Finite Group Databasebeta

← #6644822

Subgroups — #6644822

Order 512.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1285 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37524C211yesmaximal, characteristic, complemented
2#35529C211yesmaximal, characteristic, complemented
3#33018C211yesmaximal, characteristic, complemented
4#33014C211yesmaximal, characteristic
5#32457C211yesmaximal, characteristic, complemented
6#32450C211yesmaximal, characteristic, complemented
7#32431C211yesmaximal, characteristic, complemented
8#32428C211yesmaximal, characteristic, complemented
9#32371C211yesmaximal, characteristic, complemented
10#32366C211yesmaximal, characteristic, complemented
11#32349C211yesmaximal, characteristic, complemented
12#32344C211yesmaximal, characteristic, complemented
13#31654C211yesmaximal, characteristic, complemented
14#31651C211yesmaximal, characteristic, complemented
15#31646C211yesmaximal, characteristic, complemented
16#31643C211yesmaximal, characteristic, complemented
17#31538C211yesmaximal, characteristic, complemented
18#31537C211yesmaximal, characteristic, complemented
19#31530C211yesmaximal, characteristic, complemented
20#31529C211yesmaximal, characteristic, complemented
21#29648C211yesmaximal, characteristic, complemented
22#29647C211yesmaximal, characteristic, complemented
23#29115C211yesmaximal, characteristic, complemented
24#28321C211yesmaximal, characteristic
25#28120C211yesmaximal, characteristic, complemented
26#28117C211yesmaximal, characteristic
27#27970C211yesmaximal, characteristic, complemented
28#27920C211yesmaximal, characteristic, complemented
29#27652C211yesmaximal, characteristic, complemented
30#27646C211yesmaximal, characteristic, complemented
31#21921C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×#481C2211yescharacteristic
35C2×#485C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#482C2211yescharacteristic
39C2×#483C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#447C2211yescharacteristic
42#2827—21no—
43#2827—21no—
44#2667—21no—
45#2664—21no—
46#2654—21no—
47#2652—21no—
48#2629C2211yescharacteristic
49#2625C2211yescharacteristic
50#2624C2211yescharacteristic
51#2620C2211yescharacteristic
52#2566C2211yescharacteristic
53#2566C2211yescharacteristic
54#2566C2211yescharacteristic
55#2566C2211yescharacteristic
56#2563C2211yescharacteristic
57#2563C2211yescharacteristic
58#2542C2211yescharacteristic
59#2542C2211yescharacteristic
60#2512C2211yescharacteristic, complemented
61#2511C2211yescharacteristic, complemented
62#2507C2211yescharacteristic, complemented
63#2506C2211yescharacteristic, complemented
64#2466—21no—
65#2460—21no—
66#2454—21no—
67#2454—21no—
68#2454C2211yescharacteristic, complemented
69#2453C2211yescharacteristic, complemented
70#2452—21no—
71#2452—21no—
72#2448C2211yescharacteristic, complemented
73#2447C2211yescharacteristic, complemented
74#2437—21no—
75#2437—21no—
76#2437—21no—
77#2437—21no—
78#2317C2211yescharacteristic
79#2309C2211yescharacteristic
80C4×C22⋊Q8C2211yescharacteristic
81C4×#121C2211yescharacteristic
82#2296C2211yescharacteristic
83C2×#390C2211yescharacteristic
84#2285C2211yescharacteristic
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2100C2211yescharacteristic, complemented
88#2099C2211yescharacteristic, complemented
89#2097C2211yescharacteristic, complemented
90#2096C2211yescharacteristic, complemented
91#2094C2211yescharacteristic
92#2094C2211yescharacteristic, complemented
93#2093C2211yescharacteristic
94#2092C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2083C2211yescharacteristic, complemented
99#2073C2211yescharacteristic, complemented
100#2073C2211yescharacteristic, complemented
101#2072C2211yescharacteristic, complemented
102#2072C2211yescharacteristic, complemented
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2059C2211yescharacteristic, complemented
110#2059C2211yescharacteristic, complemented
111#2059C2211yescharacteristic, complemented
112#2059C2211yescharacteristic, complemented
113#2058C2211yescharacteristic, complemented
114#2058C2211yescharacteristic, complemented
115#2058C2211yescharacteristic, complemented
116#2058C2211yescharacteristic, complemented
117#2055C2211yescharacteristic
118#2055C2211yescharacteristic
119#2054C2211yescharacteristic
120#2054C2211yescharacteristic
121#2026C2211yescharacteristic, complemented
122#2026C2211yescharacteristic, complemented
123#2025C2211yescharacteristic
124#2025C2211yescharacteristic
125#2025C2211yescharacteristic, complemented
126#2025C2211yescharacteristic, complemented
127#2024C2211yescharacteristic, complemented
128#2024C2211yescharacteristic, complemented
129#2023C2211yescharacteristic, complemented
130#2023C2211yescharacteristic, complemented
131#2012C2211yescharacteristic
132#2012C2211yescharacteristic
133#1992C2211yescharacteristic, complemented
134#1991C2211yescharacteristic, complemented
135#1973C2211yescharacteristic
136#1972C2211yescharacteristic
137#1970C2211yescharacteristic
138#1968C2211yescharacteristic
139#1959C2211yescharacteristic, complemented
140#1958C2211yescharacteristic, complemented
141#1949C2211yescharacteristic, complemented
142#1949C2211yescharacteristic, complemented
143#1948C2211yescharacteristic, complemented
144#1947C2211yescharacteristic, complemented
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1917C2211yescharacteristic, complemented
154#1917C2211yescharacteristic, complemented
155#1917C2211yescharacteristic, complemented
156#1917C2211yescharacteristic, complemented
157#1916C2211yescharacteristic, complemented
158#1916C2211yescharacteristic, complemented
159#1916C2211yescharacteristic, complemented
160#1916C2211yescharacteristic, complemented
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic
172#1877C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1847C2211yescharacteristic, complemented
182#1844C2211yescharacteristic, complemented
183#1836C2211yescharacteristic, complemented
184#1834C2211yescharacteristic, complemented
185#1825C2211yescharacteristic
186#1825C2211yescharacteristic
187#1825C2211yescharacteristic
188#1825C2211yescharacteristic
189#1824C2211yescharacteristic
190#1823C2211yescharacteristic
191#1818C2211yescharacteristic
192#1818C2211yescharacteristic
193#1805C2211yescharacteristic, complemented
194#1805C2211yescharacteristic, complemented
195#1802C2211yescharacteristic, complemented
196#1802C2211yescharacteristic, complemented
197#1797C2211yescharacteristic
198#1797C2211yescharacteristic
199#1786C2211yescharacteristic
200#1786C2211yescharacteristic
201#1750C2211yescharacteristic
202#1750C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208#544—42no—
209#544—42no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#126—21no—
214C2×#125—21no—
215C2×#125—21no—
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×#121C2311yescharacteristic
228#518—42no—
229#518—42no—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C22⋊C4—21no—
245C22×C22⋊C4—21no—
246C22×C22⋊C4—21no—
247C22×C22⋊C4—21no—
248C22×C42C2311yescharacteristic
249#485—42no—
250#485—42no—
251#483—42no—
252#482—42no—
253#482—42no—
254#481—42no—
255#450—42no—
256#447—42no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#399—21no—
311#399—21no—
312#399—21no—
313#399—21no—
314#399—21no—
315#399—21no—
316#399—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#393—21no—
350#393—21no—
351#393—21no—
352#393—21no—
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#390—21no—
358#390—21no—
359#390—21no—
360#390—21no—
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389D411yescharacteristic
378#389D411yescharacteristic
379#389D411yescharacteristic
380#389D411yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#386—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385D411yescharacteristic
414#385D411yescharacteristic
415#385D411yescharacteristic
416#385D411yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#381—21no—
428#380—21no—
429#380—21no—
430#380—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#379—21no—
438#379—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8C2411yescharacteristic
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2411yescharacteristic
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×D8—22no—
521C2×D8—22no—
522C2×D8—41no—
523C2×D8—41no—
524C2×D8—41no—
525C2×D8—41no—
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—44no—
539#126—82no—
540#125—41no—
541#125—41no—
542#125—41no—
543#125—41no—
544#125—41no—
545#125—41no—
546#125—44no—
547#125—82no—
548#124—41no—
549#124—41no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—44no—
553C22⋊Q8—44no—
554C22⋊Q8—82no—
555C22⋊Q8—82no—
556C22⋊Q8—82no—
557C22⋊Q8—82no—
558#121—22no—
559#121—22no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—44no—
573C4×D4—44no—
574C4×D4—82no—
575#117—22no—
576#117—22no—
577#117—22no—
578#117—22no—
579#117—22no—
580#117—22no—
581#117—41no—
582#117—41no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—44no—
678C2×C22⋊C4—44no—
679C2×C22⋊C4—82no—
680C2×C22⋊C4—82no—
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—41no—
691C2×C42—41no—
692C2×C42C2×D411yescharacteristic
693C2×C42C2×D411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700#107—41no—
701#107—41no—
702#107—41no—
703#107—41no—
704#106—41no—
705#106—41no—
706#106—41no—
707#106—41no—
708#106—41no—
709#106—41no—
710#106—41no—
711#106—41no—
712C4⋊C8—41no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740C22⋊C8—22no—
741C22⋊C8—22no—
742C22⋊C8—22no—
743C22⋊C8—22no—
744#97—41no—
745#97—41no—
746C4×C8—41no—
747C4×C8—41no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784C24—24no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—42no—
789C24—42no—
790C24—81no—
791C24—81no—
792C24—81no—
793C24—81no—
794C24C22×D411yescharacteristic
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—42no—
802C2×Q8—42no—
803C2×Q8—81no—
804C2×Q8—81no—
805C2×Q8—81no—
806C2×Q8—81no—
807C2×D4—24no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—44no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D42−1+412yes—
834C2×D42−1+412yes—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—41no—
854C22×C4—41no—
855C22×C4—41no—
856C22×C4—41no—
857C22×C4—41no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—81no—
865C22×C4—81no—
866C22×C4—81no—
867C22×C4—81no—
868C22×C4—81no—
869C22×C4—81no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4H(5,𝔽2)12yes—
890C22×C4H(5,𝔽2)12yes—
891C22×C4C2511yescharacteristic
892SD16—82no—
893SD16—82no—
894D8—82no—
895D8—82no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—41no—
949C4⋊C4—41no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—41no—
1041C42—41no—
1042C42—42no—
1043C42—42no—
1044C42—42no—
1045C42—81no—
1046C42—81no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—22no—
1054C23—22no—
1055C23—48no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—84no—
1076C23—84no—
1077C23—162no—
1078C23—162no—
1079C23—162no—
1080C23—162no—
1081C23#53512yes—
1082C23C23×D411yescharacteristic
1083Q8—41no—
1084Q8—41no—
1085Q8—41no—
1086Q8—41no—
1087Q8—162no—
1088Q8—162no—
1089D4—22no—
1090D4—22no—
1091D4—22no—
1092D4—22no—
1093D4—48no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—41no—
1098D4—41no—
1099D4—41no—
1100D4—41no—
1101D4—41no—
1102D4—84no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
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—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
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—82no—
1184C2×C4—82no—
1185C2×C4—162no—
1186C2×C4—162no—
1187C2×C4—162no—
1188C2×C4—162no—
1189C2×C4—162no—
1190C2×C4—162no—
1191C2×C4#53512yes—
1192C2×C4#57712yes—
1193C2×C4C2×H(5,𝔽2)11yescharacteristic
1194C2×C4C2×H(5,𝔽2)11yescharacteristic
1195C2×C4C2×2−1+411yescharacteristic
1196C2×C4C2×2−1+411yescharacteristic
1197C2×C4#58511yescharacteristic
1198C2×C4#58511yescharacteristic
1199C8—41no—
1200C8—41no—
1201C8—41no—
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—168no—
1236C22C2×#53511yescharacteristic
1237C22#348511yescharacteristic
1238C22#348611yescharacteristic
1239C22C2×#57711yescharacteristic
1240C22#358411yescharacteristic
1241C22#358511yescharacteristic
1242C22#358511yescharacteristic
1243C4—22no—
1244C4—22no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4#353511yescharacteristic
1270C4#353511yescharacteristic
1271C4#353511yescharacteristic
1272C4#353511yescharacteristic
1273C2—42no—
1274C2—82no—
1275C2—82no—
1276C2—161no—
1277C2#3711811yescharacteristic
1278C2#6083311yescharacteristic
1279C2#6083411yescharacteristic
1280C2#6175811yescharacteristic
1281C2#6176111yescharacteristic
1282C2#6186411yescharacteristic
1283C2#6187211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37524C2semidirect
2. #35529C2semidirect
3. #33018C2semidirect
5. #32457C2semidirect
6. #32450C2semidirect
7. #32431C2semidirect
8. #32428C2semidirect
9. #32371C2semidirect
10. #32366C2semidirect
11. #32349C2semidirect
12. #32344C2semidirect
13. #31654C2semidirect
14. #31651C2semidirect
15. #31646C2semidirect
16. #31643C2semidirect
17. #31538C2semidirect
18. #31537C2semidirect
19. #31530C2semidirect
20. #31529C2semidirect
21. #29648C2semidirect
22. #29647C2semidirect
23. #29115C2semidirect
25. #28120C2semidirect
27. #27970C2semidirect
28. #27920C2semidirect
29. #27652C2semidirect
30. #27646C2semidirect
31. #21921C2semidirect
60. #2512C22semidirect
61. #2511C22semidirect
62. #2507C22semidirect
63. #2506C22semidirect
68. #2454C22semidirect
69. #2453C22semidirect
72. #2448C22semidirect
73. #2447C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2100C22semidirect
88. #2099C22semidirect
89. #2097C22semidirect
90. #2096C22semidirect
92. #2094C22semidirect
94. #2092C22semidirect
95. #2085C22semidirect
96. #2085C22semidirect
97. #2084C22semidirect
98. #2083C22semidirect
99. #2073C22semidirect
100. #2073C22semidirect
101. #2072C22semidirect
102. #2072C22semidirect
109. #2059C22semidirect
110. #2059C22semidirect
111. #2059C22semidirect
112. #2059C22semidirect
113. #2058C22semidirect
114. #2058C22semidirect
115. #2058C22semidirect
116. #2058C22semidirect
121. #2026C22semidirect
122. #2026C22semidirect
125. #2025C22semidirect
126. #2025C22semidirect
127. #2024C22semidirect
128. #2024C22semidirect
129. #2023C22semidirect
130. #2023C22semidirect
133. #1992C22semidirect
134. #1991C22semidirect
139. #1959C22semidirect
140. #1958C22semidirect
141. #1949C22semidirect
142. #1949C22semidirect
143. #1948C22semidirect
144. #1947C22semidirect
153. #1917C22semidirect
154. #1917C22semidirect
155. #1917C22semidirect
156. #1917C22semidirect
157. #1916C22semidirect
158. #1916C22semidirect
159. #1916C22semidirect
160. #1916C22semidirect
181. #1847C22semidirect
182. #1844C22semidirect
183. #1836C22semidirect
184. #1834C22semidirect
193. #1805C22semidirect
194. #1805C22semidirect
195. #1802C22semidirect
196. #1802C22semidirect

Maximal subgroups

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

subgroupindex
#375242
#355292
#330182
#330142
#324572
#324502
#324312
#324282
#323712
#323662
#323492
#323442
#316542
#316512
#316462
#316432
#315382
#315372
#315302
#315292
#296482
#296472
#291152
#283212
#281202
#281172
#279702
#279202
#276522
#276462
#219212