Finite Group Databasebeta

← #29712649

Subgroups — #29712649

Order 15616.

1500 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D61C211yesmaximal, characteristic
2C2×#16840094C211yesmaximal, characteristic, complemented
3C2×#16840091C211yesmaximal, characteristic, complemented
4#380×D61C211yesmaximal, characteristic
5#21447016C211yesmaximal, characteristic, complemented
6#21447015C211yesmaximal, characteristic, complemented
7#21447012C211yesmaximal, characteristic, complemented
8#21446125C211yesmaximal, characteristic, complemented
9#21446123C211yesmaximal, characteristic, complemented
10#21446013C211yesmaximal, characteristic, complemented
11#21446010C211yesmaximal, characteristic, complemented
12#21445752C211yesmaximal, characteristic, complemented
13#21445752C211yesmaximal, characteristic, complemented
14#21445728C211yesmaximal, characteristic
15C61×#2035C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C2×#14519757C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×#14519755—21no—
21C2×#14519754—21no—
22C2×#14519753C2211yescharacteristic
23C22⋊Q8×D61—24no—
24C22⋊Q8×D61—24no—
25C2×C4⋊C4×D61—21no—
26C2×C4⋊C4×D61C2211yescharacteristic
27C2×C4⋊C4×D61C2211yescharacteristic
28C2×C4⋊C4×D61C2211yescharacteristic
29C2×C22⋊C4×D61—21no—
30C2×C22⋊C4×D61—21no—
31#16840094—24no—
32#16840091—24no—
33C2×#14519709C2211yescharacteristic, complemented
34C2×#14519708C2211yescharacteristic, complemented
35C2×#14519708C2211yescharacteristic, complemented
36C2×#14519702C2211yescharacteristic, complemented
37C2×#14519702C2211yescharacteristic, complemented
38C2×#14519701C2211yescharacteristic, complemented
39C2×#14519701C2211yescharacteristic, complemented
40C2×#14519700C2211yescharacteristic, complemented
41C2×#14519700C2211yescharacteristic, complemented
42C2×C22⋊#92418C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47#16839622C2211yescharacteristic
48#16839621—21no—
49#16839620—21no—
50#16839619C2211yescharacteristic
51#16839619C2211yescharacteristic
52#95×D61—21no—
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56C2×C22⋊Q8×C61C2211yescharacteristic
57C2×#106×C61C2211yescharacteristic, complemented
58C2×#103×C61C2211yescharacteristic, complemented
59C2×#103×C61C2211yescharacteristic, complemented
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#340C2211yescharacteristic, complemented
63C24×D61D411yescharacteristic
64C22×Dic122—21no—
65C22×Dic122C2311yescharacteristic
66C2×Q8×D61—22no—
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61—22no—
70C2×Q8×D61—41no—
71C2×Q8×D61—41no—
72C23×Dic61D411yescharacteristic
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—22no—
76C22×C4×D61—22no—
77C22×C4×D61—22no—
78C22×C4×D61—22no—
79C22×C4×D61—21no—
80C22×C4×D61—21no—
81C22×C4×D61—41no—
82C22×C4×D61—41no—
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89#14519757—22no—
90#14519757D414yes—
91#14519756—22no—
92#14519756—22no—
93#14519755—28no—
94#14519754—28no—
95#14519753—22no—
96#14519753D414yes—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C4⋊C4×D61—28no—
107C4⋊C4×D61—22no—
108C4⋊C4×D61—22no—
109C4⋊C4×D61—22no—
110C4⋊C4×D61—22no—
111C4⋊C4×D61—41no—
112C4⋊C4×D61—41no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C22⋊C4×D61—28no—
120C22⋊C4×D61—44no—
121#14519709—22no—
122#14519708—22no—
123#14519708—22no—
124#14519702—22no—
125#14519702—41no—
126#14519701—22no—
127#14519701—41no—
128#14519700—22no—
129#14519700—41no—
130C22⋊#92418—41no—
131#14519689—22no—
132#14519689—22no—
133#14519689—22no—
134#14519689—22no—
135#14519684—21no—
136#14519684—21no—
137#14519684—21no—
138C22×Q8×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142C22⋊Q8×C61—22no—
143C22⋊Q8×C61—22no—
144C2×C4⋊C4×C61—21no—
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150#106×C61—22no—
151#103×C61—22no—
152#103×C61—41no—
153C22⋊C8×C61—41no—
154#95×C61—21no—
155C24×C61C2×D411yescharacteristic
156C23×D61—22no—
157C23×D61—22no—
158C23×D61—22no—
159C23×D61—22no—
160C23×D61—41no—
161C23×D61—41no—
162C23×D61SD1614yes—
163C23×D61C2×D411yescharacteristic
164C23×D61C2×D411yescharacteristic
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61C2×D412yes—
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×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2411yescharacteristic
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—41no—
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192Q8×D61—44no—
193Q8×D61—44no—
194Q8×D61—44no—
195Q8×D61—44no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
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—24no—
205C2×C4×D61—24no—
206C2×C4×D61—22no—
207C2×C4×D61—22no—
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61—44no—
211C2×C4×D61—44no—
212C2×C4×D61—44no—
213C2×C4×D61—44no—
214C2×C4×D61—41no—
215C2×C4×D61—41no—
216C2×C4×D61—42no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61—42no—
220C2×C4×D61—42no—
221C2×C4×D61—42no—
222C2×C4×D61—42no—
223C2×C4×D61—42no—
224C2×C4×D61—42no—
225C2×C4×D61—42no—
226C2×C4×D61C2×D412yes—
227C2×C4×D61C2×D412yes—
228C2×C4×D61#4112yes—
229C2×C4×D61#4112yes—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—24no—
235C2×Dic122—21no—
236C2×Dic122—42no—
237C2×Dic122—42no—
238C2×Dic122C2×D412yes—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C4⋊C4×C61—24no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61C2×D412yes—
252C22⋊C4×C61—24no—
253C22⋊C4×C61—42no—
254C22⋊Dic61—24no—
255C22⋊Dic61—42no—
256#11758198—24no—
257#11758198—24no—
258#11758198—42no—
259#11758198—42no—
260C4⋊Dic61—21no—
261C4⋊Dic61—24no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61C2×D412yes—
267#11758196—24no—
268#11758196—24no—
269#11758196—24no—
270#11758196—42no—
271#11758196—42no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61C2×SD1612yes—
285C23×C61C22×D411yescharacteristic
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—28no—
295C22×D61—28no—
296C22×D61—44no—
297C22×D61—44no—
298C22×D61—44no—
299C22×D61—44no—
300C22×D61—44no—
301C22×D61#12012yes—
302C22×D61#12312yes—
303C22×D61C2×SD1612yes—
304C22×D61C2×SD1612yes—
305C22×D61#13712yes—
306C22×D61#13712yes—
307Q8×C61—22no—
308Q8×C61—22no—
309Q8×C61—41no—
310Q8×C61—41no—
311C2×C4×C61—21no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
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×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C2×#4111yescharacteristic
333C2×C4×C61C2×#4111yescharacteristic
334C2×C4×C61H(5,𝔽2)11yescharacteristic
335C2×C4×C61H(5,𝔽2)11yescharacteristic
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—44no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61#12012yes—
354C2×Dic61#12312yes—
355C4×D61—22no—
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—44no—
364C4×D61—44no—
365C4×D61—48no—
366C4×D61—48no—
367C4×D61—84no—
368C4×D61—84no—
369Dic122—22no—
370Dic122—22no—
371Dic122—48no—
372Dic122—41no—
373Dic122—41no—
374C8×C61—41no—
375C8×C61—41no—
376#92418—41no—
377#92418—41no—
378#24003—611nomaximal, Sylow
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61C2×#12011yescharacteristic
387C22×C61C2×#12311yescharacteristic
388C22×C61#53411yescharacteristic
389C22×C61C22×SD1611yescharacteristic
390C22×C61C2×#13711yescharacteristic
391C22×C61C2×#13711yescharacteristic
392C22×C61#57511yescharacteristic
393C2×D61—22no—
394C2×D61—22no—
395C2×D61—22no—
396C2×D61—22no—
397C2×D61—22no—
398C2×D61—22no—
399C2×D61—22no—
400C2×D61—22no—
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—416no—
406C2×D61#44814yes—
407C2×D61#48314yescomplemented
408C4×C61—42no—
409C4×C61—41no—
410C4×C61—42no—
411C4×C61—81no—
412C4×C61—81no—
413C4×C61#54611yescharacteristic
414C4×C61#54611yescharacteristic
415C4×C61#54611yescharacteristic
416C4×C61#54611yescharacteristic
417Dic61—22no—
418Dic61—22no—
419Dic61—42no—
420Dic61—42no—
421Dic61—81no—
422Dic61—81no—
423C22×C22⋊Q8—611no—
424C2×#483—611no—
425C2×#483—611no—
426C2×#380—611no—
427#2035—611no—
428#2035—611no—
429#2035—611no—
430#2035D6111yescharacteristic, complemented
431#1872—611no—
432#1872—611no—
433#1853—611no—
434#1853—611no—
435#1787—611no—
436#1787—611no—
437#1779—611no—
438C2×C61—42no—
439C2×C61#240511yescharacteristic
440C2×C61C2×#44811yescharacteristic
441C2×C61#300711yescharacteristic
442C2×C61C2×#48311yescharacteristic
443C2×C61#309511yescharacteristic
444C2×C61#318711yescharacteristic
445C2×C61#319511yescharacteristic
446D61—24no—
447D61—24no—
448C23×Q8—611no—
449C24×C4—611no—
450C2×C22⋊Q8—611no—
451C2×C22⋊Q8—611no—
452C2×C22⋊Q8—611no—
453C2×C22⋊Q8—1221no—
454C2×C22⋊Q8—1221no—
455C2×C22⋊Q8—1224no—
456C2×C22⋊Q8—1224no—
457C2×C22⋊Q8C2×D6111yescharacteristic
458C22×C4⋊C4—611no—
459C22×C4⋊C4—611no—
460C22×C4⋊C4—611no—
461C22×C4⋊C4—1221no—
462C22×C22⋊C4—1221no—
463C22×C22⋊C4—1221no—
464#483—1224no—
465#483—1224no—
466C2×#106—611no—
467C2×#106—611no—
468C2×#106—611no—
469C2×#106C2×D6111yescharacteristic, complemented
470C2×#103—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#103—611no—
476C2×#103C2×D6111yescharacteristic, complemented
477C2×#103C2×D6111yescharacteristic, complemented
478C2×C22⋊C8—611no—
479C2×C22⋊C8—611no—
480C2×C22⋊C8—611no—
481C2×C22⋊C8—611no—
482C2×C22⋊C8—611no—
483C2×C22⋊C8C2×D6111yescharacteristic
484#380—611no—
485#380—611no—
486#380—611no—
487#380—1221no—
488#380—1221no—
489#380C2×D6111yescharacteristic
490C2×#95—1221no—
491#340—611no—
492#340—611no—
493#340—611no—
494#340C2×D6111yescharacteristic, complemented
495C61#2400311yescharacteristic, complemented, Sylow
496C25—611no—
497C22×Q8—611no—
498C22×Q8—1221no—
499C22×Q8—1222no—
500C22×Q8—1222no—
501C22×Q8—1222no—
502C22×Q8—1222no—
503C22×Q8—2441no—
504C22×Q8—2441no—
505C22×Q8C22×D6111yescharacteristic
506C23×C4—611no—
507C23×C4—611no—
508C23×C4—611no—
509C23×C4—611no—
510C23×C4—611no—
511C23×C4—1222no—
512C23×C4—1222no—
513C23×C4—1222no—
514C23×C4—1222no—
515C23×C4—1221no—
516C23×C4—1221no—
517C23×C4—1221no—
518C23×C4—1221no—
519C23×C4—2441no—
520C23×C4—2441no—
521C23×C4C22×D6111yescharacteristic
522C22×C8—611no—
523C22×C8—611no—
524C22×C8C22×D6111yescharacteristic
525C22×C8C22×D6111yescharacteristic
526C22⋊Q8—22no—
527C22⋊Q8—22no—
528C22⋊Q8—614no—
529C22⋊Q8—614no—
530C22⋊Q8—1228no—
531C22⋊Q8—1222no—
532C22⋊Q8—1228no—
533C22⋊Q8—1222no—
534C22⋊Q8—1222no—
535C22⋊Q8—1222no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—1222no—
541C2×C4⋊C4—1228no—
542C2×C4⋊C4—1222no—
543C2×C4⋊C4—1222no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4—1221no—
548C2×C4⋊C4—1222no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—2441no—
552C2×C4⋊C4—2441no—
553C2×C4⋊C4C22×D6111yescharacteristic
554C2×C4⋊C4C22×D6111yescharacteristic
555C2×C4⋊C4C22×D6111yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—1228no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—2444no—
566#106—22no—
567#106—1222no—
568#106—1222no—
569#106—1222no—
570#103—22no—
571#103—41no—
572#103—1222no—
573#103—1222no—
574#103—1222no—
575#103—2441no—
576#103—2441no—
577#103—2441no—
578C22⋊C8—41no—
579C22⋊C8—1222no—
580C22⋊C8—1222no—
581C22⋊C8—1222no—
582C22⋊C8—1222no—
583C22⋊C8—2441no—
584#95—21no—
585#95—1221no—
586#95—1221no—
587#95—1221no—
588C24—611no—
589C24—611no—
590C24—614no—
591C24—1222no—
592C24—1222no—
593C24—1222no—
594C24—1222no—
595C24—2441no—
596C24—2441no—
597C24D4×D6111yescharacteristic
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—612no—
604C2×Q8—1224no—
605C2×Q8—1221no—
606C2×Q8—1221no—
607C2×Q8—1221no—
608C2×Q8—1221no—
609C2×Q8—1221no—
610C2×Q8—2442no—
611C2×Q8—2442no—
612C2×Q8—2444no—
613C2×Q8—2444no—
614C2×Q8—2444no—
615C2×Q8—2444no—
616C2×Q8D4×D6112yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—612no—
630C22×C4—612no—
631C22×C4—612no—
632C22×C4—612no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1224no—
638C22×C4—1224no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—1221no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—2441no—
654C22×C4—2441no—
655C22×C4—2444no—
656C22×C4—2444no—
657C22×C4—2444no—
658C22×C4—2444no—
659C22×C4—2442no—
660C22×C4—2442no—
661C22×C4—2442no—
662C22×C4—2442no—
663C22×C4—2442no—
664C22×C4—2442no—
665C22×C4—2442no—
666C22×C4—2442no—
667C22×C4—2442no—
668C22×C4—2442no—
669C22×C4—2441no—
670C22×C4D4×D6111yescharacteristic
671C22×C4C23×D6111yescharacteristic
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—1221no—
683C2×C8—1221no—
684C4⋊C4—24no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—612no—
691C4⋊C4—1224no—
692C4⋊C4—1224no—
693C4⋊C4—1224no—
694C4⋊C4—1224no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—2442no—
701C4⋊C4—2442no—
702C4⋊C4D4×D6112yes—
703C22⋊C4—24no—
704C22⋊C4—42no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C22⋊C4—2442no—
709C22⋊C4—2442no—
710C22⋊C4—2442no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—612no—
718C23—612no—
719C23—612no—
720C23—612no—
721C23—612no—
722C23—612no—
723C23—1228no—
724C23—1228no—
725C23—1221no—
726C23—1221no—
727C23—1221no—
728C23—1221no—
729C23—1221no—
730C23—1221no—
731C23—1221no—
732C23—1221no—
733C23—2444no—
734C23—2444no—
735C23—2444no—
736C23—2444no—
737C23—2444no—
738C23SD16×D6112yes—
739C23C2×D4×D6111yescharacteristic
740Q8—22no—
741Q8—22no—
742Q8—41no—
743Q8—41no—
744Q8—1222no—
745Q8—1222no—
746Q8—2448no—
747Q8—2441no—
748Q8—2441no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—612no—
769C2×C4—612no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—4884no—
785C2×C4—4884no—
786C2×C4—2444no—
787C2×C4—2444no—
788C2×C4—2448no—
789C2×C4—2448no—
790C2×C4—2444no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4C2×D4×D6111yescharacteristic
802C2×C4C2×D4×D6111yescharacteristic
803C2×C4#41×D6111yescharacteristic
804C2×C4#41×D6111yescharacteristic
805C2×C4#1451982211yescharacteristic
806C2×C4#1451982311yescharacteristic
807C8—41no—
808C8—41no—
809C8—2441no—
810C8—2441no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—614no—
819C22—614no—
820C22—1222no—
821C22—1222no—
822C22—1222no—
823C22—1222no—
824C22—1222no—
825C22—1222no—
826C22—1222no—
827C22—1222no—
828C22—1222no—
829C22—1222no—
830C22—1222no—
831C22—1222no—
832C22—24416no—
833C22#120×D6111yescharacteristic
834C22#123×D6111yescharacteristic
835C22#1684032011yescharacteristic
836C22C2×SD16×D6111yescharacteristic
837C22#137×D6111yescharacteristic
838C22#137×D6111yescharacteristic
839C22#1684055911yescharacteristic
840C4—41no—
841C4—42no—
842C4—42no—
843C4—81no—
844C4—81no—
845C4—1222no—
846C4—1222no—
847C4—4881no—
848C4—4881no—
849C4—2442no—
850C4—2442no—
851C4#1684040111yescharacteristic
852C4#1684040411yescharacteristic
853C4#1684040511yescharacteristic
854C4#1684040911yescharacteristic
855C2—42no—
856C2—1224no—
857C2—1224no—
858C2#2144914111yescharacteristic
859C2#448×D6111yescharacteristic
860C2#2145507611yescharacteristic
861C2#483×D6111yescharacteristic
862C2#2145576611yescharacteristic
863C2#2145657111yescharacteristic
864C2#2145663911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2035C2
socleC23×C61C22×D4
prime radicalC24×D61D4
hypercenter#2035D61
hypocenterC61#24003
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
2. C2×#16840094C2semidirect
3. C2×#16840091C2semidirect
5. #21447016C2semidirect
6. #21447015C2semidirect
7. #21447012C2semidirect
8. #21446125C2semidirect
9. #21446123C2semidirect
10. #21446013C2semidirect
11. #21446010C2semidirect
12. #21445752C2semidirect
13. #21445752C2semidirect
15. C61×#2035C2semidirect
33. C2×#14519709C22semidirect
34. C2×#14519708C22semidirect
35. C2×#14519708C22semidirect
36. C2×#14519702C22semidirect
37. C2×#14519702C22semidirect
38. C2×#14519701C22semidirect
39. C2×#14519701C22semidirect
40. C2×#14519700C22semidirect
41. C2×#14519700C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
57. C2×#106×C61C22semidirect
58. C2×#103×C61C22semidirect
59. C2×#103×C61C22semidirect
62. C61×#340C22semidirect
407. C2×D61#483semidirect
430. #2035D61semidirect
469. C2×#106C2×D61semidirect
476. C2×#103C2×D61semidirect
477. C2×#103C2×D61semidirect
494. #340C2×D61semidirect
495. C61#24003semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D612
C2×#168400942
C2×#168400912
#380×D612
#214470162
#214470152
#214470122
#214461252
#214461232
#214460132
#214460102
#214457522
#214457282
C61×#20352
#2400361