Finite Group Databasebeta

← #6542041

Subgroups — #6542041

Order 512.

1422 conjugacy classes of subgroups.

The subgroup lattice has 1171 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39622C211yesmaximal, characteristic, complemented
2#34481C211yesmaximal, characteristic
3#29993C211yesmaximal, characteristic, complemented
4#29992C211yesmaximal, characteristic, complemented
5#29987C211yesmaximal, characteristic
6#29269C211yesmaximal, characteristic
7#29268C211yesmaximal, characteristic
8#29257C211yesmaximal, characteristic, complemented
9#28524C211yesmaximal, characteristic
10#28523C211yesmaximal, characteristic
11#28518C211yesmaximal, characteristic, complemented
12#26479C211yesmaximal, characteristic
13#26477C211yesmaximal, characteristic
14#26474C211yesmaximal, characteristic, complemented
15#26473C211yesmaximal, characteristic, complemented
16#26471C211yesmaximal, characteristic
17#26469C211yesmaximal, characteristic
18#26055C211yesmaximal, characteristic, complemented
19#26054C211yesmaximal, characteristic, complemented
20#26053C211yesmaximal, characteristic
21#26052C211yesmaximal, characteristic
22#26047C211yesmaximal, characteristic, complemented
23#26043C211yesmaximal, characteristic, complemented
24#23793C211yesmaximal, characteristic, complemented
25#23792C211yesmaximal, characteristic, complemented
26#23784C211yesmaximal, characteristic
27#22737C211yesmaximal, characteristic, complemented
28#22729C211yesmaximal, characteristic, complemented
29#22728C211yesmaximal, characteristic, complemented
30#22548C211yesmaximal, characteristic
31#22548C211yesmaximal, characteristic
32C2×#556C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#479C2211yescharacteristic
38C2×#479C2211yescharacteristic
39C2×#477C2211yescharacteristic
40C2×#475C2211yescharacteristic
41C2×#478C2211yescharacteristic
42C2×#478C2211yescharacteristic
43C2×#476C2211yescharacteristic
44C2×#474C2211yescharacteristic
45C2×#446C2211yescharacteristic
46C2×#446C2211yescharacteristic
47#2859C2211yescharacteristic
48#2806—21no—
49#2806—21no—
50#2792—21no—
51#2792—21no—
52#2660C2211yescharacteristic
53#2660C2211yescharacteristic
54#2586—21no—
55#2586—21no—
56#2552C2211yescharacteristic
57#2552C2211yescharacteristic
58#2550C2211yescharacteristic
59#2550C2211yescharacteristic
60#2550C2211yescharacteristic
61#2550C2211yescharacteristic
62#2507—21no—
63#2507—21no—
64#2383—21no—
65#2383—21no—
66#2367C2211yescharacteristic
67#2367C2211yescharacteristic
68#2365C2211yescharacteristic
69#2360—21no—
70#2355C2211yescharacteristic
71#2355C2211yescharacteristic
72Q8×C4⋊C4C2211yescharacteristic
73Q8×C4⋊C4C2211yescharacteristic
74Q8×C4⋊C4C2211yescharacteristic
75D4×C4⋊C4C2211yescharacteristic
76#2347—21no—
77#2334—21no—
78#2334—21no—
79#2330C2211yescharacteristic
80#2330C2211yescharacteristic
81#2326C2211yescharacteristic
82#2326C2211yescharacteristic
83#2323—21no—
84#2320C2211yescharacteristic
85#2320C2211yescharacteristic
86#2317—21no—
87C4×C4⋊Q8C2211yescharacteristic
88C4×#125C2211yescharacteristic
89#2295C2211yescharacteristic
90#2293C2211yescharacteristic
91#2101C2211yescharacteristic
92#2100C2211yescharacteristic
93#2099C2211yescharacteristic
94#2097C2211yescharacteristic
95#2097C2211yescharacteristic
96#2096C2211yescharacteristic
97#2096C2211yescharacteristic
98#2095C2211yescharacteristic
99#2095C2211yescharacteristic
100#2094C2211yescharacteristic
101#2093C2211yescharacteristic
102#2092C2211yescharacteristic
103#2088C2211yescharacteristic
104#2088C2211yescharacteristic
105#2088C2211yescharacteristic
106#2087C2211yescharacteristic
107#2086C2211yescharacteristic
108#2086C2211yescharacteristic
109#2068C2211yescharacteristic
110#2068C2211yescharacteristic
111#2067C2211yescharacteristic
112#2066C2211yescharacteristic
113#2066C2211yescharacteristic
114#2065C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2059C2211yescharacteristic
120#2058C2211yescharacteristic
121#2057C2211yescharacteristic
122#2026C2211yescharacteristic
123#2026C2211yescharacteristic
124#2026C2211yescharacteristic
125#2026C2211yescharacteristic
126#2025C2211yescharacteristic
127#2025C2211yescharacteristic
128#2025C2211yescharacteristic
129#2024C2211yescharacteristic
130#2024C2211yescharacteristic
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1983C2211yescharacteristic
134#1983C2211yescharacteristic
135#1981C2211yescharacteristic
136#1981C2211yescharacteristic
137#1960C2211yescharacteristic
138#1960C2211yescharacteristic
139#1959C2211yescharacteristic
140#1959C2211yescharacteristic
141#1958C2211yescharacteristic
142#1958C2211yescharacteristic
143#1949C2211yescharacteristic
144#1949C2211yescharacteristic
145#1949C2211yescharacteristic
146#1949C2211yescharacteristic
147#1948C2211yescharacteristic
148#1948C2211yescharacteristic
149#1948C2211yescharacteristic
150#1948C2211yescharacteristic
151#1947C2211yescharacteristic
152#1947C2211yescharacteristic
153#1947C2211yescharacteristic
154#1947C2211yescharacteristic
155#1940C2211yescharacteristic
156#1940C2211yescharacteristic
157#1940C2211yescharacteristic
158#1940C2211yescharacteristic
159#1939C2211yescharacteristic
160#1939C2211yescharacteristic
161#1865C2211yescharacteristic
162#1865C2211yescharacteristic
163#1865C2211yescharacteristic
164#1865C2211yescharacteristic
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1863C2211yescharacteristic
168#1863C2211yescharacteristic
169#1863C2211yescharacteristic
170#1863C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1847C2211yescharacteristic
174#1847C2211yescharacteristic
175#1847C2211yescharacteristic
176#1847C2211yescharacteristic
177#1845C2211yescharacteristic
178#1844C2211yescharacteristic
179#1832C2211yescharacteristic
180#1832C2211yescharacteristic
181#1831C2211yescharacteristic
182#1805C2211yescharacteristic
183#1805C2211yescharacteristic
184#1804C2211yescharacteristic
185#1804C2211yescharacteristic
186#1803C2211yescharacteristic
187#1803C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192C4×#107C2211yescharacteristic
193C4×#106C2211yescharacteristic
194#1768C2211yescharacteristic
195#1768C2211yescharacteristic
196#1767C2211yescharacteristic
197#1763C2211yescharacteristic
198#1763C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×#103C2211yescharacteristic
203#556—24no—
204#556Q818yescomplemented
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126—21no—
209C2×#126—21no—
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×C22⋊Q8—21no—
218C2×C4×Q8—21no—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×#117—21no—
230C2×#117—21no—
231C22×C4⋊C4—21no—
232#479—42no—
233#479—42no—
234#479—42no—
235#479—42no—
236#479—42no—
237#479—42no—
238#478—42no—
239#478—42no—
240#477—42no—
241#476—42no—
242#475—42no—
243#474—42no—
244#446—24no—
245#446—24no—
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
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
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#395—21no—
321#395—21no—
322#395—21no—
323#395—21no—
324#395—21no—
325#395—21no—
326#395—21no—
327#395—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391D411yescharacteristic
335#391D411yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389D411yescharacteristic
367#389D411yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—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#387D411yescharacteristic
405#387D411yescharacteristic
406#387D411yescharacteristic
407#387D411yescharacteristic
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#384—21no—
417#384—21no—
418#384—21no—
419#384—21no—
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#383—21no—
428#383—21no—
429#382—21no—
430#382—21no—
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#380—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461#376C2311yescharacteristic
462#376C2311yescharacteristic
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#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8C2×D411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4C2411yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C4⋊Q8—22no—
512C4⋊Q8—41no—
513C4⋊Q8—41no—
514C4⋊Q8—41no—
515C4⋊Q8—41no—
516C4⋊Q8C2×Q814yes—
517#126—28no—
518#126—28no—
519#125—22no—
520#125—22no—
521#125—41no—
522#125—41no—
523#125—41no—
524#125—41no—
525#125—41no—
526#125—41no—
527#125—41no—
528#125—41no—
529#124—22no—
530#124—22no—
531#124C2×Q814yes—
532#124C2×Q814yes—
533C22⋊Q8—28no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—41no—
537C4×Q8—41no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—82no—
545C4×Q8C2×Q814yes—
546C4×Q8C2×Q814yes—
547C4×Q8C2×Q814yes—
548C4×Q8#4114yes—
549C4×D4—22no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—41no—
553C4×D4—41no—
554C4×D4C2×Q814yes—
555#117—28no—
556#117—82no—
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⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
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—82no—
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
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⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
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×C42C2×D411yescharacteristic
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2×D411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661#107—22no—
662#107—22no—
663#107—22no—
664#107—22no—
665#107—41no—
666#107—41no—
667#107—41no—
668#107—41no—
669#107—41no—
670#107—41no—
671#106—22no—
672#106—22no—
673#106—22no—
674#106—22no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679#106—41no—
680#106—41no—
681C4⋊C8—22no—
682C4⋊C8—22no—
683C4⋊C8—22no—
684C4⋊C8—22no—
685C4⋊C8—22no—
686C4⋊C8—22no—
687C4⋊C8—22no—
688C4⋊C8—22no—
689C4⋊C8—22no—
690C4⋊C8—22no—
691C4⋊C8—22no—
692C4⋊C8—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—41no—
702#103—41no—
703#103—41no—
704#103—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#103—41no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#97—22no—
718#97—22no—
719#97—22no—
720#97—22no—
721C4×C8—22no—
722C4×C8—22no—
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#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774C24—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—41no—
786C2×Q8—41no—
787C2×Q8—81no—
788C2×Q8—81no—
789C2×Q8—81no—
790C2×Q8—81no—
791C2×Q8—81no—
792C2×Q8—81no—
793C2×Q8C22⋊Q814yes—
794C2×Q8C22×Q812yes—
795C2×Q8C22×Q812yes—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4C22×Q812yes—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—24no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—81no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4—81no—
824C22×C4—81no—
825C22×C4—81no—
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C2511yescharacteristic
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8H(5,𝔽2)12yes—
864C2×C8H(5,𝔽2)12yes—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—41no—
895C4⋊C4—41no—
896C4⋊C4—41no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—41no—
900C4⋊C4—42no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4C22⋊Q814yes—
939C4⋊C4C22⋊Q814yes—
940C4⋊C4C22⋊Q814yes—
941C4⋊C4C22×Q812yes—
942C4⋊C42−1+412yes—
943C4⋊C42−1+412yes—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—42no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C42—24no—
956C42—24no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—41no—
966C42—41no—
967C42—41no—
968C42—41no—
969C42—42no—
970C42—81no—
971C42—81no—
972C42—81no—
973C42—81no—
974C42—81no—
975C42—81no—
976C42—81no—
977C42—81no—
978C42—81no—
979C42—81no—
980C42—81no—
981C42—81no—
982C42C22×Q812yes—
983C42C22×Q812yes—
984C42C22×Q812yes—
985C42C2×#4112yes—
986C42C2×#4112yes—
987C42C2×#4112yes—
988C23—22no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23C23×D411yescharacteristic
996Q8—22no—
997Q8—22no—
998Q8—22no—
999Q8—22no—
1000Q8—44no—
1001Q8—41no—
1002Q8—41no—
1003Q8—41no—
1004Q8—41no—
1005Q8—162no—
1006Q8—162no—
1007D4—22no—
1008D4—22no—
1009D4—41no—
1010D4—41no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
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—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—48no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
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—162no—
1094C2×C4—162no—
1095C2×C4C2×C22⋊Q812yes—
1096C2×C4C2×C22⋊Q812yes—
1097C2×C4C2×C22⋊Q812yes—
1098C2×C4C2×C22⋊Q812yes—
1099C2×C4C2×C22⋊Q812yes—
1100C2×C4C2×C22⋊Q812yes—
1101C2×C4C23×Q811yescharacteristic
1102C2×C4C22×#4111yescharacteristic
1103C2×C4C2×H(5,𝔽2)11yescharacteristic
1104C2×C4C2×H(5,𝔽2)11yescharacteristic
1105C2×C4C2×2−1+411yescharacteristic
1106C2×C4C2×2−1+411yescharacteristic
1107C8—22no—
1108C8—22no—
1109C8—41no—
1110C8—41no—
1111C8—41no—
1112C8—41no—
1113C8—41no—
1114C8—41no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22C22×C22⋊Q811yescharacteristic
1123C22#348611yescharacteristic
1124C22#349811yescharacteristic
1125C22#358411yescharacteristic
1126C22#358511yescharacteristic
1127C22#358611yescharacteristic
1128C22#358611yescharacteristic
1129C4—22no—
1130C4—22no—
1131C4—22no—
1132C4—22no—
1133C4—22no—
1134C4—22no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—41no—
1139C4—42no—
1140C4—41no—
1141C4—42no—
1142C4—41no—
1143C4—41no—
1144C4—41no—
1145C4—41no—
1146C4—41no—
1147C4—41no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4#350311yescharacteristic
1159C4#350311yescharacteristic
1160C4#352211yescharacteristic
1161C4#352211yescharacteristic
1162C2—82no—
1163C2#3574811yescharacteristic
1164C2#6049211yescharacteristic
1165C2#6049911yescharacteristic
1166C2#6186211yescharacteristic
1167C2#6187811yescharacteristic
1168C2#6244211yescharacteristic
1169C2#6246111yescharacteristic
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
1. #39622C2semidirect
3. #29993C2semidirect
4. #29992C2semidirect
8. #29257C2semidirect
11. #28518C2semidirect
14. #26474C2semidirect
15. #26473C2semidirect
18. #26055C2semidirect
19. #26054C2semidirect
22. #26047C2semidirect
23. #26043C2semidirect
24. #23793C2semidirect
25. #23792C2semidirect
27. #22737C2semidirect
28. #22729C2semidirect
29. #22728C2semidirect
204. #556Q8semidirect

Maximal subgroups

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

subgroupindex
#396222
#344812
#299932
#299922
#299872
#292692
#292682
#292572
#285242
#285232
#285182
#264792
#264772
#264742
#264732
#264712
#264692
#260552
#260542
#260532
#260522
#260472
#260432
#237932
#237922
#237842
#227372
#227292
#227282
#225482