Finite Group Databasebeta

← #6614468

Subgroups — #6614468

Order 512.

1461 conjugacy classes of subgroups.

The subgroup lattice has 1187 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37938C211yesmaximal, characteristic, complemented
2#34306C211yesmaximal, characteristic
3#33155C211yesmaximal, characteristic, complemented
4#33154C211yesmaximal, characteristic, complemented
5#33076C211yesmaximal, characteristic, complemented
6#29322C211yesmaximal, characteristic, complemented
7#29281C211yesmaximal, characteristic, complemented
8#27655C211yesmaximal, characteristic, complemented
9#27633C211yesmaximal, characteristic, complemented
10#27483C211yesmaximal, characteristic, complemented
11#27469C211yesmaximal, characteristic, complemented
12#27386C211yesmaximal, characteristic, complemented
13#27385C211yesmaximal, characteristic, complemented
14#27056C211yesmaximal, characteristic, complemented
15#27038C211yesmaximal, characteristic, complemented
16#26874C211yesmaximal, characteristic, complemented
17#26873C211yesmaximal, characteristic, complemented
18#24959C211yesmaximal, characteristic, complemented
19#24943C211yesmaximal, characteristic, complemented
20#24851C211yesmaximal, characteristic, complemented
21#24708C211yesmaximal, characteristic, complemented
22#24105C211yesmaximal, characteristic
23#24093C211yesmaximal, characteristic
24#22938C211yesmaximal, characteristic, complemented
25#22926C211yesmaximal, characteristic, complemented
26#22753C211yesmaximal, characteristic, complemented
27#22622C211yesmaximal, characteristic, complemented
28#22620C211yesmaximal, characteristic, complemented
29#21623C211yesmaximal, characteristic, complemented
30#21366C211yesmaximal, characteristic, complemented
31#21175C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#482C2211yescharacteristic
34C2×#480C2211yescharacteristic
35C2×#476C2211yescharacteristic
36C2×#432C2211yescharacteristic
37C2×#428C2211yescharacteristic
38C2×#427C2211yescharacteristic
39C2×#424C2211yescharacteristic
40#2857C2211yescharacteristic
41#2764—21no—
42#2758—21no—
43#2743—21no—
44#2738—21no—
45#2647C2211yescharacteristic
46#2628C2211yescharacteristic
47#2611—21no—
48#2556—21no—
49#2533—21no—
50#2509C2211yescharacteristic
51#2506C2211yescharacteristic
52#2497C2211yescharacteristic
53#2495C2211yescharacteristic
54#2487C2211yescharacteristic
55#2485C2211yescharacteristic
56#2477—21no—
57#2372—21no—
58#2367—21no—
59#2365C2211yescharacteristic
60#2364—21no—
61#2363C2211yescharacteristic
62#2361C2211yescharacteristic
63#2357C2211yescharacteristic
64#2352C2211yescharacteristic
65#2347C2211yescharacteristic
66#2347C2211yescharacteristic
67#2346C2211yescharacteristic
68#2344C2211yescharacteristic
69#2343—21no—
70#2337—21no—
71#2333—21no—
72#2331C2211yescharacteristic
73#2331C2211yescharacteristic
74#2324C2211yescharacteristic
75#2317C2211yescharacteristic
76C4×#124—21no—
77C4×#121C2211yescharacteristic
78#2298—21no—
79#2290C2211yescharacteristic
80#2283C2211yescharacteristic
81#2275C2211yescharacteristic
82#2274C2211yescharacteristic
83C4×#117C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2088C2211yescharacteristic
87#2088C2211yescharacteristic
88#2085C2211yescharacteristic
89#2085C2211yescharacteristic
90#2085C2211yescharacteristic
91#2083C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2075C2211yescharacteristic
96#2073C2211yescharacteristic
97#2071C2211yescharacteristic
98#2067C2211yescharacteristic
99#2065C2211yescharacteristic
100#2058C2211yescharacteristic
101#2057C2211yescharacteristic
102#2057C2211yescharacteristic
103#2057C2211yescharacteristic
104#2034C2211yescharacteristic
105#2033C2211yescharacteristic
106#2033C2211yescharacteristic
107#2033C2211yescharacteristic
108#1988C2211yescharacteristic
109#1988C2211yescharacteristic
110#1987C2211yescharacteristic
111#1949C2211yescharacteristic
112#1949C2211yescharacteristic
113#1949C2211yescharacteristic
114#1949C2211yescharacteristic
115#1949C2211yescharacteristic
116#1949C2211yescharacteristic
117#1949C2211yescharacteristic
118#1949C2211yescharacteristic
119#1948C2211yescharacteristic
120#1948C2211yescharacteristic
121#1947C2211yescharacteristic
122#1947C2211yescharacteristic
123#1947C2211yescharacteristic
124#1943C2211yescharacteristic
125#1943C2211yescharacteristic
126#1943C2211yescharacteristic
127#1943C2211yescharacteristic
128#1942C2211yescharacteristic
129#1942C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1926C2211yescharacteristic
133#1925C2211yescharacteristic
134#1924C2211yescharacteristic
135#1923C2211yescharacteristic
136#1921C2211yescharacteristic
137#1921C2211yescharacteristic
138#1921C2211yescharacteristic
139#1921C2211yescharacteristic
140#1921C2211yescharacteristic
141#1920C2211yescharacteristic
142#1920C2211yescharacteristic
143#1920C2211yescharacteristic
144#1920C2211yescharacteristic
145#1920C2211yescharacteristic
146#1920C2211yescharacteristic
147#1920C2211yescharacteristic
148#1919C2211yescharacteristic
149#1919C2211yescharacteristic
150#1919C2211yescharacteristic
151#1919C2211yescharacteristic
152#1919C2211yescharacteristic
153#1918C2211yescharacteristic
154#1918C2211yescharacteristic
155#1918C2211yescharacteristic
156#1917C2211yescharacteristic
157#1917C2211yescharacteristic
158#1895C2211yescharacteristic
159#1893C2211yescharacteristic
160#1870C2211yescharacteristic
161#1869C2211yescharacteristic
162#1864C2211yescharacteristic
163#1864C2211yescharacteristic
164#1864C2211yescharacteristic
165#1864C2211yescharacteristic
166#1862C2211yescharacteristic
167#1862C2211yescharacteristic
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1853C2211yescharacteristic
175#1852C2211yescharacteristic
176#1832C2211yescharacteristic
177#1825C2211yescharacteristic
178#1825C2211yescharacteristic
179#1825C2211yescharacteristic
180#1825C2211yescharacteristic
181#1825C2211yescharacteristic
182#1824C2211yescharacteristic
183#1809C2211yescharacteristic
184#1807C2211yescharacteristic
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1802C2211yescharacteristic
188#1798C2211yescharacteristic
189#1797C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1768C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic
200#1752C2211yescharacteristic
201#1736C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205#555—24no—
206#555—24no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125—21no—
210C2×#124—21no—
211C2×#124—21no—
212C2×C22⋊Q8—21no—
213C2×#121—21no—
214C2×#121C2311yescharacteristic
215C2×#121C2311yescharacteristic
216C2×C4×Q8—21no—
217C2×C4×D4—21no—
218C2×C4×D4—21no—
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×#117—21no—
224C2×#117—21no—
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C42C2311yescharacteristic
233#482—24no—
234#480—24no—
235#476—24no—
236#432—24no—
237#428—24no—
238#427—24no—
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
259#424—24no—
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#399—21no—
294#399—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#397—21no—
299#397—21no—
300#396—21no—
301#395—21no—
302#394—21no—
303#393—21no—
304#391—21no—
305#391—21no—
306#391—21no—
307#391—21no—
308#391—21no—
309#391—21no—
310#390—21no—
311#390—21no—
312#390C2311yescharacteristic
313#390C2311yescharacteristic
314#389—21no—
315#389—21no—
316#389—21no—
317#389—21no—
318#389C2311yescharacteristic
319#389C2311yescharacteristic
320#389C2311yescharacteristic
321#389C2311yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#388—21no—
333#388—21no—
334#388—21no—
335#388—21no—
336#388—21no—
337#388—21no—
338#388—21no—
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388D411yescharacteristic
349#388D411yescharacteristic
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387D411yescharacteristic
364#387D411yescharacteristic
365#386—21no—
366#386—21no—
367#386—21no—
368#386—21no—
369#386—21no—
370#386—21no—
371#386D411yescharacteristic
372#386D411yescharacteristic
373#385—21no—
374#385—21no—
375#385—21no—
376#385—21no—
377#385—21no—
378#385D411yescharacteristic
379#385D411yescharacteristic
380#384C2311yescharacteristic
381#384C2311yescharacteristic
382#383—21no—
383#383—21no—
384#383—21no—
385#383—21no—
386#382—21no—
387#382C2311yescharacteristic
388#382C2311yescharacteristic
389#382C2311yescharacteristic
390#382C2311yescharacteristic
391#381—21no—
392#381—21no—
393#381—21no—
394#380—21no—
395#380C2311yescharacteristic
396#380C2311yescharacteristic
397#380C2311yescharacteristic
398#380C2311yescharacteristic
399#380C2311yescharacteristic
400#380C2311yescharacteristic
401#380C2311yescharacteristic
402#380C2311yescharacteristic
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C22⋊C4—21no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4C2311yescharacteristic
434C4×C22⋊C4C2311yescharacteristic
435#376—21no—
436#376—21no—
437#376—21no—
438#376C2311yescharacteristic
439C2×#95—21no—
440C43—21no—
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#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4C2×D411yescharacteristic
492C22×D4C2411yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4C2×D411yescharacteristic
499C23×C4C2×D411yescharacteristic
500C23×C4C2411yescharacteristic
501C23×C4C2411yescharacteristic
502C2×M16—22no—
503C2×M16—22no—
504C2×M16—41no—
505C22×C8—22no—
506C22×C8—22no—
507C22×C8—41no—
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C4⋊Q8—22no—
517C4⋊Q8—22no—
518C4⋊Q8—22no—
519C4⋊Q8—22no—
520#125—82no—
521#124—28no—
522#124—28no—
523C22⋊Q8—82no—
524#121—28no—
525#121—22no—
526#121—22no—
527#121—22no—
528#121#4114yes—
529C4×Q8—82no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—41no—
538C4×D4—82no—
539C4×D4—82no—
540#117—28no—
541#117—22no—
542#117—22no—
543#117—22no—
544#117—22no—
545#117—22no—
546#117—22no—
547#117—22no—
548#117—22no—
549#117—41no—
550#117—82no—
551#117#4114yes—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
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—41no—
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
620C2×C22⋊C4C2×D411yescharacteristic
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—22no—
630C2×C42—22no—
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—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653#107—22no—
654#107—22no—
655#107—22no—
656#107—22no—
657#107—22no—
658#107—22no—
659#107—22no—
660#107—22no—
661#107—41no—
662#107—41no—
663#106—22no—
664#106—22no—
665#106—22no—
666#106—22no—
667#106—22no—
668#106—22no—
669#106—22no—
670#106—22no—
671#106—41no—
672#106—41no—
673C4⋊C8—22no—
674C4⋊C8—22no—
675C4⋊C8—22no—
676C4⋊C8—22no—
677C4⋊C8—22no—
678C4⋊C8#4114yes—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—41no—
686#102—41no—
687C22⋊C8—22no—
688C22⋊C8—22no—
689C22⋊C8—22no—
690C22⋊C8—22no—
691C22⋊C8—41no—
692C22⋊C8—41no—
693#97—22no—
694#97—22no—
695#97—41no—
696C4×C8—41no—
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#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#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—
751C24C22×D411yescharacteristic
752C24C22×D411yescharacteristic
753C2×Q8—24no—
754C2×Q8—42no—
755C2×Q8—81no—
756C2×Q8—81no—
757C2×Q8—81no—
758C2×Q8—81no—
759C2×D4—24no—
760C2×D4—22no—
761C2×D4—24no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—41no—
768C2×D4—41no—
769C2×D4—81no—
770C2×D4—81no—
771C2×D4—81no—
772C2×D4—81no—
773C2×D4C2×#4112yes—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—24no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—41no—
803C22×C4—41no—
804C22×C4—41no—
805C22×C4—41no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—81no—
811C22×C4—81no—
812C22×C4—81no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4—81no—
819C22×C4—81no—
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C2×#4112yes—
833C22×C4C2×#4112yes—
834C22×C4C2511yescharacteristic
835M16—44no—
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×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—44no—
859C2×C8C2×#4112yes—
860C2×C8C2×#4112yes—
861C4⋊C4—24no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—22no—
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—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—41no—
892C4⋊C4—41no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
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⋊C4C2×#4112yes—
915C4⋊C4C2×#4112yes—
916C4⋊C4C2×#4112yes—
917C4⋊C42−1+412yes—
918C22⋊C4—24no—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—22no—
923C22⋊C4—24no—
924C22⋊C4—22no—
925C22⋊C4—22no—
926C22⋊C4—22no—
927C22⋊C4—41no—
928C22⋊C4—41no—
929C22⋊C4—41no—
930C22⋊C4—41no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C42—24no—
948C42—24no—
949C42—22no—
950C42—22no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—42no—
960C42—42no—
961C42—42no—
962C42—42no—
963C42—81no—
964C42—81no—
965C42—81no—
966C42—81no—
967C42—81no—
968C42—81no—
969C42—81no—
970C42—81no—
971C42—81no—
972C42—81no—
973C42—81no—
974C42C2×#4112yes—
975C422−1+412yes—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—22no—
988C23—21no—
989C23—21no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23#52512yes—
997C23C23×D411yescharacteristic
998Q8—84no—
999Q8—162no—
1000D4—22no—
1001D4—22no—
1002D4—41no—
1003D4—41no—
1004D4—82no—
1005D4—84no—
1006D4—84no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
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—22no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—22no—
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—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—82no—
1094C2×C4—82no—
1095C2×C4—84no—
1096C2×C4—84no—
1097C2×C4—162no—
1098C2×C4—162no—
1099C2×C4—162no—
1100C2×C4#52512yes—
1101C2×C4#54712yes—
1102C2×C4#54712yes—
1103C2×C4C22×#4111yescharacteristic
1104C2×C4C22×#4111yescharacteristic
1105C2×C4C22×#4111yescharacteristic
1106C2×C4C2×2−1+411yescharacteristic
1107C2×C4C2×2−1+411yescharacteristic
1108C2×C4#58511yescharacteristic
1109C8—22no—
1110C8—22no—
1111C8—41no—
1112C8—41no—
1113C8—41no—
1114C8—41no—
1115C8—41no—
1116C8—41no—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—41no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—42no—
1127C22—41no—
1128C22—41no—
1129C22—41no—
1130C22—42no—
1131C22—42no—
1132C22—41no—
1133C22—41no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22—81no—
1138C22C2×#52511yescharacteristic
1139C22C2×#54711yescharacteristic
1140C22#348911yescharacteristic
1141C22#358411yescharacteristic
1142C22#358511yescharacteristic
1143C22#358511yescharacteristic
1144C22#358611yescharacteristic
1145C4—22no—
1146C4—22no—
1147C4—22no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—41no—
1155C4—42no—
1156C4—42no—
1157C4—41no—
1158C4—42no—
1159C4—41no—
1160C4—42no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4#347511yescharacteristic
1173C4#348211yescharacteristic
1174C4#350911yescharacteristic
1175C4#351511yescharacteristic
1176C2—42no—
1177C2—81no—
1178C2—82no—
1179C2#3637511yescharacteristic
1180C2#6057411yescharacteristic
1181C2#6058611yescharacteristic
1182C2#6126811yescharacteristic
1183C2#6127411yescharacteristic
1184C2#6215911yescharacteristic
1185C2#6222911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#555C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37938C2semidirect
3. #33155C2semidirect
4. #33154C2semidirect
5. #33076C2semidirect
6. #29322C2semidirect
7. #29281C2semidirect
8. #27655C2semidirect
9. #27633C2semidirect
10. #27483C2semidirect
11. #27469C2semidirect
12. #27386C2semidirect
13. #27385C2semidirect
14. #27056C2semidirect
15. #27038C2semidirect
16. #26874C2semidirect
17. #26873C2semidirect
18. #24959C2semidirect
19. #24943C2semidirect
20. #24851C2semidirect
21. #24708C2semidirect
24. #22938C2semidirect
25. #22926C2semidirect
26. #22753C2semidirect
27. #22622C2semidirect
28. #22620C2semidirect
29. #21623C2semidirect
30. #21366C2semidirect
31. #21175C2semidirect

Maximal subgroups

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

subgroupindex
#379382
#343062
#331552
#331542
#330762
#293222
#292812
#276552
#276332
#274832
#274692
#273862
#273852
#270562
#270382
#268742
#268732
#249592
#249432
#248512
#247082
#241052
#240932
#229382
#229262
#227532
#226222
#226202
#216232
#213662
#211752