Finite Group Databasebeta

← #29685743

Subgroups — #29685743

Order 15616.

1560 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840236C211yesmaximal, characteristic
2C2×#16839912C211yesmaximal, characteristic
3C2×#16839860C211yesmaximal, characteristic, complemented
4C2×C4×#11758201C211yesmaximal, characteristic, complemented
5#21446156C211yesmaximal, characteristic, complemented
6#21446156C211yesmaximal, characteristic, complemented
7#21446132C211yesmaximal, characteristic, complemented
8#21446079C211yesmaximal, characteristic, complemented
9#21446065C211yesmaximal, characteristic, complemented
10#21446016C211yesmaximal, characteristic, complemented
11#21445749C211yesmaximal, characteristic
12#21445647C211yesmaximal, characteristic, complemented
13C4×#14519697C211yesmaximal, characteristic, complemented
14#21445585C211yesmaximal, characteristic, complemented
15C61×#2323C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19#16840236—24no—
20#16840236—24no—
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×C4×D244C2211yescharacteristic
24C2×C4×D244C2211yescharacteristic
25C2×#14519739—21no—
26C2×#14519739—21no—
27C2×#14519736C2211yescharacteristic
28C2×C22⋊C4×D61—21no—
29C2×C22⋊C4×D61—21no—
30#16839912C418yescomplemented
31#16839860—24no—
32C4×#11758201—24no—
33C2×#14519710C2211yescharacteristic, complemented
34C2×#14519708C2211yescharacteristic, complemented
35C2×#14519701C2211yescharacteristic, complemented
36C2×#14519701C2211yescharacteristic, complemented
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44C2×C22⋊#92418C2211yescharacteristic
45C2×#14519688C2211yescharacteristic, complemented
46C2×C4×#92418C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52#16839517C2211yescharacteristic, complemented
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic, complemented
55C2×#117×C61C2211yescharacteristic
56C61×#391C2211yescharacteristic, complemented
57C61×#389—21no—
58C61×#389C2211yescharacteristic, complemented
59C61×#388—21no—
60C61×#388—21no—
61C61×#387—21no—
62C61×#380C2211yescharacteristic
63C4×C4⋊C4×C61C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×D244—21no—
66C22×D244—22no—
67C22×D244—22no—
68C22×D244—22no—
69C22×D244—22no—
70C22×D244—22no—
71C22×D244C2×C414yes—
72C22×D244C2311yescharacteristic
73C22×D244C2311yescharacteristic
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61—21no—
78C2×#11758201—22no—
79C2×#11758201—22no—
80C2×#11758201—22no—
81C2×#11758201—22no—
82C2×#11758201C2×C414yescomplemented
83C2×#11758201C2×C414yescomplemented
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C4×D244—22no—
89C4×D244—22no—
90C4×D244—22no—
91C4×D244—22no—
92C4×D244—22no—
93C4×D244—22no—
94C4×D244D414yes—
95C4×D244D414yes—
96#14519739—28no—
97#14519739—28no—
98#14519736—22no—
99#14519736—22no—
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C22⋊Dic61—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C22⋊C4×D61—28no—
108C22⋊C4×D61—28no—
109C2×C4×Dic61—21no—
110#14519710—22no—
111#14519708—22no—
112#14519701—22no—
113#14519701—22no—
114#14519697—22no—
115#14519697—22no—
116#14519697—22no—
117#14519697—22no—
118#14519697C2×C414yescomplemented
119#14519697C2×C414yescomplemented
120C22⋊#92418—22no—
121C22⋊#92418C2×C414yescomplemented
122#14519688—22no—
123C4×#92418—22no—
124C22×Q8×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126C22⋊Q8×C61—22no—
127C22⋊Q8×C61C2×C414yescomplemented
128C4×Q8×C61—22no—
129C4×Q8×C61—22no—
130#117×C61—22no—
131#117×C61—22no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61D411yescharacteristic
136C2×C4⋊C4×C61D411yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61D411yescharacteristic
143C2×C22⋊C4×C61D411yescharacteristic
144C2×C42×C61—21no—
145C2×C42×C61—21no—
146C2×C42×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148#95×C61—21no—
149#95×C61—21no—
150#95×C61—21no—
151#95×C61—21no—
152#95×C61—21no—
153C24×C61C2×D411yescharacteristic
154C23×D61—21no—
155C23×D61—21no—
156C23×D61—24no—
157C23×D61—24no—
158C23×D61—24no—
159C23×D61—81no—
160C23×D61—81no—
161C23×D61—81no—
162C23×D61—81no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61C22×C412yes—
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×C61C22×C412yes—
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61#4112yes—
184C22×C4×C61C2411yescharacteristic
185C22×Dic61—21no—
186C22×Dic61—21no—
187C2×D244—24no—
188C2×D244—28no—
189C2×D244—28no—
190C2×D244—24no—
191C2×D244—24no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—28no—
199C2×D244—28no—
200C2×D244C22×C412yes—
201C2×D244C22×C412yes—
202C2×D244C2×D412yes—
203C2×D244C2×D412yes—
204C2×D244#4112yes—
205C2×D244#4112yes—
206C2×C4×D61—24no—
207C2×C4×D61—24no—
208C2×C4×D61—24no—
209C2×C4×D61—24no—
210C2×C4×D61—81no—
211C2×C4×D61—81no—
212C2×C4×D61—81no—
213C2×C4×D61—81no—
214C2×C4×D61—81no—
215C2×C4×D61—81no—
216C2×C4×D61—81no—
217C2×C4×D61—81no—
218C4⋊C4×C61—24no—
219C4⋊C4×C61—22no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—42no—
227C4⋊C4×C61—81no—
228C4⋊C4×C61C22×C412yes—
229C22⋊C4×C61—24no—
230C22⋊C4×C61—22no—
231C22⋊C4×C61—22no—
232C22⋊C4×C61—81no—
233C42×C61—21no—
234C42×C61—21no—
235C42×C61—42no—
236C42×C61—81no—
237C42×C61C2×D412yes—
238C42×C61C2×D412yes—
239C22⋊Dic61—24no—
240#11758201—28no—
241#11758201—28no—
242#11758198—24no—
243#11758198—24no—
244#11758198—24no—
245#11758198—24no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61C2×D412yes—
249C4⋊Dic61C2×D412yes—
250C4×Dic61—24no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418C22×C412yes—
262C2×#92418C22×C412yes—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61C4×D412yes—
270C23×C61C22×D411yescharacteristic
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—216no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—84no—
287C22×D61—84no—
288C22×D61—84no—
289C22×D61—84no—
290C22×D61—84no—
291C22×D61—84no—
292Q8×C61—22no—
293Q8×C61—22no—
294Q8×C61—41no—
295Q8×C61—41no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61C4×D412yes—
325C2×C4×C61#12012yes—
326C2×C4×C61#12012yes—
327C2×C4×C61C23×C411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C2×#4111yescharacteristic
331C2×C4×C61C2×#4111yescharacteristic
332C2×C4×C61C2×#4111yescharacteristic
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339D244—216no—
340D244—22no—
341D244—22no—
342D244—22no—
343D244—22no—
344D244—22no—
345D244—22no—
346D244C4×D414yes—
347D244C4×D414yes—
348C4×D61—84no—
349C4×D61—84no—
350C4×D61—84no—
351C4×D61—84no—
352#92418—22no—
353#92418—22no—
354#92418—41no—
355#92418—41no—
356#21459—611nomaximal, Sylow
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61C2×C4×D411yescharacteristic
365C22×C61C2×#12011yescharacteristic
366C22×C61#52511yescharacteristic
367C22×C61#57611yescharacteristic
368C22×C61#57711yescharacteristic
369C22×C61#57711yescharacteristic
370C22×C61#57711yescharacteristic
371C2×D61—24no—
372C2×D61—24no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—816no—
386C4×C61—22no—
387C4×C61—22no—
388C4×C61—22no—
389C4×C61—42no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—42no—
393C4×C61—81no—
394C4×C61—81no—
395C4×C61C2×C4×D411yescharacteristic
396C4×C61C2×C4×D411yescharacteristic
397C4×C61#52511yescharacteristic
398C4×C61#52511yescharacteristic
399Dic61—42no—
400Dic61—42no—
401C2×#518—611no—
402C2×#450—611no—
403C2×#440—611no—
404C2×C4×SD16—611no—
405#2323D6111yescharacteristic, complemented
406#1877—611no—
407#1877—611no—
408#1873—611no—
409#1864—611no—
410#1862—611no—
411#1854—611no—
412#1786—611no—
413#1762—611no—
414C4×#102—611no—
415#1750—611no—
416C2×C61—42no—
417C2×C61C4×#12011yescharacteristic
418C2×C61#294611yescharacteristic
419C2×C61#294911yescharacteristic
420C2×C61#300911yescharacteristic
421C2×C61#301211yescharacteristic
422C2×C61#311811yescharacteristic
423C2×C61#312311yescharacteristic
424D61—44no—
425D61—44no—
426C23×D4—611no—
427C22×SD16—611no—
428C22×SD16—611no—
429C2×C22⋊Q8C2×D6111yescharacteristic
430#518—1224no—
431#518—1224no—
432C2×C4×Q8C2×D6111yescharacteristic, complemented
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×C4×D4—1221no—
438C2×C4×D4—1221no—
439C2×#117—611no—
440C2×#117C2×D6111yescharacteristic
441C22×C22⋊C4—1221no—
442C22×C22⋊C4—1221no—
443#450—618no—
444#440—1224no—
445C4×SD16—1224no—
446C2×#107—611no—
447C2×#106—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×C22⋊C8—611no—
457C2×C22⋊C8—611no—
458C2×#97—611no—
459C2×C4×C8—611no—
460#391C2×D6111yescharacteristic, complemented
461#389—21no—
462#389C2×D6111yescharacteristic, complemented
463#388—21no—
464#388—21no—
465#387—21no—
466#380C2×D6111yescharacteristic
467C4×C4⋊C4C2×D6111yescharacteristic, complemented
468#340—611no—
469#340—611no—
470#340—611no—
471#340—611no—
472#336—611no—
473#336—611no—
474C61#2145911yescharacteristic, complemented, Sylow
475C25—1221no—
476C22×Q8C22×D6111yescharacteristic
477C22×D4—614no—
478C22×D4—611no—
479C22×D4—611no—
480C22×D4—1222no—
481C22×D4—1222no—
482C22×D4—1222no—
483C22×D4—1222no—
484C22×D4—1222no—
485C22×D4—1221no—
486C23×C4—1221no—
487C23×C4—1221no—
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4C22×D6111yescharacteristic
491C2×SD16—614no—
492C2×SD16—614no—
493C2×SD16—1222no—
494C2×SD16—1222no—
495C2×SD16—1222no—
496C2×SD16—1222no—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8—611no—
500C22×C8—611no—
501C22⋊Q8—22no—
502C22⋊Q8C4×D6114yescomplemented
503C4×Q8—22no—
504C4×Q8—22no—
505C4×D4—614no—
506C4×D4—614no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1222no—
510C4×D4—1222no—
511C4×D4—1228no—
512C4×D4—1228no—
513C4×D4—1222no—
514C4×D4—1222no—
515#117—22no—
516#117—22no—
517#117—1222no—
518#117—1222no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4C22⋊D6111yescharacteristic
525C2×C4⋊C4C22⋊D6111yescharacteristic
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C4⋊C4C22×D6111yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—1228no—
532C2×C22⋊C4—1228no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4C22⋊D6111yescharacteristic
539C2×C22⋊C4C22⋊D6111yescharacteristic
540C2×C42—21no—
541C2×C42—21no—
542C2×C42—1221no—
543C2×C42C22×D6111yescharacteristic
544C2×C42C22×D6111yescharacteristic
545#107—1222no—
546#106—1222no—
547#103—1222no—
548#103—1222no—
549#102—614no—
550#102—614no—
551#102—1222no—
552#102—1222no—
553#102—1222no—
554#102—1222no—
555C22⋊C8—614no—
556C22⋊C8—1222no—
557#97—1222no—
558C4×C8—1222no—
559#95—21no—
560#95—21no—
561#95—21no—
562#95—21no—
563#95—21no—
564C24—1224no—
565C24—1224no—
566C24—1224no—
567C24—1221no—
568C24—1221no—
569C24—4881no—
570C24—4881no—
571C24—4881no—
572C24—4881no—
573C24C2×C22⋊D6111yescharacteristic
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C2×C4×D6112yes—
580C2×D4—612no—
581C2×D4—612no—
582C2×D4—612no—
583C2×D4—612no—
584C2×D4—612no—
585C2×D4—612no—
586C2×D4—1228no—
587C2×D4—1228no—
588C2×D4—1224no—
589C2×D4—1224no—
590C2×D4—1228no—
591C2×D4—1228no—
592C2×D4—1221no—
593C2×D4—1221no—
594C2×D4—1221no—
595C2×D4—1221no—
596C2×D4—1221no—
597C2×D4—1221no—
598C2×D4—1224no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—1224no—
608C22×C4—1224no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1224no—
612C22×C4—1224no—
613C22×C4—4881no—
614C22×C4—4881no—
615C22×C4—4881no—
616C22×C4—4881no—
617C22×C4—4881no—
618C22×C4—4881no—
619C22×C4—4881no—
620C22×C4—4881no—
621C22×C4C2×C4×D6112yes—
622C22×C4#1175822212yes—
623C22×C4C2×C22⋊D6111yescharacteristic
624C22×C4C2×C22⋊D6111yescharacteristic
625C22×C4C2×C22⋊D6111yescharacteristic
626C22×C4C2×C22⋊D6111yescharacteristic
627C22×C4C2×C22⋊D6111yescharacteristic
628C22×C4C23×D6111yescharacteristic
629SD16—1228no—
630SD16—1228no—
631C2×C8—612no—
632C2×C8—612no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C4⋊C4—21no—
644C4⋊C4—24no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—42no—
652C4⋊C4—81no—
653C4⋊C4—612no—
654C4⋊C4—612no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4C2×C4×D6112yes—
658C22⋊C4—24no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—81no—
662C22⋊C4—1224no—
663C22⋊C4—1224no—
664C22⋊C4—1224no—
665C22⋊C4—1224no—
666C22⋊C4—1224no—
667C42—21no—
668C42—21no—
669C42—42no—
670C42—81no—
671C42—1224no—
672C42D4×D6112yes—
673C42D4×D6112yes—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—12216no—
681C23—1222no—
682C23—1222no—
683C23—1222no—
684C23—1222no—
685C23—1222no—
686C23—1222no—
687C23—4884no—
688C23—4884no—
689C23—4884no—
690C23—4884no—
691C23—4884no—
692C23—4884no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23C4×C22⋊D6112yes—
702C23C22×C22⋊D6111yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707D4—614no—
708D4—614no—
709D4—12216no—
710D4—1222no—
711D4—1222no—
712D4—1222no—
713D4—1222no—
714D4—1222no—
715D4—1222no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—4884no—
747C2×C4—4884no—
748C2×C4—4884no—
749C2×C4—4884no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4C4×C22⋊D6112yes—
755C2×C4#1451974512yes—
756C2×C4#1451974512yes—
757C2×C4C22×C4×D6111yescharacteristic
758C2×C4C2×D4×D6111yescharacteristic
759C2×C4C2×D4×D6111yescharacteristic
760C2×C4#41×D6111yescharacteristic
761C2×C4#41×D6111yescharacteristic
762C2×C4C2×#1175822211yescharacteristic
763C8—1222no—
764C8—1222no—
765C8—2441no—
766C8—2441no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—1224no—
775C22—1224no—
776C22—48816no—
777C22—2442no—
778C22—2442no—
779C22—2442no—
780C22—2442no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22C2×C4×C22⋊D6111yescharacteristic
790C22C2×#1451974511yescharacteristic
791C22#1684026911yescharacteristic
792C22#1684056511yescharacteristic
793C22#1684057011yescharacteristic
794C22#1684057011yescharacteristic
795C22#1684057011yescharacteristic
796C4—22no—
797C4—22no—
798C4—22no—
799C4—41no—
800C4—42no—
801C4—42no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—2442no—
806C4—2442no—
807C4C4×D4×D6111yescharacteristic
808C4C4×D4×D6111yescharacteristic
809C4#1684027111yescharacteristic
810C4#1684027111yescharacteristic
811C2—42no—
812C2—2444no—
813C2—2444no—
814C2C4×#1451974511yescharacteristic
815C2#2145464711yescharacteristic
816C2#2145467811yescharacteristic
817C2#2145509411yescharacteristic
818C2#2145512011yescharacteristic
819C2#2145599711yescharacteristic
820C2#2145606611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2323C2
socleC23×C61C22×D4
prime radicalC23×D244C22
cosocleC22×C4×C61C24
hypercenter#2323D61
hypocenterC61#21459
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
3. C2×#16839860C2semidirect
4. C2×C4×#11758201C2semidirect
5. #21446156C2semidirect
6. #21446156C2semidirect
7. #21446132C2semidirect
8. #21446079C2semidirect
9. #21446065C2semidirect
10. #21446016C2semidirect
12. #21445647C2semidirect
13. C4×#14519697C2semidirect
14. #21445585C2semidirect
15. C61×#2323C2semidirect
30. #16839912C4semidirect
33. C2×#14519710C22semidirect
34. C2×#14519708C22semidirect
35. C2×#14519701C22semidirect
36. C2×#14519701C22semidirect
45. C2×#14519688C22semidirect
46. C2×C4×#92418C22semidirect
47. #16839524C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839517C22semidirect
52. #16839517C22semidirect
54. C2×C4×Q8×C61C22semidirect
56. C61×#391C22semidirect
58. C61×#389C22semidirect
63. C4×C4⋊C4×C61C22semidirect
82. C2×#11758201C2×C4semidirect
83. C2×#11758201C2×C4semidirect
118. #14519697C2×C4semidirect
119. #14519697C2×C4semidirect
121. C22⋊#92418C2×C4semidirect
127. C22⋊Q8×C61C2×C4semidirect
405. #2323D61semidirect
432. C2×C4×Q8C2×D61semidirect
460. #391C2×D61semidirect
462. #389C2×D61semidirect
467. C4×C4⋊C4C2×D61semidirect
474. C61#21459semidirect
502. C22⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402362
C2×#168399122
C2×#168398602
C2×C4×#117582012
#214461562
#214461322
#214460792
#214460652
#214460162
#214457492
#214456472
C4×#145196972
#214455852
C61×#23232
#2145961