Finite Group Databasebeta

← #6816719

Subgroups — #6816719

Order 512.

1718 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3389C211yesmaximal, characteristic, complemented
2C2×#3347C211yesmaximal, characteristic
3#42682C211yesmaximal, characteristic, complemented
4#42681C211yesmaximal, characteristic, complemented
5#33318C211yesmaximal, characteristic, complemented
6#31106C211yesmaximal, characteristic, complemented
7#31102C211yesmaximal, characteristic, complemented
8#31100C211yesmaximal, characteristic, complemented
9#31098C211yesmaximal, characteristic, complemented
10#31092C211yesmaximal, characteristic, complemented
11#31092C211yesmaximal, characteristic, complemented
12#31082C211yesmaximal, characteristic, complemented
13#31080C211yesmaximal, characteristic, complemented
14#29872C211yesmaximal, characteristic, complemented
15#29872C211yesmaximal, characteristic, complemented
16#28714C211yesmaximal, characteristic, complemented
17#28685C211yesmaximal, characteristic, complemented
18#26076C211yesmaximal, characteristic, complemented
19#26073C211yesmaximal, characteristic, complemented
20#26069C211yesmaximal, characteristic, complemented
21#26063C211yesmaximal, characteristic, complemented
22#25843C211yesmaximal, characteristic, complemented
23#25835C211yesmaximal, characteristic, complemented
24#25707C211yesmaximal, characteristic, complemented
25#25700C211yesmaximal, characteristic, complemented
26#25046C211yesmaximal, characteristic, complemented
27#25042C211yesmaximal, characteristic, complemented
28#25038C211yesmaximal, characteristic, complemented
29#25032C211yesmaximal, characteristic, complemented
30#21637C211yesmaximal, characteristic, complemented
31#21290C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#554C2211yescharacteristic
35C2×#553C2211yescharacteristic
36#3389—28no—
37#3347—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#501C2211yescharacteristic
41C2×#499C2211yescharacteristic
42C2×#499C2211yescharacteristic
43C2×#498C2211yescharacteristic
44C2×#482C2211yescharacteristic
45C2×#482C2211yescharacteristic
46C2×#482C2211yescharacteristic
47C2×#480C2211yescharacteristic
48C2×#478C2211yescharacteristic
49C2×#478C2211yescharacteristic
50C2×#478C2211yescharacteristic
51C2×#478C2211yescharacteristic
52C2×#478C2211yescharacteristic
53C2×#474C2211yescharacteristic
54C2×#474C2211yescharacteristic
55C2×#474C2211yescharacteristic
56C2×#469C2211yescharacteristic
57C2×#466C2211yescharacteristic
58C2×#446C2211yescharacteristic
59C2×#442C2211yescharacteristic
60C2×#442C2211yescharacteristic
61C2×C4×D8C2211yescharacteristic
62C2×#435C2211yescharacteristic
63C2×#428C2211yescharacteristic
64C2×#427C2211yescharacteristic
65#2816—21no—
66#2814—21no—
67#2700—21no—
68#2700—21no—
69#2689—21no—
70#2689—21no—
71#2674—21no—
72#2674—21no—
73#2672—21no—
74#2672—21no—
75#2660C2211yescharacteristic
76#2660C2211yescharacteristic
77#2638—21no—
78#2625—21no—
79#2623—21no—
80#2618—21no—
81#2584C2211yescharacteristic
82#2562C2211yescharacteristic
83#2547C2211yescharacteristic
84#2546C2211yescharacteristic
85#2486—21no—
86#2484—21no—
87#2442C2211yescharacteristic
88#2442C2211yescharacteristic
89#2441C2211yescharacteristic
90#2441C2211yescharacteristic
91#2441C2211yescharacteristic
92#2441C2211yescharacteristic
93#2439C2211yescharacteristic
94#2439C2211yescharacteristic
95#2422C2211yescharacteristic
96#2422C2211yescharacteristic
97#2422C2211yescharacteristic
98#2422C2211yescharacteristic
99#2420C2211yescharacteristic
100#2420C2211yescharacteristic
101#2420C2211yescharacteristic
102#2420C2211yescharacteristic
103#2398C2211yescharacteristic
104#2319C2211yescharacteristic
105#2319C2211yescharacteristic
106#2088C2211yescharacteristic
107#2088C2211yescharacteristic
108#2087C2211yescharacteristic
109#2086C2211yescharacteristic
110#2085C2211yescharacteristic
111#2085C2211yescharacteristic
112#2085C2211yescharacteristic
113#2085C2211yescharacteristic
114#2083C2211yescharacteristic
115#2083C2211yescharacteristic
116#2083C2211yescharacteristic
117#2083C2211yescharacteristic
118#2077C2211yescharacteristic
119#2077C2211yescharacteristic
120#2076C2211yescharacteristic
121#2075C2211yescharacteristic
122#2073C2211yescharacteristic
123#2073C2211yescharacteristic
124#2073C2211yescharacteristic
125#2073C2211yescharacteristic
126#2071C2211yescharacteristic
127#2071C2211yescharacteristic
128#2071C2211yescharacteristic
129#2071C2211yescharacteristic
130#2059C2211yescharacteristic
131#2059C2211yescharacteristic
132#2059C2211yescharacteristic
133#2059C2211yescharacteristic
134#2059C2211yescharacteristic
135#2059C2211yescharacteristic
136#2058C2211yescharacteristic
137#2057C2211yescharacteristic
138#2034C2211yescharacteristic
139#2034C2211yescharacteristic
140#2034C2211yescharacteristic
141#2034C2211yescharacteristic
142#2034C2211yescharacteristic
143#2034C2211yescharacteristic
144#2033C2211yescharacteristic
145#2033C2211yescharacteristic
146#1989C2211yescharacteristic
147#1989C2211yescharacteristic
148#1987C2211yescharacteristic
149#1987C2211yescharacteristic
150#1984C2211yescharacteristic
151#1972C2211yescharacteristic
152#1970C2211yescharacteristic
153#1954C2211yescharacteristic
154#1944C2211yescharacteristic
155#1944C2211yescharacteristic
156#1943C2211yescharacteristic
157#1942C2211yescharacteristic
158#1941C2211yescharacteristic
159#1941C2211yescharacteristic
160#1936C2211yescharacteristic
161#1936C2211yescharacteristic
162#1934C2211yescharacteristic
163#1934C2211yescharacteristic
164#1924C2211yescharacteristic
165#1924C2211yescharacteristic
166#1923C2211yescharacteristic
167#1923C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1853C2211yescharacteristic
183#1852C2211yescharacteristic
184#1847C2211yescharacteristic
185#1847C2211yescharacteristic
186#1847C2211yescharacteristic
187#1847C2211yescharacteristic
188#1846C2211yescharacteristic
189#1846C2211yescharacteristic
190#1844C2211yescharacteristic
191#1844C2211yescharacteristic
192#1832C2211yescharacteristic
193#1809C2211yescharacteristic
194#1809C2211yescharacteristic
195#1808C2211yescharacteristic
196#1807C2211yescharacteristic
197#1776C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1752C2211yescharacteristic
203C8×C22⋊C4C2211yescharacteristic
204#1726C2211yescharacteristic
205C22×D8C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#555—24no—
209#555—42no—
210#554—24no—
211#554—24no—
212#554—42no—
213#554—42no—
214#553—24no—
215#553—42no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#126—21no—
221C2×#125C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#125C2311yescharacteristic
225C2×#125C2311yescharacteristic
226C2×#124—21no—
227C2×#124—21no—
228C2×#124—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×#123—21no—
232C2×#123—21no—
233C2×#123—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×#121—21no—
241C2×#121—21no—
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×#117—21no—
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C22×C4⋊C4—21no—
260C22×C4⋊C4—21no—
261C22×C4⋊C4C2311yescharacteristic
262#501—24no—
263#501—24no—
264#501—24no—
265#499—24no—
266#499—42no—
267#498—42no—
268#482—24no—
269#482—24no—
270#482—24no—
271#480—24no—
272#478—24no—
273#478—24no—
274#478—24no—
275#478—24no—
276#478—24no—
277#474—24no—
278#474—24no—
279#474—24no—
280#469—24no—
281#466—24no—
282#446—24no—
283#442—24no—
284#442D418yes—
285C4×D8—24no—
286#435—24no—
287#428—24no—
288#427—24no—
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×#106C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×C22⋊C8C2311yescharacteristic
339C2×C22⋊C8C2311yescharacteristic
340C2×#97C2311yescharacteristic
341C2×#97C2311yescharacteristic
342C2×#97C2311yescharacteristic
343C2×#97C2311yescharacteristic
344C2×C4×C8C2311yescharacteristic
345C2×C4×C8C2311yescharacteristic
346C2×C4×C8C2311yescharacteristic
347C2×C4×C8C2311yescharacteristic
348#400—21no—
349#400—21no—
350#400—21no—
351#400D411yescharacteristic
352#400D411yescharacteristic
353#399—21no—
354#399—21no—
355#399—21no—
356#399—21no—
357#398—21no—
358#398—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#398—21no—
365#398—21no—
366#397—21no—
367#397—21no—
368#397—21no—
369#397—21no—
370#397—21no—
371#397—21no—
372#397—21no—
373#397—21no—
374#397—21no—
375#397—21no—
376#397D411yescharacteristic
377#397D411yescharacteristic
378#396—21no—
379#396—21no—
380#396—21no—
381#396—21no—
382#396—21no—
383#396—21no—
384#395—21no—
385#395—21no—
386#395—21no—
387#395—21no—
388#395—21no—
389#394—21no—
390#394—21no—
391#394—21no—
392#394—21no—
393#394—21no—
394#394—21no—
395#394—21no—
396#394—21no—
397#394—21no—
398#394D411yescharacteristic
399#394D411yescharacteristic
400#393—21no—
401#393—21no—
402#393D411yescharacteristic
403#393D411yescharacteristic
404#391—21no—
405#391—21no—
406#391—21no—
407#391—21no—
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#390C2311yescharacteristic
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389—21no—
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#386—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#384C2311yescharacteristic
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#384C2311yescharacteristic
456#382C2311yescharacteristic
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#382C2311yescharacteristic
460#381—21no—
461#381—21no—
462#381—21no—
463#381—21no—
464#381—21no—
465#381—21no—
466#380—21no—
467#380—21no—
468#380—21no—
469#380—21no—
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473#380C2311yescharacteristic
474#380C2311yescharacteristic
475#380C2311yescharacteristic
476#380C2311yescharacteristic
477#380C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482C4×C22⋊C4C2311yescharacteristic
483C4×C22⋊C4C2311yescharacteristic
484#376C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
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#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C22×Q8—21no—
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8C2×D411yescharacteristic
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4C2×D411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C2×D8—22no—
536C2×D8—22no—
537C2×D8C2×D414yes—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16—22no—
541C22×C8—22no—
542C22×C8—22no—
543C22×C8—22no—
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C4⋊Q8—22no—
553C4⋊Q8—22no—
554C4⋊Q8—22no—
555C4⋊Q8—22no—
556C4⋊Q8—22no—
557C4⋊Q8—41no—
558C4⋊Q8—82no—
559#126—44no—
560#125—22no—
561#125—22no—
562#125—22no—
563#125—22no—
564#125—22no—
565#125—22no—
566#125—22no—
567#125—41no—
568#125—41no—
569#125—41no—
570#124—44no—
571#124—44no—
572#124—82no—
573#123—44no—
574#123—82no—
575#123—82no—
576#123—82no—
577#123—82no—
578C22⋊Q8—44no—
579C22⋊Q8—44no—
580C22⋊Q8—44no—
581C22⋊Q8—44no—
582C22⋊Q8—44no—
583C22⋊Q8—44no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—44no—
589#121—41no—
590#121—41no—
591#121—41no—
592#121—41no—
593#121—44no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—44no—
609C4×D4C2×D414yes—
610C4×D4C2×D414yes—
611#117—22no—
612#117—22no—
613#117—22no—
614#117—41no—
615#117—41no—
616#117—41no—
617#117—44no—
618C2×C4⋊C4—22no—
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—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—41no—
654C2×C4⋊C4—44no—
655C2×C4⋊C4—44no—
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
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—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723#107—22no—
724#107—22no—
725#107—22no—
726#107—22no—
727#107—22no—
728#107—22no—
729#107—22no—
730#107—22no—
731#107—22no—
732#107—22no—
733#107—22no—
734#107—41no—
735#107—41no—
736#106—22no—
737#106—22no—
738#106—22no—
739#106—22no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—41no—
744#106—41no—
745#106—41no—
746#106—41no—
747#106—41no—
748#106—41no—
749#106C2×D414yes—
750C4⋊C8—22no—
751C4⋊C8—22no—
752C4⋊C8—22no—
753C4⋊C8—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102C2×D414yes—
767#102C2×D414yes—
768C22⋊C8—22no—
769C22⋊C8—22no—
770C22⋊C8—22no—
771C22⋊C8—22no—
772C22⋊C8—22no—
773C22⋊C8—22no—
774#97—22no—
775#97—22no—
776#97—22no—
777#97C2×D414yes—
778C4×C8—22no—
779C4×C8—22no—
780C4×C8—22no—
781C4×C8—22no—
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#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#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
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
824C24—21no—
825C24—21no—
826C24C22×D411yescharacteristic
827C24C22×D411yescharacteristic
828C2×Q8—22no—
829C2×Q8—41no—
830C2×Q8—41no—
831C2×Q8—42no—
832C2×Q8—42no—
833C2×Q8—42no—
834C2×Q8—81no—
835C2×Q8—81no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×Q8—81no—
840C2×D4—22no—
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—21no—
851C2×D4—41no—
852C2×D4—41no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4C22×D412yes—
866C2×D4C22×D412yes—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C2511yescharacteristic
927D8—28no—
928M16—44no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—44no—
948C2×C8C22×D412yes—
949C2×C8C22×D412yes—
950C2×C82−1+412yes—
951C2×C82−1+412yes—
952C2×C82−1+412yes—
953C2×C82−1+412yes—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4C22×D412yes—
1019C4⋊C4C22×D412yes—
1020C22⋊C4—24no—
1021C22⋊C4—24no—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—42no—
1068C42—42no—
1069C42—42no—
1070C42—81no—
1071C42—81no—
1072C42C22×D412yes—
1073C42H(5,𝔽2)12yes—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—22no—
1083C23—22no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23C23×D411yescharacteristic
1103Q8—82no—
1104Q8—162no—
1105Q8—162no—
1106Q8—162no—
1107D4—22no—
1108D4—22no—
1109D4—22no—
1110D4—22no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—82no—
1116D4—84no—
1117D4—162no—
1118D4—162no—
1119D4—162no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—84no—
1205C2×C4—84no—
1206C2×C4—84no—
1207C2×C4—162no—
1208C2×C4—162no—
1209C2×C4—162no—
1210C2×C4—162no—
1211C2×C4D4212yes—
1212C2×C4D4212yes—
1213C2×C4C23×D411yescharacteristic
1214C2×C4C2×H(5,𝔽2)11yescharacteristic
1215C2×C4C2×2−1+411yescharacteristic
1216C2×C4C2×2−1+411yescharacteristic
1217C2×C4C2×2−1+411yescharacteristic
1218C2×C4C2×2−1+411yescharacteristic
1219C8—22no—
1220C8—22no—
1221C8—22no—
1222C8—41no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C8#53614yes—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—42no—
1246C22—42no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22C2×D4211yescharacteristic
1256C22#349911yescharacteristic
1257C22#349911yescharacteristic
1258C22#358411yescharacteristic
1259C22#358411yescharacteristic
1260C22#358511yescharacteristic
1261C22#358511yescharacteristic
1262C4—22no—
1263C4—22no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—42no—
1273C4—42no—
1274C4—41no—
1275C4—41no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4C2×#53611yescharacteristic
1289C4#349911yescharacteristic
1290C4#355211yescharacteristic
1291C4#355211yescharacteristic
1292C2—81no—
1293C2—81no—
1294C2—82no—
1295C2—82no—
1296C2#3936011yescharacteristic
1297C2#6107411yescharacteristic
1298C2#6107411yescharacteristic
1299C2#6248911yescharacteristic
1300C2#6250111yescharacteristic
1301C2#6251811yescharacteristic
1302C2#6252411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3347C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2398 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3389C2semidirect
3. #42682C2semidirect
4. #42681C2semidirect
5. #33318C2semidirect
6. #31106C2semidirect
7. #31102C2semidirect
8. #31100C2semidirect
9. #31098C2semidirect
10. #31092C2semidirect
11. #31092C2semidirect
12. #31082C2semidirect
13. #31080C2semidirect
14. #29872C2semidirect
15. #29872C2semidirect
16. #28714C2semidirect
17. #28685C2semidirect
18. #26076C2semidirect
19. #26073C2semidirect
20. #26069C2semidirect
21. #26063C2semidirect
22. #25843C2semidirect
23. #25835C2semidirect
24. #25707C2semidirect
25. #25700C2semidirect
26. #25046C2semidirect
27. #25042C2semidirect
28. #25038C2semidirect
29. #25032C2semidirect
30. #21637C2semidirect
31. #21290C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33892
C2×#33472
#426822
#426812
#333182
#311062
#311022
#311002
#310982
#310922
#310822
#310802
#298722
#287142
#286852
#260762
#260732
#260692
#260632
#258432
#258352
#257072
#257002
#250462
#250422
#250382
#250322
#216372
#212902