Finite Group Databasebeta

← #6818450

Subgroups — #6818450

Order 512.

1324 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39979C211yesmaximal, characteristic, complemented
2#39976C211yesmaximal, characteristic
3#33311C211yesmaximal, characteristic, complemented
4#32348C211yesmaximal, characteristic, complemented
5#32347C211yesmaximal, characteristic
6#32345C211yesmaximal, characteristic, complemented
7#32342C211yesmaximal, characteristic
8#30960C211yesmaximal, characteristic, complemented
9#30958C211yesmaximal, characteristic
10#30953C211yesmaximal, characteristic, complemented
11#30951C211yesmaximal, characteristic
12#29989C211yesmaximal, characteristic, complemented
13#29987C211yesmaximal, characteristic
14#28831C211yesmaximal, characteristic, complemented
15#28811C211yesmaximal, characteristic, complemented
16#28810C211yesmaximal, characteristic, complemented
17#28810C211yesmaximal, characteristic, complemented
18#28533C211yesmaximal, characteristic
19#28530C211yesmaximal, characteristic
20#27990C211yesmaximal, characteristic, complemented
21#27990C211yesmaximal, characteristic, complemented
22#26481C211yesmaximal, characteristic
23#26481C211yesmaximal, characteristic
24#26096C211yesmaximal, characteristic
25#26095C211yesmaximal, characteristic, complemented
26#26051C211yesmaximal, characteristic
27#26048C211yesmaximal, characteristic, complemented
28#22806C211yesmaximal, characteristic
29#22683C211yesmaximal, characteristic
30C8×#125C211yesmaximal, characteristic, complemented
31#21274C211yesmaximal, characteristic
32C2×#499C2211yescharacteristic
33C2×#499C2211yescharacteristic
34C2×#499C2211yescharacteristic
35C2×#499C2211yescharacteristic
36C2×#499C2211yescharacteristic
37C2×#498C2211yescharacteristic
38C2×#479C2211yescharacteristic
39C2×#475C2211yescharacteristic
40C2×#478C2211yescharacteristic
41C2×#476C2211yescharacteristic
42C2×C4×SD16C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic
44C2×C4×SD16C2211yescharacteristic
45#2859C2211yescharacteristic
46#2859C2211yescharacteristic
47#2807—21no—
48#2802—21no—
49#2792—21no—
50#2774—21no—
51#2768—21no—
52#2726—21no—
53#2720—21no—
54#2704—21no—
55#2667—21no—
56#2666—21no—
57#2612—21no—
58#2606—21no—
59#2570C2211yescharacteristic
60#2570C2211yescharacteristic
61#2567C2211yescharacteristic
62#2566C2211yescharacteristic
63#2565C2211yescharacteristic
64#2552C2211yescharacteristic
65#2552C2211yescharacteristic
66#2550C2211yescharacteristic
67#2550C2211yescharacteristic
68#2550C2211yescharacteristic
69#2550C2211yescharacteristic
70#2542C2211yescharacteristic
71#2507C2211yescharacteristic
72#2507C2211yescharacteristic
73#2506C2211yescharacteristic
74#2506C2211yescharacteristic
75#2454C2211yescharacteristic
76#2454C2211yescharacteristic
77#2453C2211yescharacteristic
78#2453C2211yescharacteristic
79#2441—21no—
80#2438—21no—
81#2357C2211yescharacteristic
82#2356C2211yescharacteristic
83#2351C2211yescharacteristic
84#2349C2211yescharacteristic
85#2330—21no—
86#2329—21no—
87C4×#125C2211yescharacteristic
88#2295C2211yescharacteristic
89#2293C2211yescharacteristic
90#2100C2211yescharacteristic
91#2100C2211yescharacteristic
92#2099C2211yescharacteristic
93#2099C2211yescharacteristic
94#2097C2211yescharacteristic
95#2096C2211yescharacteristic
96#2096C2211yescharacteristic
97#2095C2211yescharacteristic
98#2094C2211yescharacteristic
99#2094C2211yescharacteristic
100#2093C2211yescharacteristic
101#2092C2211yescharacteristic
102#2088C2211yescharacteristic
103#2088C2211yescharacteristic
104#2088C2211yescharacteristic
105#2088C2211yescharacteristic
106#2085C2211yescharacteristic
107#2085C2211yescharacteristic
108#2083C2211yescharacteristic
109#2083C2211yescharacteristic
110#2068C2211yescharacteristic
111#2068C2211yescharacteristic
112#2067C2211yescharacteristic
113#2067C2211yescharacteristic
114#2059C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2059C2211yescharacteristic
120#2059C2211yescharacteristic
121#2059C2211yescharacteristic
122#2057C2211yescharacteristic
123#2057C2211yescharacteristic
124#2057C2211yescharacteristic
125#2057C2211yescharacteristic
126#2026C2211yescharacteristic
127#2026C2211yescharacteristic
128#2025C2211yescharacteristic
129#2025C2211yescharacteristic
130#1968C2211yescharacteristic
131#1968C2211yescharacteristic
132#1968C2211yescharacteristic
133#1968C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1947C2211yescharacteristic
141#1947C2211yescharacteristic
142#1941C2211yescharacteristic
143#1941C2211yescharacteristic
144#1941C2211yescharacteristic
145#1941C2211yescharacteristic
146#1941C2211yescharacteristic
147#1941C2211yescharacteristic
148#1941C2211yescharacteristic
149#1941C2211yescharacteristic
150#1939C2211yescharacteristic
151#1939C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1933C2211yescharacteristic
155#1933C2211yescharacteristic
156#1928C2211yescharacteristic
157#1928C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1920C2211yescharacteristic
161#1920C2211yescharacteristic
162#1919C2211yescharacteristic
163#1919C2211yescharacteristic
164#1916C2211yescharacteristic
165#1916C2211yescharacteristic
166#1916C2211yescharacteristic
167#1916C2211yescharacteristic
168#1863C2211yescharacteristic
169#1863C2211yescharacteristic
170#1863C2211yescharacteristic
171#1863C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1846C2211yescharacteristic
177#1846C2211yescharacteristic
178#1846C2211yescharacteristic
179#1846C2211yescharacteristic
180#1846C2211yescharacteristic
181#1845C2211yescharacteristic
182#1845C2211yescharacteristic
183#1844C2211yescharacteristic
184#1844C2211yescharacteristic
185#1844C2211yescharacteristic
186#1831C2211yescharacteristic
187#1805C2211yescharacteristic
188#1805C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191C4×#106C2211yescharacteristic
192C4×#106C2211yescharacteristic
193C4×#106C2211yescharacteristic
194C8×C4⋊C4C2211yescharacteristic
195C8×C4⋊C4C2211yescharacteristic
196C8×C4⋊C4C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic
198C8×C4⋊C4C2211yescharacteristic
199C8×C4⋊C4C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C42×C8C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×#125—21no—
207C2×#125—21no—
208C2×#125D411yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×#117—21no—
224#499—42no—
225#499—42no—
226#499—42no—
227#499—42no—
228#499—42no—
229#498—42no—
230#479—42no—
231#478—42no—
232#476—42no—
233#475—42no—
234C4×SD16—42no—
235C4×SD16—42no—
236C4×SD16Q818yescomplemented
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#399—21no—
301#399—21no—
302#399—21no—
303#399—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#395—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#395—21no—
334#391—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389D411yescharacteristic
369#389D411yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387D411yescharacteristic
407#387D411yescharacteristic
408#387D411yescharacteristic
409#387D411yescharacteristic
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#384—21no—
417#384—21no—
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#383—21no—
425#382—21no—
426#382D411yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#381—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453#376—21no—
454#376—21no—
455C2×#95—21no—
456C43C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
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#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8C2411yescharacteristic
494C22×D4C2411yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C2×SD16—22no—
499C2×SD16—22no—
500C2×SD16C2×Q814yes—
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C4⋊Q8—41no—
510C4⋊Q8—41no—
511C4⋊Q8—41no—
512C4⋊Q8—41no—
513#125—24no—
514#125—41no—
515#125—41no—
516#125—41no—
517#125—41no—
518#125—41no—
519#125—41no—
520#125—41no—
521#125—41no—
522#125—41no—
523#125—41no—
524#125—41no—
525#125—41no—
526#125—44no—
527#125—82no—
528C22⋊Q8—44no—
529C22⋊Q8—82no—
530C4×Q8—22no—
531C4×Q8—41no—
532C4×Q8—41no—
533C4×Q8—41no—
534C4×Q8—41no—
535C4×Q8C2×Q814yes—
536C4×D4—22no—
537C4×D4—41no—
538C4×D4—41no—
539C4×D4—41no—
540C4×D4—41no—
541C4×D4C2×Q814yes—
542#117—82no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42C2×D411yescharacteristic
635C2×C42C2×D411yescharacteristic
636C2×C42C2×D411yescharacteristic
637C2×C42C2×D411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645#107—41no—
646#107—41no—
647#107—41no—
648#107—41no—
649#107—41no—
650#107—41no—
651#107—41no—
652#107—41no—
653#107—41no—
654#107—41no—
655#107—41no—
656#107—41no—
657#106—22no—
658#106—22no—
659#106—22no—
660#106—22no—
661#106—22no—
662#106—22no—
663#106—22no—
664#106—22no—
665#106—22no—
666#106—22no—
667#106—41no—
668#106—41no—
669#106—41no—
670#106—41no—
671#106C2×Q814yes—
672C4⋊C8—22no—
673C4⋊C8—22no—
674C4⋊C8—22no—
675C4⋊C8—22no—
676C4⋊C8—22no—
677C4⋊C8—22no—
678#103—22no—
679#103—22no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#103C2×Q814yes—
685#102—22no—
686#102—22no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102—41no—
691#102C2×Q814yes—
692C4×C8—22no—
693C4×C8—22no—
694C4×C8—22no—
695C4×C8—22no—
696C4×C8—22no—
697C4×C8—22no—
698C4×C8—22no—
699C4×C8—22no—
700C4×C8—22no—
701C4×C8C2×Q814yes—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756C24—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—42no—
763C2×Q8—81no—
764C2×Q8—81no—
765C2×Q8—81no—
766C2×Q8—81no—
767C2×Q8—81no—
768C2×Q8C22×Q812yes—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4C22×Q812yes—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—24no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—42no—
792C22×C4—81no—
793C22×C4—81no—
794C22×C4—81no—
795C22×C4—81no—
796C22×C4—81no—
797C22×C4—81no—
798C22×C4—81no—
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C2511yescharacteristic
814SD16—28no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8C22×Q812yes—
834C2×C8C22×Q812yes—
835C2×C8H(5,𝔽2)12yes—
836C2×C8H(5,𝔽2)12yes—
837C2×C82−1+412yes—
838C2×C82−1+412yes—
839C4⋊C4—24no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—41no—
874C4⋊C4—41no—
875C4⋊C4—41no—
876C4⋊C4—41no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4#13514yes—
922C4⋊C4C22×Q812yes—
923C4⋊C4C22×Q812yes—
924C22⋊C4—24no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C42—24no—
936C42—22no—
937C42—22no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—41no—
951C42—41no—
952C42—42no—
953C42—81no—
954C42—81no—
955C42—81no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42—81no—
960C42C22×Q812yes—
961C422−1+412yes—
962C23—22no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23C23×D411yescharacteristic
970Q8—22no—
971Q8—22no—
972Q8—41no—
973Q8—41no—
974Q8—162no—
975Q8—162no—
976D4—22no—
977D4—22no—
978D4—41no—
979D4—41no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—84no—
1062C2×C4—162no—
1063C2×C4—162no—
1064C2×C4D4×Q812yes—
1065C2×C4D4×Q812yes—
1066C2×C4C2×#13512yes—
1067C2×C4C2×#13512yes—
1068C2×C4C2×#13512yes—
1069C2×C4#57712yes—
1070C2×C4C23×Q811yescharacteristic
1071C2×C4C2×H(5,𝔽2)11yescharacteristic
1072C2×C4C2×H(5,𝔽2)11yescharacteristic
1073C2×C4C2×2−1+411yescharacteristic
1074C2×C4C2×2−1+411yescharacteristic
1075C2×C4C2×2−1+411yescharacteristic
1076C8—22no—
1077C8—22no—
1078C8—22no—
1079C8—41no—
1080C8—41no—
1081C8—41no—
1082C8—41no—
1083C8#54414yes—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22C2×D4×Q811yescharacteristic
1092C22#349811yescharacteristic
1093C22#349911yescharacteristic
1094C22C22×#13511yescharacteristic
1095C22C2×#57711yescharacteristic
1096C22#358411yescharacteristic
1097C22#358411yescharacteristic
1098C4—22no—
1099C4—22no—
1100C4—22no—
1101C4—22no—
1102C4—22no—
1103C4—22no—
1104C4—41no—
1105C4—41no—
1106C4—41no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—41no—
1111C4—41no—
1112C4—41no—
1113C4—41no—
1114C4—41no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4—81no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C4—81no—
1127C4C2×#54411yescharacteristic
1128C4#350311yescharacteristic
1129C4#354411yescharacteristic
1130C4#355211yescharacteristic
1131C2—82no—
1132C2#3936911yescharacteristic
1133C2Q8×#13511yescharacteristic
1134C2#6137111yescharacteristic
1135C2#6241411yescharacteristic
1136C2#6243311yescharacteristic
1137C2#6247511yescharacteristic
1138C2#6249111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#125 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39979C2semidirect
3. #33311C2semidirect
4. #32348C2semidirect
6. #32345C2semidirect
8. #30960C2semidirect
10. #30953C2semidirect
12. #29989C2semidirect
14. #28831C2semidirect
15. #28811C2semidirect
16. #28810C2semidirect
17. #28810C2semidirect
20. #27990C2semidirect
21. #27990C2semidirect
25. #26095C2semidirect
27. #26048C2semidirect
30. C8×#125C2semidirect
236. C4×SD16Q8semidirect

Maximal subgroups

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

subgroupindex
#399792
#399762
#333112
#323482
#323472
#323452
#323422
#309602
#309582
#309532
#309512
#299892
#299872
#288312
#288112
#288102
#285332
#285302
#279902
#264812
#260962
#260952
#260512
#260482
#228062
#226832
C8×#1252
#212742