Finite Group Databasebeta

← #30622473

Subgroups — #30622473

Order 15616.

930 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462350C211yesmaximal, characteristic, complemented
2#21462337C211yesmaximal, characteristic, complemented
3#21461969C211yesmaximal, characteristic, complemented
4#21461966C211yesmaximal, characteristic
5#21461949C211yesmaximal, characteristic, complemented
6#21461930C211yesmaximal, characteristic, complemented
7#21461899C211yesmaximal, characteristic, complemented
8#21461896C211yesmaximal, characteristic, complemented
9#21461815C211yesmaximal, characteristic, complemented
10#21461814C211yesmaximal, characteristic
11#21461620C211yesmaximal, characteristic, complemented
12#21461590C211yesmaximal, characteristic, complemented
13#21461589C211yesmaximal, characteristic, complemented
14#103×#6923C211yesmaximal, characteristic, complemented
15#463×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×#14519856—21no—
19C2×#14519846C2211yescharacteristic
20C2×#14519846C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25C2×#14519839C2211yescharacteristic
26C2×#14519839C2211yescharacteristic
27#16840721C2211yescharacteristic
28C2×#14519831C2211yescharacteristic
29C2×C8×#6923C2211yescharacteristic
30(C2×#6923)⋊Q8C2211yescharacteristic
31#16840714C2211yescharacteristic
32#16840714C2211yescharacteristic
33#16840714C2211yescharacteristic
34#16840712—21no—
35#16840712—21no—
36#16840712—21no—
37#16840712—21no—
38#16840709—21no—
39#16840708C2211yescharacteristic
40#16840704—21no—
41C4⋊C4×#6923C2211yescharacteristic
42C4⋊C4×#6923C2211yescharacteristic
43C4×C4⋊#6923C2211yescharacteristic
44C4×C4⋊#6923C2211yescharacteristic
45C22⋊C4×#6923—21no—
46#16840636C2211yescharacteristic
47#16840636C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×SD16×D61C2211yescharacteristic
53C2×D8×D61C2211yescharacteristic
54#124×D61C2211yescharacteristic
55C4×D4×D61C2211yescharacteristic
56#16839980C411yescharacteristic, complemented
57#16839979C411yescharacteristic, complemented
58#16839978C411yescharacteristic, complemented
59#16839977C411yescharacteristic, complemented
60#16839976C411yescharacteristic, complemented
61#16839975C411yescharacteristic, complemented
62#16839974C411yescharacteristic, complemented
63C4⋊C8×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#463C411yescharacteristic, complemented
67C23×#6923—21no—
68C2×D61⋊C8C2311yescharacteristic
69C2×D61⋊C8C2311yescharacteristic
70Q8×#6923—22no—
71Q8×#6923—41no—
72D4×#6923—22no—
73D4×#6923—41no—
74#14519856—44no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923D411yescharacteristic
79C2×C4⋊#6923D411yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C4⋊#6923C2311yescharacteristic
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C22⋊#6923—21no—
88C2×C22⋊#6923—21no—
89C2×C22⋊#6923—21no—
90C2×C22⋊#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923—21no—
95C2×C4×#6923C2311yescharacteristic
96C2×C4×#6923C2311yescharacteristic
97#14519846—41no—
98#14519846—41no—
99#14519840—22no—
100#14519840—41no—
101#14519839—22no—
102#14519839—22no—
103#14519839—22no—
104#14519839—41no—
105#14519832—21no—
106#14519832—21no—
107#14519831—41no—
108C8×#6923—41no—
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×D61C2311yescharacteristic
118C2×D4×D61C2311yescharacteristic
119C22×C4×D61—21no—
120C2×#11758190C2×C411yescharacteristic, complemented
121C2×#11758200C2×C411yescharacteristic, complemented
122C2×#11758201C2×C411yescharacteristic, complemented
123SD16×D61—41no—
124SD16×D61—41no—
125C2×D488C2×C411yescharacteristic
126C2×#11758199C2×C411yescharacteristic
127C2×#11758199C2×C411yescharacteristic
128D8×D61—41no—
129D8×D61—41no—
130C2×C8×D61C2311yescharacteristic
131C2×C8×D61C2311yescharacteristic
132#14519766C2×C411yescharacteristic
133#14519765C2×C411yescharacteristic
134#14519764C2×C411yescharacteristic
135#14519763—21no—
136#14519763—21no—
137C4×D244C2×C411yescharacteristic, complemented
138D4×Dic61C2×C411yescharacteristic, complemented
139#14519739C2×C411yescharacteristic, complemented
140C4×C22⋊D61—21no—
141#14519737—21no—
142C4⋊C4×D61C2311yescharacteristic
143C22⋊C4×D61—21no—
144C22⋊C4×D61—21no—
145C22⋊C4×D61—21no—
146C42×D61C2311yescharacteristic
147C4⋊#92418C2×C411yescharacteristic, complemented
148#14519706C2×C411yescharacteristic, complemented
149#14519706C2×C411yescharacteristic, complemented
150#14519702C2×C411yescharacteristic, complemented
151#14519701C2×C411yescharacteristic, complemented
152#14519700C2×C411yescharacteristic, complemented
153#14519699C2×C411yescharacteristic
154#14519698C2×C411yescharacteristic
155#14519697C2×C411yescharacteristic
156C2×SD16×C61C2×C411yescharacteristic, complemented
157C2×D8×C61C2×C411yescharacteristic
158#124×C61C2×C411yescharacteristic
159C4×D4×C61C2×C411yescharacteristic, complemented
160C4⋊C8×C61C2×C411yescharacteristic, complemented
161#103×C61C2×C411yescharacteristic, complemented
162#102×C61C2×C411yescharacteristic
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—81no—
172C22×#6923C2×D411yescharacteristic
173C22×#6923C2×D411yescharacteristic
174C22×#6923C2×D411yescharacteristic
175C22×#6923C2×D411yescharacteristic
176C2×Q8×C61C22×C411yescharacteristic
177C2×D4×C61C22×C411yescharacteristic
178C2×D4×C61C22×C411yescharacteristic
179C22×C4×C61—21no—
180C2×C22⋊D61—21no—
181C2×C22⋊D61—21no—
182C22×Dic61—21no—
183Q8×D61—21no—
184Q8×D61—21no—
185Q8×D61—21no—
186Q8×D61—21no—
187D4×D61—21no—
188D4×D61—21no—
189D4×D61—21no—
190D4×D61—21no—
191D4×D61—21no—
192D4×D61—21no—
193D4×D61—21no—
194D4×D61—21no—
195C2×D244C22×C411yescharacteristic
196C2×D244C22×C411yescharacteristic
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61C2×D411yescharacteristic
204C2×C4×D61C2×D411yescharacteristic
205C2×C4×D61C2411yescharacteristic
206C2×Dic122—21no—
207C2×Dic122C22×C411yescharacteristic
208C22⋊#6923—42no—
209C22⋊#6923—42no—
210C22⋊#6923—42no—
211C22⋊#6923—42no—
212C22⋊#6923—81no—
213C22⋊#6923—81no—
214C22⋊#6923—81no—
215C2×#92420—21no—
216C2×#92420—21no—
217C4⋊#6923—22no—
218C4⋊#6923—21no—
219C4⋊#6923—21no—
220C4⋊#6923—21no—
221C4⋊#6923—21no—
222C4⋊#6923—21no—
223C4⋊#6923—21no—
224C4⋊#6923—21no—
225C4⋊#6923—41no—
226C4⋊#6923—42no—
227C4⋊#6923—42no—
228C4⋊#6923—81no—
229C4⋊#6923#4112yes—
230C4×#6923—21no—
231C4×#6923—21no—
232C4×#6923—21no—
233C4×#6923—21no—
234C4×#6923—42no—
235C4×#6923—42no—
236C4×#6923—42no—
237C4×#6923—81no—
238D61⋊C8—21no—
239D61⋊C8—21no—
240D61⋊C8—21no—
241D61⋊C8#4112yes—
242SD16×C61—41no—
243D8×C61—41no—
244C2×C8×C61C22×C411yescharacteristic
245C2×C8×C61C22×C411yescharacteristic
246C4⋊C4×C61C22×C411yescharacteristic
247C22⋊C4×C61—21no—
248C22⋊C4×C61—21no—
249C22⋊C4×C61—21no—
250C42×C61C22×C411yescharacteristic
251C22⋊Dic61—21no—
252C22⋊Dic61—21no—
253C22⋊Dic61—21no—
254#11758201—41no—
255#11758200—41no—
256#11758199—41no—
257#11758199—41no—
258#11758198—21no—
259#11758198—21no—
260#11758198—21no—
261#11758198—21no—
262#11758198—21no—
263#11758198—21no—
264C4⋊Dic61C22×C411yescharacteristic
265#11758196—21no—
266C4×Dic61C22×C411yescharacteristic
267C4×Dic61#4111yescharacteristic
268C4×Dic61#4111yescharacteristic
269C2×#92418C22×C411yescharacteristic
270C2×#92418C22×C411yescharacteristic
271D488—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×#6923AGL(1,ℤ/8)12yes—
319Q8×C61—21no—
320Q8×C61—21no—
321D4×C61—21no—
322D4×C61—21no—
323D4×C61—21no—
324D4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—42no—
328C2×C4×C61C4×D411yescharacteristic
329C2×C4×C61C4×D411yescharacteristic
330C2×C4×C61C23×C411yescharacteristic
331C22⋊D61—41no—
332C22⋊D61—41no—
333C22⋊D61—41no—
334C22⋊D61—41no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—42no—
338C2×Dic61C4×D411yescharacteristic
339C2×Dic61C4×D411yescharacteristic
340C2×Dic61C2×#4111yescharacteristic
341D244—21no—
342D244—21no—
343D244—21no—
344D244—21no—
345C4×D61—21no—
346C4×D61—21no—
347C4×D61—21no—
348C4×D61—21no—
349C4×D61—42no—
350C4×D61—42no—
351C4×D61—41no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61C2×#4111yescharacteristic
356C4×D61C2×#4111yescharacteristic
357C4×D61H(5,𝔽2)11yescharacteristic
358C4×D61H(5,𝔽2)11yescharacteristic
359Dic122—21no—
360Dic122—21no—
361Dic122—41no—
362Dic122—41no—
363#92420—22no—
364#92420—41no—
365C8×C61—21no—
366C8×C61—21no—
367#92418—21no—
368#92418—21no—
369#23105—611nomaximal, Sylow
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61C2×C4×D411yescharacteristic
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—81no—
384C2×D61—81no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61—81no—
389C2×D61—81no—
390C2×D61—81no—
391C2×D61#54611yescharacteristic
392C2×D61#55011yescharacteristic
393C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
394C2×D61#57511yescharacteristic
395C2×D61#57611yescharacteristic
396C2×D61#57811yescharacteristic
397#6923—22no—
398#6923—41no—
399#6923—41no—
400#6923—41no—
401#6923—42no—
402#6923—81no—
403#6923—81no—
404#6923—81no—
405C4×C61—21no—
406C4×C61—21no—
407C4×C61—41no—
408C4×C61—41no—
409C4×C61C4×#4111yescharacteristic
410C4×C61#51811yescharacteristic
411Dic61—21no—
412Dic61—21no—
413Dic61—41no—
414Dic61—41no—
415Dic61#55311yescharacteristic
416Dic61#55511yescharacteristic
417C2×#463—611no—
418#2367—611no—
419#2354—611no—
420#1973—611no—
421#1970—611no—
422#1959—611no—
423#1947—611no—
424#1928—611no—
425#1925—611no—
426#1880—611no—
427#1879—611no—
428#1771—611no—
429#1762—611no—
430#1762—611no—
431C4×#103—611no—
432C2×C61—81no—
433C2×C61—81no—
434C2×C61#236311yescharacteristic
435C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
436C2×C61#295111yescharacteristic
437D61—81no—
438D61—81no—
439D61#330811yescharacteristic
440D61#331911yescharacteristic
441D61#339911yescharacteristic
442D61#340211yescharacteristic
443C22×SD16—611no—
444C22×D8—611no—
445C2×#124—611no—
446C2×C4×Q8—611no—
447C2×C4×D4—611no—
448C2×C4×D4—611no—
449C2×#117—1221no—
450#463—611no—
451#463—611no—
452#463—611no—
453#463—611no—
454#463—611no—
455#463—611no—
456#463—611no—
457#463#692311yescharacteristic, complemented
458C2×#107—611no—
459C2×#107—611no—
460C2×C4⋊C8—611no—
461C2×#103—611no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×#97—611no—
470C2×#97—611no—
471C2×C4×C8—611no—
472#391—611no—
473#390—611no—
474#390—611no—
475#390—611no—
476#388—1221no—
477#388—1221no—
478#388—1221no—
479#388—1221no—
480#385—1221no—
481#384—611no—
482#380—1221no—
483C4×C4⋊C4—611no—
484C4×C4⋊C4—611no—
485C4×C4⋊C4—611no—
486C4×C4⋊C4—611no—
487C4×C22⋊C4—1221no—
488#340—611no—
489#340—611no—
490#340—611no—
491#340—611no—
492#336—611no—
493#336—611no—
494C61#2310511yescharacteristic, complemented, Sylow
495C22×Q8—611no—
496C22×D4—611no—
497C22×D4—611no—
498C23×C4—1221no—
499C23×C4—1221no—
500C2×SD16—611no—
501C2×SD16—611no—
502C2×SD16—611no—
503C2×SD16—2441no—
504C2×SD16—2441no—
505C2×SD16C2×#692311yescharacteristic, complemented
506C2×D8—611no—
507C2×D8—611no—
508C2×D8—611no—
509C2×D8—2441no—
510C2×D8—2441no—
511C2×D8C2×#692311yescharacteristic
512C22×C8—611no—
513C22×C8—611no—
514C22×C8—611no—
515C22×C8—611no—
516#124—611no—
517#124—611no—
518#124—611no—
519#124—1221no—
520#124—1221no—
521#124C2×#692311yescharacteristic
522C4×Q8—1222no—
523C4×Q8—2441no—
524C4×D4—611no—
525C4×D4—611no—
526C4×D4—611no—
527C4×D4—1221no—
528C4×D4—1221no—
529C4×D4—1222no—
530C4×D4—2441no—
531C4×D4C2×#692311yescharacteristic, complemented
532#117—2444no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C42—611no—
554C2×C42—611no—
555C2×C42—611no—
556C2×C42—1221no—
557C2×C42—1221no—
558C2×C42—1221no—
559C2×C42—1221no—
560#107—2441no—
561#107—2441no—
562C4⋊C8—611no—
563C4⋊C8—611no—
564C4⋊C8—611no—
565C4⋊C8C2×#692311yescharacteristic, complemented
566#103—611no—
567#103—611no—
568#103—611no—
569#103—1222no—
570#103—2441no—
571#103C2×#692311yescharacteristic, complemented
572#102—611no—
573#102—611no—
574#102—611no—
575#102—1222no—
576#102—1222no—
577#102—1222no—
578#102—2441no—
579#102C2×#692311yescharacteristic
580#97—1221no—
581#97—1221no—
582#97—2441no—
583C4×C8—2441no—
584#95—611no—
585#95—611no—
586#95—1221no—
587#95—1221no—
588#95—1221no—
589#95—1221no—
590#95—1221no—
591C24—1221no—
592C24—1221no—
593C2×Q8—611no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8C22×#692311yescharacteristic
600C2×D4—611no—
601C2×D4—611no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4C22×#692311yescharacteristic
613C2×D4C22×#692311yescharacteristic
614C22×C4—21no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—4881no—
632C22×C4—2442no—
633C22×C4—2442no—
634C22×C4—2442no—
635C22×C4—2442no—
636SD16—41no—
637SD16—2441no—
638SD16—2441no—
639SD16—2441no—
640D8—41no—
641D8—2441no—
642D8—2441no—
643D8—2441no—
644C2×C8—612no—
645C2×C8—611no—
646C2×C8—611no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8C22×#692311yescharacteristic
657C2×C8C22×#692311yescharacteristic
658C4⋊C4—612no—
659C4⋊C4—611no—
660C4⋊C4—1221no—
661C4⋊C4—1222no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—4881no—
670C4⋊C4—2441no—
671C4⋊C4—2442no—
672C4⋊C4—2442no—
673C4⋊C4C22×#692311yescharacteristic
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—1221no—
678C22⋊C4—1221no—
679C22⋊C4—1221no—
680C22⋊C4—1221no—
681C22⋊C4—1221no—
682C22⋊C4—1221no—
683C22⋊C4—1221no—
684C22⋊C4—1221no—
685C22⋊C4—1221no—
686C22⋊C4—4881no—
687C22⋊C4—4881no—
688C22⋊C4—4881no—
689C22⋊C4—2442no—
690C22⋊C4—2442no—
691C22⋊C4—2442no—
692C22⋊C4—2442no—
693C42—611no—
694C42—611no—
695C42—611no—
696C42—1221no—
697C42—1221no—
698C42—1221no—
699C42—1221no—
700C42—4881no—
701C42—2442no—
702C42—2442no—
703C42—2442no—
704C42C22×#692311yescharacteristic
705C23—21no—
706C23—21no—
707C23—611no—
708C23—1221no—
709C23—1221no—
710C23—2441no—
711C23—2441no—
712C23—2441no—
713C23—2441no—
714C23—2441no—
715C23—2441no—
716C23—2441no—
717C23—2441no—
718C23—2441no—
719C23—2441no—
720C23—2441no—
721C23—2441no—
722Q8—21no—
723Q8—21no—
724Q8—1221no—
725Q8—1221no—
726Q8—2441no—
727Q8—2441no—
728D4—21no—
729D4—21no—
730D4—21no—
731D4—21no—
732D4—1221no—
733D4—1221no—
734D4—1221no—
735D4—1221no—
736D4—2441no—
737D4—2441no—
738D4—2441no—
739D4—2441no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—42no—
743C2×C4—611no—
744C2×C4—611no—
745C2×C4—611no—
746C2×C4—611no—
747C2×C4—611no—
748C2×C4—612no—
749C2×C4—611no—
750C2×C4—611no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1221no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—1222no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1221no—
768C2×C4—1221no—
769C2×C4—4884no—
770C2×C4—2442no—
771C2×C4—2442no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4—2441no—
776C2×C4—2442no—
777C2×C4—2441no—
778C2×C4—2441no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4D4×#692311yescharacteristic
789C2×C4D4×#692311yescharacteristic
790C2×C4C23×#692311yescharacteristic
791C8—21no—
792C8—21no—
793C8—1222no—
794C8—1221no—
795C8—1221no—
796C8—2441no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—611no—
804C22—611no—
805C22—611no—
806C22—611no—
807C22—611no—
808C22—611no—
809C22—4881no—
810C22—4881no—
811C22—4881no—
812C22—4881no—
813C22—4881no—
814C22—4881no—
815C22—4881no—
816C22—4881no—
817C22—2441no—
818C22—2441no—
819C22—2441no—
820C22—2441no—
821C22—2441no—
822C22—2441no—
823C22C2×D4×#692311yescharacteristic
824C4—21no—
825C4—21no—
826C4—41no—
827C4—41no—
828C4—611no—
829C4—611no—
830C4—1222no—
831C4—1221no—
832C4—1221no—
833C4—4881no—
834C4—4881no—
835C4—4881no—
836C4—2441no—
837C4—2441no—
838C4—2441no—
839C4—2442no—
840C4—2441no—
841C4—2441no—
842C4#41×#692311yescharacteristic
843C4#1684082911yescharacteristic
844C2—81no—
845C2—81no—
846C2—611no—
847C2—611no—
848C2—611no—
849C2—611no—
850C2—4881no—
851C2—4881no—
852C2#2146234611yescharacteristic
853C2AGL(1,ℤ/8)×#692311yescharacteristic
854C2#2146258111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#463C4
socleC22×C61C2×C4×D4
prime radicalC2×D8×D61C22
cosocleC2×C4×D61C24
hypercenter#463#6923
hypocenterC61#23105
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #21462350C2semidirect
2. #21462337C2semidirect
3. #21461969C2semidirect
5. #21461949C2semidirect
6. #21461930C2semidirect
7. #21461899C2semidirect
8. #21461896C2semidirect
9. #21461815C2semidirect
11. #21461620C2semidirect
12. #21461590C2semidirect
13. #21461589C2semidirect
14. #103×#6923C2semidirect
56. #16839980C4semidirect
57. #16839979C4semidirect
58. #16839978C4semidirect
59. #16839977C4semidirect
60. #16839976C4semidirect
61. #16839975C4semidirect
62. #16839974C4semidirect
66. C61×#463C4semidirect
120. C2×#11758190C2×C4semidirect
121. C2×#11758200C2×C4semidirect
122. C2×#11758201C2×C4semidirect
137. C4×D244C2×C4semidirect
138. D4×Dic61C2×C4semidirect
139. #14519739C2×C4semidirect
147. C4⋊#92418C2×C4semidirect
148. #14519706C2×C4semidirect
149. #14519706C2×C4semidirect
150. #14519702C2×C4semidirect
151. #14519701C2×C4semidirect
152. #14519700C2×C4semidirect
156. C2×SD16×C61C2×C4semidirect
159. C4×D4×C61C2×C4semidirect
160. C4⋊C8×C61C2×C4semidirect
161. #103×C61C2×C4semidirect
457. #463#6923semidirect
494. C61#23105semidirect
505. C2×SD16C2×#6923semidirect
531. C4×D4C2×#6923semidirect
565. C4⋊C8C2×#6923semidirect
571. #103C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623502
#214623372
#214619692
#214619662
#214619492
#214619302
#214618992
#214618962
#214618152
#214618142
#214616202
#214615902
#214615892
#103×#69232
#463×D612
#2310561