Finite Group Databasebeta

← #6800610

Subgroups — #6800610

Order 512.

1583 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36545C211yesmaximal, characteristic
2C2×#2568C211yesmaximal, characteristic
3#33151C211yesmaximal, characteristic
4#32641C212yesmaximal, complemented
5#32630C212yesmaximal, complemented
6#32619C212yesmaximal, complemented
7#32602C212yesmaximal, complemented
8#29957C211yesmaximal, characteristic
9#29953C211yesmaximal, characteristic
10#29111C211yesmaximal, characteristic
11#29106C211yesmaximal, characteristic
12#28652C212yesmaximal, complemented
13#28124C211yesmaximal, characteristic
14#28124C211yesmaximal, characteristic
15#26333C212yesmaximal, complemented
16#25943C212yesmaximal, complemented
17#25861C211yesmaximal, characteristic
18#25306C212yesmaximal, complemented
19#24212C211yesmaximal, characteristic
20#22510C211yesmaximal, characteristic
21#22050C211yesmaximal, characteristic
22#22044C211yesmaximal, characteristic
23#21579C211yesmaximal, characteristic
24C2×#557C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C2×#491C2212yes—
28C2×#483C2211yescharacteristic
29C2×#462C2212yes—
30C2×#451C2211yescharacteristic
31C2×#451C2211yescharacteristic
32C2×#446C2212yes—
33#2857C2211yescharacteristic
34#2851C2211yescharacteristic
35#2851C2211yescharacteristic
36#2584C2211yescharacteristic
37#2584C2211yescharacteristic
38#2582C2211yescharacteristic
39#2581C2211yescharacteristic
40#2581C2211yescharacteristic
41#2568—21no—
42#2568—21no—
43#2568—21no—
44#2568—21no—
45#2568C2212yes—
46#2568C2212yes—
47#2568C2212yes—
48#2568C2212yes—
49#2546C2211yescharacteristic
50#2473—21no—
51#2473—21no—
52#2462—21no—
53#2462—21no—
54#2446—21no—
55#2434—21no—
56C2×#400—21no—
57C2×#400—21no—
58#2365—21no—
59#2360—21no—
60#2355C2211yescharacteristic
61C4×C22⋊Q8C2211yescharacteristic
62C4×C22⋊Q8C2211yescharacteristic
63C4×C22⋊Q8C2211yescharacteristic
64C2×#391—21no—
65C2×#391C2211yescharacteristic
66C2×#391C2211yescharacteristic
67C2×#391C2211yescharacteristic
68C2×#391C2211yescharacteristic
69C2×#382—21no—
70C2×C4×C4⋊C4C2211yescharacteristic
71#2097C2212yes—
72#2095C2212yes—
73#2074C2212yes—
74#2072C2212yes—
75#2068C2212yes—
76#2068C2212yes—
77#2068C2212yes—
78#2066C2212yes—
79#2066C2212yes—
80#2066C2212yes—
81#2056C2212yes—
82#2056C2212yes—
83#2043C2212yes—
84#2043C2212yes—
85#2043C2212yes—
86#2026C2212yes—
87#2026C2212yes—
88#2024C2212yes—
89#2024C2212yes—
90#2016C2212yes—
91#1989C2212yes—
92#1985C2212yes—
93#1985C2212yes—
94#1984C2212yes—
95#1981C2212yes—
96#1971C2212yes—
97#1969C2212yes—
98#1960C2212yes—
99#1949C2212yes—
100#1935C2212yes—
101#1935C2212yes—
102#1935C2212yes—
103#1933C2212yes—
104#1933C2212yes—
105#1933C2212yes—
106#1928C2212yes—
107#1928C2212yes—
108#1927C2212yes—
109#1927C2212yes—
110#1927C2212yes—
111#1921C2212yes—
112#1919C2212yes—
113#1919C2212yes—
114#1878C2212yes—
115#1878C2212yes—
116#1878C2212yes—
117#1878C2212yes—
118#1872C2211yescharacteristic
119#1853C2211yescharacteristic
120#1852C2211yescharacteristic
121#1852C2211yescharacteristic
122#1823C2211yescharacteristic
123#1823C2211yescharacteristic
124#1823C2211yescharacteristic
125#1797C2211yescharacteristic
126#1797C2211yescharacteristic
127#1797C2211yescharacteristic
128#1787C2211yescharacteristic
129#1787C2211yescharacteristic
130#1787C2211yescharacteristic
131#1787C2211yescharacteristic
132#1787C2211yescharacteristic
133#1787C2211yescharacteristic
134#1776C2212yes—
135#1763C2212yes—
136#1749C2211yescharacteristic
137#1749C2211yescharacteristic
138C4×C22⋊C8C2211yescharacteristic
139C23×Q8D411yescharacteristic
140C23×Q8C2311yescharacteristic
141C23×Q8C2311yescharacteristic
142C22×Q16C2312yes—
143C22×Q16C2312yes—
144#557—44no—
145C2×C4⋊Q8—21no—
146C2×C4⋊Q8—21no—
147C2×C4⋊Q8—21no—
148C2×C4⋊Q8—21no—
149C2×C4⋊Q8—44no—
150C2×C4⋊Q8C2312yes—
151C2×C4⋊Q8C2312yes—
152C2×C4⋊Q8C2311yescharacteristic
153C2×#125—21no—
154C2×#125—21no—
155C2×#125C2311yescharacteristic
156C2×#125C2311yescharacteristic
157C2×C22⋊Q8—21no—
158C2×C22⋊Q8C2311yescharacteristic
159C2×C4×Q8—21no—
160C2×C4×Q8—44no—
161C2×C4×Q8D411yescharacteristic
162C2×C4×Q8D411yescharacteristic
163C2×C4×Q8D411yescharacteristic
164C2×C4×Q8D411yescharacteristic
165C2×C4×Q8C2311yescharacteristic
166C2×C4×Q8C2311yescharacteristic
167C2×C4×Q8C2311yescharacteristic
168C2×C4×Q8C2311yescharacteristic
169C2×C4×Q8C2311yescharacteristic
170C2×C4×Q8C2311yescharacteristic
171C2×C4×Q8C2311yescharacteristic
172C22×C4⋊C4—21no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4D411yescharacteristic
175C22×C4⋊C4D411yescharacteristic
176C22×C4⋊C4D411yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C42—21no—
180C22×C42C2311yescharacteristic
181C22×C42C2311yescharacteristic
182C22×C42C2311yescharacteristic
183#491—44no—
184#483—24no—
185#462—44no—
186#451—24no—
187#451—24no—
188#446—44no—
189C2×#107C2312yes—
190C2×#107C2312yes—
191C2×#106C2312yes—
192C2×#106C2312yes—
193C2×C4⋊C8C2312yes—
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#103C2312yes—
208C2×#103C2312yes—
209C2×#103C2312yes—
210C2×#103C2312yes—
211C2×#103C2312yes—
212C2×C22⋊C8C2311yescharacteristic
213C2×C22⋊C8C2311yescharacteristic
214C2×C22⋊C8C2311yescharacteristic
215C2×C22⋊C8C2311yescharacteristic
216C2×#97C2312yes—
217C2×#97C2312yes—
218C2×C4×C8C2312yes—
219#400—22no—
220#400—22no—
221#400—22no—
222#400—22no—
223#400—22no—
224#400—22no—
225#400—22no—
226#400—22no—
227#400—21no—
228#400—21no—
229#398—21no—
230#398—21no—
231#398—21no—
232#398—21no—
233#398—21no—
234#398—21no—
235#395—21no—
236#395—21no—
237#395—21no—
238#395—21no—
239#391—22no—
240#391—22no—
241#391—22no—
242#391—22no—
243#391—21no—
244#391—21no—
245#391—21no—
246#391—21no—
247#391—21no—
248#391—21no—
249#391—21no—
250#391—21no—
251#391—21no—
252#391—21no—
253#391—21no—
254#391—21no—
255#391C2311yescharacteristic
256#391C2311yescharacteristic
257#391C2312yes—
258#391C2312yes—
259#391C2312yes—
260#391C2312yes—
261#391C2312yes—
262#391C2312yes—
263#391C2312yes—
264#391C2312yes—
265#391C2311yescharacteristic
266#389—21no—
267#389—21no—
268#389—21no—
269#389—21no—
270#389—21no—
271#389—21no—
272#389C2311yescharacteristic
273#389C2311yescharacteristic
274#389C2311yescharacteristic
275#389C2311yescharacteristic
276#389C2311yescharacteristic
277#389C2311yescharacteristic
278#389C2311yescharacteristic
279#389C2311yescharacteristic
280#389C2311yescharacteristic
281#387—21no—
282#387—21no—
283#387—21no—
284#387—21no—
285#387—21no—
286#387—21no—
287#387—21no—
288#387—21no—
289#387—21no—
290#387—21no—
291#387—21no—
292#387—21no—
293#387—21no—
294#385—21no—
295#385—21no—
296#385—21no—
297#385—21no—
298#385—21no—
299#385—21no—
300#385—21no—
301#384C2311yescharacteristic
302#382—22no—
303#382—22no—
304#382—22no—
305#382—22no—
306#382C2311yescharacteristic
307#382C2311yescharacteristic
308#380—21no—
309#380C2311yescharacteristic
310#380C2311yescharacteristic
311#380C2311yescharacteristic
312C4×C4⋊C4—21no—
313C4×C4⋊C4—21no—
314C4×C4⋊C4—21no—
315C4×C4⋊C4—21no—
316C4×C4⋊C4—21no—
317C4×C4⋊C4—21no—
318C4×C4⋊C4C2312yes—
319C4×C4⋊C4C2312yes—
320C4×C4⋊C4C2311yescharacteristic
321C4×C4⋊C4C2311yescharacteristic
322C4×C4⋊C4C2311yescharacteristic
323C4×C22⋊C4—21no—
324C4×C22⋊C4—21no—
325C4×C22⋊C4—21no—
326C2×#95—21no—
327C2×#95—21no—
328C2×#95—21no—
329C2×#95—21no—
330C2×#95—21no—
331C2×#95—21no—
332C2×#95—21no—
333C2×#95—21no—
334C2×#95—21no—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#340C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348#336C2312yes—
349#336C2312yes—
350#336C2312yes—
351C22×Q8—24no—
352C22×Q8—21no—
353C22×Q8—21no—
354C22×Q8—21no—
355C22×Q8—22no—
356C22×Q8—22no—
357C22×Q8—22no—
358C22×Q8—22no—
359C22×Q8—42no—
360C22×Q8—42no—
361C22×Q8—42no—
362C22×Q8—42no—
363C22×Q8—42no—
364C22×Q8—42no—
365C22×Q8C2×D411yescharacteristic
366C22×Q8C2×D411yescharacteristic
367C22×Q8C2×D411yescharacteristic
368C22×Q8C2×D411yescharacteristic
369C22×Q8C2412yes—
370C22×Q8C2412yes—
371C22×Q8C2411yescharacteristic
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—21no—
375C23×C4—21no—
376C23×C4C2×D411yescharacteristic
377C23×C4C2×D411yescharacteristic
378C23×C4C2×D411yescharacteristic
379C23×C4C2×D411yescharacteristic
380C23×C4C2×D411yescharacteristic
381C23×C4C2×D411yescharacteristic
382C23×C4C2411yescharacteristic
383C2×Q16—24no—
384C2×Q16—24no—
385C2×Q16—42no—
386C2×Q16—42no—
387C2×Q16—42no—
388C2×Q16—42no—
389C22×C8C2412yes—
390C22×C8C2412yes—
391C22×C8C2412yes—
392C22×C8C2412yes—
393C4⋊Q8—24no—
394C4⋊Q8—24no—
395C4⋊Q8—42no—
396C4⋊Q8—42no—
397C4⋊Q8—42no—
398C4⋊Q8—44no—
399C4⋊Q8—44no—
400C4⋊Q8—44no—
401C4⋊Q8—44no—
402#125—24no—
403#125—42no—
404#125—44no—
405#125—44no—
406C22⋊Q8—22no—
407C22⋊Q8—44no—
408C22⋊Q8#4114yes—
409C4×Q8—24no—
410C4×Q8—24no—
411C4×Q8—24no—
412C4×Q8—42no—
413C4×Q8—42no—
414C4×Q8—42no—
415C4×Q8—42no—
416C4×Q8—42no—
417C4×Q8—42no—
418C4×Q8—42no—
419C4×Q8—42no—
420C4×Q8—44no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—44no—
454C2×C4⋊C4—44no—
455C2×C4⋊C4C2×D411yescharacteristic
456C2×C4⋊C4C2×D411yescharacteristic
457C2×C4⋊C4C2×D411yescharacteristic
458C2×C4⋊C4C2×D411yescharacteristic
459C2×C4⋊C4C2×D411yescharacteristic
460C2×C4⋊C4C2×D411yescharacteristic
461C2×C4⋊C4C2×D411yescharacteristic
462C2×C4⋊C4C2×D411yescharacteristic
463C2×C4⋊C4C2×D411yescharacteristic
464C2×C4⋊C4C2×D411yescharacteristic
465C2×C4⋊C4C2×D411yescharacteristic
466C2×C4⋊C4C2×D411yescharacteristic
467C2×C4⋊C4C2412yes—
468C2×C4⋊C4C2412yes—
469C2×C4⋊C4C2411yescharacteristic
470C2×C4⋊C4C2411yescharacteristic
471C2×C4⋊C4C2411yescharacteristic
472C2×C4⋊C4C2411yescharacteristic
473C2×C4⋊C4C2411yescharacteristic
474C2×C4⋊C4C2411yescharacteristic
475C2×C4⋊C4C2411yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C42—24no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—22no—
486C2×C42—22no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—42no—
490C2×C42—42no—
491C2×C42—44no—
492C2×C42C2×D411yescharacteristic
493C2×C42C2×D411yescharacteristic
494C2×C42C2×D411yescharacteristic
495C2×C42C2×D411yescharacteristic
496C2×C42C2×D411yescharacteristic
497C2×C42C2×D411yescharacteristic
498C2×C42C2411yescharacteristic
499C2×C42C2411yescharacteristic
500C2×C42C2411yescharacteristic
501C2×C42C2411yescharacteristic
502C2×C42C2411yescharacteristic
503C2×C42C2411yescharacteristic
504#107—42no—
505#107—42no—
506#106—24no—
507#106—42no—
508C4⋊C8—24no—
509C4⋊C8—42no—
510C4⋊C8—42no—
511#103—24no—
512#103—24no—
513#103—24no—
514#103—42no—
515#103—42no—
516#103—42no—
517#103—42no—
518#103—42no—
519#103—42no—
520#103—42no—
521#103—42no—
522#103—42no—
523#103—42no—
524#103—42no—
525#103—42no—
526#103—42no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C22⋊C8—22no—
530C22⋊C8—22no—
531#97—24no—
532#97—42no—
533C4×C8—42no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557#95—21no—
558#95—21no—
559#95—21no—
560#95—21no—
561#95—21no—
562#95—21no—
563#95—21no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577C24C22×D411yescharacteristic
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—21no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—22no—
598C2×Q8—41no—
599C2×Q8—41no—
600C2×Q8—41no—
601C2×Q8—41no—
602C2×Q8—41no—
603C2×Q8—41no—
604C2×Q8—416no—
605C2×Q8—42no—
606C2×Q8—42no—
607C2×Q8—42no—
608C2×Q8—42no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8—42no—
612C2×Q8—42no—
613C2×Q8—42no—
614C2×Q8—84no—
615C2×Q8—84no—
616C2×Q8—84no—
617C2×Q8—84no—
618C2×Q8#13714yes—
619C2×Q8C2×#4112yes—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4C22×D411yescharacteristic
665C22×C4C22×D411yescharacteristic
666C22×C4C22×D411yescharacteristic
667C22×C4C22×D411yescharacteristic
668C22×C4C22×D411yescharacteristic
669C22×C4C22×D411yescharacteristic
670C22×C4C22×D411yescharacteristic
671C22×C4C22×D411yescharacteristic
672C22×C4C22×D411yescharacteristic
673C22×C4C22×D411yescharacteristic
674C22×C4C22×D411yescharacteristic
675C22×C4C22×D411yescharacteristic
676C22×C4C22×D411yescharacteristic
677C22×C4C2×#4112yes—
678C22×C42−1+412yes—
679C22×C4C2511yescharacteristic
680Q16—84no—
681Q16—84no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—22no—
685C2×C8—22no—
686C2×C8—22no—
687C2×C8—22no—
688C2×C8—22no—
689C2×C8—22no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—22no—
693C2×C8—22no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—22no—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—41no—
713C4⋊C4—41no—
714C4⋊C4—41no—
715C4⋊C4—41no—
716C4⋊C4—41no—
717C4⋊C4—41no—
718C4⋊C4—42no—
719C4⋊C4—44no—
720C4⋊C4—44no—
721C4⋊C4—42no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—42no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—42no—
729C4⋊C4—44no—
730C4⋊C4—44no—
731C4⋊C4—42no—
732C4⋊C4—42no—
733C4⋊C4—42no—
734C4⋊C4—42no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4—81no—
740C4⋊C4—81no—
741C4⋊C4—81no—
742C4⋊C4—81no—
743C4⋊C4C2×#4112yes—
744C22⋊C4—24no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C42—22no—
749C42—22no—
750C42—22no—
751C42—22no—
752C42—22no—
753C42—22no—
754C42—22no—
755C42—41no—
756C42—41no—
757C42—41no—
758C42—41no—
759C42—44no—
760C42—44no—
761C42—42no—
762C42—42no—
763C42—42no—
764C42—42no—
765C42—81no—
766C42—81no—
767C42H(5,𝔽2)14yes—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23#54812yes—
773C23#57512yes—
774C23#57812yes—
775C23C23×D411yescharacteristic
776Q8—24no—
777Q8—44no—
778Q8—44no—
779Q8—44no—
780Q8—44no—
781Q8—42no—
782Q8—42no—
783Q8—42no—
784Q8—42no—
785Q8—42no—
786Q8—42no—
787Q8—42no—
788Q8—42no—
789Q8—42no—
790Q8—84no—
791Q8—84no—
792Q8—84no—
793C2×C4—28no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—42no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—42no—
868C2×C4—82no—
869C2×C4—82no—
870C2×C4—84no—
871C2×C4—84no—
872C2×C4—84no—
873C2×C4—84no—
874C2×C4#53412yes—
875C2×C4#53412yes—
876C2×C4#54812yes—
877C2×C4C2×#13712yes—
878C2×C4C2×#13712yes—
879C2×C4C2×#13712yes—
880C2×C4C22×#4111yescharacteristic
881C2×C4C2×H(5,𝔽2)12yes—
882C2×C4C2×2−1+411yescharacteristic
883C2×C4#58512yes—
884C8—42no—
885C8—42no—
886C8—42no—
887C8—42no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22#337714yes—
895C22C2×#53411yescharacteristic
896C22C2×#54811yescharacteristic
897C22#348711yescharacteristic
898C22C22×#13711yescharacteristic
899C22C2×#57511yescharacteristic
900C22C2×#57811yescharacteristic
901C22#358611yescharacteristic
902C4—22no—
903C4—22no—
904C4—22no—
905C4—22no—
906C4—22no—
907C4—22no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—42no—
916C4—42no—
917C4—81no—
918C4—81no—
919C4—81no—
920C4—82no—
921C4—81no—
922C4—81no—
923C4—82no—
924C4—81no—
925C4—82no—
926C4—82no—
927C4#351412yes—
928C4#356112yes—
929C2—24no—
930C2#3912311yescharacteristic
931C2#6075111yescharacteristic
932C2#6075911yescharacteristic
933C2C2×#337711yescharacteristic
934C2#6132211yescharacteristic
935C2#6189411yescharacteristic
936C2#6190011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #32641C2semidirect
5. #32630C2semidirect
6. #32619C2semidirect
7. #32602C2semidirect
12. #28652C2semidirect
15. #26333C2semidirect
16. #25943C2semidirect
18. #25306C2semidirect

Maximal subgroups

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

subgroupindex
#365452
C2×#25682
#331512
#326412
#326302
#326192
#326022
#299572
#299532
#291112
#291062
#286522
#281242
#263332
#259432
#258612
#253062
#242122
#225102
#220502
#220442
#215792