Finite Group Databasebeta

← #6608132

Subgroups — #6608132

Order 512.

1646 conjugacy classes of subgroups.

The subgroup lattice has 1345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39070C211yesmaximal, characteristic, complemented
2#39069C211yesmaximal, characteristic, complemented
3#33269C211yesmaximal, characteristic, complemented
4#33243C211yesmaximal, characteristic, complemented
5#33142C211yesmaximal, characteristic, complemented
6#29571C211yesmaximal, characteristic, complemented
7#29564C211yesmaximal, characteristic, complemented
8#29497C211yesmaximal, characteristic, complemented
9#29497C211yesmaximal, characteristic, complemented
10#28903C211yesmaximal, characteristic, complemented
11#28897C211yesmaximal, characteristic, complemented
12#28013C211yesmaximal, characteristic, complemented
13#27257C211yesmaximal, characteristic, complemented
14#27256C211yesmaximal, characteristic, complemented
15#26839C211yesmaximal, characteristic, complemented
16#26834C211yesmaximal, characteristic, complemented
17#26499C211yesmaximal, characteristic, complemented
18#26267C211yesmaximal, characteristic, complemented
19#26251C211yesmaximal, characteristic, complemented
20#26076C211yesmaximal, characteristic, complemented
21#25793C211yesmaximal, characteristic
22#24517C211yesmaximal, characteristic, complemented
23#24512C211yesmaximal, characteristic, complemented
24#23040C211yesmaximal, characteristic, complemented
25#22861C211yesmaximal, characteristic, complemented
26#22858C211yesmaximal, characteristic, complemented
27#22443C211yesmaximal, characteristic, complemented
28#21693C211yesmaximal, characteristic, complemented
29#21285C211yesmaximal, characteristic, complemented
30#21235C211yesmaximal, characteristic, complemented
31#20478C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#501C2211yescharacteristic, complemented
34C2×#496C2211yescharacteristic
35C2×#495C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#486C2211yescharacteristic, complemented
38C2×#468C2211yescharacteristic
39C2×#452C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#442C2211yescharacteristic
42C2×#441C2211yescharacteristic, complemented
43C2×#440C2211yescharacteristic
44C2×#440C2211yescharacteristic, complemented
45C2×C4×SD16C2211yescharacteristic
46C2×#433C2211yescharacteristic
47C2×#428C2211yescharacteristic
48C2×#416C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C2×#405C2211yescharacteristic
51#2860C2211yescharacteristic
52#2860C2211yescharacteristic, complemented
53#2756—21no—
54#2753—21no—
55#2751—21no—
56#2741—21no—
57#2741—21no—
58#2740—21no—
59#2736—21no—
60#2735—21no—
61#2641C2211yescharacteristic, complemented
62#2640C2211yescharacteristic
63#2625C2211yescharacteristic
64#2624C2211yescharacteristic
65#2602—21no—
66#2595—21no—
67#2578—21no—
68#2561—21no—
69#2560—21no—
70#2553—21no—
71#2513C2211yescharacteristic
72#2513C2211yescharacteristic, complemented
73#2480—21no—
74#2467—21no—
75#2453C2211yescharacteristic, complemented
76#2452C2211yescharacteristic
77#2448C2211yescharacteristic
78#2448C2211yescharacteristic, complemented
79#2447C2211yescharacteristic
80#2445C2211yescharacteristic, complemented
81#2442C2211yescharacteristic
82#2439C2211yescharacteristic
83#2435C2211yescharacteristic
84#2431C2211yescharacteristic
85#2362C2211yescharacteristic
86#2361C2211yescharacteristic
87#2341C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89#2320C2211yescharacteristic, complemented
90#2319C2211yescharacteristic
91#2311C2211yescharacteristic
92#2309C2211yescharacteristic
93C4×#124C2211yescharacteristic
94C4×#124C2211yescharacteristic, complemented
95#2298C2211yescharacteristic
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic, complemented
100#2067C2211yescharacteristic
101#2066C2211yescharacteristic, complemented
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic, complemented
104#2059C2211yescharacteristic, complemented
105#2058C2211yescharacteristic, complemented
106#2056C2211yescharacteristic, complemented
107#2055C2211yescharacteristic, complemented
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic, complemented
113#2041C2211yescharacteristic, complemented
114#2025C2211yescharacteristic
115#2024C2211yescharacteristic, complemented
116#2015C2211yescharacteristic
117#2012C2211yescharacteristic
118#2012C2211yescharacteristic
119#2011C2211yescharacteristic
120#1973C2211yescharacteristic
121#1973C2211yescharacteristic
122#1973C2211yescharacteristic
123#1973C2211yescharacteristic, complemented
124#1973C2211yescharacteristic, complemented
125#1972C2211yescharacteristic
126#1972C2211yescharacteristic
127#1972C2211yescharacteristic
128#1972C2211yescharacteristic
129#1972C2211yescharacteristic
130#1971C2211yescharacteristic, complemented
131#1970C2211yescharacteristic
132#1970C2211yescharacteristic
133#1970C2211yescharacteristic
134#1970C2211yescharacteristic
135#1970C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic, complemented
139#1968C2211yescharacteristic, complemented
140#1968C2211yescharacteristic, complemented
141#1958C2211yescharacteristic
142#1958C2211yescharacteristic, complemented
143#1944C2211yescharacteristic, complemented
144#1944C2211yescharacteristic, complemented
145#1943C2211yescharacteristic, complemented
146#1942C2211yescharacteristic, complemented
147#1941C2211yescharacteristic, complemented
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic, complemented
151#1936C2211yescharacteristic, complemented
152#1936C2211yescharacteristic, complemented
153#1935C2211yescharacteristic, complemented
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1934C2211yescharacteristic
157#1934C2211yescharacteristic, complemented
158#1934C2211yescharacteristic, complemented
159#1933C2211yescharacteristic, complemented
160#1933C2211yescharacteristic, complemented
161#1933C2211yescharacteristic, complemented
162#1927C2211yescharacteristic, complemented
163#1926C2211yescharacteristic
164#1926C2211yescharacteristic, complemented
165#1925C2211yescharacteristic, complemented
166#1893C2211yescharacteristic
167#1892C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic, complemented
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1878C2211yescharacteristic, complemented
176#1875C2211yescharacteristic
177#1872C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1854C2211yescharacteristic
183#1853C2211yescharacteristic
184#1846C2211yescharacteristic, complemented
185#1809C2211yescharacteristic
186#1788C2211yescharacteristic
187#1786C2211yescharacteristic
188C4×#107C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1771C2211yescharacteristic, complemented
191#1770C2211yescharacteristic, complemented
192C8×C4⋊C4C2211yescharacteristic, complemented
193#1763C2211yescharacteristic, complemented
194#1762C2211yescharacteristic
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1752C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199#1746C2211yescharacteristic, complemented
200#1744C2211yescharacteristic, complemented
201#1726C2211yescharacteristic, complemented
202C4×#97C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—24no—
207C2×AGL(1,ℤ/8)—42no—
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#126—21no—
222C2×#126—21no—
223C2×#125C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C22⋊C4—21no—
242#501—42no—
243#496—42no—
244#495—24no—
245#488—42no—
246#486—42no—
247#468—24no—
248#452—24no—
249#447—24no—
250#442—42no—
251#441—42no—
252#440—42no—
253#440—42no—
254C4×SD16—24no—
255#433—24no—
256#428—42no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270#416—42no—
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#102—42no—
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304#405—24no—
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319#400—21no—
320#400—21no—
321#400—21no—
322#399—21no—
323#399—21no—
324#399—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#397—21no—
329#397—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#396—21no—
342#396—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#393—21no—
354#393—21no—
355#393—21no—
356#393—21no—
357#392—21no—
358#392—21no—
359#391—21no—
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#390—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#389—21no—
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#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#388—21no—
420#388D411yescharacteristic
421#388D411yescharacteristic
422#388D411yescharacteristic
423#388D411yescharacteristic
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387D411yescharacteristic
430#387D411yescharacteristic
431#387D411yescharacteristic
432#387D411yescharacteristic
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#383—21no—
446#382—21no—
447#382C2311yescharacteristic
448#382C2311yescharacteristic
449#381—21no—
450#381—21no—
451#380—21no—
452#380—21no—
453#380—21no—
454#380—21no—
455#380—21no—
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#379—21no—
459#379—21no—
460#379—21no—
461#379—21no—
462#379—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4—21no—
473C4×C22⋊C4C2311yescharacteristic
474C4×C22⋊C4C2311yescharacteristic
475#376C2311yescharacteristic
476C43C2311yescharacteristic
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#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—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—22no—
516C22×D4—22no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2411yescharacteristic
530AGL(1,ℤ/8)—416no—
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—41no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16#4114yes—
546C2×D8—22no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×M16—22no—
559C2×M16—22no—
560C2×M16#4114yes—
561C22×C8—22no—
562C22×C8—22no—
563C22×C8—41no—
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C4⋊Q8—41no—
573C4⋊Q8—41no—
574#127—41no—
575#127—41no—
576#126—82no—
577#126—82no—
578#125—41no—
579#125—41no—
580#124—22no—
581#124—22no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124—41no—
586#123—82no—
587C22⋊Q8—22no—
588C22⋊Q8—22no—
589C22⋊Q8—82no—
590#121—22no—
591#121—22no—
592C4×Q8—22no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×Q8—41no—
598C4×D4—22no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—82no—
605#117—22no—
606#117—22no—
607#117—41no—
608#117—41no—
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—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—82no—
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42C2×D411yescharacteristic
705C2×C42C2×D411yescharacteristic
706C2×C42C2×D411yescharacteristic
707C2×C42C2×D411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714#107—22no—
715#107—22no—
716#107—22no—
717#107—41no—
718#107—41no—
719#106—22no—
720#106—22no—
721#106—41no—
722#106—41no—
723#106—41no—
724#106—41no—
725C4⋊C8—22no—
726C4⋊C8—22no—
727#103—22no—
728#103—22no—
729#103—22no—
730#103—22no—
731#103—22no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757C22⋊C8—22no—
758C22⋊C8#4114yes—
759#97—22no—
760#97—22no—
761#97—22no—
762#97—22no—
763#97—22no—
764#97—22no—
765#97—41no—
766C4×C8—22no—
767C4×C8—22no—
768C4×C8—22no—
769C4×C8—22no—
770C4×C8—22no—
771C4×C8—22no—
772C4×C8—41no—
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#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—42no—
820C24—42no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24—81no—
825C24—81no—
826C24C22×D411yescharacteristic
827#41—44no—
828#41—44no—
829#41—82no—
830#41—82no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8—81no—
845C2×Q8C2×#4112yes—
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—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—82no—
877C2×D4—82no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4C2×#4112yes—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C2×#4112yes—
934C22×C4C2×#4112yes—
935C22×C4C2511yescharacteristic
936Q16—44no—
937SD16—28no—
938SD16—44no—
939SD16—44no—
940SD16—82no—
941D8—44no—
942D8—44no—
943D8—44no—
944D8—82no—
945M16—28no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—44no—
964C2×C8C2×#4112yes—
965C2×C8C2×#4112yes—
966C2×C8C2×#4112yes—
967C2×C8C2×#4112yes—
968C2×C8C2×#4112yes—
969C2×C8H(5,𝔽2)12yes—
970C2×C8H(5,𝔽2)12yes—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—41no—
1018C22⋊C4—41no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
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—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—41no—
1080C42—41no—
1081C42—41no—
1082C42—41no—
1083C42—42no—
1084C42—81no—
1085C42—81no—
1086C42—81no—
1087C42—81no—
1088C42—81no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—22no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—84no—
1124C23—84no—
1125C23—162no—
1126C23—162no—
1127C23—162no—
1128C23—162no—
1129C23—162no—
1130C23#53212yes—
1131C23C23×D411yescharacteristic
1132Q8—22no—
1133Q8—22no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—162no—
1141D4—22no—
1142D4—22no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—41no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—84no—
1158D4—84no—
1159D4—84no—
1160D4—162no—
1161D4—162no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—84no—
1241C2×C4—162no—
1242C2×C4—162no—
1243C2×C4—162no—
1244C2×C4—162no—
1245C2×C4#53212yes—
1246C2×C4C22×#4111yescharacteristic
1247C2×C4C22×#4111yescharacteristic
1248C2×C4C22×#4111yescharacteristic
1249C2×C4C2×H(5,𝔽2)11yescharacteristic
1250C2×C4C2×H(5,𝔽2)11yescharacteristic
1251C2×C4#58511yescharacteristic
1252C8—22no—
1253C8—22no—
1254C8—22no—
1255C8—22no—
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C8#55114yes—
1260C22—22no—
1261C22—22no—
1262C22—22no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—168no—
1296C22C2×#53211yescharacteristic
1297C22D4×#4111yescharacteristic
1298C22#349811yescharacteristic
1299C22#358411yescharacteristic
1300C22#358411yescharacteristic
1301C22#358511yescharacteristic
1302C22#358511yescharacteristic
1303C4—22no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—42no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4C2×#55111yescharacteristic
1329C4#348111yescharacteristic
1330C4#349411yescharacteristic
1331C4#351411yescharacteristic
1332C2—42no—
1333C2—82no—
1334C2—161no—
1335C2—161no—
1336C2—161no—
1337C2#3626411yescharacteristic
1338C2#6069811yescharacteristic
1339C2#6072411yescharacteristic
1340C2#6152711yescharacteristic
1341C2#6153111yescharacteristic
1342C2#6246811yescharacteristic
1343C2#6246811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25793C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39070C2semidirect
2. #39069C2semidirect
3. #33269C2semidirect
4. #33243C2semidirect
5. #33142C2semidirect
6. #29571C2semidirect
7. #29564C2semidirect
8. #29497C2semidirect
9. #29497C2semidirect
10. #28903C2semidirect
11. #28897C2semidirect
12. #28013C2semidirect
13. #27257C2semidirect
14. #27256C2semidirect
15. #26839C2semidirect
16. #26834C2semidirect
17. #26499C2semidirect
18. #26267C2semidirect
19. #26251C2semidirect
20. #26076C2semidirect
22. #24517C2semidirect
23. #24512C2semidirect
24. #23040C2semidirect
25. #22861C2semidirect
26. #22858C2semidirect
27. #22443C2semidirect
28. #21693C2semidirect
29. #21285C2semidirect
30. #21235C2semidirect
31. #20478C2semidirect
33. C2×#501C22semidirect
37. C2×#486C22semidirect
42. C2×#441C22semidirect
44. C2×#440C22semidirect
52. #2860C22semidirect
61. #2641C22semidirect
72. #2513C22semidirect
75. #2453C22semidirect
78. #2448C22semidirect
80. #2445C22semidirect
89. #2320C22semidirect
94. C4×#124C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
99. #2073C22semidirect
101. #2066C22semidirect
103. #2065C22semidirect
104. #2059C22semidirect
105. #2058C22semidirect
106. #2056C22semidirect
107. #2055C22semidirect
112. #2042C22semidirect
113. #2041C22semidirect
115. #2024C22semidirect
123. #1973C22semidirect
124. #1973C22semidirect
130. #1971C22semidirect
138. #1968C22semidirect
139. #1968C22semidirect
140. #1968C22semidirect
142. #1958C22semidirect
143. #1944C22semidirect
144. #1944C22semidirect
145. #1943C22semidirect
146. #1942C22semidirect
147. #1941C22semidirect
150. #1936C22semidirect
151. #1936C22semidirect
152. #1936C22semidirect
153. #1935C22semidirect
157. #1934C22semidirect
158. #1934C22semidirect
159. #1933C22semidirect
160. #1933C22semidirect
161. #1933C22semidirect
162. #1927C22semidirect
164. #1926C22semidirect
165. #1925C22semidirect
170. #1880C22semidirect
175. #1878C22semidirect
179. #1864C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
184. #1846C22semidirect
188. C4×#107C22semidirect
189. #1771C22semidirect
190. #1771C22semidirect
191. #1770C22semidirect
192. C8×C4⋊C4C22semidirect
193. #1763C22semidirect
199. #1746C22semidirect
200. #1744C22semidirect
201. #1726C22semidirect
202. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
#390702
#390692
#332692
#332432
#331422
#295712
#295642
#294972
#289032
#288972
#280132
#272572
#272562
#268392
#268342
#264992
#262672
#262512
#260762
#257932
#245172
#245122
#230402
#228612
#228582
#224432
#216932
#212852
#212352
#204782