Finite Group Databasebeta

← #30622842

Subgroups — #30622842

Order 15616.

850 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462350C211yesmaximal, characteristic
2#21462348C211yesmaximal, characteristic, complemented
3#21461997C211yesmaximal, characteristic, complemented
4#21461987C211yesmaximal, characteristic
5#21461910C211yesmaximal, characteristic, complemented
6#21461909C211yesmaximal, characteristic
7#21461899C211yesmaximal, characteristic, complemented
8#21461896C211yesmaximal, characteristic
9#21461785C211yesmaximal, characteristic, complemented
10#21461784C211yesmaximal, characteristic
11#21461633C211yesmaximal, characteristic, complemented
12#21461617C211yesmaximal, characteristic, complemented
13#21461590C211yesmaximal, characteristic
14#103×#6923C211yesmaximal, characteristic, complemented
15#489×D61C211yesmaximal, characteristic
16C2×Q8×#6923—21no—
17C2×Q8×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×#14519846C2211yescharacteristic
20C2×#14519845C2211yescharacteristic
21D61⋊(C4⋊C8)C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23C2×#14519840C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25C2×#14519839C2211yescharacteristic
26C2×#14519831C2211yescharacteristic
27C2×C8×#6923C2211yescharacteristic
28(C2×#6923)⋊Q8—21no—
29(C2×#6923)⋊Q8C2211yescharacteristic
30#16840714C2211yescharacteristic
31#16840713C2211yescharacteristic
32#16840713C2211yescharacteristic
33#16840712—21no—
34#16840712—21no—
35#16840711—21no—
36#16840711—21no—
37#16840709—21no—
38C4⋊C4×#6923C2211yescharacteristic
39C4⋊C4×#6923C2211yescharacteristic
40C4×C4⋊#6923C2211yescharacteristic
41C4×C4⋊#6923C2211yescharacteristic
42C4×C4⋊#6923C2211yescharacteristic
43C22⋊C4×#6923—21no—
44#16840636C2211yescharacteristic
45#16840636C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C4⋊Q8×D61C2211yescharacteristic
53#124×D61C2211yescharacteristic
54#16840124C411yescharacteristic, complemented
55#16840123C411yescharacteristic, complemented
56#16840123C411yescharacteristic, complemented
57#16840122C411yescharacteristic, complemented
58#16840121C411yescharacteristic, complemented
59#16840120C411yescharacteristic, complemented
60#16840120C411yescharacteristic, complemented
61#103×D61C2211yescharacteristic
62#103×D61C2211yescharacteristic
63#102×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#97×D61C2211yescharacteristic
66C61×#489C411yescharacteristic, complemented
67C23×#6923—21no—
68C2×D61⋊C8C2311yescharacteristic
69C2×D61⋊C8C2311yescharacteristic
70Q8×#6923—22no—
71Q8×#6923—41no—
72Q8×#6923—44no—
73D4×#6923—22no—
74D4×#6923—41no—
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×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923C2311yescharacteristic
93C2×C4×#6923C2311yescharacteristic
94#14519846—22no—
95#14519845—22no—
96#14519844—21no—
97C4⋊#92420—21no—
98#14519840—22no—
99#14519840—41no—
100#14519839—22no—
101#14519839—41no—
102#14519831—41no—
103C8×#6923—41no—
104(C2×#6923)⋊C4—21no—
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)⋊C4D411yescharacteristic
113(C2×#6923)⋊C4D411yescharacteristic
114C2×Q8×D61—21no—
115C2×Q8×D61C2311yescharacteristic
116C2×D4×D61C2311yescharacteristic
117C2×C8×D61C2311yescharacteristic
118C2×C8×D61C2311yescharacteristic
119#14519777C2×C411yescharacteristic, complemented
120#14519776—21no—
121#14519776C2×C411yescharacteristic, complemented
122#14519776C2×C411yescharacteristic, complemented
123#14519775—21no—
124#14519766C2×C411yescharacteristic
125#14519765C2×C411yescharacteristic
126#14519764C2×C411yescharacteristic
127#14519763—21no—
128#14519763—21no—
129C4⋊C4×D61—21no—
130C4⋊C4×D61C2311yescharacteristic
131C4⋊C4×D61C2311yescharacteristic
132C22⋊C4×D61—21no—
133C22⋊C4×D61—21no—
134C42×D61C2311yescharacteristic
135#14519702C2×C411yescharacteristic, complemented
136#14519702C2×C411yescharacteristic, complemented
137#14519701C2×C411yescharacteristic, complemented
138#14519701C2×C411yescharacteristic, complemented
139#14519700C2×C411yescharacteristic, complemented
140#14519700C2×C411yescharacteristic, complemented
141#14519699C2×C411yescharacteristic
142#14519699C2×C411yescharacteristic
143#14519698C2×C411yescharacteristic
144#14519698C2×C411yescharacteristic
145#14519697C2×C411yescharacteristic
146#14519697C2×C411yescharacteristic
147#14519688C2×C411yescharacteristic, complemented
148#14519687C2×C411yescharacteristic, complemented
149#14519687C2×C411yescharacteristic, complemented
150C4⋊Q8×C61C2×C411yescharacteristic, complemented
151#124×C61C2×C411yescharacteristic
152#103×C61C2×C411yescharacteristic, complemented
153#103×C61C2×C411yescharacteristic, complemented
154#102×C61C2×C411yescharacteristic
155#102×C61C2×C411yescharacteristic
156#97×C61C2×C411yescharacteristic, complemented
157C23×D61—21no—
158C22×#6923—21no—
159C22×#6923—21no—
160C22×#6923—21no—
161C22×#6923—21no—
162C22×#6923—42no—
163C22×#6923—42no—
164C22×#6923—81no—
165C22×#6923C2×D411yescharacteristic
166C22×#6923C2×D411yescharacteristic
167C22×#6923C2×D411yescharacteristic
168C22×#6923C2×D411yescharacteristic
169C2×Q8×C61—21no—
170C2×Q8×C61C22×C411yescharacteristic
171C2×D4×C61C22×C411yescharacteristic
172C2×C22⋊D61—21no—
173Q8×D61—21no—
174Q8×D61—21no—
175Q8×D61—21no—
176Q8×D61—21no—
177Q8×D61—42no—
178Q8×D61—42no—
179D4×D61—21no—
180D4×D61—21no—
181D4×D61—21no—
182D4×D61—21no—
183C2×D244C22×C411yescharacteristic
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61C2×D411yescharacteristic
188C2×C4×D61C2×D411yescharacteristic
189C2×C4×D61C2411yescharacteristic
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122C22×C411yescharacteristic
195C22⋊#6923—42no—
196C22⋊#6923—42no—
197C22⋊#6923—81no—
198C2×#92420—21no—
199C2×#92420—21no—
200C4⋊#6923—22no—
201C4⋊#6923—21no—
202C4⋊#6923—21no—
203C4⋊#6923—21no—
204C4⋊#6923—21no—
205C4⋊#6923—21no—
206C4⋊#6923—21no—
207C4⋊#6923—41no—
208C4⋊#6923—42no—
209C4⋊#6923—42no—
210C4⋊#6923—42no—
211C4⋊#6923#4112yes—
212C4⋊#6923#4112yes—
213C4×#6923—21no—
214C4×#6923—21no—
215C4×#6923—21no—
216C4×#6923—21no—
217C4×#6923—42no—
218C4×#6923—42no—
219C4×#6923—42no—
220C4×#6923—42no—
221C4×#6923—81no—
222D61⋊C8—21no—
223D61⋊C8—21no—
224D61⋊C8—21no—
225D61⋊C8—21no—
226C2×C8×C61C22×C411yescharacteristic
227C2×C8×C61C22×C411yescharacteristic
228C4⋊C4×C61—21no—
229C4⋊C4×C61C22×C411yescharacteristic
230C4⋊C4×C61C22×C411yescharacteristic
231C22⋊C4×C61—21no—
232C22⋊C4×C61—21no—
233C42×C61C22×C411yescharacteristic
234C22⋊Dic61—21no—
235C22⋊Dic61—21no—
236#11758198—21no—
237#11758198—21no—
238#11758198—21no—
239#11758198—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61C22×C411yescharacteristic
242C4⋊Dic61C22×C411yescharacteristic
243#11758196—21no—
244#11758196—21no—
245#11758196—21no—
246#11758196—21no—
247C4×Dic61C22×C411yescharacteristic
248C4×Dic61#4111yescharacteristic
249C4×Dic61#4111yescharacteristic
250C2×#92418C22×C411yescharacteristic
251C2×#92418C22×C411yescharacteristic
252C8×D61—21no—
253C8×D61—21no—
254C8×D61—21no—
255C8×D61—21no—
256C23×C61—21no—
257C22×D61—21no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61C22×D411yescharacteristic
265C2×#6923—21no—
266C2×#6923—21no—
267C2×#6923—21no—
268C2×#6923—21no—
269C2×#6923—21no—
270C2×#6923—22no—
271C2×#6923—22no—
272C2×#6923—21no—
273C2×#6923—21no—
274C2×#6923—21no—
275C2×#6923—21no—
276C2×#6923—21no—
277C2×#6923—21no—
278C2×#6923—41no—
279C2×#6923—41no—
280C2×#6923—41no—
281C2×#6923—41no—
282C2×#6923—41no—
283C2×#6923—41no—
284C2×#6923—41no—
285C2×#6923—41no—
286C2×#6923—41no—
287C2×#6923—41no—
288C2×#6923—84no—
289C2×#6923AGL(1,ℤ/8)12yes—
290Q8×C61—21no—
291Q8×C61—21no—
292Q8×C61—42no—
293D4×C61—21no—
294D4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61C4×D411yescharacteristic
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C23×C411yescharacteristic
301C22⋊D61—41no—
302C22⋊D61—41no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61C4×D411yescharacteristic
307C2×Dic61C4×D411yescharacteristic
308C2×Dic61C2×#4111yescharacteristic
309D244—21no—
310D244—21no—
311C4×D61—21no—
312C4×D61—21no—
313C4×D61—21no—
314C4×D61—21no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—41no—
319C4×D61—41no—
320C4×D61—41no—
321C4×D61C2×#4111yescharacteristic
322C4×D61C2×#4111yescharacteristic
323C4×D61H(5,𝔽2)11yescharacteristic
324C4×D612−1+411yescharacteristic
325Dic122—21no—
326Dic122—21no—
327Dic122—42no—
328Dic122—42no—
329Dic122—42no—
330Dic122—41no—
331Dic122—41no—
332#92420—41no—
333#92420—41no—
334C8×C61—21no—
335C8×C61—21no—
336#92418—21no—
337#92418—21no—
338#23228—611nomaximal, Sylow
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61C2×C4×D411yescharacteristic
343C2×D61—41no—
344C2×D61—41no—
345C2×D61—41no—
346C2×D61—81no—
347C2×D61—81no—
348C2×D61—81no—
349C2×D61—81no—
350C2×D61#54611yescharacteristic
351C2×D61#54811yescharacteristic
352C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
353C2×D61#57511yescharacteristic
354C2×D61#57711yescharacteristic
355C2×D61#57811yescharacteristic
356#6923—22no—
357#6923—42no—
358#6923—41no—
359#6923—41no—
360#6923—41no—
361#6923—42no—
362#6923—81no—
363#6923—81no—
364C4×C61—21no—
365C4×C61—21no—
366C4×C61—41no—
367C4×C61—41no—
368C4×C61—41no—
369C4×C61C4×#4111yescharacteristic
370C4×C61#52011yescharacteristic
371Dic61—21no—
372Dic61—21no—
373Dic61—41no—
374Dic61—41no—
375Dic61—41no—
376Dic61#55611yescharacteristic
377Dic61#55911yescharacteristic
378C2×#489—611no—
379#2367—611no—
380#2365—611no—
381#1987—611no—
382#1983—611no—
383#1935—611no—
384#1934—611no—
385#1928—611no—
386#1925—611no—
387#1865—611no—
388#1864—611no—
389#1776—611no—
390#1771—611no—
391#1762—611no—
392C4×#103—611no—
393C2×C61—81no—
394C2×C61#236711yescharacteristic
395C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
396C2×C61#294711yescharacteristic
397D61—81no—
398D61#330811yescharacteristic
399D61#331111yescharacteristic
400D61#337311yescharacteristic
401D61#337711yescharacteristic
402C2×C4⋊Q8—611no—
403C2×#124—611no—
404C2×C4×Q8—611no—
405C2×C4×Q8—1221no—
406C2×C4×D4—611no—
407#489—611no—
408#489—611no—
409#489—611no—
410#489—611no—
411#489—611no—
412#489—611no—
413#489—611no—
414#489#692311yescharacteristic, complemented
415C2×#107—611no—
416C2×#106—611no—
417C2×C4⋊C8—611no—
418C2×#103—611no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#103—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×#97—611no—
427C2×#97—611no—
428C2×C4×C8—611no—
429#391—611no—
430#391—1221no—
431#390—611no—
432#389—611no—
433#389—611no—
434#388—1221no—
435#388—1221no—
436#387—1221no—
437#387—1221no—
438#385—1221no—
439C4×C4⋊C4—611no—
440C4×C4⋊C4—611no—
441C4×C4⋊C4—611no—
442C4×C4⋊C4—611no—
443C4×C4⋊C4—611no—
444C4×C22⋊C4—1221no—
445#340—611no—
446#340—611no—
447#340—611no—
448#340—611no—
449#340—611no—
450#340—611no—
451#336—611no—
452#336—611no—
453C61#2322811yescharacteristic, complemented, Sylow
454C22×Q8—611no—
455C22×Q8—1221no—
456C22×D4—611no—
457C23×C4—1221no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—611no—
462C4⋊Q8—611no—
463C4⋊Q8—611no—
464C4⋊Q8—611no—
465C4⋊Q8—1221no—
466C4⋊Q8—1221no—
467C4⋊Q8C2×#692311yescharacteristic, complemented
468#124—611no—
469#124—611no—
470#124—611no—
471#124—1221no—
472#124—1221no—
473#124C2×#692311yescharacteristic
474C4×Q8—1222no—
475C4×Q8—2441no—
476C4×Q8—2444no—
477C4×D4—1222no—
478C4×D4—2441no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C42—611no—
497C2×C42—611no—
498C2×C42—611no—
499C2×C42—1221no—
500C2×C42—1221no—
501C2×C42—1221no—
502C2×C42—1221no—
503C2×C42—1221no—
504#107—1222no—
505#106—1222no—
506C4⋊C8—1221no—
507C4⋊C8—1221no—
508#103—611no—
509#103—611no—
510#103—611no—
511#103—611no—
512#103—611no—
513#103—611no—
514#103—1222no—
515#103—2441no—
516#103C2×#692311yescharacteristic, complemented
517#103C2×#692311yescharacteristic, complemented
518#102—611no—
519#102—611no—
520#102—611no—
521#102—611no—
522#102—611no—
523#102—611no—
524#102—1222no—
525#102—2441no—
526#102C2×#692311yescharacteristic
527#102C2×#692311yescharacteristic
528#97—611no—
529#97—611no—
530#97—611no—
531#97—2441no—
532#97C2×#692311yescharacteristic, complemented
533C4×C8—2441no—
534#95—611no—
535#95—611no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539#95—1221no—
540#95—1221no—
541#95—1221no—
542#95—1221no—
543#95—1221no—
544C24—1221no—
545C2×Q8—21no—
546C2×Q8—611no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8—1221no—
551C2×Q8—1221no—
552C2×Q8—1221no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—2442no—
556C2×Q8—2442no—
557C2×Q8C22×#692311yescharacteristic
558C2×D4—611no—
559C2×D4—1221no—
560C2×D4—1221no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—1221no—
564C2×D4C22×#692311yescharacteristic
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—4881no—
580C22×C4—2442no—
581C22×C4—2442no—
582C2×C8—611no—
583C2×C8—611no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8C22×#692311yescharacteristic
595C2×C8C22×#692311yescharacteristic
596C4⋊C4—21no—
597C4⋊C4—612no—
598C4⋊C4—612no—
599C4⋊C4—611no—
600C4⋊C4—611no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1222no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—2442no—
614C4⋊C4—2441no—
615C4⋊C4—2442no—
616C4⋊C4—2442no—
617C4⋊C4C22×#692311yescharacteristic
618C4⋊C4C22×#692311yescharacteristic
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—1221no—
622C22⋊C4—1221no—
623C22⋊C4—1221no—
624C22⋊C4—1221no—
625C22⋊C4—1221no—
626C22⋊C4—1221no—
627C22⋊C4—4881no—
628C22⋊C4—2442no—
629C22⋊C4—2442no—
630C42—611no—
631C42—611no—
632C42—611no—
633C42—1221no—
634C42—1221no—
635C42—1221no—
636C42—1221no—
637C42—4881no—
638C42—2442no—
639C42—2442no—
640C42—2442no—
641C42—2442no—
642C42C22×#692311yescharacteristic
643C23—21no—
644C23—611no—
645C23—1221no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652Q8—21no—
653Q8—21no—
654Q8—42no—
655Q8—1221no—
656Q8—1221no—
657Q8—2442no—
658Q8—2441no—
659Q8—2441no—
660Q8—2442no—
661Q8—2442no—
662D4—21no—
663D4—21no—
664D4—1221no—
665D4—1221no—
666D4—2441no—
667D4—2441no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—611no—
672C2×C4—611no—
673C2×C4—611no—
674C2×C4—611no—
675C2×C4—611no—
676C2×C4—612no—
677C2×C4—611no—
678C2×C4—611no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1222no—
690C2×C4—1221no—
691C2×C4—1222no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—4884no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4D4×#692311yescharacteristic
717C2×C4D4×#692311yescharacteristic
718C2×C4C23×#692311yescharacteristic
719C8—21no—
720C8—21no—
721C8—1221no—
722C8—1221no—
723C8—2441no—
724C8—2441no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—611no—
729C22—611no—
730C22—611no—
731C22—611no—
732C22—611no—
733C22—611no—
734C22—4881no—
735C22—4881no—
736C22—4881no—
737C22—4881no—
738C22—2441no—
739C22—2441no—
740C22—2441no—
741C22C2×D4×#692311yescharacteristic
742C4—21no—
743C4—21no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—611no—
748C4—611no—
749C4—1222no—
750C4—1221no—
751C4—1221no—
752C4—4881no—
753C4—4881no—
754C4—2441no—
755C4—2441no—
756C4—2441no—
757C4—2442no—
758C4—2442no—
759C4—2441no—
760C4—2441no—
761C4—2441no—
762C4#41×#692311yescharacteristic
763C4#1684083111yescharacteristic
764C2—81no—
765C2—611no—
766C2—611no—
767C2—611no—
768C2—611no—
769C2—4881no—
770C2#2146235011yescharacteristic
771C2AGL(1,ℤ/8)×#692311yescharacteristic
772C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#489C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#489#6923
hypocenterC61#23228
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #21462348C2semidirect
3. #21461997C2semidirect
5. #21461910C2semidirect
7. #21461899C2semidirect
9. #21461785C2semidirect
11. #21461633C2semidirect
12. #21461617C2semidirect
14. #103×#6923C2semidirect
54. #16840124C4semidirect
55. #16840123C4semidirect
56. #16840123C4semidirect
57. #16840122C4semidirect
58. #16840121C4semidirect
59. #16840120C4semidirect
60. #16840120C4semidirect
66. C61×#489C4semidirect
119. #14519777C2×C4semidirect
121. #14519776C2×C4semidirect
122. #14519776C2×C4semidirect
135. #14519702C2×C4semidirect
136. #14519702C2×C4semidirect
137. #14519701C2×C4semidirect
138. #14519701C2×C4semidirect
139. #14519700C2×C4semidirect
140. #14519700C2×C4semidirect
147. #14519688C2×C4semidirect
148. #14519687C2×C4semidirect
149. #14519687C2×C4semidirect
150. C4⋊Q8×C61C2×C4semidirect
152. #103×C61C2×C4semidirect
153. #103×C61C2×C4semidirect
156. #97×C61C2×C4semidirect
414. #489#6923semidirect
453. C61#23228semidirect
467. C4⋊Q8C2×#6923semidirect
516. #103C2×#6923semidirect
517. #103C2×#6923semidirect
532. #97C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623502
#214623482
#214619972
#214619872
#214619102
#214619092
#214618992
#214618962
#214617852
#214617842
#214616332
#214616172
#214615902
#103×#69232
#489×D612
#2322861