Finite Group Databasebeta

← #7308287

Subgroups — #7308287

Order 512.

1707 conjugacy classes of subgroups.

The subgroup lattice has 1418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59103C211yesmaximal, characteristic, complemented
2#40076C211yesmaximal, characteristic, complemented
3#32187C211yesmaximal, characteristic, complemented
4#32123C211yesmaximal, characteristic, complemented
5#31826C211yesmaximal, characteristic, complemented
6#31654C211yesmaximal, characteristic, complemented
7#31516C211yesmaximal, characteristic, complemented
8#31407C211yesmaximal, characteristic, complemented
9#31221C211yesmaximal, characteristic, complemented
10#31038C211yesmaximal, characteristic, complemented
11#30543C211yesmaximal, characteristic, complemented
12#30537C211yesmaximal, characteristic, complemented
13#30470C211yesmaximal, characteristic, complemented
14#30467C211yesmaximal, characteristic, complemented
15#29717C211yesmaximal, characteristic, complemented
16#29665C211yesmaximal, characteristic, complemented
17#28116C211yesmaximal, characteristic, complemented
18#27539C211yesmaximal, characteristic, complemented
19#27251C211yesmaximal, characteristic, complemented
20#26955C211yesmaximal, characteristic, complemented
21#26917C211yesmaximal, characteristic, complemented
22#26746C211yesmaximal, characteristic, complemented
23#26610C211yesmaximal, characteristic, complemented
24#25381C211yesmaximal, characteristic, complemented
25#25334C211yesmaximal, characteristic, complemented
26#24373C211yesmaximal, characteristic, complemented
27#24367C211yesmaximal, characteristic, complemented
28#24259C211yesmaximal, characteristic, complemented
29#24159C211yesmaximal, characteristic, complemented
30#23863C211yesmaximal, characteristic
31#23324C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×#497C2211yescharacteristic, complemented
36C2×#489C2211yescharacteristic
37C2×#482C2211yescharacteristic, complemented
38C2×#478C2211yescharacteristic, complemented
39C2×#464C2211yescharacteristic
40C2×#462C2211yescharacteristic, complemented
41C2×#463C2211yescharacteristic
42C2×#463C2211yescharacteristic
43C2×#463C2211yescharacteristic
44C2×#461C2211yescharacteristic
45C2×#452C2211yescharacteristic
46C2×#452C2211yescharacteristic
47C2×#452C2211yescharacteristic
48C2×#452C2211yescharacteristic
49C2×#449C2211yescharacteristic
50C2×#450C2211yescharacteristic
51C2×#440C2211yescharacteristic
52#2857C2211yescharacteristic, complemented
53#2771—21no—
54#2743—21no—
55#2708—21no—
56#2702—21no—
57#2697—21no—
58#2696—21no—
59#2649—21no—
60#2553—21no—
61#2547C2211yescharacteristic
62#2542C2211yescharacteristic, complemented
63#2538C2211yescharacteristic
64#2511C2211yescharacteristic, complemented
65#2496C2211yescharacteristic
66#2492C2211yescharacteristic
67#2492C2211yescharacteristic, complemented
68#2489C2211yescharacteristic
69#2480—21no—
70#2470—21no—
71#2467—21no—
72#2454C2211yescharacteristic
73#2450—21no—
74#2447C2211yescharacteristic
75#2446C2211yescharacteristic, complemented
76#2435C2211yescharacteristic
77#2432C2211yescharacteristic
78#2432C2211yescharacteristic
79#2429C2211yescharacteristic
80#2427C2211yescharacteristic, complemented
81#2420—21no—
82#2418—21no—
83#2415C2211yescharacteristic
84#2407C2211yescharacteristic
85#2367C2211yescharacteristic
86#2367C2211yescharacteristic, complemented
87#2363C2211yescharacteristic
88#2342—21no—
89#2339C2211yescharacteristic
90D4×C22⋊C4C2211yescharacteristic
91#2329—21no—
92C4×#123C2211yescharacteristic
93C4×#121C2211yescharacteristic, complemented
94#2297C2211yescharacteristic
95#2100C2211yescharacteristic, complemented
96#2086C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2072C2211yescharacteristic, complemented
100#2072C2211yescharacteristic, complemented
101#2071C2211yescharacteristic
102#2068C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2056C2211yescharacteristic, complemented
106#2056C2211yescharacteristic, complemented
107#2056C2211yescharacteristic, complemented
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic, complemented
113#2055C2211yescharacteristic, complemented
114#2054C2211yescharacteristic
115#2043C2211yescharacteristic, complemented
116#2042C2211yescharacteristic, complemented
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2035C2211yescharacteristic, complemented
120#2033C2211yescharacteristic
121#2026C2211yescharacteristic, complemented
122#2026C2211yescharacteristic, complemented
123#2024C2211yescharacteristic, complemented
124#2023C2211yescharacteristic
125#2016C2211yescharacteristic, complemented
126#2016C2211yescharacteristic, complemented
127#2015C2211yescharacteristic
128#2015C2211yescharacteristic
129#2015C2211yescharacteristic
130#2015C2211yescharacteristic
131#2015C2211yescharacteristic
132#2013C2211yescharacteristic
133#2012C2211yescharacteristic
134#2012C2211yescharacteristic
135#2001C2211yescharacteristic
136#2001C2211yescharacteristic
137#2001C2211yescharacteristic, complemented
138#2001C2211yescharacteristic, complemented
139#2000C2211yescharacteristic
140#2000C2211yescharacteristic
141#2000C2211yescharacteristic, complemented
142#1999C2211yescharacteristic
143#1989C2211yescharacteristic, complemented
144#1987C2211yescharacteristic, complemented
145#1983C2211yescharacteristic
146#1981C2211yescharacteristic, complemented
147#1973C2211yescharacteristic
148#1971C2211yescharacteristic, complemented
149#1971C2211yescharacteristic, complemented
150#1959C2211yescharacteristic
151#1955C2211yescharacteristic
152#1940C2211yescharacteristic, complemented
153#1940C2211yescharacteristic, complemented
154#1936C2211yescharacteristic
155#1936C2211yescharacteristic, complemented
156#1935C2211yescharacteristic, complemented
157#1928C2211yescharacteristic, complemented
158#1927C2211yescharacteristic, complemented
159#1927C2211yescharacteristic, complemented
160#1926C2211yescharacteristic
161#1925C2211yescharacteristic
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic
164#1924C2211yescharacteristic, complemented
165#1924C2211yescharacteristic, complemented
166#1918C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1917C2211yescharacteristic, complemented
169#1894C2211yescharacteristic
170#1894C2211yescharacteristic
171#1894C2211yescharacteristic
172#1880C2211yescharacteristic, complemented
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1878C2211yescharacteristic, complemented
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic, complemented
181#1877C2211yescharacteristic, complemented
182#1873C2211yescharacteristic, complemented
183#1873C2211yescharacteristic, complemented
184#1870C2211yescharacteristic
185#1865C2211yescharacteristic, complemented
186#1864C2211yescharacteristic
187#1864C2211yescharacteristic
188#1863C2211yescharacteristic, complemented
189#1851C2211yescharacteristic
190#1851C2211yescharacteristic
191#1825C2211yescharacteristic, complemented
192#1803C2211yescharacteristic, complemented
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1797C2211yescharacteristic, complemented
196#1797C2211yescharacteristic, complemented
197#1788C2211yescharacteristic
198#1788C2211yescharacteristic
199#1786C2211yescharacteristic
200#1786C2211yescharacteristic
201#1762C2211yescharacteristic
202#1762C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×AGL(1,ℤ/8)—42no—
207C2×AGL(1,ℤ/8)—42no—
208C2×AGL(1,ℤ/8)—42no—
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×D8C2311yescharacteristic
220C22×D8C2311yescharacteristic
221C22×M16C2311yescharacteristic
222#546—42no—
223#546—42no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227#529—42no—
228#529—42no—
229C2×#126—21no—
230C2×#126—21no—
231C2×#125C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#123—21no—
237C2×#123—21no—
238C2×#123D411yescharacteristic
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2311yescharacteristic
247C2×#121—21no—
248C2×#121C2311yescharacteristic
249C2×#121C2311yescharacteristic
250C2×#120—21no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×#117—21no—
262C2×#117C2311yescharacteristic
263C22×C22⋊C4—21no—
264C22×C22⋊C4—21no—
265C22×C42C2311yescharacteristic
266#497—42no—
267#489—42no—
268#482—42no—
269#478—42no—
270#464—42no—
271#463—42no—
272#463—42no—
273#463—42no—
274#462—42no—
275#461—42no—
276#452—42no—
277#452—42no—
278#452—42no—
279#452—42no—
280#450—42no—
281#449—42no—
282#440—42no—
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×#97C2311yescharacteristic
336#400—21no—
337#400—21no—
338#400—21no—
339#400—21no—
340#400—21no—
341#400—21no—
342#400—21no—
343#399—21no—
344#399—21no—
345#399—21no—
346#398—21no—
347#398—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#393—21no—
370#393—21no—
371#392—21no—
372#391—21no—
373#391—21no—
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#390—21no—
385#390—21no—
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#389—21no—
393#389—21no—
394#389—21no—
395#389—21no—
396#389—21no—
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
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#388—21no—
411#388—21no—
412#388D411yescharacteristic
413#388D411yescharacteristic
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387D411yescharacteristic
420#387D411yescharacteristic
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386D411yescharacteristic
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385D411yescharacteristic
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#382—21no—
445#381—21no—
446#381—21no—
447#381D411yescharacteristic
448#380—21no—
449#380—21no—
450#380—21no—
451#380—21no—
452#380—21no—
453#380—21no—
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#379—21no—
459#379—21no—
460#379—21no—
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
474C4×C22⋊C4C2311yescharacteristic
475C2×#95—21no—
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#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C22×Q8—21no—
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—22no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4C2×D411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C2×D411yescharacteristic
543C23×C4C2×D411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546AGL(1,ℤ/8)—416no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—41no—
582C2×D8—41no—
583C2×M16—41no—
584C2×M16—41no—
585C2×M16—41no—
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C22×C8C2411yescharacteristic
594C4⋊Q8—41no—
595C4⋊Q8—41no—
596C4⋊Q8—41no—
597C4⋊Q8—41no—
598C4⋊Q8—41no—
599C4⋊Q8—41no—
600#126—44no—
601#126—82no—
602#125—22no—
603#125—41no—
604#124—22no—
605#124—22no—
606#124—22no—
607#124—22no—
608#124—41no—
609#124—41no—
610#124—41no—
611#124—41no—
612#123—42no—
613#123—44no—
614#123—44no—
615C22⋊Q8—22no—
616C22⋊Q8—41no—
617C22⋊Q8—41no—
618C22⋊Q8—41no—
619C22⋊Q8—44no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8—41no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626C22⋊Q8—41no—
627C22⋊Q8—41no—
628C22⋊Q8—82no—
629#121—22no—
630#121—22no—
631#121—22no—
632#121—41no—
633#121—44no—
634#120—44no—
635C4×Q8—22no—
636C4×Q8—41no—
637C4×Q8—41no—
638C4×Q8—41no—
639C4×D4—22no—
640C4×D4—22no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—41no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—41no—
648C4×D4—41no—
649C4×D4—41no—
650C4×D4—41no—
651C4×D4—44no—
652C4×D4—82no—
653#117—44no—
654#117—41no—
655#117—41no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
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—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—44no—
732C2×C22⋊C4—44no—
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—41no—
748C2×C42—41no—
749C2×C42C2×D411yescharacteristic
750C2×C42C2×D411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756#107—22no—
757#107—41no—
758#106—41no—
759#106—41no—
760C4⋊C8—41no—
761C4⋊C8—41no—
762C4⋊C8—41no—
763C4⋊C8—41no—
764C4⋊C8—41no—
765C4⋊C8—41no—
766C4⋊C8—41no—
767#103—22no—
768#103—22no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781#103—41no—
782#103—41no—
783#103—41no—
784#103—41no—
785#102—22no—
786#102—22no—
787#102—22no—
788#102—22no—
789#102—22no—
790#102—22no—
791#102—22no—
792#102—41no—
793#102—41no—
794#102—41no—
795#102—41no—
796#102—41no—
797#102—41no—
798#102—41no—
799C22⋊C8—41no—
800C22⋊C8—41no—
801C22⋊C8—41no—
802C22⋊C8—41no—
803C22⋊C8—41no—
804C22⋊C8—41no—
805C22⋊C8—41no—
806#97—41no—
807#97—41no—
808#97—41no—
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#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850C24—21no—
851C24—21no—
852C24—21no—
853C24—42no—
854C24—42no—
855C24—42no—
856C24—81no—
857C24—81no—
858C24—81no—
859C24—81no—
860C24C22×D411yescharacteristic
861C24C22×D411yescharacteristic
862#41—44no—
863#41—82no—
864#41—82no—
865#41—82no—
866#41—82no—
867#41—82no—
868#41—82no—
869#41—82no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—42no—
895C2×Q8—81no—
896C2×Q8—81no—
897C2×D4—24no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—41no—
914C2×D4—41no—
915C2×D4—41no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—44no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—81no—
925C2×D4—82no—
926C2×D4—82no—
927C2×D4—82no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4H(5,𝔽2)12yes—
935C2×D4H(5,𝔽2)12yes—
936C2×D4H(5,𝔽2)12yes—
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—21no—
950C22×C4—22no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—41no—
964C22×C4—41no—
965C22×C4—41no—
966C22×C4—41no—
967C22×C4—41no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C2511yescharacteristic
1002Q16—82no—
1003Q16—82no—
1004Q16—82no—
1005Q16—82no—
1006SD16—44no—
1007SD16—44no—
1008SD16—44no—
1009SD16—82no—
1010SD16—82no—
1011SD16—82no—
1012D8—44no—
1013D8—44no—
1014M16—44no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C4⋊C4—22no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4H(5,𝔽2)12yes—
1085C22⋊C4—24no—
1086C22⋊C4—22no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—41no—
1091C22⋊C4—41no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—41no—
1142C42—41no—
1143C42—42no—
1144C42—81no—
1145C42—81no—
1146C42—81no—
1147C42—81no—
1148C42—81no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—22no—
1156C23—21no—
1157C23—21no—
1158C23—22no—
1159C23—22no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—84no—
1185C23—84no—
1186C23—84no—
1187C23—162no—
1188C23—162no—
1189C23—162no—
1190C23—162no—
1191C23C23×D411yescharacteristic
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—41no—
1202Q8—41no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—162no—
1209D4—22no—
1210D4—22no—
1211D4—22no—
1212D4—22no—
1213D4—22no—
1214D4—22no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—84no—
1222D4—82no—
1223D4—84no—
1224D4—84no—
1225D4—84no—
1226D4—84no—
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—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
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—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—82no—
1310C2×C4—84no—
1311C2×C4—82no—
1312C2×C4—84no—
1313C2×C4—84no—
1314C2×C4—162no—
1315C2×C4—162no—
1316C2×C4—162no—
1317C2×C4—162no—
1318C2×C4#57512yes—
1319C2×C4C2×H(5,𝔽2)11yescharacteristic
1320C2×C4C2×H(5,𝔽2)11yescharacteristic
1321C2×C4C2×H(5,𝔽2)11yescharacteristic
1322C2×C4C2×H(5,𝔽2)11yescharacteristic
1323C2×C4#58511yescharacteristic
1324C2×C4#58511yescharacteristic
1325C8—41no—
1326C8—41no—
1327C8—41no—
1328C8—41no—
1329C8—41no—
1330C8—41no—
1331C8—41no—
1332C8—41no—
1333C22—41no—
1334C22—41no—
1335C22—42no—
1336C22—41no—
1337C22—41no—
1338C22—42no—
1339C22—41no—
1340C22—42no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—42no—
1345C22—41no—
1346C22—42no—
1347C22—41no—
1348C22—41no—
1349C22—42no—
1350C22—41no—
1351C22—41no—
1352C22—41no—
1353C22—42no—
1354C22—42no—
1355C22—42no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—168no—
1369C22#348411yescharacteristic
1370C22#348811yescharacteristic
1371C22#348811yescharacteristic
1372C22C2×#57511yescharacteristic
1373C22#358511yescharacteristic
1374C22#358611yescharacteristic
1375C22#358611yescharacteristic
1376C4—22no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—41no—
1384C4—41no—
1385C4—41no—
1386C4—42no—
1387C4—41no—
1388C4—41no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4#353211yescharacteristic
1402C4#354211yescharacteristic
1403C4#355811yescharacteristic
1404C4#356011yescharacteristic
1405C2—81no—
1406C2—81no—
1407C2—82no—
1408C2—82no—
1409C2—82no—
1410C2#4784411yescharacteristic
1411C2#6158011yescharacteristic
1412C2#6164711yescharacteristic
1413C2#6196811yescharacteristic
1414C2#6197311yescharacteristic
1415C2#6207611yescharacteristic
1416C2#6208011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23863C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59103C2semidirect
2. #40076C2semidirect
3. #32187C2semidirect
4. #32123C2semidirect
5. #31826C2semidirect
6. #31654C2semidirect
7. #31516C2semidirect
8. #31407C2semidirect
9. #31221C2semidirect
10. #31038C2semidirect
11. #30543C2semidirect
12. #30537C2semidirect
13. #30470C2semidirect
14. #30467C2semidirect
15. #29717C2semidirect
16. #29665C2semidirect
17. #28116C2semidirect
18. #27539C2semidirect
19. #27251C2semidirect
20. #26955C2semidirect
21. #26917C2semidirect
22. #26746C2semidirect
23. #26610C2semidirect
24. #25381C2semidirect
25. #25334C2semidirect
26. #24373C2semidirect
27. #24367C2semidirect
28. #24259C2semidirect
29. #24159C2semidirect
31. #23324C2semidirect
35. C2×#497C22semidirect
37. C2×#482C22semidirect
38. C2×#478C22semidirect
40. C2×#462C22semidirect
52. #2857C22semidirect
62. #2542C22semidirect
64. #2511C22semidirect
67. #2492C22semidirect
75. #2446C22semidirect
80. #2427C22semidirect
86. #2367C22semidirect
93. C4×#121C22semidirect
95. #2100C22semidirect
96. #2086C22semidirect
99. #2072C22semidirect
100. #2072C22semidirect
102. #2068C22semidirect
103. #2068C22semidirect
105. #2056C22semidirect
106. #2056C22semidirect
107. #2056C22semidirect
112. #2055C22semidirect
113. #2055C22semidirect
115. #2043C22semidirect
116. #2042C22semidirect
119. #2035C22semidirect
121. #2026C22semidirect
122. #2026C22semidirect
123. #2024C22semidirect
125. #2016C22semidirect
126. #2016C22semidirect
137. #2001C22semidirect
138. #2001C22semidirect
141. #2000C22semidirect
143. #1989C22semidirect
144. #1987C22semidirect
146. #1981C22semidirect
148. #1971C22semidirect
149. #1971C22semidirect
152. #1940C22semidirect
153. #1940C22semidirect
155. #1936C22semidirect
156. #1935C22semidirect
157. #1928C22semidirect
158. #1927C22semidirect
159. #1927C22semidirect
164. #1924C22semidirect
165. #1924C22semidirect
166. #1918C22semidirect
167. #1917C22semidirect
168. #1917C22semidirect
172. #1880C22semidirect
177. #1878C22semidirect
180. #1877C22semidirect
181. #1877C22semidirect
182. #1873C22semidirect
183. #1873C22semidirect
185. #1865C22semidirect
188. #1863C22semidirect
191. #1825C22semidirect
192. #1803C22semidirect
195. #1797C22semidirect
196. #1797C22semidirect
202. #1762C22semidirect

Maximal subgroups

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

subgroupindex
#591032
#400762
#321872
#321232
#318262
#316542
#315162
#314072
#312212
#310382
#305432
#305372
#304702
#304672
#297172
#296652
#281162
#275392
#272512
#269552
#269172
#267462
#266102
#253812
#253342
#243732
#243672
#242592
#241592
#238632
#233242