Finite Group Databasebeta

← #6506979

Subgroups — #6506979

Order 512.

1765 conjugacy classes of subgroups.

The subgroup lattice has 1419 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37361C211yesmaximal, characteristic, complemented
2#35523C211yesmaximal, characteristic, complemented
3#29564C211yesmaximal, characteristic, complemented
4#29506C211yesmaximal, characteristic, complemented
5#29461C211yesmaximal, characteristic, complemented
6#29457C211yesmaximal, characteristic, complemented
7#29096C211yesmaximal, characteristic, complemented
8#28995C211yesmaximal, characteristic, complemented
9#28922C211yesmaximal, characteristic, complemented
10#28878C211yesmaximal, characteristic, complemented
11#28788C211yesmaximal, characteristic, complemented
12#28630C211yesmaximal, characteristic, complemented
13#28579C211yesmaximal, characteristic, complemented
14#28569C211yesmaximal, characteristic, complemented
15#27259C211yesmaximal, characteristic, complemented
16#27256C211yesmaximal, characteristic, complemented
17#26984C211yesmaximal, characteristic, complemented
18#26819C211yesmaximal, characteristic, complemented
19#26262C211yesmaximal, characteristic, complemented
20#25793C211yesmaximal, characteristic, complemented
21#25601C211yesmaximal, characteristic, complemented
22#25506C211yesmaximal, characteristic, complemented
23#25419C211yesmaximal, characteristic, complemented
24#25129C211yesmaximal, characteristic, complemented
25#25124C211yesmaximal, characteristic, complemented
26#24277C211yesmaximal, characteristic, complemented
27#22201C211yesmaximal, characteristic, complemented
28#22059C211yesmaximal, characteristic, complemented
29#21458C211yesmaximal, characteristic, complemented
30#20929C211yesmaximal, characteristic, complemented
31#20561C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#518C2211yescharacteristic
35C2×#496C2211yescharacteristic
36C2×#495C2211yescharacteristic
37C2×#488C2211yescharacteristic
38C2×#488C2211yescharacteristic, complemented
39C2×#469C2211yescharacteristic
40C2×#469C2211yescharacteristic
41C2×#468C2211yescharacteristic
42C2×#468C2211yescharacteristic
43C2×#468C2211yescharacteristic, complemented
44C2×#452C2211yescharacteristic
45C2×#447C2211yescharacteristic
46C2×#442C2211yescharacteristic
47C2×C4×D8C2211yescharacteristic
48C2×#436C2211yescharacteristic
49C2×#435C2211yescharacteristic
50C2×#416C2211yescharacteristic
51C22×#102C2211yescharacteristic
52#2854C2211yescharacteristic, complemented
53#2850C2211yescharacteristic, complemented
54#2781—21no—
55#2778—21no—
56#2778—21no—
57#2753—21no—
58#2750—21no—
59#2708—21no—
60#2703—21no—
61#2688—21no—
62#2645C2211yescharacteristic, complemented
63#2641C2211yescharacteristic, complemented
64#2600—21no—
65#2534—21no—
66#2513C2211yescharacteristic, complemented
67#2489C2211yescharacteristic, complemented
68#2485—21no—
69#2482—21no—
70#2480—21no—
71#2466—21no—
72#2455—21no—
73#2454C2211yescharacteristic
74#2447C2211yescharacteristic
75#2447C2211yescharacteristic, complemented
76#2442C2211yescharacteristic
77#2441C2211yescharacteristic
78#2435C2211yescharacteristic
79#2431C2211yescharacteristic
80#2428C2211yescharacteristic, complemented
81#2427C2211yescharacteristic
82#2422C2211yescharacteristic
83#2418—21no—
84#2416C2211yescharacteristic
85#2415C2211yescharacteristic
86#2408C2211yescharacteristic
87#2407C2211yescharacteristic
88#2326C2211yescharacteristic
89#2324C2211yescharacteristic
90#2323C2211yescharacteristic
91#2319C2211yescharacteristic
92#2311C2211yescharacteristic
93C4×#121C2211yescharacteristic
94#2290C2211yescharacteristic
95#2086C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2076C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2072C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2065C2211yescharacteristic
103#2059C2211yescharacteristic, complemented
104#2059C2211yescharacteristic, complemented
105#2055C2211yescharacteristic
106#2055C2211yescharacteristic, complemented
107#2055C2211yescharacteristic, complemented
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic, complemented
113#2041C2211yescharacteristic, complemented
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic, complemented
116#2025C2211yescharacteristic
117#2025C2211yescharacteristic, complemented
118#2015C2211yescharacteristic
119#2012C2211yescharacteristic
120#2012C2211yescharacteristic
121#2011C2211yescharacteristic
122#2001C2211yescharacteristic, complemented
123#2000C2211yescharacteristic
124#2000C2211yescharacteristic, complemented
125#1999C2211yescharacteristic
126#1999C2211yescharacteristic
127#1992C2211yescharacteristic, complemented
128#1991C2211yescharacteristic, complemented
129#1973C2211yescharacteristic
130#1972C2211yescharacteristic
131#1971C2211yescharacteristic, complemented
132#1971C2211yescharacteristic, complemented
133#1970C2211yescharacteristic
134#1970C2211yescharacteristic
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic, complemented
137#1958C2211yescharacteristic
138#1957C2211yescharacteristic, complemented
139#1943C2211yescharacteristic, complemented
140#1941C2211yescharacteristic, complemented
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic, complemented
143#1936C2211yescharacteristic, complemented
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic, complemented
147#1934C2211yescharacteristic, complemented
148#1933C2211yescharacteristic, complemented
149#1933C2211yescharacteristic, complemented
150#1933C2211yescharacteristic, complemented
151#1928C2211yescharacteristic, complemented
152#1927C2211yescharacteristic, complemented
153#1926C2211yescharacteristic, complemented
154#1925C2211yescharacteristic, complemented
155#1921C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1895C2211yescharacteristic
158#1895C2211yescharacteristic, complemented
159#1894C2211yescharacteristic, complemented
160#1894C2211yescharacteristic, complemented
161#1893C2211yescharacteristic
162#1892C2211yescharacteristic
163#1880C2211yescharacteristic, complemented
164#1880C2211yescharacteristic, complemented
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1878C2211yescharacteristic, complemented
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic, complemented
177#1875C2211yescharacteristic
178#1872C2211yescharacteristic
179#1865C2211yescharacteristic, complemented
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic, complemented
182#1862C2211yescharacteristic
183#1854C2211yescharacteristic
184#1853C2211yescharacteristic
185#1809C2211yescharacteristic
186#1788C2211yescharacteristic
187#1786C2211yescharacteristic
188#1771C2211yescharacteristic, complemented
189C8×C4⋊C4C2211yescharacteristic, complemented
190#1768C2211yescharacteristic, complemented
191#1762C2211yescharacteristic
192C4×#102C2211yescharacteristic
193#1753C2211yescharacteristic
194#1753C2211yescharacteristic, complemented
195#1753C2211yescharacteristic, complemented
196C8×C22⋊C4C2211yescharacteristic
197#1750C2211yescharacteristic
198C4×C22⋊C8C2211yescharacteristic, complemented
199#1746C2211yescharacteristic, complemented
200#1736C2211yescharacteristic
201#1729C2211yescharacteristic
202#1728C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C2×AGL(1,ℤ/8)—42no—
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C22×M16C2311yescharacteristic
219C22×M16C2311yescharacteristic
220C23×C8C2311yescharacteristic
221C2×#127C2311yescharacteristic
222#529—42no—
223#529—42no—
224C2×#126—21no—
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#123—21no—
231C2×#123—21no—
232C2×#123—21no—
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×#121—21no—
237C2×#121—21no—
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#120—21no—
244#518—42no—
245#518—42no—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×#117—21no—
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C22⋊C4—21no—
262C22×C22⋊C4—21no—
263C22×C42C2311yescharacteristic
264#496—42no—
265#495—42no—
266#488—42no—
267#488—42no—
268#469—42no—
269#469—42no—
270#468—24no—
271#468—42no—
272#468—42no—
273#452—24no—
274#447—24no—
275#442—42no—
276C4×D8—42no—
277#436—24no—
278#435—24no—
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288#416—42no—
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#102—42no—
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
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332#401—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#400—21no—
337#400—21no—
338#399—21no—
339#399—21no—
340#398—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#392—21no—
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#390—21no—
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#389—21no—
390#389—21no—
391#389—21no—
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#388—21no—
401#388—21no—
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#388D411yescharacteristic
417#388D411yescharacteristic
418#387—21no—
419#387—21no—
420#387D411yescharacteristic
421#387D411yescharacteristic
422#386—21no—
423#386—21no—
424#386—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#386—21no—
435#386D411yescharacteristic
436#386D411yescharacteristic
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385D411yescharacteristic
447#385D411yescharacteristic
448#384C2311yescharacteristic
449#382—21no—
450#382C2311yescharacteristic
451#381—21no—
452#381—21no—
453#381—21no—
454#380—21no—
455#380—21no—
456#380—21no—
457#380—21no—
458#380—21no—
459#380—21no—
460#380C2311yescharacteristic
461#380C2311yescharacteristic
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464#379—21no—
465#379—21no—
466#379—21no—
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C22⋊C4—21no—
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473#376C2311yescharacteristic
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#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—22no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×D411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C2×D411yescharacteristic
539C23×C4C2×D411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542AGL(1,ℤ/8)—416no—
543C2×Q16—22no—
544C2×Q16—41no—
545C2×Q16—41no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×D8—22no—
559C2×D8—22no—
560C2×D8—22no—
561C2×D8—22no—
562C2×D8—22no—
563C2×D8—22no—
564C2×D8—22no—
565C2×D8—22no—
566C2×D8—41no—
567C2×D8—41no—
568C2×D8—41no—
569C2×D8—41no—
570C2×M16—22no—
571C2×M16—22no—
572C2×M16—41no—
573C2×M16—41no—
574C2×M16—41no—
575C2×M16—41no—
576C2×M16—41no—
577C2×M16—41no—
578C2×M16#4114yes—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8—41no—
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590#127—41no—
591#127—41no—
592#126—44no—
593#125—22no—
594#125—41no—
595#125—41no—
596#125—41no—
597#124—22no—
598#124—22no—
599#124—41no—
600#124—41no—
601#124—41no—
602#124—41no—
603#123—44no—
604#123—82no—
605#123—82no—
606C22⋊Q8—22no—
607C22⋊Q8—22no—
608C22⋊Q8—22no—
609C22⋊Q8—41no—
610C22⋊Q8—41no—
611C22⋊Q8—41no—
612#121—22no—
613#121—22no—
614#121—22no—
615#121—22no—
616#121—41no—
617#121—41no—
618#121—41no—
619#121—41no—
620#121—41no—
621#121—41no—
622#121—82no—
623#121—82no—
624#120—82no—
625C4×Q8—41no—
626C4×Q8—41no—
627C4×D4—22no—
628C4×D4—22no—
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—41no—
634C4×D4—41no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—44no—
640C4×D4—44no—
641C4×D4—44no—
642C4×D4—82no—
643#117—22no—
644#117—41no—
645#117—41no—
646#117—41no—
647#117—44no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
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—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—44no—
729C2×C22⋊C4—44no—
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—41no—
743C2×C42—41no—
744C2×C42C2×D411yescharacteristic
745C2×C42C2×D411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751#107—22no—
752#107—22no—
753#107—41no—
754#106—41no—
755#106—41no—
756#106—41no—
757#106—41no—
758C4⋊C8—22no—
759C4⋊C8—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—41no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790C22⋊C8—22no—
791C22⋊C8—22no—
792C22⋊C8—22no—
793C22⋊C8#4114yes—
794#97—22no—
795#97—41no—
796#97—41no—
797C4×C8—22no—
798C4×C8—41no—
799C4×C8—41no—
800C4×C8—41no—
801C4×C8—41no—
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#95—21no—
812#95—21no—
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#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—42no—
845C24—42no—
846C24—42no—
847C24—81no—
848C24—81no—
849C24—81no—
850C24—81no—
851C24C22×D411yescharacteristic
852C24C22×D411yescharacteristic
853#41—44no—
854#41—44no—
855#41—82no—
856#41—82no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×D4—28no—
870C2×D4—22no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—44no—
898C2×D4—41no—
899C2×D4—41no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
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×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4H(5,𝔽2)12yes—
926C2×D4H(5,𝔽2)12yes—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—24no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—41no—
955C22×C4—41no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C2×#4112yes—
989C22×C4C2×#4112yes—
990C22×C4C2511yescharacteristic
991Q16—82no—
992SD16—44no—
993SD16—44no—
994SD16—82no—
995SD16—82no—
996D8—44no—
997D8—44no—
998D8—44no—
999D8—44no—
1000M16—44no—
1001M16—82no—
1002M16—82no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—82no—
1024C2×C8C2×#4112yes—
1025C2×C8C2×#4112yes—
1026C2×C8C2×#4112yes—
1027C2×C8C2×#4112yes—
1028C4⋊C4—22no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—41no—
1049C4⋊C4—41no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4H(5,𝔽2)12yes—
1072C22⋊C4—24no—
1073C22⋊C4—22no—
1074C22⋊C4—22no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—41no—
1078C22⋊C4—41no—
1079C22⋊C4—41no—
1080C22⋊C4—41no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
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—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—41no—
1135C42—41no—
1136C42—42no—
1137C42—42no—
1138C42—81no—
1139C42—81no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—22no—
1152C23—21no—
1153C23—22no—
1154C23—21no—
1155C23—48no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—162no—
1183C23—162no—
1184C23—162no—
1185C23—162no—
1186C23—162no—
1187C23—162no—
1188C23#53212yes—
1189C23C23×D411yescharacteristic
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198D4—22no—
1199D4—22no—
1200D4—22no—
1201D4—22no—
1202D4—48no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—41no—
1215D4—82no—
1216D4—84no—
1217D4—84no—
1218D4—84no—
1219D4—162no—
1220D4—162no—
1221D4—162no—
1222D4—162no—
1223D4—162no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
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—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
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—22no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
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—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
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—84no—
1304C2×C4—84no—
1305C2×C4—82no—
1306C2×C4—82no—
1307C2×C4—162no—
1308C2×C4—162no—
1309C2×C4—162no—
1310C2×C4—162no—
1311C2×C4—162no—
1312C2×C4#53212yes—
1313C2×C4C22×#4111yescharacteristic
1314C2×C4C22×#4111yescharacteristic
1315C2×C4C2×H(5,𝔽2)11yescharacteristic
1316C2×C4C2×H(5,𝔽2)11yescharacteristic
1317C2×C4C2×H(5,𝔽2)11yescharacteristic
1318C2×C4#58511yescharacteristic
1319C8—22no—
1320C8—22no—
1321C8—22no—
1322C8—22no—
1323C8—41no—
1324C8—41no—
1325C8—41no—
1326C8—41no—
1327C22—22no—
1328C22—22no—
1329C22—22no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—42no—
1338C22—42no—
1339C22—41no—
1340C22—42no—
1341C22—41no—
1342C22—42no—
1343C22—41no—
1344C22—42no—
1345C22—41no—
1346C22—42no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—168no—
1370C22C2×#53211yescharacteristic
1371C22#348411yescharacteristic
1372C22#348811yescharacteristic
1373C22#358411yescharacteristic
1374C22#358411yescharacteristic
1375C22#358511yescharacteristic
1376C22#358511yescharacteristic
1377C4—22no—
1378C4—41no—
1379C4—41no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—41no—
1384C4—41no—
1385C4—41no—
1386C4—42no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4#349011yescharacteristic
1402C4#350611yescharacteristic
1403C4#351311yescharacteristic
1404C4#351911yescharacteristic
1405C2—42no—
1406C2—81no—
1407C2—82no—
1408C2—82no—
1409C2—161no—
1410C2—161no—
1411C2#3539211yescharacteristic
1412C2#6071011yescharacteristic
1413C2#6072411yescharacteristic
1414C2#6161411yescharacteristic
1415C2#6162811yescharacteristic
1416C2#6202711yescharacteristic
1417C2#6204711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37361C2semidirect
2. #35523C2semidirect
3. #29564C2semidirect
4. #29506C2semidirect
5. #29461C2semidirect
6. #29457C2semidirect
7. #29096C2semidirect
8. #28995C2semidirect
9. #28922C2semidirect
10. #28878C2semidirect
11. #28788C2semidirect
12. #28630C2semidirect
13. #28579C2semidirect
14. #28569C2semidirect
15. #27259C2semidirect
16. #27256C2semidirect
17. #26984C2semidirect
18. #26819C2semidirect
19. #26262C2semidirect
20. #25793C2semidirect
21. #25601C2semidirect
22. #25506C2semidirect
23. #25419C2semidirect
24. #25129C2semidirect
25. #25124C2semidirect
26. #24277C2semidirect
27. #22201C2semidirect
28. #22059C2semidirect
29. #21458C2semidirect
30. #20929C2semidirect
31. #20561C2semidirect
38. C2×#488C22semidirect
43. C2×#468C22semidirect
52. #2854C22semidirect
53. #2850C22semidirect
62. #2645C22semidirect
63. #2641C22semidirect
66. #2513C22semidirect
67. #2489C22semidirect
75. #2447C22semidirect
80. #2428C22semidirect
95. #2086C22semidirect
96. #2085C22semidirect
97. #2084C22semidirect
98. #2076C22semidirect
100. #2072C22semidirect
101. #2068C22semidirect
103. #2059C22semidirect
104. #2059C22semidirect
106. #2055C22semidirect
107. #2055C22semidirect
112. #2042C22semidirect
113. #2041C22semidirect
115. #2034C22semidirect
117. #2025C22semidirect
122. #2001C22semidirect
124. #2000C22semidirect
127. #1992C22semidirect
128. #1991C22semidirect
131. #1971C22semidirect
132. #1971C22semidirect
136. #1968C22semidirect
138. #1957C22semidirect
139. #1943C22semidirect
140. #1941C22semidirect
142. #1936C22semidirect
143. #1936C22semidirect
146. #1934C22semidirect
147. #1934C22semidirect
148. #1933C22semidirect
149. #1933C22semidirect
150. #1933C22semidirect
151. #1928C22semidirect
152. #1927C22semidirect
153. #1926C22semidirect
154. #1925C22semidirect
155. #1921C22semidirect
156. #1918C22semidirect
158. #1895C22semidirect
159. #1894C22semidirect
160. #1894C22semidirect
163. #1880C22semidirect
164. #1880C22semidirect
171. #1878C22semidirect
176. #1877C22semidirect
179. #1865C22semidirect
181. #1864C22semidirect
188. #1771C22semidirect
189. C8×C4⋊C4C22semidirect
190. #1768C22semidirect
194. #1753C22semidirect
195. #1753C22semidirect
198. C4×C22⋊C8C22semidirect
199. #1746C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#373612
#355232
#295642
#295062
#294612
#294572
#290962
#289952
#289222
#288782
#287882
#286302
#285792
#285692
#272592
#272562
#269842
#268192
#262622
#257932
#256012
#255062
#254192
#251292
#251242
#242772
#222012
#220592
#214582
#209292
#205612