Finite Group Databasebeta

← #6492584

Subgroups — #6492584

Order 512.

1468 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#35294C211yesmaximal, characteristic
2#34145C211yesmaximal, characteristic
3#33200C211yesmaximal, characteristic, complemented
4#33196C211yesmaximal, characteristic, complemented
5#33073C211yesmaximal, characteristic, complemented
6#33069C211yesmaximal, characteristic, complemented
7#29999C211yesmaximal, characteristic, complemented
8#29997C211yesmaximal, characteristic, complemented
9#29988C211yesmaximal, characteristic, complemented
10#29983C211yesmaximal, characteristic, complemented
11#26539C212yesmaximal, complemented
12#26520C212yesmaximal, complemented
13#26473C212yesmaximal, complemented
14#26454C212yesmaximal, complemented
15#26432C212yesmaximal
16#26428C212yesmaximal
17#26360C212yesmaximal
18#26356C212yesmaximal
19#21978C211yesmaximal, characteristic
20#21894C211yesmaximal, characteristic
21#21870C211yesmaximal, characteristic
22#21365C211yesmaximal, characteristic
23#21170C211yesmaximal, characteristic
24C2×#533C2211yescharacteristic
25C2×#479C2212yes—
26C2×#475C2212yes—
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#2550—21no—
39#2550C2212yes—
40#2441—21no—
41#2441C2212yes—
42#2439—21no—
43#2439C2212yes—
44#2370—21no—
45#2370—21no—
46#2369C2211yescharacteristic
47#2369C2211yescharacteristic
48#2368—21no—
49#2368—21no—
50#2365C2211yescharacteristic
51#2365C2211yescharacteristic
52#2360C2211yescharacteristic
53#2360C2211yescharacteristic
54#2360C2211yescharacteristic
55#2360C2211yescharacteristic
56#2331—21no—
57#2330—21no—
58#2296—21no—
59#2295—21no—
60#2295—21no—
61#2295C2211yescharacteristic
62#2295C2211yescharacteristic
63#2285C2211yescharacteristic
64#2285C2211yescharacteristic
65C42×Q8C2211yescharacteristic
66C42×Q8C2211yescharacteristic
67C4×#117—21no—
68C4×#117C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70#2101C2212yes—
71#2099C2212yes—
72#2097C2212yes—
73#2096C2212yes—
74#2088C2212yes—
75#2087C2212yes—
76#2087C2212yes—
77#2086C2212yes—
78#2068C2212yes—
79#2068C2212yes—
80#2068C2212yes—
81#2066C2212yes—
82#2059C2212yes—
83#2058C2212yes—
84#2026C2212yes—
85#2024C2212yes—
86#1993C2212yes—
87#1989C2212yes—
88#1988C2212yes—
89#1988C2212yes—
90#1981C2212yes—
91#1960C2212yes—
92#1949C2212yes—
93#1949C2212yes—
94#1949C2212yes—
95#1948C2211yescharacteristic
96#1948C2211yescharacteristic
97#1948C2211yescharacteristic
98#1948C2211yescharacteristic
99#1948C2212yes—
100#1947C2211yescharacteristic
101#1947C2211yescharacteristic
102#1947C2211yescharacteristic
103#1947C2211yescharacteristic
104#1940C2212yes—
105#1940C2212yes—
106#1921C2212yes—
107#1921C2212yes—
108#1920C2212yes—
109#1918C2212yes—
110#1894C2212yes—
111#1894C2212yes—
112#1873C2212yes—
113#1873C2212yes—
114#1865C2212yes—
115#1863C2212yes—
116#1863C2212yes—
117#1863C2212yes—
118#1853C2212yes—
119#1852C2212yes—
120#1851C2212yes—
121#1851C2212yes—
122#1842C2211yescharacteristic
123#1842C2211yescharacteristic
124#1831C2211yescharacteristic
125#1831C2211yescharacteristic
126#1805C2212yes—
127#1803C2211yescharacteristic
128#1803C2211yescharacteristic
129#1803C2211yescharacteristic
130#1803C2211yescharacteristic
131#1803C2211yescharacteristic
132#1803C2211yescharacteristic
133#1803C2211yescharacteristic
134#1803C2211yescharacteristic
135#1803C2212yes—
136#1776C2212yes—
137#1776C2212yes—
138#1736C2212yes—
139C22×M16C2312yes—
140#533—24no—
141#533Q818yescomplemented
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2312yes—
147C2×#125—21no—
148C2×#125—21no—
149C2×#125—21no—
150C2×#125C2312yes—
151C2×C22⋊Q8—21no—
152C2×C22⋊Q8C2311yescharacteristic
153C2×C22⋊Q8C2311yescharacteristic
154C2×C4×Q8—21no—
155C2×C4×Q8C2311yescharacteristic
156C2×C4×Q8C2311yescharacteristic
157C2×C4×Q8C2311yescharacteristic
158C2×C4×Q8C2311yescharacteristic
159C2×C4×Q8C2311yescharacteristic
160C2×C4×Q8C2311yescharacteristic
161C2×#117—21no—
162C2×#117—21no—
163C2×#117D411yescharacteristic
164C2×#117D411yescharacteristic
165C2×#117C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C42—21no—
169C22×C42C2311yescharacteristic
170#479—44no—
171#475—44no—
172#432—24no—
173#428—44no—
174C2×#107C2312yes—
175C2×#107C2312yes—
176C2×#107C2312yes—
177C2×#107C2312yes—
178C2×#106C2312yes—
179C2×#106C2312yes—
180C2×#106C2312yes—
181C2×#106C2312yes—
182#423—24no—
183C2×C4⋊C8C2311yescharacteristic
184C2×C4⋊C8C2311yescharacteristic
185C2×C4⋊C8C2311yescharacteristic
186C2×C4⋊C8C2311yescharacteristic
187C2×C4⋊C8C2312yes—
188C2×C4⋊C8C2312yes—
189C2×C4⋊C8C2312yes—
190C2×C4⋊C8C2312yes—
191C2×C4⋊C8C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×C22⋊C8C2312yes—
201C2×#97C2312yes—
202#400—22no—
203#399—22no—
204#398—22no—
205#398—22no—
206#396—22no—
207#396—22no—
208#395—22no—
209#393—22no—
210#391—22no—
211#391—22no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391C2311yescharacteristic
217#391C2311yescharacteristic
218#391C2311yescharacteristic
219#391C2311yescharacteristic
220#389—21no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—22no—
233#389—22no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389C2311yescharacteristic
239#389C2312yes—
240#389C2312yes—
241#389C2311yescharacteristic
242#389C2312yes—
243#389C2312yes—
244#389C2311yescharacteristic
245#389C2311yescharacteristic
246#387—21no—
247#387—21no—
248#387—21no—
249#387—21no—
250#387—22no—
251#387—22no—
252#387—22no—
253#387—22no—
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#385—21no—
263#385—21no—
264#385—21no—
265#385—21no—
266#384—21no—
267#384—21no—
268#384C2312yes—
269#384C2311yescharacteristic
270#384C2311yescharacteristic
271#384C2311yescharacteristic
272#384C2311yescharacteristic
273#382—21no—
274#382—21no—
275#382—21no—
276#382C2312yes—
277#382C2312yes—
278#380—21no—
279#380—21no—
280#380—21no—
281#380C2312yes—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4—21no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4D411yescharacteristic
300C4×C4⋊C4D411yescharacteristic
301C4×C4⋊C4C2312yes—
302C4×C4⋊C4C2311yescharacteristic
303C4×C4⋊C4C2311yescharacteristic
304C4×C4⋊C4C2311yescharacteristic
305C4×C4⋊C4C2311yescharacteristic
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C4⋊C4C2311yescharacteristic
309C4×C4⋊C4C2311yescharacteristic
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C22⋊C4—21no—
313C4×C22⋊C4—21no—
314C4×C22⋊C4—21no—
315C4×C22⋊C4—21no—
316C4×C22⋊C4D411yescharacteristic
317C4×C22⋊C4D411yescharacteristic
318C4×C22⋊C4C2311yescharacteristic
319C4×C22⋊C4C2311yescharacteristic
320#376—21no—
321#376—21no—
322#376D411yescharacteristic
323#376D411yescharacteristic
324C2×#95—21no—
325C43—21no—
326C43—21no—
327C43C2311yescharacteristic
328C43C2311yescharacteristic
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#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348#336C2312yes—
349C22×Q8—21no—
350C22×Q8—22no—
351C22×Q8C2411yescharacteristic
352C22×Q8C2411yescharacteristic
353C23×C4—21no—
354C23×C4—21no—
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D411yescharacteristic
357C23×C4C2411yescharacteristic
358C2×M16—24no—
359C2×M16—42no—
360C2×M16—42no—
361C22×C8C2412yes—
362C22×C8C2412yes—
363C22×C8C2412yes—
364C22×C8C2412yes—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—42no—
368C4⋊Q8—42no—
369C4⋊Q8—44no—
370C4⋊Q8—82no—
371C4⋊Q8C2×Q814yes—
372C4⋊Q8C2×Q814yes—
373#125—28no—
374#125—42no—
375#125—42no—
376#125—44no—
377#125—82no—
378C22⋊Q8—28no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381C22⋊Q8C2×Q814yes—
382C22⋊Q8C2×Q814yes—
383C4×Q8—28no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×Q8—22no—
389C4×Q8—22no—
390C4×Q8—41no—
391C4×Q8—41no—
392C4×Q8—41no—
393C4×Q8—41no—
394C4×Q8C2×Q814yes—
395C4×Q8C2×Q814yes—
396#117—28no—
397#117—24no—
398#117—42no—
399#117—42no—
400#117—42no—
401#117—82no—
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—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—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—41no—
439C2×C4⋊C4—41no—
440C2×C4⋊C4C2×D411yescharacteristic
441C2×C4⋊C4C2×D411yescharacteristic
442C2×C4⋊C4C2×D411yescharacteristic
443C2×C4⋊C4C2×D411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2411yescharacteristic
451C2×C4⋊C4C2411yescharacteristic
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2411yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4C2×D411yescharacteristic
459C2×C22⋊C4C2×D411yescharacteristic
460C2×C22⋊C4C2×D411yescharacteristic
461C2×C22⋊C4C2×D411yescharacteristic
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
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×C42#4114yes—
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#106—24no—
502#106—24no—
503#106—42no—
504#106—42no—
505C4⋊C8—24no—
506C4⋊C8—22no—
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8—22no—
510C4⋊C8—42no—
511C4⋊C8—42no—
512C4⋊C8—42no—
513C4⋊C8—42no—
514#103—42no—
515#103—42no—
516#103—42no—
517#103—42no—
518#103—42no—
519#103—42no—
520#103—42no—
521#103—42no—
522C22⋊C8—24no—
523#97—24no—
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—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95C2×D411yescharacteristic
555#95C2×D411yescharacteristic
556#95C2×D411yescharacteristic
557#95C2×D411yescharacteristic
558#95C2×D411yescharacteristic
559#95C2×D411yescharacteristic
560#95C2×D411yescharacteristic
561#95C2×D411yescharacteristic
562C24C22×D411yescharacteristic
563C2×Q8—24no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—44no—
575C2×Q8—81no—
576C2×Q8—81no—
577C2×Q8—82no—
578C2×Q8—82no—
579C2×Q8C22×Q812yes—
580C2×Q8C22×Q812yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
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—41no—
600C22×C4—41no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4C22⋊Q814yes—
608C22×C4C22⋊Q814yes—
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×Q812yes—
623C22×C4C2×#4112yes—
624C22×C4C2511yescharacteristic
625M16—48no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—21no—
663C4⋊C4—41no—
664C4⋊C4—41no—
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—44no—
675C4⋊C4—44no—
676C4⋊C4—42no—
677C4⋊C4—44no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—81no—
683C4⋊C4—81no—
684C4⋊C4—81no—
685C4⋊C4—81no—
686C4⋊C4—82no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C4⋊C4—82no—
692C4⋊C4C22×Q812yes—
693C4⋊C4C22×Q812yes—
694C4⋊C4H(5,𝔽2)12yes—
695C4⋊C42−1+412yes—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—22no—
699C22⋊C4—22no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C42—24no—
705C42—24no—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—41no—
718C42—41no—
719C42—41no—
720C42—41no—
721C42—42no—
722C42—42no—
723C42—42no—
724C42—42no—
725C42—42no—
726C42—42no—
727C42—42no—
728C42—42no—
729C42—81no—
730C42—81no—
731C42—81no—
732C42—81no—
733C42—82no—
734C42—82no—
735C42C22⋊Q814yes—
736C42C22⋊Q814yes—
737C42#13714yes—
738C42C22×Q812yes—
739C42C22×Q812yes—
740C42C2×#4112yes—
741C42C2×#4112yes—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23C2×C22⋊Q812yes—
749C23C23×D411yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8—41no—
755Q8—41no—
756Q8—41no—
757Q8—41no—
758Q8—84no—
759Q8—164no—
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—28no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—44no—
802C2×C4—41no—
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—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—84no—
833C2×C4—84no—
834C2×C4C2×C22⋊Q812yes—
835C2×C4C2×C22⋊Q812yes—
836C2×C4C2×C22⋊Q812yes—
837C2×C4C2×C22⋊Q812yes—
838C2×C4C2×C22⋊Q812yes—
839C2×C4C2×#13712yes—
840C2×C4C2×#13712yes—
841C2×C4C2×#13712yes—
842C2×C4#57512yes—
843C2×C4C23×Q811yescharacteristic
844C2×C4C22×#4111yescharacteristic
845C2×C4C2×H(5,𝔽2)11yescharacteristic
846C2×C4C2×2−1+411yescharacteristic
847C2×C4#58511yescharacteristic
848C2×C4#58511yescharacteristic
849C8—42no—
850C8—42no—
851C8—42no—
852C8—42no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22C22×C22⋊Q811yescharacteristic
861C22#348811yescharacteristic
862C22#348911yescharacteristic
863C22C22×#13711yescharacteristic
864C22C2×#57511yescharacteristic
865C22#358511yescharacteristic
866C22#358611yescharacteristic
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—22no—
872C4—22no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—42no—
877C4—42no—
878C4—42no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4—81no—
889C4—82no—
890C4—81no—
891C4#307814yes—
892C4#346011yescharacteristic
893C4#346111yescharacteristic
894C4#350311yescharacteristic
895C4#350411yescharacteristic
896C2—42no—
897C2#3525711yescharacteristic
898C2C2×#307811yescharacteristic
899C2#6049311yescharacteristic
900C2#6196511yescharacteristic
901C2#6196711yescharacteristic
902C2#6211311yescharacteristic
903C2#6211511yescharacteristic
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. #33200C2semidirect
4. #33196C2semidirect
5. #33073C2semidirect
6. #33069C2semidirect
7. #29999C2semidirect
8. #29997C2semidirect
9. #29988C2semidirect
10. #29983C2semidirect
11. #26539C2semidirect
12. #26520C2semidirect
13. #26473C2semidirect
14. #26454C2semidirect
141. #533Q8semidirect

Maximal subgroups

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

subgroupindex
#352942
#341452
#332002
#331962
#330732
#330692
#299992
#299972
#299882
#299832
#265392
#265202
#264732
#264542
#264322
#264282
#263602
#263562
#219782
#218942
#218702
#213652
#211702