Finite Group Databasebeta

← #7560884

Subgroups — #7560884

Order 512.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3296C211yesmaximal, characteristic
2C2×#3181C211yesmaximal, characteristic, complemented
3#59116C211yesmaximal, characteristic, complemented
4#59103C211yesmaximal, characteristic
5#30963C211yesmaximal, characteristic, complemented
6#30801C211yesmaximal, characteristic, complemented
7#30754C211yesmaximal, characteristic, complemented
8#30464C211yesmaximal, characteristic, complemented
9#28934C211yesmaximal, characteristic, complemented
10#28554C211yesmaximal, characteristic, complemented
11#28350C211yesmaximal, characteristic, complemented
12#27784C211yesmaximal, characteristic, complemented
13#27262C211yesmaximal, characteristic, complemented
14#26981C211yesmaximal, characteristic, complemented
15#26909C211yesmaximal, characteristic, complemented
16#26833C211yesmaximal, characteristic, complemented
17#26829C211yesmaximal, characteristic, complemented
18#26636C211yesmaximal, characteristic, complemented
19#26177C211yesmaximal, characteristic, complemented
20#25546C211yesmaximal, characteristic, complemented
21#25211C211yesmaximal, characteristic, complemented
22#25089C211yesmaximal, characteristic, complemented
23#24917C211yesmaximal, characteristic, complemented
24#24436C211yesmaximal, characteristic
25#24068C211yesmaximal, characteristic, complemented
26#23935C211yesmaximal, characteristic, complemented
27#23135C211yesmaximal, characteristic, complemented
28#23013C211yesmaximal, characteristic, complemented
29#22854C211yesmaximal, characteristic, complemented
30#21561C211yesmaximal, characteristic, complemented
31#21086C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#533C2211yescharacteristic, complemented
35C2×#529C2211yescharacteristic
36#3296—28no—
37#3181—28no—
38C2×#501C2211yescharacteristic, complemented
39C2×#497C2211yescharacteristic
40C2×#491C2211yescharacteristic, complemented
41C2×#489C2211yescharacteristic
42C2×#488C2211yescharacteristic
43C2×#485C2211yescharacteristic, complemented
44C2×#482C2211yescharacteristic
45C2×#483C2211yescharacteristic
46C2×#478C2211yescharacteristic
47C2×#467C2211yescharacteristic
48C2×#467C2211yescharacteristic, complemented
49C2×#467C2211yescharacteristic, complemented
50C2×#465C2211yescharacteristic
51C2×#465C2211yescharacteristic
52C2×#464C2211yescharacteristic
53C2×#464C2211yescharacteristic
54C2×#452C2211yescharacteristic
55C2×#452C2211yescharacteristic
56C2×#450C2211yescharacteristic
57C2×#450C2211yescharacteristic
58C2×#441C2211yescharacteristic, complemented
59C2×#441C2211yescharacteristic, complemented
60C2×#440C2211yescharacteristic
61C2×#440C2211yescharacteristic
62C2×C4×SD16C2211yescharacteristic
63C2×C8×D4C2211yescharacteristic
64C2×#416C2211yescharacteristic
65C2×#416C2211yescharacteristic
66C22×#102C2211yescharacteristic
67C22×#97C2211yescharacteristic, complemented
68#2708—21no—
69#2697—21no—
70#2689—21no—
71#2680—21no—
72#2553—21no—
73#2550C2211yescharacteristic, complemented
74#2547C2211yescharacteristic
75#2506—21no—
76#2499C2211yescharacteristic, complemented
77#2489C2211yescharacteristic
78#2480—21no—
79#2478—21no—
80#2475—21no—
81#2470—21no—
82#2470—21no—
83#2462—21no—
84#2454C2211yescharacteristic
85#2453C2211yescharacteristic, complemented
86#2447C2211yescharacteristic
87#2446C2211yescharacteristic, complemented
88#2440C2211yescharacteristic
89#2435C2211yescharacteristic
90#2432C2211yescharacteristic
91#2429C2211yescharacteristic
92#2429C2211yescharacteristic
93#2421C2211yescharacteristic
94#2420—21no—
95#2418—21no—
96#2415C2211yescharacteristic
97#2415C2211yescharacteristic
98#2367C2211yescharacteristic
99#2363C2211yescharacteristic
100#2362—21no—
101#2362C2211yescharacteristic, complemented
102#2360C2211yescharacteristic
103Q8×C4⋊C4C2211yescharacteristic, complemented
104#2342—21no—
105D4×C22⋊C4C2211yescharacteristic
106C4×#123C2211yescharacteristic
107#2297C2211yescharacteristic
108#2296C2211yescharacteristic, complemented
109#2095C2211yescharacteristic, complemented
110#2092C2211yescharacteristic
111#2086C2211yescharacteristic, complemented
112#2085C2211yescharacteristic, complemented
113#2075C2211yescharacteristic
114#2071C2211yescharacteristic
115#2068C2211yescharacteristic, complemented
116#2066C2211yescharacteristic, complemented
117#2059C2211yescharacteristic, complemented
118#2059C2211yescharacteristic, complemented
119#2059C2211yescharacteristic, complemented
120#2056C2211yescharacteristic, complemented
121#2055C2211yescharacteristic
122#2055C2211yescharacteristic
123#2042C2211yescharacteristic
124#2042C2211yescharacteristic
125#2042C2211yescharacteristic
126#2042C2211yescharacteristic
127#2035C2211yescharacteristic
128#2035C2211yescharacteristic
129#2026C2211yescharacteristic, complemented
130#2024C2211yescharacteristic, complemented
131#2023C2211yescharacteristic
132#2016C2211yescharacteristic, complemented
133#2016C2211yescharacteristic, complemented
134#2016C2211yescharacteristic, complemented
135#2015C2211yescharacteristic
136#2015C2211yescharacteristic
137#2013C2211yescharacteristic
138#2001C2211yescharacteristic
139#2001C2211yescharacteristic
140#2001C2211yescharacteristic
141#1981C2211yescharacteristic, complemented
142#1973C2211yescharacteristic
143#1971C2211yescharacteristic, complemented
144#1960C2211yescharacteristic, complemented
145#1959C2211yescharacteristic
146#1948C2211yescharacteristic, complemented
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic
152#1935C2211yescharacteristic, complemented
153#1935C2211yescharacteristic, complemented
154#1935C2211yescharacteristic, complemented
155#1935C2211yescharacteristic, complemented
156#1935C2211yescharacteristic, complemented
157#1933C2211yescharacteristic, complemented
158#1933C2211yescharacteristic, complemented
159#1928C2211yescharacteristic, complemented
160#1925C2211yescharacteristic
161#1924C2211yescharacteristic
162#1924C2211yescharacteristic
163#1920C2211yescharacteristic, complemented
164#1919C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1892C2211yescharacteristic
168#1892C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1875C2211yescharacteristic
180#1873C2211yescharacteristic, complemented
181#1873C2211yescharacteristic, complemented
182#1873C2211yescharacteristic, complemented
183#1872C2211yescharacteristic
184#1869C2211yescharacteristic
185#1865C2211yescharacteristic, complemented
186#1864C2211yescharacteristic
187#1864C2211yescharacteristic
188#1863C2211yescharacteristic, complemented
189#1863C2211yescharacteristic, complemented
190#1862C2211yescharacteristic
191#1852C2211yescharacteristic
192#1850C2211yescharacteristic, complemented
193#1817C2211yescharacteristic, complemented
194#1804C2211yescharacteristic
195#1786C2211yescharacteristic
196#1771C2211yescharacteristic, complemented
197#1771C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200#1752C2211yescharacteristic
201#1752C2211yescharacteristic
202#1752C2211yescharacteristic, complemented
203#1735C2211yescharacteristic, complemented
204#1735C2211yescharacteristic, complemented
205C22×#41C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C23×C8C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218#552—24no—
219#552—42no—
220#546—24no—
221#546—42no—
222#533—24no—
223#533—42no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227#529—24no—
228#529—42no—
229C2×#126—21no—
230C2×#126—21no—
231C2×#125—21no—
232C2×#125—21no—
233C2×#125C2311yescharacteristic
234C2×#125C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#124C2311yescharacteristic
237C2×#124C2311yescharacteristic
238C2×#123—21no—
239C2×#123—21no—
240C2×#123—21no—
241C2×#123D411yescharacteristic
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2311yescharacteristic
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2311yescharacteristic
249C2×C22⋊Q8C2311yescharacteristic
250C2×C22⋊Q8C2311yescharacteristic
251C2×#121—21no—
252C2×#121C2311yescharacteristic
253C2×#120—21no—
254C2×C4×Q8—21no—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×D4—21no—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×#117—21no—
266C2×#117—21no—
267C2×#117—21no—
268C2×#117C2311yescharacteristic
269C2×#117C2311yescharacteristic
270C2×#117C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C22⋊C4—21no—
273C22×C22⋊C4—21no—
274C22×C42C2311yescharacteristic
275#501—24no—
276#497—24no—
277#491—24no—
278#489—24no—
279#488—24no—
280#485—42no—
281#483—24no—
282#482—24no—
283#478—24no—
284#467—24no—
285#467—24no—
286#467—24no—
287#465—24no—
288#465D418yes—
289#464—24no—
290#464—24no—
291#452—24no—
292#452—42no—
293#450—24no—
294#450—24no—
295#441—24no—
296#441—24no—
297#440—24no—
298#440—24no—
299C4×SD16—24no—
300C8×D4—24no—
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312#416—24no—
313#416—24no—
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#102—24no—
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×C22⋊C8C2311yescharacteristic
348C2×C22⋊C8C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×C22⋊C8C2311yescharacteristic
352C2×#97—24no—
353C2×#97C2311yescharacteristic
354C2×#97C2311yescharacteristic
355C2×#97C2311yescharacteristic
356C2×#97C2311yescharacteristic
357C2×#97C2311yescharacteristic
358C2×#97C2311yescharacteristic
359C2×C4×C8C2311yescharacteristic
360#400—21no—
361#400—21no—
362#400—21no—
363#400—21no—
364#399—21no—
365#398—21no—
366#398—21no—
367#398—21no—
368#398—21no—
369#398—21no—
370#398—21no—
371#397—21no—
372#397—21no—
373#397—21no—
374#397—21no—
375#397—21no—
376#397—21no—
377#397—21no—
378#397—21no—
379#397—21no—
380#397—21no—
381#396—21no—
382#396—21no—
383#396—21no—
384#395—21no—
385#395—21no—
386#394—21no—
387#394—21no—
388#394—21no—
389#394—21no—
390#394—21no—
391#394—21no—
392#391—21no—
393#391C2311yescharacteristic
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#390—21no—
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#389—21no—
407#389—21no—
408#389—21no—
409#389—21no—
410#389—21no—
411#389—21no—
412#389—21no—
413#389—21no—
414#389—21no—
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388D411yescharacteristic
435#388D411yescharacteristic
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387D411yescharacteristic
445#387D411yescharacteristic
446#386—21no—
447#386—21no—
448#386—21no—
449#386—21no—
450#386—21no—
451#386D411yescharacteristic
452#385—21no—
453#385—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#385—21no—
459#385—21no—
460#385—21no—
461#385D411yescharacteristic
462#384—21no—
463#384C2311yescharacteristic
464#382—21no—
465#382C2311yescharacteristic
466#381—21no—
467#381D411yescharacteristic
468#380—21no—
469#380—21no—
470#380—21no—
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473#379—21no—
474#379—21no—
475#379—21no—
476C4×C4⋊C4—21no—
477C4×C4⋊C4—21no—
478C4×C4⋊C4—21no—
479C4×C4⋊C4—21no—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C22⋊C4—21no—
485C4×C22⋊C4—21no—
486C4×C22⋊C4—21no—
487C4×C22⋊C4—21no—
488C4×C22⋊C4—21no—
489C4×C22⋊C4C2311yescharacteristic
490C4×C22⋊C4C2311yescharacteristic
491C4×C22⋊C4C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518C25—21no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C22×Q8—21no—
526C22×Q8C2411yescharacteristic
527C22×Q8C2411yescharacteristic
528C22×Q8C2411yescharacteristic
529C22×Q8C2411yescharacteristic
530C22×D4—21no—
531C22×D4—22no—
532C22×D4—22no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—41no—
536C22×D4—41no—
537C22×D4—41no—
538C22×D4—41no—
539C22×D4C2×D411yescharacteristic
540C22×D4C2411yescharacteristic
541C22×D4C2411yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4C2×D411yescharacteristic
548C23×C4C2×D411yescharacteristic
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C2×Q16—22no—
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—22no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×Q16—41no—
561C2×Q16—41no—
562C2×Q16—41no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16C2×D414yes—
575C22×C8—22no—
576C22×C8—22no—
577C22×C8—22no—
578C22×C8—41no—
579C22×C8—41no—
580C22×C8—41no—
581C22×C8—41no—
582C22×C8—41no—
583C22×C8C2×D414yes—
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C4⋊Q8—22no—
593C4⋊Q8—22no—
594C4⋊Q8—41no—
595C4⋊Q8—41no—
596C4⋊Q8—41no—
597C4⋊Q8—41no—
598#126—44no—
599#126—44no—
600#125—22no—
601#125—22no—
602#125—41no—
603#125—41no—
604#125—44no—
605#125—44no—
606#124—22no—
607#124—22no—
608#124—22no—
609#124—41no—
610#124—41no—
611#124—41no—
612#123—42no—
613#123—44no—
614#123—44no—
615#123—44no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—22no—
619C22⋊Q8—22no—
620C22⋊Q8—22no—
621C22⋊Q8—22no—
622C22⋊Q8—22no—
623C22⋊Q8—22no—
624C22⋊Q8—44no—
625C22⋊Q8—44no—
626C22⋊Q8—41no—
627C22⋊Q8—41no—
628C22⋊Q8—41no—
629C22⋊Q8—41no—
630C22⋊Q8—41no—
631C22⋊Q8C2×D414yes—
632#121—22no—
633#121—44no—
634#121C2×D414yes—
635#120—44no—
636C4×Q8—22no—
637C4×Q8—22no—
638C4×Q8—22no—
639C4×Q8—22no—
640C4×Q8—22no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×Q8—41no—
644C4×Q8—41no—
645C4×Q8—41no—
646C4×Q8—44no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—41no—
654C4×D4—41no—
655C4×D4—44no—
656#117—22no—
657#117—22no—
658#117—22no—
659#117—44no—
660#117—44no—
661#117—44no—
662#117—41no—
663#117—41no—
664#117—41no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—41no—
699C2×C4⋊C4C2×D411yescharacteristic
700C2×C4⋊C4C2×D411yescharacteristic
701C2×C4⋊C4C2×D411yescharacteristic
702C2×C4⋊C4C2×D411yescharacteristic
703C2×C4⋊C4C2×D411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
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—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—44no—
745C2×C22⋊C4—44no—
746C2×C22⋊C4C2×D411yescharacteristic
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C22⋊C4C2×D411yescharacteristic
749C2×C22⋊C4C2×D411yescharacteristic
750C2×C22⋊C4C2×D411yescharacteristic
751C2×C22⋊C4C2×D411yescharacteristic
752C2×C22⋊C4C2×D411yescharacteristic
753C2×C22⋊C4C2×D411yescharacteristic
754C2×C42—22no—
755C2×C42—22no—
756C2×C42—21no—
757C2×C42—21no—
758C2×C42—21no—
759C2×C42—21no—
760C2×C42—21no—
761C2×C42—21no—
762C2×C42—21no—
763C2×C42—21no—
764C2×C42—21no—
765C2×C42—21no—
766C2×C42C2×D411yescharacteristic
767C2×C42C2×D411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770C2×C42C2411yescharacteristic
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773#107—22no—
774#107—22no—
775#107—22no—
776#107—41no—
777#106—22no—
778#106—22no—
779#106—41no—
780#106C2×D414yes—
781C4⋊C8—22no—
782C4⋊C8—22no—
783C4⋊C8—41no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—22no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—41no—
796#103—41no—
797#103—41no—
798#103—41no—
799#103—41no—
800#103—41no—
801#103—41no—
802#103—41no—
803#103C2×D414yes—
804#102—22no—
805#102—22no—
806#102—22no—
807#102—22no—
808#102—22no—
809#102—22no—
810#102—22no—
811#102—22no—
812#102—41no—
813#102—41no—
814#102C2×D414yes—
815#102#4114yes—
816C22⋊C8—22no—
817C22⋊C8—22no—
818C22⋊C8—22no—
819C22⋊C8—22no—
820C22⋊C8—41no—
821#97—22no—
822#97—22no—
823#97—22no—
824#97—22no—
825#97—41no—
826#97—41no—
827C4×C8—22no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
853#95—21no—
854#95—21no—
855#95—21no—
856#95—21no—
857#95—21no—
858#95C2×D411yescharacteristic
859#95C2×D411yescharacteristic
860#95C2×D411yescharacteristic
861#95C2×D411yescharacteristic
862#95C2×D411yescharacteristic
863#95C2×D411yescharacteristic
864#95C2×D411yescharacteristic
865#95C2×D411yescharacteristic
866#95C2×D411yescharacteristic
867#95C2×D411yescharacteristic
868C24—21no—
869C24—21no—
870C24—42no—
871C24—42no—
872C24—42no—
873C24—81no—
874C24—81no—
875C24—81no—
876C24—81no—
877C24C22×D411yescharacteristic
878C24C22×D411yescharacteristic
879#41—44no—
880#41—44no—
881#41—82no—
882#41—82no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—21no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—21no—
903C2×Q8—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×Q8—42no—
907C2×Q8—42no—
908C2×Q8—81no—
909C2×Q8C22×D412yes—
910C2×D4—22no—
911C2×D4—22no—
912C2×D4—24no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—41no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—44no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—81no—
930C2×D4—82no—
931C2×D4—82no—
932C2×D4—82no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4C22×D412yes—
937C2×D4C2×#4112yes—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—22no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—22no—
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—21no—
963C22×C4—21no—
964C22×C4—41no—
965C22×C4—41no—
966C22×C4—41no—
967C22×C4—41no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D412yes—
996C22×C4H(5,𝔽2)12yes—
997C22×C4C2511yescharacteristic
998Q16—44no—
999Q16—44no—
1000Q16—82no—
1001Q16—82no—
1002SD16—44no—
1003SD16—44no—
1004SD16—44no—
1005SD16—82no—
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×C8—21no—
1026C2×C8—21no—
1027C2×C8—44no—
1028C2×C8—44no—
1029C2×C8—82no—
1030C2×C8C22×D412yes—
1031C2×C8C22×D412yes—
1032C2×C8C2×#4112yes—
1033C4⋊C4—24no—
1034C4⋊C4—22no—
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—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4C22×D412yes—
1088C4⋊C4C22×D412yes—
1089C4⋊C4C2×#4112yes—
1090C22⋊C4—24no—
1091C22⋊C4—22no—
1092C22⋊C4—22no—
1093C22⋊C4—22no—
1094C22⋊C4—24no—
1095C22⋊C4—22no—
1096C22⋊C4—41no—
1097C22⋊C4—41no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C42—22no—
1129C42—22no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—42no—
1141C42—42no—
1142C42—42no—
1143C42—42no—
1144C42—42no—
1145C42—42no—
1146C42—42no—
1147C42—81no—
1148C42—81no—
1149C42—81no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—22no—
1163C23—22no—
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—84no—
1177C23—84no—
1178C23—84no—
1179C23—162no—
1180C23—162no—
1181C23—162no—
1182C23—162no—
1183C23D4212yes—
1184C23#57512yes—
1185C23C23×D411yescharacteristic
1186Q8—22no—
1187Q8—22no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—41no—
1202Q8—84no—
1203D4—22no—
1204D4—22no—
1205D4—22no—
1206D4—22no—
1207D4—44no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—84no—
1213D4—84no—
1214D4—84no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—22no—
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—44no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—84no—
1302C2×C4—82no—
1303C2×C4—84no—
1304C2×C4—84no—
1305C2×C4—162no—
1306C2×C4—162no—
1307C2×C4D4212yes—
1308C2×C4C23×D411yescharacteristic
1309C2×C4C22×#4111yescharacteristic
1310C2×C4C2×H(5,𝔽2)11yescharacteristic
1311C2×C4#58511yescharacteristic
1312C2×C4#58511yescharacteristic
1313C2×C4#58511yescharacteristic
1314C8—22no—
1315C8—22no—
1316C8—22no—
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C8—41no—
1321C8—41no—
1322C22—22no—
1323C22—22no—
1324C22—22no—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—168no—
1351C22C2×D4211yescharacteristic
1352C22D4×#4111yescharacteristic
1353C22#350011yescharacteristic
1354C22C2×#57511yescharacteristic
1355C22#358411yescharacteristic
1356C22#358611yescharacteristic
1357C22#358611yescharacteristic
1358C4—22no—
1359C4—41no—
1360C4—41no—
1361C4—42no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—42no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—42no—
1371C4—41no—
1372C4—41no—
1373C4—42no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4D4×#4111yescharacteristic
1385C4#348511yescharacteristic
1386C4#349411yescharacteristic
1387C4#356011yescharacteristic
1388C2—42no—
1389C2—42no—
1390C2—82no—
1391C2—82no—
1392C2#5912211yescharacteristic
1393C2#6103011yescharacteristic
1394C2#6106011yescharacteristic
1395C2#6145511yescharacteristic
1396C2#6153211yescharacteristic
1397C2#6258511yescharacteristic
1398C2#6260011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3181C2semidirect
3. #59116C2semidirect
5. #30963C2semidirect
6. #30801C2semidirect
7. #30754C2semidirect
8. #30464C2semidirect
9. #28934C2semidirect
10. #28554C2semidirect
11. #28350C2semidirect
12. #27784C2semidirect
13. #27262C2semidirect
14. #26981C2semidirect
15. #26909C2semidirect
16. #26833C2semidirect
17. #26829C2semidirect
18. #26636C2semidirect
19. #26177C2semidirect
20. #25546C2semidirect
21. #25211C2semidirect
22. #25089C2semidirect
23. #24917C2semidirect
25. #24068C2semidirect
26. #23935C2semidirect
27. #23135C2semidirect
28. #23013C2semidirect
29. #22854C2semidirect
30. #21561C2semidirect
31. #21086C2semidirect
34. C2×#533C22semidirect
38. C2×#501C22semidirect
40. C2×#491C22semidirect
43. C2×#485C22semidirect
48. C2×#467C22semidirect
49. C2×#467C22semidirect
58. C2×#441C22semidirect
59. C2×#441C22semidirect
67. C22×#97C22semidirect
73. #2550C22semidirect
76. #2499C22semidirect
85. #2453C22semidirect
87. #2446C22semidirect
101. #2362C22semidirect
103. Q8×C4⋊C4C22semidirect
108. #2296C22semidirect
109. #2095C22semidirect
111. #2086C22semidirect
112. #2085C22semidirect
115. #2068C22semidirect
116. #2066C22semidirect
117. #2059C22semidirect
118. #2059C22semidirect
119. #2059C22semidirect
120. #2056C22semidirect
129. #2026C22semidirect
130. #2024C22semidirect
132. #2016C22semidirect
133. #2016C22semidirect
134. #2016C22semidirect
141. #1981C22semidirect
143. #1971C22semidirect
144. #1960C22semidirect
146. #1948C22semidirect
152. #1935C22semidirect
153. #1935C22semidirect
154. #1935C22semidirect
155. #1935C22semidirect
156. #1935C22semidirect
157. #1933C22semidirect
158. #1933C22semidirect
159. #1928C22semidirect
163. #1920C22semidirect
164. #1919C22semidirect
165. #1917C22semidirect
166. #1917C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
180. #1873C22semidirect
181. #1873C22semidirect
182. #1873C22semidirect
185. #1865C22semidirect
188. #1863C22semidirect
189. #1863C22semidirect
192. #1850C22semidirect
193. #1817C22semidirect
196. #1771C22semidirect
197. #1771C22semidirect
198. #1763C22semidirect
202. #1752C22semidirect
203. #1735C22semidirect
204. #1735C22semidirect

Maximal subgroups

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

subgroupindex
C2×#32962
C2×#31812
#591162
#591032
#309632
#308012
#307542
#304642
#289342
#285542
#283502
#277842
#272622
#269812
#269092
#268332
#268292
#266362
#261772
#255462
#252112
#250892
#249172
#244362
#240682
#239352
#231352
#230132
#228542
#215612
#210862