Finite Group Databasebeta

← #29695478

Subgroups — #29695478

Order 15616.

1542 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840431C211yesmaximal, characteristic
2C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
3C2×#16839757C211yesmaximal, characteristic, complemented
4#21448769C211yesmaximal, characteristic, complemented
5#21446744C211yesmaximal, characteristic, complemented
6#21446623C211yesmaximal, characteristic, complemented
7#21446247C211yesmaximal, characteristic, complemented
8#21446244C211yesmaximal, characteristic, complemented
9#21446141C211yesmaximal, characteristic, complemented
10#21446138C211yesmaximal, characteristic, complemented
11#21445822C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic, complemented
13#21445758C211yesmaximal, characteristic, complemented
14#103×Dic61C211yesmaximal, characteristic, complemented
15C2×C61×#416C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
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×#14519735C2211yescharacteristic
30C8×C22⋊D61—24no—
31C2×#14519706C2211yescharacteristic
32#16839757—24no—
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×C8×Dic61C2211yescharacteristic
44#16839662—21no—
45#16839653—21no—
46#16839650—21no—
47#16839631C2211yescharacteristic
48#16839622C2211yescharacteristic
49#16839619C2211yescharacteristic
50C4⋊C4×Dic61C2211yescharacteristic
51C4×#11758196—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×D61C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C2×C8×D61—22no—
82C2×C8×D61—22no—
83C2×C8×D61—41no—
84#14519773—28no—
85#14519773—22no—
86#14519773C2×C414yes—
87#14519751—22no—
88#14519751—28no—
89#14519751C2×C414yes—
90#14519748—22no—
91#14519748—28no—
92#14519748C2×C414yes—
93Q8×Dic61—22no—
94Q8×Dic61C2×C414yes—
95C4×C22⋊D61—28no—
96C4×C22⋊D61C2×C414yes—
97C4×C22⋊D61D414yes—
98#14519735—22no—
99#14519735—41no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196D411yescharacteristic
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61D411yescharacteristic
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198D411yescharacteristic
114C2×C4×Dic61—21no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61C2311yescharacteristic
118#14519706—22no—
119#14519701—22no—
120#14519701—22no—
121#14519699—22no—
122#14519699—41no—
123#14519698—41no—
124#14519698—41no—
125#14519697—22no—
126#14519697—41no—
127C22⋊#92418—22no—
128#14519689—22no—
129C8×Dic61—22no—
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×C414yes—
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—22no—
201C2×C22⋊D61—22no—
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×D61C22×C412yes—
238C2×C4×D61C2×D412yes—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—44no—
245C2×C8×C61C2×D412yes—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61C2×D412yes—
250C22⋊C4×C61—42no—
251C42×C61—42no—
252C22⋊Dic61—24no—
253C22⋊Dic61—81no—
254C22⋊Dic61C22⋊C414yes—
255#11758198—24no—
256#11758198—42no—
257#11758198—81no—
258#11758198C22⋊C414yes—
259C4⋊Dic61—21no—
260C4⋊Dic61—24no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61C22×C412yes—
266#11758196—42no—
267#11758196—81no—
268#11758196C22⋊C414yes—
269C4×Dic61—24no—
270C4×Dic61—42no—
271C4×Dic61—42no—
272C4×Dic61C22×C412yes—
273C4×Dic61C2×D412yes—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
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—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—28no—
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—22no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61C2×C22⋊C412yes—
361C2×Dic61C2×C22⋊C412yes—
362C2×Dic61C2×C22⋊C412yes—
363C2×Dic61#13512yes—
364C2×Dic61#13512yes—
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—
375C8×C61—22no—
376C8×C61—41no—
377#92418—41no—
378#92418—41no—
379#22418—611nomaximal, Sylow
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—81no—
391C22×C61—81no—
392C22×C61—81no—
393C22×C61—81no—
394C22×C61C22×C22⋊C411yescharacteristic
395C22×C61D4211yescharacteristic
396C22×C61#54611yescharacteristic
397C22×C61C2×#13511yescharacteristic
398C22×C61C2×#13511yescharacteristic
399C22×C61#57611yescharacteristic
400C22×C61#57711yescharacteristic
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—81no—
412C2×D61—81no—
413C2×D61—81no—
414C2×D61—81no—
415C4×C61—24no—
416C4×C61—22no—
417C4×C61—42no—
418C4×C61—81no—
419C4×C61C2×C4×D411yescharacteristic
420C4×C61#51811yescharacteristic
421C4×C61D4211yescharacteristic
422C4×C61#54611yescharacteristic
423Dic61—22no—
424Dic61—22no—
425Dic61—42no—
426Dic61—81no—
427Dic61—81no—
428Dic61#41614yescomplemented
429C2×#550—611no—
430C2×C8×D4—611no—
431C2×#416—611no—
432C2×#416D6111yescharacteristic, complemented
433#2354—611no—
434#1982—611no—
435#1957—611no—
436#1893—611no—
437#1893—611no—
438#1875—611no—
439#1875—611no—
440#1803—611no—
441#1788—611no—
442#1788—611no—
443C4×#103—611no—
444C2×C61—42no—
445C2×C61—82no—
446C2×C61D4×C22⋊C411yescharacteristic
447C2×C61C2×#41611yescharacteristic
448C2×C61#289711yescharacteristic
449C2×C61#328411yescharacteristic
450C2×C61#328711yescharacteristic
451C2×C61#330411yescharacteristic
452C2×C61#330511yescharacteristic
453D61—42no—
454D61—82no—
455C22×#41—611no—
456C22×#41C2×D6111yescharacteristic
457C23×C8—611no—
458C23×C8C2×D6111yescharacteristic
459#550—618no—
460#550—1224no—
461C2×#127—611no—
462C2×#127—1221no—
463C2×#121—611no—
464C2×#121—611no—
465C2×#121—1221no—
466C2×#121—1221no—
467C2×C4×Q8—611no—
468C2×C4×D4—611no—
469C2×C4×D4—1221no—
470C2×#117—611no—
471C2×#117C2×D6111yescharacteristic
472C8×D4—1224no—
473C2×C4⋊C8—611no—
474#416—24no—
475#416—1224no—
476C2×#103—611no—
477C2×#103—611no—
478C2×#103C2×D6111yescharacteristic
479C2×#103C2×D6111yescharacteristic
480C2×#102—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102—611no—
486C2×#102C2×D6111yescharacteristic
487C2×#102C2×D6111yescharacteristic
488C2×C22⋊C8—611no—
489C2×C22⋊C8—611no—
490C2×C4×C8—611no—
491#390—1221no—
492#388—1221no—
493#388—1221no—
494#384—611no—
495#380—611no—
496#380—611no—
497C4×C4⋊C4—611no—
498C4×C4⋊C4—1221no—
499#340—611no—
500#340—611no—
501#340—611no—
502#340—611no—
503C61#2241811yescharacteristic, complemented, Sylow
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—614no—
510C2×#41—1222no—
511C2×#41—1222no—
512C2×#41—1222no—
513C2×#41—2441no—
514C2×#41—2441no—
515C2×#41C4×D6114yes—
516C22×Q8C22×D6111yescharacteristic
517C22×D4—21no—
518C22×D4—611no—
519C22×D4—611no—
520C22×D4—1221no—
521C22×D4—1221no—
522C22×D4—1221no—
523C22×D4—1221no—
524C22×D4—1221no—
525C22×D4C22×D6111yescharacteristic
526C23×C4—21no—
527C23×C4—611no—
528C23×C4—1221no—
529C23×C4C22×D6111yescharacteristic
530C22×C8—22no—
531C22×C8—22no—
532C22×C8—41no—
533C22×C8—611no—
534C22×C8—611no—
535C22×C8—1222no—
536C22×C8—1222no—
537C22×C8—2441no—
538C22×C8C22×D6111yescharacteristic
539C22×C8C22×D6111yescharacteristic
540#127—614no—
541#127—1222no—
542#127—1228no—
543#121—614no—
544#121—614no—
545#121—1228no—
546#121—1228no—
547#121—1222no—
548#121—1222no—
549C4×Q8—614no—
550C4×Q8—1222no—
551C4×D4—614no—
552C4×D4—614no—
553C4×D4—1228no—
554#117—22no—
555#117—41no—
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—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4C22×D6111yescharacteristic
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C22⋊C4—21no—
568C2×C22⋊C4—611no—
569C2×C22⋊C4—611no—
570C2×C22⋊C4—1221no—
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—
579C2×C42—1221no—
580C4⋊C8—1222no—
581#103—22no—
582#103—1222no—
583#103—1222no—
584#103C22⋊D6114yescomplemented
585#102—22no—
586#102—22no—
587#102—1222no—
588#102—1222no—
589#102—2441no—
590#102—2441no—
591#102—2441no—
592#102—2441no—
593C22⋊C8—1222no—
594C22⋊C8—1222no—
595C4×C8—1222no—
596#95—1221no—
597#95—1221no—
598#95—1221no—
599C24—21no—
600C24—611no—
601C24—1221no—
602C24D4×D6111yescharacteristic
603#41—28no—
604#41—44no—
605#41—44no—
606#41—44no—
607#41—1228no—
608#41—2444no—
609#41—2444no—
610#41—2444no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8C2×C4×D6112yes—
615C2×Q8#1175822212yes—
616C2×Q8C2×C22⋊D6112yes—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—614no—
626C2×D4—612no—
627C2×D4—1224no—
628C2×D4—1222no—
629C2×D4—1222no—
630C2×D4—1224no—
631C2×D4—1224no—
632C2×D4—1224no—
633C2×D4—1224no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—4881no—
640C2×D4—4881no—
641C2×D4—4881no—
642C2×D4—4881no—
643C2×D4—4881no—
644C2×D4—4881no—
645C2×D4—2442no—
646C2×D4—2442no—
647C2×D4—2442no—
648C2×D4—2442no—
649C2×D4C2×C4×D6112yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—1224no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—2442no—
674C22×C4—2442no—
675C22×C4C2×C4×D6112yes—
676C22×C4D4×D6112yes—
677C22×C4D4×D6111yescharacteristic
678C22×C4C23×D6111yescharacteristic
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—44no—
685C2×C8—1221no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—2444no—
692C2×C8C2×C22⋊D6112yes—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—614no—
697C4⋊C4—612no—
698C4⋊C4—1224no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—4881no—
705C4⋊C4—2442no—
706C4⋊C4C2×C22⋊D6112yes—
707C22⋊C4—42no—
708C22⋊C4—614no—
709C22⋊C4—614no—
710C22⋊C4—1224no—
711C22⋊C4—1224no—
712C22⋊C4—4881no—
713C22⋊C4—4881no—
714C22⋊C4—2442no—
715C42—42no—
716C42—612no—
717C42—612no—
718C42—1224no—
719C42—2442no—
720C42—2442no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—22no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—612no—
735C23—1221no—
736C23—1221no—
737C23—1221no—
738C23—1221no—
739C23—1221no—
740C23—1221no—
741C23—1222no—
742C23—2441no—
743C23—2441no—
744C23—2441no—
745C23—2441no—
746C23—2441no—
747C23—2441no—
748C23C22⋊C4×D6112yes—
749C23C2×D4×D6111yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8C4×C22⋊D6114yes—
754D4—22no—
755D4—22no—
756D4—48no—
757D4—41no—
758D4—41no—
759D4—1228no—
760D4—1222no—
761D4—1222no—
762D4—4884no—
763D4—4884no—
764D4—4884no—
765D4—2448no—
766D4—2448no—
767D4—2441no—
768D4—2441no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
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—612no—
786C2×C4—612no—
787C2×C4—612no—
788C2×C4—612no—
789C2×C4—612no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—2448no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4C22⋊C4×D6112yes—
809C2×C4C22×C4×D6111yescharacteristic
810C2×C4C2×D4×D6111yescharacteristic
811C2×C4C22×C22⋊D6111yescharacteristic
812C2×C4C2×#1175822211yescharacteristic
813C2×C4#1451982211yescharacteristic
814C2×C4#1451982211yescharacteristic
815C8—22no—
816C8—41no—
817C8—2441no—
818C8—2441no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—1222no—
834C22—1222no—
835C22—1222no—
836C22—4881no—
837C22—4881no—
838C22—4881no—
839C22—4881no—
840C22—2442no—
841C22—2442no—
842C22—2442no—
843C22—2441no—
844C22—2441no—
845C22—2441no—
846C22—2441no—
847C22C2×C22⋊C4×D6111yescharacteristic
848C22D4×C22⋊D6111yescharacteristic
849C22#1684040211yescharacteristic
850C22#135×D6111yescharacteristic
851C22#135×D6111yescharacteristic
852C22#1684056411yescharacteristic
853C22#1684056911yescharacteristic
854C4—22no—
855C4—24no—
856C4—42no—
857C4—81no—
858C4—614no—
859C4—1222no—
860C4—1222no—
861C4—4881no—
862C4—4881no—
863C4—2442no—
864C4C2×C4×C22⋊D6111yescharacteristic
865C4#1684023511yescharacteristic
866C4D4×C22⋊D6111yescharacteristic
867C4#1684040211yescharacteristic
868C2—42no—
869C2—82no—
870C2—4882no—
871C2—2442no—
872C2C22⋊C4×C22⋊D6111yescharacteristic
873C2#416×D6111yescharacteristic
874C2#2145434111yescharacteristic
875C2#2145754311yescharacteristic
876C2#2145757311yescharacteristic
877C2#2145775411yescharacteristic
878C2#2145776511yescharacteristic
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#22418
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×C8×C22⋊D61C2semidirect
3. C2×#16839757C2semidirect
4. #21448769C2semidirect
5. #21446744C2semidirect
6. #21446623C2semidirect
7. #21446247C2semidirect
8. #21446244C2semidirect
9. #21446141C2semidirect
10. #21446138C2semidirect
11. #21445822C2semidirect
12. #21445759C2semidirect
13. #21445758C2semidirect
14. #103×Dic61C2semidirect
15. C2×C61×#416C2semidirect
19. #16840431C4semidirect
156. #103×C61D4semidirect
428. Dic61#416semidirect
432. C2×#416D61semidirect
503. C61#22418semidirect
584. #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×C8×C22⋊D612
C2×#168397572
#214487692
#214467442
#214466232
#214462472
#214462442
#214461412
#214461382
#214458222
#214457592
#214457582
#103×Dic612
C2×C61×#4162
#2241861