Finite Group Databasebeta

← #7563009

Subgroups — #7563009

Order 512.

1768 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3371C211yesmaximal, characteristic
2C2×#3375C211yesmaximal, characteristic
3#45137C211yesmaximal, characteristic
4#35937C211yesmaximal, characteristic, complemented
5#30829C211yesmaximal, characteristic, complemented
6#30823C211yesmaximal, characteristic, complemented
7#30821C211yesmaximal, characteristic, complemented
8#30809C211yesmaximal, characteristic, complemented
9#28728C211yesmaximal, characteristic
10#28526C211yesmaximal, characteristic, complemented
11#27784C211yesmaximal, characteristic, complemented
12#27776C211yesmaximal, characteristic, complemented
13#26181C211yesmaximal, characteristic, complemented
14#26181C211yesmaximal, characteristic, complemented
15#26177C211yesmaximal, characteristic, complemented
16#26161C211yesmaximal, characteristic, complemented
17#26058C211yesmaximal, characteristic, complemented
18#26049C211yesmaximal, characteristic, complemented
19#25658C211yesmaximal, characteristic
20#25652C211yesmaximal, characteristic
21#25483C211yesmaximal, characteristic, complemented
22#25476C211yesmaximal, characteristic, complemented
23#24743C211yesmaximal, characteristic, complemented
24#24729C211yesmaximal, characteristic, complemented
25#24345C211yesmaximal, characteristic, complemented
26#24336C211yesmaximal, characteristic, complemented
27#23155C211yesmaximal, characteristic, complemented
28#22678C211yesmaximal, characteristic, complemented
29#22673C211yesmaximal, characteristic, complemented
30#21516C211yesmaximal, characteristic, complemented
31#21515C211yesmaximal, characteristic
32C2×#559C2211yescharacteristic
33C2×#559C2211yescharacteristic
34C2×Q82C2211yescharacteristic
35C2×#557C2211yescharacteristic
36#3375—28no—
37#3371—28no—
38C2×#490C2211yescharacteristic
39C2×#489C2211yescharacteristic
40C2×#489C2211yescharacteristic
41C2×#489C2211yescharacteristic
42C2×#488C2211yescharacteristic
43C2×#486C2211yescharacteristic
44C2×#479C2211yescharacteristic
45C2×#479C2211yescharacteristic
46C2×#477C2211yescharacteristic
47C2×#475C2211yescharacteristic
48C2×#478C2211yescharacteristic
49C2×#476C2211yescharacteristic
50C2×#474C2211yescharacteristic
51C2×#474C2211yescharacteristic
52C2×#464C2211yescharacteristic
53C2×#464C2211yescharacteristic
54C2×#464C2211yescharacteristic
55C2×#464C2211yescharacteristic
56C2×#462C2211yescharacteristic
57C2×#460C2211yescharacteristic
58C2×#446C2211yescharacteristic
59C2×#446C2211yescharacteristic
60C2×#441C2211yescharacteristic
61C2×#440C2211yescharacteristic
62C2×#440C2211yescharacteristic
63C2×#440C2211yescharacteristic
64C2×#440C2211yescharacteristic
65C2×C4×Q16C2211yescharacteristic
66C2×C4×SD16C2211yescharacteristic
67C2×C4×SD16C2211yescharacteristic
68#2717—21no—
69#2717—21no—
70#2717—21no—
71#2717—21no—
72#2660—21no—
73#2660C2211yescharacteristic
74#2584—21no—
75#2584C2211yescharacteristic
76#2581C2211yescharacteristic
77#2581C2211yescharacteristic
78#2551—21no—
79#2551—21no—
80#2551C2211yescharacteristic
81#2551C2211yescharacteristic
82#2550—21no—
83#2550—21no—
84#2550C2211yescharacteristic
85#2550C2211yescharacteristic
86#2547C2211yescharacteristic
87#2547C2211yescharacteristic
88#2546—21no—
89#2546C2211yescharacteristic
90#2447C2211yescharacteristic
91#2447C2211yescharacteristic
92#2447C2211yescharacteristic
93#2447C2211yescharacteristic
94#2419—21no—
95#2419—21no—
96#2419—21no—
97#2419—21no—
98#2399—21no—
99#2399C2211yescharacteristic
100#2351C2211yescharacteristic
101#2351C2211yescharacteristic
102Q8×C4⋊C4C2211yescharacteristic
103Q8×C4⋊C4C2211yescharacteristic
104#2349C2211yescharacteristic
105#2349C2211yescharacteristic
106#2328C2211yescharacteristic
107#2327C2211yescharacteristic
108#2276C2211yescharacteristic
109#2097C2211yescharacteristic
110#2097C2211yescharacteristic
111#2096C2211yescharacteristic
112#2095C2211yescharacteristic
113#2088C2211yescharacteristic
114#2087C2211yescharacteristic
115#2087C2211yescharacteristic
116#2086C2211yescharacteristic
117#2073C2211yescharacteristic
118#2073C2211yescharacteristic
119#2071C2211yescharacteristic
120#2071C2211yescharacteristic
121#2068C2211yescharacteristic
122#2068C2211yescharacteristic
123#2066C2211yescharacteristic
124#2066C2211yescharacteristic
125#2059C2211yescharacteristic
126#2058C2211yescharacteristic
127#2058C2211yescharacteristic
128#2057C2211yescharacteristic
129#2042C2211yescharacteristic
130#2042C2211yescharacteristic
131#2042C2211yescharacteristic
132#2042C2211yescharacteristic
133#2042C2211yescharacteristic
134#2042C2211yescharacteristic
135#2042C2211yescharacteristic
136#2042C2211yescharacteristic
137#2026C2211yescharacteristic
138#2024C2211yescharacteristic
139#2024C2211yescharacteristic
140#2024C2211yescharacteristic
141#1993C2211yescharacteristic
142#1991C2211yescharacteristic
143#1985C2211yescharacteristic
144#1984C2211yescharacteristic
145#1982C2211yescharacteristic
146#1981C2211yescharacteristic
147#1960C2211yescharacteristic
148#1956C2211yescharacteristic
149#1949C2211yescharacteristic
150#1949C2211yescharacteristic
151#1944C2211yescharacteristic
152#1944C2211yescharacteristic
153#1943C2211yescharacteristic
154#1942C2211yescharacteristic
155#1940C2211yescharacteristic
156#1939C2211yescharacteristic
157#1935C2211yescharacteristic
158#1935C2211yescharacteristic
159#1935C2211yescharacteristic
160#1933C2211yescharacteristic
161#1928C2211yescharacteristic
162#1927C2211yescharacteristic
163#1926C2211yescharacteristic
164#1925C2211yescharacteristic
165#1917C2211yescharacteristic
166#1917C2211yescharacteristic
167#1917C2211yescharacteristic
168#1916C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1864C2211yescharacteristic
185#1864C2211yescharacteristic
186#1863C2211yescharacteristic
187#1862C2211yescharacteristic
188#1862C2211yescharacteristic
189#1847C2211yescharacteristic
190#1846C2211yescharacteristic
191#1805C2211yescharacteristic
192#1805C2211yescharacteristic
193#1804C2211yescharacteristic
194#1804C2211yescharacteristic
195#1802C2211yescharacteristic
196#1802C2211yescharacteristic
197#1771C2211yescharacteristic
198#1770C2211yescharacteristic
199#1768C2211yescharacteristic
200#1768C2211yescharacteristic
201#1763C2211yescharacteristic
202#1762C2211yescharacteristic
203C4×#103C2211yescharacteristic
204C4×#102C2211yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209#559—24no—
210#559—24no—
211#559—42no—
212#559—42no—
213Q82—24no—
214Q82—42no—
215#557—24no—
216#557—42no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8—21no—
220C2×C4⋊Q8—21no—
221C2×C4⋊Q8—21no—
222C2×C4⋊Q8—21no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×#127C2311yescharacteristic
230C2×#125—21no—
231C2×#125—21no—
232C2×#125C2311yescharacteristic
233C2×#125C2311yescharacteristic
234C2×#124—21no—
235C2×#124—21no—
236C2×#124C2311yescharacteristic
237C2×#124C2311yescharacteristic
238C2×#124C2311yescharacteristic
239C2×#124C2311yescharacteristic
240C2×#123—21no—
241C2×#123—21no—
242C2×#123—21no—
243C2×#123—21no—
244C2×C4×Q8—21no—
245C2×C4×Q8—21no—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×D4—21no—
258C2×C4×D4—21no—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265#490—24no—
266#489—24no—
267#489—24no—
268#489—24no—
269#488—24no—
270#486—24no—
271#479—24no—
272#479—42no—
273#478—24no—
274#477—24no—
275#476—24no—
276#475—42no—
277#474—24no—
278#474—24no—
279#464—24no—
280#464—24no—
281#464—24no—
282#464—24no—
283#462—24no—
284#460D418yes—
285#446—24no—
286#446—24no—
287#441—24no—
288#440—24no—
289#440—24no—
290#440—24no—
291#440—24no—
292C4×Q16—24no—
293C4×SD16—24no—
294C4×SD16—24no—
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#97C2311yescharacteristic
348C2×#97C2311yescharacteristic
349C2×#97C2311yescharacteristic
350C2×#97C2311yescharacteristic
351C2×#97C2311yescharacteristic
352C2×C4×C8C2311yescharacteristic
353C2×C4×C8C2311yescharacteristic
354C2×C4×C8C2311yescharacteristic
355#400—21no—
356#400—21no—
357#398—21no—
358#398—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#398D411yescharacteristic
365#398D411yescharacteristic
366#398D411yescharacteristic
367#398D411yescharacteristic
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#397—21no—
377#397—21no—
378#397—21no—
379#397—21no—
380#395—21no—
381#395—21no—
382#395—21no—
383#395—21no—
384#395—21no—
385#395—21no—
386#395—21no—
387#395—21no—
388#395—21no—
389#395—21no—
390#395—21no—
391#395D411yescharacteristic
392#395D411yescharacteristic
393#395D411yescharacteristic
394#395D411yescharacteristic
395#391—21no—
396#391—21no—
397#391—21no—
398#391C2311yescharacteristic
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#389—21no—
407#389—21no—
408#389—21no—
409#389—21no—
410#389—21no—
411#389—21no—
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389—21no—
418#389—21no—
419#389—21no—
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#387—21no—
433#387—21no—
434#387—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—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#384—21no—
453#384—21no—
454#384C2311yescharacteristic
455#384C2311yescharacteristic
456#382—21no—
457#382—21no—
458#382C2311yescharacteristic
459#382C2311yescharacteristic
460#382C2311yescharacteristic
461#382C2311yescharacteristic
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#380—21no—
471#380—21no—
472C4×C4⋊C4—21no—
473C4×C4⋊C4—21no—
474C4×C4⋊C4—21no—
475C4×C4⋊C4—21no—
476C4×C4⋊C4—21no—
477C4×C4⋊C4—21no—
478C4×C4⋊C4—21no—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486#376—21no—
487#376C2311yescharacteristic
488C2×#95—21no—
489C2×#95—21no—
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#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518C22×Q8—21no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—21no—
522C22×Q8C2×D411yescharacteristic
523C22×Q8C2×D411yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×D4—21no—
528C22×D4—21no—
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C2×Q16—22no—
538C2×Q16—22no—
539C2×Q16—22no—
540C2×Q16—22no—
541C2×Q16—22no—
542C2×Q16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16C2×D414yes—
548C2×SD16C2×D414yes—
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C4⋊Q8—22no—
558C4⋊Q8—22no—
559C4⋊Q8—22no—
560C4⋊Q8—22no—
561C4⋊Q8—22no—
562C4⋊Q8—22no—
563C4⋊Q8—22no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566C4⋊Q8—41no—
567C4⋊Q8—44no—
568C4⋊Q8—44no—
569C4⋊Q8—44no—
570C4⋊Q8—44no—
571C4⋊Q8—82no—
572C4⋊Q8—82no—
573C4⋊Q8—82no—
574#127—22no—
575#127C2×D414yes—
576#125—22no—
577#125—22no—
578#125—22no—
579#125—41no—
580#125—44no—
581#125—44no—
582#124—22no—
583#124—22no—
584#124—22no—
585#124—22no—
586#124—41no—
587#124—41no—
588#124—41no—
589#124—41no—
590#124—44no—
591#124—44no—
592#123—44no—
593#123—44no—
594#123—44no—
595#123—44no—
596C4×Q8—22no—
597C4×Q8—22no—
598C4×Q8—22no—
599C4×Q8—22no—
600C4×Q8—22no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—22no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—22no—
611C4×Q8—22no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—44no—
617C4×Q8—44no—
618C4×Q8C2×D414yes—
619C4×Q8#4114yes—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—44no—
633C4×D4—44no—
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—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⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2×D411yescharacteristic
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×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731#107—22no—
732#107—22no—
733#107—22no—
734#107—22no—
735#107—22no—
736#107—41no—
737#106—22no—
738#106—22no—
739#106—22no—
740#106—41no—
741#106—41no—
742#106—41no—
743C4⋊C8—22no—
744C4⋊C8—22no—
745C4⋊C8—22no—
746C4⋊C8—22no—
747C4⋊C8—22no—
748C4⋊C8—22no—
749C4⋊C8—22no—
750C4⋊C8C2×D414yes—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—22no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
781#102C2×D414yes—
782#102C2×D414yes—
783#97—22no—
784#97—22no—
785#97—22no—
786#97—22no—
787#97—22no—
788C4×C8—22no—
789C4×C8—22no—
790C4×C8—22no—
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#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#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
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
838C24—21no—
839C24—21no—
840C2×Q8—22no—
841C2×Q8—22no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—41no—
858C2×Q8—41no—
859C2×Q8—41no—
860C2×Q8—41no—
861C2×Q8—42no—
862C2×Q8—42no—
863C2×Q8—42no—
864C2×Q8—42no—
865C2×Q8—42no—
866C2×Q8—81no—
867C2×Q8—81no—
868C2×Q8—81no—
869C2×Q8—81no—
870C2×Q8—81no—
871C2×Q8—81no—
872C2×Q8—81no—
873C2×Q8C22×D412yes—
874C2×Q8C2×#4112yes—
875C2×Q82−1+412yes—
876C2×D4—24no—
877C2×D4—24no—
878C2×D4—21no—
879C2×D4—21no—
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—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4C22×D412yes—
893C2×D4C22×D412yes—
894C22×C4—21no—
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—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C2511yescharacteristic
941Q16—44no—
942Q16—44no—
943SD16—28no—
944SD16—28no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
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×C8C22×D412yes—
968C2×C8C22×D412yes—
969C4⋊C4—24no—
970C4⋊C4—24no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—22no—
974C4⋊C4—22no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—24no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
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⋊C4C22×D412yes—
1038C4⋊C4C2×#4112yes—
1039C4⋊C42−1+412yes—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C42—24no—
1059C42—24no—
1060C42—24no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—42no—
1072C42—42no—
1073C42—42no—
1074C42—42no—
1075C42—42no—
1076C42—42no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42C22×D412yes—
1081C42C2×#4112yes—
1082C42H(5,𝔽2)12yes—
1083C422−1+412yes—
1084C23—22no—
1085C23—22no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23C23×D411yescharacteristic
1099Q8—22no—
1100Q8—22no—
1101Q8—22no—
1102Q8—44no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—82no—
1112Q8—84no—
1113Q8—162no—
1114Q8—162no—
1115Q8—162no—
1116Q8#54714yes—
1117D4—22no—
1118D4—22no—
1119D4—22no—
1120D4—22no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—84no—
1126D4—84no—
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—22no—
1136C2×C4—22no—
1137C2×C4—22no—
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—21no—
1147C2×C4—21no—
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—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—22no—
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—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—162no—
1208C2×C4—162no—
1209C2×C4—162no—
1210C2×C4—162no—
1211C2×C4—162no—
1212C2×C4—162no—
1213C2×C4D4212yes—
1214C2×C4D4212yes—
1215C2×C4#54812yes—
1216C2×C4#54812yes—
1217C2×C4C23×D411yescharacteristic
1218C2×C4C22×#4111yescharacteristic
1219C2×C4C2×H(5,𝔽2)11yescharacteristic
1220C2×C4C2×2−1+411yescharacteristic
1221C2×C4C2×2−1+411yescharacteristic
1222C2×C4C2×2−1+411yescharacteristic
1223C8—22no—
1224C8—22no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C8—41no—
1229C8—41no—
1230C8—41no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22C2×D4211yescharacteristic
1246C22C2×#54811yescharacteristic
1247C22#348611yescharacteristic
1248C22#358411yescharacteristic
1249C22#358511yescharacteristic
1250C22#358611yescharacteristic
1251C22#358611yescharacteristic
1252C4—22no—
1253C4—22no—
1254C4—22no—
1255C4—22no—
1256C4—24no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—42no—
1266C4—42no—
1267C4—41no—
1268C4—41no—
1269C4—42no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4C2×#54711yescharacteristic
1281C4#349911yescharacteristic
1282C4#351111yescharacteristic
1283C4#355211yescharacteristic
1284C2—82no—
1285C2—82no—
1286C2#5912511yescharacteristic
1287C2#6106011yescharacteristic
1288C2#6107411yescharacteristic
1289C2#6133611yescharacteristic
1290C2#6134411yescharacteristic
1291C2#6185611yescharacteristic
1292C2#6187911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#127C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #35937C2semidirect
5. #30829C2semidirect
6. #30823C2semidirect
7. #30821C2semidirect
8. #30809C2semidirect
10. #28526C2semidirect
11. #27784C2semidirect
12. #27776C2semidirect
13. #26181C2semidirect
14. #26181C2semidirect
15. #26177C2semidirect
16. #26161C2semidirect
17. #26058C2semidirect
18. #26049C2semidirect
21. #25483C2semidirect
22. #25476C2semidirect
23. #24743C2semidirect
24. #24729C2semidirect
25. #24345C2semidirect
26. #24336C2semidirect
27. #23155C2semidirect
28. #22678C2semidirect
29. #22673C2semidirect
30. #21516C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33712
C2×#33752
#451372
#359372
#308292
#308232
#308212
#308092
#287282
#285262
#277842
#277762
#261812
#261772
#261612
#260582
#260492
#256582
#256522
#254832
#254762
#247432
#247292
#243452
#243362
#231552
#226782
#226732
#215162
#215152