Finite Group Databasebeta

← #6569228

Subgroups — #6569228

Order 512.

1267 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39800C211yesmaximal, characteristic
2#38239C211yesmaximal, characteristic, complemented
3#30350C211yesmaximal, characteristic
4#30341C211yesmaximal, characteristic
5#30210C211yesmaximal, characteristic, complemented
6#29571C211yesmaximal, characteristic
7#29557C211yesmaximal, characteristic
8#29528C211yesmaximal, characteristic, complemented
9#29515C211yesmaximal, characteristic, complemented
10#29217C211yesmaximal, characteristic, complemented
11#29093C211yesmaximal, characteristic
12#29081C211yesmaximal, characteristic, complemented
13#29077C211yesmaximal, characteristic
14#29073C211yesmaximal, characteristic, complemented
15#28390C211yesmaximal, characteristic
16#28026C211yesmaximal, characteristic
17#28016C211yesmaximal, characteristic, complemented
18#28012C211yesmaximal, characteristic, complemented
19#28011C211yesmaximal, characteristic
20#25482C211yesmaximal, characteristic
21#25474C211yesmaximal, characteristic, complemented
22#25306C211yesmaximal, characteristic, complemented
23#25293C211yesmaximal, characteristic
24#23827C211yesmaximal, characteristic
25#23792C211yesmaximal, characteristic, complemented
26#23776C211yesmaximal, characteristic, complemented
27#23112C211yesmaximal, characteristic
28#23096C211yesmaximal, characteristic, complemented
29#23078C211yesmaximal, characteristic, complemented
30#23065C211yesmaximal, characteristic
31#20571C211yesmaximal, characteristic, complemented
32C2×#479C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#462C2211yescharacteristic
35C2×#461C2211yescharacteristic
36C2×#446C2211yescharacteristic
37C2×C8×Q8C2211yescharacteristic
38#2863C2211yescharacteristic
39#2861C2211yescharacteristic
40#2805—21no—
41#2789—21no—
42#2783—21no—
43#2776—21no—
44#2775—21no—
45#2762—21no—
46#2745—21no—
47#2689—21no—
48#2660C2211yescharacteristic
49#2645C2211yescharacteristic
50#2642C2211yescharacteristic
51#2640C2211yescharacteristic
52#2605—21no—
53#2594—21no—
54#2584C2211yescharacteristic
55#2581C2211yescharacteristic
56#2577—21no—
57#2568C2211yescharacteristic
58#2538C2211yescharacteristic
59#2533—21no—
60#2524—21no—
61#2514—21no—
62#2514C2211yescharacteristic
63#2514C2211yescharacteristic
64#2514C2211yescharacteristic
65#2513C2211yescharacteristic
66#2512C2211yescharacteristic
67#2511C2211yescharacteristic
68#2469—21no—
69#2465—21no—
70#2451C2211yescharacteristic
71#2451C2211yescharacteristic
72#2370C2211yescharacteristic
73#2365C2211yescharacteristic
74#2357C2211yescharacteristic
75#2355C2211yescharacteristic
76#2331C2211yescharacteristic
77#2330C2211yescharacteristic
78#2326C2211yescharacteristic
79#2320C2211yescharacteristic
80C4×C4⋊Q8C2211yescharacteristic
81#2295C2211yescharacteristic
82#2295C2211yescharacteristic
83#2100C2211yescharacteristic
84#2099C2211yescharacteristic
85#2096C2211yescharacteristic
86#2095C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2086C2211yescharacteristic
91#2074C2211yescharacteristic
92#2074C2211yescharacteristic
93#2074C2211yescharacteristic
94#2073C2211yescharacteristic
95#2072C2211yescharacteristic
96#2072C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2066C2211yescharacteristic
102#2066C2211yescharacteristic
103#2066C2211yescharacteristic
104#2066C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2058C2211yescharacteristic
108#2057C2211yescharacteristic
109#2056C2211yescharacteristic
110#2056C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2026C2211yescharacteristic
116#2026C2211yescharacteristic
117#2024C2211yescharacteristic
118#2024C2211yescharacteristic
119#2024C2211yescharacteristic
120#2023C2211yescharacteristic
121#2015C2211yescharacteristic
122#2015C2211yescharacteristic
123#1993C2211yescharacteristic
124#1992C2211yescharacteristic
125#1991C2211yescharacteristic
126#1990C2211yescharacteristic
127#1973C2211yescharacteristic
128#1973C2211yescharacteristic
129#1971C2211yescharacteristic
130#1971C2211yescharacteristic
131#1969C2211yescharacteristic
132#1969C2211yescharacteristic
133#1969C2211yescharacteristic
134#1969C2211yescharacteristic
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1960C2211yescharacteristic
140#1956C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1948C2211yescharacteristic
144#1947C2211yescharacteristic
145#1943C2211yescharacteristic
146#1942C2211yescharacteristic
147#1942C2211yescharacteristic
148#1941C2211yescharacteristic
149#1936C2211yescharacteristic
150#1935C2211yescharacteristic
151#1935C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1933C2211yescharacteristic
156#1933C2211yescharacteristic
157#1933C2211yescharacteristic
158#1933C2211yescharacteristic
159#1933C2211yescharacteristic
160#1933C2211yescharacteristic
161#1928C2211yescharacteristic
162#1928C2211yescharacteristic
163#1928C2211yescharacteristic
164#1927C2211yescharacteristic
165#1927C2211yescharacteristic
166#1927C2211yescharacteristic
167#1926C2211yescharacteristic
168#1925C2211yescharacteristic
169#1921C2211yescharacteristic
170#1921C2211yescharacteristic
171#1920C2211yescharacteristic
172#1919C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1847C2211yescharacteristic
178#1846C2211yescharacteristic
179#1776C2211yescharacteristic
180C4×#107C2211yescharacteristic
181C4×#106C2211yescharacteristic
182C4×#106C2211yescharacteristic
183#1771C2211yescharacteristic
184#1771C2211yescharacteristic
185#1770C2211yescharacteristic
186C8×C4⋊C4C2211yescharacteristic
187C8×C4⋊C4C2211yescharacteristic
188C8×C4⋊C4C2211yescharacteristic
189#1768C2211yescharacteristic
190#1768C2211yescharacteristic
191C4×C4⋊C8C2211yescharacteristic
192#1763C2211yescharacteristic
193#1763C2211yescharacteristic
194#1762C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1746C2211yescharacteristic
201#1746C2211yescharacteristic
202#1744C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#126—21no—
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×C22⋊Q8—21no—
215C2×C4×Q8—21no—
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221#479—24no—
222#478—24no—
223#462—24no—
224#461—24no—
225#446—24no—
226C8×Q8—24no—
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#97C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×#97C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
274C2×C4×C8C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281#401—21no—
282#401—21no—
283#401—21no—
284#401—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#396—21no—
311#396—21no—
312#396—21no—
313#395—21no—
314#395—21no—
315#395—21no—
316#395—21no—
317#395—21no—
318#395—21no—
319#393—21no—
320#393—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391D411yescharacteristic
328#391D411yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389D411yescharacteristic
357#389D411yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387D411yescharacteristic
408#387D411yescharacteristic
409#387D411yescharacteristic
410#387D411yescharacteristic
411#385—21no—
412#385—21no—
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#383—21no—
417#383—21no—
418#383—21no—
419#383—21no—
420#383—21no—
421#382—21no—
422#382—21no—
423#382—21no—
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#381—21no—
428#380—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C22⋊C4—21no—
446#376—21no—
447#376C2311yescharacteristic
448#376C2311yescharacteristic
449C43C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8C2×D411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4C2411yescharacteristic
491C23×C4—21no—
492C2×Q16—22no—
493C2×Q16—22no—
494C2×Q16—41no—
495C2×Q16—41no—
496C2×Q16—41no—
497C2×Q16—41no—
498C2×SD16—22no—
499C2×SD16—22no—
500C2×SD16—41no—
501C2×SD16—41no—
502C2×SD16—41no—
503C2×SD16—41no—
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C4⋊Q8—22no—
513C4⋊Q8—22no—
514C4⋊Q8—22no—
515C4⋊Q8—41no—
516C4⋊Q8—41no—
517C4⋊Q8—41no—
518#126—82no—
519#125—22no—
520#125—22no—
521#125—41no—
522#125—41no—
523#124—41no—
524#124—41no—
525C22⋊Q8—82no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—22no—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×Q8—41no—
533C4×Q8—41no—
534C4×Q8—82no—
535C4×D4—22no—
536C4×D4—22no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C42—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42C2×D411yescharacteristic
612C2×C42C2×D411yescharacteristic
613C2×C42C2×D411yescharacteristic
614C2×C42C2×D411yescharacteristic
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617C2×C42C2411yescharacteristic
618C2×C42C2411yescharacteristic
619C2×C42C2411yescharacteristic
620C2×C42C2411yescharacteristic
621C2×C42C2411yescharacteristic
622#107—22no—
623#107—22no—
624#107—41no—
625#107—41no—
626#107—41no—
627#107—41no—
628#106—22no—
629#106—22no—
630#106—41no—
631#106—41no—
632#106—41no—
633#106—41no—
634C4⋊C8—22no—
635C4⋊C8—22no—
636C4⋊C8—22no—
637C4⋊C8—22no—
638C4⋊C8#4114yes—
639C4⋊C8#4114yes—
640#103—22no—
641#103—22no—
642#103—22no—
643#103—22no—
644#103—22no—
645#103—22no—
646#103—22no—
647#103—41no—
648#103—41no—
649#103—41no—
650#103—41no—
651#103—41no—
652#103—41no—
653#103—41no—
654#103—41no—
655#103—41no—
656#103—41no—
657#103—41no—
658#102—22no—
659#102—22no—
660#102—22no—
661#102—41no—
662#102—41no—
663#102—41no—
664#97—22no—
665#97—22no—
666#97—41no—
667#97—41no—
668C4×C8—22no—
669C4×C8—22no—
670C4×C8—22no—
671C4×C8—22no—
672C4×C8—41no—
673C4×C8—41no—
674C4×C8—41no—
675C4×C8—41no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746C24—21no—
747C2×Q8—22no—
748C2×Q8—22no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—41no—
768C2×Q8—42no—
769C2×Q8—42no—
770C2×Q8—81no—
771C2×Q8—81no—
772C2×Q8—81no—
773C2×Q8—81no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—42no—
796C22×C4—81no—
797C22×C4—81no—
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C2511yescharacteristic
813Q16—82no—
814Q16—82no—
815SD16—82no—
816SD16—82no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8C2×#4112yes—
838C2×C8C2×#4112yes—
839C2×C8C2×#4112yes—
840C2×C8C2×#4112yes—
841C4⋊C4—22no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—41no—
871C4⋊C4—41no—
872C4⋊C4—41no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C42−1+412yes—
903C22⋊C4—42no—
904C22⋊C4—42no—
905C22⋊C4—42no—
906C22⋊C4—42no—
907C22⋊C4—42no—
908C22⋊C4—81no—
909C22⋊C4—81no—
910C22⋊C4—81no—
911C22⋊C4—81no—
912C22⋊C4—81no—
913C22⋊C4—81no—
914C22⋊C4—81no—
915C22⋊C4—81no—
916C42—22no—
917C42—22no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—21no—
926C42—21no—
927C42—21no—
928C42—21no—
929C42—21no—
930C42—41no—
931C42—41no—
932C42—42no—
933C42—42no—
934C42—42no—
935C42—42no—
936C42—81no—
937C42—81no—
938C42—81no—
939C42—81no—
940C42—81no—
941C42—81no—
942C42—81no—
943C42C2×#4112yes—
944C42C2×#4112yes—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23C23×D411yescharacteristic
953Q8—44no—
954Q8—41no—
955Q8—41no—
956Q8—41no—
957Q8—41no—
958Q8—41no—
959Q8—41no—
960Q8—41no—
961Q8—41no—
962Q8—41no—
963Q8—41no—
964Q8—41no—
965Q8—41no—
966Q8—84no—
967Q8—162no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—41no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—162no—
1056C2×C4#53212yes—
1057C2×C4#53212yes—
1058C2×C4#57712yes—
1059C2×C4#57812yes—
1060C2×C4C22×#4111yescharacteristic
1061C2×C4C22×#4111yescharacteristic
1062C2×C4C2×2−1+411yescharacteristic
1063C2×C4#58511yescharacteristic
1064C2×C4#58511yescharacteristic
1065C2×C4#58511yescharacteristic
1066C8—22no—
1067C8—22no—
1068C8—22no—
1069C8—22no—
1070C8—41no—
1071C8—41no—
1072C8—41no—
1073C8—41no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22C2×#53211yescharacteristic
1082C22#348711yescharacteristic
1083C22#348911yescharacteristic
1084C22C2×#57711yescharacteristic
1085C22C2×#57811yescharacteristic
1086C22#358411yescharacteristic
1087C22#358411yescharacteristic
1088C4—22no—
1089C4—22no—
1090C4—22no—
1091C4—22no—
1092C4—41no—
1093C4—41no—
1094C4—41no—
1095C4—41no—
1096C4—41no—
1097C4—41no—
1098C4—41no—
1099C4—41no—
1100C4—41no—
1101C4—41no—
1102C4—42no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C4—81no—
1111C4—81no—
1112C4—81no—
1113C4—81no—
1114C4—81no—
1115C4—81no—
1116C4—81no—
1117C4#351811yescharacteristic
1118C4#351811yescharacteristic
1119C4#352111yescharacteristic
1120C4#352111yescharacteristic
1121C2—161no—
1122C2#3604811yescharacteristic
1123C2#6069611yescharacteristic
1124C2#6070611yescharacteristic
1125C2#6192711yescharacteristic
1126C2#6192911yescharacteristic
1127C2#6220311yescharacteristic
1128C2#6220711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #38239C2semidirect
5. #30210C2semidirect
8. #29528C2semidirect
9. #29515C2semidirect
10. #29217C2semidirect
12. #29081C2semidirect
14. #29073C2semidirect
17. #28016C2semidirect
18. #28012C2semidirect
21. #25474C2semidirect
22. #25306C2semidirect
25. #23792C2semidirect
26. #23776C2semidirect
28. #23096C2semidirect
29. #23078C2semidirect
31. #20571C2semidirect

Maximal subgroups

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

subgroupindex
#398002
#382392
#303502
#303412
#302102
#295712
#295572
#295282
#295152
#292172
#290932
#290812
#290772
#290732
#283902
#280262
#280162
#280122
#280112
#254822
#254742
#253062
#252932
#238272
#237922
#237762
#231122
#230962
#230782
#230652
#205712