Finite Group Databasebeta

← #6816346

Subgroups — #6816346

Order 512.

1824 conjugacy classes of subgroups.

The subgroup lattice has 1340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3255C211yesmaximal, characteristic, complemented
2C2×#3252C211yesmaximal, characteristic
3#36140C211yesmaximal, characteristic
4#36133C211yesmaximal, characteristic, complemented
5#33186C211yesmaximal, characteristic
6#31242C211yesmaximal, characteristic, complemented
7#31240C211yesmaximal, characteristic, complemented
8#31213C211yesmaximal, characteristic, complemented
9#31211C211yesmaximal, characteristic, complemented
10#31163C211yesmaximal, characteristic, complemented
11#31159C211yesmaximal, characteristic, complemented
12#31151C211yesmaximal, characteristic, complemented
13#31149C211yesmaximal, characteristic, complemented
14#29784C211yesmaximal, characteristic
15#29783C211yesmaximal, characteristic, complemented
16#26476C211yesmaximal, characteristic, complemented
17#26473C211yesmaximal, characteristic, complemented
18#26056C211yesmaximal, characteristic, complemented
19#26054C211yesmaximal, characteristic, complemented
20#25505C211yesmaximal, characteristic
21#25504C211yesmaximal, characteristic, complemented
22#25504C211yesmaximal, characteristic, complemented
23#25503C211yesmaximal, characteristic
24#25382C211yesmaximal, characteristic, complemented
25#25379C211yesmaximal, characteristic, complemented
26#24760C211yesmaximal, characteristic, complemented
27#24757C211yesmaximal, characteristic
28#24746C211yesmaximal, characteristic, complemented
29#24741C211yesmaximal, characteristic, complemented
30#21539C211yesmaximal, characteristic, complemented
31#21146C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#529C2211yescharacteristic
36#3255—28no—
37#3252—28no—
38C2×#497C2211yescharacteristic
39C2×#479C2211yescharacteristic
40C2×#479C2211yescharacteristic
41C2×#477C2211yescharacteristic
42C2×#475C2211yescharacteristic
43C2×#475C2211yescharacteristic
44C2×#475C2211yescharacteristic
45C2×#475C2211yescharacteristic
46C2×#476C2211yescharacteristic
47C2×#470C2211yescharacteristic
48C2×#470C2211yescharacteristic
49C2×#470C2211yescharacteristic
50C2×#470C2211yescharacteristic
51C2×#470C2211yescharacteristic
52C2×#470C2211yescharacteristic
53C2×#468C2211yescharacteristic
54C2×#468C2211yescharacteristic
55C2×#468C2211yescharacteristic
56C2×#464C2211yescharacteristic
57C2×#464C2211yescharacteristic
58C2×#464C2211yescharacteristic
59C2×#462C2211yescharacteristic
60C2×#462C2211yescharacteristic
61C2×#462C2211yescharacteristic
62C2×#462C2211yescharacteristic
63C2×#462C2211yescharacteristic
64C2×#462C2211yescharacteristic
65C2×#461C2211yescharacteristic
66C2×#441C2211yescharacteristic
67C2×#423C2211yescharacteristic
68C2×#423C2211yescharacteristic
69C2×#423C2211yescharacteristic
70C2×C4×M16C2211yescharacteristic
71#2857C2211yescharacteristic
72#2855C2211yescharacteristic
73#2855C2211yescharacteristic
74#2855C2211yescharacteristic
75#2854C2211yescharacteristic
76#2850C2211yescharacteristic
77#2551C2211yescharacteristic
78#2550C2211yescharacteristic
79#2546C2211yescharacteristic
80#2545C2211yescharacteristic
81#2519—21no—
82#2506—21no—
83#2488—21no—
84#2475—21no—
85#2469—21no—
86#2462—21no—
87#2462—21no—
88#2453C2211yescharacteristic
89#2452C2211yescharacteristic
90#2451C2211yescharacteristic
91#2451C2211yescharacteristic
92#2449—21no—
93#2448C2211yescharacteristic
94#2446C2211yescharacteristic
95#2446C2211yescharacteristic
96#2446C2211yescharacteristic
97#2440—21no—
98#2438—21no—
99#2438—21no—
100#2413—21no—
101#2367C2211yescharacteristic
102#2365—21no—
103#2365C2211yescharacteristic
104#2362—21no—
105#2359—21no—
106#2351C2211yescharacteristic
107Q8×C4⋊C4C2211yescharacteristic
108#2344—21no—
109C4×C22⋊Q8C2211yescharacteristic
110C4×C22⋊Q8C2211yescharacteristic
111C2×C4×C4⋊C4C2211yescharacteristic
112#2088C2211yescharacteristic
113#2088C2211yescharacteristic
114#2087C2211yescharacteristic
115#2086C2211yescharacteristic
116#2068C2211yescharacteristic
117#2068C2211yescharacteristic
118#2068C2211yescharacteristic
119#2068C2211yescharacteristic
120#2067C2211yescharacteristic
121#2066C2211yescharacteristic
122#2066C2211yescharacteristic
123#2066C2211yescharacteristic
124#2066C2211yescharacteristic
125#2066C2211yescharacteristic
126#2065C2211yescharacteristic
127#2065C2211yescharacteristic
128#2059C2211yescharacteristic
129#2058C2211yescharacteristic
130#2058C2211yescharacteristic
131#2057C2211yescharacteristic
132#2056C2211yescharacteristic
133#2056C2211yescharacteristic
134#2056C2211yescharacteristic
135#2056C2211yescharacteristic
136#2056C2211yescharacteristic
137#2055C2211yescharacteristic
138#2055C2211yescharacteristic
139#2055C2211yescharacteristic
140#2043C2211yescharacteristic
141#2043C2211yescharacteristic
142#2043C2211yescharacteristic
143#2042C2211yescharacteristic
144#2026C2211yescharacteristic
145#2024C2211yescharacteristic
146#2024C2211yescharacteristic
147#2023C2211yescharacteristic
148#2016C2211yescharacteristic
149#2016C2211yescharacteristic
150#2015C2211yescharacteristic
151#2013C2211yescharacteristic
152#1983C2211yescharacteristic
153#1981C2211yescharacteristic
154#1969C2211yescharacteristic
155#1969C2211yescharacteristic
156#1969C2211yescharacteristic
157#1968C2211yescharacteristic
158#1968C2211yescharacteristic
159#1960C2211yescharacteristic
160#1959C2211yescharacteristic
161#1949C2211yescharacteristic
162#1948C2211yescharacteristic
163#1941C2211yescharacteristic
164#1940C2211yescharacteristic
165#1940C2211yescharacteristic
166#1940C2211yescharacteristic
167#1940C2211yescharacteristic
168#1939C2211yescharacteristic
169#1939C2211yescharacteristic
170#1939C2211yescharacteristic
171#1939C2211yescharacteristic
172#1933C2211yescharacteristic
173#1933C2211yescharacteristic
174#1895C2211yescharacteristic
175#1894C2211yescharacteristic
176#1894C2211yescharacteristic
177#1894C2211yescharacteristic
178#1894C2211yescharacteristic
179#1894C2211yescharacteristic
180#1880C2211yescharacteristic
181#1880C2211yescharacteristic
182#1878C2211yescharacteristic
183#1878C2211yescharacteristic
184#1878C2211yescharacteristic
185#1878C2211yescharacteristic
186#1878C2211yescharacteristic
187#1877C2211yescharacteristic
188#1865C2211yescharacteristic
189#1865C2211yescharacteristic
190#1865C2211yescharacteristic
191#1865C2211yescharacteristic
192#1864C2211yescharacteristic
193#1863C2211yescharacteristic
194#1863C2211yescharacteristic
195#1863C2211yescharacteristic
196#1847C2211yescharacteristic
197#1809C2211yescharacteristic
198#1805C2211yescharacteristic
199#1803C2211yescharacteristic
200#1776C2211yescharacteristic
201#1763C2211yescharacteristic
202#1763C2211yescharacteristic
203#1728C2211yescharacteristic
204#1728C2211yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×M16C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C22×M16C2311yescharacteristic
218#533—24no—
219#533—24no—
220#533—24no—
221#533—42no—
222#533—42no—
223#533—42no—
224C2×C4⋊Q8—21no—
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232#529—24no—
233#529—42no—
234C2×#126—21no—
235C2×#125—21no—
236C2×#125—21no—
237C2×#125—21no—
238C2×#125C2311yescharacteristic
239C2×#124C2311yescharacteristic
240C2×#124C2311yescharacteristic
241C2×#123—21no—
242C2×#123—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8—21no—
246C2×C22⋊Q8—21no—
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2311yescharacteristic
249C2×C22⋊Q8C2311yescharacteristic
250C2×C22⋊Q8C2311yescharacteristic
251C2×C22⋊Q8C2311yescharacteristic
252C2×#121C2311yescharacteristic
253C2×C4×Q8—21no—
254C2×C4×Q8—21no—
255C2×C4×Q8—21no—
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×D4—21no—
266C2×C4×D4C2311yescharacteristic
267C2×#117—21no—
268C2×#117—21no—
269C2×#117—21no—
270C2×#117—21no—
271C22×C4⋊C4D411yescharacteristic
272C22×C4⋊C4D411yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276#497—42no—
277#479—24no—
278#479—24no—
279#477—24no—
280#476—24no—
281#475—24no—
282#475—24no—
283#475—24no—
284#475—24no—
285#470—24no—
286#470—24no—
287#470—24no—
288#470—24no—
289#470—42no—
290#470D418yes—
291#468—24no—
292#468—24no—
293#468—42no—
294#464—24no—
295#464—24no—
296#464—42no—
297#462—24no—
298#462—24no—
299#462—24no—
300#462—24no—
301#462—24no—
302#462—42no—
303#461—24no—
304#441—42no—
305C2×#107C2311yescharacteristic
306C2×#107C2311yescharacteristic
307C2×#107C2311yescharacteristic
308C2×#107C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×#106C2311yescharacteristic
316#423—24no—
317#423—24no—
318#423—42no—
319C2×C4⋊C8C2311yescharacteristic
320C2×C4⋊C8C2311yescharacteristic
321C2×C4⋊C8C2311yescharacteristic
322C2×C4⋊C8C2311yescharacteristic
323C2×C4⋊C8C2311yescharacteristic
324C2×C4⋊C8C2311yescharacteristic
325C2×C4⋊C8C2311yescharacteristic
326C2×C4⋊C8C2311yescharacteristic
327C2×C4⋊C8C2311yescharacteristic
328C2×C4⋊C8C2311yescharacteristic
329C2×C4⋊C8C2311yescharacteristic
330C2×C4⋊C8C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#103C2311yescharacteristic
341C2×#103C2311yescharacteristic
342C2×#103C2311yescharacteristic
343C2×#103C2311yescharacteristic
344C2×#103C2311yescharacteristic
345C2×#103C2311yescharacteristic
346C2×#103C2311yescharacteristic
347C2×#103C2311yescharacteristic
348C2×#103C2311yescharacteristic
349C2×#103C2311yescharacteristic
350C2×#103C2311yescharacteristic
351C2×#103C2311yescharacteristic
352C2×#103C2311yescharacteristic
353C2×#103C2311yescharacteristic
354C2×#103C2311yescharacteristic
355C2×#103C2311yescharacteristic
356C2×#102C2311yescharacteristic
357C2×#102C2311yescharacteristic
358C2×#102C2311yescharacteristic
359C2×#102C2311yescharacteristic
360C2×#102C2311yescharacteristic
361C4×M16—42no—
362C2×#97C2311yescharacteristic
363C2×#97C2311yescharacteristic
364C2×C4×C8C2311yescharacteristic
365C2×C4×C8C2311yescharacteristic
366#400—21no—
367#400—21no—
368#400—21no—
369#400—21no—
370#399—21no—
371#398—21no—
372#398—21no—
373#398—21no—
374#398—21no—
375#398—21no—
376#398—21no—
377#398—21no—
378#398—21no—
379#398—21no—
380#397—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#393—21no—
390#391—21no—
391#391—21no—
392#391—21no—
393#391C2311yescharacteristic
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#389—21no—
408#389—21no—
409#389—21no—
410#389—21no—
411#389—21no—
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389—21no—
418#389—21no—
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#387—21no—
447#387—21no—
448#387—21no—
449#387—21no—
450#387—21no—
451#387—21no—
452#387—21no—
453#387—21no—
454#387—21no—
455#387—21no—
456#387—21no—
457#387—21no—
458#386—21no—
459#386—21no—
460#386—21no—
461#385—21no—
462#385—21no—
463#385—21no—
464#385—21no—
465#385—21no—
466#385—21no—
467#385—21no—
468#384—21no—
469#384C2311yescharacteristic
470#382—21no—
471#382C2311yescharacteristic
472#381—21no—
473#381—21no—
474#381—21no—
475#380—21no—
476#380—21no—
477#380C2311yescharacteristic
478#380C2311yescharacteristic
479C4×C4⋊C4—21no—
480C4×C4⋊C4—21no—
481C4×C4⋊C4—21no—
482C4×C4⋊C4—21no—
483C4×C4⋊C4—21no—
484C4×C4⋊C4D411yescharacteristic
485C4×C4⋊C4D411yescharacteristic
486C4×C4⋊C4D411yescharacteristic
487C4×C4⋊C4D411yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C22⋊C4—21no—
495C4×C22⋊C4—21no—
496C4×C22⋊C4—21no—
497C2×#95D411yescharacteristic
498C2×#95D411yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#340C2311yescharacteristic
512#340C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518#336C2311yescharacteristic
519#336C2311yescharacteristic
520#336C2311yescharacteristic
521C22×Q8—21no—
522C22×Q8—21no—
523C22×Q8—21no—
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×Q8C2411yescharacteristic
528C22×Q8C2411yescharacteristic
529C22×D4—21no—
530C22×D4C2411yescharacteristic
531C23×C4—21no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2×D411yescharacteristic
535C23×C4C2×D411yescharacteristic
536C23×C4C2×D411yescharacteristic
537C23×C4C2×D411yescharacteristic
538C23×C4C2411yescharacteristic
539C2×Q16—22no—
540C2×Q16—22no—
541C2×Q16—22no—
542C2×Q16—22no—
543C2×Q16—22no—
544C2×Q16—41no—
545C2×Q16—41no—
546C2×Q16—41no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16C2×D414yes—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×M16—22no—
567C2×M16—22no—
568C2×M16—22no—
569C2×M16—22no—
570C2×M16—41no—
571C2×M16—41no—
572C2×M16—41no—
573C2×M16—41no—
574C2×M16—41no—
575C2×M16—41no—
576C2×M16—41no—
577C2×M16C2×D414yes—
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C4⋊Q8—22no—
587C4⋊Q8—22no—
588C4⋊Q8—22no—
589C4⋊Q8—22no—
590C4⋊Q8—22no—
591C4⋊Q8—22no—
592C4⋊Q8—22no—
593C4⋊Q8—22no—
594C4⋊Q8—41no—
595C4⋊Q8—41no—
596C4⋊Q8—41no—
597C4⋊Q8—41no—
598C4⋊Q8—41no—
599C4⋊Q8—41no—
600C4⋊Q8—44no—
601#126—44no—
602#125—22no—
603#125—41no—
604#125—44no—
605#125—44no—
606#125—44no—
607#124—22no—
608#124—22no—
609#124—22no—
610#124—41no—
611#123—44no—
612#123—44no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—22no—
619C22⋊Q8—22no—
620C22⋊Q8—22no—
621C22⋊Q8—44no—
622C22⋊Q8—44no—
623C22⋊Q8—44no—
624C22⋊Q8—44no—
625C22⋊Q8C2×D414yes—
626C22⋊Q8C2×D414yes—
627#121—22no—
628#121—22no—
629C4×Q8—22no—
630C4×Q8—22no—
631C4×Q8—22no—
632C4×Q8—22no—
633C4×Q8—22no—
634C4×Q8—22no—
635C4×Q8—22no—
636C4×Q8—22no—
637C4×Q8—22no—
638C4×Q8—22no—
639C4×Q8—22no—
640C4×Q8—41no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×Q8—41no—
644C4×Q8—41no—
645C4×Q8—41no—
646C4×Q8—41no—
647C4×Q8—44no—
648C4×Q8—44no—
649C4×Q8—44no—
650C4×D4—22no—
651C4×D4—41no—
652C4×D4—44no—
653#117—44no—
654#117—44no—
655#117—44no—
656#117—44no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—24no—
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—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—42no—
698C2×C4⋊C4C2×D411yescharacteristic
699C2×C4⋊C4C2×D411yescharacteristic
700C2×C4⋊C4C2×D411yescharacteristic
701C2×C4⋊C4C2×D411yescharacteristic
702C2×C4⋊C4C2×D411yescharacteristic
703C2×C4⋊C4C2×D411yescharacteristic
704C2×C4⋊C4C2×D411yescharacteristic
705C2×C4⋊C4C2×D411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C42—22no—
736C2×C42—22no—
737C2×C42—22no—
738C2×C42—22no—
739C2×C42—22no—
740C2×C42—22no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42C2×D411yescharacteristic
753C2×C42C2×D411yescharacteristic
754C2×C42C2×D411yescharacteristic
755C2×C42C2×D411yescharacteristic
756C2×C42C2×D411yescharacteristic
757C2×C42C2×D411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764#107—22no—
765#107—22no—
766#107—41no—
767#107—41no—
768#106—22no—
769#106—22no—
770#106—22no—
771#106—22no—
772#106—41no—
773#106—41no—
774#106C2×D414yes—
775C4⋊C8—22no—
776C4⋊C8—22no—
777C4⋊C8—22no—
778C4⋊C8—22no—
779C4⋊C8—22no—
780C4⋊C8—22no—
781C4⋊C8—22no—
782C4⋊C8—22no—
783C4⋊C8—22no—
784C4⋊C8—22no—
785C4⋊C8—41no—
786C4⋊C8—41no—
787#103—22no—
788#103—22no—
789#103—22no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—22no—
796#103—22no—
797#103—22no—
798#103—22no—
799#103—41no—
800#103—41no—
801#103—41no—
802#103—41no—
803#103—41no—
804#103—41no—
805#103—41no—
806#103—41no—
807#103—41no—
808#103—41no—
809#103—41no—
810#103C2×D414yes—
811#103C2×D414yes—
812#102—22no—
813#102—22no—
814#102—41no—
815#102—41no—
816#102—41no—
817#97—22no—
818#97—22no—
819C4×C8—41no—
820C4×C8—41no—
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#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
853#95—21no—
854#95—21no—
855#95—21no—
856#95—21no—
857#95—21no—
858#95—21no—
859#95C2×D411yescharacteristic
860#95C2×D411yescharacteristic
861#95C2×D411yescharacteristic
862#95C2×D411yescharacteristic
863#95C2×D411yescharacteristic
864#95C2×D411yescharacteristic
865#95C2×D411yescharacteristic
866#95C2×D411yescharacteristic
867C24—21no—
868C24C22×D411yescharacteristic
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—42no—
898C2×Q8—42no—
899C2×Q8—42no—
900C2×Q8—42no—
901C2×Q8—42no—
902C2×Q8—42no—
903C2×Q8—81no—
904C2×Q8—81no—
905C2×Q8—81no—
906C2×Q8C22×D412yes—
907C2×Q8C22×D412yes—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—22no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—22no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—22no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—41no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—41no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—81no—
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D412yes—
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4H(5,𝔽2)12yes—
972C22×C4C2511yescharacteristic
973Q16—44no—
974Q16—82no—
975Q16—82no—
976Q16—82no—
977Q16—82no—
978Q16—82no—
979SD16—82no—
980SD16—82no—
981SD16—82no—
982M16—44no—
983M16—44no—
984M16—82no—
985M16—82no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8C22×D412yes—
1008C2×C8C22×D412yes—
1009C2×C82−1+412yes—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—22no—
1015C4⋊C4—22no—
1016C4⋊C4—22no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—41no—
1036C4⋊C4—41no—
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—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4#13714yes—
1075C4⋊C4C22×D412yes—
1076C4⋊C4C22×D412yes—
1077C22⋊C4—24no—
1078C22⋊C4—24no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C42—22no—
1097C42—22no—
1098C42—22no—
1099C42—22no—
1100C42—22no—
1101C42—22no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—42no—
1113C42—42no—
1114C42—42no—
1115C42—42no—
1116C42—42no—
1117C42—42no—
1118C42—42no—
1119C42—42no—
1120C42—42no—
1121C42—42no—
1122C42—81no—
1123C42H(5,𝔽2)12yes—
1124C422−1+412yes—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23D4212yes—
1139C23C23×D411yescharacteristic
1140Q8—22no—
1141Q8—22no—
1142Q8—22no—
1143Q8—22no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—84no—
1161Q8—84no—
1162Q8—84no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—84no—
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—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—21no—
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—21no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—44no—
1209C2×C4—44no—
1210C2×C4—44no—
1211C2×C4—44no—
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—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—82no—
1254C2×C4—84no—
1255C2×C4—82no—
1256C2×C4#53712yes—
1257C2×C4#53712yes—
1258C2×C4D4212yes—
1259C2×C4C2×#13712yes—
1260C2×C4C2×#13712yes—
1261C2×C4C2×#13712yes—
1262C2×C4#57512yes—
1263C2×C4C23×D411yescharacteristic
1264C2×C4C2×H(5,𝔽2)11yescharacteristic
1265C2×C4C2×H(5,𝔽2)11yescharacteristic
1266C2×C4C2×2−1+411yescharacteristic
1267C2×C4C2×2−1+411yescharacteristic
1268C2×C4#58511yescharacteristic
1269C8—22no—
1270C8—22no—
1271C8—22no—
1272C8—41no—
1273C8—41no—
1274C8—41no—
1275C8—41no—
1276C8—41no—
1277C22—22no—
1278C22—22no—
1279C22—22no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22C2×#53711yescharacteristic
1292C22C2×D4211yescharacteristic
1293C22#349711yescharacteristic
1294C22C22×#13711yescharacteristic
1295C22C2×#57511yescharacteristic
1296C22#358611yescharacteristic
1297C22#358611yescharacteristic
1298C4—22no—
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—22no—
1303C4—22no—
1304C4—22no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—42no—
1310C4—41no—
1311C4—41no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4#349611yescharacteristic
1327C4#349911yescharacteristic
1328C4#353611yescharacteristic
1329C4#355911yescharacteristic
1330C2—42no—
1331C2—161no—
1332C2#3935911yescharacteristic
1333C2#6091811yescharacteristic
1334C2#6093911yescharacteristic
1335C2#6106811yescharacteristic
1336C2D4×#13711yescharacteristic
1337C2#6239611yescharacteristic
1338C2#6239811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3255C2semidirect
4. #36133C2semidirect
6. #31242C2semidirect
7. #31240C2semidirect
8. #31213C2semidirect
9. #31211C2semidirect
10. #31163C2semidirect
11. #31159C2semidirect
12. #31151C2semidirect
13. #31149C2semidirect
15. #29783C2semidirect
16. #26476C2semidirect
17. #26473C2semidirect
18. #26056C2semidirect
19. #26054C2semidirect
21. #25504C2semidirect
22. #25504C2semidirect
24. #25382C2semidirect
25. #25379C2semidirect
26. #24760C2semidirect
28. #24746C2semidirect
29. #24741C2semidirect
30. #21539C2semidirect
31. #21146C2semidirect

Maximal subgroups

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

subgroupindex
C2×#32552
C2×#32522
#361402
#361332
#331862
#312422
#312402
#312132
#312112
#311632
#311592
#311512
#311492
#297842
#297832
#264762
#264732
#260562
#260542
#255052
#255042
#255032
#253822
#253792
#247602
#247572
#247462
#247412
#215392
#211462