Finite Group Databasebeta

← #6763580

Subgroups — #6763580

Order 512.

1850 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36180C211yesmaximal, characteristic, complemented
2#36122C211yesmaximal, characteristic
3#33042C211yesmaximal, characteristic, complemented
4#31740C214yesmaximal, complemented
5#31458C214yesmaximal, complemented
6#30203C211yesmaximal, characteristic, complemented
7#29877C211yesmaximal, characteristic, complemented
8#29218C211yesmaximal, characteristic, complemented
9#28654C211yesmaximal, characteristic, complemented
10#27973C211yesmaximal, characteristic, complemented
11#27961C211yesmaximal, characteristic, complemented
12#26410C214yesmaximal, complemented
13#26202C214yesmaximal, complemented
14#25811C211yesmaximal, characteristic, complemented
15#25671C211yesmaximal, characteristic, complemented
16#22246C211yesmaximal, characteristic, complemented
17#21859C211yesmaximal, characteristic, complemented
18C2×#1990C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic, complemented
20C2×#554—21no—
21C2×#548—21no—
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C2×#498C2211yescharacteristic
25C2×#498C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#431C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29#2868C2211yescharacteristic
30#2858C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2856C2211yescharacteristic
35#2567—21no—
36#2552—21no—
37#2552C2212yes—
38#2545—21no—
39#2502—21no—
40#2502—21no—
41#2491—21no—
42#2491C2212yes—
43#2452—21no—
44#2452C2212yes—
45#2440—21no—
46#2440—21no—
47#2440C2212yes—
48#2440C2212yes—
49#2436—21no—
50#2432—21no—
51#2416—21no—
52#2416C2212yes—
53#2361—21no—
54#2361C2212yes—
55D4×C4⋊C4—21no—
56D4×C4⋊C4C2212yes—
57C4×C4⋊Q8C2211yescharacteristic
58C4×C4⋊Q8C2211yescharacteristic
59C2×#384C2211yescharacteristic
60C2×#384C2211yescharacteristic
61C42×D4C2211yescharacteristic
62#2100C2214yes—
63#2100C2214yes—
64#2088C2214yes—
65#2077C2214yes—
66#2071C2214yes—
67#2071C2214yes—
68#2065C2214yes—
69#2058C2214yes—
70#2034C2214yes—
71#2023C2214yes—
72#1990C2211yescharacteristic
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1990C2211yescharacteristic
78#1990C2211yescharacteristic
79#1990C2214yes—
80#1987C2214yes—
81#1957C2211yescharacteristic
82#1957C2211yescharacteristic
83#1957C2211yescharacteristic
84#1934C2214yes—
85#1926C2214yes—
86#1923C2212yes—
87#1920C2214yes—
88#1919C2214yes—
89#1916C2212yes—
90#1893C2214yes—
91#1874C2214yes—
92#1874C2214yes—
93#1869C2212yes—
94#1864C2214yes—
95#1853C2214yes—
96#1850C2212yes—
97#1834C2211yescharacteristic
98#1834C2211yescharacteristic
99#1834C2211yescharacteristic
100#1824C2214yes—
101#1802C2214yes—
102C4×C4⋊C8C2211yescharacteristic
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105#1744C2211yescharacteristic
106C2×#340C2214yes—
107C22×#41—21no—
108C23×Q8—21no—
109C23×C8C2312yes—
110#554—48no—
111#548—48no—
112#532—24no—
113#532—42no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8—42no—
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2312yes—
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2312yes—
125C2×#127C2311yescharacteristic
126C2×#125—22no—
127C2×#124—22no—
128C2×#124—21no—
129C2×#124—21no—
130C2×#124—21no—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—22no—
135C2×C22⋊Q8—22no—
136C2×C22⋊Q8—22no—
137C2×#121—22no—
138C2×#121—21no—
139C2×#121—21no—
140C2×#121—21no—
141C2×#121C2312yes—
142C2×#121C2312yes—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×D4—22no—
146C2×C4×D4—22no—
147C2×C4×D4—21no—
148C2×C4×D4D411yescharacteristic
149C2×C4×D4D411yescharacteristic
150C2×C4×D4C2312yes—
151C2×C4×D4C2311yescharacteristic
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162#498—24no—
163#498—42no—
164#486—42no—
165#431—42no—
166C2×#106C2314yes—
167C2×#106C2314yes—
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2312yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2312yes—
177C2×C4×C8—42no—
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2311yescharacteristic
182C2×C4×C8C2312yes—
183#398—22no—
184#398—22no—
185#398—22no—
186#398—22no—
187#396—22no—
188#396—22no—
189#395—22no—
190#395—22no—
191#394—22no—
192#394—22no—
193#393—22no—
194#393—22no—
195#391—21no—
196#391—21no—
197#391—21no—
198#391—21no—
199#391—21no—
200#390—21no—
201#390—21no—
202#390—21no—
203#390—21no—
204#390C2312yes—
205#390C2312yes—
206#390C2312yes—
207#389—22no—
208#389—22no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389C2312yes—
215#389C2312yes—
216#389C2312yes—
217#389C2312yes—
218#389C2312yes—
219#388—22no—
220#388—22no—
221#386—22no—
222#386—22no—
223#385—22no—
224#385—22no—
225#385—22no—
226#385—22no—
227#385—22no—
228#385—22no—
229#384—21no—
230#384—21no—
231#384—21no—
232#384—21no—
233#384—21no—
234#384—21no—
235#384C2311yescharacteristic
236#384C2311yescharacteristic
237#384C2312yes—
238#384C2312yes—
239#384C2312yes—
240#384C2311yescharacteristic
241#384C2311yescharacteristic
242#380—21no—
243#380—21no—
244#380—21no—
245#380C2312yes—
246#380C2312yes—
247#380C2312yes—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4D411yescharacteristic
251C4×C4⋊C4D411yescharacteristic
252C4×C4⋊C4C2312yes—
253C4×C4⋊C4C2312yes—
254C4×C4⋊C4C2311yescharacteristic
255C4×C22⋊C4D411yescharacteristic
256C4×C22⋊C4D411yescharacteristic
257C4×C22⋊C4D411yescharacteristic
258C4×C22⋊C4D411yescharacteristic
259C4×C22⋊C4C2311yescharacteristic
260C4×C22⋊C4C2311yescharacteristic
261C43C2311yescharacteristic
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#336C2312yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277C2×#41—44no—
278C2×#41—44no—
279C2×#41—82no—
280C22×Q8—21no—
281C22×Q8—21no—
282C22×Q8—21no—
283C22×Q8—22no—
284C22×Q8—22no—
285C22×Q8—44no—
286C22×Q8—44no—
287C22×Q8—82no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4C2×D411yescharacteristic
293C22×D4C2412yes—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C22×C8—24no—
305C22×C8—42no—
306C22×C8—42no—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C22×C8C2412yes—
311C4⋊Q8—24no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—42no—
318C4⋊Q8—44no—
319C4⋊Q8—44no—
320C4⋊Q8—44no—
321C4⋊Q8—44no—
322C4⋊Q8—82no—
323C4⋊Q8#4114yes—
324#127—22no—
325#127—22no—
326#125—48no—
327#124—44no—
328#124—48no—
329#124—44no—
330#124—82no—
331C22⋊Q8—48no—
332C22⋊Q8—48no—
333C22⋊Q8—44no—
334C22⋊Q8—44no—
335C22⋊Q8—44no—
336C22⋊Q8—48no—
337#121—28no—
338#121—24no—
339#121—42no—
340#121—44no—
341#121—48no—
342#121—44no—
343#121—44no—
344C4×Q8—44no—
345C4×Q8—44no—
346C4×D4—24no—
347C4×D4—24no—
348C4×D4—24no—
349C4×D4—42no—
350C4×D4—44no—
351C4×D4—48no—
352C4×D4—48no—
353C4×D4SD1618yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—82no—
389C2×C4⋊C4—82no—
390C2×C4⋊C4C2×D411yescharacteristic
391C2×C4⋊C4C2×D411yescharacteristic
392C2×C4⋊C4C2×D411yescharacteristic
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2412yes—
398C2×C4⋊C4C2412yes—
399C2×C4⋊C4C2412yes—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4C2×D411yescharacteristic
413C2×C22⋊C4C2×D411yescharacteristic
414C2×C22⋊C4C2×D411yescharacteristic
415C2×C22⋊C4C2×D411yescharacteristic
416C2×C22⋊C4C2×D411yescharacteristic
417C2×C22⋊C4C2×D411yescharacteristic
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437#106—28no—
438#106—44no—
439C4⋊C8—42no—
440C4⋊C8—42no—
441#102—44no—
442#102—44no—
443#102—44no—
444#102—44no—
445C22⋊C8—24no—
446C22⋊C8—42no—
447C22⋊C8—42no—
448C4×C8—22no—
449C4×C8—22no—
450C4×C8—22no—
451C4×C8—22no—
452C4×C8—42no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95C2×D411yescharacteristic
464#95C2×D411yescharacteristic
465#95C2×D411yescharacteristic
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469C24—22no—
470C24C22×D411yescharacteristic
471C24C22×D411yescharacteristic
472#41—816no—
473C2×Q8—24no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—44no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—82no—
486C2×Q8—82no—
487C2×Q8—82no—
488C2×Q8—816no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—82no—
507C2×D4C2×SD1614yes—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—82no—
538C22×C4—82no—
539C22×C4—82no—
540C22×C4—82no—
541C22×C4—82no—
542C22×C4—82no—
543C22×C4C2×SD1614yes—
544C22×C4C2×SD1614yes—
545C22×C4AGL(1,ℤ/8)14yes—
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C42−1+414yes—
559C22×C4C2511yescharacteristic
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—48no—
573C4⋊C4—22no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—44no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—44no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—82no—
606C4⋊C4—82no—
607C4⋊C4—82no—
608C4⋊C4—82no—
609C4⋊C4—82no—
610C4⋊C4—82no—
611C4⋊C4C2×SD1614yes—
612C4⋊C4C2×#4114yes—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—82no—
628C22⋊C4—82no—
629C22⋊C4C2×SD1614yes—
630C22⋊C4C2×SD1614yes—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—22no—
643C42—22no—
644C42—44no—
645C42—44no—
646C42C2×SD1614yes—
647C42C2×#4112yes—
648C42H(5,𝔽2)12yes—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23#53612yes—
667C23C22×SD1612yes—
668C23C22×SD1612yes—
669C23C2×AGL(1,ℤ/8)12yes—
670C23C23×D411yescharacteristic
671Q8—48no—
672Q8—88no—
673Q8—84no—
674Q8—84no—
675Q8—164no—
676D4—28no—
677D4—44no—
678D4—44no—
679D4—88no—
680D4—88no—
681D4—84no—
682D4—84no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—24no—
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—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—88no—
737C2×C4—88no—
738C2×C4—164no—
739C2×C4—164no—
740C2×C4#53612yes—
741C2×C4#54612yes—
742C2×C4#54612yes—
743C2×C4C22×SD1612yes—
744C2×C4C22×SD1612yes—
745C2×C4C22×SD1612yes—
746C2×C4C22×SD1612yes—
747C2×C4C22×SD1612yes—
748C2×C4C2×AGL(1,ℤ/8)12yes—
749C2×C4C2×AGL(1,ℤ/8)12yes—
750C2×C4#57612yes—
751C2×C4#57812yes—
752C2×C4C22×#4111yescharacteristic
753C2×C4C2×H(5,𝔽2)11yescharacteristic
754C2×C4C2×2−1+412yes—
755C2×C4#58512yes—
756C8—42no—
757C8—42no—
758C8—42no—
759C8—42no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22#322714yes—
781C22C2×#53611yescharacteristic
782C22C2×#54611yescharacteristic
783C22#350011yescharacteristic
784C22C23×SD1611yescharacteristic
785C22C22×AGL(1,ℤ/8)11yescharacteristic
786C22C2×#57611yescharacteristic
787C22C2×#57811yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—41no—
795C4—44no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4#329514yes—
806C4#330814yes—
807C4#351612yes—
808C4#354112yes—
809C2—24no—
810C2—42no—
811C2—162no—
812C2#3808311yescharacteristic
813C2C2×#322711yescharacteristic
814C2#6088011yescharacteristic
815C2C2×#329511yescharacteristic
816C2C2×#330811yescharacteristic
817C2#6252611yescharacteristic
818C2#6253511yescharacteristic
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. #33042C2semidirect
4. #31740C2semidirect
5. #31458C2semidirect
6. #30203C2semidirect
7. #29877C2semidirect
8. #29218C2semidirect
9. #28654C2semidirect
10. #27973C2semidirect
11. #27961C2semidirect
12. #26410C2semidirect
13. #26202C2semidirect
14. #25811C2semidirect
15. #25671C2semidirect
16. #22246C2semidirect
17. #21859C2semidirect
18. C2×#1990C2semidirect
19. #21101C2semidirect

Maximal subgroups

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

subgroupindex
#361802
#361222
#330422
#317402
#314582
#302032
#298772
#292182
#286542
#279732
#279612
#264102
#262022
#258112
#256712
#222462
#218592
C2×#19902
#211012