Finite Group Databasebeta

← #7586362

Subgroups — #7586362

Order 512.

1426 conjugacy classes of subgroups.

The subgroup lattice has 1167 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59842C211yesmaximal, characteristic
2#36600C211yesmaximal, characteristic, complemented
3#32253C211yesmaximal, characteristic, complemented
4#32155C211yesmaximal, characteristic, complemented
5#30967C211yesmaximal, characteristic, complemented
6#30827C211yesmaximal, characteristic
7#29572C211yesmaximal, characteristic, complemented
8#29572C211yesmaximal, characteristic, complemented
9#29094C211yesmaximal, characteristic, complemented
10#28962C211yesmaximal, characteristic, complemented
11#27503C211yesmaximal, characteristic, complemented
12#27439C211yesmaximal, characteristic, complemented
13#27429C211yesmaximal, characteristic, complemented
14#27375C211yesmaximal, characteristic, complemented
15#27207C211yesmaximal, characteristic
16#27139C211yesmaximal, characteristic, complemented
17#27011C211yesmaximal, characteristic, complemented
18#27001C211yesmaximal, characteristic, complemented
19#26896C211yesmaximal, characteristic
20#26869C211yesmaximal, characteristic, complemented
21#26825C211yesmaximal, characteristic
22#26701C211yesmaximal, characteristic
23#26486C211yesmaximal, characteristic, complemented
24#26374C211yesmaximal, characteristic, complemented
25#23266C211yesmaximal, characteristic, complemented
26#23229C211yesmaximal, characteristic
27#23168C211yesmaximal, characteristic, complemented
28#23072C211yesmaximal, characteristic, complemented
29#22974C211yesmaximal, characteristic, complemented
30#21115C211yesmaximal, characteristic, complemented
31#21115C211yesmaximal, characteristic, complemented
32C2×#552—21no—
33C2×#501C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×C4×SD16C2211yescharacteristic
38C2×C4×SD16C2211yescharacteristic
39#2859—21no—
40#2859C2211yescharacteristic
41#2707—21no—
42#2702—21no—
43#2609—21no—
44#2585—21no—
45#2585—21no—
46#2585—21no—
47#2585—21no—
48#2570—21no—
49#2570—21no—
50#2552C2211yescharacteristic
51#2552C2211yescharacteristic
52#2512C2211yescharacteristic
53#2512C2211yescharacteristic
54#2506C2211yescharacteristic
55#2506C2211yescharacteristic
56#2481—21no—
57#2477—21no—
58#2460—21no—
59#2458—21no—
60#2453C2211yescharacteristic
61#2453C2211yescharacteristic
62#2453C2211yescharacteristic
63#2453C2211yescharacteristic
64#2452C2211yescharacteristic
65#2452C2211yescharacteristic
66#2445C2211yescharacteristic
67#2445C2211yescharacteristic
68#2370C2211yescharacteristic
69#2370C2211yescharacteristic
70#2370C2211yescharacteristic
71#2370C2211yescharacteristic
72#2366C2211yescharacteristic
73#2365C2211yescharacteristic
74#2355C2211yescharacteristic
75#2355C2211yescharacteristic
76#2354C2211yescharacteristic
77D4×C4⋊C4C2211yescharacteristic
78C4×#125—21no—
79C4×#125C2211yescharacteristic
80#2293C2211yescharacteristic
81#2293C2211yescharacteristic
82C42×Q8C2211yescharacteristic
83#2100C2211yescharacteristic
84#2099C2211yescharacteristic
85#2099C2211yescharacteristic
86#2095C2211yescharacteristic
87#2093C2211yescharacteristic
88#2093C2211yescharacteristic
89#2087C2211yescharacteristic
90#2087C2211yescharacteristic
91#2084C2211yescharacteristic
92#2083C2211yescharacteristic
93#2083C2211yescharacteristic
94#2072C2211yescharacteristic
95#2071C2211yescharacteristic
96#2071C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2065C2211yescharacteristic
100#2065C2211yescharacteristic
101#2059C2211yescharacteristic
102#2059C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2057C2211yescharacteristic
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2041C2211yescharacteristic
109#2025C2211yescharacteristic
110#2025C2211yescharacteristic
111#2025C2211yescharacteristic
112#2025C2211yescharacteristic
113#2024C2211yescharacteristic
114#2014C2211yescharacteristic
115#1992C2211yescharacteristic
116#1992C2211yescharacteristic
117#1989C2211yescharacteristic
118#1989C2211yescharacteristic
119#1987C2211yescharacteristic
120#1982C2211yescharacteristic
121#1973C2211yescharacteristic
122#1973C2211yescharacteristic
123#1948C2211yescharacteristic
124#1947C2211yescharacteristic
125#1944C2211yescharacteristic
126#1944C2211yescharacteristic
127#1942C2211yescharacteristic
128#1942C2211yescharacteristic
129#1942C2211yescharacteristic
130#1942C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1935C2211yescharacteristic
134#1935C2211yescharacteristic
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1928C2211yescharacteristic
140#1928C2211yescharacteristic
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1919C2211yescharacteristic
158#1919C2211yescharacteristic
159#1918C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1917C2211yescharacteristic
164#1917C2211yescharacteristic
165#1917C2211yescharacteristic
166#1917C2211yescharacteristic
167#1916C2211yescharacteristic
168#1916C2211yescharacteristic
169#1916C2211yescharacteristic
170#1916C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189C4×#106C2211yescharacteristic
190C4×#106C2211yescharacteristic
191#1771C2211yescharacteristic
192#1771C2211yescharacteristic
193#1771C2211yescharacteristic
194#1771C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1744C2211yescharacteristic
202#1744C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205#552—48no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×#127C2311yescharacteristic
208C2×#126—21no—
209C2×#126—21no—
210C2×#125—21no—
211C2×#125—21no—
212C2×#125—21no—
213C2×#125D411yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#123—21no—
219C2×#123—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C4×Q8—21no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117—21no—
232C2×#117—21no—
233C2×#117—21no—
234C22×C4⋊C4—21no—
235#501—24no—
236#490—24no—
237#478—24no—
238#478—24no—
239C4×SD16—24no—
240C4×SD16—24no—
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×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#397—21no—
304#397—21no—
305#396—21no—
306#396—21no—
307#396—21no—
308#396—21no—
309#394—21no—
310#394—21no—
311#394—21no—
312#394—21no—
313#393—21no—
314#393—21no—
315#391—21no—
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#390—21no—
321#390C2311yescharacteristic
322#390C2311yescharacteristic
323#390C2311yescharacteristic
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389D411yescharacteristic
342#389D411yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387D411yescharacteristic
388#387D411yescharacteristic
389#387D411yescharacteristic
390#387D411yescharacteristic
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#384—21no—
400#384—21no—
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#382—21no—
406#382—21no—
407#382—21no—
408#382D411yescharacteristic
409#380—21no—
410#380—21no—
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C43—21no—
440C43C2311yescharacteristic
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#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
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
484#336C2311yescharacteristic
485C22×Q8—21no—
486C22×Q8C2411yescharacteristic
487C22×D4—21no—
488C22×D4—21no—
489C22×D4C2411yescharacteristic
490C22×D4C2411yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C4⋊Q8—22no—
510C4⋊Q8—41no—
511#127—22no—
512#127—41no—
513#126—44no—
514#126—44no—
515#125—22no—
516#125—22no—
517#125—22no—
518#125—22no—
519#125—24no—
520#125—41no—
521#125—41no—
522#125—41no—
523#125—41no—
524#125—44no—
525#125—44no—
526#125—44no—
527#123—44no—
528#123—44no—
529C22⋊Q8—44no—
530C22⋊Q8—44no—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—22no—
535C4×Q8—41no—
536C4×Q8—41no—
537C4×Q8—44no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—41no—
543C4×D4—41no—
544C4×D4—41no—
545C4×D4—41no—
546C4×D4—44no—
547#117—44no—
548#117—44no—
549#117—44no—
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—44no—
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⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—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—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2×D411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657#107—22no—
658#107—22no—
659#107—22no—
660#107—22no—
661#107—41no—
662#107—41no—
663#107—41no—
664#107—41no—
665#106—22no—
666#106—22no—
667#106—22no—
668#106—22no—
669#106—22no—
670#106#4114yes—
671C4⋊C8—22no—
672C4⋊C8—22no—
673C4⋊C8—41no—
674C4⋊C8—41no—
675#103—22no—
676#103—22no—
677#103—22no—
678#103—22no—
679#103—41no—
680#103—41no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—22no—
689#102—22no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102#4114yes—
695#97—22no—
696#97—22no—
697#97—41no—
698#97—41no—
699C4×C8—22no—
700C4×C8—22no—
701C4×C8—41no—
702C4×C8—41no—
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#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750C24—21no—
751C24—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8—81no—
760C2×Q82−1+412yes—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—42no—
773C2×D4—42no—
774C2×D4—42no—
775C2×D4—81no—
776C2×D4—81no—
777C2×D4—81no—
778C2×D4C2×#4112yes—
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—21no—
792C22×C4—21no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—81no—
802C22×C4—81no—
803C22×C4—81no—
804C22×C4—81no—
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×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C2511yescharacteristic
820SD16—44no—
821SD16—44no—
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—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8C2×#4112yes—
845C2×C8C2×#4112yes—
846C4⋊C4—24no—
847C4⋊C4—22no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
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—41no—
879C4⋊C4—41no—
880C4⋊C4—41no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
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⋊C4C2×#4112yes—
917C4⋊C4C2×#4112yes—
918C4⋊C4C2×#4112yes—
919C4⋊C42−1+412yes—
920C22⋊C4—42no—
921C22⋊C4—42no—
922C22⋊C4—42no—
923C22⋊C4—42no—
924C22⋊C4—42no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C42—24no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—41no—
956C42—41no—
957C42—41no—
958C42—42no—
959C42—42no—
960C42—42no—
961C42—42no—
962C42—42no—
963C42—42no—
964C42—42no—
965C42—81no—
966C42—81no—
967C42—81no—
968C42—81no—
969C42—81no—
970C42—81no—
971C42AGL(1,ℤ/8)14yes—
972C23—22no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23C23×D411yescharacteristic
987Q8—22no—
988Q8—22no—
989Q8—41no—
990Q8—41no—
991Q8—84no—
992D4—22no—
993D4—22no—
994D4—41no—
995D4—41no—
996D4—41no—
997D4—41no—
998D4—41no—
999D4—41no—
1000D4—84no—
1001D4—162no—
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—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—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—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—21no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
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—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—84no—
1084C2×C4—84no—
1085C2×C4—84no—
1086C2×C4—84no—
1087C2×C4C2×AGL(1,ℤ/8)12yes—
1088C2×C4C2×AGL(1,ℤ/8)12yes—
1089C2×C4C2×AGL(1,ℤ/8)12yes—
1090C2×C4C22×#4111yescharacteristic
1091C2×C4C22×#4111yescharacteristic
1092C2×C4C2×2−1+411yescharacteristic
1093C2×C4C2×2−1+411yescharacteristic
1094C2×C4#58511yescharacteristic
1095C2×C4#58511yescharacteristic
1096C8—22no—
1097C8—22no—
1098C8—41no—
1099C8—41no—
1100C8—41no—
1101C8—41no—
1102C8—41no—
1103C8—41no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22D4×#4111yescharacteristic
1119C22D4×#4111yescharacteristic
1120C22#348611yescharacteristic
1121C22C22×AGL(1,ℤ/8)11yescharacteristic
1122C22#358411yescharacteristic
1123C22#358411yescharacteristic
1124C22#358611yescharacteristic
1125C4—22no—
1126C4—22no—
1127C4—22no—
1128C4—42no—
1129C4—41no—
1130C4—41no—
1131C4—41no—
1132C4—42no—
1133C4—41no—
1134C4—41no—
1135C4—41no—
1136C4—42no—
1137C4—41no—
1138C4—42no—
1139C4—41no—
1140C4—41no—
1141C4—41no—
1142C4—41no—
1143C4—42no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4#348211yescharacteristic
1154C4#349511yescharacteristic
1155C4#349511yescharacteristic
1156C4#355711yescharacteristic
1157C2—82no—
1158C2—161no—
1159C2#5918311yescharacteristic
1160C2#6143911yescharacteristic
1161C2#6143911yescharacteristic
1162C2#6153011yescharacteristic
1163C2#6153211yescharacteristic
1164C2#6182811yescharacteristic
1165C2#6186711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#127C23
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
2. #36600C2semidirect
3. #32253C2semidirect
4. #32155C2semidirect
5. #30967C2semidirect
7. #29572C2semidirect
8. #29572C2semidirect
9. #29094C2semidirect
10. #28962C2semidirect
11. #27503C2semidirect
12. #27439C2semidirect
13. #27429C2semidirect
14. #27375C2semidirect
16. #27139C2semidirect
17. #27011C2semidirect
18. #27001C2semidirect
20. #26869C2semidirect
23. #26486C2semidirect
24. #26374C2semidirect
25. #23266C2semidirect
27. #23168C2semidirect
28. #23072C2semidirect
29. #22974C2semidirect
30. #21115C2semidirect
31. #21115C2semidirect

Maximal subgroups

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

subgroupindex
#598422
#366002
#322532
#321552
#309672
#308272
#295722
#290942
#289622
#275032
#274392
#274292
#273752
#272072
#271392
#270112
#270012
#268962
#268692
#268252
#267012
#264862
#263742
#232662
#232292
#231682
#230722
#229742
#211152