Finite Group Databasebeta

← #29689147

Subgroups — #29689147

Order 15616.

1486 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840269C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic, complemented
3#21448200C211yesmaximal, characteristic, complemented
4#21446264C214yesmaximal, complemented
5#21446118C214yesmaximal, complemented
6#21445919C211yesmaximal, characteristic, complemented
7#21445916C211yesmaximal, characteristic, complemented
8#21445763C211yesmaximal, characteristic, complemented
9C61×#1789C211yesmaximal, characteristic, complemented
10C23×C4×D61C2211yescharacteristic
11C2×M16×D61C2212yescomplemented
12#16840269—21no—
13#16840269—21no—
14#16840269—21no—
15#16840269—21no—
16#16840269C412yescomplemented
17#16840269C412yescomplemented
18#16840269C2212yes—
19#16840269C2212yes—
20C2×#14519758—21no—
21C2×#14519753C411yescharacteristic, complemented
22C2×#14519753C411yescharacteristic, complemented
23C2×#14519748C411yescharacteristic, complemented
24C2×#14519748C411yescharacteristic, complemented
25C2×#14519745—21no—
26C2×C4×C22⋊D61—21no—
27C2×C4×C22⋊D61—21no—
28C2×#14519736C2211yescharacteristic
29C2×#14519734C2212yescomplemented
30C2×#14519704C2214yescomplemented
31#16839726C2211yescharacteristic
32#16839725C2212yescomplemented
33#16839724—21no—
34#16839724—21no—
35C22⋊C8×D61—21no—
36C22⋊C8×D61—21no—
37#16839624—21no—
38#16839621—21no—
39#16839620—21no—
40#16839617—21no—
41C4×#11758198C2212yescomplemented
42C4×C22⋊Dic61C2211yescharacteristic
43#16839523C2214yescomplemented
44#16839522C2214yescomplemented
45C22×#41×C61C2211yescharacteristic
46C2×#104×C61C2214yescomplemented
47C61×#407C2211yescharacteristic
48C4×C22⋊C4×C61C2211yescharacteristic
49C24×D61D411yescharacteristic
50C22×C22⋊D61—21no—
51C22×C22⋊D61—21no—
52C23×Dic61D411yescharacteristic
53C22×C4×D61—44no—
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C2×#11758194C2312yes—
67C2×#11758189—22no—
68M16×D61—44no—
69C2×C8×D61—22no—
70#14519758—22no—
71#14519758—22no—
72#14519758—22no—
73#14519758—22no—
74#14519753—21no—
75#14519753—21no—
76#14519753—21no—
77#14519753—21no—
78#14519753C2×C412yes—
79#14519753C2×C412yes—
80#14519753C2×C412yes—
81#14519753C2×C412yes—
82#14519748—21no—
83#14519748—21no—
84#14519748—21no—
85#14519748—21no—
86#14519748C2×C412yes—
87#14519748C2×C412yes—
88#14519748C2×C412yes—
89#14519748C2×C412yes—
90#14519745—22no—
91#14519745—22no—
92#14519745—22no—
93#14519745—22no—
94C4×C22⋊D61—22no—
95C4×C22⋊D61—22no—
96C4×C22⋊D61—22no—
97C4×C22⋊D61—22no—
98C4×C22⋊D61—22no—
99C4×C22⋊D61—22no—
100C4×C22⋊D61—22no—
101C4×C22⋊D61—22no—
102#14519736—21no—
103#14519736—21no—
104#14519736C2×C412yes—
105#14519736C2312yes—
106#14519734—44no—
107C2×C4⋊Dic61C2×C411yescharacteristic
108C2×C4⋊Dic61C2×C411yescharacteristic
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196—22no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—22no—
119C2×#11758198—22no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61C2312yes—
122#14519704—44no—
123C22⋊#92418—21no—
124C22⋊#92418—21no—
125#14519689—22no—
126#14519689—22no—
127#14519684—21no—
128#14519684—22no—
129C2×#41×C61—21no—
130C2×#41×C61—21no—
131C2×#41×C61—44no—
132C2×#41×C61C2×C412yes—
133C2×#41×C61C2312yes—
134C22×Q8×C61C2×C411yescharacteristic
135C22×D4×C61—21no—
136C22×D4×C61C2×C411yescharacteristic
137C23×C4×C61—21no—
138C23×C4×C61C2311yescharacteristic
139C2×M16×C61C2312yes—
140C2×C22⋊C4×C61—21no—
141C2×C42×C61C2312yes—
142#104×C61—44no—
143C22⋊C8×C61—21no—
144C22⋊C8×C61—21no—
145#95×C61—21no—
146C24×C61—21no—
147C24×C61C2×D411yescharacteristic
148C23×D61—42no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61C22⋊C411yescharacteristic
152C23×D61C22⋊C411yescharacteristic
153C23×D61C22⋊C411yescharacteristic
154C23×D61C22⋊C411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C23×D61C2×D411yescharacteristic
157#41×C61—24no—
158#41×C61—24no—
159#41×C61—42no—
160#41×C61—42no—
161#41×C61—44no—
162#41×C61—44no—
163C2×Q8×C61—21no—
164C2×Q8×C61—42no—
165C2×Q8×C61C22×C412yes—
166C2×D4×C61—22no—
167C2×D4×C61—22no—
168C2×D4×C61—21no—
169C2×D4×C61—42no—
170C2×D4×C61—44no—
171C2×D4×C61C22×C412yes—
172C22×C4×C61—24no—
173C22×C4×C61—21no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—44no—
178C22×C4×C61C22×C411yescharacteristic
179C22×C4×C61C22×C411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2411yescharacteristic
184C2×C22⋊D61—22no—
185C2×C22⋊D61—22no—
186C2×C22⋊D61—22no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—44no—
189C2×C22⋊D61—44no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—22no—
193C22×Dic61—42no—
194C22×Dic61C22⋊C411yescharacteristic
195C22×Dic61C22⋊C411yescharacteristic
196C22×Dic61C22⋊C411yescharacteristic
197C22×Dic61C22⋊C411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199C22×Dic61C2×D411yescharacteristic
200C2×C4×D61—24no—
201C2×C4×D61—24no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×C4×D61—42no—
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C22⋊C411yescharacteristic
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22⋊C411yescharacteristic
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C22⋊C411yescharacteristic
219C2×C4×D61C22⋊C411yescharacteristic
220C2×C4×D61C22×C411yescharacteristic
221C2×C4×D61C22×C411yescharacteristic
222C2×C4×D61C22×C411yescharacteristic
223C2×C4×D61C22×C411yescharacteristic
224C2×C4×D61C2×D411yescharacteristic
225C2×C4×D61C2×D411yescharacteristic
226C2×C4×D61C2×D411yescharacteristic
227C2×C4×D61C2×D411yescharacteristic
228M16×C61—24no—
229C2×C8×C61—22no—
230C22⋊C4×C61—42no—
231C42×C61—24no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61—22no—
235C22⋊Dic61—22no—
236C22⋊Dic61—22no—
237C22⋊Dic61—22no—
238C22⋊Dic61—42no—
239#11758198—22no—
240#11758198—22no—
241#11758198—22no—
242#11758198—22no—
243#11758198—44no—
244#11758198—44no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61C22×C412yes—
248C4⋊Dic61C22×C412yes—
249#11758196—22no—
250#11758196—22no—
251#11758196—22no—
252#11758196—22no—
253#11758196—44no—
254C4×Dic61—22no—
255C4×Dic61—22no—
256C4×Dic61—24no—
257#11758194—24no—
258C2×#92418—22no—
259#11758189—44no—
260C8×D61—44no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—41no—
265C23×C61—42no—
266C23×C61—42no—
267C23×C61—42no—
268C23×C61C2×C22⋊C411yescharacteristic
269C23×C61C2×C22⋊C411yescharacteristic
270C23×C61C22×D411yescharacteristic
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
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—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—416no—
290C22×D61C2×C22⋊C411yescharacteristic
291C22×D61C2×C22⋊C411yescharacteristic
292C22×D61C2×C22⋊C411yescharacteristic
293C22×D61C2×C22⋊C411yescharacteristic
294Q8×C61—22no—
295Q8×C61—22no—
296Q8×C61—42no—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61—42no—
300D4×C61—44no—
301D4×C61—44no—
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—44no—
309C2×C4×C61—42no—
310C2×C4×C61—44no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C23×C411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61H(5,𝔽2)14yes—
319C22⋊D61—44no—
320C22⋊D61—44no—
321C22⋊D61—44no—
322C22⋊D61—44no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61C2×C22⋊C411yescharacteristic
337C2×Dic61C2×C22⋊C411yescharacteristic
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C22⋊C411yescharacteristic
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—41no—
351C4×D61—41no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—41no—
356C8×C61—42no—
357#92418—42no—
358#21774—611nomaximal, Sylow
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—44no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—84no—
371C22×C61#42112yes—
372C22×C61C22×C22⋊C411yescharacteristic
373C22×C61#53412yes—
374C2×D61—21no—
375C2×D61—21no—
376C2×D61—21no—
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—21no—
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—21no—
384C2×D61—21no—
385C2×D61—44no—
386C2×D61—44no—
387C2×D61—44no—
388C2×D61—44no—
389C2×D61—44no—
390C2×D61—44no—
391C2×D61#42112yes—
392C4×C61—21no—
393C4×C61—21no—
394C4×C61—42no—
395C4×C61—82no—
396C4×C61#51812yes—
397C4×C61#53412yes—
398Dic61—21no—
399Dic61—21no—
400Dic61—21no—
401Dic61—21no—
402Dic61—42no—
403Dic61—42no—
404Dic61—82no—
405C2×#525—611no—
406C2×#407—611no—
407#2280—611no—
408#1897—614no—
409#1871—614no—
410#1826—611no—
411#1826—611no—
412#1789—611no—
413#1789D6111yescharacteristic, complemented
414C2×C61—22no—
415C2×C61—22no—
416C2×C61—41no—
417C2×C61—82no—
418C2×C61#230811yescharacteristic
419C2×C61C2×#42111yescharacteristic
420C2×C61C2×#42111yescharacteristic
421D61—22no—
422D61—41no—
423D61—41no—
424D61—41no—
425C22×#41C2×D6111yescharacteristic
426C24×C4—611no—
427C22×M16—612no—
428#525—612no—
429#525—612no—
430#525—612no—
431#525—612no—
432#525—1221no—
433#525—1221no—
434#525—1221no—
435#525—1221no—
436C2×#123—1221no—
437C2×C22⋊Q8—611no—
438C2×C22⋊Q8—611no—
439C2×#121—611no—
440C2×#121—611no—
441C2×#120—1221no—
442C2×C4×D4—1221no—
443C2×C4×D4—1221no—
444C2×#117—612no—
445C2×#117—611no—
446C2×#104—614no—
447C2×#104C2×D6114yescomplemented
448#407—611no—
449#407—612no—
450#407—1221no—
451#407—1221no—
452#407C2×D6111yescharacteristic
453C2×C22⋊C8—1221no—
454C2×C22⋊C8—1221no—
455#381—1221no—
456#380—1221no—
457#380—1221no—
458#379—1221no—
459C4×C22⋊C4—611no—
460C4×C22⋊C4—612no—
461C4×C22⋊C4C2×D6111yescharacteristic
462#339—614no—
463#339—614no—
464C61#2177411yescharacteristic, complemented, Sylow
465C25—611no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—44no—
469C2×#41C4×D6112yes—
470C2×#41C22×D6112yes—
471C22×Q8C4×D6111yescharacteristic
472C22×D4—21no—
473C22×D4—1221no—
474C22×D4—1221no—
475C22×D4C4×D6111yescharacteristic
476C23×C4—21no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—2444no—
491C23×C4C22×D6111yescharacteristic
492C2×M16—612no—
493C2×M16—1222no—
494C2×M16—2444no—
495C2×M16C22×D6112yes—
496C22×C8—1222no—
497#123—1222no—
498#123—1222no—
499#123—1222no—
500#123—1222no—
501C22⋊Q8—612no—
502C22⋊Q8—612no—
503C22⋊Q8—612no—
504C22⋊Q8—612no—
505C22⋊Q8—1221no—
506C22⋊Q8—1221no—
507C22⋊Q8—1221no—
508C22⋊Q8—1221no—
509#121—612no—
510#121—612no—
511#121—612no—
512#121—612no—
513#121—1221no—
514#121—1221no—
515#121—1221no—
516#121—1221no—
517#120—1222no—
518#120—1222no—
519#120—1222no—
520#120—1222no—
521C4×D4—1222no—
522C4×D4—1222no—
523C4×D4—1222no—
524C4×D4—1222no—
525C4×D4—1222no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—1222no—
529#117—612no—
530#117—612no—
531#117—1221no—
532#117—1221no—
533#117—2444no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—1221no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1222no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1222no—
546C2×C22⋊C4—1222no—
547C2×C22⋊C4—1221no—
548C2×C42—612no—
549C2×C42—1221no—
550C2×C42C22×D6112yes—
551#104—44no—
552#104—2444no—
553C22⋊C8—21no—
554C22⋊C8—21no—
555C22⋊C8—1222no—
556C22⋊C8—1222no—
557C22⋊C8—1221no—
558C22⋊C8—1221no—
559#95—21no—
560#95—1222no—
561#95—1221no—
562C24—21no—
563C24—611no—
564C24—611no—
565C24—611no—
566C24—611no—
567C24—611no—
568C24—611no—
569C24—2442no—
570C24—2442no—
571C24—2442no—
572C24D4×D6111yescharacteristic
573#41—24no—
574#41—24no—
575#41—42no—
576#41—42no—
577#41—44no—
578#41—44no—
579C2×Q8—21no—
580C2×Q8—42no—
581C2×Q8C2×C4×D6112yes—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—42no—
586C2×D4—44no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—2444no—
592C2×D4—2444no—
593C2×D4C2×C4×D6112yes—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—44no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—1224no—
623C22×C4—1224no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1222no—
627C22×C4—2442no—
628C22×C4—2442no—
629C22×C4—2442no—
630C22×C4—2442no—
631C22×C4—2442no—
632C22×C4—2442no—
633C22×C4—2442no—
634C22×C4—2442no—
635C22×C4—2442no—
636C22×C4—2442no—
637C22×C4—2442no—
638C22×C4C2×C4×D6111yescharacteristic
639C22×C4C2×C4×D6111yescharacteristic
640C22×C4D4×D6111yescharacteristic
641C22×C4D4×D6111yescharacteristic
642C22×C4D4×D6111yescharacteristic
643C22×C4C23×D6111yescharacteristic
644M16—24no—
645M16—1224no—
646M16—2444no—
647C2×C8—22no—
648C2×C8—1222no—
649C2×C8—2444no—
650C4⋊C4—612no—
651C4⋊C4—612no—
652C4⋊C4—1222no—
653C4⋊C4—1222no—
654C4⋊C4—1222no—
655C4⋊C4—1222no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—2444no—
659C22⋊C4—42no—
660C22⋊C4—1222no—
661C22⋊C4—1222no—
662C22⋊C4—1222no—
663C22⋊C4—1222no—
664C22⋊C4—1222no—
665C22⋊C4—1222no—
666C22⋊C4—1222no—
667C22⋊C4—1222no—
668C22⋊C4—1222no—
669C22⋊C4—1222no—
670C22⋊C4—2444no—
671C22⋊C4—2444no—
672C22⋊C4—2442no—
673C42—24no—
674C42—1222no—
675C42—1222no—
676C42—1224no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—41no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—611no—
685C23—611no—
686C23—611no—
687C23—611no—
688C23—1222no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23—1222no—
695C23—2441no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23—2441no—
704C23—2441no—
705C23—2441no—
706C23—24416no—
707C23C22⋊C4×D6111yescharacteristic
708C23C22⋊C4×D6111yescharacteristic
709C23C2×D4×D6111yescharacteristic
710Q8—22no—
711Q8—22no—
712Q8—42no—
713D4—22no—
714D4—22no—
715D4—42no—
716D4—44no—
717D4—44no—
718D4—2444no—
719D4—2444no—
720D4—2444no—
721D4—2444no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—611no—
735C2×C4—611no—
736C2×C4—611no—
737C2×C4—611no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4—2442no—
767C2×C4C22⋊C4×D6111yescharacteristic
768C2×C4C22⋊C4×D6111yescharacteristic
769C2×C4C22×C4×D6111yescharacteristic
770C2×C4C2×D4×D6111yescharacteristic
771C2×C4#1451982214yes—
772C8—42no—
773C8—2442no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—84no—
786C22—612no—
787C22—1221no—
788C22—1221no—
789C22—1221no—
790C22—1221no—
791C22—1221no—
792C22—1221no—
793C22—1221no—
794C22—1221no—
795C22—1221no—
796C22—1221no—
797C22—1221no—
798C22—2444no—
799C22—2444no—
800C22—2444no—
801C22—2444no—
802C22—2444no—
803C22—2444no—
804C22#1683977712yes—
805C22C2×C22⋊C4×D6111yescharacteristic
806C22#1684032212yes—
807C4—21no—
808C4—21no—
809C4—42no—
810C4—82no—
811C4—1221no—
812C4—1221no—
813C4—1221no—
814C4—1221no—
815C4—4882no—
816C4—2442no—
817C4—2442no—
818C4#1684023512yes—
819C4#1684032212yes—
820C2—22no—
821C2—22no—
822C2—41no—
823C2—82no—
824C2—1222no—
825C2—2441no—
826C2—2441no—
827C2—2441no—
828C2#2144839511yescharacteristic
829C2#421×D6111yescharacteristic
830C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1789C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840269C2
cosocleC22×C4×C61C24
hypercenter#1789D61
hypocenterC61#21774
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. #21448200C2semidirect
4. #21446264C2semidirect
5. #21446118C2semidirect
6. #21445919C2semidirect
7. #21445916C2semidirect
8. #21445763C2semidirect
9. C61×#1789C2semidirect
11. C2×M16×D61C22semidirect
16. #16840269C4semidirect
17. #16840269C4semidirect
21. C2×#14519753C4semidirect
22. C2×#14519753C4semidirect
23. C2×#14519748C4semidirect
24. C2×#14519748C4semidirect
29. C2×#14519734C22semidirect
30. C2×#14519704C22semidirect
32. #16839725C22semidirect
41. C4×#11758198C22semidirect
43. #16839523C22semidirect
44. #16839522C22semidirect
46. C2×#104×C61C22semidirect
413. #1789D61semidirect
447. C2×#104C2×D61semidirect
464. C61#21774semidirect

Maximal subgroups

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

subgroupindex
C2×#168402692
#407×D612
#214482002
#214462642
#214461182
#214459192
#214459162
#214457632
C61×#17892
#2177461