Finite Group Databasebeta

← #6579878

Subgroups — #6579878

Order 512.

1821 conjugacy classes of subgroups.

The subgroup lattice has 1381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36459C211yesmaximal, characteristic, complemented
2#36218C211yesmaximal, characteristic
3#33112C211yesmaximal, characteristic, complemented
4#33051C211yesmaximal, characteristic, complemented
5#32955C211yesmaximal, characteristic, complemented
6#29066C211yesmaximal, characteristic, complemented
7#29054C211yesmaximal, characteristic, complemented
8#27765C211yesmaximal, characteristic, complemented
9#27542C211yesmaximal, characteristic, complemented
10#27539C211yesmaximal, characteristic, complemented
11#27420C211yesmaximal, characteristic, complemented
12#27417C211yesmaximal, characteristic, complemented
13#26211C211yesmaximal, characteristic, complemented
14#26209C211yesmaximal, characteristic, complemented
15#26124C211yesmaximal, characteristic, complemented
16#25897C211yesmaximal, characteristic, complemented
17#25356C211yesmaximal, characteristic, complemented
18#25287C211yesmaximal, characteristic, complemented
19#25251C211yesmaximal, characteristic, complemented
20#25237C211yesmaximal, characteristic, complemented
21#24980C211yesmaximal, characteristic, complemented
22#24043C211yesmaximal, characteristic, complemented
23#24037C211yesmaximal, characteristic, complemented
24#22979C211yesmaximal, characteristic, complemented
25#22580C211yesmaximal, characteristic, complemented
26#22568C211yesmaximal, characteristic, complemented
27#22424C211yesmaximal, characteristic, complemented
28#22424C211yesmaximal, characteristic, complemented
29#22417C211yesmaximal, characteristic, complemented
30#21489C211yesmaximal, characteristic, complemented
31#20411C211yesmaximal, characteristic, complemented
32C2×#547C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#546C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C2×#489C2211yescharacteristic
37C2×#485C2211yescharacteristic, complemented
38C2×#482C2211yescharacteristic
39C2×#475C2211yescharacteristic, complemented
40C2×#474C2211yescharacteristic
41C2×#435C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C2×C8×D4C2211yescharacteristic, complemented
44C2×#418C2211yescharacteristic
45C2×#416C2211yescharacteristic
46C2×#416C2211yescharacteristic
47C2×#416C2211yescharacteristic
48C22×#97C2211yescharacteristic, complemented
49#2860—21no—
50#2857C2211yescharacteristic, complemented
51#2854—21no—
52#2850C2211yescharacteristic
53#2563C2211yescharacteristic
54#2560—21no—
55#2560—21no—
56#2552C2211yescharacteristic, complemented
57#2545C2211yescharacteristic
58#2543—21no—
59#2536C2211yescharacteristic
60#2534—21no—
61#2532—21no—
62#2532—21no—
63#2496C2211yescharacteristic
64#2496C2211yescharacteristic, complemented
65#2495—21no—
66#2490—21no—
67#2485C2211yescharacteristic
68#2485C2211yescharacteristic, complemented
69#2429C2211yescharacteristic
70#2426C2211yescharacteristic
71#2425—21no—
72#2424—21no—
73#2415C2211yescharacteristic
74#2414C2211yescharacteristic
75#2413—21no—
76#2411—21no—
77#2369C2211yescharacteristic, complemented
78#2354C2211yescharacteristic
79#2354C2211yescharacteristic
80#2354C2211yescharacteristic, complemented
81#2349C2211yescharacteristic
82#2347C2211yescharacteristic
83#2347C2211yescharacteristic, complemented
84#2339C2211yescharacteristic
85D4×C22⋊C4C2211yescharacteristic
86C4×#125—21no—
87C4×#121C2211yescharacteristic
88C2×#388—21no—
89C4×#117C2211yescharacteristic, complemented
90#2100C2211yescharacteristic, complemented
91#2099C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic, complemented
97#2076C2211yescharacteristic, complemented
98#2072C2211yescharacteristic, complemented
99#2071C2211yescharacteristic
100#2066C2211yescharacteristic, complemented
101#2065C2211yescharacteristic
102#2043C2211yescharacteristic, complemented
103#2043C2211yescharacteristic, complemented
104#2042C2211yescharacteristic
105#2042C2211yescharacteristic
106#2036C2211yescharacteristic
107#2036C2211yescharacteristic
108#2036C2211yescharacteristic
109#2036C2211yescharacteristic, complemented
110#2035C2211yescharacteristic
111#2035C2211yescharacteristic, complemented
112#2033C2211yescharacteristic
113#2033C2211yescharacteristic
114#1993C2211yescharacteristic, complemented
115#1983C2211yescharacteristic
116#1983C2211yescharacteristic
117#1983C2211yescharacteristic
118#1981C2211yescharacteristic, complemented
119#1959C2211yescharacteristic
120#1959C2211yescharacteristic
121#1956C2211yescharacteristic, complemented
122#1955C2211yescharacteristic
123#1949C2211yescharacteristic, complemented
124#1949C2211yescharacteristic, complemented
125#1943C2211yescharacteristic, complemented
126#1942C2211yescharacteristic, complemented
127#1940C2211yescharacteristic, complemented
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1935C2211yescharacteristic, complemented
131#1935C2211yescharacteristic, complemented
132#1935C2211yescharacteristic, complemented
133#1934C2211yescharacteristic
134#1928C2211yescharacteristic, complemented
135#1927C2211yescharacteristic, complemented
136#1927C2211yescharacteristic, complemented
137#1926C2211yescharacteristic
138#1926C2211yescharacteristic
139#1925C2211yescharacteristic
140#1924C2211yescharacteristic
141#1924C2211yescharacteristic, complemented
142#1921C2211yescharacteristic, complemented
143#1918C2211yescharacteristic, complemented
144#1894C2211yescharacteristic
145#1894C2211yescharacteristic
146#1893C2211yescharacteristic
147#1893C2211yescharacteristic
148#1893C2211yescharacteristic
149#1892C2211yescharacteristic, complemented
150#1892C2211yescharacteristic, complemented
151#1892C2211yescharacteristic, complemented
152#1875C2211yescharacteristic
153#1875C2211yescharacteristic
154#1873C2211yescharacteristic
155#1873C2211yescharacteristic
156#1873C2211yescharacteristic, complemented
157#1873C2211yescharacteristic, complemented
158#1869C2211yescharacteristic
159#1869C2211yescharacteristic, complemented
160#1864C2211yescharacteristic
161#1864C2211yescharacteristic
162#1864C2211yescharacteristic
163#1864C2211yescharacteristic
164#1863C2211yescharacteristic, complemented
165#1863C2211yescharacteristic, complemented
166#1862C2211yescharacteristic
167#1862C2211yescharacteristic
168#1854C2211yescharacteristic, complemented
169#1854C2211yescharacteristic, complemented
170#1836C2211yescharacteristic, complemented
171#1825C2211yescharacteristic
172#1825C2211yescharacteristic, complemented
173#1809C2211yescharacteristic
174#1807C2211yescharacteristic, complemented
175#1803C2211yescharacteristic, complemented
176#1802C2211yescharacteristic
177#1802C2211yescharacteristic
178#1802C2211yescharacteristic
179#1797C2211yescharacteristic, complemented
180#1788C2211yescharacteristic
181#1788C2211yescharacteristic
182#1788C2211yescharacteristic
183#1788C2211yescharacteristic
184#1788C2211yescharacteristic
185#1786C2211yescharacteristic
186#1786C2211yescharacteristic
187#1786C2211yescharacteristic
188#1771C2211yescharacteristic, complemented
189#1763C2211yescharacteristic, complemented
190#1763C2211yescharacteristic, complemented
191#1763C2211yescharacteristic, complemented
192#1763C2211yescharacteristic, complemented
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic
200#1752C2211yescharacteristic, complemented
201#1735C2211yescharacteristic, complemented
202#1735C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#547—24no—
211#547—42no—
212#546—24no—
213#546—24no—
214#546—42no—
215#546—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#126—21no—
220C2×#125—21no—
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×#123—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121D411yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120—21no—
240C4×#41—24no—
241C4×#41—42no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×#117—21no—
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C22×C4⋊C4—21no—
260C22×C22⋊C4—21no—
261C22×C22⋊C4—21no—
262C22×C22⋊C4—21no—
263C22×C42—21no—
264C22×C42C2311yescharacteristic
265#489—42no—
266#485—42no—
267#482—42no—
268#475—42no—
269#474—24no—
270#435—42no—
271#435—42no—
272C8×D4—42no—
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285#418—24no—
286#416—24no—
287#416—24no—
288#416—24no—
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×#97—42no—
330C2×#97C2311yescharacteristic
331C2×#97C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×C4×C8C2311yescharacteristic
336#400—21no—
337#400—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#393—21no—
358#393—21no—
359#392—21no—
360#391—21no—
361#391—21no—
362#391—21no—
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#390—21no—
366#390—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390—21no—
371#390D411yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389D411yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
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#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388D411yescharacteristic
411#388D411yescharacteristic
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386D411yescharacteristic
423#386D411yescharacteristic
424#385—21no—
425#385—21no—
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#383—21no—
430#383—21no—
431#382—21no—
432#382C2311yescharacteristic
433#381—21no—
434#380—21no—
435#380—21no—
436#380D411yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#379—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465#376—21no—
466C2×#95—21no—
467C2×#95—21no—
468C43—21no—
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#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41#4114yes—
512C22×Q8—21no—
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×D411yescharacteristic
527C22×D4C2×D411yescharacteristic
528C22×D4C2×D411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4C2×D411yescharacteristic
538C23×C4C2×D411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C2×M16—22no—
543C2×M16—41no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—22no—
548C22×C8—22no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8—41no—
553C22×C8—41no—
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C4⋊Q8—22no—
563C4⋊Q8—22no—
564C4⋊Q8—22no—
565C4⋊Q8—41no—
566#126—82no—
567#126—82no—
568#125—44no—
569#124—22no—
570#124—22no—
571#124—22no—
572#124—41no—
573#123—44no—
574#123—44no—
575#123—44no—
576#123—44no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—82no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—42no—
590#121—44no—
591#121—44no—
592#121—41no—
593#121—44no—
594#120—44no—
595#120—44no—
596C4×Q8—22no—
597C4×Q8—22no—
598C4×Q8—22no—
599C4×Q8—41no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—44no—
614C4×D4—44no—
615C4×D4#4114yes—
616#117—22no—
617#117—22no—
618#117—22no—
619#117—22no—
620#117—22no—
621#117—22no—
622#117—44no—
623#117—41no—
624#117—41no—
625#117—41no—
626#117—41no—
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—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—44no—
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—44no—
702C2×C22⋊C4—44no—
703C2×C22⋊C4—44no—
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
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×C42—22no—
715C2×C42—22no—
716C2×C42—21no—
717C2×C42—21no—
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×C42—21no—
728C2×C42—21no—
729C2×C42—44no—
730C2×C42C2×D411yescharacteristic
731C2×C42C2×D411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#107—22no—
737#107—22no—
738#107—41no—
739#107—41no—
740#106—41no—
741#106—41no—
742#106—41no—
743#106—41no—
744C4⋊C8—22no—
745C4⋊C8—22no—
746C4⋊C8—41no—
747C4⋊C8—41no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102#4114yes—
780C22⋊C8—22no—
781C22⋊C8—22no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785C22⋊C8—41no—
786C22⋊C8—41no—
787C22⋊C8—41no—
788#97—22no—
789#97—22no—
790#97—41no—
791#97—41no—
792#97—41no—
793C4×C8—41no—
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#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830C24—21no—
831C24—21no—
832C24—42no—
833C24—42no—
834C24—42no—
835C24—42no—
836C24—81no—
837C24—81no—
838C24—81no—
839C24C22×D411yescharacteristic
840C24C22×D411yescharacteristic
841C24C22×D411yescharacteristic
842#41—28no—
843#41—44no—
844#41—44no—
845#41—44no—
846#41—44no—
847#41—82no—
848#41—82no—
849#41—82no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—42no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8C2×#4112yes—
865C2×D4—22no—
866C2×D4—24no—
867C2×D4—22no—
868C2×D4—22no—
869C2×D4—22no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—82no—
896C2×D4—82no—
897C2×D4—82no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4C2×#4112yes—
903C2×D4C2×#4112yes—
904C2×D4C2×#4112yes—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—24no—
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—22no—
926C22×C4—22no—
927C22×C4—24no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—41no—
940C22×C4—41no—
941C22×C4—41no—
942C22×C4—41no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C2×#4112yes—
971C22×C4H(5,𝔽2)12yes—
972C22×C4C2511yescharacteristic
973M16—82no—
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—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—44no—
998C2×C8—44no—
999C2×C8—82no—
1000C2×C8C2×#4112yes—
1001C4⋊C4—22no—
1002C4⋊C4—22no—
1003C4⋊C4—22no—
1004C4⋊C4—22no—
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—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—41no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4C2×#4112yes—
1052C4⋊C4C2×#4112yes—
1053C22⋊C4—22no—
1054C22⋊C4—22no—
1055C22⋊C4—24no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
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—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
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—22no—
1097C42—22no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—42no—
1105C42—42no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—42no—
1110C42—42no—
1111C42—42no—
1112C42—42no—
1113C42—42no—
1114C42—81no—
1115C42—81no—
1116C42—81no—
1117C42C2×#4112yes—
1118C42H(5,𝔽2)12yes—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—22no—
1123C23—21no—
1124C23—22no—
1125C23—21no—
1126C23—22no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
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—162no—
1158C23—162no—
1159C23—162no—
1160C23#54612yes—
1161C23C23×D411yescharacteristic
1162Q8—22no—
1163Q8—22no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—162no—
1171D4—22no—
1172D4—22no—
1173D4—22no—
1174D4—44no—
1175D4—48no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—82no—
1181D4—82no—
1182D4—84no—
1183D4—84no—
1184D4—162no—
1185D4—162no—
1186D4#52914yes—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—48no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—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—82no—
1272C2×C4—82no—
1273C2×C4—84no—
1274C2×C4—84no—
1275C2×C4—84no—
1276C2×C4—84no—
1277C2×C4—162no—
1278C2×C4#54612yes—
1279C2×C4#54612yes—
1280C2×C4#54612yes—
1281C2×C4#57512yes—
1282C2×C4C22×#4111yescharacteristic
1283C2×C4C22×#4111yescharacteristic
1284C2×C4C22×#4111yescharacteristic
1285C2×C4C2×H(5,𝔽2)11yescharacteristic
1286C2×C4C2×H(5,𝔽2)11yescharacteristic
1287C2×C4#58511yescharacteristic
1288C8—22no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C8—41no—
1293C8—41no—
1294C8—41no—
1295C8—41no—
1296C22—22no—
1297C22—24no—
1298C22—22no—
1299C22—22no—
1300C22—41no—
1301C22—42no—
1302C22—41no—
1303C22—42no—
1304C22—42no—
1305C22—41no—
1306C22—42no—
1307C22—42no—
1308C22—41no—
1309C22—42no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—168no—
1332C22C2×#54611yescharacteristic
1333C22C2×#54611yescharacteristic
1334C22D4×#4111yescharacteristic
1335C22C2×#57511yescharacteristic
1336C22#358411yescharacteristic
1337C22#358511yescharacteristic
1338C22#358611yescharacteristic
1339C4—22no—
1340C4—22no—
1341C4—22no—
1342C4—22no—
1343C4—41no—
1344C4—42no—
1345C4—41no—
1346C4—41no—
1347C4—42no—
1348C4—41no—
1349C4—41no—
1350C4—42no—
1351C4—41no—
1352C4—41no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4C2×#52911yescharacteristic
1365C4#349411yescharacteristic
1366C4#350511yescharacteristic
1367C4#351911yescharacteristic
1368C2—42no—
1369C2—44no—
1370C2—81no—
1371C2—81no—
1372C2—161no—
1373C2#3610711yescharacteristic
1374C2#6114111yescharacteristic
1375C2#6116511yescharacteristic
1376C2#6118711yescharacteristic
1377C2#6122211yescharacteristic
1378C2#6145911yescharacteristic
1379C2#6153211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36218C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36459C2semidirect
3. #33112C2semidirect
4. #33051C2semidirect
5. #32955C2semidirect
6. #29066C2semidirect
7. #29054C2semidirect
8. #27765C2semidirect
9. #27542C2semidirect
10. #27539C2semidirect
11. #27420C2semidirect
12. #27417C2semidirect
13. #26211C2semidirect
14. #26209C2semidirect
15. #26124C2semidirect
16. #25897C2semidirect
17. #25356C2semidirect
18. #25287C2semidirect
19. #25251C2semidirect
20. #25237C2semidirect
21. #24980C2semidirect
22. #24043C2semidirect
23. #24037C2semidirect
24. #22979C2semidirect
25. #22580C2semidirect
26. #22568C2semidirect
27. #22424C2semidirect
28. #22424C2semidirect
29. #22417C2semidirect
30. #21489C2semidirect
31. #20411C2semidirect
37. C2×#485C22semidirect
39. C2×#475C22semidirect
43. C2×C8×D4C22semidirect
48. C22×#97C22semidirect
50. #2857C22semidirect
56. #2552C22semidirect
64. #2496C22semidirect
68. #2485C22semidirect
77. #2369C22semidirect
80. #2354C22semidirect
83. #2347C22semidirect
89. C4×#117C22semidirect
90. #2100C22semidirect
91. #2099C22semidirect
92. #2088C22semidirect
93. #2087C22semidirect
96. #2077C22semidirect
97. #2076C22semidirect
98. #2072C22semidirect
100. #2066C22semidirect
102. #2043C22semidirect
103. #2043C22semidirect
109. #2036C22semidirect
111. #2035C22semidirect
114. #1993C22semidirect
118. #1981C22semidirect
121. #1956C22semidirect
123. #1949C22semidirect
124. #1949C22semidirect
125. #1943C22semidirect
126. #1942C22semidirect
127. #1940C22semidirect
130. #1935C22semidirect
131. #1935C22semidirect
132. #1935C22semidirect
134. #1928C22semidirect
135. #1927C22semidirect
136. #1927C22semidirect
141. #1924C22semidirect
142. #1921C22semidirect
143. #1918C22semidirect
149. #1892C22semidirect
150. #1892C22semidirect
151. #1892C22semidirect
156. #1873C22semidirect
157. #1873C22semidirect
159. #1869C22semidirect
164. #1863C22semidirect
165. #1863C22semidirect
168. #1854C22semidirect
169. #1854C22semidirect
170. #1836C22semidirect
172. #1825C22semidirect
174. #1807C22semidirect
175. #1803C22semidirect
179. #1797C22semidirect
188. #1771C22semidirect
189. #1763C22semidirect
190. #1763C22semidirect
191. #1763C22semidirect
192. #1763C22semidirect
200. #1752C22semidirect
201. #1735C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#364592
#362182
#331122
#330512
#329552
#290662
#290542
#277652
#275422
#275392
#274202
#274172
#262112
#262092
#261242
#258972
#253562
#252872
#252512
#252372
#249802
#240432
#240372
#229792
#225802
#225682
#224242
#224172
#214892
#204112