Finite Group Databasebeta

← #7604071

Subgroups — #7604071

Order 512.

1220 conjugacy classes of subgroups.

The subgroup lattice has 1089 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45164C211yesmaximal, characteristic, complemented
2#45163C211yesmaximal, characteristic
3#32495C211yesmaximal, characteristic, complemented
4#32493C211yesmaximal, characteristic, complemented
5#32491C211yesmaximal, characteristic
6#32489C211yesmaximal, characteristic
7#29292C211yesmaximal, characteristic, complemented
8#28642C211yesmaximal, characteristic
9#28641C211yesmaximal, characteristic
10#28293C211yesmaximal, characteristic
11#28037C211yesmaximal, characteristic
12#28035C211yesmaximal, characteristic, complemented
13#28033C211yesmaximal, characteristic, complemented
14#28031C211yesmaximal, characteristic
15#27730C211yesmaximal, characteristic, complemented
16#27728C211yesmaximal, characteristic
17#26331C211yesmaximal, characteristic
18#26329C211yesmaximal, characteristic
19#26291C211yesmaximal, characteristic, complemented
20#26289C211yesmaximal, characteristic, complemented
21#26105C211yesmaximal, characteristic, complemented
22#26103C211yesmaximal, characteristic
23#25468C211yesmaximal, characteristic, complemented
24#25466C211yesmaximal, characteristic
25#23065C211yesmaximal, characteristic
26#23064C211yesmaximal, characteristic, complemented
27#22741C211yesmaximal, characteristic, complemented
28#22739C211yesmaximal, characteristic, complemented
29#21730C211yesmaximal, characteristic, complemented
30#21715C211yesmaximal, characteristic, complemented
31#21643C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#488C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×C8×Q8C2211yescharacteristic
37C2×C8×Q8C2211yescharacteristic
38#2805—21no—
39#2805—21no—
40#2774—21no—
41#2774—21no—
42#2759—21no—
43#2759—21no—
44#2745—21no—
45#2745—21no—
46#2592C2211yescharacteristic
47#2592C2211yescharacteristic
48#2590—21no—
49#2590—21no—
50#2584C2211yescharacteristic
51#2584C2211yescharacteristic
52#2577—21no—
53#2577—21no—
54#2571C2211yescharacteristic
55#2571C2211yescharacteristic
56#2568C2211yescharacteristic
57#2563C2211yescharacteristic
58#2532—21no—
59#2532—21no—
60#2514C2211yescharacteristic
61#2514C2211yescharacteristic
62#2513C2211yescharacteristic
63#2513C2211yescharacteristic
64#2509C2211yescharacteristic
65#2509C2211yescharacteristic
66#2508—21no—
67#2508—21no—
68#2508C2211yescharacteristic
69#2508C2211yescharacteristic
70#2399C2211yescharacteristic
71#2370C2211yescharacteristic
72#2370C2211yescharacteristic
73#2357C2211yescharacteristic
74#2356C2211yescharacteristic
75#2355C2211yescharacteristic
76#2355C2211yescharacteristic
77#2355C2211yescharacteristic
78#2355C2211yescharacteristic
79#2331C2211yescharacteristic
80#2330C2211yescharacteristic
81#2330C2211yescharacteristic
82#2326C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2097C2211yescharacteristic
88#2097C2211yescharacteristic
89#2092C2211yescharacteristic
90#2092C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2087C2211yescharacteristic
94#2086C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2074C2211yescharacteristic
100#2074C2211yescharacteristic
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2068C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2066C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#1992C2211yescharacteristic
116#1991C2211yescharacteristic
117#1990C2211yescharacteristic
118#1989C2211yescharacteristic
119#1989C2211yescharacteristic
120#1988C2211yescharacteristic
121#1987C2211yescharacteristic
122#1985C2211yescharacteristic
123#1985C2211yescharacteristic
124#1983C2211yescharacteristic
125#1983C2211yescharacteristic
126#1959C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1948C2211yescharacteristic
138#1948C2211yescharacteristic
139#1947C2211yescharacteristic
140#1947C2211yescharacteristic
141#1944C2211yescharacteristic
142#1943C2211yescharacteristic
143#1942C2211yescharacteristic
144#1941C2211yescharacteristic
145#1940C2211yescharacteristic
146#1940C2211yescharacteristic
147#1940C2211yescharacteristic
148#1940C2211yescharacteristic
149#1936C2211yescharacteristic
150#1935C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1933C2211yescharacteristic
157#1933C2211yescharacteristic
158#1933C2211yescharacteristic
159#1933C2211yescharacteristic
160#1933C2211yescharacteristic
161#1928C2211yescharacteristic
162#1928C2211yescharacteristic
163#1927C2211yescharacteristic
164#1927C2211yescharacteristic
165#1926C2211yescharacteristic
166#1926C2211yescharacteristic
167#1925C2211yescharacteristic
168#1925C2211yescharacteristic
169#1921C2211yescharacteristic
170#1921C2211yescharacteristic
171#1920C2211yescharacteristic
172#1920C2211yescharacteristic
173#1919C2211yescharacteristic
174#1919C2211yescharacteristic
175#1918C2211yescharacteristic
176#1918C2211yescharacteristic
177#1847C2211yescharacteristic
178#1843C2211yescharacteristic
179#1835C2211yescharacteristic
180#1835C2211yescharacteristic
181#1835C2211yescharacteristic
182#1835C2211yescharacteristic
183#1834C2211yescharacteristic
184#1803C2211yescharacteristic
185#1802C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188C4×#107C2211yescharacteristic
189C4×#107C2211yescharacteristic
190C4×#107C2211yescharacteristic
191C4×#106C2211yescharacteristic
192C4×#106C2211yescharacteristic
193C4×#106C2211yescharacteristic
194C8×C4⋊C4C2211yescharacteristic
195C8×C4⋊C4C2211yescharacteristic
196C8×C4⋊C4C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic
198#1763C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1726C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×#125C2311yescharacteristic
205C2×#125C2311yescharacteristic
206C2×#124C2311yescharacteristic
207C2×C4×Q8C2311yescharacteristic
208C2×C4×Q8C2311yescharacteristic
209C2×C4×Q8C2311yescharacteristic
210C2×C4×D4C2311yescharacteristic
211#501—24no—
212#488—24no—
213#479—24no—
214#478—24no—
215C8×Q8—24no—
216C8×Q8—24no—
217C2×#107C2311yescharacteristic
218C2×#107C2311yescharacteristic
219C2×#107C2311yescharacteristic
220C2×#107C2311yescharacteristic
221C2×#107C2311yescharacteristic
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#106C2311yescharacteristic
226C2×#106C2311yescharacteristic
227C2×#106C2311yescharacteristic
228C2×#106C2311yescharacteristic
229C2×#106C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×C4⋊C8C2311yescharacteristic
234C2×C4⋊C8C2311yescharacteristic
235C2×C4⋊C8C2311yescharacteristic
236C2×C4⋊C8C2311yescharacteristic
237C2×C4⋊C8C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#102C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#97C2311yescharacteristic
260C2×#97C2311yescharacteristic
261C2×#97C2311yescharacteristic
262C2×C4×C8C2311yescharacteristic
263C2×C4×C8C2311yescharacteristic
264C2×C4×C8C2311yescharacteristic
265C2×C4×C8C2311yescharacteristic
266C2×C4×C8C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269#401—21no—
270#401—21no—
271#400—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398D411yescharacteristic
290#398D411yescharacteristic
291#398D411yescharacteristic
292#398D411yescharacteristic
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#395—21no—
300#395—21no—
301#395D411yescharacteristic
302#395D411yescharacteristic
303#395D411yescharacteristic
304#395D411yescharacteristic
305#393—21no—
306#393—21no—
307#393—21no—
308#393—21no—
309#391—21no—
310#391—21no—
311#391—21no—
312#391—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#390C2311yescharacteristic
323#390C2311yescharacteristic
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#389—21no—
328#389—21no—
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#389C2311yescharacteristic
342#389C2311yescharacteristic
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#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
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#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#385—21no—
394#385—21no—
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#383—21no—
399#383—21no—
400#383—21no—
401#382—21no—
402#382—21no—
403#382—21no—
404#382—21no—
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#381—21no—
415#380—21no—
416#380—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442#376—21no—
443#376C2311yescharacteristic
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#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8C2×D411yescharacteristic
486C22×Q8C2×D411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×D4C2411yescharacteristic
489C23×C4—21no—
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C4⋊Q8—22no—
499C4⋊Q8—22no—
500#125—22no—
501#125—22no—
502#125—22no—
503#125#4114yes—
504#124—22no—
505#124—22no—
506C4×Q8—22no—
507C4×Q8—22no—
508C4×Q8—22no—
509C4×Q8—22no—
510C4×Q8—22no—
511C4×Q8—22no—
512C4×D4—22no—
513C4×D4—22no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4C2×D411yescharacteristic
541C2×C4⋊C4C2×D411yescharacteristic
542C2×C4⋊C4C2×D411yescharacteristic
543C2×C4⋊C4C2×D411yescharacteristic
544C2×C4⋊C4C2×D411yescharacteristic
545C2×C4⋊C4C2×D411yescharacteristic
546C2×C4⋊C4C2×D411yescharacteristic
547C2×C4⋊C4C2×D411yescharacteristic
548C2×C4⋊C4C2×D411yescharacteristic
549C2×C4⋊C4C2×D411yescharacteristic
550C2×C4⋊C4C2×D411yescharacteristic
551C2×C4⋊C4C2×D411yescharacteristic
552C2×C4⋊C4C2×D411yescharacteristic
553C2×C4⋊C4C2×D411yescharacteristic
554C2×C4⋊C4C2411yescharacteristic
555C2×C4⋊C4C2411yescharacteristic
556C2×C4⋊C4C2411yescharacteristic
557C2×C4⋊C4C2411yescharacteristic
558C2×C4⋊C4C2411yescharacteristic
559C2×C4⋊C4C2411yescharacteristic
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2411yescharacteristic
562C2×C4⋊C4C2411yescharacteristic
563C2×C4⋊C4C2411yescharacteristic
564C2×C4⋊C4C2411yescharacteristic
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2411yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C42—21no—
582C2×C42—21no—
583C2×C42—21no—
584C2×C42—21no—
585C2×C42—21no—
586C2×C42—21no—
587C2×C42—21no—
588C2×C42—21no—
589C2×C42—21no—
590C2×C42—21no—
591C2×C42—21no—
592C2×C42—21no—
593C2×C42—21no—
594C2×C42—21no—
595C2×C42—21no—
596C2×C42C2411yescharacteristic
597C2×C42C2411yescharacteristic
598C2×C42C2411yescharacteristic
599C2×C42C2411yescharacteristic
600C2×C42C2411yescharacteristic
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603#107—22no—
604#107—22no—
605#107—22no—
606#107—22no—
607#107—22no—
608#107—41no—
609#107—41no—
610#107—41no—
611#106—22no—
612#106—22no—
613#106—22no—
614#106—22no—
615#106—22no—
616#106—41no—
617#106—41no—
618#106—41no—
619C4⋊C8—22no—
620C4⋊C8—22no—
621C4⋊C8—22no—
622C4⋊C8—22no—
623C4⋊C8—22no—
624C4⋊C8—22no—
625C4⋊C8—22no—
626C4⋊C8—22no—
627C4⋊C8—41no—
628C4⋊C8—41no—
629#103—22no—
630#103—22no—
631#103—22no—
632#103—22no—
633#103—22no—
634#103—41no—
635#103—41no—
636#103—41no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—41no—
643#102—41no—
644#102—41no—
645#97—22no—
646#97—22no—
647#97—41no—
648C4×C8—22no—
649C4×C8—22no—
650C4×C8—22no—
651C4×C8—22no—
652C4×C8—22no—
653C4×C8—22no—
654C4×C8#4114yes—
655#95—21no—
656#95—21no—
657#95—21no—
658#95—21no—
659#95—21no—
660#95—21no—
661#95—21no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
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#95C2×D411yescharacteristic
712#95C2×D411yescharacteristic
713#95C2×D411yescharacteristic
714#95C2×D411yescharacteristic
715#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723C24—21no—
724C2×Q8—22no—
725C2×Q8—22no—
726C2×Q8—21no—
727C2×Q8—21no—
728C2×Q8—21no—
729C2×Q8—21no—
730C2×Q8—21no—
731C2×Q8—21no—
732C2×Q8—41no—
733C2×Q8—41no—
734C2×Q8—41no—
735C2×Q8—41no—
736C2×Q8—42no—
737C2×Q8—81no—
738C2×Q8—81no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—42no—
761C22×C4—81no—
762C22×C4—81no—
763C22×C4C22×D411yescharacteristic
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C22×D411yescharacteristic
767C22×C4C22×D411yescharacteristic
768C22×C4C22×D411yescharacteristic
769C22×C4C22×D411yescharacteristic
770C22×C4C22×D411yescharacteristic
771C22×C4C22×D411yescharacteristic
772C22×C4C22×D411yescharacteristic
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D411yescharacteristic
775C22×C4C22×D411yescharacteristic
776C22×C4C22×D411yescharacteristic
777C22×C4C2511yescharacteristic
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8C2×#4112yes—
800C2×C8C2×#4112yes—
801C2×C82−1+412yes—
802C4⋊C4—22no—
803C4⋊C4—22no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—41no—
837C4⋊C4—41no—
838C4⋊C4—41no—
839C4⋊C4—41no—
840C4⋊C4—41no—
841C4⋊C4—41no—
842C4⋊C4—41no—
843C4⋊C4—41no—
844C4⋊C4—42no—
845C4⋊C4—42no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—81no—
849C4⋊C4—81no—
850C4⋊C4—81no—
851C4⋊C4—81no—
852C4⋊C4—81no—
853C4⋊C4—81no—
854C4⋊C4—81no—
855C4⋊C4—81no—
856C4⋊C4—81no—
857C4⋊C4—81no—
858C4⋊C4—81no—
859C4⋊C4—81no—
860C4⋊C4—81no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4—81no—
868C4⋊C4C2×#4112yes—
869C4⋊C4C2×#4112yes—
870C22⋊C4—42no—
871C22⋊C4—42no—
872C22⋊C4—42no—
873C22⋊C4—81no—
874C22⋊C4—81no—
875C22⋊C4—81no—
876C22⋊C4—81no—
877C22⋊C4—81no—
878C22⋊C4—81no—
879C22⋊C4—81no—
880C22⋊C4—81no—
881C22⋊C4—81no—
882C22⋊C4—81no—
883C42—21no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42—21no—
889C42—21no—
890C42—21no—
891C42—21no—
892C42—21no—
893C42—42no—
894C42—81no—
895C42—81no—
896C42—81no—
897C42—81no—
898C42—81no—
899C42—81no—
900C42—81no—
901C42—81no—
902C42—81no—
903C42—81no—
904C42—81no—
905C42—81no—
906C42—81no—
907C42—81no—
908C42C2×#4112yes—
909C42C2×#4112yes—
910C422−1+412yes—
911C422−1+412yes—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23C23×D411yescharacteristic
920Q8—44no—
921Q8—44no—
922Q8—41no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—162no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—162no—
1015C2×C4#54712yes—
1016C2×C4#54712yes—
1017C2×C4#54812yes—
1018C2×C4#54812yes—
1019C2×C4C22×#4111yescharacteristic
1020C2×C4C22×#4111yescharacteristic
1021C2×C4C2×2−1+411yescharacteristic
1022C2×C4C2×2−1+411yescharacteristic
1023C2×C4C2×2−1+411yescharacteristic
1024C2×C4#58511yescharacteristic
1025C8—22no—
1026C8—22no—
1027C8—22no—
1028C8—41no—
1029C8—41no—
1030C8—41no—
1031C8—41no—
1032C8—41no—
1033C22—81no—
1034C22—81no—
1035C22—81no—
1036C22—81no—
1037C22—81no—
1038C22—81no—
1039C22—81no—
1040C22C2×#54711yescharacteristic
1041C22C2×#54811yescharacteristic
1042C22#349711yescharacteristic
1043C22#358411yescharacteristic
1044C22#358411yescharacteristic
1045C22#358411yescharacteristic
1046C22#358411yescharacteristic
1047C4—22no—
1048C4—22no—
1049C4—22no—
1050C4—22no—
1051C4—41no—
1052C4—41no—
1053C4—41no—
1054C4—41no—
1055C4—41no—
1056C4—41no—
1057C4—41no—
1058C4—41no—
1059C4—42no—
1060C4—42no—
1061C4—41no—
1062C4—41no—
1063C4—81no—
1064C4—81no—
1065C4—81no—
1066C4—81no—
1067C4—81no—
1068C4—81no—
1069C4—81no—
1070C4—81no—
1071C4—81no—
1072C4—81no—
1073C4—81no—
1074C4—81no—
1075C4—81no—
1076C4#348011yescharacteristic
1077C4#350911yescharacteristic
1078C4#352311yescharacteristic
1079C4#355511yescharacteristic
1080C2—161no—
1081C2#5965311yescharacteristic
1082C2#6126011yescharacteristic
1083C2#6126111yescharacteristic
1084C2#6133111yescharacteristic
1085C2#6133111yescharacteristic
1086C2#6238311yescharacteristic
1087C2#6238311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45164C2semidirect
3. #32495C2semidirect
4. #32493C2semidirect
7. #29292C2semidirect
12. #28035C2semidirect
13. #28033C2semidirect
15. #27730C2semidirect
19. #26291C2semidirect
20. #26289C2semidirect
21. #26105C2semidirect
23. #25468C2semidirect
26. #23064C2semidirect
27. #22741C2semidirect
28. #22739C2semidirect
29. #21730C2semidirect
30. #21715C2semidirect

Maximal subgroups

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

subgroupindex
#451642
#451632
#324952
#324932
#324912
#324892
#292922
#286422
#286412
#282932
#280372
#280352
#280332
#280312
#277302
#277282
#263312
#263292
#262912
#262892
#261052
#261032
#254682
#254662
#230652
#230642
#227412
#227392
#217302
#217152
#216432