Finite Group Databasebeta

← #6680197

Subgroups — #6680197

Order 512.

1744 conjugacy classes of subgroups.

The subgroup lattice has 1362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39604C211yesmaximal, characteristic, complemented
2#36529C211yesmaximal, characteristic
3#33009C211yesmaximal, characteristic, complemented
4#31878C211yesmaximal, characteristic, complemented
5#31838C211yesmaximal, characteristic, complemented
6#31810C211yesmaximal, characteristic, complemented
7#31534C211yesmaximal, characteristic, complemented
8#31510C211yesmaximal, characteristic, complemented
9#31474C211yesmaximal, characteristic, complemented
10#30629C211yesmaximal, characteristic, complemented
11#30612C211yesmaximal, characteristic, complemented
12#29906C211yesmaximal, characteristic, complemented
13#29775C211yesmaximal, characteristic, complemented
14#27254C211yesmaximal, characteristic, complemented
15#27109C211yesmaximal, characteristic, complemented
16#27081C211yesmaximal, characteristic, complemented
17#26771C211yesmaximal, characteristic, complemented
18#26671C211yesmaximal, characteristic, complemented
19#26526C211yesmaximal, characteristic, complemented
20#26427C211yesmaximal, characteristic, complemented
21#25994C211yesmaximal, characteristic, complemented
22#25535C211yesmaximal, characteristic, complemented
23#25322C211yesmaximal, characteristic, complemented
24#25223C211yesmaximal, characteristic, complemented
25#25128C211yesmaximal, characteristic, complemented
26#25080C211yesmaximal, characteristic, complemented
27#24861C211yesmaximal, characteristic, complemented
28#22922C211yesmaximal, characteristic, complemented
29#22493C211yesmaximal, characteristic, complemented
30#22067C211yesmaximal, characteristic, complemented
31C2×#1802C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#484C2211yescharacteristic
36C2×#480C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#460C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#435C2211yescharacteristic
42C22×C4⋊C8C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2855C2211yescharacteristic
46#2854C2211yescharacteristic
47#2847—21no—
48#2792—21no—
49#2791—21no—
50#2790—21no—
51#2720—21no—
52#2627—21no—
53#2567C2211yescharacteristic, complemented
54#2552C2211yescharacteristic, complemented
55#2539—21no—
56#2534—21no—
57#2511C2211yescharacteristic, complemented
58#2507C2211yescharacteristic, complemented
59#2502C2211yescharacteristic, complemented
60#2497C2211yescharacteristic, complemented
61#2473—21no—
62#2467—21no—
63#2467—21no—
64#2456—21no—
65#2456—21no—
66#2454C2211yescharacteristic
67#2454C2211yescharacteristic
68#2449—21no—
69#2440C2211yescharacteristic
70#2440C2211yescharacteristic, complemented
71#2433C2211yescharacteristic
72#2428C2211yescharacteristic
73#2428C2211yescharacteristic
74#2423C2211yescharacteristic, complemented
75#2417C2211yescharacteristic
76#2408C2211yescharacteristic
77#2366C2211yescharacteristic
78#2366C2211yescharacteristic
79#2363C2211yescharacteristic
80#2363C2211yescharacteristic
81#2360C2211yescharacteristic
82D4×C4⋊C4C2211yescharacteristic
83#2345C2211yescharacteristic
84#2322—21no—
85C4×#123C2211yescharacteristic
86C4×#120—21no—
87C2×#384C2211yescharacteristic
88#2100C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2093C2211yescharacteristic
92#2093C2211yescharacteristic, complemented
93#2093C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2087C2211yescharacteristic, complemented
97#2087C2211yescharacteristic, complemented
98#2083C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic, complemented
103#2071C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2068C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic, complemented
108#2067C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic, complemented
111#2057C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic, complemented
115#2055C2211yescharacteristic, complemented
116#2041C2211yescharacteristic
117#2041C2211yescharacteristic
118#2041C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic, complemented
123#2026C2211yescharacteristic, complemented
124#2023C2211yescharacteristic
125#2014C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic, complemented
128#1992C2211yescharacteristic, complemented
129#1989C2211yescharacteristic, complemented
130#1987C2211yescharacteristic, complemented
131#1982C2211yescharacteristic
132#1973C2211yescharacteristic
133#1957C2211yescharacteristic
134#1947C2211yescharacteristic, complemented
135#1942C2211yescharacteristic, complemented
136#1939C2211yescharacteristic, complemented
137#1939C2211yescharacteristic, complemented
138#1936C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1933C2211yescharacteristic, complemented
142#1928C2211yescharacteristic, complemented
143#1926C2211yescharacteristic
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic
146#1923C2211yescharacteristic, complemented
147#1923C2211yescharacteristic, complemented
148#1921C2211yescharacteristic, complemented
149#1921C2211yescharacteristic, complemented
150#1921C2211yescharacteristic, complemented
151#1921C2211yescharacteristic, complemented
152#1917C2211yescharacteristic, complemented
153#1917C2211yescharacteristic, complemented
154#1895C2211yescharacteristic
155#1895C2211yescharacteristic, complemented
156#1893C2211yescharacteristic
157#1892C2211yescharacteristic
158#1880C2211yescharacteristic
159#1877C2211yescharacteristic
160#1877C2211yescharacteristic
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic
163#1877C2211yescharacteristic, complemented
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic
166#1874C2211yescharacteristic
167#1874C2211yescharacteristic, complemented
168#1873C2211yescharacteristic, complemented
169#1869C2211yescharacteristic
170#1863C2211yescharacteristic, complemented
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic, complemented
176#1854C2211yescharacteristic, complemented
177#1852C2211yescharacteristic
178#1852C2211yescharacteristic
179#1851C2211yescharacteristic, complemented
180#1851C2211yescharacteristic, complemented
181#1850C2211yescharacteristic
182#1825C2211yescharacteristic, complemented
183#1824C2211yescharacteristic
184#1817C2211yescharacteristic
185#1808C2211yescharacteristic
186#1802C2211yescharacteristic
187#1802C2211yescharacteristic
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic
190#1802C2211yescharacteristic
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic, complemented
195#1786C2211yescharacteristic
196C4×#107C2211yescharacteristic, complemented
197#1762C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199C8×C22⋊C4C2211yescharacteristic
200#1736C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C24×C4—21no—
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#553—24no—
212#553—42no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#126—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#123—21no—
220C2×#123—21no—
221C2×#123D411yescharacteristic
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121—21no—
227C2×#121—21no—
228C2×#121—21no—
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#120—21no—
234C2×#120—21no—
235C2×#120—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4—24no—
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4—42no—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C22×C4⋊C4—21no—
253C22×C4⋊C4—21no—
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C22⋊C4—21no—
259C22×C42C2311yescharacteristic
260#486—42no—
261#484—24no—
262#480—42no—
263#468—42no—
264#465—42no—
265#460—42no—
266#450—42no—
267#435—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×C4⋊C8—42no—
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#102—42no—
291C2×#102—42no—
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321#400—21no—
322#400—21no—
323#400—21no—
324#399—21no—
325#399—21no—
326#399—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#395—21no—
342#395—21no—
343#395—21no—
344#395—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#392—21no—
349#392—21no—
350#392—21no—
351#392—21no—
352#392—21no—
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#390—21no—
358#390—21no—
359#390—21no—
360#390—21no—
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388D411yescharacteristic
390#388D411yescharacteristic
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387D411yescharacteristic
402#387D411yescharacteristic
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386D411yescharacteristic
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385D411yescharacteristic
425#384—21no—
426#384—21no—
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#381—21no—
434#381D411yescharacteristic
435#380—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#379—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8C2411yescharacteristic
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4C2×D411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—44no—
525C23×C4—82no—
526C23×C4—82no—
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16—41no—
543C22×C8—22no—
544C22×C8—22no—
545C22×C8—41no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8—41no—
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559#127—22no—
560#127—22no—
561#127—41no—
562#127—41no—
563#126—44no—
564#125—22no—
565#125—41no—
566#125—82no—
567#123—24no—
568#123—44no—
569#123—82no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—82no—
575C22⋊Q8—82no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—41no—
582#121—41no—
583#121—41no—
584#121—44no—
585#121—82no—
586#121—82no—
587#120—44no—
588#120—82no—
589#120—82no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—44no—
605C4×D4—44no—
606C4×D4—44no—
607C4×D4—82no—
608C4×D4—82no—
609C4×D4—82no—
610#117—22no—
611#117—41no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
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—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4—82no—
652C2×C4⋊C4—82no—
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4#4114yes—
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
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—44no—
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42C2×D411yescharacteristic
717C2×C42C2×D411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723#107—22no—
724#107—22no—
725#107—41no—
726#107—41no—
727#107—41no—
728#107—41no—
729#107—41no—
730#107—41no—
731#106—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739#103—22no—
740#103—22no—
741#103—41no—
742#103—41no—
743#103—41no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765C22⋊C8—22no—
766C22⋊C8—22no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770#97—41no—
771C4×C8—41no—
772C4×C8—41no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
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#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809C24—21no—
810C24—21no—
811C24—21no—
812C24—42no—
813C24—42no—
814C24—42no—
815C24—42no—
816C24—42no—
817C24—81no—
818C24—81no—
819C24C22×D411yescharacteristic
820C24C22×D411yescharacteristic
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—81no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×D4—28no—
831C2×D4—22no—
832C2×D4—22no—
833C2×D4—22no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—44no—
851C2×D4—44no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—44no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4H(5,𝔽2)12yes—
881C2×D42−1+412yes—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—24no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—816no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C2×#4112yes—
952C22×C4H(5,𝔽2)12yes—
953C22×C4C2511yescharacteristic
954SD16—82no—
955SD16—82no—
956SD16—82no—
957M16—82no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—82no—
983C2×C8—82no—
984C4⋊C4—24no—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4C2×#4112yes—
1044C4⋊C4C2×#4112yes—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—22no—
1049C22⋊C4—22no—
1050C22⋊C4—22no—
1051C22⋊C4—22no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
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#13714yes—
1081C42—22no—
1082C42—22no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—42no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—22no—
1105C23—21no—
1106C23—22no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—48no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—84no—
1133C23—84no—
1134C23—84no—
1135C23—84no—
1136C23—84no—
1137C23—84no—
1138C23#54612yes—
1139C23C2×#13712yes—
1140C23#57612yes—
1141C23C23×D411yescharacteristic
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—162no—
1147D4—22no—
1148D4—22no—
1149D4—22no—
1150D4—22no—
1151D4—48no—
1152D4—44no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—84no—
1162D4—84no—
1163D4—84no—
1164D4—162no—
1165D4—162no—
1166D4—162no—
1167D4—162no—
1168D4—162no—
1169C2×C4—28no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
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—44no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
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—84no—
1250C2×C4—84no—
1251C2×C4—84no—
1252C2×C4—84no—
1253C2×C4—84no—
1254C2×C4—162no—
1255C2×C4—162no—
1256C2×C4—162no—
1257C2×C4—162no—
1258C2×C4#54612yes—
1259C2×C4C2×#13712yes—
1260C2×C4C2×#13712yes—
1261C2×C4#57612yes—
1262C2×C4#57712yes—
1263C2×C4C22×#4111yescharacteristic
1264C2×C4C2×H(5,𝔽2)11yescharacteristic
1265C2×C4C2×H(5,𝔽2)11yescharacteristic
1266C2×C4C2×2−1+411yescharacteristic
1267C2×C4#58511yescharacteristic
1268C2×C4#58511yescharacteristic
1269C8—41no—
1270C8—41no—
1271C8—41no—
1272C8—41no—
1273C8—41no—
1274C8—41no—
1275C8—41no—
1276C8—41no—
1277C22—22no—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—42no—
1284C22—41no—
1285C22—41no—
1286C22—42no—
1287C22—42no—
1288C22—41no—
1289C22—42no—
1290C22—42no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—42no—
1296C22—816no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22#333314yes—
1313C22C2×#54611yescharacteristic
1314C22#348811yescharacteristic
1315C22#348911yescharacteristic
1316C22C22×#13711yescharacteristic
1317C22C2×#57611yescharacteristic
1318C22C2×#57611yescharacteristic
1319C22C2×#57711yescharacteristic
1320C4—22no—
1321C4—22no—
1322C4—22no—
1323C4—22no—
1324C4—22no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—42no—
1332C4—42no—
1333C4—41no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4#345511yescharacteristic
1346C4#349211yescharacteristic
1347C4#353411yescharacteristic
1348C4#353511yescharacteristic
1349C2—24no—
1350C2—81no—
1351C2—82no—
1352C2—82no—
1353C2—161no—
1354C2#3766611yescharacteristic
1355C2C2×#333311yescharacteristic
1356C2#6116711yescharacteristic
1357C2#6198011yescharacteristic
1358C2#6205111yescharacteristic
1359C2#6212711yescharacteristic
1360C2#6220011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36529C2
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
1. #39604C2semidirect
3. #33009C2semidirect
4. #31878C2semidirect
5. #31838C2semidirect
6. #31810C2semidirect
7. #31534C2semidirect
8. #31510C2semidirect
9. #31474C2semidirect
10. #30629C2semidirect
11. #30612C2semidirect
12. #29906C2semidirect
13. #29775C2semidirect
14. #27254C2semidirect
15. #27109C2semidirect
16. #27081C2semidirect
17. #26771C2semidirect
18. #26671C2semidirect
19. #26526C2semidirect
20. #26427C2semidirect
21. #25994C2semidirect
22. #25535C2semidirect
23. #25322C2semidirect
24. #25223C2semidirect
25. #25128C2semidirect
26. #25080C2semidirect
27. #24861C2semidirect
28. #22922C2semidirect
29. #22493C2semidirect
30. #22067C2semidirect
31. C2×#1802C2semidirect
53. #2567C22semidirect
54. #2552C22semidirect
57. #2511C22semidirect
58. #2507C22semidirect
59. #2502C22semidirect
60. #2497C22semidirect
70. #2440C22semidirect
74. #2423C22semidirect
88. #2100C22semidirect
89. #2099C22semidirect
90. #2099C22semidirect
92. #2093C22semidirect
93. #2093C22semidirect
94. #2088C22semidirect
95. #2088C22semidirect
96. #2087C22semidirect
97. #2087C22semidirect
98. #2083C22semidirect
99. #2083C22semidirect
102. #2071C22semidirect
103. #2071C22semidirect
104. #2068C22semidirect
105. #2068C22semidirect
107. #2067C22semidirect
108. #2067C22semidirect
110. #2059C22semidirect
111. #2057C22semidirect
114. #2055C22semidirect
115. #2055C22semidirect
122. #2033C22semidirect
123. #2026C22semidirect
127. #2000C22semidirect
128. #1992C22semidirect
129. #1989C22semidirect
130. #1987C22semidirect
134. #1947C22semidirect
135. #1942C22semidirect
136. #1939C22semidirect
137. #1939C22semidirect
141. #1933C22semidirect
142. #1928C22semidirect
146. #1923C22semidirect
147. #1923C22semidirect
148. #1921C22semidirect
149. #1921C22semidirect
150. #1921C22semidirect
151. #1921C22semidirect
152. #1917C22semidirect
153. #1917C22semidirect
155. #1895C22semidirect
163. #1877C22semidirect
167. #1874C22semidirect
168. #1873C22semidirect
170. #1863C22semidirect
175. #1862C22semidirect
176. #1854C22semidirect
179. #1851C22semidirect
180. #1851C22semidirect
182. #1825C22semidirect
194. #1802C22semidirect
196. C4×#107C22semidirect
197. #1762C22semidirect
198. C4×#103C22semidirect
200. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#396042
#365292
#330092
#318782
#318382
#318102
#315342
#315102
#314742
#306292
#306122
#299062
#297752
#272542
#271092
#270812
#267712
#266712
#265262
#264272
#259942
#255352
#253222
#252232
#251282
#250802
#248612
#229222
#224932
#220672
C2×#18022