Finite Group Databasebeta

← #6777145

Subgroups — #6777145

Order 512.

1325 conjugacy classes of subgroups.

The subgroup lattice has 1205 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38113C211yesmaximal, characteristic, complemented
2#35553C211yesmaximal, characteristic
3#33090C211yesmaximal, characteristic, complemented
4#32448C211yesmaximal, characteristic, complemented
5#32393C211yesmaximal, characteristic, complemented
6#32268C211yesmaximal, characteristic, complemented
7#32004C211yesmaximal, characteristic
8#31540C211yesmaximal, characteristic, complemented
9#31477C211yesmaximal, characteristic, complemented
10#31263C211yesmaximal, characteristic, complemented
11#30419C211yesmaximal, characteristic
12#30167C211yesmaximal, characteristic, complemented
13#30025C211yesmaximal, characteristic, complemented
14#29526C211yesmaximal, characteristic, complemented
15#29402C211yesmaximal, characteristic, complemented
16#28987C211yesmaximal, characteristic, complemented
17#28856C211yesmaximal, characteristic, complemented
18#28076C211yesmaximal, characteristic, complemented
19#27881C211yesmaximal, characteristic, complemented
20#27870C211yesmaximal, characteristic, complemented
21#27643C211yesmaximal, characteristic, complemented
22#27586C211yesmaximal, characteristic, complemented
23#27537C211yesmaximal, characteristic, complemented
24#27460C211yesmaximal, characteristic, complemented
25#27178C211yesmaximal, characteristic, complemented
26#25036C211yesmaximal, characteristic, complemented
27#24894C211yesmaximal, characteristic, complemented
28#22794C211yesmaximal, characteristic, complemented
29#22201C211yesmaximal, characteristic, complemented
30#22047C211yesmaximal, characteristic, complemented
31#21130C211yesmaximal, characteristic, complemented
32C2×#468C2211yescharacteristic
33C2×#448C2211yescharacteristic
34C2×C4×SD16C2211yescharacteristic
35#2851C2211yescharacteristic
36#2798—21no—
37#2789—21no—
38#2758—21no—
39#2754—21no—
40#2645C2211yescharacteristic
41#2625C2211yescharacteristic
42#2575—21no—
43#2570C2211yescharacteristic
44#2563C2211yescharacteristic
45#2560—21no—
46#2542C2211yescharacteristic
47#2535C2211yescharacteristic
48#2517—21no—
49#2514C2211yescharacteristic
50#2510—21no—
51#2510—21no—
52#2505—21no—
53#2505—21no—
54#2497C2211yescharacteristic
55#2496C2211yescharacteristic
56#2489C2211yescharacteristic
57#2488—21no—
58#2487C2211yescharacteristic
59#2477—21no—
60#2471—21no—
61#2467—21no—
62#2453C2211yescharacteristic
63#2450—21no—
64#2422C2211yescharacteristic
65#2421C2211yescharacteristic
66#2420C2211yescharacteristic
67#2409C2211yescharacteristic
68#2345C2211yescharacteristic
69Q8×C22⋊C4C2211yescharacteristic
70#2331C2211yescharacteristic
71#2324C2211yescharacteristic
72#2323C2211yescharacteristic
73#2320C2211yescharacteristic
74#2314C2211yescharacteristic
75C4×#121C2211yescharacteristic
76C2×#391C2211yescharacteristic
77#2290C2211yescharacteristic
78#2285C2211yescharacteristic
79#2275C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2097C2211yescharacteristic
83#2097C2211yescharacteristic
84#2095C2211yescharacteristic
85#2095C2211yescharacteristic
86#2087C2211yescharacteristic
87#2085C2211yescharacteristic
88#2085C2211yescharacteristic
89#2083C2211yescharacteristic
90#2077C2211yescharacteristic
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2076C2211yescharacteristic
94#2076C2211yescharacteristic
95#2076C2211yescharacteristic
96#2076C2211yescharacteristic
97#2075C2211yescharacteristic
98#2075C2211yescharacteristic
99#2074C2211yescharacteristic
100#2073C2211yescharacteristic
101#2072C2211yescharacteristic
102#2072C2211yescharacteristic
103#2072C2211yescharacteristic
104#2067C2211yescharacteristic
105#2066C2211yescharacteristic
106#2059C2211yescharacteristic
107#2057C2211yescharacteristic
108#2057C2211yescharacteristic
109#2055C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2035C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2033C2211yescharacteristic
116#2025C2211yescharacteristic
117#2024C2211yescharacteristic
118#2024C2211yescharacteristic
119#2000C2211yescharacteristic
120#1992C2211yescharacteristic
121#1992C2211yescharacteristic
122#1973C2211yescharacteristic
123#1973C2211yescharacteristic
124#1949C2211yescharacteristic
125#1947C2211yescharacteristic
126#1943C2211yescharacteristic
127#1942C2211yescharacteristic
128#1935C2211yescharacteristic
129#1935C2211yescharacteristic
130#1935C2211yescharacteristic
131#1933C2211yescharacteristic
132#1928C2211yescharacteristic
133#1928C2211yescharacteristic
134#1928C2211yescharacteristic
135#1928C2211yescharacteristic
136#1928C2211yescharacteristic
137#1928C2211yescharacteristic
138#1928C2211yescharacteristic
139#1928C2211yescharacteristic
140#1927C2211yescharacteristic
141#1925C2211yescharacteristic
142#1924C2211yescharacteristic
143#1923C2211yescharacteristic
144#1921C2211yescharacteristic
145#1921C2211yescharacteristic
146#1921C2211yescharacteristic
147#1920C2211yescharacteristic
148#1920C2211yescharacteristic
149#1920C2211yescharacteristic
150#1920C2211yescharacteristic
151#1920C2211yescharacteristic
152#1918C2211yescharacteristic
153#1918C2211yescharacteristic
154#1918C2211yescharacteristic
155#1918C2211yescharacteristic
156#1917C2211yescharacteristic
157#1917C2211yescharacteristic
158#1894C2211yescharacteristic
159#1893C2211yescharacteristic
160#1892C2211yescharacteristic
161#1892C2211yescharacteristic
162#1880C2211yescharacteristic
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1874C2211yescharacteristic
169#1870C2211yescharacteristic
170#1869C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1864C2211yescharacteristic
174#1863C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1852C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1847C2211yescharacteristic
183#1840C2211yescharacteristic
184#1836C2211yescharacteristic
185#1817C2211yescharacteristic
186#1809C2211yescharacteristic
187#1809C2211yescharacteristic
188#1808C2211yescharacteristic
189#1805C2211yescharacteristic
190#1803C2211yescharacteristic
191#1798C2211yescharacteristic
192#1787C2211yescharacteristic
193#1787C2211yescharacteristic
194#1787C2211yescharacteristic
195C4×#107C2211yescharacteristic
196#1763C2211yescharacteristic
197#1762C2211yescharacteristic
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic
200#1749C2211yescharacteristic
201#1746C2211yescharacteristic
202#1729C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#126—21no—
210C2×#125C2311yescharacteristic
211C2×#123—21no—
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4—21no—
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×#117—21no—
226C2×#117C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C42C2311yescharacteristic
229#468—24no—
230#448—24no—
231C4×SD16—24no—
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×C22⋊C8C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278#401—21no—
279#401—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
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#399—21no—
293#399—21no—
294#399—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#396—21no—
307#395—21no—
308#394—21no—
309#394—21no—
310#393—21no—
311#393—21no—
312#393—21no—
313#392—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#391—21no—
319#391—21no—
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#390—21no—
329#390—21no—
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#389—21no—
333#389—21no—
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388D411yescharacteristic
354#388D411yescharacteristic
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#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387D411yescharacteristic
374#387D411yescharacteristic
375#386—21no—
376#386—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#386—21no—
382#386D411yescharacteristic
383#386D411yescharacteristic
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385D411yescharacteristic
391#385D411yescharacteristic
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#384C2311yescharacteristic
395#383—21no—
396#383—21no—
397#382—21no—
398#382—21no—
399#382—21no—
400#382—21no—
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#381—21no—
405#380—21no—
406#380—21no—
407#380—21no—
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418C4×C4⋊C4—21no—
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
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#376C2311yescharacteristic
436C2×#95—21no—
437C2×#95—21no—
438C2×#95—21no—
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8—21no—
482C22×Q8—21no—
483C22×Q8—22no—
484C22×Q8—41no—
485C22×Q8—41no—
486C22×Q8—41no—
487C22×Q8—41no—
488C22×Q8—41no—
489C22×Q8C2411yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×D4—21no—
492C22×D4—21no—
493C22×D4C2×D411yescharacteristic
494C22×D4C2411yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4C2×D411yescharacteristic
501C23×C4C2×D411yescharacteristic
502C23×C4C2411yescharacteristic
503C23×C4C2411yescharacteristic
504C2×SD16—22no—
505C2×SD16—41no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×SD16—41no—
509C2×SD16#4114yes—
510C2×M16—22no—
511C2×M16—41no—
512C2×M16—41no—
513C22×C8—41no—
514C22×C8—41no—
515C22×C8—41no—
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526#126—82no—
527#125—41no—
528#125—41no—
529#123—82no—
530C22⋊Q8—22no—
531C22⋊Q8—41no—
532C22⋊Q8—41no—
533C22⋊Q8—41no—
534C22⋊Q8—82no—
535C22⋊Q8—82no—
536#121—22no—
537#121—22no—
538#121—41no—
539#121—41no—
540C4×Q8—22no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×D4—22no—
545C4×D4—41no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—82no—
553#117—41no—
554#117—41no—
555#117—82no—
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—41no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
620C2×C22⋊C4—21no—
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×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—41no—
639C2×C42—41no—
640C2×C42C2×D411yescharacteristic
641C2×C42C2×D411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647#107—22no—
648#107—41no—
649#107—41no—
650#107—41no—
651#107—41no—
652#107—41no—
653#107—41no—
654#107—41no—
655#107—41no—
656#107—41no—
657#106—22no—
658#106—41no—
659#106—41no—
660#106—41no—
661C4⋊C8—41no—
662C4⋊C8—41no—
663#103—22no—
664#103—22no—
665#103—22no—
666#103—22no—
667#103—41no—
668#103—41no—
669#103—41no—
670#103—41no—
671#103—41no—
672#103—41no—
673#103—41no—
674#103—41no—
675#103—41no—
676#103—41no—
677#102—22no—
678#102—22no—
679#102—41no—
680#102—41no—
681#102—41no—
682#102—41no—
683C22⋊C8—22no—
684C22⋊C8—41no—
685C22⋊C8—41no—
686C22⋊C8—41no—
687C22⋊C8—41no—
688C22⋊C8—41no—
689#97—41no—
690#97—41no—
691#97—41no—
692C4×C8—22no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#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#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752C24—21no—
753C24C22×D411yescharacteristic
754C24C22×D411yescharacteristic
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—42no—
767C2×Q8—42no—
768C2×Q8—42no—
769C2×Q8—81no—
770C2×Q8—81no—
771C2×Q8—81no—
772C2×Q8—82no—
773C2×Q8—82no—
774C2×Q8—82no—
775C2×Q8—82no—
776C2×Q8C2×#4112yes—
777C2×D4—22no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—41no—
784C2×D4—41no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—81no—
791C2×D4C2×#4112yes—
792C22×C4—22no—
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—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C2511yescharacteristic
853SD16—44no—
854SD16—82no—
855M16—82no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
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—82no—
880C2×C8C2×#4112yes—
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—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
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—41no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C22⋊C4—22no—
937C22⋊C4—41no—
938C22⋊C4—41no—
939C22⋊C4—41no—
940C22⋊C4—41no—
941C22⋊C4—41no—
942C22⋊C4—41no—
943C22⋊C4—41no—
944C22⋊C4—42no—
945C22⋊C4—42no—
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—81no—
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—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—41no—
976C42—41no—
977C42—42no—
978C42—81no—
979C42—81no—
980C42—81no—
981C42—81no—
982C42—81no—
983C42—81no—
984C42—81no—
985C42—81no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—22no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23#57812yes—
1007C23C23×D411yescharacteristic
1008Q8—22no—
1009Q8—22no—
1010Q8—41no—
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—84no—
1017Q8—162no—
1018D4—22no—
1019D4—22no—
1020D4—41no—
1021D4—41no—
1022D4—82no—
1023D4—84no—
1024D4—162no—
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—21no—
1037C2×C4—21no—
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—22no—
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—44no—
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—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—82no—
1116C2×C4—84no—
1117C2×C4—162no—
1118C2×C4—162no—
1119C2×C4—162no—
1120C2×C4—162no—
1121C2×C4C22×#4111yescharacteristic
1122C2×C4#58511yescharacteristic
1123C2×C4#58511yescharacteristic
1124C2×C4#58511yescharacteristic
1125C2×C4#58511yescharacteristic
1126C2×C4#58511yescharacteristic
1127C8—22no—
1128C8—41no—
1129C8—41no—
1130C8—41no—
1131C8—41no—
1132C8—41no—
1133C8—41no—
1134C8—41no—
1135C22—22no—
1136C22—22no—
1137C22—22no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—42no—
1145C22—41no—
1146C22—42no—
1147C22—41no—
1148C22—41no—
1149C22—41no—
1150C22—41no—
1151C22—42no—
1152C22—81no—
1153C22—81no—
1154C22—81no—
1155C22—81no—
1156C22#344911yescharacteristic
1157C22D4×#4111yescharacteristic
1158C22#348511yescharacteristic
1159C22C2×#57811yescharacteristic
1160C22#358511yescharacteristic
1161C22#358511yescharacteristic
1162C22#358611yescharacteristic
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—41no—
1173C4—41no—
1174C4—41no—
1175C4—42no—
1176C4—81no—
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—81no—
1190C4#349111yescharacteristic
1191C4#352111yescharacteristic
1192C4#356611yescharacteristic
1193C4#356811yescharacteristic
1194C2—42no—
1195C2—81no—
1196C2—82no—
1197C2#3837611yescharacteristic
1198C2#6098311yescharacteristic
1199C2#6101711yescharacteristic
1200C2#6151311yescharacteristic
1201C2#6152411yescharacteristic
1202C2#6174711yescharacteristic
1203C2#6178211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2535C22
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. #38113C2semidirect
3. #33090C2semidirect
4. #32448C2semidirect
5. #32393C2semidirect
6. #32268C2semidirect
8. #31540C2semidirect
9. #31477C2semidirect
10. #31263C2semidirect
12. #30167C2semidirect
13. #30025C2semidirect
14. #29526C2semidirect
15. #29402C2semidirect
16. #28987C2semidirect
17. #28856C2semidirect
18. #28076C2semidirect
19. #27881C2semidirect
20. #27870C2semidirect
21. #27643C2semidirect
22. #27586C2semidirect
23. #27537C2semidirect
24. #27460C2semidirect
25. #27178C2semidirect
26. #25036C2semidirect
27. #24894C2semidirect
28. #22794C2semidirect
29. #22201C2semidirect
30. #22047C2semidirect
31. #21130C2semidirect

Maximal subgroups

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

subgroupindex
#381132
#355532
#330902
#324482
#323932
#322682
#320042
#315402
#314772
#312632
#304192
#301672
#300252
#295262
#294022
#289872
#288562
#280762
#278812
#278702
#276432
#275862
#275372
#274602
#271782
#250362
#248942
#227942
#222012
#220472
#211302