Finite Group Databasebeta

← #7566222

Subgroups — #7566222

Order 512.

1447 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59424C211yesmaximal, characteristic
2#36480C211yesmaximal, characteristic, complemented
3#32638C211yesmaximal, characteristic, complemented
4#32568C211yesmaximal, characteristic, complemented
5#32230C211yesmaximal, characteristic, complemented
6#30821C211yesmaximal, characteristic, complemented
7#29166C211yesmaximal, characteristic, complemented
8#29103C211yesmaximal, characteristic
9#29014C211yesmaximal, characteristic, complemented
10#28038C211yesmaximal, characteristic, complemented
11#27721C211yesmaximal, characteristic, complemented
12#27365C211yesmaximal, characteristic, complemented
13#27281C211yesmaximal, characteristic
14#27147C211yesmaximal, characteristic, complemented
15#27126C211yesmaximal, characteristic, complemented
16#26766C211yesmaximal, characteristic, complemented
17#26693C211yesmaximal, characteristic, complemented
18#26691C211yesmaximal, characteristic, complemented
19#26325C211yesmaximal, characteristic, complemented
20#26010C211yesmaximal, characteristic, complemented
21#25966C211yesmaximal, characteristic
22#25007C211yesmaximal, characteristic, complemented
23#24596C211yesmaximal, characteristic, complemented
24#24493C211yesmaximal, characteristic
25#23239C211yesmaximal, characteristic, complemented
26#23228C211yesmaximal, characteristic, complemented
27#23060C211yesmaximal, characteristic, complemented
28#22623C211yesmaximal, characteristic, complemented
29#22580C211yesmaximal, characteristic
30C4×#485C211yesmaximal, characteristic, complemented
31#21060C211yesmaximal, characteristic
32C2×#489C2211yescharacteristic
33C2×#485C2211yescharacteristic
34C2×#474C2211yescharacteristic
35C2×#428C2211yescharacteristic
36C2×#418C2211yescharacteristic
37C2×#418C2211yescharacteristic
38#2863—21no—
39#2857C2211yescharacteristic
40#2786—21no—
41#2740—21no—
42#2605—21no—
43#2605—21no—
44#2601—21no—
45#2592C2211yescharacteristic
46#2567C2211yescharacteristic, complemented
47#2560—21no—
48#2551C2211yescharacteristic, complemented
49#2538C2211yescharacteristic
50#2512C2211yescharacteristic
51#2512C2211yescharacteristic
52#2509C2211yescharacteristic, complemented
53#2509C2211yescharacteristic, complemented
54#2502C2211yescharacteristic
55#2497—21no—
56#2492—21no—
57#2480—21no—
58#2480—21no—
59#2465—21no—
60#2465—21no—
61#2448C2211yescharacteristic
62#2447C2211yescharacteristic
63#2439C2211yescharacteristic
64#2439C2211yescharacteristic
65#2437—21no—
66#2435C2211yescharacteristic
67#2369C2211yescharacteristic, complemented
68#2367C2211yescharacteristic
69#2365C2211yescharacteristic, complemented
70#2365C2211yescharacteristic, complemented
71#2355C2211yescharacteristic, complemented
72#2354C2211yescharacteristic
73#2347C2211yescharacteristic
74#2347C2211yescharacteristic
75#2345C2211yescharacteristic
76#2342—21no—
77D4×C22⋊C4C2211yescharacteristic
78C4×C4⋊Q8—21no—
79C4×C22⋊Q8C2211yescharacteristic
80C4×C22⋊Q8C2211yescharacteristic
81C2×#390C2211yescharacteristic
82C4×#117C2211yescharacteristic
83#2101C2211yescharacteristic, complemented
84#2100C2211yescharacteristic, complemented
85#2100C2211yescharacteristic, complemented
86#2099C2211yescharacteristic, complemented
87#2095C2211yescharacteristic, complemented
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2084C2211yescharacteristic, complemented
92#2084C2211yescharacteristic, complemented
93#2074C2211yescharacteristic, complemented
94#2073C2211yescharacteristic
95#2071C2211yescharacteristic
96#2071C2211yescharacteristic
97#2067C2211yescharacteristic
98#2066C2211yescharacteristic, complemented
99#2066C2211yescharacteristic, complemented
100#2065C2211yescharacteristic
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic
103#2058C2211yescharacteristic, complemented
104#2057C2211yescharacteristic, complemented
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2024C2211yescharacteristic, complemented
110#2024C2211yescharacteristic, complemented
111#2023C2211yescharacteristic
112#2023C2211yescharacteristic
113#2023C2211yescharacteristic
114#2023C2211yescharacteristic
115#1990C2211yescharacteristic, complemented
116#1987C2211yescharacteristic, complemented
117#1985C2211yescharacteristic, complemented
118#1984C2211yescharacteristic, complemented
119#1983C2211yescharacteristic
120#1983C2211yescharacteristic
121#1958C2211yescharacteristic
122#1949C2211yescharacteristic, complemented
123#1947C2211yescharacteristic, complemented
124#1947C2211yescharacteristic, complemented
125#1944C2211yescharacteristic, complemented
126#1941C2211yescharacteristic, complemented
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1935C2211yescharacteristic, complemented
130#1934C2211yescharacteristic
131#1934C2211yescharacteristic
132#1934C2211yescharacteristic
133#1934C2211yescharacteristic
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic
136#1933C2211yescharacteristic, complemented
137#1928C2211yescharacteristic, complemented
138#1928C2211yescharacteristic, complemented
139#1928C2211yescharacteristic, complemented
140#1927C2211yescharacteristic, complemented
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1921C2211yescharacteristic, complemented
154#1920C2211yescharacteristic, complemented
155#1919C2211yescharacteristic, complemented
156#1919C2211yescharacteristic, complemented
157#1919C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1918C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1918C2211yescharacteristic, complemented
163#1917C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1894C2211yescharacteristic
168#1894C2211yescharacteristic
169#1873C2211yescharacteristic
170#1865C2211yescharacteristic, complemented
171#1865C2211yescharacteristic, complemented
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1862C2211yescharacteristic
176#1854C2211yescharacteristic
177#1851C2211yescharacteristic
178#1851C2211yescharacteristic
179#1836C2211yescharacteristic, complemented
180#1825C2211yescharacteristic
181#1823C2211yescharacteristic
182#1823C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1804C2211yescharacteristic
186#1786C2211yescharacteristic
187#1786C2211yescharacteristic
188#1776C2211yescharacteristic, complemented
189C4×#107C2211yescharacteristic, complemented
190C4×#107C2211yescharacteristic, complemented
191C4×#106C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193C8×C4⋊C4C2211yescharacteristic, complemented
194#1762C2211yescharacteristic
195C4×#103C2211yescharacteristic, complemented
196C4×#103C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1736C2211yescharacteristic
202#1728C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#126—21no—
211C2×#126—21no—
212C2×#124C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8D411yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×C4×Q8—21no—
219C2×C4×Q8—21no—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×#117—21no—
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C22⋊C4—21no—
229C22×C22⋊C4—21no—
230C22×C22⋊C4—21no—
231C22×C42C2311yescharacteristic
232#489—24no—
233#485—24no—
234#474—24no—
235#428—24no—
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252#418—24no—
253#418—24no—
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#399—21no—
291#398—21no—
292#398—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#396—21no—
300#396—21no—
301#396—21no—
302#396—21no—
303#396—21no—
304#396—21no—
305#395—21no—
306#395—21no—
307#395—21no—
308#395—21no—
309#394—21no—
310#394—21no—
311#393—21no—
312#393—21no—
313#393—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#391—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391D411yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#390—21no—
328#390—21no—
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389D411yescharacteristic
343#389C2311yescharacteristic
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#388—21no—
369#388—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#387D411yescharacteristic
384#387D411yescharacteristic
385#386—21no—
386#386—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385D411yescharacteristic
393#385D411yescharacteristic
394#384—21no—
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#383—21no—
399#383—21no—
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#381—21no—
403#380—21no—
404#380—21no—
405#380—21no—
406#380—21no—
407#380D411yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#379—21no—
412#379—21no—
413#379—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440#376—21no—
441C43—21no—
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
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#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C25—21no—
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8—21no—
488C22×Q8C2×D411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4—22no—
491C22×D4—21no—
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—41no—
495C22×D4—41no—
496C22×D4—41no—
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2×D411yescharacteristic
503C23×C4C2×D411yescharacteristic
504C23×C4C2411yescharacteristic
505C2×M16—22no—
506C2×M16—22no—
507C2×M16—22no—
508C2×M16—41no—
509C2×M16—41no—
510C2×M16—41no—
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C4⋊Q8—22no—
520C4⋊Q8—22no—
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525C4⋊Q8—44no—
526#126—82no—
527#126—82no—
528#124—22no—
529#124—41no—
530#124—41no—
531#124—41no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534C22⋊Q8—42no—
535C22⋊Q8—82no—
536C22⋊Q8—82no—
537C4×Q8—41no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—82no—
542C4×Q8—82no—
543C4×D4—22no—
544C4×D4—41no—
545C4×D4—41no—
546C4×D4—41no—
547#117—22no—
548#117—22no—
549#117—41no—
550#117—82no—
551#117#4114yes—
552C2×C4⋊C4—22no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊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⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
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—44no—
630C2×C22⋊C4—82no—
631C2×C22⋊C4—82no—
632C2×C22⋊C4C2×D411yescharacteristic
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C22⋊C4C2×D411yescharacteristic
635C2×C22⋊C4C2×D411yescharacteristic
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×C42—41no—
651C2×C42—41no—
652C2×C42C2×D411yescharacteristic
653C2×C42C2×D411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660#107—22no—
661#107—22no—
662#107—22no—
663#107—22no—
664#107—22no—
665#107—41no—
666#106—22no—
667#106—22no—
668#106—22no—
669#106—41no—
670#106—41no—
671#106—41no—
672C4⋊C8—22no—
673C4⋊C8—41no—
674C4⋊C8—41no—
675C4⋊C8—41no—
676#103—22no—
677#103—22no—
678#103—22no—
679#103—22no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#102—22no—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—22no—
689#102—22no—
690#102—22no—
691#102—22no—
692#102—22no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102#4114yes—
700C22⋊C8—22no—
701C22⋊C8—22no—
702#97—22no—
703#97—41no—
704C4×C8—41no—
705C4×C8—41no—
706C4×C8—41no—
707C4×C8—41no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#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#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755C24—21no—
756C24—21no—
757C24—42no—
758C24—42no—
759C24—42no—
760C24—42no—
761C24—81no—
762C24—81no—
763C24—81no—
764C24C22×D411yescharacteristic
765C2×Q8—22no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—41no—
773C2×Q8—41no—
774C2×Q8—42no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×Q8—42no—
778C2×Q8—42no—
779C2×Q8—81no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—82no—
799C2×D4—82no—
800C2×D4—81no—
801C2×D4C2×#4112yes—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—81no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
849C22×C42−1+412yes—
850C22×C4C2511yescharacteristic
851M16—44no—
852M16—82no—
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×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×C8C2×#4112yes—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—22no—
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—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—41no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—41no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
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⋊C4C2×#4112yes—
935C4⋊C4C2×#4112yes—
936C4⋊C4C2×#4112yes—
937C22⋊C4—24no—
938C22⋊C4—22no—
939C22⋊C4—41no—
940C22⋊C4—41no—
941C22⋊C4—41no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C42—24no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—41no—
983C42—41no—
984C42—42no—
985C42—42no—
986C42—42no—
987C42—42no—
988C42—42no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C42—81no—
994C42—81no—
995C42—81no—
996C42—81no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—22no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—84no—
1018C23—84no—
1019C23—84no—
1020C23—84no—
1021C23—162no—
1022C23—162no—
1023C23—162no—
1024C23#54812yes—
1025C23C23×D411yescharacteristic
1026Q8—41no—
1027Q8—41no—
1028Q8—41no—
1029Q8—41no—
1030Q8—82no—
1031Q8—84no—
1032Q8—84no—
1033Q8—162no—
1034D4—22no—
1035D4—22no—
1036D4—41no—
1037D4—41no—
1038D4—41no—
1039D4—41no—
1040D4—41no—
1041D4—41no—
1042D4—84no—
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—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
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—21no—
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—41no—
1123C2×C4—41no—
1124C2×C4—82no—
1125C2×C4—82no—
1126C2×C4—84no—
1127C2×C4—162no—
1128C2×C4—162no—
1129C2×C4#54812yes—
1130C2×C4#57512yes—
1131C2×C4#57612yes—
1132C2×C4#57712yes—
1133C2×C4C22×#4111yescharacteristic
1134C2×C4C22×#4111yescharacteristic
1135C2×C4C2×2−1+411yescharacteristic
1136C2×C4#58511yescharacteristic
1137C2×C4#58511yescharacteristic
1138C2×C4#58511yescharacteristic
1139C8—22no—
1140C8—41no—
1141C8—41no—
1142C8—41no—
1143C8—41no—
1144C8—41no—
1145C8—41no—
1146C8—41no—
1147C22—22no—
1148C22—22no—
1149C22—22no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—81no—
1158C22—81no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22—81no—
1168C22—168no—
1169C22C2×#54811yescharacteristic
1170C22D4×#4111yescharacteristic
1171C22#348511yescharacteristic
1172C22C2×#57511yescharacteristic
1173C22C2×#57611yescharacteristic
1174C22C2×#57711yescharacteristic
1175C22#358611yescharacteristic
1176C4—22no—
1177C4—22no—
1178C4—22no—
1179C4—22no—
1180C4—41no—
1181C4—42no—
1182C4—41no—
1183C4—41no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—41no—
1190C4—42no—
1191C4—42no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4#347511yescharacteristic
1204C4#349511yescharacteristic
1205C4#351011yescharacteristic
1206C4#356411yescharacteristic
1207C2—42no—
1208C2—82no—
1209C2—161no—
1210C2#5913211yescharacteristic
1211C2#6132311yescharacteristic
1212C2#6132911yescharacteristic
1213C2#6144411yescharacteristic
1214C2#6155711yescharacteristic
1215C2#6173911yescharacteristic
1216C2#6175911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36480C2semidirect
3. #32638C2semidirect
4. #32568C2semidirect
5. #32230C2semidirect
6. #30821C2semidirect
7. #29166C2semidirect
9. #29014C2semidirect
10. #28038C2semidirect
11. #27721C2semidirect
12. #27365C2semidirect
14. #27147C2semidirect
15. #27126C2semidirect
16. #26766C2semidirect
17. #26693C2semidirect
18. #26691C2semidirect
19. #26325C2semidirect
20. #26010C2semidirect
22. #25007C2semidirect
23. #24596C2semidirect
25. #23239C2semidirect
26. #23228C2semidirect
27. #23060C2semidirect
28. #22623C2semidirect
30. C4×#485C2semidirect
46. #2567C22semidirect
48. #2551C22semidirect
52. #2509C22semidirect
53. #2509C22semidirect
67. #2369C22semidirect
69. #2365C22semidirect
70. #2365C22semidirect
71. #2355C22semidirect
83. #2101C22semidirect
84. #2100C22semidirect
85. #2100C22semidirect
86. #2099C22semidirect
87. #2095C22semidirect
89. #2088C22semidirect
90. #2088C22semidirect
91. #2084C22semidirect
92. #2084C22semidirect
93. #2074C22semidirect
98. #2066C22semidirect
99. #2066C22semidirect
103. #2058C22semidirect
104. #2057C22semidirect
109. #2024C22semidirect
110. #2024C22semidirect
115. #1990C22semidirect
116. #1987C22semidirect
117. #1985C22semidirect
118. #1984C22semidirect
122. #1949C22semidirect
123. #1947C22semidirect
124. #1947C22semidirect
125. #1944C22semidirect
126. #1941C22semidirect
129. #1935C22semidirect
136. #1933C22semidirect
137. #1928C22semidirect
138. #1928C22semidirect
139. #1928C22semidirect
140. #1927C22semidirect
153. #1921C22semidirect
154. #1920C22semidirect
155. #1919C22semidirect
156. #1919C22semidirect
157. #1919C22semidirect
158. #1918C22semidirect
159. #1918C22semidirect
160. #1918C22semidirect
161. #1918C22semidirect
162. #1918C22semidirect
163. #1917C22semidirect
164. #1916C22semidirect
165. #1916C22semidirect
166. #1916C22semidirect
170. #1865C22semidirect
171. #1865C22semidirect
179. #1836C22semidirect
188. #1776C22semidirect
189. C4×#107C22semidirect
190. C4×#107C22semidirect
191. C4×#106C22semidirect
192. #1771C22semidirect
193. C8×C4⋊C4C22semidirect
195. C4×#103C22semidirect
196. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#594242
#364802
#326382
#325682
#322302
#308212
#291662
#291032
#290142
#280382
#277212
#273652
#272812
#271472
#271262
#267662
#266932
#266912
#263252
#260102
#259662
#250072
#245962
#244932
#232392
#232282
#230602
#226232
#225802
C4×#4852
#210602