Finite Group Databasebeta

← #6797207

Subgroups — #6797207

Order 512.

1785 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36211C211yesmaximal, characteristic, complemented
2#36122C211yesmaximal, characteristic, complemented
3#33277C211yesmaximal, characteristic, complemented
4#31815C214yesmaximal, complemented
5#31727C214yesmaximal, complemented
6#29843C211yesmaximal, characteristic, complemented
7#29806C211yesmaximal, characteristic, complemented
8#29176C211yesmaximal, characteristic, complemented
9#28615C211yesmaximal, characteristic, complemented
10#27962C211yesmaximal, characteristic, complemented
11#27890C211yesmaximal, characteristic, complemented
12#26729C214yesmaximal, complemented
13#26657C214yesmaximal, complemented
14#25903C211yesmaximal, characteristic, complemented
15#25599C211yesmaximal, characteristic, complemented
16#21863C211yesmaximal, characteristic, complemented
17#21834C211yesmaximal, characteristic, complemented
18C4×#486C211yesmaximal, characteristic, complemented
19#21264C211yesmaximal, characteristic, complemented
20C2×#548—21no—
21C2×#532C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C2×#493C2211yescharacteristic
24C2×#486C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#431C2211yescharacteristic
27C2×#431C2211yescharacteristic
28#2859C2211yescharacteristic
29#2858C2211yescharacteristic
30#2857C2211yescharacteristic
31#2856C2211yescharacteristic
32#2856C2211yescharacteristic
33#2856C2211yescharacteristic
34#2545—21no—
35#2535—21no—
36#2513—21no—
37#2513C2212yes—
38#2491—21no—
39#2491C2212yes—
40#2490—21no—
41#2490—21no—
42#2452—21no—
43#2452C2212yes—
44#2436—21no—
45#2432—21no—
46#2420—21no—
47#2420C2212yes—
48#2416—21no—
49#2416C2212yes—
50#2414—21no—
51#2414C2212yes—
52#2363—21no—
53#2363C2212yes—
54#2361—21no—
55#2361C2212yes—
56#2357—21no—
57C4×C4⋊Q8C2211yescharacteristic
58C4×#127C2211yescharacteristic
59#2285C2211yescharacteristic
60#2285C2211yescharacteristic
61C42×D4C2211yescharacteristic
62#2101C2214yes—
63#2088C2214yes—
64#2065C2214yes—
65#2054C2214yes—
66#2054C2214yes—
67#2034C2214yes—
68#2034C2214yes—
69#2023C2214yes—
70#1999C2214yes—
71#1999C2214yes—
72#1990C2211yescharacteristic
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1990C2211yescharacteristic
78#1987C2214yes—
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1957C2211yescharacteristic
82#1957C2211yescharacteristic
83#1954C2212yes—
84#1939C2212yes—
85#1934C2214yes—
86#1934C2214yes—
87#1934C2214yes—
88#1926C2214yes—
89#1923C2212yes—
90#1923C2212yes—
91#1920C2214yes—
92#1879C2214yes—
93#1879C2214yes—
94#1875C2214yes—
95#1874C2214yes—
96#1844C2211yescharacteristic
97#1834C2211yescharacteristic
98#1834C2211yescharacteristic
99#1825C2214yes—
100#1824C2214yes—
101#1804C2214yes—
102C4×C4⋊C8C2211yescharacteristic
103C4×#102C2214yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C42×C8C2211yescharacteristic
107C22×#41—21no—
108C23×Q8—21no—
109C22×D8C2314yes—
110#548—48no—
111#532—24no—
112#532—42no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—42no—
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2312yes—
119C2×C4⋊Q8C2311yescharacteristic
120C2×#127C2311yescharacteristic
121C2×#127C2311yescharacteristic
122C2×#125—21no—
123C2×#124—22no—
124C2×#124—21no—
125C2×#124—21no—
126C2×#124—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—22no—
129C2×#121—22no—
130C2×#121—21no—
131C2×#121—21no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121C2312yes—
138C2×#121C2312yes—
139C2×#121C2312yes—
140C2×#121C2312yes—
141C2×C4×Q8—21no—
142C2×C4×D4—22no—
143C2×C4×D4—21no—
144C2×C4×D4—21no—
145C2×C4×D4—21no—
146C2×C4×D4D411yescharacteristic
147C2×C4×D4D411yescharacteristic
148C2×C4×D4C2312yes—
149C2×C4×D4C2312yes—
150C2×C4×D4C2311yescharacteristic
151C2×#117—21no—
152C2×#117C2312yes—
153C22×C4⋊C4—21no—
154C22×C4⋊C4C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#493—42no—
158#486—24no—
159#486—42no—
160#431—42no—
161#431—42no—
162C2×#106C2314yes—
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2312yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2312yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2312yes—
181C2×C4×C8C2312yes—
182#397—22no—
183#397—22no—
184#397—22no—
185#396—22no—
186#396—22no—
187#394—22no—
188#394—22no—
189#394—22no—
190#394—22no—
191#393—22no—
192#393—22no—
193#392—22no—
194#391—21no—
195#391—21no—
196#390—22no—
197#390—22no—
198#390—21no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390—21no—
203#390—21no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390—21no—
208#390C2312yes—
209#390C2312yes—
210#390C2312yes—
211#390C2312yes—
212#390C2312yes—
213#390C2312yes—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389C2312yes—
219#389C2312yes—
220#389C2312yes—
221#389C2312yes—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#386—22no—
229#386—22no—
230#386—22no—
231#386—22no—
232#385—22no—
233#385—22no—
234#384C2311yescharacteristic
235#384C2311yescharacteristic
236#384C2311yescharacteristic
237#384C2311yescharacteristic
238#382—21no—
239#382—21no—
240#382C2312yes—
241#381—22no—
242#380—21no—
243#380—21no—
244#380—21no—
245#380—21no—
246#380C2312yes—
247#380C2312yes—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4D411yescharacteristic
253C4×C4⋊C4D411yescharacteristic
254C4×C4⋊C4C2312yes—
255C4×C4⋊C4C2312yes—
256C4×C4⋊C4C2311yescharacteristic
257C4×C22⋊C4—22no—
258C4×C22⋊C4D411yescharacteristic
259C4×C22⋊C4D411yescharacteristic
260C4×C22⋊C4D411yescharacteristic
261C4×C22⋊C4D411yescharacteristic
262C4×C22⋊C4C2311yescharacteristic
263C4×C22⋊C4C2311yescharacteristic
264C43C2311yescharacteristic
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276C2×#41—44no—
277C2×#41—44no—
278C2×#41—82no—
279C22×Q8—21no—
280C22×Q8—21no—
281C22×Q8—22no—
282C22×Q8—44no—
283C22×Q8—44no—
284C22×Q8—82no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4C2×D411yescharacteristic
294C22×D4C2412yes—
295C22×D4C2412yes—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C2×D8—44no—
306C2×D8—44no—
307C2×D8—44no—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C4⋊Q8—24no—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—42no—
317C4⋊Q8—44no—
318C4⋊Q8—44no—
319C4⋊Q8#4114yes—
320#127—22no—
321#127—22no—
322#127—22no—
323#127—22no—
324#125—82no—
325#124—44no—
326#124—48no—
327#124—44no—
328#124—82no—
329C22⋊Q8—48no—
330C22⋊Q8—44no—
331#121—24no—
332#121—44no—
333#121—44no—
334#121—42no—
335#121—44no—
336#121—44no—
337#121—48no—
338#121—44no—
339#121—44no—
340#121—44no—
341#121—82no—
342#121—82no—
343#121—82no—
344C4×Q8—44no—
345C4×D4—24no—
346C4×D4—24no—
347C4×D4—24no—
348C4×D4—42no—
349C4×D4—44no—
350C4×D4—42no—
351C4×D4—44no—
352C4×D4—48no—
353C4×D4—44no—
354C4×D4—82no—
355#117—44no—
356#117—82no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
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—42no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4C2×D411yescharacteristic
377C2×C4⋊C4C2×D411yescharacteristic
378C2×C4⋊C4C2×D411yescharacteristic
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C22⋊C4C2×D411yescharacteristic
409C2×C22⋊C4C2×D411yescharacteristic
410C2×C22⋊C4C2×D411yescharacteristic
411C2×C22⋊C4C2×D411yescharacteristic
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432#106—44no—
433C4⋊C8—42no—
434C4⋊C8—42no—
435C4⋊C8—42no—
436#102—28no—
437#102—44no—
438#102—44no—
439#102—44no—
440#102—44no—
441#102—44no—
442C22⋊C8—42no—
443C22⋊C8—42no—
444C22⋊C8—42no—
445C22⋊C8—42no—
446C4×C8—22no—
447C4×C8—22no—
448C4×C8—22no—
449C4×C8—22no—
450C4×C8—42no—
451C4×C8—42no—
452#95—22no—
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#95C2×D411yescharacteristic
463#95C2×D411yescharacteristic
464#95C2×D411yescharacteristic
465#95C2×D411yescharacteristic
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468C24—22no—
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—42no—
480C2×Q8—42no—
481C2×Q8—82no—
482C2×Q8—816no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—24no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—24no—
493C2×D4—41no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—82no—
514C2×D4—82no—
515C2×D4—82no—
516C2×D4—82no—
517C2×D4—82no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
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—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—82no—
549C22×C4—82no—
550C22×C4—82no—
551C22×C4—82no—
552C22×C4#13514yes—
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C2511yescharacteristic
566D8—88no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C4⋊C4—24no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—41no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—44no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—82no—
604C4⋊C4—82no—
605C4⋊C4C2×#4114yes—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—82no—
624C22⋊C4—82no—
625C22⋊C4—82no—
626C22⋊C4—82no—
627C22⋊C4—82no—
628C22⋊C4—82no—
629C22⋊C4—82no—
630C22⋊C4—82no—
631C22⋊C4—82no—
632C22⋊C4—82no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—22no—
645C42—22no—
646C42—44no—
647C42—82no—
648C42—82no—
649C42AGL(1,ℤ/8)14yes—
650C42C2×#4112yes—
651C42H(5,𝔽2)12yes—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23C2×#13512yes—
680C23C23×D411yescharacteristic
681Q8—48no—
682Q8—88no—
683Q8—84no—
684D4—44no—
685D4—44no—
686D4—44no—
687D4—44no—
688D4—44no—
689D4—88no—
690D4—88no—
691D4—84no—
692D4—84no—
693D4—84no—
694D4—84no—
695D4—164no—
696D4—164no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—28no—
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—24no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
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—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—88no—
751C2×C4—88no—
752C2×C4—164no—
753C2×C4#54612yes—
754C2×C4#54612yes—
755C2×C4C2×#13512yes—
756C2×C4C2×#13512yes—
757C2×C4C2×AGL(1,ℤ/8)12yes—
758C2×C4C2×AGL(1,ℤ/8)12yes—
759C2×C4C2×AGL(1,ℤ/8)12yes—
760C2×C4#57612yes—
761C2×C4#57712yes—
762C2×C4C22×#4111yescharacteristic
763C2×C4C2×H(5,𝔽2)11yescharacteristic
764C2×C4#58512yes—
765C2×C4#58512yes—
766C8—42no—
767C8—42no—
768C8—42no—
769C8—42no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22#344911yescharacteristic
799C22C2×#54611yescharacteristic
800C22#350011yescharacteristic
801C22C22×#13511yescharacteristic
802C22C22×AGL(1,ℤ/8)11yescharacteristic
803C22C2×#57611yescharacteristic
804C22C2×#57711yescharacteristic
805C4—22no—
806C4—22no—
807C4—22no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—44no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4#330114yes—
822C4#332514yes—
823C4#352412yes—
824C4#355112yes—
825C2—42no—
826C2—81no—
827C2—162no—
828C2—162no—
829C2#3894811yescharacteristic
830C2#6094611yescharacteristic
831C2#6100611yescharacteristic
832C2C2×#330111yescharacteristic
833C2C2×#332511yescharacteristic
834C2#6252711yescharacteristic
835C2#6254111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
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. #36211C2semidirect
2. #36122C2semidirect
3. #33277C2semidirect
4. #31815C2semidirect
5. #31727C2semidirect
6. #29843C2semidirect
7. #29806C2semidirect
8. #29176C2semidirect
9. #28615C2semidirect
10. #27962C2semidirect
11. #27890C2semidirect
12. #26729C2semidirect
13. #26657C2semidirect
14. #25903C2semidirect
15. #25599C2semidirect
16. #21863C2semidirect
17. #21834C2semidirect
18. C4×#486C2semidirect
19. #21264C2semidirect

Maximal subgroups

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

subgroupindex
#362112
#361222
#332772
#318152
#317272
#298432
#298062
#291762
#286152
#279622
#278902
#267292
#266572
#259032
#255992
#218632
#218342
C4×#4862
#212642