Finite Group Databasebeta

← #6541997

Subgroups — #6541997

Order 512.

1526 conjugacy classes of subgroups.

The subgroup lattice has 1213 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36565C211yesmaximal, characteristic, complemented
2#34331C211yesmaximal, characteristic
3#29986C211yesmaximal, characteristic, complemented
4#29985C211yesmaximal, characteristic, complemented
5#29982C211yesmaximal, characteristic, complemented
6#29261C211yesmaximal, characteristic, complemented
7#29261C211yesmaximal, characteristic, complemented
8#29256C211yesmaximal, characteristic
9#28521C211yesmaximal, characteristic
10#28517C211yesmaximal, characteristic, complemented
11#28510C211yesmaximal, characteristic, complemented
12#26478C211yesmaximal, characteristic, complemented
13#26476C211yesmaximal, characteristic, complemented
14#26475C211yesmaximal, characteristic
15#26472C211yesmaximal, characteristic
16#26471C211yesmaximal, characteristic, complemented
17#26469C211yesmaximal, characteristic, complemented
18#26058C211yesmaximal, characteristic, complemented
19#26058C211yesmaximal, characteristic, complemented
20#26055C211yesmaximal, characteristic, complemented
21#26054C211yesmaximal, characteristic, complemented
22#26051C211yesmaximal, characteristic, complemented
23#26049C211yesmaximal, characteristic, complemented
24#23785C211yesmaximal, characteristic, complemented
25#23784C211yesmaximal, characteristic, complemented
26#23778C211yesmaximal, characteristic, complemented
27#22736C211yesmaximal, characteristic, complemented
28#22731C211yesmaximal, characteristic, complemented
29#22730C211yesmaximal, characteristic, complemented
30#22549C211yesmaximal, characteristic
31#22549C211yesmaximal, characteristic
32C2×#559C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#477C2211yescharacteristic
36C2×#475C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#476C2211yescharacteristic
40C2×#476C2211yescharacteristic
41C2×#476C2211yescharacteristic
42C2×#474C2211yescharacteristic
43C2×#474C2211yescharacteristic
44C2×#474C2211yescharacteristic
45C2×#446C2211yescharacteristic
46C2×#446C2211yescharacteristic
47#2862C2211yescharacteristic
48#2862C2211yescharacteristic
49#2859C2211yescharacteristic
50#2586—21no—
51#2586—21no—
52#2586—21no—
53#2586—21no—
54#2551C2211yescharacteristic
55#2551C2211yescharacteristic
56#2550C2211yescharacteristic
57#2550C2211yescharacteristic
58#2550C2211yescharacteristic
59#2550C2211yescharacteristic
60#2451—21no—
61#2451—21no—
62#2369—21no—
63#2369—21no—
64#2367—21no—
65#2367C2211yescharacteristic
66#2367C2211yescharacteristic
67#2366C2211yescharacteristic
68#2359—21no—
69#2359—21no—
70#2355C2211yescharacteristic
71#2355C2211yescharacteristic
72#2355C2211yescharacteristic
73#2354—21no—
74Q8×C4⋊C4C2211yescharacteristic
75#2349C2211yescharacteristic
76#2349C2211yescharacteristic
77#2335—21no—
78#2335—21no—
79#2326—21no—
80C4×#127C2211yescharacteristic
81C4×#125C2211yescharacteristic
82C4×#125C2211yescharacteristic
83C4×#125C2211yescharacteristic
84C4×#124C2211yescharacteristic
85C4×#124C2211yescharacteristic
86#2295C2211yescharacteristic
87#2293C2211yescharacteristic
88#2293C2211yescharacteristic
89#2275—21no—
90C42×Q8C2211yescharacteristic
91#2101C2211yescharacteristic
92#2101C2211yescharacteristic
93#2101C2211yescharacteristic
94#2097C2211yescharacteristic
95#2097C2211yescharacteristic
96#2097C2211yescharacteristic
97#2092C2211yescharacteristic
98#2092C2211yescharacteristic
99#2092C2211yescharacteristic
100#2092C2211yescharacteristic
101#2092C2211yescharacteristic
102#2092C2211yescharacteristic
103#2088C2211yescharacteristic
104#2088C2211yescharacteristic
105#2088C2211yescharacteristic
106#2087C2211yescharacteristic
107#2087C2211yescharacteristic
108#2086C2211yescharacteristic
109#2068C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2066C2211yescharacteristic
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2058C2211yescharacteristic
119#2058C2211yescharacteristic
120#2057C2211yescharacteristic
121#2057C2211yescharacteristic
122#2026C2211yescharacteristic
123#2025C2211yescharacteristic
124#2025C2211yescharacteristic
125#2025C2211yescharacteristic
126#2025C2211yescharacteristic
127#2024C2211yescharacteristic
128#2024C2211yescharacteristic
129#2023C2211yescharacteristic
130#2023C2211yescharacteristic
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1983C2211yescharacteristic
134#1983C2211yescharacteristic
135#1982C2211yescharacteristic
136#1982C2211yescharacteristic
137#1961C2211yescharacteristic
138#1961C2211yescharacteristic
139#1959C2211yescharacteristic
140#1959C2211yescharacteristic
141#1958C2211yescharacteristic
142#1958C2211yescharacteristic
143#1949C2211yescharacteristic
144#1949C2211yescharacteristic
145#1949C2211yescharacteristic
146#1949C2211yescharacteristic
147#1949C2211yescharacteristic
148#1949C2211yescharacteristic
149#1949C2211yescharacteristic
150#1949C2211yescharacteristic
151#1948C2211yescharacteristic
152#1948C2211yescharacteristic
153#1947C2211yescharacteristic
154#1947C2211yescharacteristic
155#1940C2211yescharacteristic
156#1940C2211yescharacteristic
157#1940C2211yescharacteristic
158#1940C2211yescharacteristic
159#1939C2211yescharacteristic
160#1939C2211yescharacteristic
161#1865C2211yescharacteristic
162#1865C2211yescharacteristic
163#1864C2211yescharacteristic
164#1864C2211yescharacteristic
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1863C2211yescharacteristic
168#1863C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1847C2211yescharacteristic
174#1847C2211yescharacteristic
175#1847C2211yescharacteristic
176#1847C2211yescharacteristic
177#1846C2211yescharacteristic
178#1846C2211yescharacteristic
179#1831C2211yescharacteristic
180#1831C2211yescharacteristic
181#1831C2211yescharacteristic
182#1805C2211yescharacteristic
183#1805C2211yescharacteristic
184#1804C2211yescharacteristic
185#1804C2211yescharacteristic
186#1802C2211yescharacteristic
187#1802C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192C4×#107C2211yescharacteristic
193C4×#106C2211yescharacteristic
194#1767C2211yescharacteristic
195#1767C2211yescharacteristic
196C4×C4⋊C8C2211yescharacteristic
197#1763C2211yescharacteristic
198#1763C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic
203#559—24no—
204#559Q818yescomplemented
205C2×C4⋊Q8—21no—
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#124—21no—
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#123—21no—
219C2×#123—21no—
220C2×C4×Q8D411yescharacteristic
221C2×C4×Q8D411yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4—21no—
229C2×C4×D4—21no—
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×#117—21no—
237C2×#117—21no—
238#479—42no—
239#479—42no—
240#478—42no—
241#478—42no—
242#477—42no—
243#476—42no—
244#476—42no—
245#476—42no—
246#475—42no—
247#474—42no—
248#474—42no—
249#474—42no—
250#446—24no—
251#446—24no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#395—21no—
319#395—21no—
320#395—21no—
321#395—21no—
322#395—21no—
323#395—21no—
324#395—21no—
325#395—21no—
326#391—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#390—21no—
344#390—21no—
345#390—21no—
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
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#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
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#388—21no—
382#388—21no—
383#388—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#386—21no—
399#386—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#384—21no—
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
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⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4D411yescharacteristic
433C4×C4⋊C4D411yescharacteristic
434C4×C4⋊C4D411yescharacteristic
435C4×C4⋊C4D411yescharacteristic
436C4×C4⋊C4D411yescharacteristic
437C4×C4⋊C4D411yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458#376—21no—
459C2×#95—21no—
460C2×#95—21no—
461C43C2311yescharacteristic
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#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×Q8—21no—
497C22×Q8—21no—
498C22×Q8C2×D411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×D4—21no—
501C22×D4—21no—
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C4⋊Q8—41no—
519C4⋊Q8—41no—
520C4⋊Q8—41no—
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—44no—
527C4⋊Q8—44no—
528#127—22no—
529#127C2×Q814yes—
530#125—22no—
531#125—22no—
532#125—41no—
533#125—41no—
534#125—41no—
535#125—41no—
536#124—28no—
537#124—22no—
538#124—22no—
539#124C2×Q814yes—
540#124C2×Q814yes—
541#123—28no—
542#123—28no—
543C4×Q8—22no—
544C4×Q8—42no—
545C4×Q8—42no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8C2×Q814yes—
551C4×Q8C2×Q814yes—
552C4×Q8#4114yes—
553C4×D4—28no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—44no—
557C4×D4—41no—
558C4×D4—41no—
559C4×D4—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—44no—
566C4×D4—82no—
567C4×D4C2×Q814yes—
568C4×D4C2×Q814yes—
569#117—82no—
570#117—82no—
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⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
623C2×C22⋊C4—21no—
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×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—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×C42—21no—
651C2×C42—21no—
652C2×C42C2×D411yescharacteristic
653C2×C42C2×D411yescharacteristic
654C2×C42C2×D411yescharacteristic
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×C42C2411yescharacteristic
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#107—41no—
678#107—41no—
679#107—41no—
680#107—41no—
681#106—22no—
682#106—22no—
683#106—22no—
684#106—22no—
685#106—41no—
686#106—41no—
687#106—41no—
688#106—41no—
689#106—41no—
690#106—41no—
691C4⋊C8—22no—
692C4⋊C8—22no—
693C4⋊C8—22no—
694C4⋊C8—22no—
695C4⋊C8—22no—
696C4⋊C8—22no—
697C4⋊C8—22no—
698C4⋊C8—22no—
699C4⋊C8—22no—
700C4⋊C8—22no—
701C4⋊C8—22no—
702C4⋊C8—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#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#97—22no—
728#97—22no—
729#97—22no—
730#97—22no—
731C4×C8—22no—
732C4×C8—22no—
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#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780C24—21no—
781C24—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—41no—
788C2×Q8—41no—
789C2×Q8—42no—
790C2×Q8—42no—
791C2×Q8—42no—
792C2×Q8—42no—
793C2×Q8—81no—
794C2×Q8—81no—
795C2×Q8—81no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×Q8—81no—
799C2×Q8—81no—
800C2×Q8—81no—
801C2×Q8C22⋊Q814yes—
802C2×Q8C22×Q812yes—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—81no—
818C2×D4—81no—
819C2×D4C22×Q812yes—
820C2×D4C22×Q812yes—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—24no—
826C22×C4—24no—
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—21no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C2511yescharacteristic
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—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8H(5,𝔽2)12yes—
891C2×C8H(5,𝔽2)12yes—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—22no—
896C4⋊C4—22no—
897C4⋊C4—22no—
898C4⋊C4—22no—
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—21no—
921C4⋊C4—21no—
922C4⋊C4—41no—
923C4⋊C4—41no—
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—81no—
933C4⋊C4—81no—
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⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4C22⋊Q814yes—
951C4⋊C4C22⋊Q814yes—
952C4⋊C4C22⋊Q814yes—
953C4⋊C4C22×Q812yes—
954C4⋊C42−1+412yes—
955C4⋊C42−1+412yes—
956C22⋊C4—24no—
957C22⋊C4—24no—
958C22⋊C4—24no—
959C22⋊C4—24no—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C42—24no—
975C42—22no—
976C42—22no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—41no—
986C42—41no—
987C42—41no—
988C42—41no—
989C42—41no—
990C42—41no—
991C42—41no—
992C42—41no—
993C42—41no—
994C42—41no—
995C42—42no—
996C42—42no—
997C42—42no—
998C42—81no—
999C42—81no—
1000C42—81no—
1001C42—81no—
1002C42—81no—
1003C42—81no—
1004C42—81no—
1005C42—81no—
1006C42C22×Q812yes—
1007C42C22×Q812yes—
1008C42C22×Q812yes—
1009C42C2×#4112yes—
1010C42C2×#4112yes—
1011C42C2×#4112yes—
1012C23—22no—
1013C23—22no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23C23×D411yescharacteristic
1027Q8—22no—
1028Q8—22no—
1029Q8—44no—
1030Q8—41no—
1031Q8—41no—
1032Q8—162no—
1033Q8—162no—
1034Q8—162no—
1035Q8—162no—
1036D4—22no—
1037D4—22no—
1038D4—22no—
1039D4—22no—
1040D4—48no—
1041D4—41no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—84no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
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—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—84no—
1123C2×C4—84no—
1124C2×C4—162no—
1125C2×C4—162no—
1126C2×C4—162no—
1127C2×C4—162no—
1128C2×C4C2×C22⋊Q812yes—
1129C2×C4C2×C22⋊Q812yes—
1130C2×C4C2×C22⋊Q812yes—
1131C2×C4C2×C22⋊Q812yes—
1132C2×C4C2×C22⋊Q812yes—
1133C2×C4C2×C22⋊Q812yes—
1134C2×C4#57512yes—
1135C2×C4#57512yes—
1136C2×C4C23×Q811yescharacteristic
1137C2×C4C22×#4111yescharacteristic
1138C2×C4C2×H(5,𝔽2)11yescharacteristic
1139C2×C4C2×H(5,𝔽2)11yescharacteristic
1140C2×C4C2×2−1+411yescharacteristic
1141C2×C4C2×2−1+411yescharacteristic
1142C8—22no—
1143C8—22no—
1144C8—41no—
1145C8—41no—
1146C8—41no—
1147C8—41no—
1148C8—41no—
1149C8—41no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22—81no—
1157C22—81no—
1158C22—81no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22C22×C22⋊Q811yescharacteristic
1165C22#348611yescharacteristic
1166C22#349811yescharacteristic
1167C22C2×#57511yescharacteristic
1168C22C2×#57511yescharacteristic
1169C22#358411yescharacteristic
1170C22#358511yescharacteristic
1171C4—22no—
1172C4—22no—
1173C4—22no—
1174C4—22no—
1175C4—22no—
1176C4—22no—
1177C4—22no—
1178C4—22no—
1179C4—42no—
1180C4—41no—
1181C4—42no—
1182C4—41no—
1183C4—42no—
1184C4—42no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4#350311yescharacteristic
1200C4#350311yescharacteristic
1201C4#352211yescharacteristic
1202C4#352211yescharacteristic
1203C2—82no—
1204C2—82no—
1205C2#3574811yescharacteristic
1206C2#6048411yescharacteristic
1207C2#6049611yescharacteristic
1208C2#6183311yescharacteristic
1209C2#6183911yescharacteristic
1210C2#6242811yescharacteristic
1211C2#6244911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#127C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36565C2semidirect
3. #29986C2semidirect
4. #29985C2semidirect
5. #29982C2semidirect
6. #29261C2semidirect
7. #29261C2semidirect
10. #28517C2semidirect
11. #28510C2semidirect
12. #26478C2semidirect
13. #26476C2semidirect
16. #26471C2semidirect
17. #26469C2semidirect
18. #26058C2semidirect
19. #26058C2semidirect
20. #26055C2semidirect
21. #26054C2semidirect
22. #26051C2semidirect
23. #26049C2semidirect
24. #23785C2semidirect
25. #23784C2semidirect
26. #23778C2semidirect
27. #22736C2semidirect
28. #22731C2semidirect
29. #22730C2semidirect
204. #559Q8semidirect

Maximal subgroups

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

subgroupindex
#365652
#343312
#299862
#299852
#299822
#292612
#292562
#285212
#285172
#285102
#264782
#264762
#264752
#264722
#264712
#264692
#260582
#260552
#260542
#260512
#260492
#237852
#237842
#237782
#227362
#227312
#227302
#225492