Finite Group Databasebeta

← #6520653

Subgroups — #6520653

Order 512.

1518 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35275C211yesmaximal, characteristic
2#34966C211yesmaximal, characteristic
3#29320C211yesmaximal, characteristic, complemented
4#29319C211yesmaximal, characteristic, complemented
5#29314C211yesmaximal, characteristic, complemented
6#29314C211yesmaximal, characteristic, complemented
7#29213C211yesmaximal, characteristic, complemented
8#29208C211yesmaximal, characteristic, complemented
9#28838C212yesmaximal, complemented
10#28821C212yesmaximal, complemented
11#28804C212yesmaximal, complemented
12#28801C212yesmaximal, complemented
13#28775C212yesmaximal
14#28771C212yesmaximal
15#28694C211yesmaximal, characteristic, complemented
16#28689C211yesmaximal, characteristic, complemented
17#26071C212yesmaximal
18#26065C212yesmaximal
19#21987C211yesmaximal, characteristic
20#21962C211yesmaximal, characteristic
21#21365C211yesmaximal, characteristic
22C2×#1947C211yesmaximal, characteristic
23#20546C211yesmaximal, characteristic
24C2×#544—21no—
25C2×#501C2212yes—
26C2×#500C2212yes—
27C2×#432C2211yescharacteristic
28C22×#107C2212yes—
29C22×C4⋊C8C2211yescharacteristic
30#2868C2211yescharacteristic
31#2868C2211yescharacteristic
32#2859C2211yescharacteristic
33#2859C2211yescharacteristic
34#2660—21no—
35#2660—21no—
36#2606—21no—
37#2605—21no—
38#2570C2211yescharacteristic
39#2570C2211yescharacteristic
40#2552—21no—
41#2552C2212yes—
42#2551—21no—
43#2551C2212yes—
44#2550C2211yescharacteristic
45#2550C2211yescharacteristic
46#2442C2211yescharacteristic
47#2442C2211yescharacteristic
48#2440—21no—
49#2440—21no—
50#2440C2211yescharacteristic
51#2440C2212yes—
52#2440C2212yes—
53#2440C2211yescharacteristic
54#2438—21no—
55#2438—21no—
56#2402—21no—
57#2399—21no—
58#2317—21no—
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61C4×#125C2211yescharacteristic
62C4×#125C2211yescharacteristic
63C4×C22⋊Q8—21no—
64C4×C22⋊Q8—21no—
65#2285C2211yescharacteristic
66C2×#384C2211yescharacteristic
67#2283C2211yescharacteristic
68C4×#117C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70#2085C2212yes—
71#2085C2212yes—
72#2084C2212yes—
73#2084C2212yes—
74#2083C2212yes—
75#2083C2212yes—
76#2083C2212yes—
77#2083C2212yes—
78#2059C2212yes—
79#2059C2212yes—
80#2058C2212yes—
81#2058C2212yes—
82#2057C2212yes—
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#1947C2211yescharacteristic
99#1947C2211yescharacteristic
100#1947C2211yescharacteristic
101#1947C2211yescharacteristic
102#1947C2211yescharacteristic
103#1947C2211yescharacteristic
104#1947C2211yescharacteristic
105#1947C2211yescharacteristic
106#1947C2211yescharacteristic
107#1947C2212yes—
108#1947C2211yescharacteristic
109#1947C2212yes—
110#1944C2212yes—
111#1944C2212yes—
112#1943C2212yes—
113#1943C2212yes—
114#1942C2212yes—
115#1942C2212yes—
116#1941C2212yes—
117#1941C2212yes—
118#1853C2212yes—
119#1853C2212yes—
120#1852C2212yes—
121#1852C2212yes—
122#1847C2212yes—
123#1847C2212yes—
124#1845C2212yes—
125#1836C2212yes—
126#1808C2212yes—
127#1807C2212yes—
128#1776C2212yes—
129#1776C2212yes—
130#1771C2212yes—
131#1771C2212yes—
132#1767C2211yescharacteristic
133#1767C2211yescharacteristic
134C4×C4⋊C8C2211yescharacteristic
135C4×C4⋊C8C2211yescharacteristic
136#1752C2212yes—
137C8×C22⋊C4C2212yes—
138C2×#340C2212yes—
139C23×C8C2312yes—
140#544—48no—
141C2×C4⋊Q8—22no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8—21no—
145C2×C4⋊Q8—21no—
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2311yescharacteristic
148C2×C4⋊Q8C2312yes—
149C2×C4⋊Q8C2312yes—
150C2×#125—22no—
151C2×#125—21no—
152C2×#125—21no—
153C2×#125C2311yescharacteristic
154C2×#125C2311yescharacteristic
155C2×C22⋊Q8—22no—
156C2×C22⋊Q8—22no—
157C2×C22⋊Q8—21no—
158C2×C22⋊Q8—21no—
159C2×C4×Q8—21no—
160C2×C4×Q8—21no—
161C2×#117—21no—
162C2×#117D411yescharacteristic
163C2×#117D411yescharacteristic
164C22×C4⋊C4—21no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C42—21no—
170C22×C42C2311yescharacteristic
171#501—44no—
172#500—44no—
173#432Q818yescomplemented
174C2×#107—44no—
175C2×#107C2312yes—
176C2×#107C2312yes—
177C2×#107C2312yes—
178C2×#107C2312yes—
179C2×#107C2312yes—
180C2×#107C2312yes—
181C2×#107C2312yes—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#107C2312yes—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×#106C2312yes—
191C2×C4⋊C8Q818yescomplemented
192C2×C4⋊C8C2311yescharacteristic
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2311yescharacteristic
196C2×C4⋊C8C2311yescharacteristic
197C2×C22⋊C8C2312yes—
198C2×#97C2312yes—
199C2×#97C2312yes—
200C2×#97C2312yes—
201C2×C4×C8C2312yes—
202C2×C4×C8C2312yes—
203#400—21no—
204#400—21no—
205#400—21no—
206#400—21no—
207#398—21no—
208#398—21no—
209#398—21no—
210#398—21no—
211#398—21no—
212#398—21no—
213#398—21no—
214#398—21no—
215#398—22no—
216#398—22no—
217#398—22no—
218#398—22no—
219#395—21no—
220#395—21no—
221#395—21no—
222#395—21no—
223#395—22no—
224#395—22no—
225#395—22no—
226#395—22no—
227#391—21no—
228#391—21no—
229#391—21no—
230#391—21no—
231#389—22no—
232#389—22no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389C2311yescharacteristic
242#389C2311yescharacteristic
243#389C2311yescharacteristic
244#389C2311yescharacteristic
245#389C2311yescharacteristic
246#389C2311yescharacteristic
247#389C2311yescharacteristic
248#389C2311yescharacteristic
249#389C2312yes—
250#389C2312yes—
251#389C2312yes—
252#389C2312yes—
253#387—21no—
254#387—21no—
255#387—21no—
256#387—21no—
257#387—21no—
258#387—21no—
259#387—21no—
260#387—21no—
261#385—22no—
262#385—22no—
263#385—21no—
264#385—21no—
265#385—21no—
266#385—21no—
267#384—21no—
268#384—21no—
269#384—21no—
270#384—21no—
271#384—21no—
272#384—21no—
273#384C2311yescharacteristic
274#384C2311yescharacteristic
275#384C2312yes—
276#384C2312yes—
277#384C2311yescharacteristic
278#384C2311yescharacteristic
279#384C2311yescharacteristic
280#384C2312yes—
281#384C2311yescharacteristic
282#383—21no—
283#382—21no—
284#382—21no—
285#382—21no—
286#382C2311yescharacteristic
287#382C2311yescharacteristic
288#382C2311yescharacteristic
289#382C2311yescharacteristic
290#381—21no—
291#380—21no—
292#380—21no—
293#380—21no—
294#380C2311yescharacteristic
295#380C2312yes—
296#380C2311yescharacteristic
297C4×C4⋊C4—21no—
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⋊C4D411yescharacteristic
307C4×C4⋊C4D411yescharacteristic
308C4×C4⋊C4C2311yescharacteristic
309C4×C4⋊C4C2311yescharacteristic
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2312yes—
315C4×C4⋊C4C2311yescharacteristic
316C4×C4⋊C4C2311yescharacteristic
317C4×C22⋊C4—21no—
318C4×C22⋊C4D411yescharacteristic
319C4×C22⋊C4D411yescharacteristic
320C4×C22⋊C4C2311yescharacteristic
321C4×C22⋊C4C2311yescharacteristic
322#376—21no—
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—22no—
351C22×Q8—22no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—22no—
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D411yescharacteristic
357C23×C4C2411yescharacteristic
358C22×C8—42no—
359C22×C8—42no—
360C22×C8C2×Q818yes—
361C22×C8C2412yes—
362C22×C8C2412yes—
363C22×C8C2412yes—
364C22×C8C2412yes—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—41no—
368C4⋊Q8—41no—
369C4⋊Q8—42no—
370C4⋊Q8—42no—
371C4⋊Q8—42no—
372C4⋊Q8—42no—
373C4⋊Q8—44no—
374C4⋊Q8—44no—
375C4⋊Q8—48no—
376C4⋊Q8—82no—
377C4⋊Q8—82no—
378#125—22no—
379#125—22no—
380#125—41no—
381#125—41no—
382#125—44no—
383#125—44no—
384#125—48no—
385C22⋊Q8—48no—
386C22⋊Q8—44no—
387C22⋊Q8—48no—
388C22⋊Q8—44no—
389C4×Q8—82no—
390C4×Q8—82no—
391#117—24no—
392#117—24no—
393#117—44no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
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—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
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—21no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—41no—
438C2×C4⋊C4—41no—
439C2×C4⋊C4—42no—
440C2×C4⋊C4—42no—
441C2×C4⋊C4—44no—
442C2×C4⋊C4—82no—
443C2×C4⋊C4C2×D411yescharacteristic
444C2×C4⋊C4C2×D411yescharacteristic
445C2×C4⋊C4C2×D411yescharacteristic
446C2×C4⋊C4C2×D411yescharacteristic
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2411yescharacteristic
450C2×C4⋊C4C2411yescharacteristic
451C2×C4⋊C4C2411yescharacteristic
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2412yes—
457C2×C4⋊C4C2411yescharacteristic
458C2×C4⋊C4C2411yescharacteristic
459C2×C22⋊C4—22no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4C2×D411yescharacteristic
463C2×C22⋊C4C2×D411yescharacteristic
464C2×C22⋊C4C2×D411yescharacteristic
465C2×C22⋊C4C2×D411yescharacteristic
466C2×C42—22no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—82no—
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D411yescharacteristic
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2×Q814yes—
485C2×C42C2×Q814yes—
486C2×C42C2411yescharacteristic
487C2×C42C2411yescharacteristic
488C2×C42C2411yescharacteristic
489C2×C42C2411yescharacteristic
490C2×C42C2411yescharacteristic
491C2×C42C2411yescharacteristic
492#107—24no—
493#107—24no—
494#107—24no—
495#107—42no—
496#107—42no—
497#107—42no—
498#107—42no—
499#107—42no—
500#107—42no—
501#107—42no—
502#106—24no—
503#106—42no—
504#106—42no—
505#106—42no—
506#106—42no—
507#106—42no—
508C4⋊C8C2×Q814yes—
509C4⋊C8C2×Q814yes—
510C4⋊C8C2×Q818yes—
511C4⋊C8C2×Q814yes—
512C4⋊C8C2×Q814yes—
513C22⋊C8C2×Q818yes—
514#97—42no—
515#97—42no—
516#97C2×Q818yes—
517C4×C8—42no—
518C4×C8—42no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—22no—
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—22no—
543#95—21no—
544#95—21no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95C2×D411yescharacteristic
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552#95C2×D411yescharacteristic
553#95C2×D411yescharacteristic
554#95C2×D411yescharacteristic
555#95C2×D411yescharacteristic
556#95C2×D411yescharacteristic
557C24C22×D411yescharacteristic
558C2×Q8—42no—
559C2×Q8—42no—
560C2×Q8—44no—
561C2×Q8—42no—
562C2×Q8—44no—
563C2×Q8—42no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8—82no—
567C2×Q8—82no—
568C2×Q8—82no—
569C2×Q8—82no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4C4⋊Q814yes—
600C22×C4C4⋊Q814yes—
601C22×C4C22×D411yescharacteristic
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×Q812yes—
615C22×C4C22×Q812yes—
616C22×C4C2511yescharacteristic
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—48no—
626C2×C8C22×Q814yes—
627C2×C8C22×Q814yes—
628C2×C8C22×Q814yes—
629C2×C8C22×Q814yes—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—22no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—42no—
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—44no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—82no—
686C4⋊C4—82no—
687C4⋊C4—81no—
688C4⋊C4—81no—
689C4⋊C4—81no—
690C4⋊C4—81no—
691C4⋊C4—81no—
692C4⋊C4—81no—
693C4⋊C4—82no—
694C4⋊C4—82no—
695C4⋊C4—82no—
696C4⋊C4—82no—
697C4⋊C4H(5,𝔽2)12yes—
698C4⋊C42−1+412yes—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—44no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4AGL(1,ℤ/8)14yes—
705C22⋊C4#13714yes—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—22no—
711C42—22no—
712C42—22no—
713C42—22no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—44no—
723C42—42no—
724C42—42no—
725C42—42no—
726C42—42no—
727C42—81no—
728C42—81no—
729C42C4⋊Q814yes—
730C42C4⋊Q814yes—
731C42C22×Q812yes—
732C42C22×Q812yes—
733C42C22×Q812yes—
734C42C22×Q812yes—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23C2×C4⋊Q812yes—
740C23C2×AGL(1,ℤ/8)12yes—
741C23C2×#13712yes—
742C23C23×D411yescharacteristic
743Q8—84no—
744Q8—84no—
745Q8—164no—
746Q8—164no—
747C2×C4—28no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
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—28no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—84no—
818C2×C4—84no—
819C2×C4—164no—
820C2×C4C2×C4⋊Q812yes—
821C2×C4C2×C4⋊Q812yes—
822C2×C4C2×C4⋊Q812yes—
823C2×C4C2×C4⋊Q812yes—
824C2×C4C2×C4⋊Q812yes—
825C2×C4C2×AGL(1,ℤ/8)12yes—
826C2×C4C2×AGL(1,ℤ/8)12yes—
827C2×C4C2×#13712yes—
828C2×C4C2×#13712yes—
829C2×C4#57612yes—
830C2×C4#57812yes—
831C2×C4C23×Q811yescharacteristic
832C2×C4C23×Q811yescharacteristic
833C2×C4C2×H(5,𝔽2)11yescharacteristic
834C2×C4C2×2−1+411yescharacteristic
835C2×C4#58511yescharacteristic
836C2×C4#58511yescharacteristic
837C8—24no—
838C8—24no—
839C8—24no—
840C8—24no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22#316514yes—
848C22C22×C4⋊Q811yescharacteristic
849C22#348811yescharacteristic
850C22#348911yescharacteristic
851C22C22×AGL(1,ℤ/8)11yescharacteristic
852C22C22×#13711yescharacteristic
853C22C2×#57611yescharacteristic
854C22C2×#57811yescharacteristic
855C4—22no—
856C4—22no—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—22no—
861C4—22no—
862C4—22no—
863C4—41no—
864C4—42no—
865C4—41no—
866C4—41no—
867C4—42no—
868C4—41no—
869C4—81no—
870C4—82no—
871C4—82no—
872C4—81no—
873C4—82no—
874C4—81no—
875C4—81no—
876C4—81no—
877C4—81no—
878C4—82no—
879C4#316414yes—
880C4#350111yescharacteristic
881C4#350211yescharacteristic
882C4#350311yescharacteristic
883C4#350411yescharacteristic
884C2—24no—
885C2#3556611yescharacteristic
886C2C2×#316411yescharacteristic
887C2C2×#316511yescharacteristic
888C2#6197911yescharacteristic
889C2#6198411yescharacteristic
890C2#6212711yescharacteristic
891C2#6213211yescharacteristic
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. #29314C2semidirect
6. #29314C2semidirect
7. #29213C2semidirect
8. #29208C2semidirect
9. #28838C2semidirect
10. #28821C2semidirect
11. #28804C2semidirect
12. #28801C2semidirect
15. #28694C2semidirect
16. #28689C2semidirect
173. #432Q8semidirect
191. C2×C4⋊C8Q8semidirect

Maximal subgroups

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

subgroupindex
#352752
#349662
#293202
#293192
#293142
#292132
#292082
#288382
#288212
#288042
#288012
#287752
#287712
#286942
#286892
#260712
#260652
#219872
#219622
#213652
C2×#19472
#205462