Finite Group Databasebeta

← #7043705

Subgroups — #7043705

Order 512.

1713 conjugacy classes of subgroups.

The subgroup lattice has 1395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44972C211yesmaximal, characteristic, complemented
2#44929C211yesmaximal, characteristic
3#32206C211yesmaximal, characteristic, complemented
4#32048C211yesmaximal, characteristic, complemented
5#31839C211yesmaximal, characteristic, complemented
6#31574C211yesmaximal, characteristic, complemented
7#31486C211yesmaximal, characteristic, complemented
8#31454C211yesmaximal, characteristic, complemented
9#31395C211yesmaximal, characteristic, complemented
10#30404C211yesmaximal, characteristic, complemented
11#28130C211yesmaximal, characteristic, complemented
12#27688C211yesmaximal, characteristic, complemented
13#27523C211yesmaximal, characteristic, complemented
14#27435C211yesmaximal, characteristic, complemented
15#27203C211yesmaximal, characteristic, complemented
16#27039C211yesmaximal, characteristic, complemented
17#26199C211yesmaximal, characteristic, complemented
18#25552C211yesmaximal, characteristic, complemented
19#25233C211yesmaximal, characteristic, complemented
20#25205C211yesmaximal, characteristic, complemented
21#25112C211yesmaximal, characteristic, complemented
22#24955C211yesmaximal, characteristic, complemented
23#24886C211yesmaximal, characteristic, complemented
24#24869C211yesmaximal, characteristic, complemented
25#24530C211yesmaximal, characteristic, complemented
26#24448C211yesmaximal, characteristic, complemented
27#23632C211yesmaximal, characteristic, complemented
28#22489C211yesmaximal, characteristic, complemented
29D4×#102C211yesmaximal, characteristic, complemented
30#22200C211yesmaximal, characteristic, complemented
31#22169C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×D42C2211yescharacteristic
34C2×#485C2211yescharacteristic, complemented
35C2×#482C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×C8×D4C2211yescharacteristic
41C2×C8×D4C2211yescharacteristic, complemented
42C2×#418C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2770—21no—
46#2757—21no—
47#2757—21no—
48#2725—21no—
49#2684—21no—
50#2678—21no—
51#2676—21no—
52#2670—21no—
53#2606—21no—
54#2603—21no—
55#2587—21no—
56#2552C2211yescharacteristic, complemented
57#2538C2211yescharacteristic, complemented
58#2502C2211yescharacteristic, complemented
59#2499C2211yescharacteristic, complemented
60#2496C2211yescharacteristic, complemented
61#2495C2211yescharacteristic, complemented
62#2491C2211yescharacteristic
63#2485C2211yescharacteristic
64#2476—21no—
65#2460—21no—
66#2452C2211yescharacteristic
67#2445C2211yescharacteristic
68#2435—21no—
69#2428C2211yescharacteristic
70#2417C2211yescharacteristic, complemented
71#2415C2211yescharacteristic
72#2414C2211yescharacteristic
73#2411—21no—
74#2410—21no—
75#2408C2211yescharacteristic
76#2408C2211yescharacteristic
77#2392C2211yescharacteristic
78#2363C2211yescharacteristic
79#2356C2211yescharacteristic, complemented
80#2354C2211yescharacteristic, complemented
81#2352C2211yescharacteristic, complemented
82D4×C4⋊C4C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84#2324C2211yescharacteristic
85#2323C2211yescharacteristic, complemented
86#2317C2211yescharacteristic, complemented
87#2309C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2094C2211yescharacteristic, complemented
92#2094C2211yescharacteristic, complemented
93#2092C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2077C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2076C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic, complemented
102#2073C2211yescharacteristic, complemented
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic
106#2071C2211yescharacteristic, complemented
107#2071C2211yescharacteristic, complemented
108#2068C2211yescharacteristic, complemented
109#2067C2211yescharacteristic, complemented
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic, complemented
112#2057C2211yescharacteristic, complemented
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic, complemented
116#2041C2211yescharacteristic
117#2035C2211yescharacteristic, complemented
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic, complemented
122#2033C2211yescharacteristic, complemented
123#2024C2211yescharacteristic, complemented
124#2014C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic, complemented
127#2000C2211yescharacteristic, complemented
128#1990C2211yescharacteristic, complemented
129#1987C2211yescharacteristic, complemented
130#1982C2211yescharacteristic
131#1968C2211yescharacteristic, complemented
132#1957C2211yescharacteristic
133#1949C2211yescharacteristic, complemented
134#1948C2211yescharacteristic, complemented
135#1941C2211yescharacteristic, complemented
136#1934C2211yescharacteristic
137#1933C2211yescharacteristic, complemented
138#1927C2211yescharacteristic, complemented
139#1926C2211yescharacteristic, complemented
140#1926C2211yescharacteristic, complemented
141#1925C2211yescharacteristic
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic, complemented
144#1923C2211yescharacteristic, complemented
145#1923C2211yescharacteristic, complemented
146#1921C2211yescharacteristic, complemented
147#1920C2211yescharacteristic, complemented
148#1918C2211yescharacteristic, complemented
149#1918C2211yescharacteristic, complemented
150#1916C2211yescharacteristic, complemented
151#1916C2211yescharacteristic, complemented
152#1893C2211yescharacteristic
153#1893C2211yescharacteristic
154#1893C2211yescharacteristic, complemented
155#1893C2211yescharacteristic, complemented
156#1892C2211yescharacteristic, complemented
157#1892C2211yescharacteristic, complemented
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic, complemented
160#1880C2211yescharacteristic, complemented
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic, complemented
163#1877C2211yescharacteristic, complemented
164#1875C2211yescharacteristic
165#1875C2211yescharacteristic, complemented
166#1875C2211yescharacteristic, complemented
167#1874C2211yescharacteristic
168#1874C2211yescharacteristic
169#1873C2211yescharacteristic, complemented
170#1870C2211yescharacteristic
171#1870C2211yescharacteristic, complemented
172#1869C2211yescharacteristic, complemented
173#1869C2211yescharacteristic, complemented
174#1864C2211yescharacteristic, complemented
175#1863C2211yescharacteristic, complemented
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic, complemented
178#1854C2211yescharacteristic, complemented
179#1854C2211yescharacteristic, complemented
180#1853C2211yescharacteristic, complemented
181#1853C2211yescharacteristic, complemented
182#1850C2211yescharacteristic, complemented
183#1850C2211yescharacteristic, complemented
184#1825C2211yescharacteristic, complemented
185#1825C2211yescharacteristic, complemented
186#1824C2211yescharacteristic, complemented
187#1809C2211yescharacteristic, complemented
188#1808C2211yescharacteristic, complemented
189#1804C2211yescharacteristic, complemented
190#1802C2211yescharacteristic
191#1802C2211yescharacteristic, complemented
192#1802C2211yescharacteristic, complemented
193#1798C2211yescharacteristic, complemented
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic, complemented
199#1736C2211yescharacteristic, complemented
200#1735C2211yescharacteristic, complemented
201#1735C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#555—24no—
214#555—42no—
215D42—24no—
216D42—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#126—21no—
220C2×#125—21no—
221C2×#124—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#120—21no—
238C2×#120—21no—
239C2×#120—21no—
240C2×#120—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×D4—21no—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117—21no—
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C22⋊C4—21no—
258#485—42no—
259#482—42no—
260#468—24no—
261#465—42no—
262#450—42no—
263#450—42no—
264C8×D4—42no—
265C8×D4—42no—
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279#418—42no—
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#102—42no—
286C2×#102—42no—
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×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318#400—21no—
319#400—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398D411yescharacteristic
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397D411yescharacteristic
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396D411yescharacteristic
338#396D411yescharacteristic
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394D411yescharacteristic
349#394D411yescharacteristic
350#394D411yescharacteristic
351#393—21no—
352#393—21no—
353#392—21no—
354#392—21no—
355#392—21no—
356#392—21no—
357#392D411yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#390—21no—
362#390—21no—
363#390—21no—
364#390—21no—
365#390—21no—
366#390—21no—
367#390—21no—
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
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#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
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#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#383—21no—
429#383—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#380—21no—
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#379—21no—
442#379—21no—
443#379—21no—
444#379—21no—
445#379—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456#376—21no—
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#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C25—21no—
495C22×Q8—21no—
496C22×Q8C2411yescharacteristic
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—44no—
519C22×D4—82no—
520C22×D4—82no—
521C22×D4C2×D411yescharacteristic
522C22×D4C2×D411yescharacteristic
523C22×D4C2×D411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×M16—22no—
545C2×M16—41no—
546C2×M16—41no—
547C22×C8—22no—
548C22×C8—41no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8—41no—
553C22×C8—41no—
554C22×C8—41no—
555C22×C8—41no—
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C4⋊Q8—22no—
565C4⋊Q8—41no—
566#127—22no—
567#127—41no—
568#126—82no—
569#125—82no—
570#124—44no—
571#124—44no—
572#124—82no—
573#123—82no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—82no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—22no—
585#121—44no—
586#121—41no—
587#121—41no—
588#121—41no—
589#121—44no—
590#121—41no—
591#121—41no—
592#121—82no—
593#121#4114yes—
594#120—44no—
595#120—44no—
596#120—82no—
597#120—82no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—82no—
613#117—22no—
614#117—22no—
615#117—22no—
616#117—41no—
617#117—41no—
618#117—44no—
619#117—41no—
620#117—41no—
621#117—41no—
622#117—41no—
623#117—41no—
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—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
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—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—82no—
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731#107—22no—
732#107—41no—
733#107—41no—
734#107—41no—
735#106—41no—
736#106—41no—
737#106—41no—
738#106—41no—
739#106—41no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743C4⋊C8—41no—
744#103—22no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770C22⋊C8—22no—
771C22⋊C8—22no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C4×C8—41no—
779C4×C8—41no—
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#95—21no—
807#95—21no—
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814C24—21no—
815C24—21no—
816C24—21no—
817C24—42no—
818C24—42no—
819C24—42no—
820C24—42no—
821C24—42no—
822C24—81no—
823C24—81no—
824C24—81no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24C22×D411yescharacteristic
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—42no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—22no—
846C2×D4—24no—
847C2×D4—22no—
848C2×D4—22no—
849C2×D4—22no—
850C2×D4—21no—
851C2×D4—21no—
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—44no—
867C2×D4—44no—
868C2×D4—41no—
869C2×D4—41no—
870C2×D4—41no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—44no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—82no—
884C2×D4—82no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—82no—
891C2×D4—82no—
892C2×D4—82no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—816no—
904C2×D4C2×#4112yes—
905C2×D4H(5,𝔽2)12yes—
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—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C2×#4112yes—
962C22×C4H(5,𝔽2)12yes—
963C22×C4C2511yescharacteristic
964SD16—82no—
965SD16—82no—
966SD16—82no—
967M16—82no—
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×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—82no—
993C2×C8—82no—
994C2×C8—82no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—22no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4C2×#4112yes—
1047C22⋊C4—22no—
1048C22⋊C4—22no—
1049C22⋊C4—22no—
1050C22⋊C4—24no—
1051C22⋊C4—22no—
1052C22⋊C4—22no—
1053C22⋊C4—22no—
1054C22⋊C4—22no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—42no—
1105C42—42no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—81no—
1110C42—81no—
1111C42—81no—
1112C42—81no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—22no—
1128C23—21no—
1129C23—22no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—84no—
1154C23—84no—
1155C23—84no—
1156C23—84no—
1157C23—84no—
1158C23—162no—
1159C23—162no—
1160C23—162no—
1161C23—162no—
1162C23—162no—
1163C23—162no—
1164C23—162no—
1165C23—162no—
1166C23—162no—
1167C23#54612yes—
1168C23#57712yes—
1169C23C23×D411yescharacteristic
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—162no—
1175D4—28no—
1176D4—22no—
1177D4—22no—
1178D4—22no—
1179D4—22no—
1180D4—44no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—84no—
1190D4—84no—
1191D4—82no—
1192D4—84no—
1193D4—84no—
1194D4—84no—
1195D4—162no—
1196D4—162no—
1197D4—162no—
1198D4—162no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—84no—
1281C2×C4—84no—
1282C2×C4—162no—
1283C2×C4—162no—
1284C2×C4—162no—
1285C2×C4#54612yes—
1286C2×C4#57612yes—
1287C2×C4#57712yes—
1288C2×C4C22×#4111yescharacteristic
1289C2×C4C2×H(5,𝔽2)11yescharacteristic
1290C2×C4C2×H(5,𝔽2)11yescharacteristic
1291C2×C4#58511yescharacteristic
1292C2×C4#58511yescharacteristic
1293C2×C4#58511yescharacteristic
1294C8—41no—
1295C8—41no—
1296C8—41no—
1297C8—41no—
1298C8—41no—
1299C8—41no—
1300C8—41no—
1301C8—41no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—42no—
1318C22—42no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—42no—
1323C22—41no—
1324C22—42no—
1325C22—42no—
1326C22—41no—
1327C22—42no—
1328C22—41no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—168no—
1345C22—168no—
1346C22C2×#54611yescharacteristic
1347C22#348511yescharacteristic
1348C22#348811yescharacteristic
1349C22C2×#57611yescharacteristic
1350C22C2×#57711yescharacteristic
1351C22C2×#57711yescharacteristic
1352C22#358411yescharacteristic
1353C4—22no—
1354C4—22no—
1355C4—22no—
1356C4—41no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—42no—
1364C4—41no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4#351311yescharacteristic
1378C4#352111yescharacteristic
1379C4#353411yescharacteristic
1380C4#356011yescharacteristic
1381C2—42no—
1382C2—42no—
1383C2—81no—
1384C2—82no—
1385C2—82no—
1386C2—161no—
1387C2#4353011yescharacteristic
1388C2#6116711yescharacteristic
1389C2#6117211yescharacteristic
1390C2#6177011yescharacteristic
1391C2#6178811yescharacteristic
1392C2#6205211yescharacteristic
1393C2#6206711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#44929C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #44972C2semidirect
3. #32206C2semidirect
4. #32048C2semidirect
5. #31839C2semidirect
6. #31574C2semidirect
7. #31486C2semidirect
8. #31454C2semidirect
9. #31395C2semidirect
10. #30404C2semidirect
11. #28130C2semidirect
12. #27688C2semidirect
13. #27523C2semidirect
14. #27435C2semidirect
15. #27203C2semidirect
16. #27039C2semidirect
17. #26199C2semidirect
18. #25552C2semidirect
19. #25233C2semidirect
20. #25205C2semidirect
21. #25112C2semidirect
22. #24955C2semidirect
23. #24886C2semidirect
24. #24869C2semidirect
25. #24530C2semidirect
26. #24448C2semidirect
27. #23632C2semidirect
28. #22489C2semidirect
29. D4×#102C2semidirect
30. #22200C2semidirect
31. #22169C2semidirect
34. C2×#485C22semidirect
41. C2×C8×D4C22semidirect
56. #2552C22semidirect
57. #2538C22semidirect
58. #2502C22semidirect
59. #2499C22semidirect
60. #2496C22semidirect
61. #2495C22semidirect
70. #2417C22semidirect
79. #2356C22semidirect
80. #2354C22semidirect
81. #2352C22semidirect
85. #2323C22semidirect
86. #2317C22semidirect
88. #2101C22semidirect
89. #2099C22semidirect
90. #2099C22semidirect
91. #2094C22semidirect
92. #2094C22semidirect
93. #2092C22semidirect
94. #2086C22semidirect
95. #2084C22semidirect
96. #2077C22semidirect
97. #2077C22semidirect
98. #2076C22semidirect
101. #2073C22semidirect
102. #2073C22semidirect
106. #2071C22semidirect
107. #2071C22semidirect
108. #2068C22semidirect
109. #2067C22semidirect
111. #2065C22semidirect
112. #2057C22semidirect
115. #2055C22semidirect
117. #2035C22semidirect
121. #2033C22semidirect
122. #2033C22semidirect
123. #2024C22semidirect
126. #2000C22semidirect
127. #2000C22semidirect
128. #1990C22semidirect
129. #1987C22semidirect
131. #1968C22semidirect
133. #1949C22semidirect
134. #1948C22semidirect
135. #1941C22semidirect
137. #1933C22semidirect
138. #1927C22semidirect
139. #1926C22semidirect
140. #1926C22semidirect
143. #1925C22semidirect
144. #1923C22semidirect
145. #1923C22semidirect
146. #1921C22semidirect
147. #1920C22semidirect
148. #1918C22semidirect
149. #1918C22semidirect
150. #1916C22semidirect
151. #1916C22semidirect
154. #1893C22semidirect
155. #1893C22semidirect
156. #1892C22semidirect
157. #1892C22semidirect
159. #1880C22semidirect
160. #1880C22semidirect
162. #1877C22semidirect
163. #1877C22semidirect
165. #1875C22semidirect
166. #1875C22semidirect
169. #1873C22semidirect
171. #1870C22semidirect
172. #1869C22semidirect
173. #1869C22semidirect
174. #1864C22semidirect
175. #1863C22semidirect
177. #1862C22semidirect
178. #1854C22semidirect
179. #1854C22semidirect
180. #1853C22semidirect
181. #1853C22semidirect
182. #1850C22semidirect
183. #1850C22semidirect
184. #1825C22semidirect
185. #1825C22semidirect
186. #1824C22semidirect
187. #1809C22semidirect
188. #1808C22semidirect
189. #1804C22semidirect
191. #1802C22semidirect
192. #1802C22semidirect
193. #1798C22semidirect
198. C4×#102C22semidirect
199. #1736C22semidirect
200. #1735C22semidirect
201. #1735C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#449722
#449292
#322062
#320482
#318392
#315742
#314862
#314542
#313952
#304042
#281302
#276882
#275232
#274352
#272032
#270392
#261992
#255522
#252332
#252052
#251122
#249552
#248862
#248692
#245302
#244482
#236322
#224892
D4×#1022
#222002
#221692