Finite Group Databasebeta

← #7187314

Subgroups — #7187314

Order 512.

1211 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45151C211yesmaximal, characteristic
2#44949C211yesmaximal, characteristic, complemented
3#32645C211yesmaximal, characteristic, complemented
4#32644C211yesmaximal, characteristic, complemented
5#32639C211yesmaximal, characteristic
6#32638C211yesmaximal, characteristic
7#32105C211yesmaximal, characteristic
8#32103C211yesmaximal, characteristic
9#32100C211yesmaximal, characteristic, complemented
10#32098C211yesmaximal, characteristic, complemented
11#29267C211yesmaximal, characteristic
12#28213C211yesmaximal, characteristic, complemented
13#27754C211yesmaximal, characteristic
14#27754C211yesmaximal, characteristic
15#27385C211yesmaximal, characteristic
16#27384C211yesmaximal, characteristic, complemented
17#27383C211yesmaximal, characteristic
18#27382C211yesmaximal, characteristic, complemented
19#26335C211yesmaximal, characteristic, complemented
20#26333C211yesmaximal, characteristic, complemented
21#26331C211yesmaximal, characteristic
22#26329C211yesmaximal, characteristic
23#26101C211yesmaximal, characteristic, complemented
24#26100C211yesmaximal, characteristic, complemented
25#25287C211yesmaximal, characteristic
26#25286C211yesmaximal, characteristic
27#23829C211yesmaximal, characteristic, complemented
28#23069C211yesmaximal, characteristic, complemented
29#23068C211yesmaximal, characteristic, complemented
30#22312C211yesmaximal, characteristic, complemented
31#22233C211yesmaximal, characteristic
32C2×#489C2211yescharacteristic
33C2×#477C2211yescharacteristic
34C2×#475C2211yescharacteristic
35#2799—21no—
36#2799—21no—
37#2791—21no—
38#2775—21no—
39#2775—21no—
40#2744—21no—
41#2744—21no—
42#2713—21no—
43#2592C2211yescharacteristic
44#2592C2211yescharacteristic
45#2588—21no—
46#2574—21no—
47#2574—21no—
48#2570C2211yescharacteristic
49#2570C2211yescharacteristic
50#2568C2211yescharacteristic
51#2568C2211yescharacteristic
52#2567C2211yescharacteristic
53#2565—21no—
54#2547C2211yescharacteristic
55#2546C2211yescharacteristic
56#2546C2211yescharacteristic
57#2545C2211yescharacteristic
58#2545C2211yescharacteristic
59#2529—21no—
60#2529—21no—
61#2520—21no—
62#2509C2211yescharacteristic
63#2508C2211yescharacteristic
64#2507C2211yescharacteristic
65#2506C2211yescharacteristic
66#2451—21no—
67#2399C2211yescharacteristic
68#2369C2211yescharacteristic
69#2365C2211yescharacteristic
70#2357C2211yescharacteristic
71#2356C2211yescharacteristic
72#2355C2211yescharacteristic
73#2355C2211yescharacteristic
74#2355C2211yescharacteristic
75#2355C2211yescharacteristic
76#2331C2211yescharacteristic
77#2331C2211yescharacteristic
78#2327C2211yescharacteristic
79#2326C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2097C2211yescharacteristic
83#2097C2211yescharacteristic
84#2097C2211yescharacteristic
85#2096C2211yescharacteristic
86#2095C2211yescharacteristic
87#2092C2211yescharacteristic
88#2085C2211yescharacteristic
89#2085C2211yescharacteristic
90#2074C2211yescharacteristic
91#2074C2211yescharacteristic
92#2073C2211yescharacteristic
93#2073C2211yescharacteristic
94#2072C2211yescharacteristic
95#2072C2211yescharacteristic
96#2068C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2067C2211yescharacteristic
100#2066C2211yescharacteristic
101#2066C2211yescharacteristic
102#2066C2211yescharacteristic
103#2065C2211yescharacteristic
104#2043C2211yescharacteristic
105#2043C2211yescharacteristic
106#2043C2211yescharacteristic
107#2043C2211yescharacteristic
108#2043C2211yescharacteristic
109#2043C2211yescharacteristic
110#2043C2211yescharacteristic
111#2043C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2024C2211yescharacteristic
117#2024C2211yescharacteristic
118#2024C2211yescharacteristic
119#2023C2211yescharacteristic
120#1990C2211yescharacteristic
121#1985C2211yescharacteristic
122#1985C2211yescharacteristic
123#1985C2211yescharacteristic
124#1985C2211yescharacteristic
125#1983C2211yescharacteristic
126#1983C2211yescharacteristic
127#1983C2211yescharacteristic
128#1983C2211yescharacteristic
129#1981C2211yescharacteristic
130#1981C2211yescharacteristic
131#1960C2211yescharacteristic
132#1960C2211yescharacteristic
133#1959C2211yescharacteristic
134#1959C2211yescharacteristic
135#1958C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1948C2211yescharacteristic
139#1948C2211yescharacteristic
140#1947C2211yescharacteristic
141#1947C2211yescharacteristic
142#1940C2211yescharacteristic
143#1940C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1935C2211yescharacteristic
147#1935C2211yescharacteristic
148#1935C2211yescharacteristic
149#1935C2211yescharacteristic
150#1935C2211yescharacteristic
151#1935C2211yescharacteristic
152#1928C2211yescharacteristic
153#1928C2211yescharacteristic
154#1928C2211yescharacteristic
155#1928C2211yescharacteristic
156#1928C2211yescharacteristic
157#1928C2211yescharacteristic
158#1927C2211yescharacteristic
159#1927C2211yescharacteristic
160#1927C2211yescharacteristic
161#1927C2211yescharacteristic
162#1927C2211yescharacteristic
163#1927C2211yescharacteristic
164#1926C2211yescharacteristic
165#1926C2211yescharacteristic
166#1925C2211yescharacteristic
167#1925C2211yescharacteristic
168#1921C2211yescharacteristic
169#1920C2211yescharacteristic
170#1920C2211yescharacteristic
171#1920C2211yescharacteristic
172#1919C2211yescharacteristic
173#1918C2211yescharacteristic
174#1918C2211yescharacteristic
175#1918C2211yescharacteristic
176#1917C2211yescharacteristic
177#1917C2211yescharacteristic
178#1917C2211yescharacteristic
179#1917C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1862C2211yescharacteristic
187#1862C2211yescharacteristic
188#1847C2211yescharacteristic
189#1832C2211yescharacteristic
190#1805C2211yescharacteristic
191#1805C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195#1776C2211yescharacteristic
196#1770C2211yescharacteristic
197#1770C2211yescharacteristic
198#1763C2211yescharacteristic
199#1763C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#103C2211yescharacteristic
202#1746C2211yescharacteristic
203C2×C4⋊Q8—21no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125—21no—
210C2×#124C2311yescharacteristic
211C2×#124C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×C4×Q8—21no—
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220#489—24no—
221#477—24no—
222#475—24no—
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#106C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×C4⋊C8C2311yescharacteristic
236C2×C4⋊C8C2311yescharacteristic
237C2×C4⋊C8C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×#103C2311yescharacteristic
242C2×#103C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398D411yescharacteristic
300#398D411yescharacteristic
301#398D411yescharacteristic
302#398D411yescharacteristic
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#396—21no—
308#396—21no—
309#396—21no—
310#396—21no—
311#395—21no—
312#395—21no—
313#395D411yescharacteristic
314#395D411yescharacteristic
315#395D411yescharacteristic
316#395D411yescharacteristic
317#393—21no—
318#393—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—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#385—21no—
402#385—21no—
403#384—21no—
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#383—21no—
408#382—21no—
409#382—21no—
410#382—21no—
411#382—21no—
412#382—21no—
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#381—21no—
419#380—21no—
420#380—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
443#376—21no—
444#376C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
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#336C2311yescharacteristic
466#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8—21no—
482C22×Q8—21no—
483C22×Q8C2×D411yescharacteristic
484C22×Q8C2×D411yescharacteristic
485C22×Q8C2411yescharacteristic
486C22×Q8C2411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×D4C2411yescharacteristic
489C23×C4—21no—
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C4⋊Q8—22no—
499C4⋊Q8—41no—
500C4⋊Q8—41no—
501C4⋊Q8—41no—
502C4⋊Q8—41no—
503C4⋊Q8—41no—
504C4⋊Q8—41no—
505C4⋊Q8—41no—
506C4⋊Q8—41no—
507C4⋊Q8—82no—
508C4⋊Q8#4114yes—
509#125—82no—
510#124—22no—
511#124—22no—
512#124—41no—
513#124—41no—
514#124—41no—
515#124—41no—
516C4×Q8—22no—
517C4×Q8—22no—
518C4×Q8—22no—
519C4×Q8—22no—
520C4×Q8—41no—
521C4×Q8—41no—
522C4×Q8—41no—
523C4×Q8—41no—
524C4×Q8—41no—
525C4×Q8—41no—
526C4×Q8—82no—
527C4×D4—41no—
528C4×D4—41no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
559C2×C4⋊C4C2×D411yescharacteristic
560C2×C4⋊C4C2×D411yescharacteristic
561C2×C4⋊C4C2×D411yescharacteristic
562C2×C4⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
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×C42—21no—
598C2×C42—21no—
599C2×C42—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×C42—21no—
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617C2×C42C2411yescharacteristic
618C2×C42C2411yescharacteristic
619#107—22no—
620#107—22no—
621#107—41no—
622#107—41no—
623#107—41no—
624#107—41no—
625#106—22no—
626#106—22no—
627#106—41no—
628#106—41no—
629#106—41no—
630#106—41no—
631C4⋊C8—22no—
632C4⋊C8—22no—
633C4⋊C8—41no—
634C4⋊C8—41no—
635C4⋊C8—41no—
636C4⋊C8—41no—
637#103—22no—
638#103—22no—
639#103—22no—
640#103—22no—
641#103—22no—
642#103—22no—
643#103—41no—
644#103—41no—
645#103—41no—
646#103—41no—
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#103—41no—
659#103—41no—
660#103—41no—
661#102—22no—
662#102—22no—
663#102—41no—
664#102—41no—
665#102—41no—
666#102—41no—
667#102—41no—
668#102—41no—
669#97—22no—
670#97—41no—
671#97—41no—
672#97—41no—
673#97—41no—
674C4×C8—22no—
675#95—21no—
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#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739C24—21no—
740C2×Q8—24no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
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—41no—
760C2×Q8—41no—
761C2×Q8—41no—
762C2×Q8—41no—
763C2×Q8—41no—
764C2×Q8—41no—
765C2×Q8—42no—
766C2×Q8—81no—
767C2×Q8—81no—
768C2×Q8—81no—
769C2×Q8—81no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—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—42no—
792C22×C4—81no—
793C22×C4—81no—
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
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—
833C4⋊C4—24no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
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—41no—
857C4⋊C4—41no—
858C4⋊C4—41no—
859C4⋊C4—41no—
860C4⋊C4—41no—
861C4⋊C4—41no—
862C4⋊C4—41no—
863C4⋊C4—41no—
864C4⋊C4—41no—
865C4⋊C4—41no—
866C4⋊C4—41no—
867C4⋊C4—41no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
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⋊C4C2×#4112yes—
899C4⋊C4C2×#4112yes—
900C22⋊C4—42no—
901C22⋊C4—42no—
902C22⋊C4—42no—
903C22⋊C4—42no—
904C22⋊C4—42no—
905C22⋊C4—81no—
906C22⋊C4—81no—
907C22⋊C4—81no—
908C22⋊C4—81no—
909C22⋊C4—81no—
910C22⋊C4—81no—
911C22⋊C4—81no—
912C22⋊C4—81no—
913C42—21no—
914C42—21no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—42no—
926C42—42no—
927C42—42no—
928C42—42no—
929C42—81no—
930C42—81no—
931C42—81no—
932C42—81no—
933C42—81no—
934C42—81no—
935C42—81no—
936C42—81no—
937C42—81no—
938C42—81no—
939C42—81no—
940C42C2×#4112yes—
941C422−1+412yes—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23C23×D411yescharacteristic
950Q8—41no—
951Q8—41no—
952Q8—41no—
953Q8—41no—
954Q8—41no—
955Q8—41no—
956Q8—41no—
957Q8—41no—
958Q8—41no—
959Q8—41no—
960Q8—41no—
961Q8—41no—
962Q8—84no—
963Q8—82no—
964Q8—82no—
965Q8—162no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970C2×C4—21no—
971C2×C4—21no—
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—22no—
999C2×C4—22no—
1000C2×C4—21no—
1001C2×C4—21no—
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—21no—
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#54812yes—
1057C2×C4#54812yes—
1058C2×C4C22×#4111yescharacteristic
1059C2×C4C2×2−1+411yescharacteristic
1060C2×C4#58511yescharacteristic
1061C2×C4#58511yescharacteristic
1062C2×C4#58511yescharacteristic
1063C2×C4#58511yescharacteristic
1064C8—41no—
1065C8—41no—
1066C8—41no—
1067C8—41no—
1068C8—41no—
1069C8—41no—
1070C8—41no—
1071C8—41no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22C2×#54811yescharacteristic
1080C22#348511yescharacteristic
1081C22#348711yescharacteristic
1082C22#358511yescharacteristic
1083C22#358611yescharacteristic
1084C22#358611yescharacteristic
1085C22#358611yescharacteristic
1086C4—22no—
1087C4—22no—
1088C4—41no—
1089C4—41no—
1090C4—41no—
1091C4—41no—
1092C4—41no—
1093C4—41no—
1094C4—41no—
1095C4—41no—
1096C4—41no—
1097C4—41no—
1098C4—42no—
1099C4—42no—
1100C4—41no—
1101C4—41no—
1102C4—81no—
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#352411yescharacteristic
1116C4#352411yescharacteristic
1117C4#356511yescharacteristic
1118C4#356511yescharacteristic
1119C2—161no—
1120C2#4527011yescharacteristic
1121C2#6133311yescharacteristic
1122C2#6133511yescharacteristic
1123C2#6178111yescharacteristic
1124C2#6178211yescharacteristic
1125C2#6194411yescharacteristic
1126C2#6194611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #44949C2semidirect
3. #32645C2semidirect
4. #32644C2semidirect
9. #32100C2semidirect
10. #32098C2semidirect
12. #28213C2semidirect
16. #27384C2semidirect
18. #27382C2semidirect
19. #26335C2semidirect
20. #26333C2semidirect
23. #26101C2semidirect
24. #26100C2semidirect
27. #23829C2semidirect
28. #23069C2semidirect
29. #23068C2semidirect
30. #22312C2semidirect

Maximal subgroups

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

subgroupindex
#451512
#449492
#326452
#326442
#326392
#326382
#321052
#321032
#321002
#320982
#292672
#282132
#277542
#273852
#273842
#273832
#273822
#263352
#263332
#263312
#263292
#261012
#261002
#252872
#252862
#238292
#230692
#230682
#223122
#222332