Finite Group Databasebeta

← #6672380

Subgroups — #6672380

Order 512.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3385C211yesmaximal, characteristic, complemented
2C2×#3110C211yesmaximal, characteristic
3#39597C211yesmaximal, characteristic, complemented
4#36215C211yesmaximal, characteristic
5#32953C211yesmaximal, characteristic
6#31165C211yesmaximal, characteristic, complemented
7#31157C211yesmaximal, characteristic, complemented
8#31105C211yesmaximal, characteristic, complemented
9#31081C211yesmaximal, characteristic, complemented
10#30962C211yesmaximal, characteristic, complemented
11#30946C211yesmaximal, characteristic, complemented
12#30795C211yesmaximal, characteristic, complemented
13#30779C211yesmaximal, characteristic, complemented
14#29884C211yesmaximal, characteristic, complemented
15#29695C211yesmaximal, characteristic, complemented
16#28543C211yesmaximal, characteristic, complemented
17#28200C211yesmaximal, characteristic, complemented
18#27245C211yesmaximal, characteristic
19#27224C211yesmaximal, characteristic
20#26182C211yesmaximal, characteristic, complemented
21#26170C211yesmaximal, characteristic, complemented
22#26058C211yesmaximal, characteristic, complemented
23#26040C211yesmaximal, characteristic, complemented
24#24921C211yesmaximal, characteristic
25#24901C211yesmaximal, characteristic
26#24833C211yesmaximal, characteristic, complemented
27#24689C211yesmaximal, characteristic, complemented
28#24349C211yesmaximal, characteristic, complemented
29#24341C211yesmaximal, characteristic, complemented
30#22776C211yesmaximal, characteristic, complemented
31#22108C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic, complemented
33C2×#554C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36#3385—28no—
37C2×#501C2211yescharacteristic, complemented
38C2×#501C2211yescharacteristic, complemented
39C2×#500C2211yescharacteristic, complemented
40#3110—28no—
41C2×#484C2211yescharacteristic
42C2×#484C2211yescharacteristic
43C2×#479C2211yescharacteristic, complemented
44C2×#479C2211yescharacteristic, complemented
45C2×#479C2211yescharacteristic, complemented
46C2×#477C2211yescharacteristic, complemented
47C2×#476C2211yescharacteristic
48C2×#474C2211yescharacteristic
49C2×#474C2211yescharacteristic
50C2×#474C2211yescharacteristic
51C2×#474C2211yescharacteristic
52C2×#474C2211yescharacteristic
53C2×#461C2211yescharacteristic
54C2×#461C2211yescharacteristic
55C2×#450C2211yescharacteristic
56C2×#450C2211yescharacteristic
57C2×#446C2211yescharacteristic, complemented
58C2×#440C2211yescharacteristic
59C2×#440C2211yescharacteristic
60C2×#440C2211yescharacteristic
61C2×#440C2211yescharacteristic
62C2×#440C2211yescharacteristic
63C2×C4×SD16C2211yescharacteristic
64C2×#432C2211yescharacteristic
65#2857C2211yescharacteristic
66#2851C2211yescharacteristic
67#2848—21no—
68#2713—21no—
69#2713—21no—
70#2677—21no—
71#2677—21no—
72#2628—21no—
73#2582C2211yescharacteristic, complemented
74#2581—21no—
75#2580C2211yescharacteristic
76#2579—21no—
77#2567C2211yescharacteristic, complemented
78#2566C2211yescharacteristic
79#2564—21no—
80#2551C2211yescharacteristic, complemented
81#2551C2211yescharacteristic, complemented
82#2546—21no—
83#2492C2211yescharacteristic
84#2492C2211yescharacteristic
85#2454C2211yescharacteristic
86#2452C2211yescharacteristic
87#2450—21no—
88#2449—21no—
89#2446C2211yescharacteristic, complemented
90#2446C2211yescharacteristic, complemented
91#2442C2211yescharacteristic
92#2440C2211yescharacteristic
93#2437—21no—
94#2437—21no—
95#2423C2211yescharacteristic
96#2423C2211yescharacteristic
97#2355C2211yescharacteristic, complemented
98#2349C2211yescharacteristic
99#2349C2211yescharacteristic
100D4×C4⋊C4C2211yescharacteristic
101D4×C22⋊C4C2211yescharacteristic
102D4×C22⋊C4C2211yescharacteristic
103#2323—21no—
104C4×C22⋊Q8C2211yescharacteristic
105C2×#385—21no—
106#2097C2211yescharacteristic, complemented
107#2095C2211yescharacteristic, complemented
108#2094C2211yescharacteristic
109#2093C2211yescharacteristic
110#2088C2211yescharacteristic, complemented
111#2088C2211yescharacteristic, complemented
112#2087C2211yescharacteristic, complemented
113#2086C2211yescharacteristic, complemented
114#2086C2211yescharacteristic, complemented
115#2086C2211yescharacteristic, complemented
116#2083C2211yescharacteristic, complemented
117#2083C2211yescharacteristic, complemented
118#2077C2211yescharacteristic
119#2077C2211yescharacteristic
120#2076C2211yescharacteristic
121#2076C2211yescharacteristic
122#2074C2211yescharacteristic, complemented
123#2072C2211yescharacteristic, complemented
124#2068C2211yescharacteristic, complemented
125#2068C2211yescharacteristic, complemented
126#2059C2211yescharacteristic, complemented
127#2058C2211yescharacteristic, complemented
128#2057C2211yescharacteristic, complemented
129#2057C2211yescharacteristic, complemented
130#2057C2211yescharacteristic, complemented
131#2057C2211yescharacteristic, complemented
132#2055C2211yescharacteristic
133#2055C2211yescharacteristic
134#2055C2211yescharacteristic
135#2055C2211yescharacteristic
136#2043C2211yescharacteristic, complemented
137#2043C2211yescharacteristic, complemented
138#2036C2211yescharacteristic
139#2036C2211yescharacteristic
140#2035C2211yescharacteristic
141#2035C2211yescharacteristic
142#2026C2211yescharacteristic, complemented
143#2024C2211yescharacteristic, complemented
144#2023C2211yescharacteristic
145#2023C2211yescharacteristic
146#1993C2211yescharacteristic, complemented
147#1992C2211yescharacteristic, complemented
148#1985C2211yescharacteristic, complemented
149#1973C2211yescharacteristic
150#1968C2211yescharacteristic
151#1949C2211yescharacteristic, complemented
152#1947C2211yescharacteristic, complemented
153#1940C2211yescharacteristic, complemented
154#1940C2211yescharacteristic, complemented
155#1939C2211yescharacteristic, complemented
156#1936C2211yescharacteristic
157#1935C2211yescharacteristic, complemented
158#1935C2211yescharacteristic, complemented
159#1934C2211yescharacteristic
160#1933C2211yescharacteristic, complemented
161#1933C2211yescharacteristic, complemented
162#1926C2211yescharacteristic
163#1925C2211yescharacteristic
164#1924C2211yescharacteristic
165#1924C2211yescharacteristic
166#1923C2211yescharacteristic
167#1923C2211yescharacteristic
168#1921C2211yescharacteristic, complemented
169#1918C2211yescharacteristic, complemented
170#1917C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1864C2211yescharacteristic
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic
187#1862C2211yescharacteristic
188#1852C2211yescharacteristic
189#1852C2211yescharacteristic
190#1847C2211yescharacteristic, complemented
191#1845C2211yescharacteristic, complemented
192#1836C2211yescharacteristic, complemented
193#1805C2211yescharacteristic, complemented
194#1805C2211yescharacteristic, complemented
195#1802C2211yescharacteristic
196#1802C2211yescharacteristic
197#1802C2211yescharacteristic
198#1802C2211yescharacteristic
199#1797C2211yescharacteristic
200#1786C2211yescharacteristic
201#1786C2211yescharacteristic
202#1771C2211yescharacteristic, complemented
203#1762C2211yescharacteristic
204C4×#102C2211yescharacteristic
205C23×D4C2311yescharacteristic
206C24×C4—21no—
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211Q82—24no—
212Q82—42no—
213#554—24no—
214#554—42no—
215#533—24no—
216#533—42no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8—21no—
220C2×C4⋊Q8—21no—
221C2×C4⋊Q8—21no—
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×#125—21no—
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8D411yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C4×Q8—21no—
242C2×C4×Q8—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×D4—24no—
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4—42no—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×#117—21no—
261C22×C4⋊C4—21no—
262C22×C4⋊C4—21no—
263C22×C4⋊C4C2311yescharacteristic
264C22×C22⋊C4—21no—
265C22×C22⋊C4—21no—
266C22×C22⋊C4—21no—
267C22×C42C2311yescharacteristic
268#501—24no—
269#501—24no—
270#500—24no—
271#484—24no—
272#484—24no—
273#479—24no—
274#479—24no—
275#479—42no—
276#477—24no—
277#476—24no—
278#474—24no—
279#474—24no—
280#474—24no—
281#474—24no—
282#474—42no—
283#461—24no—
284#461—24no—
285#450—24no—
286#450—24no—
287#446—24no—
288#440—24no—
289#440—24no—
290#440—24no—
291#440—24no—
292#440D418yes—
293C4×SD16—24no—
294#432—24no—
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#107C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×C22⋊C8C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×C22⋊C8C2311yescharacteristic
346C2×C22⋊C8C2311yescharacteristic
347C2×#97C2311yescharacteristic
348C2×#97C2311yescharacteristic
349C2×#97C2311yescharacteristic
350C2×#97C2311yescharacteristic
351C2×C4×C8C2311yescharacteristic
352C2×C4×C8C2311yescharacteristic
353#400—21no—
354#400—21no—
355#400—21no—
356#400—21no—
357#400—21no—
358#399—21no—
359#399—21no—
360#399—21no—
361#399—21no—
362#398—21no—
363#398—21no—
364#398—21no—
365#398—21no—
366#398—21no—
367#398—21no—
368#398—21no—
369#398—21no—
370#396—21no—
371#396—21no—
372#396—21no—
373#396—21no—
374#395—21no—
375#395—21no—
376#395—21no—
377#395—21no—
378#395—21no—
379#395—21no—
380#395—21no—
381#393—21no—
382#393—21no—
383#393—21no—
384#393—21no—
385#391—21no—
386#391—21no—
387#391—21no—
388#391—21no—
389#391D411yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#391C2311yescharacteristic
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#389—21no—
401#389—21no—
402#389—21no—
403#389—21no—
404#389—21no—
405#389—21no—
406#389D411yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387D411yescharacteristic
432#387D411yescharacteristic
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#385D411yescharacteristic
454#385D411yescharacteristic
455#384C2311yescharacteristic
456#384C2311yescharacteristic
457#384C2311yescharacteristic
458#384C2311yescharacteristic
459#382—21no—
460#382C2311yescharacteristic
461#382C2311yescharacteristic
462#380—21no—
463#380—21no—
464#380—21no—
465#380—21no—
466#380—21no—
467#380—21no—
468#380D411yescharacteristic
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473#379—21no—
474#379—21no—
475C4×C4⋊C4—21no—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482C4×C22⋊C4C2311yescharacteristic
483C2×#95—21no—
484C2×#95—21no—
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#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C25—21no—
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8—21no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8C2×D411yescharacteristic
522C22×Q8C2411yescharacteristic
523C22×Q8C2411yescharacteristic
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—22no—
527C22×D4—22no—
528C22×D4—21no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—44no—
543C23×C4—82no—
544C23×C4—82no—
545C23×C4C2×D411yescharacteristic
546C23×C4C2×D411yescharacteristic
547C23×C4C2411yescharacteristic
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16C2×D414yes—
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C4⋊Q8—22no—
569C4⋊Q8—22no—
570C4⋊Q8—22no—
571C4⋊Q8—22no—
572C4⋊Q8—22no—
573C4⋊Q8—22no—
574C4⋊Q8—22no—
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579C4⋊Q8—44no—
580C4⋊Q8—41no—
581C4⋊Q8—44no—
582C4⋊Q8—44no—
583C4⋊Q8—82no—
584C4⋊Q8—82no—
585#125—22no—
586#125—22no—
587#125—22no—
588#125—41no—
589#125—44no—
590C22⋊Q8—24no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593C22⋊Q8—44no—
594C22⋊Q8—44no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—44no—
598C22⋊Q8—44no—
599C22⋊Q8—82no—
600C22⋊Q8—82no—
601C22⋊Q8—82no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—22no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—22no—
609C4×Q8—44no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—44no—
613C4×Q8C2×D414yes—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—44no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—44no—
631C4×D4C2×D414yes—
632#117—44no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—22no—
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—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—44no—
672C2×C4⋊C4—82no—
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—44no—
717C2×C22⋊C4—44no—
718C2×C22⋊C4—82no—
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C42—21no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42C2×D411yescharacteristic
732C2×C42C2×D411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739#107—22no—
740#107—22no—
741#107—22no—
742#107—22no—
743#107—22no—
744#107—22no—
745#107—22no—
746#107—22no—
747#107—41no—
748#107—41no—
749#107—41no—
750#107C2×D414yes—
751#106—22no—
752#106—22no—
753#106—22no—
754#106—41no—
755C4⋊C8—22no—
756C4⋊C8—22no—
757C4⋊C8—22no—
758C4⋊C8—22no—
759C4⋊C8—22no—
760C4⋊C8—22no—
761C4⋊C8—41no—
762C4⋊C8—41no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103C2×D414yes—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—22no—
784#102—41no—
785#102—41no—
786#102C2×D414yes—
787C22⋊C8—22no—
788C22⋊C8—22no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791#97—22no—
792#97—22no—
793#97—41no—
794#97C2×D414yes—
795C4×C8—22no—
796C4×C8—41no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839C24—21no—
840C24—24no—
841C24—21no—
842C24—42no—
843C24—42no—
844C24—42no—
845C24—42no—
846C24—81no—
847C24—81no—
848C24C22×D411yescharacteristic
849C2×Q8—22no—
850C2×Q8—22no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—41no—
863C2×Q8—42no—
864C2×Q8—42no—
865C2×Q8—42no—
866C2×Q8—42no—
867C2×Q8—42no—
868C2×Q8—42no—
869C2×Q8—81no—
870C2×Q8—81no—
871C2×Q8—81no—
872C2×Q8—81no—
873C2×Q8—81no—
874C2×Q8—81no—
875C2×Q8—81no—
876C2×Q8—81no—
877C2×Q8—81no—
878C2×Q8C22×D412yes—
879C2×D4—24no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4C22×D412yes—
895C2×D42−1+412yes—
896C2×D42−1+412yes—
897C2×D42−1+412yes—
898C22×C4—22no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—24no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—41no—
924C22×C4—41no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—816no—
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C2511yescharacteristic
966SD16—28no—
967SD16—44no—
968SD16—44no—
969SD16—44no—
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—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8C22×D412yes—
993C2×C8C22×D412yes—
994C4⋊C4—24no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—22no—
1001C4⋊C4—22no—
1002C4⋊C4—22no—
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—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—41no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4C22×D412yes—
1062C4⋊C4C22×D412yes—
1063C22⋊C4—22no—
1064C22⋊C4—24no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4#13714yes—
1089C42—22no—
1090C42—22no—
1091C42—24no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—42no—
1103C42—42no—
1104C42—42no—
1105C42—81no—
1106C42—81no—
1107C42C22×D412yes—
1108C42H(5,𝔽2)12yes—
1109C23—21no—
1110C23—21no—
1111C23—22no—
1112C23—21no—
1113C23—21no—
1114C23—22no—
1115C23—22no—
1116C23—21no—
1117C23—21no—
1118C23—22no—
1119C23—48no—
1120C23—48no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—84no—
1132C23—84no—
1133C23—84no—
1134C23—84no—
1135C23—84no—
1136C23C2×#13712yes—
1137C23C23×D411yescharacteristic
1138Q8—22no—
1139Q8—22no—
1140Q8—44no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—84no—
1148Q8—162no—
1149Q8—162no—
1150Q8—162no—
1151Q8—162no—
1152D4—22no—
1153D4—22no—
1154D4—22no—
1155D4—22no—
1156D4—22no—
1157D4—48no—
1158D4—41no—
1159D4—41no—
1160D4#53614yes—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
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—21no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—21no—
1184C2×C4—22no—
1185C2×C4—21no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—44no—
1199C2×C4—44no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
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—84no—
1244C2×C4—84no—
1245C2×C4—84no—
1246C2×C4—84no—
1247C2×C4—84no—
1248C2×C4—84no—
1249C2×C4—84no—
1250C2×C4—162no—
1251C2×C4—162no—
1252C2×C4D4212yes—
1253C2×C4D4212yes—
1254C2×C4C2×#13712yes—
1255C2×C4C2×#13712yes—
1256C2×C4#57612yes—
1257C2×C4C23×D411yescharacteristic
1258C2×C4C2×H(5,𝔽2)11yescharacteristic
1259C2×C4C2×2−1+411yescharacteristic
1260C2×C4C2×2−1+411yescharacteristic
1261C2×C4C2×2−1+411yescharacteristic
1262C2×C4#58511yescharacteristic
1263C8—22no—
1264C8—22no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C22—24no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—41no—
1276C22—42no—
1277C22—41no—
1278C22—42no—
1279C22—42no—
1280C22—41no—
1281C22—42no—
1282C22—41no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—816no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22C2×D4211yescharacteristic
1294C22#348611yescharacteristic
1295C22#348911yescharacteristic
1296C22C22×#13711yescharacteristic
1297C22C2×#57611yescharacteristic
1298C22#358511yescharacteristic
1299C22#358611yescharacteristic
1300C4—22no—
1301C4—22no—
1302C4—22no—
1303C4—22no—
1304C4—22no—
1305C4—41no—
1306C4—42no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—42no—
1314C4—42no—
1315C4—41no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4C2×#53611yescharacteristic
1328C4#348911yescharacteristic
1329C4#353811yescharacteristic
1330C4#354111yescharacteristic
1331C2—42no—
1332C2—44no—
1333C2—82no—
1334C2#3765111yescharacteristic
1335C2D4×#13711yescharacteristic
1336C2#6107211yescharacteristic
1337C2#6182611yescharacteristic
1338C2#6184911yescharacteristic
1339C2#6212711yescharacteristic
1340C2#6223211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3385C2semidirect
3. #39597C2semidirect
6. #31165C2semidirect
7. #31157C2semidirect
8. #31105C2semidirect
9. #31081C2semidirect
10. #30962C2semidirect
11. #30946C2semidirect
12. #30795C2semidirect
13. #30779C2semidirect
14. #29884C2semidirect
15. #29695C2semidirect
16. #28543C2semidirect
17. #28200C2semidirect
20. #26182C2semidirect
21. #26170C2semidirect
22. #26058C2semidirect
23. #26040C2semidirect
26. #24833C2semidirect
27. #24689C2semidirect
28. #24349C2semidirect
29. #24341C2semidirect
30. #22776C2semidirect
31. #22108C2semidirect
32. C2×Q82C22semidirect
37. C2×#501C22semidirect
38. C2×#501C22semidirect
39. C2×#500C22semidirect
43. C2×#479C22semidirect
44. C2×#479C22semidirect
45. C2×#479C22semidirect
46. C2×#477C22semidirect
57. C2×#446C22semidirect
73. #2582C22semidirect
77. #2567C22semidirect
80. #2551C22semidirect
81. #2551C22semidirect
89. #2446C22semidirect
90. #2446C22semidirect
97. #2355C22semidirect
106. #2097C22semidirect
107. #2095C22semidirect
110. #2088C22semidirect
111. #2088C22semidirect
112. #2087C22semidirect
113. #2086C22semidirect
114. #2086C22semidirect
115. #2086C22semidirect
116. #2083C22semidirect
117. #2083C22semidirect
122. #2074C22semidirect
123. #2072C22semidirect
124. #2068C22semidirect
125. #2068C22semidirect
126. #2059C22semidirect
127. #2058C22semidirect
128. #2057C22semidirect
129. #2057C22semidirect
130. #2057C22semidirect
131. #2057C22semidirect
136. #2043C22semidirect
137. #2043C22semidirect
142. #2026C22semidirect
143. #2024C22semidirect
146. #1993C22semidirect
147. #1992C22semidirect
148. #1985C22semidirect
151. #1949C22semidirect
152. #1947C22semidirect
153. #1940C22semidirect
154. #1940C22semidirect
155. #1939C22semidirect
157. #1935C22semidirect
158. #1935C22semidirect
160. #1933C22semidirect
161. #1933C22semidirect
168. #1921C22semidirect
169. #1918C22semidirect
170. #1917C22semidirect
171. #1916C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
190. #1847C22semidirect
191. #1845C22semidirect
192. #1836C22semidirect
193. #1805C22semidirect
194. #1805C22semidirect
202. #1771C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33852
C2×#31102
#395972
#362152
#329532
#311652
#311572
#311052
#310812
#309622
#309462
#307952
#307792
#298842
#296952
#285432
#282002
#272452
#272242
#261822
#261702
#260582
#260402
#249212
#249012
#248332
#246892
#243492
#243412
#227762
#221082