Finite Group Databasebeta

← #30622474

Subgroups — #30622474

Order 15616.

946 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462349C211yesmaximal, characteristic
2#21462339C211yesmaximal, characteristic, complemented
3#21461969C211yesmaximal, characteristic, complemented
4#21461964C211yesmaximal, characteristic, complemented
5#21461951C211yesmaximal, characteristic
6#21461932C211yesmaximal, characteristic, complemented
7#21461897C211yesmaximal, characteristic, complemented
8#21461896C211yesmaximal, characteristic, complemented
9#21461812C211yesmaximal, characteristic, complemented
10#21461812C211yesmaximal, characteristic, complemented
11#21461620C211yesmaximal, characteristic, complemented
12#21461591C211yesmaximal, characteristic, complemented
13#21461590C211yesmaximal, characteristic, complemented
14#102×#6923C211yesmaximal, characteristic, complemented
15#460×D61C211yesmaximal, characteristic
16C2×D4×#6923—21no—
17C2×D4×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×#14519846C2211yescharacteristic
20C2×#14519845C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25C2×#14519839C2211yescharacteristic
26C2×#14519839C2211yescharacteristic
27#16840721C2211yescharacteristic
28C2×#14519831C2211yescharacteristic
29C2×C8×#6923C2211yescharacteristic
30(C2×#6923)⋊Q8C2211yescharacteristic
31(C2×#6923)⋊Q8C2211yescharacteristic
32#16840714—21no—
33#16840714C2211yescharacteristic
34#16840714C2211yescharacteristic
35#16840711—21no—
36#16840711—21no—
37#16840710—21no—
38#16840710—21no—
39#16840707—21no—
40#16840706C2211yescharacteristic
41C4⋊C4×#6923C2211yescharacteristic
42C4⋊C4×#6923C2211yescharacteristic
43C4×C4⋊#6923C2211yescharacteristic
44C4×C4⋊#6923C2211yescharacteristic
45#16840698—21no—
46#16840636C2211yescharacteristic
47#16840636C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×SD16×D61C2211yescharacteristic
53C2×SD16×D61C2211yescharacteristic
54#127×D61C2211yescharacteristic
55C4×Q8×D61C2211yescharacteristic
56#16839963C411yescharacteristic, complemented
57#16839962C411yescharacteristic, complemented
58#16839961C411yescharacteristic, complemented
59#16839961C411yescharacteristic, complemented
60#16839960C411yescharacteristic, complemented
61#16839960C411yescharacteristic, complemented
62#16839959C411yescharacteristic, complemented
63C4⋊C8×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#460C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71D4×#6923—22no—
72D4×#6923—22no—
73D4×#6923—41no—
74D4×#6923—41no—
75D4×#6923—44no—
76C2×C4⋊#6923D411yescharacteristic
77C2×C4⋊#6923D411yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C22⋊#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923C2311yescharacteristic
92C2×C4×#6923C2311yescharacteristic
93#14519846—41no—
94#14519845—41no—
95#14519840—22no—
96#14519840—22no—
97#14519839—22no—
98#14519839—22no—
99#14519839—41no—
100#14519839—41no—
101#14519832—21no—
102#14519832—21no—
103#14519831—41no—
104C8×#6923—41no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4D411yescharacteristic
115(C2×#6923)⋊C4D411yescharacteristic
116C2×Q8×D61C2311yescharacteristic
117C2×D4×D61—21no—
118C2×D4×D61—21no—
119C2×D4×D61C2311yescharacteristic
120C2×D4×D61C2311yescharacteristic
121C2×#11758190C2×C411yescharacteristic, complemented
122C2×#11758190C2×C411yescharacteristic, complemented
123C2×#11758200C2×C411yescharacteristic, complemented
124C2×#11758200C2×C411yescharacteristic, complemented
125C2×#11758201C2×C411yescharacteristic, complemented
126C2×#11758201C2×C411yescharacteristic, complemented
127SD16×D61—41no—
128SD16×D61—41no—
129SD16×D61—41no—
130SD16×D61—41no—
131C2×C8×D61C2311yescharacteristic
132C2×C8×D61C2311yescharacteristic
133#14519774C2×C411yescharacteristic
134#14519773—21no—
135#14519773—21no—
136#14519773C2×C411yescharacteristic
137#14519773C2×C411yescharacteristic
138Q8×Dic61C2×C411yescharacteristic, complemented
139C4×Dic122—21no—
140C4×Dic122C2×C411yescharacteristic, complemented
141#14519742—21no—
142#14519742C2×C411yescharacteristic, complemented
143C4⋊C4×D61—21no—
144C4⋊C4×D61C2311yescharacteristic
145C42×D61—21no—
146C42×D61C2311yescharacteristic
147C4⋊#92418C2×C411yescharacteristic, complemented
148#14519706C2×C411yescharacteristic, complemented
149#14519706C2×C411yescharacteristic, complemented
150#14519699C2×C411yescharacteristic, complemented
151#14519699C2×C411yescharacteristic, complemented
152#14519698C2×C411yescharacteristic, complemented
153#14519698C2×C411yescharacteristic, complemented
154#14519697C2×C411yescharacteristic, complemented
155#14519697C2×C411yescharacteristic, complemented
156C2×SD16×C61C2×C411yescharacteristic, complemented
157C2×SD16×C61C2×C411yescharacteristic, complemented
158#127×C61C2×C411yescharacteristic
159C4×Q8×C61C2×C411yescharacteristic, complemented
160C4⋊C8×C61C2×C411yescharacteristic, complemented
161#102×C61C2×C411yescharacteristic, complemented
162#102×C61C2×C411yescharacteristic, complemented
163C23×D61—21no—
164C23×D61—21no—
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923—21no—
169C22×#6923—42no—
170C22×#6923—42no—
171C22×#6923—42no—
172C22×#6923—42no—
173C22×#6923—81no—
174C22×#6923—81no—
175C22×#6923C2×D411yescharacteristic
176C22×#6923C2×D411yescharacteristic
177C22×#6923C2×D411yescharacteristic
178C22×#6923C2×D411yescharacteristic
179C2×Q8×C61C22×C411yescharacteristic
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61C22×C411yescharacteristic
183C2×D4×C61C22×C411yescharacteristic
184C2×C22⋊D61—21no—
185C2×C22⋊D61—21no—
186C2×C22⋊D61—21no—
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190Q8×D61—21no—
191Q8×D61—21no—
192Q8×D61—21no—
193Q8×D61—21no—
194D4×D61—21no—
195D4×D61—21no—
196D4×D61—21no—
197D4×D61—21no—
198D4×D61—21no—
199D4×D61—21no—
200D4×D61—21no—
201D4×D61—21no—
202D4×D61—42no—
203D4×D61—42no—
204D4×D61—81no—
205D4×D61—81no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244C22×C411yescharacteristic
209C2×D244C22×C411yescharacteristic
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2411yescharacteristic
215C2×Dic122—21no—
216C2×Dic122C22×C411yescharacteristic
217C22⋊#6923—42no—
218C22⋊#6923—42no—
219C22⋊#6923—42no—
220C22⋊#6923—42no—
221C22⋊#6923—81no—
222C22⋊#6923—81no—
223C2×#92420—21no—
224C2×#92420—21no—
225C4⋊#6923—22no—
226C4⋊#6923—21no—
227C4⋊#6923—21no—
228C4⋊#6923—21no—
229C4⋊#6923—21no—
230C4⋊#6923—21no—
231C4⋊#6923—21no—
232C4⋊#6923—21no—
233C4⋊#6923—41no—
234C4⋊#6923#4112yes—
235C4×#6923—21no—
236C4×#6923—21no—
237C4×#6923—21no—
238C4×#6923—21no—
239C4×#6923—42no—
240C4×#6923—42no—
241C4×#6923—42no—
242D61⋊C8—21no—
243D61⋊C8—21no—
244D61⋊C8—21no—
245D61⋊C8#4112yes—
246SD16×C61—41no—
247SD16×C61—41no—
248C2×C8×C61C22×C411yescharacteristic
249C2×C8×C61C22×C411yescharacteristic
250C4⋊C4×C61—21no—
251C4⋊C4×C61C22×C411yescharacteristic
252C42×C61—21no—
253C42×C61C22×C411yescharacteristic
254#11758201—41no—
255#11758201—41no—
256#11758200—41no—
257#11758200—41no—
258C4⋊Dic61—21no—
259C4⋊Dic61C22×C411yescharacteristic
260#11758196—21no—
261#11758196—21no—
262#11758196—21no—
263C4×Dic61—21no—
264C4×Dic61—21no—
265C4×Dic61—21no—
266C4×Dic61C22×C411yescharacteristic
267C4×Dic61#4111yescharacteristic
268C4×Dic61#4111yescharacteristic
269C2×#92418C22×C411yescharacteristic
270C2×#92418C22×C411yescharacteristic
271#11758190—41no—
272#11758190—41no—
273C8×D61—21no—
274C8×D61—21no—
275C8×D61—21no—
276C8×D61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61C22×D411yescharacteristic
294C2×#6923—21no—
295C2×#6923—21no—
296C2×#6923—21no—
297C2×#6923—21no—
298C2×#6923—21no—
299C2×#6923—22no—
300C2×#6923—21no—
301C2×#6923—21no—
302C2×#6923—21no—
303C2×#6923—21no—
304C2×#6923—21no—
305C2×#6923—21no—
306C2×#6923—41no—
307C2×#6923—41no—
308C2×#6923—41no—
309C2×#6923—41no—
310C2×#6923—41no—
311C2×#6923—41no—
312C2×#6923—41no—
313C2×#6923—41no—
314C2×#6923—41no—
315C2×#6923—41no—
316C2×#6923—41no—
317C2×#6923—84no—
318C2×#6923—84no—
319C2×#6923AGL(1,ℤ/8)12yes—
320Q8×C61—21no—
321Q8×C61—21no—
322D4×C61—21no—
323D4×C61—21no—
324D4×C61—21no—
325D4×C61—21no—
326D4×C61—42no—
327D4×C61—81no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61C4×D411yescharacteristic
331C2×C4×C61C4×D411yescharacteristic
332C2×C4×C61C23×C411yescharacteristic
333C22⋊D61—42no—
334C22⋊D61—42no—
335C22⋊D61—41no—
336C22⋊D61—41no—
337C22⋊D61—41no—
338C22⋊D61—41no—
339C22⋊D61—81no—
340C22⋊D61—81no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61C4×D411yescharacteristic
344C2×Dic61C4×D411yescharacteristic
345C2×Dic61C2×#4111yescharacteristic
346D244—21no—
347D244—21no—
348D244—21no—
349D244—21no—
350D244—42no—
351D244—81no—
352C4×D61—21no—
353C4×D61—21no—
354C4×D61—21no—
355C4×D61—21no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—41no—
360C4×D61C2×#4111yescharacteristic
361C4×D61C2×#4111yescharacteristic
362C4×D61H(5,𝔽2)11yescharacteristic
363C4×D61H(5,𝔽2)11yescharacteristic
364Dic122—21no—
365Dic122—21no—
366Dic122—41no—
367Dic122—41no—
368#92420—22no—
369#92420—41no—
370C8×C61—21no—
371C8×C61—21no—
372#92418—21no—
373#92418—21no—
374#23106—611nomaximal, Sylow
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61C2×C4×D411yescharacteristic
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—81no—
389C2×D61—81no—
390C2×D61—81no—
391C2×D61—81no—
392C2×D61—81no—
393C2×D61—81no—
394C2×D61—81no—
395C2×D61—81no—
396C2×D61#54611yescharacteristic
397C2×D61#55011yescharacteristic
398C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
399C2×D61#57511yescharacteristic
400C2×D61#57711yescharacteristic
401C2×D61#57711yescharacteristic
402#6923—22no—
403#6923—41no—
404#6923—42no—
405#6923—41no—
406#6923—41no—
407#6923—81no—
408#6923—81no—
409#6923—81no—
410C4×C61—21no—
411C4×C61—21no—
412C4×C61—41no—
413C4×C61—41no—
414C4×C61C4×#4111yescharacteristic
415C4×C61#51811yescharacteristic
416Dic61—21no—
417Dic61—21no—
418Dic61—41no—
419Dic61—41no—
420Dic61#55311yescharacteristic
421Dic61#55511yescharacteristic
422C2×#460—611no—
423#2366—611no—
424#2356—611no—
425#1973—611no—
426#1968—611no—
427#1961—611no—
428#1949—611no—
429#1926—611no—
430#1925—611no—
431#1877—611no—
432#1877—611no—
433#1771—611no—
434#1763—611no—
435#1762—611no—
436C4×#102—611no—
437C2×C61—81no—
438C2×C61—81no—
439C2×C61#236311yescharacteristic
440C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
441C2×C61#294911yescharacteristic
442D61—81no—
443D61—81no—
444D61#331011yescharacteristic
445D61#331711yescharacteristic
446D61#339711yescharacteristic
447D61#340111yescharacteristic
448C22×SD16—611no—
449C22×SD16—611no—
450C2×#127—611no—
451C2×C4×Q8—611no—
452C2×C4×D4—611no—
453C2×C4×D4—611no—
454C2×C4×D4—1221no—
455#460—611no—
456#460—611no—
457#460—611no—
458#460—611no—
459#460—611no—
460#460—611no—
461#460—611no—
462#460#692311yescharacteristic, complemented
463C2×#107—611no—
464C2×#106—611no—
465C2×C4⋊C8—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×#102—611no—
471C2×#102—611no—
472C2×#102—611no—
473C2×#102—611no—
474C2×#97—611no—
475C2×#97—611no—
476C2×C4×C8—611no—
477#391—611no—
478#391—611no—
479#390—611no—
480#390—611no—
481#390—1221no—
482#387—1221no—
483#387—1221no—
484#386—1221no—
485#386—1221no—
486#383—1221no—
487#382—611no—
488C4×C4⋊C4—611no—
489C4×C4⋊C4—611no—
490C4×C4⋊C4—611no—
491C4×C4⋊C4—611no—
492#376—1221no—
493#340—611no—
494#340—611no—
495#340—611no—
496#340—611no—
497#336—611no—
498#336—611no—
499C61#2310611yescharacteristic, complemented, Sylow
500C22×Q8—611no—
501C22×D4—611no—
502C22×D4—611no—
503C22×D4—1221no—
504C22×D4—1221no—
505C23×C4—1221no—
506C23×C4—1221no—
507C2×SD16—611no—
508C2×SD16—611no—
509C2×SD16—611no—
510C2×SD16—611no—
511C2×SD16—611no—
512C2×SD16—611no—
513C2×SD16—2441no—
514C2×SD16—2441no—
515C2×SD16—2441no—
516C2×SD16—2441no—
517C2×SD16C2×#692311yescharacteristic, complemented
518C2×SD16C2×#692311yescharacteristic, complemented
519C22×C8—611no—
520C22×C8—611no—
521C22×C8—611no—
522C22×C8—611no—
523#127—611no—
524#127—611no—
525#127—611no—
526#127—1221no—
527#127—1221no—
528#127C2×#692311yescharacteristic
529C4×Q8—611no—
530C4×Q8—611no—
531C4×Q8—611no—
532C4×Q8—1221no—
533C4×Q8—1221no—
534C4×Q8C2×#692311yescharacteristic, complemented
535C4×D4—1222no—
536C4×D4—1222no—
537C4×D4—2441no—
538C4×D4—2441no—
539C4×D4—2444no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—611no—
547C2×C4⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C42—611no—
555C2×C42—611no—
556C2×C42—611no—
557C2×C42—1221no—
558C2×C42—1221no—
559C2×C42—1221no—
560C2×C42—1221no—
561#107—2441no—
562#106—2441no—
563C4⋊C8—611no—
564C4⋊C8—611no—
565C4⋊C8—611no—
566C4⋊C8C2×#692311yescharacteristic, complemented
567#103—1222no—
568#103—1222no—
569#102—611no—
570#102—611no—
571#102—611no—
572#102—611no—
573#102—611no—
574#102—611no—
575#102—1222no—
576#102—1222no—
577#102—2441no—
578#102—2441no—
579#102C2×#692311yescharacteristic, complemented
580#102C2×#692311yescharacteristic, complemented
581#97—1221no—
582#97—1221no—
583#97—2441no—
584C4×C8—2441no—
585#95—611no—
586#95—611no—
587#95—1221no—
588#95—1221no—
589#95—1221no—
590#95—1221no—
591#95—1221no—
592#95—1221no—
593#95—1221no—
594#95—1221no—
595#95—1221no—
596C24—1221no—
597C24—1221no—
598C2×Q8—611no—
599C2×Q8—1221no—
600C2×Q8—1221no—
601C2×Q8—1221no—
602C2×Q8—1221no—
603C2×Q8—1221no—
604C2×Q8C22×#692311yescharacteristic
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—611no—
608C2×D4—611no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—1221no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—1221no—
625C2×D4—4881no—
626C2×D4—4881no—
627C2×D4—2442no—
628C2×D4—2442no—
629C2×D4C22×#692311yescharacteristic
630C2×D4C22×#692311yescharacteristic
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—4881no—
645C22×C4—4881no—
646C22×C4—2442no—
647C22×C4—2442no—
648C22×C4—2442no—
649C22×C4—2442no—
650SD16—41no—
651SD16—41no—
652SD16—2441no—
653SD16—2441no—
654SD16—2441no—
655SD16—2441no—
656SD16—2441no—
657SD16—2441no—
658C2×C8—612no—
659C2×C8—611no—
660C2×C8—611no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8—1221no—
668C2×C8—1221no—
669C2×C8—1221no—
670C2×C8C22×#692311yescharacteristic
671C2×C8C22×#692311yescharacteristic
672C4⋊C4—21no—
673C4⋊C4—612no—
674C4⋊C4—611no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1222no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4—1221no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—1221no—
686C4⋊C4—1221no—
687C4⋊C4—2441no—
688C4⋊C4C22×#692311yescharacteristic
689C22⋊C4—4881no—
690C22⋊C4—4881no—
691C22⋊C4—2442no—
692C22⋊C4—2442no—
693C22⋊C4—2442no—
694C22⋊C4—2442no—
695C42—21no—
696C42—611no—
697C42—611no—
698C42—611no—
699C42—1221no—
700C42—1221no—
701C42—1221no—
702C42—1221no—
703C42—1221no—
704C42—1221no—
705C42—1221no—
706C42—2442no—
707C42—2442no—
708C42—2442no—
709C42C22×#692311yescharacteristic
710C23—21no—
711C23—21no—
712C23—611no—
713C23—1221no—
714C23—1221no—
715C23—2441no—
716C23—2441no—
717C23—2441no—
718C23—2441no—
719C23—2441no—
720C23—2441no—
721C23—2441no—
722C23—2441no—
723C23—2441no—
724C23—2441no—
725C23—2441no—
726C23—2441no—
727Q8—21no—
728Q8—21no—
729Q8—1221no—
730Q8—1221no—
731Q8—2441no—
732Q8—2441no—
733D4—21no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—42no—
738D4—81no—
739D4—1221no—
740D4—1221no—
741D4—1221no—
742D4—1221no—
743D4—4881no—
744D4—4881no—
745D4—4881no—
746D4—2442no—
747D4—2441no—
748D4—2441no—
749D4—2441no—
750D4—2441no—
751D4—2442no—
752D4—2442no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—611no—
756C2×C4—611no—
757C2×C4—611no—
758C2×C4—611no—
759C2×C4—611no—
760C2×C4—612no—
761C2×C4—611no—
762C2×C4—611no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1221no—
768C2×C4—1221no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1222no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—4884no—
782C2×C4—4884no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4D4×#692311yescharacteristic
799C2×C4D4×#692311yescharacteristic
800C2×C4C23×#692311yescharacteristic
801C8—21no—
802C8—21no—
803C8—1222no—
804C8—1221no—
805C8—1221no—
806C8—2441no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—611no—
814C22—611no—
815C22—611no—
816C22—611no—
817C22—611no—
818C22—611no—
819C22—4881no—
820C22—4881no—
821C22—4881no—
822C22—4881no—
823C22—4881no—
824C22—4881no—
825C22—4881no—
826C22—4881no—
827C22—2441no—
828C22—2441no—
829C22—2441no—
830C22—2441no—
831C22—2441no—
832C22—2441no—
833C22C2×D4×#692311yescharacteristic
834C4—21no—
835C4—21no—
836C4—41no—
837C4—41no—
838C4—611no—
839C4—611no—
840C4—1222no—
841C4—1221no—
842C4—1221no—
843C4—4881no—
844C4—4881no—
845C4—4881no—
846C4—2441no—
847C4—2441no—
848C4—2441no—
849C4—2442no—
850C4—2441no—
851C4—2441no—
852C4#41×#692311yescharacteristic
853C4#1684082911yescharacteristic
854C2—81no—
855C2—81no—
856C2—611no—
857C2—611no—
858C2—611no—
859C2—611no—
860C2—4881no—
861C2—4881no—
862C2#2146234611yescharacteristic
863C2AGL(1,ℤ/8)×#692311yescharacteristic
864C2#2146257911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#460C4
socleC22×C61C2×C4×D4
prime radical#127×D61C22
cosocleC2×C4×D61C24
hypercenter#460#6923
hypocenterC61#23106
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #21462339C2semidirect
3. #21461969C2semidirect
4. #21461964C2semidirect
6. #21461932C2semidirect
7. #21461897C2semidirect
8. #21461896C2semidirect
9. #21461812C2semidirect
10. #21461812C2semidirect
11. #21461620C2semidirect
12. #21461591C2semidirect
13. #21461590C2semidirect
14. #102×#6923C2semidirect
56. #16839963C4semidirect
57. #16839962C4semidirect
58. #16839961C4semidirect
59. #16839961C4semidirect
60. #16839960C4semidirect
61. #16839960C4semidirect
62. #16839959C4semidirect
66. C61×#460C4semidirect
121. C2×#11758190C2×C4semidirect
122. C2×#11758190C2×C4semidirect
123. C2×#11758200C2×C4semidirect
124. C2×#11758200C2×C4semidirect
125. C2×#11758201C2×C4semidirect
126. C2×#11758201C2×C4semidirect
138. Q8×Dic61C2×C4semidirect
140. C4×Dic122C2×C4semidirect
142. #14519742C2×C4semidirect
147. C4⋊#92418C2×C4semidirect
148. #14519706C2×C4semidirect
149. #14519706C2×C4semidirect
150. #14519699C2×C4semidirect
151. #14519699C2×C4semidirect
152. #14519698C2×C4semidirect
153. #14519698C2×C4semidirect
154. #14519697C2×C4semidirect
155. #14519697C2×C4semidirect
156. C2×SD16×C61C2×C4semidirect
157. C2×SD16×C61C2×C4semidirect
159. C4×Q8×C61C2×C4semidirect
160. C4⋊C8×C61C2×C4semidirect
161. #102×C61C2×C4semidirect
162. #102×C61C2×C4semidirect
462. #460#6923semidirect
499. C61#23106semidirect
517. C2×SD16C2×#6923semidirect
518. C2×SD16C2×#6923semidirect
534. C4×Q8C2×#6923semidirect
566. C4⋊C8C2×#6923semidirect
579. #102C2×#6923semidirect
580. #102C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623492
#214623392
#214619692
#214619642
#214619512
#214619322
#214618972
#214618962
#214618122
#214616202
#214615912
#214615902
#102×#69232
#460×D612
#2310661