Finite Group Databasebeta

← #6583324

Subgroups — #6583324

Order 512.

1906 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3165C211yesmaximal, characteristic, complemented
2C2×#3160C211yesmaximal, characteristic, complemented
3#36134C211yesmaximal, characteristic
4#36129C211yesmaximal, characteristic
5#33314C211yesmaximal, characteristic, complemented
6#33210C211yesmaximal, characteristic, complemented
7#33209C211yesmaximal, characteristic, complemented
8#28820C214yesmaximal, complemented
9#28689C211yesmaximal, characteristic, complemented
10#28688C211yesmaximal, characteristic, complemented
11#26073C214yesmaximal, complemented
12#26069C214yesmaximal, complemented
13#25813C211yesmaximal, characteristic, complemented
14#25812C211yesmaximal, characteristic, complemented
15#25812C211yesmaximal, characteristic, complemented
16#25812C211yesmaximal, characteristic, complemented
17#22660C214yesmaximal
18#21727C211yesmaximal, characteristic, complemented
19C4×#435C211yesmaximal, characteristic
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24#3165—28no—
25C2×#501C2214yes—
26#3160—28no—
27C2×#500C2211yescharacteristic
28C2×#500C2211yescharacteristic
29C2×#500C2211yescharacteristic
30C2×#500C2211yescharacteristic
31C2×#500C2211yescharacteristic
32C2×#499C2214yes—
33C2×#498C2211yescharacteristic
34C2×#498C2211yescharacteristic
35C2×#498C2211yescharacteristic
36C2×#498C2211yescharacteristic
37C2×#435C2212yes—
38C2×#428C2214yes—
39C2×#427C2214yes—
40C2×C4×M16C2211yescharacteristic
41C22×C4×C8C2211yescharacteristic
42#2868C2211yescharacteristic
43#2862C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2552C2212yes—
49#2550C2212yes—
50#2542—21no—
51#2538—21no—
52#2492—21no—
53#2451—21no—
54#2446—21no—
55#2442C2212yes—
56#2441C2212yes—
57#2441C2212yes—
58#2439C2212yes—
59#2429—21no—
60#2429—21no—
61#2429—21no—
62#2423—21no—
63#2423—21no—
64#2417—21no—
65#2409—21no—
66#2365—21no—
67#2360—21no—
68#2354C2212yes—
69#2352C2212yes—
70Q8×C4⋊C4—21no—
71Q8×C22⋊C4—21no—
72C4×C4⋊Q8C2211yescharacteristic
73C4×C4⋊Q8C2211yescharacteristic
74C42×D4C2211yescharacteristic
75#2085C2214yes—
76#2083C2214yes—
77#2059C2214yes—
78#2059C2214yes—
79#2059C2214yes—
80#2057C2214yes—
81#1990C2211yescharacteristic
82#1990C2211yescharacteristic
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1949C2214yes—
88#1947C2214yes—
89#1944C2214yes—
90#1943C2214yes—
91#1942C2214yes—
92#1854C2214yes—
93#1854C2214yes—
94#1854C2214yes—
95#1852C2214yes—
96#1847C2214yes—
97#1847C2214yes—
98#1845C2211yescharacteristic
99#1809C2214yes—
100#1808C2214yes—
101#1776C2214yes—
102#1771C2212yes—
103C4×C4⋊C8C2211yescharacteristic
104#1753C2212yes—
105#1752C2212yes—
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C4×#97C2211yescharacteristic
109C23×Q8—21no—
110C22×M16C2312yes—
111C23×C8C2312yes—
112#533—24no—
113#533—24no—
114#533—24no—
115#533—42no—
116#533—42no—
117#533—42no—
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⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2311yescharacteristic
128C2×C4⋊Q8C2312yes—
129C2×C4⋊Q8C2311yescharacteristic
130C2×C4⋊Q8C2311yescharacteristic
131C2×#125C2312yes—
132C2×#125C2312yes—
133C2×#125C2312yes—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8—21no—
142C2×C22⋊Q8—21no—
143C2×C22⋊Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×Q8—21no—
147C2×C4×Q8—21no—
148C2×C4×Q8—21no—
149C2×C4×Q8—21no—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×D4D411yescharacteristic
153C2×C4×D4D411yescharacteristic
154C2×C4×D4C2311yescharacteristic
155C2×#117C2312yes—
156C2×#117C2312yes—
157C2×#117C2312yes—
158C22×C4⋊C4—21no—
159C22×C4⋊C4C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162#501—216no—
163#500—24no—
164#500—24no—
165#500—24no—
166#500—24no—
167#500—42no—
168#499—216no—
169#498—24no—
170#498—24no—
171#498—42no—
172#498D418yescomplemented
173#435Q8116yescomplemented
174#428—216no—
175#427—216no—
176C2×#107C2314yes—
177C2×#107C2314yes—
178C2×#107C2314yes—
179C2×#107C2314yes—
180C2×#107C2314yes—
181C2×#107C2314yes—
182C2×#106C2314yes—
183C2×#106C2314yes—
184C2×#106C2314yes—
185C2×#106C2314yes—
186C2×C4⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C4×M16—24no—
190C2×#97C2312yes—
191C2×#97C2312yes—
192C2×#97C2312yes—
193C2×C4×C8—24no—
194C2×C4×C8C2312yes—
195C2×C4×C8C2311yescharacteristic
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2311yescharacteristic
199#400—22no—
200#399—22no—
201#399—22no—
202#398—22no—
203#398—22no—
204#398—22no—
205#398—22no—
206#396—22no—
207#396—22no—
208#396—22no—
209#395—22no—
210#393—22no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—22no—
222#391—22no—
223#390—22no—
224#389—22no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—22no—
232#389—22no—
233#389—22no—
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#389C2312yes—
240#388—22no—
241#388—22no—
242#388—22no—
243#387—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#386—22no—
248#385—22no—
249#384—22no—
250#384—21no—
251#384—21no—
252#384C2311yescharacteristic
253#384C2311yescharacteristic
254#384C2312yes—
255#384C2312yes—
256#382C2312yes—
257#382C2312yes—
258#380—21no—
259#380—21no—
260#380—21no—
261#380—21no—
262#380—22no—
263#380C2312yes—
264#380C2312yes—
265#380C2312yes—
266#380C2312yes—
267C4×C4⋊C4—22no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4D411yescharacteristic
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2311yescharacteristic
275C4×C22⋊C4—22no—
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4D411yescharacteristic
280C4×C22⋊C4C2311yescharacteristic
281C4×C22⋊C4C2311yescharacteristic
282C43C2311yescharacteristic
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#340C2314yes—
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×Q8—22no—
299C22×Q8—44no—
300C22×Q8—44no—
301C22×Q8—82no—
302C22×D4C2×D411yescharacteristic
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×M16C2×Q818yes—
313C22×C8—24no—
314C22×C8—24no—
315C22×C8C2×Q818yescomplemented
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—22no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—42no—
332C4⋊Q8—44no—
333C4⋊Q8—44no—
334C4⋊Q8—44no—
335C4⋊Q8—82no—
336C4⋊Q8C2×D414yes—
337C4⋊Q8C2×D414yes—
338#125—24no—
339#125—24no—
340#125—24no—
341#125—42no—
342#125—42no—
343#125—42no—
344C22⋊Q8—44no—
345C22⋊Q8—44no—
346C22⋊Q8—44no—
347C22⋊Q8—44no—
348C22⋊Q8—44no—
349C22⋊Q8—44no—
350C22⋊Q8—44no—
351C22⋊Q8—82no—
352C22⋊Q8—82no—
353C22⋊Q8—82no—
354C4×Q8—44no—
355C4×Q8—44no—
356C4×Q8—44no—
357C4×Q8—44no—
358C4×Q8—44no—
359C4×Q8—44no—
360C4×Q8—44no—
361C4×Q8—82no—
362C4×D4—42no—
363C4×D4—42no—
364C4×D4C2×Q818yes—
365#117—24no—
366#117—24no—
367#117—24no—
368#117—42no—
369#117—42no—
370#117—42no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
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—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—42no—
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×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
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⋊C4—22no—
420C2×C22⋊C4C2×D411yescharacteristic
421C2×C22⋊C4C2×D411yescharacteristic
422C2×C22⋊C4C2×D411yescharacteristic
423C2×C22⋊C4C2×D411yescharacteristic
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2411yescharacteristic
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448#107—28no—
449#107—28no—
450#107—28no—
451#107—28no—
452#107—28no—
453#107—44no—
454#106—28no—
455#106—28no—
456#106—44no—
457#106C2×D4116yes—
458C4⋊C8C2×Q818yescomplemented
459C22⋊C8C2×Q818yes—
460C22⋊C8C2×Q818yescomplemented
461#97—24no—
462#97—24no—
463#97C2×Q818yescomplemented
464C4×C8—24no—
465C4×C8—22no—
466C4×C8—22no—
467C4×C8—22no—
468C4×C8C2×D414yes—
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#95C2×D411yescharacteristic
486#95C2×D411yescharacteristic
487#95C2×D411yescharacteristic
488#95C2×D411yescharacteristic
489#95C2×D411yescharacteristic
490#95C2×D411yescharacteristic
491C24C22×D411yescharacteristic
492C24C22×D411yescharacteristic
493C2×Q8—24no—
494C2×Q8—24no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—82no—
514C2×Q8—816no—
515C2×D4—41no—
516C2×D4—41no—
517C2×D4C4⋊Q814yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
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—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—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—82no—
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×C4C22×D411yescharacteristic
559C22×C4C22×Q814yes—
560C22×C4C22×Q814yes—
561C22×C4C2511yescharacteristic
562M16—216no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—216no—
570C2×C8C22×D414yes—
571C2×C8C22×Q814yes—
572C2×C8C22×Q814yes—
573C2×C8C22×Q814yes—
574C2×C8C22×Q814yes—
575C2×C82−1+414yes—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—82no—
613C4⋊C4—82no—
614C4⋊C4—82no—
615C4⋊C4—82no—
616C4⋊C4—82no—
617C4⋊C4—82no—
618C4⋊C4C4⋊Q814yes—
619C4⋊C4C22×D414yes—
620C4⋊C4C22×D414yes—
621C22⋊C4—41no—
622C22⋊C4—41no—
623C22⋊C4—41no—
624C22⋊C4—41no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—82no—
630C22⋊C4—82no—
631C22⋊C4—82no—
632C22⋊C4C4⋊Q814yes—
633C22⋊C4C4⋊Q814yes—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—22no—
647C42—44no—
648C42—44no—
649C42—44no—
650C42—44no—
651C42—82no—
652C42C22×D412yes—
653C42C22×Q814yes—
654C42H(5,𝔽2)12yes—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23C2×C4⋊Q812yes—
668C23C2×C4⋊Q812yes—
669C23C23×D411yescharacteristic
670Q8—48no—
671Q8—48no—
672Q8—88no—
673Q8—84no—
674Q8—84no—
675Q8—84no—
676Q8—84no—
677D4—44no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
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—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
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×C4C2×C4⋊Q812yes—
738C2×C4C2×C4⋊Q812yes—
739C2×C4C2×C4⋊Q812yes—
740C2×C4C2×C4⋊Q812yes—
741C2×C4D4212yes—
742C2×C4D4212yes—
743C2×C4#57512yes—
744C2×C4#57512yes—
745C2×C4#57612yes—
746C2×C4#57812yes—
747C2×C4C23×D411yescharacteristic
748C2×C4C23×Q812yes—
749C2×C4C2×H(5,𝔽2)11yescharacteristic
750C2×C4C2×2−1+412yes—
751C8—24no—
752C8—24no—
753C8—24no—
754C8D4×Q818yes—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22C22×C4⋊Q811yescharacteristic
770C22C2×D4211yescharacteristic
771C22#349911yescharacteristic
772C22C2×#57511yescharacteristic
773C22C2×#57511yescharacteristic
774C22C2×#57611yescharacteristic
775C22C2×#57811yescharacteristic
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—44no—
785C4—41no—
786C4—41no—
787C4—44no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4#326814yes—
795C4#326914yes—
796C4C2×D4×Q812yes—
797C4#350312yes—
798C2—42no—
799C2—42no—
800C2D4×C4⋊Q811yescharacteristic
801C2#6066311yescharacteristic
802C2#6066711yescharacteristic
803C2C2×#326811yescharacteristic
804C2C2×#326911yescharacteristic
805C2#6248111yescharacteristic
806C2#6248211yescharacteristic
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×#3165C2semidirect
2. C2×#3160C2semidirect
5. #33314C2semidirect
6. #33210C2semidirect
7. #33209C2semidirect
8. #28820C2semidirect
9. #28689C2semidirect
10. #28688C2semidirect
11. #26073C2semidirect
12. #26069C2semidirect
13. #25813C2semidirect
14. #25812C2semidirect
15. #25812C2semidirect
16. #25812C2semidirect
18. #21727C2semidirect
172. #498D4semidirect
173. #435Q8semidirect
315. C22×C8C2×Q8semidirect
458. C4⋊C8C2×Q8semidirect
460. C22⋊C8C2×Q8semidirect
463. #97C2×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#31652
C2×#31602
#361342
#361292
#333142
#332102
#332092
#288202
#286892
#286882
#260732
#260692
#258132
#258122
#226602
#217272
C4×#4352