Finite Group Databasebeta

← #29713078

Subgroups — #29713078

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×Q8×D244C211yesmaximal, characteristic
2C2×#16840099C211yesmaximal, characteristic, complemented
3C2×#103×D61C211yesmaximal, characteristic, complemented
4#21450134C211yesmaximal, characteristic
5#21447066C211yesmaximal, characteristic, complemented
6#21447065C211yesmaximal, characteristic, complemented
7#21447025C211yesmaximal, characteristic, complemented
8#21447024C211yesmaximal, characteristic, complemented
9#21446241C211yesmaximal, characteristic, complemented
10#21446110C211yesmaximal, characteristic
11#21446073C211yesmaximal, characteristic, complemented
12#21445752C211yesmaximal, characteristic, complemented
13#21445752C211yesmaximal, characteristic, complemented
14#21445752C211yesmaximal, characteristic, complemented
15C61×#1863C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19Q8×D244—24no—
20Q8×D244—24no—
21C2×#14519777—21no—
22C2×#14519777C2211yescharacteristic
23C2×#14519757—21no—
24C2×#14519757—21no—
25C2×#14519757C2211yescharacteristic
26C2×#14519757C2211yescharacteristic
27C2×C4×D244—21no—
28C2×C4×D244C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30#16840099—24no—
31C2×#14519710C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42#103×D61—24no—
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46#16839704—21no—
47#16839697—21no—
48#16839660C2211yescharacteristic
49#16839640—21no—
50#16839633—21no—
51#16839619C2211yescharacteristic
52#16839619C2211yescharacteristic
53#16839619C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839517C2211yescharacteristic
56C2×C4×Q8×C61C2211yescharacteristic
57C2×#107×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C61×#389C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122—21no—
65C22×Dic122C2311yescharacteristic
66C22×Dic122C2311yescharacteristic
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—22no—
74C2×Q8×D61—41no—
75C2×Q8×D61—41no—
76C2×Q8×D61—41no—
77C2×Q8×D61—41no—
78C2×Q8×D61D414yes—
79C22×D244D411yescharacteristic
80C22×C4×D61—21no—
81C22×C4×D61—21no—
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C2×C8×D61—22no—
88C2×C8×D61—41no—
89C2×C8×D61—41no—
90#14519777—28no—
91#14519777—22no—
92#14519777—22no—
93#14519757—28no—
94#14519757—28no—
95#14519757—22no—
96#14519757—22no—
97#14519757—22no—
98#14519757D414yes—
99C4×D244—28no—
100C4×D244—22no—
101C4×D244—22no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61—21no—
106C2×C4⋊Dic61D411yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758196—21no—
110C2×#11758196—21no—
111C4⋊C4×D61—22no—
112C4⋊C4×D61—22no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198D411yescharacteristic
119C2×#11758198D411yescharacteristic
120#14519710—22no—
121#14519702—22no—
122#14519702—22no—
123#14519702—41no—
124#14519702—41no—
125#14519701—22no—
126#14519701—22no—
127#14519700—22no—
128#14519700—22no—
129#14519700—41no—
130#14519700—41no—
131#14519689—22no—
132#14519689—41no—
133#14519689—41no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137#14519684—21no—
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×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C42×C61—21no—
149C2×C42×C61C2311yescharacteristic
150#107×C61—22no—
151#103×C61—22no—
152#103×C61—22no—
153#95×C61—21no—
154C23×D61C2×D411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61C2×D412yes—
160C2×Q8×C61#4112yes—
161C2×Q8×C61#4112yes—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2411yescharacteristic
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175Q8×D61—28no—
176Q8×D61—44no—
177Q8×D61—44no—
178Q8×D61—44no—
179Q8×D61—44no—
180Q8×D61—44no—
181Q8×D61—44no—
182Q8×D61—44no—
183C2×D244—22no—
184C2×D244—22no—
185C2×D244Q1614yes—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—24no—
191C2×C4×D61—24no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—81no—
204C2×C4×D61—81no—
205C2×C4×D61C2×D412yes—
206C2×C4×D61C2×D412yes—
207C2×Dic122—21no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—24no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—24no—
219C2×Dic122—42no—
220C2×Dic122—42no—
221C2×Dic122—42no—
222C2×Dic122—42no—
223C2×Dic122C2×D412yes—
224C2×Dic122C2×D412yes—
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—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—81no—
238C4⋊C4×C61C2×D412yes—
239C42×C61—24no—
240C42×C61—21no—
241C42×C61—21no—
242#11758198—24no—
243#11758198—24no—
244#11758198—22no—
245#11758198—22no—
246#11758198—42no—
247#11758198—81no—
248#11758198—81no—
249C4⋊Dic61—24no—
250C4⋊Dic61—24no—
251C4⋊Dic61—24no—
252C4⋊Dic61—24no—
253C4⋊Dic61—22no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258#11758196—42no—
259#11758196—81no—
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#12314yes—
286C2×C4×C61—21no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—22no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
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×C61C2×Q1612yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C2×C4×C61H(5,𝔽2)11yescharacteristic
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61#12012yes—
328D244—28no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—48no—
334C4×D61—48no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—84no—
340Dic122—22no—
341Dic122—22no—
342Dic122—22no—
343Dic122—22no—
344Dic122—48no—
345Dic122—48no—
346Dic122—41no—
347Dic122—41no—
348Dic122—41no—
349Dic122—41no—
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—24no—
377C4×C61—22no—
378C4×C61—41no—
379C4×C61—42no—
380C4×C61—81no—
381C4×C61—81no—
382C4×C61C2×#12311yescharacteristic
383C4×C61#53411yescharacteristic
384C4×C61#54611yescharacteristic
385C4×C61#54611yescharacteristic
386Dic61—22no—
387Dic61—42no—
388Dic61—42no—
389Dic61—41no—
390Dic61—81no—
391Dic61—81no—
392C2×D4×Q8—611no—
393C2×#484—611no—
394C22×#103—611no—
395#2487—611no—
396#2043—611no—
397#2043—611no—
398#2036—611no—
399#2036—611no—
400#1892—611no—
401#1869—611no—
402#1863—611no—
403#1863D6111yescharacteristic, complemented
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—611no—
422C2×C4⋊Q8—1221no—
423C2×C22⋊Q8—611no—
424C2×C22⋊Q8—611no—
425C2×C22⋊Q8—1221no—
426C2×C22⋊Q8—1221no—
427C2×C4×Q8C2×D6111yescharacteristic
428C2×C4×D4—611no—
429C2×C4×D4—1221no—
430C22×C4⋊C4—611no—
431#484—1224no—
432C2×#107—611no—
433C2×#107C2×D6111yescharacteristic
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—611no—
443C2×#103—611no—
444C2×#103—1224no—
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#340C2×D6111yescharacteristic
461#336—611no—
462#336C2×D6111yescharacteristic
463C61#2404211yescharacteristic, complemented, Sylow
464C22×Q8—614no—
465C22×Q8—611no—
466C22×Q8—611no—
467C22×Q8—1221no—
468C22×Q8—1221no—
469C22×Q8—1222no—
470C22×Q8—1222no—
471C22×Q8—1222no—
472C22×Q8—1222no—
473C22×Q8—1222no—
474C22×Q8—1222no—
475C22×Q8—1222no—
476C22×Q8—2441no—
477C22×Q8—2441no—
478C22×Q8—2441no—
479C22×Q8—2441no—
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—1222no—
495C4⋊Q8—1222no—
496C4⋊Q8—1228no—
497C22⋊Q8—614no—
498C22⋊Q8—1222no—
499C22⋊Q8—1222no—
500C22⋊Q8—1228no—
501C22⋊Q8—1228no—
502C22⋊Q8—1222no—
503C4×Q8—22no—
504C4×Q8—22no—
505C4×D4—1222no—
506C4×D4—1222no—
507C4×D4—1228no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—1222no—
514C2×C4⋊C4—1222no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4C22×D6111yescharacteristic
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—21no—
532C2×C42C22×D6111yescharacteristic
533#107—22no—
534#107—1222no—
535#103—22no—
536#103—22no—
537#103—1222no—
538#103—1222no—
539#103—1222no—
540#103—1222no—
541#103—1222no—
542#103—1222no—
543#103—2441no—
544#103—2441no—
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—612no—
561C2×Q8—612no—
562C2×Q8—1224no—
563C2×Q8—1224no—
564C2×Q8—1221no—
565C2×Q8—1221no—
566C2×Q8—1228no—
567C2×Q8—1221no—
568C2×Q8—1221no—
569C2×Q8—1221no—
570C2×Q8—1221no—
571C2×Q8—1221no—
572C2×Q8—1221no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8—2442no—
576C2×Q8—2442no—
577C2×Q8—2442no—
578C2×Q8—2442no—
579C2×Q8—2444no—
580C2×Q8—2444no—
581C2×Q8—2444no—
582C2×Q8—2444no—
583C2×Q8—2444no—
584C2×Q8—2444no—
585C2×Q8—2444no—
586C2×Q8#1175822212yes—
587C2×Q8D4×D6112yes—
588C2×Q8#1175822612yes—
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—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—81no—
646C4⋊C4—1222no—
647C4⋊C4—1224no—
648C4⋊C4—1224no—
649C4⋊C4—1224no—
650C4⋊C4—1224no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—4881no—
656C4⋊C4—2442no—
657C4⋊C4D4×D6112yes—
658C22⋊C4—1222no—
659C22⋊C4—1222no—
660C22⋊C4—1224no—
661C22⋊C4—1224no—
662C22⋊C4—4881no—
663C22⋊C4—4881no—
664C22⋊C4—2442no—
665C42—24no—
666C42—21no—
667C42—21no—
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—1222no—
687Q8—1222no—
688Q8—1222no—
689Q8—1222no—
690Q8—2448no—
691Q8—2448no—
692Q8—2441no—
693Q8—2441no—
694Q8—2441no—
695Q8—2441no—
696Q8#1451976214yes—
697D4—1228no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
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—1221no—
717C2×C4—1221no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1221no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1221no—
726C2×C4—1221no—
727C2×C4—4884no—
728C2×C4—2448no—
729C2×C4—2448no—
730C2×C4—2441no—
731C2×C4—2441no—
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×C4C2×#1175822211yescharacteristic
748C2×C4C2×#1175822611yescharacteristic
749C2×C4#1451982311yescharacteristic
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#1684040311yescharacteristic
771C22#1684040811yescharacteristic
772C22C2×Q16×D6111yescharacteristic
773C22#137×D6111yescharacteristic
774C22#1684056911yescharacteristic
775C22#1684057211yescharacteristic
776C4—22no—
777C4—24no—
778C4—41no—
779C4—42no—
780C4—81no—
781C4—81no—
782C4—1222no—
783C4—4881no—
784C4—4881no—
785C4—2441no—
786C4—2442no—
787C4—2442no—
788C4C2×#1451976211yescharacteristic
789C4#1684032311yescharacteristic
790C4#1684040311yescharacteristic
791C4#1684040811yescharacteristic
792C2—1224no—
793C2—2442no—
794C2#2144914811yescharacteristic
795C2#451×D6111yescharacteristic
796C2#2145510211yescharacteristic
797C2#2145769211yescharacteristic
798C2#2145769711yescharacteristic
799C2#2145798711yescharacteristic
800C2#2145799511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1863C2
socleC23×C61C22×D4
prime radicalC22×D244D4
hypercenter#1863D61
hypocenterC61#24042
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
2. C2×#16840099C2semidirect
3. C2×#103×D61C2semidirect
5. #21447066C2semidirect
6. #21447065C2semidirect
7. #21447025C2semidirect
8. #21447024C2semidirect
9. #21446241C2semidirect
11. #21446073C2semidirect
12. #21445752C2semidirect
13. #21445752C2semidirect
14. #21445752C2semidirect
15. C61×#1863C2semidirect
403. #1863D61semidirect
463. C61#24042semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×D2442
C2×#168400992
C2×#103×D612
#214501342
#214470662
#214470652
#214470252
#214470242
#214462412
#214461102
#214460732
#214457522
C61×#18632
#2404261