Finite Group Databasebeta

← #6774830

Subgroups — #6774830

Order 512.

1705 conjugacy classes of subgroups.

The subgroup lattice has 1420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39042C211yesmaximal, characteristic, complemented
2#35571C211yesmaximal, characteristic, complemented
3#33086C211yesmaximal, characteristic, complemented
4#32240C211yesmaximal, characteristic, complemented
5#32178C211yesmaximal, characteristic, complemented
6#32045C211yesmaximal, characteristic, complemented
7#32013C211yesmaximal, characteristic, complemented
8#30974C211yesmaximal, characteristic, complemented
9#30874C211yesmaximal, characteristic, complemented
10#30509C211yesmaximal, characteristic, complemented
11#30416C211yesmaximal, characteristic, complemented
12#30179C211yesmaximal, characteristic, complemented
13#30006C211yesmaximal, characteristic, complemented
14#29505C211yesmaximal, characteristic, complemented
15#29376C211yesmaximal, characteristic, complemented
16#29000C211yesmaximal, characteristic, complemented
17#28921C211yesmaximal, characteristic, complemented
18#27794C211yesmaximal, characteristic, complemented
19#27418C211yesmaximal, characteristic, complemented
20#27335C211yesmaximal, characteristic, complemented
21#27243C211yesmaximal, characteristic, complemented
22#26968C211yesmaximal, characteristic, complemented
23#25685C211yesmaximal, characteristic, complemented
24#25502C211yesmaximal, characteristic, complemented
25#25148C211yesmaximal, characteristic, complemented
26#24152C211yesmaximal, characteristic, complemented
27#23939C211yesmaximal, characteristic, complemented
28#22792C211yesmaximal, characteristic, complemented
29#22187C211yesmaximal, characteristic, complemented
30#22056C211yesmaximal, characteristic, complemented
31#21134C211yesmaximal, characteristic, complemented
32C2×#540C2211yescharacteristic
33C2×#532C2211yescharacteristic, complemented
34C2×#501C2211yescharacteristic, complemented
35C2×#486C2211yescharacteristic, complemented
36C2×#476C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#469C2211yescharacteristic
39C2×#469C2211yescharacteristic
40C2×#459C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#447C2211yescharacteristic
43C2×#447C2211yescharacteristic
44C2×C4×D8C2211yescharacteristic
45#2854C2211yescharacteristic
46#2749—21no—
47#2737—21no—
48#2735—21no—
49#2684—21no—
50#2644C2211yescharacteristic
51#2628C2211yescharacteristic
52#2602—21no—
53#2597—21no—
54#2561—21no—
55#2557—21no—
56#2555—21no—
57#2550C2211yescharacteristic, complemented
58#2543—21no—
59#2541C2211yescharacteristic
60#2541C2211yescharacteristic, complemented
61#2535C2211yescharacteristic
62#2513C2211yescharacteristic
63#2491C2211yescharacteristic
64#2491C2211yescharacteristic
65#2490C2211yescharacteristic, complemented
66#2485C2211yescharacteristic
67#2464—21no—
68#2461—21no—
69#2452C2211yescharacteristic
70#2431—21no—
71#2430—21no—
72#2428—21no—
73#2428C2211yescharacteristic
74#2428C2211yescharacteristic, complemented
75#2420C2211yescharacteristic
76#2418—21no—
77#2408C2211yescharacteristic
78#2347C2211yescharacteristic
79D4×C22⋊C4C2211yescharacteristic
80#2328C2211yescharacteristic, complemented
81#2324C2211yescharacteristic
82#2319C2211yescharacteristic
83#2309C2211yescharacteristic
84C4×#121C2211yescharacteristic
85C4×#121C2211yescharacteristic, complemented
86#2290C2211yescharacteristic
87#2275C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2092C2211yescharacteristic
90#2086C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2075C2211yescharacteristic, complemented
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic, complemented
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic, complemented
100#2058C2211yescharacteristic, complemented
101#2058C2211yescharacteristic, complemented
102#2054C2211yescharacteristic
103#2041C2211yescharacteristic, complemented
104#2041C2211yescharacteristic, complemented
105#2041C2211yescharacteristic, complemented
106#2034C2211yescharacteristic
107#2034C2211yescharacteristic
108#2034C2211yescharacteristic
109#2034C2211yescharacteristic, complemented
110#2034C2211yescharacteristic, complemented
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2033C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic, complemented
116#2025C2211yescharacteristic
117#2025C2211yescharacteristic
118#2023C2211yescharacteristic
119#2023C2211yescharacteristic, complemented
120#2011C2211yescharacteristic
121#2011C2211yescharacteristic
122#2011C2211yescharacteristic
123#2011C2211yescharacteristic
124#2011C2211yescharacteristic
125#1999C2211yescharacteristic
126#1999C2211yescharacteristic
127#1999C2211yescharacteristic
128#1991C2211yescharacteristic, complemented
129#1987C2211yescharacteristic, complemented
130#1982C2211yescharacteristic, complemented
131#1972C2211yescharacteristic
132#1972C2211yescharacteristic
133#1970C2211yescharacteristic
134#1970C2211yescharacteristic
135#1961C2211yescharacteristic, complemented
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic, complemented
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic, complemented
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic, complemented
145#1926C2211yescharacteristic, complemented
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic, complemented
148#1924C2211yescharacteristic
149#1923C2211yescharacteristic
150#1920C2211yescharacteristic, complemented
151#1919C2211yescharacteristic, complemented
152#1919C2211yescharacteristic, complemented
153#1918C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1917C2211yescharacteristic, complemented
157#1916C2211yescharacteristic, complemented
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic, complemented
160#1895C2211yescharacteristic, complemented
161#1895C2211yescharacteristic, complemented
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1875C2211yescharacteristic
175#1875C2211yescharacteristic
176#1875C2211yescharacteristic
177#1870C2211yescharacteristic
178#1870C2211yescharacteristic
179#1864C2211yescharacteristic, complemented
180#1864C2211yescharacteristic, complemented
181#1864C2211yescharacteristic, complemented
182#1864C2211yescharacteristic, complemented
183#1864C2211yescharacteristic, complemented
184#1864C2211yescharacteristic, complemented
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic, complemented
187#1862C2211yescharacteristic, complemented
188#1862C2211yescharacteristic, complemented
189#1854C2211yescharacteristic
190#1840C2211yescharacteristic, complemented
191#1818C2211yescharacteristic
192#1809C2211yescharacteristic, complemented
193#1797C2211yescharacteristic, complemented
194#1786C2211yescharacteristic
195C4×#106C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic, complemented
198#1753C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200#1750C2211yescharacteristic
201#1746C2211yescharacteristic, complemented
202#1728C2211yescharacteristic, complemented
203C22×#41—21no—
204C23×D4C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213#540—42no—
214#540—42no—
215#532—42no—
216#532—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#127—21no—
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#124—21no—
225C2×#124—21no—
226C2×#124—21no—
227C2×#123—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×C22⋊Q8—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#120—21no—
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C22×C22⋊C4—21no—
261C22×C42C2311yescharacteristic
262#501—42no—
263#486—42no—
264#476—42no—
265#469—24no—
266#469—42no—
267#469—42no—
268#459—42no—
269#447—24no—
270#447—42no—
271#447—42no—
272C4×D8—24no—
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323#400—21no—
324#399—21no—
325#398—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#396—21no—
336#396—21no—
337#395—21no—
338#395—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#393—21no—
348#393—21no—
349#393—21no—
350#393—21no—
351#392—21no—
352#392—21no—
353#392—21no—
354#392—21no—
355#392—21no—
356#392—21no—
357#392—21no—
358#392—21no—
359#391—21no—
360#390—21no—
361#390—21no—
362#390—21no—
363#390—21no—
364#390—21no—
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#389—21no—
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388D411yescharacteristic
402#388D411yescharacteristic
403#387—21no—
404#387D411yescharacteristic
405#387D411yescharacteristic
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386D411yescharacteristic
422#386D411yescharacteristic
423#385—21no—
424#385—21no—
425#385D411yescharacteristic
426#385D411yescharacteristic
427#383—21no—
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#381—21no—
431#381—21no—
432#380—21no—
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441#379—21no—
442#379—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457#376C2311yescharacteristic
458C2×#95—21no—
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—44no—
495C2×#41—82no—
496C2×#41—82no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C2×D411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C2×D411yescharacteristic
534C23×C4C2×D411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C2×D8—41no—
550C2×D8—41no—
551C2×D8—41no—
552C2×D8—41no—
553C2×D8—41no—
554C2×D8—41no—
555C2×M16—22no—
556C2×M16—41no—
557C2×M16—41no—
558C2×M16—41no—
559C2×M16—41no—
560C2×M16—41no—
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C4⋊Q8—22no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572C4⋊Q8—41no—
573#127—22no—
574#127—22no—
575#127—41no—
576#127—41no—
577#127—41no—
578#127—41no—
579#127—82no—
580#125—22no—
581#125—41no—
582#124—44no—
583#124—82no—
584#124—82no—
585#123—44no—
586#123—44no—
587#123—82no—
588C22⋊Q8—82no—
589#121—22no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—44no—
597#121—44no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—41no—
602#121—41no—
603#121—41no—
604#121—41no—
605#121—44no—
606#121—41no—
607#121—41no—
608#121—82no—
609#121—82no—
610#121—82no—
611#121—82no—
612#120—82no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—44no—
630C4×D4—82no—
631C4×D4—82no—
632#117—41no—
633#117—41no—
634#117—41no—
635#117—41no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—82no—
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—41no—
726C2×C42—41no—
727C2×C42C2×D411yescharacteristic
728C2×C42C2×D411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734#107—22no—
735#107—41no—
736#107—41no—
737#107—41no—
738#106—22no—
739#106—22no—
740#106—22no—
741#106—41no—
742#106—41no—
743#106—41no—
744C4⋊C8—41no—
745C4⋊C8—41no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102#4114yescomplemented
774C22⋊C8—22no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780#97—41no—
781#97—41no—
782C4×C8—22no—
783C4×C8—41no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—42no—
823C24—42no—
824C24—81no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
831#41—816no—
832C2×Q8—42no—
833C2×Q8—42no—
834C2×Q8—81no—
835C2×Q8—81no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—41no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—82no—
903C2×D4—82no—
904C2×D4—82no—
905C2×D4—82no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4C2×#4112yes—
919C2×D4H(5,𝔽2)12yes—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—24no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—22no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—41no—
946C22×C4—41no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—41no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C2511yescharacteristic
983D8—44no—
984D8—82no—
985D8—82no—
986D8—82no—
987D8—82no—
988D8—82no—
989M16—82no—
990M16—82no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8C2×#4112yes—
1015C4⋊C4—22no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—41no—
1037C4⋊C4—41no—
1038C4⋊C4—41no—
1039C4⋊C4—41no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4C2×#4112yes—
1053C4⋊C4H(5,𝔽2)12yes—
1054C22⋊C4—24no—
1055C22⋊C4—22no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—41no—
1119C42—41no—
1120C42—42no—
1121C42—81no—
1122C42—81no—
1123C42—81no—
1124C42—81no—
1125C42—81no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—22no—
1135C23—21no—
1136C23—21no—
1137C23—22no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—84no—
1176C23—84no—
1177C23—162no—
1178C23—162no—
1179C23—162no—
1180C23—162no—
1181C23—162no—
1182C23C23×D411yescharacteristic
1183Q8—84no—
1184Q8—162no—
1185D4—22no—
1186D4—22no—
1187D4—22no—
1188D4—22no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—84no—
1206D4—82no—
1207D4—84no—
1208D4—84no—
1209D4—84no—
1210D4—84no—
1211D4—84no—
1212D4—84no—
1213D4—162no—
1214D4—162no—
1215D4—162no—
1216D4—162no—
1217D4—162no—
1218D4—162no—
1219D4—162no—
1220D4—162no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—22no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—44no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—82no—
1299C2×C4—84no—
1300C2×C4—84no—
1301C2×C4—162no—
1302C2×C4—162no—
1303C2×C4—162no—
1304C2×C4—162no—
1305C2×C4—162no—
1306C2×C4#57612yes—
1307C2×C4C22×#4111yescharacteristic
1308C2×C4C2×H(5,𝔽2)11yescharacteristic
1309C2×C4C2×H(5,𝔽2)11yescharacteristic
1310C2×C4#58511yescharacteristic
1311C2×C4#58511yescharacteristic
1312C2×C4#58511yescharacteristic
1313C8—22no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C8—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—42no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—42no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—42no—
1333C22—41no—
1334C22—41no—
1335C22—42no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—42no—
1340C22—42no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—168no—
1371C22#344911yescharacteristic
1372C22D4×#4111yescharacteristic
1373C22#348411yescharacteristic
1374C22C2×#57611yescharacteristic
1375C22#358511yescharacteristic
1376C22#358511yescharacteristic
1377C22#358511yescharacteristic
1378C4—22no—
1379C4—41no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—42no—
1384C4—41no—
1385C4—41no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—42no—
1390C4—41no—
1391C4—41no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4#349411yescharacteristic
1402C4#351411yescharacteristic
1403C4#356011yescharacteristic
1404C4#356211yescharacteristic
1405C2—81no—
1406C2—81no—
1407C2—82no—
1408C2—82no—
1409C2—161no—
1410C2—161no—
1411C2—161no—
1412C2#3837211yescharacteristic
1413C2#6099011yescharacteristic
1414C2#6100311yescharacteristic
1415C2#6150711yescharacteristic
1416C2#6153911yescharacteristic
1417C2#6161711yescharacteristic
1418C2#6164411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39042C2semidirect
2. #35571C2semidirect
3. #33086C2semidirect
4. #32240C2semidirect
5. #32178C2semidirect
6. #32045C2semidirect
7. #32013C2semidirect
8. #30974C2semidirect
9. #30874C2semidirect
10. #30509C2semidirect
11. #30416C2semidirect
12. #30179C2semidirect
13. #30006C2semidirect
14. #29505C2semidirect
15. #29376C2semidirect
16. #29000C2semidirect
17. #28921C2semidirect
18. #27794C2semidirect
19. #27418C2semidirect
20. #27335C2semidirect
21. #27243C2semidirect
22. #26968C2semidirect
23. #25685C2semidirect
24. #25502C2semidirect
25. #25148C2semidirect
26. #24152C2semidirect
27. #23939C2semidirect
28. #22792C2semidirect
29. #22187C2semidirect
30. #22056C2semidirect
31. #21134C2semidirect
33. C2×#532C22semidirect
34. C2×#501C22semidirect
35. C2×#486C22semidirect
57. #2550C22semidirect
60. #2541C22semidirect
65. #2490C22semidirect
74. #2428C22semidirect
80. #2328C22semidirect
85. C4×#121C22semidirect
87. #2275C22semidirect
88. #2101C22semidirect
90. #2086C22semidirect
91. #2085C22semidirect
92. #2085C22semidirect
95. #2075C22semidirect
97. #2073C22semidirect
99. #2067C22semidirect
100. #2058C22semidirect
101. #2058C22semidirect
103. #2041C22semidirect
104. #2041C22semidirect
105. #2041C22semidirect
109. #2034C22semidirect
110. #2034C22semidirect
115. #2033C22semidirect
119. #2023C22semidirect
128. #1991C22semidirect
129. #1987C22semidirect
130. #1982C22semidirect
135. #1961C22semidirect
137. #1936C22semidirect
139. #1934C22semidirect
144. #1926C22semidirect
145. #1926C22semidirect
147. #1925C22semidirect
150. #1920C22semidirect
151. #1919C22semidirect
152. #1919C22semidirect
153. #1918C22semidirect
154. #1918C22semidirect
155. #1918C22semidirect
156. #1917C22semidirect
157. #1916C22semidirect
159. #1895C22semidirect
160. #1895C22semidirect
161. #1895C22semidirect
179. #1864C22semidirect
180. #1864C22semidirect
181. #1864C22semidirect
182. #1864C22semidirect
183. #1864C22semidirect
184. #1864C22semidirect
186. #1862C22semidirect
187. #1862C22semidirect
188. #1862C22semidirect
190. #1840C22semidirect
192. #1809C22semidirect
193. #1797C22semidirect
195. C4×#106C22semidirect
197. #1762C22semidirect
198. #1753C22semidirect
199. #1753C22semidirect
201. #1746C22semidirect
202. #1728C22semidirect
773. #102#41semidirect

Maximal subgroups

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

subgroupindex
#390422
#355712
#330862
#322402
#321782
#320452
#320132
#309742
#308742
#305092
#304162
#301792
#300062
#295052
#293762
#290002
#289212
#277942
#274182
#273352
#272432
#269682
#256852
#255022
#251482
#241522
#239392
#227922
#221872
#220562
#211342