Finite Group Databasebeta

← #29695565

Subgroups — #29695565

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×#16840407C211yesmaximal, characteristic
2C2×#16839832C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic, complemented
4C2×#16839755C211yesmaximal, characteristic, complemented
5#21448770C211yesmaximal, characteristic, complemented
6#21446749C211yesmaximal, characteristic, complemented
7#21446633C211yesmaximal, characteristic, complemented
8#21446251C211yesmaximal, characteristic, complemented
9#21446246C211yesmaximal, characteristic, complemented
10#21446140C211yesmaximal, characteristic, complemented
11#21446130C211yesmaximal, characteristic, complemented
12#21445756C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445644C211yesmaximal, characteristic, complemented
15C61×#1802C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic, complemented
20#16840407—24no—
21#16840407C418yescomplemented
22C2×#14519765C2211yescharacteristic
23C2×#14519761—21no—
24C2×#14519757C2211yescharacteristic
25C2×#14519752C2211yescharacteristic
26C2×#14519751—21no—
27C2×#14519747—21no—
28C2×C4×D244C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C2×#14519735C2211yescharacteristic, complemented
31C22×#11758198—21no—
32#16839832—24no—
33#16839765—24no—
34#16839755—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×#14519689C2211yescharacteristic
46C2×#14519689C2211yescharacteristic, complemented
47C2×#14519688C2211yescharacteristic, complemented
48#16839663—21no—
49#16839652—21no—
50#16839652—21no—
51#16839619C2211yescharacteristic
52#16839619C2211yescharacteristic, complemented
53C4⋊C4×Dic61—21no—
54C4×C4⋊Dic61C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C2×C4×D4×C61C2211yescharacteristic
58C2×C4⋊C8×C61C2211yescharacteristic, complemented
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C61×#384C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—41no—
69C2×#11758224—41no—
70C2×#11758224C2×C414yes—
71C22×Dic122C2311yescharacteristic
72C22×D244—21no—
73C22×D244D411yescharacteristic
74C22×D244C2311yescharacteristic
75C22×C22⋊D61—21no—
76C22×C22⋊D61—21no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—22no—
80C2×D4×D61—41no—
81C2×D4×D61—41no—
82C2×D4×D61C2×C414yes—
83C23×Dic61—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#14519765—22no—
95#14519765C2×C414yes—
96#14519761—28no—
97#14519757—22no—
98#14519757C2×C414yes—
99#14519752—22no—
100#14519752C2×C414yes—
101#14519751—28no—
102#14519747—28no—
103C4×D244C2×C414yes—
104C4×D244D414yes—
105#14519735—22no—
106#14519735—22no—
107#14519735—41no—
108#14519735—41no—
109C2×C4⋊Dic61—21no—
110C2×C4⋊Dic61D411yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—28no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198D411yescharacteristic
123C2×#11758198D411yescharacteristic
124C2×C4×Dic61—21no—
125C2×C4×Dic61—21no—
126C2×C4×Dic61—21no—
127#14519702—22no—
128#14519702—41no—
129#14519700—22no—
130#14519700—41no—
131#14519699—22no—
132#14519699—41no—
133#14519698—22no—
134#14519698D414yescomplemented
135#14519697—22no—
136#14519697—41no—
137#14519689—22no—
138#14519689—22no—
139#14519688—22no—
140#14519684—21no—
141#14519684—21no—
142#14519684—21no—
143C22×D4×C61C2311yescharacteristic
144C23×C4×C61—21no—
145C22×C8×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C4×D4×C61—22no—
148C4×D4×C61C2×C414yes—
149C2×C4⋊C4×C61—21no—
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C22⋊C4×C61—21no—
155C2×C42×C61C2311yescharacteristic
156C4⋊C8×C61—22no—
157#102×C61—22no—
158#102×C61—22no—
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×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61C22×C412yes—
174C2×D4×C61C2×D412yes—
175C2×D4×C61#4112yes—
176C22×C4×C61—21no—
177C22×C4×C61—24no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—81no—
181C22×C4×C61—81no—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2411yescharacteristic
185C2×C22⋊D61—24no—
186C2×C22⋊D61—24no—
187C2×C22⋊D61—42no—
188C2×C22⋊D61—42no—
189C2×C22⋊D61—42no—
190C2×C22⋊D61—42no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—24no—
194C22×Dic61—21no—
195C22×Dic61—42no—
196C22×Dic61—42no—
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199#11758224—28no—
200#11758224—44no—
201#11758224—44no—
202#11758224—44no—
203D4×D61—28no—
204D4×D61—44no—
205D4×D61—44no—
206D4×D61—44no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244—24no—
213C2×D244—41no—
214C2×D244—41no—
215C2×D244—81no—
216C2×D244—81no—
217C2×D244C22⋊C414yes—
218C2×D244C22×C412yes—
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×D61C22×C412yes—
228C2×C4×D61C22×C412yes—
229C2×C4×D61C2×D412yes—
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—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—42no—
249C4⋊C4×C61—81no—
250C4⋊C4×C61C22×C412yes—
251C22⋊C4×C61—24no—
252C42×C61C22×C412yes—
253C42×C61C2×D412yes—
254#11758198—24no—
255#11758198—24no—
256#11758198—24no—
257#11758198—24no—
258#11758198—42no—
259#11758198—42no—
260#11758198—81no—
261#11758198—81no—
262#11758198C22⋊C414yes—
263#11758198C22⋊C414yes—
264C4⋊Dic61—21no—
265C4⋊Dic61—24no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61C22⋊C414yes—
269C4⋊Dic61C2×D412yes—
270C4×Dic61—42no—
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—22no—
283C23×C61—22no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61C22×D411yescharacteristic
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—22no—
302C22×D61—48no—
303C22×D61—48no—
304C22×D61—41no—
305C22×D61—41no—
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—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61C4×D414yes—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—22no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—84no—
335C2×C4×C61C2×C22⋊C412yes—
336C2×C4×C61C2×C22⋊C412yes—
337C2×C4×C61C23×C411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C2×C4×C61H(5,𝔽2)11yescharacteristic
342C2×C4×C61H(5,𝔽2)11yescharacteristic
343C22⋊D61—48no—
344C22⋊D61—48no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—48no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61C2×C22⋊C412yes—
360C2×Dic61C2×C22⋊C412yes—
361D244—22no—
362D244—22no—
363D244—44no—
364D244—41no—
365D244—41no—
366D244—84no—
367C4×D61—22no—
368C4×D61—22no—
369C4×D61—22no—
370C4×D61—22no—
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—42no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—42no—
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—22no—
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—41no—
411C2×D61—41no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—816no—
416C2×D61—81no—
417C2×D61—81no—
418C2×D61—81no—
419C2×D61—81no—
420C4×C61—22no—
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—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#1802D6111yescharacteristic, complemented
446#1788—611no—
447#1786—611no—
448#1762—611no—
449C2×C61—44no—
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—82no—
460C22×#41—611no—
461C23×D4—611no—
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×D4C2×D6111yescharacteristic
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×#103—611no—
484C2×#103—611no—
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#384C2×D6111yescharacteristic, complemented
500#380—611no—
501#380—611no—
502C4×C4⋊C4—611no—
503C4×C4⋊C4—1221no—
504#340—611no—
505#340—611no—
506#340C2×D6111yescharacteristic, complemented
507#340C2×D6111yescharacteristic, complemented
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×Q8—611no—
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—21no—
530C23×C4—611no—
531C23×C4—611no—
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—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—22no—
553C4×D4—614no—
554C4×D4—614no—
555C4×D4C4×D6114yes—
556#117—1222no—
557#117—1222no—
558#117—2441no—
559#117—2441no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4C22×D6111yescharacteristic
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—1221no—
582C2×C42—1221no—
583C2×C42—1221no—
584C2×C42C22×D6111yescharacteristic
585C4⋊C8—22no—
586#103—1222no—
587#103—1222no—
588#103—2441no—
589#103—2441no—
590#102—22no—
591#102—22no—
592#102—614no—
593#102—1222no—
594#102—1222no—
595#102—1222no—
596#102—2441no—
597#102—2441no—
598C22⋊C8—1222no—
599C22⋊C8—1222no—
600#97—1222no—
601#95—1221no—
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—612no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—612no—
629C2×D4—614no—
630C2×D4—1224no—
631C2×D4—1224no—
632C2×D4—1228no—
633C2×D4—1224no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—4881no—
640C2×D4—4881no—
641C2×D4—2441no—
642C2×D4—2441no—
643C2×D4—2444no—
644C2×D4—2444no—
645C2×D4—2444no—
646C2×D4—2442no—
647C2×D4—2442no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4C2×C4×D6112yes—
651C2×D4D4×D6112yes—
652C2×D4#1175822612yes—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—81no—
658C22×C4—81no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—612no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—612no—
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—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
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—21no—
700C4⋊C4—21no—
701C4⋊C4—42no—
702C4⋊C4—81no—
703C4⋊C4—614no—
704C4⋊C4—612no—
705C4⋊C4—1224no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4C2×C4×D6112yes—
710C22⋊C4—24no—
711C22⋊C4—614no—
712C22⋊C4—614no—
713C22⋊C4—1224no—
714C22⋊C4—1224no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—4881no—
718C22⋊C4—4881no—
719C22⋊C4—2442no—
720C22⋊C4—2442no—
721C42—2442no—
722C42—2442no—
723C42—2442no—
724C42C2×C4×D6112yes—
725C42D4×D6112yes—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—612no—
734C23—612no—
735C23—1221no—
736C23—1221no—
737C23—1221no—
738C23—1221no—
739C23—1221no—
740C23—1221no—
741C23—1221no—
742C23—1221no—
743C23—1221no—
744C23—1221no—
745C23—1221no—
746C23—1221no—
747C23—1222no—
748C23—4884no—
749C23—4884no—
750C23—4884no—
751C23—4884no—
752C23—4884no—
753C23—2448no—
754C23—2448no—
755C23—2441no—
756C23—2441no—
757C23—2441no—
758C23—2441no—
759C23—2441no—
760C23—2441no—
761C23C2×D4×D6111yescharacteristic
762Q8—1222no—
763Q8—1222no—
764Q8—2441no—
765Q8—2441no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—1222no—
770D4—1222no—
771D4—4884no—
772D4—2444no—
773D4—2448no—
774D4—2448no—
775D4—2441no—
776D4—2441no—
777D4#1451973914yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—84no—
792C2×C4—612no—
793C2×C4—612no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
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—1222no—
807C2×C4—1222no—
808C2×C4—2448no—
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×C4C2×#1175822611yescharacteristic
822C2×C4#1451982311yescharacteristic
823C2×C4#1451982311yescharacteristic
824C8—41no—
825C8—41no—
826C8—1222no—
827C8—2441no—
828C22—24no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—1222no—
836C22—1222no—
837C22—1222no—
838C22—1222no—
839C22—1222no—
840C22—1222no—
841C22—48816no—
842C22—4881no—
843C22—4881no—
844C22—4881no—
845C22—4881no—
846C22—2442no—
847C22—2442no—
848C22—2442no—
849C22—2441no—
850C22—2441no—
851C22—2441no—
852C22—2441no—
853C22—2441no—
854C22—2441no—
855C22—2441no—
856C22—2441no—
857C22C2×C22⋊C4×D6111yescharacteristic
858C22#1684039611yescharacteristic
859C22#1684040311yescharacteristic
860C22#1684055811yescharacteristic
861C22#1684056111yescharacteristic
862C22#1684056311yescharacteristic
863C22#1684056811yescharacteristic
864C4—22no—
865C4—22no—
866C4—42no—
867C4—81no—
868C4—81no—
869C4—1222no—
870C4—1222no—
871C4—4881no—
872C4—2442no—
873C4—2442no—
874C4C2×#1451973911yescharacteristic
875C4#1684023611yescharacteristic
876C4#1684039611yescharacteristic
877C4#1684040311yescharacteristic
878C2—44no—
879C2—4882no—
880C2—2442no—
881C2—2442no—
882C2#2144863911yescharacteristic
883C2#2145433511yescharacteristic
884C2#2145434011yescharacteristic
885C2#2145735011yescharacteristic
886C2#2145736511yescharacteristic
887C2#2145785211yescharacteristic
888C2#2145797211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1802C2
socleC23×C61C22×D4
prime radicalC2×#16840407C2
cosocleC22×C4×C61C24
hypercenter#1802D61
hypocenterC61#22424
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#16839832C2semidirect
3. C2×#16839765C2semidirect
4. C2×#16839755C2semidirect
5. #21448770C2semidirect
6. #21446749C2semidirect
7. #21446633C2semidirect
8. #21446251C2semidirect
9. #21446246C2semidirect
10. #21446140C2semidirect
11. #21446130C2semidirect
12. #21445756C2semidirect
13. #21445748C2semidirect
14. #21445644C2semidirect
15. C61×#1802C2semidirect
19. C22×C8×D61C22semidirect
21. #16840407C4semidirect
30. C2×#14519735C22semidirect
35. C2×#14519702C22semidirect
36. C2×#14519702C22semidirect
37. C2×#14519700C22semidirect
38. C2×#14519700C22semidirect
46. C2×#14519689C22semidirect
47. C2×#14519688C22semidirect
52. #16839619C22semidirect
54. C4×C4⋊Dic61C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
58. C2×C4⋊C8×C61C22semidirect
61. C61×#384C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
134. #14519698D4semidirect
445. #1802D61semidirect
478. C2×C4⋊C8C2×D61semidirect
499. #384C2×D61semidirect
506. #340C2×D61semidirect
507. #340C2×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×#168404072
C2×#168398322
C2×#168397652
C2×#168397552
#214487702
#214467492
#214466332
#214462512
#214462462
#214461402
#214461302
#214457562
#214457482
#214456442
C61×#18022
#2242461