Finite Group Databasebeta

← #6815595

Subgroups — #6815595

Order 512.

1874 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3229C211yesmaximal, characteristic, complemented
2C2×#3209C211yesmaximal, characteristic, complemented
3#36129C211yesmaximal, characteristic
4#36129C211yesmaximal, characteristic
5#33255C211yesmaximal, characteristic, complemented
6#31173C214yesmaximal, complemented
7#31035C214yesmaximal
8#29877C211yesmaximal, characteristic, complemented
9#29808C211yesmaximal, characteristic, complemented
10#28653C211yesmaximal, characteristic, complemented
11#28616C211yesmaximal, characteristic, complemented
12#27241C214yesmaximal, complemented
13#26949C214yesmaximal, complemented
14#25902C211yesmaximal, characteristic, complemented
15#25856C211yesmaximal, characteristic, complemented
16#25672C211yesmaximal, characteristic, complemented
17#25600C211yesmaximal, characteristic, complemented
18#21647C211yesmaximal, characteristic, complemented
19#21265C211yesmaximal, characteristic
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24#3229—28no—
25#3209—28no—
26C2×#498C2211yescharacteristic
27C2×#498C2211yescharacteristic
28C2×#494C2211yescharacteristic
29C2×#494C2211yescharacteristic
30C2×#487C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#483C2214yes—
36C2×#475C2214yes—
37C2×#462C2214yes—
38C2×#451C2214yes—
39C2×#431C2211yescharacteristic
40C2×#431C2211yescharacteristic
41#2862C2211yescharacteristic
42#2862C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2550—21no—
48#2550—21no—
49#2492—21no—
50#2492C2212yes—
51#2451—21no—
52#2451C2212yes—
53#2446—21no—
54#2446C2212yes—
55#2442—21no—
56#2442—21no—
57#2439—21no—
58#2439—21no—
59#2429—21no—
60#2429C2212yes—
61#2417—21no—
62#2417C2212yes—
63#2409—21no—
64#2409C2212yes—
65#2360—21no—
66#2360C2212yes—
67#2352—21no—
68#2352—21no—
69Q8×C22⋊C4—21no—
70Q8×C22⋊C4C2212yes—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2088C2214yes—
75#2077C2214yes—
76#2066C2214yes—
77#2056C2214yes—
78#2056C2214yes—
79#2043C2214yes—
80#2035C2214yes—
81#2024C2214yes—
82#2001C2214yes—
83#2001C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1971C2214yes—
88#1971C2214yes—
89#1956C2211yescharacteristic
90#1956C2211yescharacteristic
91#1956C2211yescharacteristic
92#1955C2212yes—
93#1940C2212yes—
94#1935C2214yes—
95#1927C2214yes—
96#1924C2212yes—
97#1924C2212yes—
98#1878C2214yes—
99#1878C2214yes—
100#1872C2214yes—
101#1865C2214yes—
102#1834C2211yescharacteristic
103#1787C2214yes—
104C4×C4⋊C8C2211yescharacteristic
105#1763C2214yes—
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C4×#97C2211yescharacteristic
109C23×Q8—21no—
110C23×Q8C2312yes—
111C22×Q16C2314yes—
112C22×Q16C2314yes—
113#533—24no—
114#533—24no—
115#533—42no—
116#533—42no—
117C2×C4⋊Q8—24no—
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8—21no—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8—42no—
124C2×C4⋊Q8—42no—
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2312yes—
128C2×C4⋊Q8C2311yescharacteristic
129C2×C4⋊Q8C2311yescharacteristic
130C2×C4⋊Q8C2311yescharacteristic
131C2×C4⋊Q8C2312yes—
132C2×C4⋊Q8C2311yescharacteristic
133C2×#125—21no—
134C2×#125—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8C2312yes—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2312yes—
142C2×C22⋊Q8C2312yes—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×Q8C2312yes—
147C2×C4×Q8C2312yes—
148C2×C4×Q8C2312yes—
149C2×C4×D4D411yescharacteristic
150C2×C4×D4D411yescharacteristic
151C2×C4×D4C2311yescharacteristic
152C2×#117—21no—
153C2×#117—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4C2312yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160#498—24no—
161#498—24no—
162#494—24no—
163#494—24no—
164#487—24no—
165#487—24no—
166#487—42no—
167#487—42no—
168#487D418yescomplemented
169#483—216no—
170#475—216no—
171#462—216no—
172#451—216no—
173#431—24no—
174#431—24no—
175C2×#106C2314yes—
176C2×#106C2314yes—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2312yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C2×#97C2312yes—
193C2×#97C2312yes—
194C2×C4×C8C2311yescharacteristic
195C2×C4×C8C2311yescharacteristic
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198#400—22no—
199#400—22no—
200#398—22no—
201#398—22no—
202#398—22no—
203#398—22no—
204#396—22no—
205#396—22no—
206#395—22no—
207#395—22no—
208#393—22no—
209#393—22no—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—22no—
218#391—22no—
219#391—22no—
220#391—22no—
221#391C2312yes—
222#391C2312yes—
223#391C2312yes—
224#391C2312yes—
225#391C2312yes—
226#391C2312yes—
227#391C2312yes—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—22no—
238#389—22no—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#388—22no—
243#388—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#386—22no—
249#386—22no—
250#385—22no—
251#385—22no—
252#384C2311yescharacteristic
253#384C2311yescharacteristic
254#382—21no—
255#382—21no—
256#382—21no—
257#382—21no—
258#380—21no—
259#380—21no—
260#380—21no—
261#380—21no—
262#380—21no—
263#380—21no—
264#380—22no—
265#380—22no—
266#380C2312yes—
267#380C2312yes—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4D411yescharacteristic
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2311yescharacteristic
275C4×C22⋊C4—22no—
276C4×C22⋊C4—22no—
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4D411yescharacteristic
280C4×C22⋊C4D411yescharacteristic
281C4×C22⋊C4C2311yescharacteristic
282C4×C22⋊C4C2311yescharacteristic
283C43C2311yescharacteristic
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291C22×Q8—21no—
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8—22no—
295C22×Q8—22no—
296C22×Q8—24no—
297C22×Q8—42no—
298C22×Q8—44no—
299C22×Q8—44no—
300C22×Q8—44no—
301C22×Q8—44no—
302C22×Q8—82no—
303C22×Q8C2412yes—
304C22×Q8C2412yes—
305C22×Q8C2412yes—
306C22×D4C2×D411yescharacteristic
307C23×C4—22no—
308C23×C4—22no—
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C2×Q16—28no—
316C2×Q16—28no—
317C2×Q16—44no—
318C2×Q16—44no—
319C2×Q16—44no—
320C2×Q16—44no—
321C22×C8C2412yes—
322C22×C8C2412yes—
323C22×C8C2412yes—
324C22×C8C2412yes—
325C4⋊Q8—24no—
326C4⋊Q8—24no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—42no—
338C4⋊Q8—44no—
339C4⋊Q8—44no—
340C4⋊Q8—44no—
341C4⋊Q8—42no—
342C4⋊Q8—44no—
343C4⋊Q8C2×D414yes—
344C4⋊Q8C2×D414yes—
345#125—44no—
346#125—44no—
347C22⋊Q8—24no—
348C22⋊Q8—24no—
349C22⋊Q8—44no—
350C22⋊Q8—42no—
351C22⋊Q8—42no—
352C22⋊Q8—44no—
353C22⋊Q8—44no—
354C22⋊Q8—44no—
355C22⋊Q8—44no—
356C22⋊Q8—82no—
357C4×Q8—24no—
358C4×Q8—24no—
359C4×Q8—42no—
360C4×Q8—42no—
361C4×Q8—44no—
362C4×Q8—44no—
363C4×Q8—44no—
364C4×Q8—82no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—42no—
368#117—44no—
369#117—44no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—44no—
400C2×C4⋊C4—44no—
401C2×C4⋊C4—44no—
402C2×C4⋊C4C2×D411yescharacteristic
403C2×C4⋊C4C2×D411yescharacteristic
404C2×C4⋊C4C2×D411yescharacteristic
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
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⋊C4C2×D411yescharacteristic
417C2×C22⋊C4C2×D411yescharacteristic
418C2×C22⋊C4C2×D411yescharacteristic
419C2×C22⋊C4C2×D411yescharacteristic
420C2×C22⋊C4C2×D411yescharacteristic
421C2×C22⋊C4C2×D411yescharacteristic
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443#106—28no—
444#106—28no—
445C4⋊C8—24no—
446C4⋊C8—24no—
447C4⋊C8—42no—
448#103—28no—
449#103—28no—
450#103—44no—
451#103—44no—
452#103—44no—
453#103—44no—
454#103—44no—
455#103C2×D4116yes—
456C22⋊C8—24no—
457C22⋊C8—24no—
458C22⋊C8—42no—
459C22⋊C8—42no—
460#97—42no—
461#97—42no—
462C4×C8—22no—
463C4×C8—22no—
464C4×C8—22no—
465C4×C8C2×D414yes—
466#95—22no—
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#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95C2×D411yescharacteristic
487#95C2×D411yescharacteristic
488#95C2×D411yescharacteristic
489#95C2×D411yescharacteristic
490#95C2×D411yescharacteristic
491#95C2×D411yescharacteristic
492C24C22×D411yescharacteristic
493C24C22×D411yescharacteristic
494C2×Q8—24no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—24no—
501C2×Q8—24no—
502C2×Q8—24no—
503C2×Q8—24no—
504C2×Q8—24no—
505C2×Q8—24no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8—44no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—44no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—42no—
518C2×Q8—82no—
519C2×Q8—82no—
520C2×Q8—816no—
521C2×Q8—88no—
522C2×Q8—88no—
523C2×Q8C22×D414yes—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—41no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—82no—
558C22×C4—82no—
559C22×C4#13714yes—
560C22×C4#13714yes—
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
574Q16—88no—
575Q16—88no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
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×C8C22×D414yes—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—41no—
601C4⋊C4—44no—
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—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—44no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—82no—
622C4⋊C4—82no—
623C4⋊C4—82no—
624C4⋊C4—82no—
625C4⋊C4C22×D414yes—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—41no—
631C22⋊C4—41no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—82no—
637C22⋊C4—82no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—22no—
651C42—22no—
652C42—44no—
653C42—44no—
654C42—82no—
655C42—82no—
656C42C22×D412yes—
657C42H(5,𝔽2)12yes—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23C2×#13712yes—
671C23C2×#13712yes—
672C23C23×D411yescharacteristic
673Q8—28no—
674Q8—48no—
675Q8—44no—
676Q8—44no—
677Q8—44no—
678Q8—44no—
679Q8—44no—
680Q8—88no—
681Q8—88no—
682Q8—84no—
683Q8—84no—
684D4—44no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—21no—
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—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—44no—
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—42no—
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—88no—
746C2×C4—88no—
747C2×C4D4212yes—
748C2×C4D4212yes—
749C2×C4C2×#13712yes—
750C2×C4C2×#13712yes—
751C2×C4C2×#13712yes—
752C2×C4C2×#13712yes—
753C2×C4#57712yes—
754C2×C4#57812yes—
755C2×C4C23×D411yescharacteristic
756C2×C4C2×H(5,𝔽2)11yescharacteristic
757C2×C4#58512yes—
758C2×C4#58512yes—
759C8—24no—
760C8—42no—
761C8—42no—
762C8—42no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22#344911yescharacteristic
778C22C2×D4211yescharacteristic
779C22#350011yescharacteristic
780C22C22×#13711yescharacteristic
781C22C22×#13711yescharacteristic
782C22C2×#57711yescharacteristic
783C22C2×#57811yescharacteristic
784C4—22no—
785C4—22no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—44no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—44no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4#326614yes—
803C4#327014yes—
804C4#350012yes—
805C4#356212yes—
806C2—42no—
807C2—42no—
808C2#3935711yescharacteristic
809C2#6097111yescharacteristic
810C2#6100811yescharacteristic
811C2C2×#326611yescharacteristic
812C2C2×#327011yescharacteristic
813C2#6253611yescharacteristic
814C2#6254211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
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. C2×#3229C2semidirect
2. C2×#3209C2semidirect
5. #33255C2semidirect
6. #31173C2semidirect
8. #29877C2semidirect
9. #29808C2semidirect
10. #28653C2semidirect
11. #28616C2semidirect
12. #27241C2semidirect
13. #26949C2semidirect
14. #25902C2semidirect
15. #25856C2semidirect
16. #25672C2semidirect
17. #25600C2semidirect
18. #21647C2semidirect
168. #487D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32292
C2×#32092
#361292
#332552
#311732
#310352
#298772
#298082
#286532
#286162
#272412
#269492
#259022
#258562
#256722
#256002
#216472
#212652