Finite Group Databasebeta

← #6798362

Subgroups — #6798362

Order 512.

1584 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36196C211yesmaximal, characteristic
2D4×C4⋊Q8C211yesmaximal, characteristic
3#33297C211yesmaximal, characteristic, complemented
4#31692C212yesmaximal, complemented
5#31690C212yesmaximal, complemented
6#31688C212yesmaximal, complemented
7#31686C212yesmaximal, complemented
8#29884C211yesmaximal, characteristic, complemented
9#29883C211yesmaximal, characteristic, complemented
10#29223C211yesmaximal, characteristic, complemented
11#28694C211yesmaximal, characteristic, complemented
12#27883C211yesmaximal, characteristic, complemented
13#27882C211yesmaximal, characteristic, complemented
14#26458C212yesmaximal, complemented
15#26456C212yesmaximal, complemented
16#26310C212yesmaximal
17#26308C212yesmaximal
18#25816C211yesmaximal, characteristic, complemented
19#25816C211yesmaximal, characteristic, complemented
20#21841C211yesmaximal, characteristic, complemented
21#21840C211yesmaximal, characteristic, complemented
22#21731C211yesmaximal, characteristic, complemented
23#21271C211yesmaximal, characteristic
24C2×D4×Q8—21no—
25C22×C4⋊Q8C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C2×#501C2211yescharacteristic
28C2×#501C2211yescharacteristic
29C2×#501C2211yescharacteristic
30C2×#432C2211yescharacteristic
31C2×#432C2211yescharacteristic
32#2868C2211yescharacteristic
33#2859C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2851C2211yescharacteristic
37#2851C2211yescharacteristic
38#2573—21no—
39#2573—21no—
40#2562C2211yescharacteristic
41#2562C2211yescharacteristic
42#2551—21no—
43#2551C2212yes—
44#2546—21no—
45#2533—21no—
46#2533—21no—
47#2497C2211yescharacteristic
48#2497C2211yescharacteristic
49#2496C2211yescharacteristic
50#2496C2211yescharacteristic
51#2466—21no—
52#2466—21no—
53#2440—21no—
54#2440—21no—
55#2440C2212yes—
56#2440C2212yes—
57#2434—21no—
58#2434—21no—
59#2373—21no—
60#2373—21no—
61#2370C2211yescharacteristic
62#2370C2211yescharacteristic
63D4×C4⋊C4—21no—
64D4×C4⋊C4C2212yes—
65C4×C4⋊Q8C2211yescharacteristic
66C4×#125C2211yescharacteristic
67#2283C2211yescharacteristic
68#2283C2211yescharacteristic
69C42×D4C2211yescharacteristic
70#2100C2212yes—
71#2099C2212yes—
72#2088C2212yes—
73#2088C2212yes—
74#2087C2212yes—
75#2086C2212yes—
76#2084C2212yes—
77#2083C2212yes—
78#2077C2212yes—
79#2077C2212yes—
80#2077C2212yes—
81#2077C2212yes—
82#2076C2212yes—
83#2076C2212yes—
84#2075C2212yes—
85#2075C2212yes—
86#2058C2212yes—
87#2058C2212yes—
88#2057C2212yes—
89#2057C2212yes—
90#1993C2211yescharacteristic
91#1993C2211yescharacteristic
92#1993C2211yescharacteristic
93#1993C2211yescharacteristic
94#1993C2211yescharacteristic
95#1993C2211yescharacteristic
96#1993C2211yescharacteristic
97#1993C2211yescharacteristic
98#1993C2211yescharacteristic
99#1992C2212yes—
100#1992C2212yes—
101#1992C2211yescharacteristic
102#1989C2212yes—
103#1989C2212yes—
104#1988C2212yes—
105#1988C2212yes—
106#1987C2212yes—
107#1987C2212yes—
108#1955C2212yes—
109#1948C2212yes—
110#1947C2212yes—
111#1942C2212yes—
112#1941C2212yes—
113#1940C2212yes—
114#1923C2212yes—
115#1923C2212yes—
116#1921C2212yes—
117#1920C2212yes—
118#1919C2212yes—
119#1918C2212yes—
120#1853C2212yes—
121#1853C2212yes—
122#1852C2212yes—
123#1852C2212yes—
124#1847C2211yescharacteristic
125#1836C2211yescharacteristic
126#1836C2211yescharacteristic
127#1834C2212yes—
128#1834C2212yes—
129#1824C2212yes—
130#1824C2212yes—
131#1823C2212yes—
132#1823C2212yes—
133#1776C2212yes—
134#1776C2212yes—
135#1767C2211yescharacteristic
136#1749C2211yescharacteristic
137#1749C2211yescharacteristic
138C4×#97C2211yescharacteristic
139C23×Q8—21no—
140C23×Q8—21no—
141D4×Q8—48no—
142C2×C4⋊Q8—22no—
143C2×C4⋊Q8—24no—
144C2×C4⋊Q8—24no—
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—42no—
152C2×C4⋊Q8—42no—
153C2×C4⋊Q8C2311yescharacteristic
154C2×C4⋊Q8C2311yescharacteristic
155C2×C4⋊Q8C2312yes—
156C2×C4⋊Q8C2312yes—
157C2×C4⋊Q8C2311yescharacteristic
158C2×#126—21no—
159C2×#126—21no—
160C2×#125C2311yescharacteristic
161C2×#125C2311yescharacteristic
162C2×#125C2311yescharacteristic
163C2×C22⋊Q8—21no—
164C2×C22⋊Q8—21no—
165C2×C22⋊Q8—22no—
166C2×C22⋊Q8—22no—
167C2×C4×Q8—21no—
168C2×C4×D4—22no—
169C2×C4×D4D411yescharacteristic
170C2×C4×D4D411yescharacteristic
171C2×C4×D4C2311yescharacteristic
172C22×C4⋊C4—21no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178#501—24no—
179#501—42no—
180#501—42no—
181#432—42no—
182#432—42no—
183C2×#107C2312yes—
184C2×#107C2312yes—
185C2×#107C2312yes—
186C2×#107C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×#106C2312yes—
191C2×C4⋊C8C2312yes—
192C2×C4⋊C8C2312yes—
193C2×C4⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C2×#97C2311yescharacteristic
199C2×#97C2311yescharacteristic
200C2×#97C2311yescharacteristic
201C2×#97C2311yescharacteristic
202C2×#97C2312yes—
203C2×C4×C8C2312yes—
204#400—21no—
205#400—21no—
206#400—21no—
207#400—21no—
208#400—21no—
209#400—21no—
210#398—22no—
211#398—22no—
212#397—21no—
213#397—21no—
214#396—21no—
215#396—21no—
216#395—22no—
217#395—22no—
218#395—22no—
219#395—22no—
220#394—21no—
221#394—21no—
222#391—21no—
223#391—21no—
224#391—21no—
225#389—22no—
226#389—22no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389C2311yescharacteristic
237#389C2311yescharacteristic
238#389C2312yes—
239#389C2311yescharacteristic
240#389C2311yescharacteristic
241#389C2311yescharacteristic
242#389C2311yescharacteristic
243#389C2312yes—
244#389C2312yes—
245#388—21no—
246#388—21no—
247#388—21no—
248#388—21no—
249#388—21no—
250#388—21no—
251#387—21no—
252#387—21no—
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#387—21no—
262#387—21no—
263#387—21no—
264#387—21no—
265#385—21no—
266#385—21no—
267#385—21no—
268#385—21no—
269#385—22no—
270#385—22no—
271#385—22no—
272#385—22no—
273#384—21no—
274#384—21no—
275#384C2311yescharacteristic
276#384C2312yes—
277#384C2311yescharacteristic
278#384C2311yescharacteristic
279#384C2312yes—
280#383—21no—
281#383—21no—
282#382C2311yescharacteristic
283#382C2311yescharacteristic
284#382C2311yescharacteristic
285#381—21no—
286#381—21no—
287#380—21no—
288#380—21no—
289#380C2311yescharacteristic
290#380C2311yescharacteristic
291#380C2311yescharacteristic
292#380C2311yescharacteristic
293#380C2311yescharacteristic
294#380C2311yescharacteristic
295#380C2311yescharacteristic
296#380C2311yescharacteristic
297#380C2312yes—
298#380C2312yes—
299C4×C4⋊C4—21no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4—21no—
303C4×C4⋊C4—21no—
304C4×C4⋊C4D411yescharacteristic
305C4×C4⋊C4D411yescharacteristic
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C4⋊C4C2312yes—
309C4×C4⋊C4C2311yescharacteristic
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C22⋊C4—21no—
315C4×C22⋊C4—21no—
316C4×C22⋊C4D411yescharacteristic
317C4×C22⋊C4D411yescharacteristic
318C4×C22⋊C4D411yescharacteristic
319C4×C22⋊C4D411yescharacteristic
320C4×C22⋊C4C2311yescharacteristic
321C4×C22⋊C4C2311yescharacteristic
322#376—21no—
323#376—21no—
324C43C2311yescharacteristic
325#340C2312yes—
326#340C2312yes—
327#340C2312yes—
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#340C2312yes—
345#340C2312yes—
346#340C2312yes—
347#340C2312yes—
348#340C2312yes—
349#336C2312yes—
350#336C2312yes—
351#336C2312yes—
352C22×Q8—21no—
353C22×Q8—21no—
354C22×Q8—21no—
355C22×Q8—22no—
356C22×Q8—22no—
357C22×Q8—44no—
358C22×Q8—44no—
359C22×Q8—44no—
360C22×Q8—44no—
361C22×Q8—82no—
362C22×Q8—82no—
363C22×D4C2×D411yescharacteristic
364C23×C4—22no—
365C23×C4—22no—
366C23×C4C2×D411yescharacteristic
367C23×C4C2×D411yescharacteristic
368C23×C4C2×D411yescharacteristic
369C23×C4C2×D411yescharacteristic
370C23×C4C2411yescharacteristic
371C23×C4C2411yescharacteristic
372C22×C8C2412yes—
373C22×C8C2412yes—
374C22×C8C2412yes—
375C22×C8C2412yes—
376C4⋊Q8—24no—
377C4⋊Q8—24no—
378C4⋊Q8—22no—
379C4⋊Q8—22no—
380C4⋊Q8—22no—
381C4⋊Q8—22no—
382C4⋊Q8—22no—
383C4⋊Q8—42no—
384C4⋊Q8—42no—
385C4⋊Q8—44no—
386C4⋊Q8—44no—
387C4⋊Q8—44no—
388C4⋊Q8—44no—
389C4⋊Q8—44no—
390C4⋊Q8—48no—
391C4⋊Q8—82no—
392C4⋊Q8#4114yes—
393#126—44no—
394#126—44no—
395#125—22no—
396#125—22no—
397#125—24no—
398#125—24no—
399C22⋊Q8—48no—
400C22⋊Q8—44no—
401C22⋊Q8—44no—
402C22⋊Q8—48no—
403C4×Q8—44no—
404C4×D4—24no—
405C4×D4—24no—
406C4×D4—24no—
407C4×D4—48no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
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—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
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—42no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—44no—
445C2×C4⋊C4—44no—
446C2×C4⋊C4C2×D411yescharacteristic
447C2×C4⋊C4C2×D411yescharacteristic
448C2×C4⋊C4C2×D411yescharacteristic
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2411yescharacteristic
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2411yescharacteristic
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2411yescharacteristic
457C2×C4⋊C4C2411yescharacteristic
458C2×C4⋊C4C2411yescharacteristic
459C2×C4⋊C4C2412yes—
460C2×C4⋊C4C2412yes—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4C2×D411yescharacteristic
472C2×C22⋊C4C2×D411yescharacteristic
473C2×C22⋊C4C2×D411yescharacteristic
474C2×C22⋊C4C2×D411yescharacteristic
475C2×C22⋊C4C2×D411yescharacteristic
476C2×C22⋊C4C2×D411yescharacteristic
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—22no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42C2×D411yescharacteristic
489C2×C42C2×D411yescharacteristic
490C2×C42C2×D411yescharacteristic
491C2×C42C2×D411yescharacteristic
492C2×C42C2×D411yescharacteristic
493C2×C42C2×D411yescharacteristic
494C2×C42C2×D411yescharacteristic
495C2×C42C2×D411yescharacteristic
496C2×C42C2411yescharacteristic
497C2×C42C2411yescharacteristic
498C2×C42C2411yescharacteristic
499C2×C42C2411yescharacteristic
500C2×C42C2411yescharacteristic
501#107—24no—
502#107—24no—
503#107—42no—
504#107—42no—
505#106—24no—
506#106—24no—
507#106—42no—
508#106—42no—
509C4⋊C8—24no—
510C4⋊C8—42no—
511C4⋊C8—42no—
512C22⋊C8—24no—
513C22⋊C8—24no—
514C22⋊C8—42no—
515C22⋊C8—42no—
516#97—22no—
517#97—22no—
518#97—22no—
519#97—22no—
520#97—24no—
521C4×C8—24no—
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—22no—
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—22no—
542#95—21no—
543#95—21no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95C2×D411yescharacteristic
555#95C2×D411yescharacteristic
556#95C2×D411yescharacteristic
557#95C2×D411yescharacteristic
558#95C2×D411yescharacteristic
559#95C2×D411yescharacteristic
560C24C22×D411yescharacteristic
561C24C22×D411yescharacteristic
562C2×Q8—24no—
563C2×Q8—44no—
564C2×Q8—44no—
565C2×Q8—42no—
566C2×Q8—42no—
567C2×Q8—42no—
568C2×Q8—42no—
569C2×Q8—44no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8—42no—
574C2×Q8—44no—
575C2×Q8—82no—
576C2×Q8—82no—
577C2×Q8—816no—
578C2×Q8—816no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—82no—
619C22×C4—82no—
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C2511yescharacteristic
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C82−1+414yes—
645C4⋊C4—22no—
646C4⋊C4—24no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—44no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—42no—
671C4⋊C4—44no—
672C4⋊C4—42no—
673C4⋊C4—44no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—44no—
683C4⋊C4—44no—
684C4⋊C4—44no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—81no—
692C4⋊C4—81no—
693C4⋊C4—81no—
694C4⋊C4—81no—
695C4⋊C4—82no—
696C4⋊C4—82no—
697C4⋊C4C2×#4114yes—
698C22⋊C4—22no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—44no—
703C22⋊C4—44no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4AGL(1,ℤ/8)14yes—
713C22⋊C4#13714yes—
714C42—22no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—22no—
719C42—22no—
720C42—21no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—22no—
725C42—41no—
726C42—41no—
727C42—44no—
728C42—42no—
729C42—42no—
730C42—81no—
731C42—81no—
732C42—81no—
733C42—81no—
734C42C2×#4112yes—
735C42H(5,𝔽2)12yes—
736C422−1+414yes—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23C2×AGL(1,ℤ/8)12yes—
750C23C2×#13712yes—
751C23C23×D411yescharacteristic
752Q8—48no—
753Q8—88no—
754Q8—84no—
755Q8—84no—
756Q8—88no—
757D4—28no—
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—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—24no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
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—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—88no—
831C2×C4—88no—
832C2×C4#53612yes—
833C2×C4#53612yes—
834C2×C4#54612yes—
835C2×C4#54612yes—
836C2×C4C2×AGL(1,ℤ/8)12yes—
837C2×C4C2×AGL(1,ℤ/8)12yes—
838C2×C4C2×#13712yes—
839C2×C4C2×#13712yes—
840C2×C4C22×#4111yescharacteristic
841C2×C4C2×H(5,𝔽2)11yescharacteristic
842C2×C4C2×2−1+412yes—
843C2×C4C2×2−1+412yes—
844C8—24no—
845C8—42no—
846C8—42no—
847C8—42no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22C2×#53611yescharacteristic
863C22C2×#54611yescharacteristic
864C22#349911yescharacteristic
865C22C22×AGL(1,ℤ/8)11yescharacteristic
866C22C22×#13711yescharacteristic
867C22#358511yescharacteristic
868C22#358611yescharacteristic
869C4—22no—
870C4—22no—
871C4—22no—
872C4—22no—
873C4—22no—
874C4—22no—
875C4—22no—
876C4—22no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—44no—
881C4—41no—
882C4—81no—
883C4—82no—
884C4—81no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4—81no—
889C4—81no—
890C4—82no—
891C4—82no—
892C4—81no—
893C4#352312yes—
894C4#355012yes—
895C2—42no—
896C2—42no—
897C2#3895411yescharacteristic
898C2#6086011yescharacteristic
899C2#6088711yescharacteristic
900C2#6115511yescharacteristic
901C2#6115711yescharacteristic
902C2#6250311yescharacteristic
903C2#6250411yescharacteristic
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. #33297C2semidirect
4. #31692C2semidirect
5. #31690C2semidirect
6. #31688C2semidirect
7. #31686C2semidirect
8. #29884C2semidirect
9. #29883C2semidirect
10. #29223C2semidirect
11. #28694C2semidirect
12. #27883C2semidirect
13. #27882C2semidirect
14. #26458C2semidirect
15. #26456C2semidirect
18. #25816C2semidirect
19. #25816C2semidirect
20. #21841C2semidirect
21. #21840C2semidirect
22. #21731C2semidirect

Maximal subgroups

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

subgroupindex
#361962
D4×C4⋊Q82
#332972
#316922
#316902
#316882
#316862
#298842
#298832
#292232
#286942
#278832
#278822
#264582
#264562
#263102
#263082
#258162
#218412
#218402
#217312
#212712