Finite Group Databasebeta

← #30622588

Subgroups — #30622588

Order 15616.

954 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462345C211yesmaximal, characteristic, complemented
2#21462344C211yesmaximal, characteristic
3#21461910C211yesmaximal, characteristic, complemented
4#21461909C211yesmaximal, characteristic, complemented
5#21461883C211yesmaximal, characteristic, complemented
6#21461880C211yesmaximal, characteristic, complemented
7#21461815C211yesmaximal, characteristic, complemented
8#21461812C211yesmaximal, characteristic, complemented
9#21461807C211yesmaximal, characteristic
10#21461804C211yesmaximal, characteristic, complemented
11#21461590C211yesmaximal, characteristic, complemented
12#103×#6923C211yesmaximal, characteristic, complemented
13#21461559C211yesmaximal, characteristic, complemented
14#21461507C211yesmaximal, characteristic, complemented
15#468×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×D4×#6923—21no—
18C2×D4×#6923C2211yescharacteristic
19C2×#14519856C2211yescharacteristic
20C22×C4⋊#6923C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25D61⋊(C22⋊C8)C2211yescharacteristic
26C2×#14519831C2211yescharacteristic
27C2×C8×#6923C2211yescharacteristic
28(C2×#6923)⋊Q8C2211yescharacteristic
29#16840714C2211yescharacteristic
30#16840713C2211yescharacteristic
31#16840713C2211yescharacteristic
32#16840712—21no—
33#16840712—21no—
34#16840712—21no—
35#16840711—21no—
36#16840710—21no—
37#16840709—21no—
38C4⋊C4×#6923—21no—
39C4⋊C4×#6923C2211yescharacteristic
40C4⋊C4×#6923C2211yescharacteristic
41C4×C22⋊#6923C2211yescharacteristic
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840636C2211yescharacteristic
45#16840636C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×SD16×D61C2211yescharacteristic
53C2×M16×D61C2211yescharacteristic
54C22⋊Q8×D61C2211yescharacteristic
55#121×D61C2211yescharacteristic
56#16840011C411yescharacteristic, complemented
57#16840010C411yescharacteristic, complemented
58#16840009C411yescharacteristic, complemented
59#16840008C411yescharacteristic, complemented
60#16840007C411yescharacteristic, complemented
61#16840006C411yescharacteristic, complemented
62#16840005C411yescharacteristic, complemented
63#107×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#468C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71Q8×#6923—22no—
72Q8×#6923—41no—
73D4×#6923—22no—
74D4×#6923—41no—
75D4×#6923—44no—
76#14519856—22no—
77#14519856—41no—
78C2×C4⋊#6923—22no—
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—41no—
84C2×C4⋊#6923C2311yescharacteristic
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C22⋊#6923—21no—
89C2×C22⋊#6923—21no—
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923D411yescharacteristic
93C2×C22⋊#6923D411yescharacteristic
94C2×C4×#6923—21no—
95C2×C4×#6923—21no—
96C2×C4×#6923—21no—
97C2×C4×#6923—21no—
98C2×C4×#6923C2311yescharacteristic
99C2×C4×#6923C2311yescharacteristic
100#14519840—22no—
101#14519840—41no—
102#14519839—22no—
103#14519839—41no—
104#14519834—21no—
105C22⋊#92420—21no—
106#14519831—41no—
107C8×#6923—41no—
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×D61C2311yescharacteristic
119C22×C4×D61C2311yescharacteristic
120C2×#11758190C2×C411yescharacteristic, complemented
121C2×#11758200C2×C411yescharacteristic, complemented
122C2×#11758201C2×C411yescharacteristic, complemented
123SD16×D61—41no—
124SD16×D61—41no—
125C2×#11758194C2×C411yescharacteristic, complemented
126C2×#11758189C2×C411yescharacteristic, complemented
127C2×#11758189C2×C411yescharacteristic, complemented
128M16×D61—41no—
129M16×D61—41no—
130C2×C8×D61C2311yescharacteristic
131C2×C8×D61C2311yescharacteristic
132#14519757C2×C411yescharacteristic, complemented
133#14519756C2×C411yescharacteristic, complemented
134#14519755—21no—
135#14519754—21no—
136#14519753C2×C411yescharacteristic, complemented
137#14519752C2×C411yescharacteristic
138#14519751C2×C411yescharacteristic
139#14519750—21no—
140#14519749—21no—
141#14519748C2×C411yescharacteristic
142C4⋊C4×D61—21no—
143C4⋊C4×D61C2311yescharacteristic
144C4⋊C4×D61C2311yescharacteristic
145C22⋊C4×D61—21no—
146C22⋊C4×D61—21no—
147#14519711C2×C411yescharacteristic, complemented
148#14519710C2×C411yescharacteristic, complemented
149#14519710C2×C411yescharacteristic, complemented
150#14519702C2×C411yescharacteristic, complemented
151#14519701C2×C411yescharacteristic, complemented
152#14519700C2×C411yescharacteristic, complemented
153#14519699C2×C411yescharacteristic, complemented
154#14519698C2×C411yescharacteristic, complemented
155#14519697C2×C411yescharacteristic, complemented
156C2×SD16×C61C2×C411yescharacteristic, complemented
157C2×M16×C61C2×C411yescharacteristic, complemented
158C22⋊Q8×C61C2×C411yescharacteristic, complemented
159#121×C61C2×C411yescharacteristic
160#107×C61C2×C411yescharacteristic, complemented
161#103×C61C2×C411yescharacteristic, complemented
162#102×C61C2×C411yescharacteristic, complemented
163C23×D61—21no—
164C23×D61C2×D411yescharacteristic
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×C61C22×C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C2×C22⋊D61—21no—
184C2×C22⋊D61—21no—
185C2×C22⋊D61—21no—
186C22×Dic61#4111yescharacteristic
187Q8×D61—21no—
188Q8×D61—21no—
189Q8×D61—21no—
190Q8×D61—21no—
191D4×D61—21no—
192D4×D61—21no—
193D4×D61—21no—
194D4×D61—21no—
195D4×D61—42no—
196D4×D61—42no—
197C2×D244—21no—
198C2×D244C22×C411yescharacteristic
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61C22×C411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61#4111yescharacteristic
209C2×C4×D61C2411yescharacteristic
210C2×Dic122—21no—
211C2×Dic122C22×C411yescharacteristic
212C22⋊#6923—22no—
213C22⋊#6923—41no—
214C22⋊#6923—42no—
215C22⋊#6923—42no—
216C22⋊#6923—42no—
217C22⋊#6923—81no—
218C2×#92420—21no—
219C2×#92420—21no—
220C4⋊#6923—21no—
221C4⋊#6923—21no—
222C4⋊#6923—21no—
223C4⋊#6923—21no—
224C4⋊#6923—21no—
225C4⋊#6923—21no—
226C4⋊#6923—42no—
227C4⋊#6923—42no—
228C4⋊#6923—42no—
229C4⋊#6923—42no—
230C4⋊#6923#4112yes—
231C4⋊#6923#4112yes—
232C4×#6923—21no—
233C4×#6923—21no—
234C4×#6923—21no—
235C4×#6923—21no—
236C4×#6923—42no—
237C4×#6923—42no—
238C4×#6923—42no—
239C4×#6923—42no—
240D61⋊C8—21no—
241D61⋊C8—21no—
242D61⋊C8—21no—
243D61⋊C8—21no—
244SD16×C61—41no—
245M16×C61—41no—
246C2×C8×C61C22×C411yescharacteristic
247C2×C8×C61C22×C411yescharacteristic
248C4⋊C4×C61—21no—
249C4⋊C4×C61C22×C411yescharacteristic
250C4⋊C4×C61C22×C411yescharacteristic
251C22⋊C4×C61—21no—
252C22⋊C4×C61—21no—
253C22⋊Dic61—21no—
254C22⋊Dic61—21no—
255#11758201—41no—
256#11758200—41no—
257#11758198—21no—
258#11758198—21no—
259#11758198—21no—
260#11758198—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61C22×C411yescharacteristic
263C4⋊Dic61C22×C411yescharacteristic
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758194—41no—
269C2×#92418C22×C411yescharacteristic
270C2×#92418C22×C411yescharacteristic
271#11758190—41no—
272#11758189—41no—
273#11758189—41no—
274C8×D61—21no—
275C8×D61—21no—
276C8×D61—21no—
277C8×D61—21no—
278C23×C61—21no—
279C23×C61C4×D411yescharacteristic
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61C4×D411yescharacteristic
294C22×D61C22×D411yescharacteristic
295C2×#6923—21no—
296C2×#6923—21no—
297C2×#6923—21no—
298C2×#6923—21no—
299C2×#6923—21no—
300C2×#6923—22no—
301C2×#6923—22no—
302C2×#6923—21no—
303C2×#6923—21no—
304C2×#6923—21no—
305C2×#6923—21no—
306C2×#6923—21no—
307C2×#6923—21no—
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—41no—
318C2×#6923—84no—
319C2×#6923—84no—
320C2×#6923AGL(1,ℤ/8)12yes—
321Q8×C61—21no—
322Q8×C61—21no—
323D4×C61—21no—
324D4×C61—21no—
325D4×C61—42no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61C4×D411yescharacteristic
332C2×C4×C61C23×C411yescharacteristic
333C22⋊D61—42no—
334C22⋊D61—42no—
335C22⋊D61—41no—
336C22⋊D61—41no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61C4×D411yescharacteristic
343C2×Dic61C2×#4111yescharacteristic
344D244—21no—
345D244—21no—
346D244—42no—
347C4×D61—21no—
348C4×D61—21no—
349C4×D61—21no—
350C4×D61—21no—
351C4×D61—21no—
352C4×D61—21no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61C2×#4111yescharacteristic
360C4×D61C2×#4111yescharacteristic
361C4×D61H(5,𝔽2)11yescharacteristic
362C4×D61H(5,𝔽2)11yescharacteristic
363Dic122—21no—
364Dic122—21no—
365Dic122—41no—
366Dic122—41no—
367#92420—41no—
368#92420—41no—
369C8×C61—21no—
370C8×C61—21no—
371#92418—21no—
372#92418—21no—
373#23141—611nomaximal, Sylow
374C22×C61—21no—
375C22×C61—21no—
376C22×C61—21no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61C2×C4×D411yescharacteristic
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—21no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—81no—
392C2×D61—81no—
393C2×D61—81no—
394C2×D61—81no—
395C2×D61#54611yescharacteristic
396C2×D61#54611yescharacteristic
397C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
398C2×D61#57511yescharacteristic
399C2×D61#57711yescharacteristic
400C2×D61#57811yescharacteristic
401#6923—22no—
402#6923—41no—
403#6923—42no—
404#6923—41no—
405#6923—42no—
406#6923—41no—
407#6923—81no—
408#6923—81no—
409C4×C61—21no—
410C4×C61—41no—
411C4×C61—41no—
412C4×C61—41no—
413C4×C61C4×#4111yescharacteristic
414C4×C61#51811yescharacteristic
415Dic61—21no—
416Dic61—41no—
417Dic61—41no—
418Dic61—41no—
419Dic61#55311yescharacteristic
420Dic61#55311yescharacteristic
421C2×#468—611no—
422#2362—611no—
423#2361—611no—
424#1935—611no—
425#1934—611no—
426#1921—611no—
427#1918—611no—
428#1880—611no—
429#1877—611no—
430#1875—611no—
431#1872—611no—
432#1762—611no—
433C4×#103—611no—
434#1753—611no—
435#1736—611no—
436C2×C61—41no—
437C2×C61—81no—
438C2×C61#236411yescharacteristic
439C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
440C2×C61#294711yescharacteristic
441D61—41no—
442D61—81no—
443D61#330711yescharacteristic
444D61#330811yescharacteristic
445D61#332411yescharacteristic
446D61#332711yescharacteristic
447C22×SD16—611no—
448C22×M16—611no—
449C2×C22⋊Q8—611no—
450C2×#121—611no—
451C2×C4×Q8—611no—
452C2×C4×D4—611no—
453C2×C4×D4—1221no—
454C2×#117—611no—
455C22×C4⋊C4—611no—
456#468—611no—
457#468—611no—
458#468—611no—
459#468—611no—
460#468—611no—
461#468—611no—
462#468—611no—
463#468#692311yescharacteristic, complemented
464C2×#107—611no—
465C2×#103—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×#102—611no—
471C2×C22⋊C8—611no—
472C2×#97—611no—
473C2×C4×C8—611no—
474#391—611no—
475#390—611no—
476#389—611no—
477#389—611no—
478#388—1221no—
479#388—1221no—
480#388—1221no—
481#387—1221no—
482#386—1221no—
483#385—1221no—
484C4×C4⋊C4—611no—
485C4×C4⋊C4—611no—
486C4×C4⋊C4—1221no—
487C4×C22⋊C4—611no—
488#340—611no—
489#340—611no—
490#340—611no—
491#340—611no—
492#340—611no—
493#340—611no—
494#340—611no—
495#340—611no—
496#336—611no—
497#336—611no—
498C61#2314111yescharacteristic, complemented, Sylow
499C22×Q8—611no—
500C22×D4—611no—
501C22×D4—1221no—
502C23×C4—611no—
503C23×C4—1221no—
504C23×C4—1221no—
505C2×SD16—611no—
506C2×SD16—611no—
507C2×SD16—611no—
508C2×SD16—2441no—
509C2×SD16—2441no—
510C2×SD16C2×#692311yescharacteristic, complemented
511C2×M16—611no—
512C2×M16—611no—
513C2×M16—611no—
514C2×M16—2441no—
515C2×M16—2441no—
516C2×M16C2×#692311yescharacteristic, complemented
517C22×C8—611no—
518C22×C8—611no—
519C22×C8—611no—
520C22×C8—611no—
521C22⋊Q8—611no—
522C22⋊Q8—611no—
523C22⋊Q8—611no—
524C22⋊Q8—1221no—
525C22⋊Q8—1221no—
526C22⋊Q8C2×#692311yescharacteristic, complemented
527#121—611no—
528#121—611no—
529#121—611no—
530#121—1221no—
531#121—1221no—
532#121C2×#692311yescharacteristic
533C4×Q8—1222no—
534C4×Q8—2441no—
535C4×D4—1222no—
536C4×D4—2441no—
537C4×D4—2444no—
538#117—1222no—
539#117—2441no—
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—1221no—
547C2×C4⋊C4—1222no—
548C2×C4⋊C4—1221no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—2441no—
553C2×C22⋊C4—611no—
554C2×C22⋊C4—611no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C42—611no—
562C2×C42—611no—
563C2×C42—1221no—
564C2×C42—1221no—
565C2×C42—1221no—
566C2×C42—1221no—
567#107—611no—
568#107—611no—
569#107—611no—
570#107C2×#692311yescharacteristic, complemented
571#103—611no—
572#103—611no—
573#103—611no—
574#103—1222no—
575#103—2441no—
576#103C2×#692311yescharacteristic, complemented
577#102—611no—
578#102—611no—
579#102—611no—
580#102—1222no—
581#102—2441no—
582#102C2×#692311yescharacteristic, complemented
583C22⋊C8—1221no—
584C22⋊C8—1221no—
585#97—2441no—
586C4×C8—2441no—
587#95—611no—
588#95—611no—
589#95—1221no—
590#95—1221no—
591#95—1221no—
592#95—1221no—
593#95—1221no—
594#95—1221no—
595C24—611no—
596C24—1221no—
597C2×Q8—611no—
598C2×Q8—1221no—
599C2×Q8—1221no—
600C2×Q8—1221no—
601C2×Q8—1221no—
602C2×Q8—1221no—
603C2×Q8C22×#692311yescharacteristic
604C2×D4—21no—
605C2×D4—611no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—2442no—
615C2×D4—2442no—
616C2×D4C22×#692311yescharacteristic
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—4881no—
638C22×C4—4881no—
639C22×C4—2442no—
640C22×C4—2442no—
641C22×C4—2442no—
642C22×C4—2442no—
643C22×C4C22×#692311yescharacteristic
644SD16—41no—
645SD16—2441no—
646SD16—2441no—
647SD16—2441no—
648M16—41no—
649M16—2441no—
650M16—2441no—
651M16—2441no—
652C2×C8—611no—
653C2×C8—611no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8C22×#692311yescharacteristic
665C2×C8C22×#692311yescharacteristic
666C4⋊C4—21no—
667C4⋊C4—612no—
668C4⋊C4—612no—
669C4⋊C4—611no—
670C4⋊C4—611no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4—2442no—
683C4⋊C4—2442no—
684C4⋊C4—2442no—
685C4⋊C4—2442no—
686C4⋊C4C22×#692311yescharacteristic
687C4⋊C4C22×#692311yescharacteristic
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—1221no—
691C22⋊C4—1221no—
692C22⋊C4—1221no—
693C22⋊C4—1221no—
694C22⋊C4—1222no—
695C22⋊C4—1221no—
696C22⋊C4—1221no—
697C22⋊C4—4881no—
698C22⋊C4—2442no—
699C22⋊C4—2441no—
700C22⋊C4—2442no—
701C22⋊C4—2442no—
702C42—1221no—
703C42—1221no—
704C42—1221no—
705C42—1221no—
706C42—2442no—
707C42—2442no—
708C42—2442no—
709C42—2442no—
710C23—21no—
711C23—611no—
712C23—611no—
713C23—1221no—
714C23—1221no—
715C23—1221no—
716C23—1221no—
717C23—1221no—
718C23—1221no—
719C23—1221no—
720C23—2441no—
721C23—2441no—
722C23—2441no—
723C23—2441no—
724C23—2441no—
725C23—2441no—
726C23D4×#692311yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—1221no—
730Q8—1221no—
731Q8—2441no—
732Q8—2441no—
733D4—21no—
734D4—21no—
735D4—42no—
736D4—1221no—
737D4—1221no—
738D4—2442no—
739D4—2441no—
740D4—2441no—
741D4—2442no—
742D4—2442no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—611no—
749C2×C4—611no—
750C2×C4—611no—
751C2×C4—611no—
752C2×C4—611no—
753C2×C4—612no—
754C2×C4—611no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1221no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1221no—
768C2×C4—1222no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1222no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—4884no—
780C2×C4—4884no—
781C2×C4—2441no—
782C2×C4—2441no—
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×C4D4×#692311yescharacteristic
798C2×C4C23×#692311yescharacteristic
799C8—21no—
800C8—21no—
801C8—1221no—
802C8—1221no—
803C8—2441no—
804C8—2441no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—611no—
812C22—611no—
813C22—611no—
814C22—611no—
815C22—611no—
816C22—611no—
817C22—1221no—
818C22—1221no—
819C22—1221no—
820C22—4881no—
821C22—4881no—
822C22—4881no—
823C22—4881no—
824C22—2441no—
825C22—2441no—
826C22—2441no—
827C22—2441no—
828C22—2441no—
829C22—2441no—
830C22—2441no—
831C22C2×D4×#692311yescharacteristic
832C4—21no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—611no—
837C4—611no—
838C4—1222no—
839C4—1221no—
840C4—4881no—
841C4—4881no—
842C4—2441no—
843C4—2441no—
844C4—2441no—
845C4—2442no—
846C4—2442no—
847C4—2441no—
848C4—2441no—
849C4—2441no—
850C4#41×#692311yescharacteristic
851C4#1684082911yescharacteristic
852C2—41no—
853C2—81no—
854C2—611no—
855C2—611no—
856C2—611no—
857C2—611no—
858C2—4881no—
859C2—2441no—
860C2#2146234711yescharacteristic
861C2AGL(1,ℤ/8)×#692311yescharacteristic
862C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#468C4
socleC22×C61C2×C4×D4
prime radical#121×D61C22
cosocleC2×C4×D61C24
hypercenter#468#6923
hypocenterC61#23141
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #21462345C2semidirect
3. #21461910C2semidirect
4. #21461909C2semidirect
5. #21461883C2semidirect
6. #21461880C2semidirect
7. #21461815C2semidirect
8. #21461812C2semidirect
10. #21461804C2semidirect
11. #21461590C2semidirect
12. #103×#6923C2semidirect
13. #21461559C2semidirect
14. #21461507C2semidirect
56. #16840011C4semidirect
57. #16840010C4semidirect
58. #16840009C4semidirect
59. #16840008C4semidirect
60. #16840007C4semidirect
61. #16840006C4semidirect
62. #16840005C4semidirect
66. C61×#468C4semidirect
120. C2×#11758190C2×C4semidirect
121. C2×#11758200C2×C4semidirect
122. C2×#11758201C2×C4semidirect
125. C2×#11758194C2×C4semidirect
126. C2×#11758189C2×C4semidirect
127. C2×#11758189C2×C4semidirect
132. #14519757C2×C4semidirect
133. #14519756C2×C4semidirect
136. #14519753C2×C4semidirect
147. #14519711C2×C4semidirect
148. #14519710C2×C4semidirect
149. #14519710C2×C4semidirect
150. #14519702C2×C4semidirect
151. #14519701C2×C4semidirect
152. #14519700C2×C4semidirect
153. #14519699C2×C4semidirect
154. #14519698C2×C4semidirect
155. #14519697C2×C4semidirect
156. C2×SD16×C61C2×C4semidirect
157. C2×M16×C61C2×C4semidirect
158. C22⋊Q8×C61C2×C4semidirect
160. #107×C61C2×C4semidirect
161. #103×C61C2×C4semidirect
162. #102×C61C2×C4semidirect
463. #468#6923semidirect
498. C61#23141semidirect
510. C2×SD16C2×#6923semidirect
516. C2×M16C2×#6923semidirect
526. C22⋊Q8C2×#6923semidirect
570. #107C2×#6923semidirect
576. #103C2×#6923semidirect
582. #102C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623452
#214623442
#214619102
#214619092
#214618832
#214618802
#214618152
#214618122
#214618072
#214618042
#214615902
#103×#69232
#214615592
#214615072
#468×D612
#2314161