Finite Group Databasebeta

← #29695531

Subgroups — #29695531

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×#16840431C211yesmaximal, characteristic
2C2×#16839836C211yesmaximal, characteristic, complemented
3C2×#16839763C211yesmaximal, characteristic, complemented
4C2×#16839757C211yesmaximal, characteristic, complemented
5#21448750C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446641C211yesmaximal, characteristic, complemented
8#21446255C211yesmaximal, characteristic, complemented
9#21446244C211yesmaximal, characteristic, complemented
10#21446138C211yesmaximal, characteristic, complemented
11#21446134C211yesmaximal, characteristic, complemented
12#21445832C211yesmaximal, characteristic, complemented
13#21445758C211yesmaximal, characteristic, complemented
14#21445651C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840431—24no—
20#16840431C418yescomplemented
21C2×#14519773—21no—
22C2×#14519773C2211yescharacteristic
23C2×#14519751—21no—
24C2×#14519751C2211yescharacteristic
25C2×#14519748—21no—
26C2×#14519748C2211yescharacteristic
27C2×Q8×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61—21no—
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×#14519735C2211yescharacteristic
31C22×C4⋊Dic61C2211yescharacteristic
32#16839836—24no—
33C2×#14519706C2211yescharacteristic
34#16839763—24no—
35#16839757—24no—
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519699C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519687C2211yescharacteristic
46#16839654—21no—
47#16839649—21no—
48#16839639—21no—
49#16839627C2211yescharacteristic
50#16839619C2211yescharacteristic
51C4⋊C4×Dic61C2211yescharacteristic
52C22⋊C4×Dic61—21no—
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C22×#41×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—41no—
68C2×#11758226—41no—
69C2×#11758226C2×C414yescomplemented
70C22×D244—21no—
71C22×D244C2311yescharacteristic
72C22×C22⋊D61—21no—
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C22×C22⋊D61—21no—
76C22×C22⋊D61D411yescharacteristic
77C23×Dic61—21no—
78C22×C4×D61—21no—
79C22×C4×D61C2311yescharacteristic
80C2×#11758194—22no—
81C2×#11758194—22no—
82C2×#11758194—41no—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C2×C8×D61—22no—
86C2×C8×D61—22no—
87C2×C8×D61—41no—
88#14519773—28no—
89#14519773—22no—
90#14519773C2×C414yescomplemented
91#14519751—22no—
92#14519751—28no—
93#14519751C2×C414yes—
94#14519748—22no—
95#14519748—28no—
96#14519748C2×C414yescomplemented
97Q8×Dic61—22no—
98Q8×Dic61C2×C414yescomplemented
99C4×C22⋊D61—28no—
100C4×C22⋊D61C2×C414yes—
101C4×C22⋊D61D414yes—
102#14519735—22no—
103#14519735—41no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61—22no—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61—41no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×#11758196D411yescharacteristic
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61D411yescharacteristic
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198D411yescharacteristic
118C2×C4×Dic61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61C2311yescharacteristic
122#14519706—22no—
123#14519701—22no—
124#14519701D414yescomplemented
125#14519699—22no—
126#14519699—41no—
127#14519698—22no—
128#14519698—22no—
129#14519697—22no—
130#14519697—41no—
131#14519689—22no—
132#14519687—22no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137C2×#41×C61—22no—
138C2×#41×C61—22no—
139C2×#41×C61—22no—
140C2×#41×C61—41no—
141C2×#41×C61—41no—
142C2×#41×C61C2×C414yes—
143C22×Q8×C61C2311yescharacteristic
144C22×D4×C61—21no—
145C22×D4×C61C2311yescharacteristic
146C23×C4×C61—21no—
147C23×C4×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C22⋊C4×C61—21no—
153#103×C61—22no—
154#103×C61—22no—
155#102×C61—41no—
156#102×C61—41no—
157C22⋊C8×C61—22no—
158#95×C61—21no—
159C24×C61—21no—
160C24×C61C2×D411yescharacteristic
161C23×D61—21no—
162C23×D61C2×D411yescharacteristic
163#41×C61—28no—
164#41×C61—44no—
165#41×C61—44no—
166#41×C61—44no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61C22×C412yes—
171C2×Q8×C61C2×D412yes—
172C2×Q8×C61#4112yes—
173C2×D4×C61—24no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—42no—
180C2×D4×C61—42no—
181C2×D4×C61C22×C412yes—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—24no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—42no—
191C22×C4×C61—42no—
192C22×C4×C61C22×C412yes—
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D412yes—
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—24no—
197C2×C22⋊D61—24no—
198C2×C22⋊D61—24no—
199C2×C22⋊D61—24no—
200C2×C22⋊D61—41no—
201C2×C22⋊D61—41no—
202C2×C22⋊D61—42no—
203C2×C22⋊D61—42no—
204C2×C22⋊D61—81no—
205C2×C22⋊D61—81no—
206C2×C22⋊D61—81no—
207C2×C22⋊D61—81no—
208C2×C22⋊D61—81no—
209C2×C22⋊D61—81no—
210C2×C22⋊D61C22⋊C414yes—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—42no—
215C22×Dic61—42no—
216C22×Dic61—81no—
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220#11758226—28no—
221#11758226—44no—
222#11758226—44no—
223#11758226—44no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—24no—
229C2×D244—21no—
230C2×D244—42no—
231C2×D244—42no—
232C2×D244C22×C412yes—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—24no—
238C2×C4×D61—42no—
239C2×C4×D61—42no—
240C2×C4×D61C22×C412yes—
241C2×C4×D61C2×D412yes—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C22⋊C4×C61—42no—
253C22⋊Dic61—24no—
254C22⋊Dic61C22⋊C414yes—
255#11758198—24no—
256#11758198—42no—
257#11758198—81no—
258#11758198C22⋊C414yes—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—24no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—42no—
265C4⋊Dic61C22×C412yes—
266C4⋊Dic61C2×D412yes—
267#11758196C22⋊C414yes—
268C4×Dic61—24no—
269C4×Dic61—42no—
270C4×Dic61—81no—
271C4×Dic61C22×C412yes—
272C4×Dic61C2×D412yes—
273#11758194—44no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418C2×D412yes—
280C8×D61—44no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—22no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61C2×C22⋊C412yes—
295C23×C61C22×D411yescharacteristic
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—22no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61C2×C22⋊C412yes—
310Q8×C61—22no—
311Q8×C61—22no—
312Q8×C61—22no—
313Q8×C61C4×D414yes—
314D4×C61—22no—
315D4×C61—22no—
316D4×C61—48no—
317D4×C61—41no—
318D4×C61—41no—
319C2×C4×C61—22no—
320C2×C4×C61—21no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—21no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—48no—
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×C61C2×C22⋊C412yes—
336C2×C4×C61C23×C411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C2×#4111yescharacteristic
340C2×C4×C61H(5,𝔽2)11yescharacteristic
341C2×C4×C61H(5,𝔽2)11yescharacteristic
342C22⋊D61—44no—
343C22⋊D61—48no—
344C22⋊D61—84no—
345C22⋊D61—84no—
346C22⋊D61—84no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—84no—
363C2×Dic61C2×C22⋊C412yes—
364C2×Dic61C2×C22⋊C412yes—
365C2×Dic61C2×C22⋊C412yes—
366D244—22no—
367D244—22no—
368D244—48no—
369D244—41no—
370D244—41no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—48no—
376C8×C61—41no—
377C8×C61—41no—
378#92418—22no—
379#92418—41no—
380#22422—611nomaximal, Sylow
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—42no—
391C22×C61—81no—
392C22×C61—81no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61C22×C22⋊C411yescharacteristic
396C22×C61D4211yescharacteristic
397C22×C61#54611yescharacteristic
398C22×C61#57511yescharacteristic
399C22×C61#57511yescharacteristic
400C22×C61#57611yescharacteristic
401C22×C61#57711yescharacteristic
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—81no—
413C2×D61—81no—
414C2×D61—81no—
415C2×D61—81no—
416C4×C61—24no—
417C4×C61—22no—
418C4×C61—81no—
419C4×C61—81no—
420C4×C61C2×C4×D411yescharacteristic
421C4×C61#51811yescharacteristic
422C4×C61D4211yescharacteristic
423C4×C61#54611yescharacteristic
424Dic61—22no—
425Dic61—22no—
426Dic61—22no—
427Dic61—42no—
428Dic61—42no—
429Dic61—81no—
430C2×#550—611no—
431C2×#435—611no—
432C2×#417—611no—
433C2×#416—611no—
434#2352—611no—
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#1788D6111yescharacteristic, complemented
444#1763—611no—
445C2×C61—42no—
446C2×C61—82no—
447C2×C61D4×C22⋊C411yescharacteristic
448C2×C61#289611yescharacteristic
449C2×C61#289711yescharacteristic
450C2×C61#326811yescharacteristic
451C2×C61#327111yescharacteristic
452C2×C61#330911yescharacteristic
453C2×C61#331711yescharacteristic
454D61—42no—
455D61—82no—
456C22×#41—611no—
457C22×#41C2×D6111yescharacteristic
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—611no—
470C2×C4×D4—1221no—
471C2×#117—611no—
472C22×C4⋊C4—611no—
473#435—1224no—
474C2×C4⋊C8—611no—
475#417—1224no—
476#416—1224no—
477C2×#103—611no—
478C2×#103—611no—
479C2×#103C2×D6111yescharacteristic
480C2×#103C2×D6111yescharacteristic
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102C2×D6111yescharacteristic
488C2×#102C2×D6111yescharacteristic
489C2×C22⋊C8—611no—
490C2×C22⋊C8C2×D6111yescharacteristic
491C2×#97—611no—
492#388—1221no—
493#387—1221no—
494#386—1221no—
495#382—611no—
496#380—611no—
497#380C2×D6111yescharacteristic
498C4×C4⋊C4—611no—
499C4×C22⋊C4—1221no—
500#340—611no—
501#340—611no—
502#340—611no—
503#340—611no—
504C61#2242211yescharacteristic, complemented, Sylow
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—614no—
511C2×#41—1222no—
512C2×#41—1222no—
513C2×#41—1222no—
514C2×#41—2441no—
515C2×#41—2441no—
516C2×#41C4×D6114yes—
517C22×Q8C22×D6111yescharacteristic
518C22×D4—21no—
519C22×D4—611no—
520C22×D4—611no—
521C22×D4—1221no—
522C22×D4—1221no—
523C22×D4—1221no—
524C22×D4—1221no—
525C22×D4—1221no—
526C22×D4C22×D6111yescharacteristic
527C23×C4—21no—
528C23×C4—611no—
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4C22×D6111yescharacteristic
532C2×M16—1222no—
533C2×M16—1222no—
534C2×M16—2441no—
535C22×C8—611no—
536C22×C8—611no—
537C22×C8—1222no—
538C22×C8—1222no—
539C22×C8—2441no—
540C22×C8C22×D6111yescharacteristic
541C22×C8C22×D6111yescharacteristic
542#127—614no—
543#127—1222no—
544#127—1228no—
545#121—614no—
546#121—614no—
547#121—1228no—
548#121—1228no—
549#121—1222no—
550#121—1222no—
551C4×Q8—614no—
552C4×Q8—1222no—
553C4×D4—614no—
554C4×D4—614no—
555C4×D4—1228no—
556#117—1222no—
557#117—2441no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—1222no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—2441no—
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—611no—
570C2×C22⋊C4—611no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C42—611no—
576C2×C42—1221no—
577C2×C42—1221no—
578C2×C42—1221no—
579C4⋊C8—1222no—
580#103—22no—
581#103—22no—
582#103—614no—
583#103—1222no—
584#102—41no—
585#102—41no—
586#102—1222no—
587#102—1222no—
588#102—1222no—
589#102—1222no—
590#102—2441no—
591#102—2441no—
592C22⋊C8—22no—
593C22⋊C8—1222no—
594#97—1222no—
595#95—21no—
596#95—1221no—
597#95—1221no—
598#95—1221no—
599#95—1221no—
600C24—21no—
601C24—611no—
602C24—1221no—
603C24D4×D6111yescharacteristic
604#41—28no—
605#41—44no—
606#41—44no—
607#41—44no—
608#41—1228no—
609#41—2444no—
610#41—2444no—
611#41—2444no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8C2×C4×D6112yes—
616C2×Q8D4×D6112yes—
617C2×Q8#1175822412yes—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—614no—
627C2×D4—612no—
628C2×D4—1224no—
629C2×D4—1224no—
630C2×D4—1224no—
631C2×D4—1224no—
632C2×D4—1224no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
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—2441no—
647C2×D4—2441no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4C2×C4×D6112yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—612no—
665C22×C4—612no—
666C22×C4—1224no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—4881no—
675C22×C4—2442no—
676C22×C4—2442no—
677C22×C4—2442no—
678C22×C4—2442no—
679C22×C4C2×C4×D6112yes—
680C22×C4D4×D6112yes—
681C22×C4D4×D6111yescharacteristic
682C22×C4C23×D6111yescharacteristic
683M16—2444no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—612no—
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—614no—
702C4⋊C4—612no—
703C4⋊C4—612no—
704C4⋊C4—1224no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—2442no—
710C22⋊C4—42no—
711C22⋊C4—614no—
712C22⋊C4—614no—
713C22⋊C4—1224no—
714C22⋊C4—1224no—
715C22⋊C4—4881no—
716C22⋊C4—2442no—
717C42—612no—
718C42—612no—
719C42—1224no—
720C42—4881no—
721C42—2442no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—612no—
736C23—1221no—
737C23—1221no—
738C23—1221no—
739C23—1221no—
740C23—1221no—
741C23—1221no—
742C23—1222no—
743C23—2441no—
744C23—2441no—
745C23—2441no—
746C23—2441no—
747C23—2441no—
748C23—2441no—
749C23C22⋊C4×D6112yes—
750C23C2×D4×D6111yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8#1451973714yes—
755D4—22no—
756D4—22no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—1222no—
761D4—1222no—
762D4—4884no—
763D4—4884no—
764D4—4884no—
765D4—2448no—
766D4—2444no—
767D4—2448no—
768D4—2441no—
769D4—2441no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—48no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—612no—
787C2×C4—612no—
788C2×C4—612no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—4884no—
802C2×C4—2448no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4C22⋊C4×D6112yes—
811C2×C4C22×C4×D6111yescharacteristic
812C2×C4C2×D4×D6111yescharacteristic
813C2×C4C2×D4×D6111yescharacteristic
814C2×C4C2×#1175822411yescharacteristic
815C2×C4#1451982211yescharacteristic
816C2×C4#1451982211yescharacteristic
817C8—41no—
818C8—41no—
819C8—1222no—
820C8—2441no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—1222no—
836C22—1222no—
837C22—1222no—
838C22—4881no—
839C22—4881no—
840C22—4881no—
841C22—4881no—
842C22—2442no—
843C22—2442no—
844C22—2442no—
845C22—2441no—
846C22—2441no—
847C22—2441no—
848C22—2441no—
849C22C2×C22⋊C4×D6111yescharacteristic
850C22#1684039411yescharacteristic
851C22#1684039911yescharacteristic
852C22#1684055811yescharacteristic
853C22#1684056111yescharacteristic
854C22#1684056411yescharacteristic
855C22#1684056911yescharacteristic
856C4—22no—
857C4—24no—
858C4—81no—
859C4—81no—
860C4—1222no—
861C4—1222no—
862C4—1222no—
863C4—4881no—
864C4—2442no—
865C4—2442no—
866C4C2×#1451973711yescharacteristic
867C4#1684023511yescharacteristic
868C4#1684039411yescharacteristic
869C4#1684039911yescharacteristic
870C2—42no—
871C2—82no—
872C2—4882no—
873C2—2442no—
874C2#2144863511yescharacteristic
875C2#2145433511yescharacteristic
876C2#2145434111yescharacteristic
877C2#2145736211yescharacteristic
878C2#2145740211yescharacteristic
879C2#2145781811yescharacteristic
880C2#2145793811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1788C2
socleC23×C61C22×D4
prime radicalC2×#16840431C2
cosocleC22×C4×C61C24
hypercenter#1788D61
hypocenterC61#22422
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#16839836C2semidirect
3. C2×#16839763C2semidirect
4. C2×#16839757C2semidirect
5. #21448750C2semidirect
6. #21446744C2semidirect
7. #21446641C2semidirect
8. #21446255C2semidirect
9. #21446244C2semidirect
10. #21446138C2semidirect
11. #21446134C2semidirect
12. #21445832C2semidirect
13. #21445758C2semidirect
14. #21445651C2semidirect
15. C61×#1788C2semidirect
20. #16840431C4semidirect
69. C2×#11758226C2×C4semidirect
90. #14519773C2×C4semidirect
96. #14519748C2×C4semidirect
98. Q8×Dic61C2×C4semidirect
124. #14519701D4semidirect
443. #1788D61semidirect
504. C61#22422semidirect

Maximal subgroups

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

subgroupindex
C2×#168404312
C2×#168398362
C2×#168397632
C2×#168397572
#214487502
#214467442
#214466412
#214462552
#214462442
#214461382
#214461342
#214458322
#214457582
#214456512
C61×#17882
#2242261