Finite Group Databasebeta

← #44470714

Subgroups — #44470714

Order 29888.

248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28417948C211yesmaximal, characteristic, complemented
2#28417948C211yesmaximal, characteristic, complemented
3#28417942C211yesmaximal, characteristic, complemented
4#28417938C211yesmaximal, characteristic, complemented
5#28417938C211yesmaximal, characteristic, complemented
6#28417937C211yesmaximal, characteristic, complemented
7#28417929C211yesmaximal, characteristic, complemented
8#28417923C211yesmaximal, characteristic
9#28417915C211yesmaximal, characteristic, complemented
10C4×C22⋊D467C211yesmaximal, characteristic, complemented
11#28417911C211yesmaximal, characteristic, complemented
12#28417909C211yesmaximal, characteristic, complemented
13C2×(C2×D467)⋊C4C211yesmaximal, characteristic, complemented
14C22⋊C4×D467C211yesmaximal, characteristic, complemented
15C22⋊Q8×C467C211yesmaximal, characteristic, complemented
16C23×D467C2211yescharacteristic
17C2×D1868C2211yescharacteristic
18C2×D1868C2211yescharacteristic
19C2×C22⋊D467C2211yescharacteristic
20C22×Dic467C2211yescharacteristic
21C2×C4×D467C2211yescharacteristic
22C2×C4×D467C2211yescharacteristic
23C2×C4×D467C2211yescharacteristic, complemented
24C4⋊Dic467C2211yescharacteristic, complemented
25C4⋊Dic467C2211yescharacteristic, complemented
26Dic467⋊C4C2211yescharacteristic, complemented
27Dic467⋊C4C2211yescharacteristic, complemented
28Dic467⋊C4C2211yescharacteristic, complemented
29C22⋊Dic467C2211yescharacteristic
30(C2×D467)⋊C4C2211yescharacteristic
31(C2×D467)⋊C4C2211yescharacteristic
32(C2×D467)⋊C4C2211yescharacteristic
33(C2×D467)⋊C4C2211yescharacteristic
34(C2×D467)⋊C4C2211yescharacteristic
35(C2×D467)⋊C4C2211yescharacteristic
36(C2×D467)⋊C4C2211yescharacteristic
37(C2×D467)⋊C4C2211yescharacteristic
38(C2×D467)⋊C4C2211yescharacteristic, complemented
39(C2×D467)⋊C4C2211yescharacteristic, complemented
40(C2×D467)⋊C4C2211yescharacteristic, complemented
41C4×Dic467C2211yescharacteristic, complemented
42C4×Dic467C2211yescharacteristic, complemented
43C4×Dic467C2211yescharacteristic, complemented
44C2×Q8×C467C2211yescharacteristic, complemented
45C22×C4×C467C2211yescharacteristic
46C4⋊C4×C467C2211yescharacteristic, complemented
47C4⋊C4×C467C2211yescharacteristic, complemented
48C4⋊C4×C467C2211yescharacteristic, complemented
49C22⋊C4×C467C2211yescharacteristic
50C22⋊C4×C467C2211yescharacteristic
51C22×D467—22no—
52C22×D467—22no—
53C22×D467—41no—
54C22×D467C2311yescharacteristic
55C22×D467C2311yescharacteristic
56C22×D467C2311yescharacteristic
57D1868—22no—
58D1868—41no—
59C22⋊D467—22no—
60C2×Dic467—22no—
61C2×Dic467C2311yescharacteristic
62C2×Dic467C2311yescharacteristic
63C2×Dic467C2311yescharacteristic
64C2×Dic467C2311yescharacteristic
65C2×Dic467C2311yescharacteristic
66C4×D467—22no—
67C4×D467—41no—
68C4×D467—41no—
69C23×C467C2311yescharacteristic
70Q8×C467—41no—
71C2×C4×C467—41no—
72C2×C4×C467C2311yescharacteristic
73C2×C4×C467C2311yescharacteristic
74C2×C4×C467C2311yescharacteristic
75C2×C4×C467C2311yescharacteristic
76C2×C4×C467C2311yescharacteristic
77C2×C4×C467C2311yescharacteristic
78C22×C467—21no—
79C22×C467—21no—
80C22×C467#4112yes—
81C22×C467C2411yescharacteristic
82C2×D467—21no—
83C2×D467—21no—
84C2×D467—21no—
85C2×D467—21no—
86C2×D467—21no—
87C2×D467—21no—
88C2×D467—21no—
89C2×D467—21no—
90C2×D467—44no—
91C2×D467#4112yes—
92C4×C467—21no—
93C4×C467—21no—
94C4×C467—21no—
95C4×C467—21no—
96C4×C467—21no—
97C4×C467—21no—
98Dic467—21no—
99Dic467—21no—
100Dic467—21no—
101Dic467—21no—
102Dic467—21no—
103C2×C467—22no—
104C2×C467C2×#4111yescharacteristic
105C2×C467C2×#4111yescharacteristic
106C2×C467H(5,𝔽2)11yescharacteristic
107D467—22no—
108D467—41no—
109D467—41no—
110C467#55111yescharacteristic, complemented, Sylow
111#551—4671nomaximal, Sylow
112#126—4671no—
113#126—4671no—
114#124—4671no—
115#123—4671no—
116#123—4671no—
117#123—4671no—
118C22⋊Q8—4671no—
119C22⋊Q8D46711yescharacteristic, complemented
120#120—4671no—
121C4×D4—4671no—
122C4×D4—4671no—
123#117—4671no—
124#117—4671no—
125C2×C22⋊C4—4671no—
126C2×C22⋊C4—4671no—
127C24—4671no—
128C2×Q8C2×D46711yescharacteristic, complemented
129C2×D4—4671no—
130C2×D4—4671no—
131C2×D4—4671no—
132C22×C4—4671no—
133C22×C4—4671no—
134C22×C4—4671no—
135C22×C4—4671no—
136C22×C4C2×D46711yescharacteristic
137C4⋊C4—4671no—
138C4⋊C4—4671no—
139C4⋊C4—4671no—
140C4⋊C4—4671no—
141C4⋊C4—4671no—
142C4⋊C4C2×D46711yescharacteristic, complemented
143C4⋊C4C2×D46711yescharacteristic, complemented
144C4⋊C4C2×D46711yescharacteristic, complemented
145C22⋊C4—4671no—
146C22⋊C4—4671no—
147C22⋊C4—4671no—
148C22⋊C4—4671no—
149C22⋊C4—4671no—
150C22⋊C4—4671no—
151C22⋊C4—4671no—
152C22⋊C4—4671no—
153C22⋊C4—4671no—
154C22⋊C4—4671no—
155C22⋊C4—4671no—
156C22⋊C4—4671no—
157C22⋊C4C2×D46711yescharacteristic
158C22⋊C4C2×D46711yescharacteristic
159C42—4671no—
160C42—4671no—
161C42—4671no—
162C23—18681no—
163C23—9342no—
164C23—9342no—
165C23—4671no—
166C23—4671no—
167C23—4671no—
168C23C22×D46711yescharacteristic
169Q8—41no—
170D4—18681no—
171D4—9342no—
172D4—9342no—
173C2×C4—41no—
174C2×C4—18681no—
175C2×C4—18681no—
176C2×C4—9342no—
177C2×C4—9342no—
178C2×C4—4671no—
179C2×C4—4671no—
180C2×C4—4671no—
181C2×C4—4671no—
182C2×C4—4671no—
183C2×C4C22×D46711yescharacteristic
184C2×C4C22×D46711yescharacteristic
185C2×C4C22×D46711yescharacteristic
186C2×C4C22×D46711yescharacteristic
187C2×C4C22×D46711yescharacteristic
188C2×C4C22×D46711yescharacteristic
189C22—21no—
190C22—21no—
191C22—18684no—
192C22—9341no—
193C22—9341no—
194C22—9341no—
195C22—9341no—
196C22—9341no—
197C22—9341no—
198C22—9341no—
199C22—9341no—
200C22—4672no—
201C22#2141874412yes—
202C22C23×D46711yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—9341no—
210C4—9341no—
211C4—9341no—
212C4—9341no—
213C4—9341no—
214C2—22no—
215C2—18681no—
216C2—18681no—
217C2—9342no—
218C2#41×D46711yescharacteristic
219C2C2×#2141874411yescharacteristic
220C2#2841799811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D467
commutator, socle, cosocleC22×C467C24
FittingC22⋊Q8×C467C2
prime radical#28417923C2
hypercenterC22⋊Q8D467
hypocenterC467#551
LCSG ▷ C22×C467 ▷ C467
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #28417948C2semidirect
2. #28417948C2semidirect
3. #28417942C2semidirect
4. #28417938C2semidirect
5. #28417938C2semidirect
6. #28417937C2semidirect
7. #28417929C2semidirect
9. #28417915C2semidirect
10. C4×C22⋊D467C2semidirect
11. #28417911C2semidirect
12. #28417909C2semidirect
13. C2×(C2×D467)⋊C4C2semidirect
14. C22⋊C4×D467C2semidirect
15. C22⋊Q8×C467C2semidirect
23. C2×C4×D467C22semidirect
24. C4⋊Dic467C22semidirect
25. C4⋊Dic467C22semidirect
26. Dic467⋊C4C22semidirect
27. Dic467⋊C4C22semidirect
28. Dic467⋊C4C22semidirect
38. (C2×D467)⋊C4C22semidirect
39. (C2×D467)⋊C4C22semidirect
40. (C2×D467)⋊C4C22semidirect
41. C4×Dic467C22semidirect
42. C4×Dic467C22semidirect
43. C4×Dic467C22semidirect
44. C2×Q8×C467C22semidirect
46. C4⋊C4×C467C22semidirect
47. C4⋊C4×C467C22semidirect
48. C4⋊C4×C467C22semidirect
110. C467#551semidirect
119. C22⋊Q8D467semidirect
128. C2×Q8C2×D467semidirect
142. C4⋊C4C2×D467semidirect
143. C4⋊C4C2×D467semidirect
144. C4⋊C4C2×D467semidirect

Maximal subgroups

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

subgroupindex
#284179482
#284179422
#284179382
#284179372
#284179292
#284179232
#284179152
C4×C22⋊D4672
#284179112
#284179092
C2×(C2×D467)⋊C42
C22⋊C4×D4672
C22⋊Q8×C4672
#551467