Finite Group Databasebeta

← #7522930

Subgroups — #7522930

Order 512.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3375C211yesmaximal, characteristic, complemented
2C22×#474C211yesmaximal, characteristic, complemented
3#59151C211yesmaximal, characteristic, complemented
4#36441C211yesmaximal, characteristic
5#31166C211yesmaximal, characteristic, complemented
6#31152C211yesmaximal, characteristic, complemented
7#30821C211yesmaximal, characteristic, complemented
8#30805C211yesmaximal, characteristic, complemented
9#28428C211yesmaximal, characteristic, complemented
10#27262C211yesmaximal, characteristic, complemented
11#27254C211yesmaximal, characteristic
12#26912C211yesmaximal, characteristic, complemented
13#26893C211yesmaximal, characteristic, complemented
14#26478C211yesmaximal, characteristic, complemented
15#26460C211yesmaximal, characteristic, complemented
16#26342C211yesmaximal, characteristic, complemented
17#26336C211yesmaximal, characteristic, complemented
18#25908C211yesmaximal, characteristic, complemented
19#25660C211yesmaximal, characteristic, complemented
20#25481C211yesmaximal, characteristic, complemented
21#25285C211yesmaximal, characteristic, complemented
22#25084C211yesmaximal, characteristic, complemented
23#25080C211yesmaximal, characteristic
24#24755C211yesmaximal, characteristic, complemented
25#24696C211yesmaximal, characteristic, complemented
26#24341C211yesmaximal, characteristic, complemented
27#23079C211yesmaximal, characteristic, complemented
28#23032C211yesmaximal, characteristic, complemented
29#23024C211yesmaximal, characteristic, complemented
30#22954C211yesmaximal, characteristic, complemented
31#21453C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×Q82C2211yescharacteristic, complemented
34C22×C4⋊Q8C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36#3375—28no—
37C2×#489C2211yescharacteristic
38C2×#489C2211yescharacteristic, complemented
39C2×#489C2211yescharacteristic, complemented
40C2×#486C2211yescharacteristic
41C2×#477C2211yescharacteristic, complemented
42C2×#474—28no—
43C2×#474C2211yescharacteristic
44C2×#474C2211yescharacteristic
45C2×#474C2211yescharacteristic
46C2×#474C2211yescharacteristic
47C2×#474C2211yescharacteristic
48C2×#474C2211yescharacteristic
49C2×#474C2211yescharacteristic
50C2×#474C2211yescharacteristic
51C2×#474C2211yescharacteristic, complemented
52C2×#467C2211yescharacteristic
53C2×#465C2211yescharacteristic
54C2×#464C2211yescharacteristic
55C2×#464C2211yescharacteristic, complemented
56C2×#460C2211yescharacteristic
57C2×#450C2211yescharacteristic
58C2×#446C2211yescharacteristic, complemented
59C2×#440C2211yescharacteristic
60C2×#440C2211yescharacteristic
61C2×#440C2211yescharacteristic, complemented
62C2×C4×Q16C2211yescharacteristic, complemented
63C22×#107C2211yescharacteristic
64C22×#107C2211yescharacteristic
65C22×C4⋊C8C2211yescharacteristic
66C22×#102C2211yescharacteristic
67C22×#102C2211yescharacteristic
68#2850C2211yescharacteristic
69#2849—21no—
70#2734—21no—
71#2734—21no—
72#2602—21no—
73#2600—21no—
74#2580C2211yescharacteristic
75#2567C2211yescharacteristic, complemented
76#2567C2211yescharacteristic, complemented
77#2551—21no—
78#2551C2211yescharacteristic, complemented
79#2551C2211yescharacteristic, complemented
80#2544C2211yescharacteristic
81#2472—21no—
82#2459—21no—
83#2455—21no—
84#2451—21no—
85#2451C2211yescharacteristic, complemented
86#2451C2211yescharacteristic, complemented
87#2447C2211yescharacteristic
88#2445C2211yescharacteristic
89#2440—21no—
90#2440C2211yescharacteristic
91#2440C2211yescharacteristic
92#2435C2211yescharacteristic
93#2434—21no—
94#2434—21no—
95#2433C2211yescharacteristic
96#2418—21no—
97#2369C2211yescharacteristic, complemented
98#2367C2211yescharacteristic
99#2366C2211yescharacteristic
100#2361C2211yescharacteristic
101#2360—21no—
102#2360C2211yescharacteristic
103#2360C2211yescharacteristic
104#2360C2211yescharacteristic
105#2357C2211yescharacteristic
106C4×C22⋊Q8C2211yescharacteristic
107C4×C22⋊Q8C2211yescharacteristic
108C4×#120—21no—
109#2095C2211yescharacteristic, complemented
110#2093C2211yescharacteristic, complemented
111#2087C2211yescharacteristic, complemented
112#2086C2211yescharacteristic, complemented
113#2071C2211yescharacteristic
114#2071C2211yescharacteristic
115#2068C2211yescharacteristic, complemented
116#2067C2211yescharacteristic
117#2067C2211yescharacteristic, complemented
118#2067C2211yescharacteristic, complemented
119#2066C2211yescharacteristic, complemented
120#2065C2211yescharacteristic
121#2057C2211yescharacteristic, complemented
122#2057C2211yescharacteristic, complemented
123#2056C2211yescharacteristic, complemented
124#2055C2211yescharacteristic
125#2055C2211yescharacteristic
126#2055C2211yescharacteristic, complemented
127#2042C2211yescharacteristic
128#2042C2211yescharacteristic
129#2042C2211yescharacteristic
130#2041C2211yescharacteristic
131#2041C2211yescharacteristic
132#2041C2211yescharacteristic
133#2024C2211yescharacteristic, complemented
134#2024C2211yescharacteristic, complemented
135#2023C2211yescharacteristic
136#2023C2211yescharacteristic
137#2023C2211yescharacteristic, complemented
138#2023C2211yescharacteristic, complemented
139#2015C2211yescharacteristic
140#2014C2211yescharacteristic
141#1993C2211yescharacteristic, complemented
142#1993C2211yescharacteristic, complemented
143#1985C2211yescharacteristic, complemented
144#1983C2211yescharacteristic
145#1983C2211yescharacteristic, complemented
146#1982C2211yescharacteristic
147#1973C2211yescharacteristic, complemented
148#1969C2211yescharacteristic, complemented
149#1959C2211yescharacteristic
150#1957C2211yescharacteristic
151#1949C2211yescharacteristic, complemented
152#1947C2211yescharacteristic, complemented
153#1947C2211yescharacteristic, complemented
154#1944C2211yescharacteristic, complemented
155#1942C2211yescharacteristic, complemented
156#1940C2211yescharacteristic, complemented
157#1940C2211yescharacteristic, complemented
158#1939C2211yescharacteristic, complemented
159#1936C2211yescharacteristic
160#1936C2211yescharacteristic
161#1934C2211yescharacteristic
162#1934C2211yescharacteristic
163#1928C2211yescharacteristic, complemented
164#1928C2211yescharacteristic, complemented
165#1928C2211yescharacteristic, complemented
166#1926C2211yescharacteristic
167#1925C2211yescharacteristic
168#1925C2211yescharacteristic, complemented
169#1921C2211yescharacteristic, complemented
170#1918C2211yescharacteristic, complemented
171#1917C2211yescharacteristic, complemented
172#1916C2211yescharacteristic, complemented
173#1893C2211yescharacteristic
174#1892C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1874C2211yescharacteristic
180#1874C2211yescharacteristic
181#1872C2211yescharacteristic
182#1872C2211yescharacteristic
183#1872C2211yescharacteristic
184#1863C2211yescharacteristic, complemented
185#1863C2211yescharacteristic, complemented
186#1863C2211yescharacteristic, complemented
187#1863C2211yescharacteristic, complemented
188#1862C2211yescharacteristic
189#1862C2211yescharacteristic
190#1862C2211yescharacteristic, complemented
191#1862C2211yescharacteristic, complemented
192#1852C2211yescharacteristic
193#1850C2211yescharacteristic
194#1850C2211yescharacteristic
195#1805C2211yescharacteristic, complemented
196#1786C2211yescharacteristic
197#1776C2211yescharacteristic, complemented
198C4×#107C2211yescharacteristic, complemented
199#1771C2211yescharacteristic, complemented
200#1762C2211yescharacteristic
201#1762C2211yescharacteristic
202#1752C2211yescharacteristic
203C8×C22⋊C4C2211yescharacteristic
204#1749C2211yescharacteristic
205C23×Q8—21no—
206C23×D4C2311yescharacteristic
207C24×C4—21no—
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#559—24no—
215#559—42no—
216Q82—24no—
217Q82—42no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8—21no—
220C2×C4⋊Q8—21no—
221C2×C4⋊Q8—21no—
222C2×C4⋊Q8—21no—
223C2×C4⋊Q8—24no—
224C2×C4⋊Q8—21no—
225C2×C4⋊Q8—21no—
226C2×C4⋊Q8—42no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×#127C2311yescharacteristic
234C2×#127C2311yescharacteristic
235C2×#124—21no—
236C2×#124C2311yescharacteristic
237C2×#124C2311yescharacteristic
238C2×#124C2311yescharacteristic
239C2×#123—21no—
240C2×#123—21no—
241C2×#123—21no—
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8D411yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#120—21no—
249C2×#120—21no—
250C2×C4×Q8—21no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×D4—21no—
257C2×C4×D4—21no—
258C2×C4×D4—21no—
259C2×C4×D4—24no—
260C2×C4×D4—21no—
261C2×C4×D4—21no—
262C2×C4×D4—42no—
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C22×C4⋊C4—21no—
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C22⋊C4—21no—
273C22×C42C2311yescharacteristic
274#489—24no—
275#489—24no—
276#489—42no—
277#486—24no—
278#477—24no—
279#474—24no—
280#474—24no—
281#474—24no—
282#474—24no—
283#474—24no—
284#474—24no—
285#474—24no—
286#474—24no—
287#474D418yescomplemented
288#467—24no—
289#465—24no—
290#464—24no—
291#464—24no—
292#460—24no—
293#450—24no—
294#446—24no—
295#440—24no—
296#440—24no—
297#440—42no—
298C4×Q16—24no—
299C2×#107—24no—
300C2×#107—24no—
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#107C2311yescharacteristic
307C2×#107C2311yescharacteristic
308C2×#107C2311yescharacteristic
309C2×#107C2311yescharacteristic
310C2×#107C2311yescharacteristic
311C2×#107C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×C4⋊C8—24no—
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320C2×C4⋊C8C2311yescharacteristic
321C2×C4⋊C8C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#102—24no—
334C2×#102—24no—
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×#102C2311yescharacteristic
351C2×#102C2311yescharacteristic
352C2×#102C2311yescharacteristic
353C2×#102C2311yescharacteristic
354C2×#102C2311yescharacteristic
355C2×#102C2311yescharacteristic
356C2×C22⋊C8C2311yescharacteristic
357C2×C22⋊C8C2311yescharacteristic
358C2×#97C2311yescharacteristic
359C2×#97C2311yescharacteristic
360C2×#97C2311yescharacteristic
361C2×#97C2311yescharacteristic
362C2×C4×C8C2311yescharacteristic
363C2×C4×C8C2311yescharacteristic
364#399—21no—
365#398—21no—
366#398—21no—
367#398—21no—
368#398—21no—
369#397—21no—
370#397—21no—
371#395—21no—
372#395—21no—
373#395—21no—
374#395—21no—
375#395—21no—
376#395—21no—
377#395—21no—
378#395—21no—
379#395—21no—
380#395—21no—
381#395—21no—
382#395—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#394—21no—
387#394—21no—
388#394—21no—
389#393—21no—
390#392—21no—
391#392—21no—
392#391—21no—
393#391—21no—
394#391—21no—
395#391—21no—
396#391—21no—
397#391D411yescharacteristic
398#391C2311yescharacteristic
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#390—21no—
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#389—21no—
411#389—21no—
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389—21no—
418#389D411yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387D411yescharacteristic
442#387D411yescharacteristic
443#386—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#386—21no—
448#386—21no—
449#386—21no—
450#386—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#385—21no—
461#385—21no—
462#385D411yescharacteristic
463#385D411yescharacteristic
464#384—21no—
465#384C2311yescharacteristic
466#384C2311yescharacteristic
467#382C2311yescharacteristic
468#381—21no—
469#381—21no—
470#380D411yescharacteristic
471#380C2311yescharacteristic
472#379—21no—
473#379—21no—
474C4×C4⋊C4—21no—
475C4×C4⋊C4—21no—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C22⋊C4—21no—
485C4×C22⋊C4—21no—
486C4×C22⋊C4—21no—
487C4×C22⋊C4—21no—
488C4×C22⋊C4—21no—
489C4×C22⋊C4—21no—
490C4×C22⋊C4C2311yescharacteristic
491C4×C22⋊C4C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518C25—21no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—21no—
522C22×Q8—21no—
523C22×Q8—21no—
524C22×Q8—21no—
525C22×Q8—44no—
526C22×Q8—82no—
527C22×Q8—82no—
528C22×Q8C2×D411yescharacteristic
529C22×Q8C2411yescharacteristic
530C22×Q8C2411yescharacteristic
531C22×D4—22no—
532C22×D4—22no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—41no—
542C22×D4—41no—
543C22×D4C2411yescharacteristic
544C22×D4C2411yescharacteristic
545C22×D4C2411yescharacteristic
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4—21no—
554C23×C4—44no—
555C23×C4—82no—
556C23×C4—82no—
557C23×C4C2×D411yescharacteristic
558C23×C4C2×D411yescharacteristic
559C23×C4C2411yescharacteristic
560C2×Q16—22no—
561C2×Q16—22no—
562C2×Q16—41no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C22×C8—22no—
573C22×C8—22no—
574C22×C8—22no—
575C22×C8—22no—
576C22×C8—41no—
577C22×C8—41no—
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C4⋊Q8—22no—
587C4⋊Q8—22no—
588C4⋊Q8—22no—
589C4⋊Q8—22no—
590C4⋊Q8—22no—
591C4⋊Q8—22no—
592C4⋊Q8—22no—
593C4⋊Q8—41no—
594C4⋊Q8—41no—
595C4⋊Q8—41no—
596C4⋊Q8—41no—
597C4⋊Q8—44no—
598C4⋊Q8—44no—
599C4⋊Q8—44no—
600C4⋊Q8—44no—
601C4⋊Q8—44no—
602C4⋊Q8—82no—
603C4⋊Q8—82no—
604C4⋊Q8C2×D414yes—
605#127—22no—
606#127—22no—
607#127—41no—
608#127—41no—
609#124—22no—
610#124—22no—
611#124—22no—
612#124—22no—
613#124—41no—
614#124—41no—
615#124—44no—
616#123—44no—
617#123—44no—
618#123—82no—
619C22⋊Q8—22no—
620C22⋊Q8—24no—
621C22⋊Q8—22no—
622C22⋊Q8—22no—
623C22⋊Q8—82no—
624C22⋊Q8—82no—
625C22⋊Q8#4114yes—
626#121—22no—
627#121—22no—
628#120—44no—
629#120—82no—
630C4×Q8—22no—
631C4×Q8—22no—
632C4×Q8—22no—
633C4×Q8—22no—
634C4×Q8—22no—
635C4×Q8—22no—
636C4×Q8—22no—
637C4×Q8—41no—
638C4×Q8—41no—
639C4×Q8—41no—
640C4×Q8—44no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—22no—
647C4×D4—44no—
648C4×D4—41no—
649C4×D4—41no—
650C4×D4—41no—
651C4×D4—44no—
652C4×D4—44no—
653C4×D4—82no—
654C4×D4—82no—
655C4×D4C2×D414yes—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
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—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—41no—
688C2×C4⋊C4—41no—
689C2×C4⋊C4—41no—
690C2×C4⋊C4—44no—
691C2×C4⋊C4C2×D411yescharacteristic
692C2×C4⋊C4C2×D411yescharacteristic
693C2×C4⋊C4C2×D411yescharacteristic
694C2×C4⋊C4C2×D411yescharacteristic
695C2×C4⋊C4C2×D411yescharacteristic
696C2×C4⋊C4C2×D411yescharacteristic
697C2×C4⋊C4C2×D411yescharacteristic
698C2×C4⋊C4C2×D411yescharacteristic
699C2×C4⋊C4C2×D411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—44no—
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C42—22no—
744C2×C42—22no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42C2×D411yescharacteristic
755C2×C42C2×D411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762#107—22no—
763#107—22no—
764#107—22no—
765#107—22no—
766#107—22no—
767#107—22no—
768#107—22no—
769#107—22no—
770#107—41no—
771#107C2×D414yes—
772#107C2×D414yes—
773#106—22no—
774C4⋊C8—22no—
775C4⋊C8—22no—
776C4⋊C8—22no—
777C4⋊C8—22no—
778C4⋊C8—22no—
779C4⋊C8—41no—
780C4⋊C8—41no—
781C4⋊C8C2×D414yes—
782#103—22no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—41no—
790#103—41no—
791#103—41no—
792#103—41no—
793#102—22no—
794#102—22no—
795#102—22no—
796#102—22no—
797#102—22no—
798#102—22no—
799#102—22no—
800#102—22no—
801#102—22no—
802#102—22no—
803#102—22no—
804#102—22no—
805#102—22no—
806#102—22no—
807#102—41no—
808#102—41no—
809#102—41no—
810#102—41no—
811#102—41no—
812#102C2×D414yes—
813#102C2×D414yes—
814C22⋊C8—22no—
815C22⋊C8—22no—
816#97—22no—
817#97—22no—
818#97—22no—
819#97—41no—
820C4×C8—22no—
821C4×C8—41no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95C2×D411yescharacteristic
850#95C2×D411yescharacteristic
851#95C2×D411yescharacteristic
852#95C2×D411yescharacteristic
853#95C2×D411yescharacteristic
854#95C2×D411yescharacteristic
855#95C2×D411yescharacteristic
856#95C2×D411yescharacteristic
857#95C2×D411yescharacteristic
858#95C2×D411yescharacteristic
859C24—21no—
860C24—21no—
861C24—21no—
862C24—42no—
863C24—42no—
864C24—42no—
865C24—42no—
866C24—42no—
867C24—81no—
868C24—81no—
869C24C22×D411yescharacteristic
870C2×Q8—22no—
871C2×Q8—24no—
872C2×Q8—22no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—41no—
885C2×Q8—42no—
886C2×Q8—42no—
887C2×Q8—42no—
888C2×Q8—42no—
889C2×Q8—42no—
890C2×Q8—42no—
891C2×Q8—42no—
892C2×Q8—81no—
893C2×Q8—81no—
894C2×Q8—81no—
895C2×Q8—81no—
896C2×Q8—81no—
897C2×Q8—81no—
898C2×Q8—81no—
899C2×Q8—81no—
900C2×Q8—81no—
901C2×Q8—81no—
902C2×Q8—816no—
903C2×Q8C2×#4112yes—
904C2×D4—28no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—44no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4—81no—
940C2×D4—81no—
941C2×D4—81no—
942C2×D4C22×D412yes—
943C2×D42−1+412yes—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—22no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—22no—
958C22×C4—24no—
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—41no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—816no—
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×C4C22×D411yescharacteristic
1005C22×C4C2×#4112yes—
1006C22×C42−1+412yes—
1007C22×C4C2511yescharacteristic
1008Q16—44no—
1009SD16—44no—
1010SD16—44no—
1011SD16—44no—
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—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—44no—
1035C2×C8—44no—
1036C2×C8C22×D412yes—
1037C2×C8C22×D412yes—
1038C4⋊C4—24no—
1039C4⋊C4—22no—
1040C4⋊C4—22no—
1041C4⋊C4—22no—
1042C4⋊C4—24no—
1043C4⋊C4—22no—
1044C4⋊C4—22no—
1045C4⋊C4—22no—
1046C4⋊C4—22no—
1047C4⋊C4—22no—
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—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—41no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
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⋊C4C22×D412yes—
1094C4⋊C4C22×D412yes—
1095C4⋊C4C22×D412yes—
1096C4⋊C4C2×#4112yes—
1097C22⋊C4—24no—
1098C22⋊C4—22no—
1099C22⋊C4—22no—
1100C22⋊C4—22no—
1101C22⋊C4—24no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—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#13714yes—
1128C42—22no—
1129C42—22no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—42no—
1141C42—42no—
1142C42—42no—
1143C42—42no—
1144C42—42no—
1145C42—81no—
1146C42—81no—
1147C42—81no—
1148C42—81no—
1149C42C22×D412yes—
1150C42H(5,𝔽2)12yes—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—22no—
1156C23—22no—
1157C23—48no—
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—84no—
1178C23—84no—
1179C23—84no—
1180C23—84no—
1181C23—84no—
1182C23—84no—
1183C23#54812yes—
1184C23C2×#13712yes—
1185C23#57612yes—
1186C23C23×D411yescharacteristic
1187Q8—22no—
1188Q8—22no—
1189Q8—44no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—84no—
1197Q8—84no—
1198Q8—84no—
1199Q8—84no—
1200Q8—162no—
1201Q8—162no—
1202D4—22no—
1203D4—22no—
1204D4—22no—
1205D4—22no—
1206D4—48no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—41no—
1215D4—84no—
1216D4—84no—
1217D4—84no—
1218D4—162no—
1219D4—162no—
1220C2×C4—28no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
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—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
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—44no—
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—84no—
1299C2×C4—84no—
1300C2×C4—84no—
1301C2×C4—84no—
1302C2×C4—84no—
1303C2×C4—84no—
1304C2×C4—84no—
1305C2×C4—162no—
1306C2×C4D4212yes—
1307C2×C4D4212yes—
1308C2×C4#54812yes—
1309C2×C4C2×#13712yes—
1310C2×C4C2×#13712yes—
1311C2×C4#57612yes—
1312C2×C4C23×D411yescharacteristic
1313C2×C4C22×#4111yescharacteristic
1314C2×C4C2×H(5,𝔽2)11yescharacteristic
1315C2×C4C2×2−1+411yescharacteristic
1316C2×C4C2×2−1+411yescharacteristic
1317C2×C4#58511yescharacteristic
1318C8—22no—
1319C8—22no—
1320C8—41no—
1321C8—41no—
1322C8—41no—
1323C8—41no—
1324C8—41no—
1325C8—41no—
1326C22—22no—
1327C22—22no—
1328C22—22no—
1329C22—22no—
1330C22—22no—
1331C22—22no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—816no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22#337514yescomplemented
1355C22C2×D4211yescharacteristic
1356C22C2×#54811yescharacteristic
1357C22#348911yescharacteristic
1358C22C22×#13711yescharacteristic
1359C22C2×#57611yescharacteristic
1360C22C2×#57611yescharacteristic
1361C22#358611yescharacteristic
1362C4—22no—
1363C4—22no—
1364C4—22no—
1365C4—22no—
1366C4—22no—
1367C4—22no—
1368C4—41no—
1369C4—41no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—42no—
1374C4—41no—
1375C4—41no—
1376C4—42no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4D4×#4111yescharacteristic
1389C4#348611yescharacteristic
1390C4#352011yescharacteristic
1391C4#354111yescharacteristic
1392C2—24no—
1393C2—82no—
1394C2—82no—
1395C2—161no—
1396C2#5900511yescharacteristic
1397C2#6104911yescharacteristic
1398C2D4×#13711yescharacteristic
1399C2C2×#337511yescharacteristic
1400C2#6134511yescharacteristic
1401C2#6212711yescharacteristic
1402C2#6215511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2433C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3375C2semidirect
2. C22×#474C2semidirect
3. #59151C2semidirect
5. #31166C2semidirect
6. #31152C2semidirect
7. #30821C2semidirect
8. #30805C2semidirect
9. #28428C2semidirect
10. #27262C2semidirect
12. #26912C2semidirect
13. #26893C2semidirect
14. #26478C2semidirect
15. #26460C2semidirect
16. #26342C2semidirect
17. #26336C2semidirect
18. #25908C2semidirect
19. #25660C2semidirect
20. #25481C2semidirect
21. #25285C2semidirect
22. #25084C2semidirect
24. #24755C2semidirect
25. #24696C2semidirect
26. #24341C2semidirect
27. #23079C2semidirect
28. #23032C2semidirect
29. #23024C2semidirect
30. #22954C2semidirect
31. #21453C2semidirect
33. C2×Q82C22semidirect
38. C2×#489C22semidirect
39. C2×#489C22semidirect
41. C2×#477C22semidirect
51. C2×#474C22semidirect
55. C2×#464C22semidirect
58. C2×#446C22semidirect
61. C2×#440C22semidirect
62. C2×C4×Q16C22semidirect
75. #2567C22semidirect
76. #2567C22semidirect
78. #2551C22semidirect
79. #2551C22semidirect
85. #2451C22semidirect
86. #2451C22semidirect
97. #2369C22semidirect
109. #2095C22semidirect
110. #2093C22semidirect
111. #2087C22semidirect
112. #2086C22semidirect
115. #2068C22semidirect
117. #2067C22semidirect
118. #2067C22semidirect
119. #2066C22semidirect
121. #2057C22semidirect
122. #2057C22semidirect
123. #2056C22semidirect
126. #2055C22semidirect
133. #2024C22semidirect
134. #2024C22semidirect
137. #2023C22semidirect
138. #2023C22semidirect
141. #1993C22semidirect
142. #1993C22semidirect
143. #1985C22semidirect
145. #1983C22semidirect
147. #1973C22semidirect
148. #1969C22semidirect
151. #1949C22semidirect
152. #1947C22semidirect
153. #1947C22semidirect
154. #1944C22semidirect
155. #1942C22semidirect
156. #1940C22semidirect
157. #1940C22semidirect
158. #1939C22semidirect
163. #1928C22semidirect
164. #1928C22semidirect
165. #1928C22semidirect
168. #1925C22semidirect
169. #1921C22semidirect
170. #1918C22semidirect
171. #1917C22semidirect
172. #1916C22semidirect
184. #1863C22semidirect
185. #1863C22semidirect
186. #1863C22semidirect
187. #1863C22semidirect
190. #1862C22semidirect
191. #1862C22semidirect
195. #1805C22semidirect
197. #1776C22semidirect
198. C4×#107C22semidirect
199. #1771C22semidirect
287. #474D4semidirect
1354. C22#3375semidirect

Maximal subgroups

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

subgroupindex
C2×#33752
C22×#4742
#591512
#364412
#311662
#311522
#308212
#308052
#284282
#272622
#272542
#269122
#268932
#264782
#264602
#263422
#263362
#259082
#256602
#254812
#252852
#250842
#250802
#247552
#246962
#243412
#230792
#230322
#230242
#229542
#214532