Finite Group Databasebeta

← #6490297

Subgroups — #6490297

Order 512.

1427 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37337C211yesmaximal, characteristic, complemented
2#34332C211yesmaximal, characteristic, complemented
3#33088C211yesmaximal, characteristic
4#33080C211yesmaximal, characteristic
5#33074C211yesmaximal, characteristic, complemented
6#33072C211yesmaximal, characteristic, complemented
7#30161C211yesmaximal, characteristic, complemented
8#30145C211yesmaximal, characteristic, complemented
9#30103C211yesmaximal, characteristic, complemented
10#30095C211yesmaximal, characteristic, complemented
11#27571C211yesmaximal, characteristic
12#27557C211yesmaximal, characteristic
13#27317C211yesmaximal, characteristic, complemented
14#27294C211yesmaximal, characteristic, complemented
15#27148C211yesmaximal, characteristic, complemented
16#27135C211yesmaximal, characteristic, complemented
17#26880C211yesmaximal, characteristic, complemented
18#26862C211yesmaximal, characteristic, complemented
19#26516C211yesmaximal, characteristic, complemented
20#26282C211yesmaximal, characteristic, complemented
21#26119C211yesmaximal, characteristic, complemented
22#25850C211yesmaximal, characteristic, complemented
23#25465C211yesmaximal, characteristic, complemented
24#25002C211yesmaximal, characteristic, complemented
25#24811C211yesmaximal, characteristic
26#24335C211yesmaximal, characteristic
27#22255C211yesmaximal, characteristic, complemented
28#22126C211yesmaximal, characteristic, complemented
29#22027C211yesmaximal, characteristic, complemented
30#21624C211yesmaximal, characteristic, complemented
31#21129C211yesmaximal, characteristic
32C2×#554C2211yescharacteristic
33C2×#501C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#474C2211yescharacteristic
36C2×C4×D8C2211yescharacteristic
37#2860C2211yescharacteristic
38#2859C2211yescharacteristic
39#2798—21no—
40#2754—21no—
41#2721—21no—
42#2721—21no—
43#2704—21no—
44#2698—21no—
45#2690—21no—
46#2689—21no—
47#2647C2211yescharacteristic
48#2644C2211yescharacteristic
49#2580C2211yescharacteristic
50#2570C2211yescharacteristic
51#2567C2211yescharacteristic
52#2542C2211yescharacteristic
53#2513C2211yescharacteristic
54#2512C2211yescharacteristic
55#2507C2211yescharacteristic
56#2506C2211yescharacteristic
57#2370C2211yescharacteristic
58#2370C2211yescharacteristic
59#2369C2211yescharacteristic
60#2360—21no—
61#2360—21no—
62#2360—21no—
63Q8×C4⋊C4C2211yescharacteristic
64D4×C4⋊C4C2211yescharacteristic
65D4×C4⋊C4C2211yescharacteristic
66D4×C4⋊C4C2211yescharacteristic
67#2345—21no—
68#2331C2211yescharacteristic
69#2330C2211yescharacteristic
70#2330C2211yescharacteristic
71#2329—21no—
72#2329—21no—
73#2319C2211yescharacteristic
74C4×C4⋊Q8C2211yescharacteristic
75C4×C22⋊Q8—21no—
76#2295C2211yescharacteristic
77C2×#389—21no—
78#2275C2211yescharacteristic
79#2275C2211yescharacteristic
80C42×D4C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2100C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2100C2211yescharacteristic
87#2100C2211yescharacteristic
88#2099C2211yescharacteristic
89#2087C2211yescharacteristic
90#2086C2211yescharacteristic
91#2086C2211yescharacteristic
92#2086C2211yescharacteristic
93#2084C2211yescharacteristic
94#2083C2211yescharacteristic
95#2083C2211yescharacteristic
96#2083C2211yescharacteristic
97#2083C2211yescharacteristic
98#2083C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2065C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2057C2211yescharacteristic
109#2057C2211yescharacteristic
110#2057C2211yescharacteristic
111#2025C2211yescharacteristic
112#2023C2211yescharacteristic
113#1991C2211yescharacteristic
114#1990C2211yescharacteristic
115#1989C2211yescharacteristic
116#1987C2211yescharacteristic
117#1985C2211yescharacteristic
118#1984C2211yescharacteristic
119#1949C2211yescharacteristic
120#1949C2211yescharacteristic
121#1948C2211yescharacteristic
122#1947C2211yescharacteristic
123#1947C2211yescharacteristic
124#1947C2211yescharacteristic
125#1944C2211yescharacteristic
126#1942C2211yescharacteristic
127#1940C2211yescharacteristic
128#1939C2211yescharacteristic
129#1936C2211yescharacteristic
130#1934C2211yescharacteristic
131#1926C2211yescharacteristic
132#1926C2211yescharacteristic
133#1925C2211yescharacteristic
134#1925C2211yescharacteristic
135#1925C2211yescharacteristic
136#1925C2211yescharacteristic
137#1925C2211yescharacteristic
138#1925C2211yescharacteristic
139#1921C2211yescharacteristic
140#1921C2211yescharacteristic
141#1921C2211yescharacteristic
142#1921C2211yescharacteristic
143#1921C2211yescharacteristic
144#1921C2211yescharacteristic
145#1921C2211yescharacteristic
146#1921C2211yescharacteristic
147#1921C2211yescharacteristic
148#1921C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1919C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1918C2211yescharacteristic
161#1917C2211yescharacteristic
162#1917C2211yescharacteristic
163#1916C2211yescharacteristic
164#1916C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic
183#1840C2211yescharacteristic
184#1839C2211yescharacteristic
185#1836C2211yescharacteristic
186#1832C2211yescharacteristic
187#1831C2211yescharacteristic
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic
190#1802C2211yescharacteristic
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#107C2211yescharacteristic
196C4×#107C2211yescharacteristic
197#1768C2211yescharacteristic
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1746C2211yescharacteristic
203C22×D8C2311yescharacteristic
204#554—24no—
205#554—24no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126—21no—
209C2×#126—21no—
210C2×#125—21no—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C4×Q8—21no—
220C2×C4×Q8—21no—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C22×C4⋊C4—21no—
231C22×C4⋊C4—21no—
232C22×C4⋊C4—21no—
233C22×C4⋊C4—21no—
234C22×C42—21no—
235#501—24no—
236#478—24no—
237#474—24no—
238C4×D8—24no—
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#399—21no—
283#399—21no—
284#399—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#397—21no—
292#397—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#396—21no—
298#396—21no—
299#395—21no—
300#395—21no—
301#393—21no—
302#391—21no—
303#391—21no—
304#391—21no—
305#391—21no—
306#391—21no—
307#391—21no—
308#391D411yescharacteristic
309#391D411yescharacteristic
310#390C2311yescharacteristic
311#390C2311yescharacteristic
312#390C2311yescharacteristic
313#390C2311yescharacteristic
314#390C2311yescharacteristic
315#390C2311yescharacteristic
316#389—21no—
317#389—21no—
318#389—21no—
319#389—21no—
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389D411yescharacteristic
331#389D411yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387D411yescharacteristic
373#387D411yescharacteristic
374#387D411yescharacteristic
375#387D411yescharacteristic
376#385—21no—
377#385—21no—
378#385—21no—
379#385—21no—
380#385—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#384—21no—
385#384C2311yescharacteristic
386#384C2311yescharacteristic
387#384C2311yescharacteristic
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#382—21no—
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#381—21no—
395#380—21no—
396#380—21no—
397#380—21no—
398#380—21no—
399C4×C4⋊C4—21no—
400C4×C4⋊C4—21no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4C2311yescharacteristic
404C4×C4⋊C4C2311yescharacteristic
405C4×C4⋊C4C2311yescharacteristic
406C4×C4⋊C4C2311yescharacteristic
407C4×C4⋊C4C2311yescharacteristic
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C22⋊C4—21no—
419C4×C22⋊C4—21no—
420C4×C22⋊C4—21no—
421C4×C22⋊C4—21no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427#376C2311yescharacteristic
428#376C2311yescharacteristic
429C2×#95—21no—
430C2×#95—21no—
431C43C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8C2×D411yescharacteristic
487C22×D4C2411yescharacteristic
488C22×D4C2411yescharacteristic
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C2×D8—22no—
498C2×D8—22no—
499C2×D8—22no—
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C4⋊Q8—22no—
509C4⋊Q8—22no—
510C4⋊Q8—22no—
511C4⋊Q8—22no—
512#126—82no—
513#126—82no—
514#125—22no—
515#125—22no—
516#125—22no—
517#125—82no—
518#125—82no—
519#125#4114yes—
520C22⋊Q8—28no—
521C22⋊Q8—28no—
522C22⋊Q8—28no—
523C22⋊Q8—82no—
524C22⋊Q8—82no—
525C4×Q8—22no—
526C4×Q8—22no—
527C4×Q8—82no—
528C4×Q8—82no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—41no—
542C4×D4—41no—
543C4×D4—41no—
544C4×D4#4114yes—
545C2×C4⋊C4—28no—
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—82no—
583C2×C4⋊C4—82no—
584C2×C4⋊C4—82no—
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
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×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—82no—
641C2×C42C2×D411yescharacteristic
642C2×C42C2×D411yescharacteristic
643C2×C42C2×D411yescharacteristic
644C2×C42C2×D411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652#107—22no—
653#107—22no—
654#107—22no—
655#107—22no—
656#107—22no—
657#107—22no—
658#107—22no—
659#107—22no—
660#107—41no—
661#107—41no—
662#107—41no—
663#106—22no—
664#106—22no—
665#106—22no—
666#106—22no—
667C4⋊C8—22no—
668C4⋊C8—22no—
669C4⋊C8—41no—
670C4⋊C8—41no—
671C4⋊C8—41no—
672C4⋊C8—41no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—22no—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—41no—
685#102—41no—
686#102—41no—
687#97—22no—
688#97—41no—
689C4×C8—22no—
690C4×C8—41no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
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#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739C24—21no—
740C24—21no—
741C2×Q8—24no—
742C2×Q8—22no—
743C2×Q8—22no—
744C2×Q8—41no—
745C2×Q8—42no—
746C2×Q8—81no—
747C2×Q8—81no—
748C2×Q8—81no—
749C2×Q8—81no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4C2×#4112yes—
760C2×D42−1+412yes—
761C2×D42−1+412yes—
762C22×C4—24no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—81no—
788C22×C4—81no—
789C22×C4—81no—
790C22×C4—81no—
791C22×C4—81no—
792C22×C4—81no—
793C22×C4—81no—
794C22×C4—81no—
795C22×C4—81no—
796C22×C4—81no—
797C22×C4—81no—
798C22×C4—81no—
799C22×C4—81no—
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×C4C22×D411yescharacteristic
814C22×C4C2511yescharacteristic
815D8—44no—
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×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—22no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—22no—
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—21no—
874C4⋊C4—21no—
875C4⋊C4—41no—
876C4⋊C4—41no—
877C4⋊C4—41no—
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—81no—
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⋊C4C2×#4112yes—
910C4⋊C4C2×#4112yes—
911C4⋊C4C2×#4112yes—
912C4⋊C42−1+412yes—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—24no—
916C22⋊C4—24no—
917C22⋊C4—42no—
918C22⋊C4—42no—
919C22⋊C4—42no—
920C22⋊C4—42no—
921C22⋊C4—42no—
922C22⋊C4—42no—
923C22⋊C4—42no—
924C22⋊C4—81no—
925C22⋊C4—81no—
926C22⋊C4—81no—
927C22⋊C4—81no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C42—22no—
934C42—22no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—41no—
948C42—41no—
949C42—42no—
950C42—81no—
951C42—81no—
952C42—81no—
953C42—81no—
954C42—81no—
955C42—81no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42—81no—
960C42—81no—
961C42C2×#4112yes—
962C42C2×#4112yes—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23C23×D411yescharacteristic
978Q8—44no—
979Q8—84no—
980Q8—162no—
981D4—22no—
982D4—22no—
983D4—22no—
984D4—41no—
985D4—41no—
986D4—41no—
987D4—41no—
988D4#54114yes—
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—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—48no—
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—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—84no—
1071C2×C4—84no—
1072C2×C4—84no—
1073C2×C4—84no—
1074C2×C4—162no—
1075C2×C4—162no—
1076C2×C4—162no—
1077C2×C4#52512yes—
1078C2×C4#52512yes—
1079C2×C4#57612yes—
1080C2×C4#57812yes—
1081C2×C4C22×#4111yescharacteristic
1082C2×C4C22×#4111yescharacteristic
1083C2×C4C2×2−1+411yescharacteristic
1084C2×C4C2×2−1+411yescharacteristic
1085C2×C4C2×2−1+411yescharacteristic
1086C2×C4#58511yescharacteristic
1087C8—41no—
1088C8—41no—
1089C8—41no—
1090C8—41no—
1091C8—41no—
1092C8—41no—
1093C8—41no—
1094C8—41no—
1095C22—24no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22C2×#52511yescharacteristic
1110C22#348611yescharacteristic
1111C22#348911yescharacteristic
1112C22C2×#57611yescharacteristic
1113C22C2×#57811yescharacteristic
1114C22#358511yescharacteristic
1115C22#358511yescharacteristic
1116C4—22no—
1117C4—22no—
1118C4—22no—
1119C4—22no—
1120C4—41no—
1121C4—42no—
1122C4—41no—
1123C4—41no—
1124C4—42no—
1125C4—42no—
1126C4—41no—
1127C4—41no—
1128C4—42no—
1129C4—41no—
1130C4—41no—
1131C4—41no—
1132C4—41no—
1133C4—41no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4C2×#54111yescharacteristic
1145C4#346111yescharacteristic
1146C4#351611yescharacteristic
1147C4#352311yescharacteristic
1148C2—44no—
1149C2—161no—
1150C2#3524411yescharacteristic
1151C2#6058911yescharacteristic
1152C2#6059011yescharacteristic
1153C2#6187011yescharacteristic
1154C2#6187211yescharacteristic
1155C2#6216311yescharacteristic
1156C2#6218111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D8C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37337C2semidirect
2. #34332C2semidirect
5. #33074C2semidirect
6. #33072C2semidirect
7. #30161C2semidirect
8. #30145C2semidirect
9. #30103C2semidirect
10. #30095C2semidirect
13. #27317C2semidirect
14. #27294C2semidirect
15. #27148C2semidirect
16. #27135C2semidirect
17. #26880C2semidirect
18. #26862C2semidirect
19. #26516C2semidirect
20. #26282C2semidirect
21. #26119C2semidirect
22. #25850C2semidirect
23. #25465C2semidirect
24. #25002C2semidirect
27. #22255C2semidirect
28. #22126C2semidirect
29. #22027C2semidirect
30. #21624C2semidirect

Maximal subgroups

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

subgroupindex
#373372
#343322
#330882
#330802
#330742
#330722
#301612
#301452
#301032
#300952
#275712
#275572
#273172
#272942
#271482
#271352
#268802
#268622
#265162
#262822
#261192
#258502
#254652
#250022
#248112
#243352
#222552
#221262
#220272
#216242
#211292