Finite Group Databasebeta

← #29695532

Subgroups — #29695532

Order 15616.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840433C211yesmaximal, characteristic
2C2×#16839834C211yesmaximal, characteristic, complemented
3C2×#16839761C211yesmaximal, characteristic, complemented
4C2×#16839756C211yesmaximal, characteristic, complemented
5#21446746C211yesmaximal, characteristic, complemented
6#21446642C211yesmaximal, characteristic, complemented
7#21446255C211yesmaximal, characteristic, complemented
8#21446245C211yesmaximal, characteristic, complemented
9#21446141C211yesmaximal, characteristic, complemented
10#21446136C211yesmaximal, characteristic, complemented
11#21445831C211yesmaximal, characteristic, complemented
12#21445757C211yesmaximal, characteristic, complemented
13#21445757C211yesmaximal, characteristic, complemented
14#21445652C211yesmaximal, characteristic, complemented
15C61×#2352C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758222C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20#16840433—24no—
21#16840433C418yescomplemented
22C2×#14519774C2211yescharacteristic
23C2×#14519773—21no—
24C2×#14519751C2211yescharacteristic
25C2×#14519751C2211yescharacteristic
26C2×#14519750—21no—
27C2×#14519750—21no—
28C2×C4×Dic122C2211yescharacteristic
29C2×#14519739—21no—
30#16839834—24no—
31C2×C4⋊#92418C2211yescharacteristic
32#16839761—24no—
33#16839756—24no—
34C2×#14519700C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46C2×C22⋊#92418C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic
48C2×#14519688C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×#117×C61C2211yescharacteristic
55C22×C4⋊C4×C61C2211yescharacteristic
56C61×#388—21no—
57C61×#387—21no—
58C61×#386—21no—
59C61×#382C2211yescharacteristic
60C61×#380C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C4×C4⋊C4×C61C2211yescharacteristic
63C4×C22⋊C4×C61—21no—
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222—22no—
70C2×#11758222—41no—
71C2×#11758222—41no—
72C2×#11758222—41no—
73C2×#11758222—41no—
74C2×#11758222C2×C414yes—
75C2×#11758222C2×C414yescomplemented
76C22×Dic122C2311yescharacteristic
77C22×D244—21no—
78C22×D244—21no—
79C22×D244C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C2×#11758194—22no—
88C2×#11758194—22no—
89C2×#11758194—41no—
90C22×#92418—22no—
91C22×#92418—22no—
92C22×#92418—41no—
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97#14519774—22no—
98#14519774C2×C414yescomplemented
99#14519773—28no—
100#14519751—22no—
101#14519751—22no—
102#14519751C2×C414yes—
103#14519751C2×C414yescomplemented
104#14519750—28no—
105#14519750—28no—
106C4×Dic122—22no—
107C4×Dic122C2×C414yescomplemented
108#14519739—28no—
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×C4×Dic61—21no—
114C4⋊#92418—22no—
115#14519700—22no—
116#14519700—22no—
117#14519700—22no—
118#14519700D414yescomplemented
119#14519697—22no—
120#14519697—22no—
121#14519697—22no—
122#14519697—22no—
123#14519697—41no—
124#14519697—41no—
125#14519697—41no—
126#14519697—41no—
127C22⋊#92418—22no—
128C22⋊#92418—22no—
129#14519688—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—
163C2×D4×C61—41no—
164C2×D4×C61—41no—
165C2×D4×C61C22⋊C414yes—
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—42no—
179C22×C4×C61—42no—
180C22×C4×C61—81no—
181C22×C4×C61C22×C412yes—
182C22×C4×C61C22×C412yes—
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D412yes—
188C22×C4×C61C2×D412yes—
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—24no—
191C2×C22⋊D61—24no—
192C2×C22⋊D61—24no—
193C2×C22⋊D61—24no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—42no—
197C2×C22⋊D61—42no—
198C2×C22⋊D61—81no—
199C2×C22⋊D61—81no—
200C2×C22⋊D61—81no—
201C2×C22⋊D61—81no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204#11758222—28no—
205#11758222—28no—
206#11758222—44no—
207#11758222—44no—
208#11758222—44no—
209#11758222—44no—
210#11758222—44no—
211#11758222—44no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—24no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—24no—
224C2×D244—42no—
225C2×D244—42no—
226C2×D244—81no—
227C2×D244—81no—
228C2×D244C22×C412yes—
229C2×D244C22×C412yes—
230C2×C4×D61—24no—
231C2×C4×D61—24no—
232C2×C4×D61—42no—
233C2×C4×D61—42no—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122C22×C412yes—
240C2×Dic122C2×D412yes—
241C2×Dic122#4112yes—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—42no—
250C4⋊C4×C61C22⋊C414yes—
251C4⋊C4×C61C2×D412yes—
252C22⋊C4×C61—42no—
253C22⋊C4×C61—42no—
254C22⋊C4×C61—81no—
255C22⋊C4×C61C22⋊C414yes—
256C22⋊C4×C61C22⋊C414yes—
257C42×C61—42no—
258C42×C61—81no—
259C42×C61C22×C412yes—
260C42×C61C2×D412yes—
261#11758198—24no—
262#11758198—24no—
263C4⋊Dic61—21no—
264C4⋊Dic61C22×C412yes—
265#11758196—24no—
266C4×Dic61—24no—
267#11758194—44no—
268C2×#92418—21no—
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—44no—
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—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310D4×C61—44no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
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—84no—
340C2×C4×C61C2×C22⋊C412yes—
341C2×C4×C61C2×C22⋊C412yes—
342C2×C4×C61C2×C22⋊C412yes—
343C2×C4×C61C2×C22⋊C412yes—
344C2×C4×C61C23×C411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C2×#4111yescharacteristic
348C2×C4×C61H(5,𝔽2)11yescharacteristic
349C2×C4×C61H(5,𝔽2)11yescharacteristic
350C22⋊D61—48no—
351C22⋊D61—48no—
352C22⋊D61—84no—
353C22⋊D61—84no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360D244—22no—
361D244—22no—
362D244—22no—
363D244—22no—
364D244—48no—
365D244—41no—
366D244—41no—
367D244—41no—
368D244—41no—
369D244—84no—
370C4×D61—48no—
371C4×D61—48no—
372Dic122—22no—
373Dic122—22no—
374Dic122—22no—
375Dic122C4×D414yes—
376#92418—22no—
377#92418—41no—
378#92418—41no—
379#92418—41no—
380#22422—611nomaximal, Sylow
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61C22×C22⋊C411yescharacteristic
396C22×C61D4211yescharacteristic
397C22×C61#54611yescharacteristic
398C22×C61#57511yescharacteristic
399C22×C61#57511yescharacteristic
400C22×C61#57611yescharacteristic
401C22×C61#57711yescharacteristic
402C2×D61—42no—
403C2×D61—42no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—42no—
408C2×D61—81no—
409C2×D61—81no—
410C2×D61—81no—
411C2×D61—81no—
412C2×D61—81no—
413C2×D61—81no—
414C2×D61—81no—
415C2×D61—81no—
416C4×C61—22no—
417C4×C61—22no—
418C4×C61—22no—
419C4×C61—22no—
420C4×C61—42no—
421C4×C61—81no—
422C4×C61—81no—
423C4×C61—81no—
424C4×C61C2×C4×D411yescharacteristic
425C4×C61#51811yescharacteristic
426C4×C61D4211yescharacteristic
427C4×C61#54611yescharacteristic
428Dic61—24no—
429Dic61—42no—
430C2×#550—611no—
431C2×#435—611no—
432C2×#417—611no—
433C2×#416—611no—
434#2352D6111yescharacteristic, complemented
435#1982—611no—
436#1961—611no—
437#1895—611no—
438#1893—611no—
439#1875—611no—
440#1874—611no—
441#1805—611no—
442#1788—611no—
443#1788—611no—
444#1763—611no—
445C2×C61—42no—
446C2×C61—42no—
447C2×C61D4×C22⋊C411yescharacteristic
448C2×C61#289611yescharacteristic
449C2×C61#289711yescharacteristic
450C2×C61#326811yescharacteristic
451C2×C61#327111yescharacteristic
452C2×C61#330911yescharacteristic
453C2×C61#331711yescharacteristic
454D61—82no—
455D61—82no—
456C22×#41—611no—
457C22×#41—611no—
458C22×M16—611no—
459C23×C8—611no—
460#550—618no—
461#550—1224no—
462C2×#127—611no—
463C2×#127—1221no—
464C2×#121—611no—
465C2×#121—611no—
466C2×#121—1221no—
467C2×#121—1221no—
468C2×C4×Q8—611no—
469C2×C4×D4—1221no—
470C2×C4×D4C2×D6111yescharacteristic
471C2×#117C2×D6111yescharacteristic
472C22×C4⋊C4C2×D6111yescharacteristic
473#435—1224no—
474C2×C4⋊C8—611no—
475#417—1224no—
476#416—1224no—
477C2×#103—611no—
478C2×#103—611no—
479C2×#103—611no—
480C2×#103—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×C22⋊C8—611no—
490C2×C22⋊C8—611no—
491C2×#97—611no—
492#388—21no—
493#387—21no—
494#386—21no—
495#382C2×D6111yescharacteristic
496#380C2×D6111yescharacteristic
497#380C2×D6111yescharacteristic
498C4×C4⋊C4C2×D6111yescharacteristic
499C4×C22⋊C4—21no—
500#340—611no—
501#340—611no—
502#340—611no—
503#340—611no—
504C61#2242211yescharacteristic, complemented, Sylow
505C2×#41—614no—
506C2×#41—614no—
507C2×#41—1222no—
508C2×#41—1222no—
509C2×#41—1222no—
510C2×#41—1222no—
511C2×#41—1222no—
512C2×#41—1222no—
513C2×#41—2441no—
514C2×#41—2441no—
515C2×#41—2441no—
516C2×#41—2441no—
517C22×Q8—611no—
518C22×D4—611no—
519C22×D4—611no—
520C22×D4—1221no—
521C22×D4—1221no—
522C22×D4—1221no—
523C22×D4—1221no—
524C22×D4—1221no—
525C22×D4—1221no—
526C22×D4C22⋊D6111yescharacteristic
527C23×C4—21no—
528C23×C4—1221no—
529C23×C4—1221no—
530C23×C4C22×D6111yescharacteristic
531C23×C4C22×D6111yescharacteristic
532C2×M16—1222no—
533C2×M16—1222no—
534C2×M16—2441no—
535C22×C8—611no—
536C22×C8—611no—
537C22×C8—611no—
538C22×C8—611no—
539C22×C8—1222no—
540C22×C8—1222no—
541C22×C8—2441no—
542#127—614no—
543#127—1228no—
544#127—1222no—
545#121—614no—
546#121—614no—
547#121—1222no—
548#121—1222no—
549#121—1228no—
550#121—1228no—
551C4×Q8—614no—
552C4×Q8—1222no—
553C4×D4—1228no—
554C4×D4C4×D6114yes—
555C4×D4D24414yes—
556#117—22no—
557#117—41no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4C22⋊D6111yescharacteristic
564C2×C4⋊C4C22×D6111yescharacteristic
565C2×C4⋊C4C22×D6111yescharacteristic
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4C22⋊D6111yescharacteristic
574C2×C22⋊C4C22⋊D6111yescharacteristic
575C2×C42—21no—
576C2×C42—21no—
577C2×C42—1221no—
578C2×C42C22×D6111yescharacteristic
579C4⋊C8—1222no—
580#103—614no—
581#103—1222no—
582#103—1222no—
583#103—1222no—
584#102—1222no—
585#102—1222no—
586#102—1222no—
587#102—1222no—
588#102—2441no—
589#102—2441no—
590#102—2441no—
591#102—2441no—
592C22⋊C8—1222no—
593C22⋊C8—1222no—
594#97—1222no—
595#95—21no—
596#95—21no—
597#95—21no—
598#95—21no—
599#95—21no—
600C24—1221no—
601C24—1221no—
602C24C2×C22⋊D6111yescharacteristic
603C24C2×C22⋊D6111yescharacteristic
604#41—1228no—
605#41—1228no—
606#41—2444no—
607#41—2444no—
608#41—2444no—
609#41—2444no—
610#41—2444no—
611#41—2444no—
612C2×Q8—612no—
613C2×Q8—612no—
614C2×Q8—612no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8—1221no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—612no—
621C2×D4—612no—
622C2×D4—1224no—
623C2×D4—1224no—
624C2×D4—1224no—
625C2×D4—1224no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1221no—
631C2×D4—1221no—
632C2×D4—1221no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1224no—
637C2×D4—1224no—
638C2×D4—4881no—
639C2×D4—4881no—
640C2×D4—4881no—
641C2×D4—4881no—
642C2×D4—4881no—
643C2×D4—4881no—
644C2×D4—2442no—
645C2×D4—2442no—
646C2×D4—2442no—
647C2×D4—2442no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4#1175819814yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
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—42no—
664C22×C4—42no—
665C22×C4—81no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1224no—
669C22×C4—1224no—
670C22×C4—2442no—
671C22×C4—2442no—
672C22×C4—2442no—
673C22×C4—2442no—
674C22×C4C2×C4×D6112yes—
675C22×C4C2×C4×D6112yes—
676C22×C4C2×D24412yes—
677C22×C4C2×D24412yes—
678C22×C4C2×C22⋊D6111yescharacteristic
679C22×C4C2×C22⋊D6111yescharacteristic
680C22×C4C2×C22⋊D6111yescharacteristic
681C22×C4C2×C22⋊D6111yescharacteristic
682C22×C4C23×D6111yescharacteristic
683M16—2444no—
684C2×C8—612no—
685C2×C8—1221no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—2444no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—42no—
705C4⋊C4—612no—
706C4⋊C4—1221no—
707C4⋊C4—1224no—
708C4⋊C4#1175819814yes—
709C4⋊C4D4×D6112yes—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—81no—
713C22⋊C4—1224no—
714C22⋊C4—1224no—
715C22⋊C4#1175819814yes—
716C22⋊C4#1175819814yes—
717C42—42no—
718C42—81no—
719C42—1224no—
720C42C2×C4×D6112yes—
721C42C2×D24412yes—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—1222no—
735C23—1222no—
736C23—2441no—
737C23—2441no—
738C23—2441no—
739C23—2441no—
740C23—2441no—
741C23—2441no—
742C23—2441no—
743C23—2441no—
744C23—2441no—
745C23—2441no—
746C23—2441no—
747C23—2441no—
748C23C2×#1175819812yes—
749C23C2×#1175819812yes—
750C23C22×C22⋊D6111yescharacteristic
751Q8—614no—
752Q8—1222no—
753Q8—1222no—
754Q8—1222no—
755D4—44no—
756D4—1222no—
757D4—1222no—
758D4—1222no—
759D4—1222no—
760D4—4884no—
761D4—4884no—
762D4—4884no—
763D4—2448no—
764D4—2448no—
765D4—2448no—
766D4—2441no—
767D4—2441no—
768D4—2441no—
769D4—2441no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—84no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—2448no—
804C2×C4—2448no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4C2×#1175819812yes—
808C2×C4C2×#1175819812yes—
809C2×C4C2×#1175819812yes—
810C2×C4C2×#1175819812yes—
811C2×C4C22×C4×D6111yescharacteristic
812C2×C4C2×D4×D6111yescharacteristic
813C2×C4C22×D24411yescharacteristic
814C2×C4#41×D6111yescharacteristic
815C2×C4#1451982211yescharacteristic
816C2×C4#1451982311yescharacteristic
817C8—1222no—
818C8—2441no—
819C8—2441no—
820C8—2441no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—4881no—
836C22—4881no—
837C22—4881no—
838C22—4881no—
839C22—4881no—
840C22—4881no—
841C22—4881no—
842C22—4881no—
843C22—2442no—
844C22—2442no—
845C22—2442no—
846C22—2442no—
847C22—2442no—
848C22—2442no—
849C22C22×#1175819811yescharacteristic
850C22D4×C22⋊D6111yescharacteristic
851C22#1684040011yescharacteristic
852C22#1684056011yescharacteristic
853C22#1684056011yescharacteristic
854C22#1684056511yescharacteristic
855C22#1684057011yescharacteristic
856C4—22no—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—42no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4—1224no—
865C4—2442no—
866C4C4×D4×D6111yescharacteristic
867C4#1684023411yescharacteristic
868C4D4×D24411yescharacteristic
869C4#1684040711yescharacteristic
870C2—42no—
871C2—42no—
872C2—4882no—
873C2—4882no—
874C2D4×#1175819811yescharacteristic
875C2#2145433611yescharacteristic
876C2#2145434211yescharacteristic
877C2#2145735511yescharacteristic
878C2#2145740511yescharacteristic
879C2#2145781911yescharacteristic
880C2#2145793911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2352C2
socleC23×C61C22×D4
prime radicalC2×#16840433C2
cosocleC22×C4×C61C24
hypercenter#2352D61
hypocenterC61#22422
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×#16839834C2semidirect
3. C2×#16839761C2semidirect
4. C2×#16839756C2semidirect
5. #21446746C2semidirect
6. #21446642C2semidirect
7. #21446255C2semidirect
8. #21446245C2semidirect
9. #21446141C2semidirect
10. #21446136C2semidirect
11. #21445831C2semidirect
12. #21445757C2semidirect
13. #21445757C2semidirect
14. #21445652C2semidirect
15. C61×#2352C2semidirect
21. #16840433C4semidirect
75. C2×#11758222C2×C4semidirect
98. #14519774C2×C4semidirect
103. #14519751C2×C4semidirect
107. C4×Dic122C2×C4semidirect
118. #14519700D4semidirect
434. #2352D61semidirect
504. C61#22422semidirect

Maximal subgroups

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

subgroupindex
C2×#168404332
C2×#168398342
C2×#168397612
C2×#168397562
#214467462
#214466422
#214462552
#214462452
#214461412
#214461362
#214458312
#214457572
#214456522
C61×#23522
#2242261