Finite Group Databasebeta

← #6520663

Subgroups — #6520663

Order 512.

1484 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35294C211yesmaximal, characteristic
2#34938C211yesmaximal, characteristic
3#29320C211yesmaximal, characteristic, complemented
4#29319C211yesmaximal, characteristic, complemented
5#29312C211yesmaximal, characteristic, complemented
6#29312C211yesmaximal, characteristic, complemented
7#29212C211yesmaximal, characteristic, complemented
8#29206C211yesmaximal, characteristic, complemented
9#28837C212yesmaximal, complemented
10#28819C212yesmaximal, complemented
11#28804C212yesmaximal, complemented
12#28801C212yesmaximal, complemented
13#28784C212yesmaximal
14#28781C212yesmaximal
15#28693C211yesmaximal, characteristic, complemented
16#28687C211yesmaximal, characteristic, complemented
17#26078C212yesmaximal
18#26072C212yesmaximal
19#21988C211yesmaximal, characteristic
20#21964C211yesmaximal, characteristic
21#21365C211yesmaximal, characteristic
22#21170C211yesmaximal, characteristic
23#20549C211yesmaximal, characteristic
24C2×#533—21no—
25C2×#501C2212yes—
26C2×#498C2212yes—
27C2×#432C2211yescharacteristic
28C2×#428C2212yes—
29C2×#423C2211yescharacteristic
30#2868C2211yescharacteristic
31#2859C2211yescharacteristic
32#2859C2211yescharacteristic
33#2859C2211yescharacteristic
34#2629—21no—
35#2628—21no—
36#2570—21no—
37#2570C2212yes—
38#2552C2211yescharacteristic
39#2552C2211yescharacteristic
40#2551C2211yescharacteristic
41#2551C2211yescharacteristic
42#2550—21no—
43#2550—21no—
44#2550—21no—
45#2550C2212yes—
46#2549—21no—
47#2549—21no—
48#2441—21no—
49#2441C2212yes—
50#2440C2211yescharacteristic
51#2440C2211yescharacteristic
52#2440C2211yescharacteristic
53#2440C2211yescharacteristic
54#2439—21no—
55#2439C2212yes—
56#2399—21no—
57#2399—21no—
58#2331—21no—
59#2330—21no—
60C4×C4⋊Q8C2211yescharacteristic
61C4×C4⋊Q8C2211yescharacteristic
62C4×C4⋊Q8C2211yescharacteristic
63C4×C4⋊Q8C2211yescharacteristic
64#2296—21no—
65#2285C2211yescharacteristic
66#2285C2211yescharacteristic
67#2285C2211yescharacteristic
68C4×#117C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70#2085C2212yes—
71#2085C2212yes—
72#2084C2212yes—
73#2084C2212yes—
74#2084C2212yes—
75#2083C2212yes—
76#2083C2212yes—
77#2083C2212yes—
78#2059C2212yes—
79#2059C2212yes—
80#2058C2212yes—
81#2058C2212yes—
82#2058C2212yes—
83#2057C2212yes—
84#2057C2212yes—
85#2057C2212yes—
86#1993C2212yes—
87#1992C2212yes—
88#1990C2212yes—
89#1990C2212yes—
90#1949C2212yes—
91#1949C2212yes—
92#1948C2211yescharacteristic
93#1948C2211yescharacteristic
94#1948C2211yescharacteristic
95#1948C2211yescharacteristic
96#1948C2211yescharacteristic
97#1948C2211yescharacteristic
98#1948C2211yescharacteristic
99#1948C2211yescharacteristic
100#1948C2212yes—
101#1947C2211yescharacteristic
102#1947C2211yescharacteristic
103#1947C2211yescharacteristic
104#1947C2211yescharacteristic
105#1947C2211yescharacteristic
106#1947C2211yescharacteristic
107#1947C2211yescharacteristic
108#1947C2211yescharacteristic
109#1947C2212yes—
110#1944C2212yes—
111#1944C2212yes—
112#1943C2212yes—
113#1943C2212yes—
114#1942C2212yes—
115#1942C2212yes—
116#1942C2212yes—
117#1942C2212yes—
118#1854C2212yes—
119#1854C2212yes—
120#1853C2212yes—
121#1852C2212yes—
122#1847C2212yes—
123#1847C2212yes—
124#1844C2212yes—
125#1836C2212yes—
126#1809C2212yes—
127#1809C2212yes—
128#1776C2212yes—
129#1776C2212yes—
130#1771C2212yes—
131#1771C2212yes—
132#1767C2211yescharacteristic
133#1767C2211yescharacteristic
134C4×C4⋊C8C2211yescharacteristic
135C4×C4⋊C8C2211yescharacteristic
136#1753C2212yes—
137#1753C2212yes—
138#1736C2212yes—
139C22×M16C2312yes—
140#533—48no—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8—21no—
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2311yescharacteristic
148C2×C4⋊Q8C2311yescharacteristic
149C2×C4⋊Q8C2312yes—
150C2×#125—21no—
151C2×#125—21no—
152C2×#125—21no—
153C2×#125—21no—
154C2×#125C2312yes—
155C2×C22⋊Q8—21no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8—21no—
158C2×C22⋊Q8—21no—
159C2×C4×Q8—21no—
160C2×C4×Q8—21no—
161C2×C4×Q8—21no—
162C2×C4×Q8—21no—
163C2×#117—21no—
164C2×#117—21no—
165C2×#117D411yescharacteristic
166C2×#117D411yescharacteristic
167C2×#117C2312yes—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C42—21no—
171C22×C42C2311yescharacteristic
172#501—44no—
173#498—44no—
174#432Q818yescomplemented
175#428—44no—
176C2×#107C2312yes—
177C2×#107C2312yes—
178C2×#107C2312yes—
179C2×#107C2312yes—
180C2×#107C2312yes—
181C2×#107C2312yes—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#106C2312yes—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×#106C2312yes—
191C2×#106C2312yes—
192#423Q818yescomplemented
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2311yescharacteristic
195C2×C4⋊C8C2312yes—
196C2×C4⋊C8C2311yescharacteristic
197C2×C4⋊C8C2311yescharacteristic
198C2×C22⋊C8C2312yes—
199C2×#97C2312yes—
200C2×#97C2312yes—
201C2×#97C2312yes—
202C2×C4×C8C2312yes—
203C2×C4×C8C2312yes—
204#400—22no—
205#399—22no—
206#398—22no—
207#398—22no—
208#398—21no—
209#398—21no—
210#398—21no—
211#398—21no—
212#398—21no—
213#398—21no—
214#398—21no—
215#398—21no—
216#396—22no—
217#396—22no—
218#395—22no—
219#395—21no—
220#395—21no—
221#395—21no—
222#395—21no—
223#395—21no—
224#395—21no—
225#395—21no—
226#395—21no—
227#393—22no—
228#391—21no—
229#391—21no—
230#391—21no—
231#391—21no—
232#391—22no—
233#391—22no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—21no—
242#389—21no—
243#389—21no—
244#389—21no—
245#389—21no—
246#389—21no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389—22no—
251#389—22no—
252#389C2311yescharacteristic
253#389C2311yescharacteristic
254#389C2311yescharacteristic
255#389C2311yescharacteristic
256#389C2311yescharacteristic
257#389C2311yescharacteristic
258#389C2311yescharacteristic
259#389C2311yescharacteristic
260#389C2312yes—
261#389C2312yes—
262#389C2312yes—
263#389C2312yes—
264#387—22no—
265#387—22no—
266#387—22no—
267#387—22no—
268#385—21no—
269#385—21no—
270#385—21no—
271#385—21no—
272#384—21no—
273#384—21no—
274#384C2311yescharacteristic
275#384C2311yescharacteristic
276#384C2311yescharacteristic
277#384C2311yescharacteristic
278#384C2312yes—
279#384C2311yescharacteristic
280#384C2311yescharacteristic
281#384C2311yescharacteristic
282#384C2311yescharacteristic
283#384C2311yescharacteristic
284#384C2311yescharacteristic
285#382—21no—
286#382—21no—
287#382—21no—
288#382—21no—
289#382C2312yes—
290#382C2312yes—
291#380—21no—
292#380—21no—
293#380—21no—
294#380—21no—
295#380C2312yes—
296#380C2311yescharacteristic
297#380C2311yescharacteristic
298C4×C4⋊C4—21no—
299C4×C4⋊C4—21no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4—21no—
303C4×C4⋊C4—21no—
304C4×C4⋊C4—21no—
305C4×C4⋊C4—21no—
306C4×C4⋊C4—21no—
307C4×C4⋊C4—21no—
308C4×C4⋊C4D411yescharacteristic
309C4×C4⋊C4D411yescharacteristic
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2312yes—
315C4×C4⋊C4C2311yescharacteristic
316C4×C4⋊C4C2311yescharacteristic
317C4×C4⋊C4C2311yescharacteristic
318C4×C4⋊C4C2311yescharacteristic
319C4×C22⋊C4D411yescharacteristic
320C4×C22⋊C4D411yescharacteristic
321C4×C22⋊C4C2311yescharacteristic
322C4×C22⋊C4C2311yescharacteristic
323#376D411yescharacteristic
324#376D411yescharacteristic
325C2×#95—21no—
326C43C2311yescharacteristic
327C43C2311yescharacteristic
328#340C2312yes—
329#340C2312yes—
330#340C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#336C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348C22×Q8—21no—
349C22×Q8—21no—
350C22×Q8—21no—
351C22×Q8—21no—
352C22×Q8—22no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D411yescharacteristic
357C23×C4C2411yescharacteristic
358C2×M16—42no—
359C2×M16—42no—
360C2×M16C2×Q818yes—
361C22×C8C2412yes—
362C22×C8C2412yes—
363C22×C8C2412yes—
364C22×C8C2412yes—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C4⋊Q8—41no—
370C4⋊Q8—41no—
371C4⋊Q8—41no—
372C4⋊Q8—41no—
373C4⋊Q8—42no—
374C4⋊Q8—42no—
375C4⋊Q8—44no—
376C4⋊Q8—44no—
377C4⋊Q8—44no—
378C4⋊Q8—82no—
379#125—42no—
380#125—42no—
381#125—44no—
382#125—44no—
383#125—44no—
384#125—82no—
385C22⋊Q8—44no—
386C22⋊Q8—44no—
387C22⋊Q8—44no—
388C22⋊Q8—44no—
389C4×Q8—44no—
390C4×Q8—44no—
391C4×Q8—44no—
392C4×Q8—44no—
393#117—24no—
394#117—24no—
395#117—44no—
396#117—42no—
397#117—42no—
398#117—82no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
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—41no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4C2×D411yescharacteristic
447C2×C4⋊C4C2×D411yescharacteristic
448C2×C4⋊C4C2×D411yescharacteristic
449C2×C4⋊C4C2×D411yescharacteristic
450C2×C4⋊C4C2411yescharacteristic
451C2×C4⋊C4C2411yescharacteristic
452C2×C4⋊C4C2412yes—
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2412yes—
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2411yescharacteristic
457C2×C4⋊C4C2411yescharacteristic
458C2×C4⋊C4C2411yescharacteristic
459C2×C4⋊C4C2412yes—
460C2×C4⋊C4C2411yescharacteristic
461C2×C4⋊C4C2411yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4C2×D411yescharacteristic
467C2×C22⋊C4C2×D411yescharacteristic
468C2×C22⋊C4C2×D411yescharacteristic
469C2×C22⋊C4C2×D411yescharacteristic
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42—44no—
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D411yescharacteristic
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2×D411yescharacteristic
485C2×C42C2×D411yescharacteristic
486C2×C42C2×D411yescharacteristic
487C2×C42C2×D411yescharacteristic
488C2×C42C2×D411yescharacteristic
489C2×C42C2×Q814yes—
490C2×C42C2×Q814yes—
491C2×C42C2411yescharacteristic
492C2×C42C2411yescharacteristic
493C2×C42C2411yescharacteristic
494C2×C42C2411yescharacteristic
495C2×C42C2411yescharacteristic
496C2×C42C2411yescharacteristic
497#107—24no—
498#107—24no—
499#107—42no—
500#107—42no—
501#107—42no—
502#107—42no—
503#107—42no—
504#107—42no—
505#106—24no—
506#106—24no—
507#106—42no—
508#106—42no—
509#106—42no—
510#106—42no—
511#106—42no—
512#106—42no—
513C4⋊C8C2×Q814yes—
514C4⋊C8C2×Q814yes—
515C4⋊C8C2×Q818yes—
516C4⋊C8C2×Q814yes—
517C4⋊C8C2×Q814yes—
518C22⋊C8C2×Q818yes—
519#97—42no—
520#97—42no—
521#97C2×Q818yes—
522C4×C8—42no—
523C4×C8—42no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552#95C2×D411yescharacteristic
553#95C2×D411yescharacteristic
554#95C2×D411yescharacteristic
555#95C2×D411yescharacteristic
556#95C2×D411yescharacteristic
557#95C2×D411yescharacteristic
558C24C22×D411yescharacteristic
559C2×Q8—42no—
560C2×Q8—42no—
561C2×Q8—42no—
562C2×Q8—42no—
563C2×Q8—42no—
564C2×Q8—42no—
565C2×Q8—42no—
566C2×Q8—42no—
567C2×Q8—44no—
568C2×Q8—81no—
569C2×Q8—81no—
570C2×Q8—81no—
571C2×Q8—81no—
572C2×Q8—82no—
573C2×Q8—82no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—81no—
599C22×C4—81no—
600C22×C4C4⋊Q814yes—
601C22×C4C4⋊Q814yes—
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×Q812yes—
616C22×C4C22×Q812yes—
617C22×C4C2511yescharacteristic
618M16—48no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8C22×Q814yes—
628C2×C8C22×Q814yes—
629C2×C8C22×Q814yes—
630C2×C8C22×Q814yes—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—44no—
682C4⋊C4—44no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—44no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—81no—
689C4⋊C4—81no—
690C4⋊C4—81no—
691C4⋊C4—81no—
692C4⋊C4—81no—
693C4⋊C4—81no—
694C4⋊C4—82no—
695C4⋊C4—82no—
696C4⋊C4—82no—
697C4⋊C4—82no—
698C4⋊C4—82no—
699C4⋊C4—82no—
700C4⋊C4H(5,𝔽2)12yes—
701C4⋊C42−1+412yes—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—82no—
709C22⋊C4—82no—
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—21no—
720C42—41no—
721C42—41no—
722C42—41no—
723C42—41no—
724C42—42no—
725C42—42no—
726C42—42no—
727C42—42no—
728C42—42no—
729C42—42no—
730C42—82no—
731C42—82no—
732C42C4⋊Q814yes—
733C42C4⋊Q814yes—
734C42AGL(1,ℤ/8)14yes—
735C42#13714yes—
736C42C22×Q812yes—
737C42C22×Q812yes—
738C42C22×Q812yes—
739C42C22×Q812yes—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23C2×C4⋊Q812yes—
747C23C23×D411yescharacteristic
748Q8—84no—
749Q8—84no—
750Q8—84no—
751Q8—84no—
752Q8—164no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—28no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—44no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—84no—
824C2×C4—84no—
825C2×C4C2×C4⋊Q812yes—
826C2×C4C2×C4⋊Q812yes—
827C2×C4C2×C4⋊Q812yes—
828C2×C4C2×C4⋊Q812yes—
829C2×C4C2×C4⋊Q812yes—
830C2×C4C2×AGL(1,ℤ/8)12yes—
831C2×C4C2×AGL(1,ℤ/8)12yes—
832C2×C4C2×AGL(1,ℤ/8)12yes—
833C2×C4C2×#13712yes—
834C2×C4C2×#13712yes—
835C2×C4C2×#13712yes—
836C2×C4C23×Q811yescharacteristic
837C2×C4C23×Q811yescharacteristic
838C2×C4C2×H(5,𝔽2)11yescharacteristic
839C2×C4C2×2−1+411yescharacteristic
840C2×C4#58511yescharacteristic
841C2×C4#58511yescharacteristic
842C8—24no—
843C8—24no—
844C8—24no—
845C8—24no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22C22×C4⋊Q811yescharacteristic
854C22#348811yescharacteristic
855C22#348911yescharacteristic
856C22C22×AGL(1,ℤ/8)11yescharacteristic
857C22C22×#13711yescharacteristic
858C22#358511yescharacteristic
859C22#358611yescharacteristic
860C4—22no—
861C4—22no—
862C4—22no—
863C4—22no—
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—41no—
869C4—42no—
870C4—41no—
871C4—41no—
872C4—42no—
873C4—41no—
874C4—82no—
875C4—81no—
876C4—81no—
877C4—81no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—81no—
882C4—81no—
883C4—81no—
884C4#316514yes—
885C4#350111yescharacteristic
886C4#350211yescharacteristic
887C4#350311yescharacteristic
888C4#350411yescharacteristic
889C2—42no—
890C2#3556611yescharacteristic
891C2C2×#316511yescharacteristic
892C2#6066411yescharacteristic
893C2#6196211yescharacteristic
894C2#6196511yescharacteristic
895C2#6211011yescharacteristic
896C2#6211311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #29320C2semidirect
4. #29319C2semidirect
5. #29312C2semidirect
6. #29312C2semidirect
7. #29212C2semidirect
8. #29206C2semidirect
9. #28837C2semidirect
10. #28819C2semidirect
11. #28804C2semidirect
12. #28801C2semidirect
15. #28693C2semidirect
16. #28687C2semidirect
174. #432Q8semidirect
192. #423Q8semidirect

Maximal subgroups

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

subgroupindex
#352942
#349382
#293202
#293192
#293122
#292122
#292062
#288372
#288192
#288042
#288012
#287842
#287812
#286932
#286872
#260782
#260722
#219882
#219642
#213652
#211702
#205492