Finite Group Databasebeta

← #29888821

Subgroups — #29888821

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#21454111C211yesmaximal, characteristic, complemented
2#21453762C211yesmaximal, characteristic, complemented
3#21453672C211yesmaximal, characteristic, complemented
4#21453561C211yesmaximal, characteristic, complemented
5#21453516C211yesmaximal, characteristic, complemented
6#21453464C211yesmaximal, characteristic, complemented
7#21453440C211yesmaximal, characteristic, complemented
8#21453072C211yesmaximal, characteristic, complemented
9#21453057C211yesmaximal, characteristic, complemented
10#21452984C211yesmaximal, characteristic, complemented
11#21452609C211yesmaximal, characteristic, complemented
12#21452561C211yesmaximal, characteristic, complemented
13#21452537C211yesmaximal, characteristic, complemented
14#21452531C211yesmaximal, characteristic, complemented
15#21452354C211yesmaximal, characteristic, complemented
16#21452221C211yesmaximal, characteristic, complemented
17#21452180C211yesmaximal, characteristic, complemented
18#21451774C211yesmaximal, characteristic, complemented
19#21451749C211yesmaximal, characteristic, complemented
20#21450087C211yesmaximal, characteristic, complemented
21#21449944C211yesmaximal, characteristic, complemented
22#21449550C211yesmaximal, characteristic, complemented
23#21449501C211yesmaximal, characteristic, complemented
24#21449425C211yesmaximal, characteristic, complemented
25#21449359C211yesmaximal, characteristic, complemented
26#21449200C211yesmaximal, characteristic, complemented
27#21449135C211yesmaximal, characteristic, complemented
28#21448493C211yesmaximal, characteristic, complemented
29#21448406C211yesmaximal, characteristic, complemented
30C2×#16839635C211yesmaximal, characteristic, complemented
31C61×#2847C211yesmaximal, characteristic, complemented
32C22×#11758224C2211yescharacteristic
33C2×#14519772C2211yescharacteristic, complemented
34C2×#14519764C2211yescharacteristic
35C2×#14519760C2211yescharacteristic
36C2×#14519760C2211yescharacteristic
37C2×#14519758C2211yescharacteristic
38C2×#14519758C2211yescharacteristic, complemented
39C2×#14519754C2211yescharacteristic
40C2×#14519749C2211yescharacteristic
41C2×#14519749C2211yescharacteristic
42C2×#14519746C2211yescharacteristic
43C2×D4×Dic61C2211yescharacteristic
44C2×#14519733C2211yescharacteristic
45C22×#11758196C2211yescharacteristic
46C22×#11758196C2211yescharacteristic
47C22×C22⋊Dic61C2211yescharacteristic
48C22×C22⋊Dic61C2211yescharacteristic
49C61⋊#401C2211yescharacteristic, complemented
50#16839704C2211yescharacteristic, complemented
51#16839704C2211yescharacteristic, complemented
52#16839704C2211yescharacteristic, complemented
53#16839703C2211yescharacteristic, complemented
54#16839703C2211yescharacteristic, complemented
55#16839703C2211yescharacteristic, complemented
56#16839702C2211yescharacteristic, complemented
57#16839700C2211yescharacteristic, complemented
58#16839698C2211yescharacteristic, complemented
59#16839696C2211yescharacteristic, complemented
60#16839693C2211yescharacteristic, complemented
61#16839692C2211yescharacteristic, complemented
62#16839691C2211yescharacteristic, complemented
63#16839691C2211yescharacteristic, complemented
64#16839690C2211yescharacteristic, complemented
65#16839690C2211yescharacteristic, complemented
66#16839690C2211yescharacteristic, complemented
67#16839690C2211yescharacteristic, complemented
68#16839687C2211yescharacteristic
69#16839687C2211yescharacteristic, complemented
70#16839685C2211yescharacteristic
71#16839685C2211yescharacteristic
72#16839685C2211yescharacteristic
73#16839685C2211yescharacteristic, complemented
74#16839684C2211yescharacteristic, complemented
75#16839682C2211yescharacteristic, complemented
76#16839682C2211yescharacteristic, complemented
77#16839678C2211yescharacteristic
78#16839678C2211yescharacteristic, complemented
79#16839677C2211yescharacteristic, complemented
80#16839677C2211yescharacteristic, complemented
81#16839676C2211yescharacteristic
82#16839676C2211yescharacteristic
83#16839676C2211yescharacteristic
84#16839676C2211yescharacteristic
85#16839676C2211yescharacteristic
86#16839676C2211yescharacteristic, complemented
87#16839675C2211yescharacteristic, complemented
88#16839674C2211yescharacteristic
89#16839674C2211yescharacteristic
90#16839674C2211yescharacteristic
91#16839674C2211yescharacteristic, complemented
92#16839674C2211yescharacteristic, complemented
93#16839670C2211yescharacteristic
94#16839670C2211yescharacteristic
95#16839670C2211yescharacteristic
96#16839670C2211yescharacteristic, complemented
97#16839666C2211yescharacteristic, complemented
98#16839666C2211yescharacteristic, complemented
99#16839666C2211yescharacteristic, complemented
100#16839665C2211yescharacteristic
101#16839665C2211yescharacteristic
102#16839665C2211yescharacteristic
103#16839662C2211yescharacteristic
104#16839662C2211yescharacteristic, complemented
105#16839662C2211yescharacteristic, complemented
106#16839659C2211yescharacteristic, complemented
107#16839659C2211yescharacteristic, complemented
108#16839657C2211yescharacteristic, complemented
109#16839656C2211yescharacteristic
110#16839656C2211yescharacteristic
111#16839656C2211yescharacteristic
112#16839651C2211yescharacteristic, complemented
113#16839650C2211yescharacteristic
114#16839650C2211yescharacteristic
115#16839650C2211yescharacteristic, complemented
116#16839650C2211yescharacteristic, complemented
117#16839650C2211yescharacteristic, complemented
118#16839648C2211yescharacteristic, complemented
119#16839645C2211yescharacteristic, complemented
120#16839644C2211yescharacteristic, complemented
121#16839644C2211yescharacteristic, complemented
122#16839644C2211yescharacteristic, complemented
123#16839643C2211yescharacteristic, complemented
124#16839643C2211yescharacteristic, complemented
125#16839642C2211yescharacteristic
126#16839642C2211yescharacteristic
127#16839642C2211yescharacteristic
128#16839642C2211yescharacteristic
129#16839642C2211yescharacteristic
130#16839642C2211yescharacteristic
131#16839642C2211yescharacteristic
132#16839642C2211yescharacteristic, complemented
133#16839641C2211yescharacteristic
134#16839641C2211yescharacteristic
135#16839641C2211yescharacteristic
136#16839641C2211yescharacteristic
137#16839639C2211yescharacteristic
138#16839639C2211yescharacteristic
139#16839638C2211yescharacteristic
140#16839638C2211yescharacteristic
141#16839638C2211yescharacteristic, complemented
142#16839637C2211yescharacteristic
143#16839635C2211yescharacteristic
144#16839635C2211yescharacteristic
145#16839635C2211yescharacteristic
146#16839635C2211yescharacteristic
147#16839635C2211yescharacteristic
148#16839635C2211yescharacteristic
149#16839635C2211yescharacteristic
150#16839635C2211yescharacteristic
151#16839635C2211yescharacteristic
152#16839635C2211yescharacteristic
153#16839635C2211yescharacteristic
154#16839635C2211yescharacteristic
155#16839634C2211yescharacteristic
156#16839634C2211yescharacteristic, complemented
157#16839634C2211yescharacteristic, complemented
158#16839634C2211yescharacteristic, complemented
159#16839634C2211yescharacteristic, complemented
160#16839633C2211yescharacteristic, complemented
161#16839625C2211yescharacteristic
162#16839625C2211yescharacteristic
163#16839623C2211yescharacteristic
164#16839621C2211yescharacteristic, complemented
165#16839621C2211yescharacteristic, complemented
166#16839620C2211yescharacteristic, complemented
167#16839620C2211yescharacteristic, complemented
168#16839618C2211yescharacteristic
169C22⋊C4×Dic61C2211yescharacteristic
170C2×#14519684C2211yescharacteristic
171C2×#14519684C2211yescharacteristic
172C24×C4×C61C2211yescharacteristic
173C2×#121×C61C2211yescharacteristic
174C2×#121×C61C2211yescharacteristic
175C2×#121×C61C2211yescharacteristic
176C2×#120×C61C2211yescharacteristic
177C2×#120×C61C2211yescharacteristic
178C61×#386C2211yescharacteristic
179C61×#386C2211yescharacteristic
180C61×#386C2211yescharacteristic
181C61×#386C2211yescharacteristic
182C61×#386C2211yescharacteristic
183C61×#386C2211yescharacteristic
184C61×#380C2211yescharacteristic
185C61×#380C2211yescharacteristic
186C61×#380C2211yescharacteristic
187C2×#11758224—24no—
188C2×#11758224—42no—
189C2×#11758224—42no—
190C22×Dic122C2311yescharacteristic
191C22×Dic122C2311yescharacteristic
192C22×C22⋊D61C2311yescharacteristic
193C22×C22⋊D61C2311yescharacteristic
194C22×C22⋊D61C2311yescharacteristic
195C22×C22⋊D61C2311yescharacteristic
196C22×C22⋊D61C2311yescharacteristic
197C23×Dic61C2311yescharacteristic
198C23×Dic61C2311yescharacteristic
199C23×Dic61C2311yescharacteristic
200C23×Dic61C2311yescharacteristic
201C23×Dic61C2311yescharacteristic
202C23×Dic61C2311yescharacteristic
203C22×C4×D61C2311yescharacteristic
204#14519772—42no—
205#14519764—42no—
206#14519760—42no—
207#14519760—42no—
208#14519758—24no—
209#14519758—42no—
210#14519754—42no—
211#14519749—42no—
212#14519749—42no—
213#14519746—42no—
214D4×Dic61—42no—
215#14519733—42no—
216C2×C4⋊Dic61C2311yescharacteristic
217C2×C4⋊Dic61C2311yescharacteristic
218C2×C4⋊Dic61C2311yescharacteristic
219C2×C4⋊Dic61C2311yescharacteristic
220C2×#11758196—42no—
221C2×#11758196—42no—
222C2×#11758196C2311yescharacteristic
223C2×#11758196C2311yescharacteristic
224C2×#11758196C2311yescharacteristic
225C2×#11758196C2311yescharacteristic
226C2×#11758196C2311yescharacteristic
227C2×#11758196C2311yescharacteristic
228C2×#11758196C2311yescharacteristic
229C2×#11758196C2311yescharacteristic
230C2×#11758196C2311yescharacteristic
231C2×#11758196C2311yescharacteristic
232C2×#11758196C2311yescharacteristic
233C2×#11758196C2311yescharacteristic
234C2×#11758196C2311yescharacteristic
235C2×#11758196C2311yescharacteristic
236C2×#11758196C2311yescharacteristic
237C2×#11758196C2311yescharacteristic
238C2×#11758196C2311yescharacteristic
239C2×#11758196C2311yescharacteristic
240C2×#11758196C2311yescharacteristic
241C2×#11758196C2311yescharacteristic
242C2×#11758196C2311yescharacteristic
243C2×C22⋊Dic61—24no—
244C2×C22⋊Dic61—42no—
245C2×C22⋊Dic61C2311yescharacteristic
246C2×C22⋊Dic61C2311yescharacteristic
247C2×C22⋊Dic61C2311yescharacteristic
248C2×C22⋊Dic61C2311yescharacteristic
249C2×C22⋊Dic61C2311yescharacteristic
250C2×C22⋊Dic61C2311yescharacteristic
251C2×C22⋊Dic61C2311yescharacteristic
252C2×C22⋊Dic61C2311yescharacteristic
253C2×C22⋊Dic61C2311yescharacteristic
254C2×C22⋊Dic61C2311yescharacteristic
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×C22⋊Dic61C2311yescharacteristic
267C2×C22⋊Dic61C2311yescharacteristic
268C2×C22⋊Dic61C2311yescharacteristic
269C2×C22⋊Dic61C2311yescharacteristic
270C2×C22⋊Dic61C2311yescharacteristic
271C2×C22⋊Dic61C2311yescharacteristic
272C2×C22⋊Dic61C2311yescharacteristic
273C2×C22⋊Dic61C2311yescharacteristic
274C2×#11758198C2311yescharacteristic
275C2×#11758198C2311yescharacteristic
276C2×#11758198C2311yescharacteristic
277C2×#11758198C2311yescharacteristic
278C2×#11758198C2311yescharacteristic
279C2×#11758198C2311yescharacteristic
280C2×#11758198C2311yescharacteristic
281C2×#11758198C2311yescharacteristic
282C2×#11758198C2311yescharacteristic
283C2×C4×Dic61C2311yescharacteristic
284C2×C4×Dic61C2311yescharacteristic
285C2×C4×Dic61C2311yescharacteristic
286C2×C4×Dic61C2311yescharacteristic
287C2×C4×Dic61C2311yescharacteristic
288#14519684C2311yescharacteristic
289#14519684C2311yescharacteristic
290#14519684C2311yescharacteristic
291#14519684C2311yescharacteristic
292#14519684C2311yescharacteristic
293#14519684C2311yescharacteristic
294#14519684C2311yescharacteristic
295#14519684C2311yescharacteristic
296#14519684C2311yescharacteristic
297#14519684C2311yescharacteristic
298#14519684C2311yescharacteristic
299#14519684C2311yescharacteristic
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
326C25×C61C2311yescharacteristic
327C22×D4×C61C2311yescharacteristic
328C22×D4×C61C2311yescharacteristic
329C22×D4×C61C2311yescharacteristic
330C22×D4×C61C2311yescharacteristic
331C22×D4×C61C2311yescharacteristic
332C22×D4×C61C2311yescharacteristic
333C22×D4×C61C2311yescharacteristic
334C23×C4×C61—42no—
335C23×C4×C61—42no—
336C23×C4×C61—42no—
337C23×C4×C61C2311yescharacteristic
338C23×C4×C61C2311yescharacteristic
339C23×C4×C61C2311yescharacteristic
340C23×C4×C61C2311yescharacteristic
341C23×C4×C61C2311yescharacteristic
342C23×C4×C61C2311yescharacteristic
343#121×C61—42no—
344#121×C61—42no—
345#121×C61—42no—
346#120×C61—42no—
347#120×C61—42no—
348C2×C4⋊C4×C61C2311yescharacteristic
349C2×C4⋊C4×C61C2311yescharacteristic
350C2×C4⋊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
357C2×C22⋊C4×C61C2311yescharacteristic
358C2×C22⋊C4×C61C2311yescharacteristic
359C2×C22⋊C4×C61C2311yescharacteristic
360C2×C22⋊C4×C61C2311yescharacteristic
361C2×C22⋊C4×C61C2311yescharacteristic
362C2×C22⋊C4×C61C2311yescharacteristic
363#95×C61C2311yescharacteristic
364#95×C61C2311yescharacteristic
365#95×C61C2311yescharacteristic
366#95×C61C2311yescharacteristic
367#95×C61C2311yescharacteristic
368#95×C61C2311yescharacteristic
369C24×C61—22no—
370C24×C61—22no—
371C24×C61—22no—
372C24×C61—22no—
373C24×C61—22no—
374C24×C61—41no—
375C24×C61—41no—
376C24×C61C2411yescharacteristic
377C24×C61C2411yescharacteristic
378C24×C61C2411yescharacteristic
379C24×C61C2411yescharacteristic
380C24×C61C2411yescharacteristic
381C23×D61C2411yescharacteristic
382C2×D4×C61—22no—
383C2×D4×C61—22no—
384C2×D4×C61—22no—
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—22no—
392C2×D4×C61—22no—
393C2×D4×C61—41no—
394C2×D4×C61—41no—
395C2×D4×C61—41no—
396C2×D4×C61—41no—
397C2×D4×C61—41no—
398C2×D4×C61—41no—
399C2×D4×C61—41no—
400C2×D4×C61—41no—
401C2×D4×C61—41no—
402C2×D4×C61—41no—
403C22×C4×C61—22no—
404C22×C4×C61—22no—
405C22×C4×C61—22no—
406C22×C4×C61—22no—
407C22×C4×C61—22no—
408C22×C4×C61—22no—
409C22×C4×C61—22no—
410C22×C4×C61—41no—
411C22×C4×C61—41no—
412C22×C4×C61—41no—
413C22×C4×C61—41no—
414C22×C4×C61—41no—
415C22×C4×C61—41no—
416C22×C4×C61—41no—
417C22×C4×C61—41no—
418C22×C4×C61—41no—
419C22×C4×C61—41no—
420C22×C4×C61—41no—
421C22×C4×C61—416no—
422C22×C4×C61C2411yescharacteristic
423C22×C4×C61C2411yescharacteristic
424C22×C4×C61C2411yescharacteristic
425C22×C4×C61C2411yescharacteristic
426C22×C4×C61C2411yescharacteristic
427C22×C4×C61C2411yescharacteristic
428C22×C4×C61C2411yescharacteristic
429C22×C4×C61C2411yescharacteristic
430C22×C4×C61C2411yescharacteristic
431C22×C4×C61C2411yescharacteristic
432C2×C22⋊D61—22no—
433C2×C22⋊D61—22no—
434C2×C22⋊D61—22no—
435C2×C22⋊D61—22no—
436C2×C22⋊D61—22no—
437C2×C22⋊D61—22no—
438C2×C22⋊D61—41no—
439C2×C22⋊D61—41no—
440C2×C22⋊D61—41no—
441C2×C22⋊D61—41no—
442C2×C22⋊D61—41no—
443C2×C22⋊D61—41no—
444C2×C22⋊D61—41no—
445C2×C22⋊D61—41no—
446C2×C22⋊D61—41no—
447C22×Dic61—22no—
448C22×Dic61—22no—
449C22×Dic61—22no—
450C22×Dic61—22no—
451C22×Dic61—22no—
452C22×Dic61—22no—
453C22×Dic61—41no—
454C22×Dic61—41no—
455C22×Dic61—41no—
456C22×Dic61—41no—
457C22×Dic61—41no—
458C22×Dic61—41no—
459C22×Dic61—41no—
460C22×Dic61—41no—
461C22×Dic61—41no—
462C22×Dic61—41no—
463C22×Dic61—41no—
464C22×Dic61#4114yes—
465C22×Dic61C2411yescharacteristic
466C22×Dic61C2411yescharacteristic
467C22×Dic61C2411yescharacteristic
468C22×Dic61C2411yescharacteristic
469C22×Dic61C2411yescharacteristic
470C22×Dic61C2411yescharacteristic
471C22×Dic61C2411yescharacteristic
472C22×Dic61C2411yescharacteristic
473C22×Dic61C2411yescharacteristic
474C22×Dic61C2411yescharacteristic
475C22×Dic61C2411yescharacteristic
476C22×Dic61C2411yescharacteristic
477C22×Dic61C2411yescharacteristic
478C22×Dic61C2411yescharacteristic
479C22×Dic61C2411yescharacteristic
480#11758224—416no—
481C2×C4×D61—22no—
482C2×C4×D61—41no—
483C2×C4×D61—41no—
484C2×Dic122—22no—
485C2×Dic122—41no—
486C2×Dic122—41no—
487C2×Dic122—41no—
488C2×Dic122—41no—
489C2×Dic122—41no—
490C4⋊C4×C61—22no—
491C4⋊C4×C61—41no—
492C4⋊C4×C61—41no—
493C22⋊C4×C61—22no—
494C22⋊C4×C61—22no—
495C22⋊C4×C61—41no—
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⋊Dic61—22no—
506C22⋊Dic61—22no—
507C22⋊Dic61—22no—
508C22⋊Dic61—22no—
509C22⋊Dic61—22no—
510C22⋊Dic61—22no—
511C22⋊Dic61—22no—
512C22⋊Dic61—22no—
513C22⋊Dic61—22no—
514C22⋊Dic61—22no—
515C22⋊Dic61—22no—
516C22⋊Dic61—22no—
517C22⋊Dic61—22no—
518C22⋊Dic61—41no—
519C22⋊Dic61—41no—
520C22⋊Dic61—41no—
521C22⋊Dic61—41no—
522C22⋊Dic61—41no—
523C22⋊Dic61—41no—
524C22⋊Dic61—41no—
525C22⋊Dic61—41no—
526C22⋊Dic61—41no—
527C22⋊Dic61—41no—
528C22⋊Dic61—41no—
529C22⋊Dic61—41no—
530C22⋊Dic61—41no—
531C22⋊Dic61—41no—
532C22⋊Dic61—41no—
533C22⋊Dic61—41no—
534#11758198—22no—
535#11758198—41no—
536#11758198—41no—
537#11758198—41no—
538#11758198—41no—
539#11758198—41no—
540#11758198—41no—
541#11758198—41no—
542#11758198—41no—
543C4⋊Dic61—41no—
544C4⋊Dic61—41no—
545C4⋊Dic61—41no—
546C4⋊Dic61—41no—
547#11758196—22no—
548#11758196—22no—
549#11758196—22no—
550#11758196—22no—
551#11758196—22no—
552#11758196—41no—
553#11758196—41no—
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—28no—
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×C61—21no—
592C23×C61—21no—
593C23×C61—21no—
594C23×C61—21no—
595C23×C61—21no—
596C23×C61—21no—
597C23×C61—21no—
598C23×C61—21no—
599C23×C61—21no—
600C23×C61—21no—
601C23×C61—21no—
602C23×C61—21no—
603C23×C61—21no—
604C23×C61—44no—
605C23×C61—44no—
606C23×C61—44no—
607C23×C61—44no—
608C23×C61—44no—
609C23×C61—44no—
610C23×C61C2×#4112yes—
611C23×C61H(5,𝔽2)12yes—
612C23×C61H(5,𝔽2)12yes—
613C23×C61H(5,𝔽2)12yes—
614C23×C612−1+412yes—
615C23×C61C2511yescharacteristic
616C22×D61—21no—
617C22×D61—21no—
618C22×D61—21no—
619C22×D61—21no—
620C22×D61—21no—
621C22×D61—21no—
622C22×D61—21no—
623D4×C61—44no—
624D4×C61—44no—
625D4×C61—82no—
626D4×C61—82no—
627D4×C61—82no—
628D4×C61—82no—
629D4×C61—82no—
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—44no—
660C2×C4×C61—44no—
661C2×C4×C61—44no—
662C2×C4×C61—44no—
663C2×C4×C61—44no—
664C2×C4×C61—44no—
665C2×C4×C61H(5,𝔽2)12yes—
666C22⋊D61—44no—
667C22⋊D61—44no—
668C22⋊D61—82no—
669C22⋊D61—82no—
670C22⋊D61—82no—
671C2×Dic61—28no—
672C2×Dic61—21no—
673C2×Dic61—21no—
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—21no—
711C2×Dic61—21no—
712C2×Dic61—21no—
713C2×Dic61—21no—
714C2×Dic61—21no—
715C2×Dic61—44no—
716C2×Dic61—44no—
717C2×Dic61—82no—
718C2×Dic61—82no—
719C2×Dic61—82no—
720C2×Dic61C2×#4112yes—
721C2×Dic61C2×#4112yes—
722C4×D61—44no—
723Dic122—44no—
724Dic122—82no—
725#36791—611nomaximal, Sylow
726C22×C61—22no—
727C22×C61—22no—
728C22×C61—22no—
729C22×C61—22no—
730C22×C61—22no—
731C22×C61—22no—
732C22×C61—22no—
733C22×C61—22no—
734C22×C61—22no—
735C22×C61—22no—
736C22×C61—22no—
737C22×C61—22no—
738C22×C61—416no—
739C22×C61—41no—
740C22×C61—41no—
741C22×C61—41no—
742C22×C61—41no—
743C22×C61—41no—
744C22×C61—41no—
745C22×C61—41no—
746C22×C61—41no—
747C22×C61—41no—
748C22×C61—41no—
749C22×C61—41no—
750C22×C61—41no—
751C22×C61—41no—
752C22×C61—41no—
753C22×C61—41no—
754C22×C61—41no—
755C22×C61—41no—
756C22×C61—41no—
757C22×C61—41no—
758C22×C61—41no—
759C22×C61—41no—
760C22×C61—41no—
761C22×C61#53814yes—
762C22×C61C22×#4111yescharacteristic
763C22×C61C2×H(5,𝔽2)11yescharacteristic
764C22×C61C2×H(5,𝔽2)11yescharacteristic
765C22×C61C2×H(5,𝔽2)11yescharacteristic
766C22×C61C2×H(5,𝔽2)11yescharacteristic
767C22×C61C2×2−1+411yescharacteristic
768C22×C61#58511yescharacteristic
769C2×D61—41no—
770C2×D61—41no—
771C2×D61—41no—
772C2×D61—41no—
773C2×D61—41no—
774C2×D61—41no—
775C2×D61—41no—
776C4×C61—22no—
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—
786Dic61—22no—
787Dic61—22no—
788Dic61—41no—
789Dic61—41no—
790Dic61—41no—
791Dic61—41no—
792Dic61—41no—
793Dic61—41no—
794Dic61—41no—
795Dic61—41no—
796Dic61—41no—
797Dic61—41no—
798Dic61—41no—
799Dic61—41no—
800Dic61—41no—
801#2849—611no—
802#2847D6111yescharacteristic, complemented
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#2639—611no—
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—42no—
834C2×C61—42no—
835C2×C61—81no—
836C2×C61—81no—
837C2×C61C2×#53811yescharacteristic
838C2×C61#349211yescharacteristic
839C2×C61#350611yescharacteristic
840C2×C61#353211yescharacteristic
841C2×C61#353411yescharacteristic
842C2×C61#353511yescharacteristic
843C2×C61#353611yescharacteristic
844D61—81no—
845C22×#41—611no—
846C24×C4C2×D6111yescharacteristic
847C2×#126—611no—
848C2×#124—611no—
849C2×#123—611no—
850C2×#123—611no—
851C2×#123—611no—
852C2×#123—611no—
853C2×C22⋊Q8—611no—
854C2×#121—611no—
855C2×#121—611no—
856C2×#121C2×D6111yescharacteristic
857C2×#121C2×D6111yescharacteristic
858C2×#121C2×D6111yescharacteristic
859C2×#120—611no—
860C2×#120C2×D6111yescharacteristic
861C2×#120C2×D6111yescharacteristic
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#400—611no—
876#400—611no—
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#397—611no—
888#397—611no—
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#394—611no—
905#394—611no—
906#393—611no—
907#393—611no—
908#393—611no—
909#393—611no—
910#393—611no—
911#393—611no—
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#386C2×D6111yescharacteristic
962#386C2×D6111yescharacteristic
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#380C2×D6111yescharacteristic
994#380C2×D6111yescharacteristic
995#380C2×D6111yescharacteristic
996#379—611no—
997C4×C22⋊C4—611no—
998C2×#95—611no—
999C2×#95—611no—
1000C61#3679111yescharacteristic, complemented, Sylow
1001C25C22×D6111yescharacteristic
1002C2×#41—1224no—
1003C2×#41—2442no—
1004C2×#41—2442no—
1005C22×Q8—611no—
1006C22×Q8—611no—
1007C22×D4—611no—
1008C22×D4—611no—
1009C22×D4—611no—
1010C22×D4—611no—
1011C22×D4—611no—
1012C22×D4C22×D6111yescharacteristic
1013C22×D4C22×D6111yescharacteristic
1014C22×D4C22×D6111yescharacteristic
1015C22×D4C22×D6111yescharacteristic
1016C22×D4C22×D6111yescharacteristic
1017C22×D4C22×D6111yescharacteristic
1018C22×D4C22×D6111yescharacteristic
1019C23×C4—42no—
1020C23×C4—42no—
1021C23×C4—42no—
1022C23×C4—611no—
1023C23×C4—611no—
1024C23×C4—611no—
1025C23×C4—611no—
1026C23×C4—611no—
1027C23×C4—611no—
1028C23×C4—611no—
1029C23×C4C22×D6111yescharacteristic
1030C23×C4C22×D6111yescharacteristic
1031C23×C4C22×D6111yescharacteristic
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—2442no—
1042#121—42no—
1043#121—42no—
1044#121—42no—
1045#121—2442no—
1046#121—2442no—
1047#120—42no—
1048#120—42no—
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—611no—
1077C2×C4⋊C4—2442no—
1078C2×C4⋊C4—2442no—
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#95—611no—
1172#95—611no—
1173#95—611no—
1174#95—611no—
1175#95—611no—
1176#95—611no—
1177#95C22×D6111yescharacteristic
1178#95C22×D6111yescharacteristic
1179#95C22×D6111yescharacteristic
1180#95C22×D6111yescharacteristic
1181#95C22×D6111yescharacteristic
1182#95C22×D6111yescharacteristic
1183C24—22no—
1184C24—22no—
1185C24—22no—
1186C24—22no—
1187C24—22no—
1188C24—41no—
1189C24—41no—
1190C24—611no—
1191C24C23×D6111yescharacteristic
1192C24C23×D6111yescharacteristic
1193C24C23×D6111yescharacteristic
1194C24C23×D6111yescharacteristic
1195C24C23×D6111yescharacteristic
1196#41—24416no—
1197C2×Q8—1222no—
1198C2×Q8—2441no—
1199C2×Q8—2441no—
1200C2×Q8—2441no—
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—22no—
1210C2×D4—22no—
1211C2×D4—22no—
1212C2×D4—22no—
1213C2×D4—22no—
1214C2×D4—41no—
1215C2×D4—41no—
1216C2×D4—41no—
1217C2×D4—41no—
1218C2×D4—41no—
1219C2×D4—41no—
1220C2×D4—41no—
1221C2×D4—41no—
1222C2×D4—41no—
1223C2×D4—41no—
1224C2×D4—1222no—
1225C2×D4—1222no—
1226C2×D4—1222no—
1227C2×D4—1222no—
1228C2×D4—1222no—
1229C2×D4—1222no—
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—22no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—41no—
1247C22×C4—41no—
1248C22×C4—41no—
1249C22×C4—41no—
1250C22×C4—41no—
1251C22×C4—41no—
1252C22×C4—41no—
1253C22×C4—41no—
1254C22×C4—41no—
1255C22×C4—41no—
1256C22×C4—41no—
1257C22×C4—416no—
1258C22×C4—614no—
1259C22×C4—611no—
1260C22×C4—611no—
1261C22×C4—611no—
1262C22×C4—611no—
1263C22×C4—611no—
1264C22×C4—611no—
1265C22×C4—611no—
1266C22×C4—611no—
1267C22×C4—611no—
1268C22×C4—611no—
1269C22×C4—611no—
1270C22×C4—611no—
1271C22×C4—611no—
1272C22×C4—611no—
1273C22×C4—611no—
1274C22×C4—1222no—
1275C22×C4—1222no—
1276C22×C4—1222no—
1277C22×C4—1222no—
1278C22×C4—1222no—
1279C22×C4—1222no—
1280C22×C4—1222no—
1281C22×C4—2441no—
1282C22×C4—2441no—
1283C22×C4—2441no—
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×C4—2441no—
1293C22×C4—2441no—
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—22no—
1305C4⋊C4—41no—
1306C4⋊C4—41no—
1307C4⋊C4—1222no—
1308C4⋊C4—1222no—
1309C4⋊C4—1222no—
1310C4⋊C4—1222no—
1311C4⋊C4—1222no—
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—
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—28no—
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—21no—
1406C23—21no—
1407C23—21no—
1408C23—21no—
1409C23—21no—
1410C23—21no—
1411C23—21no—
1412C23—21no—
1413C23—21no—
1414C23—21no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—44no—
1419C23—44no—
1420C23—44no—
1421C23—44no—
1422C23—44no—
1423C23—44no—
1424C23—1221no—
1425C23—1221no—
1426C23—1221no—
1427C23—1221no—
1428C23—1221no—
1429C23—1221no—
1430C23—1221no—
1431C23#41×D6112yes—
1432C23#1451982212yes—
1433C23#1451982212yes—
1434C23#1451982212yes—
1435C23#1451982412yes—
1436C23C24×D6111yescharacteristic
1437Q8—4882no—
1438Q8—2444no—
1439D4—44no—
1440D4—44no—
1441D4—82no—
1442D4—82no—
1443D4—82no—
1444D4—82no—
1445D4—82no—
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—44no—
1481C2×C4—44no—
1482C2×C4—44no—
1483C2×C4—44no—
1484C2×C4—44no—
1485C2×C4—44no—
1486C2×C4—612no—
1487C2×C4—612no—
1488C2×C4—1221no—
1489C2×C4—1221no—
1490C2×C4—1221no—
1491C2×C4—1221no—
1492C2×C4—1228no—
1493C2×C4—1221no—
1494C2×C4—1221no—
1495C2×C4—1221no—
1496C2×C4—1221no—
1497C2×C4—1221no—
1498C2×C4—1221no—
1499C2×C4—1221no—
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—1221no—
1531C2×C4—1221no—
1532C2×C4—4882no—
1533C2×C4—4882no—
1534C2×C4—4882no—
1535C2×C4—2444no—
1536C2×C4—2444no—
1537C2×C4—2444no—
1538C2×C4#1451982212yes—
1539C22—22no—
1540C22—22no—
1541C22—22no—
1542C22—22no—
1543C22—22no—
1544C22—22no—
1545C22—22no—
1546C22—22no—
1547C22—22no—
1548C22—22no—
1549C22—22no—
1550C22—22no—
1551C22—416no—
1552C22—41no—
1553C22—41no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—41no—
1559C22—41no—
1560C22—41no—
1561C22—41no—
1562C22—41no—
1563C22—41no—
1564C22—41no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—41no—
1569C22—41no—
1570C22—41no—
1571C22—41no—
1572C22—41no—
1573C22—41no—
1574C22—2441no—
1575C22—2441no—
1576C22—2441no—
1577C22—2441no—
1578C22—2441no—
1579C22—2441no—
1580C22—2441no—
1581C22#1684034414yes—
1582C22C2×#41×D6111yescharacteristic
1583C22C2×#1451982211yescharacteristic
1584C22C2×#1451982211yescharacteristic
1585C22C2×#1451982211yescharacteristic
1586C22C2×#1451982211yescharacteristic
1587C22C2×#1451982411yescharacteristic
1588C22#1684059811yescharacteristic
1589C4—22no—
1590C4—41no—
1591C4—41no—
1592C4—41no—
1593C4—41no—
1594C4—41no—
1595C4—41no—
1596C4—41no—
1597C4—41no—
1598C4—41no—
1599C4—1222no—
1600C4—1222no—
1601C4—2441no—
1602C4—2441no—
1603C4—2441no—
1604C4—2441no—
1605C4—2441no—
1606C4—2441no—
1607C4—2441no—
1608C4—2441no—
1609C4—2441no—
1610C4—2441no—
1611C4—2441no—
1612C4—2441no—
1613C4—2441no—
1614C2—24no—
1615C2—42no—
1616C2—42no—
1617C2—81no—
1618C2—81no—
1619C2—4881no—
1620C2C2×#1684034411yescharacteristic
1621C2#2145952011yescharacteristic
1622C2#2145966211yescharacteristic
1623C2#2145997411yescharacteristic
1624C2#2146000911yescharacteristic
1625C2#2146002211yescharacteristic
1626C2#2146004111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2847C2
hypercenter#2847D61
hypocenterC61#36791
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. #21454111C2semidirect
2. #21453762C2semidirect
3. #21453672C2semidirect
4. #21453561C2semidirect
5. #21453516C2semidirect
6. #21453464C2semidirect
7. #21453440C2semidirect
8. #21453072C2semidirect
9. #21453057C2semidirect
10. #21452984C2semidirect
11. #21452609C2semidirect
12. #21452561C2semidirect
13. #21452537C2semidirect
14. #21452531C2semidirect
15. #21452354C2semidirect
16. #21452221C2semidirect
17. #21452180C2semidirect
18. #21451774C2semidirect
19. #21451749C2semidirect
20. #21450087C2semidirect
21. #21449944C2semidirect
22. #21449550C2semidirect
23. #21449501C2semidirect
24. #21449425C2semidirect
25. #21449359C2semidirect
26. #21449200C2semidirect
27. #21449135C2semidirect
28. #21448493C2semidirect
29. #21448406C2semidirect
30. C2×#16839635C2semidirect
31. C61×#2847C2semidirect
33. C2×#14519772C22semidirect
38. C2×#14519758C22semidirect
49. C61⋊#401C22semidirect
50. #16839704C22semidirect
51. #16839704C22semidirect
52. #16839704C22semidirect
53. #16839703C22semidirect
54. #16839703C22semidirect
55. #16839703C22semidirect
56. #16839702C22semidirect
57. #16839700C22semidirect
58. #16839698C22semidirect
59. #16839696C22semidirect
60. #16839693C22semidirect
61. #16839692C22semidirect
62. #16839691C22semidirect
63. #16839691C22semidirect
64. #16839690C22semidirect
65. #16839690C22semidirect
66. #16839690C22semidirect
67. #16839690C22semidirect
69. #16839687C22semidirect
73. #16839685C22semidirect
74. #16839684C22semidirect
75. #16839682C22semidirect
76. #16839682C22semidirect
78. #16839678C22semidirect
79. #16839677C22semidirect
80. #16839677C22semidirect
86. #16839676C22semidirect
87. #16839675C22semidirect
91. #16839674C22semidirect
92. #16839674C22semidirect
96. #16839670C22semidirect
97. #16839666C22semidirect
98. #16839666C22semidirect
99. #16839666C22semidirect
104. #16839662C22semidirect
105. #16839662C22semidirect
106. #16839659C22semidirect
107. #16839659C22semidirect
108. #16839657C22semidirect
112. #16839651C22semidirect
115. #16839650C22semidirect
116. #16839650C22semidirect
117. #16839650C22semidirect
118. #16839648C22semidirect
119. #16839645C22semidirect
120. #16839644C22semidirect
121. #16839644C22semidirect
122. #16839644C22semidirect
123. #16839643C22semidirect
124. #16839643C22semidirect
132. #16839642C22semidirect
141. #16839638C22semidirect
156. #16839634C22semidirect
157. #16839634C22semidirect
158. #16839634C22semidirect
159. #16839634C22semidirect
160. #16839633C22semidirect
164. #16839621C22semidirect
165. #16839621C22semidirect
166. #16839620C22semidirect
167. #16839620C22semidirect
802. #2847D61semidirect
1000. C61#36791semidirect

Maximal subgroups

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

subgroupindex
#214541112
#214537622
#214536722
#214535612
#214535162
#214534642
#214534402
#214530722
#214530572
#214529842
#214526092
#214525612
#214525372
#214525312
#214523542
#214522212
#214521802
#214517742
#214517492
#214500872
#214499442
#214495502
#214495012
#214494252
#214493592
#214492002
#214491352
#214484932
#214484062
C2×#168396352
C61×#28472
#3679161