Finite Group Databasebeta

← #29695608

Subgroups — #29695608

Order 15616.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840409C211yesmaximal, characteristic
2C2×#16839838C211yesmaximal, characteristic, complemented
3C2×#16839764C211yesmaximal, characteristic, complemented
4C2×#16839765C211yesmaximal, characteristic, complemented
5#21448750C211yesmaximal, characteristic, complemented
6#21446750C211yesmaximal, characteristic, complemented
7#21446629C211yesmaximal, characteristic, complemented
8#21446251C211yesmaximal, characteristic, complemented
9#21446137C211yesmaximal, characteristic, complemented
10#21446130C211yesmaximal, characteristic, complemented
11#21445828C211yesmaximal, characteristic, complemented
12#21445757C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445633C211yesmaximal, characteristic, complemented
15C61×#1895C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19#16840409—24no—
20#16840409C418yescomplemented
21C2×#14519764C2211yescharacteristic
22C2×#14519759—21no—
23C2×#14519757C2211yescharacteristic
24C2×#14519748—21no—
25C2×#14519745—21no—
26C2×#14519739C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519735C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic, complemented
30C2×C22⋊C4×D61—21no—
31#16839838—24no—
32C2×#14519706C2211yescharacteristic, complemented
33#16839765—24no—
34#16839764—24no—
35C2×#14519702C2211yescharacteristic, complemented
36C2×#14519702C2211yescharacteristic, complemented
37C2×#14519700C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39C2×#14519699C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×C22⋊#92418C2211yescharacteristic, complemented
46C2×#14519689C2211yescharacteristic
47C2×C8×Dic61C2211yescharacteristic, complemented
48#16839654—21no—
49#16839649—21no—
50#16839639—21no—
51#16839627C2211yescharacteristic, complemented
52#16839619C2211yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic, complemented
54C22⋊C4×Dic61—21no—
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C22×M16×C61C2211yescharacteristic, complemented
58C2×#121×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—41no—
69C2×#11758222—41no—
70C2×#11758222C2×C414yes—
71C22×Dic122C2311yescharacteristic
72C22×D244C2311yescharacteristic
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C22×C22⋊D61D411yescharacteristic
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—41no—
80C2×D4×D61—41no—
81C2×D4×D61C2×C414yescomplemented
82C23×Dic61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C2×#11758189—22no—
87C2×#11758189—22no—
88C2×#11758189—41no—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91#14519764—22no—
92#14519764C2×C414yescomplemented
93#14519759—28no—
94#14519757—22no—
95#14519757C2×C414yescomplemented
96#14519748—28no—
97#14519745—28no—
98#14519739—22no—
99#14519739C2×C414yescomplemented
100C4×C22⋊D61C2×C414yes—
101C4×C22⋊D61D414yes—
102#14519735—22no—
103#14519735—41no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61—22no—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61—41no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196D411yescharacteristic
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61D411yescharacteristic
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198D411yescharacteristic
119C22⋊C4×D61—28no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61C2311yescharacteristic
123#14519706—22no—
124#14519702—22no—
125#14519702—22no—
126#14519700—41no—
127#14519700—41no—
128#14519699—22no—
129#14519699D414yescomplemented
130#14519698—22no—
131#14519698—41no—
132#14519697—22no—
133#14519697—22no—
134C22⋊#92418—22no—
135#14519689—22no—
136C8×Dic61—22no—
137#14519684—21no—
138#14519684—21no—
139#14519684—21no—
140#14519684—21no—
141C22×D4×C61—21no—
142C22×D4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C2×M16×C61—22no—
145C2×M16×C61—22no—
146C2×M16×C61—41no—
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149#121×C61—22no—
150#121×C61C2×C414yes—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61—21no—
156#102×C61—22no—
157#102×C61—41no—
158#95×C61—21no—
159C24×C61—21no—
160C24×C61C2×D411yescharacteristic
161C23×D61—21no—
162C23×D61—24no—
163C23×D61—42no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—81no—
168C23×D61—81no—
169C23×D61C2×D411yescharacteristic
170C2×D4×C61—24no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—81no—
177C2×D4×C61—81no—
178C2×D4×C61C22×C412yes—
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×C61C22×C412yes—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D412yes—
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—24no—
191C2×C22⋊D61—24no—
192C2×C22⋊D61—41no—
193C2×C22⋊D61—41no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—42no—
197C2×C22⋊D61—42no—
198C2×C22⋊D61C22⋊C414yes—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—42no—
203C22×Dic61—42no—
204C22×Dic61—81no—
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208D4×D61—28no—
209D4×D61—44no—
210D4×D61—44no—
211D4×D61—44no—
212#11758222—28no—
213#11758222—44no—
214#11758222—44no—
215#11758222—44no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244C22×C412yes—
220C2×D244C2×D412yes—
221C2×D244#4112yes—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—24no—
227C2×C4×D61—24no—
228C2×C4×D61—42no—
229C2×C4×D61—42no—
230C2×C4×D61—81no—
231C2×C4×D61—81no—
232C2×C4×D61C22×C412yes—
233C2×C4×D61C2×D412yes—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122C22×C412yes—
240M16×C61—44no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61C2×D412yes—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61C22×C412yes—
253C22⋊C4×C61—24no—
254C22⋊C4×C61—42no—
255C22⋊Dic61—24no—
256C22⋊Dic61—24no—
257C22⋊Dic61C22⋊C414yes—
258#11758198—24no—
259#11758198—24no—
260#11758198—42no—
261#11758198—81no—
262#11758198C22⋊C414yes—
263C4⋊Dic61—21no—
264C4⋊Dic61—24no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—42no—
268C4⋊Dic61C2×D412yes—
269#11758196C22⋊C414yes—
270C4×Dic61—42no—
271C4×Dic61—81no—
272C4×Dic61C22×C412yes—
273C4×Dic61C2×D412yes—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280#11758189—44no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—22no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61C2×C22⋊C412yes—
295C23×C61C22×D411yescharacteristic
296C22×D61—22no—
297C22×D61—21no—
298C22×D61—22no—
299C22×D61—21no—
300C22×D61—22no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—48no—
306C22×D61—48no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—84no—
312C22×D61—84no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61—84no—
316C22×D61C2×C22⋊C412yes—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—41no—
320D4×C61—41no—
321D4×C61—84no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61C2×C22⋊C412yes—
338C2×C4×C61C23×C411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C2×#4111yescharacteristic
342C2×C4×C61H(5,𝔽2)11yescharacteristic
343C2×C4×C61H(5,𝔽2)11yescharacteristic
344C22⋊D61—44no—
345C22⋊D61—48no—
346C22⋊D61—48no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—84no—
363C2×Dic61C2×C22⋊C412yes—
364C2×Dic61C2×C22⋊C412yes—
365C2×Dic61C2×C22⋊C412yes—
366D244—22no—
367D244—22no—
368D244—22no—
369D244C4×D414yes—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—48no—
375C4×D61—84no—
376Dic122—22no—
377Dic122—22no—
378Dic122—41no—
379Dic122—41no—
380C8×C61—22no—
381C8×C61—41no—
382#92418—41no—
383#92418—41no—
384#22427—611nomaximal, Sylow
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—42no—
395C22×C61—81no—
396C22×C61—81no—
397C22×C61—81no—
398C22×C61—81no—
399C22×C61C22×C22⋊C411yescharacteristic
400C22×C61D4211yescharacteristic
401C22×C61#54611yescharacteristic
402C22×C61#57511yescharacteristic
403C22×C61#57511yescharacteristic
404C22×C61#57611yescharacteristic
405C22×C61#57711yescharacteristic
406C2×D61—22no—
407C2×D61—24no—
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—41no—
413C2×D61—42no—
414C2×D61—41no—
415C2×D61—42no—
416C2×D61—41no—
417C2×D61—42no—
418C2×D61—41no—
419C2×D61—42no—
420C2×D61—816no—
421C4×C61—22no—
422C4×C61—42no—
423C4×C61—81no—
424C4×C61—81no—
425C4×C61C2×C4×D411yescharacteristic
426C4×C61#51811yescharacteristic
427C4×C61D4211yescharacteristic
428C4×C61#54611yescharacteristic
429Dic61—22no—
430Dic61—22no—
431Dic61—22no—
432Dic61—42no—
433Dic61—42no—
434Dic61—81no—
435C2×#546—611no—
436C2×#436—611no—
437C2×#417—611no—
438C2×#418—611no—
439#2352—611no—
440#1983—611no—
441#1958—611no—
442#1895D6111yescharacteristic, complemented
443#1894—611no—
444#1874—611no—
445#1873—611no—
446#1804—611no—
447#1788—611no—
448#1786—611no—
449C4×#102—611no—
450C2×C61—42no—
451C2×C61—82no—
452C2×C61D4×C22⋊C411yescharacteristic
453C2×C61#289611yescharacteristic
454C2×C61#289711yescharacteristic
455C2×C61#327311yescharacteristic
456C2×C61#327511yescharacteristic
457C2×C61#332211yescharacteristic
458C2×C61#332311yescharacteristic
459D61—42no—
460D61—44no—
461C22×#41—611no—
462C23×D4—611no—
463C22×M16—611no—
464C22×M16C2×D6111yescharacteristic, complemented
465#546—618no—
466#546—1224no—
467C2×#124—611no—
468C2×#123—1221no—
469C2×C22⋊Q8—611no—
470C2×#121—1221no—
471C2×#121C2×D6111yescharacteristic
472C2×#120—1221no—
473C2×C4×D4—611no—
474C2×C4×D4—611no—
475C2×#117—611no—
476C22×C4⋊C4—611no—
477C22×C22⋊C4—1221no—
478#436—1224no—
479C2×C4⋊C8—611no—
480#418—1224no—
481#417—1224no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102C2×D6111yescharacteristic
493C2×#102C2×D6111yescharacteristic
494C2×C22⋊C8—611no—
495C2×C22⋊C8—611no—
496C2×C4×C8—611no—
497#388—1221no—
498#387—1221no—
499#386—1221no—
500#382—611no—
501#380—611no—
502#380C2×D6111yescharacteristic, complemented
503C4×C4⋊C4—611no—
504C4×C22⋊C4—1221no—
505#340—611no—
506#340—611no—
507#340C2×D6111yescharacteristic, complemented
508#340C2×D6111yescharacteristic, complemented
509C61#2242711yescharacteristic, complemented, Sylow
510C25—1221no—
511C2×#41—614no—
512C2×#41—1222no—
513C2×#41—1222no—
514C2×#41—1222no—
515C2×#41—2441no—
516C2×#41—2441no—
517C22×Q8—611no—
518C22×D4—21no—
519C22×D4—611no—
520C22×D4—614no—
521C22×D4—611no—
522C22×D4—1222no—
523C22×D4—1221no—
524C22×D4—1222no—
525C22×D4—1222no—
526C22×D4—1221no—
527C22×D4—2441no—
528C22×D4—2441no—
529C22×D4C22×D6111yescharacteristic
530C23×C4—611no—
531C23×C4—1221no—
532C23×C4—1221no—
533C23×C4—1221no—
534C23×C4C22×D6111yescharacteristic
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—1222no—
539C2×M16—1222no—
540C2×M16—2441no—
541C22×C8—611no—
542C22×C8—611no—
543C22×C8C22×D6111yescharacteristic
544C22×C8C22×D6111yescharacteristic
545#124—614no—
546#124—1222no—
547#123—1228no—
548C22⋊Q8—614no—
549C22⋊Q8—1222no—
550#121—22no—
551#121—1228no—
552#121C4×D6114yes—
553#120—1228no—
554C4×D4—614no—
555C4×D4—614no—
556C4×D4—614no—
557C4×D4—1222no—
558#117—1222no—
559#117—2441no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—1222no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—2441no—
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C4⋊C4C22×D6111yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—611no—
573C2×C22⋊C4—611no—
574C2×C22⋊C4—1228no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C42—611no—
582C2×C42—1221no—
583C2×C42—1221no—
584C4⋊C8—1222no—
585#103—1222no—
586#103—1222no—
587#103—2441no—
588#103—2441no—
589#102—22no—
590#102—41no—
591#102—614no—
592#102—1222no—
593#102—1222no—
594#102—1222no—
595#102—1222no—
596#102—2441no—
597C22⋊C8—1222no—
598C22⋊C8—1222no—
599C4×C8—1222no—
600#95—21no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605C24—21no—
606C24—611no—
607C24—1224no—
608C24—1221no—
609C24—4881no—
610C24—4881no—
611C24—2442no—
612C24—2442no—
613C24—2442no—
614C24—2442no—
615C24D4×D6111yescharacteristic
616#41—1228no—
617#41—2444no—
618#41—2444no—
619#41—2444no—
620C2×Q8—612no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×D4—24no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—614no—
635C2×D4—612no—
636C2×D4—612no—
637C2×D4—612no—
638C2×D4—1224no—
639C2×D4—1228no—
640C2×D4—1224no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—2444no—
645C2×D4—2444no—
646C2×D4—2444no—
647C2×D4—2441no—
648C2×D4—2441no—
649C2×D4—2442no—
650C2×D4—2442no—
651C2×D4—2442no—
652C2×D4—2442no—
653C2×D4C2×C4×D6112yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—612no—
665C22×C4—612no—
666C22×C4—1224no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1224no—
674C22×C4—1221no—
675C22×C4—4881no—
676C22×C4—4881no—
677C22×C4—4881no—
678C22×C4—2442no—
679C22×C4—2442no—
680C22×C4—2442no—
681C22×C4—2442no—
682C22×C4C2×C4×D6112yes—
683C22×C4D4×D6112yes—
684C22×C4D4×D6111yescharacteristic
685C22×C4C23×D6111yescharacteristic
686M16—44no—
687M16—2444no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8D4×D6112yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—614no—
706C4⋊C4—612no—
707C4⋊C4—1224no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—2442no—
712C4⋊C4C2×C4×D6112yes—
713C22⋊C4—24no—
714C22⋊C4—42no—
715C22⋊C4—614no—
716C22⋊C4—614no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C22⋊C4—1224no—
721C22⋊C4—4881no—
722C22⋊C4—2442no—
723C42—612no—
724C42—612no—
725C42—4881no—
726C42—2442no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—612no—
741C23—1222no—
742C23—1221no—
743C23—1221no—
744C23—1221no—
745C23—1221no—
746C23—1221no—
747C23—1222no—
748C23—1221no—
749C23—1222no—
750C23—4884no—
751C23—4884no—
752C23—4884no—
753C23—4884no—
754C23—4884no—
755C23—2448no—
756C23—2448no—
757C23—2441no—
758C23—2441no—
759C23—2441no—
760C23—2441no—
761C23C22⋊C4×D6112yes—
762C23C2×D4×D6111yescharacteristic
763Q8—1222no—
764Q8—1222no—
765Q8—2441no—
766Q8—2441no—
767D4—22no—
768D4—22no—
769D4—41no—
770D4—41no—
771D4—84no—
772D4—614no—
773D4—1222no—
774D4—1222no—
775D4—1222no—
776D4—2444no—
777D4—2448no—
778D4—2448no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—612no—
795C2×C4—612no—
796C2×C4—612no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—4884no—
810C2×C4—4884no—
811C2×C4—2448no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4C22⋊C4×D6112yes—
820C2×C4C22×C4×D6111yescharacteristic
821C2×C4C2×D4×D6111yescharacteristic
822C2×C4C2×D4×D6111yescharacteristic
823C2×C4#41×D6111yescharacteristic
824C2×C4#1451982211yescharacteristic
825C2×C4#1451982311yescharacteristic
826C8—22no—
827C8—41no—
828C8—2441no—
829C8—2441no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—1222no—
845C22—1222no—
846C22—1224no—
847C22—1222no—
848C22—48816no—
849C22—2442no—
850C22—2441no—
851C22—2442no—
852C22—2441no—
853C22—2442no—
854C22—2441no—
855C22—2442no—
856C22—2441no—
857C22—2442no—
858C22—2442no—
859C22C2×C22⋊C4×D6111yescharacteristic
860C22#1684039611yescharacteristic
861C22#1684040111yescharacteristic
862C22#1684055811yescharacteristic
863C22#1684056111yescharacteristic
864C22#1684056611yescharacteristic
865C22#1684057211yescharacteristic
866C4—22no—
867C4—42no—
868C4—81no—
869C4—81no—
870C4—1222no—
871C4—1222no—
872C4—1222no—
873C4—4881no—
874C4—2442no—
875C4—2442no—
876C4C4×D4×D6111yescharacteristic
877C4#1684023411yescharacteristic
878C4#1684039411yescharacteristic
879C4#1684040411yescharacteristic
880C2—42no—
881C2—82no—
882C2—2442no—
883C2—2444no—
884C2#2144863711yescharacteristic
885C2#2145433511yescharacteristic
886C2#2145434411yescharacteristic
887C2#2145742711yescharacteristic
888C2#2145745711yescharacteristic
889C2#2145801511yescharacteristic
890C2#2145803011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1895C2
socleC23×C61C22×D4
prime radicalC2×#16840409C2
cosocleC22×C4×C61C24
hypercenter#1895D61
hypocenterC61#22427
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
2. C2×#16839838C2semidirect
3. C2×#16839764C2semidirect
4. C2×#16839765C2semidirect
5. #21448750C2semidirect
6. #21446750C2semidirect
7. #21446629C2semidirect
8. #21446251C2semidirect
9. #21446137C2semidirect
10. #21446130C2semidirect
11. #21445828C2semidirect
12. #21445757C2semidirect
13. #21445748C2semidirect
14. #21445633C2semidirect
15. C61×#1895C2semidirect
20. #16840409C4semidirect
29. C22×C4⋊Dic61C22semidirect
32. C2×#14519706C22semidirect
35. C2×#14519702C22semidirect
36. C2×#14519702C22semidirect
37. C2×#14519700C22semidirect
38. C2×#14519700C22semidirect
45. C2×C22⋊#92418C22semidirect
47. C2×C8×Dic61C22semidirect
51. #16839627C22semidirect
53. C4⋊C4×Dic61C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
57. C22×M16×C61C22semidirect
61. C61×#380C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
81. C2×D4×D61C2×C4semidirect
92. #14519764C2×C4semidirect
95. #14519757C2×C4semidirect
99. #14519739C2×C4semidirect
129. #14519699D4semidirect
442. #1895D61semidirect
464. C22×M16C2×D61semidirect
502. #380C2×D61semidirect
507. #340C2×D61semidirect
508. #340C2×D61semidirect
509. C61#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#168404092
C2×#168398382
C2×#168397642
C2×#168397652
#214487502
#214467502
#214466292
#214462512
#214461372
#214461302
#214458282
#214457572
#214457482
#214456332
C61×#18952
#2242761