Finite Group Databasebeta

← #7327527

Subgroups — #7327527

Order 512.

1721 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#59042C211yesmaximal, characteristic, complemented
2#45701C211yesmaximal, characteristic
3#32441C211yesmaximal, characteristic, complemented
4#31943C211yesmaximal, characteristic, complemented
5#31647C211yesmaximal, characteristic, complemented
6#31603C211yesmaximal, characteristic, complemented
7#31392C211yesmaximal, characteristic, complemented
8#31320C211yesmaximal, characteristic, complemented
9#31260C211yesmaximal, characteristic, complemented
10#30996C211yesmaximal, characteristic, complemented
11#30598C211yesmaximal, characteristic, complemented
12#30508C211yesmaximal, characteristic, complemented
13#30411C211yesmaximal, characteristic, complemented
14#30408C211yesmaximal, characteristic, complemented
15#30018C211yesmaximal, characteristic, complemented
16#29668C211yesmaximal, characteristic, complemented
17#28576C211yesmaximal, characteristic, complemented
18#28145C211yesmaximal, characteristic, complemented
19#27519C211yesmaximal, characteristic, complemented
20#27069C211yesmaximal, characteristic, complemented
21#26591C211yesmaximal, characteristic, complemented
22#25497C211yesmaximal, characteristic, complemented
23#25389C211yesmaximal, characteristic, complemented
24#25149C211yesmaximal, characteristic, complemented
25#25114C211yesmaximal, characteristic, complemented
26#24533C211yesmaximal, characteristic, complemented
27#24437C211yesmaximal, characteristic, complemented
28#24357C211yesmaximal, characteristic, complemented
29#24264C211yesmaximal, characteristic, complemented
30#23855C211yesmaximal, characteristic, complemented
31#22168C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#533C2211yescharacteristic, complemented
35C2×#467C2211yescharacteristic, complemented
36C2×#467C2211yescharacteristic, complemented
37C2×#465C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#464C2211yescharacteristic
42C2×#464C2211yescharacteristic
43C2×#451C2211yescharacteristic
44C2×#451C2211yescharacteristic, complemented
45C2×#448C2211yescharacteristic
46C2×#448C2211yescharacteristic
47C2×#450C2211yescharacteristic
48C2×C4×Q16C2211yescharacteristic, complemented
49C2×C8×D4C2211yescharacteristic
50C2×C8×D4C2211yescharacteristic, complemented
51C22×#103C2211yescharacteristic, complemented
52#2854C2211yescharacteristic
53#2850C2211yescharacteristic
54#2837—21no—
55#2756—21no—
56#2756—21no—
57#2735—21no—
58#2703—21no—
59#2697—21no—
60#2690—21no—
61#2690—21no—
62#2668—21no—
63#2568C2211yescharacteristic, complemented
64#2547C2211yescharacteristic
65#2540C2211yescharacteristic
66#2536C2211yescharacteristic
67#2536C2211yescharacteristic
68#2536C2211yescharacteristic, complemented
69#2513C2211yescharacteristic
70#2504C2211yescharacteristic
71#2495C2211yescharacteristic
72#2492—21no—
73#2477—21no—
74#2477—21no—
75#2451—21no—
76#2448C2211yescharacteristic
77#2435C2211yescharacteristic
78#2427—21no—
79#2426C2211yescharacteristic
80#2421C2211yescharacteristic
81#2421C2211yescharacteristic, complemented
82#2417C2211yescharacteristic
83#2416C2211yescharacteristic
84#2409C2211yescharacteristic
85#2409C2211yescharacteristic, complemented
86#2408C2211yescharacteristic
87#2408C2211yescharacteristic
88#2375—21no—
89#2367—21no—
90#2365C2211yescharacteristic, complemented
91Q8×C22⋊C4C2211yescharacteristic
92Q8×C22⋊C4C2211yescharacteristic, complemented
93C4×C22⋊Q8C2211yescharacteristic, complemented
94C4×#121C2211yescharacteristic
95#2101C2211yescharacteristic, complemented
96#2097C2211yescharacteristic, complemented
97#2092C2211yescharacteristic
98#2087C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2077C2211yescharacteristic
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2075C2211yescharacteristic, complemented
104#2074C2211yescharacteristic, complemented
105#2074C2211yescharacteristic, complemented
106#2073C2211yescharacteristic
107#2073C2211yescharacteristic
108#2068C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2065C2211yescharacteristic
111#2058C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2043C2211yescharacteristic, complemented
117#2042C2211yescharacteristic
118#2036C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic, complemented
121#2035C2211yescharacteristic, complemented
122#2035C2211yescharacteristic, complemented
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2024C2211yescharacteristic, complemented
127#2023C2211yescharacteristic
128#2023C2211yescharacteristic
129#2016C2211yescharacteristic, complemented
130#2015C2211yescharacteristic
131#2015C2211yescharacteristic
132#2015C2211yescharacteristic
133#2013C2211yescharacteristic
134#2013C2211yescharacteristic
135#2001C2211yescharacteristic
136#2001C2211yescharacteristic, complemented
137#2001C2211yescharacteristic, complemented
138#2000C2211yescharacteristic
139#2000C2211yescharacteristic
140#2000C2211yescharacteristic
141#2000C2211yescharacteristic
142#2000C2211yescharacteristic
143#1968C2211yescharacteristic
144#1968C2211yescharacteristic
145#1968C2211yescharacteristic
146#1958C2211yescharacteristic
147#1949C2211yescharacteristic, complemented
148#1933C2211yescharacteristic, complemented
149#1928C2211yescharacteristic, complemented
150#1927C2211yescharacteristic, complemented
151#1927C2211yescharacteristic, complemented
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic, complemented
156#1920C2211yescharacteristic, complemented
157#1916C2211yescharacteristic, complemented
158#1916C2211yescharacteristic, complemented
159#1893C2211yescharacteristic
160#1893C2211yescharacteristic
161#1893C2211yescharacteristic
162#1892C2211yescharacteristic
163#1892C2211yescharacteristic
164#1892C2211yescharacteristic, complemented
165#1892C2211yescharacteristic, complemented
166#1892C2211yescharacteristic, complemented
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1878C2211yescharacteristic, complemented
177#1872C2211yescharacteristic, complemented
178#1869C2211yescharacteristic
179#1869C2211yescharacteristic
180#1869C2211yescharacteristic
181#1869C2211yescharacteristic, complemented
182#1865C2211yescharacteristic, complemented
183#1865C2211yescharacteristic, complemented
184#1863C2211yescharacteristic, complemented
185#1863C2211yescharacteristic, complemented
186#1853C2211yescharacteristic, complemented
187#1850C2211yescharacteristic
188#1850C2211yescharacteristic, complemented
189#1835C2211yescharacteristic, complemented
190#1824C2211yescharacteristic, complemented
191#1807C2211yescharacteristic
192#1805C2211yescharacteristic, complemented
193#1805C2211yescharacteristic, complemented
194#1805C2211yescharacteristic, complemented
195#1805C2211yescharacteristic, complemented
196#1797C2211yescharacteristic, complemented
197#1787C2211yescharacteristic
198#1787C2211yescharacteristic
199#1786C2211yescharacteristic
200#1786C2211yescharacteristic
201C4×#103C2211yescharacteristic, complemented
202C2×#336C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16—42no—
210C22×SD16—42no—
211C22×SD16—42no—
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C23×C8C2311yescharacteristic
220C23×C8C2311yescharacteristic
221C23×C8C2311yescharacteristic
222D4×Q8—42no—
223D4×Q8—42no—
224#533—42no—
225#533—42no—
226C2×C4⋊Q8—21no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×#125—21no—
230C2×#124—21no—
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#123—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×C22⋊Q8C2311yescharacteristic
245C2×#121—21no—
246C2×#121D411yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#121C2311yescharacteristic
250C2×#121C2311yescharacteristic
251C2×#120—21no—
252C2×#120—21no—
253C2×C4×Q8—21no—
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×D4—21no—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×#117—21no—
265C22×C4⋊C4C2311yescharacteristic
266C22×C42C2311yescharacteristic
267#467—42no—
268#467—42no—
269#465—42no—
270#465—42no—
271#465—42no—
272#464—42no—
273#464—42no—
274#464—42no—
275#451—42no—
276#451—42no—
277#450—42no—
278#448—42no—
279#448—42no—
280C4×Q16—42no—
281C8×D4—42no—
282C8×D4—42no—
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×#103—42no—
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C4×C8C2311yescharacteristic
334C2×C4×C8C2311yescharacteristic
335#400—21no—
336#400—21no—
337#400—21no—
338#400—21no—
339#400—21no—
340#399—21no—
341#399—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#395—21no—
360#395—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#393—21no—
371#393—21no—
372#392—21no—
373#392—21no—
374#392—21no—
375#391—21no—
376#391—21no—
377#391—21no—
378#391—21no—
379#391—21no—
380#391—21no—
381#391—21no—
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#390—21no—
389#390—21no—
390#390—21no—
391#390D411yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#389—21no—
399#389D411yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
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#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388D411yescharacteristic
423#388D411yescharacteristic
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386D411yescharacteristic
439#386D411yescharacteristic
440#385—21no—
441#385—21no—
442#385—21no—
443#383—21no—
444#382C2311yescharacteristic
445#382C2311yescharacteristic
446#382C2311yescharacteristic
447#382C2311yescharacteristic
448#380—21no—
449#380—21no—
450#380—21no—
451#380D411yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#379—21no—
461#379—21no—
462#379—21no—
463#379—21no—
464C4×C4⋊C4—21no—
465C4×C4⋊C4—21no—
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
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—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8—21no—
506C22×Q8—22no—
507C22×Q8—22no—
508C22×Q8—22no—
509C22×Q8—22no—
510C22×Q8—41no—
511C22×Q8—41no—
512C22×Q8—41no—
513C22×Q8—41no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8—41no—
517C22×Q8—41no—
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4C2×D411yescharacteristic
534C22×D4C2×D411yescharacteristic
535C22×D4C2×D411yescharacteristic
536C22×D4C2411yescharacteristic
537C22×D4C2411yescharacteristic
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4C2×D411yescharacteristic
542C23×C4C2×D411yescharacteristic
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—416no—
574C22×C8—22no—
575C22×C8—22no—
576C22×C8—41no—
577C22×C8—41no—
578C22×C8—41no—
579C22×C8—41no—
580C22×C8—41no—
581C22×C8—41no—
582C22×C8—41no—
583C22×C8—41no—
584C22×C8—41no—
585C22×C8—41no—
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C22×C8C2411yescharacteristic
594C4⋊Q8—22no—
595C4⋊Q8—22no—
596C4⋊Q8—41no—
597C4⋊Q8—41no—
598C4⋊Q8—44no—
599#125—44no—
600#124—41no—
601#124—41no—
602#124—41no—
603#124—41no—
604#124—44no—
605#123—82no—
606C22⋊Q8—22no—
607C22⋊Q8—22no—
608C22⋊Q8—22no—
609C22⋊Q8—22no—
610C22⋊Q8—22no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613C22⋊Q8—41no—
614C22⋊Q8—41no—
615C22⋊Q8—41no—
616C22⋊Q8—44no—
617C22⋊Q8—44no—
618C22⋊Q8—44no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8—41no—
624C22⋊Q8—41no—
625#121—24no—
626#121—41no—
627#121—41no—
628#121—41no—
629#121—41no—
630#121—41no—
631#121—41no—
632#121—41no—
633#121—41no—
634#121—82no—
635#120—44no—
636#120—82no—
637C4×Q8—22no—
638C4×Q8—22no—
639C4×Q8—41no—
640C4×Q8—41no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×Q8—41no—
644C4×Q8—41no—
645C4×Q8—41no—
646C4×Q8—41no—
647C4×Q8—41no—
648C4×Q8—41no—
649C4×Q8—44no—
650C4×D4—41no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—41no—
654C4×D4—41no—
655C4×D4—41no—
656C4×D4—44no—
657#117—44no—
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—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—41no—
681C2×C4⋊C4—41no—
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2×D411yescharacteristic
686C2×C4⋊C4C2×D411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C42—21no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—41no—
752C2×C42—41no—
753C2×C42C2×D411yescharacteristic
754C2×C42C2×D411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759#107—41no—
760#107—41no—
761#107—41no—
762#106—41no—
763#106—41no—
764#106—41no—
765#106—41no—
766C4⋊C8—22no—
767C4⋊C8—41no—
768C4⋊C8—41no—
769C4⋊C8—41no—
770#103—22no—
771#103—22no—
772#103—22no—
773#103—22no—
774#103—22no—
775#103—22no—
776#103—22no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781#103—41no—
782#103—41no—
783#103—41no—
784#103—41no—
785#103—41no—
786#103—41no—
787#103—41no—
788#103—41no—
789#103—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795#102—41no—
796#102—41no—
797#102—41no—
798#102—41no—
799#102—41no—
800C22⋊C8—22no—
801C22⋊C8—41no—
802C22⋊C8—41no—
803C22⋊C8—41no—
804C22⋊C8—41no—
805C22⋊C8—41no—
806C22⋊C8—41no—
807C22⋊C8—41no—
808C4×C8—22no—
809C4×C8—41no—
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#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#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850C24—21no—
851C24—21no—
852C24—42no—
853C24—81no—
854C24—81no—
855C24—81no—
856C24—81no—
857C24—81no—
858C24—81no—
859C24C22×D411yescharacteristic
860C24C22×D411yescharacteristic
861C24C22×D411yescharacteristic
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
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—42no—
884C2×Q8—42no—
885C2×Q8—42no—
886C2×Q8—42no—
887C2×Q8—42no—
888C2×Q8—42no—
889C2×Q8—42no—
890C2×Q8—44no—
891C2×Q8—44no—
892C2×Q8—81no—
893C2×Q8—81no—
894C2×Q8—82no—
895C2×Q8—82no—
896C2×Q8—82no—
897C2×Q8—82no—
898C2×Q8—82no—
899C2×Q8—82no—
900C2×Q8H(5,𝔽2)12yes—
901C2×Q8H(5,𝔽2)12yes—
902C2×Q8H(5,𝔽2)12yes—
903C2×D4—22no—
904C2×D4—22no—
905C2×D4—22no—
906C2×D4—22no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—41no—
920C2×D4—41no—
921C2×D4—41no—
922C2×D4—41no—
923C2×D4—44no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—82no—
932C2×D4—82no—
933C2×D4—82no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4—81no—
940C2×D4—81no—
941C2×D4—81no—
942C2×D4#13514yes—
943C22×C4—22no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—22no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—41no—
978C22×C4—41no—
979C22×C4—41no—
980C22×C4—41no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
1002Q16—44no—
1003Q16—82no—
1004Q16—82no—
1005SD16—44no—
1006SD16—44no—
1007SD16—44no—
1008SD16—44no—
1009SD16—82no—
1010SD16—82no—
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—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—82no—
1036C2×C8—82no—
1037C2×C8—82no—
1038C2×C8H(5,𝔽2)12yes—
1039C4⋊C4—24no—
1040C4⋊C4—24no—
1041C4⋊C4—22no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—42no—
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—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C22⋊C4—22no—
1087C22⋊C4—22no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—41no—
1091C22⋊C4—41no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—41no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
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—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—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—41no—
1141C42—41no—
1142C42—42no—
1143C42—42no—
1144C42—42no—
1145C42—42no—
1146C42—81no—
1147C42—81no—
1148C42—81no—
1149C42—81no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
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—84no—
1183C23—162no—
1184C23—162no—
1185C23—162no—
1186C23—162no—
1187C23—162no—
1188C23—162no—
1189C23C2×#13512yes—
1190C23C2×#13512yes—
1191C23#57712yes—
1192C23C23×D411yescharacteristic
1193Q8—22no—
1194Q8—22no—
1195Q8—22no—
1196Q8—22no—
1197Q8—22no—
1198Q8—22no—
1199Q8—41no—
1200Q8—41no—
1201Q8—41no—
1202Q8—41no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—41no—
1209Q8—84no—
1210Q8—84no—
1211Q8—84no—
1212D4—44no—
1213D4—44no—
1214D4—44no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—84no—
1224D4—162no—
1225D4—162no—
1226D4—162no—
1227D4—162no—
1228C2×C4—21no—
1229C2×C4—21no—
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—22no—
1242C2×C4—22no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—22no—
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—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—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—82no—
1316C2×C4—84no—
1317C2×C4—84no—
1318C2×C4—162no—
1319C2×C4C2×#13512yes—
1320C2×C4C2×H(5,𝔽2)11yescharacteristic
1321C2×C4C2×H(5,𝔽2)11yescharacteristic
1322C2×C4C2×H(5,𝔽2)11yescharacteristic
1323C2×C4C2×H(5,𝔽2)11yescharacteristic
1324C2×C4#58511yescharacteristic
1325C2×C4#58511yescharacteristic
1326C8—22no—
1327C8—41no—
1328C8—41no—
1329C8—41no—
1330C8—41no—
1331C8—41no—
1332C8—41no—
1333C8—41no—
1334C22—22no—
1335C22—22no—
1336C22—22no—
1337C22—22no—
1338C22—22no—
1339C22—22no—
1340C22—22no—
1341C22—22no—
1342C22—22no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—41no—
1350C22—41no—
1351C22—41no—
1352C22—41no—
1353C22—41no—
1354C22—41no—
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—
1370C22#348411yescharacteristic
1371C22#348811yescharacteristic
1372C22#349611yescharacteristic
1373C22C22×#13511yescharacteristic
1374C22C2×#57711yescharacteristic
1375C22#358611yescharacteristic
1376C22#358611yescharacteristic
1377C4—22no—
1378C4—41no—
1379C4—41no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—41no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4#353211yescharacteristic
1403C4#353411yescharacteristic
1404C4#354211yescharacteristic
1405C4#356011yescharacteristic
1406C2—42no—
1407C2—42no—
1408C2—42no—
1409C2—161no—
1410C2—161no—
1411C2#4793411yescharacteristic
1412C2#6156411yescharacteristic
1413C2#6161111yescharacteristic
1414C2#6195611yescharacteristic
1415C2#6201911yescharacteristic
1416C2#6225011yescharacteristic
1417C2#6233711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45701C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59042C2semidirect
3. #32441C2semidirect
4. #31943C2semidirect
5. #31647C2semidirect
6. #31603C2semidirect
7. #31392C2semidirect
8. #31320C2semidirect
9. #31260C2semidirect
10. #30996C2semidirect
11. #30598C2semidirect
12. #30508C2semidirect
13. #30411C2semidirect
14. #30408C2semidirect
15. #30018C2semidirect
16. #29668C2semidirect
17. #28576C2semidirect
18. #28145C2semidirect
19. #27519C2semidirect
20. #27069C2semidirect
21. #26591C2semidirect
22. #25497C2semidirect
23. #25389C2semidirect
24. #25149C2semidirect
25. #25114C2semidirect
26. #24533C2semidirect
27. #24437C2semidirect
28. #24357C2semidirect
29. #24264C2semidirect
30. #23855C2semidirect
31. #22168C2semidirect
34. C2×#533C22semidirect
35. C2×#467C22semidirect
36. C2×#467C22semidirect
44. C2×#451C22semidirect
48. C2×C4×Q16C22semidirect
50. C2×C8×D4C22semidirect
51. C22×#103C22semidirect
63. #2568C22semidirect
68. #2536C22semidirect
81. #2421C22semidirect
85. #2409C22semidirect
90. #2365C22semidirect
92. Q8×C22⋊C4C22semidirect
93. C4×C22⋊Q8C22semidirect
95. #2101C22semidirect
96. #2097C22semidirect
98. #2087C22semidirect
99. #2085C22semidirect
103. #2075C22semidirect
104. #2074C22semidirect
105. #2074C22semidirect
108. #2068C22semidirect
109. #2066C22semidirect
111. #2058C22semidirect
116. #2043C22semidirect
120. #2035C22semidirect
121. #2035C22semidirect
122. #2035C22semidirect
126. #2024C22semidirect
129. #2016C22semidirect
136. #2001C22semidirect
137. #2001C22semidirect
147. #1949C22semidirect
148. #1933C22semidirect
149. #1928C22semidirect
150. #1927C22semidirect
151. #1927C22semidirect
155. #1923C22semidirect
156. #1920C22semidirect
157. #1916C22semidirect
158. #1916C22semidirect
164. #1892C22semidirect
165. #1892C22semidirect
166. #1892C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
176. #1878C22semidirect
177. #1872C22semidirect
181. #1869C22semidirect
182. #1865C22semidirect
183. #1865C22semidirect
184. #1863C22semidirect
185. #1863C22semidirect
186. #1853C22semidirect
188. #1850C22semidirect
189. #1835C22semidirect
190. #1824C22semidirect
192. #1805C22semidirect
193. #1805C22semidirect
194. #1805C22semidirect
195. #1805C22semidirect
196. #1797C22semidirect
201. C4×#103C22semidirect
202. C2×#336C22semidirect

Maximal subgroups

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

subgroupindex
#590422
#457012
#324412
#319432
#316472
#316032
#313922
#313202
#312602
#309962
#305982
#305082
#304112
#304082
#300182
#296682
#285762
#281452
#275192
#270692
#265912
#254972
#253892
#251492
#251142
#245332
#244372
#243572
#242642
#238552
#221682