Finite Group Databasebeta

← #29610102

Subgroups — #29610102

Order 15616.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839675C211yesmaximal, characteristic
2C2×#16839667C211yesmaximal, characteristic, complemented
3C2×#16839666C211yesmaximal, characteristic, complemented
4C2×#16839633C211yesmaximal, characteristic
5C2×#16839633C211yesmaximal, characteristic
6#21444082C211yesmaximal, characteristic, complemented
7#21444078C211yesmaximal, characteristic, complemented
8#21444077C211yesmaximal, characteristic, complemented
9#21444061C211yesmaximal, characteristic
10#21444055C211yesmaximal, characteristic
11#21444055C211yesmaximal, characteristic
12#21444045C211yesmaximal, characteristic, complemented
13#21444044C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic
15C61×#1444C211yesmaximal, characteristic, complemented
16C23×Dic122C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×C4×Dic61C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28#16839675C418yescomplemented
29#16839667—24no—
30#16839666—24no—
31#16839633—24no—
32#16839633—24no—
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C22×C4⋊C4×C61C2211yescharacteristic
50C22×C4⋊C4×C61C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C24×D61C2311yescharacteristic
57C22×Dic122—22no—
58C22×Dic122—22no—
59C22×Dic122—22no—
60C22×Dic122—22no—
61C22×Dic122—41no—
62C22×Dic122—41no—
63C22×Dic122C2×C414yescomplemented
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C22×C4×D61—22no—
72C22×C4×D61—22no—
73C22×C4×D61—22no—
74C22×C4×D61—41no—
75C22×C4×D61—41no—
76C22×C4×D61—41no—
77C22×C4×D61—41no—
78C2×#11758196—22no—
79C2×#11758196—22no—
80C2×#11758196—22no—
81C2×#11758196—41no—
82C2×#11758196—41no—
83C2×#11758196—41no—
84C2×#11758198—22no—
85C2×#11758198—22no—
86C2×#11758198—22no—
87C2×#11758198—22no—
88C2×#11758198—22no—
89C2×#11758198—22no—
90C2×#11758198—22no—
91C2×#11758198—22no—
92C2×#11758198—41no—
93C2×#11758198—41no—
94C2×#11758198—41no—
95C2×#11758198—41no—
96C2×#11758198—41no—
97C2×#11758198—41no—
98C2×#11758198C2×C414yes—
99C2×#11758198C2×C414yes—
100C2×#11758198C2×C414yes—
101C2×#11758198Q814yescomplemented
102C2×C4×Dic61—22no—
103C2×C4×Dic61—22no—
104C2×C4×Dic61—22no—
105C2×C4×Dic61—22no—
106C2×C4×Dic61—41no—
107C2×C4×Dic61—41no—
108#14519684—22no—
109#14519684—22no—
110#14519684—22no—
111#14519684—22no—
112#14519684—22no—
113#14519684—22no—
114#14519684—22no—
115#14519684—41no—
116#14519684—41no—
117#14519684—41no—
118#14519684—41no—
119#14519684—41no—
120#14519684C2×C414yescomplemented
121#14519684C2×C414yescomplemented
122#14519684D414yes—
123#14519684D414yes—
124C23×C4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61—22no—
132C2×C4⋊C4×C61—22no—
133C2×C4⋊C4×C61—22no—
134C2×C4⋊C4×C61—41no—
135C2×C4⋊C4×C61—41no—
136C2×C4⋊C4×C61—41no—
137C2×C4⋊C4×C61—41no—
138C2×C4⋊C4×C61—41no—
139C2×C4⋊C4×C61—41no—
140#95×C61—22no—
141#95×C61—41no—
142#95×C61—41no—
143#95×C61C2×C414yescomplemented
144C24×C61C2411yescharacteristic
145C23×D61—21no—
146C23×D61—21no—
147C23×D61—21no—
148C23×D61—21no—
149C23×D61—21no—
150C23×D61—21no—
151C23×D61—21no—
152C23×D61—21no—
153C23×D61—21no—
154C23×D61—21no—
155C23×D61—21no—
156C23×D61—21no—
157C23×D61C22×C412yes—
158C23×D61C2×Q812yes—
159C23×D61#4112yes—
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—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61C22×C412yes—
203C22×C4×C61C22×C412yes—
204C22×C4×C61C22×C412yes—
205C22×C4×C61C2×D412yes—
206C22×C4×C61C2×D412yes—
207C22×C4×C61C2×Q812yes—
208C22×C4×C61#4112yes—
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×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61C22×C412yes—
250C22×Dic61C22×C412yes—
251C22×Dic61C22×C412yes—
252C22×Dic61C2×D412yes—
253C22×Dic61C2×D412yes—
254C22×Dic61C2×D412yes—
255C22×Dic61C2×D412yes—
256C22×Dic61C2×Q812yes—
257C22×Dic61#4112yes—
258C2×C4×D61—44no—
259C2×C4×D61—44no—
260C2×C4×D61—44no—
261C2×C4×D61—44no—
262C2×C4×D61—44no—
263C2×C4×D61—44no—
264C2×C4×D61—44no—
265C2×Dic122—28no—
266C2×Dic122—28no—
267C2×Dic122—44no—
268C2×Dic122—44no—
269C2×Dic122—44no—
270C2×Dic122—44no—
271C2×Dic122—44no—
272C4⋊C4×C61—44no—
273C4⋊C4×C61—44no—
274C4⋊C4×C61—44no—
275#11758198—28no—
276#11758198—28no—
277#11758198—44no—
278#11758198—44no—
279#11758198—44no—
280#11758198—44no—
281#11758196—44no—
282#11758196—44no—
283C4×Dic61—44no—
284C4×Dic61—44no—
285C23×C61C23×C411yescharacteristic
286C23×C61C22×D411yescharacteristic
287C23×C61C22×D411yescharacteristic
288C23×C61C22×Q811yescharacteristic
289C23×C61C2×#4111yescharacteristic
290C23×C61C2×#4111yescharacteristic
291C23×C61C2×#4111yescharacteristic
292C23×C61H(5,𝔽2)11yescharacteristic
293C23×C61H(5,𝔽2)11yescharacteristic
294C23×C61H(5,𝔽2)11yescharacteristic
295C23×C61H(5,𝔽2)11yescharacteristic
296C23×C61H(5,𝔽2)11yescharacteristic
297C23×C612−1+411yescharacteristic
298C23×C612−1+411yescharacteristic
299C23×C612−1+411yescharacteristic
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61—41no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61C4×Q814yes—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61C4×D414yes—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—22no—
393C2×Dic61—22no—
394C2×Dic61—22no—
395C2×Dic61—22no—
396C2×Dic61—22no—
397C2×Dic61—22no—
398C2×Dic61—22no—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—22no—
402C2×Dic61—22no—
403C2×Dic61—22no—
404C2×Dic61—22no—
405C2×Dic61—22no—
406C2×Dic61—22no—
407C2×Dic61—22no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61—41no—
417C2×Dic61—41no—
418C2×Dic61—41no—
419C2×Dic61—41no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422C2×Dic61—41no—
423C2×Dic61—41no—
424C2×Dic61—41no—
425C2×Dic61—41no—
426C2×Dic61—41no—
427C2×Dic61—41no—
428C2×Dic61—41no—
429C2×Dic61—41no—
430C2×Dic61—41no—
431C2×Dic61—41no—
432C2×Dic61C4×D414yes—
433C4×D61—416no—
434Dic122—416no—
435#14575—611nomaximal, Sylow
436C22×C61C2×C4×D411yescharacteristic
437C22×C61C2×C4×D411yescharacteristic
438C22×C61C2×C4×Q811yescharacteristic
439C22×C61#51811yescharacteristic
440C22×C61#52011yescharacteristic
441C22×C61#52011yescharacteristic
442C22×C61#52011yescharacteristic
443C22×C61#53511yescharacteristic
444C22×C61#53511yescharacteristic
445C22×C61#53611yescharacteristic
446C22×C61#53611yescharacteristic
447C22×C61#53811yescharacteristic
448C22×C61#53911yescharacteristic
449C22×C61#54211yescharacteristic
450C22×C61#54211yescharacteristic
451C22×C61#54211yescharacteristic
452C22×C61#54211yescharacteristic
453C22×C61#54311yescharacteristic
454C22×C61#54411yescharacteristic
455C22×C61D4211yescharacteristic
456C22×C61#54611yescharacteristic
457C22×C61#54611yescharacteristic
458C22×C61#54611yescharacteristic
459C22×C61#54611yescharacteristic
460C22×C61D4×Q811yescharacteristic
461C22×C61D4×Q811yescharacteristic
462C22×C61#55111yescharacteristic
463C22×C61#55211yescharacteristic
464C22×C61#55211yescharacteristic
465C22×C61#55411yescharacteristic
466C22×C61#55411yescharacteristic
467C22×C61H(3,𝔽4)11yescharacteristic
468C22×C61#56211yescharacteristic
469C22×C61#56211yescharacteristic
470C22×C61#56311yescharacteristic
471C2×D61—24no—
472C2×D61—24no—
473C2×D61—24no—
474C2×D61—42no—
475C2×D61—42no—
476C2×D61—42no—
477C2×D61—42no—
478C2×D61—42no—
479C2×D61—42no—
480C2×D61—42no—
481C2×D61—42no—
482C2×D61—42no—
483C2×D61—42no—
484C2×D61—42no—
485C2×D61—42no—
486C4×C61—24no—
487C4×C61—42no—
488C4×C61—42no—
489C4×C61—42no—
490C4×C61—42no—
491C4×C61—81no—
492C4×C61—81no—
493Dic61—24no—
494Dic61—42no—
495Dic61—42no—
496Dic61—42no—
497Dic61—42no—
498Dic61—42no—
499Dic61—42no—
500C2×#393—611no—
501C2×#391—611no—
502C2×#391—611no—
503C2×#385—611no—
504C2×#385—611no—
505#1444—611no—
506#1444D6111yescharacteristic, complemented
507#1442—611no—
508#1442—611no—
509#1439—611no—
510#1437—611no—
511#1437—611no—
512#1434—611no—
513#1434—611no—
514C22⋊#95—611no—
515C2×C61#232611yescharacteristic
516C2×C61#232611yescharacteristic
517C2×C61#232911yescharacteristic
518C2×C61#235811yescharacteristic
519C2×C61#236011yescharacteristic
520C2×C61#236011yescharacteristic
521C2×C61#237911yescharacteristic
522C2×C61#267011yescharacteristic
523C2×C61#267711yescharacteristic
524C2×C61#268711yescharacteristic
525C2×C61#268711yescharacteristic
526C2×C61#269211yescharacteristic
527C2×C61#269211yescharacteristic
528C2×C61#276311yescharacteristic
529C2×C61#276411yescharacteristic
530D61—44no—
531C23×Q8—611no—
532C24×C4—611no—
533C22×C4⋊C4—611no—
534C22×C4⋊C4—611no—
535C22×C4⋊C4C2×D6111yescharacteristic
536C22×C4⋊C4C2×D6111yescharacteristic
537C22×C4⋊C4C2×D6111yescharacteristic
538C22×C22⋊C4—611no—
539C22×C22⋊C4—611no—
540C22×C22⋊C4—611no—
541C22×C22⋊C4—611no—
542C22×C22⋊C4—611no—
543C22×C22⋊C4—611no—
544C22×C42—611no—
545C22×C42—611no—
546#393—618no—
547#391—1224no—
548#391—1224no—
549#385—1224no—
550#385—1224no—
551C2×#95—611no—
552C2×#95—611no—
553C2×#95—611no—
554C2×#95—611no—
555C2×#95—611no—
556C2×#95—611no—
557C2×#95—611no—
558C2×#95—611no—
559C2×#95—611no—
560C2×#95—611no—
561C2×#95—611no—
562C2×#95—611no—
563C2×#95—611no—
564C2×#95—611no—
565C2×#95—611no—
566C2×#95—611no—
567C2×#95C2×D6111yescharacteristic
568C2×#95C2×D6111yescharacteristic
569C2×#95C2×D6111yescharacteristic
570C2×#95C2×D6111yescharacteristic
571C61#1457511yescharacteristic, complemented, Sylow
572C25—611no—
573C22×Q8—614no—
574C22×Q8—1222no—
575C22×Q8—1222no—
576C22×Q8—1222no—
577C22×Q8—1222no—
578C22×Q8—2441no—
579C22×Q8—2441no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C23×C4—611no—
584C23×C4—611no—
585C23×C4—611no—
586C23×C4—611no—
587C23×C4—1222no—
588C23×C4—1222no—
589C23×C4—1222no—
590C23×C4—2441no—
591C23×C4—2441no—
592C23×C4—2441no—
593C23×C4—2441no—
594C23×C4C22×D6111yescharacteristic
595C23×C4C22×D6111yescharacteristic
596C23×C4C22×D6111yescharacteristic
597C23×C4C22×D6111yescharacteristic
598C23×C4C22×D6111yescharacteristic
599C23×C4C22×D6111yescharacteristic
600C23×C4C22×D6111yescharacteristic
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—1222no—
611C2×C4⋊C4—1222no—
612C2×C4⋊C4—1222no—
613C2×C4⋊C4—2441no—
614C2×C4⋊C4—2441no—
615C2×C4⋊C4—2441no—
616C2×C22⋊C4—614no—
617C2×C22⋊C4—614no—
618C2×C22⋊C4—614no—
619C2×C22⋊C4—614no—
620C2×C22⋊C4—1222no—
621C2×C22⋊C4—1222no—
622C2×C22⋊C4—1222no—
623C2×C22⋊C4—1222no—
624C2×C22⋊C4—1222no—
625C2×C22⋊C4—1222no—
626C2×C22⋊C4—1222no—
627C2×C22⋊C4—1222no—
628C2×C22⋊C4—2441no—
629C2×C22⋊C4—2441no—
630C2×C22⋊C4—2441no—
631C2×C22⋊C4—2441no—
632C2×C22⋊C4—2441no—
633C2×C22⋊C4—2441no—
634C2×C42—1222no—
635C2×C42—1222no—
636C2×C42—1222no—
637C2×C42—1222no—
638C2×C42—2441no—
639C2×C42—2441no—
640#95—22no—
641#95—41no—
642#95—41no—
643#95—614no—
644#95—614no—
645#95—614no—
646#95—614no—
647#95—1222no—
648#95—1222no—
649#95—1222no—
650#95—1222no—
651#95—1222no—
652#95—1222no—
653#95—1222no—
654#95—2441no—
655#95—2441no—
656#95—2441no—
657#95—2441no—
658#95—2441no—
659#95C4×D6114yescomplemented
660C24—612no—
661C24—612no—
662C24—612no—
663C24—1221no—
664C24—1221no—
665C24—1221no—
666C24—1221no—
667C24—1221no—
668C24—1221no—
669C24—1221no—
670C24—1221no—
671C24—1221no—
672C24—1221no—
673C24—1221no—
674C24—1221no—
675C24C23×D6111yescharacteristic
676C2×Q8—1228no—
677C2×Q8—1228no—
678C2×Q8—2444no—
679C2×Q8—2444no—
680C2×Q8—2444no—
681C2×Q8—2444no—
682C2×Q8—2444no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—612no—
726C22×C4—612no—
727C22×C4—612no—
728C22×C4—612no—
729C22×C4—612no—
730C22×C4—612no—
731C22×C4—612no—
732C22×C4—612no—
733C22×C4—612no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—2444no—
775C22×C4—2444no—
776C22×C4—2444no—
777C22×C4—2444no—
778C22×C4—2444no—
779C22×C4—2444no—
780C22×C4—2444no—
781C22×C4C2×C4×D6112yes—
782C22×C4C2×C4×D6112yes—
783C22×C4C2×C4×D6112yes—
784C22×C4D4×D6112yes—
785C22×C4D4×D6112yes—
786C22×C4Q8×D6112yes—
787C22×C4#1175822612yes—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—2444no—
792C4⋊C4—2444no—
793C22⋊C4—1228no—
794C22⋊C4—1228no—
795C22⋊C4—2444no—
796C22⋊C4—2444no—
797C22⋊C4—2444no—
798C22⋊C4—2444no—
799C42—2444no—
800C42—2444no—
801C23—614no—
802C23—1222no—
803C23—1222no—
804C23—1222no—
805C23—1222no—
806C23—1222no—
807C23—1222no—
808C23—1222no—
809C23—1222no—
810C23—1222no—
811C23—1222no—
812C23—1222no—
813C23—1222no—
814C23—1222no—
815C23—1222no—
816C23—1222no—
817C23—1222no—
818C23—1222no—
819C23—1222no—
820C23—2441no—
821C23—2441no—
822C23—2441no—
823C23—2441no—
824C23—2441no—
825C23—2441no—
826C23—2441no—
827C23—2441no—
828C23—2441no—
829C23—2441no—
830C23—2441no—
831C23—2441no—
832C23—2441no—
833C23—2441no—
834C23—2441no—
835C23—2441no—
836C23C22×C4×D6111yescharacteristic
837C23C2×D4×D6111yescharacteristic
838C23C2×D4×D6111yescharacteristic
839C23C2×Q8×D6111yescharacteristic
840C23#41×D6111yescharacteristic
841C23#41×D6111yescharacteristic
842C23C2×#1175822611yescharacteristic
843C23#1451982211yescharacteristic
844C23#1451982211yescharacteristic
845C23#1451982211yescharacteristic
846C23#1451982211yescharacteristic
847C23#1451982311yescharacteristic
848C23#1451982411yescharacteristic
849C23#1451982511yescharacteristic
850C23#1451982511yescharacteristic
851Q8—24416no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—614no—
901C2×C4—1222no—
902C2×C4—1222no—
903C2×C4—1222no—
904C2×C4—1222no—
905C2×C4—1222no—
906C2×C4—1222no—
907C2×C4—1222no—
908C2×C4—1222no—
909C2×C4—1222no—
910C2×C4—1222no—
911C2×C4—1222no—
912C2×C4—1222no—
913C2×C4—1222no—
914C2×C4—1222no—
915C2×C4—1222no—
916C2×C4—1222no—
917C2×C4—1222no—
918C2×C4—1222no—
919C2×C4—1222no—
920C2×C4—1222no—
921C2×C4—1222no—
922C2×C4—1222no—
923C2×C4—1222no—
924C2×C4—1222no—
925C2×C4—24416no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4—2441no—
944C2×C4—2441no—
945C2×C4—2441no—
946C2×C4—2441no—
947C2×C4—2441no—
948C2×C4—2441no—
949C2×C4—2441no—
950C2×C4#1451973914yes—
951C22—1224no—
952C22—1224no—
953C22—1224no—
954C22—2442no—
955C22—2442no—
956C22—2442no—
957C22—2442no—
958C22—2442no—
959C22—2442no—
960C22—2442no—
961C22—2442no—
962C22—2442no—
963C22—2442no—
964C22—2442no—
965C22—2442no—
966C22C4×D4×D6111yescharacteristic
967C22C2×#1451973911yescharacteristic
968C22C4×Q8×D6111yescharacteristic
969C22#1684023411yescharacteristic
970C22#1684024111yescharacteristic
971C22#1684024311yescharacteristic
972C22#1684024311yescharacteristic
973C22#1684032511yescharacteristic
974C22#1684032711yescharacteristic
975C22#1684033511yescharacteristic
976C22#1684033711yescharacteristic
977C22#1684034411yescharacteristic
978C22#1684036011yescharacteristic
979C22#1684038011yescharacteristic
980C22#1684038211yescharacteristic
981C22#1684038611yescharacteristic
982C22#1684038611yescharacteristic
983C22#1684038711yescharacteristic
984C22#1684038911yescharacteristic
985C22#1684039411yescharacteristic
986C22#1684040111yescharacteristic
987C22#1684040311yescharacteristic
988C22#1684040411yescharacteristic
989C22#1684040911yescharacteristic
990C22#1684042511yescharacteristic
991C22#1684042711yescharacteristic
992C22#1684043911yescharacteristic
993C22#1684044411yescharacteristic
994C22#1684045011yescharacteristic
995C22#1684046611yescharacteristic
996C22#1684047311yescharacteristic
997C22#1684050511yescharacteristic
998C22#1684050811yescharacteristic
999C22#1684050911yescharacteristic
1000C22#1684051311yescharacteristic
1001C4—24no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—81no—
1007C4—81no—
1008C4—1224no—
1009C4—2442no—
1010C4—2442no—
1011C4—2442no—
1012C4—2442no—
1013C4—2442no—
1014C4—2442no—
1015C2—2444no—
1016C2#2144852511yescharacteristic
1017C2#2144852711yescharacteristic
1018C2#2144855311yescharacteristic
1019C2#2144879511yescharacteristic
1020C2#2144882111yescharacteristic
1021C2#2144882311yescharacteristic
1022C2#2144899211yescharacteristic
1023C2#2145204411yescharacteristic
1024C2#2145213311yescharacteristic
1025C2#2145223311yescharacteristic
1026C2#2145224711yescharacteristic
1027C2#2145230811yescharacteristic
1028C2#2145232211yescharacteristic
1029C2#2145322911yescharacteristic
1030C2#2145323811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1444C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1444D61
hypocenterC61#14575
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
2. C2×#16839667C2semidirect
3. C2×#16839666C2semidirect
6. #21444082C2semidirect
7. #21444078C2semidirect
8. #21444077C2semidirect
12. #21444045C2semidirect
13. #21444044C2semidirect
15. C61×#1444C2semidirect
28. #16839675C4semidirect
63. C22×Dic122C2×C4semidirect
101. C2×#11758198Q8semidirect
120. #14519684C2×C4semidirect
121. #14519684C2×C4semidirect
143. #95×C61C2×C4semidirect
506. #1444D61semidirect
571. C61#14575semidirect
659. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396752
C2×#168396672
C2×#168396662
C2×#168396332
#214440822
#214440782
#214440772
#214440612
#214440552
#214440452
#214440442
#214440402
C61×#14442
#1457561