Finite Group Databasebeta

← #29713072

Subgroups — #29713072

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×C22⋊D61C211yesmaximal, characteristic
2C2×#16840096C211yesmaximal, characteristic, complemented
3C2×#103×D61C211yesmaximal, characteristic, complemented
4#21450132C211yesmaximal, characteristic
5#21447064C211yesmaximal, characteristic, complemented
6#21447063C211yesmaximal, characteristic, complemented
7#21447023C211yesmaximal, characteristic, complemented
8#21447022C211yesmaximal, characteristic, complemented
9#21446239C211yesmaximal, characteristic, complemented
10#21446108C211yesmaximal, characteristic
11#21446075C211yesmaximal, characteristic, complemented
12#21446071C211yesmaximal, characteristic, complemented
13#21445754C211yesmaximal, characteristic, complemented
14#21445752C211yesmaximal, characteristic, complemented
15C61×#1787C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18Q8×C22⋊D61—24no—
19Q8×C22⋊D61—24no—
20C2×#14519775—21no—
21C2×#14519775C2211yescharacteristic
22C2×#14519756—21no—
23C2×#14519756C2211yescharacteristic
24C2×#14519753—21no—
25C2×#14519753C2211yescharacteristic
26C2×Q8×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61—21no—
28C2×C4×C22⋊D61C2211yescharacteristic
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×C22⋊#92418C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44#16839703—21no—
45#16839698—21no—
46#16839661C2211yescharacteristic
47#16839658C2211yescharacteristic
48#16839638—21no—
49#16839636—21no—
50#16839622C2211yescharacteristic
51#16839619C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C23×Q8×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C61×#380C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122C2311yescharacteristic
65C2×Q8×D61—22no—
66C2×Q8×D61—22no—
67C2×Q8×D61—22no—
68C2×Q8×D61—41no—
69C2×Q8×D61—41no—
70C2×Q8×D61D414yes—
71C22×C22⋊D61D411yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C2×C8×D61—22no—
78C2×C8×D61—41no—
79C2×C8×D61—41no—
80#14519775—28no—
81#14519775—22no—
82#14519775—22no—
83#14519756—28no—
84#14519756—22no—
85#14519756—22no—
86#14519753—28no—
87#14519753—22no—
88#14519753D414yes—
89Q8×Dic61—22no—
90Q8×Dic61—22no—
91C4×C22⋊D61—28no—
92C4×C22⋊D61—22no—
93C4×C22⋊D61—22no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196D411yescharacteristic
106C4⋊C4×D61—22no—
107C4⋊C4×D61—22no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61D411yescharacteristic
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198D411yescharacteristic
114C2×C4×Dic61—21no—
115C2×C4×Dic61C2311yescharacteristic
116#14519711—22no—
117#14519710—22no—
118#14519702—22no—
119#14519702—41no—
120#14519701—22no—
121#14519701—22no—
122#14519701—22no—
123#14519701—41no—
124#14519700—22no—
125#14519700—41no—
126C22⋊#92418—41no—
127#14519689—22no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131#14519684—21no—
132C22×Q8×C61—22no—
133C22×Q8×C61—22no—
134C22×Q8×C61—21no—
135C22×Q8×C61—22no—
136C22×Q8×C61—22no—
137C22×Q8×C61—41no—
138C22×Q8×C61—41no—
139C22×Q8×C61C2311yescharacteristic
140C22×Q8×C61C2311yescharacteristic
141C23×C4×C61—21no—
142C23×C4×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C22⋊C4×C61—21no—
148#103×C61—22no—
149#103×C61—22no—
150#103×C61—22no—
151#103×C61—41no—
152C22⋊C8×C61—41no—
153#95×C61—21no—
154C24×C61C2×D411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C2×Q8×C61—24no—
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—42no—
166C2×Q8×C61—42no—
167C2×Q8×C61—44no—
168C2×Q8×C61—44no—
169C2×Q8×C61—44no—
170C2×Q8×C61—44no—
171C2×Q8×C61C2×D412yes—
172C2×Q8×C61C2×D412yes—
173C2×Q8×C61#4112yes—
174C2×Q8×C61#4112yes—
175C22×C4×C61—21no—
176C22×C4×C61—24no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—42no—
187C22×C4×C61—42no—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—22no—
191C2×C22⋊D61—22no—
192C2×C22⋊D61Q1614yes—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199C22×Dic61C2×D411yescharacteristic
200Q8×D61—28no—
201Q8×D61—44no—
202Q8×D61—44no—
203Q8×D61—44no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—24no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×C4×D61—42no—
212C2×C4×D61—81no—
213C2×C4×D61—81no—
214C2×C4×D61C2×D412yes—
215C2×C4×D61C2×D412yes—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—21no—
219C2×Dic122—21no—
220C2×Dic122—21no—
221C2×Dic122—24no—
222C2×Dic122—42no—
223C2×Dic122—42no—
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—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C22⋊C4×C61—81no—
236C22⋊Dic61—24no—
237C22⋊Dic61—22no—
238C22⋊Dic61—81no—
239#11758198—24no—
240#11758198—22no—
241#11758198—42no—
242C4⋊Dic61—24no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—81no—
249C4⋊Dic61C2×D412yes—
250#11758196—24no—
251#11758196—24no—
252#11758196—24no—
253#11758196—24no—
254#11758196—22no—
255#11758196—42no—
256#11758196—81no—
257C4×Dic61—24no—
258C4×Dic61—21no—
259C4×Dic61—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C8×D61—44no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61C2×Q1612yes—
274C23×C61C22×D411yescharacteristic
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61#12012yes—
280C22×D61C2×Q1612yes—
281C22×D61#13712yes—
282Q8×C61—22no—
283Q8×C61—22no—
284Q8×C61—22no—
285Q8×C61—22no—
286Q8×C61—22no—
287Q8×C61—48no—
288Q8×C61—41no—
289Q8×C61—41no—
290Q8×C61#12314yes—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—48no—
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×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61H(5,𝔽2)11yescharacteristic
316C2×C4×C61H(5,𝔽2)11yescharacteristic
317C22⋊D61—28no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61#12012yes—
338C2×Dic61C2×Q1612yes—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—48no—
344C4×D61—84no—
345Dic122—22no—
346Dic122—22no—
347Dic122—48no—
348Dic122—41no—
349Dic122—41no—
350C8×C61—41no—
351C8×C61—41no—
352#92418—41no—
353#92418—41no—
354#24042—611nomaximal, Sylow
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—22no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61C2×#12011yescharacteristic
363C22×C61#54611yescharacteristic
364C22×C61#54611yescharacteristic
365C22×C61C22×Q1611yescharacteristic
366C22×C61C2×#13711yescharacteristic
367C22×C61#57711yescharacteristic
368C22×C61#57711yescharacteristic
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—22no—
375C2×D61#45114yes—
376C4×C61—24no—
377C4×C61—41no—
378C4×C61—42no—
379C4×C61—81no—
380C4×C61—81no—
381C4×C61C2×#12311yescharacteristic
382C4×C61#53411yescharacteristic
383C4×C61#54611yescharacteristic
384C4×C61#54611yescharacteristic
385Dic61—22no—
386Dic61—22no—
387Dic61—42no—
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#2043—611no—
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#1787D6111yescharacteristic, complemented
407C2×C61—42no—
408C2×C61#240511yescharacteristic
409C2×C61C2×#45111yescharacteristic
410C2×C61#301011yescharacteristic
411C2×C61#329911yescharacteristic
412C2×C61#329911yescharacteristic
413C2×C61#332011yescharacteristic
414C2×C61#332011yescharacteristic
415D61—24no—
416C23×Q8—611no—
417C23×Q8C2×D6111yescharacteristic
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×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⋊C8C2×D6111yescharacteristic
450#400—1221no—
451#399—1221no—
452#389—611no—
453#389—611no—
454#386—1221no—
455#385—1221no—
456#380—611no—
457#380—611no—
458#380C2×D6111yescharacteristic
459#340—611no—
460#340—611no—
461#336—611no—
462#336—611no—
463C61#2404211yescharacteristic, complemented, Sylow
464C22×Q8—22no—
465C22×Q8—22no—
466C22×Q8—21no—
467C22×Q8—22no—
468C22×Q8—22no—
469C22×Q8—41no—
470C22×Q8—41no—
471C22×Q8—614no—
472C22×Q8—611no—
473C22×Q8—1221no—
474C22×Q8—1222no—
475C22×Q8—1222no—
476C22×Q8—1222no—
477C22×Q8—2441no—
478C22×Q8—2441no—
479C22×Q8C22×D6111yescharacteristic
480C22×Q8C22×D6111yescharacteristic
481C22×D4—611no—
482C23×C4—21no—
483C23×C4—611no—
484C23×C4—1221no—
485C23×C4—1221no—
486C23×C4C22×D6111yescharacteristic
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—1228no—
496C4⋊Q8—1222no—
497C22⋊Q8—614no—
498C22⋊Q8—1222no—
499C22⋊Q8—1222no—
500C22⋊Q8—1228no—
501C22⋊Q8—1222no—
502C22⋊Q8—1228no—
503C4×Q8—1222no—
504C4×Q8—1222no—
505C4×D4—1222no—
506C4×D4—1222no—
507C4×D4—1228no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—1222no—
513C2×C4⋊C4—1222no—
514C2×C4⋊C4—1221no—
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⋊C4—1221no—
522C2×C4⋊C4C22×D6111yescharacteristic
523C2×C4⋊C4C22×D6111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C42—611no—
532C2×C42—1221no—
533#107—1222no—
534#107—1222no—
535#103—22no—
536#103—22no—
537#103—22no—
538#103—41no—
539#103—1222no—
540#103—1222no—
541#103—1222no—
542#103—1222no—
543#103—1222no—
544#103—2441no—
545#103—2441no—
546#103—2441no—
547C22⋊C8—41no—
548C22⋊C8—1222no—
549C22⋊C8—2441no—
550#95—21no—
551#95—1221no—
552#95—1221no—
553#95—1221no—
554#95—1221no—
555C24—611no—
556C24D4×D6111yescharacteristic
557C2×Q8—24no—
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—42no—
567C2×Q8—42no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8—44no—
571C2×Q8—44no—
572C2×Q8—612no—
573C2×Q8—1224no—
574C2×Q8—1221no—
575C2×Q8—1228no—
576C2×Q8—1221no—
577C2×Q8—1221no—
578C2×Q8—1221no—
579C2×Q8—1221no—
580C2×Q8—2442no—
581C2×Q8—2442no—
582C2×Q8—2444no—
583C2×Q8—2444no—
584C2×Q8—2444no—
585C2×Q8#1175822212yes—
586C2×Q8D4×D6112yes—
587C2×Q8D4×D6112yes—
588C2×Q8#1175822412yes—
589C2×D4—614no—
590C2×D4—1222no—
591C2×D4—1222no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—612no—
608C22×C4—612no—
609C22×C4—611no—
610C22×C4—1224no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—4881no—
620C22×C4—4881no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4—2442no—
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—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—612no—
644C4⋊C4—1222no—
645C4⋊C4—1224no—
646C4⋊C4—1224no—
647C4⋊C4—1224no—
648C4⋊C4—1224no—
649C4⋊C4—1224no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—4881no—
656C4⋊C4—4881no—
657C4⋊C4—2442no—
658C22⋊C4—81no—
659C22⋊C4—1222no—
660C22⋊C4—1224no—
661C22⋊C4—1222no—
662C22⋊C4—1224no—
663C22⋊C4—4881no—
664C22⋊C4—2442no—
665C42—1224no—
666C42—1221no—
667C42—1221no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—612no—
675C23—612no—
676C23—612no—
677C23—1221no—
678C23—1221no—
679C23—1221no—
680C23—1221no—
681C23Q16×D6112yes—
682C23C2×D4×D6111yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—22no—
688Q8—48no—
689Q8—41no—
690Q8—41no—
691Q8—1222no—
692Q8—1222no—
693Q8—2448no—
694Q8—2441no—
695Q8—2441no—
696Q8#1451975914yes—
697D4—1228no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—48no—
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—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—612no—
719C2×C4—612no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1221no—
730C2×C4—1222no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—4884no—
734C2×C4—2448no—
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×C4—2441no—
745C2×C4C2×D4×D6111yescharacteristic
746C2×C4C2×D4×D6111yescharacteristic
747C2×C4C2×#1175822411yescharacteristic
748C2×C4C2×#1175822211yescharacteristic
749C2×C4#1451982211yescharacteristic
750C2×C4#1451982211yescharacteristic
751C8—41no—
752C8—41no—
753C8—2441no—
754C8—2441no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—614no—
763C22—1222no—
764C22—1222no—
765C22—1222no—
766C22—1222no—
767C22—1222no—
768C22—1222no—
769C22#120×D6111yescharacteristic
770C22#1684039911yescharacteristic
771C22#1684040211yescharacteristic
772C22C2×Q16×D6111yescharacteristic
773C22#137×D6111yescharacteristic
774C22#1684056811yescharacteristic
775C22#1684057111yescharacteristic
776C4—24no—
777C4—41no—
778C4—42no—
779C4—81no—
780C4—81no—
781C4—1222no—
782C4—1222no—
783C4—4881no—
784C4—4881no—
785C4—2442no—
786C4—2441no—
787C4—2442no—
788C4C2×#1451975911yescharacteristic
789C4#1684032211yescharacteristic
790C4#1684039911yescharacteristic
791C4#1684040211yescharacteristic
792C2—42no—
793C2—1224no—
794C2#2144914411yescharacteristic
795C2#451×D6111yescharacteristic
796C2#2145510011yescharacteristic
797C2#2145768811yescharacteristic
798C2#2145769111yescharacteristic
799C2#2145798311yescharacteristic
800C2#2145799111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1787C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#1787D61
hypocenterC61#24042
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
2. C2×#16840096C2semidirect
3. C2×#103×D61C2semidirect
5. #21447064C2semidirect
6. #21447063C2semidirect
7. #21447023C2semidirect
8. #21447022C2semidirect
9. #21446239C2semidirect
11. #21446075C2semidirect
12. #21446071C2semidirect
13. #21445754C2semidirect
14. #21445752C2semidirect
15. C61×#1787C2semidirect
406. #1787D61semidirect
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×C22⋊D612
C2×#168400962
C2×#103×D612
#214501322
#214470642
#214470632
#214470232
#214470222
#214462392
#214461082
#214460752
#214460712
#214457542
#214457522
C61×#17872
#2404261