Finite Group Databasebeta

← #29695607

Subgroups — #29695607

Order 15616.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840408C211yesmaximal, characteristic
2C2×#16839840C211yesmaximal, characteristic, complemented
3C2×#16839761C211yesmaximal, characteristic, complemented
4C2×#16839766C211yesmaximal, characteristic, complemented
5#21446751C211yesmaximal, characteristic, complemented
6#21446628C211yesmaximal, characteristic, complemented
7#21446255C211yesmaximal, characteristic, complemented
8#21446250C211yesmaximal, characteristic, complemented
9#21446136C211yesmaximal, characteristic, complemented
10#21446131C211yesmaximal, characteristic, complemented
11#21445826C211yesmaximal, characteristic, complemented
12#21445757C211yesmaximal, characteristic, complemented
13#21445749C211yesmaximal, characteristic, complemented
14C4×#14519697C211yesmaximal, characteristic, complemented
15C61×#2352C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C22×#11758194C2211yescharacteristic, complemented
20#16840408—24no—
21#16840408C418yescomplemented
22C2×#14519765C2211yescharacteristic
23C2×#14519762—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519751C2211yescharacteristic
26C2×#14519750—21no—
27C2×#14519745—21no—
28C2×C4×D244C2211yescharacteristic
29C2×C22⋊C4×D61—21no—
30#16839840—24no—
31C2×C4⋊#92418C2211yescharacteristic, complemented
32#16839766—24no—
33#16839761—24no—
34C2×#14519700C2211yescharacteristic, complemented
35C2×#14519700C2211yescharacteristic, complemented
36C2×#14519700C2211yescharacteristic, complemented
37C2×#14519700C2211yescharacteristic, complemented
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46C2×C22⋊#92418C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic, complemented
48C2×C4×#92418C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53C2×C4×D4×C61C2211yescharacteristic
54C2×#117×C61C2211yescharacteristic
55C22×C4⋊C4×C61C2211yescharacteristic, complemented
56C61×#388—21no—
57C61×#387—21no—
58C61×#386—21no—
59C61×#382C2211yescharacteristic, complemented
60C61×#380C2211yescharacteristic
61C61×#380C2211yescharacteristic, complemented
62C4×C4⋊C4×C61C2211yescharacteristic, complemented
63C4×C22⋊C4×C61—21no—
64C24×D61—21no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—41no—
69C2×#11758222—41no—
70C2×#11758222C2×C414yes—
71C22×Dic122C2311yescharacteristic
72C22×D244—22no—
73C22×D244—22no—
74C22×D244—21no—
75C22×D244—22no—
76C22×D244—41no—
77C22×D244—41no—
78C22×D244C2×C414yescomplemented
79C22×D244C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C2×#11758194—22no—
86C2×#11758194—22no—
87C2×#11758194—22no—
88C2×#11758194—22no—
89C2×#11758194—41no—
90C2×#11758194—41no—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95#14519765—22no—
96#14519765C2×C414yescomplemented
97#14519762—28no—
98#14519756—22no—
99#14519756C2×C414yescomplemented
100#14519751—22no—
101#14519751C2×C414yes—
102#14519750—28no—
103#14519745—28no—
104C4×D244—22no—
105C4×D244C2×C414yescomplemented
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×C22⋊Dic61—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C22⋊C4×D61—28no—
114C4⋊#92418—22no—
115#14519700—22no—
116#14519700—22no—
117#14519700—41no—
118#14519700—41no—
119#14519697—22no—
120#14519697—22no—
121#14519697—22no—
122#14519697—22no—
123#14519697—22no—
124#14519697—41no—
125#14519697—41no—
126#14519697D414yescomplemented
127C22⋊#92418—22no—
128C22⋊#92418—22no—
129C4×#92418—22no—
130C22×D4×C61D411yescharacteristic
131C23×C4×C61—21no—
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C4×D4×C61C2×C414yes—
135C4×D4×C61D414yes—
136#117×C61—22no—
137#117×C61—41no—
138C2×C4⋊C4×C61—22no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61—41no—
141C2×C4⋊C4×C61D411yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61D411yescharacteristic
150C2×C22⋊C4×C61D411yescharacteristic
151C2×C42×C61—21no—
152C2×C42×C61—21no—
153C2×C42×C61C2311yescharacteristic
154#95×C61—21no—
155#95×C61—21no—
156#95×C61—21no—
157#95×C61—21no—
158#95×C61—21no—
159C24×C61C2×D411yescharacteristic
160C24×C61C2×D411yescharacteristic
161C23×D61—21no—
162C23×D61—21no—
163C23×D61—24no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—42no—
168C23×D61—81no—
169C23×D61—81no—
170C2×D4×C61—41no—
171C2×D4×C61—41no—
172C2×D4×C61C22⋊C414yes—
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—42no—
186C22×C4×C61—42no—
187C22×C4×C61—81no—
188C22×C4×C61C22×C412yes—
189C22×C4×C61C22×C412yes—
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D412yes—
195C22×C4×C61C2×D412yes—
196C22×C4×C61C2411yescharacteristic
197C2×C22⋊D61—24no—
198C2×C22⋊D61—24no—
199C2×C22⋊D61—42no—
200C2×C22⋊D61—42no—
201C2×C22⋊D61—81no—
202C2×C22⋊D61—81no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205#11758222—28no—
206#11758222—44no—
207#11758222—44no—
208#11758222—44no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—28no—
217C2×D244—24no—
218C2×D244—21no—
219C2×D244—44no—
220C2×D244—44no—
221C2×D244—44no—
222C2×D244—42no—
223C2×D244—42no—
224C2×D244C22×C412yes—
225C2×D244C22×C412yes—
226C2×D244C2×D412yes—
227C2×D244#4112yes—
228C2×C4×D61—24no—
229C2×C4×D61—24no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—81no—
233C2×C4×D61—81no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122C22×C412yes—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—42no—
248C4⋊C4×C61C22⋊C414yes—
249C4⋊C4×C61C2×D412yes—
250C22⋊C4×C61—42no—
251C22⋊C4×C61—42no—
252C22⋊C4×C61—81no—
253C22⋊C4×C61C22⋊C414yes—
254C22⋊C4×C61C22⋊C414yes—
255C42×C61—42no—
256C42×C61—81no—
257C42×C61C22×C412yes—
258C42×C61C2×D412yes—
259C22⋊Dic61—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264C4⋊Dic61—21no—
265C4⋊Dic61C22×C412yes—
266#11758196—24no—
267#11758194—44no—
268#11758194—44no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418C2×D412yes—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61C2×C22⋊C412yes—
294C23×C61C2×C22⋊C412yes—
295C23×C61C22×D411yescharacteristic
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—48no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—48no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—84no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61—84no—
316C22×D61—84no—
317D4×C61—44no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
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—84no—
347C2×C4×C61C2×C22⋊C412yes—
348C2×C4×C61C2×C22⋊C412yes—
349C2×C4×C61C2×C22⋊C412yes—
350C2×C4×C61C2×C22⋊C412yes—
351C2×C4×C61C23×C411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C2×#4111yescharacteristic
355C2×C4×C61H(5,𝔽2)11yescharacteristic
356C2×C4×C61H(5,𝔽2)11yescharacteristic
357C22⋊D61—48no—
358C22⋊D61—84no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365D244—22no—
366D244—22no—
367D244—22no—
368D244—22no—
369D244—22no—
370D244—48no—
371D244—41no—
372D244—41no—
373D244C4×D414yes—
374C4×D61—48no—
375C4×D61—84no—
376Dic122—22no—
377Dic122—22no—
378Dic122—41no—
379Dic122—41no—
380#92418—22no—
381#92418—41no—
382#92418—41no—
383#92418—41no—
384#22427—611nomaximal, Sylow
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61C22×C22⋊C411yescharacteristic
400C22×C61D4211yescharacteristic
401C22×C61#54611yescharacteristic
402C22×C61#57511yescharacteristic
403C22×C61#57511yescharacteristic
404C22×C61#57611yescharacteristic
405C22×C61#57711yescharacteristic
406C2×D61—24no—
407C2×D61—42no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—816no—
417C2×D61—81no—
418C2×D61—81no—
419C2×D61—81no—
420C2×D61—81no—
421C4×C61—22no—
422C4×C61—22no—
423C4×C61—22no—
424C4×C61—22no—
425C4×C61—42no—
426C4×C61—81no—
427C4×C61—81no—
428C4×C61—81no—
429C4×C61C2×C4×D411yescharacteristic
430C4×C61#51811yescharacteristic
431C4×C61D4211yescharacteristic
432C4×C61#54611yescharacteristic
433Dic61—42no—
434Dic61—42no—
435C2×#546—611no—
436C2×#436—611no—
437C2×#417—611no—
438C2×#418—611no—
439#2352D6111yescharacteristic, complemented
440#1983—611no—
441#1958—611no—
442#1895—611no—
443#1894—611no—
444#1874—611no—
445#1873—611no—
446#1804—611no—
447#1788—611no—
448#1786—611no—
449C4×#102—611no—
450C2×C61—42no—
451C2×C61—42no—
452C2×C61D4×C22⋊C411yescharacteristic
453C2×C61#289611yescharacteristic
454C2×C61#289711yescharacteristic
455C2×C61#327311yescharacteristic
456C2×C61#327511yescharacteristic
457C2×C61#332211yescharacteristic
458C2×C61#332311yescharacteristic
459D61—44no—
460D61—82no—
461C22×#41—611no—
462C23×D4—611no—
463C22×M16—611no—
464C22×M16—611no—
465#546—618no—
466#546—1224no—
467C2×#124—611no—
468C2×#123—1221no—
469C2×C22⋊Q8—611no—
470C2×#121—611no—
471C2×#121—1221no—
472C2×#120—1221no—
473C2×C4×D4—611no—
474C2×C4×D4C2×D6111yescharacteristic
475C2×#117C2×D6111yescharacteristic
476C22×C4⋊C4C2×D6111yescharacteristic, complemented
477C22×C22⋊C4—1221no—
478#436—1224no—
479C2×C4⋊C8—611no—
480#418—1224no—
481#417—1224no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×C22⋊C8—611no—
495C2×C22⋊C8—611no—
496C2×C4×C8—611no—
497#388—21no—
498#387—21no—
499#386—21no—
500#382C2×D6111yescharacteristic, complemented
501#380C2×D6111yescharacteristic
502#380C2×D6111yescharacteristic, complemented
503C4×C4⋊C4C2×D6111yescharacteristic, complemented
504C4×C22⋊C4—21no—
505#340—611no—
506#340—611no—
507#340—611no—
508#340—611no—
509C61#2242711yescharacteristic, complemented, Sylow
510C25—1221no—
511C2×#41—614no—
512C2×#41—1222no—
513C2×#41—1222no—
514C2×#41—1222no—
515C2×#41—2441no—
516C2×#41—2441no—
517C22×Q8—611no—
518C22×D4—614no—
519C22×D4—611no—
520C22×D4—611no—
521C22×D4—1222no—
522C22×D4—1222no—
523C22×D4—1221no—
524C22×D4—1221no—
525C22×D4—1222no—
526C22×D4—1221no—
527C22×D4—2441no—
528C22×D4—2441no—
529C22×D4C22⋊D6111yescharacteristic
530C23×C4—21no—
531C23×C4—1221no—
532C23×C4—1221no—
533C23×C4C22×D6111yescharacteristic
534C23×C4C22×D6111yescharacteristic
535C2×M16—1222no—
536C2×M16—1222no—
537C2×M16—1222no—
538C2×M16—1222no—
539C2×M16—2441no—
540C2×M16—2441no—
541C22×C8—611no—
542C22×C8—611no—
543C22×C8—611no—
544C22×C8—611no—
545#124—614no—
546#124—1222no—
547#123—1228no—
548C22⋊Q8—614no—
549C22⋊Q8—1222no—
550#121—614no—
551#121—1222no—
552#121—1228no—
553#120—1228no—
554C4×D4—614no—
555C4×D4—1222no—
556C4×D4C4×D6114yes—
557C4×D4D24414yes—
558#117—22no—
559#117—41no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4C22⋊D6111yescharacteristic
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C4⋊C4C22×D6111yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1228no—
579C2×C22⋊C4C22⋊D6111yescharacteristic
580C2×C22⋊C4C22⋊D6111yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42C22×D6111yescharacteristic
584C4⋊C8—1222no—
585#103—1222no—
586#103—1222no—
587#103—2441no—
588#103—2441no—
589#102—614no—
590#102—1222no—
591#102—1222no—
592#102—1222no—
593#102—1222no—
594#102—1222no—
595#102—2441no—
596#102—2441no—
597C22⋊C8—1222no—
598C22⋊C8—1222no—
599C4×C8—1222no—
600#95—21no—
601#95—21no—
602#95—21no—
603#95—21no—
604#95—21no—
605C24—1221no—
606C24—1224no—
607C24—1221no—
608C24—4881no—
609C24—4881no—
610C24—2442no—
611C24—2442no—
612C24—2442no—
613C24—2442no—
614C24C2×C22⋊D6111yescharacteristic
615C24C2×C22⋊D6111yescharacteristic
616#41—1228no—
617#41—2444no—
618#41—2444no—
619#41—2444no—
620C2×Q8—612no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×D4—41no—
627C2×D4—41no—
628C2×D4—612no—
629C2×D4—612no—
630C2×D4—612no—
631C2×D4—612no—
632C2×D4—1228no—
633C2×D4—1224no—
634C2×D4—1224no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1224no—
644C2×D4—4881no—
645C2×D4—4881no—
646C2×D4—2444no—
647C2×D4—2444no—
648C2×D4—2444no—
649C2×D4—2442no—
650C2×D4—2442no—
651C2×D4—2442no—
652C2×D4—2442no—
653C2×D4#1175819814yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
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—42no—
667C22×C4—42no—
668C22×C4—81no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1224no—
672C22×C4—1224no—
673C22×C4—4881no—
674C22×C4—4881no—
675C22×C4—2442no—
676C22×C4—2442no—
677C22×C4C2×C4×D6112yes—
678C22×C4C2×C4×D6112yes—
679C22×C4C2×D24412yes—
680C22×C4C2×D24412yes—
681C22×C4C2×C22⋊D6111yescharacteristic
682C22×C4C2×C22⋊D6111yescharacteristic
683C22×C4C2×C22⋊D6111yescharacteristic
684C22×C4C2×C22⋊D6111yescharacteristic
685C22×C4C23×D6111yescharacteristic
686M16—2444no—
687M16—2444no—
688C2×C8—612no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8—1221no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—42no—
708C4⋊C4—612no—
709C4⋊C4—1221no—
710C4⋊C4—1224no—
711C4⋊C4#1175819814yes—
712C4⋊C4D4×D6112yes—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—81no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C22⋊C4—1224no—
721C22⋊C4#1175819814yes—
722C22⋊C4#1175819814yes—
723C42—42no—
724C42—81no—
725C42C2×C4×D6112yes—
726C42C2×D24412yes—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—1222no—
740C23—1222no—
741C23—1222no—
742C23—1222no—
743C23—4884no—
744C23—4884no—
745C23—4884no—
746C23—4884no—
747C23—4884no—
748C23—2448no—
749C23—2448no—
750C23—2441no—
751C23—2441no—
752C23—2441no—
753C23—2441no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23—2441no—
758C23—2441no—
759C23—2441no—
760C23C2×#1175819812yes—
761C23C2×#1175819812yes—
762C23C22×C22⋊D6111yescharacteristic
763Q8—1222no—
764Q8—1222no—
765Q8—2441no—
766Q8—2441no—
767D4—44no—
768D4—614no—
769D4—1222no—
770D4—1222no—
771D4—1222no—
772D4—1222no—
773D4—1222no—
774D4—4884no—
775D4—2448no—
776D4—2448no—
777D4—2441no—
778D4—2441no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—84no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—4884no—
811C2×C4—2448no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4C2×#1175819812yes—
817C2×C4C2×#1175819812yes—
818C2×C4C2×#1175819812yes—
819C2×C4C2×#1175819812yes—
820C2×C4C22×C4×D6111yescharacteristic
821C2×C4C2×D4×D6111yescharacteristic
822C2×C4C22×D24411yescharacteristic
823C2×C4#41×D6111yescharacteristic
824C2×C4#1451982211yescharacteristic
825C2×C4#1451982311yescharacteristic
826C8—1222no—
827C8—2441no—
828C8—2441no—
829C8—2441no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—1224no—
845C22—48816no—
846C22—4881no—
847C22—4881no—
848C22—4881no—
849C22—4881no—
850C22—2442no—
851C22—2442no—
852C22—2442no—
853C22—2442no—
854C22—2442no—
855C22—2442no—
856C22—2442no—
857C22—2442no—
858C22—2442no—
859C22C22×#1175819811yescharacteristic
860C22D4×C22⋊D6111yescharacteristic
861C22#1684040011yescharacteristic
862C22#1684056011yescharacteristic
863C22#1684056011yescharacteristic
864C22#1684056511yescharacteristic
865C22#1684057011yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—2442no—
875C4—2442no—
876C4C4×D4×D6111yescharacteristic
877C4#1684023411yescharacteristic
878C4D4×D24411yescharacteristic
879C4#1684040711yescharacteristic
880C2—42no—
881C2—42no—
882C2—4882no—
883C2—2444no—
884C2D4×#1175819811yescharacteristic
885C2#2145433611yescharacteristic
886C2#2145434211yescharacteristic
887C2#2145742611yescharacteristic
888C2#2145745111yescharacteristic
889C2#2145801411yescharacteristic
890C2#2145802911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2352C2
socleC23×C61C22×D4
prime radicalC2×#16840408C2
cosocleC22×C4×C61C24
hypercenter#2352D61
hypocenterC61#22427
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#16839840C2semidirect
3. C2×#16839761C2semidirect
4. C2×#16839766C2semidirect
5. #21446751C2semidirect
6. #21446628C2semidirect
7. #21446255C2semidirect
8. #21446250C2semidirect
9. #21446136C2semidirect
10. #21446131C2semidirect
11. #21445826C2semidirect
12. #21445757C2semidirect
13. #21445749C2semidirect
14. C4×#14519697C2semidirect
15. C61×#2352C2semidirect
19. C22×#11758194C22semidirect
21. #16840408C4semidirect
31. C2×C4⋊#92418C22semidirect
34. C2×#14519700C22semidirect
35. C2×#14519700C22semidirect
36. C2×#14519700C22semidirect
37. C2×#14519700C22semidirect
47. C2×C22⋊#92418C22semidirect
48. C2×C4×#92418C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
55. C22×C4⋊C4×C61C22semidirect
59. C61×#382C22semidirect
61. C61×#380C22semidirect
62. C4×C4⋊C4×C61C22semidirect
78. C22×D244C2×C4semidirect
96. #14519765C2×C4semidirect
99. #14519756C2×C4semidirect
105. C4×D244C2×C4semidirect
126. #14519697D4semidirect
439. #2352D61semidirect
476. C22×C4⋊C4C2×D61semidirect
500. #382C2×D61semidirect
502. #380C2×D61semidirect
503. C4×C4⋊C4C2×D61semidirect
509. C61#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#168404082
C2×#168398402
C2×#168397612
C2×#168397662
#214467512
#214466282
#214462552
#214462502
#214461362
#214461312
#214458262
#214457572
#214457492
C4×#145196972
C61×#23522
#2242761