Finite Group Databasebeta

← #6763750

Subgroups — #6763750

Order 512.

1844 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36181C211yesmaximal, characteristic
2D4×C4⋊Q8C211yesmaximal, characteristic
3#33043C211yesmaximal, characteristic, complemented
4#32082C214yesmaximal, complemented
5#31288C214yesmaximal, complemented
6#30220C211yesmaximal, characteristic, complemented
7#29845C211yesmaximal, characteristic, complemented
8#29191C211yesmaximal, characteristic, complemented
9#28748C211yesmaximal, characteristic, complemented
10#27905C211yesmaximal, characteristic, complemented
11#27889C211yesmaximal, characteristic, complemented
12#25856C211yesmaximal, characteristic, complemented
13#25856C211yesmaximal, characteristic, complemented
14#24480C214yesmaximal, complemented
15#24041C214yesmaximal
16#22218C211yesmaximal, characteristic, complemented
17#21804C211yesmaximal, characteristic, complemented
18C2×#1956C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic
20C2×#552—21no—
21C2×D4×Q8C2212yes—
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C2×#487C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#487C2211yescharacteristic
27C2×#483C2214yes—
28C2×#431C2211yescharacteristic
29C22×#103C2214yes—
30C22×C4×C8C2211yescharacteristic
31#2868C2211yescharacteristic
32#2859C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2565—21no—
38#2551—21no—
39#2551—21no—
40#2546C2212yes—
41#2506—21no—
42#2506C2212yes—
43#2503—21no—
44#2499—21no—
45#2496—21no—
46#2496C2212yes—
47#2486—21no—
48#2486C2212yes—
49#2440—21no—
50#2440—21no—
51#2440—21no—
52#2440—21no—
53#2434C2212yes—
54#2434C2212yes—
55D4×C4⋊C4—21no—
56D4×C4⋊C4—21no—
57#2344—21no—
58#2344C2212yes—
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61#2285C2211yescharacteristic
62C2×#384C2211yescharacteristic
63C42×D4C2211yescharacteristic
64#2096C2214yes—
65#2066C2214yes—
66#2066C2214yes—
67#2043C2214yes—
68#2043C2214yes—
69#2043C2214yes—
70#2043C2214yes—
71#2043C2214yes—
72#2035C2214yes—
73#2035C2214yes—
74#1990C2211yescharacteristic
75#1981C2214yes—
76#1981C2214yes—
77#1956C2211yescharacteristic
78#1956C2211yescharacteristic
79#1956C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2211yescharacteristic
85#1956C2214yes—
86#1956C2211yescharacteristic
87#1933C2214yes—
88#1927C2214yes—
89#1927C2214yes—
90#1923C2212yes—
91#1916C2212yes—
92#1892C2214yes—
93#1869C2212yes—
94#1865C2214yes—
95#1865C2214yes—
96#1850C2212yes—
97#1844C2211yescharacteristic
98#1844C2211yescharacteristic
99#1834C2211yescharacteristic
100#1787C2214yes—
101#1787C2214yes—
102#1787C2214yes—
103C4×C4⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106#1744C2211yescharacteristic
107C23×Q8C2312yes—
108C23×Q8C2312yes—
109C23×C8C2312yes—
110#552—48no—
111D4×Q8—48no—
112C2×C4⋊Q8—22no—
113C2×C4⋊Q8—24no—
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⋊Q8—42no—
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2312yes—
124C2×C4⋊Q8C2312yes—
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2312yes—
127C2×C4⋊Q8C2312yes—
128C2×C4⋊Q8C2311yescharacteristic
129C2×#126—22no—
130C2×#125—22no—
131C2×#125—21no—
132C2×#123—22no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—22no—
136C2×C22⋊Q8—22no—
137C2×C22⋊Q8C2312yes—
138C2×C22⋊Q8C2312yes—
139C2×C4×Q8—21no—
140C2×C4×Q8C2312yes—
141C2×C4×D4—22no—
142C2×C4×D4D411yescharacteristic
143C2×C4×D4D411yescharacteristic
144C2×C4×D4C2311yescharacteristic
145C2×#117—21no—
146C2×#117—22no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4C2312yes—
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#487—24no—
157#487—42no—
158#487—42no—
159#483—48no—
160#431—42no—
161C2×#106C2314yes—
162C2×#106C2314yes—
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2312yes—
165C2×#103—48no—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2312yes—
181C2×C4×C8—42no—
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2311yescharacteristic
184C2×C4×C8C2311yescharacteristic
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2312yes—
187#400—22no—
188#400—22no—
189#398—22no—
190#398—22no—
191#398—22no—
192#398—22no—
193#397—22no—
194#397—22no—
195#395—22no—
196#395—22no—
197#395—22no—
198#395—22no—
199#391—21no—
200#391—21no—
201#391—21no—
202#391C2312yes—
203#391C2312yes—
204#391C2312yes—
205#389—22no—
206#389—22no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389C2312yes—
219#389C2312yes—
220#389C2312yes—
221#389C2312yes—
222#389C2312yes—
223#387—22no—
224#387—22no—
225#387—22no—
226#387—22no—
227#385—22no—
228#385—22no—
229#385—22no—
230#385—22no—
231#384—21no—
232#384—21no—
233#384—21no—
234#384—21no—
235#384—21no—
236#384—21no—
237#384C2311yescharacteristic
238#384C2311yescharacteristic
239#384C2311yescharacteristic
240#384C2311yescharacteristic
241#384C2312yes—
242#382—21no—
243#382—21no—
244#381—22no—
245#381—22no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380—21no—
251#380—21no—
252#380—21no—
253#380C2312yes—
254#380C2312yes—
255#380C2312yes—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4D411yescharacteristic
261C4×C4⋊C4D411yescharacteristic
262C4×C4⋊C4C2312yes—
263C4×C4⋊C4C2312yes—
264C4×C4⋊C4C2311yescharacteristic
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4D411yescharacteristic
268C4×C22⋊C4D411yescharacteristic
269C4×C22⋊C4C2311yescharacteristic
270C4×C22⋊C4C2311yescharacteristic
271C43C2311yescharacteristic
272#340C2314yes—
273#340C2314yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278#336C2312yes—
279C22×Q8—21no—
280C22×Q8—22no—
281C22×Q8—22no—
282C22×Q8—24no—
283C22×Q8—24no—
284C22×Q8—28no—
285C22×Q8—42no—
286C22×Q8—42no—
287C22×Q8—44no—
288C22×Q8—44no—
289C22×Q8—44no—
290C22×Q8C2412yes—
291C22×Q8C2412yes—
292C22×Q8C2412yes—
293C22×D4C2×D411yescharacteristic
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C22×C8—24no—
304C22×C8—42no—
305C22×C8—42no—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C4⋊Q8—24no—
311C4⋊Q8—24no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—44no—
320C4⋊Q8—44no—
321C4⋊Q8—44no—
322C4⋊Q8—44no—
323C4⋊Q8—42no—
324C4⋊Q8—42no—
325C4⋊Q8—44no—
326C4⋊Q8—44no—
327C4⋊Q8—48no—
328C4⋊Q8#4114yes—
329#126—48no—
330#125—48no—
331#125—44no—
332#123—48no—
333C22⋊Q8—28no—
334C22⋊Q8—48no—
335C22⋊Q8—48no—
336C22⋊Q8—44no—
337C22⋊Q8—44no—
338C22⋊Q8—44no—
339C4×Q8—44no—
340C4×Q8—44no—
341C4×D4—24no—
342C4×D4—24no—
343C4×D4—48no—
344C4×D4SD1618yes—
345#117—44no—
346#117—48no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2×D411yescharacteristic
390C2×C4⋊C4C2×D411yescharacteristic
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4C2×D411yescharacteristic
402C2×C22⋊C4C2×D411yescharacteristic
403C2×C22⋊C4C2×D411yescharacteristic
404C2×C22⋊C4C2×D411yescharacteristic
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427#106—44no—
428#106—44no—
429C4⋊C8—42no—
430C4⋊C8—42no—
431#103—28no—
432#103—44no—
433#103—44no—
434#103—44no—
435#103—44no—
436#103—44no—
437#103—44no—
438#103—44no—
439#103—44no—
440#103—44no—
441#103—44no—
442#103—44no—
443C22⋊C8—24no—
444C22⋊C8—42no—
445C22⋊C8—42no—
446C4×C8—22no—
447C4×C8—22no—
448C4×C8—22no—
449C4×C8—22no—
450C4×C8—42no—
451#95—22no—
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#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469#95C2×D411yescharacteristic
470#95C2×D411yescharacteristic
471#95C2×D411yescharacteristic
472#95C2×D411yescharacteristic
473C24C22×D411yescharacteristic
474C24C22×D411yescharacteristic
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—24no—
479C2×Q8—24no—
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—24no—
484C2×Q8—24no—
485C2×Q8—24no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—416no—
490C2×Q8—44no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—82no—
495C2×Q8—82no—
496C2×Q8—88no—
497C2×Q8—88no—
498C2×Q8—88no—
499C2×Q8C2×#4114yes—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4C2×SD1614yes—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
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—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—82no—
535C22×C4—82no—
536C22×C4C2×SD1614yes—
537C22×C4C2×SD1614yes—
538C22×C4#13714yes—
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4H(5,𝔽2)14yes—
552C22×C4C2511yescharacteristic
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—48no—
566C4⋊C4—22no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—44no—
594C4⋊C4—42no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—82no—
607C4⋊C4—82no—
608C4⋊C4C2×SD1614yes—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4C2×SD1614yes—
619C22⋊C4C2×SD1614yes—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—22no—
632C42—22no—
633C42—44no—
634C42—44no—
635C42—44no—
636C42C2×SD1614yes—
637C42C2×#4112yes—
638C42H(5,𝔽2)12yes—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23#53512yes—
650C23C22×SD1612yes—
651C23C22×SD1612yes—
652C23C2×#13712yes—
653C23C23×D411yescharacteristic
654Q8—28no—
655Q8—44no—
656Q8—44no—
657Q8—44no—
658Q8—44no—
659Q8—44no—
660Q8—88no—
661Q8—88no—
662Q8—84no—
663D4—28no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—28no—
679C2×C4—28no—
680C2×C4—28no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—24no—
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—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—88no—
721C2×C4—88no—
722C2×C4—88no—
723C2×C4#53512yes—
724C2×C4#54612yes—
725C2×C4#54612yes—
726C2×C4C22×SD1612yes—
727C2×C4C22×SD1612yes—
728C2×C4C22×SD1612yes—
729C2×C4C22×SD1612yes—
730C2×C4C22×SD1612yes—
731C2×C4C2×#13712yes—
732C2×C4C2×#13712yes—
733C2×C4#57812yes—
734C2×C4#57812yes—
735C2×C4C22×#4111yescharacteristic
736C2×C4C2×H(5,𝔽2)12yes—
737C2×C4C2×H(5,𝔽2)11yescharacteristic
738C2×C4#58512yes—
739C8—42no—
740C8—42no—
741C8—42no—
742C8—42no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22#320614yes—
757C22C2×#53511yescharacteristic
758C22C2×#54611yescharacteristic
759C22#350011yescharacteristic
760C22C23×SD1611yescharacteristic
761C22C22×#13711yescharacteristic
762C22C2×#57811yescharacteristic
763C22C2×#57811yescharacteristic
764C4—22no—
765C4—22no—
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—44no—
774C4—41no—
775C4—82no—
776C4—82no—
777C4—82no—
778C4—82no—
779C4—82no—
780C4—82no—
781C4—82no—
782C4#329814yes—
783C4#331214yes—
784C4#351312yes—
785C4#354212yes—
786C2—24no—
787C2—42no—
788C2#3808411yescharacteristic
789C2C2×#320611yescharacteristic
790C2#6082111yescharacteristic
791C2C2×#329811yescharacteristic
792C2C2×#331211yescharacteristic
793C2#6252611yescharacteristic
794C2#6253611yescharacteristic
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
3. #33043C2semidirect
4. #32082C2semidirect
5. #31288C2semidirect
6. #30220C2semidirect
7. #29845C2semidirect
8. #29191C2semidirect
9. #28748C2semidirect
10. #27905C2semidirect
11. #27889C2semidirect
12. #25856C2semidirect
13. #25856C2semidirect
14. #24480C2semidirect
16. #22218C2semidirect
17. #21804C2semidirect
18. C2×#1956C2semidirect

Maximal subgroups

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

subgroupindex
#361812
D4×C4⋊Q82
#330432
#320822
#312882
#302202
#298452
#291912
#287482
#279052
#278892
#258562
#244802
#240412
#222182
#218042
C2×#19562
#211012