Finite Group Databasebeta

← #7338740

Subgroups — #7338740

Order 512.

1616 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53025C211yesmaximal, characteristic, complemented
2#45018C211yesmaximal, characteristic, complemented
3#31855C211yesmaximal, characteristic, complemented
4#31740C211yesmaximal, characteristic, complemented
5#31727C211yesmaximal, characteristic, complemented
6#31643C211yesmaximal, characteristic, complemented
7#31459C211yesmaximal, characteristic, complemented
8#31403C211yesmaximal, characteristic, complemented
9#31163C211yesmaximal, characteristic, complemented
10#31000C211yesmaximal, characteristic, complemented
11#30934C211yesmaximal, characteristic, complemented
12#30746C211yesmaximal, characteristic, complemented
13#30527C211yesmaximal, characteristic, complemented
14#30446C211yesmaximal, characteristic, complemented
15#29727C211yesmaximal, characteristic, complemented
16#29697C211yesmaximal, characteristic, complemented
17#29116C211yesmaximal, characteristic, complemented
18#28913C211yesmaximal, characteristic, complemented
19#27766C211yesmaximal, characteristic, complemented
20#27270C211yesmaximal, characteristic, complemented
21#27250C211yesmaximal, characteristic, complemented
22#26897C211yesmaximal, characteristic, complemented
23#26828C211yesmaximal, characteristic, complemented
24#26750C211yesmaximal, characteristic, complemented
25#26664C211yesmaximal, characteristic, complemented
26#25610C211yesmaximal, characteristic, complemented
27#25321C211yesmaximal, characteristic, complemented
28#24543C211yesmaximal, characteristic, complemented
29#24444C211yesmaximal, characteristic, complemented
30#24247C211yesmaximal, characteristic, complemented
31#22360C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#495C2211yescharacteristic, complemented
35C2×#489C2211yescharacteristic, complemented
36C2×#486C2211yescharacteristic
37C2×#475C2211yescharacteristic, complemented
38C2×#476C2211yescharacteristic, complemented
39C2×#469C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#459C2211yescharacteristic
42C2×#452C2211yescharacteristic
43C2×#449C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#447C2211yescharacteristic
46C2×C4×SD16C2211yescharacteristic
47C2×#417C2211yescharacteristic
48#2841—21no—
49#2832—21no—
50#2831—21no—
51#2816—21no—
52#2743—21no—
53#2741—21no—
54#2714—21no—
55#2700—21no—
56#2696—21no—
57#2686—21no—
58#2678—21no—
59#2670—21no—
60#2628C2211yescharacteristic
61#2620C2211yescharacteristic
62#2570C2211yescharacteristic, complemented
63#2563C2211yescharacteristic, complemented
64#2554—21no—
65#2548C2211yescharacteristic
66#2540—21no—
67#2536C2211yescharacteristic
68#2503C2211yescharacteristic, complemented
69#2492C2211yescharacteristic
70#2491C2211yescharacteristic
71#2491C2211yescharacteristic, complemented
72#2472—21no—
73#2452C2211yescharacteristic
74#2451C2211yescharacteristic, complemented
75#2448C2211yescharacteristic
76#2448C2211yescharacteristic, complemented
77#2440C2211yescharacteristic, complemented
78#2433C2211yescharacteristic
79#2431C2211yescharacteristic
80#2428C2211yescharacteristic
81#2427C2211yescharacteristic, complemented
82#2420C2211yescharacteristic
83#2418—21no—
84#2416C2211yescharacteristic
85#2414C2211yescharacteristic
86#2395C2211yescharacteristic
87#2366C2211yescharacteristic
88#2362C2211yescharacteristic
89#2341C2211yescharacteristic
90#2309C2211yescharacteristic
91#2101C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2077C2211yescharacteristic, complemented
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic, complemented
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic, complemented
103#2058C2211yescharacteristic, complemented
104#2058C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2054C2211yescharacteristic
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic, complemented
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic, complemented
114#2042C2211yescharacteristic, complemented
115#2041C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic, complemented
122#2024C2211yescharacteristic, complemented
123#2023C2211yescharacteristic
124#2023C2211yescharacteristic
125#2023C2211yescharacteristic
126#2014C2211yescharacteristic
127#2014C2211yescharacteristic
128#2012C2211yescharacteristic
129#2012C2211yescharacteristic
130#2012C2211yescharacteristic
131#2011C2211yescharacteristic
132#2001C2211yescharacteristic
133#2000C2211yescharacteristic
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic, complemented
137#1999C2211yescharacteristic
138#1999C2211yescharacteristic, complemented
139#1990C2211yescharacteristic, complemented
140#1987C2211yescharacteristic, complemented
141#1982C2211yescharacteristic
142#1972C2211yescharacteristic
143#1968C2211yescharacteristic
144#1961C2211yescharacteristic
145#1959C2211yescharacteristic, complemented
146#1958C2211yescharacteristic
147#1954C2211yescharacteristic
148#1939C2211yescharacteristic, complemented
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1935C2211yescharacteristic, complemented
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic, complemented
155#1934C2211yescharacteristic, complemented
156#1933C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1926C2211yescharacteristic
159#1924C2211yescharacteristic
160#1924C2211yescharacteristic, complemented
161#1923C2211yescharacteristic
162#1923C2211yescharacteristic, complemented
163#1920C2211yescharacteristic, complemented
164#1920C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1895C2211yescharacteristic, complemented
168#1894C2211yescharacteristic, complemented
169#1880C2211yescharacteristic, complemented
170#1880C2211yescharacteristic, complemented
171#1880C2211yescharacteristic, complemented
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1878C2211yescharacteristic, complemented
177#1877C2211yescharacteristic, complemented
178#1877C2211yescharacteristic, complemented
179#1875C2211yescharacteristic
180#1874C2211yescharacteristic
181#1874C2211yescharacteristic, complemented
182#1873C2211yescharacteristic
183#1870C2211yescharacteristic
184#1865C2211yescharacteristic, complemented
185#1864C2211yescharacteristic
186#1851C2211yescharacteristic, complemented
187#1825C2211yescharacteristic
188#1825C2211yescharacteristic
189#1824C2211yescharacteristic, complemented
190#1805C2211yescharacteristic, complemented
191#1805C2211yescharacteristic, complemented
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic, complemented
194#1798C2211yescharacteristic
195#1788C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1771C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic, complemented
201#1753C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×M16C2311yescharacteristic
214#546—42no—
215#546—42no—
216#542—42no—
217#542—42no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#126—21no—
224C2×#124—21no—
225C2×#124—21no—
226C2×#124—21no—
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#123—21no—
231C2×#123—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#120—21no—
247C2×#120—21no—
248C2×#120—21no—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×D4—21no—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C22⋊C4—21no—
261#495—42no—
262#489—42no—
263#486—42no—
264#476—42no—
265#475—42no—
266#469—42no—
267#464—42no—
268#459—42no—
269#452—42no—
270#450—42no—
271#449—42no—
272#447—42no—
273C4×SD16—42no—
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283#417—42no—
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#400D411yescharacteristic
334#399—21no—
335#399—21no—
336#399—21no—
337#399D411yescharacteristic
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398D411yescharacteristic
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397D411yescharacteristic
348#397D411yescharacteristic
349#397D411yescharacteristic
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#395—21no—
355#395—21no—
356#395—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394D411yescharacteristic
370#394D411yescharacteristic
371#393—21no—
372#393—21no—
373#393—21no—
374#393—21no—
375#393—21no—
376#393—21no—
377#393—21no—
378#392—21no—
379#392—21no—
380#392—21no—
381#392—21no—
382#392—21no—
383#392—21no—
384#391—21no—
385#391—21no—
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#390—21no—
391#390—21no—
392#390—21no—
393#390—21no—
394#390—21no—
395#390—21no—
396#390—21no—
397#390—21no—
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#385—21no—
439#385—21no—
440#384C2311yescharacteristic
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#382C2311yescharacteristic
444#381—21no—
445#381—21no—
446#381—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380—21no—
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#379—21no—
456#379—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4—21no—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8—21no—
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×D4—22no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×D411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C2×Q16—22no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×D8—22no—
553C2×D8—41no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×M16—41no—
562C2×M16—41no—
563C2×M16—41no—
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C4⋊Q8—22no—
573C4⋊Q8—41no—
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577C4⋊Q8—41no—
578#127—22no—
579#127—41no—
580#127—41no—
581#127—41no—
582#126—44no—
583#124—22no—
584#124—22no—
585#124—41no—
586#124—41no—
587#124—41no—
588#124—41no—
589#124—44no—
590#124—82no—
591#124—82no—
592#123—44no—
593#123—44no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—44no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—82no—
602C22⋊Q8—82no—
603#121—22no—
604#121—41no—
605#121—41no—
606#121—41no—
607#121—44no—
608#121—41no—
609#121—41no—
610#121—41no—
611#121—41no—
612#121—41no—
613#121—41no—
614#121—82no—
615#121—82no—
616#120—44no—
617#120—82no—
618#120—82no—
619C4×Q8—22no—
620C4×Q8—41no—
621C4×Q8—41no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×Q8—41no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—82no—
634#117—41no—
635#117—41no—
636#117—41no—
637#117—41no—
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⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
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—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—44no—
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739#106—22no—
740#106—22no—
741#106—41no—
742#106—41no—
743C4⋊C8—41no—
744C4⋊C8—41no—
745C4⋊C8—41no—
746C4⋊C8—41no—
747C4⋊C8—41no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
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—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785C22⋊C8—41no—
786C22⋊C8—41no—
787#97—41no—
788#97—41no—
789C4×C8—41no—
790C4×C8—41no—
791C4×C8—41no—
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#95—21no—
808#95—21no—
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#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—42no—
833C24—42no—
834C24—81no—
835C24—81no—
836C24—81no—
837C24—81no—
838C24—81no—
839C24C22×D411yescharacteristic
840C24C22×D411yescharacteristic
841#41—44no—
842#41—82no—
843#41—82no—
844#41—82no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—42no—
857C2×Q8—81no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×Q8—81no—
861C2×Q8—81no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8—81no—
865C2×Q8H(5,𝔽2)12yes—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
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—41no—
890C2×D4—41no—
891C2×D4—41no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—82no—
913C2×D4—82no—
914C2×D4—82no—
915C2×D4—82no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4H(5,𝔽2)12yes—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
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—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
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×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
982Q16—82no—
983SD16—44no—
984SD16—82no—
985SD16—82no—
986SD16—82no—
987D8—82no—
988D8—82no—
989D8—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×C8—21no—
1015C4⋊C4—24no—
1016C4⋊C4—22no—
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—41no—
1041C4⋊C4—41no—
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⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4H(5,𝔽2)12yes—
1060C22⋊C4—24no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
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—42no—
1081C22⋊C4—42no—
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—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—42no—
1123C42—42no—
1124C42—81no—
1125C42—81no—
1126C42—81no—
1127C42—81no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—22no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
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—84no—
1171C23—84no—
1172C23—162no—
1173C23—162no—
1174C23—162no—
1175C23—162no—
1176C23—162no—
1177C23C23×D411yescharacteristic
1178Q8—22no—
1179Q8—22no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—162no—
1187Q8—162no—
1188Q8—162no—
1189D4—22no—
1190D4—22no—
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—162no—
1210D4—162no—
1211D4—162no—
1212D4—162no—
1213D4—162no—
1214D4—162no—
1215D4—162no—
1216D4—162no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
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—22no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
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—84no—
1297C2×C4—162no—
1298C2×C4—162no—
1299C2×C4—162no—
1300C2×C4—162no—
1301C2×C4#57712yes—
1302C2×C4C2×H(5,𝔽2)11yescharacteristic
1303C2×C4C2×H(5,𝔽2)11yescharacteristic
1304C2×C4C2×H(5,𝔽2)11yescharacteristic
1305C2×C4#58511yescharacteristic
1306C2×C4#58511yescharacteristic
1307C2×C4#58511yescharacteristic
1308C8—41no—
1309C8—41no—
1310C8—41no—
1311C8—41no—
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C22—41no—
1317C22—41no—
1318C22—42no—
1319C22—42no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—42no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
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—168no—
1359C22#348411yescharacteristic
1360C22#348811yescharacteristic
1361C22#350011yescharacteristic
1362C22C2×#57711yescharacteristic
1363C22#358411yescharacteristic
1364C22#358511yescharacteristic
1365C22#358511yescharacteristic
1366C4—22no—
1367C4—41no—
1368C4—41no—
1369C4—42no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—41no—
1379C4—42no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4#353411yescharacteristic
1391C4#354211yescharacteristic
1392C4#354511yescharacteristic
1393C4#356211yescharacteristic
1394C2—81no—
1395C2—81no—
1396C2—82no—
1397C2—161no—
1398C2—161no—
1399C2—161no—
1400C2#4795511yescharacteristic
1401C2#6161611yescharacteristic
1402C2#6168911yescharacteristic
1403C2#6206311yescharacteristic
1404C2#6208811yescharacteristic
1405C2#6261411yescharacteristic
1406C2#6261711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53025C2semidirect
2. #45018C2semidirect
3. #31855C2semidirect
4. #31740C2semidirect
5. #31727C2semidirect
6. #31643C2semidirect
7. #31459C2semidirect
8. #31403C2semidirect
9. #31163C2semidirect
10. #31000C2semidirect
11. #30934C2semidirect
12. #30746C2semidirect
13. #30527C2semidirect
14. #30446C2semidirect
15. #29727C2semidirect
16. #29697C2semidirect
17. #29116C2semidirect
18. #28913C2semidirect
19. #27766C2semidirect
20. #27270C2semidirect
21. #27250C2semidirect
22. #26897C2semidirect
23. #26828C2semidirect
24. #26750C2semidirect
25. #26664C2semidirect
26. #25610C2semidirect
27. #25321C2semidirect
28. #24543C2semidirect
29. #24444C2semidirect
30. #24247C2semidirect
31. #22360C2semidirect
34. C2×#495C22semidirect
35. C2×#489C22semidirect
37. C2×#475C22semidirect
38. C2×#476C22semidirect
62. #2570C22semidirect
63. #2563C22semidirect
68. #2503C22semidirect
71. #2491C22semidirect
74. #2451C22semidirect
76. #2448C22semidirect
77. #2440C22semidirect
81. #2427C22semidirect
91. #2101C22semidirect
92. #2101C22semidirect
93. #2088C22semidirect
94. #2077C22semidirect
98. #2073C22semidirect
102. #2065C22semidirect
103. #2058C22semidirect
104. #2058C22semidirect
105. #2056C22semidirect
111. #2054C22semidirect
113. #2042C22semidirect
114. #2042C22semidirect
121. #2034C22semidirect
122. #2024C22semidirect
136. #2000C22semidirect
138. #1999C22semidirect
139. #1990C22semidirect
140. #1987C22semidirect
145. #1959C22semidirect
148. #1939C22semidirect
151. #1935C22semidirect
154. #1934C22semidirect
155. #1934C22semidirect
156. #1933C22semidirect
157. #1927C22semidirect
160. #1924C22semidirect
162. #1923C22semidirect
163. #1920C22semidirect
164. #1920C22semidirect
165. #1916C22semidirect
166. #1916C22semidirect
167. #1895C22semidirect
168. #1894C22semidirect
169. #1880C22semidirect
170. #1880C22semidirect
171. #1880C22semidirect
174. #1879C22semidirect
175. #1878C22semidirect
176. #1878C22semidirect
177. #1877C22semidirect
178. #1877C22semidirect
181. #1874C22semidirect
184. #1865C22semidirect
186. #1851C22semidirect
189. #1824C22semidirect
190. #1805C22semidirect
191. #1805C22semidirect
193. #1804C22semidirect
198. #1771C22semidirect
199. #1763C22semidirect
200. C4×#102C22semidirect
201. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#530252
#450182
#318552
#317402
#317272
#316432
#314592
#314032
#311632
#310002
#309342
#307462
#305272
#304462
#297272
#296972
#291162
#289132
#277662
#272702
#272502
#268972
#268282
#267502
#266642
#256102
#253212
#245432
#244442
#242472
#223602