Finite Group Databasebeta

← #7611348

Subgroups — #7611348

Order 512.

1701 conjugacy classes of subgroups.

The subgroup lattice has 1394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45254C211yesmaximal, characteristic, complemented
2#44957C211yesmaximal, characteristic, complemented
3#32193C211yesmaximal, characteristic, complemented
4#32178C211yesmaximal, characteristic, complemented
5#31597C211yesmaximal, characteristic, complemented
6#31587C211yesmaximal, characteristic, complemented
7#28903C211yesmaximal, characteristic, complemented
8#28873C211yesmaximal, characteristic, complemented
9#28354C211yesmaximal, characteristic, complemented
10#28353C211yesmaximal, characteristic, complemented
11#27760C211yesmaximal, characteristic, complemented
12#27760C211yesmaximal, characteristic, complemented
13#27750C211yesmaximal, characteristic, complemented
14#27655C211yesmaximal, characteristic, complemented
15#26534C211yesmaximal, characteristic, complemented
16#26321C211yesmaximal, characteristic, complemented
17#25304C211yesmaximal, characteristic, complemented
18#24626C211yesmaximal, characteristic, complemented
19#24535C211yesmaximal, characteristic, complemented
20#24531C211yesmaximal, characteristic, complemented
21#24484C211yesmaximal, characteristic, complemented
22#24476C211yesmaximal, characteristic, complemented
23#24218C211yesmaximal, characteristic, complemented
24#24192C211yesmaximal, characteristic, complemented
25#23105C211yesmaximal, characteristic, complemented
26#22583C211yesmaximal, characteristic, complemented
27#22580C211yesmaximal, characteristic, complemented
28#22549C211yesmaximal, characteristic, complemented
29#21606C211yesmaximal, characteristic, complemented
30#21536C211yesmaximal, characteristic, complemented
31#21206C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#480C2211yescharacteristic
36C2×#469C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#459C2211yescharacteristic
39C2×#449C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#446C2211yescharacteristic, complemented
42C2×C4×D8C2211yescharacteristic, complemented
43C2×#417C2211yescharacteristic
44C2×#418C2211yescharacteristic
45C2×#416C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C2×#405C2211yescharacteristic
48#2775—21no—
49#2770—21no—
50#2751—21no—
51#2750—21no—
52#2703—21no—
53#2678—21no—
54#2671—21no—
55#2670—21no—
56#2609—21no—
57#2596—21no—
58#2580C2211yescharacteristic, complemented
59#2571C2211yescharacteristic, complemented
60#2570C2211yescharacteristic, complemented
61#2570C2211yescharacteristic, complemented
62#2555—21no—
63#2548C2211yescharacteristic
64#2548C2211yescharacteristic
65#2541C2211yescharacteristic
66#2541C2211yescharacteristic
67#2539—21no—
68#2513C2211yescharacteristic, complemented
69#2512C2211yescharacteristic, complemented
70#2504C2211yescharacteristic
71#2500C2211yescharacteristic
72#2479—21no—
73#2478—21no—
74#2464—21no—
75#2448C2211yescharacteristic
76#2445C2211yescharacteristic
77#2433C2211yescharacteristic
78#2431C2211yescharacteristic
79#2424—21no—
80#2396C2211yescharacteristic
81#2367C2211yescharacteristic
82#2355C2211yescharacteristic, complemented
83#2354C2211yescharacteristic, complemented
84#2347C2211yescharacteristic
85#2344C2211yescharacteristic
86#2341C2211yescharacteristic
87D4×C22⋊C4C2211yescharacteristic
88#2324C2211yescharacteristic
89#2324C2211yescharacteristic
90#2317C2211yescharacteristic
91#2097C2211yescharacteristic, complemented
92#2094C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic, complemented
100#2073C2211yescharacteristic, complemented
101#2071C2211yescharacteristic, complemented
102#2071C2211yescharacteristic, complemented
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2066C2211yescharacteristic, complemented
106#2065C2211yescharacteristic, complemented
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic, complemented
110#2054C2211yescharacteristic, complemented
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic, complemented
113#2041C2211yescharacteristic
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic, complemented
117#2012C2211yescharacteristic
118#2012C2211yescharacteristic, complemented
119#2011C2211yescharacteristic
120#2011C2211yescharacteristic
121#2011C2211yescharacteristic
122#2011C2211yescharacteristic, complemented
123#1984C2211yescharacteristic, complemented
124#1983C2211yescharacteristic
125#1983C2211yescharacteristic, complemented
126#1982C2211yescharacteristic
127#1982C2211yescharacteristic
128#1982C2211yescharacteristic
129#1982C2211yescharacteristic, complemented
130#1973C2211yescharacteristic, complemented
131#1972C2211yescharacteristic
132#1972C2211yescharacteristic, complemented
133#1970C2211yescharacteristic
134#1970C2211yescharacteristic, complemented
135#1961C2211yescharacteristic
136#1961C2211yescharacteristic
137#1961C2211yescharacteristic
138#1961C2211yescharacteristic, complemented
139#1959C2211yescharacteristic
140#1959C2211yescharacteristic
141#1958C2211yescharacteristic
142#1958C2211yescharacteristic
143#1958C2211yescharacteristic, complemented
144#1957C2211yescharacteristic
145#1957C2211yescharacteristic
146#1957C2211yescharacteristic
147#1949C2211yescharacteristic, complemented
148#1947C2211yescharacteristic, complemented
149#1944C2211yescharacteristic, complemented
150#1939C2211yescharacteristic, complemented
151#1936C2211yescharacteristic
152#1936C2211yescharacteristic, complemented
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic, complemented
155#1934C2211yescharacteristic, complemented
156#1934C2211yescharacteristic, complemented
157#1928C2211yescharacteristic, complemented
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic, complemented
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic, complemented
164#1925C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1893C2211yescharacteristic
168#1893C2211yescharacteristic
169#1880C2211yescharacteristic, complemented
170#1880C2211yescharacteristic, complemented
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1865C2211yescharacteristic, complemented
174#1864C2211yescharacteristic
175#1863C2211yescharacteristic, complemented
176#1862C2211yescharacteristic
177#1850C2211yescharacteristic
178#1850C2211yescharacteristic
179#1825C2211yescharacteristic
180#1824C2211yescharacteristic
181#1809C2211yescharacteristic
182#1805C2211yescharacteristic, complemented
183#1804C2211yescharacteristic
184#1804C2211yescharacteristic
185#1804C2211yescharacteristic, complemented
186#1803C2211yescharacteristic, complemented
187#1802C2211yescharacteristic, complemented
188#1798C2211yescharacteristic
189#1788C2211yescharacteristic
190#1786C2211yescharacteristic
191C4×#106C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194C8×C4⋊C4C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic, complemented
198#1762C2211yescharacteristic, complemented
199C4×#103C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#559—24no—
213#559—42no—
214#535—24no—
215#535—42no—
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#126—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120—21no—
240C2×#120—21no—
241C2×#120—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4—21no—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117—21no—
251C2×#117—21no—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C22⋊C4—21no—
256#482—42no—
257#480—42no—
258#469—24no—
259#463—24no—
260#459—42no—
261#449—42no—
262#447—42no—
263#446—42no—
264C4×D8—42no—
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278#418—24no—
279#417—24no—
280#416—42no—
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#102—42no—
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322#405—42no—
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#400D411yescharacteristic
336#399—21no—
337#399—21no—
338#399D411yescharacteristic
339#398—21no—
340#398—21no—
341#398D411yescharacteristic
342#398D411yescharacteristic
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#396—21no—
350#396D411yescharacteristic
351#396D411yescharacteristic
352#395D411yescharacteristic
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#393—21no—
362#393D411yescharacteristic
363#392—21no—
364#392—21no—
365#392—21no—
366#392—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#391—21no—
372#391C2311yescharacteristic
373#390—21no—
374#390—21no—
375#390—21no—
376#390—21no—
377#390—21no—
378#390—21no—
379#390—21no—
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#389—21no—
394#389—21no—
395#389—21no—
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#383—21no—
445#382—21no—
446#382C2311yescharacteristic
447#382C2311yescharacteristic
448#382C2311yescharacteristic
449#382C2311yescharacteristic
450#382C2311yescharacteristic
451#381—21no—
452#380—21no—
453#380—21no—
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#379—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8C2×D411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×D4—22no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C2411yescharacteristic
537C2×SD16—22no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C2×D8—41no—
550C2×D8—41no—
551C2×D8—41no—
552C2×M16—41no—
553C2×M16—41no—
554C2×M16#4114yes—
555C22×C8—22no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566#127—22no—
567#127—22no—
568#127—22no—
569#127—22no—
570#127—41no—
571#127—41no—
572#127—41no—
573#127—41no—
574#127—41no—
575#127—41no—
576#126—82no—
577#124—22no—
578#124—22no—
579#124—22no—
580#124—41no—
581#124—41no—
582#124—44no—
583#124—82no—
584#124#4114yes—
585#123—44no—
586#123—44no—
587#123—82no—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—22no—
592#121—44no—
593#121—44no—
594#121—82no—
595#121—82no—
596#121—82no—
597#121—82no—
598#120—44no—
599#120—44no—
600#120—82no—
601#120—82no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—44no—
617#117—22no—
618#117—22no—
619#117—22no—
620#117—22no—
621#117—82no—
622#117—82no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—82no—
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724#107—41no—
725#107—41no—
726#107—41no—
727#107—41no—
728#106—22no—
729#106—41no—
730#106—41no—
731C4⋊C8—22no—
732C4⋊C8—22no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737#103—22no—
738#103—22no—
739#103—22no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775C22⋊C8—22no—
776C22⋊C8—22no—
777#97—22no—
778#97—41no—
779#97—41no—
780#97—41no—
781C4×C8—22no—
782C4×C8—41no—
783C4×C8—41no—
784C4×C8—41no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—42no—
827C24—42no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24C22×D411yescharacteristic
834#41—44no—
835#41—44no—
836#41—82no—
837#41—82no—
838C2×Q8—22no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—41no—
845C2×Q8—41no—
846C2×Q8C2×#4112yes—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—82no—
894C2×D4—82no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4C2×#4112yes—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C2×#4112yes—
970C22×C4H(5,𝔽2)12yes—
971C22×C4C2511yescharacteristic
972SD16—82no—
973D8—44no—
974D8—82no—
975D8—82no—
976D8—82no—
977M16—44no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—44no—
1001C2×C8C2×#4112yes—
1002C2×C8C2×#4112yes—
1003C4⋊C4—22no—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—22no—
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—41no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C22⋊C4—24no—
1050C22⋊C4—24no—
1051C22⋊C4—22no—
1052C22⋊C4—22no—
1053C22⋊C4—22no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—81no—
1110C42—81no—
1111C42—81no—
1112C42—81no—
1113C42—81no—
1114C42—81no—
1115C42C2×#4112yes—
1116C42H(5,𝔽2)12yes—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—22no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—84no—
1159C23—84no—
1160C23—162no—
1161C23—162no—
1162C23—162no—
1163C23—162no—
1164C23—162no—
1165C23#55012yes—
1166C23C23×D411yescharacteristic
1167Q8—22no—
1168Q8—22no—
1169Q8—41no—
1170Q8—41no—
1171Q8—82no—
1172D4—22no—
1173D4—22no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—84no—
1193D4—84no—
1194D4—84no—
1195D4—162no—
1196D4—162no—
1197D4—162no—
1198D4—162no—
1199D4—162no—
1200D4—162no—
1201D4—162no—
1202D4—162no—
1203D4—162no—
1204D4—162no—
1205D4—162no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—22no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—84no—
1279C2×C4—84no—
1280C2×C4—84no—
1281C2×C4—162no—
1282C2×C4—162no—
1283C2×C4—162no—
1284C2×C4#54612yes—
1285C2×C4#54612yes—
1286C2×C4#55012yes—
1287C2×C4#57612yes—
1288C2×C4C22×#4111yescharacteristic
1289C2×C4C22×#4111yescharacteristic
1290C2×C4C2×H(5,𝔽2)11yescharacteristic
1291C2×C4C2×H(5,𝔽2)11yescharacteristic
1292C2×C4#58511yescharacteristic
1293C2×C4#58511yescharacteristic
1294C8—22no—
1295C8—22no—
1296C8—41no—
1297C8—41no—
1298C8—41no—
1299C8—41no—
1300C8—41no—
1301C8—41no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—168no—
1345C22C2×#54611yescharacteristic
1346C22C2×#55011yescharacteristic
1347C22#350011yescharacteristic
1348C22C2×#57611yescharacteristic
1349C22#358411yescharacteristic
1350C22#358511yescharacteristic
1351C22#358511yescharacteristic
1352C4—22no—
1353C4—22no—
1354C4—22no—
1355C4—22no—
1356C4—41no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—42no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4#347511yescharacteristic
1377C4#350511yescharacteristic
1378C4#351311yescharacteristic
1379C4#354211yescharacteristic
1380C2—42no—
1381C2—82no—
1382C2—161no—
1383C2—161no—
1384C2—161no—
1385C2—161no—
1386C2#5980711yescharacteristic
1387C2#6119511yescharacteristic
1388C2#6120511yescharacteristic
1389C2#6141911yescharacteristic
1390C2#6142411yescharacteristic
1391C2#6255811yescharacteristic
1392C2#6256411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45254C2semidirect
2. #44957C2semidirect
3. #32193C2semidirect
4. #32178C2semidirect
5. #31597C2semidirect
6. #31587C2semidirect
7. #28903C2semidirect
8. #28873C2semidirect
9. #28354C2semidirect
10. #28353C2semidirect
11. #27760C2semidirect
12. #27760C2semidirect
13. #27750C2semidirect
14. #27655C2semidirect
15. #26534C2semidirect
16. #26321C2semidirect
17. #25304C2semidirect
18. #24626C2semidirect
19. #24535C2semidirect
20. #24531C2semidirect
21. #24484C2semidirect
22. #24476C2semidirect
23. #24218C2semidirect
24. #24192C2semidirect
25. #23105C2semidirect
26. #22583C2semidirect
27. #22580C2semidirect
28. #22549C2semidirect
29. #21606C2semidirect
30. #21536C2semidirect
31. #21206C2semidirect
41. C2×#446C22semidirect
42. C2×C4×D8C22semidirect
58. #2580C22semidirect
59. #2571C22semidirect
60. #2570C22semidirect
61. #2570C22semidirect
68. #2513C22semidirect
69. #2512C22semidirect
82. #2355C22semidirect
83. #2354C22semidirect
91. #2097C22semidirect
94. #2092C22semidirect
95. #2085C22semidirect
96. #2083C22semidirect
99. #2073C22semidirect
100. #2073C22semidirect
101. #2071C22semidirect
102. #2071C22semidirect
105. #2066C22semidirect
106. #2065C22semidirect
109. #2054C22semidirect
110. #2054C22semidirect
112. #2042C22semidirect
116. #2041C22semidirect
118. #2012C22semidirect
122. #2011C22semidirect
123. #1984C22semidirect
125. #1983C22semidirect
129. #1982C22semidirect
130. #1973C22semidirect
132. #1972C22semidirect
134. #1970C22semidirect
138. #1961C22semidirect
143. #1958C22semidirect
147. #1949C22semidirect
148. #1947C22semidirect
149. #1944C22semidirect
150. #1939C22semidirect
152. #1936C22semidirect
154. #1934C22semidirect
155. #1934C22semidirect
156. #1934C22semidirect
157. #1928C22semidirect
159. #1926C22semidirect
163. #1925C22semidirect
164. #1925C22semidirect
165. #1917C22semidirect
166. #1917C22semidirect
169. #1880C22semidirect
170. #1880C22semidirect
173. #1865C22semidirect
175. #1863C22semidirect
182. #1805C22semidirect
185. #1804C22semidirect
186. #1803C22semidirect
187. #1802C22semidirect
191. C4×#106C22semidirect
192. #1771C22semidirect
193. #1771C22semidirect
194. C8×C4⋊C4C22semidirect
195. #1763C22semidirect
197. #1762C22semidirect
198. #1762C22semidirect
199. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#452542
#449572
#321932
#321782
#315972
#315872
#289032
#288732
#283542
#283532
#277602
#277502
#276552
#265342
#263212
#253042
#246262
#245352
#245312
#244842
#244762
#242182
#241922
#231052
#225832
#225802
#225492
#216062
#215362
#212062