758198—41no—
545#11758198—41no—
546#11758198—41no—
547#11758198—41no—
548#11758198—41no—
549#11758198—41no—
550#11758198—41no—
551C4⋊Dic61—41no—
552C4⋊Dic61—41no—
553#11758196—22no—
554#11758196—22no—
555#11758196—22no—
556#11758196—41no—
557#11758196—41no—
558#11758196—41no—
559#11758196—41no—
560#11758196—41no—
561#11758196—41no—
562#11758196—41no—
563#11758196—41no—
564#11758196—41no—
565#11758196—41no—
566#11758196—41no—
567#11758196—41no—
568#11758196—41no—
569#11758196—41no—
570C4×Dic61—22no—
571C4×Dic61—41no—
572C4×Dic61—41no—
573C23×C61—21no—
574C23×C61—21no—
575C23×C61—21no—
576C23×C61—21no—
577C23×C61C2×#4112yes—
578C23×C61H(5,𝔽2)12yes—
579C23×C612−1+412yes—
580C23×C61C2511yescharacteristic
581C22×D61—28no—
582C22×D61—21no—
583C22×D61—21no—
584C22×D61—21no—
585C22×D61—21no—
586C22×D61—21no—
587C22×D61—21no—
588C22×D61—21no—
589C22×D61—21no—
590C22×D61—21no—
591C22×D61—21no—
592C22×D61—21no—
593C22×D61—21no—
594C22×D61—21no—
595C22×D61—21no—
596C22×D61—21no—
597C22×D61—21no—
598C22×D61—21no—
599C22×D61—21no—
600C22×D61—21no—
601C22×D61—21no—
602C22×D61—21no—
603C22×D61—21no—
604C22×D61—21no—
605C22×D61—21no—
606C22×D61—21no—
607C22×D61—21no—
608C22×D61—21no—
609C22×D61—21no—
610C22×D61—21no—
611C22×D61—21no—
612C22×D61—21no—
613C22×D61—21no—
614C22×D61—21no—
615C22×D61—44no—
616C22×D61—44no—
617C22×D61—44no—
618C22×D61—44no—
619C22×D61—44no—
620C22×D61—44no—
621C22×D61—44no—
622C22×D61—44no—
623C22×D61—44no—
624C22×D61—82no—
625C22×D61—82no—
626C22×D61—82no—
627C22×D61—82no—
628C22×D61H(5,𝔽2)12yes—
629C22×D61H(5,𝔽2)12yes—
630Q8×C61—82no—
631C2×C4×C61—21no—
632C2×C4×C61—21no—
633C2×C4×C61—21no—
634C2×C4×C61—21no—
635C2×C4×C61—21no—
636C2×C4×C61—21no—
637C2×C4×C61—21no—
638C2×C4×C61—21no—
639C2×C4×C61—21no—
640C2×C4×C61—21no—
641C2×C4×C61—21no—
642C2×C4×C61—21no—
643C2×C4×C61—21no—
644C2×C4×C61—21no—
645C2×C4×C61—21no—
646C2×C4×C61—21no—
647C2×C4×C61—21no—
648C2×C4×C61—21no—
649C2×C4×C61—21no—
650C2×C4×C61—21no—
651C2×C4×C61—21no—
652C2×C4×C61—21no—
653C2×C4×C61—21no—
654C2×C4×C61—21no—
655C2×C4×C61—21no—
656C2×C4×C61—21no—
657C2×C4×C61—21no—
658C2×C4×C61—21no—
659C2×C4×C61—21no—
660C2×C4×C61—21no—
661C2×C4×C61—21no—
662C2×C4×C61—21no—
663C2×C4×C61—21no—
664C2×C4×C61—21no—
665C2×C4×C61—21no—
666C2×C4×C61—21no—
667C2×C4×C61—21no—
668C2×C4×C61—21no—
669C2×C4×C61—21no—
670C2×C4×C61—21no—
671C2×C4×C61—44no—
672C2×C4×C61—44no—
673C2×C4×C61—82no—
674C2×C4×C61C2×#4112yes—
675C2×C4×C61C2×#4112yes—
676C22⋊D61—44no—
677C2×Dic61—21no—
678C2×Dic61—21no—
679C2×Dic61—21no—
680C2×Dic61—21no—
681C2×Dic61—21no—
682C2×Dic61—21no—
683C2×Dic61—21no—
684C2×Dic61—21no—
685C2×Dic61—21no—
686C2×Dic61—21no—
687C2×Dic61—21no—
688C2×Dic61—21no—
689C2×Dic61—21no—
690C2×Dic61—21no—
691C2×Dic61—21no—
692C2×Dic61—21no—
693C2×Dic61—21no—
694C2×Dic61—21no—
695C2×Dic61—21no—
696C2×Dic61—21no—
697C2×Dic61—21no—
698C2×Dic61—21no—
699C2×Dic61—21no—
700C2×Dic61—21no—
701C2×Dic61—21no—
702C2×Dic61—21no—
703C2×Dic61—21no—
704C2×Dic61—21no—
705C2×Dic61—21no—
706C2×Dic61—21no—
707C2×Dic61—21no—
708C2×Dic61—21no—
709C2×Dic61—44no—
710C2×Dic61—82no—
711C2×Dic61H(5,𝔽2)12yes—
712D244—44no—
713D244—44no—
714D244—44no—
715D244—44no—
716D244—82no—
717D244—82no—
718D244—82no—
719D244—82no—
720C4×D61—44no—
721C4×D61—44no—
722C4×D61—44no—
723C4×D61—44no—
724C4×D61—82no—
725Dic122—82no—
726Dic122—82no—
727#36793—611nomaximal, Sylow
728C22×C61—22no—
729C22×C61—22no—
730C22×C61—22no—
731C22×C61—22no—
732C22×C61—22no—
733C22×C61—22no—
734C22×C61#54214yes—
735C22×C61C22×#4111yescharacteristic
736C22×C61C2×H(5,𝔽2)11yescharacteristic
737C22×C61C2×H(5,𝔽2)11yescharacteristic
738C22×C61C2×H(5,𝔽2)11yescharacteristic
739C22×C61C2×H(5,𝔽2)11yescharacteristic
740C22×C61C2×2−1+411yescharacteristic
741C22×C61#58511yescharacteristic
742C2×D61—22no—
743C2×D61—22no—
744C2×D61—22no—
745C2×D61—22no—
746C2×D61—22no—
747C2×D61—22no—
748C2×D61—416no—
749C2×D61—41no—
750C2×D61—41no—
751C2×D61—41no—
752C2×D61—41no—
753C2×D61—41no—
754C2×D61—41no—
755C2×D61—41no—
756C2×D61—41no—
757C2×D61—41no—
758C2×D61—41no—
759C2×D61—41no—
760C2×D61—41no—
761C2×D61—41no—
762C2×D61—41no—
763C2×D61—41no—
764C2×D61—41no—
765C2×D61—41no—
766C2×D61—41no—
767C2×D61—41no—
768C2×D61—41no—
769C2×D61—41no—
770C2×D61—41no—
771C2×D61—41no—
772C2×D61—41no—
773C2×D61—41no—
774C2×D61—41no—
775C2×D61—41no—
776C2×D61—41no—
777C2×D61—41no—
778C2×D61—88no—
779C4×C61—22no—
780C4×C61—22no—
781C4×C61—41no—
782C4×C61—41no—
783C4×C61—41no—
784C4×C61—41no—
785C4×C61—41no—
786C4×C61—41no—
787C4×C61—41no—
788C4×C61—41no—
789C4×C61—41no—
790C4×C61—41no—
791C4×C61—41no—
792C4×C61—41no—
793Dic61—22no—
794Dic61—41no—
795Dic61—41no—
796Dic61—41no—
797Dic61—41no—
798Dic61—41no—
799Dic61—41no—
800Dic61—41no—
801Dic61—41no—
802Dic61—41no—
803Dic61—41no—
804#2849—611no—
805#2848—611no—
806#2796—611no—
807#2761—611no—
808#2757—611no—
809#2751—611no—
810#2737—611no—
811#2730—611no—
812#2723—611no—
813#2715—611no—
814#2712—611no—
815#2710—611no—
816#2705—611no—
817#2701—611no—
818#2700—611no—
819#2691—611no—
820#2686—611no—
821#2672—611no—
822#2626—611no—
823#2622—611no—
824#2564—611no—
825#2549—611no—
826#2480—611no—
827#2480—611no—
828#2472—611no—
829#2472—611no—
830#2435—611no—
831#2408—611no—
832#2329D6111yescharacteristic, complemented
833#2318—611no—
834C2×#386—611no—
835C2×C61—24no—
836C2×C61C2×#54211yescharacteristic
837C2×C61#349011yescharacteristic
838C2×C61#350611yescharacteristic
839C2×C61#353211yescharacteristic
840C2×C61#353411yescharacteristic
841C2×C61#353511yescharacteristic
842C2×C61#353611yescharacteristic
843D61—42no—
844D61—42no—
845D61—81no—
846D61—81no—
847D61—81no—
848C23×D4—611no—
849C24×C4—611no—
850C2×#126—611no—
851C2×#126—611no—
852C2×#124—611no—
853C2×#124—611no—
854C2×#124—611no—
855C2×#124—611no—
856C2×#123—611no—
857C2×#123—611no—
858C2×C22⋊Q8—611no—
859C2×C22⋊Q8—611no—
860C2×C22⋊Q8—611no—
861C2×C22⋊Q8—611no—
862C2×C22⋊Q8C2×D6111yescharacteristic
863C2×#121—611no—
864C2×#121—611no—
865C2×#120—611no—
866C2×#120—611no—
867C2×C4×D4—611no—
868C22×C22⋊C4—611no—
869C22×C22⋊C4—611no—
870C22×C22⋊C4—611no—
871#400—611no—
872#399—611no—
873#399—611no—
874#399—611no—
875#398—611no—
876#398—611no—
877#397—611no—
878#397—611no—
879#397—611no—
880#397—611no—
881#397—611no—
882#397—611no—
883#397—611no—
884#397—611no—
885#397—611no—
886#397—611no—
887#397—611no—
888#397—611no—
889#396—611no—
890#396—611no—
891#396—611no—
892#396—611no—
893#396—611no—
894#396—611no—
895#395—611no—
896#395—611no—
897#395—611no—
898#394—611no—
899#394—611no—
900#394—611no—
901#394—611no—
902#394—611no—
903#394—611no—
904#394—611no—
905#394—611no—
906#394—611no—
907#394—611no—
908#394—611no—
909#394—611no—
910#394—611no—
911#394—611no—
912#393—611no—
913#393—611no—
914#393—611no—
915#393—611no—
916#393—611no—
917#392—611no—
918#392—611no—
919#391—611no—
920#391—611no—
921#391C2×D6111yescharacteristic, complemented
922#391C2×D6111yescharacteristic, complemented
923#390—611no—
924#390—611no—
925#390—611no—
926#390—611no—
927#390—611no—
928#390—611no—
929#389—611no—
930#389—611no—
931#389C2×D6111yescharacteristic, complemented
932#389C2×D6111yescharacteristic, complemented
933#388—611no—
934#388—611no—
935#388—611no—
936#388—611no—
937#388—611no—
938#388—611no—
939#388—611no—
940#388—611no—
941#388—611no—
942#388—611no—
943#388—611no—
944#388—611no—
945#387—611no—
946#387—611no—
947#387—611no—
948#387—611no—
949#387C2×D6111yescharacteristic, complemented
950#387C2×D6111yescharacteristic, complemented
951#387C2×D6111yescharacteristic, complemented
952#387C2×D6111yescharacteristic, complemented
953#386—611no—
954#386—611no—
955#386—611no—
956#386—611no—
957#386—611no—
958#386—611no—
959#386—611no—
960#386—611no—
961#386—611no—
962#386—611no—
963#386—611no—
964#386—611no—
965#386—611no—
966#386—611no—
967#385—611no—
968#385—611no—
969#385—611no—
970#385—611no—
971#385—611no—
972#385—611no—
973#385—611no—
974#385—611no—
975#385—611no—
976#385—611no—
977#385—611no—
978#385—611no—
979#385C2×D6111yescharacteristic
980#385C2×D6111yescharacteristic
981#383—611no—
982#382—611no—
983#381—611no—
984#381—611no—
985#381—611no—
986#380—611no—
987#380—611no—
988#380—611no—
989#380—611no—
990#380—611no—
991#380C2×D6111yescharacteristic
992#379—611no—
993#379—611no—
994#379—611no—
995#379—611no—
996#379—611no—
997#379—611no—
998C4×C22⋊C4—611no—
999C4×C22⋊C4C2×D6111yescharacteristic
1000C4×C22⋊C4C2×D6111yescharacteristic
1001C2×#95—611no—
1002C2×#95C2×D6111yescharacteristic
1003C61#3679311yescharacteristic, complemented, Sylow
1004C25—611no—
1005C25—611no—
1006C22×Q8—611no—
1007C22×Q8—611no—
1008C22×Q8C22×D6111yescharacteristic
1009C22×D4—611no—
1010C22×D4—611no—
1011C22×D4—611no—
1012C22×D4—611no—
1013C22×D4—611no—
1014C22×D4—611no—
1015C22×D4—611no—
1016C22×D4—611no—
1017C22×D4—611no—
1018C22×D4—1224no—
1019C22×D4—2442no—
1020C22×D4—2442no—
1021C23×C4—611no—
1022C23×C4—611no—
1023C23×C4—611no—
1024C23×C4—611no—
1025C23×C4—611no—
1026C23×C4—611no—
1027C23×C4—611no—
1028C23×C4—2442no—
1029C23×C4—2442no—
1030C23×C4—2442no—
1031C23×C4C22×D6111yescharacteristic
1032C23×C4C22×D6111yescharacteristic
1033C23×C4C22×D6111yescharacteristic
1034#126—2442no—
1035#126—2442no—
1036#124—2442no—
1037#124—2442no—
1038#124—2442no—
1039#124—2442no—
1040#123—2442no—
1041#123—2442no—
1042C22⋊Q8—24no—
1043C22⋊Q8—2442no—
1044C22⋊Q8—2442no—
1045C22⋊Q8—2442no—
1046C22⋊Q8—2442no—
1047#121—2442no—
1048#121—2442no—
1049#120—2442no—
1050#120—2442no—
1051C4×D4—1224no—
1052C2×C4⋊C4—611no—
1053C2×C4⋊C4—611no—
1054C2×C4⋊C4—611no—
1055C2×C4⋊C4—611no—
1056C2×C4⋊C4—611no—
1057C2×C4⋊C4—611no—
1058C2×C4⋊C4—611no—
1059C2×C4⋊C4—611no—
1060C2×C4⋊C4—611no—
1061C2×C4⋊C4—611no—
1062C2×C4⋊C4—611no—
1063C2×C4⋊C4—611no—
1064C2×C4⋊C4—611no—
1065C2×C4⋊C4—611no—
1066C2×C4⋊C4—611no—
1067C2×C4⋊C4—611no—
1068C2×C4⋊C4—611no—
1069C2×C4⋊C4—611no—
1070C2×C4⋊C4—611no—
1071C2×C4⋊C4C22×D6111yescharacteristic
1072C2×C4⋊C4C22×D6111yescharacteristic
1073C2×C4⋊C4C22×D6111yescharacteristic
1074C2×C4⋊C4C22×D6111yescharacteristic
1075C2×C4⋊C4C22×D6111yescharacteristic
1076C2×C4⋊C4C22×D6111yescharacteristic
1077C2×C4⋊C4C22×D6111yescharacteristic
1078C2×C4⋊C4C22×D6111yescharacteristic
1079C2×C4⋊C4C22×D6111yescharacteristic
1080C2×C22⋊C4—611no—
1081C2×C22⋊C4—611no—
1082C2×C22⋊C4—611no—
1083C2×C22⋊C4—611no—
1084C2×C22⋊C4—611no—
1085C2×C22⋊C4—611no—
1086C2×C22⋊C4—611no—
1087C2×C22⋊C4—611no—
1088C2×C22⋊C4—611no—
1089C2×C22⋊C4—611no—
1090C2×C22⋊C4—611no—
1091C2×C22⋊C4—611no—
1092C2×C22⋊C4—611no—
1093C2×C22⋊C4—611no—
1094C2×C22⋊C4—611no—
1095C2×C22⋊C4—611no—
1096C2×C22⋊C4—611no—
1097C2×C22⋊C4—611no—
1098C2×C22⋊C4—611no—
1099C2×C22⋊C4—611no—
1100C2×C22⋊C4—611no—
1101C2×C22⋊C4—611no—
1102C2×C22⋊C4—611no—
1103C2×C22⋊C4—611no—
1104C2×C22⋊C4—611no—
1105C2×C22⋊C4—611no—
1106C2×C22⋊C4—611no—
1107C2×C22⋊C4—611no—
1108C2×C22⋊C4—611no—
1109C2×C22⋊C4—611no—
1110C2×C22⋊C4—611no—
1111C2×C22⋊C4—611no—
1112C2×C22⋊C4—611no—
1113C2×C22⋊C4—611no—
1114C2×C22⋊C4—611no—
1115C2×C22⋊C4—611no—
1116C2×C22⋊C4—611no—
1117C2×C22⋊C4—611no—
1118C2×C22⋊C4—611no—
1119C2×C22⋊C4—611no—
1120C2×C22⋊C4—611no—
1121C2×C22⋊C4—611no—
1122C2×C22⋊C4—611no—
1123C2×C22⋊C4—611no—
1124C2×C22⋊C4—611no—
1125C2×C22⋊C4—611no—
1126C2×C22⋊C4—611no—
1127C2×C22⋊C4—611no—
1128C2×C22⋊C4—611no—
1129C2×C22⋊C4—611no—
1130C2×C22⋊C4—611no—
1131C2×C22⋊C4—611no—
1132C2×C22⋊C4—2442no—
1133C2×C22⋊C4—2442no—
1134C2×C22⋊C4—2442no—
1135C2×C22⋊C4C22×D6111yescharacteristic
1136C2×C22⋊C4C22×D6111yescharacteristic
1137C2×C22⋊C4C22×D6111yescharacteristic
1138C2×C22⋊C4C22×D6111yescharacteristic
1139C2×C42—611no—
1140C2×C42—611no—
1141C2×C42—611no—
1142C2×C42C22×D6111yescharacteristic
1143C2×C42C22×D6111yescharacteristic
1144C2×C42C22×D6111yescharacteristic
1145C2×C42C22×D6111yescharacteristic
1146#95—611no—
1147#95—611no—
1148#95—611no—
1149#95—611no—
1150#95—611no—
1151#95—611no—
1152#95—611no—
1153#95—611no—
1154#95—611no—
1155#95—611no—
1156#95—611no—
1157#95—611no—
1158#95—611no—
1159#95—611no—
1160#95—611no—
1161#95—611no—
1162#95—611no—
1163#95—611no—
1164#95—611no—
1165#95—611no—
1166#95—611no—
1167#95—611no—
1168#95—611no—
1169#95—611no—
1170#95—611no—
1171#95—611no—
1172#95C22×D6111yescharacteristic
1173#95C22×D6111yescharacteristic
1174#95C22×D6111yescharacteristic
1175#95C22×D6111yescharacteristic
1176#95C22×D6111yescharacteristic
1177#95C22×D6111yescharacteristic
1178#95C22×D6111yescharacteristic
1179#95C22×D6111yescharacteristic
1180#95C22×D6111yescharacteristic
1181#95C22×D6111yescharacteristic
1182#95C22×D6111yescharacteristic
1183#95C22×D6111yescharacteristic
1184#95C22×D6111yescharacteristic
1185#95C22×D6111yescharacteristic
1186C24—611no—
1187C24—611no—
1188C24—611no—
1189C24—611no—
1190C24—611no—
1191C24—1222no—
1192C24—1222no—
1193C24—1222no—
1194C24—1222no—
1195C24—1222no—
1196C24—1222no—
1197C24—1222no—
1198C24—1222no—
1199C24—2441no—
1200C24—2441no—
1201C24—2441no—
1202C24—2441no—
1203C24—2441no—
1204C24—2441no—
1205C24C23×D6111yescharacteristic
1206C2×Q8—22no—
1207C2×Q8—41no—
1208C2×Q8—41no—
1209C2×Q8—1222no—
1210C2×Q8—2441no—
1211C2×Q8—2441no—
1212C2×Q8—2441no—
1213C2×Q8—2441no—
1214C2×Q8—2441no—
1215C2×D4—1222no—
1216C2×D4—1222no—
1217C2×D4—1222no—
1218C2×D4—1222no—
1219C2×D4—1222no—
1220C2×D4—1222no—
1221C2×D4—1222no—
1222C2×D4—1222no—
1223C2×D4—1222no—
1224C2×D4—1222no—
1225C2×D4—1222no—
1226C2×D4—1222no—
1227C2×D4—1222no—
1228C2×D4—2441no—
1229C2×D4—2441no—
1230C2×D4—2441no—
1231C2×D4—2441no—
1232C2×D4—2441no—
1233C2×D4—2441no—
1234C2×D4—2441no—
1235C2×D4—2441no—
1236C2×D4—2441no—
1237C2×D4—2441no—
1238C2×D4—2441no—
1239C2×D4—2441no—
1240C2×D4—2441no—
1241C2×D4—2441no—
1242C2×D4—24416no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—41no—
1246C22×C4—41no—
1247C22×C4—41no—
1248C22×C4—41no—
1249C22×C4—41no—
1250C22×C4—41no—
1251C22×C4—611no—
1252C22×C4—611no—
1253C22×C4—611no—
1254C22×C4—611no—
1255C22×C4—611no—
1256C22×C4—611no—
1257C22×C4—611no—
1258C22×C4—611no—
1259C22×C4—611no—
1260C22×C4—611no—
1261C22×C4—611no—
1262C22×C4—1222no—
1263C22×C4—1222no—
1264C22×C4—1222no—
1265C22×C4—1222no—
1266C22×C4—1222no—
1267C22×C4—1222no—
1268C22×C4—1222no—
1269C22×C4—1222no—
1270C22×C4—2441no—
1271C22×C4—2441no—
1272C22×C4—2441no—
1273C22×C4—2441no—
1274C22×C4—2441no—
1275C22×C4—2441no—
1276C22×C4—2441no—
1277C22×C4—2441no—
1278C22×C4—2441no—
1279C22×C4—2441no—
1280C22×C4—24416no—
1281C22×C4—2441no—
1282C22×C4—2441no—
1283C22×C4—2441no—
1284C22×C4#1175822214yes—
1285C22×C4C23×D6111yescharacteristic
1286C22×C4C23×D6111yescharacteristic
1287C22×C4C23×D6111yescharacteristic
1288C22×C4C23×D6111yescharacteristic
1289C22×C4C23×D6111yescharacteristic
1290C22×C4C23×D6111yescharacteristic
1291C22×C4C23×D6111yescharacteristic
1292C22×C4C23×D6111yescharacteristic
1293C22×C4C23×D6111yescharacteristic
1294C22×C4C23×D6111yescharacteristic
1295C22×C4C23×D6111yescharacteristic
1296C22×C4C23×D6111yescharacteristic
1297C22×C4C23×D6111yescharacteristic
1298C22×C4C23×D6111yescharacteristic
1299C4⋊C4—22no—
1300C4⋊C4—22no—
1301C4⋊C4—22no—
1302C4⋊C4—41no—
1303C4⋊C4—41no—
1304C4⋊C4—41no—
1305C4⋊C4—41no—
1306C4⋊C4—41no—
1307C4⋊C4—41no—
1308C4⋊C4—1222no—
1309C4⋊C4—1222no—
1310C4⋊C4—1222no—
1311C4⋊C4—2441no—
1312C4⋊C4—2441no—
1313C4⋊C4—2441no—
1314C4⋊C4—2441no—
1315C4⋊C4—2441no—
1316C4⋊C4—2441no—
1317C4⋊C4—2441no—
1318C4⋊C4—2441no—
1319C4⋊C4—2441no—
1320C4⋊C4—2441no—
1321C4⋊C4—2441no—
1322C4⋊C4—2441no—
1323C4⋊C4—2441no—
1324C4⋊C4—2441no—
1325C4⋊C4—2441no—
1326C4⋊C4—2441no—
1327C22⋊C4—22no—
1328C22⋊C4—22no—
1329C22⋊C4—22no—
1330C22⋊C4—22no—
1331C22⋊C4—1222no—
1332C22⋊C4—1222no—
1333C22⋊C4—1222no—
1334C22⋊C4—1222no—
1335C22⋊C4—1222no—
1336C22⋊C4—1222no—
1337C22⋊C4—1222no—
1338C22⋊C4—1222no—
1339C22⋊C4—1222no—
1340C22⋊C4—1222no—
1341C22⋊C4—1222no—
1342C22⋊C4—1222no—
1343C22⋊C4—1222no—
1344C22⋊C4—1222no—
1345C22⋊C4—1222no—
1346C22⋊C4—2441no—
1347C22⋊C4—2441no—
1348C22⋊C4—2441no—
1349C22⋊C4—2441no—
1350C22⋊C4—2441no—
1351C22⋊C4—2441no—
1352C22⋊C4—2441no—
1353C22⋊C4—2441no—
1354C22⋊C4—2441no—
1355C22⋊C4—2441no—
1356C22⋊C4—2441no—
1357C22⋊C4—2441no—
1358C22⋊C4—2441no—
1359C22⋊C4—2441no—
1360C22⋊C4—2441no—
1361C22⋊C4—2441no—
1362C22⋊C4—2441no—
1363C22⋊C4—2441no—
1364C22⋊C4—2441no—
1365C22⋊C4—2441no—
1366C22⋊C4—2441no—
1367C22⋊C4—2441no—
1368C22⋊C4—2441no—
1369C22⋊C4—2441no—
1370C22⋊C4—2441no—
1371C22⋊C4—2441no—
1372C22⋊C4—2441no—
1373C22⋊C4—2441no—
1374C22⋊C4—2441no—
1375C22⋊C4—2441no—
1376C22⋊C4—2441no—
1377C22⋊C4—2441no—
1378C22⋊C4—2441no—
1379C22⋊C4—2441no—
1380C22⋊C4—2441no—
1381C22⋊C4—2441no—
1382C22⋊C4—2441no—
1383C42—41no—
1384C42—41no—
1385C42—41no—
1386C42—41no—
1387C42—1222no—
1388C42—2441no—
1389C42—2441no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—612no—
1395C23—612no—
1396C23—1228no—
1397C23—1221no—
1398C23—1221no—
1399C23—1221no—
1400C23—1221no—
1401C23—1221no—
1402C23—1221no—
1403C23—1221no—
1404C23—1221no—
1405C23—1221no—
1406C23—1221no—
1407C23—1221no—
1408C23—1221no—
1409C23—1221no—
1410C23—1221no—
1411C23—1221no—
1412C23—1221no—
1413C23—1221no—
1414C23—1221no—
1415C23—1221no—
1416C23—1221no—
1417C23—1221no—
1418C23—1221no—
1419C23—1221no—
1420C23—1221no—
1421C23—1221no—
1422C23—1221no—
1423C23—1221no—
1424C23—1221no—
1425C23—1221no—
1426C23—1221no—
1427C23—1221no—
1428C23—1221no—
1429C23—1221no—
1430C23—4882no—
1431C23—4882no—
1432C23—4882no—
1433C23—4882no—
1434C23—2444no—
1435C23—2444no—
1436C23—2444no—
1437C23—2444no—
1438C23—2444no—
1439C23—2444no—
1440C23—2444no—
1441C23—2444no—
1442C23—2444no—
1443C23C2×#1175822212yes—
1444C23#1451982312yes—
1445C23#1451982512yes—
1446C23C24×D6111yescharacteristic
1447Q8—82no—
1448Q8—4882no—
1449Q8—4882no—
1450D4—4882no—
1451D4—4882no—
1452D4—4882no—
1453D4—4882no—
1454D4—2444no—
1455D4—2444no—
1456D4—2444no—
1457D4—2444no—
1458D4—2444no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—44no—
1500C2×C4—44no—
1501C2×C4—82no—
1502C2×C4—612no—
1503C2×C4—1221no—
1504C2×C4—1221no—
1505C2×C4—1221no—
1506C2×C4—1221no—
1507C2×C4—1221no—
1508C2×C4—1221no—
1509C2×C4—1221no—
1510C2×C4—1221no—
1511C2×C4—1221no—
1512C2×C4—1221no—
1513C2×C4—1221no—
1514C2×C4—1221no—
1515C2×C4—1221no—
1516C2×C4—1221no—
1517C2×C4—1221no—
1518C2×C4—1221no—
1519C2×C4—1221no—
1520C2×C4—1221no—
1521C2×C4—1221no—
1522C2×C4—1221no—
1523C2×C4—1221no—
1524C2×C4—1221no—
1525C2×C4—1221no—
1526C2×C4—1221no—
1527C2×C4—1221no—
1528C2×C4—1221no—
1529C2×C4—1221no—
1530C2×C4—1221no—
1531C2×C4—1221no—
1532C2×C4—1221no—
1533C2×C4—1221no—
1534C2×C4—1221no—
1535C2×C4—4882no—
1536C2×C4—4882no—
1537C2×C4—2444no—
1538C2×C4—2444no—
1539C2×C4—2444no—
1540C2×C4—2444no—
1541C2×C4—2444no—
1542C2×C4C2×#1175822212yes—
1543C2×C4C2×#1175822212yes—
1544C22—22no—
1545C22—22no—
1546C22—22no—
1547C22—22no—
1548C22—22no—
1549C22—22no—
1550C22—1222no—
1551C22—1222no—
1552C22—1222no—
1553C22—1222no—
1554C22—1222no—
1555C22—1222no—
1556C22—4888no—
1557C22—24416no—
1558C22—2441no—
1559C22—2441no—
1560C22—2441no—
1561C22—2441no—
1562C22—2441no—
1563C22—2441no—
1564C22—2441no—
1565C22—2441no—
1566C22—2441no—
1567C22—2441no—
1568C22—2441no—
1569C22—2441no—
1570C22—2441no—
1571C22—2441no—
1572C22—2441no—
1573C22—2441no—
1574C22—2441no—
1575C22—2441no—
1576C22—2441no—
1577C22—2441no—
1578C22—2441no—
1579C22—2441no—
1580C22—2441no—
1581C22—2441no—
1582C22—2441no—
1583C22—2441no—
1584C22—2441no—
1585C22—2441no—
1586C22—2441no—
1587C22#1684038414yes—
1588C22C22×#1175822211yescharacteristic
1589C22H(5,𝔽2)×D6111yescharacteristic
1590C22H(5,𝔽2)×D6111yescharacteristic
1591C22H(5,𝔽2)×D6111yescharacteristic
1592C22C2×#1451982311yescharacteristic
1593C22C2×#1451982511yescharacteristic
1594C22#1684059911yescharacteristic
1595C4—22no—
1596C4—22no—
1597C4—41no—
1598C4—41no—
1599C4—41no—
1600C4—41no—
1601C4—41no—
1602C4—41no—
1603C4—41no—
1604C4—41no—
1605C4—41no—
1606C4—41no—
1607C4—41no—
1608C4—41no—
1609C4—1222no—
1610C4—2441no—
1611C4—2441no—
1612C4—2441no—
1613C4—2441no—
1614C4—2441no—
1615C4—2441no—
1616C4—2441no—
1617C4—2441no—
1618C4—2441no—
1619C4—2441no—
1620C2—24no—
1621C2—4881no—
1622C2—4881no—
1623C2—4881no—
1624C2—2442no—
1625C2—2442no—
1626C2C2×#1684038411yescharacteristic
1627C2#2145950411yescharacteristic
1628C2#2145966411yescharacteristic
1629C2#2145997011yescharacteristic
1630C2#2146000711yescharacteristic
1631C2#2146002911yescharacteristic
1632C2#2146004511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2329C2
prime radical#21449176C2
hypercenter#2329D61
hypocenterC61#36793
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2329

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #21454114C2semidirect
2. #21454105C2semidirect
3. #21453656C2semidirect
4. #21453201C2semidirect
5. #21453154C2semidirect
6. #21453067C2semidirect
7. #21452875C2semidirect
8. #21452820C2semidirect
9. #21452738C2semidirect
10. #21452630C2semidirect
11. #21452589C2semidirect
12. #21452556C2semidirect
13. #21452493C2semidirect
14. #21452427C2semidirect
15. #21452414C2semidirect
16. #21452303C2semidirect
17. #21452228C2semidirect
18. #21452067C2semidirect
19. #21451630C2semidirect
20. #21451597C2semidirect
21. #21451001C2semidirect
22. #21450831C2semidirect
23. #21450065C2semidirect
24. #21450065C2semidirect
25. #21449945C2semidirect
26. #21449945C2semidirect
27. #21449471C2semidirect
29. #21448453C2semidirect
30. C2×#16839640C2semidirect
31. C61×#2329C2semidirect
34. C2×#14519771C22semidirect
35. C2×#14519771C22semidirect
38. C2×#14519765C22semidirect
39. C2×#14519765C22semidirect
40. C2×#14519762C22semidirect
41. C2×#14519762C22semidirect
42. C2×#14519755C22semidirect
43. C2×#14519755C22semidirect
54. #16839700C22semidirect
55. #16839697C22semidirect
56. #16839697C22semidirect
57. #16839697C22semidirect
58. #16839695C22semidirect
59. #16839695C22semidirect
60. #16839691C22semidirect
61. #16839691C22semidirect
62. #16839691C22semidirect
63. #16839691C22semidirect
64. #16839691C22semidirect
65. #16839691C22semidirect
66. #16839691C22semidirect
67. #16839691C22semidirect
68. #16839689C22semidirect
69. #16839689C22semidirect
70. #16839688C22semidirect
71. #16839688C22semidirect
72. #16839686C22semidirect
73. #16839686C22semidirect
74. #16839686C22semidirect
75. #16839686C22semidirect
76. #16839684C22semidirect
77. #16839684C22semidirect
78. #16839682C22semidirect
79. #16839682C22semidirect
80. #16839681C22semidirect
83. #16839680C22semidirect
84. #16839680C22semidirect
85. #16839680C22semidirect
86. #16839680C22semidirect
87. #16839680C22semidirect
88. #16839680C22semidirect
93. #16839679C22semidirect
94. #16839679C22semidirect
95. #16839675C22semidirect
96. #16839675C22semidirect
97. #16839675C22semidirect
98. #16839675C22semidirect
99. #16839673C22semidirect
102. #16839666C22semidirect
103. #16839666C22semidirect
104. #16839664C22semidirect
105. #16839664C22semidirect
110. #16839659C22semidirect
111. #16839659C22semidirect
112. #16839653C22semidirect
113. #16839653C22semidirect
114. #16839653C22semidirect
115. #16839653C22semidirect
116. #16839653C22semidirect
117. #16839653C22semidirect
118. #16839653C22semidirect
119. #16839653C22semidirect
120. #16839653C22semidirect
121. #16839653C22semidirect
122. #16839651C22semidirect
123. #16839651C22semidirect
124. #16839644C22semidirect
125. #16839644C22semidirect
126. #16839643C22semidirect
127. #16839643C22semidirect
138. #16839640C22semidirect
139. #16839640C22semidirect
142. #16839636C22semidirect
143. #16839636C22semidirect
148. #16839633C22semidirect
149. #16839633C22semidirect
150. #16839633C22semidirect
151. #16839633C22semidirect
152. #16839633C22semidirect
153. #16839633C22semidirect
154. #16839629C22semidirect
155. #16839626C22semidirect
156. #16839624C22semidirect
157. #16839624C22semidirect
158. #16839624C22semidirect
159. #16839621C22semidirect
160. #16839621C22semidirect
161. #16839621C22semidirect
173. C61×#391C22semidirect
174. C61×#391C22semidirect
175. C61×#389C22semidirect
176. C61×#389C22semidirect
177. C61×#387C22semidirect
178. C61×#387C22semidirect
179. C61×#387C22semidirect
180. C61×#387C22semidirect
832. #2329D61semidirect
921. #391C2×D61semidirect
922. #391C2×D61semidirect
931. #389C2×D61semidirect
932. #389C2×D61semidirect
949. #387C2×D61semidirect
950. #387C2×D61semidirect
951. #387C2×D61semidirect
952. #387C2×D61semidirect
1003. C61#36793semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214541142
#214541052
#214536562
#214532012
#214531542
#214530672
#214528752
#214528202
#214527382
#214526302
#214525892
#214525562
#214524932
#214524272
#214524142
#214523032
#214522282
#214520672
#214516302
#214515972
#214510012
#214508312
#214500652
#214499452
#214494712
#214491762
#214484532
C2×#168396402
C61×#23292
#3679361