Finite Group Databasebeta

← #29695575

Subgroups — #29695575

Order 15616.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840405C211yesmaximal, characteristic
2C2×#16839832C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic, complemented
4C2×#16839757C211yesmaximal, characteristic, complemented
5#21448766C211yesmaximal, characteristic, complemented
6#21446636C211yesmaximal, characteristic, complemented
7#21446249C211yesmaximal, characteristic, complemented
8#21446244C211yesmaximal, characteristic, complemented
9#21446138C211yesmaximal, characteristic, complemented
10#21446128C211yesmaximal, characteristic, complemented
11#21445820C211yesmaximal, characteristic, complemented
12#21445758C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445647C211yesmaximal, characteristic, complemented
15C61×#1983C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic, complemented
20#16840405—24no—
21#16840405C418yescomplemented
22C2×#14519759—21no—
23C2×#14519753C2211yescharacteristic
24C2×#14519750—21no—
25C2×#14519748C2211yescharacteristic
26C2×#14519747—21no—
27C2×C4×D244C2211yescharacteristic
28C2×C4×D244C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C2×#14519735C2211yescharacteristic, complemented
31C2×C22⋊C4×D61—21no—
32#16839832—24no—
33#16839765—24no—
34#16839757—24no—
35C2×#14519701C2211yescharacteristic, complemented
36C2×#14519701C2211yescharacteristic, complemented
37C2×#14519699C2211yescharacteristic
38C2×#14519699C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic, complemented
45C2×#14519688C2211yescharacteristic, complemented
46#16839664—21no—
47#16839654—21no—
48#16839654—21no—
49#16839632C2211yescharacteristic, complemented
50#16839619C2211yescharacteristic
51#16839619C2211yescharacteristic, complemented
52C4×C4⋊Dic61—21no—
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C2×#124×C61C2211yescharacteristic
58C2×C4⋊C8×C61C2211yescharacteristic, complemented
59C2×#103×C61C2211yescharacteristic, complemented
60C2×#103×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C4×C4⋊C4×C61C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—41no—
69C2×#11758226—41no—
70C2×#11758226C2×C414yes—
71C22×D244—21no—
72C22×D244D411yescharacteristic
73C22×D244C2311yescharacteristic
74C22×C22⋊D61—21no—
75C22×C22⋊D61—21no—
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—41no—
80C2×D4×D61—41no—
81C2×D4×D61C2×C414yes—
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C2×#11758189—22no—
87C2×#11758189—22no—
88C2×#11758189—41no—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C2×C8×D61—22no—
92C2×C8×D61—22no—
93C2×C8×D61—41no—
94#14519759—28no—
95#14519753—22no—
96#14519753C2×C414yes—
97#14519750—28no—
98#14519748—22no—
99#14519748C2×C414yes—
100#14519747—28no—
101C4×D244—22no—
102C4×D244C2×C414yes—
103C4×D244C2×C414yes—
104C4×D244D414yes—
105#14519735—22no—
106#14519735—22no—
107#14519735—41no—
108#14519735—41no—
109C2×C4⋊Dic61—21no—
110C2×C4⋊Dic61—21no—
111C2×C4⋊Dic61D411yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×C4⋊Dic61C2311yescharacteristic
114C2×C4⋊Dic61C2311yescharacteristic
115C2×#11758196—21no—
116C2×C22⋊Dic61—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198D411yescharacteristic
124C2×#11758198D411yescharacteristic
125C22⋊C4×D61—28no—
126C2×C4×Dic61—21no—
127C2×C4×Dic61—21no—
128#14519701—22no—
129#14519701—41no—
130#14519699—22no—
131#14519699—22no—
132#14519698—22no—
133#14519698—41no—
134#14519697—22no—
135#14519697D414yescomplemented
136#14519689—22no—
137#14519689—22no—
138#14519688—22no—
139#14519684—21no—
140#14519684—21no—
141C22×Q8×C61C2311yescharacteristic
142C22×D4×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145#124×C61—22no—
146#124×C61C2×C414yes—
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C22⋊C4×C61—21no—
150C2×C22⋊C4×C61—21no—
151C2×C42×C61—21no—
152C2×C42×C61C2311yescharacteristic
153C4⋊C8×C61—22no—
154#103×C61—22no—
155#103×C61—41no—
156#102×C61—22no—
157#102×C61—41no—
158#95×C61—21no—
159C24×C61—21no—
160C23×D61—21no—
161C23×D61—24no—
162C23×D61—42no—
163C23×D61—42no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—81no—
167C23×D61—81no—
168C23×D61C2×D411yescharacteristic
169C23×D61C2×D411yescharacteristic
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61C22×C412yes—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61C22×C412yes—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2411yescharacteristic
188C2×C22⋊D61—24no—
189C2×C22⋊D61—24no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—81no—
193C2×C22⋊D61—81no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199#11758226—28no—
200#11758226—44no—
201#11758226—44no—
202#11758226—44no—
203D4×D61—28no—
204D4×D61—44no—
205D4×D61—44no—
206D4×D61—44no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—24no—
211C2×D244—41no—
212C2×D244—41no—
213C2×D244—42no—
214C2×D244—42no—
215C2×D244C22⋊C414yes—
216C2×D244C22×C412yes—
217C2×D244C2×D412yes—
218C2×D244#4112yes—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—24no—
228C2×C4×D61—24no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61—81no—
232C2×C4×D61—81no—
233C2×C4×D61C22×C412yes—
234C2×C4×D61C22×C412yes—
235C2×C4×D61C2×D412yes—
236C2×C4×D61C2×D412yes—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61C2×D412yes—
247C22⋊C4×C61—24no—
248C22⋊C4×C61—24no—
249C42×C61—42no—
250C42×C61C22×C412yes—
251C42×C61C2×D412yes—
252C22⋊Dic61—24no—
253#11758198—24no—
254#11758198—24no—
255#11758198—42no—
256#11758198—42no—
257#11758198—81no—
258#11758198—81no—
259#11758198C22⋊C414yes—
260#11758198C22⋊C414yes—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—42no—
267C4⋊Dic61—81no—
268C4⋊Dic61C22⋊C414yes—
269C4⋊Dic61C22×C412yes—
270#11758196—24no—
271C4×Dic61—42no—
272C4×Dic61—42no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418C2×D412yes—
279#11758189—44no—
280C8×D61—44no—
281C23×C61—22no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61C22×D411yescharacteristic
289C22×D61—22no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—22no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—22no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—48no—
305C22×D61—48no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—84no—
311C22×D61—84no—
312C22×D61—84no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61C2×C22⋊C412yes—
316C22×D61C2×C22⋊C412yes—
317Q8×C61—22no—
318Q8×C61—22no—
319Q8×C61—41no—
320Q8×C61—41no—
321D4×C61—22no—
322D4×C61—22no—
323D4×C61—41no—
324D4×C61—41no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
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×C61—41no—
338C2×C4×C61C2×C22⋊C412yes—
339C2×C4×C61C2×C22⋊C412yes—
340C2×C4×C61C23×C411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C2×#4111yescharacteristic
344C2×C4×C61H(5,𝔽2)11yescharacteristic
345C2×C4×C61H(5,𝔽2)11yescharacteristic
346C22⋊D61—48no—
347C22⋊D61—84no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—22no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61C2×C22⋊C412yes—
362C2×Dic61C2×C22⋊C412yes—
363D244—22no—
364D244—22no—
365D244—22no—
366D244—44no—
367D244—48no—
368D244C4×D414yes—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—22no—
376C4×D61—22no—
377C4×D61—48no—
378C4×D61—84no—
379C8×C61—41no—
380C8×C61—41no—
381#92418—22no—
382#92418—41no—
383#22424—611nomaximal, Sylow
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61—81no—
391C22×C61C22×C22⋊C411yescharacteristic
392C22×C61D4211yescharacteristic
393C22×C61#54611yescharacteristic
394C22×C61#57511yescharacteristic
395C22×C61#57511yescharacteristic
396C22×C61#57611yescharacteristic
397C22×C61#57711yescharacteristic
398C2×D61—22no—
399C2×D61—22no—
400C2×D61—24no—
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—42no—
410C2×D61—41no—
411C2×D61—41no—
412C2×D61—42no—
413C2×D61—41no—
414C2×D61—41no—
415C2×D61—42no—
416C2×D61—41no—
417C2×D61—41no—
418C2×D61—42no—
419C2×D61—816no—
420C4×C61—22no—
421C4×C61—22no—
422C4×C61—42no—
423C4×C61—42no—
424C4×C61—81no—
425C4×C61C2×C4×D411yescharacteristic
426C4×C61#51811yescharacteristic
427C4×C61D4211yescharacteristic
428C4×C61#54611yescharacteristic
429Dic61—22no—
430Dic61—22no—
431Dic61—42no—
432Dic61—81no—
433Dic61—81no—
434C2×#546—611no—
435C2×#435—611no—
436C2×#418—611no—
437C2×#416—611no—
438#2354—611no—
439#1983D6111yescharacteristic, complemented
440#1959—611no—
441#1894—611no—
442#1893—611no—
443#1875—611no—
444#1873—611no—
445#1802—611no—
446#1788—611no—
447#1786—611no—
448#1762—611no—
449C2×C61—82no—
450C2×C61D4×C22⋊C411yescharacteristic
451C2×C61#289611yescharacteristic
452C2×C61#289711yescharacteristic
453C2×C61#326711yescharacteristic
454C2×C61#326811yescharacteristic
455C2×C61#331111yescharacteristic
456C2×C61#331911yescharacteristic
457D61—42no—
458D61—42no—
459D61—44no—
460C22×#41—611no—
461C23×D4—611no—
462C22×M16—611no—
463C23×C8—611no—
464#546—618no—
465#546—1224no—
466C2×#124C2×D6111yescharacteristic
467C2×#123—1221no—
468C2×C22⋊Q8—611no—
469C2×#121—611no—
470C2×#121—1221no—
471C2×#120—1221no—
472C2×C4×D4—611no—
473C2×C4×D4—611no—
474C2×#117—611no—
475C2×#117—611no—
476C22×C22⋊C4—1221no—
477#435—1224no—
478C2×C4⋊C8C2×D6111yescharacteristic, complemented
479#418—1224no—
480#416—1224no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103C2×D6111yescharacteristic, complemented
484C2×#103C2×D6111yescharacteristic, complemented
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102C2×D6111yescharacteristic
492C2×#102C2×D6111yescharacteristic
493C2×C22⋊C8—611no—
494C2×C22⋊C8—611no—
495C2×#97—611no—
496#390—1221no—
497#388—1221no—
498#388—1221no—
499#384—611no—
500#380—611no—
501#380—611no—
502C4×C4⋊C4—1221no—
503C4×C4⋊C4C2×D6111yescharacteristic, complemented
504#340—611no—
505#340—611no—
506#340—611no—
507#340—611no—
508C61#2242411yescharacteristic, complemented, Sylow
509C25—1221no—
510C2×#41—614no—
511C2×#41—1222no—
512C2×#41—1222no—
513C2×#41—1222no—
514C2×#41—2441no—
515C2×#41—2441no—
516C22×Q8C22×D6111yescharacteristic
517C22×D4—614no—
518C22×D4—611no—
519C22×D4—611no—
520C22×D4—1221no—
521C22×D4—1222no—
522C22×D4—1221no—
523C22×D4—1222no—
524C22×D4—1222no—
525C22×D4—1221no—
526C22×D4—2441no—
527C22×D4—2441no—
528C22×D4C22×D6111yescharacteristic
529C23×C4—611no—
530C23×C4—611no—
531C23×C4—1221no—
532C23×C4—1221no—
533C2×M16—1222no—
534C2×M16—1222no—
535C2×M16—2441no—
536C22×C8—611no—
537C22×C8—611no—
538C22×C8—1222no—
539C22×C8—1222no—
540C22×C8—2441no—
541C22×C8C22×D6111yescharacteristic
542C22×C8C22×D6111yescharacteristic
543#124—22no—
544#124C4×D6114yes—
545#123—1228no—
546C22⋊Q8—614no—
547C22⋊Q8—1222no—
548#121—614no—
549#121—1228no—
550#121—1222no—
551#120—1228no—
552C4×D4—614no—
553C4×D4—614no—
554C4×D4—614no—
555C4×D4—1222no—
556#117—1222no—
557#117—1222no—
558#117—2441no—
559#117—2441no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—611no—
573C2×C22⋊C4—1228no—
574C2×C22⋊C4—1221no—
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—21no—
582C2×C42—1221no—
583C2×C42—1221no—
584C2×C42C22×D6111yescharacteristic
585C4⋊C8—22no—
586#103—22no—
587#103—41no—
588#103—1222no—
589#103—2441no—
590#102—22no—
591#102—41no—
592#102—614no—
593#102—1222no—
594#102—1222no—
595#102—1222no—
596#102—1222no—
597#102—2441no—
598C22⋊C8—1222no—
599C22⋊C8—1222no—
600#97—1222no—
601#95—21no—
602#95—1221no—
603#95—1221no—
604C24—21no—
605C24—611no—
606C24—611no—
607C24—1224no—
608C24—1221no—
609C24—4881no—
610C24—4881no—
611C24—2442no—
612C24—2442no—
613C24—2442no—
614C24—2442no—
615#41—1228no—
616#41—2444no—
617#41—2444no—
618#41—2444no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C2×C4×D6112yes—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—612no—
631C2×D4—612no—
632C2×D4—612no—
633C2×D4—614no—
634C2×D4—1224no—
635C2×D4—1224no—
636C2×D4—1228no—
637C2×D4—1224no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—4881no—
642C2×D4—4881no—
643C2×D4—2441no—
644C2×D4—2441no—
645C2×D4—2442no—
646C2×D4—2442no—
647C2×D4—2444no—
648C2×D4—2444no—
649C2×D4—2444no—
650C2×D4—2442no—
651C2×D4—2442no—
652C2×D4C2×C4×D6112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—612no—
659C22×C4—612no—
660C22×C4—612no—
661C22×C4—612no—
662C22×C4—1224no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1224no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—4881no—
676C22×C4—4881no—
677C22×C4—2442no—
678C22×C4—2442no—
679C22×C4D4×D6111yescharacteristic
680C22×C4D4×D6111yescharacteristic
681C22×C4C23×D6111yescharacteristic
682M16—2444no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—612no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—2444no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—614no—
700C4⋊C4—612no—
701C4⋊C4—1224no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—4881no—
708C4⋊C4—2442no—
709C4⋊C4D4×D6112yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—614no—
713C22⋊C4—614no—
714C22⋊C4—1224no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—4881no—
718C22⋊C4—4881no—
719C22⋊C4—2442no—
720C22⋊C4—2442no—
721C42—42no—
722C42—2442no—
723C42—2442no—
724C42C2×C4×D6112yes—
725C42D4×D6112yes—
726C23—22no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—612no—
734C23—612no—
735C23—1222no—
736C23—1221no—
737C23—1221no—
738C23—1221no—
739C23—1221no—
740C23—1221no—
741C23—1221no—
742C23—1221no—
743C23—1221no—
744C23—1221no—
745C23—1221no—
746C23—1222no—
747C23—1221no—
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—
761C23C2×D4×D6111yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—41no—
769D4—41no—
770D4—614no—
771D4—1222no—
772D4—1222no—
773D4—1222no—
774D4—4884no—
775D4—2444no—
776D4—2448no—
777D4—2448no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—612no—
792C2×C4—612no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—4884no—
807C2×C4—2448no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4C22⋊C4×D6112yes—
817C2×C4C22⋊C4×D6112yes—
818C2×C4C22×C4×D6111yescharacteristic
819C2×C4C2×D4×D6111yescharacteristic
820C2×C4C2×D4×D6111yescharacteristic
821C2×C4#41×D6111yescharacteristic
822C2×C4#1451982211yescharacteristic
823C2×C4#1451982311yescharacteristic
824C8—41no—
825C8—41no—
826C8—1222no—
827C8—2441no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—1222no—
836C22—1222no—
837C22—1222no—
838C22—1222no—
839C22—1224no—
840C22—1222no—
841C22—1222no—
842C22—48816no—
843C22—2442no—
844C22—2441no—
845C22—2441no—
846C22—2442no—
847C22—2441no—
848C22—2441no—
849C22—2442no—
850C22—2441no—
851C22—2441no—
852C22—2442no—
853C22—2441no—
854C22—2441no—
855C22—2442no—
856C22—2442no—
857C22C2×C22⋊C4×D6111yescharacteristic
858C22#1684039611yescharacteristic
859C22#1684040911yescharacteristic
860C22#1684055811yescharacteristic
861C22#1684056111yescharacteristic
862C22#1684056411yescharacteristic
863C22#1684056911yescharacteristic
864C4—22no—
865C4—22no—
866C4—42no—
867C4—42no—
868C4—81no—
869C4—1222no—
870C4—1222no—
871C4—4881no—
872C4—4881no—
873C4—2442no—
874C4C4×D4×D6111yescharacteristic
875C4#1684023411yescharacteristic
876C4#1684039711yescharacteristic
877C4#1684040511yescharacteristic
878C2—82no—
879C2—2442no—
880C2—2442no—
881C2—2444no—
882C2#2144864011yescharacteristic
883C2#2145433511yescharacteristic
884C2#2145434111yescharacteristic
885C2#2145733911yescharacteristic
886C2#2145735411yescharacteristic
887C2#2145786211yescharacteristic
888C2#2145798211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1983C2
socleC23×C61C22×D4
prime radicalC2×#16840405C2
cosocleC22×C4×C61C24
hypercenter#1983D61
hypocenterC61#22424
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×#16839832C2semidirect
3. C2×#16839765C2semidirect
4. C2×#16839757C2semidirect
5. #21448766C2semidirect
6. #21446636C2semidirect
7. #21446249C2semidirect
8. #21446244C2semidirect
9. #21446138C2semidirect
10. #21446128C2semidirect
11. #21445820C2semidirect
12. #21445758C2semidirect
13. #21445748C2semidirect
14. #21445647C2semidirect
15. C61×#1983C2semidirect
19. C22×C8×D61C22semidirect
21. #16840405C4semidirect
30. C2×#14519735C22semidirect
35. C2×#14519701C22semidirect
36. C2×#14519701C22semidirect
44. C2×#14519689C22semidirect
45. C2×#14519688C22semidirect
49. #16839632C22semidirect
51. #16839619C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
58. C2×C4⋊C8×C61C22semidirect
59. C2×#103×C61C22semidirect
60. C2×#103×C61C22semidirect
63. C4×C4⋊C4×C61C22semidirect
135. #14519697D4semidirect
439. #1983D61semidirect
478. C2×C4⋊C8C2×D61semidirect
483. C2×#103C2×D61semidirect
484. C2×#103C2×D61semidirect
503. C4×C4⋊C4C2×D61semidirect
508. C61#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#168404052
C2×#168398322
C2×#168397652
C2×#168397572
#214487662
#214466362
#214462492
#214462442
#214461382
#214461282
#214458202
#214457582
#214457482
#214456472
C61×#19832
#2242461