Finite Group Databasebeta

← #29713069

Subgroups — #29713069

Order 15616.

1318 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840427C211yesmaximal, characteristic
2C2×#16840096C211yesmaximal, characteristic, complemented
3C2×#103×D61C211yesmaximal, characteristic, complemented
4#21450134C211yesmaximal, characteristic
5#21447062C211yesmaximal, characteristic, complemented
6#21447021C211yesmaximal, characteristic, complemented
7#21447020C211yesmaximal, characteristic, complemented
8#21446239C211yesmaximal, characteristic, complemented
9#21446110C211yesmaximal, characteristic
10#21446076C211yesmaximal, characteristic, complemented
11#21446072C211yesmaximal, characteristic, complemented
12#21445752C211yesmaximal, characteristic, complemented
13#21445752C211yesmaximal, characteristic, complemented
14#21445752C211yesmaximal, characteristic, complemented
15C61×#2043C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840427—24no—
20#16840427—24no—
21C2×#14519776—21no—
22C2×#14519755—21no—
23C2×#14519755—21no—
24C2×#14519753C2211yescharacteristic
25C2×#14519753C2211yescharacteristic
26C2×C4×Dic122C2211yescharacteristic
27C2×C4×D244C2211yescharacteristic
28C2×#14519739—21no—
29C2×C4⋊C4×D61C2211yescharacteristic
30#16840096—24no—
31C2×#14519711C2211yescharacteristic
32C2×#14519710C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41#103×D61—24no—
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45#16839704—21no—
46#16839697—21no—
47#16839660C2211yescharacteristic
48#16839640—21no—
49#16839633—21no—
50#16839619C2211yescharacteristic
51#16839619C2211yescharacteristic
52#16839619C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839517C2211yescharacteristic
56C2×C4⋊Q8×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C61×#389C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122—21no—
65C22×Dic122C2311yescharacteristic
66C2×Q8×D61—22no—
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61—22no—
70C2×Q8×D61—22no—
71C2×Q8×D61—22no—
72C2×Q8×D61—22no—
73C2×Q8×D61—41no—
74C2×Q8×D61—41no—
75C2×Q8×D61—41no—
76C2×Q8×D61—41no—
77C2×Q8×D61D414yes—
78C22×D244D411yescharacteristic
79C22×C4×D61—21no—
80C22×C4×D61—21no—
81C22×C4×D61—21no—
82C22×C4×D61C2311yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C2×C8×D61—22no—
87C2×C8×D61—41no—
88C2×C8×D61—41no—
89#14519776—28no—
90#14519755—28no—
91#14519755—28no—
92#14519753—22no—
93#14519753—22no—
94#14519753—22no—
95#14519753D414yes—
96C4×Dic122—22no—
97C4×Dic122—22no—
98C4×D244—22no—
99C4×D244—22no—
100#14519739—28no—
101C2×C4⋊Dic61D411yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196—21no—
110C4⋊C4×D61—22no—
111C4⋊C4×D61—22no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198D411yescharacteristic
118C2×#11758198D411yescharacteristic
119C2×C4×Dic61—21no—
120#14519711—22no—
121#14519710—22no—
122#14519702—22no—
123#14519702—22no—
124#14519701—22no—
125#14519701—22no—
126#14519701—41no—
127#14519701—41no—
128#14519700—22no—
129#14519700—22no—
130#14519689—22no—
131#14519689—41no—
132#14519689—41no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137C22×Q8×C61C2311yescharacteristic
138C22×Q8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C4⋊Q8×C61—22no—
142C4⋊Q8×C61—22no—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61—21no—
145C2×C4⋊C4×C61—21no—
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C42×C61C2311yescharacteristic
149#103×C61—22no—
150#103×C61—22no—
151#103×C61—41no—
152#103×C61—41no—
153#95×C61—21no—
154C23×D61C2×D411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61C2×D412yes—
167C2×Q8×C61C2×D412yes—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2411yescharacteristic
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181Q8×D61—28no—
182Q8×D61—44no—
183Q8×D61—44no—
184Q8×D61—44no—
185Q8×D61—44no—
186Q8×D61—44no—
187Q8×D61—44no—
188Q8×D61—44no—
189C2×D244—22no—
190C2×D244—22no—
191C2×D244Q1614yes—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—24no—
197C2×C4×D61—24no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—81no—
210C2×C4×D61—81no—
211C2×C4×D61C2×D412yes—
212C2×C4×D61C2×D412yes—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—24no—
217C2×Dic122—24no—
218C2×Dic122—42no—
219C2×Dic122—42no—
220C2×Dic122—42no—
221C2×Dic122—42no—
222C2×Dic122C2×D412yes—
223C2×Dic122#4112yes—
224C2×Dic122#4112yes—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—81no—
238C42×C61—21no—
239C42×C61—21no—
240#11758198—24no—
241#11758198—24no—
242#11758198—22no—
243#11758198—22no—
244#11758198—42no—
245#11758198—81no—
246#11758198—81no—
247C4⋊Dic61—21no—
248C4⋊Dic61—22no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61C2×D412yes—
254#11758196—24no—
255#11758196—24no—
256#11758196—24no—
257#11758196—42no—
258#11758196—81no—
259C4×Dic61—24no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C8×D61—44no—
267C23×C61C22×D411yescharacteristic
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61#12012yes—
279C22×D61C2×Q1612yes—
280C22×D61C2×Q1612yes—
281C22×D61#13712yes—
282Q8×C61—22no—
283Q8×C61—22no—
284Q8×C61—22no—
285Q8×C61—22no—
286Q8×C61—41no—
287Q8×C61—41no—
288Q8×C61—41no—
289Q8×C61—41no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61C2×Q1612yes—
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61C22×D411yescharacteristic
310C2×C4×C61C2×#4111yescharacteristic
311C2×C4×C61C2×#4111yescharacteristic
312C2×C4×C61H(5,𝔽2)11yescharacteristic
313C2×C4×C61H(5,𝔽2)11yescharacteristic
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—22no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61#12012yes—
332D244—28no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—48no—
338C4×D61—48no—
339C4×D61—41no—
340C4×D61—41no—
341C4×D61—41no—
342C4×D61—41no—
343C4×D61—84no—
344Dic122—22no—
345Dic122—22no—
346Dic122—22no—
347Dic122—48no—
348Dic122—48no—
349Dic122#12314yes—
350C8×C61—41no—
351C8×C61—41no—
352#92418—41no—
353#92418—41no—
354#24042—611nomaximal, Sylow
355C22×C61C2×#12011yescharacteristic
356C22×C61#54611yescharacteristic
357C22×C61#54611yescharacteristic
358C22×C61C22×Q1611yescharacteristic
359C22×C61C2×#13711yescharacteristic
360C22×C61#57711yescharacteristic
361C22×C61#57711yescharacteristic
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61#45114yes—
376C4×C61—22no—
377C4×C61—42no—
378C4×C61—42no—
379C4×C61—41no—
380C4×C61—81no—
381C4×C61—81no—
382C4×C61C2×#12311yescharacteristic
383C4×C61#53411yescharacteristic
384C4×C61#54611yescharacteristic
385C4×C61#54611yescharacteristic
386Dic61—24no—
387Dic61—22no—
388Dic61—41no—
389Dic61—42no—
390Dic61—81no—
391Dic61—81no—
392C2×D4×Q8—611no—
393C2×#484—611no—
394C22×#103—611no—
395#2487—611no—
396#2043—611no—
397#2043D6111yescharacteristic, complemented
398#2036—611no—
399#2036—611no—
400#1892—611no—
401#1869—611no—
402#1863—611no—
403#1863—611no—
404#1787—611no—
405#1787—611no—
406#1787—611no—
407C2×C61#240511yescharacteristic
408C2×C61C2×#45111yescharacteristic
409C2×C61#301011yescharacteristic
410C2×C61#329911yescharacteristic
411C2×C61#329911yescharacteristic
412C2×C61#332011yescharacteristic
413C2×C61#332011yescharacteristic
414D61—24no—
415D61—42no—
416C23×Q8—611no—
417C23×Q8—611no—
418C23×C8—611no—
419D4×Q8—1224no—
420D4×Q8—1224no—
421C2×C4⋊Q8—1221no—
422C2×C4⋊Q8C2×D6111yescharacteristic
423C2×C22⋊Q8—611no—
424C2×C22⋊Q8—611no—
425C2×C22⋊Q8—1221no—
426C2×C22⋊Q8—1221no—
427C2×C4×Q8—611no—
428C2×C4×D4—611no—
429C2×C4×D4—1221no—
430C22×C4⋊C4—611no—
431#484—1224no—
432C2×#107—611no—
433C2×#107—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#103—611no—
442C2×#103—1224no—
443C2×#103C2×D6111yescharacteristic
444C2×#103C2×D6111yescharacteristic
445C2×#103C2×D6111yescharacteristic
446C2×#103C2×D6111yescharacteristic
447C2×C22⋊C8—611no—
448C2×C22⋊C8—611no—
449C2×C22⋊C8—611no—
450#400—1221no—
451#399—1221no—
452#389—611no—
453#389C2×D6111yescharacteristic
454#386—1221no—
455#385—1221no—
456#380—611no—
457#380—611no—
458#380—611no—
459#340—611no—
460#340—611no—
461#336—611no—
462#336C2×D6111yescharacteristic
463C61#2404211yescharacteristic, complemented, Sylow
464C22×Q8—614no—
465C22×Q8—611no—
466C22×Q8—1221no—
467C22×Q8—1221no—
468C22×Q8—1222no—
469C22×Q8—1222no—
470C22×Q8—1222no—
471C22×Q8—1222no—
472C22×Q8—1222no—
473C22×Q8—1222no—
474C22×Q8—1222no—
475C22×Q8—2441no—
476C22×Q8—2441no—
477C22×Q8—2441no—
478C22×Q8—2441no—
479C22×Q8C22×D6111yescharacteristic
480C22×Q8C22×D6111yescharacteristic
481C22×D4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—1221no—
485C23×C4—1221no—
486C23×C4—1221no—
487C22×C8—611no—
488C22×C8—611no—
489C22×C8—1222no—
490C22×C8—2441no—
491C22×C8—2441no—
492C22×C8C22×D6111yescharacteristic
493C22×C8C22×D6111yescharacteristic
494C4⋊Q8—22no—
495C4⋊Q8—22no—
496C4⋊Q8—1228no—
497C22⋊Q8—614no—
498C22⋊Q8—1228no—
499C22⋊Q8—1228no—
500C22⋊Q8—1222no—
501C22⋊Q8—1222no—
502C22⋊Q8—1222no—
503C4×Q8—1222no—
504C4×Q8—1222no—
505C4×D4—1222no—
506C4×D4—1222no—
507C4×D4—1228no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—1222no—
516C2×C4⋊C4—1222no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4C22×D6111yescharacteristic
523C2×C4⋊C4C22×D6111yescharacteristic
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C42—1221no—
532C2×C42C22×D6111yescharacteristic
533#107—1222no—
534#107—1222no—
535#103—22no—
536#103—22no—
537#103—41no—
538#103—41no—
539#103—1222no—
540#103—1222no—
541#103—1222no—
542#103—1222no—
543#103—1222no—
544#103—1222no—
545#103—2441no—
546#103—2441no—
547C22⋊C8—1222no—
548C22⋊C8—2441no—
549C22⋊C8—2441no—
550#95—21no—
551#95—1221no—
552#95—1221no—
553#95—1221no—
554#95—1221no—
555C24—611no—
556C24—611no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—612no—
568C2×Q8—612no—
569C2×Q8—612no—
570C2×Q8—1224no—
571C2×Q8—1224no—
572C2×Q8—1221no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8—1228no—
576C2×Q8—2442no—
577C2×Q8—2442no—
578C2×Q8—2442no—
579C2×Q8—2442no—
580C2×Q8—2444no—
581C2×Q8—2444no—
582C2×Q8—2444no—
583C2×Q8—2444no—
584C2×Q8—2444no—
585C2×Q8—2444no—
586C2×Q8—2444no—
587C2×Q8D4×D6112yes—
588C2×Q8D4×D6112yes—
589C2×D4—614no—
590C2×D4—1222no—
591C2×D4—1222no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—611no—
597C22×C4—612no—
598C22×C4—612no—
599C22×C4—611no—
600C22×C4—1224no—
601C22×C4—1224no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—4881no—
617C22×C4—4881no—
618C22×C4—2442no—
619C22×C4—2442no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4D4×D6111yescharacteristic
624C22×C4D4×D6111yescharacteristic
625C22×C4C23×D6111yescharacteristic
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—2444no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—81no—
646C4⋊C4—612no—
647C4⋊C4—1222no—
648C4⋊C4—1224no—
649C4⋊C4—1224no—
650C4⋊C4—1224no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—4881no—
657C4⋊C4—2442no—
658C22⋊C4—1222no—
659C22⋊C4—1222no—
660C22⋊C4—1224no—
661C22⋊C4—1224no—
662C22⋊C4—4881no—
663C22⋊C4—4881no—
664C22⋊C4—2442no—
665C42—21no—
666C42—21no—
667C42—1224no—
668C23—612no—
669C23—612no—
670C23—612no—
671C23—612no—
672C23—1221no—
673C23—1221no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23—1221no—
680C23—1221no—
681C23—1221no—
682C23C2×D4×D6111yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8—614no—
692Q8—1222no—
693Q8—1222no—
694Q8—1222no—
695Q8—2448no—
696Q8—2448no—
697D4—1228no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—612no—
716C2×C4—1222no—
717C2×C4—1221no—
718C2×C4—1222no—
719C2×C4—1221no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—4884no—
730C2×C4—2448no—
731C2×C4—2448no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4Q16×D6112yes—
745C2×C4C2×D4×D6111yescharacteristic
746C2×C4C2×D4×D6111yescharacteristic
747C2×C4#41×D6111yescharacteristic
748C2×C4#41×D6111yescharacteristic
749C2×C4#1451982211yescharacteristic
750C2×C4#1451982311yescharacteristic
751C8—41no—
752C8—41no—
753C8—2441no—
754C8—2441no—
755C22—614no—
756C22—1222no—
757C22—1222no—
758C22—1222no—
759C22—1222no—
760C22—1222no—
761C22—1222no—
762C22—1222no—
763C22—1222no—
764C22—1222no—
765C22—2441no—
766C22—2441no—
767C22—2441no—
768C22—2441no—
769C22#120×D6111yescharacteristic
770C22#1684040511yescharacteristic
771C22#1684040911yescharacteristic
772C22C2×Q16×D6111yescharacteristic
773C22#137×D6111yescharacteristic
774C22#1684056811yescharacteristic
775C22#1684057111yescharacteristic
776C4—22no—
777C4—42no—
778C4—42no—
779C4—41no—
780C4—81no—
781C4—81no—
782C4—1222no—
783C4—1224no—
784C4—4881no—
785C4—4881no—
786C4—2441no—
787C4—2442no—
788C4#123×D6111yescharacteristic
789C4#1684032011yescharacteristic
790C4#1684040111yescharacteristic
791C4#1684040411yescharacteristic
792C2—1224no—
793C2—2442no—
794C2#2144914111yescharacteristic
795C2#451×D6111yescharacteristic
796C2#2145510011yescharacteristic
797C2#2145769411yescharacteristic
798C2#2145769811yescharacteristic
799C2#2145798911yescharacteristic
800C2#2145799711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2043C2
socleC23×C61C22×D4
prime radicalC22×D244D4
hypercenter#2043D61
hypocenterC61#24042
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
2. C2×#16840096C2semidirect
3. C2×#103×D61C2semidirect
5. #21447062C2semidirect
6. #21447021C2semidirect
7. #21447020C2semidirect
8. #21446239C2semidirect
10. #21446076C2semidirect
11. #21446072C2semidirect
12. #21445752C2semidirect
13. #21445752C2semidirect
14. #21445752C2semidirect
15. C61×#2043C2semidirect
397. #2043D61semidirect
463. C61#24042semidirect

Maximal subgroups

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

subgroupindex
C2×#168404272
C2×#168400962
C2×#103×D612
#214501342
#214470622
#214470212
#214470202
#214462392
#214461102
#214460762
#214460722
#214457522
C61×#20432
#2404261