Finite Group Databasebeta

← #7337228

Subgroups — #7337228

Order 512.

1684 conjugacy classes of subgroups.

The subgroup lattice has 1434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53047C211yesmaximal, characteristic, complemented
2#45187C211yesmaximal, characteristic, complemented
3#32169C211yesmaximal, characteristic, complemented
4#31915C211yesmaximal, characteristic, complemented
5#31045C211yesmaximal, characteristic, complemented
6#30991C211yesmaximal, characteristic, complemented
7#30886C211yesmaximal, characteristic, complemented
8#30760C211yesmaximal, characteristic, complemented
9#30712C211yesmaximal, characteristic, complemented
10#30598C211yesmaximal, characteristic, complemented
11#30533C211yesmaximal, characteristic, complemented
12#30464C211yesmaximal, characteristic, complemented
13#30451C211yesmaximal, characteristic, complemented
14#30448C211yesmaximal, characteristic, complemented
15#29727C211yesmaximal, characteristic, complemented
16#29674C211yesmaximal, characteristic, complemented
17#29084C211yesmaximal, characteristic, complemented
18#28989C211yesmaximal, characteristic, complemented
19#28469C211yesmaximal, characteristic, complemented
20#28320C211yesmaximal, characteristic, complemented
21#27089C211yesmaximal, characteristic, complemented
22#26953C211yesmaximal, characteristic, complemented
23#26622C211yesmaximal, characteristic, complemented
24#25786C211yesmaximal, characteristic, complemented
25#25769C211yesmaximal, characteristic, complemented
26#25612C211yesmaximal, characteristic, complemented
27#25382C211yesmaximal, characteristic, complemented
28#24908C211yesmaximal, characteristic, complemented
29#24363C211yesmaximal, characteristic, complemented
30#23850C211yesmaximal, characteristic
31#22372C211yesmaximal, characteristic, complemented
32C22×#135C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#541C2211yescharacteristic
35C2×#497C2211yescharacteristic
36C2×#497C2211yescharacteristic
37C2×#497C2211yescharacteristic, complemented
38C2×#495C2211yescharacteristic
39C2×#488C2211yescharacteristic, complemented
40C2×#485C2211yescharacteristic
41C2×#485C2211yescharacteristic
42C2×#467C2211yescharacteristic, complemented
43C2×#464C2211yescharacteristic
44C2×#464C2211yescharacteristic
45C2×#464C2211yescharacteristic, complemented
46C2×#462C2211yescharacteristic, complemented
47C2×#462C2211yescharacteristic, complemented
48C2×#461C2211yescharacteristic
49C2×#452C2211yescharacteristic
50C2×#452C2211yescharacteristic
51C2×#452C2211yescharacteristic, complemented
52C2×#449C2211yescharacteristic
53C2×#450C2211yescharacteristic
54C2×#450C2211yescharacteristic
55C2×#450C2211yescharacteristic
56C2×#447C2211yescharacteristic
57C2×C4×Q16C2211yescharacteristic, complemented
58#2837—21no—
59#2837—21no—
60#2829—21no—
61#2827—21no—
62#2803—21no—
63#2796—21no—
64#2790—21no—
65#2790—21no—
66#2711—21no—
67#2694—21no—
68#2685—21no—
69#2685—21no—
70#2621C2211yescharacteristic
71#2620C2211yescharacteristic
72#2558—21no—
73#2546C2211yescharacteristic, complemented
74#2545C2211yescharacteristic
75#2545C2211yescharacteristic, complemented
76#2542C2211yescharacteristic
77#2513C2211yescharacteristic, complemented
78#2511C2211yescharacteristic, complemented
79#2490—21no—
80#2490C2211yescharacteristic
81#2480—21no—
82#2480—21no—
83#2454C2211yescharacteristic
84#2448C2211yescharacteristic
85#2435C2211yescharacteristic
86#2432C2211yescharacteristic
87#2432C2211yescharacteristic, complemented
88#2432C2211yescharacteristic, complemented
89#2429C2211yescharacteristic
90#2426C2211yescharacteristic
91#2426C2211yescharacteristic
92#2423C2211yescharacteristic, complemented
93#2421C2211yescharacteristic, complemented
94#2415C2211yescharacteristic
95#2407C2211yescharacteristic
96#2395C2211yescharacteristic
97#2367C2211yescharacteristic
98#2362C2211yescharacteristic
99#2341C2211yescharacteristic
100#2309C2211yescharacteristic
101#2092C2211yescharacteristic
102#2092C2211yescharacteristic
103#2087C2211yescharacteristic, complemented
104#2076C2211yescharacteristic, complemented
105#2071C2211yescharacteristic
106#2071C2211yescharacteristic
107#2066C2211yescharacteristic, complemented
108#2065C2211yescharacteristic, complemented
109#2056C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic
115#2054C2211yescharacteristic
116#2043C2211yescharacteristic, complemented
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic, complemented
120#2035C2211yescharacteristic, complemented
121#2035C2211yescharacteristic, complemented
122#2026C2211yescharacteristic, complemented
123#2026C2211yescharacteristic, complemented
124#2016C2211yescharacteristic, complemented
125#2016C2211yescharacteristic, complemented
126#2016C2211yescharacteristic, complemented
127#2016C2211yescharacteristic, complemented
128#2015C2211yescharacteristic
129#2015C2211yescharacteristic
130#2013C2211yescharacteristic
131#2013C2211yescharacteristic
132#2013C2211yescharacteristic
133#2012C2211yescharacteristic
134#2012C2211yescharacteristic
135#2012C2211yescharacteristic
136#2012C2211yescharacteristic
137#2012C2211yescharacteristic
138#2001C2211yescharacteristic
139#2001C2211yescharacteristic
140#2001C2211yescharacteristic
141#2001C2211yescharacteristic
142#2001C2211yescharacteristic
143#2001C2211yescharacteristic
144#2001C2211yescharacteristic, complemented
145#2000C2211yescharacteristic
146#2000C2211yescharacteristic
147#2000C2211yescharacteristic
148#2000C2211yescharacteristic
149#1992C2211yescharacteristic, complemented
150#1983C2211yescharacteristic
151#1981C2211yescharacteristic, complemented
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic
154#1973C2211yescharacteristic, complemented
155#1973C2211yescharacteristic, complemented
156#1968C2211yescharacteristic
157#1968C2211yescharacteristic
158#1956C2211yescharacteristic, complemented
159#1955C2211yescharacteristic
160#1940C2211yescharacteristic, complemented
161#1936C2211yescharacteristic
162#1935C2211yescharacteristic, complemented
163#1934C2211yescharacteristic
164#1933C2211yescharacteristic, complemented
165#1927C2211yescharacteristic, complemented
166#1926C2211yescharacteristic, complemented
167#1924C2211yescharacteristic
168#1923C2211yescharacteristic
169#1923C2211yescharacteristic, complemented
170#1923C2211yescharacteristic, complemented
171#1918C2211yescharacteristic, complemented
172#1918C2211yescharacteristic, complemented
173#1917C2211yescharacteristic, complemented
174#1916C2211yescharacteristic, complemented
175#1893C2211yescharacteristic
176#1892C2211yescharacteristic, complemented
177#1880C2211yescharacteristic
178#1880C2211yescharacteristic
179#1880C2211yescharacteristic, complemented
180#1880C2211yescharacteristic, complemented
181#1879C2211yescharacteristic
182#1878C2211yescharacteristic, complemented
183#1878C2211yescharacteristic, complemented
184#1878C2211yescharacteristic, complemented
185#1878C2211yescharacteristic, complemented
186#1877C2211yescharacteristic
187#1875C2211yescharacteristic
188#1873C2211yescharacteristic
189#1869C2211yescharacteristic
190#1865C2211yescharacteristic, complemented
191#1865C2211yescharacteristic, complemented
192#1850C2211yescharacteristic, complemented
193#1805C2211yescharacteristic, complemented
194#1805C2211yescharacteristic, complemented
195#1798C2211yescharacteristic
196#1788C2211yescharacteristic
197#1788C2211yescharacteristic, complemented
198#1770C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200#1762C2211yescharacteristic
201#1752C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×#135—42no—
207C2×#135—42no—
208C2×#135—42no—
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×Q16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×SD16C2311yescharacteristic
223C22×D8C2311yescharacteristic
224C22×D8C2311yescharacteristic
225C23×C8C2311yescharacteristic
226#546—42no—
227#546—42no—
228#541—42no—
229#541—42no—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×#126—21no—
235C2×#126—21no—
236C2×#125—21no—
237C2×#125—21no—
238C2×#125C2311yescharacteristic
239C2×#124C2311yescharacteristic
240C2×#124C2311yescharacteristic
241C2×#124C2311yescharacteristic
242C2×#124C2311yescharacteristic
243C2×#124C2311yescharacteristic
244C2×#123—21no—
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2311yescharacteristic
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2311yescharacteristic
249C2×C22⋊Q8C2311yescharacteristic
250C2×C22⋊Q8C2311yescharacteristic
251C2×C22⋊Q8C2311yescharacteristic
252C2×C22⋊Q8C2311yescharacteristic
253C2×#121—21no—
254C2×#121C2311yescharacteristic
255C2×#121C2311yescharacteristic
256C2×#120—21no—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C22×C22⋊C4—21no—
267#497—42no—
268#497—42no—
269#497—42no—
270#495—42no—
271#488—42no—
272#485—42no—
273#485—42no—
274#467—42no—
275#464—42no—
276#464—42no—
277#464—42no—
278#462—42no—
279#462—42no—
280#461—42no—
281#452—42no—
282#452—42no—
283#452—42no—
284#450—42no—
285#450—42no—
286#450—42no—
287#449—42no—
288#447—42no—
289C4×Q16—42no—
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#106C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296C2×C4⋊C8C2311yescharacteristic
297C2×C4⋊C8C2311yescharacteristic
298C2×C4⋊C8C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×#97C2311yescharacteristic
339C2×#97C2311yescharacteristic
340C2×#97C2311yescharacteristic
341C2×C4×C8C2311yescharacteristic
342C2×C4×C8C2311yescharacteristic
343#400—21no—
344#400—21no—
345#400—21no—
346#400D411yescharacteristic
347#399—21no—
348#399—21no—
349#399—21no—
350#399—21no—
351#399—21no—
352#399D411yescharacteristic
353#398—21no—
354#398—21no—
355#398—21no—
356#398—21no—
357#398—21no—
358#398—21no—
359#398D411yescharacteristic
360#397—21no—
361#397—21no—
362#397—21no—
363#397—21no—
364#397—21no—
365#397—21no—
366#397—21no—
367#397—21no—
368#397D411yescharacteristic
369#397D411yescharacteristic
370#397D411yescharacteristic
371#396—21no—
372#396—21no—
373#396—21no—
374#396—21no—
375#396—21no—
376#396—21no—
377#396—21no—
378#396—21no—
379#396—21no—
380#396—21no—
381#394—21no—
382#394—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#394—21no—
387#394—21no—
388#394—21no—
389#394—21no—
390#394—21no—
391#394—21no—
392#394—21no—
393#394—21no—
394#394—21no—
395#394—21no—
396#394D411yescharacteristic
397#394D411yescharacteristic
398#392—21no—
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#390—21no—
407#390—21no—
408#390—21no—
409#390—21no—
410#390—21no—
411#390—21no—
412#390—21no—
413#390—21no—
414#390C2311yescharacteristic
415#390C2311yescharacteristic
416#390C2311yescharacteristic
417#390C2311yescharacteristic
418#390C2311yescharacteristic
419#390C2311yescharacteristic
420#390C2311yescharacteristic
421#390C2311yescharacteristic
422#390C2311yescharacteristic
423#389—21no—
424#389—21no—
425#389—21no—
426#389—21no—
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#388—21no—
441#388—21no—
442#388—21no—
443#388—21no—
444#388—21no—
445#388—21no—
446#388—21no—
447#388—21no—
448#388—21no—
449#388—21no—
450#387—21no—
451#387—21no—
452#387—21no—
453#387—21no—
454#387—21no—
455#386—21no—
456#385—21no—
457#385—21no—
458#385—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#385—21no—
463#385—21no—
464#385—21no—
465#384—21no—
466#384C2311yescharacteristic
467#382C2311yescharacteristic
468#380—21no—
469#380—21no—
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472#379—21no—
473#379—21no—
474#379—21no—
475#379—21no—
476C4×C4⋊C4—21no—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C22⋊C4—21no—
482C4×C22⋊C4—21no—
483C4×C22⋊C4C2311yescharacteristic
484C4×C22⋊C4C2311yescharacteristic
485C4×C22⋊C4C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502#336C2311yescharacteristic
503#336C2311yescharacteristic
504#336C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508C25—21no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41—41no—
517C2×#41—41no—
518C2×#41—41no—
519C2×#41—41no—
520C2×#41—41no—
521C22×Q8C2411yescharacteristic
522C22×Q8C2411yescharacteristic
523C22×Q8C2411yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×D4—22no—
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
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546#135—416no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×Q16—41no—
561C2×Q16—41no—
562C2×Q16—41no—
563C2×Q16—41no—
564C2×Q16—41no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×SD16—22no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×SD16—41no—
582C2×SD16—41no—
583C2×SD16—41no—
584C2×SD16—41no—
585C2×SD16—41no—
586C2×SD16—41no—
587C2×SD16—41no—
588C2×SD16—41no—
589C2×D8—22no—
590C2×D8—41no—
591C2×D8—41no—
592C2×D8—41no—
593C2×D8—41no—
594C2×D8—41no—
595C22×C8—22no—
596C22×C8—41no—
597C22×C8—41no—
598C22×C8C2411yescharacteristic
599C22×C8C2411yescharacteristic
600C22×C8C2411yescharacteristic
601C22×C8C2411yescharacteristic
602C22×C8C2411yescharacteristic
603C22×C8C2411yescharacteristic
604C22×C8C2411yescharacteristic
605C22×C8C2411yescharacteristic
606C4⋊Q8—22no—
607C4⋊Q8—41no—
608C4⋊Q8—41no—
609C4⋊Q8—41no—
610C4⋊Q8—41no—
611C4⋊Q8—41no—
612C4⋊Q8—41no—
613C4⋊Q8—41no—
614#126—44no—
615#126—44no—
616#125—22no—
617#125—41no—
618#125—44no—
619#125—44no—
620#124—22no—
621#124—22no—
622#124—41no—
623#124—41no—
624#124—41no—
625#124—41no—
626#124—41no—
627#124—41no—
628#124—41no—
629#124—41no—
630#123—44no—
631C22⋊Q8—22no—
632C22⋊Q8—22no—
633C22⋊Q8—41no—
634C22⋊Q8—41no—
635C22⋊Q8—41no—
636C22⋊Q8—41no—
637C22⋊Q8—41no—
638C22⋊Q8—41no—
639C22⋊Q8—41no—
640C22⋊Q8—41no—
641C22⋊Q8—41no—
642C22⋊Q8—41no—
643C22⋊Q8—41no—
644C22⋊Q8—41no—
645C22⋊Q8—41no—
646C22⋊Q8—41no—
647#121—22no—
648#121—41no—
649#121—44no—
650#121—41no—
651#121—41no—
652#120—44no—
653C4×Q8—22no—
654C4×Q8—22no—
655C4×Q8—41no—
656C4×Q8—41no—
657C4×Q8—41no—
658C4×Q8—41no—
659C4×Q8—41no—
660C4×Q8—41no—
661C4×Q8—41no—
662C4×Q8—41no—
663C4×D4—22no—
664C4×D4—41no—
665C4×D4—41no—
666C4×D4—41no—
667#117—41no—
668#117—41no—
669#117—41no—
670#117—41no—
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⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4C2×D411yescharacteristic
701C2×C4⋊C4C2×D411yescharacteristic
702C2×C4⋊C4C2×D411yescharacteristic
703C2×C4⋊C4C2×D411yescharacteristic
704C2×C4⋊C4C2×D411yescharacteristic
705C2×C4⋊C4C2×D411yescharacteristic
706C2×C4⋊C4C2×D411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
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—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—21no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—21no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—21no—
750C2×C22⋊C4—21no—
751C2×C22⋊C4—21no—
752C2×C22⋊C4—21no—
753C2×C22⋊C4—21no—
754C2×C22⋊C4—21no—
755C2×C22⋊C4—21no—
756C2×C22⋊C4—21no—
757C2×C22⋊C4—44no—
758C2×C22⋊C4C2×D411yescharacteristic
759C2×C22⋊C4C2×D411yescharacteristic
760C2×C22⋊C4C2×D411yescharacteristic
761C2×C22⋊C4C2×D411yescharacteristic
762C2×C22⋊C4C2×D411yescharacteristic
763C2×C22⋊C4C2×D411yescharacteristic
764C2×C22⋊C4C2×D411yescharacteristic
765C2×C22⋊C4C2×D411yescharacteristic
766C2×C22⋊C4C2×D411yescharacteristic
767C2×C22⋊C4C2×D411yescharacteristic
768C2×C42—21no—
769C2×C42—21no—
770C2×C42—21no—
771C2×C42—21no—
772C2×C42—21no—
773C2×C42—21no—
774C2×C42—21no—
775C2×C42—21no—
776C2×C42C2411yescharacteristic
777C2×C42C2411yescharacteristic
778C2×C42C2411yescharacteristic
779C2×C42C2411yescharacteristic
780C2×C42C2411yescharacteristic
781#107—22no—
782#107—22no—
783#106—41no—
784#106—41no—
785C4⋊C8—22no—
786C4⋊C8—41no—
787C4⋊C8—41no—
788C4⋊C8—41no—
789C4⋊C8—41no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—41no—
796#103—41no—
797#103—41no—
798#103—41no—
799#103—41no—
800#103—41no—
801#103—41no—
802#103—41no—
803#103—41no—
804#103—41no—
805#103—41no—
806#103—41no—
807#103—41no—
808#103—41no—
809#103—41no—
810#102—22no—
811#102—22no—
812#102—22no—
813#102—22no—
814#102—22no—
815#102—41no—
816#102—41no—
817#102—41no—
818#102—41no—
819#102—41no—
820#102—41no—
821#102—41no—
822C22⋊C8—22no—
823C22⋊C8—22no—
824C22⋊C8—22no—
825C22⋊C8—41no—
826C22⋊C8—41no—
827C22⋊C8—41no—
828C22⋊C8—41no—
829#97—41no—
830#97—41no—
831#97—41no—
832C4×C8—22no—
833C4×C8—41no—
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#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
853#95—21no—
854#95—21no—
855#95—21no—
856#95—21no—
857#95—21no—
858#95C2×D411yescharacteristic
859#95C2×D411yescharacteristic
860#95C2×D411yescharacteristic
861#95C2×D411yescharacteristic
862#95C2×D411yescharacteristic
863#95C2×D411yescharacteristic
864#95C2×D411yescharacteristic
865#95C2×D411yescharacteristic
866#95C2×D411yescharacteristic
867#95C2×D411yescharacteristic
868C24—21no—
869C24—21no—
870C24—21no—
871C24—42no—
872C24—42no—
873C24—81no—
874C24—81no—
875C24—81no—
876C24—81no—
877C24—81no—
878C24C22×D411yescharacteristic
879C24C22×D411yescharacteristic
880#41—44no—
881#41—44no—
882#41—82no—
883#41—82no—
884#41—82no—
885#41—82no—
886#41—82no—
887#41—82no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—21no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—21no—
903C2×Q8—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×Q8—21no—
907C2×Q8—21no—
908C2×Q8—21no—
909C2×Q8—21no—
910C2×Q8—21no—
911C2×Q8—21no—
912C2×Q8—21no—
913C2×Q8—21no—
914C2×Q8—21no—
915C2×Q8—21no—
916C2×Q8—21no—
917C2×Q8H(5,𝔽2)12yes—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—21no—
929C2×D4—21no—
930C2×D4—21no—
931C2×D4—21no—
932C2×D4—21no—
933C2×D4—21no—
934C2×D4—21no—
935C2×D4—41no—
936C2×D4—41no—
937C2×D4—41no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4—42no—
943C2×D4—81no—
944C2×D4—82no—
945C2×D4—82no—
946C2×D4—82no—
947C2×D4—82no—
948C2×D4—81no—
949C2×D4—81no—
950C2×D4—81no—
951C2×D4—81no—
952C2×D4—81no—
953C2×D4—81no—
954C2×D4—81no—
955C2×D4—81no—
956C2×D4—81no—
957C2×D4H(5,𝔽2)12yes—
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—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C22×D411yescharacteristic
1002C22×C4C22×D411yescharacteristic
1003C22×C4C22×D411yescharacteristic
1004C22×C4C2511yescharacteristic
1005Q16—44no—
1006Q16—44no—
1007Q16—82no—
1008Q16—82no—
1009Q16—82no—
1010Q16—82no—
1011SD16—44no—
1012SD16—44no—
1013SD16—82no—
1014SD16—82no—
1015SD16—82no—
1016SD16—82no—
1017SD16—82no—
1018SD16—82no—
1019D8—44no—
1020D8—82no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
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—44no—
1044C2×C8H(5,𝔽2)12yes—
1045C2×C8H(5,𝔽2)12yes—
1046C4⋊C4—24no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
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—41no—
1063C4⋊C4—41no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—41no—
1068C4⋊C4—41no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
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—
1092C4⋊C4—81no—
1093C4⋊C4—81no—
1094C4⋊C4—81no—
1095C4⋊C4—81no—
1096C4⋊C4—81no—
1097C4⋊C4H(5,𝔽2)12yes—
1098C22⋊C4—24no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
1106C22⋊C4—41no—
1107C22⋊C4—41no—
1108C22⋊C4—41no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
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—
1145C22⋊C4—81no—
1146C22⋊C4—81no—
1147C22⋊C4—81no—
1148C22⋊C4—81no—
1149C22⋊C4—81no—
1150C42—21no—
1151C42—21no—
1152C42—21no—
1153C42—21no—
1154C42—21no—
1155C42—21no—
1156C42—21no—
1157C42—21no—
1158C42—21no—
1159C42—21no—
1160C42—42no—
1161C42—42no—
1162C42—81no—
1163C42—81no—
1164C42—81no—
1165C42—81no—
1166C42—81no—
1167C42—81no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—21no—
1177C23—21no—
1178C23—22no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
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—41no—
1203C23—84no—
1204C23—84no—
1205C23—162no—
1206C23—162no—
1207C23—162no—
1208C23—162no—
1209C23—162no—
1210C23C23×D411yescharacteristic
1211Q8—22no—
1212Q8—22no—
1213Q8—41no—
1214Q8—41no—
1215Q8—41no—
1216Q8—41no—
1217Q8—41no—
1218Q8—41no—
1219Q8—41no—
1220Q8—41no—
1221Q8—41no—
1222Q8—41no—
1223Q8—41no—
1224Q8—41no—
1225Q8—41no—
1226Q8—41no—
1227Q8—41no—
1228Q8—41no—
1229Q8—41no—
1230Q8—41no—
1231D4—22no—
1232D4—22no—
1233D4—41no—
1234D4—41no—
1235D4—41no—
1236D4—41no—
1237D4—41no—
1238D4—41no—
1239D4—41no—
1240D4—41no—
1241D4—41no—
1242D4—41no—
1243D4—82no—
1244D4—84no—
1245D4—84no—
1246D4—84no—
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—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—22no—
1276C2×C4—22no—
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—21no—
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—41no—
1330C2×C4—41no—
1331C2×C4—41no—
1332C2×C4—84no—
1333C2×C4—84no—
1334C2×C4—162no—
1335C2×C4C2×H(5,𝔽2)11yescharacteristic
1336C2×C4C2×H(5,𝔽2)11yescharacteristic
1337C2×C4C2×H(5,𝔽2)11yescharacteristic
1338C2×C4C2×H(5,𝔽2)11yescharacteristic
1339C2×C4C2×H(5,𝔽2)11yescharacteristic
1340C2×C4#58511yescharacteristic
1341C8—22no—
1342C8—22no—
1343C8—41no—
1344C8—41no—
1345C8—41no—
1346C8—41no—
1347C8—41no—
1348C8—41no—
1349C22—41no—
1350C22—41no—
1351C22—42no—
1352C22—41no—
1353C22—41no—
1354C22—42no—
1355C22—41no—
1356C22—41no—
1357C22—42no—
1358C22—41no—
1359C22—41no—
1360C22—41no—
1361C22—41no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—41no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—168no—
1385C22#348411yescharacteristic
1386C22#348811yescharacteristic
1387C22#349811yescharacteristic
1388C22#358411yescharacteristic
1389C22#358411yescharacteristic
1390C22#358611yescharacteristic
1391C22#358611yescharacteristic
1392C4—41no—
1393C4—41no—
1394C4—42no—
1395C4—41no—
1396C4—41no—
1397C4—41no—
1398C4—41no—
1399C4—41no—
1400C4—41no—
1401C4—41no—
1402C4—41no—
1403C4—42no—
1404C4—41no—
1405C4—41no—
1406C4—81no—
1407C4—81no—
1408C4—81no—
1409C4—81no—
1410C4—81no—
1411C4—81no—
1412C4—81no—
1413C4—81no—
1414C4—81no—
1415C4—81no—
1416C4—81no—
1417C4#353211yescharacteristic
1418C4#353411yescharacteristic
1419C4#354311yescharacteristic
1420C4#354611yescharacteristic
1421C2—81no—
1422C2—81no—
1423C2—82no—
1424C2—161no—
1425C2—161no—
1426C2#4795211yescharacteristic
1427C2#6161511yescharacteristic
1428C2#6169111yescharacteristic
1429C2#6206011yescharacteristic
1430C2#6208011yescharacteristic
1431C2#6246211yescharacteristic
1432C2#6246211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23850C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53047C2semidirect
2. #45187C2semidirect
3. #32169C2semidirect
4. #31915C2semidirect
5. #31045C2semidirect
6. #30991C2semidirect
7. #30886C2semidirect
8. #30760C2semidirect
9. #30712C2semidirect
10. #30598C2semidirect
11. #30533C2semidirect
12. #30464C2semidirect
13. #30451C2semidirect
14. #30448C2semidirect
15. #29727C2semidirect
16. #29674C2semidirect
17. #29084C2semidirect
18. #28989C2semidirect
19. #28469C2semidirect
20. #28320C2semidirect
21. #27089C2semidirect
22. #26953C2semidirect
23. #26622C2semidirect
24. #25786C2semidirect
25. #25769C2semidirect
26. #25612C2semidirect
27. #25382C2semidirect
28. #24908C2semidirect
29. #24363C2semidirect
31. #22372C2semidirect
37. C2×#497C22semidirect
39. C2×#488C22semidirect
42. C2×#467C22semidirect
45. C2×#464C22semidirect
46. C2×#462C22semidirect
47. C2×#462C22semidirect
51. C2×#452C22semidirect
57. C2×C4×Q16C22semidirect
73. #2546C22semidirect
75. #2545C22semidirect
77. #2513C22semidirect
78. #2511C22semidirect
87. #2432C22semidirect
88. #2432C22semidirect
92. #2423C22semidirect
93. #2421C22semidirect
103. #2087C22semidirect
104. #2076C22semidirect
107. #2066C22semidirect
108. #2065C22semidirect
109. #2056C22semidirect
116. #2043C22semidirect
119. #2042C22semidirect
120. #2035C22semidirect
121. #2035C22semidirect
122. #2026C22semidirect
123. #2026C22semidirect
124. #2016C22semidirect
125. #2016C22semidirect
126. #2016C22semidirect
127. #2016C22semidirect
144. #2001C22semidirect
149. #1992C22semidirect
151. #1981C22semidirect
154. #1973C22semidirect
155. #1973C22semidirect
158. #1956C22semidirect
160. #1940C22semidirect
162. #1935C22semidirect
164. #1933C22semidirect
165. #1927C22semidirect
166. #1926C22semidirect
169. #1923C22semidirect
170. #1923C22semidirect
171. #1918C22semidirect
172. #1918C22semidirect
173. #1917C22semidirect
174. #1916C22semidirect
176. #1892C22semidirect
179. #1880C22semidirect
180. #1880C22semidirect
182. #1878C22semidirect
183. #1878C22semidirect
184. #1878C22semidirect
185. #1878C22semidirect
190. #1865C22semidirect
191. #1865C22semidirect
192. #1850C22semidirect
193. #1805C22semidirect
194. #1805C22semidirect
197. #1788C22semidirect
198. #1770C22semidirect
199. #1763C22semidirect
201. #1752C22semidirect

Maximal subgroups

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

subgroupindex
#530472
#451872
#321692
#319152
#310452
#309912
#308862
#307602
#307122
#305982
#305332
#304642
#304512
#304482
#297272
#296742
#290842
#289892
#284692
#283202
#270892
#269532
#266222
#257862
#257692
#256122
#253822
#249082
#243632
#238502
#223722