Finite Group Databasebeta

← #29695561

Subgroups — #29695561

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×#16840406C211yesmaximal, characteristic
2C2×#16839836C211yesmaximal, characteristic, complemented
3C2×#16839767C211yesmaximal, characteristic, complemented
4C2×#16839755C211yesmaximal, characteristic, complemented
5#21448763C211yesmaximal, characteristic, complemented
6#21446750C211yesmaximal, characteristic, complemented
7#21446634C211yesmaximal, characteristic, complemented
8#21446250C211yesmaximal, characteristic, complemented
9#21446244C211yesmaximal, characteristic, complemented
10#21446138C211yesmaximal, characteristic, complemented
11#21446129C211yesmaximal, characteristic, complemented
12#21445817C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14#21445646C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic, complemented
19#16840406—24no—
20#16840406C418yescomplemented
21C2×#14519764C2211yescharacteristic
22C2×#14519758—21no—
23C2×#14519756C2211yescharacteristic
24C2×#14519749—21no—
25C2×#14519748C2211yescharacteristic
26C2×#14519746—21no—
27C2×D4×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519736C2211yescharacteristic
30C2×#14519735C2211yescharacteristic, complemented
31C22×C22⋊Dic61—21no—
32#16839836—24no—
33C2×#14519706C2211yescharacteristic, complemented
34#16839767—24no—
35#16839755—24no—
36C2×#14519702C2211yescharacteristic, complemented
37C2×#14519702C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39C2×#14519700C2211yescharacteristic, complemented
40C2×#14519698C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519698C2211yescharacteristic
44C2×#14519689C2211yescharacteristic, complemented
45C2×#14519687C2211yescharacteristic, complemented
46#16839662—21no—
47#16839656—21no—
48#16839651—21no—
49#16839631C2211yescharacteristic, complemented
50#16839619C2211yescharacteristic, complemented
51C4⋊C4×Dic61C2211yescharacteristic, complemented
52#16839613—21no—
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C23×D4×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—41no—
68C2×#11758224—41no—
69C2×#11758224C2×C414yes—
70C22×Dic122C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C22×C22⋊D61D411yescharacteristic
74C23×Dic61—21no—
75C23×Dic61—21no—
76C22×C4×D61C2311yescharacteristic
77C2×#11758194—22no—
78C2×#11758194—22no—
79C2×#11758194—41no—
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C2×C8×D61—22no—
83C2×C8×D61—22no—
84C2×C8×D61—41no—
85#14519764—22no—
86#14519764C2×C414yes—
87#14519758—28no—
88#14519756—22no—
89#14519756C2×C414yes—
90#14519749—28no—
91#14519748—22no—
92#14519748C2×C414yes—
93#14519746—28no—
94D4×Dic61—22no—
95D4×Dic61C2×C414yes—
96C4×C22⋊D61C2×C414yes—
97C4×C22⋊D61D414yes—
98#14519736—22no—
99#14519736—41no—
100#14519735—22no—
101#14519735—41no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196D411yescharacteristic
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—28no—
115C2×C22⋊Dic61—21no—
116C2×C22⋊Dic61D411yescharacteristic
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198D411yescharacteristic
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123C2×C4×Dic61C2311yescharacteristic
124#14519706—22no—
125#14519702—22no—
126#14519702—41no—
127#14519700—22no—
128#14519700—41no—
129#14519698—22no—
130#14519698—22no—
131#14519698—22no—
132#14519698D414yescomplemented
133#14519689—22no—
134#14519687—22no—
135#14519684—21no—
136#14519684—21no—
137C25×C61—21no—
138C22×D4×C61—22no—
139C22×D4×C61—22no—
140C22×D4×C61—21no—
141C22×D4×C61—22no—
142C22×D4×C61—41no—
143C22×D4×C61—41no—
144C22×D4×C61C2×C414yes—
145C22×D4×C61C2311yescharacteristic
146C22×D4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C22⋊C4×C61—21no—
153#102×C61—22no—
154#102×C61—22no—
155#102×C61—41no—
156#102×C61—41no—
157C22⋊C8×C61—22no—
158#95×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—24no—
162C24×C61—42no—
163C24×C61—42no—
164C24×C61—42no—
165C24×C61—42no—
166C24×C61—81no—
167C24×C61—81no—
168C24×C61C2×D411yescharacteristic
169C23×D61C2×D411yescharacteristic
170C2×D4×C61—28no—
171C2×D4×C61—24no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—44no—
181C2×D4×C61—44no—
182C2×D4×C61—44no—
183C2×D4×C61—42no—
184C2×D4×C61—42no—
185C2×D4×C61C22×C412yes—
186C2×D4×C61C22×C412yes—
187C2×D4×C61C2×D412yes—
188C2×D4×C61#4112yes—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61C22×C412yes—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D412yes—
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—24no—
200C2×C22⋊D61—24no—
201C2×C22⋊D61—41no—
202C2×C22⋊D61—41no—
203C2×C22⋊D61—42no—
204C2×C22⋊D61—42no—
205C2×C22⋊D61—81no—
206C2×C22⋊D61—81no—
207C2×C22⋊D61C22⋊C414yes—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—24no—
212C22×Dic61—24no—
213C22×Dic61—21no—
214C22×Dic61—42no—
215C22×Dic61—42no—
216C22×Dic61—81no—
217C22×Dic61—81no—
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221#11758224—28no—
222#11758224—44no—
223#11758224—44no—
224#11758224—44no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61C22×C412yes—
230C2×C4×D61C2×D412yes—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122C22×C412yes—
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×C61—21no—
247C22⋊C4×C61—81no—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250C22⋊Dic61—24no—
251C22⋊Dic61—24no—
252C22⋊Dic61—24no—
253C22⋊Dic61—42no—
254C22⋊Dic61C22⋊C414yes—
255#11758198—42no—
256#11758198—81no—
257#11758198C22⋊C414yes—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61C22×C412yes—
263C4⋊Dic61C2×D412yes—
264#11758196—24no—
265#11758196—42no—
266#11758196—81no—
267#11758196C22⋊C414yes—
268C4×Dic61—42no—
269C4×Dic61—42no—
270C4×Dic61—42no—
271C4×Dic61C22×C412yes—
272C4×Dic61C2×D412yes—
273#11758194—44no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418C2×D412yes—
280C8×D61—44no—
281C23×C61—22no—
282C23×C61—21no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—22no—
291C23×C61—48no—
292C23×C61—48no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—84no—
304C23×C61—84no—
305C23×C61—84no—
306C23×C61—84no—
307C23×C61—84no—
308C23×C61C2×C22⋊C412yes—
309C23×C61C22×D411yescharacteristic
310C22×D61—21no—
311C22×D61—21no—
312C22×D61—21no—
313C22×D61—21no—
314C22×D61—21no—
315C22×D61—21no—
316C22×D61C2×C22⋊C412yes—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—22no—
322D4×C61—48no—
323D4×C61—41no—
324D4×C61—41no—
325D4×C61C4×D414yes—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
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×C61C23×C411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C2×#4111yescharacteristic
343C2×C4×C61H(5,𝔽2)11yescharacteristic
344C2×C4×C61H(5,𝔽2)11yescharacteristic
345C22⋊D61—44no—
346C22⋊D61—48no—
347C22⋊D61—84no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—48no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—84no—
368C2×Dic61C2×C22⋊C412yes—
369C2×Dic61C2×C22⋊C412yes—
370C2×Dic61C2×C22⋊C412yes—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—22no—
375Dic122—22no—
376Dic122—22no—
377Dic122—41no—
378Dic122—41no—
379C8×C61—41no—
380C8×C61—41no—
381#92418—22no—
382#92418—41no—
383#22424—611nomaximal, Sylow
384C22×C61—24no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—41no—
391C22×C61—42no—
392C22×C61—41no—
393C22×C61—42no—
394C22×C61—41no—
395C22×C61—42no—
396C22×C61—41no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—816no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61C22×C22⋊C411yescharacteristic
407C22×C61D4211yescharacteristic
408C22×C61#54611yescharacteristic
409C22×C61#57511yescharacteristic
410C22×C61#57511yescharacteristic
411C22×C61#57611yescharacteristic
412C22×C61#57711yescharacteristic
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—41no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—41no—
420C4×C61—22no—
421C4×C61—81no—
422C4×C61—81no—
423C4×C61C2×C4×D411yescharacteristic
424C4×C61#51811yescharacteristic
425C4×C61D4211yescharacteristic
426C4×C61#54611yescharacteristic
427Dic61—22no—
428Dic61—22no—
429Dic61—22no—
430Dic61—42no—
431Dic61—42no—
432Dic61—42no—
433Dic61—81no—
434C2×#546—611no—
435C2×#435—611no—
436C2×#418—611no—
437C2×#416—611no—
438#2354—611no—
439#1983—611no—
440#1959—611no—
441#1894—611no—
442#1893—611no—
443#1875—611no—
444#1873—611no—
445#1802—611no—
446#1788—611no—
447#1786D6111yescharacteristic, complemented
448#1762—611no—
449C2×C61—42no—
450C2×C61—44no—
451C2×C61—82no—
452C2×C61D4×C22⋊C411yescharacteristic
453C2×C61#289611yescharacteristic
454C2×C61#289711yescharacteristic
455C2×C61#326711yescharacteristic
456C2×C61#326811yescharacteristic
457C2×C61#331111yescharacteristic
458C2×C61#331911yescharacteristic
459D61—42no—
460C22×#41—611no—
461C23×D4C2×D6111yescharacteristic
462C22×M16—611no—
463C23×C8—611no—
464#546—618no—
465#546—1224no—
466C2×#124—611no—
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⋊C8—611no—
479#418—1224no—
480#416—1224no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102C2×D6111yescharacteristic
490C2×#102C2×D6111yescharacteristic
491C2×#102C2×D6111yescharacteristic
492C2×#102C2×D6111yescharacteristic
493C2×C22⋊C8—611no—
494C2×C22⋊C8C2×D6111yescharacteristic
495C2×#97—611no—
496#390—1221no—
497#388—1221no—
498#388—1221no—
499#384—611no—
500#380—611no—
501#380C2×D6111yescharacteristic
502C4×C4⋊C4—611no—
503C4×C4⋊C4—1221no—
504#340—611no—
505#340—611no—
506#340—611no—
507#340—611no—
508C61#2242411yescharacteristic, complemented, Sylow
509C25—21no—
510C2×#41—614no—
511C2×#41—1222no—
512C2×#41—1222no—
513C2×#41—1222no—
514C2×#41—2441no—
515C2×#41—2441no—
516C22×Q8—611no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—611no—
524C22×D4—1221no—
525C22×D4—1221no—
526C22×D4C4×D6114yes—
527C22×D4C22×D6111yescharacteristic
528C22×D4C22×D6111yescharacteristic
529C23×C4—611no—
530C23×C4—1221no—
531C23×C4—1221no—
532C23×C4C22×D6111yescharacteristic
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—614no—
544#124—1222no—
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—611no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—1228no—
573C2×C22⋊C4—1221no—
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—611no—
582C2×C42—1221no—
583C2×C42—1221no—
584C2×C42—1221no—
585C4⋊C8—1222no—
586#103—1222no—
587#103—1222no—
588#103—2441no—
589#103—2441no—
590#102—22no—
591#102—22no—
592#102—41no—
593#102—41no—
594#102—614no—
595#102—1222no—
596#102—1222no—
597#102—1222no—
598C22⋊C8—22no—
599C22⋊C8—1222no—
600#97—1222no—
601#95—21no—
602#95—1221no—
603#95—1221no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24—611no—
614C24D4×D6111yescharacteristic
615#41—1228no—
616#41—2444no—
617#41—2444no—
618#41—2444no—
619C2×Q8—612no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×D4—28no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—24no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—614no—
641C2×D4—1224no—
642C2×D4—1224no—
643C2×D4—4881no—
644C2×D4—4881no—
645C2×D4—2441no—
646C2×D4—2441no—
647C2×D4—2442no—
648C2×D4—2442no—
649C2×D4C2×C4×D6112yes—
650C2×D4C2×C4×D6112yes—
651C2×D4D4×D6112yes—
652C2×D4#1175822412yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—1224no—
665C22×C4—1224no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—4881no—
675C22×C4—4881no—
676C22×C4—2442no—
677C22×C4—2442no—
678C22×C4C2×C4×D6112yes—
679C22×C4D4×D6112yes—
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—21no—
700C4⋊C4—614no—
701C4⋊C4—612no—
702C4⋊C4—612no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1224no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—4881no—
709C4⋊C4—2442no—
710C22⋊C4—81no—
711C22⋊C4—614no—
712C22⋊C4—614no—
713C22⋊C4—1224no—
714C22⋊C4—1224no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—4881no—
719C22⋊C4—2442no—
720C22⋊C4—2442no—
721C42—612no—
722C42—612no—
723C42—2442no—
724C42—2442no—
725C42—2442no—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—48no—
737C23—48no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—84no—
749C23—84no—
750C23—84no—
751C23—84no—
752C23—84no—
753C23—612no—
754C23—1221no—
755C23—1221no—
756C23—1221no—
757C23—1221no—
758C23—1221no—
759C23—1221no—
760C23C22⋊C4×D6112yes—
761C23C2×D4×D6111yescharacteristic
762Q8—1222no—
763Q8—1222no—
764Q8—2441no—
765Q8—2441no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—41no—
773D4—41no—
774D4—4884no—
775D4—2444no—
776D4—2448no—
777D4#1451973714yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
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—612no—
791C2×C4—612no—
792C2×C4—612no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1221no—
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×C4—2441no—
817C2×C4C22⋊C4×D6112yes—
818C2×C4C22×C4×D6111yescharacteristic
819C2×C4C2×D4×D6111yescharacteristic
820C2×C4C2×D4×D6111yescharacteristic
821C2×C4C2×#1175822411yescharacteristic
822C2×C4#1451982211yescharacteristic
823C2×C4#1451982211yescharacteristic
824C8—41no—
825C8—41no—
826C8—1222no—
827C8—2441no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—22no—
832C22—42no—
833C22—41no—
834C22—42no—
835C22—41no—
836C22—42no—
837C22—41no—
838C22—42no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—816no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—1222no—
851C22—1222no—
852C22—1222no—
853C22—2441no—
854C22—2441no—
855C22—2441no—
856C22—2441no—
857C22C2×C22⋊C4×D6111yescharacteristic
858C22#1684039411yescharacteristic
859C22#1684039911yescharacteristic
860C22#1684055811yescharacteristic
861C22#1684055811yescharacteristic
862C22#1684056311yescharacteristic
863C22#1684056811yescharacteristic
864C4—22no—
865C4—81no—
866C4—81no—
867C4—1222no—
868C4—1222no—
869C4—1222no—
870C4—4881no—
871C4—2442no—
872C4—2442no—
873C4—2442no—
874C4C2×#1451973711yescharacteristic
875C4#1684023511yescharacteristic
876C4#1684039411yescharacteristic
877C4#1684039911yescharacteristic
878C2—42no—
879C2—44no—
880C2—82no—
881C2—2442no—
882C2#2144863511yescharacteristic
883C2#2145433311yescharacteristic
884C2#2145434011yescharacteristic
885C2#2145734211yescharacteristic
886C2#2145735711yescharacteristic
887C2#2145784811yescharacteristic
888C2#2145796811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1786C2
socleC23×C61C22×D4
prime radicalC2×#16840406C2
cosocleC22×C4×C61C24
hypercenter#1786D61
hypocenterC61#22424
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#16839836C2semidirect
3. C2×#16839767C2semidirect
4. C2×#16839755C2semidirect
5. #21448763C2semidirect
6. #21446750C2semidirect
7. #21446634C2semidirect
8. #21446250C2semidirect
9. #21446244C2semidirect
10. #21446138C2semidirect
11. #21446129C2semidirect
12. #21445817C2semidirect
13. #21445756C2semidirect
14. #21445646C2semidirect
15. C61×#1786C2semidirect
18. C22×C8×D61C22semidirect
20. #16840406C4semidirect
30. C2×#14519735C22semidirect
33. C2×#14519706C22semidirect
36. C2×#14519702C22semidirect
37. C2×#14519702C22semidirect
38. C2×#14519700C22semidirect
39. C2×#14519700C22semidirect
44. C2×#14519689C22semidirect
45. C2×#14519687C22semidirect
49. #16839631C22semidirect
50. #16839619C22semidirect
51. C4⋊C4×Dic61C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
132. #14519698D4semidirect
447. #1786D61semidirect
508. C61#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#168404062
C2×#168398362
C2×#168397672
C2×#168397552
#214487632
#214467502
#214466342
#214462502
#214462442
#214461382
#214461292
#214458172
#214457562
#214456462
C61×#17862
#2242461