Finite Group Databasebeta

← #29888809

Subgroups — #29888809

Order 15616.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454110C211yesmaximal, characteristic, complemented
2#21454100C211yesmaximal, characteristic, complemented
3#21453760C211yesmaximal, characteristic, complemented
4#21453681C211yesmaximal, characteristic, complemented
5#21453572C211yesmaximal, characteristic, complemented
6#21453514C211yesmaximal, characteristic, complemented
7#21453466C211yesmaximal, characteristic, complemented
8#21453442C211yesmaximal, characteristic, complemented
9#21453077C211yesmaximal, characteristic, complemented
10#21453062C211yesmaximal, characteristic, complemented
11#21452981C211yesmaximal, characteristic, complemented
12#21452621C211yesmaximal, characteristic, complemented
13#21452554C211yesmaximal, characteristic, complemented
14#21452543C211yesmaximal, characteristic, complemented
15#21452530C211yesmaximal, characteristic, complemented
16#21452347C211yesmaximal, characteristic, complemented
17#21452230C211yesmaximal, characteristic, complemented
18#21452187C211yesmaximal, characteristic, complemented
19#21451772C211yesmaximal, characteristic, complemented
20#21450079C211yesmaximal, characteristic, complemented
21#21449952C211yesmaximal, characteristic, complemented
22#21449552C211yesmaximal, characteristic, complemented
23#21449491C211yesmaximal, characteristic, complemented
24#21449425C211yesmaximal, characteristic, complemented
25#21449361C211yesmaximal, characteristic, complemented
26#21449207C211yesmaximal, characteristic, complemented
27#21449137C211yesmaximal, characteristic, complemented
28#21448493C211yesmaximal, characteristic, complemented
29#21448406C211yesmaximal, characteristic, complemented
30C2×#16839636C211yesmaximal, characteristic, complemented
31C61×#2639C211yesmaximal, characteristic, complemented
32C22×#11758224C2211yescharacteristic
33C23×C4×D61C2211yescharacteristic
34C2×#14519770C2211yescharacteristic, complemented
35C2×#14519766C2211yescharacteristic
36C2×#14519761C2211yescharacteristic, complemented
37C2×#14519759C2211yescharacteristic
38C2×#14519759C2211yescharacteristic
39C2×#14519758C2211yescharacteristic
40C2×#14519750C2211yescharacteristic
41C2×#14519750C2211yescharacteristic
42C2×#14519749C2211yescharacteristic
43C2×#14519749C2211yescharacteristic
44C2×#14519747C2211yescharacteristic
45C2×#14519745C2211yescharacteristic
46C2×#14519745C2211yescharacteristic
47C2×D4×Dic61C2211yescharacteristic
48C2×#14519733C2211yescharacteristic
49C22×C4⋊Dic61C2211yescharacteristic
50C22×#11758196C2211yescharacteristic
51C22×#11758198C2211yescharacteristic
52C22×#11758198C2211yescharacteristic
53C61⋊#401C2211yescharacteristic, complemented
54#16839704C2211yescharacteristic, complemented
55#16839703C2211yescharacteristic, complemented
56#16839703C2211yescharacteristic, complemented
57#16839703C2211yescharacteristic, complemented
58#16839702C2211yescharacteristic, complemented
59#16839700C2211yescharacteristic, complemented
60#16839699C2211yescharacteristic, complemented
61#16839695C2211yescharacteristic, complemented
62#16839695C2211yescharacteristic, complemented
63#16839694C2211yescharacteristic, complemented
64#16839691C2211yescharacteristic, complemented
65#16839691C2211yescharacteristic, complemented
66#16839691C2211yescharacteristic, complemented
67#16839688C2211yescharacteristic
68#16839687C2211yescharacteristic, complemented
69#16839687C2211yescharacteristic, complemented
70#16839686C2211yescharacteristic
71#16839686C2211yescharacteristic
72#16839686C2211yescharacteristic, complemented
73#16839685C2211yescharacteristic, complemented
74#16839684C2211yescharacteristic
75#16839682C2211yescharacteristic, complemented
76#16839681C2211yescharacteristic, complemented
77#16839679C2211yescharacteristic
78#16839679C2211yescharacteristic
79#16839678C2211yescharacteristic
80#16839678C2211yescharacteristic, complemented
81#16839677C2211yescharacteristic
82#16839677C2211yescharacteristic
83#16839677C2211yescharacteristic
84#16839677C2211yescharacteristic, complemented
85#16839675C2211yescharacteristic
86#16839675C2211yescharacteristic
87#16839674C2211yescharacteristic, complemented
88#16839673C2211yescharacteristic
89#16839671C2211yescharacteristic
90#16839671C2211yescharacteristic
91#16839670C2211yescharacteristic
92#16839670C2211yescharacteristic, complemented
93#16839669C2211yescharacteristic, complemented
94#16839666C2211yescharacteristic, complemented
95#16839666C2211yescharacteristic, complemented
96#16839663C2211yescharacteristic
97#16839662C2211yescharacteristic
98#16839662C2211yescharacteristic
99#16839662C2211yescharacteristic
100#16839662C2211yescharacteristic, complemented
101#16839662C2211yescharacteristic, complemented
102#16839659C2211yescharacteristic, complemented
103#16839659C2211yescharacteristic, complemented
104#16839658C2211yescharacteristic, complemented
105#16839655C2211yescharacteristic, complemented
106#16839654C2211yescharacteristic, complemented
107#16839652C2211yescharacteristic
108#16839652C2211yescharacteristic
109#16839652C2211yescharacteristic
110#16839651C2211yescharacteristic
111#16839651C2211yescharacteristic
112#16839650C2211yescharacteristic, complemented
113#16839650C2211yescharacteristic, complemented
114#16839649C2211yescharacteristic, complemented
115#16839647C2211yescharacteristic, complemented
116#16839647C2211yescharacteristic, complemented
117#16839644C2211yescharacteristic, complemented
118#16839644C2211yescharacteristic, complemented
119#16839643C2211yescharacteristic, complemented
120#16839643C2211yescharacteristic, complemented
121#16839642C2211yescharacteristic
122#16839642C2211yescharacteristic
123#16839642C2211yescharacteristic, complemented
124#16839641C2211yescharacteristic
125#16839641C2211yescharacteristic
126#16839641C2211yescharacteristic
127#16839640C2211yescharacteristic
128#16839640C2211yescharacteristic
129#16839640C2211yescharacteristic
130#16839640C2211yescharacteristic
131#16839639C2211yescharacteristic
132#16839639C2211yescharacteristic
133#16839639C2211yescharacteristic
134#16839639C2211yescharacteristic
135#16839638C2211yescharacteristic
136#16839638C2211yescharacteristic
137#16839638C2211yescharacteristic
138#16839638C2211yescharacteristic
139#16839638C2211yescharacteristic, complemented
140#16839637C2211yescharacteristic
141#16839637C2211yescharacteristic, complemented
142#16839636C2211yescharacteristic
143#16839636C2211yescharacteristic
144#16839636C2211yescharacteristic
145#16839636C2211yescharacteristic
146#16839636C2211yescharacteristic
147#16839636C2211yescharacteristic
148#16839636C2211yescharacteristic
149#16839636C2211yescharacteristic
150#16839636C2211yescharacteristic
151#16839636C2211yescharacteristic
152#16839635C2211yescharacteristic
153#16839635C2211yescharacteristic
154#16839635C2211yescharacteristic
155#16839634C2211yescharacteristic, complemented
156#16839634C2211yescharacteristic, complemented
157#16839634C2211yescharacteristic, complemented
158#16839633C2211yescharacteristic, complemented
159#16839624C2211yescharacteristic
160#16839624C2211yescharacteristic
161#16839623C2211yescharacteristic
162#16839621C2211yescharacteristic
163#16839621C2211yescharacteristic
164#16839621C2211yescharacteristic, complemented
165#16839621C2211yescharacteristic, complemented
166#16839620C2211yescharacteristic
167#16839620C2211yescharacteristic, complemented
168#16839620C2211yescharacteristic, complemented
169#16839617C2211yescharacteristic
170C22⋊C4×Dic61C2211yescharacteristic
171C2×#14519684C2211yescharacteristic
172C2×C22⋊Q8×C61C2211yescharacteristic
173C2×#121×C61C2211yescharacteristic
174C61×#400C2211yescharacteristic, complemented
175C61×#400C2211yescharacteristic, complemented
176C61×#397C2211yescharacteristic, complemented
177C61×#397C2211yescharacteristic, complemented
178C61×#394C2211yescharacteristic, complemented
179C61×#394C2211yescharacteristic, complemented
180C61×#393C2211yescharacteristic, complemented
181C61×#393C2211yescharacteristic, complemented
182C61×#386C2211yescharacteristic
183C61×#386C2211yescharacteristic
184C61×#386C2211yescharacteristic
185C61×#386C2211yescharacteristic
186C2×#95×C61C2211yescharacteristic
187C24×D61C2311yescharacteristic
188C2×#11758224—24no—
189C2×#11758224—42no—
190C2×#11758224—42no—
191C22×Dic122C2311yescharacteristic
192C22×D244C2311yescharacteristic
193C22×D244C2311yescharacteristic
194C22×C22⋊D61C2311yescharacteristic
195C22×C22⋊D61C2311yescharacteristic
196C22×C22⋊D61C2311yescharacteristic
197C22×C22⋊D61C2311yescharacteristic
198C22×C22⋊D61C2311yescharacteristic
199C22×C22⋊D61C2311yescharacteristic
200C22×C22⋊D61C2311yescharacteristic
201C23×Dic61C2311yescharacteristic
202C23×Dic61C2311yescharacteristic
203C23×Dic61C2311yescharacteristic
204C23×Dic61C2311yescharacteristic
205C23×Dic61C2311yescharacteristic
206C22×C4×D61—42no—
207C22×C4×D61—42no—
208C22×C4×D61—42no—
209C22×C4×D61C2311yescharacteristic
210C22×C4×D61C2311yescharacteristic
211C22×C4×D61C2311yescharacteristic
212C22×C4×D61C2311yescharacteristic
213C22×C4×D61C2311yescharacteristic
214#14519770—42no—
215#14519766—42no—
216#14519761—42no—
217#14519759—42no—
218#14519759—42no—
219#14519758—24no—
220#14519750—42no—
221#14519750—42no—
222#14519749—42no—
223#14519749—42no—
224#14519747—42no—
225#14519745—42no—
226#14519745—42no—
227D4×Dic61—42no—
228#14519733—42no—
229C2×C4⋊Dic61—42no—
230C2×C4⋊Dic61C2311yescharacteristic
231C2×C4⋊Dic61C2311yescharacteristic
232C2×C4⋊Dic61C2311yescharacteristic
233C2×C4⋊Dic61C2311yescharacteristic
234C2×C4⋊Dic61C2311yescharacteristic
235C2×C4⋊Dic61C2311yescharacteristic
236C2×C4⋊Dic61C2311yescharacteristic
237C2×#11758196—42no—
238C2×#11758196C2311yescharacteristic
239C2×#11758196C2311yescharacteristic
240C2×#11758196C2311yescharacteristic
241C2×#11758196C2311yescharacteristic
242C2×#11758196C2311yescharacteristic
243C2×#11758196C2311yescharacteristic
244C2×#11758196C2311yescharacteristic
245C2×#11758196C2311yescharacteristic
246C2×#11758196C2311yescharacteristic
247C2×#11758196C2311yescharacteristic
248C2×#11758196C2311yescharacteristic
249C2×#11758196C2311yescharacteristic
250C2×#11758196C2311yescharacteristic
251C2×#11758196C2311yescharacteristic
252C2×#11758196C2311yescharacteristic
253C2×#11758196C2311yescharacteristic
254C2×#11758196C2311yescharacteristic
255C2×C22⋊Dic61C2311yescharacteristic
256C2×C22⋊Dic61C2311yescharacteristic
257C2×C22⋊Dic61C2311yescharacteristic
258C2×C22⋊Dic61C2311yescharacteristic
259C2×C22⋊Dic61C2311yescharacteristic
260C2×C22⋊Dic61C2311yescharacteristic
261C2×C22⋊Dic61C2311yescharacteristic
262C2×C22⋊Dic61C2311yescharacteristic
263C2×C22⋊Dic61C2311yescharacteristic
264C2×C22⋊Dic61C2311yescharacteristic
265C2×C22⋊Dic61C2311yescharacteristic
266C2×#11758198—24no—
267C2×#11758198—42no—
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×C4×Dic61C2311yescharacteristic
296C2×C4×Dic61C2311yescharacteristic
297C2×C4×Dic61C2311yescharacteristic
298C2×C4×Dic61C2311yescharacteristic
299C2×C4×Dic61C2311yescharacteristic
300#14519684C2311yescharacteristic
301#14519684C2311yescharacteristic
302#14519684C2311yescharacteristic
303#14519684C2311yescharacteristic
304#14519684C2311yescharacteristic
305#14519684C2311yescharacteristic
306#14519684C2311yescharacteristic
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
332C22×Q8×C61C2311yescharacteristic
333C22×D4×C61C2311yescharacteristic
334C22×D4×C61C2311yescharacteristic
335C22×D4×C61C2311yescharacteristic
336C23×C4×C61C2311yescharacteristic
337C23×C4×C61C2311yescharacteristic
338C23×C4×C61C2311yescharacteristic
339C22⋊Q8×C61—42no—
340#121×C61—42no—
341C2×C4⋊C4×C61C2311yescharacteristic
342C2×C4⋊C4×C61C2311yescharacteristic
343C2×C4⋊C4×C61C2311yescharacteristic
344C2×C4⋊C4×C61C2311yescharacteristic
345C2×C22⋊C4×C61C2311yescharacteristic
346C2×C22⋊C4×C61C2311yescharacteristic
347C2×C22⋊C4×C61C2311yescharacteristic
348C2×C22⋊C4×C61C2311yescharacteristic
349C2×C22⋊C4×C61C2311yescharacteristic
350C2×C22⋊C4×C61C2311yescharacteristic
351C2×C22⋊C4×C61C2311yescharacteristic
352C2×C22⋊C4×C61C2311yescharacteristic
353C2×C22⋊C4×C61C2311yescharacteristic
354C2×C22⋊C4×C61C2311yescharacteristic
355C2×C22⋊C4×C61C2311yescharacteristic
356C2×C22⋊C4×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
370C24×C61C2411yescharacteristic
371C24×C61C2411yescharacteristic
372C23×D61—22no—
373C23×D61—22no—
374C23×D61—22no—
375C23×D61—22no—
376C23×D61—22no—
377C23×D61—41no—
378C23×D61—41no—
379C23×D61C2411yescharacteristic
380C23×D61C2411yescharacteristic
381C23×D61C2411yescharacteristic
382C2×Q8×C61—41no—
383C2×Q8×C61—41no—
384C2×Q8×C61—41no—
385C2×D4×C61—22no—
386C2×D4×C61—22no—
387C2×D4×C61—22no—
388C2×D4×C61—22no—
389C2×D4×C61—22no—
390C2×D4×C61—22no—
391C2×D4×C61—41no—
392C2×D4×C61—41no—
393C2×D4×C61—41no—
394C22×C4×C61—22no—
395C22×C4×C61—22no—
396C22×C4×C61—22no—
397C22×C4×C61—41no—
398C22×C4×C61—41no—
399C22×C4×C61—41no—
400C22×C4×C61—41no—
401C22×C4×C61—41no—
402C22×C4×C61—41no—
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—
418C2×C22⋊D61—22no—
419C2×C22⋊D61—22no—
420C2×C22⋊D61—22no—
421C2×C22⋊D61—22no—
422C2×C22⋊D61—22no—
423C2×C22⋊D61—22no—
424C2×C22⋊D61—41no—
425C2×C22⋊D61—41no—
426C2×C22⋊D61—41no—
427C2×C22⋊D61—41no—
428C2×C22⋊D61—41no—
429C2×C22⋊D61—41no—
430C2×C22⋊D61—41no—
431C2×C22⋊D61—41no—
432C2×C22⋊D61—41no—
433C2×C22⋊D61—41no—
434C2×C22⋊D61—41no—
435C2×C22⋊D61—41no—
436C22×Dic61—22no—
437C22×Dic61—22no—
438C22×Dic61—22no—
439C22×Dic61—22no—
440C22×Dic61—22no—
441C22×Dic61—22no—
442C22×Dic61—41no—
443C22×Dic61—41no—
444C22×Dic61—41no—
445C22×Dic61—41no—
446C22×Dic61—41no—
447C22×Dic61—41no—
448C22×Dic61—41no—
449C22×Dic61—41no—
450C22×Dic61#4114yes—
451C22×Dic61C2411yescharacteristic
452C22×Dic61C2411yescharacteristic
453C22×Dic61C2411yescharacteristic
454C22×Dic61C2411yescharacteristic
455C22×Dic61C2411yescharacteristic
456C22×Dic61C2411yescharacteristic
457C22×Dic61C2411yescharacteristic
458C22×Dic61C2411yescharacteristic
459C22×Dic61C2411yescharacteristic
460C22×Dic61C2411yescharacteristic
461C22×Dic61C2411yescharacteristic
462C22×Dic61C2411yescharacteristic
463C22×Dic61C2411yescharacteristic
464#11758224—416no—
465C2×D244—22no—
466C2×D244—22no—
467C2×D244—41no—
468C2×D244—41no—
469C2×D244—41no—
470C2×D244—41no—
471C2×C4×D61—22no—
472C2×C4×D61—22no—
473C2×C4×D61—22no—
474C2×C4×D61—22no—
475C2×C4×D61—22no—
476C2×C4×D61—41no—
477C2×C4×D61—41no—
478C2×C4×D61—41no—
479C2×C4×D61—41no—
480C2×C4×D61—41no—
481C2×C4×D61—41no—
482C2×C4×D61—41no—
483C2×C4×D61—41no—
484C2×C4×D61—41no—
485C2×C4×D61—41no—
486C2×C4×D61—416no—
487C2×Dic122—22no—
488C2×Dic122—41no—
489C2×Dic122—41no—
490C4⋊C4×C61—41no—
491C4⋊C4×C61—41no—
492C4⋊C4×C61—41no—
493C4⋊C4×C61—41no—
494C22⋊C4×C61—22no—
495C22⋊C4×C61—22no—
496C22⋊C4×C61—41no—
497C22⋊C4×C61—41no—
498C22⋊C4×C61—41no—
499C22⋊C4×C61—41no—
500C22⋊C4×C61—41no—
501C22⋊C4×C61—41no—
502C22⋊C4×C61—41no—
503C22⋊C4×C61—41no—
504C22⋊C4×C61—41no—
505C22⋊C4×C61—41no—
506C22⋊Dic61—22no—
507C22⋊Dic61—22no—
508C22⋊Dic61—22no—
509C22⋊Dic61—22no—
510C22⋊Dic61—22no—
511C22⋊Dic61—22no—
512C22⋊Dic61—41no—
513C22⋊Dic61—41no—
514C22⋊Dic61—41no—
515C22⋊Dic61—41no—
516C22⋊Dic61—41no—
517#11758198—22no—
518#11758198—22no—
519#11758198—22no—
520#11758198—22no—
521#11758198—22no—
522#11758198—22no—
523#11758198—22no—
524#11758198—22no—
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—
544C4⋊Dic61—22no—
545C4⋊Dic61—22no—
546C4⋊Dic61—22no—
547C4⋊Dic61—41no—
548C4⋊Dic61—41no—
549C4⋊Dic61—41no—
550C4⋊Dic61—41no—
551#11758196—22no—
552#11758196—22no—
553#11758196—22no—
554#11758196—41no—
555#11758196—41no—
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—
568C4×Dic61—41no—
569C4×Dic61—41no—
570C4×Dic61—41no—
571C4×Dic61—41no—
572C4×Dic61—41no—
573C23×C61—21no—
574C23×C61—21no—
575C23×C61—21no—
576C23×C61—21no—
577C23×C61—21no—
578C23×C61—21no—
579C23×C61—21no—
580C23×C61—21no—
581C23×C61—21no—
582C23×C61—21no—
583C23×C61—21no—
584C23×C61—21no—
585C23×C61—21no—
586C23×C61—21no—
587C23×C61—21no—
588C23×C61—21no—
589C23×C61—21no—
590C23×C61—21no—
591C23×C61C2×#4112yes—
592C23×C61H(5,𝔽2)12yes—
593C23×C61H(5,𝔽2)12yes—
594C23×C61C2511yescharacteristic
595C22×D61—28no—
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×D61H(5,𝔽2)12yes—
622C22×D612−1+412yes—
623Q8×C61—82no—
624D4×C61—44no—
625D4×C61—44no—
626D4×C61—82no—
627C2×C4×C61—21no—
628C2×C4×C61—21no—
629C2×C4×C61—21no—
630C2×C4×C61—21no—
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—44no—
664C2×C4×C61—44no—
665C2×C4×C61—82no—
666C22⋊D61—44no—
667C22⋊D61—44no—
668C22⋊D61—82no—
669C22⋊D61—82no—
670C22⋊D61—82no—
671C22⋊D61—82no—
672C22⋊D61—82no—
673C2×Dic61—28no—
674C2×Dic61—21no—
675C2×Dic61—21no—
676C2×Dic61—21no—
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—21no—
710C2×Dic61—44no—
711C2×Dic61—44no—
712C2×Dic61—82no—
713C2×Dic61—82no—
714C2×Dic61C2×#4112yes—
715C2×Dic61C2×#4112yes—
716C2×Dic61H(5,𝔽2)12yes—
717D244—82no—
718D244—82no—
719C4×D61—44no—
720C4×D61—44no—
721C4×D61—44no—
722C4×D61—44no—
723C4×D61—44no—
724Dic122—44no—
725#36791—611nomaximal, Sylow
726C22×C61—22no—
727C22×C61—22no—
728C22×C61—22no—
729C22×C61—22no—
730C22×C61—22no—
731C22×C61—22no—
732C22×C61—41no—
733C22×C61—41no—
734C22×C61—41no—
735C22×C61—41no—
736C22×C61—41no—
737C22×C61—41no—
738C22×C61—41no—
739C22×C61—41no—
740C22×C61—41no—
741C22×C61—41no—
742C22×C61—41no—
743C22×C61—41no—
744C22×C61—41no—
745C22×C61—41no—
746C22×C61#53814yes—
747C22×C61C22×#4111yescharacteristic
748C22×C61C2×H(5,𝔽2)11yescharacteristic
749C22×C61C2×H(5,𝔽2)11yescharacteristic
750C22×C61C2×H(5,𝔽2)11yescharacteristic
751C22×C61C2×H(5,𝔽2)11yescharacteristic
752C22×C61C2×2−1+411yescharacteristic
753C22×C61#58511yescharacteristic
754C2×D61—22no—
755C2×D61—22no—
756C2×D61—22no—
757C2×D61—22no—
758C2×D61—22no—
759C2×D61—22no—
760C2×D61—416no—
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—
776C4×C61—41no—
777C4×C61—41no—
778C4×C61—41no—
779C4×C61—41no—
780C4×C61—41no—
781C4×C61—41no—
782C4×C61—41no—
783C4×C61—41no—
784C4×C61—41no—
785C4×C61—41no—
786C4×C61—41no—
787C4×C61—41no—
788Dic61—22no—
789Dic61—22no—
790Dic61—22no—
791Dic61—41no—
792Dic61—41no—
793Dic61—41no—
794Dic61—41no—
795Dic61—41no—
796Dic61—41no—
797Dic61—41no—
798Dic61—41no—
799Dic61—41no—
800Dic61—41no—
801#2849—611no—
802#2847—611no—
803#2804—611no—
804#2797—611no—
805#2788—611no—
806#2784—611no—
807#2780—611no—
808#2778—611no—
809#2751—611no—
810#2750—611no—
811#2745—611no—
812#2714—611no—
813#2710—611no—
814#2708—611no—
815#2708—611no—
816#2695—611no—
817#2686—611no—
818#2682—611no—
819#2643—611no—
820#2639D6111yescharacteristic, complemented
821#2481—611no—
822#2472—611no—
823#2443—611no—
824#2438—611no—
825#2430—611no—
826#2424—611no—
827#2411—611no—
828#2404—611no—
829#2322—611no—
830#2311—611no—
831C2×#385—611no—
832C2×C61—24no—
833C2×C61—81no—
834C2×C61—81no—
835C2×C61C2×#53811yescharacteristic
836C2×C61#349211yescharacteristic
837C2×C61#350611yescharacteristic
838C2×C61#353211yescharacteristic
839C2×C61#353411yescharacteristic
840C2×C61#353511yescharacteristic
841C2×C61#353611yescharacteristic
842D61—42no—
843D61—42no—
844D61—81no—
845C22×#41—611no—
846C24×C4—611no—
847C2×#126—611no—
848C2×#124—611no—
849C2×#123—611no—
850C2×#123—611no—
851C2×#123—611no—
852C2×#123—611no—
853C2×C22⋊Q8C2×D6111yescharacteristic
854C2×#121—611no—
855C2×#121—611no—
856C2×#121—611no—
857C2×#121—611no—
858C2×#121C2×D6111yescharacteristic
859C2×#120—611no—
860C2×#120—611no—
861C2×#120—611no—
862C2×C4×D4—611no—
863C2×#117—611no—
864C22×C4⋊C4—611no—
865C22×C4⋊C4—611no—
866C22×C22⋊C4—611no—
867C22×C22⋊C4—611no—
868#401—611no—
869#400—611no—
870#400—611no—
871#400—611no—
872#400—611no—
873#400—611no—
874#400—611no—
875#400C2×D6111yescharacteristic, complemented
876#400C2×D6111yescharacteristic, complemented
877#399—611no—
878#398—611no—
879#398—611no—
880#398—611no—
881#397—611no—
882#397—611no—
883#397—611no—
884#397—611no—
885#397—611no—
886#397—611no—
887#397C2×D6111yescharacteristic, complemented
888#397C2×D6111yescharacteristic, complemented
889#396—611no—
890#396—611no—
891#396—611no—
892#396—611no—
893#396—611no—
894#395—611no—
895#395—611no—
896#394—611no—
897#394—611no—
898#394—611no—
899#394—611no—
900#394—611no—
901#394—611no—
902#394—611no—
903#394—611no—
904#394C2×D6111yescharacteristic, complemented
905#394C2×D6111yescharacteristic, complemented
906#393—611no—
907#393—611no—
908#393—611no—
909#393—611no—
910#393C2×D6111yescharacteristic, complemented
911#393C2×D6111yescharacteristic, complemented
912#392—611no—
913#392—611no—
914#392—611no—
915#392—611no—
916#391—611no—
917#391—611no—
918#391—611no—
919#390—611no—
920#390—611no—
921#390—611no—
922#390—611no—
923#390—611no—
924#390—611no—
925#389—611no—
926#389—611no—
927#389—611no—
928#388—611no—
929#388—611no—
930#388—611no—
931#388—611no—
932#388—611no—
933#388—611no—
934#388—611no—
935#388—611no—
936#388—611no—
937#387—611no—
938#387—611no—
939#387—611no—
940#387—611no—
941#387—611no—
942#387—611no—
943#387—611no—
944#386—611no—
945#386—611no—
946#386—611no—
947#386—611no—
948#386—611no—
949#386—611no—
950#386—611no—
951#386—611no—
952#386—611no—
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#386C2×D6111yescharacteristic
964#386C2×D6111yescharacteristic
965#386C2×D6111yescharacteristic
966#386C2×D6111yescharacteristic
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#385—611no—
980#385—611no—
981#385—611no—
982#385—611no—
983#385—611no—
984#385—611no—
985#385—611no—
986#381—611no—
987#381—611no—
988#381—611no—
989#380—611no—
990#380—611no—
991#380—611no—
992#380—611no—
993#380—611no—
994#380—611no—
995#380—611no—
996#379—611no—
997C4×C22⋊C4—611no—
998C2×#95—611no—
999C2×#95C2×D6111yescharacteristic
1000C61#3679111yescharacteristic, complemented, Sylow
1001C25—611no—
1002C2×#41—1224no—
1003C2×#41—2442no—
1004C2×#41—2442no—
1005C22×Q8—611no—
1006C22×Q8C22×D6111yescharacteristic
1007C22×D4—611no—
1008C22×D4—611no—
1009C22×D4—611no—
1010C22×D4—611no—
1011C22×D4—611no—
1012C22×D4—611no—
1013C22×D4—611no—
1014C22×D4—611no—
1015C22×D4—611no—
1016C22×D4C22×D6111yescharacteristic
1017C22×D4C22×D6111yescharacteristic
1018C22×D4C22×D6111yescharacteristic
1019C23×C4—611no—
1020C23×C4—611no—
1021C23×C4—611no—
1022C23×C4—611no—
1023C23×C4—611no—
1024C23×C4—611no—
1025C23×C4—611no—
1026C23×C4—611no—
1027C23×C4—611no—
1028C23×C4—611no—
1029C23×C4—2442no—
1030C23×C4—2442no—
1031C23×C4—2442no—
1032C23×C4C22×D6111yescharacteristic
1033C23×C4C22×D6111yescharacteristic
1034C23×C4C22×D6111yescharacteristic
1035#126—2442no—
1036#124—2442no—
1037#123—1224no—
1038#123—2442no—
1039#123—2442no—
1040#123—2442no—
1041C22⋊Q8—42no—
1042#121—42no—
1043#121—2442no—
1044#121—2442no—
1045#121—2442no—
1046#121—2442no—
1047#120—2442no—
1048#120—2442no—
1049#120—2442no—
1050C4×D4—2442no—
1051#117—2442no—
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⋊C4—611no—
1072C2×C4⋊C4—611no—
1073C2×C4⋊C4—611no—
1074C2×C4⋊C4—611no—
1075C2×C4⋊C4—611no—
1076C2×C4⋊C4—2442no—
1077C2×C4⋊C4—2442no—
1078C2×C4⋊C4C22×D6111yescharacteristic
1079C2×C4⋊C4C22×D6111yescharacteristic
1080C2×C4⋊C4C22×D6111yescharacteristic
1081C2×C4⋊C4C22×D6111yescharacteristic
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—1224no—
1121C2×C22⋊C4—2442no—
1122C2×C22⋊C4C22×D6111yescharacteristic
1123C2×C22⋊C4C22×D6111yescharacteristic
1124C2×C22⋊C4C22×D6111yescharacteristic
1125C2×C22⋊C4C22×D6111yescharacteristic
1126C2×C22⋊C4C22×D6111yescharacteristic
1127C2×C22⋊C4C22×D6111yescharacteristic
1128C2×C22⋊C4C22×D6111yescharacteristic
1129C2×C22⋊C4C22×D6111yescharacteristic
1130C2×C22⋊C4C22×D6111yescharacteristic
1131C2×C22⋊C4C22×D6111yescharacteristic
1132C2×C22⋊C4C22×D6111yescharacteristic
1133C2×C22⋊C4C22×D6111yescharacteristic
1134C2×C42—611no—
1135C2×C42—611no—
1136C2×C42—611no—
1137C2×C42—611no—
1138C2×C42—611no—
1139#95—611no—
1140#95—611no—
1141#95—611no—
1142#95—611no—
1143#95—611no—
1144#95—611no—
1145#95—611no—
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#95C22×D6111yescharacteristic
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
1183C24—611no—
1184C24—611no—
1185C24—611no—
1186C24—1222no—
1187C24—1222no—
1188C24—1222no—
1189C24—1222no—
1190C24—1222no—
1191C24—2441no—
1192C24—2441no—
1193C24C23×D6111yescharacteristic
1194C24C23×D6111yescharacteristic
1195C24C23×D6111yescharacteristic
1196#41—24416no—
1197C2×Q8—41no—
1198C2×Q8—41no—
1199C2×Q8—41no—
1200C2×Q8—1222no—
1201C2×Q8—2441no—
1202C2×Q8—2441no—
1203C2×D4—22no—
1204C2×D4—22no—
1205C2×D4—22no—
1206C2×D4—22no—
1207C2×D4—22no—
1208C2×D4—22no—
1209C2×D4—41no—
1210C2×D4—41no—
1211C2×D4—41no—
1212C2×D4—1222no—
1213C2×D4—1222no—
1214C2×D4—1222no—
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—2441no—
1224C2×D4—2441no—
1225C2×D4—2441no—
1226C2×D4—2441no—
1227C2×D4—2441no—
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—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—41no—
1243C22×C4—41no—
1244C22×C4—41no—
1245C22×C4—41no—
1246C22×C4—41no—
1247C22×C4—41no—
1248C22×C4—614no—
1249C22×C4—611no—
1250C22×C4—611no—
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—1222no—
1271C22×C4—1222no—
1272C22×C4—1222no—
1273C22×C4—2441no—
1274C22×C4—2441no—
1275C22×C4—2441no—
1276C22×C4—2441no—
1277C22×C4—2441no—
1278C22×C4—2441no—
1279C22×C4—2441no—
1280C22×C4—2441no—
1281C22×C4—2441no—
1282C22×C4—2441no—
1283C22×C4—24416no—
1284C22×C4—2441no—
1285C22×C4—2441no—
1286C22×C4—2441no—
1287C22×C4—2441no—
1288C22×C4—2441no—
1289C22×C4—2441no—
1290C22×C4—2441no—
1291C22×C4—2441no—
1292C22×C4C23×D6111yescharacteristic
1293C22×C4C23×D6111yescharacteristic
1294C22×C4C23×D6111yescharacteristic
1295C22×C4C23×D6111yescharacteristic
1296C22×C4C23×D6111yescharacteristic
1297C22×C4C23×D6111yescharacteristic
1298C22×C4C23×D6111yescharacteristic
1299C22×C4C23×D6111yescharacteristic
1300C22×C4C23×D6111yescharacteristic
1301C22×C4C23×D6111yescharacteristic
1302C22×C4C23×D6111yescharacteristic
1303C22×C4C23×D6111yescharacteristic
1304C4⋊C4—41no—
1305C4⋊C4—41no—
1306C4⋊C4—41no—
1307C4⋊C4—41no—
1308C4⋊C4—1222no—
1309C4⋊C4—1222no—
1310C4⋊C4—1222no—
1311C4⋊C4—1222no—
1312C4⋊C4—1222no—
1313C4⋊C4—1222no—
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—
1327C4⋊C4—2441no—
1328C4⋊C4—2441no—
1329C4⋊C4—2441no—
1330C4⋊C4—2441no—
1331C4⋊C4—2441no—
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—41no—
1335C22⋊C4—41no—
1336C22⋊C4—41no—
1337C22⋊C4—41no—
1338C22⋊C4—41no—
1339C22⋊C4—41no—
1340C22⋊C4—41no—
1341C22⋊C4—41no—
1342C22⋊C4—41no—
1343C22⋊C4—41no—
1344C22⋊C4—1222no—
1345C22⋊C4—1222no—
1346C22⋊C4—1222no—
1347C22⋊C4—1222no—
1348C22⋊C4—1222no—
1349C22⋊C4—1222no—
1350C22⋊C4—1222no—
1351C22⋊C4—1222no—
1352C22⋊C4—1222no—
1353C22⋊C4—1222no—
1354C22⋊C4—1222no—
1355C22⋊C4—1222no—
1356C22⋊C4—1222no—
1357C22⋊C4—1222no—
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—
1382C42—2441no—
1383C42—2441no—
1384C42—2441no—
1385C42—2441no—
1386C42—2441no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—612no—
1406C23—612no—
1407C23—1228no—
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—2444no—
1428C23—2444no—
1429C23—2444no—
1430C23—2444no—
1431C23—2444no—
1432C23—2444no—
1433C23#41×D6112yes—
1434C23#1451982212yes—
1435C23#1451982312yes—
1436C23C24×D6111yescharacteristic
1437Q8—82no—
1438Q8—2444no—
1439D4—44no—
1440D4—44no—
1441D4—82no—
1442D4—4882no—
1443D4—4882no—
1444D4—4882no—
1445D4—4882no—
1446D4—4882no—
1447D4—4882no—
1448D4—4882no—
1449D4—2444no—
1450D4—2444no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
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—44no—
1488C2×C4—44no—
1489C2×C4—82no—
1490C2×C4—612no—
1491C2×C4—612no—
1492C2×C4—612no—
1493C2×C4—1221no—
1494C2×C4—1221no—
1495C2×C4—1221no—
1496C2×C4—1221no—
1497C2×C4—1221no—
1498C2×C4—1221no—
1499C2×C4—1228no—
1500C2×C4—1221no—
1501C2×C4—1221no—
1502C2×C4—1221no—
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—4882no—
1531C2×C4—4882no—
1532C2×C4—2444no—
1533C2×C4—2444no—
1534C2×C4—2444no—
1535C2×C4—2444no—
1536C2×C4—2444no—
1537C2×C4—2444no—
1538C2×C4—2444no—
1539C22—22no—
1540C22—22no—
1541C22—22no—
1542C22—22no—
1543C22—22no—
1544C22—22no—
1545C22—41no—
1546C22—41no—
1547C22—41no—
1548C22—41no—
1549C22—41no—
1550C22—41no—
1551C22—41no—
1552C22—41no—
1553C22—41no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—41no—
1559C22—1222no—
1560C22—1222no—
1561C22—1222no—
1562C22—1222no—
1563C22—1222no—
1564C22—1222no—
1565C22—24416no—
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#1684034614yes—
1582C22C2×#41×D6111yescharacteristic
1583C22H(5,𝔽2)×D6111yescharacteristic
1584C22H(5,𝔽2)×D6111yescharacteristic
1585C22C2×#1451982211yescharacteristic
1586C22C2×#1451982311yescharacteristic
1587C222−1+4×D6111yescharacteristic
1588C22#1684059711yescharacteristic
1589C4—41no—
1590C4—41no—
1591C4—41no—
1592C4—41no—
1593C4—41no—
1594C4—41no—
1595C4—41no—
1596C4—41no—
1597C4—41no—
1598C4—41no—
1599C4—41no—
1600C4—41no—
1601C4—1222no—
1602C4—1222no—
1603C4—1222no—
1604C4—2441no—
1605C4—2441no—
1606C4—2441no—
1607C4—2441no—
1608C4—2441no—
1609C4—2441no—
1610C4—2441no—
1611C4—2441no—
1612C4—2441no—
1613C4—2441no—
1614C2—24no—
1615C2—81no—
1616C2—81no—
1617C2—4881no—
1618C2—2442no—
1619C2—2442no—
1620C2C2×#1684034611yescharacteristic
1621C2#2145952411yescharacteristic
1622C2#2145966611yescharacteristic
1623C2#2145997011yescharacteristic
1624C2#2146000611yescharacteristic
1625C2#2146002611yescharacteristic
1626C2#2146003611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2639C2
hypercenter#2639D61
hypocenterC61#36791
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2639

Complements

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

NH ≅ G/Ntype
1. #21454110C2semidirect
2. #21454100C2semidirect
3. #21453760C2semidirect
4. #21453681C2semidirect
5. #21453572C2semidirect
6. #21453514C2semidirect
7. #21453466C2semidirect
8. #21453442C2semidirect
9. #21453077C2semidirect
10. #21453062C2semidirect
11. #21452981C2semidirect
12. #21452621C2semidirect
13. #21452554C2semidirect
14. #21452543C2semidirect
15. #21452530C2semidirect
16. #21452347C2semidirect
17. #21452230C2semidirect
18. #21452187C2semidirect
19. #21451772C2semidirect
20. #21450079C2semidirect
21. #21449952C2semidirect
22. #21449552C2semidirect
23. #21449491C2semidirect
24. #21449425C2semidirect
25. #21449361C2semidirect
26. #21449207C2semidirect
27. #21449137C2semidirect
28. #21448493C2semidirect
29. #21448406C2semidirect
30. C2×#16839636C2semidirect
31. C61×#2639C2semidirect
34. C2×#14519770C22semidirect
36. C2×#14519761C22semidirect
53. C61⋊#401C22semidirect
54. #16839704C22semidirect
55. #16839703C22semidirect
56. #16839703C22semidirect
57. #16839703C22semidirect
58. #16839702C22semidirect
59. #16839700C22semidirect
60. #16839699C22semidirect
61. #16839695C22semidirect
62. #16839695C22semidirect
63. #16839694C22semidirect
64. #16839691C22semidirect
65. #16839691C22semidirect
66. #16839691C22semidirect
68. #16839687C22semidirect
69. #16839687C22semidirect
72. #16839686C22semidirect
73. #16839685C22semidirect
75. #16839682C22semidirect
76. #16839681C22semidirect
80. #16839678C22semidirect
84. #16839677C22semidirect
87. #16839674C22semidirect
92. #16839670C22semidirect
93. #16839669C22semidirect
94. #16839666C22semidirect
95. #16839666C22semidirect
100. #16839662C22semidirect
101. #16839662C22semidirect
102. #16839659C22semidirect
103. #16839659C22semidirect
104. #16839658C22semidirect
105. #16839655C22semidirect
106. #16839654C22semidirect
112. #16839650C22semidirect
113. #16839650C22semidirect
114. #16839649C22semidirect
115. #16839647C22semidirect
116. #16839647C22semidirect
117. #16839644C22semidirect
118. #16839644C22semidirect
119. #16839643C22semidirect
120. #16839643C22semidirect
123. #16839642C22semidirect
139. #16839638C22semidirect
141. #16839637C22semidirect
155. #16839634C22semidirect
156. #16839634C22semidirect
157. #16839634C22semidirect
158. #16839633C22semidirect
164. #16839621C22semidirect
165. #16839621C22semidirect
167. #16839620C22semidirect
168. #16839620C22semidirect
174. C61×#400C22semidirect
175. C61×#400C22semidirect
176. C61×#397C22semidirect
177. C61×#397C22semidirect
178. C61×#394C22semidirect
179. C61×#394C22semidirect
180. C61×#393C22semidirect
181. C61×#393C22semidirect
820. #2639D61semidirect
875. #400C2×D61semidirect
876. #400C2×D61semidirect
887. #397C2×D61semidirect
888. #397C2×D61semidirect
904. #394C2×D61semidirect
905. #394C2×D61semidirect
910. #393C2×D61semidirect
911. #393C2×D61semidirect
1000. C61#36791semidirect

Maximal subgroups

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

subgroupindex
#214541102
#214541002
#214537602
#214536812
#214535722
#214535142
#214534662
#214534422
#214530772
#214530622
#214529812
#214526212
#214525542
#214525432
#214525302
#214523472
#214522302
#214521872
#214517722
#214500792
#214499522
#214495522
#214494912
#214494252
#214493612
#214492072
#214491372
#214484932
#214484062
C2×#168396362
C61×#26392
#3679161