Finite Group Databasebeta

← #7090343

Subgroups — #7090343

Order 512.

1754 conjugacy classes of subgroups.

The subgroup lattice has 1443 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45141C211yesmaximal, characteristic, complemented
2#42627C211yesmaximal, characteristic, complemented
3#32651C211yesmaximal, characteristic, complemented
4#32603C211yesmaximal, characteristic, complemented
5#31961C211yesmaximal, characteristic, complemented
6#31287C211yesmaximal, characteristic, complemented
7#30992C211yesmaximal, characteristic, complemented
8#30580C211yesmaximal, characteristic, complemented
9#30470C211yesmaximal, characteristic, complemented
10#30408C211yesmaximal, characteristic, complemented
11#29508C211yesmaximal, characteristic, complemented
12#29505C211yesmaximal, characteristic, complemented
13#28862C211yesmaximal, characteristic, complemented
14#28339C211yesmaximal, characteristic, complemented
15#26986C211yesmaximal, characteristic, complemented
16#26960C211yesmaximal, characteristic, complemented
17#26635C211yesmaximal, characteristic, complemented
18#25796C211yesmaximal, characteristic, complemented
19#25635C211yesmaximal, characteristic, complemented
20#25411C211yesmaximal, characteristic, complemented
21#25178C211yesmaximal, characteristic, complemented
22#25160C211yesmaximal, characteristic, complemented
23#24903C211yesmaximal, characteristic, complemented
24#24427C211yesmaximal, characteristic, complemented
25#24192C211yesmaximal, characteristic, complemented
26#23869C211yesmaximal, characteristic
27#23808C211yesmaximal, characteristic, complemented
28#23275C211yesmaximal, characteristic, complemented
29#22872C211yesmaximal, characteristic, complemented
30#22442C211yesmaximal, characteristic, complemented
31#22278C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#559C2211yescharacteristic, complemented
34C2×#550C2211yescharacteristic
35C2×#497C2211yescharacteristic
36C2×#495C2211yescharacteristic
37C2×#485C2211yescharacteristic, complemented
38C2×#470C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#465C2211yescharacteristic, complemented
41C2×#463C2211yescharacteristic
42C2×#463C2211yescharacteristic
43C2×#452C2211yescharacteristic
44C2×#452C2211yescharacteristic, complemented
45C2×#449C2211yescharacteristic
46C2×#449C2211yescharacteristic
47C2×#450C2211yescharacteristic
48C2×#447C2211yescharacteristic
49C2×#442C2211yescharacteristic
50C2×#440C2211yescharacteristic, complemented
51C2×C4×SD16C2211yescharacteristic, complemented
52C2×C4×D8C2211yescharacteristic
53C2×C4×D8C2211yescharacteristic
54C2×#416C2211yescharacteristic, complemented
55#2824—21no—
56#2797—21no—
57#2779—21no—
58#2736—21no—
59#2709—21no—
60#2709—21no—
61#2686—21no—
62#2686—21no—
63#2685—21no—
64#2649—21no—
65#2644C2211yescharacteristic
66#2622—21no—
67#2592C2211yescharacteristic
68#2581C2211yescharacteristic, complemented
69#2580C2211yescharacteristic
70#2536C2211yescharacteristic
71#2500C2211yescharacteristic
72#2496C2211yescharacteristic
73#2480—21no—
74#2444—21no—
75#2444—21no—
76#2435C2211yescharacteristic
77#2432C2211yescharacteristic
78#2432C2211yescharacteristic, complemented
79#2427C2211yescharacteristic
80#2427C2211yescharacteristic
81#2427C2211yescharacteristic, complemented
82#2426C2211yescharacteristic
83#2421C2211yescharacteristic
84#2420C2211yescharacteristic
85#2420C2211yescharacteristic, complemented
86#2419—21no—
87#2419—21no—
88#2415C2211yescharacteristic
89#2408C2211yescharacteristic
90#2398C2211yescharacteristic
91#2363C2211yescharacteristic
92#2339C2211yescharacteristic
93#2339C2211yescharacteristic, complemented
94D4×C22⋊C4C2211yescharacteristic
95#2328C2211yescharacteristic, complemented
96#2327C2211yescharacteristic, complemented
97#2326C2211yescharacteristic
98#2097C2211yescharacteristic, complemented
99#2097C2211yescharacteristic, complemented
100#2094C2211yescharacteristic, complemented
101#2093C2211yescharacteristic, complemented
102#2092C2211yescharacteristic
103#2085C2211yescharacteristic, complemented
104#2085C2211yescharacteristic, complemented
105#2085C2211yescharacteristic, complemented
106#2077C2211yescharacteristic
107#2073C2211yescharacteristic
108#2073C2211yescharacteristic
109#2068C2211yescharacteristic, complemented
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2056C2211yescharacteristic, complemented
113#2043C2211yescharacteristic, complemented
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic, complemented
116#2041C2211yescharacteristic, complemented
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic, complemented
121#2034C2211yescharacteristic
122#2033C2211yescharacteristic
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic, complemented
125#2014C2211yescharacteristic, complemented
126#2013C2211yescharacteristic
127#2012C2211yescharacteristic
128#2012C2211yescharacteristic
129#2012C2211yescharacteristic
130#2012C2211yescharacteristic
131#2011C2211yescharacteristic
132#2011C2211yescharacteristic
133#2001C2211yescharacteristic, complemented
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#1999C2211yescharacteristic
137#1999C2211yescharacteristic
138#1984C2211yescharacteristic, complemented
139#1984C2211yescharacteristic, complemented
140#1983C2211yescharacteristic, complemented
141#1973C2211yescharacteristic
142#1972C2211yescharacteristic
143#1970C2211yescharacteristic
144#1968C2211yescharacteristic
145#1968C2211yescharacteristic
146#1968C2211yescharacteristic
147#1958C2211yescharacteristic
148#1958C2211yescharacteristic, complemented
149#1956C2211yescharacteristic, complemented
150#1941C2211yescharacteristic, complemented
151#1936C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1934C2211yescharacteristic, complemented
154#1933C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1928C2211yescharacteristic, complemented
157#1924C2211yescharacteristic, complemented
158#1924C2211yescharacteristic, complemented
159#1923C2211yescharacteristic
160#1923C2211yescharacteristic
161#1920C2211yescharacteristic, complemented
162#1895C2211yescharacteristic
163#1893C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic, complemented
180#1875C2211yescharacteristic, complemented
181#1870C2211yescharacteristic
182#1869C2211yescharacteristic
183#1865C2211yescharacteristic, complemented
184#1864C2211yescharacteristic
185#1864C2211yescharacteristic, complemented
186#1863C2211yescharacteristic, complemented
187#1862C2211yescharacteristic, complemented
188#1862C2211yescharacteristic, complemented
189#1854C2211yescharacteristic, complemented
190#1836C2211yescharacteristic, complemented
191#1809C2211yescharacteristic
192#1804C2211yescharacteristic, complemented
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195#1786C2211yescharacteristic
196C4×#102C2211yescharacteristic, complemented
197#1753C2211yescharacteristic
198#1753C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic, complemented
200C8×C22⋊C4C2211yescharacteristic, complemented
201#1746C2211yescharacteristic, complemented
202#1746C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×AGL(1,ℤ/8)—24no—
207C2×AGL(1,ℤ/8)—42no—
208C2×AGL(1,ℤ/8)—42no—
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×D8C2311yescharacteristic
218C22×D8C2311yescharacteristic
219C22×D8C2311yescharacteristic
220C22×D8C2311yescharacteristic
221C22×M16C2311yescharacteristic
222C23×C8C2311yescharacteristic
223#559—42no—
224#559—42no—
225#550—42no—
226#550—42no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×#127—21no—
229C2×#127C2311yescharacteristic
230C2×#126—21no—
231C2×#124—21no—
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#123—21no—
237C2×#123—21no—
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×#121—21no—
243C2×#121—21no—
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#120—21no—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C22×C22⋊C4—21no—
264#497—24no—
265#495—42no—
266#485—42no—
267#470—42no—
268#465—42no—
269#465—42no—
270#463—42no—
271#463—42no—
272#452—42no—
273#452—42no—
274#450—42no—
275#449—24no—
276#449—42no—
277#447—42no—
278#442—42no—
279#440—42no—
280C4×SD16—42no—
281C4×D8—42no—
282C4×D8—42no—
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293#416—42no—
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×C4×C8C2311yescharacteristic
335C2×C4×C8C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338#400—21no—
339#400—21no—
340#400—21no—
341#400D411yescharacteristic
342#400D411yescharacteristic
343#399—21no—
344#398—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#397—21no—
357#397D411yescharacteristic
358#397D411yescharacteristic
359#396—21no—
360#396—21no—
361#395—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394—21no—
376#394—21no—
377#394—21no—
378#394—21no—
379#394D411yescharacteristic
380#394D411yescharacteristic
381#393—21no—
382#393—21no—
383#393D411yescharacteristic
384#393D411yescharacteristic
385#392—21no—
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#390—21no—
393#390—21no—
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#389—21no—
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
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#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#384C2311yescharacteristic
454#382C2311yescharacteristic
455#382C2311yescharacteristic
456#382C2311yescharacteristic
457#381—21no—
458#381—21no—
459#381—21no—
460#381—21no—
461#380—21no—
462#380—21no—
463#380—21no—
464#380C2311yescharacteristic
465#380C2311yescharacteristic
466#380C2311yescharacteristic
467#380C2311yescharacteristic
468#379—21no—
469#379—21no—
470#379—21no—
471#379—21no—
472C4×C4⋊C4C2311yescharacteristic
473C4×C22⋊C4—21no—
474C4×C22⋊C4C2311yescharacteristic
475C4×C22⋊C4C2311yescharacteristic
476C4×C22⋊C4C2311yescharacteristic
477C4×C22⋊C4C2311yescharacteristic
478#376C2311yescharacteristic
479C2×#95—21no—
480C2×#95—21no—
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502#336C2311yescharacteristic
503#336C2311yescharacteristic
504#336C2311yescharacteristic
505C25—21no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41—41no—
517C2×#41—41no—
518C22×Q8C2×D411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×D4—22no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—41no—
533C22×D4—41no—
534C22×D4—41no—
535C22×D4—41no—
536C22×D4—41no—
537C22×D4C2×D411yescharacteristic
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C22×D4C2411yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552AGL(1,ℤ/8)—416no—
553C2×Q16—22no—
554C2×Q16—22no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16#4114yes—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—41no—
586C2×D8—41no—
587C2×D8—41no—
588C2×D8—41no—
589C2×M16—22no—
590C2×M16—22no—
591C2×M16—41no—
592C22×C8—22no—
593C22×C8—41no—
594C22×C8—41no—
595C22×C8C2411yescharacteristic
596C22×C8C2411yescharacteristic
597C22×C8C2411yescharacteristic
598C22×C8C2411yescharacteristic
599C22×C8C2411yescharacteristic
600C22×C8C2411yescharacteristic
601C22×C8C2411yescharacteristic
602C22×C8C2411yescharacteristic
603C4⋊Q8—22no—
604C4⋊Q8—41no—
605#127—22no—
606#127—22no—
607#127—44no—
608#126—82no—
609#124—22no—
610#124—22no—
611#124—22no—
612#124—41no—
613#124—41no—
614#124—41no—
615#124—41no—
616#124—41no—
617#124—44no—
618#123—44no—
619#123—44no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8—41no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626C22⋊Q8—41no—
627C22⋊Q8—41no—
628#121—22no—
629#121—22no—
630#121—22no—
631#121—41no—
632#121—41no—
633#121—41no—
634#121—44no—
635#121—44no—
636#121—41no—
637#121—41no—
638#120—82no—
639C4×Q8—41no—
640C4×Q8—41no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×Q8—41no—
644C4×Q8—41no—
645C4×Q8—41no—
646C4×Q8—41no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—41no—
650C4×D4—41no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—41no—
654C4×D4—41no—
655C4×D4—41no—
656C4×D4—41no—
657C4×D4—41no—
658C4×D4—41no—
659C4×D4—41no—
660C4×D4—41no—
661C4×D4—44no—
662C4×D4—44no—
663#117—41no—
664#117—41no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2×D411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
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—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—82no—
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C22⋊C4C2×D411yescharacteristic
746C2×C22⋊C4C2×D411yescharacteristic
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C22⋊C4C2×D411yescharacteristic
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759#107—41no—
760#107—41no—
761#107—41no—
762#107—41no—
763#106—22no—
764#106—22no—
765#106—41no—
766#106—41no—
767C4⋊C8—41no—
768C4⋊C8—41no—
769#103—22no—
770#103—22no—
771#103—22no—
772#103—22no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781#103—41no—
782#103—41no—
783#102—22no—
784#102—22no—
785#102—22no—
786#102—22no—
787#102—22no—
788#102—22no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795#102—41no—
796#102—41no—
797#102—41no—
798#102—41no—
799#102—41no—
800#102—41no—
801C22⋊C8—22no—
802C22⋊C8—22no—
803C22⋊C8—22no—
804C22⋊C8—41no—
805C22⋊C8—41no—
806C22⋊C8—41no—
807#97—22no—
808#97—22no—
809C4×C8—22no—
810C4×C8—41no—
811C4×C8—41no—
812C4×C8—41no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850#95C2×D411yescharacteristic
851#95C2×D411yescharacteristic
852#95C2×D411yescharacteristic
853#95C2×D411yescharacteristic
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—42no—
859C24—42no—
860C24—81no—
861C24—81no—
862C24—81no—
863C24—81no—
864C24—81no—
865C24C22×D411yescharacteristic
866C24C22×D411yescharacteristic
867#41—44no—
868#41—44no—
869#41—82no—
870#41—82no—
871#41—82no—
872#41—82no—
873#41—82no—
874#41—82no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—41no—
893C2×Q8—41no—
894C2×Q8—41no—
895C2×Q8C2×#4112yes—
896C2×D4—24no—
897C2×D4—24no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—41no—
920C2×D4—41no—
921C2×D4—41no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—44no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—82no—
938C2×D4—82no—
939C2×D4—82no—
940C2×D4—81no—
941C2×D4—81no—
942C2×D4—81no—
943C2×D4—81no—
944C2×D4—81no—
945C2×D4—81no—
946C2×D4—81no—
947C2×D4—81no—
948C2×D4—81no—
949C2×D4—81no—
950C2×D4—81no—
951C2×D4C2×#4112yes—
952C2×D4H(5,𝔽2)12yes—
953C2×D4H(5,𝔽2)12yes—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4—81no—
993C22×C4—81no—
994C22×C4—81no—
995C22×C4—81no—
996C22×C4—81no—
997C22×C4—81no—
998C22×C4—81no—
999C22×C4—81no—
1000C22×C4—81no—
1001C22×C4—81no—
1002C22×C4C22×D411yescharacteristic
1003C22×C4C22×D411yescharacteristic
1004C22×C4C22×D411yescharacteristic
1005C22×C4C22×D411yescharacteristic
1006C22×C4C22×D411yescharacteristic
1007C22×C4C22×D411yescharacteristic
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D411yescharacteristic
1010C22×C4C22×D411yescharacteristic
1011C22×C4C22×D411yescharacteristic
1012C22×C4C22×D411yescharacteristic
1013C22×C4C22×D411yescharacteristic
1014C22×C4C2511yescharacteristic
1015Q16—82no—
1016Q16—82no—
1017SD16—44no—
1018SD16—44no—
1019SD16—44no—
1020SD16—44no—
1021SD16—82no—
1022SD16—82no—
1023D8—28no—
1024D8—44no—
1025D8—44no—
1026D8—82no—
1027M16—44no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—21no—
1046C2×C8—21no—
1047C2×C8—21no—
1048C2×C8—21no—
1049C2×C8—82no—
1050C2×C8C2×#4112yes—
1051C2×C8H(5,𝔽2)12yes—
1052C2×C8H(5,𝔽2)12yes—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—41no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C4⋊C4—81no—
1090C4⋊C4—81no—
1091C4⋊C4—81no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—41no—
1096C22⋊C4—41no—
1097C22⋊C4—41no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C22⋊C4—81no—
1135C22⋊C4—81no—
1136C22⋊C4—81no—
1137C22⋊C4—81no—
1138C22⋊C4—81no—
1139C22⋊C4—81no—
1140C22⋊C4—81no—
1141C22⋊C4—81no—
1142C22⋊C4—81no—
1143C22⋊C4—81no—
1144C22⋊C4—81no—
1145C42—21no—
1146C42—21no—
1147C42—21no—
1148C42—21no—
1149C42—21no—
1150C42—21no—
1151C42—21no—
1152C42—21no—
1153C42—21no—
1154C42—21no—
1155C42—42no—
1156C42—42no—
1157C42—81no—
1158C42—81no—
1159C42—81no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—22no—
1169C23—21no—
1170C23—21no—
1171C23—22no—
1172C23—22no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—21no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—41no—
1195C23—41no—
1196C23—41no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—41no—
1201C23—41no—
1202C23—84no—
1203C23—84no—
1204C23—162no—
1205C23—162no—
1206C23—162no—
1207C23—162no—
1208C23—162no—
1209C23C23×D411yescharacteristic
1210Q8—22no—
1211Q8—22no—
1212Q8—41no—
1213Q8—41no—
1214Q8—41no—
1215Q8—41no—
1216Q8—41no—
1217Q8—41no—
1218Q8—41no—
1219Q8—41no—
1220Q8—41no—
1221Q8—41no—
1222Q8—82no—
1223D4—22no—
1224D4—22no—
1225D4—22no—
1226D4—22no—
1227D4—22no—
1228D4—22no—
1229D4—41no—
1230D4—41no—
1231D4—41no—
1232D4—41no—
1233D4—41no—
1234D4—41no—
1235D4—41no—
1236D4—41no—
1237D4—41no—
1238D4—41no—
1239D4—84no—
1240D4—84no—
1241D4—82no—
1242D4—84no—
1243D4—84no—
1244D4—84no—
1245D4—162no—
1246D4—162no—
1247D4—162no—
1248D4—162no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—22no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—41no—
1325C2×C4—41no—
1326C2×C4—41no—
1327C2×C4—41no—
1328C2×C4—41no—
1329C2×C4—84no—
1330C2×C4—84no—
1331C2×C4—162no—
1332C2×C4—162no—
1333C2×C4—162no—
1334C2×C4—162no—
1335C2×C4—162no—
1336C2×C4—162no—
1337C2×C4C22×#4111yescharacteristic
1338C2×C4C2×H(5,𝔽2)11yescharacteristic
1339C2×C4C2×H(5,𝔽2)11yescharacteristic
1340C2×C4C2×H(5,𝔽2)11yescharacteristic
1341C2×C4C2×H(5,𝔽2)11yescharacteristic
1342C2×C4#58511yescharacteristic
1343C8—22no—
1344C8—22no—
1345C8—22no—
1346C8—41no—
1347C8—41no—
1348C8—41no—
1349C8—41no—
1350C8—41no—
1351C22—41no—
1352C22—41no—
1353C22—41no—
1354C22—41no—
1355C22—42no—
1356C22—41no—
1357C22—42no—
1358C22—41no—
1359C22—42no—
1360C22—42no—
1361C22—41no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—42no—
1366C22—42no—
1367C22—42no—
1368C22—42no—
1369C22—42no—
1370C22—41no—
1371C22—41no—
1372C22—41no—
1373C22—41no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—81no—
1385C22—81no—
1386C22—81no—
1387C22—81no—
1388C22—81no—
1389C22—81no—
1390C22—81no—
1391C22—81no—
1392C22—81no—
1393C22—168no—
1394C22D4×#4111yescharacteristic
1395C22#348411yescharacteristic
1396C22#349811yescharacteristic
1397C22#358411yescharacteristic
1398C22#358411yescharacteristic
1399C22#358411yescharacteristic
1400C22#358511yescharacteristic
1401C4—41no—
1402C4—41no—
1403C4—41no—
1404C4—41no—
1405C4—41no—
1406C4—41no—
1407C4—41no—
1408C4—41no—
1409C4—42no—
1410C4—41no—
1411C4—41no—
1412C4—41no—
1413C4—41no—
1414C4—81no—
1415C4—81no—
1416C4—81no—
1417C4—81no—
1418C4—81no—
1419C4—81no—
1420C4—81no—
1421C4—81no—
1422C4—81no—
1423C4—81no—
1424C4—81no—
1425C4#349011yescharacteristic
1426C4#351911yescharacteristic
1427C4#353411yescharacteristic
1428C4#354211yescharacteristic
1429C2—81no—
1430C2—81no—
1431C2—82no—
1432C2—82no—
1433C2—82no—
1434C2—161no—
1435C2#4422811yescharacteristic
1436C2#6150011yescharacteristic
1437C2#6154711yescharacteristic
1438C2#6161411yescharacteristic
1439C2#6163611yescharacteristic
1440C2#6243311yescharacteristic
1441C2#6246811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23869C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2398 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45141C2semidirect
2. #42627C2semidirect
3. #32651C2semidirect
4. #32603C2semidirect
5. #31961C2semidirect
6. #31287C2semidirect
7. #30992C2semidirect
8. #30580C2semidirect
9. #30470C2semidirect
10. #30408C2semidirect
11. #29508C2semidirect
12. #29505C2semidirect
13. #28862C2semidirect
14. #28339C2semidirect
15. #26986C2semidirect
16. #26960C2semidirect
17. #26635C2semidirect
18. #25796C2semidirect
19. #25635C2semidirect
20. #25411C2semidirect
21. #25178C2semidirect
22. #25160C2semidirect
23. #24903C2semidirect
24. #24427C2semidirect
25. #24192C2semidirect
27. #23808C2semidirect
28. #23275C2semidirect
29. #22872C2semidirect
30. #22442C2semidirect
31. #22278C2semidirect
33. C2×#559C22semidirect
37. C2×#485C22semidirect
40. C2×#465C22semidirect
44. C2×#452C22semidirect
50. C2×#440C22semidirect
51. C2×C4×SD16C22semidirect
54. C2×#416C22semidirect
68. #2581C22semidirect
78. #2432C22semidirect
81. #2427C22semidirect
85. #2420C22semidirect
93. #2339C22semidirect
95. #2328C22semidirect
96. #2327C22semidirect
98. #2097C22semidirect
99. #2097C22semidirect
100. #2094C22semidirect
101. #2093C22semidirect
103. #2085C22semidirect
104. #2085C22semidirect
105. #2085C22semidirect
109. #2068C22semidirect
112. #2056C22semidirect
113. #2043C22semidirect
115. #2042C22semidirect
116. #2041C22semidirect
120. #2036C22semidirect
124. #2015C22semidirect
125. #2014C22semidirect
133. #2001C22semidirect
138. #1984C22semidirect
139. #1984C22semidirect
140. #1983C22semidirect
148. #1958C22semidirect
149. #1956C22semidirect
150. #1941C22semidirect
151. #1936C22semidirect
152. #1935C22semidirect
153. #1934C22semidirect
154. #1933C22semidirect
155. #1933C22semidirect
156. #1928C22semidirect
157. #1924C22semidirect
158. #1924C22semidirect
161. #1920C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
179. #1877C22semidirect
180. #1875C22semidirect
183. #1865C22semidirect
185. #1864C22semidirect
186. #1863C22semidirect
187. #1862C22semidirect
188. #1862C22semidirect
189. #1854C22semidirect
190. #1836C22semidirect
192. #1804C22semidirect
196. C4×#102C22semidirect
199. C8×C22⋊C4C22semidirect
200. C8×C22⋊C4C22semidirect
201. #1746C22semidirect
202. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#451412
#426272
#326512
#326032
#319612
#312872
#309922
#305802
#304702
#304082
#295082
#295052
#288622
#283392
#269862
#269602
#266352
#257962
#256352
#254112
#251782
#251602
#249032
#244272
#241922
#238692
#238082
#232752
#228722
#224422
#222782