Finite Group Databasebeta

← #6697005

Subgroups — #6697005

Order 512.

1718 conjugacy classes of subgroups.

The subgroup lattice has 1397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40214C211yesmaximal, characteristic, complemented
2#36457C211yesmaximal, characteristic, complemented
3#33081C211yesmaximal, characteristic, complemented
4#32674C211yesmaximal, characteristic, complemented
5#32627C211yesmaximal, characteristic, complemented
6#32194C211yesmaximal, characteristic, complemented
7#32046C211yesmaximal, characteristic, complemented
8#31324C211yesmaximal, characteristic, complemented
9#31279C211yesmaximal, characteristic, complemented
10#30937C211yesmaximal, characteristic, complemented
11#30545C211yesmaximal, characteristic, complemented
12#30336C211yesmaximal, characteristic, complemented
13#30041C211yesmaximal, characteristic, complemented
14#28981C211yesmaximal, characteristic, complemented
15#28919C211yesmaximal, characteristic, complemented
16#27546C211yesmaximal, characteristic, complemented
17#27231C211yesmaximal, characteristic, complemented
18#26724C211yesmaximal, characteristic, complemented
19#25942C211yesmaximal, characteristic, complemented
20#25163C211yesmaximal, characteristic, complemented
21#25151C211yesmaximal, characteristic, complemented
22#24904C211yesmaximal, characteristic, complemented
23#24542C211yesmaximal, characteristic, complemented
24#24443C211yesmaximal, characteristic, complemented
25#24363C211yesmaximal, characteristic, complemented
26#24333C211yesmaximal, characteristic, complemented
27#23857C211yesmaximal, characteristic
28#22879C211yesmaximal, characteristic, complemented
29#22451C211yesmaximal, characteristic, complemented
30#22389C211yesmaximal, characteristic, complemented
31C4×#462C211yesmaximal, characteristic, complemented
32C22×#135C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#489C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#464C2211yescharacteristic
39C2×#462C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#452C2211yescharacteristic
43C2×#449C2211yescharacteristic
44C2×#449C2211yescharacteristic
45C2×C4×Q16C2211yescharacteristic
46C2×C4×Q16C2211yescharacteristic
47C2×C4×Q16C2211yescharacteristic
48C2×#417C2211yescharacteristic
49#2860C2211yescharacteristic
50#2858—21no—
51#2858C2211yescharacteristic
52#2768—21no—
53#2727—21no—
54#2710—21no—
55#2695—21no—
56#2651—21no—
57#2592C2211yescharacteristic
58#2589—21no—
59#2582C2211yescharacteristic
60#2563—21no—
61#2563C2211yescharacteristic
62#2554—21no—
63#2548—21no—
64#2548C2211yescharacteristic
65#2501C2211yescharacteristic
66#2496C2211yescharacteristic
67#2491—21no—
68#2491—21no—
69#2491—21no—
70#2491—21no—
71#2491C2211yescharacteristic
72#2491C2211yescharacteristic
73#2491C2211yescharacteristic
74#2491C2211yescharacteristic
75#2432C2211yescharacteristic
76#2429C2211yescharacteristic
77#2426C2211yescharacteristic
78#2423C2211yescharacteristic
79#2417C2211yescharacteristic
80#2407C2211yescharacteristic
81#2360C2211yescharacteristic
82#2341C2211yescharacteristic
83#2341C2211yescharacteristic
84#2341C2211yescharacteristic
85#2341C2211yescharacteristic
86#2341C2211yescharacteristic
87#2335—21no—
88C4×C4⋊Q8C2211yescharacteristic
89C4×#124—21no—
90C4×#124C2211yescharacteristic
91C42×Q8C2211yescharacteristic
92#2093C2211yescharacteristic
93#2077C2211yescharacteristic
94#2076C2211yescharacteristic
95#2075C2211yescharacteristic
96#2071C2211yescharacteristic
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2057C2211yescharacteristic
103#2057C2211yescharacteristic
104#2055C2211yescharacteristic
105#2055C2211yescharacteristic
106#2054C2211yescharacteristic
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic
109#2041C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic
113#2035C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2024C2211yescharacteristic
117#2024C2211yescharacteristic
118#2024C2211yescharacteristic
119#2024C2211yescharacteristic
120#2023C2211yescharacteristic
121#2023C2211yescharacteristic
122#2014C2211yescharacteristic
123#2014C2211yescharacteristic
124#2013C2211yescharacteristic
125#2013C2211yescharacteristic
126#2012C2211yescharacteristic
127#2012C2211yescharacteristic
128#2011C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#1999C2211yescharacteristic
132#1990C2211yescharacteristic
133#1988C2211yescharacteristic
134#1985C2211yescharacteristic
135#1984C2211yescharacteristic
136#1981C2211yescharacteristic
137#1973C2211yescharacteristic
138#1970C2211yescharacteristic
139#1970C2211yescharacteristic
140#1970C2211yescharacteristic
141#1968C2211yescharacteristic
142#1947C2211yescharacteristic
143#1936C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1928C2211yescharacteristic
147#1928C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1924C2211yescharacteristic
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic
156#1923C2211yescharacteristic
157#1921C2211yescharacteristic
158#1920C2211yescharacteristic
159#1918C2211yescharacteristic
160#1895C2211yescharacteristic
161#1894C2211yescharacteristic
162#1893C2211yescharacteristic
163#1892C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1874C2211yescharacteristic
179#1870C2211yescharacteristic
180#1869C2211yescharacteristic
181#1865C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1852C2211yescharacteristic
186#1851C2211yescharacteristic
187#1850C2211yescharacteristic
188#1839C2211yescharacteristic
189#1824C2211yescharacteristic
190#1808C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197C4×C4⋊C8C2211yescharacteristic
198#1763C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201#1753C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C22×#41C2311yescharacteristic
206C2×#135—24no—
207C2×#135—42no—
208C2×#135—42no—
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×D8C2311yescharacteristic
218C22×M16C2311yescharacteristic
219C23×C8C2311yescharacteristic
220Q82—42no—
221Q82—42no—
222#550—42no—
223#550—42no—
224C2×C4⋊Q8—21no—
225C2×C4⋊Q8—21no—
226C2×C4⋊Q8—21no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×#127—21no—
232C2×#127C2311yescharacteristic
233C2×#126—21no—
234C2×#126—21no—
235C2×#124—21no—
236C2×#124—21no—
237C2×#124—21no—
238C2×#124—21no—
239C2×#124—21no—
240C2×#124—21no—
241C2×#124—21no—
242C2×#124D411yescharacteristic
243C2×#124C2311yescharacteristic
244C2×#123—21no—
245C2×#123—21no—
246C2×C22⋊Q8C2311yescharacteristic
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2311yescharacteristic
249C2×#121—21no—
250C2×#121—21no—
251C2×#121C2311yescharacteristic
252C2×#121C2311yescharacteristic
253C2×#121C2311yescharacteristic
254C2×C4×Q8—21no—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×D4—21no—
265C2×C4×D4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267#489—42no—
268#477—42no—
269#468—42no—
270#464—42no—
271#462—24no—
272#452—24no—
273#452—42no—
274#452—42no—
275#449—42no—
276#449—42no—
277C4×Q16—42no—
278C4×Q16—42no—
279C4×Q16—42no—
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291#417—42no—
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332#400—21no—
333#399—21no—
334#399—21no—
335#399—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#397—21no—
342#397—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#393—21no—
357#393—21no—
358#393—21no—
359#393—21no—
360#393—21no—
361#393—21no—
362#393—21no—
363#392—21no—
364#391—21no—
365#391D411yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390—21no—
376#390—21no—
377#390—21no—
378#390—21no—
379#390—21no—
380#390—21no—
381#390—21no—
382#390—21no—
383#390—21no—
384#390—21no—
385#390D411yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#389—21no—
399#389—21no—
400#389—21no—
401#389—21no—
402#389—21no—
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
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#388—21no—
417#388—21no—
418#388—21no—
419#388D411yescharacteristic
420#388D411yescharacteristic
421#388D411yescharacteristic
422#388D411yescharacteristic
423#387—21no—
424#387—21no—
425#387—21no—
426#386—21no—
427#386—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#382—21no—
435#382D411yescharacteristic
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380—21no—
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467C43—21no—
468C43C2311yescharacteristic
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#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41—41no—
517C22×Q8—21no—
518C22×Q8—21no—
519C22×Q8—21no—
520C22×Q8C2×D411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×Q8C2411yescharacteristic
523C22×Q8C2411yescharacteristic
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4C2×D411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542#135—416no—
543C2×Q16—22no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16#4114yes—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
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—41no—
563C2×SD16—41no—
564C2×D8—22no—
565C2×D8—41no—
566C2×D8—41no—
567C2×D8—41no—
568C2×D8—41no—
569C2×D8—41no—
570C2×M16—41no—
571C2×M16—41no—
572C2×M16—41no—
573C22×C8—22no—
574C22×C8—41no—
575C22×C8—41no—
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C4⋊Q8—22no—
585C4⋊Q8—22no—
586C4⋊Q8—22no—
587C4⋊Q8—41no—
588C4⋊Q8—41no—
589C4⋊Q8—41no—
590C4⋊Q8—41no—
591C4⋊Q8—41no—
592C4⋊Q8—44no—
593C4⋊Q8—44no—
594C4⋊Q8—44no—
595#127—41no—
596#127—41no—
597#127—44no—
598#126—82no—
599#126—82no—
600#124—41no—
601#124—41no—
602#124—42no—
603#124—44no—
604#124—82no—
605#124—82no—
606#124—82no—
607#124—82no—
608#124—82no—
609#124—82no—
610#123—44no—
611#123—82no—
612C22⋊Q8—22no—
613C22⋊Q8—41no—
614C22⋊Q8—41no—
615C22⋊Q8—41no—
616C22⋊Q8—41no—
617C22⋊Q8—41no—
618#121—22no—
619#121—22no—
620#121—41no—
621#121—41no—
622#121—44no—
623#121—44no—
624#121—41no—
625#121—41no—
626C4×Q8—22no—
627C4×Q8—22no—
628C4×Q8—22no—
629C4×Q8—22no—
630C4×Q8—22no—
631C4×Q8—22no—
632C4×Q8—41no—
633C4×Q8—41no—
634C4×Q8—41no—
635C4×Q8—41no—
636C4×Q8—41no—
637C4×Q8—41no—
638C4×Q8—44no—
639C4×Q8—41no—
640C4×Q8—41no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×Q8—41no—
644C4×Q8—41no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—44no—
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—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—41no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
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—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⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42C2×D411yescharacteristic
750C2×C42C2×D411yescharacteristic
751C2×C42C2×D411yescharacteristic
752C2×C42C2×D411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758#107—22no—
759#107—41no—
760#107—41no—
761#107—41no—
762#107—41no—
763#107—41no—
764#106—41no—
765C4⋊C8—22no—
766C4⋊C8—41no—
767C4⋊C8—41no—
768C4⋊C8—41no—
769#103—22no—
770#103—22no—
771#103—22no—
772#103—22no—
773#103—22no—
774#103—22no—
775#103—22no—
776#103—22no—
777#103—22no—
778#103—41no—
779#103—41no—
780#103—41no—
781#103—41no—
782#103—41no—
783#103—41no—
784#102—22no—
785#102—22no—
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—
799C22⋊C8—22no—
800C22⋊C8—41no—
801C22⋊C8—41no—
802C22⋊C8—41no—
803C22⋊C8—41no—
804C22⋊C8—41no—
805#97—41no—
806C4×C8—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#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839C24—21no—
840C24—21no—
841C24—21no—
842C24C22×D411yescharacteristic
843C24C22×D411yescharacteristic
844#41—44no—
845#41—44no—
846#41—44no—
847#41—82no—
848#41—82no—
849#41—82no—
850#41—82no—
851#41—82no—
852#41—82no—
853#41—82no—
854#41—82no—
855#41—82no—
856C2×Q8—22no—
857C2×Q8—22no—
858C2×Q8—21no—
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—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—41no—
873C2×Q8—42no—
874C2×Q8—42no—
875C2×Q8—42no—
876C2×Q8—81no—
877C2×Q8—81no—
878C2×Q8—81no—
879C2×Q8—81no—
880C2×Q8—81no—
881C2×Q8—81no—
882C2×Q8C2×#4112yes—
883C2×Q8C2×#4112yes—
884C2×Q8H(5,𝔽2)12yes—
885C2×Q8H(5,𝔽2)12yes—
886C2×D4—22no—
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—41no—
906C2×D4—41no—
907C2×D4—42no—
908C2×D4—42no—
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—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
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—21no—
955C22×C4—21no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
981Q16—28no—
982Q16—44no—
983SD16—44no—
984SD16—44no—
985SD16—82no—
986SD16—82no—
987SD16—82no—
988D8—44no—
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—44no—
1015C2×C8C2×#4112yes—
1016C4⋊C4—24no—
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—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4H(5,𝔽2)12yes—
1065C22⋊C4—22no—
1066C22⋊C4—22no—
1067C22⋊C4—22no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
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—
1112C22⋊C4—81no—
1113C42—24no—
1114C42—22no—
1115C42—22no—
1116C42—22no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—41no—
1128C42—42no—
1129C42—42no—
1130C42—42no—
1131C42—42no—
1132C42—42no—
1133C42—42no—
1134C42—42no—
1135C42—81no—
1136C42—81no—
1137C42—81no—
1138C42—81no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
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—
1174C23C23×D411yescharacteristic
1175Q8—22no—
1176Q8—22no—
1177Q8—22no—
1178Q8—22no—
1179Q8—22no—
1180Q8—44no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—162no—
1188Q8—162no—
1189Q8—162no—
1190Q8#53814yes—
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—82no—
1204D4—84no—
1205D4—84no—
1206D4—84no—
1207D4—84no—
1208D4—162no—
1209D4—162no—
1210D4—162no—
1211D4—162no—
1212C2×C4—21no—
1213C2×C4—22no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—22no—
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—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
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—84no—
1292C2×C4—84no—
1293C2×C4—84no—
1294C2×C4—162no—
1295C2×C4#57512yes—
1296C2×C4#57612yes—
1297C2×C4#57712yes—
1298C2×C4#57812yes—
1299C2×C4C22×#4111yescharacteristic
1300C2×C4C2×H(5,𝔽2)11yescharacteristic
1301C2×C4C2×H(5,𝔽2)11yescharacteristic
1302C2×C4C2×H(5,𝔽2)11yescharacteristic
1303C2×C4#58511yescharacteristic
1304C2×C4#58511yescharacteristic
1305C8—22no—
1306C8—41no—
1307C8—41no—
1308C8—41no—
1309C8—41no—
1310C8—41no—
1311C8—41no—
1312C8—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
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—
1348C22D4×#4111yescharacteristic
1349C22#348411yescharacteristic
1350C22#348811yescharacteristic
1351C22C2×#57511yescharacteristic
1352C22C2×#57611yescharacteristic
1353C22C2×#57711yescharacteristic
1354C22C2×#57811yescharacteristic
1355C4—22no—
1356C4—24no—
1357C4—22no—
1358C4—22no—
1359C4—22no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—42no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—42no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4C2×#53811yescharacteristic
1381C4#351411yescharacteristic
1382C4#354511yescharacteristic
1383C4#355811yescharacteristic
1384C2—81no—
1385C2—81no—
1386C2—161no—
1387C2—161no—
1388C2—161no—
1389C2#3771611yescharacteristic
1390C2#6145011yescharacteristic
1391C2#6148511yescharacteristic
1392C2#6160311yescharacteristic
1393C2#6166811yescharacteristic
1394C2#6198811yescharacteristic
1395C2#6205811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23857C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40214C2semidirect
2. #36457C2semidirect
3. #33081C2semidirect
4. #32674C2semidirect
5. #32627C2semidirect
6. #32194C2semidirect
7. #32046C2semidirect
8. #31324C2semidirect
9. #31279C2semidirect
10. #30937C2semidirect
11. #30545C2semidirect
12. #30336C2semidirect
13. #30041C2semidirect
14. #28981C2semidirect
15. #28919C2semidirect
16. #27546C2semidirect
17. #27231C2semidirect
18. #26724C2semidirect
19. #25942C2semidirect
20. #25163C2semidirect
21. #25151C2semidirect
22. #24904C2semidirect
23. #24542C2semidirect
24. #24443C2semidirect
25. #24363C2semidirect
26. #24333C2semidirect
28. #22879C2semidirect
29. #22451C2semidirect
30. #22389C2semidirect
31. C4×#462C2semidirect

Maximal subgroups

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

subgroupindex
#402142
#364572
#330812
#326742
#326272
#321942
#320462
#313242
#312792
#309372
#305452
#303362
#300412
#289812
#289192
#275462
#272312
#267242
#259422
#251632
#251512
#249042
#245422
#244432
#243632
#243332
#238572
#228792
#224512
#223892
C4×#4622