Finite Group Databasebeta

← #29737190

Subgroups — #29737190

Order 15616.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840052C211yesmaximal, characteristic, complemented
2C22×#14519698C211yesmaximal, characteristic
3#21449521C211yesmaximal, characteristic, complemented
4#21447352C211yesmaximal, characteristic, complemented
5#21447193C211yesmaximal, characteristic, complemented
6#21447193C211yesmaximal, characteristic, complemented
7#21446955C211yesmaximal, characteristic, complemented
8#21446080C211yesmaximal, characteristic, complemented
9#21446080C211yesmaximal, characteristic, complemented
10#21446011C211yesmaximal, characteristic, complemented
11#21445999C211yesmaximal, characteristic, complemented
12#21445842C211yesmaximal, characteristic, complemented
13#21445819C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic
15D4×C22⋊C4×C61C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C2×#14519777C2211yescharacteristic, complemented
18C2×#14519754—21no—
19C22×C4⋊Dic61C2211yescharacteristic
20#16840052—24no—
21C2×#14519708C2211yescharacteristic, complemented
22C2×#14519708C2211yescharacteristic, complemented
23C2×#14519708C2211yescharacteristic, complemented
24C2×#14519708C2211yescharacteristic, complemented
25C2×C4⋊#92418C2211yescharacteristic, complemented
26C2×C4⋊#92418C2211yescharacteristic, complemented
27C2×#14519698—24no—
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37#16839694—21no—
38#16839683—21no—
39#16839660C2211yescharacteristic, complemented
40#16839660C2211yescharacteristic, complemented
41#16839637—21no—
42#16839632C2211yescharacteristic, complemented
43#16839622C2211yescharacteristic
44#16839524C2211yescharacteristic, complemented
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50C23×D4×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C22×C22⋊C4×C61—21no—
54C61×#390C2211yescharacteristic
55C61×#390C2211yescharacteristic
56C61×#386—21no—
57C61×#386—21no—
58C61×#380C2211yescharacteristic
59C61×#379—21no—
60C4×C22⋊C4×C61C2211yescharacteristic
61C22×Dic122—21no—
62C23×Dic61—21no—
63C22×#92418—22no—
64C22×#92418—22no—
65C22×#92418—41no—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70#14519777—22no—
71#14519777—41no—
72#14519754—44no—
73C2×C4⋊Dic61—22no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—41no—
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×C22⋊Dic61—21no—
86#14519708—22no—
87#14519708—22no—
88#14519708—41no—
89#14519708—41no—
90C4⋊#92418—22no—
91C4⋊#92418—41no—
92#14519698—22no—
93#14519698—22no—
94#14519698—22no—
95#14519698—22no—
96#14519698—22no—
97#14519698—41no—
98#14519698—41no—
99#14519698D414yes—
100C22⋊#92418—22no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104C25×C61—21no—
105C22×D4×C61—22no—
106C22×D4×C61—22no—
107C22×D4×C61—21no—
108C22×D4×C61—22no—
109C22×D4×C61—41no—
110C22×D4×C61—41no—
111C22×D4×C61Q814yescomplemented
112C22×D4×C61C2311yescharacteristic
113C22×D4×C61C2311yescharacteristic
114C23×C4×C61—21no—
115C23×C4×C61—21no—
116C23×C4×C61C2311yescharacteristic
117C4×D4×C61—22no—
118C4×D4×C61—22no—
119C4×D4×C61—41no—
120C4×D4×C61—41no—
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—44no—
131C2×C22⋊C4×C61D411yescharacteristic
132C2×C22⋊C4×C61D411yescharacteristic
133C2×C42×C61C2311yescharacteristic
134C2×C42×C61C2311yescharacteristic
135#95×C61—21no—
136#95×C61D411yescharacteristic
137#95×C61D411yescharacteristic
138C24×C61—21no—
139C24×C61—21no—
140C24×C61—24no—
141C24×C61—42no—
142C24×C61—42no—
143C24×C61—42no—
144C24×C61—42no—
145C24×C61—81no—
146C24×C61—81no—
147C24×C61C2×D411yescharacteristic
148C2×D4×C61—28no—
149C2×D4×C61—24no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—44no—
159C2×D4×C61—44no—
160C2×D4×C61—44no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61C2×D412yes—
164C2×D4×C61C2×Q812yes—
165C2×D4×C61C2×Q812yes—
166C2×D4×C61#4112yes—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—42no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61—42no—
177C22×C4×C61—81no—
178C22×C4×C61—81no—
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×Q812yes—
185C22×C4×C61#4112yes—
186C22×C4×C61C2411yescharacteristic
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—42no—
192C22×Dic61—42no—
193C22×Dic61—81no—
194C2×Dic122—42no—
195C2×Dic122—42no—
196C2×Dic122—81no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C22⋊C4×C61—22no—
202C22⋊C4×C61—42no—
203C22⋊C4×C61—42no—
204C22⋊C4×C61—42no—
205C22⋊C4×C61—42no—
206C22⋊C4×C61—42no—
207C22⋊C4×C61—81no—
208C22⋊C4×C61—81no—
209C22⋊C4×C61SD1614yes—
210C42×C61—21no—
211C42×C61—21no—
212C42×C61—21no—
213C42×C61—21no—
214C22⋊Dic61—42no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—42no—
223C4⋊Dic61—42no—
224C4⋊Dic61—42no—
225C4⋊Dic61—81no—
226C4⋊Dic61C2×D412yes—
227#11758196—42no—
228#11758196—42no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—44no—
241C2×#92418C2×D412yes—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—22no—
247C23×C61—22no—
248C23×C61—22no—
249C23×C61—22no—
250C23×C61—48no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—48no—
262C23×C61—84no—
263C23×C61—84no—
264C23×C61—84no—
265C23×C61—84no—
266C23×C61—84no—
267C23×C61C22⋊Q812yes—
268C23×C61C2×SD1612yes—
269C23×C61AGL(1,ℤ/8)12yes—
270C23×C61C22×D411yescharacteristic
271D4×C61—22no—
272D4×C61—22no—
273D4×C61—22no—
274D4×C61—22no—
275D4×C61—22no—
276D4×C61—48no—
277D4×C61—41no—
278D4×C61—41no—
279D4×C61C22⋊Q814yescomplemented
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—84no—
303C2×C4×C61—84no—
304C2×C4×C61C22⋊Q812yes—
305C2×C4×C61C2×SD1612yes—
306C2×C4×C61C2×SD1612yes—
307C2×C4×C61C22×D411yescharacteristic
308C2×C4×C61C22×Q811yescharacteristic
309C2×C4×C61C2×#4111yescharacteristic
310C2×C4×C61C2×#4111yescharacteristic
311C2×C4×C61H(5,𝔽2)11yescharacteristic
312C2×C4×C61H(5,𝔽2)11yescharacteristic
313C2×Dic61—22no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—84no—
326Dic122—84no—
327#92418—22no—
328#92418—41no—
329#92418—41no—
330#92418—41no—
331#25958—611nomaximal, Sylow
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—24no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—816no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61#47614yescomplemented
354C22×C61C2×C22⋊Q811yescharacteristic
355C22×C61D4211yescharacteristic
356C22×C61#54611yescharacteristic
357C22×C61C22×SD1611yescharacteristic
358C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
359C22×C61#57611yescharacteristic
360C22×C61#57711yescharacteristic
361C4×C61—22no—
362C4×C61—22no—
363C4×C61—22no—
364C4×C61—41no—
365C4×C61—41no—
366C4×C61—81no—
367C4×C61—81no—
368C4×C61C2×C22⋊Q811yescharacteristic
369C4×C61#54311yescharacteristic
370C4×C61#54611yescharacteristic
371C4×C61#55111yescharacteristic
372Dic61—42no—
373Dic61—81no—
374Dic61—81no—
375Dic61—81no—
376C2×#476—611no—
377C22×#102—611no—
378#2440—611no—
379D4×C22⋊C4D6111yescharacteristic
380#2094—611no—
381#2065—611no—
382#2065—611no—
383#2023—611no—
384#1864—611no—
385#1864—611no—
386#1853—611no—
387#1850—611no—
388#1807—611no—
389#1802—611no—
390#1786—611no—
391C2×C61—24no—
392C2×C61—44no—
393C2×C61—82no—
394C2×C61#243711yescharacteristic
395C2×C61C2×#47611yescharacteristic
396C2×C61#308111yescharacteristic
397C2×C61#326411yescharacteristic
398C2×C61D4×SD1611yescharacteristic
399C2×C61#329511yescharacteristic
400C2×C61#330611yescharacteristic
401C23×D4C2×D6111yescharacteristic
402C23×C8—611no—
403C2×C4⋊Q8—611no—
404C2×C22⋊Q8—1221no—
405C2×C4×D4C2×D6111yescharacteristic
406C2×C4×D4C2×D6111yescharacteristic
407C22×C4⋊C4—611no—
408C22×C22⋊C4—21no—
409#476—1224no—
410C2×#106—611no—
411C2×#106—611no—
412C2×#106—611no—
413C2×#106—611no—
414C2×C4⋊C8—611no—
415C2×C4⋊C8—611no—
416C2×#102—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#102—1224no—
425C2×C22⋊C8—611no—
426#398—1221no—
427#395—1221no—
428#390C2×D6111yescharacteristic
429#390C2×D6111yescharacteristic
430#389—611no—
431#389—611no—
432#386—21no—
433#386—21no—
434#385—1221no—
435#384—611no—
436#380—611no—
437#380C2×D6111yescharacteristic
438#379—21no—
439C4×C22⋊C4C2×D6111yescharacteristic
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#336—611no—
445#336—611no—
446C61#2595811yescharacteristic, complemented, Sylow
447C25—21no—
448C22×Q8—1221no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4—22no—
452C22×D4—21no—
453C22×D4—41no—
454C22×D4—41no—
455C22×D4Dic12214yescomplemented
456C22×D4C22×D6111yescharacteristic
457C22×D4C22×D6111yescharacteristic
458C23×C4—21no—
459C23×C4—21no—
460C23×C4—1221no—
461C23×C4C22×D6111yescharacteristic
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—1222no—
467C22×C8—1222no—
468C22×C8—2441no—
469C4⋊Q8—1222no—
470C4⋊Q8—2441no—
471C22⋊Q8—2444no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—41no—
475C4×D4—41no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—1222no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—2441no—
488C2×C4⋊C4C22×D6111yescharacteristic
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—44no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4C22⋊D6111yescharacteristic
500C2×C22⋊C4C22⋊D6111yescharacteristic
501C2×C42C22×D6111yescharacteristic
502C2×C42C22×D6111yescharacteristic
503#106—1222no—
504#106—1222no—
505#106—2441no—
506#106—2441no—
507C4⋊C8—1222no—
508C4⋊C8—2441no—
509#102—614no—
510#102—1222no—
511#102—1222no—
512#102—1222no—
513#102—1222no—
514#102—1222no—
515#102—2441no—
516#102—2441no—
517C22⋊C8—1222no—
518#95—21no—
519#95—1221no—
520#95—1221no—
521#95—1221no—
522#95C22⋊D6111yescharacteristic
523#95C22⋊D6111yescharacteristic
524C24—21no—
525C24—21no—
526C24—24no—
527C24—42no—
528C24—42no—
529C24—42no—
530C24—42no—
531C24—81no—
532C24—81no—
533C24C2×C22⋊D6111yescharacteristic
534C2×Q8—4881no—
535C2×Q8—2442no—
536C2×Q8—2442no—
537C2×D4—28no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—24no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4C2×Dic12212yes—
553C2×D4C2×Dic12212yes—
554C2×D4D4×D6112yes—
555C2×D4#1175822412yes—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—81no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—4881no—
573C22×C4—2442no—
574C22×C4—2442no—
575C22×C4C2×Dic12212yes—
576C22×C4#1175822212yes—
577C22×C4C2×C22⋊D6111yescharacteristic
578C22×C4C2×C22⋊D6111yescharacteristic
579C22×C4C2×C22⋊D6111yescharacteristic
580C22×C4C2×C22⋊D6111yescharacteristic
581C22×C4C2×C22⋊D6111yescharacteristic
582C22×C4C23×D6111yescharacteristic
583C2×C8—612no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—2444no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—612no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—4881no—
609C4⋊C4—2442no—
610C4⋊C4—2442no—
611C4⋊C4—2442no—
612C4⋊C4—2442no—
613C4⋊C4—2442no—
614C22⋊C4—22no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—81no—
621C22⋊C4—81no—
622C22⋊C4—2442no—
623C22⋊C4#1175820014yes—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—48no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23#1451975612yes—
654C23C2×#1175820012yes—
655C23#1451980212yes—
656C23C22×C22⋊D6111yescharacteristic
657Q8—4884no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—41no—
665D4—41no—
666D4#1451975414yescomplemented
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—84no—
690C2×C4—84no—
691C2×C4—1222no—
692C2×C4—4884no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4#1451975612yes—
705C2×C4C2×#1175820012yes—
706C2×C4C2×#1175820012yes—
707C2×C4C2×D4×D6111yescharacteristic
708C2×C4C22×Dic12211yescharacteristic
709C2×C4C2×#1175822411yescharacteristic
710C2×C4C2×#1175822211yescharacteristic
711C2×C4#1451982211yescharacteristic
712C2×C4#1451982211yescharacteristic
713C8—1222no—
714C8—2441no—
715C8—2441no—
716C8—2441no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—816no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22#1684005214yescomplemented
739C22C2×#1451975611yescharacteristic
740C22D4×C22⋊D6111yescharacteristic
741C22#1684040611yescharacteristic
742C22C22×#1175820011yescharacteristic
743C22C2×#1451980211yescharacteristic
744C22#1684056511yescharacteristic
745C22#1684057311yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—81no—
752C4—81no—
753C4—4881no—
754C4—4881no—
755C4—4881no—
756C4—2442no—
757C4C2×#1451975411yescharacteristic
758C4#1684038811yescharacteristic
759C4#1684040211yescharacteristic
760C4#1684043811yescharacteristic
761C2—24no—
762C2—44no—
763C2—82no—
764C2#2144948011yescharacteristic
765C2C2×#1684005211yescharacteristic
766C2#2145565011yescharacteristic
767C2#2145730011yescharacteristic
768C2D4×#1175820011yescharacteristic
769C2#2145764311yescharacteristic
770C2#2145778011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingD4×C22⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC23×D4×C61C22
hypercenterD4×C22⋊C4D61
hypocenterC61#25958
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16840052C2semidirect
3. #21449521C2semidirect
4. #21447352C2semidirect
5. #21447193C2semidirect
6. #21447193C2semidirect
7. #21446955C2semidirect
8. #21446080C2semidirect
9. #21446080C2semidirect
10. #21446011C2semidirect
11. #21445999C2semidirect
12. #21445842C2semidirect
13. #21445819C2semidirect
17. C2×#14519777C22semidirect
21. C2×#14519708C22semidirect
22. C2×#14519708C22semidirect
23. C2×#14519708C22semidirect
24. C2×#14519708C22semidirect
25. C2×C4⋊#92418C22semidirect
26. C2×C4⋊#92418C22semidirect
39. #16839660C22semidirect
40. #16839660C22semidirect
42. #16839632C22semidirect
44. #16839524C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839517C22semidirect
49. #16839517C22semidirect
111. C22×D4×C61Q8semidirect
279. D4×C61C22⋊Q8semidirect
353. C22×C61#476semidirect
446. C61#25958semidirect
455. C22×D4Dic122semidirect
666. D4#14519754semidirect
738. C22#16840052semidirect

Maximal subgroups

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

subgroupindex
C2×#168400522
C22×#145196982
#214495212
#214473522
#214471932
#214469552
#214460802
#214460112
#214459992
#214458422
#214458192
#214457502
D4×C22⋊C4×C612
#2595861