Finite Group Databasebeta

← #7092636

Subgroups — #7092636

Order 512.

1341 conjugacy classes of subgroups.

The subgroup lattice has 1203 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59585C211yesmaximal, characteristic
2#59547C211yesmaximal, characteristic, complemented
3#32538C211yesmaximal, characteristic, complemented
4#32185C211yesmaximal, characteristic, complemented
5#32171C211yesmaximal, characteristic, complemented
6#32086C211yesmaximal, characteristic
7#31923C211yesmaximal, characteristic, complemented
8#30904C211yesmaximal, characteristic, complemented
9#30734C211yesmaximal, characteristic
10#30734C211yesmaximal, characteristic
11#29375C211yesmaximal, characteristic, complemented
12#29375C211yesmaximal, characteristic, complemented
13#29017C211yesmaximal, characteristic, complemented
14#27579C211yesmaximal, characteristic, complemented
15#27564C211yesmaximal, characteristic, complemented
16#27366C211yesmaximal, characteristic, complemented
17#27219C211yesmaximal, characteristic, complemented
18#27205C211yesmaximal, characteristic, complemented
19#27127C211yesmaximal, characteristic, complemented
20#26908C211yesmaximal, characteristic, complemented
21#26840C211yesmaximal, characteristic, complemented
22#26768C211yesmaximal, characteristic
23#26607C211yesmaximal, characteristic, complemented
24#26396C211yesmaximal, characteristic, complemented
25#25284C211yesmaximal, characteristic
26#24743C211yesmaximal, characteristic, complemented
27#23687C211yesmaximal, characteristic, complemented
28#23190C211yesmaximal, characteristic
29#23103C211yesmaximal, characteristic, complemented
30#22383C211yesmaximal, characteristic, complemented
31#22156C211yesmaximal, characteristic, complemented
32C2×#492C2211yescharacteristic
33C2×#489C2211yescharacteristic
34C2×#476C2211yescharacteristic
35C2×#464C2211yescharacteristic
36C2×#464C2211yescharacteristic
37C2×#462C2211yescharacteristic
38C2×#441C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×#440C2211yescharacteristic
41#2779—21no—
42#2766—21no—
43#2762—21no—
44#2757—21no—
45#2612—21no—
46#2578—21no—
47#2576—21no—
48#2547C2211yescharacteristic
49#2545C2211yescharacteristic
50#2544C2211yescharacteristic
51#2544C2211yescharacteristic
52#2531—21no—
53#2528—21no—
54#2528—21no—
55#2524—21no—
56#2514C2211yescharacteristic
57#2514C2211yescharacteristic
58#2514C2211yescharacteristic
59#2513C2211yescharacteristic
60#2510—21no—
61#2508C2211yescharacteristic
62#2508C2211yescharacteristic
63#2462—21no—
64#2460—21no—
65#2451C2211yescharacteristic
66#2451C2211yescharacteristic
67#2447C2211yescharacteristic
68#2446C2211yescharacteristic
69#2446C2211yescharacteristic
70#2446C2211yescharacteristic
71#2367C2211yescharacteristic
72#2366C2211yescharacteristic
73#2365C2211yescharacteristic
74#2365C2211yescharacteristic
75#2356—21no—
76#2356C2211yescharacteristic
77#2356C2211yescharacteristic
78#2353—21no—
79#2351C2211yescharacteristic
80#2349C2211yescharacteristic
81C4×#125C2211yescharacteristic
82C4×#124C2211yescharacteristic
83C4×#124C2211yescharacteristic
84#2295C2211yescharacteristic
85#2295C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2097C2211yescharacteristic
90#2097C2211yescharacteristic
91#2092C2211yescharacteristic
92#2085C2211yescharacteristic
93#2074C2211yescharacteristic
94#2074C2211yescharacteristic
95#2073C2211yescharacteristic
96#2068C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2066C2211yescharacteristic
101#2066C2211yescharacteristic
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic
104#2057C2211yescharacteristic
105#2056C2211yescharacteristic
106#2056C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2043C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic
116#2024C2211yescharacteristic
117#2016C2211yescharacteristic
118#2016C2211yescharacteristic
119#2016C2211yescharacteristic
120#2015C2211yescharacteristic
121#2015C2211yescharacteristic
122#2015C2211yescharacteristic
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic
125#2015C2211yescharacteristic
126#1983C2211yescharacteristic
127#1983C2211yescharacteristic
128#1982C2211yescharacteristic
129#1981C2211yescharacteristic
130#1973C2211yescharacteristic
131#1973C2211yescharacteristic
132#1971C2211yescharacteristic
133#1971C2211yescharacteristic
134#1969C2211yescharacteristic
135#1960C2211yescharacteristic
136#1958C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1943C2211yescharacteristic
140#1940C2211yescharacteristic
141#1940C2211yescharacteristic
142#1936C2211yescharacteristic
143#1935C2211yescharacteristic
144#1935C2211yescharacteristic
145#1934C2211yescharacteristic
146#1933C2211yescharacteristic
147#1933C2211yescharacteristic
148#1928C2211yescharacteristic
149#1928C2211yescharacteristic
150#1928C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1920C2211yescharacteristic
157#1919C2211yescharacteristic
158#1919C2211yescharacteristic
159#1918C2211yescharacteristic
160#1917C2211yescharacteristic
161#1917C2211yescharacteristic
162#1917C2211yescharacteristic
163#1917C2211yescharacteristic
164#1916C2211yescharacteristic
165#1916C2211yescharacteristic
166#1916C2211yescharacteristic
167#1916C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic
182#1877C2211yescharacteristic
183#1877C2211yescharacteristic
184#1865C2211yescharacteristic
185#1865C2211yescharacteristic
186#1865C2211yescharacteristic
187#1864C2211yescharacteristic
188#1863C2211yescharacteristic
189#1862C2211yescharacteristic
190#1862C2211yescharacteristic
191#1862C2211yescharacteristic
192#1839C2211yescharacteristic
193#1805C2211yescharacteristic
194#1804C2211yescharacteristic
195C4×#107C2211yescharacteristic
196#1770C2211yescharacteristic
197#1770C2211yescharacteristic
198#1767C2211yescharacteristic
199#1763C2211yescharacteristic
200#1762C2211yescharacteristic
201#1762C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#125D411yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×C4×Q8—21no—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232#492—24no—
233#489—42no—
234#476—42no—
235#464—24no—
236#464—24no—
237#462—42no—
238#441—42no—
239#440—42no—
240#440—42no—
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293#401—21no—
294#401—21no—
295#401—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#396—21no—
318#396—21no—
319#395—21no—
320#395—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#391—21no—
326#391—21no—
327#391—21no—
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#390—21no—
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#389—21no—
348#389—21no—
349#389—21no—
350#389D411yescharacteristic
351#389D411yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—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#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387D411yescharacteristic
398#387D411yescharacteristic
399#387D411yescharacteristic
400#387D411yescharacteristic
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#383—21no—
412#383—21no—
413#383—21no—
414#383—21no—
415#383—21no—
416#382—21no—
417#382—21no—
418#382—21no—
419#382D411yescharacteristic
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#381—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449#376—21no—
450#376—21no—
451#376—21no—
452#376—21no—
453C2×#95—21no—
454C43C2311yescharacteristic
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#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
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×Q8C2411yescharacteristic
492C22×D4—21no—
493C22×D4—21no—
494C22×D4C2411yescharacteristic
495C22×D4C2411yescharacteristic
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C2×Q16—22no—
501C2×Q16—22no—
502C2×Q16—41no—
503C2×Q16—41no—
504C2×Q16—41no—
505C2×Q16—41no—
506C2×Q16—41no—
507C2×Q16—41no—
508C2×Q16—41no—
509C2×Q16—41no—
510C2×Q16—41no—
511C2×Q16—41no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16#4114yes—
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C4⋊Q8—22no—
533C4⋊Q8—22no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538#127—22no—
539#127—41no—
540#125—42no—
541#124—22no—
542#124—22no—
543#124—41no—
544#124—41no—
545#124—41no—
546#124—41no—
547#124—41no—
548#124—41no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—41no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×Q8—41no—
561C4×Q8—44no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—44no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×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×C22⋊C4—21no—
633C2×C22⋊C4—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—41no—
659#107—41no—
660#107—41no—
661#106—22no—
662#106—41no—
663#106—41no—
664#106—41no—
665C4⋊C8—22no—
666C4⋊C8—22no—
667C4⋊C8—41no—
668C4⋊C8—41no—
669C4⋊C8—41no—
670C4⋊C8—41no—
671#103—22no—
672#103—22no—
673#103—22no—
674#103—22no—
675#103—41no—
676#103—41no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#102—22no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#97—41no—
704#97—41no—
705#97—41no—
706#97—41no—
707C4×C8—22no—
708C4×C8—41no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773C24—21no—
774C24—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—42no—
799C2×Q8—42no—
800C2×Q8—81no—
801C2×Q8C2×#4112yes—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—81no—
817C2×D4—81no—
818C2×D4—81no—
819C2×D4C2×#4112yes—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C2511yescharacteristic
861Q16—44no—
862Q16—82no—
863Q16—82no—
864Q16—82no—
865SD16—44no—
866SD16—44no—
867SD16—82no—
868SD16—82no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8C2×#4112yes—
893C4⋊C4—22no—
894C4⋊C4—22no—
895C4⋊C4—22no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—41no—
921C4⋊C4—41no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4H(5,𝔽2)12yes—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—41no—
981C42—41no—
982C42—41no—
983C42—41no—
984C42—42no—
985C42—42no—
986C42—42no—
987C42—42no—
988C42—42no—
989C42—42no—
990C42—42no—
991C42—42no—
992C42—42no—
993C42—42no—
994C42—81no—
995C42—81no—
996C23—22no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23C23×D411yescharacteristic
1011Q8—22no—
1012Q8—22no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—41no—
1017Q8—41no—
1018Q8—41no—
1019Q8—41no—
1020Q8—41no—
1021Q8—41no—
1022Q8—41no—
1023Q8—41no—
1024Q8—41no—
1025Q8—41no—
1026Q8—41no—
1027Q8—84no—
1028D4—22no—
1029D4—22no—
1030D4—41no—
1031D4—41no—
1032D4—41no—
1033D4—41no—
1034D4—41no—
1035D4—41no—
1036D4—84no—
1037D4—162no—
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—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
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—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—162no—
1122C2×C4—162no—
1123C2×C4—162no—
1124C2×C4—162no—
1125C2×C4#57512yes—
1126C2×C4C22×#4111yescharacteristic
1127C2×C4C2×H(5,𝔽2)11yescharacteristic
1128C2×C4#58511yescharacteristic
1129C2×C4#58511yescharacteristic
1130C2×C4#58511yescharacteristic
1131C2×C4#58511yescharacteristic
1132C8—22no—
1133C8—41no—
1134C8—41no—
1135C8—41no—
1136C8—41no—
1137C8—41no—
1138C8—41no—
1139C8—41no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22—81no—
1154C22D4×#4111yescharacteristic
1155C22#348711yescharacteristic
1156C22#348811yescharacteristic
1157C22C2×#57511yescharacteristic
1158C22#358411yescharacteristic
1159C22#358611yescharacteristic
1160C22#358611yescharacteristic
1161C4—22no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—42no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—41no—
1173C4—41no—
1174C4—41no—
1175C4—42no—
1176C4—41no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4—81no—
1189C4#350511yescharacteristic
1190C4#352111yescharacteristic
1191C4#353911yescharacteristic
1192C4#356611yescharacteristic
1193C2—82no—
1194C2—161no—
1195C2#4425311yescharacteristic
1196C2#6145511yescharacteristic
1197C2#6152811yescharacteristic
1198C2#6189711yescharacteristic
1199C2#6192511yescharacteristic
1200C2#6200411yescharacteristic
1201C2#6207711yescharacteristic
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. #59547C2semidirect
3. #32538C2semidirect
4. #32185C2semidirect
5. #32171C2semidirect
7. #31923C2semidirect
8. #30904C2semidirect
11. #29375C2semidirect
12. #29375C2semidirect
13. #29017C2semidirect
14. #27579C2semidirect
15. #27564C2semidirect
16. #27366C2semidirect
17. #27219C2semidirect
18. #27205C2semidirect
19. #27127C2semidirect
20. #26908C2semidirect
21. #26840C2semidirect
23. #26607C2semidirect
24. #26396C2semidirect
26. #24743C2semidirect
27. #23687C2semidirect
29. #23103C2semidirect
30. #22383C2semidirect
31. #22156C2semidirect

Maximal subgroups

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

subgroupindex
#595852
#595472
#325382
#321852
#321712
#320862
#319232
#309042
#307342
#293752
#290172
#275792
#275642
#273662
#272192
#272052
#271272
#269082
#268402
#267682
#266072
#263962
#252842
#247432
#236872
#231902
#231032
#223832
#221562