Finite Group Databasebeta

← #30622261

Subgroups — #30622261

Order 15616.

942 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840802C211yesmaximal, characteristic, complemented
2C2×#16840773C211yesmaximal, characteristic
3#21462345C211yesmaximal, characteristic
4#21462343C211yesmaximal, characteristic
5#21461965C211yesmaximal, characteristic, complemented
6#21461925C211yesmaximal, characteristic, complemented
7#21461899C211yesmaximal, characteristic, complemented
8#21461898C211yesmaximal, characteristic, complemented
9#21461805C211yesmaximal, characteristic
10#21461804C211yesmaximal, characteristic
11#21461785C211yesmaximal, characteristic, complemented
12#21461783C211yesmaximal, characteristic, complemented
13#106×#6923C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic
15#470×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20#16840802—24no—
21#16840773—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519846C2211yescharacteristic
24C2×#14519845C2211yescharacteristic
25C2×#14519845C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519840C2211yescharacteristic
30D61⋊(C22⋊C8)C2211yescharacteristic
31C2×#14519831C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33(C2×#6923)⋊Q8C2211yescharacteristic
34(C2×#6923)⋊Q8C2211yescharacteristic
35#16840713—21no—
36#16840713C2211yescharacteristic
37#16840713C2211yescharacteristic
38#16840712—21no—
39#16840712—21no—
40#16840711—21no—
41#16840711—21no—
42#16840709—21no—
43C4⋊C4×#6923—21no—
44C4⋊C4×#6923C2211yescharacteristic
45C4⋊C4×#6923C2211yescharacteristic
46C22⋊C4×#6923—21no—
47C4×C22⋊#6923C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×Q16×D61C2211yescharacteristic
55C2×M16×D61C2211yescharacteristic
56C22⋊Q8×D61C2211yescharacteristic
57C22⋊Q8×D61C2211yescharacteristic
58#16840021C411yescharacteristic, complemented
59#16840020C411yescharacteristic, complemented
60#16840019C411yescharacteristic, complemented
61#16840019C411yescharacteristic, complemented
62#16840018C411yescharacteristic, complemented
63#16840018C411yescharacteristic, complemented
64#16840017C411yescharacteristic, complemented
65#106×D61C2211yescharacteristic
66#103×D61C2211yescharacteristic
67#103×D61C2211yescharacteristic
68C61×#470C411yescharacteristic, complemented
69C23×#6923—21no—
70C2×D61⋊C8C2311yescharacteristic
71C2×D61⋊C8C2311yescharacteristic
72Q8×#6923—22no—
73Q8×#6923—22no—
74Q8×#6923—41no—
75Q8×#6923—41no—
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—21no—
84C2×C4⋊#6923—41no—
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C22⋊#6923—21no—
90C2×C22⋊#6923D411yescharacteristic
91C2×C22⋊#6923D411yescharacteristic
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923—21no—
95C2×C4×#6923—21no—
96C2×C4×#6923—21no—
97C2×C4×#6923C2311yescharacteristic
98C2×C4×#6923C2311yescharacteristic
99#14519846—22no—
100#14519846—22no—
101#14519845—22no—
102#14519845D414yes—
103#14519840—22no—
104#14519840—22no—
105#14519840—41no—
106#14519840—41no—
107#14519834—21no—
108C22⋊#92420—21no—
109#14519831—22no—
110C8×#6923—22no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4D411yescharacteristic
120(C2×#6923)⋊C4D411yescharacteristic
121C2×Q8×D61C2311yescharacteristic
122C2×Q8×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C2×Dic244C2×C411yescharacteristic, complemented
125C2×#11758202C2×C411yescharacteristic, complemented
126C2×#11758202C2×C411yescharacteristic, complemented
127Q16×D61—22no—
128Q16×D61—22no—
129C2×#11758194C2×C411yescharacteristic
130C2×#11758189C2×C411yescharacteristic
131C2×#11758189C2×C411yescharacteristic
132M16×D61—22no—
133M16×D61—22no—
134C2×C8×D61C2311yescharacteristic
135C2×C8×D61C2311yescharacteristic
136#14519757C2×C411yescharacteristic
137#14519757C2×C411yescharacteristic
138#14519756C2×C411yescharacteristic
139#14519756C2×C411yescharacteristic
140#14519755—21no—
141#14519755—21no—
142#14519754—21no—
143#14519754—21no—
144#14519753C2×C411yescharacteristic
145#14519753C2×C411yescharacteristic
146C4⋊C4×D61—21no—
147C4⋊C4×D61—21no—
148C4⋊C4×D61C2311yescharacteristic
149C4⋊C4×D61C2311yescharacteristic
150C22⋊C4×D61—21no—
151C22⋊C4×D61—21no—
152#14519709C2×C411yescharacteristic, complemented
153#14519708C2×C411yescharacteristic, complemented
154#14519708C2×C411yescharacteristic, complemented
155#14519702C2×C411yescharacteristic, complemented
156#14519702C2×C411yescharacteristic, complemented
157#14519701C2×C411yescharacteristic, complemented
158#14519701C2×C411yescharacteristic, complemented
159#14519700C2×C411yescharacteristic, complemented
160#14519700C2×C411yescharacteristic, complemented
161C2×Q16×C61C2×C411yescharacteristic, complemented
162C2×M16×C61C2×C411yescharacteristic
163C22⋊Q8×C61C2×C411yescharacteristic
164C22⋊Q8×C61C2×C411yescharacteristic
165#106×C61C2×C411yescharacteristic, complemented
166#103×C61C2×C411yescharacteristic, complemented
167#103×C61C2×C411yescharacteristic, complemented
168C23×D61C2×D411yescharacteristic
169C22×#6923—21no—
170C22×#6923—21no—
171C22×#6923—21no—
172C22×#6923—21no—
173C22×#6923—42no—
174C22×#6923—42no—
175C22×#6923—81no—
176C22×#6923C2×D411yescharacteristic
177C22×#6923C2×D411yescharacteristic
178C22×#6923C2×D411yescharacteristic
179C22×#6923C2×D411yescharacteristic
180C2×Q8×C61C22×C411yescharacteristic
181C2×Q8×C61C22×C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C22×Dic61#4111yescharacteristic
184Q8×D61—21no—
185Q8×D61—21no—
186Q8×D61—21no—
187Q8×D61—21no—
188Q8×D61—21no—
189Q8×D61—21no—
190Q8×D61—21no—
191Q8×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61C22×C411yescharacteristic
201C2×C4×D61C2×D411yescharacteristic
202C2×C4×D61#4111yescharacteristic
203C2×C4×D61C2411yescharacteristic
204C2×Dic122—21no—
205C2×Dic122—21no—
206C2×Dic122C22×C411yescharacteristic
207C2×Dic122C22×C411yescharacteristic
208C22⋊#6923—22no—
209C22⋊#6923—41no—
210C22⋊#6923—42no—
211C2×#92420—21no—
212C2×#92420—21no—
213C4⋊#6923—21no—
214C4⋊#6923—21no—
215C4⋊#6923—21no—
216C4⋊#6923—21no—
217C4⋊#6923—21no—
218C4⋊#6923—21no—
219C4⋊#6923—42no—
220C4⋊#6923—42no—
221C4⋊#6923—42no—
222C4⋊#6923—42no—
223C4⋊#6923—81no—
224C4⋊#6923C2×D412yes—
225C4⋊#6923C2×D412yes—
226C4×#6923—21no—
227C4×#6923—21no—
228C4×#6923—21no—
229C4×#6923—21no—
230C4×#6923—42no—
231C4×#6923—42no—
232C4×#6923—42no—
233C4×#6923—42no—
234C4×#6923—81no—
235D61⋊C8—21no—
236D61⋊C8—21no—
237D61⋊C8—21no—
238D61⋊C8—21no—
239Q16×C61—22no—
240M16×C61—22no—
241C2×C8×C61C22×C411yescharacteristic
242C2×C8×C61C22×C411yescharacteristic
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61C22×C411yescharacteristic
246C4⋊C4×C61C22×C411yescharacteristic
247C22⋊C4×C61—21no—
248C22⋊C4×C61—21no—
249C22⋊Dic61—21no—
250C22⋊Dic61—21no—
251#11758202—22no—
252#11758202—22no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256#11758198—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61C22×C411yescharacteristic
260C4⋊Dic61C22×C411yescharacteristic
261#11758196—21no—
262#11758196—21no—
263#11758196—21no—
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267#11758194—22no—
268C2×#92418C22×C411yescharacteristic
269C2×#92418C22×C411yescharacteristic
270Dic244—22no—
271#11758189—22no—
272#11758189—22no—
273C8×D61—21no—
274C8×D61—21no—
275C8×D61C2×D412yes—
276C8×D61#4112yes—
277C23×C61C4×D411yescharacteristic
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61C4×D411yescharacteristic
285C22×D61C22×D411yescharacteristic
286C2×#6923—21no—
287C2×#6923—21no—
288C2×#6923—21no—
289C2×#6923—21no—
290C2×#6923—22no—
291C2×#6923—22no—
292C2×#6923—21no—
293C2×#6923—21no—
294C2×#6923—21no—
295C2×#6923—21no—
296C2×#6923—21no—
297C2×#6923—21no—
298C2×#6923—21no—
299C2×#6923—41no—
300C2×#6923—41no—
301C2×#6923—41no—
302C2×#6923—41no—
303C2×#6923—41no—
304C2×#6923—41no—
305C2×#6923—41no—
306C2×#6923—41no—
307C2×#6923—41no—
308C2×#6923—41no—
309C2×#6923—84no—
310C2×#6923#13712yes—
311Q8×C61—21no—
312Q8×C61—21no—
313Q8×C61—21no—
314Q8×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61C4×D411yescharacteristic
322C2×C4×C61C23×C411yescharacteristic
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61C4×D411yescharacteristic
330C2×Dic61C2×#4111yescharacteristic
331C4×D61—21no—
332C4×D61—21no—
333C4×D61—21no—
334C4×D61—21no—
335C4×D61—21no—
336C4×D61—21no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—41no—
341C4×D61—41no—
342C4×D61—41no—
343C4×D61—41no—
344C4×D61—41no—
345C4×D61C22×D411yescharacteristic
346C4×D61C2×#4111yescharacteristic
347C4×D61H(5,𝔽2)11yescharacteristic
348C4×D612−1+411yescharacteristic
349Dic122—21no—
350Dic122—21no—
351Dic122—21no—
352Dic122—21no—
353Dic122—41no—
354Dic122—41no—
355Dic122—41no—
356Dic122—41no—
357#92420—41no—
358#92420—41no—
359C8×C61—21no—
360C8×C61C4×D412yes—
361#92418—21no—
362#92418C4×D412yes—
363#23038—611nomaximal, Sylow
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—21no—
367C22×C61C2×C4×D411yescharacteristic
368C2×D61—21no—
369C2×D61—21no—
370C2×D61—21no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61D4211yescharacteristic
376C2×D61#54711yescharacteristic
377C2×D61C2×#13711yescharacteristic
378C2×D61#57511yescharacteristic
379C2×D61#57711yescharacteristic
380C2×D61#57811yescharacteristic
381#6923—22no—
382#6923—41no—
383#6923—41no—
384#6923—42no—
385#6923—41no—
386#6923—42no—
387#6923—81no—
388#6923—81no—
389C4×C61—21no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61—41no—
394C4×C61C2×C4×D411yescharacteristic
395C4×C61#52011yescharacteristic
396Dic61—21no—
397Dic61—41no—
398Dic61—41no—
399Dic61—41no—
400Dic61—41no—
401Dic61#54811yescharacteristic
402Dic61#55311yescharacteristic
403C2×#470—611no—
404C2×#441—611no—
405C2×#428—611no—
406#2362—611no—
407#2360—611no—
408#1969—611no—
409#1944—611no—
410#1928—611no—
411#1927—611no—
412#1873—611no—
413#1872—611no—
414#1865—611no—
415#1863—611no—
416C4×#106—611no—
417#1753—611no—
418C2×C61—41no—
419C2×C61#236111yescharacteristic
420C2×C61C4×#13711yescharacteristic
421C2×C61#294711yescharacteristic
422D61—41no—
423D61#327511yescharacteristic
424D61#327611yescharacteristic
425D61#334411yescharacteristic
426D61#334911yescharacteristic
427C22×Q16—611no—
428C22×M16—611no—
429C2×C22⋊Q8—611no—
430C2×C22⋊Q8—611no—
431C2×C4×Q8—611no—
432C2×C4×Q8—611no—
433C2×#117—611no—
434C22×C4⋊C4—611no—
435#470—611no—
436#470—611no—
437#470—611no—
438#470—611no—
439#470—611no—
440#470—611no—
441#470—611no—
442#470#692311yescharacteristic, complemented
443#441—1224no—
444#428—1224no—
445C2×#107—611no—
446C2×#107—611no—
447C2×#106—611no—
448C2×#106—611no—
449C2×#106—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103—611no—
454C2×#103—611no—
455C2×#103—611no—
456C2×C22⋊C8—611no—
457C2×#97—611no—
458C2×C4×C8—611no—
459#391—611no—
460#391—611no—
461#389—611no—
462#389—611no—
463#389—1221no—
464#388—1221no—
465#388—1221no—
466#387—1221no—
467#387—1221no—
468#385—1221no—
469C4×C4⋊C4—611no—
470C4×C4⋊C4—611no—
471C4×C4⋊C4—1221no—
472C4×C22⋊C4—611no—
473C4×C22⋊C4—1221no—
474#340—611no—
475#340—611no—
476#340—611no—
477#340—611no—
478#336—611no—
479#336—611no—
480C61#2303811yescharacteristic, complemented, Sylow
481C22×Q8—611no—
482C22×Q8—611no—
483C23×C4—611no—
484C23×C4—1221no—
485C2×Q16—611no—
486C2×Q16—611no—
487C2×Q16—611no—
488C2×Q16—1222no—
489C2×Q16—1222no—
490C2×Q16C2×#692311yescharacteristic, complemented
491C2×M16—611no—
492C2×M16—611no—
493C2×M16—611no—
494C2×M16—1222no—
495C2×M16—1222no—
496C2×M16C2×#692311yescharacteristic
497C22×C8—611no—
498C22×C8—611no—
499C22×C8—611no—
500C22×C8—611no—
501C22⋊Q8—611no—
502C22⋊Q8—611no—
503C22⋊Q8—611no—
504C22⋊Q8—611no—
505C22⋊Q8—611no—
506C22⋊Q8—611no—
507C22⋊Q8—1221no—
508C22⋊Q8—1221no—
509C22⋊Q8—1221no—
510C22⋊Q8—1221no—
511C22⋊Q8C2×#692311yescharacteristic
512C22⋊Q8C2×#692311yescharacteristic
513C4×Q8—1222no—
514C4×Q8—1222no—
515C4×Q8—2441no—
516C4×Q8—2441no—
517#117—1222no—
518#117—2441no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1222no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4—2441no—
534C2×C22⋊C4—611no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C42—611no—
540C2×C42—611no—
541C2×C42—1221no—
542C2×C42—1221no—
543C2×C42—1221no—
544C2×C42—1221no—
545C2×C42—1221no—
546#107—1222no—
547#107—1222no—
548#106—614no—
549#106—611no—
550#106—611no—
551#106—611no—
552#106—1222no—
553#106C2×#692311yescharacteristic, complemented
554#103—611no—
555#103—611no—
556#103—611no—
557#103—611no—
558#103—611no—
559#103—611no—
560#103—1222no—
561#103—1222no—
562#103—2441no—
563#103—2441no—
564#103C2×#692311yescharacteristic, complemented
565#103C2×#692311yescharacteristic, complemented
566C22⋊C8—1221no—
567C22⋊C8—1221no—
568#97—1222no—
569C4×C8—1222no—
570#95—611no—
571#95—611no—
572#95—1221no—
573#95—1221no—
574#95—1221no—
575#95—1221no—
576#95—1221no—
577#95—1221no—
578#95—1221no—
579#95—1221no—
580C24—611no—
581C2×Q8—611no—
582C2×Q8—611no—
583C2×Q8—1221no—
584C2×Q8—1221no—
585C2×Q8—1221no—
586C2×Q8—1221no—
587C2×Q8—1221no—
588C2×Q8—1221no—
589C2×Q8—1221no—
590C2×Q8—1221no—
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8C22×#692311yescharacteristic
594C2×Q8C22×#692311yescharacteristic
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—4881no—
617C22×C4—2442no—
618C22×C4—2442no—
619C22×C4C22×#692311yescharacteristic
620Q16—22no—
621Q16—1222no—
622Q16—1222no—
623Q16—1222no—
624M16—22no—
625M16—1222no—
626M16—1222no—
627M16—1222no—
628C2×C8—611no—
629C2×C8—612no—
630C2×C8—612no—
631C2×C8—611no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8C22×#692311yescharacteristic
641C2×C8C22×#692311yescharacteristic
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—612no—
645C4⋊C4—612no—
646C4⋊C4—611no—
647C4⋊C4—611no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—4881no—
663C4⋊C4—2442no—
664C4⋊C4—2442no—
665C4⋊C4—2442no—
666C4⋊C4—2442no—
667C4⋊C4C22×#692311yescharacteristic
668C4⋊C4C22×#692311yescharacteristic
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—1221no—
672C22⋊C4—1221no—
673C22⋊C4—1221no—
674C22⋊C4—1221no—
675C22⋊C4—1222no—
676C22⋊C4—1221no—
677C22⋊C4—1221no—
678C22⋊C4—2441no—
679C22⋊C4—2442no—
680C42—1221no—
681C42—1221no—
682C42—1221no—
683C42—1221no—
684C42—4881no—
685C42—2442no—
686C42—2442no—
687C42—2442no—
688C42—2442no—
689C23—611no—
690C23—611no—
691C23—1221no—
692C23—1221no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23—1221no—
697C23D4×#692311yescharacteristic
698Q8—21no—
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—1221no—
703Q8—1221no—
704Q8—1221no—
705Q8—1221no—
706Q8—2441no—
707Q8—2441no—
708Q8—2441no—
709Q8—2441no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—611no—
717C2×C4—611no—
718C2×C4—611no—
719C2×C4—611no—
720C2×C4—611no—
721C2×C4—612no—
722C2×C4—611no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—4884no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4D4×#692311yescharacteristic
768C2×C4C23×#692311yescharacteristic
769C8—21no—
770C8—612no—
771C8—1221no—
772C8—2441no—
773C8—2441no—
774C8D4×#692312yes—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—611no—
779C22—611no—
780C22—611no—
781C22—611no—
782C22—611no—
783C22—611no—
784C22—1221no—
785C22—1221no—
786C22—1221no—
787C22—2441no—
788C22—2441no—
789C22—2441no—
790C22—2441no—
791C22C2×D4×#692311yescharacteristic
792C4—21no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—611no—
798C4—611no—
799C4—1222no—
800C4—1221no—
801C4—4881no—
802C4—4881no—
803C4—2441no—
804C4—2441no—
805C4—2441no—
806C4—2442no—
807C4—2442no—
808C4—2441no—
809C4—2441no—
810C4—2441no—
811C4—2441no—
812C4C2×D4×#692311yescharacteristic
813C4#1684083111yescharacteristic
814C2—41no—
815C2—611no—
816C2—611no—
817C2—611no—
818C2—611no—
819C2—2441no—
820C2#2146234411yescharacteristic
821C2#137×#692311yescharacteristic
822C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#470C4
socleC22×C61C2×C4×D4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenter#470#6923
hypocenterC61#23038
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×#16840802C2semidirect
5. #21461965C2semidirect
6. #21461925C2semidirect
7. #21461899C2semidirect
8. #21461898C2semidirect
11. #21461785C2semidirect
12. #21461783C2semidirect
13. #106×#6923C2semidirect
58. #16840021C4semidirect
59. #16840020C4semidirect
60. #16840019C4semidirect
61. #16840019C4semidirect
62. #16840018C4semidirect
63. #16840018C4semidirect
64. #16840017C4semidirect
68. C61×#470C4semidirect
124. C2×Dic244C2×C4semidirect
125. C2×#11758202C2×C4semidirect
126. C2×#11758202C2×C4semidirect
152. #14519709C2×C4semidirect
153. #14519708C2×C4semidirect
154. #14519708C2×C4semidirect
155. #14519702C2×C4semidirect
156. #14519702C2×C4semidirect
157. #14519701C2×C4semidirect
158. #14519701C2×C4semidirect
159. #14519700C2×C4semidirect
160. #14519700C2×C4semidirect
161. C2×Q16×C61C2×C4semidirect
165. #106×C61C2×C4semidirect
166. #103×C61C2×C4semidirect
167. #103×C61C2×C4semidirect
442. #470#6923semidirect
480. C61#23038semidirect
490. C2×Q16C2×#6923semidirect
553. #106C2×#6923semidirect
564. #103C2×#6923semidirect
565. #103C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408022
C2×#168407732
#214623452
#214623432
#214619652
#214619252
#214618992
#214618982
#214618052
#214618042
#214617852
#214617832
#106×#69232
#214615592
#470×D612
#2303861