Finite Group Databasebeta

← #7081840

Subgroups — #7081840

Order 512.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59046C211yesmaximal, characteristic
2#39604C211yesmaximal, characteristic, complemented
3#32109C211yesmaximal, characteristic, complemented
4#32070C211yesmaximal, characteristic, complemented
5#31908C211yesmaximal, characteristic, complemented
6#31592C211yesmaximal, characteristic, complemented
7#31534C211yesmaximal, characteristic, complemented
8#31303C211yesmaximal, characteristic, complemented
9#30629C211yesmaximal, characteristic, complemented
10#30612C211yesmaximal, characteristic, complemented
11#28957C211yesmaximal, characteristic, complemented
12#28418C211yesmaximal, characteristic, complemented
13#28360C211yesmaximal, characteristic, complemented
14#28072C211yesmaximal, characteristic, complemented
15#27254C211yesmaximal, characteristic, complemented
16#27081C211yesmaximal, characteristic, complemented
17#26526C211yesmaximal, characteristic, complemented
18#26342C211yesmaximal, characteristic, complemented
19#26126C211yesmaximal, characteristic, complemented
20#25975C211yesmaximal, characteristic, complemented
21#25499C211yesmaximal, characteristic, complemented
22#25080C211yesmaximal, characteristic, complemented
23#24904C211yesmaximal, characteristic, complemented
24#24787C211yesmaximal, characteristic, complemented
25#24507C211yesmaximal, characteristic, complemented
26#24426C211yesmaximal, characteristic, complemented
27C2×#2093C211yesmaximal, characteristic, complemented
28#23024C211yesmaximal, characteristic, complemented
29#22910C211yesmaximal, characteristic, complemented
30#22419C211yesmaximal, characteristic, complemented
31#21867C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#480C2211yescharacteristic, complemented
36C2×#477C2211yescharacteristic, complemented
37C2×#468C2211yescharacteristic, complemented
38C2×#467C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#460C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×C4×Q16C2211yescharacteristic, complemented
44C2×#435C2211yescharacteristic
45C2×#432C2211yescharacteristic
46C22×#107C2211yescharacteristic
47C22×#107C2211yescharacteristic
48C2×#417C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×#102C2211yescharacteristic
51#2855C2211yescharacteristic
52#2792—21no—
53#2791—21no—
54#2790—21no—
55#2720—21no—
56#2714—21no—
57#2705—21no—
58#2627—21no—
59#2567C2211yescharacteristic, complemented
60#2552C2211yescharacteristic, complemented
61#2548C2211yescharacteristic
62#2539—21no—
63#2511C2211yescharacteristic, complemented
64#2507C2211yescharacteristic, complemented
65#2502C2211yescharacteristic, complemented
66#2497C2211yescharacteristic, complemented
67#2490C2211yescharacteristic
68#2473—21no—
69#2471—21no—
70#2454C2211yescharacteristic
71#2449—21no—
72#2448C2211yescharacteristic
73#2440C2211yescharacteristic
74#2440C2211yescharacteristic, complemented
75#2433C2211yescharacteristic
76#2431C2211yescharacteristic
77#2428C2211yescharacteristic
78#2424—21no—
79#2423C2211yescharacteristic, complemented
80#2417C2211yescharacteristic
81#2416C2211yescharacteristic
82#2414—21no—
83#2412—21no—
84#2366C2211yescharacteristic
85#2360C2211yescharacteristic
86#2360C2211yescharacteristic
87#2358—21no—
88D4×C4⋊C4C2211yescharacteristic
89#2341C2211yescharacteristic
90#2322—21no—
91C4×#123C2211yescharacteristic
92C2×#390C2211yescharacteristic
93C2×#384C2211yescharacteristic
94#2095C2211yescharacteristic, complemented
95#2093C2211yescharacteristic
96#2093C2211yescharacteristic
97#2093C2211yescharacteristic
98#2093C2211yescharacteristic
99#2093C2211yescharacteristic
100#2093C2211yescharacteristic
101#2093C2211yescharacteristic
102#2093C2211yescharacteristic
103#2093C2211yescharacteristic, complemented
104#2087C2211yescharacteristic, complemented
105#2083C2211yescharacteristic, complemented
106#2075C2211yescharacteristic, complemented
107#2071C2211yescharacteristic
108#2068C2211yescharacteristic, complemented
109#2068C2211yescharacteristic, complemented
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2067C2211yescharacteristic, complemented
113#2065C2211yescharacteristic
114#2059C2211yescharacteristic, complemented
115#2057C2211yescharacteristic, complemented
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2055C2211yescharacteristic
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic, complemented
121#2041C2211yescharacteristic
122#2041C2211yescharacteristic
123#2041C2211yescharacteristic
124#2036C2211yescharacteristic, complemented
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic, complemented
127#2033C2211yescharacteristic, complemented
128#2026C2211yescharacteristic, complemented
129#2023C2211yescharacteristic
130#2015C2211yescharacteristic
131#2015C2211yescharacteristic, complemented
132#2014C2211yescharacteristic
133#2000C2211yescharacteristic
134#1992C2211yescharacteristic, complemented
135#1992C2211yescharacteristic, complemented
136#1983C2211yescharacteristic
137#1982C2211yescharacteristic
138#1973C2211yescharacteristic
139#1973C2211yescharacteristic
140#1973C2211yescharacteristic, complemented
141#1969C2211yescharacteristic, complemented
142#1959C2211yescharacteristic
143#1959C2211yescharacteristic, complemented
144#1959C2211yescharacteristic, complemented
145#1957C2211yescharacteristic
146#1947C2211yescharacteristic, complemented
147#1943C2211yescharacteristic, complemented
148#1942C2211yescharacteristic, complemented
149#1939C2211yescharacteristic, complemented
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1928C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1926C2211yescharacteristic
157#1925C2211yescharacteristic, complemented
158#1924C2211yescharacteristic, complemented
159#1923C2211yescharacteristic, complemented
160#1921C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1917C2211yescharacteristic, complemented
163#1917C2211yescharacteristic, complemented
164#1895C2211yescharacteristic
165#1893C2211yescharacteristic
166#1892C2211yescharacteristic
167#1880C2211yescharacteristic
168#1878C2211yescharacteristic, complemented
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic, complemented
171#1874C2211yescharacteristic
172#1874C2211yescharacteristic
173#1874C2211yescharacteristic
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic
176#1872C2211yescharacteristic
177#1869C2211yescharacteristic
178#1865C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic, complemented
184#1852C2211yescharacteristic
185#1852C2211yescharacteristic, complemented
186#1851C2211yescharacteristic, complemented
187#1850C2211yescharacteristic
188#1809C2211yescharacteristic, complemented
189#1803C2211yescharacteristic, complemented
190#1803C2211yescharacteristic, complemented
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic, complemented
193#1802C2211yescharacteristic, complemented
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1786C2211yescharacteristic
197C4×#107C2211yescharacteristic, complemented
198#1770C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200#1753C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#546—24no—
213#546—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217#529—24no—
218#529—42no—
219C2×#126—21no—
220C2×#125—21no—
221C2×#125C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#123—21no—
225C2×#123—21no—
226C2×#123D411yescharacteristic
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120—21no—
240C2×#120—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117—21no—
251C22×C4⋊C4—21no—
252C22×C4⋊C4—21no—
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C22⋊C4—21no—
258C22×C22⋊C4—21no—
259C22×C22⋊C4—21no—
260C22×C42C2311yescharacteristic
261#486—42no—
262#480—42no—
263#477—42no—
264#468—42no—
265#467—24no—
266#465—42no—
267#460—42no—
268#452—42no—
269#450—42no—
270C4×Q16—42no—
271#435—42no—
272#432—42no—
273C2×#107—42no—
274C2×#107—42no—
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292#417—42no—
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#102—42no—
305C2×#102—42no—
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×C4×C8C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337#400—21no—
338#400—21no—
339#400—21no—
340#399—21no—
341#399—21no—
342#399—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#398—21no—
351#398—21no—
352#398—21no—
353#397—21no—
354#397—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#395—21no—
360#395—21no—
361#395—21no—
362#395—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#392—21no—
372#392—21no—
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#390—21no—
379#390—21no—
380#390—21no—
381#390—21no—
382#390—21no—
383#390—21no—
384#390—21no—
385#390—21no—
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#389—21no—
394#389—21no—
395#389—21no—
396#389—21no—
397#389—21no—
398#389—21no—
399#389—21no—
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388D411yescharacteristic
414#388D411yescharacteristic
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387D411yescharacteristic
425#387D411yescharacteristic
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386D411yescharacteristic
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385D411yescharacteristic
445#384—21no—
446#384—21no—
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#384C2311yescharacteristic
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#381—21no—
454#381D411yescharacteristic
455#380—21no—
456#380—21no—
457#380—21no—
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#380C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
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—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—22no—
520C22×D4—22no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4C2×D411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4C2×D411yescharacteristic
536C23×C4C2×D411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C2×Q16—22no—
540C2×Q16—22no—
541C2×Q16—41no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×M16—22no—
552C2×M16—41no—
553C2×M16—41no—
554C22×C8—22no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—22no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570#127—22no—
571#127—41no—
572#127—41no—
573#127—41no—
574#126—44no—
575#125—22no—
576#125—41no—
577#125—82no—
578#124—22no—
579#124—22no—
580#124—41no—
581#124—41no—
582#123—24no—
583#123—44no—
584#123—44no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—22no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—82no—
591C22⋊Q8—82no—
592C22⋊Q8#4114yes—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—44no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—82no—
601#121—82no—
602#120—44no—
603#120—44no—
604#120—82no—
605C4×Q8—22no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—44no—
618C4×D4—82no—
619C4×D4—82no—
620#117—44no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—82no—
663C2×C4⋊C4—82no—
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×C4⋊C4C2411yescharacteristic
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—44no—
711C2×C22⋊C4—82no—
712C2×C22⋊C4—82no—
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42C2×D411yescharacteristic
730C2×C42C2×D411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#107—22no—
737#107—22no—
738#107—22no—
739#107—22no—
740#107—22no—
741#107—41no—
742#107—41no—
743#107—41no—
744#107—41no—
745#107—41no—
746#107—41no—
747#106—41no—
748C4⋊C8—22no—
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#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
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—22no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790#97—41no—
791#97—41no—
792#97—41no—
793C4×C8—22no—
794C4×C8—41no—
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#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830C24—21no—
831C24—21no—
832C24—21no—
833C24—42no—
834C24—42no—
835C24—42no—
836C24—42no—
837C24—81no—
838C24—81no—
839C24—81no—
840C24C22×D411yescharacteristic
841C24C22×D411yescharacteristic
842#41—44no—
843#41—82no—
844#41—82no—
845#41—82no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—81no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×Q8C2×#4112yes—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—22no—
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—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
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—82no—
896C2×D4—82no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D42−1+412yes—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—22no—
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—21no—
941C22×C4—41no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
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×C4—81no—
962C22×C4—81no—
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×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C2×#4112yes—
976C22×C4H(5,𝔽2)12yes—
977C22×C4C2511yescharacteristic
978Q16—44no—
979SD16—82no—
980SD16—82no—
981SD16—82no—
982M16—82no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—44no—
1006C2×C8—44no—
1007C2×C8H(5,𝔽2)12yes—
1008C2×C8H(5,𝔽2)12yes—
1009C4⋊C4—24no—
1010C4⋊C4—22no—
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—41no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊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—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4C2×#4112yes—
1069C22⋊C4—24no—
1070C22⋊C4—22no—
1071C22⋊C4—22no—
1072C22⋊C4—22no—
1073C22⋊C4—22no—
1074C22⋊C4—22no—
1075C22⋊C4—22no—
1076C22⋊C4—41no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
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#13714yes—
1107C42—22no—
1108C42—22no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—42no—
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—22no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
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—84no—
1158C23—84no—
1159C23—84no—
1160C23—84no—
1161C23—162no—
1162C23—162no—
1163C23—162no—
1164C23#54612yes—
1165C23C2×#13712yes—
1166C23#57612yes—
1167C23C23×D411yescharacteristic
1168Q8—22no—
1169Q8—22no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—162no—
1177D4—22no—
1178D4—22no—
1179D4—44no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—84no—
1191D4—84no—
1192D4—84no—
1193D4—84no—
1194D4—162no—
1195D4—162no—
1196D4—162no—
1197D4—162no—
1198D4—162no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
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—22no—
1220C2×C4—22no—
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—44no—
1238C2×C4—41no—
1239C2×C4—44no—
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—84no—
1281C2×C4—84no—
1282C2×C4—162no—
1283C2×C4—162no—
1284C2×C4—162no—
1285C2×C4—162no—
1286C2×C4—162no—
1287C2×C4#54612yes—
1288C2×C4C2×#13712yes—
1289C2×C4C2×#13712yes—
1290C2×C4#57612yes—
1291C2×C4C22×#4111yescharacteristic
1292C2×C4C2×H(5,𝔽2)11yescharacteristic
1293C2×C4C2×H(5,𝔽2)11yescharacteristic
1294C2×C4C2×H(5,𝔽2)11yescharacteristic
1295C2×C4C2×2−1+411yescharacteristic
1296C2×C4#58511yescharacteristic
1297C8—22no—
1298C8—22no—
1299C8—41no—
1300C8—41no—
1301C8—41no—
1302C8—41no—
1303C8—41no—
1304C8—41no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—22no—
1311C22—41no—
1312C22—42no—
1313C22—41no—
1314C22—42no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—42no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
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—
1340C22#333314yes—
1341C22C2×#54611yescharacteristic
1342C22#348911yescharacteristic
1343C22#349811yescharacteristic
1344C22C22×#13711yescharacteristic
1345C22C2×#57611yescharacteristic
1346C22C2×#57611yescharacteristic
1347C22#358611yescharacteristic
1348C4—22no—
1349C4—22no—
1350C4—22no—
1351C4—22no—
1352C4—41no—
1353C4—41no—
1354C4—42no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—42no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4#351311yescharacteristic
1374C4#352011yescharacteristic
1375C4#353411yescharacteristic
1376C4#353611yescharacteristic
1377C2—24no—
1378C2—81no—
1379C2—82no—
1380C2—161no—
1381C2—161no—
1382C2#4402211yescharacteristic
1383C2C2×#333311yescharacteristic
1384C2#6119111yescharacteristic
1385C2#6212711yescharacteristic
1386C2#6215511yescharacteristic
1387C2#6243111yescharacteristic
1388C2#6244811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59046C2
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
2. #39604C2semidirect
3. #32109C2semidirect
4. #32070C2semidirect
5. #31908C2semidirect
6. #31592C2semidirect
7. #31534C2semidirect
8. #31303C2semidirect
9. #30629C2semidirect
10. #30612C2semidirect
11. #28957C2semidirect
12. #28418C2semidirect
13. #28360C2semidirect
14. #28072C2semidirect
15. #27254C2semidirect
16. #27081C2semidirect
17. #26526C2semidirect
18. #26342C2semidirect
19. #26126C2semidirect
20. #25975C2semidirect
21. #25499C2semidirect
22. #25080C2semidirect
23. #24904C2semidirect
24. #24787C2semidirect
25. #24507C2semidirect
26. #24426C2semidirect
27. C2×#2093C2semidirect
28. #23024C2semidirect
29. #22910C2semidirect
30. #22419C2semidirect
31. #21867C2semidirect
35. C2×#480C22semidirect
36. C2×#477C22semidirect
37. C2×#468C22semidirect
43. C2×C4×Q16C22semidirect
59. #2567C22semidirect
60. #2552C22semidirect
63. #2511C22semidirect
64. #2507C22semidirect
65. #2502C22semidirect
66. #2497C22semidirect
74. #2440C22semidirect
79. #2423C22semidirect
94. #2095C22semidirect
103. #2093C22semidirect
104. #2087C22semidirect
105. #2083C22semidirect
106. #2075C22semidirect
108. #2068C22semidirect
109. #2068C22semidirect
112. #2067C22semidirect
114. #2059C22semidirect
115. #2057C22semidirect
120. #2042C22semidirect
124. #2036C22semidirect
126. #2033C22semidirect
127. #2033C22semidirect
128. #2026C22semidirect
131. #2015C22semidirect
134. #1992C22semidirect
135. #1992C22semidirect
140. #1973C22semidirect
141. #1969C22semidirect
143. #1959C22semidirect
144. #1959C22semidirect
146. #1947C22semidirect
147. #1943C22semidirect
148. #1942C22semidirect
149. #1939C22semidirect
154. #1928C22semidirect
155. #1928C22semidirect
157. #1925C22semidirect
158. #1924C22semidirect
159. #1923C22semidirect
160. #1921C22semidirect
161. #1918C22semidirect
162. #1917C22semidirect
163. #1917C22semidirect
168. #1878C22semidirect
170. #1877C22semidirect
178. #1865C22semidirect
179. #1863C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
183. #1862C22semidirect
185. #1852C22semidirect
186. #1851C22semidirect
188. #1809C22semidirect
189. #1803C22semidirect
190. #1803C22semidirect
192. #1802C22semidirect
193. #1802C22semidirect
197. C4×#107C22semidirect
198. #1770C22semidirect
200. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#590462
#396042
#321092
#320702
#319082
#315922
#315342
#313032
#306292
#306122
#289572
#284182
#283602
#280722
#272542
#270812
#265262
#263422
#261262
#259752
#254992
#250802
#249042
#247872
#245072
#244262
C2×#20932
#230242
#229102
#224192
#218672