Finite Group Databasebeta

← #49133108

Subgroups — #49133108

Order 36224.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827168C211yesmaximal, characteristic, complemented
2#31827110C211yesmaximal, characteristic, complemented
3#31826822C211yesmaximal, characteristic, complemented
4#31826802C211yesmaximal, characteristic, complemented
5#31826791C211yesmaximal, characteristic, complemented
6#31826702C211yesmaximal, characteristic, complemented
7#31826695C211yesmaximal, characteristic, complemented
8#31826681C211yesmaximal, characteristic, complemented
9#31826611C211yesmaximal, characteristic, complemented
10#31826600C211yesmaximal, characteristic, complemented
11C4×#17985377C211yesmaximal, characteristic, complemented
12#31826530C211yesmaximal, characteristic, complemented
13#31826458C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#478×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×D4×D283C2211yescharacteristic
18C2×#17985381C2211yescharacteristic, complemented
19C2×D2264C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21C2×C8×D283C2211yescharacteristic
22C2×C8×D283C2211yescharacteristic, complemented
23#22583605—21no—
24#22583598C2211yescharacteristic
25#22583595—21no—
26#22583594—21no—
27#22583590C2211yescharacteristic
28#22583585—21no—
29#22583585C2211yescharacteristic
30#22583585C2211yescharacteristic
31#22583585C2211yescharacteristic, complemented
32#22583584—21no—
33#22583580—21no—
34C4×D1132C2211yescharacteristic
35C4×D1132C2211yescharacteristic, complemented
36#22583572—21no—
37#22583568C2211yescharacteristic, complemented
38C4⋊C4×D283C2211yescharacteristic
39C2×(C2×D283)⋊C4—21no—
40#22583543C2211yescharacteristic, complemented
41#22583535C2211yescharacteristic, complemented
42#22583533C2211yescharacteristic, complemented
43#22583533C2211yescharacteristic, complemented
44#22583532C2211yescharacteristic
45#22583531C2211yescharacteristic
46#22583530C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic, complemented
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51C4×C283⋊C8C2211yescharacteristic, complemented
52#125×C283C2211yescharacteristic, complemented
53C4×D4×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic, complemented
55#106×C283C2211yescharacteristic, complemented
56C4⋊C8×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C23×D283—21no—
60#17985391—22no—
61#17985391—41no—
62C2×Dic566C2311yescharacteristic
63C2×D1132—21no—
64C2×D1132—21no—
65C2×D1132—21no—
66C2×D1132D411yescharacteristic
67C2×D1132C2311yescharacteristic
68C2×D1132C2311yescharacteristic
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71D4×D283—22no—
72D4×D283—41no—
73C22×Dic283—21no—
74C2×C4×D283—21no—
75C2×C4×D283—21no—
76C2×C4×D283C2311yescharacteristic
77C2×C4×D283C2311yescharacteristic
78#17985381—41no—
79D2264—41no—
80#17985377—22no—
81C2×C283⋊C8C2311yescharacteristic
82C2×C283⋊C8C2311yescharacteristic
83C8×D283—41no—
84C8×D283—41no—
85C4⋊Dic283—21no—
86C4⋊Dic283D411yescharacteristic
87C4⋊Dic283C2311yescharacteristic
88Dic283⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4—21no—
97(C2×D283)⋊C4D411yescharacteristic
98(C2×D283)⋊C4D411yescharacteristic
99C4×Dic283—21no—
100C2×D4×C283C2311yescharacteristic
101C22×C4×C283—21no—
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C4⋊C4×C283—21no—
105C4⋊C4×C283—21no—
106C4⋊C4×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C4⋊C4×C283C2311yescharacteristic
109C22⋊C4×C283—21no—
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112C22×D283—21no—
113C22×D283—42no—
114C22×D283—42no—
115C22×D283—81no—
116C22×D283C2×D411yescharacteristic
117C22×D283C2×D411yescharacteristic
118Dic566—21no—
119Dic566—21no—
120D1132—22no—
121D1132—21no—
122D1132—21no—
123D1132—21no—
124D1132—21no—
125D1132—42no—
126D1132—81no—
127D1132—81no—
128C22⋊D283—42no—
129C22⋊D283—42no—
130C2×Dic283—21no—
131C2×Dic283—21no—
132C2×Dic283—42no—
133C2×Dic283C2×D411yescharacteristic
134C2×Dic283C2×D411yescharacteristic
135C4×D283—21no—
136C4×D283—21no—
137C4×D283—21no—
138C4×D283—21no—
139C4×D283—81no—
140C4×D283—81no—
141C283⋊C8—21no—
142C283⋊C8—21no—
143C23×C283—21no—
144D4×C283—21no—
145D4×C283#4112yes—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—81no—
150C2×C4×C283C2×D411yescharacteristic
151C2×C4×C283C2×D411yescharacteristic
152C2×C4×C283C2411yescharacteristic
153C8×C283—21no—
154C8×C283—21no—
155C22×C283—22no—
156C22×C283—41no—
157C22×C283—41no—
158C22×C283C22×D411yescharacteristic
159C2×D283—21no—
160C2×D283—21no—
161C2×D283—21no—
162C2×D283—21no—
163C2×D283—21no—
164C2×D283—41no—
165C2×D283—41no—
166C2×D283—41no—
167C2×D283—41no—
168C2×D283—41no—
169C2×D283—41no—
170C2×D283—84no—
171C2×D283#13512yes—
172C4×C283—21no—
173C4×C283—21no—
174C4×C283—41no—
175C4×C283—41no—
176C4×C283—41no—
177C4×C283C2×#4111yescharacteristic
178C4×C283H(5,𝔽2)11yescharacteristic
179Dic283—21no—
180Dic283—21no—
181Dic283—41no—
182Dic283—41no—
183C2×C283—42no—
184C2×C283#54611yescharacteristic
185C2×C283C2×#13511yescharacteristic
186C2×C283#57611yescharacteristic
187D283—22no—
188D283—41no—
189D283—81no—
190D283—81no—
191C283#329711yescharacteristic, complemented, Sylow
192#3297—2831nomaximal, Sylow
193#553—2831no—
194#546—2831no—
195#488—2831no—
196#484—2831no—
197#482—2831no—
198#478D28311yescharacteristic, complemented
199#466—2831no—
200#465—2831no—
201#463—2831no—
202#449—2831no—
203#447—2831no—
204C4×D8—2831no—
205C8×D4—2831no—
206#416—2831no—
207C2×#102—2831no—
208C2×#41—2831no—
209C22×D4—2831no—
210C2×SD16—2831no—
211C2×D8—2831no—
212C2×D8—2831no—
213C22×C8—2831no—
214C22×C8—2831no—
215#126—5661no—
216#125C2×D28311yescharacteristic, complemented
217#124—2831no—
218#123—5661no—
219#123—5661no—
220C22⋊Q8—2831no—
221#121—2831no—
222#121—2831no—
223#121—2831no—
224#121—5661no—
225#121—5661no—
226#120—5661no—
227C4×D4—2831no—
228C4×D4—2831no—
229C4×D4—5661no—
230C4×D4C2×D28311yescharacteristic
231#117—2831no—
232C2×C4⋊C4—2831no—
233C2×C22⋊C4—5661no—
234#107—2831no—
235#107C2×D28311yescharacteristic, complemented
236#106C2×D28311yescharacteristic, complemented
237C4⋊C8C2×D28311yescharacteristic, complemented
238#103—2831no—
239#103—2831no—
240#103—2831no—
241#102—2831no—
242#102—2831no—
243#102—2831no—
244#102—2831no—
245#102—2831no—
246#102C2×D28311yescharacteristic
247#102C2×D28311yescharacteristic
248C22⋊C8—2831no—
249C22⋊C8—2831no—
250C4×C8—2831no—
251C24—5661no—
252#41—5662no—
253#41—11321no—
254C2×Q8—2831no—
255C2×D4—2831no—
256C2×D4—2831no—
257C2×D4—2831no—
258C2×D4—5661no—
259C2×D4—5661no—
260C2×D4—5661no—
261C2×D4—5661no—
262C2×D4—5662no—
263C2×D4—5661no—
264C2×D4—11321no—
265C2×D4C22×D28311yescharacteristic
266C22×C4—21no—
267C22×C4—2831no—
268C22×C4—2831no—
269C22×C4—5661no—
270C22×C4—5661no—
271C22×C4—5661no—
272SD16—11321no—
273D8—5662no—
274D8—11321no—
275C2×C8—2831no—
276C2×C8—2831no—
277C2×C8—11321no—
278C2×C8—11321no—
279C2×C8C22×D28311yescharacteristic
280C2×C8C22×D28311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—2831no—
284C4⋊C4—2831no—
285C4⋊C4—5661no—
286C4⋊C4—5661no—
287C4⋊C4C22×D28311yescharacteristic
288C4⋊C4C22×D28311yescharacteristic
289C4⋊C4C22×D28311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—2831no—
292C22⋊C4—2831no—
293C22⋊C4—5661no—
294C22⋊C4—5661no—
295C22⋊C4—5661no—
296C22⋊C4—5661no—
297C22⋊C4—5661no—
298C22⋊C4—5661no—
299C22⋊C4—5661no—
300C22⋊C4—5661no—
301C42—5661no—
302C42C22×D28311yescharacteristic
303C23—21no—
304C23—2831no—
305C23—2831no—
306C23—5661no—
307C23—5661no—
308C23—11322no—
309C23—11322no—
310C23—22641no—
311Q8—5661no—
312Q8—5661no—
313D4—21no—
314D4—5662no—
315D4—5661no—
316D4—5661no—
317D4—5661no—
318D4—5661no—
319D4—11322no—
320D4—11322no—
321D4—11322no—
322D4—22641no—
323D4—22641no—
324D4#1798539312yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—81no—
329C2×C4—2831no—
330C2×C4—2831no—
331C2×C4—5661no—
332C2×C4—5661no—
333C2×C4—5661no—
334C2×C4—5661no—
335C2×C4—5661no—
336C2×C4—5661no—
337C2×C4—11322no—
338C2×C4—22641no—
339C2×C4—22641no—
340C2×C4D4×D28311yescharacteristic
341C2×C4D4×D28311yescharacteristic
342C2×C4C23×D28311yescharacteristic
343C8—21no—
344C8—21no—
345C8—5661no—
346C8—5661no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—2832no—
351C22—5661no—
352C22—5661no—
353C22—5661no—
354C22—5661no—
355C22—5661no—
356C22—11321no—
357C22—11321no—
358C22—11321no—
359C22—11321no—
360C22—11321no—
361C22—11321no—
362C22—22644no—
363C22C2×D4×D28311yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—5661no—
370C4—5661no—
371C4—11321no—
372C4—11321no—
373C4C2×#1798539311yescharacteristic
374C4#2258365611yescharacteristic
375C2—42no—
376C2—5662no—
377C2—11321no—
378C2—22641no—
379C2—22641no—
380C2#3182710611yescharacteristic
381C2#135×D28311yescharacteristic
382C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#478×C283C2
socleC22×C283C22×D4
hypercenter#478D283
hypocenterC283#3297
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #31827168C2semidirect
2. #31827110C2semidirect
3. #31826822C2semidirect
4. #31826802C2semidirect
5. #31826791C2semidirect
6. #31826702C2semidirect
7. #31826695C2semidirect
8. #31826681C2semidirect
9. #31826611C2semidirect
10. #31826600C2semidirect
11. C4×#17985377C2semidirect
12. #31826530C2semidirect
13. #31826458C2semidirect
14. #102×D283C2semidirect
15. #478×C283C2semidirect
18. C2×#17985381C22semidirect
22. C2×C8×D283C22semidirect
31. #22583585C22semidirect
35. C4×D1132C22semidirect
37. #22583568C22semidirect
40. #22583543C22semidirect
41. #22583535C22semidirect
42. #22583533C22semidirect
43. #22583533C22semidirect
48. #22583530C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. C4×C283⋊C8C22semidirect
52. #125×C283C22semidirect
54. #107×C283C22semidirect
55. #106×C283C22semidirect
56. C4⋊C8×C283C22semidirect
191. C283#3297semidirect
198. #478D283semidirect
216. #125C2×D283semidirect
235. #107C2×D283semidirect
236. #106C2×D283semidirect
237. C4⋊C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271682
#318271102
#318268222
#318268022
#318267912
#318267022
#318266952
#318266812
#318266112
#318266002
C4×#179853772
#318265302
#318264582
#102×D2832
#478×C2832
#3297283