Finite Group Databasebeta

← #6840518

Subgroups — #6840518

Order 512.

1479 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42635C211yesmaximal, characteristic, complemented
2#42634C211yesmaximal, characteristic, complemented
3#33245C211yesmaximal, characteristic, complemented
4#32430C211yesmaximal, characteristic, complemented
5#31932C211yesmaximal, characteristic, complemented
6#30954C211yesmaximal, characteristic, complemented
7#30883C211yesmaximal, characteristic, complemented
8#30777C211yesmaximal, characteristic, complemented
9#30748C211yesmaximal, characteristic, complemented
10#30531C211yesmaximal, characteristic, complemented
11#30452C211yesmaximal, characteristic
12#30074C211yesmaximal, characteristic, complemented
13#30055C211yesmaximal, characteristic, complemented
14#29080C211yesmaximal, characteristic, complemented
15#28985C211yesmaximal, characteristic, complemented
16#28929C211yesmaximal, characteristic, complemented
17#28909C211yesmaximal, characteristic, complemented
18#28895C211yesmaximal, characteristic, complemented
19#28419C211yesmaximal, characteristic, complemented
20#28343C211yesmaximal, characteristic
21#27785C211yesmaximal, characteristic, complemented
22#27262C211yesmaximal, characteristic, complemented
23#27243C211yesmaximal, characteristic
24#27208C211yesmaximal, characteristic, complemented
25#27088C211yesmaximal, characteristic, complemented
26#26949C211yesmaximal, characteristic, complemented
27#26828C211yesmaximal, characteristic, complemented
28#23109C211yesmaximal, characteristic, complemented
29#22874C211yesmaximal, characteristic, complemented
30#21669C211yesmaximal, characteristic, complemented
31#21643C211yesmaximal, characteristic, complemented
32C2×#498C2211yescharacteristic, complemented
33C2×#495C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#489C2211yescharacteristic, complemented
36C2×#488C2211yescharacteristic
37C2×#487C2211yescharacteristic, complemented
38C2×#483C2211yescharacteristic
39C2×#476C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#462C2211yescharacteristic, complemented
42C2×#463C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#447C2211yescharacteristic
45C2×C4×SD16C2211yescharacteristic
46C22×#102C2211yescharacteristic
47#2838—21no—
48#2827—21no—
49#2779—21no—
50#2773—21no—
51#2742—21no—
52#2736—21no—
53#2735—21no—
54#2717—21no—
55#2702—21no—
56#2674—21no—
57#2663—21no—
58#2653—21no—
59#2640C2211yescharacteristic
60#2640C2211yescharacteristic, complemented
61#2628—21no—
62#2626—21no—
63#2567C2211yescharacteristic, complemented
64#2551C2211yescharacteristic, complemented
65#2547C2211yescharacteristic
66#2545C2211yescharacteristic
67#2512C2211yescharacteristic
68#2511C2211yescharacteristic, complemented
69#2501C2211yescharacteristic
70#2492C2211yescharacteristic
71#2491C2211yescharacteristic
72#2489C2211yescharacteristic
73#2480—21no—
74#2470—21no—
75#2454C2211yescharacteristic, complemented
76#2452C2211yescharacteristic
77#2448C2211yescharacteristic
78#2448C2211yescharacteristic, complemented
79#2440C2211yescharacteristic
80#2435C2211yescharacteristic
81#2435C2211yescharacteristic
82#2429C2211yescharacteristic
83#2427C2211yescharacteristic
84#2423C2211yescharacteristic
85#2401C2211yescharacteristic
86#2367C2211yescharacteristic
87#2360C2211yescharacteristic
88#2354C2211yescharacteristic, complemented
89D4×C22⋊C4C2211yescharacteristic
90#2330C2211yescharacteristic, complemented
91#2326C2211yescharacteristic
92#2096C2211yescharacteristic, complemented
93#2096C2211yescharacteristic, complemented
94#2094C2211yescharacteristic
95#2094C2211yescharacteristic
96#2088C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2077C2211yescharacteristic
99#2072C2211yescharacteristic, complemented
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic, complemented
102#2066C2211yescharacteristic, complemented
103#2065C2211yescharacteristic, complemented
104#2058C2211yescharacteristic, complemented
105#2058C2211yescharacteristic, complemented
106#2058C2211yescharacteristic, complemented
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2054C2211yescharacteristic
110#2043C2211yescharacteristic, complemented
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2035C2211yescharacteristic
115#2034C2211yescharacteristic
116#2026C2211yescharacteristic, complemented
117#2025C2211yescharacteristic
118#2024C2211yescharacteristic, complemented
119#2023C2211yescharacteristic
120#2023C2211yescharacteristic
121#2015C2211yescharacteristic
122#2015C2211yescharacteristic
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic, complemented
125#2013C2211yescharacteristic, complemented
126#2012C2211yescharacteristic
127#2012C2211yescharacteristic
128#2012C2211yescharacteristic
129#2001C2211yescharacteristic
130#2001C2211yescharacteristic
131#2000C2211yescharacteristic
132#1992C2211yescharacteristic, complemented
133#1983C2211yescharacteristic
134#1972C2211yescharacteristic
135#1972C2211yescharacteristic
136#1972C2211yescharacteristic
137#1971C2211yescharacteristic, complemented
138#1971C2211yescharacteristic, complemented
139#1971C2211yescharacteristic, complemented
140#1968C2211yescharacteristic
141#1968C2211yescharacteristic
142#1968C2211yescharacteristic, complemented
143#1968C2211yescharacteristic, complemented
144#1959C2211yescharacteristic
145#1959C2211yescharacteristic
146#1959C2211yescharacteristic
147#1948C2211yescharacteristic, complemented
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1935C2211yescharacteristic, complemented
151#1935C2211yescharacteristic, complemented
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1927C2211yescharacteristic, complemented
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1924C2211yescharacteristic
163#1923C2211yescharacteristic
164#1923C2211yescharacteristic
165#1919C2211yescharacteristic, complemented
166#1919C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1916C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1892C2211yescharacteristic
171#1892C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic, complemented
174#1880C2211yescharacteristic, complemented
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1878C2211yescharacteristic, complemented
179#1878C2211yescharacteristic, complemented
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic, complemented
182#1872C2211yescharacteristic
183#1865C2211yescharacteristic, complemented
184#1864C2211yescharacteristic
185#1853C2211yescharacteristic
186#1840C2211yescharacteristic, complemented
187#1834C2211yescharacteristic, complemented
188#1803C2211yescharacteristic, complemented
189#1786C2211yescharacteristic
190#1771C2211yescharacteristic, complemented
191#1771C2211yescharacteristic, complemented
192#1770C2211yescharacteristic, complemented
193#1763C2211yescharacteristic, complemented
194#1763C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199#1752C2211yescharacteristic
200#1752C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202#1726C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C22×C4⋊C4C2311yescharacteristic
242C22×C22⋊C4—21no—
243#498—42no—
244#495—42no—
245#489—42no—
246#489—42no—
247#488—24no—
248#487—42no—
249#483—42no—
250#476—42no—
251#465—42no—
252#463—24no—
253#462—42no—
254#450—24no—
255#447—42no—
256C4×SD16—42no—
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#102—42no—
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313#401D411yescharacteristic
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400D411yescharacteristic
319#400D411yescharacteristic
320#400D411yescharacteristic
321#399—21no—
322#399—21no—
323#399—21no—
324#399—21no—
325#399—21no—
326#399—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397D411yescharacteristic
342#397D411yescharacteristic
343#397D411yescharacteristic
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396D411yescharacteristic
351#395—21no—
352#395—21no—
353#395—21no—
354#395—21no—
355#395—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#393—21no—
363#393—21no—
364#393—21no—
365#393—21no—
366#393—21no—
367#393—21no—
368#393—21no—
369#391—21no—
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#389—21no—
389#389—21no—
390#389—21no—
391#389—21no—
392#389—21no—
393#389—21no—
394#389—21no—
395#389C2311yescharacteristic
396#389C2311yescharacteristic
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#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#382—21no—
440#380—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380—21no—
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#379—21no—
448#379—21no—
449#379—21no—
450#379—21no—
451#379—21no—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464#376C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4C2411yescharacteristic
516C2×Q16—22no—
517C2×Q16—41no—
518C2×Q16—41no—
519C2×Q16—41no—
520C2×Q16—41no—
521C2×Q16—41no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—41no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8—41no—
540C22×C8—22no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554C4⋊Q8—41no—
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559C4⋊Q8—82no—
560#126—82no—
561#125—22no—
562#125—41no—
563#124—22no—
564#124—22no—
565#124—41no—
566#124—41no—
567#124—41no—
568#124—41no—
569#124—41no—
570#124—41no—
571#124—41no—
572#124—41no—
573#124—82no—
574#123—82no—
575#123—82no—
576C22⋊Q8—22no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—82no—
583C22⋊Q8—82no—
584#121—41no—
585#121—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×D4—22no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598#117—82no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
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—41no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—82no—
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704#106—22no—
705#106—22no—
706#106—41no—
707#106—41no—
708#106—41no—
709#106—41no—
710#106—41no—
711#106—41no—
712C4⋊C8—22no—
713C4⋊C8—22no—
714C4⋊C8—41no—
715#103—22no—
716#103—22no—
717#103—22no—
718#103—22no—
719#103—22no—
720#103—22no—
721#103—22no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102#4114yes—
747C22⋊C8—22no—
748C22⋊C8—22no—
749C22⋊C8—41no—
750#97—22no—
751#97—41no—
752#97—41no—
753#97—41no—
754#97—41no—
755C4×C8—22no—
756C4×C8—22no—
757C4×C8—22no—
758C4×C8—41no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803C24—21no—
804C24—21no—
805C24—21no—
806C24—42no—
807C24—42no—
808C24—81no—
809C24—81no—
810C24—81no—
811C24—81no—
812C24—81no—
813C24C22×D411yescharacteristic
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—81no—
833C2×Q8—81no—
834C2×Q8—81no—
835C2×Q8—81no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—42no—
859C2×D4—44no—
860C2×D4—42no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—82no—
864C2×D4—82no—
865C2×D4—82no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4C2×#4112yes—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C2511yescharacteristic
914Q16—82no—
915Q16—82no—
916SD16—44no—
917SD16—82no—
918SD16—82no—
919SD16—82no—
920D8—82no—
921D8—82no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—82no—
944C2×C8C2×#4112yes—
945C2×C8H(5,𝔽2)12yes—
946C2×C8H(5,𝔽2)12yes—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4C2×#4112yes—
1001C22⋊C4—22no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—42no—
1059C42—81no—
1060C42—81no—
1061C42—81no—
1062C42—81no—
1063C42—81no—
1064C42—81no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—22no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—84no—
1093C23—84no—
1094C23—162no—
1095C23—162no—
1096C23—162no—
1097C23—162no—
1098C23—162no—
1099C23#57712yes—
1100C23C23×D411yescharacteristic
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—162no—
1114Q8—162no—
1115Q8—162no—
1116D4—22no—
1117D4—22no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—84no—
1129D4—162no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—84no—
1212C2×C4—162no—
1213C2×C4—162no—
1214C2×C4—162no—
1215C2×C4#57712yes—
1216C2×C4C22×#4111yescharacteristic
1217C2×C4C2×H(5,𝔽2)11yescharacteristic
1218C2×C4C2×H(5,𝔽2)11yescharacteristic
1219C2×C4#58511yescharacteristic
1220C2×C4#58511yescharacteristic
1221C2×C4#58511yescharacteristic
1222C8—22no—
1223C8—22no—
1224C8—22no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C8—41no—
1229C8—41no—
1230C22—22no—
1231C22—22no—
1232C22—22no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—168no—
1259C22D4×#4111yescharacteristic
1260C22#349811yescharacteristic
1261C22#350011yescharacteristic
1262C22C2×#57711yescharacteristic
1263C22C2×#57711yescharacteristic
1264C22#358511yescharacteristic
1265C22#358611yescharacteristic
1266C4—22no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—42no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—41no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4#346011yescharacteristic
1293C4#351411yescharacteristic
1294C4#354511yescharacteristic
1295C4#356011yescharacteristic
1296C2—42no—
1297C2—82no—
1298C2—161no—
1299C2—161no—
1300C2#3944311yescharacteristic
1301C2#6148311yescharacteristic
1302C2#6151011yescharacteristic
1303C2#6245711yescharacteristic
1304C2#6245811yescharacteristic
1305C2#6260311yescharacteristic
1306C2#6261711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2401 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42635C2semidirect
2. #42634C2semidirect
3. #33245C2semidirect
4. #32430C2semidirect
5. #31932C2semidirect
6. #30954C2semidirect
7. #30883C2semidirect
8. #30777C2semidirect
9. #30748C2semidirect
10. #30531C2semidirect
12. #30074C2semidirect
13. #30055C2semidirect
14. #29080C2semidirect
15. #28985C2semidirect
16. #28929C2semidirect
17. #28909C2semidirect
18. #28895C2semidirect
19. #28419C2semidirect
21. #27785C2semidirect
22. #27262C2semidirect
24. #27208C2semidirect
25. #27088C2semidirect
26. #26949C2semidirect
27. #26828C2semidirect
28. #23109C2semidirect
29. #22874C2semidirect
30. #21669C2semidirect
31. #21643C2semidirect
32. C2×#498C22semidirect
35. C2×#489C22semidirect
37. C2×#487C22semidirect
41. C2×#462C22semidirect
60. #2640C22semidirect
63. #2567C22semidirect
64. #2551C22semidirect
68. #2511C22semidirect
75. #2454C22semidirect
78. #2448C22semidirect
88. #2354C22semidirect
90. #2330C22semidirect
92. #2096C22semidirect
93. #2096C22semidirect
96. #2088C22semidirect
97. #2084C22semidirect
99. #2072C22semidirect
101. #2071C22semidirect
102. #2066C22semidirect
103. #2065C22semidirect
104. #2058C22semidirect
105. #2058C22semidirect
106. #2058C22semidirect
110. #2043C22semidirect
116. #2026C22semidirect
118. #2024C22semidirect
124. #2015C22semidirect
125. #2013C22semidirect
132. #1992C22semidirect
137. #1971C22semidirect
138. #1971C22semidirect
139. #1971C22semidirect
142. #1968C22semidirect
143. #1968C22semidirect
147. #1948C22semidirect
150. #1935C22semidirect
151. #1935C22semidirect
154. #1934C22semidirect
155. #1933C22semidirect
156. #1927C22semidirect
157. #1927C22semidirect
158. #1927C22semidirect
165. #1919C22semidirect
166. #1919C22semidirect
167. #1917C22semidirect
168. #1916C22semidirect
169. #1916C22semidirect
173. #1880C22semidirect
174. #1880C22semidirect
178. #1878C22semidirect
179. #1878C22semidirect
181. #1877C22semidirect
183. #1865C22semidirect
186. #1840C22semidirect
187. #1834C22semidirect
188. #1803C22semidirect
190. #1771C22semidirect
191. #1771C22semidirect
192. #1770C22semidirect
193. #1763C22semidirect
194. #1763C22semidirect
196. #1762C22semidirect
197. C4×#103C22semidirect
202. #1726C22semidirect

Maximal subgroups

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

subgroupindex
#426352
#426342
#332452
#324302
#319322
#309542
#308832
#307772
#307482
#305312
#304522
#300742
#300552
#290802
#289852
#289292
#289092
#288952
#284192
#283432
#277852
#272622
#272432
#272082
#270882
#269492
#268282
#231092
#228742
#216692
#216432