Finite Group Databasebeta

← #7594442

Subgroups — #7594442

Order 512.

1520 conjugacy classes of subgroups.

The subgroup lattice has 1276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59381C211yesmaximal, characteristic, complemented
2#59374C211yesmaximal, characteristic, complemented
3#31567C211yesmaximal, characteristic, complemented
4#31563C211yesmaximal, characteristic, complemented
5#31278C211yesmaximal, characteristic, complemented
6#31274C211yesmaximal, characteristic, complemented
7#29414C211yesmaximal, characteristic, complemented
8#29411C211yesmaximal, characteristic, complemented
9#28714C211yesmaximal, characteristic, complemented
10#27845C211yesmaximal, characteristic, complemented
11#27836C211yesmaximal, characteristic, complemented
12#27548C211yesmaximal, characteristic, complemented
13#27545C211yesmaximal, characteristic, complemented
14#27528C211yesmaximal, characteristic, complemented
15#27526C211yesmaximal, characteristic, complemented
16#27452C211yesmaximal, characteristic, complemented
17#27449C211yesmaximal, characteristic, complemented
18#27435C211yesmaximal, characteristic, complemented
19#27423C211yesmaximal, characteristic, complemented
20#26497C211yesmaximal, characteristic, complemented
21#26488C211yesmaximal, characteristic, complemented
22#25049C211yesmaximal, characteristic, complemented
23#25038C211yesmaximal, characteristic, complemented
24#24271C211yesmaximal, characteristic
25#22818C211yesmaximal, characteristic, complemented
26#22816C211yesmaximal, characteristic, complemented
27#22448C211yesmaximal, characteristic, complemented
28#22441C211yesmaximal, characteristic, complemented
29#21562C211yesmaximal, characteristic, complemented
30#21539C211yesmaximal, characteristic, complemented
31C4×#469C211yesmaximal, characteristic, complemented
32C22×#135C2211yescharacteristic
33C2×#501C2211yescharacteristic
34C2×#470C2211yescharacteristic
35C2×#469C2211yescharacteristic
36C2×#441C2211yescharacteristic
37C2×#441C2211yescharacteristic
38C2×C4×D8C2211yescharacteristic
39C2×C4×D8C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×C4×M16C2211yescharacteristic
42#2761—21no—
43#2749—21no—
44#2746—21no—
45#2745—21no—
46#2602—21no—
47#2595—21no—
48#2576—21no—
49#2573—21no—
50#2562C2211yescharacteristic
51#2557—21no—
52#2547C2211yescharacteristic
53#2531—21no—
54#2516—21no—
55#2497C2211yescharacteristic
56#2495C2211yescharacteristic
57#2494C2211yescharacteristic
58#2494C2211yescharacteristic
59#2493—21no—
60#2461—21no—
61#2454C2211yescharacteristic
62#2453C2211yescharacteristic
63#2452C2211yescharacteristic
64#2451C2211yescharacteristic
65#2422C2211yescharacteristic
66#2421C2211yescharacteristic
67#2421C2211yescharacteristic
68#2420C2211yescharacteristic
69#2419—21no—
70#2407C2211yescharacteristic
71#2407C2211yescharacteristic
72#2368—21no—
73#2357C2211yescharacteristic
74#2357C2211yescharacteristic
75#2356C2211yescharacteristic
76#2355C2211yescharacteristic
77#2353—21no—
78#2341C2211yescharacteristic
79#2341C2211yescharacteristic
80#2339C2211yescharacteristic
81#2339C2211yescharacteristic
82C4×C22⋊Q8C2211yescharacteristic
83C4×C22⋊Q8C2211yescharacteristic
84C4×#123C2211yescharacteristic
85C4×#121C2211yescharacteristic
86C4×#121C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2101C2211yescharacteristic
90#2099C2211yescharacteristic
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2076C2211yescharacteristic
95#2076C2211yescharacteristic
96#2076C2211yescharacteristic
97#2075C2211yescharacteristic
98#2075C2211yescharacteristic
99#2074C2211yescharacteristic
100#2074C2211yescharacteristic
101#2073C2211yescharacteristic
102#2071C2211yescharacteristic
103#2068C2211yescharacteristic
104#2067C2211yescharacteristic
105#2066C2211yescharacteristic
106#2065C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2036C2211yescharacteristic
110#2036C2211yescharacteristic
111#2034C2211yescharacteristic
112#2033C2211yescharacteristic
113#2026C2211yescharacteristic
114#2025C2211yescharacteristic
115#2024C2211yescharacteristic
116#2023C2211yescharacteristic
117#2000C2211yescharacteristic
118#2000C2211yescharacteristic
119#1989C2211yescharacteristic
120#1987C2211yescharacteristic
121#1972C2211yescharacteristic
122#1972C2211yescharacteristic
123#1972C2211yescharacteristic
124#1971C2211yescharacteristic
125#1969C2211yescharacteristic
126#1969C2211yescharacteristic
127#1944C2211yescharacteristic
128#1943C2211yescharacteristic
129#1941C2211yescharacteristic
130#1941C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1933C2211yescharacteristic
134#1933C2211yescharacteristic
135#1928C2211yescharacteristic
136#1928C2211yescharacteristic
137#1927C2211yescharacteristic
138#1927C2211yescharacteristic
139#1925C2211yescharacteristic
140#1925C2211yescharacteristic
141#1925C2211yescharacteristic
142#1925C2211yescharacteristic
143#1924C2211yescharacteristic
144#1923C2211yescharacteristic
145#1921C2211yescharacteristic
146#1920C2211yescharacteristic
147#1918C2211yescharacteristic
148#1918C2211yescharacteristic
149#1917C2211yescharacteristic
150#1916C2211yescharacteristic
151#1895C2211yescharacteristic
152#1895C2211yescharacteristic
153#1894C2211yescharacteristic
154#1894C2211yescharacteristic
155#1880C2211yescharacteristic
156#1880C2211yescharacteristic
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1877C2211yescharacteristic
160#1877C2211yescharacteristic
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic
163#1870C2211yescharacteristic
164#1865C2211yescharacteristic
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1863C2211yescharacteristic
168#1863C2211yescharacteristic
169#1863C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1851C2211yescharacteristic
173#1847C2211yescharacteristic
174#1846C2211yescharacteristic
175#1817C2211yescharacteristic
176#1809C2211yescharacteristic
177#1809C2211yescharacteristic
178#1808C2211yescharacteristic
179#1807C2211yescharacteristic
180#1807C2211yescharacteristic
181#1805C2211yescharacteristic
182#1804C2211yescharacteristic
183#1804C2211yescharacteristic
184#1803C2211yescharacteristic
185#1788C2211yescharacteristic
186#1788C2211yescharacteristic
187#1788C2211yescharacteristic
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1776C2211yescharacteristic
192#1776C2211yescharacteristic
193C4×#106C2211yescharacteristic
194#1771C2211yescharacteristic
195#1770C2211yescharacteristic
196#1763C2211yescharacteristic
197#1763C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1752C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C2×#135—24no—
206C2×#135—24no—
207C2×#135—42no—
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#124—21no—
218C2×#123—21no—
219C2×#123D411yescharacteristic
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4—21no—
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C22×C42C2311yescharacteristic
237#501—42no—
238#470—24no—
239#469—24no—
240#441—24no—
241#441—42no—
242C4×D8—24no—
243C4×D8—42no—
244#435—42no—
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C4×M16—42no—
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297#401—21no—
298#401—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#399—21no—
306#398—21no—
307#398—21no—
308#397—21no—
309#397—21no—
310#397—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#396—21no—
320#395—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#393—21no—
327#392—21no—
328#392—21no—
329#391—21no—
330#391—21no—
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#390—21no—
338#390—21no—
339#390—21no—
340#390—21no—
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#389—21no—
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
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#388—21no—
368#388—21no—
369#388—21no—
370#388D411yescharacteristic
371#388D411yescharacteristic
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#387D411yescharacteristic
386#387D411yescharacteristic
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386D411yescharacteristic
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385D411yescharacteristic
405#384C2311yescharacteristic
406#383—21no—
407#383—21no—
408#382—21no—
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#381—21no—
413#381—21no—
414#381—21no—
415#381—21no—
416#381—21no—
417#381D411yescharacteristic
418#380—21no—
419#380—21no—
420#380—21no—
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
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×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453#376—21no—
454C2×#95—21no—
455C2×#95—21no—
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#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C22×Q8—21no—
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4C2×D411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2×D411yescharacteristic
519C23×C4C2×D411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522#135—416no—
523C2×Q16—22no—
524C2×Q16—22no—
525C2×Q16#4114yes—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×D8—22no—
533C2×D8—22no—
534C2×D8#4114yes—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—22no—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C22×C8—22no—
542C22×C8—22no—
543C22×C8—22no—
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554#125—41no—
555#125—41no—
556#124—82no—
557#123—42no—
558#123—82no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—41no—
562C22⋊Q8—41no—
563C22⋊Q8—44no—
564#121—22no—
565#121—22no—
566#121—41no—
567#121—41no—
568C4×Q8—22no—
569C4×Q8—22no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×Q8—41no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—44no—
587C4×D4—82no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—41no—
673C2×C42—41no—
674C2×C42C2×D411yescharacteristic
675C2×C42C2×D411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681#107—22no—
682#107—22no—
683#107—41no—
684#107—41no—
685#107—41no—
686#107—41no—
687#106—22no—
688#106—22no—
689#106—22no—
690#106—22no—
691#106—41no—
692#106—41no—
693C4⋊C8—41no—
694C4⋊C8—41no—
695C4⋊C8—41no—
696#103—22no—
697#103—22no—
698#103—22no—
699#103—22no—
700#103—41no—
701#103—41no—
702#103—41no—
703#103—41no—
704#103—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720C22⋊C8—41no—
721C22⋊C8—41no—
722C22⋊C8—41no—
723C22⋊C8—41no—
724C22⋊C8—41no—
725#97—22no—
726#97—22no—
727#97—22no—
728#97—41no—
729C4×C8—22no—
730C4×C8—22no—
731C4×C8—41no—
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#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784C24—21no—
785C24—21no—
786C24C22×D411yescharacteristic
787C24C22×D411yescharacteristic
788#41—44no—
789#41—44no—
790#41—82no—
791#41—82no—
792#41—82no—
793#41—82no—
794#41—82no—
795#41—82no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—42no—
807C2×Q8—81no—
808C2×Q8—81no—
809C2×Q8C2×#4112yes—
810C2×Q8C2×#4112yes—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—41no—
822C2×D4—41no—
823C2×D4—41no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4C2×#4112yes—
837C2×D4C2×#4112yes—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C2511yescharacteristic
901Q16—28no—
902SD16—44no—
903SD16—44no—
904D8—28no—
905M16—44no—
906M16—44no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—44no—
929C2×C8C2×#4112yes—
930C2×C8C2×#4112yes—
931C2×C8H(5,𝔽2)12yes—
932C4⋊C4—22no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C22⋊C4—22no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—41no—
1029C42—41no—
1030C42—42no—
1031C42—42no—
1032C42—42no—
1033C42—81no—
1034C42—81no—
1035C42—81no—
1036C42—81no—
1037C42—81no—
1038C42—81no—
1039C42—81no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—22no—
1048C23—22no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23C23×D411yescharacteristic
1069Q8—22no—
1070Q8—22no—
1071Q8—22no—
1072Q8—22no—
1073Q8—41no—
1074Q8—41no—
1075Q8—41no—
1076Q8—41no—
1077Q8—162no—
1078D4—22no—
1079D4—22no—
1080D4—22no—
1081D4—22no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—82no—
1087D4—84no—
1088D4—84no—
1089D4—84no—
1090D4—84no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—82no—
1177C2×C4—82no—
1178C2×C4—84no—
1179C2×C4—84no—
1180C2×C4—162no—
1181C2×C4—162no—
1182C2×C4—162no—
1183C2×C4—162no—
1184C2×C4#57512yes—
1185C2×C4C22×#4111yescharacteristic
1186C2×C4C22×#4111yescharacteristic
1187C2×C4C2×H(5,𝔽2)11yescharacteristic
1188C2×C4#58511yescharacteristic
1189C2×C4#58511yescharacteristic
1190C2×C4#58511yescharacteristic
1191C8—41no—
1192C8—41no—
1193C8—41no—
1194C8—41no—
1195C8—41no—
1196C8—41no—
1197C8—41no—
1198C8#55114yes—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—42no—
1203C22—41no—
1204C22—42no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—42no—
1210C22—42no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—42no—
1218C22—42no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22D4×#4111yescharacteristic
1228C22D4×#4111yescharacteristic
1229C22#349611yescharacteristic
1230C22C2×#57511yescharacteristic
1231C22#358411yescharacteristic
1232C22#358511yescharacteristic
1233C22#358611yescharacteristic
1234C4—22no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—42no—
1247C4—42no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4C2×#55111yescharacteristic
1261C4#352111yescharacteristic
1262C4#352111yescharacteristic
1263C4#354011yescharacteristic
1264C2—81no—
1265C2—81no—
1266C2—82no—
1267C2—82no—
1268C2#5937511yescharacteristic
1269C2#6144311yescharacteristic
1270C2#6146111yescharacteristic
1271C2#6151611yescharacteristic
1272C2#6153611yescharacteristic
1273C2#6230111yescharacteristic
1274C2#6232211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24271C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59381C2semidirect
2. #59374C2semidirect
3. #31567C2semidirect
4. #31563C2semidirect
5. #31278C2semidirect
6. #31274C2semidirect
7. #29414C2semidirect
8. #29411C2semidirect
9. #28714C2semidirect
10. #27845C2semidirect
11. #27836C2semidirect
12. #27548C2semidirect
13. #27545C2semidirect
14. #27528C2semidirect
15. #27526C2semidirect
16. #27452C2semidirect
17. #27449C2semidirect
18. #27435C2semidirect
19. #27423C2semidirect
20. #26497C2semidirect
21. #26488C2semidirect
22. #25049C2semidirect
23. #25038C2semidirect
25. #22818C2semidirect
26. #22816C2semidirect
27. #22448C2semidirect
28. #22441C2semidirect
29. #21562C2semidirect
30. #21539C2semidirect
31. C4×#469C2semidirect

Maximal subgroups

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

subgroupindex
#593812
#593742
#315672
#315632
#312782
#312742
#294142
#294112
#287142
#278452
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C4×#4692