Finite Group Databasebeta

← #30622203

Subgroups — #30622203

Order 15616.

954 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840802C211yesmaximal, characteristic, complemented
2C2×SD16×#6923C211yesmaximal, characteristic
3#21462350C211yesmaximal, characteristic
4Q8×C4⋊#6923C211yesmaximal, characteristic, complemented
5#21461949C211yesmaximal, characteristic
6#21461931C211yesmaximal, characteristic, complemented
7#21461911C211yesmaximal, characteristic
8#21461908C211yesmaximal, characteristic, complemented
9#21461815C211yesmaximal, characteristic
10#21461813C211yesmaximal, characteristic, complemented
11#21461785C211yesmaximal, characteristic, complemented
12#21461784C211yesmaximal, characteristic
13#21461620C211yesmaximal, characteristic, complemented
14#21461591C211yesmaximal, characteristic, complemented
15#464×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×Q8×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20#16840802—24no—
21SD16×#6923—24no—
22C2×#14519845C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24C2×#14519840C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30#16840721C2211yescharacteristic
31C2×#14519831C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33(C2×#6923)⋊Q8C2211yescharacteristic
34#16840714C2211yescharacteristic
35#16840713—21no—
36#16840713—21no—
37#16840713C2211yescharacteristic
38#16840713C2211yescharacteristic
39#16840712—21no—
40#16840712—21no—
41#16840709—21no—
42#16840708—21no—
43#16840708C2211yescharacteristic
44C4×C4⋊#6923—21no—
45C4×C4⋊#6923C2211yescharacteristic
46C4×C4⋊#6923C2211yescharacteristic
47C22⋊C4×#6923—21no—
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×Q16×D61C2211yescharacteristic
55C2×SD16×D61C2211yescharacteristic
56#124×D61C2211yescharacteristic
57C4×Q8×D61C2211yescharacteristic
58#16839987C411yescharacteristic, complemented
59#16839986C411yescharacteristic, complemented
60#16839985C411yescharacteristic, complemented
61#16839984C411yescharacteristic, complemented
62#16839983C411yescharacteristic, complemented
63#16839982C411yescharacteristic, complemented
64#16839981C411yescharacteristic, complemented
65C4⋊C8×D61C2211yescharacteristic
66#103×D61C2211yescharacteristic
67#102×D61C2211yescharacteristic
68C61×#464C411yescharacteristic, complemented
69C23×#6923—21no—
70C2×D61⋊C8C2311yescharacteristic
71C2×D61⋊C8C2311yescharacteristic
72Q8×#6923—22no—
73Q8×#6923—22no—
74Q8×#6923—22no—
75Q8×#6923—41no—
76Q8×#6923—41no—
77Q8×#6923—41no—
78D4×#6923—22no—
79D4×#6923—41no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923—21no—
86C2×C4⋊#6923—21no—
87C2×C4⋊#6923D411yescharacteristic
88C2×C4⋊#6923D411yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C4⋊#6923C2311yescharacteristic
91C2×C4⋊#6923C2311yescharacteristic
92C2×C4⋊#6923C2311yescharacteristic
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923—21no—
96C2×C4×#6923—21no—
97C2×C4×#6923—21no—
98C2×C4×#6923—21no—
99C2×C4×#6923—21no—
100C2×C4×#6923C2311yescharacteristic
101C2×C4×#6923C2311yescharacteristic
102#14519845—22no—
103#14519845—22no—
104#14519840—22no—
105#14519840—22no—
106#14519840—41no—
107#14519840D414yes—
108#14519839—22no—
109#14519839—41no—
110#14519832—21no—
111#14519832—21no—
112#14519831—22no—
113C8×#6923—22no—
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
123C2×D4×D61C2311yescharacteristic
124C2×Dic244C2×C411yescharacteristic, complemented
125C2×#11758202C2×C411yescharacteristic, complemented
126C2×#11758202C2×C411yescharacteristic, complemented
127Q16×D61—22no—
128Q16×D61—22no—
129C2×#11758190C2×C411yescharacteristic
130C2×#11758200C2×C411yescharacteristic
131C2×#11758201C2×C411yescharacteristic
132SD16×D61—22no—
133SD16×D61—22no—
134C2×C8×D61C2311yescharacteristic
135C2×C8×D61C2311yescharacteristic
136#14519766C2×C411yescharacteristic
137#14519765C2×C411yescharacteristic
138#14519764C2×C411yescharacteristic
139#14519763—21no—
140#14519763—21no—
141Q8×Dic61C2×C411yescharacteristic, complemented
142C4×Dic122—21no—
143C4×Dic122C2×C411yescharacteristic, complemented
144#14519742—21no—
145#14519742C2×C411yescharacteristic, complemented
146C4⋊C4×D61—21no—
147C4⋊C4×D61C2311yescharacteristic
148C22⋊C4×D61—21no—
149C22⋊C4×D61—21no—
150C42×D61—21no—
151C42×D61C2311yescharacteristic
152C4⋊#92418C2×C411yescharacteristic, complemented
153#14519706C2×C411yescharacteristic, complemented
154#14519706C2×C411yescharacteristic, complemented
155#14519702C2×C411yescharacteristic, complemented
156#14519701C2×C411yescharacteristic, complemented
157#14519700C2×C411yescharacteristic, complemented
158#14519699C2×C411yescharacteristic
159#14519698C2×C411yescharacteristic
160#14519697C2×C411yescharacteristic
161C2×Q16×C61C2×C411yescharacteristic, complemented
162C2×SD16×C61C2×C411yescharacteristic
163#124×C61C2×C411yescharacteristic
164C4×Q8×C61C2×C411yescharacteristic, complemented
165C4⋊C8×C61C2×C411yescharacteristic, complemented
166#103×C61C2×C411yescharacteristic, complemented
167#102×C61C2×C411yescharacteristic
168C23×D61—21no—
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
182C2×D4×C61C22×C411yescharacteristic
183C2×C22⋊D61—21no—
184Q8×D61—21no—
185Q8×D61—21no—
186Q8×D61—21no—
187Q8×D61—21no—
188Q8×D61—21no—
189Q8×D61—21no—
190Q8×D61C2×D412yes—
191Q8×D61#4112yes—
192D4×D61—21no—
193D4×D61—21no—
194D4×D61—21no—
195D4×D61—21no—
196C2×D244C22×C411yescharacteristic
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61C2×D411yescharacteristic
201C2×C4×D61C2×D411yescharacteristic
202C2×C4×D61C2411yescharacteristic
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122C22×C411yescharacteristic
206C2×Dic122C22×C411yescharacteristic
207C22⋊#6923—42no—
208C22⋊#6923—42no—
209C22⋊#6923—81no—
210C2×#92420—21no—
211C2×#92420—21no—
212C4⋊#6923—22no—
213C4⋊#6923—21no—
214C4⋊#6923—21no—
215C4⋊#6923—21no—
216C4⋊#6923—21no—
217C4⋊#6923—21no—
218C4⋊#6923—21no—
219C4⋊#6923—21no—
220C4⋊#6923—41no—
221C4⋊#6923—42no—
222C4⋊#6923—42no—
223C4⋊#6923—42no—
224C4⋊#6923—42no—
225C4⋊#6923—81no—
226C4⋊#6923—81no—
227C4⋊#6923—81no—
228C4⋊#6923C2×D412yes—
229C4×#6923—21no—
230C4×#6923—21no—
231C4×#6923—21no—
232C4×#6923—21no—
233C4×#6923—42no—
234C4×#6923—42no—
235C4×#6923—42no—
236C4×#6923—81no—
237D61⋊C8—21no—
238D61⋊C8—21no—
239D61⋊C8—21no—
240D61⋊C8C2×D412yes—
241Q16×C61—22no—
242SD16×C61—22no—
243C2×C8×C61C22×C411yescharacteristic
244C2×C8×C61C22×C411yescharacteristic
245C4⋊C4×C61—21no—
246C4⋊C4×C61C22×C411yescharacteristic
247C22⋊C4×C61—21no—
248C22⋊C4×C61—21no—
249C42×C61—21no—
250C42×C61C22×C411yescharacteristic
251C22⋊Dic61—21no—
252C22⋊Dic61—21no—
253#11758202—22no—
254#11758202—22no—
255#11758201—22no—
256#11758200—22no—
257#11758198—21no—
258#11758198—21no—
259#11758198—21no—
260#11758198—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61C22×C411yescharacteristic
263#11758196—21no—
264#11758196—21no—
265#11758196—21no—
266C4×Dic61—21no—
267C4×Dic61—21no—
268C4×Dic61—21no—
269C4×Dic61C22×C411yescharacteristic
270C4×Dic61#4111yescharacteristic
271C4×Dic61#4111yescharacteristic
272C2×#92418C22×C411yescharacteristic
273C2×#92418C22×C411yescharacteristic
274Dic244—22no—
275#11758190—22no—
276C8×D61—21no—
277C8×D61—21no—
278C8×D61—21no—
279C8×D61—21no—
280C23×C61—21no—
281C22×D61—21no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61C22×D411yescharacteristic
289C2×#6923—21no—
290C2×#6923—21no—
291C2×#6923—21no—
292C2×#6923—21no—
293C2×#6923—21no—
294C2×#6923—22no—
295C2×#6923—21no—
296C2×#6923—21no—
297C2×#6923—21no—
298C2×#6923—21no—
299C2×#6923—21no—
300C2×#6923—21no—
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—41no—
310C2×#6923—41no—
311C2×#6923—41no—
312C2×#6923—84no—
313C2×#6923#13712yes—
314Q8×C61—21no—
315Q8×C61—21no—
316Q8×C61—21no—
317Q8×C61C4×D412yes—
318D4×C61—21no—
319D4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61C4×D411yescharacteristic
324C2×C4×C61C4×D411yescharacteristic
325C2×C4×C61C23×C411yescharacteristic
326C22⋊D61—41no—
327C22⋊D61—41no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61C4×D411yescharacteristic
332C2×Dic61C4×D411yescharacteristic
333C2×Dic61C2×#4111yescharacteristic
334D244—21no—
335D244—21no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—21no—
339C4×D61—21no—
340C4×D61—21no—
341C4×D61—21no—
342C4×D61—41no—
343C4×D61—41no—
344C4×D61—41no—
345C4×D61—41no—
346C4×D61C22×D411yescharacteristic
347C4×D61C2×#4111yescharacteristic
348C4×D61H(5,𝔽2)11yescharacteristic
349C4×D612−1+411yescharacteristic
350Dic122—21no—
351Dic122—22no—
352Dic122—22no—
353Dic122—21no—
354Dic122—21no—
355Dic122—41no—
356Dic122—41no—
357Dic122C4×D412yes—
358#92420—22no—
359#92420—41no—
360C8×C61—21no—
361C8×C61—21no—
362#92418—21no—
363#92418—21no—
364#23013—611nomaximal, Sylow
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61C2×C4×D411yescharacteristic
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—81no—
375C2×D61—81no—
376C2×D61D4211yescharacteristic
377C2×D61#54811yescharacteristic
378C2×D61C2×#13711yescharacteristic
379C2×D61#57511yescharacteristic
380C2×D61#57711yescharacteristic
381C2×D61#57711yescharacteristic
382#6923—22no—
383#6923—41no—
384#6923—42no—
385#6923—41no—
386#6923—41no—
387#6923—81no—
388#6923—81no—
389#6923—81no—
390C4×C61—22no—
391C4×C61—21no—
392C4×C61—21no—
393C4×C61—41no—
394C4×C61—41no—
395C4×C61C2×C4×D411yescharacteristic
396C4×C61#52011yescharacteristic
397Dic61—22no—
398Dic61—21no—
399Dic61—21no—
400Dic61—41no—
401Dic61—41no—
402Dic61#54711yescharacteristic
403Dic61#55311yescharacteristic
404C2×#464—611no—
405C2×#441—611no—
406C2×C4×SD16—611no—
407#2367—611no—
408Q8×C4⋊C4—611no—
409#1959—611no—
410#1948—611no—
411#1936—611no—
412#1933—611no—
413#1880—611no—
414#1878—611no—
415#1865—611no—
416#1864—611no—
417#1771—611no—
418#1763—611no—
419C2×C61—81no—
420C2×C61#236111yescharacteristic
421C2×C61C4×#13711yescharacteristic
422C2×C61#295211yescharacteristic
423D61—81no—
424D61#326611yescharacteristic
425D61#327111yescharacteristic
426D61#336911yescharacteristic
427D61#337111yescharacteristic
428C22×Q16—611no—
429C22×SD16—611no—
430C2×#124—611no—
431C2×C4×Q8—611no—
432C2×C4×Q8—611no—
433C2×C4×Q8—611no—
434C2×C4×Q8—611no—
435C2×C4×D4—611no—
436#464—611no—
437#464—611no—
438#464—611no—
439#464—611no—
440#464—611no—
441#464—611no—
442#464—611no—
443#464#692311yescharacteristic, complemented
444#441—1224no—
445C4×SD16—1224no—
446C2×#106—611no—
447C2×#106—611no—
448C2×C4⋊C8—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×#102—611no—
457C2×#97—611no—
458C2×#97—611no—
459C2×C4×C8—611no—
460#391—611no—
461#390—611no—
462#389—611no—
463#389—611no—
464#389—1221no—
465#389—1221no—
466#388—1221no—
467#388—1221no—
468#385—1221no—
469#384—611no—
470#384—1221no—
471C4×C4⋊C4—611no—
472C4×C4⋊C4—611no—
473C4×C4⋊C4—1221no—
474C4×C22⋊C4—1221no—
475#340—611no—
476#340—611no—
477#340—611no—
478#340—611no—
479#336—611no—
480#336—611no—
481C61#2301311yescharacteristic, complemented, Sylow
482C22×Q8—611no—
483C22×Q8—611no—
484C22×D4—611no—
485C23×C4—1221no—
486C2×Q16—611no—
487C2×Q16—611no—
488C2×Q16—611no—
489C2×Q16—1222no—
490C2×Q16—1222no—
491C2×Q16C2×#692311yescharacteristic, complemented
492C2×SD16—611no—
493C2×SD16—611no—
494C2×SD16—611no—
495C2×SD16—1222no—
496C2×SD16—1222no—
497C2×SD16C2×#692311yescharacteristic
498C22×C8—611no—
499C22×C8—611no—
500C22×C8—611no—
501C22×C8—611no—
502#124—611no—
503#124—611no—
504#124—611no—
505#124—1221no—
506#124—1221no—
507#124C2×#692311yescharacteristic
508C4×Q8—611no—
509C4×Q8—611no—
510C4×Q8—611no—
511C4×Q8—1221no—
512C4×Q8—1221no—
513C4×Q8—1222no—
514C4×Q8—1222no—
515C4×Q8—1222no—
516C4×Q8—2441no—
517C4×Q8—2441no—
518C4×Q8—2441no—
519C4×Q8C2×#692311yescharacteristic, complemented
520C4×D4—1222no—
521C4×D4—2441no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—611no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4—1221no—
536C2×C4⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C42—611no—
543C2×C42—611no—
544C2×C42—611no—
545C2×C42—1221no—
546C2×C42—1221no—
547C2×C42—1221no—
548C2×C42—1221no—
549C2×C42—1221no—
550#106—1222no—
551#106—1222no—
552C4⋊C8—611no—
553C4⋊C8—611no—
554C4⋊C8—611no—
555C4⋊C8C2×#692311yescharacteristic, complemented
556#103—614no—
557#103—611no—
558#103—611no—
559#103—611no—
560#103—1222no—
561#103—1222no—
562#103—2441no—
563#103C2×#692311yescharacteristic, complemented
564#102—611no—
565#102—611no—
566#102—611no—
567#102—1222no—
568#102—2441no—
569#102C2×#692311yescharacteristic
570#97—1221no—
571#97—1221no—
572#97—1222no—
573C4×C8—1222no—
574#95—611no—
575#95—611no—
576#95—1221no—
577#95—1221no—
578#95—1221no—
579#95—1221no—
580#95—1221no—
581C24—1221no—
582C2×Q8—612no—
583C2×Q8—612no—
584C2×Q8—611no—
585C2×Q8—611no—
586C2×Q8—1221no—
587C2×Q8—1221no—
588C2×Q8—1221no—
589C2×Q8—1221no—
590C2×Q8—1221no—
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8C22×#692311yescharacteristic
595C2×Q8C22×#692311yescharacteristic
596C2×D4—611no—
597C2×D4—1221no—
598C2×D4—1221no—
599C2×D4—1221no—
600C2×D4—1221no—
601C2×D4—1221no—
602C2×D4C22×#692311yescharacteristic
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—4881no—
618C22×C4—2442no—
619C22×C4—2442no—
620Q16—22no—
621Q16—1222no—
622Q16—1222no—
623Q16—1222no—
624SD16—22no—
625SD16—1222no—
626SD16—1222no—
627SD16—1222no—
628C2×C8—612no—
629C2×C8—611no—
630C2×C8—611no—
631C2×C8—1221no—
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—612no—
644C4⋊C4—611no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1221no—
648C4⋊C4—1221no—
649C4⋊C4—1222no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4—4881no—
658C4⋊C4—4881no—
659C4⋊C4—4881no—
660C4⋊C4—2441no—
661C4⋊C4—2442no—
662C4⋊C4—2442no—
663C4⋊C4—2442no—
664C4⋊C4—2442no—
665C4⋊C4C22×#692311yescharacteristic
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—1221no—
669C22⋊C4—1221no—
670C22⋊C4—1221no—
671C22⋊C4—1221no—
672C22⋊C4—1221no—
673C22⋊C4—1221no—
674C22⋊C4—4881no—
675C22⋊C4—2442no—
676C22⋊C4—2442no—
677C42—21no—
678C42—611no—
679C42—611no—
680C42—611no—
681C42—1221no—
682C42—1221no—
683C42—1221no—
684C42—1221no—
685C42—1221no—
686C42—1221no—
687C42—1221no—
688C42—4881no—
689C42—2442no—
690C42—2442no—
691C42—2442no—
692C42C22×#692311yescharacteristic
693C23—21no—
694C23—611no—
695C23—1221no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702Q8—21no—
703Q8—21no—
704Q8—21no—
705Q8—612no—
706Q8—1222no—
707Q8—1222no—
708Q8—1221no—
709Q8—1221no—
710Q8—1221no—
711Q8—2441no—
712Q8—2441no—
713Q8D4×#692312yes—
714D4—21no—
715D4—21no—
716D4—1221no—
717D4—1221no—
718D4—2441no—
719D4—2441no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—611no—
724C2×C4—611no—
725C2×C4—611no—
726C2×C4—611no—
727C2×C4—611no—
728C2×C4—612no—
729C2×C4—611no—
730C2×C4—611no—
731C2×C4—1221no—
732C2×C4—1222no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1222no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1222no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—4884no—
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×C4—2441no—
768C2×C4D4×#692311yescharacteristic
769C2×C4D4×#692311yescharacteristic
770C2×C4C23×#692311yescharacteristic
771C8—21no—
772C8—21no—
773C8—1222no—
774C8—1221no—
775C8—1221no—
776C8—2441no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—611no—
781C22—611no—
782C22—611no—
783C22—611no—
784C22—611no—
785C22—611no—
786C22—4881no—
787C22—4881no—
788C22—4881no—
789C22—4881no—
790C22—2441no—
791C22—2441no—
792C22—2441no—
793C22C2×D4×#692311yescharacteristic
794C4—21no—
795C4—21no—
796C4—22no—
797C4—41no—
798C4—41no—
799C4—611no—
800C4—611no—
801C4—1222no—
802C4—1221no—
803C4—1221no—
804C4—1222no—
805C4—4881no—
806C4—4881no—
807C4—4881no—
808C4—2441no—
809C4—2441no—
810C4—2441no—
811C4—2442no—
812C4—2441no—
813C4—2441no—
814C4C2×D4×#692311yescharacteristic
815C4#1684083111yescharacteristic
816C2—81no—
817C2—611no—
818C2—611no—
819C2—611no—
820C2—611no—
821C2—4881no—
822C2#2146234411yescharacteristic
823C2#137×#692311yescharacteristic
824C2#2146258211yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#464C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#464#6923
hypocenterC61#23013
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#16840802C2semidirect
4. Q8×C4⋊#6923C2semidirect
6. #21461931C2semidirect
8. #21461908C2semidirect
10. #21461813C2semidirect
11. #21461785C2semidirect
13. #21461620C2semidirect
14. #21461591C2semidirect
58. #16839987C4semidirect
59. #16839986C4semidirect
60. #16839985C4semidirect
61. #16839984C4semidirect
62. #16839983C4semidirect
63. #16839982C4semidirect
64. #16839981C4semidirect
68. C61×#464C4semidirect
124. C2×Dic244C2×C4semidirect
125. C2×#11758202C2×C4semidirect
126. C2×#11758202C2×C4semidirect
141. Q8×Dic61C2×C4semidirect
143. C4×Dic122C2×C4semidirect
145. #14519742C2×C4semidirect
152. C4⋊#92418C2×C4semidirect
153. #14519706C2×C4semidirect
154. #14519706C2×C4semidirect
155. #14519702C2×C4semidirect
156. #14519701C2×C4semidirect
157. #14519700C2×C4semidirect
161. C2×Q16×C61C2×C4semidirect
164. C4×Q8×C61C2×C4semidirect
165. C4⋊C8×C61C2×C4semidirect
166. #103×C61C2×C4semidirect
443. #464#6923semidirect
481. C61#23013semidirect
491. C2×Q16C2×#6923semidirect
519. C4×Q8C2×#6923semidirect
555. C4⋊C8C2×#6923semidirect
563. #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×SD16×#69232
#214623502
Q8×C4⋊#69232
#214619492
#214619312
#214619112
#214619082
#214618152
#214618132
#214617852
#214617842
#214616202
#214615912
#464×D612
#2301361