Finite Group Databasebeta

← #6560373

Subgroups — #6560373

Order 512.

1598 conjugacy classes of subgroups.

The subgroup lattice has 1307 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38112C211yesmaximal, characteristic
2#37705C211yesmaximal, characteristic, complemented
3#30373C211yesmaximal, characteristic, complemented
4#30355C211yesmaximal, characteristic, complemented
5#30190C211yesmaximal, characteristic, complemented
6#29568C211yesmaximal, characteristic, complemented
7#29529C211yesmaximal, characteristic, complemented
8#29168C211yesmaximal, characteristic, complemented
9#29102C211yesmaximal, characteristic, complemented
10#29078C211yesmaximal, characteristic, complemented
11#29004C211yesmaximal, characteristic, complemented
12#28980C211yesmaximal, characteristic, complemented
13#28302C211yesmaximal, characteristic, complemented
14#27801C211yesmaximal, characteristic, complemented
15#27788C211yesmaximal, characteristic, complemented
16#26494C211yesmaximal, characteristic, complemented
17#26481C211yesmaximal, characteristic, complemented
18#25815C211yesmaximal, characteristic, complemented
19#25511C211yesmaximal, characteristic, complemented
20#25254C211yesmaximal, characteristic, complemented
21#25236C211yesmaximal, characteristic, complemented
22#25128C211yesmaximal, characteristic
23#25112C211yesmaximal, characteristic
24#23790C211yesmaximal, characteristic, complemented
25#23584C211yesmaximal, characteristic, complemented
26C2×#2025C211yesmaximal, characteristic, complemented
27#22934C211yesmaximal, characteristic, complemented
28#22920C211yesmaximal, characteristic, complemented
29#22874C211yesmaximal, characteristic, complemented
30#22854C211yesmaximal, characteristic, complemented
31#20557C211yesmaximal, characteristic, complemented
32C2×#541C2211yescharacteristic, complemented
33C22×#125C2211yescharacteristic
34C2×#499C2211yescharacteristic, complemented
35C2×#499C2211yescharacteristic, complemented
36C2×#483C2211yescharacteristic
37C2×#483C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#440C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic
44C2×#435C2211yescharacteristic
45C2×C8×D4C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48#2857C2211yescharacteristic
49#2851C2211yescharacteristic
50#2797—21no—
51#2786—21no—
52#2752—21no—
53#2740—21no—
54#2725—21no—
55#2725—21no—
56#2719—21no—
57#2719—21no—
58#2644C2211yescharacteristic
59#2642C2211yescharacteristic, complemented
60#2629C2211yescharacteristic, complemented
61#2624C2211yescharacteristic
62#2513C2211yescharacteristic
63#2490C2211yescharacteristic
64#2489C2211yescharacteristic, complemented
65#2489C2211yescharacteristic, complemented
66#2486C2211yescharacteristic
67#2483—21no—
68#2482—21no—
69#2481—21no—
70#2481—21no—
71#2454C2211yescharacteristic
72#2453C2211yescharacteristic, complemented
73#2453C2211yescharacteristic, complemented
74#2442—21no—
75#2442—21no—
76#2420C2211yescharacteristic
77#2417C2211yescharacteristic
78#2417C2211yescharacteristic
79#2412—21no—
80#2411—21no—
81#2408C2211yescharacteristic
82#2360C2211yescharacteristic
83#2360C2211yescharacteristic
84#2344C2211yescharacteristic
85D4×C22⋊C4C2211yescharacteristic
86#2330C2211yescharacteristic, complemented
87#2324C2211yescharacteristic
88#2319C2211yescharacteristic
89C2×#390C2211yescharacteristic
90#2290C2211yescharacteristic
91#2099C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2094C2211yescharacteristic
94#2094C2211yescharacteristic
95#2088C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2077C2211yescharacteristic, complemented
99#2074C2211yescharacteristic, complemented
100#2074C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2067C2211yescharacteristic
103#2066C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2059C2211yescharacteristic, complemented
106#2059C2211yescharacteristic, complemented
107#2059C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2043C2211yescharacteristic, complemented
112#2043C2211yescharacteristic, complemented
113#2036C2211yescharacteristic, complemented
114#2035C2211yescharacteristic, complemented
115#2034C2211yescharacteristic
116#2033C2211yescharacteristic
117#2026C2211yescharacteristic, complemented
118#2026C2211yescharacteristic, complemented
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic
121#2025C2211yescharacteristic
122#2025C2211yescharacteristic
123#2025C2211yescharacteristic
124#2025C2211yescharacteristic
125#2025C2211yescharacteristic
126#2025C2211yescharacteristic
127#2013C2211yescharacteristic
128#2013C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#1991C2211yescharacteristic, complemented
132#1991C2211yescharacteristic, complemented
133#1973C2211yescharacteristic
134#1973C2211yescharacteristic
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1968C2211yescharacteristic
140#1968C2211yescharacteristic
141#1944C2211yescharacteristic, complemented
142#1943C2211yescharacteristic, complemented
143#1941C2211yescharacteristic, complemented
144#1941C2211yescharacteristic, complemented
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1935C2211yescharacteristic, complemented
148#1935C2211yescharacteristic, complemented
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1933C2211yescharacteristic, complemented
152#1933C2211yescharacteristic, complemented
153#1928C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1926C2211yescharacteristic
156#1925C2211yescharacteristic
157#1920C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1919C2211yescharacteristic, complemented
161#1895C2211yescharacteristic
162#1894C2211yescharacteristic, complemented
163#1893C2211yescharacteristic
164#1892C2211yescharacteristic
165#1892C2211yescharacteristic
166#1892C2211yescharacteristic
167#1892C2211yescharacteristic
168#1892C2211yescharacteristic, complemented
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1877C2211yescharacteristic
172#1877C2211yescharacteristic
173#1865C2211yescharacteristic, complemented
174#1864C2211yescharacteristic
175#1863C2211yescharacteristic, complemented
176#1862C2211yescharacteristic
177#1853C2211yescharacteristic
178#1853C2211yescharacteristic
179#1852C2211yescharacteristic
180#1852C2211yescharacteristic
181#1809C2211yescharacteristic, complemented
182#1807C2211yescharacteristic, complemented
183#1776C2211yescharacteristic, complemented
184C4×#106C2211yescharacteristic, complemented
185#1771C2211yescharacteristic, complemented
186C8×C4⋊C4C2211yescharacteristic, complemented
187#1768C2211yescharacteristic, complemented
188#1763C2211yescharacteristic, complemented
189#1762C2211yescharacteristic
190C4×#103C2211yescharacteristic, complemented
191C4×#102C2211yescharacteristic
192#1753C2211yescharacteristic, complemented
193#1752C2211yescharacteristic
194C8×C22⋊C4C2211yescharacteristic
195C8×C22⋊C4C2211yescharacteristic, complemented
196#1750C2211yescharacteristic, complemented
197C4×C22⋊C8C2211yescharacteristic
198#1746C2211yescharacteristic, complemented
199C2×#340C2211yescharacteristic
200C2×#340C2211yescharacteristic
201#1729C2211yescharacteristic, complemented
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#541—42no—
213#541—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×#126—21no—
216C2×#126—21no—
217C2×#125—21no—
218C2×#125—21no—
219C2×#125—21no—
220C2×#125—21no—
221C2×#125—42no—
222C2×#125—42no—
223C2×#125C2311yescharacteristic
224C2×#125C2311yescharacteristic
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#123—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117—21no—
242C2×#117C2311yescharacteristic
243C22×C4⋊C4—21no—
244C22×C4⋊C4—21no—
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C22⋊C4—21no—
251C22×C42C2311yescharacteristic
252#499—42no—
253#499—42no—
254#483—24no—
255#483—24no—
256#468—42no—
257#465—42no—
258#450—24no—
259#450—24no—
260#440—42no—
261C4×SD16—42no—
262#435—24no—
263C8×D4—24no—
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#102—42no—
291C2×#102—42no—
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×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#399—21no—
325#399—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#397—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#396—21no—
349#396—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#392—21no—
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#390—21no—
363#390—21no—
364#390—21no—
365#390—21no—
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388D411yescharacteristic
401#388D411yescharacteristic
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387D411yescharacteristic
413#387D411yescharacteristic
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386D411yescharacteristic
421#386D411yescharacteristic
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385D411yescharacteristic
429#385D411yescharacteristic
430#384C2311yescharacteristic
431#382—21no—
432#382—21no—
433#382C2311yescharacteristic
434#381—21no—
435#381—21no—
436#381—21no—
437#381—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#379—21no—
451#379—21no—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#376C2311yescharacteristic
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#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4C2×D411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C2×D411yescharacteristic
517C23×C4C2×D411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×M16—22no—
533C2×M16—41no—
534C2×M16—41no—
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—41no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554#126—44no—
555#126—44no—
556#125—22no—
557#125—22no—
558#125—22no—
559#125—22no—
560#125—41no—
561#125—41no—
562#125—41no—
563#125—41no—
564#125—41no—
565#125—41no—
566#125—44no—
567#125—44no—
568#125—44no—
569#125—44no—
570#123—82no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579#121—22no—
580#121—41no—
581#121—41no—
582#121—41no—
583#120—82no—
584C4×Q8—22no—
585C4×Q8—22no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594#117—41no—
595#117—41no—
596#117—82no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
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⋊C4—21no—
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⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—44no—
637C2×C4⋊C4—44no—
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
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—82no—
686C2×C22⋊C4—82no—
687C2×C22⋊C4—82no—
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—41no—
703C2×C42—41no—
704C2×C42C2×D411yescharacteristic
705C2×C42C2×D411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711#107—22no—
712#107—22no—
713#107—41no—
714#107—41no—
715#106—22no—
716#106—22no—
717#106—22no—
718#106—22no—
719#106—22no—
720#106—22no—
721#106—41no—
722#106—41no—
723C4⋊C8—22no—
724C4⋊C8—22no—
725#103—22no—
726#103—22no—
727#103—22no—
728#103—22no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749C22⋊C8—22no—
750C22⋊C8—22no—
751C22⋊C8#4114yes—
752C22⋊C8#4114yes—
753#97—22no—
754#97—41no—
755#97—41no—
756C4×C8—22no—
757C4×C8—41no—
758C4×C8—41no—
759C4×C8—41no—
760C4×C8—41no—
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#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#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805C24—21no—
806C24—21no—
807C24—42no—
808C24—42no—
809C24—42no—
810C24—42no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24C22×D411yescharacteristic
815C24C22×D411yescharacteristic
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—22no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—44no—
843C2×D4—44no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—82no—
848C2×D4—82no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D42−1+412yes—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C2×#4112yes—
914C22×C4C2×#4112yes—
915C22×C4C2511yescharacteristic
916SD16—44no—
917SD16—44no—
918SD16—82no—
919SD16—82no—
920M16—82no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—82no—
942C2×C8—82no—
943C2×C8—82no—
944C2×C8C2×#4112yes—
945C2×C8C2×#4112yes—
946C2×C8C2×#4112yes—
947C2×C8C2×#4112yes—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—22no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4H(5,𝔽2)12yes—
1009C4⋊C4H(5,𝔽2)12yes—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—41no—
1059C42—41no—
1060C42—42no—
1061C42—42no—
1062C42—81no—
1063C42—81no—
1064C42—81no—
1065C42—81no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—22no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—84no—
1092C23—84no—
1093C23—84no—
1094C23—84no—
1095C23—162no—
1096C23—162no—
1097C23—162no—
1098C23#53212yes—
1099C23#57712yes—
1100C23#57712yes—
1101C23C23×D411yescharacteristic
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110D4—22no—
1111D4—22no—
1112D4—44no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—84no—
1120D4—162no—
1121D4—162no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
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—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—22no—
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—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—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—82no—
1208C2×C4—82no—
1209C2×C4—84no—
1210C2×C4—84no—
1211C2×C4—84no—
1212C2×C4—162no—
1213C2×C4—162no—
1214C2×C4#53212yes—
1215C2×C4C22×#4111yescharacteristic
1216C2×C4C22×#4111yescharacteristic
1217C2×C4C2×H(5,𝔽2)11yescharacteristic
1218C2×C4C2×H(5,𝔽2)11yescharacteristic
1219C2×C4C2×2−1+411yescharacteristic
1220C2×C4#58511yescharacteristic
1221C8—22no—
1222C8—22no—
1223C8—22no—
1224C8—22no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C8—41no—
1229C22—22no—
1230C22—22no—
1231C22—22no—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—42no—
1236C22—41no—
1237C22—42no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—42no—
1243C22—41no—
1244C22—41no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—168no—
1257C22#317414yes—
1258C22C2×#53211yescharacteristic
1259C22#348411yescharacteristic
1260C22#348911yescharacteristic
1261C22C2×#57711yescharacteristic
1262C22C2×#57711yescharacteristic
1263C22#358411yescharacteristic
1264C22#358411yescharacteristic
1265C4—22no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—42no—
1278C4—42no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4#351411yescharacteristic
1292C4#351411yescharacteristic
1293C4#352011yescharacteristic
1294C4#352011yescharacteristic
1295C2—24no—
1296C2—81no—
1297C2—82no—
1298C2—161no—
1299C2#3594011yescharacteristic
1300C2C2×#317411yescharacteristic
1301C2#6072411yescharacteristic
1302C2#6164111yescharacteristic
1303C2#6164111yescharacteristic
1304C2#6221211yescharacteristic
1305C2#6221211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #37705C2semidirect
3. #30373C2semidirect
4. #30355C2semidirect
5. #30190C2semidirect
6. #29568C2semidirect
7. #29529C2semidirect
8. #29168C2semidirect
9. #29102C2semidirect
10. #29078C2semidirect
11. #29004C2semidirect
12. #28980C2semidirect
13. #28302C2semidirect
14. #27801C2semidirect
15. #27788C2semidirect
16. #26494C2semidirect
17. #26481C2semidirect
18. #25815C2semidirect
19. #25511C2semidirect
20. #25254C2semidirect
21. #25236C2semidirect
24. #23790C2semidirect
25. #23584C2semidirect
26. C2×#2025C2semidirect
27. #22934C2semidirect
28. #22920C2semidirect
29. #22874C2semidirect
30. #22854C2semidirect
31. #20557C2semidirect
32. C2×#541C22semidirect
34. C2×#499C22semidirect
35. C2×#499C22semidirect
59. #2642C22semidirect
60. #2629C22semidirect
64. #2489C22semidirect
65. #2489C22semidirect
72. #2453C22semidirect
73. #2453C22semidirect
86. #2330C22semidirect
91. #2099C22semidirect
92. #2099C22semidirect
95. #2088C22semidirect
96. #2088C22semidirect
97. #2077C22semidirect
98. #2077C22semidirect
99. #2074C22semidirect
100. #2074C22semidirect
101. #2068C22semidirect
103. #2066C22semidirect
105. #2059C22semidirect
106. #2059C22semidirect
107. #2059C22semidirect
108. #2059C22semidirect
111. #2043C22semidirect
112. #2043C22semidirect
113. #2036C22semidirect
114. #2035C22semidirect
117. #2026C22semidirect
118. #2026C22semidirect
131. #1991C22semidirect
132. #1991C22semidirect
141. #1944C22semidirect
142. #1943C22semidirect
143. #1941C22semidirect
144. #1941C22semidirect
147. #1935C22semidirect
148. #1935C22semidirect
151. #1933C22semidirect
152. #1933C22semidirect
153. #1928C22semidirect
154. #1927C22semidirect
157. #1920C22semidirect
158. #1920C22semidirect
159. #1919C22semidirect
160. #1919C22semidirect
162. #1894C22semidirect
168. #1892C22semidirect
173. #1865C22semidirect
175. #1863C22semidirect
181. #1809C22semidirect
182. #1807C22semidirect
183. #1776C22semidirect
184. C4×#106C22semidirect
185. #1771C22semidirect
186. C8×C4⋊C4C22semidirect
187. #1768C22semidirect
188. #1763C22semidirect
190. C4×#103C22semidirect
192. #1753C22semidirect
195. C8×C22⋊C4C22semidirect
196. #1750C22semidirect
198. #1746C22semidirect
201. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#381122
#377052
#303732
#303552
#301902
#295682
#295292
#291682
#291022
#290782
#290042
#289802
#283022
#278012
#277882
#264942
#264812
#258152
#255112
#252542
#252362
#251282
#251122
#237902
#235842
C2×#20252
#229342
#229202
#228742
#228542
#205572