Finite Group Databasebeta

← #6771976

Subgroups — #6771976

Order 512.

1830 conjugacy classes of subgroups.

The subgroup lattice has 1437 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38056C211yesmaximal, characteristic, complemented
2#35249C211yesmaximal, characteristic, complemented
3#33003C211yesmaximal, characteristic, complemented
4#32442C211yesmaximal, characteristic, complemented
5#32177C211yesmaximal, characteristic, complemented
6#31638C211yesmaximal, characteristic, complemented
7#31638C211yesmaximal, characteristic, complemented
8#31534C211yesmaximal, characteristic, complemented
9#30887C211yesmaximal, characteristic, complemented
10#30763C211yesmaximal, characteristic, complemented
11#30763C211yesmaximal, characteristic, complemented
12#30142C211yesmaximal, characteristic, complemented
13#30053C211yesmaximal, characteristic, complemented
14#29507C211yesmaximal, characteristic, complemented
15#29381C211yesmaximal, characteristic, complemented
16#28630C211yesmaximal, characteristic, complemented
17#28329C211yesmaximal, characteristic, complemented
18#28171C211yesmaximal, characteristic, complemented
19#27717C211yesmaximal, characteristic, complemented
20#27260C211yesmaximal, characteristic, complemented
21#25783C211yesmaximal, characteristic, complemented
22#25496C211yesmaximal, characteristic, complemented
23#25200C211yesmaximal, characteristic, complemented
24#25090C211yesmaximal, characteristic, complemented
25#24526C211yesmaximal, characteristic, complemented
26#24359C211yesmaximal, characteristic, complemented
27#23930C211yesmaximal, characteristic, complemented
28#22595C211yesmaximal, characteristic, complemented
29#22279C211yesmaximal, characteristic, complemented
30#22157C211yesmaximal, characteristic, complemented
31C2×#1880C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35C2×#496C2211yescharacteristic
36C2×#496C2211yescharacteristic
37C2×#488C2211yescharacteristic, complemented
38C2×#480C2211yescharacteristic
39C2×#466C2211yescharacteristic
40C2×#466C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#463C2211yescharacteristic
43C2×#463C2211yescharacteristic, complemented
44C2×#448C2211yescharacteristic
45C2×#447C2211yescharacteristic
46C2×#447C2211yescharacteristic
47C22×#103C2211yescharacteristic
48C22×#102C2211yescharacteristic
49#2854—21no—
50#2854—21no—
51#2854C2211yescharacteristic
52#2756—21no—
53#2753—21no—
54#2749—21no—
55#2706—21no—
56#2644C2211yescharacteristic
57#2641C2211yescharacteristic
58#2632—21no—
59#2632—21no—
60#2580—21no—
61#2580—21no—
62#2567C2211yescharacteristic, complemented
63#2567C2211yescharacteristic, complemented
64#2548C2211yescharacteristic, complemented
65#2548C2211yescharacteristic, complemented
66#2534—21no—
67#2513C2211yescharacteristic
68#2501C2211yescharacteristic
69#2501C2211yescharacteristic
70#2454C2211yescharacteristic
71#2445C2211yescharacteristic
72#2445C2211yescharacteristic
73#2442C2211yescharacteristic
74#2436C2211yescharacteristic
75#2436C2211yescharacteristic
76#2433C2211yescharacteristic
77#2418—21no—
78#2412—21no—
79#2412—21no—
80#2406—21no—
81#2406—21no—
82#2361C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84#2328C2211yescharacteristic
85#2326C2211yescharacteristic, complemented
86#2326C2211yescharacteristic, complemented
87#2326C2211yescharacteristic, complemented
88#2326C2211yescharacteristic, complemented
89#2319C2211yescharacteristic
90C2×#390C2211yescharacteristic
91#2283C2211yescharacteristic
92#2100C2211yescharacteristic, complemented
93#2100C2211yescharacteristic, complemented
94#2093C2211yescharacteristic
95#2093C2211yescharacteristic
96#2083C2211yescharacteristic, complemented
97#2074C2211yescharacteristic, complemented
98#2073C2211yescharacteristic, complemented
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2067C2211yescharacteristic, complemented
104#2057C2211yescharacteristic, complemented
105#2055C2211yescharacteristic
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic, complemented
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic
110#2054C2211yescharacteristic, complemented
111#2042C2211yescharacteristic, complemented
112#2042C2211yescharacteristic, complemented
113#2042C2211yescharacteristic, complemented
114#2041C2211yescharacteristic, complemented
115#2026C2211yescharacteristic, complemented
116#2025C2211yescharacteristic, complemented
117#2023C2211yescharacteristic
118#2023C2211yescharacteristic
119#2023C2211yescharacteristic, complemented
120#2014C2211yescharacteristic
121#2014C2211yescharacteristic
122#2012C2211yescharacteristic
123#2012C2211yescharacteristic
124#2012C2211yescharacteristic
125#2012C2211yescharacteristic
126#2012C2211yescharacteristic, complemented
127#2011C2211yescharacteristic
128#2011C2211yescharacteristic
129#2011C2211yescharacteristic
130#2011C2211yescharacteristic
131#2011C2211yescharacteristic, complemented
132#1992C2211yescharacteristic, complemented
133#1983C2211yescharacteristic, complemented
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic
136#1970C2211yescharacteristic
137#1970C2211yescharacteristic
138#1958C2211yescharacteristic, complemented
139#1957C2211yescharacteristic
140#1957C2211yescharacteristic
141#1947C2211yescharacteristic, complemented
142#1936C2211yescharacteristic, complemented
143#1936C2211yescharacteristic, complemented
144#1933C2211yescharacteristic, complemented
145#1933C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1925C2211yescharacteristic, complemented
148#1917C2211yescharacteristic, complemented
149#1917C2211yescharacteristic, complemented
150#1916C2211yescharacteristic, complemented
151#1916C2211yescharacteristic, complemented
152#1893C2211yescharacteristic
153#1893C2211yescharacteristic
154#1880C2211yescharacteristic
155#1880C2211yescharacteristic
156#1880C2211yescharacteristic
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic, complemented
163#1880C2211yescharacteristic, complemented
164#1880C2211yescharacteristic, complemented
165#1880C2211yescharacteristic, complemented
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic, complemented
173#1879C2211yescharacteristic, complemented
174#1879C2211yescharacteristic, complemented
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic, complemented
178#1874C2211yescharacteristic
179#1874C2211yescharacteristic
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1863C2211yescharacteristic, complemented
184#1862C2211yescharacteristic, complemented
185#1862C2211yescharacteristic, complemented
186#1850C2211yescharacteristic
187#1850C2211yescharacteristic
188#1840C2211yescharacteristic, complemented
189#1836C2211yescharacteristic, complemented
190#1832C2211yescharacteristic, complemented
191#1823C2211yescharacteristic
192#1817C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic, complemented
196#1787C2211yescharacteristic
197#1768C2211yescharacteristic, complemented
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1746C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×#41—21no—
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16—24no—
207C22×SD16—42no—
208C22×SD16—42no—
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×D8C2311yescharacteristic
218C22×D8C2311yescharacteristic
219C22×D8C2311yescharacteristic
220C22×D8C2311yescharacteristic
221C23×C8C2311yescharacteristic
222C23×C8C2311yescharacteristic
223#532—42no—
224#532—42no—
225C2×C4⋊Q8C2311yescharacteristic
226C2×#127C2311yescharacteristic
227C2×#127C2311yescharacteristic
228C2×#127C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#124—21no—
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#123—21no—
236C2×#123—21no—
237C2×#123—21no—
238C2×#123—21no—
239C2×#123—21no—
240C2×#123—21no—
241C2×#123—21no—
242C2×#121—21no—
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#120—21no—
247C2×#120—21no—
248C2×C4×Q8—21no—
249C2×C4×Q8—21no—
250C2×C4×Q8—42no—
251C2×C4×Q8—42no—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×D4—21no—
257C2×C4×D4—21no—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C22×C4⋊C4—21no—
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C22⋊C4—21no—
267C22×C22⋊C4—21no—
268C22×C22⋊C4—21no—
269C22×C42—21no—
270C22×C42C2311yescharacteristic
271#496—24no—
272#496—42no—
273#488—42no—
274#480—42no—
275#466—42no—
276#466—42no—
277#463—24no—
278#463—42no—
279#463—42no—
280#448—42no—
281#447—42no—
282#447—42no—
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×#103—42no—
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#102—42no—
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331#400—21no—
332#399—21no—
333#399—21no—
334#399—21no—
335#399—21no—
336#399—21no—
337#398—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#396—21no—
344#396—21no—
345#395—21no—
346#395—21no—
347#395—21no—
348#395—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#393—21no—
362#393—21no—
363#393—21no—
364#393—21no—
365#392—21no—
366#392—21no—
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390—21no—
376#390—21no—
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#389—21no—
393#389—21no—
394#389—21no—
395#389—21no—
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#384C2311yescharacteristic
445#383D411yescharacteristic
446#383D411yescharacteristic
447#382D411yescharacteristic
448#382D411yescharacteristic
449#382C2311yescharacteristic
450#381—21no—
451#381D411yescharacteristic
452#381D411yescharacteristic
453#380—21no—
454#380—21no—
455#380—21no—
456#380D411yescharacteristic
457#380D411yescharacteristic
458#380C2311yescharacteristic
459#379—21no—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465#376C2311yescharacteristic
466#376C2311yescharacteristic
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#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—44no—
501C2×#41—82no—
502C2×#41—82no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8—22no—
506C22×Q8—22no—
507C22×Q8—22no—
508C22×Q8—22no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×D4—22no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C2×D411yescharacteristic
543C23×C4C2×D411yescharacteristic
544C23×C4C2411yescharacteristic
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—416no—
563C2×SD16#4114yescomplemented
564C2×D8—22no—
565C2×D8—22no—
566C2×D8—22no—
567C2×D8—41no—
568C2×D8—41no—
569C2×D8—41no—
570C2×D8—41no—
571C2×D8—41no—
572C2×D8—41no—
573C2×D8—41no—
574C2×D8—41no—
575C2×D8—41no—
576C2×D8—41no—
577C2×D8—41no—
578C2×D8—41no—
579C2×D8—41no—
580C2×D8—41no—
581C2×D8—41no—
582C22×C8—22no—
583C22×C8—22no—
584C22×C8—22no—
585C22×C8—41no—
586C22×C8—41no—
587C22×C8—41no—
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C22×C8C2411yescharacteristic
594C22×C8C2411yescharacteristic
595C22×C8C2411yescharacteristic
596C4⋊Q8—41no—
597C4⋊Q8—41no—
598#127—22no—
599#127—41no—
600#127—41no—
601#127—41no—
602#127—41no—
603#127—41no—
604#125—41no—
605#125—41no—
606#124—22no—
607#124—22no—
608#124—22no—
609#124—22no—
610#124—41no—
611#124—41no—
612#124—41no—
613#124—41no—
614#124—44no—
615#123—82no—
616#123—82no—
617#123—82no—
618#123—82no—
619#123—82no—
620#123—82no—
621#123—82no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—22no—
628#121—44no—
629#120—82no—
630#120—82no—
631C4×Q8—41no—
632C4×Q8—41no—
633C4×Q8—41no—
634C4×Q8—41no—
635C4×Q8—41no—
636C4×Q8—41no—
637C4×Q8—41no—
638C4×Q8—41no—
639C4×Q8—44no—
640C4×Q8—44no—
641C4×D4—22no—
642C4×D4—41no—
643C4×D4—41no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—44no—
648C4×D4—41no—
649C4×D4—41no—
650C4×D4—41no—
651C4×D4—41no—
652C4×D4—82no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4—41no—
679C2×C4⋊C4—44no—
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
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—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—82no—
741C2×C22⋊C4—82no—
742C2×C22⋊C4—82no—
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C22⋊C4C2×D411yescharacteristic
746C2×C22⋊C4C2×D411yescharacteristic
747C2×C42—22no—
748C2×C42—22no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—44no—
755C2×C42C2×D411yescharacteristic
756C2×C42C2×D411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763#107—41no—
764#107—41no—
765#107—41no—
766#107—41no—
767C4⋊C8—22no—
768C4⋊C8—41no—
769C4⋊C8—41no—
770C4⋊C8—41no—
771#103—22no—
772#103—22no—
773#103—22no—
774#103—22no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781#102—22no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795#102—41no—
796#102—41no—
797#102—41no—
798#102—41no—
799#102—41no—
800#102—41no—
801#102—41no—
802#102—41no—
803C22⋊C8—22no—
804C22⋊C8—22no—
805#97—22no—
806#97—41no—
807C4×C8—41no—
808C4×C8—41no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—42no—
848C24—42no—
849C24—42no—
850C24—42no—
851C24—81no—
852C24—81no—
853C24—81no—
854C24C22×D411yescharacteristic
855#41—816no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—28no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—42no—
868C2×Q8—42no—
869C2×Q8—44no—
870C2×Q8—44no—
871C2×Q8—44no—
872C2×Q8—42no—
873C2×Q8—42no—
874C2×Q8—81no—
875C2×Q8—81no—
876C2×Q8C2×#4112yes—
877C2×Q8H(5,𝔽2)12yes—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—82no—
927C2×D4—82no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4—81no—
940C2×D4—81no—
941C2×D4C2×#4112yes—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—22no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—41no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4H(5,𝔽2)12yes—
1001C22×C4H(5,𝔽2)12yes—
1002C22×C4C2511yescharacteristic
1003SD16—44no—
1004SD16—44no—
1005SD16—44no—
1006SD16—44no—
1007SD16—82no—
1008SD16—82no—
1009D8—82no—
1010D8—82no—
1011D8—82no—
1012D8—82no—
1013D8—82no—
1014D8—82no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—44no—
1039C2×C8—82no—
1040C2×C8C2×#4112yes—
1041C4⋊C4—22no—
1042C4⋊C4—22no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4—81no—
1085C22⋊C4—22no—
1086C22⋊C4—22no—
1087C22⋊C4—22no—
1088C22⋊C4—22no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C22⋊C4—81no—
1135C22⋊C4—81no—
1136C42—22no—
1137C42—22no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—21no—
1143C42—21no—
1144C42—21no—
1145C42—21no—
1146C42—21no—
1147C42—21no—
1148C42—21no—
1149C42—21no—
1150C42—42no—
1151C42—42no—
1152C42—42no—
1153C42—42no—
1154C42—81no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—22no—
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—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—84no—
1195C23—84no—
1196C23—84no—
1197C23—84no—
1198C23—162no—
1199C23—162no—
1200C23—162no—
1201C23#53512yes—
1202C23#57612yes—
1203C23#57612yes—
1204C23C23×D411yescharacteristic
1205Q8—22no—
1206Q8—22no—
1207Q8—22no—
1208Q8—22no—
1209Q8—48no—
1210Q8—41no—
1211Q8—41no—
1212Q8—41no—
1213Q8—41no—
1214Q8—84no—
1215D4—22no—
1216D4—22no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—41no—
1224D4—41no—
1225D4—41no—
1226D4—41no—
1227D4—41no—
1228D4—41no—
1229D4—41no—
1230D4—41no—
1231D4—41no—
1232D4—41no—
1233D4—41no—
1234D4—41no—
1235D4—84no—
1236D4—84no—
1237D4—84no—
1238D4—84no—
1239D4—84no—
1240D4—84no—
1241D4—162no—
1242D4—162no—
1243D4—162no—
1244D4—162no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—22no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—44no—
1289C2×C4—48no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—44no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—84no—
1323C2×C4—84no—
1324C2×C4—84no—
1325C2×C4—162no—
1326C2×C4—162no—
1327C2×C4—162no—
1328C2×C4—162no—
1329C2×C4#53512yes—
1330C2×C4#57712yes—
1331C2×C4C22×#4111yescharacteristic
1332C2×C4C2×H(5,𝔽2)11yescharacteristic
1333C2×C4C2×H(5,𝔽2)11yescharacteristic
1334C2×C4C2×H(5,𝔽2)11yescharacteristic
1335C2×C4#58511yescharacteristic
1336C2×C4#58511yescharacteristic
1337C8—22no—
1338C8—41no—
1339C8—41no—
1340C8—41no—
1341C8—41no—
1342C8—41no—
1343C8—41no—
1344C8—41no—
1345C22—22no—
1346C22—22no—
1347C22—22no—
1348C22—22no—
1349C22—22no—
1350C22—22no—
1351C22—42no—
1352C22—42no—
1353C22—42no—
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—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—81no—
1385C22—81no—
1386C22—168no—
1387C22#322014yes—
1388C22C2×#53511yescharacteristic
1389C22D4×#4111yescharacteristic
1390C22#348811yescharacteristic
1391C22C2×#57611yescharacteristic
1392C22C2×#57611yescharacteristic
1393C22C2×#57711yescharacteristic
1394C22#358611yescharacteristic
1395C4—22no—
1396C4—22no—
1397C4—41no—
1398C4—41no—
1399C4—41no—
1400C4—41no—
1401C4—41no—
1402C4—41no—
1403C4—41no—
1404C4—41no—
1405C4—41no—
1406C4—41no—
1407C4—41no—
1408C4—42no—
1409C4—42no—
1410C4—81no—
1411C4—81no—
1412C4—81no—
1413C4—81no—
1414C4—81no—
1415C4—81no—
1416C4—81no—
1417C4—81no—
1418C4—81no—
1419C4#349011yescharacteristic
1420C4#351311yescharacteristic
1421C4#353311yescharacteristic
1422C4#353411yescharacteristic
1423C2—24no—
1424C2—82no—
1425C2—161no—
1426C2—161no—
1427C2—161no—
1428C2—161no—
1429C2#3836611yescharacteristic
1430C2C2×#322011yescharacteristic
1431C2#6081311yescharacteristic
1432C2#6149811yescharacteristic
1433C2#6152311yescharacteristic
1434C2#6202211yescharacteristic
1435C2#6205711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38056C2semidirect
2. #35249C2semidirect
3. #33003C2semidirect
4. #32442C2semidirect
5. #32177C2semidirect
6. #31638C2semidirect
7. #31638C2semidirect
8. #31534C2semidirect
9. #30887C2semidirect
10. #30763C2semidirect
11. #30763C2semidirect
12. #30142C2semidirect
13. #30053C2semidirect
14. #29507C2semidirect
15. #29381C2semidirect
16. #28630C2semidirect
17. #28329C2semidirect
18. #28171C2semidirect
19. #27717C2semidirect
20. #27260C2semidirect
21. #25783C2semidirect
22. #25496C2semidirect
23. #25200C2semidirect
24. #25090C2semidirect
25. #24526C2semidirect
26. #24359C2semidirect
27. #23930C2semidirect
28. #22595C2semidirect
29. #22279C2semidirect
30. #22157C2semidirect
31. C2×#1880C2semidirect
37. C2×#488C22semidirect
43. C2×#463C22semidirect
62. #2567C22semidirect
63. #2567C22semidirect
64. #2548C22semidirect
65. #2548C22semidirect
85. #2326C22semidirect
86. #2326C22semidirect
87. #2326C22semidirect
88. #2326C22semidirect
92. #2100C22semidirect
93. #2100C22semidirect
96. #2083C22semidirect
97. #2074C22semidirect
98. #2073C22semidirect
101. #2071C22semidirect
102. #2068C22semidirect
103. #2067C22semidirect
104. #2057C22semidirect
107. #2055C22semidirect
110. #2054C22semidirect
111. #2042C22semidirect
112. #2042C22semidirect
113. #2042C22semidirect
114. #2041C22semidirect
115. #2026C22semidirect
116. #2025C22semidirect
119. #2023C22semidirect
126. #2012C22semidirect
131. #2011C22semidirect
132. #1992C22semidirect
133. #1983C22semidirect
138. #1958C22semidirect
141. #1947C22semidirect
142. #1936C22semidirect
143. #1936C22semidirect
144. #1933C22semidirect
145. #1933C22semidirect
146. #1928C22semidirect
147. #1925C22semidirect
148. #1917C22semidirect
149. #1917C22semidirect
150. #1916C22semidirect
151. #1916C22semidirect
162. #1880C22semidirect
163. #1880C22semidirect
164. #1880C22semidirect
165. #1880C22semidirect
172. #1879C22semidirect
173. #1879C22semidirect
174. #1879C22semidirect
177. #1877C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
183. #1863C22semidirect
184. #1862C22semidirect
185. #1862C22semidirect
188. #1840C22semidirect
189. #1836C22semidirect
190. #1832C22semidirect
195. #1802C22semidirect
197. #1768C22semidirect
200. #1746C22semidirect
563. C2×SD16#41semidirect

Maximal subgroups

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

subgroupindex
#380562
#352492
#330032
#324422
#321772
#316382
#315342
#308872
#307632
#301422
#300532
#295072
#293812
#286302
#283292
#281712
#277172
#272602
#257832
#254962
#252002
#250902
#245262
#243592
#239302
#225952
#222792
#221572
C2×#18802