Finite Group Databasebeta

← #6611329

Subgroups — #6611329

Order 512.

2018 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36180C211yesmaximal, characteristic, complemented
2#36122C211yesmaximal, characteristic
3#33230C211yesmaximal, characteristic, complemented
4#33049C211yesmaximal, characteristic, complemented
5#33042C211yesmaximal, characteristic, complemented
6#29141C211yesmaximal, characteristic, complemented
7#28750C211yesmaximal, characteristic, complemented
8#27973C211yesmaximal, characteristic, complemented
9#27972C211yesmaximal, characteristic, complemented
10#27765C214yesmaximal, complemented
11#27278C214yesmaximal, complemented
12#27266C214yesmaximal, complemented
13#25857C211yesmaximal, characteristic, complemented
14#25856C211yesmaximal, characteristic, complemented
15#22421C214yesmaximal, complemented
16#21647C211yesmaximal, characteristic, complemented
17#21200C211yesmaximal, characteristic, complemented
18C2×#1956C211yesmaximal, characteristic, complemented
19C4×#435C211yesmaximal, characteristic, complemented
20C2×#554—21no—
21C2×#548C2212yes—
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C2×#489C2214yes—
25C2×#487C2211yescharacteristic
26C2×#487C2211yescharacteristic
27C2×#486C2211yescharacteristic
28C2×#435C2212yes—
29C2×#417C2214yes—
30C22×#103C2214yes—
31C2×C4×M16C2211yescharacteristic
32C22×C4×C8C2211yescharacteristic
33#2868C2211yescharacteristic
34#2858C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2856C2211yescharacteristic
39#2567—21no—
40#2552—21no—
41#2552C2212yes—
42#2545C2212yes—
43#2502—21no—
44#2502—21no—
45#2491—21no—
46#2491—21no—
47#2452—21no—
48#2452—21no—
49#2440—21no—
50#2440—21no—
51#2440C2212yes—
52#2440C2212yes—
53#2436C2212yes—
54#2432C2212yes—
55#2416—21no—
56#2416—21no—
57#2361—21no—
58#2361—21no—
59D4×C4⋊C4—21no—
60D4×C4⋊C4C2212yes—
61C4×C4⋊Q8C2211yescharacteristic
62C4×C4⋊Q8C2211yescharacteristic
63C2×#384C2211yescharacteristic
64C2×#384C2211yescharacteristic
65C42×D4C2211yescharacteristic
66#2072C2214yes—
67#2071C2214yes—
68#2043C2214yes—
69#2042C2214yes—
70#2042C2214yes—
71#2024C2214yes—
72#1990C2211yescharacteristic
73#1983C2214yes—
74#1959C2214yes—
75#1959C2214yes—
76#1957C2211yescharacteristic
77#1957C2211yescharacteristic
78#1957C2211yescharacteristic
79#1956C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2214yes—
85#1956C2211yescharacteristic
86#1935C2214yes—
87#1935C2214yes—
88#1934C2214yes—
89#1894C2214yes—
90#1893C2214yes—
91#1874C2214yes—
92#1872C2214yes—
93#1834C2211yescharacteristic
94#1834C2211yescharacteristic
95#1834C2211yescharacteristic
96#1803C2214yes—
97#1788C2214yes—
98#1787C2214yes—
99#1771C2212yes—
100C4×C4⋊C8C2211yescharacteristic
101#1763C2214yes—
102#1753C2212yes—
103#1752C2212yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C22×#41C2312yes—
108C23×Q8C2312yes—
109C22×M16C2312yes—
110C23×C8C2312yes—
111#554—48no—
112#548—216no—
113#532—24no—
114#532—42no—
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8—21no—
120C2×C4⋊Q8—42no—
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2312yes—
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2312yes—
126C2×#127C2311yescharacteristic
127C2×#125—22no—
128C2×#124—22no—
129C2×#124C2312yes—
130C2×#124C2312yes—
131C2×#124C2312yes—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—22no—
135C2×C22⋊Q8—22no—
136C2×C22⋊Q8—22no—
137C2×C22⋊Q8C2312yes—
138C2×#121—22no—
139C2×#121—21no—
140C2×#121—21no—
141C2×#121—21no—
142C2×#121—21no—
143C2×#121C2312yes—
144C2×C4×Q8—21no—
145C2×C4×Q8C2312yes—
146C2×C4×D4—22no—
147C2×C4×D4—22no—
148C2×C4×D4—21no—
149C2×C4×D4—21no—
150C2×C4×D4D411yescharacteristic
151C2×C4×D4D411yescharacteristic
152C2×C4×D4C2311yescharacteristic
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4—21no—
158C22×C4⋊C4—21no—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163#489—48no—
164#487—24no—
165#487—42no—
166#486—42no—
167#435—28no—
168C2×C4⋊C8C2312yes—
169#417—48no—
170C2×#103—48no—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×#103C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×C22⋊C8C2312yes—
184C2×C22⋊C8C2312yes—
185C4×M16—42no—
186C2×#97C2312yes—
187C2×#97C2312yes—
188C2×#97C2312yes—
189C2×C4×C8—42no—
190C2×C4×C8C2311yescharacteristic
191C2×C4×C8C2311yescharacteristic
192C2×C4×C8C2311yescharacteristic
193C2×C4×C8C2311yescharacteristic
194C2×C4×C8C2312yes—
195#398—22no—
196#398—22no—
197#398—22no—
198#398—22no—
199#396—22no—
200#396—22no—
201#395—22no—
202#395—22no—
203#394—22no—
204#394—22no—
205#393—22no—
206#393—22no—
207#391—21no—
208#391—21no—
209#391—21no—
210#391C2312yes—
211#391C2312yes—
212#390—21no—
213#390—21no—
214#390—21no—
215#390—21no—
216#390—21no—
217#390—21no—
218#390C2312yes—
219#389—22no—
220#389—22no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389C2312yes—
229#389C2312yes—
230#389C2312yes—
231#388—22no—
232#388—22no—
233#386—22no—
234#386—22no—
235#385—22no—
236#385—22no—
237#385—22no—
238#385—22no—
239#385—22no—
240#385—22no—
241#384—21no—
242#384—21no—
243#384—21no—
244#384—21no—
245#384—21no—
246#384—21no—
247#384C2311yescharacteristic
248#384C2311yescharacteristic
249#384C2312yes—
250#384C2312yes—
251#384C2312yes—
252#384C2311yescharacteristic
253#384C2311yescharacteristic
254#380—21no—
255#380—21no—
256#380—21no—
257#380—21no—
258#380C2312yes—
259#380C2312yes—
260C4×C4⋊C4—21no—
261C4×C4⋊C4—21no—
262C4×C4⋊C4—21no—
263C4×C4⋊C4D411yescharacteristic
264C4×C4⋊C4D411yescharacteristic
265C4×C4⋊C4C2312yes—
266C4×C4⋊C4C2311yescharacteristic
267C4×C22⋊C4D411yescharacteristic
268C4×C22⋊C4D411yescharacteristic
269C4×C22⋊C4D411yescharacteristic
270C4×C22⋊C4D411yescharacteristic
271C4×C22⋊C4C2311yescharacteristic
272C4×C22⋊C4C2311yescharacteristic
273C43C2311yescharacteristic
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#336C2312yes—
279#336C2312yes—
280#336C2312yes—
281C2×#41—24no—
282C2×#41—28no—
283C2×#41—42no—
284C2×#41—44no—
285C22×Q8—21no—
286C22×Q8—22no—
287C22×Q8—22no—
288C22×Q8—24no—
289C22×Q8—28no—
290C22×Q8—42no—
291C22×Q8—44no—
292C22×Q8C2412yes—
293C22×Q8C2412yes—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—21no—
297C22×D4—21no—
298C22×D4C2×D411yescharacteristic
299C22×D4C2412yes—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C2×M16—24no—
311C2×M16—24no—
312C2×M16—42no—
313C22×C8—24no—
314C22×C8—24no—
315C22×C8—42no—
316C22×C8C2412yes—
317C22×C8C2412yes—
318C22×C8C2412yes—
319C22×C8C2412yes—
320C4⋊Q8—24no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—44no—
327C4⋊Q8—44no—
328C4⋊Q8—44no—
329C4⋊Q8—42no—
330C4⋊Q8—44no—
331C4⋊Q8—82no—
332C4⋊Q8#4114yes—
333#127—22no—
334#127—22no—
335#125—48no—
336#124—24no—
337#124—28no—
338#124—42no—
339#124—44no—
340#124—48no—
341C22⋊Q8—28no—
342C22⋊Q8—48no—
343C22⋊Q8—48no—
344C22⋊Q8—44no—
345C22⋊Q8—44no—
346C22⋊Q8—48no—
347#121—28no—
348#121—44no—
349#121—44no—
350#121—48no—
351#121—44no—
352#121—44no—
353C4×Q8—28no—
354C4×Q8—44no—
355C4×D4—24no—
356C4×D4—24no—
357C4×D4—44no—
358C4×D4—44no—
359C4×D4—48no—
360C4×D4—48no—
361C4×D4#4118yes—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4—44no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4—44no—
396C2×C4⋊C4—44no—
397C2×C4⋊C4—82no—
398C2×C4⋊C4—82no—
399C2×C4⋊C4C2×D411yescharacteristic
400C2×C4⋊C4C2×D411yescharacteristic
401C2×C4⋊C4C2×D411yescharacteristic
402C2×C4⋊C4C2412yes—
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4C2×D411yescharacteristic
420C2×C22⋊C4C2×D411yescharacteristic
421C2×C22⋊C4C2×D411yescharacteristic
422C2×C22⋊C4C2×D411yescharacteristic
423C2×C22⋊C4C2×D411yescharacteristic
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443C2×C42C2411yescharacteristic
444C4⋊C8—24no—
445#103—28no—
446#103—28no—
447#103—28no—
448#103—44no—
449#103—44no—
450#103—44no—
451#103—44no—
452#103—44no—
453#102—28no—
454#102—44no—
455#102—44no—
456#102—44no—
457C22⋊C8—24no—
458C22⋊C8—24no—
459#97—24no—
460#97—24no—
461#97—42no—
462C4×C8—22no—
463C4×C8—22no—
464C4×C8—22no—
465C4×C8—22no—
466C4×C8—42no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95C2×D411yescharacteristic
478#95C2×D411yescharacteristic
479#95C2×D411yescharacteristic
480#95C2×D411yescharacteristic
481#95C2×D411yescharacteristic
482#95C2×D411yescharacteristic
483C24—22no—
484C24C22×D411yescharacteristic
485C24C22×D411yescharacteristic
486#41—416no—
487#41—88no—
488C2×Q8—22no—
489C2×Q8—24no—
490C2×Q8—24no—
491C2×Q8—22no—
492C2×Q8—24no—
493C2×Q8—24no—
494C2×Q8—22no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—416no—
498C2×Q8—44no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8—82no—
503C2×Q8—82no—
504C2×Q8—82no—
505C2×Q8—88no—
506C2×Q8C2×#4114yes—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—24no—
510C2×D4—22no—
511C2×D4—24no—
512C2×D4—22no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—82no—
525C2×D4#12414yes—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—82no—
556C22×C4—82no—
557C22×C4—82no—
558C22×C4—82no—
559C22×C4—82no—
560C22×C4—82no—
561C22×C4AGL(1,ℤ/8)14yes—
562C22×C4#13714yes—
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C2×#4114yes—
576C22×C4C2×#4114yes—
577C22×C4C2511yescharacteristic
578M16—48no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—48no—
591C2×C8H(5,𝔽2)14yes—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—22no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—44no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—44no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—82no—
624C4⋊C4—82no—
625C4⋊C4—82no—
626C4⋊C4—82no—
627C4⋊C4—82no—
628C4⋊C4—82no—
629C4⋊C4#12414yes—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—82no—
645C22⋊C4—82no—
646C22⋊C4#12414yes—
647C22⋊C4#12414yes—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—22no—
660C42—21no—
661C42—44no—
662C42—44no—
663C42C2×#4114yes—
664C42C2×#4112yes—
665C42H(5,𝔽2)12yes—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23C2×#12412yes—
684C23C2×#12412yes—
685C23C2×AGL(1,ℤ/8)12yes—
686C23C2×#13712yes—
687C23C23×D411yescharacteristic
688Q8—28no—
689Q8—44no—
690Q8—44no—
691Q8—44no—
692Q8—88no—
693Q8—84no—
694Q8—164no—
695D4—28no—
696D4—44no—
697D4—44no—
698D4—88no—
699D4—88no—
700D4—84no—
701D4—84no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—24no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—88no—
756C2×C4—88no—
757C2×C4—164no—
758C2×C4—164no—
759C2×C4C2×#12412yes—
760C2×C4C2×#12412yes—
761C2×C4C2×#12412yes—
762C2×C4C2×#12412yes—
763C2×C4#54612yes—
764C2×C4#54612yes—
765C2×C4C2×AGL(1,ℤ/8)12yes—
766C2×C4C2×AGL(1,ℤ/8)12yes—
767C2×C4C2×#13712yes—
768C2×C4C2×#13712yes—
769C2×C4#57712yes—
770C2×C4#57812yes—
771C2×C4C22×#4111yescharacteristic
772C2×C4C22×#4112yes—
773C2×C4C2×H(5,𝔽2)12yes—
774C2×C4C2×H(5,𝔽2)11yescharacteristic
775C8—24no—
776C8—42no—
777C8—42no—
778C8—42no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22#314114yes—
800C22C22×#12411yescharacteristic
801C22C2×#54611yescharacteristic
802C22#349811yescharacteristic
803C22C22×AGL(1,ℤ/8)11yescharacteristic
804C22C22×#13711yescharacteristic
805C22C2×#57711yescharacteristic
806C22C2×#57811yescharacteristic
807C4—22no—
808C4—22no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—22no—
813C4—44no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4#330814yes—
825C4#331614yes—
826C4#348112yes—
827C4#351912yes—
828C2—24no—
829C2—42no—
830C2—162no—
831C2#3628911yescharacteristic
832C2C2×#314111yescharacteristic
833C2#6062311yescharacteristic
834C2C2×#330811yescharacteristic
835C2C2×#331611yescharacteristic
836C2#6242111yescharacteristic
837C2#6242411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36122C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36180C2semidirect
3. #33230C2semidirect
4. #33049C2semidirect
5. #33042C2semidirect
6. #29141C2semidirect
7. #28750C2semidirect
8. #27973C2semidirect
9. #27972C2semidirect
10. #27765C2semidirect
11. #27278C2semidirect
12. #27266C2semidirect
13. #25857C2semidirect
14. #25856C2semidirect
15. #22421C2semidirect
16. #21647C2semidirect
17. #21200C2semidirect
18. C2×#1956C2semidirect
19. C4×#435C2semidirect

Maximal subgroups

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

subgroupindex
#361802
#361222
#332302
#330492
#330422
#291412
#287502
#279732
#279722
#277652
#272782
#272662
#258572
#258562
#224212
#216472
#212002
C2×#19562
C4×#4352