Finite Group Databasebeta

← #7236797

Subgroups — #7236797

Order 512.

1661 conjugacy classes of subgroups.

The subgroup lattice has 1413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42486C211yesmaximal, characteristic, complemented
2#42444C211yesmaximal, characteristic, complemented
3#32785C211yesmaximal, characteristic, complemented
4#32666C211yesmaximal, characteristic, complemented
5#32659C211yesmaximal, characteristic, complemented
6#31538C211yesmaximal, characteristic, complemented
7#31537C211yesmaximal, characteristic, complemented
8#31147C211yesmaximal, characteristic, complemented
9#31135C211yesmaximal, characteristic, complemented
10#30898C211yesmaximal, characteristic, complemented
11#30891C211yesmaximal, characteristic, complemented
12#30891C211yesmaximal, characteristic, complemented
13#30890C211yesmaximal, characteristic, complemented
14#30658C211yesmaximal, characteristic, complemented
15#30646C211yesmaximal, characteristic, complemented
16#28430C211yesmaximal, characteristic, complemented
17#28421C211yesmaximal, characteristic, complemented
18#28321C211yesmaximal, characteristic, complemented
19#26494C211yesmaximal, characteristic, complemented
20#26492C211yesmaximal, characteristic, complemented
21#26392C211yesmaximal, characteristic, complemented
22#26390C211yesmaximal, characteristic, complemented
23#25682C211yesmaximal, characteristic, complemented
24#25172C211yesmaximal, characteristic, complemented
25#25168C211yesmaximal, characteristic, complemented
26#25168C211yesmaximal, characteristic, complemented
27#25164C211yesmaximal, characteristic, complemented
28#24204C211yesmaximal, characteristic, complemented
29#24198C211yesmaximal, characteristic, complemented
30#23939C211yesmaximal, characteristic, complemented
31#22326C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic, complemented
33C2×#540C2211yescharacteristic
34C2×#499C2211yescharacteristic, complemented
35C2×#490C2211yescharacteristic, complemented
36C2×#490C2211yescharacteristic, complemented
37C2×#489C2211yescharacteristic, complemented
38C2×#485C2211yescharacteristic
39C2×#482C2211yescharacteristic
40C2×#478C2211yescharacteristic, complemented
41C2×#476C2211yescharacteristic, complemented
42C2×#463C2211yescharacteristic
43C2×#463C2211yescharacteristic
44C2×#459C2211yescharacteristic
45C2×#459C2211yescharacteristic
46C2×#450C2211yescharacteristic
47C2×#447C2211yescharacteristic
48C2×#447C2211yescharacteristic
49C2×#447C2211yescharacteristic
50C2×#442C2211yescharacteristic
51C2×#442C2211yescharacteristic
52C2×#442C2211yescharacteristic
53C2×#440C2211yescharacteristic
54#2842—21no—
55#2813—21no—
56#2780—21no—
57#2748—21no—
58#2732—21no—
59#2693—21no—
60#2692—21no—
61#2676—21no—
62#2672—21no—
63#2671—21no—
64#2630—21no—
65#2629C2211yescharacteristic
66#2626—21no—
67#2626—21no—
68#2620C2211yescharacteristic
69#2618—21no—
70#2580C2211yescharacteristic
71#2566C2211yescharacteristic
72#2544C2211yescharacteristic, complemented
73#2544C2211yescharacteristic, complemented
74#2542C2211yescharacteristic
75#2541C2211yescharacteristic, complemented
76#2538C2211yescharacteristic
77#2538C2211yescharacteristic, complemented
78#2454C2211yescharacteristic
79#2454C2211yescharacteristic
80#2454C2211yescharacteristic
81#2454C2211yescharacteristic, complemented
82#2453C2211yescharacteristic, complemented
83#2452C2211yescharacteristic
84#2441C2211yescharacteristic
85#2439C2211yescharacteristic
86#2437—21no—
87#2428C2211yescharacteristic
88#2428C2211yescharacteristic
89#2427C2211yescharacteristic
90#2426C2211yescharacteristic
91#2416—21no—
92#2396C2211yescharacteristic
93D4×C4⋊C4C2211yescharacteristic, complemented
94D4×C22⋊C4C2211yescharacteristic
95D4×C22⋊C4C2211yescharacteristic
96#2309C2211yescharacteristic
97#2096C2211yescharacteristic, complemented
98#2094C2211yescharacteristic
99#2094C2211yescharacteristic, complemented
100#2094C2211yescharacteristic, complemented
101#2093C2211yescharacteristic
102#2092C2211yescharacteristic, complemented
103#2085C2211yescharacteristic, complemented
104#2084C2211yescharacteristic, complemented
105#2084C2211yescharacteristic, complemented
106#2084C2211yescharacteristic, complemented
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic, complemented
109#2067C2211yescharacteristic, complemented
110#2066C2211yescharacteristic, complemented
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic, complemented
115#2059C2211yescharacteristic, complemented
116#2058C2211yescharacteristic, complemented
117#2042C2211yescharacteristic, complemented
118#2042C2211yescharacteristic, complemented
119#2042C2211yescharacteristic, complemented
120#2042C2211yescharacteristic, complemented
121#2041C2211yescharacteristic, complemented
122#2041C2211yescharacteristic, complemented
123#2035C2211yescharacteristic
124#2035C2211yescharacteristic
125#2034C2211yescharacteristic
126#2034C2211yescharacteristic
127#2034C2211yescharacteristic
128#2034C2211yescharacteristic
129#2033C2211yescharacteristic
130#2033C2211yescharacteristic
131#2026C2211yescharacteristic, complemented
132#2026C2211yescharacteristic, complemented
133#2025C2211yescharacteristic
134#2025C2211yescharacteristic
135#2025C2211yescharacteristic, complemented
136#2023C2211yescharacteristic, complemented
137#2012C2211yescharacteristic
138#2012C2211yescharacteristic
139#2012C2211yescharacteristic
140#2012C2211yescharacteristic
141#2011C2211yescharacteristic
142#2011C2211yescharacteristic
143#2011C2211yescharacteristic
144#2011C2211yescharacteristic
145#1992C2211yescharacteristic, complemented
146#1985C2211yescharacteristic, complemented
147#1985C2211yescharacteristic, complemented
148#1973C2211yescharacteristic
149#1973C2211yescharacteristic
150#1972C2211yescharacteristic
151#1972C2211yescharacteristic
152#1972C2211yescharacteristic
153#1972C2211yescharacteristic
154#1970C2211yescharacteristic
155#1968C2211yescharacteristic
156#1961C2211yescharacteristic, complemented
157#1959C2211yescharacteristic, complemented
158#1957C2211yescharacteristic, complemented
159#1944C2211yescharacteristic, complemented
160#1944C2211yescharacteristic, complemented
161#1943C2211yescharacteristic, complemented
162#1943C2211yescharacteristic, complemented
163#1924C2211yescharacteristic
164#1924C2211yescharacteristic
165#1924C2211yescharacteristic
166#1924C2211yescharacteristic
167#1917C2211yescharacteristic, complemented
168#1917C2211yescharacteristic, complemented
169#1917C2211yescharacteristic, complemented
170#1917C2211yescharacteristic, complemented
171#1880C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic
180#1879C2211yescharacteristic
181#1879C2211yescharacteristic
182#1877C2211yescharacteristic
183#1875C2211yescharacteristic
184#1875C2211yescharacteristic
185#1865C2211yescharacteristic, complemented
186#1864C2211yescharacteristic
187#1864C2211yescharacteristic
188#1864C2211yescharacteristic
189#1864C2211yescharacteristic, complemented
190#1864C2211yescharacteristic, complemented
191#1864C2211yescharacteristic, complemented
192#1862C2211yescharacteristic
193#1862C2211yescharacteristic, complemented
194#1862C2211yescharacteristic, complemented
195#1862C2211yescharacteristic, complemented
196#1862C2211yescharacteristic, complemented
197#1818C2211yescharacteristic
198#1805C2211yescharacteristic, complemented
199#1802C2211yescharacteristic, complemented
200#1771C2211yescharacteristic, complemented
201#1771C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212#559—42no—
213#559—42no—
214#540—42no—
215#540—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8C2311yescharacteristic
237C2×#121—21no—
238C2×#121—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121—21no—
242C2×#121—21no—
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×D4—21no—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C22×C4⋊C4—21no—
261C22×C22⋊C4—21no—
262C22×C22⋊C4—21no—
263#499—42no—
264#490—42no—
265#490—42no—
266#489—42no—
267#485—42no—
268#482—42no—
269#478—42no—
270#476—42no—
271#463—42no—
272#463—42no—
273#459—42no—
274#459—42no—
275#450—42no—
276#447—42no—
277#447—42no—
278#447—42no—
279#442—42no—
280#442—42no—
281#442—42no—
282#440—42no—
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×#106C2311yescharacteristic
292C2×#106C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296C2×C4⋊C8C2311yescharacteristic
297C2×C4⋊C8C2311yescharacteristic
298C2×C4⋊C8C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×#97C2311yescharacteristic
337C2×#97C2311yescharacteristic
338C2×#97C2311yescharacteristic
339C2×#97C2311yescharacteristic
340C2×C4×C8C2311yescharacteristic
341#400—21no—
342#400D411yescharacteristic
343#399—21no—
344#399—21no—
345#399—21no—
346#399—21no—
347#399—21no—
348#399—21no—
349#399—21no—
350#399—21no—
351#399D411yescharacteristic
352#398—21no—
353#398—21no—
354#398—21no—
355#398D411yescharacteristic
356#398D411yescharacteristic
357#397—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#396—21no—
362#396—21no—
363#396—21no—
364#396—21no—
365#396—21no—
366#396—21no—
367#396—21no—
368#396—21no—
369#396—21no—
370#396—21no—
371#396—21no—
372#396—21no—
373#396—21no—
374#396—21no—
375#396—21no—
376#396D411yescharacteristic
377#396D411yescharacteristic
378#395D411yescharacteristic
379#394—21no—
380#394—21no—
381#394—21no—
382#394—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#394—21no—
387#394—21no—
388#394—21no—
389#393—21no—
390#393—21no—
391#393—21no—
392#393D411yescharacteristic
393#392—21no—
394#392—21no—
395#392—21no—
396#392—21no—
397#391—21no—
398#391C2311yescharacteristic
399#391C2311yescharacteristic
400#390—21no—
401#390—21no—
402#390—21no—
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#390C2311yescharacteristic
412#390C2311yescharacteristic
413#390C2311yescharacteristic
414#390C2311yescharacteristic
415#389—21no—
416#389—21no—
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#388—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#384C2311yescharacteristic
456#382C2311yescharacteristic
457#380—21no—
458#380—21no—
459#380—21no—
460#380—21no—
461#380—21no—
462#380—21no—
463#380—21no—
464#380—21no—
465#380C2311yescharacteristic
466#380C2311yescharacteristic
467#379—21no—
468#379—21no—
469#379—21no—
470#379—21no—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2311yescharacteristic
474C4×C22⋊C4C2311yescharacteristic
475C4×C22⋊C4C2311yescharacteristic
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
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C22×Q8—21no—
504C22×Q8C2×D411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—22no—
507C22×D4—22no—
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—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C2411yescharacteristic
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—22no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—41no—
553C2×D8—41no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571#127—22no—
572#127—22no—
573#127—41no—
574#127—41no—
575#127—41no—
576#127—41no—
577#125—22no—
578#125—41no—
579#125—41no—
580#125—41no—
581#125—41no—
582#125—41no—
583#124—22no—
584#124—41no—
585#124—41no—
586#124—41no—
587#124—41no—
588#124—41no—
589#124—44no—
590#123—44no—
591#123—44no—
592#123—44no—
593#123—44no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—82no—
597C22⋊Q8—82no—
598C22⋊Q8—82no—
599C22⋊Q8—82no—
600C22⋊Q8—82no—
601#121—22no—
602#121—22no—
603#121—44no—
604#121—41no—
605#121—41no—
606#121—44no—
607#121—41no—
608#121—41no—
609#121—82no—
610#121—82no—
611#121—82no—
612#121—82no—
613C4×Q8—22no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—41no—
635C4×D4—44no—
636#117—41no—
637#117—41no—
638#117—41no—
639#117—41no—
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—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—82no—
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—82no—
734C2×C22⋊C4—82no—
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C42—21no—
742C2×C42—21no—
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749#107—22no—
750#107—22no—
751#107—41no—
752#107—41no—
753#106—22no—
754#106—22no—
755#106—41no—
756#106—41no—
757#106—41no—
758#106—41no—
759#106—41no—
760#106—41no—
761C4⋊C8—22no—
762C4⋊C8—22no—
763C4⋊C8—41no—
764C4⋊C8—41no—
765#103—22no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#102—22no—
772#102—22no—
773#102—22no—
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—
797C22⋊C8—22no—
798C22⋊C8—22no—
799C22⋊C8—41no—
800C22⋊C8—41no—
801#97—22no—
802#97—22no—
803#97—41no—
804#97—41no—
805#97—41no—
806C4×C8—41no—
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#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835C24—24no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—81no—
842C24—81no—
843C24—81no—
844C24—81no—
845C24—81no—
846C24—81no—
847C24C22×D411yescharacteristic
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—41no—
855C2×Q8—41no—
856C2×Q8—41no—
857C2×Q8—42no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×D4—24no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
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—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—82no—
911C2×D4—82no—
912C2×D4—82no—
913C2×D4—82no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4H(5,𝔽2)12yes—
922C2×D42−1+412yes—
923C2×D42−1+412yes—
924C22×C4—21no—
925C22×C4—24no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×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×C4C22×D411yescharacteristic
981C22×C4C2511yescharacteristic
982SD16—44no—
983SD16—82no—
984D8—44no—
985D8—44no—
986D8—44no—
987D8—82no—
988D8—82no—
989D8—82no—
990C2×C8—21no—
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×C8H(5,𝔽2)12yes—
1013C2×C8H(5,𝔽2)12yes—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—41no—
1036C4⋊C4—41no—
1037C4⋊C4—41no—
1038C4⋊C4—41no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—41no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
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⋊C4—81no—
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⋊C4H(5,𝔽2)12yes—
1070C22⋊C4—24no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
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—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—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—42no—
1135C42—81no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—22no—
1141C23—21no—
1142C23—21no—
1143C23—22no—
1144C23—22no—
1145C23—21no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—84no—
1179C23—84no—
1180C23—84no—
1181C23—162no—
1182C23—162no—
1183C23—162no—
1184C23—162no—
1185C23C23×D411yescharacteristic
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—82no—
1191Q8—162no—
1192D4—22no—
1193D4—22no—
1194D4—22no—
1195D4—22no—
1196D4—22no—
1197D4—22no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—84no—
1213D4—84no—
1214D4—162no—
1215D4—162no—
1216D4—162no—
1217D4—162no—
1218D4—162no—
1219D4—162no—
1220D4—162no—
1221D4—162no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—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—22no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—84no—
1299C2×C4—162no—
1300C2×C4—162no—
1301C2×C4—162no—
1302C2×C4—162no—
1303C2×C4—162no—
1304C2×C4—162no—
1305C2×C4—162no—
1306C2×C4—162no—
1307C2×C4C2×H(5,𝔽2)11yescharacteristic
1308C2×C4C2×H(5,𝔽2)11yescharacteristic
1309C2×C4C2×H(5,𝔽2)11yescharacteristic
1310C2×C4C2×H(5,𝔽2)11yescharacteristic
1311C2×C4C2×2−1+411yescharacteristic
1312C2×C4C2×2−1+411yescharacteristic
1313C8—22no—
1314C8—22no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C8—41no—
1321C22—41no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22—41no—
1326C22—41no—
1327C22—42no—
1328C22—42no—
1329C22—42no—
1330C22—42no—
1331C22—42no—
1332C22—41no—
1333C22—42no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
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—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—168no—
1364C22#348411yescharacteristic
1365C22#348611yescharacteristic
1366C22#349811yescharacteristic
1367C22#358511yescharacteristic
1368C22#358511yescharacteristic
1369C22#358511yescharacteristic
1370C22#358511yescharacteristic
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—42no—
1381C4—41no—
1382C4—41no—
1383C4—41no—
1384C4—41no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4#353611yescharacteristic
1396C4#353611yescharacteristic
1397C4#353611yescharacteristic
1398C4#353611yescharacteristic
1399C2—81no—
1400C2—82no—
1401C2—82no—
1402C2—82no—
1403C2—161no—
1404C2—161no—
1405C2#4635611yescharacteristic
1406C2#6165311yescharacteristic
1407C2#6166911yescharacteristic
1408C2#6187211yescharacteristic
1409C2#6187211yescharacteristic
1410C2#6244111yescharacteristic
1411C2#6244111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42486C2semidirect
2. #42444C2semidirect
3. #32785C2semidirect
4. #32666C2semidirect
5. #32659C2semidirect
6. #31538C2semidirect
7. #31537C2semidirect
8. #31147C2semidirect
9. #31135C2semidirect
10. #30898C2semidirect
11. #30891C2semidirect
12. #30891C2semidirect
13. #30890C2semidirect
14. #30658C2semidirect
15. #30646C2semidirect
16. #28430C2semidirect
17. #28421C2semidirect
18. #28321C2semidirect
19. #26494C2semidirect
20. #26492C2semidirect
21. #26392C2semidirect
22. #26390C2semidirect
23. #25682C2semidirect
24. #25172C2semidirect
25. #25168C2semidirect
26. #25168C2semidirect
27. #25164C2semidirect
28. #24204C2semidirect
29. #24198C2semidirect
30. #23939C2semidirect
31. #22326C2semidirect
32. C2×#559C22semidirect
34. C2×#499C22semidirect
35. C2×#490C22semidirect
36. C2×#490C22semidirect
37. C2×#489C22semidirect
40. C2×#478C22semidirect
41. C2×#476C22semidirect
72. #2544C22semidirect
73. #2544C22semidirect
75. #2541C22semidirect
77. #2538C22semidirect
81. #2454C22semidirect
82. #2453C22semidirect
93. D4×C4⋊C4C22semidirect
97. #2096C22semidirect
99. #2094C22semidirect
100. #2094C22semidirect
102. #2092C22semidirect
103. #2085C22semidirect
104. #2084C22semidirect
105. #2084C22semidirect
106. #2084C22semidirect
108. #2067C22semidirect
109. #2067C22semidirect
110. #2066C22semidirect
114. #2065C22semidirect
115. #2059C22semidirect
116. #2058C22semidirect
117. #2042C22semidirect
118. #2042C22semidirect
119. #2042C22semidirect
120. #2042C22semidirect
121. #2041C22semidirect
122. #2041C22semidirect
131. #2026C22semidirect
132. #2026C22semidirect
135. #2025C22semidirect
136. #2023C22semidirect
145. #1992C22semidirect
146. #1985C22semidirect
147. #1985C22semidirect
156. #1961C22semidirect
157. #1959C22semidirect
158. #1957C22semidirect
159. #1944C22semidirect
160. #1944C22semidirect
161. #1943C22semidirect
162. #1943C22semidirect
167. #1917C22semidirect
168. #1917C22semidirect
169. #1917C22semidirect
170. #1917C22semidirect
185. #1865C22semidirect
189. #1864C22semidirect
190. #1864C22semidirect
191. #1864C22semidirect
193. #1862C22semidirect
194. #1862C22semidirect
195. #1862C22semidirect
196. #1862C22semidirect
198. #1805C22semidirect
199. #1802C22semidirect
200. #1771C22semidirect
201. #1771C22semidirect

Maximal subgroups

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

subgroupindex
#424862
#424442
#327852
#326662
#326592
#315382
#315372
#311472
#311352
#308982
#308912
#308902
#306582
#306462
#284302
#284212
#283212
#264942
#264922
#263922
#263902
#256822
#251722
#251682
#251642
#242042
#241982
#239392
#223262