Finite Group Databasebeta

← #29695534

Subgroups — #29695534

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×#16839833C211yesmaximal, characteristic, complemented
3C2×#16839762C211yesmaximal, characteristic, complemented
4#21448749C211yesmaximal, characteristic, complemented
5#21446744C211yesmaximal, characteristic, complemented
6#21446641C211yesmaximal, characteristic, complemented
7#21446254C211yesmaximal, characteristic, complemented
8#21446247C211yesmaximal, characteristic, complemented
9#21446141C211yesmaximal, characteristic, complemented
10#21446133C211yesmaximal, characteristic, complemented
11#21445832C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic, complemented
13#21445758C211yesmaximal, characteristic, complemented
14#21445651C211yesmaximal, characteristic, complemented
15C2×C61×#416C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18#16840431—24no—
19#16840431C418yescomplemented
20C2×#14519773—21no—
21C2×#14519773C2211yescharacteristic
22C2×#14519751—21no—
23C2×#14519751C2211yescharacteristic
24C2×#14519748—21no—
25C2×#14519748C2211yescharacteristic
26C2×Q8×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61—21no—
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30#16839833—24no—
31C2×#14519706C2211yescharacteristic
32#16839762—24no—
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519687C2211yescharacteristic
44#16839656—21no—
45#16839646—21no—
46#16839638—21no—
47#16839627C2211yescharacteristic
48#16839622C2211yescharacteristic
49#16839619C2211yescharacteristic
50C4⋊C4×Dic61C2211yescharacteristic
51C4×#11758198—21no—
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56C22×#41×C61C2211yescharacteristic
57C23×C8×C61C2211yescharacteristic
58C2×#117×C61C2211yescharacteristic
59C61×#416—24no—
60C2×#103×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C2×#102×C61C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—41no—
68C2×#11758226—41no—
69C2×#11758226C2×C414yes—
70C22×D244—21no—
71C22×D244C2311yescharacteristic
72C22×C22⋊D61—21no—
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C22×C22⋊D61—21no—
76C22×C22⋊D61D411yescharacteristic
77C22×C4×D61—21no—
78C22×C4×D61—21no—
79C22×C4×D61C2311yescharacteristic
80C2×#11758189—22no—
81C2×#11758189—22no—
82C2×#11758189—41no—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85#14519773—28no—
86#14519773—22no—
87#14519773C2×C414yescomplemented
88#14519751—22no—
89#14519751—28no—
90#14519751C2×C414yescomplemented
91#14519748—22no—
92#14519748—28no—
93#14519748C2×C414yes—
94Q8×Dic61—22no—
95Q8×Dic61C2×C414yescomplemented
96C4×C22⋊D61—28no—
97C4×C22⋊D61C2×C414yes—
98C4×C22⋊D61D414yes—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×#11758196—21no—
104C2×#11758196D411yescharacteristic
105C4⋊C4×D61—22no—
106C4⋊C4×D61—41no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61D411yescharacteristic
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198D411yescharacteristic
113C2×C4×Dic61—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61C2311yescharacteristic
116#14519706—22no—
117#14519701—22no—
118#14519701—22no—
119#14519699—22no—
120#14519699—41no—
121#14519698—41no—
122#14519698—41no—
123#14519697—22no—
124#14519697—41no—
125C22⋊#92418—22no—
126#14519689—22no—
127#14519687—22no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131#14519684—21no—
132#14519684—21no—
133C2×#41×C61—22no—
134C2×#41×C61—22no—
135C2×#41×C61—22no—
136C2×#41×C61—41no—
137C2×#41×C61—41no—
138C2×#41×C61C2×C414yescomplemented
139C22×Q8×C61C2311yescharacteristic
140C22×D4×C61—21no—
141C22×D4×C61C2311yescharacteristic
142C23×C4×C61—21no—
143C23×C4×C61C2311yescharacteristic
144C22×C8×C61—22no—
145C22×C8×C61—22no—
146C22×C8×C61—41no—
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149#117×C61—22no—
150#117×C61—41no—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C22⋊C4×C61—21no—
154C2×C42×C61—21no—
155#103×C61—22no—
156#103×C61D414yescomplemented
157#102×C61—22no—
158#102×C61—22no—
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—21no—
188C22×C4×C61—24no—
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×Dic61C2×D411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217#11758226—28no—
218#11758226—44no—
219#11758226—44no—
220#11758226—44no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—24no—
226C2×D244—21no—
227C2×D244—42no—
228C2×D244—42no—
229C2×D244C22×C412yes—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—24no—
235C2×C4×D61—42no—
236C2×C4×D61—42no—
237C2×C4×D61—42no—
238C2×C4×D61—42no—
239C2×C4×D61—81no—
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—44no—
248C2×C8×C61C2×D412yes—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61C2×D412yes—
253C22⋊C4×C61—42no—
254C42×C61—42no—
255C22⋊Dic61—24no—
256C22⋊Dic61—81no—
257C22⋊Dic61C22⋊C414yes—
258#11758198—24no—
259#11758198—42no—
260#11758198C22⋊C414yes—
261C4⋊Dic61—21no—
262C4⋊Dic61—24no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61C22×C412yes—
268#11758196—42no—
269#11758196C22⋊C414yes—
270C4×Dic61—24no—
271C4×Dic61—81no—
272C4×Dic61C22×C412yes—
273C4×Dic61C2×D412yes—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280#11758189—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—22no—
329C2×C4×C61—48no—
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—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61C2×C22⋊C412yes—
363C2×Dic61C2×C22⋊C412yes—
364C2×Dic61C2×C22⋊C412yes—
365D244—22no—
366D244—22no—
367D244—48no—
368D244—41no—
369D244—41no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—48no—
375C4×D61—84no—
376C8×C61—22no—
377C8×C61—41no—
378#92418—41no—
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—42no—
419C4×C61—81no—
420C4×C61C2×C4×D411yescharacteristic
421C4×C61#51811yescharacteristic
422C4×C61D4211yescharacteristic
423C4×C61#54611yescharacteristic
424Dic61—22no—
425Dic61—22no—
426Dic61—22no—
427Dic61—42no—
428Dic61—81no—
429Dic61—81no—
430C2×#550—611no—
431C2×#435—611no—
432C2×#417—611no—
433C2×#416D6111yescharacteristic, complemented
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#1788—611no—
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×C8C2×D6111yescharacteristic
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×#117C2×D6111yescharacteristic
472C22×C4⋊C4—611no—
473#435—1224no—
474C2×C4⋊C8—611no—
475#417—1224no—
476#416—24no—
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⋊C8—611no—
491C2×#97—611no—
492#388—1221no—
493#387—1221no—
494#386—1221no—
495#382—611no—
496#380—611no—
497#380—611no—
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×D6114yescomplemented
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—22no—
536C22×C8—22no—
537C22×C8—41no—
538C22×C8—611no—
539C22×C8—611no—
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—22no—
557#117—41no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1222no—
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—21no—
576C2×C42—611no—
577C2×C42—1221no—
578C2×C42—1221no—
579C4⋊C8—1222no—
580#103—22no—
581#103—1222no—
582#103—1222no—
583#103C22⋊D6114yescomplemented
584#102—22no—
585#102—22no—
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—1221no—
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×Q8#1175822212yes—
617C2×Q8C2×C22⋊D6112yes—
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—21no—
657C22×C4—24no—
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—44no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8C2×C22⋊D6112yes—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—614no—
701C4⋊C4—612no—
702C4⋊C4—1224no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—2442no—
709C4⋊C4C2×C22⋊D6112yes—
710C22⋊C4—42no—
711C22⋊C4—614no—
712C22⋊C4—614no—
713C22⋊C4—1224no—
714C22⋊C4—1224no—
715C22⋊C4—4881no—
716C22⋊C4—2442no—
717C42—42no—
718C42—612no—
719C42—612no—
720C42—1224no—
721C42—4881no—
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—
754Q8C4×C22⋊D6114yes—
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—22no—
780C2×C4—48no—
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—4884no—
801C2×C4—2448no—
802C2×C4—2441no—
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×C4C22×C22⋊D6111yescharacteristic
814C2×C4C2×#1175822211yescharacteristic
815C2×C4#1451982211yescharacteristic
816C2×C4#1451982211yescharacteristic
817C8—22no—
818C8—41no—
819C8—2441no—
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
850C22D4×C22⋊D6111yescharacteristic
851C22#1684040211yescharacteristic
852C22#1684055911yescharacteristic
853C22#1684055911yescharacteristic
854C22#1684056411yescharacteristic
855C22#1684056911yescharacteristic
856C4—22no—
857C4—24no—
858C4—42no—
859C4—81no—
860C4—1222no—
861C4—1222no—
862C4—1222no—
863C4—4881no—
864C4—4881no—
865C4—2442no—
866C4C2×C4×C22⋊D6111yescharacteristic
867C4#1684023511yescharacteristic
868C4D4×C22⋊D6111yescharacteristic
869C4#1684040211yescharacteristic
870C2—42no—
871C2—82no—
872C2—4882no—
873C2—2442no—
874C2C22⋊C4×C22⋊D6111yescharacteristic
875C2#2145433411yescharacteristic
876C2#2145434111yescharacteristic
877C2#2145735911yescharacteristic
878C2#2145740411yescharacteristic
879C2#2145782111yescharacteristic
880C2#2145794111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#416C2
socleC23×C61C22×D4
prime radicalC2×#16840431C2
cosocleC22×C4×C61C24
hypercenterC2×#416D61
hypocenterC61#22422
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#16839833C2semidirect
3. C2×#16839762C2semidirect
4. #21448749C2semidirect
5. #21446744C2semidirect
6. #21446641C2semidirect
7. #21446254C2semidirect
8. #21446247C2semidirect
9. #21446141C2semidirect
10. #21446133C2semidirect
11. #21445832C2semidirect
12. #21445759C2semidirect
13. #21445758C2semidirect
14. #21445651C2semidirect
15. C2×C61×#416C2semidirect
19. #16840431C4semidirect
87. #14519773C2×C4semidirect
90. #14519751C2×C4semidirect
95. Q8×Dic61C2×C4semidirect
138. C2×#41×C61C2×C4semidirect
156. #103×C61D4semidirect
433. C2×#416D61semidirect
504. C61#22422semidirect
516. C2×#41C4×D61semidirect
583. #103C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404312
C2×#168398332
C2×#168397622
#214487492
#214467442
#214466412
#214462542
#214462472
#214461412
#214461332
#214458322
#214457592
#214457582
#214456512
C2×C61×#4162
#2242261