Finite Group Databasebeta

← #7092648

Subgroups — #7092648

Order 512.

1369 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45414C211yesmaximal, characteristic, complemented
2#44970C211yesmaximal, characteristic
3#32539C211yesmaximal, characteristic, complemented
4#32181C211yesmaximal, characteristic, complemented
5#32180C211yesmaximal, characteristic
6#32097C211yesmaximal, characteristic, complemented
7#31927C211yesmaximal, characteristic, complemented
8#30900C211yesmaximal, characteristic, complemented
9#30756C211yesmaximal, characteristic, complemented
10#30756C211yesmaximal, characteristic, complemented
11#29382C211yesmaximal, characteristic, complemented
12#29377C211yesmaximal, characteristic, complemented
13#29028C211yesmaximal, characteristic, complemented
14#27575C211yesmaximal, characteristic, complemented
15#27566C211yesmaximal, characteristic, complemented
16#27376C211yesmaximal, characteristic, complemented
17#27221C211yesmaximal, characteristic, complemented
18#27213C211yesmaximal, characteristic, complemented
19#27148C211yesmaximal, characteristic, complemented
20#26912C211yesmaximal, characteristic, complemented
21#26830C211yesmaximal, characteristic, complemented
22#26783C211yesmaximal, characteristic, complemented
23#26605C211yesmaximal, characteristic, complemented
24#26384C211yesmaximal, characteristic, complemented
25#25285C211yesmaximal, characteristic, complemented
26#24742C211yesmaximal, characteristic
27#23695C211yesmaximal, characteristic, complemented
28#23194C211yesmaximal, characteristic, complemented
29#23106C211yesmaximal, characteristic, complemented
30#22382C211yesmaximal, characteristic, complemented
31#22160C211yesmaximal, characteristic, complemented
32C2×#497C2211yescharacteristic
33C2×#489C2211yescharacteristic
34C2×#474C2211yescharacteristic
35C2×#460C2211yescharacteristic
36C2×#460C2211yescharacteristic
37C2×#460C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×C4×Q16C2211yescharacteristic
41#2778—21no—
42#2778—21no—
43#2774—21no—
44#2769—21no—
45#2762—21no—
46#2758—21no—
47#2756—21no—
48#2708—21no—
49#2606—21no—
50#2598—21no—
51#2591—21no—
52#2544C2211yescharacteristic
53#2544C2211yescharacteristic
54#2544C2211yescharacteristic
55#2541C2211yescharacteristic
56#2528—21no—
57#2524—21no—
58#2514—21no—
59#2514C2211yescharacteristic
60#2514C2211yescharacteristic
61#2514C2211yescharacteristic
62#2513C2211yescharacteristic
63#2509C2211yescharacteristic
64#2509C2211yescharacteristic
65#2476—21no—
66#2451C2211yescharacteristic
67#2451C2211yescharacteristic
68#2448C2211yescharacteristic
69#2446C2211yescharacteristic
70#2446C2211yescharacteristic
71#2445C2211yescharacteristic
72#2443—21no—
73#2402C2211yescharacteristic
74#2369C2211yescharacteristic
75#2367C2211yescharacteristic
76#2366C2211yescharacteristic
77#2365C2211yescharacteristic
78#2356C2211yescharacteristic
79#2354C2211yescharacteristic
80#2351C2211yescharacteristic
81D4×C4⋊C4C2211yescharacteristic
82#2328C2211yescharacteristic
83#2326C2211yescharacteristic
84#2320C2211yescharacteristic
85#2320C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2099C2211yescharacteristic
89#2097C2211yescharacteristic
90#2097C2211yescharacteristic
91#2095C2211yescharacteristic
92#2083C2211yescharacteristic
93#2074C2211yescharacteristic
94#2073C2211yescharacteristic
95#2072C2211yescharacteristic
96#2068C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2066C2211yescharacteristic
103#2065C2211yescharacteristic
104#2057C2211yescharacteristic
105#2056C2211yescharacteristic
106#2056C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2041C2211yescharacteristic
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic
116#2023C2211yescharacteristic
117#2015C2211yescharacteristic
118#2015C2211yescharacteristic
119#2015C2211yescharacteristic
120#2015C2211yescharacteristic
121#2014C2211yescharacteristic
122#2014C2211yescharacteristic
123#2014C2211yescharacteristic
124#2013C2211yescharacteristic
125#2013C2211yescharacteristic
126#1983C2211yescharacteristic
127#1983C2211yescharacteristic
128#1982C2211yescharacteristic
129#1981C2211yescharacteristic
130#1973C2211yescharacteristic
131#1973C2211yescharacteristic
132#1973C2211yescharacteristic
133#1971C2211yescharacteristic
134#1968C2211yescharacteristic
135#1961C2211yescharacteristic
136#1961C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1944C2211yescharacteristic
140#1940C2211yescharacteristic
141#1940C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1935C2211yescharacteristic
146#1935C2211yescharacteristic
147#1934C2211yescharacteristic
148#1928C2211yescharacteristic
149#1928C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1921C2211yescharacteristic
159#1918C2211yescharacteristic
160#1917C2211yescharacteristic
161#1917C2211yescharacteristic
162#1917C2211yescharacteristic
163#1917C2211yescharacteristic
164#1917C2211yescharacteristic
165#1917C2211yescharacteristic
166#1917C2211yescharacteristic
167#1917C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic
182#1877C2211yescharacteristic
183#1877C2211yescharacteristic
184#1864C2211yescharacteristic
185#1864C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1862C2211yescharacteristic
189#1862C2211yescharacteristic
190#1862C2211yescharacteristic
191#1862C2211yescharacteristic
192#1840C2211yescharacteristic
193#1805C2211yescharacteristic
194#1804C2211yescharacteristic
195#1776C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1768C2211yescharacteristic
199#1763C2211yescharacteristic
200#1763C2211yescharacteristic
201#1762C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#123—21no—
220C2×#121—21no—
221C2×#121—21no—
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×#117—21no—
234C22×C4⋊C4—21no—
235#497—24no—
236#489—42no—
237#474—42no—
238#460—24no—
239#460—24no—
240#460—42no—
241#440—42no—
242#440—42no—
243C4×Q16—42no—
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296#401—21no—
297#401—21no—
298#401—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400D411yescharacteristic
309#400D411yescharacteristic
310#400D411yescharacteristic
311#400D411yescharacteristic
312#399—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398D411yescharacteristic
318#398D411yescharacteristic
319#398D411yescharacteristic
320#398D411yescharacteristic
321#397—21no—
322#397—21no—
323#397—21no—
324#395—21no—
325#395—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#392—21no—
335#392—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#390—21no—
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—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#386—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#384C2311yescharacteristic
423#383—21no—
424#383—21no—
425#383—21no—
426#383—21no—
427#383—21no—
428#383—21no—
429#382—21no—
430#382—21no—
431#382—21no—
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#380—21no—
436#380—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453#376—21no—
454#376C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C22×D4C2411yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C2×Q16—22no—
506C2×Q16—22no—
507C2×Q16—41no—
508C2×Q16—41no—
509C2×Q16—41no—
510C2×Q16—41no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16#4114yes—
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C4⋊Q8—22no—
538C4⋊Q8—22no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541#127—22no—
542#127—22no—
543#127—41no—
544#127—41no—
545#127—41no—
546#127—41no—
547#124—22no—
548#124—41no—
549#124—41no—
550#124—41no—
551#124—41no—
552#124—41no—
553#123—82no—
554#121—82no—
555#121—82no—
556C4×Q8—22no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—82no—
577#117—82no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—82no—
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664#107—22no—
665#107—22no—
666#107—41no—
667#107—41no—
668#107—41no—
669#107—41no—
670#106—41no—
671#106—41no—
672C4⋊C8—22no—
673C4⋊C8—22no—
674C4⋊C8—41no—
675C4⋊C8—41no—
676C4⋊C8—41no—
677C4⋊C8—41no—
678#103—22no—
679#103—41no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#97—22no—
711#97—41no—
712#97—41no—
713#97—41no—
714#97—41no—
715C4×C8—41no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776C24—21no—
777C24—21no—
778C24—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—42no—
797C2×Q8—81no—
798C2×Q8—81no—
799C2×Q8C2×#4112yes—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4—81no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—81no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4C2×#4112yes—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C2511yescharacteristic
879Q16—44no—
880Q16—82no—
881SD16—44no—
882SD16—44no—
883SD16—82no—
884SD16—82no—
885SD16—82no—
886SD16—82no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8C2×#4112yes—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—41no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—41no—
934C4⋊C4—41no—
935C4⋊C4—41no—
936C4⋊C4—41no—
937C4⋊C4—41no—
938C4⋊C4—41no—
939C4⋊C4—41no—
940C4⋊C4—41no—
941C4⋊C4—41no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4H(5,𝔽2)12yes—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—42no—
1003C42—42no—
1004C42—42no—
1005C42—42no—
1006C42—42no—
1007C42—42no—
1008C42—81no—
1009C42—81no—
1010C42—81no—
1011C42—81no—
1012C42—81no—
1013C23—22no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23C23×D411yescharacteristic
1035Q8—22no—
1036Q8—22no—
1037Q8—41no—
1038Q8—41no—
1039Q8—41no—
1040Q8—41no—
1041Q8—41no—
1042Q8—41no—
1043Q8—41no—
1044Q8—41no—
1045Q8—41no—
1046Q8—41no—
1047Q8—162no—
1048D4—22no—
1049D4—22no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—41no—
1057D4—41no—
1058D4—41no—
1059D4—41no—
1060D4—84no—
1061D4—162no—
1062D4—162no—
1063D4—162no—
1064D4—162no—
1065D4—162no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—22no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—84no—
1148C2×C4—84no—
1149C2×C4—162no—
1150C2×C4—162no—
1151C2×C4—162no—
1152C2×C4C22×#4111yescharacteristic
1153C2×C4C2×H(5,𝔽2)11yescharacteristic
1154C2×C4#58511yescharacteristic
1155C2×C4#58511yescharacteristic
1156C2×C4#58511yescharacteristic
1157C2×C4#58511yescharacteristic
1158C8—22no—
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C8—41no—
1163C8—41no—
1164C8—41no—
1165C8—41no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22D4×#4111yescharacteristic
1188C22#348711yescharacteristic
1189C22#348811yescharacteristic
1190C22#358511yescharacteristic
1191C22#358511yescharacteristic
1192C22#358611yescharacteristic
1193C22#358611yescharacteristic
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—41no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—42no—
1207C4—42no—
1208C4—41no—
1209C4—41no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4—81no—
1218C4—81no—
1219C4—81no—
1220C4—81no—
1221C4#350511yescharacteristic
1222C4#352111yescharacteristic
1223C4#353911yescharacteristic
1224C4#356611yescharacteristic
1225C2—82no—
1226C2—161no—
1227C2—161no—
1228C2#4425311yescharacteristic
1229C2#6150311yescharacteristic
1230C2#6151311yescharacteristic
1231C2#6193911yescharacteristic
1232C2#6193911yescharacteristic
1233C2#6207711yescharacteristic
1234C2#6207911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2541C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2402 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45414C2semidirect
3. #32539C2semidirect
4. #32181C2semidirect
6. #32097C2semidirect
7. #31927C2semidirect
8. #30900C2semidirect
9. #30756C2semidirect
10. #30756C2semidirect
11. #29382C2semidirect
12. #29377C2semidirect
13. #29028C2semidirect
14. #27575C2semidirect
15. #27566C2semidirect
16. #27376C2semidirect
17. #27221C2semidirect
18. #27213C2semidirect
19. #27148C2semidirect
20. #26912C2semidirect
21. #26830C2semidirect
22. #26783C2semidirect
23. #26605C2semidirect
24. #26384C2semidirect
25. #25285C2semidirect
27. #23695C2semidirect
28. #23194C2semidirect
29. #23106C2semidirect
30. #22382C2semidirect
31. #22160C2semidirect

Maximal subgroups

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

subgroupindex
#454142
#449702
#325392
#321812
#321802
#320972
#319272
#309002
#307562
#293822
#293772
#290282
#275752
#275662
#273762
#272212
#272132
#271482
#269122
#268302
#267832
#266052
#263842
#252852
#247422
#236952
#231942
#231062
#223822
#221602