Finite Group Databasebeta

← #7087264

Subgroups — #7087264

Order 512.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45342C211yesmaximal, characteristic, complemented
2#42589C211yesmaximal, characteristic
3#32532C211yesmaximal, characteristic, complemented
4#32164C211yesmaximal, characteristic, complemented
5#32096C211yesmaximal, characteristic, complemented
6#32059C211yesmaximal, characteristic, complemented
7#30894C211yesmaximal, characteristic, complemented
8#30613C211yesmaximal, characteristic, complemented
9#30456C211yesmaximal, characteristic, complemented
10#30456C211yesmaximal, characteristic, complemented
11#29569C211yesmaximal, characteristic, complemented
12#28944C211yesmaximal, characteristic, complemented
13#28918C211yesmaximal, characteristic, complemented
14#28623C211yesmaximal, characteristic, complemented
15#28461C211yesmaximal, characteristic, complemented
16#28365C211yesmaximal, characteristic, complemented
17#27069C211yesmaximal, characteristic, complemented
18#26630C211yesmaximal, characteristic, complemented
19#26603C211yesmaximal, characteristic, complemented
20#26553C211yesmaximal, characteristic, complemented
21#26250C211yesmaximal, characteristic, complemented
22#26179C211yesmaximal, characteristic, complemented
23#25428C211yesmaximal, characteristic, complemented
24#25366C211yesmaximal, characteristic, complemented
25#25156C211yesmaximal, characteristic, complemented
26#25093C211yesmaximal, characteristic, complemented
27#23811C211yesmaximal, characteristic, complemented
28#23287C211yesmaximal, characteristic, complemented
29#22997C211yesmaximal, characteristic, complemented
30#22864C211yesmaximal, characteristic, complemented
31#22160C211yesmaximal, characteristic, complemented
32C2×#492C2211yescharacteristic
33C2×#492C2211yescharacteristic
34C2×#492C2211yescharacteristic, complemented
35C2×#491C2211yescharacteristic, complemented
36C2×#482C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#460C2211yescharacteristic
40C2×#460C2211yescharacteristic
41C2×#460C2211yescharacteristic
42C2×#461C2211yescharacteristic
43C2×#461C2211yescharacteristic, complemented
44C2×#450C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#450C2211yescharacteristic
47C2×#440C2211yescharacteristic
48C2×#440C2211yescharacteristic, complemented
49C2×C4×SD16C2211yescharacteristic
50C2×C4×SD16C2211yescharacteristic, complemented
51C2×C4×SD16C2211yescharacteristic, complemented
52C2×#418C2211yescharacteristic
53#2825—21no—
54#2793—21no—
55#2783—21no—
56#2776—21no—
57#2772—21no—
58#2703—21no—
59#2688—21no—
60#2678—21no—
61#2668—21no—
62#2641C2211yescharacteristic
63#2635—21no—
64#2617—21no—
65#2590—21no—
66#2585—21no—
67#2570—21no—
68#2546C2211yescharacteristic, complemented
69#2541C2211yescharacteristic
70#2541C2211yescharacteristic
71#2525—21no—
72#2513C2211yescharacteristic
73#2511C2211yescharacteristic, complemented
74#2508C2211yescharacteristic, complemented
75#2499C2211yescharacteristic
76#2490C2211yescharacteristic
77#2454C2211yescharacteristic
78#2446C2211yescharacteristic, complemented
79#2445C2211yescharacteristic
80#2433C2211yescharacteristic
81#2433C2211yescharacteristic
82#2429C2211yescharacteristic
83#2429C2211yescharacteristic
84#2429C2211yescharacteristic
85#2428C2211yescharacteristic
86#2424—21no—
87#2420C2211yescharacteristic
88#2401C2211yescharacteristic
89#2366C2211yescharacteristic
90#2365C2211yescharacteristic, complemented
91#2362C2211yescharacteristic
92#2362C2211yescharacteristic
93Q8×C4⋊C4C2211yescharacteristic, complemented
94D4×C22⋊C4C2211yescharacteristic
95#2328C2211yescharacteristic
96#2327C2211yescharacteristic, complemented
97#2320C2211yescharacteristic, complemented
98#2097C2211yescharacteristic, complemented
99#2097C2211yescharacteristic, complemented
100#2093C2211yescharacteristic
101#2092C2211yescharacteristic
102#2092C2211yescharacteristic, complemented
103#2087C2211yescharacteristic, complemented
104#2071C2211yescharacteristic, complemented
105#2068C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2065C2211yescharacteristic
108#2059C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic, complemented
113#2055C2211yescharacteristic, complemented
114#2055C2211yescharacteristic, complemented
115#2043C2211yescharacteristic, complemented
116#2043C2211yescharacteristic, complemented
117#2041C2211yescharacteristic
118#2041C2211yescharacteristic
119#2041C2211yescharacteristic
120#2041C2211yescharacteristic, complemented
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic
123#2026C2211yescharacteristic, complemented
124#2014C2211yescharacteristic
125#2014C2211yescharacteristic
126#2014C2211yescharacteristic
127#2014C2211yescharacteristic
128#2014C2211yescharacteristic
129#2014C2211yescharacteristic, complemented
130#2013C2211yescharacteristic
131#2013C2211yescharacteristic
132#2013C2211yescharacteristic
133#2013C2211yescharacteristic, complemented
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic
138#1991C2211yescharacteristic, complemented
139#1982C2211yescharacteristic
140#1982C2211yescharacteristic, complemented
141#1973C2211yescharacteristic
142#1973C2211yescharacteristic, complemented
143#1968C2211yescharacteristic
144#1968C2211yescharacteristic
145#1968C2211yescharacteristic
146#1968C2211yescharacteristic, complemented
147#1968C2211yescharacteristic, complemented
148#1961C2211yescharacteristic
149#1957C2211yescharacteristic
150#1949C2211yescharacteristic, complemented
151#1948C2211yescharacteristic, complemented
152#1942C2211yescharacteristic, complemented
153#1941C2211yescharacteristic, complemented
154#1939C2211yescharacteristic, complemented
155#1936C2211yescharacteristic
156#1936C2211yescharacteristic, complemented
157#1934C2211yescharacteristic
158#1934C2211yescharacteristic
159#1934C2211yescharacteristic, complemented
160#1928C2211yescharacteristic, complemented
161#1928C2211yescharacteristic, complemented
162#1926C2211yescharacteristic, complemented
163#1925C2211yescharacteristic
164#1925C2211yescharacteristic
165#1923C2211yescharacteristic
166#1923C2211yescharacteristic
167#1923C2211yescharacteristic
168#1920C2211yescharacteristic, complemented
169#1917C2211yescharacteristic, complemented
170#1917C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1894C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic
177#1880C2211yescharacteristic
178#1880C2211yescharacteristic, complemented
179#1880C2211yescharacteristic, complemented
180#1880C2211yescharacteristic, complemented
181#1880C2211yescharacteristic, complemented
182#1877C2211yescharacteristic
183#1877C2211yescharacteristic
184#1877C2211yescharacteristic, complemented
185#1875C2211yescharacteristic
186#1864C2211yescharacteristic
187#1864C2211yescharacteristic
188#1864C2211yescharacteristic, complemented
189#1863C2211yescharacteristic, complemented
190#1862C2211yescharacteristic, complemented
191#1862C2211yescharacteristic, complemented
192#1854C2211yescharacteristic
193#1851C2211yescharacteristic
194#1805C2211yescharacteristic, complemented
195C8×C4⋊C4C2211yescharacteristic, complemented
196C8×C4⋊C4C2211yescharacteristic, complemented
197#1768C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1746C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#127C2311yescharacteristic
225C2×#125C2311yescharacteristic
226C2×#123—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#120—21no—
238C2×#120—21no—
239C2×#120—21no—
240C2×#120—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4—21no—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C22×C22⋊C4—21no—
253#492—42no—
254#492—42no—
255#492—42no—
256#491—42no—
257#482—42no—
258#468—42no—
259#468—42no—
260#461—42no—
261#461—42no—
262#460—24no—
263#460—24no—
264#460—42no—
265#450—24no—
266#450—42no—
267#450—42no—
268#440—42no—
269#440—42no—
270C4×SD16—42no—
271C4×SD16—42no—
272C4×SD16—42no—
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286#418—42no—
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329#401D411yescharacteristic
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#400D411yescharacteristic
335#400D411yescharacteristic
336#400D411yescharacteristic
337#399—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397D411yescharacteristic
352#397D411yescharacteristic
353#397D411yescharacteristic
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396D411yescharacteristic
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#392—21no—
372#392—21no—
373#392—21no—
374#392—21no—
375#392—21no—
376#392—21no—
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#390—21no—
385#390—21no—
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#389—21no—
397#389—21no—
398#389—21no—
399#389—21no—
400#389—21no—
401#389—21no—
402#389—21no—
403#389—21no—
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
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#388—21no—
420#388—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
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#387—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#386—21no—
448#386—21no—
449#385—21no—
450#384—21no—
451#384C2311yescharacteristic
452#383—21no—
453#382—21no—
454#382—21no—
455#382C2311yescharacteristic
456#382C2311yescharacteristic
457#381—21no—
458#380—21no—
459#380C2311yescharacteristic
460#379—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4—21no—
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
474#376C2311yescharacteristic
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
499C25—21no—
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×D4—22no—
504C22×D4—21no—
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—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C2411yescharacteristic
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
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—41no—
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×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×M16—22no—
568C2×M16—41no—
569C2×M16—41no—
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C4⋊Q8—22no—
579C4⋊Q8—22no—
580C4⋊Q8—41no—
581C4⋊Q8—41no—
582C4⋊Q8—41no—
583C4⋊Q8—41no—
584#127—22no—
585#127—22no—
586#127—41no—
587#127—41no—
588#127—41no—
589#127—41no—
590#127—41no—
591#127—41no—
592#127—41no—
593#127—41no—
594#125—41no—
595#125—41no—
596#123—82no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603#121—41no—
604#121—41no—
605#121—41no—
606#121—41no—
607#121—82no—
608#121—82no—
609#121—82no—
610#121—82no—
611#121—82no—
612#120—82no—
613#120—82no—
614#120—82no—
615#120—82no—
616C4×Q8—22no—
617C4×Q8—22no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×Q8—41no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×Q8—41no—
625C4×Q8—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—82no—
635#117—41no—
636#117—41no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—82no—
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730#107—22no—
731#107—41no—
732#107—41no—
733#107—41no—
734#106—22no—
735#106—41no—
736#106—41no—
737#106—41no—
738C4⋊C8—22no—
739C4⋊C8—22no—
740C4⋊C8—22no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102#4114yes—
775C22⋊C8—22no—
776C22⋊C8—22no—
777C22⋊C8—41no—
778#97—22no—
779#97—41no—
780C4×C8—22no—
781C4×C8—22no—
782C4×C8—41no—
783C4×C8—41no—
784C4×C8—41no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—42no—
835C24—42no—
836C24—81no—
837C24—81no—
838C24—81no—
839C24—81no—
840C24—81no—
841C24C22×D411yescharacteristic
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8H(5,𝔽2)12yes—
860C2×D4—21no—
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—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—44no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—81no—
895C2×D4—81no—
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—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—82no—
920C2×D4—82no—
921C2×D4—82no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4C2×#4112yes—
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—21no—
943C22×C4—21no—
944C22×C4—21no—
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×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C2511yescharacteristic
971SD16—44no—
972SD16—44no—
973SD16—44no—
974SD16—44no—
975SD16—44no—
976SD16—82no—
977SD16—82no—
978SD16—82no—
979SD16—82no—
980SD16—82no—
981SD16—82no—
982SD16—82no—
983M16—82no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
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×C8C2×#4112yes—
1006C2×C8H(5,𝔽2)12yes—
1007C2×C8H(5,𝔽2)12yes—
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
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—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4C2×#4112yes—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—81no—
1110C42—81no—
1111C42—81no—
1112C42—81no—
1113C42—81no—
1114C42—81no—
1115C23—21no—
1116C23—21no—
1117C23—22no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—84no—
1151C23—84no—
1152C23—162no—
1153C23—162no—
1154C23—162no—
1155C23—162no—
1156C23—162no—
1157C23C23×D411yescharacteristic
1158Q8—22no—
1159Q8—22no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170D4—22no—
1171D4—22no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—84no—
1187D4—84no—
1188D4—162no—
1189D4—162no—
1190D4—162no—
1191D4—162no—
1192D4—162no—
1193D4—162no—
1194D4—162no—
1195D4—162no—
1196D4—162no—
1197D4—162no—
1198D4—162no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—22no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
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—162no—
1276C2×C4—162no—
1277C2×C4—162no—
1278C2×C4—162no—
1279C2×C4#57712yes—
1280C2×C4#57712yes—
1281C2×C4#57712yes—
1282C2×C4C22×#4111yescharacteristic
1283C2×C4C2×H(5,𝔽2)11yescharacteristic
1284C2×C4C2×H(5,𝔽2)11yescharacteristic
1285C2×C4C2×H(5,𝔽2)11yescharacteristic
1286C2×C4#58511yescharacteristic
1287C2×C4#58511yescharacteristic
1288C8—22no—
1289C8—22no—
1290C8—22no—
1291C8—41no—
1292C8—41no—
1293C8—41no—
1294C8—41no—
1295C8—41no—
1296C22—41no—
1297C22—42no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—42no—
1302C22—41no—
1303C22—41no—
1304C22—42no—
1305C22—41no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—168no—
1332C22D4×#4111yescharacteristic
1333C22#348811yescharacteristic
1334C22#349811yescharacteristic
1335C22C2×#57711yescharacteristic
1336C22C2×#57711yescharacteristic
1337C22C2×#57711yescharacteristic
1338C22#358511yescharacteristic
1339C4—22no—
1340C4—22no—
1341C4—22no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—42no—
1351C4—41no—
1352C4—42no—
1353C4—41no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4#350611yescharacteristic
1365C4#351911yescharacteristic
1366C4#353311yescharacteristic
1367C4#353411yescharacteristic
1368C2—81no—
1369C2—82no—
1370C2—161no—
1371C2—161no—
1372C2—161no—
1373C2#4418411yescharacteristic
1374C2#6148111yescharacteristic
1375C2#6155111yescharacteristic
1376C2#6203511yescharacteristic
1377C2#6205511yescharacteristic
1378C2#6243011yescharacteristic
1379C2#6246511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#42589C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2401 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45342C2semidirect
3. #32532C2semidirect
4. #32164C2semidirect
5. #32096C2semidirect
6. #32059C2semidirect
7. #30894C2semidirect
8. #30613C2semidirect
9. #30456C2semidirect
10. #30456C2semidirect
11. #29569C2semidirect
12. #28944C2semidirect
13. #28918C2semidirect
14. #28623C2semidirect
15. #28461C2semidirect
16. #28365C2semidirect
17. #27069C2semidirect
18. #26630C2semidirect
19. #26603C2semidirect
20. #26553C2semidirect
21. #26250C2semidirect
22. #26179C2semidirect
23. #25428C2semidirect
24. #25366C2semidirect
25. #25156C2semidirect
26. #25093C2semidirect
27. #23811C2semidirect
28. #23287C2semidirect
29. #22997C2semidirect
30. #22864C2semidirect
31. #22160C2semidirect
34. C2×#492C22semidirect
35. C2×#491C22semidirect
43. C2×#461C22semidirect
48. C2×#440C22semidirect
50. C2×C4×SD16C22semidirect
51. C2×C4×SD16C22semidirect
68. #2546C22semidirect
73. #2511C22semidirect
74. #2508C22semidirect
78. #2446C22semidirect
90. #2365C22semidirect
93. Q8×C4⋊C4C22semidirect
96. #2327C22semidirect
97. #2320C22semidirect
98. #2097C22semidirect
99. #2097C22semidirect
102. #2092C22semidirect
103. #2087C22semidirect
104. #2071C22semidirect
105. #2068C22semidirect
108. #2059C22semidirect
112. #2055C22semidirect
113. #2055C22semidirect
114. #2055C22semidirect
115. #2043C22semidirect
116. #2043C22semidirect
120. #2041C22semidirect
123. #2026C22semidirect
129. #2014C22semidirect
133. #2013C22semidirect
138. #1991C22semidirect
140. #1982C22semidirect
142. #1973C22semidirect
146. #1968C22semidirect
147. #1968C22semidirect
150. #1949C22semidirect
151. #1948C22semidirect
152. #1942C22semidirect
153. #1941C22semidirect
154. #1939C22semidirect
156. #1936C22semidirect
159. #1934C22semidirect
160. #1928C22semidirect
161. #1928C22semidirect
162. #1926C22semidirect
168. #1920C22semidirect
169. #1917C22semidirect
170. #1917C22semidirect
171. #1916C22semidirect
178. #1880C22semidirect
179. #1880C22semidirect
180. #1880C22semidirect
181. #1880C22semidirect
184. #1877C22semidirect
188. #1864C22semidirect
189. #1863C22semidirect
190. #1862C22semidirect
191. #1862C22semidirect
194. #1805C22semidirect
195. C8×C4⋊C4C22semidirect
196. C8×C4⋊C4C22semidirect
197. #1768C22semidirect
198. C4×#103C22semidirect
202. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#453422
#425892
#325322
#321642
#320962
#320592
#308942
#306132
#304562
#295692
#289442
#289182
#286232
#284612
#283652
#270692
#266302
#266032
#265532
#262502
#261792
#254282
#253662
#251562
#250932
#238112
#232872
#229972
#228642
#221602