Finite Group Databasebeta

← #7080739

Subgroups — #7080739

Order 512.

1699 conjugacy classes of subgroups.

The subgroup lattice has 1389 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45259C211yesmaximal, characteristic, complemented
2#45108C211yesmaximal, characteristic, complemented
3#32173C211yesmaximal, characteristic, complemented
4#32126C211yesmaximal, characteristic, complemented
5#31926C211yesmaximal, characteristic, complemented
6#31837C211yesmaximal, characteristic, complemented
7#31815C211yesmaximal, characteristic, complemented
8#31649C211yesmaximal, characteristic, complemented
9#30620C211yesmaximal, characteristic, complemented
10#30535C211yesmaximal, characteristic, complemented
11#27597C211yesmaximal, characteristic, complemented
12#27426C211yesmaximal, characteristic, complemented
13#27278C211yesmaximal, characteristic, complemented
14#27071C211yesmaximal, characteristic, complemented
15#26750C211yesmaximal, characteristic, complemented
16#26410C211yesmaximal, characteristic, complemented
17#26206C211yesmaximal, characteristic, complemented
18#25337C211yesmaximal, characteristic, complemented
19#25135C211yesmaximal, characteristic, complemented
20#25105C211yesmaximal, characteristic, complemented
21#24901C211yesmaximal, characteristic, complemented
22#24629C211yesmaximal, characteristic, complemented
23#24539C211yesmaximal, characteristic, complemented
24#24363C211yesmaximal, characteristic, complemented
25#23947C211yesmaximal, characteristic, complemented
26#23850C211yesmaximal, characteristic
27#23543C211yesmaximal, characteristic, complemented
28#22883C211yesmaximal, characteristic, complemented
29#22427C211yesmaximal, characteristic, complemented
30#22074C211yesmaximal, characteristic, complemented
31#21896C211yesmaximal, characteristic, complemented
32C22×#135C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#542C2211yescharacteristic
35C2×#489C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#464C2211yescharacteristic
38C2×#462C2211yescharacteristic, complemented
39C2×#452C2211yescharacteristic, complemented
40C2×#449C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#447C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic
44C2×#436C2211yescharacteristic
45C2×#424C2211yescharacteristic, complemented
46C2×#417C2211yescharacteristic
47C2×#417C2211yescharacteristic, complemented
48C2×#418C2211yescharacteristic
49#2753—21no—
50#2747—21no—
51#2741—21no—
52#2730—21no—
53#2708—21no—
54#2695—21no—
55#2687—21no—
56#2684—21no—
57#2597—21no—
58#2574—21no—
59#2568C2211yescharacteristic, complemented
60#2560—21no—
61#2547C2211yescharacteristic
62#2534—21no—
63#2521—21no—
64#2513C2211yescharacteristic, complemented
65#2512C2211yescharacteristic, complemented
66#2500C2211yescharacteristic
67#2492C2211yescharacteristic
68#2491C2211yescharacteristic
69#2480—21no—
70#2452C2211yescharacteristic
71#2447C2211yescharacteristic
72#2440C2211yescharacteristic, complemented
73#2437—21no—
74#2435C2211yescharacteristic
75#2432C2211yescharacteristic
76#2429C2211yescharacteristic
77#2427—21no—
78#2423C2211yescharacteristic
79#2417C2211yescharacteristic
80#2407C2211yescharacteristic
81#2395C2211yescharacteristic
82#2367C2211yescharacteristic
83#2362C2211yescharacteristic
84#2361C2211yescharacteristic
85#2355C2211yescharacteristic, complemented
86#2352C2211yescharacteristic
87#2341C2211yescharacteristic, complemented
88D4×C22⋊C4C2211yescharacteristic
89#2314C2211yescharacteristic, complemented
90#2311C2211yescharacteristic
91#2311C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2100C2211yescharacteristic, complemented
94#2096C2211yescharacteristic, complemented
95#2094C2211yescharacteristic
96#2088C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2074C2211yescharacteristic, complemented
99#2074C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2071C2211yescharacteristic
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic, complemented
104#2056C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2056C2211yescharacteristic, complemented
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic, complemented
110#2055C2211yescharacteristic, complemented
111#2055C2211yescharacteristic, complemented
112#2054C2211yescharacteristic
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic
115#2043C2211yescharacteristic, complemented
116#2042C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2024C2211yescharacteristic, complemented
120#2024C2211yescharacteristic, complemented
121#2023C2211yescharacteristic
122#2023C2211yescharacteristic, complemented
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic
125#2013C2211yescharacteristic, complemented
126#2012C2211yescharacteristic
127#2012C2211yescharacteristic
128#2012C2211yescharacteristic
129#2001C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#1988C2211yescharacteristic, complemented
133#1987C2211yescharacteristic, complemented
134#1987C2211yescharacteristic, complemented
135#1983C2211yescharacteristic
136#1983C2211yescharacteristic
137#1983C2211yescharacteristic
138#1972C2211yescharacteristic
139#1968C2211yescharacteristic, complemented
140#1958C2211yescharacteristic
141#1956C2211yescharacteristic, complemented
142#1940C2211yescharacteristic, complemented
143#1939C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic, complemented
147#1933C2211yescharacteristic, complemented
148#1927C2211yescharacteristic, complemented
149#1927C2211yescharacteristic, complemented
150#1927C2211yescharacteristic, complemented
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic, complemented
154#1924C2211yescharacteristic
155#1923C2211yescharacteristic
156#1920C2211yescharacteristic, complemented
157#1919C2211yescharacteristic, complemented
158#1916C2211yescharacteristic, complemented
159#1916C2211yescharacteristic, complemented
160#1895C2211yescharacteristic
161#1895C2211yescharacteristic
162#1894C2211yescharacteristic
163#1894C2211yescharacteristic, complemented
164#1893C2211yescharacteristic
165#1892C2211yescharacteristic, complemented
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic, complemented
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1874C2211yescharacteristic
177#1873C2211yescharacteristic
178#1873C2211yescharacteristic
179#1872C2211yescharacteristic, complemented
180#1869C2211yescharacteristic
181#1865C2211yescharacteristic, complemented
182#1864C2211yescharacteristic
183#1853C2211yescharacteristic, complemented
184#1853C2211yescharacteristic, complemented
185#1851C2211yescharacteristic
186#1851C2211yescharacteristic
187#1850C2211yescharacteristic, complemented
188#1825C2211yescharacteristic
189#1818C2211yescharacteristic, complemented
190#1805C2211yescharacteristic, complemented
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic
193#1803C2211yescharacteristic, complemented
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic
196#1788C2211yescharacteristic
197#1788C2211yescharacteristic
198#1786C2211yescharacteristic
199#1763C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic
201#1753C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×#135—42no—
207C2×#135—42no—
208C2×#135—42no—
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C22×M16C2311yescharacteristic
219C23×C8C2311yescharacteristic
220#546—24no—
221#546—42no—
222#542—24no—
223#542—42no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×#126—21no—
228C2×#126—21no—
229C2×#124—21no—
230C2×#124—21no—
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#123—21no—
235C2×#123—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×#121—21no—
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#120—21no—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4—21no—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C22⋊C4—21no—
260C22×C22⋊C4—21no—
261#489—42no—
262#470—42no—
263#464—42no—
264#462—42no—
265#452—42no—
266#450—42no—
267#449—24no—
268#447—42no—
269C4×SD16—42no—
270#436—42no—
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275#424—42no—
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283#418—42no—
284#417—42no—
285#417—42no—
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326#400—21no—
327#400—21no—
328#400—21no—
329#400D411yescharacteristic
330#399—21no—
331#399D411yescharacteristic
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398D411yescharacteristic
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397D411yescharacteristic
345#397D411yescharacteristic
346#397D411yescharacteristic
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#395—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394D411yescharacteristic
361#394D411yescharacteristic
362#393—21no—
363#393—21no—
364#393—21no—
365#392—21no—
366#391—21no—
367#391—21no—
368#391—21no—
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#390—21no—
377#390—21no—
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#389—21no—
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#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#387—21no—
410#387—21no—
411#387—21no—
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#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#382—21no—
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#381—21no—
440#380—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#379—21no—
453#379—21no—
454#379—21no—
455C4×C4⋊C4—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
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—41no—
512C22×Q8—21no—
513C22×Q8—21no—
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4C2×D411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541#135—416no—
542C2×Q16—22no—
543C2×Q16—22no—
544C2×Q16—41no—
545C2×Q16—41no—
546C2×Q16—41no—
547C2×Q16—41no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×D8—22no—
561C2×D8—22no—
562C2×D8—41no—
563C2×D8—41no—
564C2×D8—41no—
565C2×D8—41no—
566C2×M16—22no—
567C2×M16—41no—
568C2×M16—41no—
569C2×M16—41no—
570C2×M16—41no—
571C2×M16—41no—
572C22×C8—22no—
573C22×C8—41no—
574C22×C8—41no—
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C4⋊Q8—22no—
584C4⋊Q8—41no—
585C4⋊Q8—41no—
586C4⋊Q8—41no—
587C4⋊Q8—41no—
588C4⋊Q8—41no—
589#126—44no—
590#126—82no—
591#124—22no—
592#124—22no—
593#124—22no—
594#124—41no—
595#124—41no—
596#124—41no—
597#124—44no—
598#124—82no—
599#123—44no—
600#123—44no—
601C22⋊Q8—22no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—44no—
606C22⋊Q8—41no—
607C22⋊Q8—41no—
608C22⋊Q8—41no—
609C22⋊Q8—41no—
610C22⋊Q8—82no—
611C22⋊Q8—82no—
612#121—22no—
613#121—44no—
614#121—41no—
615#121—41no—
616#121#4114yes—
617#120—44no—
618C4×Q8—22no—
619C4×Q8—22no—
620C4×Q8—41no—
621C4×Q8—41no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—82no—
633#117—22no—
634#117—22no—
635#117—41no—
636#117—41no—
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—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—44no—
718C2×C22⋊C4—82no—
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742#106—41no—
743#106—41no—
744#106—41no—
745#106—41no—
746C4⋊C8—41no—
747C4⋊C8—41no—
748C4⋊C8—41no—
749C4⋊C8—41no—
750C4⋊C8—41no—
751C4⋊C8—41no—
752C4⋊C8—41no—
753#103—22no—
754#103—22no—
755#103—22no—
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#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785C22⋊C8—22no—
786C22⋊C8—22no—
787C22⋊C8—41no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790#97—41no—
791C4×C8—41no—
792C4×C8—41no—
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#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833C24—21no—
834C24—21no—
835C24—21no—
836C24—42no—
837C24—42no—
838C24—42no—
839C24—81no—
840C24—81no—
841C24—81no—
842C24—81no—
843C24C22×D411yescharacteristic
844C24C22×D411yescharacteristic
845#41—44no—
846#41—44no—
847#41—44no—
848#41—44no—
849#41—82no—
850#41—82no—
851#41—82no—
852#41—82no—
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—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—42no—
871C2×Q8—42no—
872C2×Q8—81no—
873C2×Q8—81no—
874C2×Q8—81no—
875C2×Q8—81no—
876C2×Q8H(5,𝔽2)12yes—
877C2×D4—22no—
878C2×D4—24no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—41no—
896C2×D4—41no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—44no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—81no—
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—81no—
914C2×D4—81no—
915C2×D4C2×#4112yes—
916C2×D4H(5,𝔽2)12yes—
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—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
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×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C2×#4112yes—
974C22×C4H(5,𝔽2)12yes—
975C22×C4C2511yescharacteristic
976Q16—44no—
977Q16—82no—
978SD16—44no—
979SD16—44no—
980SD16—44no—
981SD16—82no—
982D8—44no—
983D8—82no—
984M16—82no—
985M16—82no—
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—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—44no—
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—22no—
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—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—41no—
1035C4⋊C4—41no—
1036C4⋊C4—41no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—81no—
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⋊C4C2×#4112yes—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—24no—
1063C22⋊C4—22no—
1064C22⋊C4—22no—
1065C22⋊C4—22no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
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—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—21no—
1116C42—21no—
1117C42—42no—
1118C42—42no—
1119C42—81no—
1120C42—81no—
1121C42—81no—
1122C42—81no—
1123C42—81no—
1124C42—81no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—22no—
1135C23—21no—
1136C23—21no—
1137C23—22no—
1138C23—21no—
1139C23—21no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—84no—
1160C23—84no—
1161C23—84no—
1162C23—162no—
1163C23—162no—
1164C23—162no—
1165C23—162no—
1166C23#54612yes—
1167C23C23×D411yescharacteristic
1168Q8—22no—
1169Q8—22no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180Q8—162no—
1181Q8—162no—
1182D4—22no—
1183D4—22no—
1184D4—22no—
1185D4—22no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—82no—
1195D4—84no—
1196D4—84no—
1197D4—84no—
1198D4—84no—
1199D4—162no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
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—22no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—22no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—84no—
1282C2×C4—84no—
1283C2×C4—162no—
1284C2×C4—162no—
1285C2×C4—162no—
1286C2×C4—162no—
1287C2×C4—162no—
1288C2×C4#54612yes—
1289C2×C4#57712yes—
1290C2×C4C22×#4111yescharacteristic
1291C2×C4C2×H(5,𝔽2)11yescharacteristic
1292C2×C4C2×H(5,𝔽2)11yescharacteristic
1293C2×C4C2×H(5,𝔽2)11yescharacteristic
1294C2×C4#58511yescharacteristic
1295C2×C4#58511yescharacteristic
1296C8—41no—
1297C8—41no—
1298C8—41no—
1299C8—41no—
1300C8—41no—
1301C8—41no—
1302C8—41no—
1303C8—41no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—42no—
1313C22—42no—
1314C22—41no—
1315C22—41no—
1316C22—42no—
1317C22—41no—
1318C22—42no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—42no—
1323C22—42no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—168no—
1340C22C2×#54611yescharacteristic
1341C22#348811yescharacteristic
1342C22#348811yescharacteristic
1343C22C2×#57711yescharacteristic
1344C22#358411yescharacteristic
1345C22#358511yescharacteristic
1346C22#358611yescharacteristic
1347C4—22no—
1348C4—22no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—42no—
1356C4—41no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—42no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4#351311yescharacteristic
1373C4#351311yescharacteristic
1374C4#353211yescharacteristic
1375C4#354511yescharacteristic
1376C2—42no—
1377C2—81no—
1378C2—82no—
1379C2—82no—
1380C2—161no—
1381C2#4400111yescharacteristic
1382C2#6119711yescharacteristic
1383C2#6120011yescharacteristic
1384C2#6204211yescharacteristic
1385C2#6204711yescharacteristic
1386C2#6206611yescharacteristic
1387C2#6209411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23850C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45259C2semidirect
2. #45108C2semidirect
3. #32173C2semidirect
4. #32126C2semidirect
5. #31926C2semidirect
6. #31837C2semidirect
7. #31815C2semidirect
8. #31649C2semidirect
9. #30620C2semidirect
10. #30535C2semidirect
11. #27597C2semidirect
12. #27426C2semidirect
13. #27278C2semidirect
14. #27071C2semidirect
15. #26750C2semidirect
16. #26410C2semidirect
17. #26206C2semidirect
18. #25337C2semidirect
19. #25135C2semidirect
20. #25105C2semidirect
21. #24901C2semidirect
22. #24629C2semidirect
23. #24539C2semidirect
24. #24363C2semidirect
25. #23947C2semidirect
27. #23543C2semidirect
28. #22883C2semidirect
29. #22427C2semidirect
30. #22074C2semidirect
31. #21896C2semidirect
38. C2×#462C22semidirect
39. C2×#452C22semidirect
45. C2×#424C22semidirect
47. C2×#417C22semidirect
59. #2568C22semidirect
64. #2513C22semidirect
65. #2512C22semidirect
72. #2440C22semidirect
85. #2355C22semidirect
87. #2341C22semidirect
89. #2314C22semidirect
91. #2311C22semidirect
92. #2101C22semidirect
93. #2100C22semidirect
94. #2096C22semidirect
96. #2088C22semidirect
98. #2074C22semidirect
99. #2074C22semidirect
103. #2065C22semidirect
104. #2056C22semidirect
105. #2056C22semidirect
106. #2056C22semidirect
109. #2055C22semidirect
110. #2055C22semidirect
111. #2055C22semidirect
115. #2043C22semidirect
119. #2024C22semidirect
120. #2024C22semidirect
122. #2023C22semidirect
125. #2013C22semidirect
132. #1988C22semidirect
133. #1987C22semidirect
134. #1987C22semidirect
139. #1968C22semidirect
141. #1956C22semidirect
142. #1940C22semidirect
143. #1939C22semidirect
144. #1935C22semidirect
146. #1934C22semidirect
147. #1933C22semidirect
148. #1927C22semidirect
149. #1927C22semidirect
150. #1927C22semidirect
153. #1926C22semidirect
156. #1920C22semidirect
157. #1919C22semidirect
158. #1916C22semidirect
159. #1916C22semidirect
163. #1894C22semidirect
165. #1892C22semidirect
168. #1880C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
179. #1872C22semidirect
181. #1865C22semidirect
183. #1853C22semidirect
184. #1853C22semidirect
187. #1850C22semidirect
189. #1818C22semidirect
190. #1805C22semidirect
193. #1803C22semidirect
199. #1763C22semidirect
201. #1753C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#452592
#451082
#321732
#321262
#319262
#318372
#318152
#316492
#306202
#305352
#275972
#274262
#272782
#270712
#267502
#264102
#262062
#253372
#251352
#251052
#249012
#246292
#245392
#243632
#239472
#238502
#235432
#228832
#224272
#220742
#218962