Finite Group Databasebeta

← #6469253

Subgroups — #6469253

Order 512.

1511 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35321C211yesmaximal, characteristic
2#34085C211yesmaximal, characteristic
3#29447C211yesmaximal, characteristic, complemented
4#29446C211yesmaximal, characteristic, complemented
5#29431C211yesmaximal, characteristic, complemented
6#29430C211yesmaximal, characteristic, complemented
7#29359C211yesmaximal, characteristic, complemented
8#29325C211yesmaximal, characteristic, complemented
9#29138C211yesmaximal, characteristic, complemented
10#28391C211yesmaximal, characteristic, complemented
11#27866C211yesmaximal, characteristic
12#27860C211yesmaximal, characteristic
13#25504C211yesmaximal, characteristic
14#25498C211yesmaximal, characteristic
15#24854C211yesmaximal, characteristic
16#24850C211yesmaximal, characteristic
17#24764C211yesmaximal, characteristic
18#24764C211yesmaximal, characteristic
19#23789C211yesmaximal, characteristic, complemented
20#23788C211yesmaximal, characteristic, complemented
21#23691C211yesmaximal, characteristic, complemented
22#23691C211yesmaximal, characteristic, complemented
23#21618C211yesmaximal, characteristic, complemented
24C4×#479C211yesmaximal, characteristic, complemented
25#21542C211yesmaximal, characteristic
26#21537C211yesmaximal, characteristic
27#21530C211yesmaximal, characteristic
28#21525C211yesmaximal, characteristic
29#21506C211yesmaximal, characteristic, complemented
30C4×#462C211yesmaximal, characteristic, complemented
31#20430C211yesmaximal, characteristic
32C2×#533C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#470C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#467C2211yescharacteristic
39C2×#462C2211yescharacteristic
40C2×#462C2211yescharacteristic
41C2×#441C2211yescharacteristic
42C2×#441C2211yescharacteristic
43C2×C4×Q16C2211yescharacteristic
44C2×C4×Q16C2211yescharacteristic
45C2×#424C2211yescharacteristic
46C2×#424C2211yescharacteristic
47C2×#405C2211yescharacteristic
48C2×#405C2211yescharacteristic
49#2863C2211yescharacteristic
50#2863C2211yescharacteristic
51#2855C2211yescharacteristic
52#2855C2211yescharacteristic
53#2647C2211yescharacteristic
54#2642C2211yescharacteristic
55#2629C2211yescharacteristic
56#2621C2211yescharacteristic
57#2585—21no—
58#2585—21no—
59#2573—21no—
60#2573—21no—
61#2524—21no—
62#2524—21no—
63#2515—21no—
64#2515—21no—
65#2336—21no—
66#2336—21no—
67#2332—21no—
68#2332—21no—
69#2331C2211yescharacteristic
70#2331C2211yescharacteristic
71#2327C2211yescharacteristic
72#2327C2211yescharacteristic
73#2323C2211yescharacteristic
74#2323C2211yescharacteristic
75#2323C2211yescharacteristic
76#2323C2211yescharacteristic
77#2323C2211yescharacteristic
78#2323C2211yescharacteristic
79#2320C2211yescharacteristic
80#2320C2211yescharacteristic
81C4×C4⋊Q8C2211yescharacteristic
82C4×#125C2211yescharacteristic
83#2298—21no—
84#2298—21no—
85#2295—21no—
86#2295—21no—
87#2295C2211yescharacteristic
88#2295C2211yescharacteristic
89#2283C2211yescharacteristic
90C42×Q8C2211yescharacteristic
91C42×Q8C2211yescharacteristic
92C4×#117C2211yescharacteristic
93#2101C2211yescharacteristic
94#2101C2211yescharacteristic
95#2097C2211yescharacteristic
96#2097C2211yescharacteristic
97#2088C2211yescharacteristic
98#2088C2211yescharacteristic
99#2087C2211yescharacteristic
100#2086C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2074C2211yescharacteristic
104#2074C2211yescharacteristic
105#2068C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2068C2211yescharacteristic
109#2066C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2066C2211yescharacteristic
113#2058C2211yescharacteristic
114#2057C2211yescharacteristic
115#2056C2211yescharacteristic
116#2056C2211yescharacteristic
117#2056C2211yescharacteristic
118#2056C2211yescharacteristic
119#2043C2211yescharacteristic
120#2043C2211yescharacteristic
121#2024C2211yescharacteristic
122#2024C2211yescharacteristic
123#2016C2211yescharacteristic
124#2016C2211yescharacteristic
125#1989C2211yescharacteristic
126#1989C2211yescharacteristic
127#1981C2211yescharacteristic
128#1981C2211yescharacteristic
129#1971C2211yescharacteristic
130#1971C2211yescharacteristic
131#1969C2211yescharacteristic
132#1969C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1948C2211yescharacteristic
136#1947C2211yescharacteristic
137#1944C2211yescharacteristic
138#1943C2211yescharacteristic
139#1942C2211yescharacteristic
140#1941C2211yescharacteristic
141#1935C2211yescharacteristic
142#1935C2211yescharacteristic
143#1935C2211yescharacteristic
144#1935C2211yescharacteristic
145#1933C2211yescharacteristic
146#1933C2211yescharacteristic
147#1933C2211yescharacteristic
148#1933C2211yescharacteristic
149#1928C2211yescharacteristic
150#1928C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1921C2211yescharacteristic
154#1920C2211yescharacteristic
155#1919C2211yescharacteristic
156#1918C2211yescharacteristic
157#1894C2211yescharacteristic
158#1894C2211yescharacteristic
159#1894C2211yescharacteristic
160#1894C2211yescharacteristic
161#1892C2211yescharacteristic
162#1892C2211yescharacteristic
163#1892C2211yescharacteristic
164#1892C2211yescharacteristic
165#1878C2211yescharacteristic
166#1878C2211yescharacteristic
167#1878C2211yescharacteristic
168#1878C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1863C2211yescharacteristic
172#1863C2211yescharacteristic
173#1809C2211yescharacteristic
174#1809C2211yescharacteristic
175#1808C2211yescharacteristic
176#1807C2211yescharacteristic
177#1805C2211yescharacteristic
178#1805C2211yescharacteristic
179#1803C2211yescharacteristic
180#1803C2211yescharacteristic
181#1776C2211yescharacteristic
182#1776C2211yescharacteristic
183C4×#107C2211yescharacteristic
184C4×#106C2211yescharacteristic
185#1768C2211yescharacteristic
186#1768C2211yescharacteristic
187#1768C2211yescharacteristic
188#1768C2211yescharacteristic
189#1767C2211yescharacteristic
190#1767C2211yescharacteristic
191C4×C4⋊C8C2211yescharacteristic
192C4×C4⋊C8C2211yescharacteristic
193#1763C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201#1728C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#533—24no—
212#533—24no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#125—21no—
217C2×#125C2311yescharacteristic
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C4×Q8—21no—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×#117—21no—
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C22×C42C2311yescharacteristic
236#479—24no—
237#479—24no—
238#470—24no—
239#470—24no—
240#467—24no—
241#467—24no—
242#462—24no—
243#462—24no—
244#441—42no—
245#441—42no—
246C4×Q16—42no—
247C4×Q16—42no—
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260#424—24no—
261#424—24no—
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294#405—42no—
295#405—42no—
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#397—21no—
317#397—21no—
318#396—21no—
319#396—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—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#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#385—21no—
407#385—21no—
408#384C2311yescharacteristic
409#383—21no—
410#383—21no—
411#383—21no—
412#383—21no—
413#383—21no—
414#382—21no—
415#382—21no—
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#381—21no—
420#381—21no—
421#381—21no—
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4D411yescharacteristic
439C4×C4⋊C4D411yescharacteristic
440C4×C4⋊C4D411yescharacteristic
441C4×C4⋊C4D411yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4D411yescharacteristic
452C4×C22⋊C4D411yescharacteristic
453C4×C22⋊C4D411yescharacteristic
454C4×C22⋊C4D411yescharacteristic
455#376—21no—
456#376—21no—
457#376—21no—
458#376C2311yescharacteristic
459#376C2311yescharacteristic
460C43—21no—
461C43—21no—
462C43C2311yescharacteristic
463C43C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
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#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C22×Q8—21no—
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C23×C4C2×D411yescharacteristic
502C23×C4C2×D411yescharacteristic
503C23×C4C2411yescharacteristic
504C2×Q16—22no—
505C2×Q16—22no—
506C2×Q16—22no—
507C2×Q16—22no—
508C2×Q16—22no—
509C2×Q16—22no—
510C2×Q16—22no—
511C2×Q16—22no—
512C2×Q16—41no—
513C2×Q16—41no—
514C2×Q16—41no—
515C2×Q16—41no—
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—22no—
519C2×M16—22no—
520C2×M16—41no—
521C2×M16—41no—
522C22×C8—22no—
523C22×C8—22no—
524C22×C8—22no—
525C22×C8—22no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C4⋊Q8—22no—
537C4⋊Q8—22no—
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540C4⋊Q8—22no—
541C4⋊Q8—22no—
542#125—28no—
543#125—22no—
544#125—22no—
545C22⋊Q8—28no—
546C22⋊Q8—22no—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8#4114yes—
553C22⋊Q8#4114yes—
554C4×Q8—28no—
555C4×Q8—22no—
556C4×Q8—22no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—22no—
564C4×Q8—22no—
565C4×Q8—22no—
566C4×Q8—22no—
567C4×Q8—22no—
568C4×Q8—22no—
569C4×Q8—22no—
570C4×Q8—22no—
571#117—28no—
572#117—22no—
573#117—22no—
574#117—22no—
575#117—22no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C22⋊C4C2×D411yescharacteristic
635C2×C22⋊C4C2×D411yescharacteristic
636C2×C22⋊C4C2×D411yescharacteristic
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—22no—
640C2×C42—22no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42C2×D411yescharacteristic
656C2×C42C2×D411yescharacteristic
657C2×C42C2×D411yescharacteristic
658C2×C42C2×D411yescharacteristic
659C2×C42C2×D411yescharacteristic
660C2×C42C2×D411yescharacteristic
661C2×C42C2×D411yescharacteristic
662C2×C42C2×D411yescharacteristic
663C2×C42C2×D411yescharacteristic
664C2×C42C2×D411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671#107—22no—
672#107—22no—
673#107—22no—
674#107—22no—
675#107—41no—
676#107—41no—
677#106—22no—
678#106—22no—
679#106—22no—
680#106—22no—
681#106—41no—
682#106—41no—
683C4⋊C8—22no—
684C4⋊C8—22no—
685C4⋊C8—22no—
686C4⋊C8—22no—
687C4⋊C8—22no—
688C4⋊C8—22no—
689C4⋊C8#4114yes—
690C4⋊C8#4114yes—
691#103—22no—
692#103—22no—
693#103—22no—
694#103—22no—
695#103—22no—
696#103—22no—
697#103—22no—
698#103—22no—
699#103—22no—
700#103—22no—
701#103—22no—
702#103—22no—
703#103—22no—
704#103—22no—
705#103—22no—
706#103—22no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#97—22no—
716#97—22no—
717#97—41no—
718#97—41no—
719C4×C8—22no—
720C4×C8—22no—
721C4×C8—41no—
722C4×C8—41no—
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#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785C24C22×D411yescharacteristic
786C2×Q8—24no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—81no—
810C2×Q8—81no—
811C2×Q8C2×#4112yes—
812C2×Q8C2×#4112yes—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C2×#4112yes—
853C22×C4C2×#4112yes—
854C22×C4C2511yescharacteristic
855Q16—44no—
856Q16—44no—
857Q16—44no—
858Q16—44no—
859M16—44no—
860M16—44no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—44no—
882C2×C8—44no—
883C2×C8C2×#4112yes—
884C2×C8C2×#4112yes—
885C2×C8C2×#4112yes—
886C2×C8C2×#4112yes—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—22no—
895C4⋊C4—22no—
896C4⋊C4—22no—
897C4⋊C4—22no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4C2×#4112yes—
947C4⋊C4C2×#4112yes—
948C22⋊C4—24no—
949C22⋊C4—24no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C42—24no—
961C42—24no—
962C42—22no—
963C42—22no—
964C42—22no—
965C42—22no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—41no—
975C42—41no—
976C42—41no—
977C42—41no—
978C42—41no—
979C42—41no—
980C42—42no—
981C42—42no—
982C42—42no—
983C42—42no—
984C42—42no—
985C42—42no—
986C42—42no—
987C42—42no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C42—81no—
994C42C2×#4112yes—
995C42C2×#4112yes—
996C42H(5,𝔽2)12yes—
997C422−1+412yes—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23#52512yes—
1005C23C23×D411yescharacteristic
1006Q8—22no—
1007Q8—22no—
1008Q8—22no—
1009Q8—22no—
1010Q8—41no—
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—41no—
1017Q8—41no—
1018Q8—41no—
1019Q8—41no—
1020Q8—41no—
1021Q8—41no—
1022Q8—84no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—44no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—82no—
1110C2×C4#52512yes—
1111C2×C4#53212yes—
1112C2×C4#53212yes—
1113C2×C4#53712yes—
1114C2×C4#53712yes—
1115C2×C4#57812yes—
1116C2×C4C22×#4111yescharacteristic
1117C2×C4C22×#4111yescharacteristic
1118C2×C4C22×#4111yescharacteristic
1119C2×C4C22×#4111yescharacteristic
1120C2×C4C2×H(5,𝔽2)11yescharacteristic
1121C2×C4C2×2−1+411yescharacteristic
1122C8—22no—
1123C8—22no—
1124C8—22no—
1125C8—22no—
1126C8—41no—
1127C8—41no—
1128C8—41no—
1129C8—41no—
1130C22—22no—
1131C22—22no—
1132C22—22no—
1133C22—41no—
1134C22—41no—
1135C22—41no—
1136C22—41no—
1137C22C2×#52511yescharacteristic
1138C22C2×#53211yescharacteristic
1139C22C2×#53711yescharacteristic
1140C22C2×#57811yescharacteristic
1141C22#358411yescharacteristic
1142C22#358611yescharacteristic
1143C22#358611yescharacteristic
1144C4—22no—
1145C4—22no—
1146C4—22no—
1147C4—22no—
1148C4—22no—
1149C4—22no—
1150C4—41no—
1151C4—41no—
1152C4—41no—
1153C4—42no—
1154C4—42no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—42no—
1159C4—42no—
1160C4—41no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4#348111yescharacteristic
1174C4#348111yescharacteristic
1175C4#348211yescharacteristic
1176C4#348211yescharacteristic
1177C2—42no—
1178C2#3496411yescharacteristic
1179C2#6058311yescharacteristic
1180C2#6058611yescharacteristic
1181C2#6069611yescharacteristic
1182C2#6069911yescharacteristic
1183C2#6092511yescharacteristic
1184C2#6093211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #29447C2semidirect
4. #29446C2semidirect
5. #29431C2semidirect
6. #29430C2semidirect
7. #29359C2semidirect
8. #29325C2semidirect
9. #29138C2semidirect
10. #28391C2semidirect
19. #23789C2semidirect
20. #23788C2semidirect
21. #23691C2semidirect
22. #23691C2semidirect
23. #21618C2semidirect
24. C4×#479C2semidirect
29. #21506C2semidirect
30. C4×#462C2semidirect

Maximal subgroups

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

subgroupindex
#353212
#340852
#294472
#294462
#294312
#294302
#293592
#293252
#291382
#283912
#278662
#278602
#255042
#254982
#248542
#248502
#247642
#237892
#237882
#236912
#216182
C4×#4792
#215422
#215372
#215302
#215252
#215062
C4×#4622
#204302