Finite Group Databasebeta

← #7087199

Subgroups — #7087199

Order 512.

1731 conjugacy classes of subgroups.

The subgroup lattice has 1424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59699C211yesmaximal, characteristic, complemented
2#39405C211yesmaximal, characteristic, complemented
3#32524C211yesmaximal, characteristic, complemented
4#32162C211yesmaximal, characteristic, complemented
5#32094C211yesmaximal, characteristic, complemented
6#32069C211yesmaximal, characteristic, complemented
7#30902C211yesmaximal, characteristic, complemented
8#30615C211yesmaximal, characteristic, complemented
9#30472C211yesmaximal, characteristic, complemented
10#30472C211yesmaximal, characteristic, complemented
11#29561C211yesmaximal, characteristic, complemented
12#28959C211yesmaximal, characteristic, complemented
13#28919C211yesmaximal, characteristic, complemented
14#28621C211yesmaximal, characteristic, complemented
15#28480C211yesmaximal, characteristic, complemented
16#28365C211yesmaximal, characteristic, complemented
17#27066C211yesmaximal, characteristic, complemented
18#26634C211yesmaximal, characteristic, complemented
19#26600C211yesmaximal, characteristic, complemented
20#26569C211yesmaximal, characteristic, complemented
21#26268C211yesmaximal, characteristic, complemented
22#26179C211yesmaximal, characteristic, complemented
23#25428C211yesmaximal, characteristic, complemented
24#25366C211yesmaximal, characteristic, complemented
25#25176C211yesmaximal, characteristic, complemented
26#25093C211yesmaximal, characteristic, complemented
27#23806C211yesmaximal, characteristic, complemented
28#23290C211yesmaximal, characteristic, complemented
29#23003C211yesmaximal, characteristic, complemented
30#22868C211yesmaximal, characteristic, complemented
31#22153C211yesmaximal, characteristic, complemented
32C2×#538—21no—
33C2×#496C2211yescharacteristic
34C2×#496C2211yescharacteristic
35C2×#492C2211yescharacteristic, complemented
36C2×#489C2211yescharacteristic, complemented
37C2×#482C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#460C2211yescharacteristic
41C2×#460C2211yescharacteristic
42C2×#460C2211yescharacteristic
43C2×#463C2211yescharacteristic, complemented
44C2×#461C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#450C2211yescharacteristic
47C2×#447C2211yescharacteristic
48C2×#442C2211yescharacteristic
49C2×#442C2211yescharacteristic, complemented
50C2×#440C2211yescharacteristic
51C2×#440C2211yescharacteristic, complemented
52C2×#440C2211yescharacteristic, complemented
53C2×#418C2211yescharacteristic
54#2858C2211yescharacteristic
55#2800—21no—
56#2793—21no—
57#2714—21no—
58#2678—21no—
59#2676—21no—
60#2670—21no—
61#2631—21no—
62#2608—21no—
63#2597—21no—
64#2545C2211yescharacteristic, complemented
65#2541C2211yescharacteristic
66#2541C2211yescharacteristic
67#2526—21no—
68#2525—21no—
69#2512—21no—
70#2512C2211yescharacteristic
71#2512C2211yescharacteristic, complemented
72#2509C2211yescharacteristic, complemented
73#2499C2211yescharacteristic
74#2491C2211yescharacteristic
75#2456—21no—
76#2452C2211yescharacteristic
77#2447C2211yescharacteristic, complemented
78#2445C2211yescharacteristic
79#2433C2211yescharacteristic
80#2433C2211yescharacteristic
81#2429C2211yescharacteristic
82#2428C2211yescharacteristic
83#2426C2211yescharacteristic
84#2426C2211yescharacteristic
85#2424—21no—
86#2422C2211yescharacteristic
87#2373—21no—
88#2366C2211yescharacteristic
89#2365C2211yescharacteristic, complemented
90#2363C2211yescharacteristic
91#2362C2211yescharacteristic
92Q8×C4⋊C4C2211yescharacteristic, complemented
93D4×C22⋊C4C2211yescharacteristic
94C4×#127C2211yescharacteristic
95C4×#126C2211yescharacteristic
96C4×#124C2211yescharacteristic, complemented
97#2295C2211yescharacteristic, complemented
98#2096C2211yescharacteristic, complemented
99#2093C2211yescharacteristic
100#2093C2211yescharacteristic, complemented
101#2092C2211yescharacteristic
102#2092C2211yescharacteristic, complemented
103#2087C2211yescharacteristic, complemented
104#2071C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic, complemented
108#2057C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic, complemented
111#2055C2211yescharacteristic, complemented
112#2054C2211yescharacteristic
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic, complemented
115#2043C2211yescharacteristic, complemented
116#2042C2211yescharacteristic, complemented
117#2041C2211yescharacteristic
118#2041C2211yescharacteristic
119#2041C2211yescharacteristic
120#2041C2211yescharacteristic, complemented
121#2036C2211yescharacteristic
122#2036C2211yescharacteristic
123#2024C2211yescharacteristic, complemented
124#2014C2211yescharacteristic
125#2014C2211yescharacteristic
126#2014C2211yescharacteristic
127#2013C2211yescharacteristic
128#2012C2211yescharacteristic
129#2012C2211yescharacteristic
130#2012C2211yescharacteristic, complemented
131#2011C2211yescharacteristic
132#2011C2211yescharacteristic
133#2011C2211yescharacteristic, complemented
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#1999C2211yescharacteristic
137#1999C2211yescharacteristic
138#1993C2211yescharacteristic, complemented
139#1982C2211yescharacteristic
140#1982C2211yescharacteristic, complemented
141#1973C2211yescharacteristic
142#1973C2211yescharacteristic
143#1973C2211yescharacteristic, complemented
144#1973C2211yescharacteristic, complemented
145#1970C2211yescharacteristic
146#1970C2211yescharacteristic, complemented
147#1968C2211yescharacteristic
148#1961C2211yescharacteristic
149#1957C2211yescharacteristic
150#1947C2211yescharacteristic, complemented
151#1947C2211yescharacteristic, complemented
152#1943C2211yescharacteristic, complemented
153#1942C2211yescharacteristic, complemented
154#1939C2211yescharacteristic, complemented
155#1936C2211yescharacteristic
156#1936C2211yescharacteristic
157#1936C2211yescharacteristic
158#1936C2211yescharacteristic, complemented
159#1936C2211yescharacteristic, complemented
160#1927C2211yescharacteristic, complemented
161#1926C2211yescharacteristic
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic, complemented
164#1925C2211yescharacteristic, complemented
165#1924C2211yescharacteristic
166#1924C2211yescharacteristic
167#1924C2211yescharacteristic
168#1919C2211yescharacteristic, complemented
169#1917C2211yescharacteristic, complemented
170#1917C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1895C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic
177#1880C2211yescharacteristic, complemented
178#1880C2211yescharacteristic, complemented
179#1880C2211yescharacteristic, complemented
180#1879C2211yescharacteristic
181#1879C2211yescharacteristic
182#1879C2211yescharacteristic, complemented
183#1877C2211yescharacteristic
184#1877C2211yescharacteristic, complemented
185#1875C2211yescharacteristic
186#1864C2211yescharacteristic, complemented
187#1863C2211yescharacteristic, complemented
188#1862C2211yescharacteristic
189#1862C2211yescharacteristic
190#1862C2211yescharacteristic, complemented
191#1862C2211yescharacteristic, complemented
192#1854C2211yescharacteristic
193#1851C2211yescharacteristic
194#1803C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1767C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1745C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×M16C2311yescharacteristic
217#538—48no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#127C2311yescharacteristic
225C2×#126—21no—
226C2×#126—21no—
227C2×#126D411yescharacteristic
228C2×#124—21no—
229C2×#124—21no—
230C2×#124—21no—
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#123—21no—
234C2×#123—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121—21no—
242C2×#121—21no—
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#120—21no—
247C2×#120—21no—
248C2×#120—21no—
249C2×#120—21no—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×D4—21no—
255C2×C4×D4—21no—
256C2×C4×D4—21no—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C22×C22⋊C4—21no—
264#496—42no—
265#496—42no—
266#492—42no—
267#489—42no—
268#482—42no—
269#468—42no—
270#468—42no—
271#463—42no—
272#461—42no—
273#460—24no—
274#460—24no—
275#460—42no—
276#450—42no—
277#450—42no—
278#447—24no—
279#442—42no—
280#442—42no—
281#440—42no—
282#440—42no—
283#440—42no—
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×#106C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296C2×C4⋊C8C2311yescharacteristic
297#418—42no—
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×#97C2311yescharacteristic
337C2×#97C2311yescharacteristic
338C2×C4×C8C2311yescharacteristic
339C2×C4×C8C2311yescharacteristic
340#400—21no—
341#400—21no—
342#398—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#393—21no—
366#393—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#392—21no—
372#392—21no—
373#392—21no—
374#392—21no—
375#392—21no—
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#390—21no—
381#390—21no—
382#390—21no—
383#390—21no—
384#390—21no—
385#390—21no—
386#390—21no—
387#390—21no—
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#389—21no—
402#389—21no—
403#389—21no—
404#389—21no—
405#389—21no—
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#388—21no—
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#388D411yescharacteristic
427#388D411yescharacteristic
428#388D411yescharacteristic
429#387—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#387—21no—
436#387—21no—
437#387D411yescharacteristic
438#387D411yescharacteristic
439#387D411yescharacteristic
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#384—21no—
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#383D411yescharacteristic
454#382C2311yescharacteristic
455#381—21no—
456#380C2311yescharacteristic
457#379—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4—21no—
460C4×C4⋊C4—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
474#376—21no—
475C43C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500C25—21no—
501C22×Q8—21no—
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4C2411yescharacteristic
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×D8—22no—
560C2×D8—22no—
561C2×D8—22no—
562C2×D8—41no—
563C2×D8—41no—
564C2×D8—41no—
565C2×D8—41no—
566C2×D8—41no—
567C2×D8—41no—
568C2×D8—41no—
569C2×D8—41no—
570C2×D8—41no—
571C2×M16—22no—
572C2×M16—41no—
573C2×M16—41no—
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C4⋊Q8—22no—
583C4⋊Q8—41no—
584C4⋊Q8—41no—
585C4⋊Q8—41no—
586#127—22no—
587#127—22no—
588#127—41no—
589#127—41no—
590#127—41no—
591#127—41no—
592#127—41no—
593#127—41no—
594#127—41no—
595#127—41no—
596#126—24no—
597#126—44no—
598#126—44no—
599#124—22no—
600#124—41no—
601#124—44no—
602#124—41no—
603#124—41no—
604#124—44no—
605#124—82no—
606#123—44no—
607#123—44no—
608C22⋊Q8—22no—
609C22⋊Q8—41no—
610C22⋊Q8—44no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613#121—22no—
614#121—44no—
615#121—41no—
616#121—44no—
617#121—44no—
618#121—41no—
619#121—41no—
620#121—41no—
621#121—41no—
622#121—82no—
623#121—82no—
624#120—44no—
625#120—44no—
626#120—82no—
627#120—82no—
628C4×Q8—22no—
629C4×Q8—22no—
630C4×Q8—41no—
631C4×Q8—41no—
632C4×Q8—41no—
633C4×Q8—41no—
634C4×Q8—41no—
635C4×Q8—41no—
636C4×D4—44no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—41no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—41no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—44no—
648C4×D4—82no—
649#117—41no—
650#117—41no—
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⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
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—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—44no—
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×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42C2×D411yescharacteristic
744C2×C42C2×D411yescharacteristic
745C2×C42C2×D411yescharacteristic
746C2×C42C2×D411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753#107—22no—
754#107—41no—
755#107—41no—
756#107—41no—
757#107—41no—
758#107—41no—
759#106—22no—
760#106—41no—
761C4⋊C8—22no—
762C4⋊C8—22no—
763C4⋊C8—22no—
764C4⋊C8—41no—
765C4⋊C8—41no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
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#4114yes—
798C22⋊C8—22no—
799C22⋊C8—22no—
800C22⋊C8—41no—
801#97—22no—
802#97—22no—
803#97—22no—
804#97—41no—
805#97—41no—
806C4×C8—41no—
807C4×C8—41no—
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#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#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
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—42no—
847C24—42no—
848C24—81no—
849C24—81no—
850C24—81no—
851C24—81no—
852C24—81no—
853C24C22×D411yescharacteristic
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—42no—
866C2×Q8—81no—
867C2×Q8—81no—
868C2×Q8H(5,𝔽2)12yes—
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—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—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—44no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—81no—
915C2×D4—81no—
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×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—82no—
936C2×D4—82no—
937C2×D4—82no—
938C2×D4—81no—
939C2×D4—81no—
940C2×D4—81no—
941C2×D4—81no—
942C2×D4—81no—
943C2×D4—81no—
944C2×D4C2×#4112yes—
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—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C2511yescharacteristic
991SD16—44no—
992SD16—44no—
993SD16—44no—
994SD16—82no—
995SD16—82no—
996SD16—82no—
997SD16—82no—
998SD16—82no—
999D8—44no—
1000D8—44no—
1001D8—82no—
1002D8—82no—
1003M16—82no—
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—
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×C8C2×#4112yes—
1026C2×C8H(5,𝔽2)12yes—
1027C2×C8H(5,𝔽2)12yes—
1028C4⋊C4—22no—
1029C4⋊C4—22no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—41no—
1048C4⋊C4—41no—
1049C4⋊C4—41no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4AGL(1,ℤ/8)14yes—
1071C4⋊C4C2×#4112yes—
1072C22⋊C4—22no—
1073C22⋊C4—22no—
1074C22⋊C4—22no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—41no—
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—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—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—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C42—22no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—41no—
1134C42—41no—
1135C42—41no—
1136C42—42no—
1137C42—42no—
1138C42—42no—
1139C42—42no—
1140C42—81no—
1141C42—81no—
1142C42—81no—
1143C42—81no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—22no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—84no—
1187C23—84no—
1188C23—162no—
1189C23—162no—
1190C23—162no—
1191C23—162no—
1192C23—162no—
1193C23C23×D411yescharacteristic
1194Q8—22no—
1195Q8—22no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—41no—
1202Q8—162no—
1203D4—22no—
1204D4—22no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—41no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—84no—
1224D4—84no—
1225D4—84no—
1226D4—84no—
1227D4—162no—
1228D4—162no—
1229D4—162no—
1230D4—162no—
1231D4—162no—
1232D4—162no—
1233D4—162no—
1234D4—162no—
1235D4—162no—
1236D4—162no—
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—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—22no—
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—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—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—162no—
1311C2×C4—162no—
1312C2×C4—162no—
1313C2×C4—162no—
1314C2×C4—162no—
1315C2×C4C2×AGL(1,ℤ/8)12yes—
1316C2×C4C2×AGL(1,ℤ/8)12yes—
1317C2×C4C2×AGL(1,ℤ/8)12yes—
1318C2×C4C22×#4111yescharacteristic
1319C2×C4C2×H(5,𝔽2)11yescharacteristic
1320C2×C4C2×H(5,𝔽2)11yescharacteristic
1321C2×C4C2×H(5,𝔽2)11yescharacteristic
1322C2×C4#58511yescharacteristic
1323C2×C4#58511yescharacteristic
1324C8—22no—
1325C8—22no—
1326C8—22no—
1327C8—41no—
1328C8—41no—
1329C8—41no—
1330C8—41no—
1331C8—41no—
1332C22—41no—
1333C22—42no—
1334C22—41no—
1335C22—42no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—42no—
1340C22—41no—
1341C22—41no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22—168no—
1375C22D4×#4111yescharacteristic
1376C22#348811yescharacteristic
1377C22#349811yescharacteristic
1378C22C22×AGL(1,ℤ/8)11yescharacteristic
1379C22#358511yescharacteristic
1380C22#358511yescharacteristic
1381C22#358611yescharacteristic
1382C4—22no—
1383C4—22no—
1384C4—22no—
1385C4—41no—
1386C4—41no—
1387C4—41no—
1388C4—42no—
1389C4—41no—
1390C4—41no—
1391C4—41no—
1392C4—42no—
1393C4—41no—
1394C4—41no—
1395C4—41no—
1396C4—41no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4#350611yescharacteristic
1407C4#351911yescharacteristic
1408C4#353311yescharacteristic
1409C4#353411yescharacteristic
1410C2—81no—
1411C2—82no—
1412C2—161no—
1413C2—161no—
1414C2—161no—
1415C2—161no—
1416C2#4418411yescharacteristic
1417C2#6145211yescharacteristic
1418C2#6150611yescharacteristic
1419C2#6196311yescharacteristic
1420C2#6209211yescharacteristic
1421C2#6244611yescharacteristic
1422C2#6245311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59699C2semidirect
2. #39405C2semidirect
3. #32524C2semidirect
4. #32162C2semidirect
5. #32094C2semidirect
6. #32069C2semidirect
7. #30902C2semidirect
8. #30615C2semidirect
9. #30472C2semidirect
10. #30472C2semidirect
11. #29561C2semidirect
12. #28959C2semidirect
13. #28919C2semidirect
14. #28621C2semidirect
15. #28480C2semidirect
16. #28365C2semidirect
17. #27066C2semidirect
18. #26634C2semidirect
19. #26600C2semidirect
20. #26569C2semidirect
21. #26268C2semidirect
22. #26179C2semidirect
23. #25428C2semidirect
24. #25366C2semidirect
25. #25176C2semidirect
26. #25093C2semidirect
27. #23806C2semidirect
28. #23290C2semidirect
29. #23003C2semidirect
30. #22868C2semidirect
31. #22153C2semidirect
35. C2×#492C22semidirect
36. C2×#489C22semidirect
43. C2×#463C22semidirect
49. C2×#442C22semidirect
51. C2×#440C22semidirect
52. C2×#440C22semidirect
64. #2545C22semidirect
71. #2512C22semidirect
72. #2509C22semidirect
77. #2447C22semidirect
89. #2365C22semidirect
92. Q8×C4⋊C4C22semidirect
96. C4×#124C22semidirect
97. #2295C22semidirect
98. #2096C22semidirect
100. #2093C22semidirect
102. #2092C22semidirect
103. #2087C22semidirect
104. #2071C22semidirect
107. #2067C22semidirect
108. #2057C22semidirect
110. #2055C22semidirect
111. #2055C22semidirect
114. #2054C22semidirect
115. #2043C22semidirect
116. #2042C22semidirect
120. #2041C22semidirect
123. #2024C22semidirect
130. #2012C22semidirect
133. #2011C22semidirect
138. #1993C22semidirect
140. #1982C22semidirect
143. #1973C22semidirect
144. #1973C22semidirect
146. #1970C22semidirect
150. #1947C22semidirect
151. #1947C22semidirect
152. #1943C22semidirect
153. #1942C22semidirect
154. #1939C22semidirect
158. #1936C22semidirect
159. #1936C22semidirect
160. #1927C22semidirect
163. #1925C22semidirect
164. #1925C22semidirect
168. #1919C22semidirect
169. #1917C22semidirect
170. #1917C22semidirect
171. #1916C22semidirect
177. #1880C22semidirect
178. #1880C22semidirect
179. #1880C22semidirect
182. #1879C22semidirect
184. #1877C22semidirect
186. #1864C22semidirect
187. #1863C22semidirect
190. #1862C22semidirect
191. #1862C22semidirect
194. #1803C22semidirect
195. #1771C22semidirect
196. #1770C22semidirect
197. #1767C22semidirect
198. C4×#103C22semidirect
202. #1745C22semidirect

Maximal subgroups

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

subgroupindex
#596992
#394052
#325242
#321622
#320942
#320692
#309022
#306152
#304722
#295612
#289592
#289192
#286212
#284802
#283652
#270662
#266342
#266002
#265692
#262682
#261792
#254282
#253662
#251762
#250932
#238062
#232902
#230032
#228682
#221532