Finite Group Databasebeta

← #6673757

Subgroups — #6673757

Order 512.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3233C211yesmaximal, characteristic, complemented
2C2×#3123C211yesmaximal, characteristic, complemented
3#37799C211yesmaximal, characteristic, complemented
4#35515C211yesmaximal, characteristic, complemented
5#33014C211yesmaximal, characteristic
6#31250C211yesmaximal, characteristic, complemented
7#31241C211yesmaximal, characteristic, complemented
8#31165C211yesmaximal, characteristic, complemented
9#31159C211yesmaximal, characteristic, complemented
10#30959C211yesmaximal, characteristic, complemented
11#30951C211yesmaximal, characteristic, complemented
12#30886C211yesmaximal, characteristic, complemented
13#30886C211yesmaximal, characteristic, complemented
14#29769C211yesmaximal, characteristic, complemented
15#29645C211yesmaximal, characteristic, complemented
16#28321C211yesmaximal, characteristic
17#28130C211yesmaximal, characteristic, complemented
18#26916C211yesmaximal, characteristic, complemented
19#26901C211yesmaximal, characteristic, complemented
20#26837C211yesmaximal, characteristic, complemented
21#26821C211yesmaximal, characteristic, complemented
22#26494C211yesmaximal, characteristic, complemented
23#26481C211yesmaximal, characteristic, complemented
24#26397C211yesmaximal, characteristic, complemented
25#26373C211yesmaximal, characteristic, complemented
26#24617C211yesmaximal, characteristic, complemented
27#24501C211yesmaximal, characteristic, complemented
28#24072C211yesmaximal, characteristic, complemented
29#23936C211yesmaximal, characteristic
30#22604C211yesmaximal, characteristic, complemented
31#22092C211yesmaximal, characteristic, complemented
32C2×#541C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×#518C2211yescharacteristic
36#3233—28no—
37C2×#499C2211yescharacteristic, complemented
38C2×#499C2211yescharacteristic, complemented
39C2×#488C2211yescharacteristic, complemented
40C2×#488C2211yescharacteristic, complemented
41#3123—28no—
42C2×#485C2211yescharacteristic
43C2×#485C2211yescharacteristic
44C2×#485C2211yescharacteristic
45C2×#485C2211yescharacteristic
46C2×#482C2211yescharacteristic
47C2×#482C2211yescharacteristic
48C2×#477C2211yescharacteristic, complemented
49C2×#475C2211yescharacteristic, complemented
50C2×#478C2211yescharacteristic
51C2×#478C2211yescharacteristic
52C2×#476C2211yescharacteristic, complemented
53C2×#474C2211yescharacteristic, complemented
54C2×#461C2211yescharacteristic
55C2×#461C2211yescharacteristic
56C2×#450C2211yescharacteristic
57C2×#450C2211yescharacteristic
58C2×#447C2211yescharacteristic
59C2×#440C2211yescharacteristic
60C2×#440C2211yescharacteristic
61C2×C4×SD16C2211yescharacteristic
62C2×C4×SD16C2211yescharacteristic
63C2×#433C2211yescharacteristic
64C2×#431C2211yescharacteristic
65#2855C2211yescharacteristic
66#2725—21no—
67#2721—21no—
68#2718—21no—
69#2718—21no—
70#2624C2211yescharacteristic
71#2620C2211yescharacteristic
72#2580—21no—
73#2580—21no—
74#2552C2211yescharacteristic, complemented
75#2545C2211yescharacteristic, complemented
76#2538—21no—
77#2538—21no—
78#2475—21no—
79#2468—21no—
80#2466—21no—
81#2454C2211yescharacteristic
82#2454C2211yescharacteristic
83#2454C2211yescharacteristic
84#2454C2211yescharacteristic
85#2454C2211yescharacteristic, complemented
86#2453C2211yescharacteristic, complemented
87#2452C2211yescharacteristic
88#2452C2211yescharacteristic
89#2452C2211yescharacteristic
90#2452C2211yescharacteristic
91#2448C2211yescharacteristic, complemented
92#2446C2211yescharacteristic, complemented
93#2441—21no—
94#2437—21no—
95#2437—21no—
96#2437—21no—
97#2437—21no—
98#2367C2211yescharacteristic, complemented
99Q8×C4⋊C4C2211yescharacteristic, complemented
100#2323C2211yescharacteristic
101#2317C2211yescharacteristic
102#2316C2211yescharacteristic
103#2309C2211yescharacteristic
104#2296C2211yescharacteristic
105C2×#390C2211yescharacteristic
106#2094C2211yescharacteristic
107#2093C2211yescharacteristic
108#2088C2211yescharacteristic, complemented
109#2086C2211yescharacteristic, complemented
110#2084C2211yescharacteristic, complemented
111#2083C2211yescharacteristic, complemented
112#2068C2211yescharacteristic, complemented
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic, complemented
115#2066C2211yescharacteristic, complemented
116#2065C2211yescharacteristic
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic, complemented
120#2065C2211yescharacteristic, complemented
121#2065C2211yescharacteristic, complemented
122#2059C2211yescharacteristic, complemented
123#2059C2211yescharacteristic, complemented
124#2059C2211yescharacteristic, complemented
125#2059C2211yescharacteristic, complemented
126#2058C2211yescharacteristic, complemented
127#2057C2211yescharacteristic, complemented
128#2055C2211yescharacteristic
129#2055C2211yescharacteristic
130#2055C2211yescharacteristic
131#2055C2211yescharacteristic
132#2043C2211yescharacteristic, complemented
133#2043C2211yescharacteristic, complemented
134#2042C2211yescharacteristic, complemented
135#2042C2211yescharacteristic, complemented
136#2026C2211yescharacteristic, complemented
137#2026C2211yescharacteristic, complemented
138#2025C2211yescharacteristic
139#2025C2211yescharacteristic
140#2024C2211yescharacteristic, complemented
141#2024C2211yescharacteristic, complemented
142#2012C2211yescharacteristic
143#2012C2211yescharacteristic
144#2012C2211yescharacteristic
145#2012C2211yescharacteristic
146#1973C2211yescharacteristic
147#1972C2211yescharacteristic
148#1970C2211yescharacteristic
149#1968C2211yescharacteristic
150#1968C2211yescharacteristic
151#1968C2211yescharacteristic
152#1944C2211yescharacteristic, complemented
153#1943C2211yescharacteristic, complemented
154#1941C2211yescharacteristic, complemented
155#1941C2211yescharacteristic, complemented
156#1940C2211yescharacteristic, complemented
157#1939C2211yescharacteristic, complemented
158#1936C2211yescharacteristic, complemented
159#1935C2211yescharacteristic, complemented
160#1934C2211yescharacteristic
161#1934C2211yescharacteristic
162#1934C2211yescharacteristic, complemented
163#1933C2211yescharacteristic, complemented
164#1926C2211yescharacteristic
165#1925C2211yescharacteristic
166#1921C2211yescharacteristic, complemented
167#1920C2211yescharacteristic, complemented
168#1917C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1916C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic
180#1879C2211yescharacteristic
181#1879C2211yescharacteristic
182#1874C2211yescharacteristic
183#1872C2211yescharacteristic
184#1872C2211yescharacteristic
185#1865C2211yescharacteristic, complemented
186#1865C2211yescharacteristic, complemented
187#1865C2211yescharacteristic, complemented
188#1865C2211yescharacteristic, complemented
189#1864C2211yescharacteristic
190#1864C2211yescharacteristic
191#1863C2211yescharacteristic, complemented
192#1863C2211yescharacteristic, complemented
193#1862C2211yescharacteristic
194#1862C2211yescharacteristic
195#1853C2211yescharacteristic
196#1825C2211yescharacteristic
197#1825C2211yescharacteristic
198#1818C2211yescharacteristic
199#1817C2211yescharacteristic
200#1798C2211yescharacteristic
201#1786C2211yescharacteristic
202#1771C2211yescharacteristic, complemented
203C8×C4⋊C4C2211yescharacteristic, complemented
204#1750C2211yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212#541—24no—
213#541—42no—
214#533—24no—
215#533—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219#529—24no—
220#529—42no—
221C2×#126—21no—
222C2×#126—21no—
223C2×#126—21no—
224C2×#125—21no—
225C2×#125—21no—
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#123—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×#121C2311yescharacteristic
242#518—24no—
243#518—42no—
244C2×C4×Q8—21no—
245C2×C4×Q8—21no—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4—21no—
251C2×C4×D4—21no—
252C2×C4×D4—21no—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×#117—21no—
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C22⋊C4—21no—
265C22×C22⋊C4—21no—
266C22×C22⋊C4—21no—
267C22×C22⋊C4—21no—
268C22×C42C2311yescharacteristic
269#499—24no—
270#499—24no—
271#488—24no—
272#488—24no—
273#485—24no—
274#485—24no—
275#485—42no—
276#485D418yes—
277#482—24no—
278#482—24no—
279#478—24no—
280#478—24no—
281#477—24no—
282#476—24no—
283#475—24no—
284#474—24no—
285#461—24no—
286#461—24no—
287#450—24no—
288#450—24no—
289#447—42no—
290#440—24no—
291#440—24no—
292C4×SD16—24no—
293C4×SD16—24no—
294#433—24no—
295#431—24no—
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×C22⋊C8C2311yescharacteristic
346C2×C22⋊C8C2311yescharacteristic
347C2×C22⋊C8C2311yescharacteristic
348C2×#97C2311yescharacteristic
349C2×#97C2311yescharacteristic
350C2×C4×C8C2311yescharacteristic
351C2×C4×C8C2311yescharacteristic
352C2×C4×C8C2311yescharacteristic
353C2×C4×C8C2311yescharacteristic
354#400—21no—
355#400—21no—
356#399—21no—
357#399—21no—
358#399—21no—
359#399—21no—
360#399—21no—
361#399—21no—
362#399—21no—
363#398—21no—
364#398—21no—
365#398—21no—
366#398—21no—
367#397—21no—
368#397—21no—
369#396—21no—
370#396—21no—
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#396—21no—
382#394—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#393—21no—
387#393—21no—
388#393—21no—
389#393—21no—
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#391C2311yescharacteristic
394#390—21no—
395#390—21no—
396#390—21no—
397#390—21no—
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#389—21no—
410#389—21no—
411#389—21no—
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389D411yescharacteristic
417#389D411yescharacteristic
418#389D411yescharacteristic
419#389D411yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
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#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#387—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#385—21no—
459#385—21no—
460#385D411yescharacteristic
461#385D411yescharacteristic
462#385D411yescharacteristic
463#385D411yescharacteristic
464#384—21no—
465#384—21no—
466#384—21no—
467#384C2311yescharacteristic
468#382—21no—
469#381—21no—
470#380—21no—
471#380—21no—
472#380—21no—
473#380—21no—
474#380—21no—
475#380—21no—
476#380—21no—
477#380C2311yescharacteristic
478#379—21no—
479#379—21no—
480C4×C4⋊C4—21no—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C22⋊C4—21no—
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#336C2311yescharacteristic
504#336C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C25—21no—
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—41no—
527C22×D4—41no—
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×C4C2×D411yescharacteristic
538C23×C4C2×D411yescharacteristic
539C23×C4C2411yescharacteristic
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C4⋊Q8—22no—
567C4⋊Q8—22no—
568C4⋊Q8—22no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572#126—44no—
573#126—44no—
574#126—44no—
575#125—22no—
576#125—22no—
577#125—22no—
578#125—22no—
579#125—41no—
580#125—41no—
581#125—41no—
582#125—41no—
583#125—44no—
584#125—44no—
585#124—22no—
586#124—41no—
587#124—41no—
588#124—41no—
589#123—44no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593C22⋊Q8—44no—
594C22⋊Q8—44no—
595C22⋊Q8—82no—
596C22⋊Q8—82no—
597C22⋊Q8—82no—
598C22⋊Q8—82no—
599C22⋊Q8C2×D414yes—
600#121—22no—
601#121—22no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—44no—
606C4×Q8—44no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—44no—
623C4×D4—44no—
624C4×D4—44no—
625#117—22no—
626#117—22no—
627#117—22no—
628#117—22no—
629#117—22no—
630#117—41no—
631#117—41no—
632#117—44no—
633#117C2×D414yes—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
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—21no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
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—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—44no—
731C2×C22⋊C4—44no—
732C2×C22⋊C4—82no—
733C2×C22⋊C4—82no—
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C42—21no—
739C2×C42—22no—
740C2×C42—22no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42C2×D411yescharacteristic
748C2×C42C2×D411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755#107—22no—
756#107—22no—
757#107—22no—
758#107—22no—
759#107—41no—
760#107C2×D414yes—
761#106—22no—
762#106—22no—
763#106—22no—
764#106—22no—
765#106—41no—
766#106—41no—
767#106—41no—
768#106C2×D414yes—
769C4⋊C8—22no—
770C4⋊C8—22no—
771C4⋊C8—22no—
772C4⋊C8—22no—
773C4⋊C8—41no—
774C4⋊C8—41no—
775#103—22no—
776#103—22no—
777#103—22no—
778#103—22no—
779#103—41no—
780#103—41no—
781#103—41no—
782#103—41no—
783#103—41no—
784#103—41no—
785#103C2×D414yes—
786#103C2×D414yes—
787#102—22no—
788#102—22no—
789#102—22no—
790#102—22no—
791#102—22no—
792#102—22no—
793#102—22no—
794#102—22no—
795#102—22no—
796#102—22no—
797#102—41no—
798#102—41no—
799#102—41no—
800#102—41no—
801#102—41no—
802#102—41no—
803C22⋊C8—22no—
804C22⋊C8—22no—
805C22⋊C8—22no—
806C22⋊C8C2×D414yes—
807#97—22no—
808#97—41no—
809C4×C8—22no—
810C4×C8—22no—
811C4×C8—22no—
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#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844C24—24no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—42no—
849C24—42no—
850C24—81no—
851C24—81no—
852C24—81no—
853C24—81no—
854C24C22×D411yescharacteristic
855C2×Q8—21no—
856C2×Q8—21no—
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—42no—
867C2×Q8—42no—
868C2×Q8—42no—
869C2×Q8—42no—
870C2×Q8—81no—
871C2×Q8—81no—
872C2×Q8C22×D412yes—
873C2×D4—24no—
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—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D42−1+412yes—
900C2×D42−1+412yes—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—22no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—41no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D412yes—
955C22×C4C22×D411yescharacteristic
956C22×C4H(5,𝔽2)12yes—
957C22×C4C2511yescharacteristic
958SD16—44no—
959SD16—44no—
960SD16—44no—
961SD16—44no—
962D8—82no—
963D8—82no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8C22×D412yes—
987C2×C8C22×D412yes—
988C4⋊C4—24no—
989C4⋊C4—22no—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4C22×D412yes—
1054C4⋊C4C22×D412yes—
1055C4⋊C4C22×D412yes—
1056C22⋊C4—24no—
1057C22⋊C4—24no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C42—22no—
1098C42—22no—
1099C42—24no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—42no—
1113C42—42no—
1114C42—42no—
1115C42—42no—
1116C42—42no—
1117C42—81no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—22no—
1125C23—22no—
1126C23—48no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—84no—
1147C23—84no—
1148C23—162no—
1149C23—162no—
1150C23—162no—
1151C23—162no—
1152C23D4212yes—
1153C23C23×D411yescharacteristic
1154Q8—22no—
1155Q8—22no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—84no—
1163Q8—84no—
1164D4—22no—
1165D4—22no—
1166D4—22no—
1167D4—22no—
1168D4—48no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—84no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—44no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—84no—
1260C2×C4—82no—
1261C2×C4—162no—
1262C2×C4—162no—
1263C2×C4—162no—
1264C2×C4—162no—
1265C2×C4—162no—
1266C2×C4D4212yes—
1267C2×C4#57712yes—
1268C2×C4C23×D411yescharacteristic
1269C2×C4C2×H(5,𝔽2)11yescharacteristic
1270C2×C4C2×2−1+411yescharacteristic
1271C2×C4C2×2−1+411yescharacteristic
1272C2×C4#58511yescharacteristic
1273C2×C4#58511yescharacteristic
1274C8—22no—
1275C8—22no—
1276C8—41no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—168no—
1311C22#344911yescharacteristic
1312C22C2×D4211yescharacteristic
1313C22#348611yescharacteristic
1314C22C2×#57711yescharacteristic
1315C22#358411yescharacteristic
1316C22#358411yescharacteristic
1317C22#358511yescharacteristic
1318C4—22no—
1319C4—22no—
1320C4—42no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—42no—
1329C4—42no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—42no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4#348911yescharacteristic
1345C4#348911yescharacteristic
1346C4#353511yescharacteristic
1347C4#353511yescharacteristic
1348C2—42no—
1349C2—82no—
1350C2—82no—
1351C2—161no—
1352C2#3765311yescharacteristic
1353C2#6099411yescharacteristic
1354C2#6101011yescharacteristic
1355C2#6105511yescharacteristic
1356C2#6107711yescharacteristic
1357C2#6185511yescharacteristic
1358C2#6186411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3233C2semidirect
2. C2×#3123C2semidirect
3. #37799C2semidirect
4. #35515C2semidirect
6. #31250C2semidirect
7. #31241C2semidirect
8. #31165C2semidirect
9. #31159C2semidirect
10. #30959C2semidirect
11. #30951C2semidirect
12. #30886C2semidirect
13. #30886C2semidirect
14. #29769C2semidirect
15. #29645C2semidirect
17. #28130C2semidirect
18. #26916C2semidirect
19. #26901C2semidirect
20. #26837C2semidirect
21. #26821C2semidirect
22. #26494C2semidirect
23. #26481C2semidirect
24. #26397C2semidirect
25. #26373C2semidirect
26. #24617C2semidirect
27. #24501C2semidirect
28. #24072C2semidirect
30. #22604C2semidirect
31. #22092C2semidirect
37. C2×#499C22semidirect
38. C2×#499C22semidirect
39. C2×#488C22semidirect
40. C2×#488C22semidirect
48. C2×#477C22semidirect
49. C2×#475C22semidirect
52. C2×#476C22semidirect
53. C2×#474C22semidirect
74. #2552C22semidirect
75. #2545C22semidirect
85. #2454C22semidirect
86. #2453C22semidirect
91. #2448C22semidirect
92. #2446C22semidirect
98. #2367C22semidirect
99. Q8×C4⋊C4C22semidirect
108. #2088C22semidirect
109. #2086C22semidirect
110. #2084C22semidirect
111. #2083C22semidirect
112. #2068C22semidirect
114. #2067C22semidirect
115. #2066C22semidirect
119. #2065C22semidirect
120. #2065C22semidirect
121. #2065C22semidirect
122. #2059C22semidirect
123. #2059C22semidirect
124. #2059C22semidirect
125. #2059C22semidirect
126. #2058C22semidirect
127. #2057C22semidirect
132. #2043C22semidirect
133. #2043C22semidirect
134. #2042C22semidirect
135. #2042C22semidirect
136. #2026C22semidirect
137. #2026C22semidirect
140. #2024C22semidirect
141. #2024C22semidirect
152. #1944C22semidirect
153. #1943C22semidirect
154. #1941C22semidirect
155. #1941C22semidirect
156. #1940C22semidirect
157. #1939C22semidirect
158. #1936C22semidirect
159. #1935C22semidirect
162. #1934C22semidirect
163. #1933C22semidirect
166. #1921C22semidirect
167. #1920C22semidirect
168. #1917C22semidirect
169. #1916C22semidirect
170. #1916C22semidirect
171. #1916C22semidirect
185. #1865C22semidirect
186. #1865C22semidirect
187. #1865C22semidirect
188. #1865C22semidirect
191. #1863C22semidirect
192. #1863C22semidirect
202. #1771C22semidirect
203. C8×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
C2×#32332
C2×#31232
#377992
#355152
#330142
#312502
#312412
#311652
#311592
#309592
#309512
#308862
#297692
#296452
#283212
#281302
#269162
#269012
#268372
#268212
#264942
#264812
#263972
#263732
#246172
#245012
#240722
#239362
#226042
#220922