Finite Group Databasebeta

← #29609208

Subgroups — #29609208

Order 15616.

1406 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839625C211yesmaximal, characteristic
2#21444080C211yesmaximal, characteristic, complemented
3#21444079C211yesmaximal, characteristic, complemented
4#21444077C211yesmaximal, characteristic, complemented
5#21444074C211yesmaximal, characteristic, complemented
6#21444062C211yesmaximal, characteristic
7#21444062C211yesmaximal, characteristic
8#21444056C211yesmaximal, characteristic
9#21444056C211yesmaximal, characteristic
10#21444054C211yesmaximal, characteristic, complemented
11#21444050C211yesmaximal, characteristic, complemented
12#21444045C211yesmaximal, characteristic, complemented
13#21444043C211yesmaximal, characteristic, complemented
14#21444042C211yesmaximal, characteristic
15C61×C22⋊#95C211yesmaximal, characteristic
16C22×#11758196C2211yescharacteristic
17C22×#11758196C2211yescharacteristic
18C22×C22⋊Dic61C2211yescharacteristic
19C22×C22⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C4×Dic61C2211yescharacteristic
23C22×C4×Dic61C2211yescharacteristic
24#16839625C418yescomplemented
25C2×#14519684C2211yescharacteristic
26C2×#14519684C2211yescharacteristic
27C2×#14519684C2211yescharacteristic
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2211yescharacteristic
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C24×C4×C61C2211yescharacteristic
46C22×C22⋊C4×C61C2211yescharacteristic
47C22×C22⋊C4×C61C2211yescharacteristic
48C2×#95×C61C2211yescharacteristic
49C2×#95×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C2×#95×C61C2211yescharacteristic
52C23×Dic61C2311yescharacteristic
53C23×Dic61C2311yescharacteristic
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2311yescharacteristic
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2311yescharacteristic
58C23×Dic61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C2×#11758196—22no—
61C2×#11758196—22no—
62C2×#11758196—41no—
63C2×#11758196—41no—
64C2×#11758196—41no—
65C2×#11758196—41no—
66C2×C22⋊Dic61—22no—
67C2×C22⋊Dic61—22no—
68C2×C22⋊Dic61—22no—
69C2×C22⋊Dic61—22no—
70C2×C22⋊Dic61—41no—
71C2×C22⋊Dic61—41no—
72C2×C22⋊Dic61—41no—
73C2×C22⋊Dic61—41no—
74C2×C22⋊Dic61—41no—
75C2×C22⋊Dic61—41no—
76C2×C22⋊Dic61C2×C414yes—
77C2×C22⋊Dic61C2×C414yes—
78C2×C4×Dic61—22no—
79C2×C4×Dic61—22no—
80C2×C4×Dic61—41no—
81C2×C4×Dic61—41no—
82C2×C4×Dic61—41no—
83C2×C4×Dic61—41no—
84#14519684—22no—
85#14519684—22no—
86#14519684—22no—
87#14519684—22no—
88#14519684—41no—
89#14519684—41no—
90#14519684—41no—
91#14519684—41no—
92#14519684—41no—
93#14519684—41no—
94#14519684—41no—
95#14519684—41no—
96#14519684—41no—
97#14519684—41no—
98#14519684—41no—
99#14519684—41no—
100#14519684C2×C414yes—
101#14519684C2×C414yes—
102#14519684C2×C414yes—
103#14519684C2×C414yes—
104C25×C61C2311yescharacteristic
105C23×C4×C61—22no—
106C23×C4×C61—22no—
107C23×C4×C61—41no—
108C23×C4×C61—41no—
109C23×C4×C61—41no—
110C23×C4×C61—41no—
111C23×C4×C61C2×C414yes—
112C23×C4×C61C2311yescharacteristic
113C23×C4×C61C2311yescharacteristic
114C23×C4×C61C2311yescharacteristic
115C23×C4×C61C2311yescharacteristic
116C23×C4×C61C2311yescharacteristic
117C23×C4×C61C2311yescharacteristic
118C2×C22⋊C4×C61—22no—
119C2×C22⋊C4×C61—22no—
120C2×C22⋊C4×C61—22no—
121C2×C22⋊C4×C61—22no—
122C2×C22⋊C4×C61—41no—
123C2×C22⋊C4×C61—41no—
124#95×C61—41no—
125#95×C61—41no—
126#95×C61—41no—
127#95×C61—41no—
128C24×C61—21no—
129C24×C61—21no—
130C24×C61—21no—
131C24×C61—21no—
132C24×C61—21no—
133C24×C61—21no—
134C24×C61—21no—
135C24×C61—21no—
136C24×C61—21no—
137C24×C61—21no—
138C24×C61—21no—
139C24×C61—21no—
140C24×C61C22×C412yes—
141C24×C61#4112yes—
142C24×C61#4112yes—
143C24×C61C2411yescharacteristic
144C22×C4×C61—28no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—44no—
184C22×C4×C61—44no—
185C22×C4×C61—44no—
186C22×C4×C61—44no—
187C22×C4×C61—44no—
188C22×C4×C61—44no—
189C22×C4×C61C22×C412yes—
190C22×C4×C61C22×C412yes—
191C22×C4×C61#4112yes—
192C22×C4×C61#4112yes—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61C22×C412yes—
244C22×Dic61C22×C412yes—
245C22×Dic61C22×C412yes—
246C22×Dic61C22×C412yes—
247C22×Dic61#4112yes—
248C22×Dic61#4112yes—
249C22⋊C4×C61—44no—
250C22⋊C4×C61—44no—
251C22⋊Dic61—44no—
252C22⋊Dic61—44no—
253C22⋊Dic61—44no—
254C22⋊Dic61—44no—
255#11758196—44no—
256#11758196—44no—
257C4×Dic61—44no—
258C4×Dic61—44no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61#11714yes—
294C23×C61C23×C411yescharacteristic
295C23×C61C2×#4111yescharacteristic
296C23×C61C2×#4111yescharacteristic
297C23×C61C2×#4111yescharacteristic
298C23×C61C2×#4111yescharacteristic
299C23×C61C2×#4111yescharacteristic
300C23×C61C2×#4111yescharacteristic
301C23×C61H(5,𝔽2)11yescharacteristic
302C23×C61H(5,𝔽2)11yescharacteristic
303C23×C61H(5,𝔽2)11yescharacteristic
304C23×C61H(5,𝔽2)11yescharacteristic
305C23×C61H(5,𝔽2)11yescharacteristic
306C23×C61H(5,𝔽2)11yescharacteristic
307C23×C612−1+411yescharacteristic
308C23×C612−1+411yescharacteristic
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—416no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—41no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408#14508—611nomaximal, Sylow
409C22×C61—24no—
410C22×C61—24no—
411C22×C61—24no—
412C22×C61—42no—
413C22×C61—42no—
414C22×C61—42no—
415C22×C61—42no—
416C22×C61—42no—
417C22×C61—42no—
418C22×C61—42no—
419C22×C61—42no—
420C22×C61—42no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—42no—
424C22×C61C2×#11711yescharacteristic
425C22×C61C4×#4111yescharacteristic
426C22×C61C4×#4111yescharacteristic
427C22×C61#51811yescharacteristic
428C22×C61#51811yescharacteristic
429C22×C61#52011yescharacteristic
430C22×C61#52011yescharacteristic
431C22×C61#53811yescharacteristic
432C22×C61#53811yescharacteristic
433C22×C61#53811yescharacteristic
434C22×C61#53811yescharacteristic
435C22×C61#53811yescharacteristic
436C22×C61#53811yescharacteristic
437C22×C61#53911yescharacteristic
438C22×C61#53911yescharacteristic
439C22×C61#54011yescharacteristic
440C22×C61#54011yescharacteristic
441C22×C61#54211yescharacteristic
442C22×C61#54211yescharacteristic
443C22×C61#55111yescharacteristic
444C22×C61#55111yescharacteristic
445C22×C61#55111yescharacteristic
446C22×C61#55111yescharacteristic
447C22×C61#55111yescharacteristic
448C22×C61#55211yescharacteristic
449C22×C61#55211yescharacteristic
450C22×C61#55211yescharacteristic
451C22×C61#55211yescharacteristic
452C22×C61#55311yescharacteristic
453C22×C61#55311yescharacteristic
454C22×C61#55911yescharacteristic
455C22×C61#56011yescharacteristic
456C22×C61#56211yescharacteristic
457C22×C61#56211yescharacteristic
458C22×C61#56311yescharacteristic
459C4×C61—42no—
460C4×C61—42no—
461C4×C61—42no—
462C4×C61—42no—
463C4×C61—81no—
464C4×C61—81no—
465Dic61—42no—
466Dic61—42no—
467Dic61—42no—
468Dic61—42no—
469Dic61—42no—
470Dic61—42no—
471Dic61—81no—
472Dic61—81no—
473C2×#381—611no—
474#1443—611no—
475#1443—611no—
476#1442—611no—
477#1442—611no—
478#1439—611no—
479#1439—611no—
480#1437—611no—
481#1437—611no—
482#1436—611no—
483#1436—611no—
484#1434—611no—
485#1434—611no—
486C22⋊#95—611no—
487C22⋊#95D6111yescharacteristic
488C2×C61—44no—
489C2×C61#231211yescharacteristic
490C2×C61#233511yescharacteristic
491C2×C61#233511yescharacteristic
492C2×C61#234311yescharacteristic
493C2×C61#234311yescharacteristic
494C2×C61#237411yescharacteristic
495C2×C61#237611yescharacteristic
496C2×C61#275011yescharacteristic
497C2×C61#275011yescharacteristic
498C2×C61#275211yescharacteristic
499C2×C61#276011yescharacteristic
500C2×C61#276111yescharacteristic
501C2×C61#276111yescharacteristic
502C2×C61#276411yescharacteristic
503C2×C61#277111yescharacteristic
504C24×C4C2×D6111yescharacteristic
505C22×C4⋊C4—611no—
506C22×C4⋊C4—611no—
507C22×C22⋊C4—611no—
508C22×C22⋊C4—611no—
509C22×C22⋊C4—611no—
510C22×C22⋊C4—611no—
511C22×C22⋊C4C2×D6111yescharacteristic
512C22×C22⋊C4C2×D6111yescharacteristic
513C22×C42—611no—
514C22×C42—611no—
515#381—618no—
516C2×#95—611no—
517C2×#95—611no—
518C2×#95—611no—
519C2×#95—611no—
520C2×#95—611no—
521C2×#95—611no—
522C2×#95—611no—
523C2×#95—611no—
524C2×#95—611no—
525C2×#95—611no—
526C2×#95—611no—
527C2×#95—611no—
528C2×#95—611no—
529C2×#95—611no—
530C2×#95—611no—
531C2×#95—611no—
532C2×#95—611no—
533C2×#95—611no—
534C2×#95—611no—
535C2×#95—611no—
536C2×#95C2×D6111yescharacteristic
537C2×#95C2×D6111yescharacteristic
538C2×#95C2×D6111yescharacteristic
539C2×#95C2×D6111yescharacteristic
540C61#1450811yescharacteristic, complemented, Sylow
541C25C22×D6111yescharacteristic
542C23×C4—22no—
543C23×C4—22no—
544C23×C4—41no—
545C23×C4—41no—
546C23×C4—41no—
547C23×C4—41no—
548C23×C4—611no—
549C23×C4—611no—
550C23×C4—611no—
551C23×C4—611no—
552C23×C4—611no—
553C23×C4—611no—
554C23×C4—611no—
555C23×C4—611no—
556C23×C4C4×D6114yes—
557C23×C4C22×D6111yescharacteristic
558C23×C4C22×D6111yescharacteristic
559C23×C4C22×D6111yescharacteristic
560C23×C4C22×D6111yescharacteristic
561C23×C4C22×D6111yescharacteristic
562C23×C4C22×D6111yescharacteristic
563C2×C4⋊C4—1222no—
564C2×C4⋊C4—1222no—
565C2×C4⋊C4—2441no—
566C2×C4⋊C4—2441no—
567C2×C4⋊C4—2441no—
568C2×C4⋊C4—2441no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—41no—
575C2×C22⋊C4—614no—
576C2×C22⋊C4—614no—
577C2×C22⋊C4—1222no—
578C2×C22⋊C4—1222no—
579C2×C22⋊C4—1222no—
580C2×C22⋊C4—1222no—
581C2×C22⋊C4—2441no—
582C2×C22⋊C4—2441no—
583C2×C22⋊C4—2441no—
584C2×C22⋊C4—2441no—
585C2×C22⋊C4—2441no—
586C2×C22⋊C4—2441no—
587C2×C42—1222no—
588C2×C42—1222no—
589C2×C42—2441no—
590C2×C42—2441no—
591C2×C42—2441no—
592C2×C42—2441no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—614no—
598#95—614no—
599#95—614no—
600#95—614no—
601#95—1222no—
602#95—1222no—
603#95—1222no—
604#95—1222no—
605#95—2441no—
606#95—2441no—
607#95—2441no—
608#95—2441no—
609#95—2441no—
610#95—2441no—
611#95—2441no—
612#95—2441no—
613#95—2441no—
614#95—2441no—
615#95—2441no—
616#95—2441no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24C2×C4×D6112yes—
630C24#1175822412yes—
631C24#1175822412yes—
632C24C23×D6111yescharacteristic
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—28no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—612no—
679C22×C4—612no—
680C22×C4—612no—
681C22×C4—612no—
682C22×C4—612no—
683C22×C4—612no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4C2×C4×D6112yes—
735C22×C4C2×C4×D6112yes—
736C22×C4#1175822212yes—
737C22×C4#1175822212yes—
738C4⋊C4—2444no—
739C4⋊C4—2444no—
740C22⋊C4—44no—
741C22⋊C4—44no—
742C22⋊C4—2444no—
743C22⋊C4—2444no—
744C22⋊C4—2444no—
745C22⋊C4—2444no—
746C42—2444no—
747C42—2444no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23#1451973314yes—
783C23C22×C4×D6111yescharacteristic
784C23#41×D6111yescharacteristic
785C23#41×D6111yescharacteristic
786C23C2×#1175822411yescharacteristic
787C23C2×#1175822411yescharacteristic
788C23C2×#1175822211yescharacteristic
789C23C2×#1175822211yescharacteristic
790C23#1451982211yescharacteristic
791C23#1451982211yescharacteristic
792C23#1451982211yescharacteristic
793C23#1451982211yescharacteristic
794C23#1451982211yescharacteristic
795C23#1451982311yescharacteristic
796C23#1451982411yescharacteristic
797C23#1451982511yescharacteristic
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—416no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—1222no—
842C2×C4—1222no—
843C2×C4—1222no—
844C2×C4—1222no—
845C2×C4—1222no—
846C2×C4—1222no—
847C2×C4—1222no—
848C2×C4—1222no—
849C2×C4—1222no—
850C2×C4—1222no—
851C2×C4—1222no—
852C2×C4—1222no—
853C2×C4—1222no—
854C2×C4—1222no—
855C2×C4—1222no—
856C2×C4—1222no—
857C2×C4—1222no—
858C2×C4—1222no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4—2441no—
862C2×C4—2441no—
863C2×C4—2441no—
864C2×C4—2441no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22C2×#1451973311yescharacteristic
913C22#1684023011yescharacteristic
914C22C4×#1175822211yescharacteristic
915C22#1684023511yescharacteristic
916C22#1684023511yescharacteristic
917C22#1684024211yescharacteristic
918C22#1684024311yescharacteristic
919C22#1684034411yescharacteristic
920C22#1684034511yescharacteristic
921C22#1684034711yescharacteristic
922C22#1684034711yescharacteristic
923C22#1684034711yescharacteristic
924C22#1684034711yescharacteristic
925C22#1684035411yescharacteristic
926C22#1684035811yescharacteristic
927C22#1684036211yescharacteristic
928C22#1684036311yescharacteristic
929C22#1684037711yescharacteristic
930C22#1684038211yescharacteristic
931C22#1684043511yescharacteristic
932C22#1684043511yescharacteristic
933C22#1684043811yescharacteristic
934C22#1684043811yescharacteristic
935C22#1684044111yescharacteristic
936C22#1684044711yescharacteristic
937C22#1684044711yescharacteristic
938C22#1684044911yescharacteristic
939C22#1684044911yescharacteristic
940C22#1684046111yescharacteristic
941C22#1684046211yescharacteristic
942C22#1684049511yescharacteristic
943C22#1684050011yescharacteristic
944C22#1684050711yescharacteristic
945C22#1684050811yescharacteristic
946C22#1684051311yescharacteristic
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—81no—
952C4—81no—
953C4—4881no—
954C4—4881no—
955C4—2442no—
956C4—2442no—
957C4—2442no—
958C4—2442no—
959C4—2442no—
960C4—2442no—
961C2—44no—
962C2#2144841511yescharacteristic
963C2#2144860511yescharacteristic
964C2#2144860911yescharacteristic
965C2#2144867511yescharacteristic
966C2#2144868111yescharacteristic
967C2#2144895011yescharacteristic
968C2#2144896311yescharacteristic
969C2#2145305711yescharacteristic
970C2#2145306111yescharacteristic
971C2#2145308611yescharacteristic
972C2#2145319511yescharacteristic
973C2#2145320611yescharacteristic
974C2#2145321011yescharacteristic
975C2#2145324011yescharacteristic
976C2#2145333711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC22⋊#95D61
hypocenterC61#14508
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. #21444080C2semidirect
3. #21444079C2semidirect
4. #21444077C2semidirect
5. #21444074C2semidirect
10. #21444054C2semidirect
11. #21444050C2semidirect
12. #21444045C2semidirect
13. #21444043C2semidirect
24. #16839625C4semidirect
540. C61#14508semidirect

Maximal subgroups

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

subgroupindex
C2×#168396252
#214440802
#214440792
#214440772
#214440742
#214440622
#214440562
#214440542
#214440502
#214440452
#214440432
#214440422
C61×C22⋊#952
#1450861