Finite Group Databasebeta

← #6608057

Subgroups — #6608057

Order 512.

1671 conjugacy classes of subgroups.

The subgroup lattice has 1355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38255C211yesmaximal, characteristic, complemented
2#38250C211yesmaximal, characteristic, complemented
3#33274C211yesmaximal, characteristic, complemented
4#33251C211yesmaximal, characteristic, complemented
5#33132C211yesmaximal, characteristic, complemented
6#29556C211yesmaximal, characteristic, complemented
7#29555C211yesmaximal, characteristic, complemented
8#29510C211yesmaximal, characteristic, complemented
9#29504C211yesmaximal, characteristic, complemented
10#28877C211yesmaximal, characteristic, complemented
11#28876C211yesmaximal, characteristic, complemented
12#28018C211yesmaximal, characteristic, complemented
13#27285C211yesmaximal, characteristic, complemented
14#27279C211yesmaximal, characteristic, complemented
15#26842C211yesmaximal, characteristic, complemented
16#26841C211yesmaximal, characteristic, complemented
17#26486C211yesmaximal, characteristic, complemented
18#26258C211yesmaximal, characteristic, complemented
19#26257C211yesmaximal, characteristic, complemented
20#26070C211yesmaximal, characteristic, complemented
21#25783C211yesmaximal, characteristic
22#24518C211yesmaximal, characteristic, complemented
23#24512C211yesmaximal, characteristic, complemented
24#23027C211yesmaximal, characteristic, complemented
25#22868C211yesmaximal, characteristic, complemented
26#22865C211yesmaximal, characteristic, complemented
27C22⋊C4×SD16C211yesmaximal, characteristic, complemented
28#21704C211yesmaximal, characteristic, complemented
29#21279C211yesmaximal, characteristic, complemented
30#21231C211yesmaximal, characteristic, complemented
31#20478C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#501C2211yescharacteristic, complemented
34C2×#496C2211yescharacteristic
35C2×#496C2211yescharacteristic
36C2×#490C2211yescharacteristic
37C2×#489C2211yescharacteristic, complemented
38C2×#466C2211yescharacteristic
39C2×#448C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#442C2211yescharacteristic
42C2×#440C2211yescharacteristic, complemented
43C2×C4×SD16C2211yescharacteristic
44C2×C4×SD16C2211yescharacteristic
45C2×C4×D8C2211yescharacteristic, complemented
46C2×#433C2211yescharacteristic
47C2×#427C2211yescharacteristic
48C2×#419C2211yescharacteristic
49C2×#418C2211yescharacteristic
50C2×#405C2211yescharacteristic
51#2861C2211yescharacteristic, complemented
52#2858C2211yescharacteristic
53#2798—21no—
54#2798—21no—
55#2797—21no—
56#2746—21no—
57#2743—21no—
58#2730—21no—
59#2697—21no—
60#2684—21no—
61#2645C2211yescharacteristic, complemented
62#2644C2211yescharacteristic
63#2624C2211yescharacteristic
64#2624C2211yescharacteristic
65#2589—21no—
66#2557—21no—
67#2527—21no—
68#2526—21no—
69#2516—21no—
70#2513C2211yescharacteristic
71#2511C2211yescharacteristic, complemented
72#2472—21no—
73#2471—21no—
74#2453C2211yescharacteristic, complemented
75#2452C2211yescharacteristic
76#2448C2211yescharacteristic, complemented
77#2447C2211yescharacteristic, complemented
78#2445C2211yescharacteristic
79#2445C2211yescharacteristic
80#2441C2211yescharacteristic
81#2439C2211yescharacteristic
82#2436C2211yescharacteristic
83#2433C2211yescharacteristic
84#2411—21no—
85#2363C2211yescharacteristic
86#2363C2211yescharacteristic
87Q8×C22⋊C4C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89#2328C2211yescharacteristic
90#2326C2211yescharacteristic, complemented
91#2310C2211yescharacteristic
92#2309C2211yescharacteristic
93#2298C2211yescharacteristic
94#2295C2211yescharacteristic, complemented
95#2293C2211yescharacteristic
96#2085C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2074C2211yescharacteristic, complemented
99#2071C2211yescharacteristic
100#2068C2211yescharacteristic, complemented
101#2067C2211yescharacteristic
102#2066C2211yescharacteristic, complemented
103#2065C2211yescharacteristic
104#2059C2211yescharacteristic, complemented
105#2058C2211yescharacteristic, complemented
106#2055C2211yescharacteristic, complemented
107#2055C2211yescharacteristic, complemented
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic
110#2042C2211yescharacteristic, complemented
111#2042C2211yescharacteristic, complemented
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2025C2211yescharacteristic
115#2024C2211yescharacteristic, complemented
116#2014C2211yescharacteristic
117#2014C2211yescharacteristic
118#2012C2211yescharacteristic
119#2012C2211yescharacteristic
120#1973C2211yescharacteristic
121#1973C2211yescharacteristic
122#1973C2211yescharacteristic
123#1973C2211yescharacteristic
124#1973C2211yescharacteristic
125#1973C2211yescharacteristic
126#1973C2211yescharacteristic, complemented
127#1972C2211yescharacteristic
128#1972C2211yescharacteristic, complemented
129#1972C2211yescharacteristic, complemented
130#1970C2211yescharacteristic
131#1970C2211yescharacteristic
132#1970C2211yescharacteristic, complemented
133#1968C2211yescharacteristic
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1968C2211yescharacteristic, complemented
140#1968C2211yescharacteristic, complemented
141#1958C2211yescharacteristic, complemented
142#1957C2211yescharacteristic
143#1944C2211yescharacteristic, complemented
144#1944C2211yescharacteristic, complemented
145#1944C2211yescharacteristic, complemented
146#1943C2211yescharacteristic, complemented
147#1942C2211yescharacteristic, complemented
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1935C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1935C2211yescharacteristic, complemented
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1934C2211yescharacteristic, complemented
157#1934C2211yescharacteristic, complemented
158#1934C2211yescharacteristic, complemented
159#1934C2211yescharacteristic, complemented
160#1933C2211yescharacteristic, complemented
161#1933C2211yescharacteristic, complemented
162#1928C2211yescharacteristic, complemented
163#1926C2211yescharacteristic
164#1926C2211yescharacteristic, complemented
165#1926C2211yescharacteristic, complemented
166#1895C2211yescharacteristic
167#1895C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic, complemented
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic, complemented
176#1875C2211yescharacteristic
177#1875C2211yescharacteristic
178#1865C2211yescharacteristic, complemented
179#1864C2211yescharacteristic, complemented
180#1864C2211yescharacteristic, complemented
181#1862C2211yescharacteristic
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1847C2211yescharacteristic, complemented
185#1807C2211yescharacteristic
186#1787C2211yescharacteristic
187#1786C2211yescharacteristic
188C4×#107C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1771C2211yescharacteristic, complemented
191#1770C2211yescharacteristic, complemented
192C8×C4⋊C4C2211yescharacteristic, complemented
193C4×#103C2211yescharacteristic, complemented
194C4×#102C2211yescharacteristic
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1752C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199#1746C2211yescharacteristic, complemented
200#1744C2211yescharacteristic, complemented
201#1726C2211yescharacteristic, complemented
202C4×#97C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16—24no—
206C22×SD16—24no—
207C22×SD16—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#124—21no—
224C2×#124—21no—
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×#123—21no—
229C2×C22⋊Q8—21no—
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#120—21no—
233C2×#120—21no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C22×C22⋊C4—21no—
245#501—42no—
246#496—24no—
247#496—42no—
248#490—42no—
249#489—42no—
250#466—24no—
251#448—24no—
252#447—24no—
253#442—42no—
254#440—42no—
255C4×SD16—24no—
256C4×SD16—42no—
257C4×D8—42no—
258#433—24no—
259#427—42no—
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273#419—42no—
274#418—42no—
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307#405—24no—
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#401—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#399—21no—
330#399—21no—
331#399—21no—
332#399—21no—
333#398—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#393—21no—
357#393—21no—
358#393—21no—
359#393—21no—
360#392—21no—
361#392—21no—
362#391—21no—
363#391—21no—
364#391—21no—
365#391—21no—
366#391—21no—
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#390—21no—
376#390—21no—
377#390—21no—
378#390—21no—
379#390—21no—
380#390—21no—
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#389—21no—
396#389—21no—
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388D411yescharacteristic
422#388D411yescharacteristic
423#388D411yescharacteristic
424#388D411yescharacteristic
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387D411yescharacteristic
433#387D411yescharacteristic
434#387D411yescharacteristic
435#387D411yescharacteristic
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#386—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#384C2311yescharacteristic
453#382C2311yescharacteristic
454#381—21no—
455#381—21no—
456#381—21no—
457#380—21no—
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#379—21no—
461#379—21no—
462#379—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
474#376—21no—
475#376C2311yescharacteristic
476C43C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—22no—
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C2411yescharacteristic
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—416no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16#4114yes—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×M16—22no—
562C2×M16—22no—
563C2×M16—41no—
564C22×C8—22no—
565C22×C8—22no—
566C22×C8#4114yes—
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577#127—22no—
578#127—41no—
579#127—41no—
580#127—41no—
581#125—41no—
582#125—41no—
583#124—22no—
584#124—41no—
585#124—41no—
586#124—41no—
587#124—82no—
588#124—82no—
589#123—82no—
590#123—82no—
591C22⋊Q8—82no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#120—82no—
597#120—82no—
598C4×Q8—22no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×D4—22no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610#117—22no—
611#117—22no—
612#117—41no—
613#117—41no—
614#117—41no—
615#117—41no—
616#117—82no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
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—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—82no—
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42C2×D411yescharacteristic
706C2×C42C2×D411yescharacteristic
707C2×C42C2×D411yescharacteristic
708C2×C42C2×D411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715#107—22no—
716#107—22no—
717#107—22no—
718#107—41no—
719#107—41no—
720#106—22no—
721#106—22no—
722#106—41no—
723#106—41no—
724#106—41no—
725#106—41no—
726C4⋊C8—22no—
727C4⋊C8—22no—
728#103—22no—
729#103—22no—
730#103—22no—
731#103—22no—
732#103—22no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758C22⋊C8—22no—
759C22⋊C8#4114yes—
760#97—22no—
761#97—22no—
762#97—22no—
763#97—22no—
764#97—22no—
765#97—22no—
766#97—22no—
767C4×C8—22no—
768C4×C8—22no—
769C4×C8—22no—
770C4×C8—22no—
771C4×C8—22no—
772C4×C8—41no—
773C4×C8—41no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—42no—
823C24—42no—
824C24—81no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24C22×D411yescharacteristic
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—42no—
842C2×Q8—42no—
843C2×Q8—44no—
844C2×Q8—44no—
845C2×Q8—42no—
846C2×Q8—81no—
847C2×Q8—81no—
848C2×Q8—81no—
849C2×Q8—82no—
850C2×Q8—82no—
851C2×Q8C2×#4112yes—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—82no—
886C2×D4—82no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4C2×#4112yes—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
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×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C2×#4112yes—
946C22×C4C2×#4112yes—
947C22×C4C2511yescharacteristic
948SD16—28no—
949SD16—44no—
950SD16—44no—
951SD16—44no—
952SD16—44no—
953SD16—82no—
954D8—44no—
955D8—44no—
956D8—82no—
957M16—44no—
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—28no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8C2×#4112yes—
977C2×C8C2×#4112yes—
978C2×C8C2×#4112yes—
979C2×C8C2×#4112yes—
980C2×C8C2×#4112yes—
981C2×C8H(5,𝔽2)12yes—
982C2×C8H(5,𝔽2)12yes—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—22no—
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—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C42—22no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—41no—
1088C42—41no—
1089C42—41no—
1090C42—42no—
1091C42—81no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—22no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—84no—
1131C23—84no—
1132C23—162no—
1133C23—162no—
1134C23—162no—
1135C23—162no—
1136C23—162no—
1137C23#53212yes—
1138C23C23×D411yescharacteristic
1139Q8—22no—
1140Q8—22no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—84no—
1148Q8—162no—
1149D4—22no—
1150D4—22no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—84no—
1166D4—162no—
1167D4—162no—
1168D4—162no—
1169D4—162no—
1170D4—162no—
1171D4—162no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
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—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
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—84no—
1250C2×C4—84no—
1251C2×C4—162no—
1252C2×C4—162no—
1253C2×C4—162no—
1254C2×C4#53212yes—
1255C2×C4#57712yes—
1256C2×C4C22×#4111yescharacteristic
1257C2×C4C22×#4111yescharacteristic
1258C2×C4C22×#4111yescharacteristic
1259C2×C4C2×H(5,𝔽2)11yescharacteristic
1260C2×C4C2×H(5,𝔽2)11yescharacteristic
1261C2×C4#58511yescharacteristic
1262C8—22no—
1263C8—22no—
1264C8—22no—
1265C8—22no—
1266C8—41no—
1267C8—41no—
1268C8—41no—
1269C8#55114yes—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—168no—
1306C22C2×#53211yescharacteristic
1307C22D4×#4111yescharacteristic
1308C22#349811yescharacteristic
1309C22C2×#57711yescharacteristic
1310C22#358411yescharacteristic
1311C22#358511yescharacteristic
1312C22#358511yescharacteristic
1313C4—22no—
1314C4—22no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—42no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4C2×#55111yescharacteristic
1339C4#348111yescharacteristic
1340C4#349411yescharacteristic
1341C4#351411yescharacteristic
1342C2—42no—
1343C2—82no—
1344C2—161no—
1345C2—161no—
1346C2—161no—
1347C2#3626411yescharacteristic
1348C2#6069411yescharacteristic
1349C2#6071911yescharacteristic
1350C2#6152111yescharacteristic
1351C2#6152711yescharacteristic
1352C2#6246511yescharacteristic
1353C2#6246811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25783C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38255C2semidirect
2. #38250C2semidirect
3. #33274C2semidirect
4. #33251C2semidirect
5. #33132C2semidirect
6. #29556C2semidirect
7. #29555C2semidirect
8. #29510C2semidirect
9. #29504C2semidirect
10. #28877C2semidirect
11. #28876C2semidirect
12. #28018C2semidirect
13. #27285C2semidirect
14. #27279C2semidirect
15. #26842C2semidirect
16. #26841C2semidirect
17. #26486C2semidirect
18. #26258C2semidirect
19. #26257C2semidirect
20. #26070C2semidirect
22. #24518C2semidirect
23. #24512C2semidirect
24. #23027C2semidirect
25. #22868C2semidirect
26. #22865C2semidirect
27. C22⋊C4×SD16C2semidirect
28. #21704C2semidirect
29. #21279C2semidirect
30. #21231C2semidirect
31. #20478C2semidirect
33. C2×#501C22semidirect
37. C2×#489C22semidirect
42. C2×#440C22semidirect
45. C2×C4×D8C22semidirect
51. #2861C22semidirect
61. #2645C22semidirect
71. #2511C22semidirect
74. #2453C22semidirect
76. #2448C22semidirect
77. #2447C22semidirect
90. #2326C22semidirect
94. #2295C22semidirect
96. #2085C22semidirect
97. #2084C22semidirect
98. #2074C22semidirect
100. #2068C22semidirect
102. #2066C22semidirect
104. #2059C22semidirect
105. #2058C22semidirect
106. #2055C22semidirect
107. #2055C22semidirect
110. #2042C22semidirect
111. #2042C22semidirect
115. #2024C22semidirect
126. #1973C22semidirect
128. #1972C22semidirect
129. #1972C22semidirect
132. #1970C22semidirect
139. #1968C22semidirect
140. #1968C22semidirect
141. #1958C22semidirect
143. #1944C22semidirect
144. #1944C22semidirect
145. #1944C22semidirect
146. #1943C22semidirect
147. #1942C22semidirect
151. #1935C22semidirect
152. #1935C22semidirect
153. #1935C22semidirect
156. #1934C22semidirect
157. #1934C22semidirect
158. #1934C22semidirect
159. #1934C22semidirect
160. #1933C22semidirect
161. #1933C22semidirect
162. #1928C22semidirect
164. #1926C22semidirect
165. #1926C22semidirect
170. #1880C22semidirect
175. #1877C22semidirect
178. #1865C22semidirect
179. #1864C22semidirect
180. #1864C22semidirect
184. #1847C22semidirect
188. C4×#107C22semidirect
189. #1771C22semidirect
190. #1771C22semidirect
191. #1770C22semidirect
192. C8×C4⋊C4C22semidirect
193. C4×#103C22semidirect
199. #1746C22semidirect
200. #1744C22semidirect
201. #1726C22semidirect
202. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
#382552
#382502
#332742
#332512
#331322
#295562
#295552
#295102
#295042
#288772
#288762
#280182
#272852
#272792
#268422
#268412
#264862
#262582
#262572
#260702
#257832
#245182
#245122
#230272
#228682
#228652
C22⋊C4×SD162
#217042
#212792
#212312
#204782