Finite Group Databasebeta

← #7330016

Subgroups — #7330016

Order 512.

1737 conjugacy classes of subgroups.

The subgroup lattice has 1407 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59041C211yesmaximal, characteristic
2#45664C211yesmaximal, characteristic, complemented
3#32353C211yesmaximal, characteristic, complemented
4#32268C211yesmaximal, characteristic, complemented
5#32011C211yesmaximal, characteristic, complemented
6#31553C211yesmaximal, characteristic, complemented
7#31549C211yesmaximal, characteristic, complemented
8#31379C211yesmaximal, characteristic, complemented
9#31329C211yesmaximal, characteristic, complemented
10#31271C211yesmaximal, characteristic, complemented
11#31088C211yesmaximal, characteristic, complemented
12#30683C211yesmaximal, characteristic, complemented
13#30583C211yesmaximal, characteristic, complemented
14#30424C211yesmaximal, characteristic, complemented
15#30008C211yesmaximal, characteristic, complemented
16#29694C211yesmaximal, characteristic, complemented
17#29167C211yesmaximal, characteristic, complemented
18#28229C211yesmaximal, characteristic, complemented
19#28110C211yesmaximal, characteristic, complemented
20#27238C211yesmaximal, characteristic, complemented
21#26897C211yesmaximal, characteristic, complemented
22#26768C211yesmaximal, characteristic, complemented
23#25974C211yesmaximal, characteristic, complemented
24#25960C211yesmaximal, characteristic, complemented
25#25501C211yesmaximal, characteristic, complemented
26#25354C211yesmaximal, characteristic, complemented
27#25128C211yesmaximal, characteristic, complemented
28#24905C211yesmaximal, characteristic, complemented
29#24448C211yesmaximal, characteristic, complemented
30#24033C211yesmaximal, characteristic, complemented
31#22174C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#481C2211yescharacteristic
35C2×#478C2211yescharacteristic, complemented
36C2×#478C2211yescharacteristic, complemented
37C2×#476C2211yescharacteristic, complemented
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic, complemented
40C2×#468C2211yescharacteristic, complemented
41C2×#450C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic, complemented
44C2×#436C2211yescharacteristic, complemented
45C2×#435C2211yescharacteristic, complemented
46C2×#418C2211yescharacteristic
47C22×#102C2211yescharacteristic
48#2855C2211yescharacteristic, complemented
49#2851C2211yescharacteristic, complemented
50#2827—21no—
51#2786—21no—
52#2755—21no—
53#2754—21no—
54#2747—21no—
55#2739—21no—
56#2686—21no—
57#2684—21no—
58#2684—21no—
59#2563C2211yescharacteristic
60#2563C2211yescharacteristic
61#2547C2211yescharacteristic, complemented
62#2536C2211yescharacteristic, complemented
63#2535—21no—
64#2535C2211yescharacteristic
65#2535C2211yescharacteristic
66#2508C2211yescharacteristic, complemented
67#2489C2211yescharacteristic, complemented
68#2487C2211yescharacteristic
69#2485C2211yescharacteristic, complemented
70#2451C2211yescharacteristic, complemented
71#2442C2211yescharacteristic, complemented
72#2439C2211yescharacteristic, complemented
73#2421C2211yescharacteristic, complemented
74#2420—21no—
75#2420C2211yescharacteristic
76#2420C2211yescharacteristic
77#2417C2211yescharacteristic, complemented
78#2415C2211yescharacteristic
79#2408—21no—
80#2408C2211yescharacteristic
81#2408C2211yescharacteristic
82#2404—21no—
83#2404—21no—
84#2379—21no—
85#2366C2211yescharacteristic
86D4×C22⋊C4—21no—
87D4×C22⋊C4C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89C4×#121C2211yescharacteristic
90C4×#121C2211yescharacteristic
91#2101C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic
96#2088C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2077C2211yescharacteristic, complemented
100#2077C2211yescharacteristic, complemented
101#2077C2211yescharacteristic, complemented
102#2077C2211yescharacteristic, complemented
103#2075C2211yescharacteristic, complemented
104#2075C2211yescharacteristic, complemented
105#2073C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2066C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic, complemented
111#2059C2211yescharacteristic, complemented
112#2058C2211yescharacteristic, complemented
113#2057C2211yescharacteristic, complemented
114#2057C2211yescharacteristic, complemented
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic, complemented
117#2041C2211yescharacteristic
118#2041C2211yescharacteristic
119#2041C2211yescharacteristic
120#2036C2211yescharacteristic, complemented
121#2035C2211yescharacteristic, complemented
122#2035C2211yescharacteristic, complemented
123#2035C2211yescharacteristic, complemented
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2034C2211yescharacteristic
127#2034C2211yescharacteristic, complemented
128#2034C2211yescharacteristic, complemented
129#2033C2211yescharacteristic
130#2033C2211yescharacteristic, complemented
131#2033C2211yescharacteristic, complemented
132#2025C2211yescharacteristic
133#2024C2211yescharacteristic, complemented
134#2023C2211yescharacteristic
135#2023C2211yescharacteristic, complemented
136#2014C2211yescharacteristic
137#2000C2211yescharacteristic
138#2000C2211yescharacteristic
139#1993C2211yescharacteristic, complemented
140#1973C2211yescharacteristic
141#1949C2211yescharacteristic, complemented
142#1936C2211yescharacteristic, complemented
143#1934C2211yescharacteristic
144#1934C2211yescharacteristic, complemented
145#1927C2211yescharacteristic, complemented
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic, complemented
148#1924C2211yescharacteristic, complemented
149#1923C2211yescharacteristic, complemented
150#1920C2211yescharacteristic, complemented
151#1920C2211yescharacteristic, complemented
152#1918C2211yescharacteristic, complemented
153#1917C2211yescharacteristic, complemented
154#1916C2211yescharacteristic, complemented
155#1895C2211yescharacteristic
156#1895C2211yescharacteristic
157#1895C2211yescharacteristic, complemented
158#1895C2211yescharacteristic, complemented
159#1893C2211yescharacteristic
160#1892C2211yescharacteristic, complemented
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic, complemented
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic, complemented
165#1877C2211yescharacteristic, complemented
166#1877C2211yescharacteristic, complemented
167#1875C2211yescharacteristic
168#1870C2211yescharacteristic
169#1870C2211yescharacteristic, complemented
170#1870C2211yescharacteristic, complemented
171#1869C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic, complemented
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic, complemented
177#1862C2211yescharacteristic, complemented
178#1862C2211yescharacteristic, complemented
179#1862C2211yescharacteristic, complemented
180#1854C2211yescharacteristic, complemented
181#1852C2211yescharacteristic, complemented
182#1852C2211yescharacteristic, complemented
183#1851C2211yescharacteristic, complemented
184#1850C2211yescharacteristic, complemented
185#1846C2211yescharacteristic, complemented
186#1825C2211yescharacteristic, complemented
187#1809C2211yescharacteristic, complemented
188#1809C2211yescharacteristic, complemented
189#1809C2211yescharacteristic, complemented
190#1809C2211yescharacteristic, complemented
191#1807C2211yescharacteristic, complemented
192#1805C2211yescharacteristic, complemented
193#1804C2211yescharacteristic, complemented
194#1804C2211yescharacteristic, complemented
195#1804C2211yescharacteristic, complemented
196#1797C2211yescharacteristic, complemented
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1786C2211yescharacteristic
200#1786C2211yescharacteristic
201#1762C2211yescharacteristic, complemented
202#1728C2211yescharacteristic, complemented
203C22×#41—21no—
204C23×D4—21no—
205C23×D4C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214D42—42no—
215D42—42no—
216#532—42no—
217#532—42no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#124—21no—
223C2×#124—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×#121—21no—
228C2×#121—21no—
229C2×#121D411yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237C2×#120—21no—
238C2×#120—21no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255C22×C42C2311yescharacteristic
256#481—42no—
257#478—42no—
258#478—42no—
259#476—42no—
260#468—42no—
261#468—42no—
262#468—42no—
263#450—42no—
264#450—42no—
265C4×SD16—42no—
266#436—42no—
267#435—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285#418—42no—
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#102—42no—
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#399—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#396—21no—
345#396—21no—
346#395—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#393—21no—
355#393—21no—
356#393—21no—
357#393—21no—
358#393—21no—
359#392—21no—
360#392—21no—
361#392—21no—
362#392—21no—
363#391—21no—
364#391—21no—
365#391—21no—
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#390—21no—
370#390—21no—
371#390D411yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#389—21no—
378#389D411yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388D411yescharacteristic
395#388D411yescharacteristic
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#387—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#386—21no—
418#386—21no—
419#386—21no—
420#386D411yescharacteristic
421#386D411yescharacteristic
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#382—21no—
428#382—21no—
429#382—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#381—21no—
435#381—21no—
436#381—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380D411yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#379—21no—
455#379—21no—
456#379—21no—
457#379—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C22⋊C4—21no—
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C25—21no—
498C2×#41—44no—
499C2×#41—82no—
500C2×#41—82no—
501C22×Q8—21no—
502C22×Q8—21no—
503C22×Q8C2411yescharacteristic
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—44no—
526C22×D4—44no—
527C22×D4—82no—
528C22×D4C2×D411yescharacteristic
529C22×D4C2×D411yescharacteristic
530C22×D4C2×D411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C2×D411yescharacteristic
541C23×C4C2×D411yescharacteristic
542C23×C4C2411yescharacteristic
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×M16—22no—
555C2×M16—22no—
556C2×M16—41no—
557C2×M16—41no—
558C2×M16—41no—
559C2×M16—41no—
560C2×M16—41no—
561C2×M16—41no—
562C2×M16—41no—
563C22×C8—41no—
564C22×C8—41no—
565C22×C8—41no—
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577C4⋊Q8—41no—
578#127—22no—
579#127—22no—
580#125—41no—
581#125—41no—
582#124—44no—
583#124—44no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—42no—
596#121—41no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—44no—
602#121—44no—
603#120—44no—
604#120—44no—
605#120—82no—
606#120—82no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—44no—
626C4×D4—82no—
627C4×D4—82no—
628#117—41no—
629#117—41no—
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—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⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—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—82no—
703C2×C22⋊C4—82no—
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—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—41no—
719C2×C42—41no—
720C2×C42C2×D411yescharacteristic
721C2×C42C2×D411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726#107—41no—
727#107—41no—
728#107—41no—
729#107—41no—
730#107—41no—
731#107—41no—
732#106—22no—
733#106—41no—
734#106—41no—
735#106—41no—
736#106—41no—
737#106—41no—
738#106—41no—
739C4⋊C8—22no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
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—
769C22⋊C8—22no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777#97—41no—
778C4×C8—22no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#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#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821C24—21no—
822C24—21no—
823C24—21no—
824C24—42no—
825C24—42no—
826C24—42no—
827C24—42no—
828C24—42no—
829C24—42no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24—81no—
836C24—81no—
837C24—81no—
838C24C22×D411yescharacteristic
839C24C22×D411yescharacteristic
840C24C22×D411yescharacteristic
841#41—816no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—42no—
849C2×Q8—42no—
850C2×Q8—81no—
851C2×Q8—81no—
852C2×Q8—81no—
853C2×Q8—81no—
854C2×D4—24no—
855C2×D4—22no—
856C2×D4—24no—
857C2×D4—22no—
858C2×D4—22no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—41no—
875C2×D4—42no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—82no—
903C2×D4—82no—
904C2×D4—82no—
905C2×D4—82no—
906C2×D4—82no—
907C2×D4—82no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—816no—
914C2×D4H(5,𝔽2)12yes—
915C2×D4H(5,𝔽2)12yes—
916C2×D42−1+412yes—
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—22no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—41no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C2511yescharacteristic
984SD16—44no—
985SD16—82no—
986SD16—82no—
987M16—82no—
988M16—82no—
989M16—82no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—82no—
1014C2×C8H(5,𝔽2)12yes—
1015C4⋊C4—22no—
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—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—41no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C22⋊C4—22no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
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—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—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—41no—
1116C42—41no—
1117C42—42no—
1118C42—42no—
1119C42—81no—
1120C42—81no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—22no—
1132C23—22no—
1133C23—21no—
1134C23—21no—
1135C23—22no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—84no—
1163C23—84no—
1164C23—84no—
1165C23—84no—
1166C23—84no—
1167C23—84no—
1168C23—162no—
1169C23—162no—
1170C23—162no—
1171C23—162no—
1172C23—162no—
1173C23—162no—
1174C23—162no—
1175C23—162no—
1176C23#57512yes—
1177C23C23×D411yescharacteristic
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—84no—
1183Q8—162no—
1184D4—22no—
1185D4—22no—
1186D4—22no—
1187D4—22no—
1188D4—22no—
1189D4—22no—
1190D4—44no—
1191D4—48no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—82no—
1199D4—84no—
1200D4—82no—
1201D4—84no—
1202D4—84no—
1203D4—84no—
1204D4—84no—
1205D4—84no—
1206D4—84no—
1207D4—84no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
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—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—44no—
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—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—82no—
1293C2×C4—84no—
1294C2×C4—84no—
1295C2×C4—84no—
1296C2×C4—162no—
1297C2×C4—162no—
1298C2×C4—162no—
1299C2×C4#57712yes—
1300C2×C4C2×H(5,𝔽2)11yescharacteristic
1301C2×C4C2×H(5,𝔽2)11yescharacteristic
1302C2×C4C2×H(5,𝔽2)11yescharacteristic
1303C2×C4C2×2−1+411yescharacteristic
1304C2×C4#58511yescharacteristic
1305C2×C4#58511yescharacteristic
1306C8—22no—
1307C8—41no—
1308C8—41no—
1309C8—41no—
1310C8—41no—
1311C8—41no—
1312C8—41no—
1313C8—41no—
1314C22—22no—
1315C22—22no—
1316C22—22no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—42no—
1333C22—42no—
1334C22—41no—
1335C22—41no—
1336C22—42no—
1337C22—41no—
1338C22—42no—
1339C22—42no—
1340C22—41no—
1341C22—41no—
1342C22—42no—
1343C22—41no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—168no—
1357C22—168no—
1358C22#348411yescharacteristic
1359C22#348911yescharacteristic
1360C22#349611yescharacteristic
1361C22C2×#57511yescharacteristic
1362C22C2×#57711yescharacteristic
1363C22#358511yescharacteristic
1364C22#358511yescharacteristic
1365C4—22no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4#353411yescharacteristic
1390C4#353511yescharacteristic
1391C4#353611yescharacteristic
1392C4#354511yescharacteristic
1393C2—42no—
1394C2—81no—
1395C2—81no—
1396C2—82no—
1397C2—82no—
1398C2—82no—
1399C2#4793811yescharacteristic
1400C2#6160111yescharacteristic
1401C2#6164411yescharacteristic
1402C2#6211911yescharacteristic
1403C2#6218811yescharacteristic
1404C2#6229811yescharacteristic
1405C2#6234611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59041C2
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
2. #45664C2semidirect
3. #32353C2semidirect
4. #32268C2semidirect
5. #32011C2semidirect
6. #31553C2semidirect
7. #31549C2semidirect
8. #31379C2semidirect
9. #31329C2semidirect
10. #31271C2semidirect
11. #31088C2semidirect
12. #30683C2semidirect
13. #30583C2semidirect
14. #30424C2semidirect
15. #30008C2semidirect
16. #29694C2semidirect
17. #29167C2semidirect
18. #28229C2semidirect
19. #28110C2semidirect
20. #27238C2semidirect
21. #26897C2semidirect
22. #26768C2semidirect
23. #25974C2semidirect
24. #25960C2semidirect
25. #25501C2semidirect
26. #25354C2semidirect
27. #25128C2semidirect
28. #24905C2semidirect
29. #24448C2semidirect
30. #24033C2semidirect
31. #22174C2semidirect
35. C2×#478C22semidirect
36. C2×#478C22semidirect
37. C2×#476C22semidirect
39. C2×#468C22semidirect
40. C2×#468C22semidirect
43. C2×C4×SD16C22semidirect
44. C2×#436C22semidirect
45. C2×#435C22semidirect
48. #2855C22semidirect
49. #2851C22semidirect
61. #2547C22semidirect
62. #2536C22semidirect
66. #2508C22semidirect
67. #2489C22semidirect
69. #2485C22semidirect
70. #2451C22semidirect
71. #2442C22semidirect
72. #2439C22semidirect
73. #2421C22semidirect
77. #2417C22semidirect
91. #2101C22semidirect
92. #2101C22semidirect
93. #2097C22semidirect
96. #2088C22semidirect
97. #2085C22semidirect
98. #2085C22semidirect
99. #2077C22semidirect
100. #2077C22semidirect
101. #2077C22semidirect
102. #2077C22semidirect
103. #2075C22semidirect
104. #2075C22semidirect
105. #2073C22semidirect
108. #2066C22semidirect
110. #2065C22semidirect
111. #2059C22semidirect
112. #2058C22semidirect
113. #2057C22semidirect
114. #2057C22semidirect
116. #2055C22semidirect
120. #2036C22semidirect
121. #2035C22semidirect
122. #2035C22semidirect
123. #2035C22semidirect
127. #2034C22semidirect
128. #2034C22semidirect
130. #2033C22semidirect
131. #2033C22semidirect
133. #2024C22semidirect
135. #2023C22semidirect
139. #1993C22semidirect
141. #1949C22semidirect
142. #1936C22semidirect
144. #1934C22semidirect
145. #1927C22semidirect
147. #1926C22semidirect
148. #1924C22semidirect
149. #1923C22semidirect
150. #1920C22semidirect
151. #1920C22semidirect
152. #1918C22semidirect
153. #1917C22semidirect
154. #1916C22semidirect
157. #1895C22semidirect
158. #1895C22semidirect
160. #1892C22semidirect
162. #1880C22semidirect
164. #1877C22semidirect
165. #1877C22semidirect
166. #1877C22semidirect
169. #1870C22semidirect
170. #1870C22semidirect
174. #1864C22semidirect
176. #1862C22semidirect
177. #1862C22semidirect
178. #1862C22semidirect
179. #1862C22semidirect
180. #1854C22semidirect
181. #1852C22semidirect
182. #1852C22semidirect
183. #1851C22semidirect
184. #1850C22semidirect
185. #1846C22semidirect
186. #1825C22semidirect
187. #1809C22semidirect
188. #1809C22semidirect
189. #1809C22semidirect
190. #1809C22semidirect
191. #1807C22semidirect
192. #1805C22semidirect
193. #1804C22semidirect
194. #1804C22semidirect
195. #1804C22semidirect
196. #1797C22semidirect
201. #1762C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#590412
#456642
#323532
#322682
#320112
#315532
#315492
#313792
#313292
#312712
#310882
#306832
#305832
#304242
#300082
#296942
#291672
#282292
#281102
#272382
#268972
#267682
#259742
#259602
#255012
#253542
#251282
#249052
#244482
#240332
#221742