Finite Group Databasebeta

← #20261412

Subgroups — #20261412

Order 6208.

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#15690805C211yesmaximal, characteristic, complemented
2#15690805C211yesmaximal, characteristic, complemented
3#15690799C211yesmaximal, characteristic, complemented
4#15690795C211yesmaximal, characteristic, complemented
5#15690795C211yesmaximal, characteristic, complemented
6#15690794C211yesmaximal, characteristic, complemented
7#15690786C211yesmaximal, characteristic, complemented
8#15690780C211yesmaximal, characteristic
9#15690772C211yesmaximal, characteristic, complemented
10C4×C22⋊D97C211yesmaximal, characteristic, complemented
11#15690768C211yesmaximal, characteristic, complemented
12#15690766C211yesmaximal, characteristic, complemented
13C2×#13095488C211yesmaximal, characteristic, complemented
14C22⋊C4×D97C211yesmaximal, characteristic, complemented
15C22⋊Q8×C97C211yesmaximal, characteristic, complemented
16C23×D97C2211yescharacteristic
17C2×D388C2211yescharacteristic
18C2×D388C2211yescharacteristic
19C2×C22⋊D97C2211yescharacteristic
20C22×Dic97C2211yescharacteristic
21C2×C4×D97C2211yescharacteristic
22C2×C4×D97C2211yescharacteristic
23C2×C4×D97C2211yescharacteristic, complemented
24C4⋊Dic97C2211yescharacteristic, complemented
25C4⋊Dic97C2211yescharacteristic, complemented
26#13095490C2211yescharacteristic, complemented
27#13095490C2211yescharacteristic, complemented
28#13095490C2211yescharacteristic, complemented
29C22⋊Dic97C2211yescharacteristic
30#13095488C2211yescharacteristic
31#13095488C2211yescharacteristic
32#13095488C2211yescharacteristic
33#13095488C2211yescharacteristic
34#13095488C2211yescharacteristic
35#13095488C2211yescharacteristic
36#13095488C2211yescharacteristic
37#13095488C2211yescharacteristic
38#13095488C2211yescharacteristic, complemented
39#13095488C2211yescharacteristic, complemented
40#13095488C2211yescharacteristic, complemented
41C4×Dic97C2211yescharacteristic, complemented
42C4×Dic97C2211yescharacteristic, complemented
43C4×Dic97C2211yescharacteristic, complemented
44C2×Q8×C97C2211yescharacteristic, complemented
45C22×C4×C97C2211yescharacteristic
46C4⋊C4×C97C2211yescharacteristic, complemented
47C4⋊C4×C97C2211yescharacteristic, complemented
48C4⋊C4×C97C2211yescharacteristic, complemented
49C22⋊C4×C97C2211yescharacteristic
50C22⋊C4×C97C2211yescharacteristic
51C23×C97C2311yescharacteristic
52C22×D97—22no—
53C22×D97—22no—
54C22×D97—41no—
55C22×D97C2311yescharacteristic
56C22×D97C2311yescharacteristic
57C22×D97C2311yescharacteristic
58Q8×C97—41no—
59C2×C4×C97—41no—
60C2×C4×C97C2311yescharacteristic
61C2×C4×C97C2311yescharacteristic
62C2×C4×C97C2311yescharacteristic
63C2×C4×C97C2311yescharacteristic
64C2×C4×C97C2311yescharacteristic
65C2×C4×C97C2311yescharacteristic
66C22⋊D97—22no—
67C2×Dic97—22no—
68C2×Dic97C2311yescharacteristic
69C2×Dic97C2311yescharacteristic
70C2×Dic97C2311yescharacteristic
71C2×Dic97C2311yescharacteristic
72C2×Dic97C2311yescharacteristic
73D388—22no—
74D388—41no—
75C4×D97—22no—
76C4×D97—41no—
77C4×D97—41no—
78C22×C97—21no—
79C22×C97—21no—
80C22×C97#4112yes—
81C22×C97C2411yescharacteristic
82C2×D97—21no—
83C2×D97—21no—
84C2×D97—21no—
85C2×D97—21no—
86C2×D97—21no—
87C2×D97—21no—
88C2×D97—21no—
89C2×D97—21no—
90C2×D97—44no—
91C2×D97#4112yes—
92C4×C97—21no—
93C4×C97—21no—
94C4×C97—21no—
95C4×C97—21no—
96C4×C97—21no—
97C4×C97—21no—
98Dic97—21no—
99Dic97—21no—
100Dic97—21no—
101Dic97—21no—
102Dic97—21no—
103C2×C97—22no—
104C2×C97C2×#4111yescharacteristic
105C2×C97C2×#4111yescharacteristic
106C2×C97H(5,𝔽2)11yescharacteristic
107D97—22no—
108D97—41no—
109D97—41no—
110C97#55111yescharacteristic, complemented, Sylow
111#551—971nomaximal, Sylow
112#126—971no—
113#126—971no—
114#124—971no—
115#123—971no—
116#123—971no—
117#123—971no—
118C22⋊Q8—971no—
119C22⋊Q8D9711yescharacteristic, complemented
120#120—971no—
121C4×D4—971no—
122C4×D4—971no—
123#117—971no—
124#117—971no—
125C2×C22⋊C4—971no—
126C2×C22⋊C4—971no—
127C24—971no—
128C2×Q8C2×D9711yescharacteristic, complemented
129C2×D4—971no—
130C2×D4—971no—
131C2×D4—971no—
132C22×C4—971no—
133C22×C4—971no—
134C22×C4—971no—
135C22×C4—971no—
136C22×C4C2×D9711yescharacteristic
137C4⋊C4—971no—
138C4⋊C4—971no—
139C4⋊C4—971no—
140C4⋊C4—971no—
141C4⋊C4—971no—
142C4⋊C4C2×D9711yescharacteristic, complemented
143C4⋊C4C2×D9711yescharacteristic, complemented
144C4⋊C4C2×D9711yescharacteristic, complemented
145C22⋊C4—971no—
146C22⋊C4—971no—
147C22⋊C4—971no—
148C22⋊C4—971no—
149C22⋊C4—971no—
150C22⋊C4—971no—
151C22⋊C4—971no—
152C22⋊C4—971no—
153C22⋊C4—971no—
154C22⋊C4—971no—
155C22⋊C4—971no—
156C22⋊C4—971no—
157C22⋊C4C2×D9711yescharacteristic
158C22⋊C4C2×D9711yescharacteristic
159C42—971no—
160C42—971no—
161C42—971no—
162C23—971no—
163C23—971no—
164C23—971no—
165C23—3881no—
166C23—1942no—
167C23—1942no—
168C23C22×D9711yescharacteristic
169Q8—41no—
170D4—3881no—
171D4—1942no—
172D4—1942no—
173C2×C4—41no—
174C2×C4—971no—
175C2×C4—971no—
176C2×C4—971no—
177C2×C4—971no—
178C2×C4—971no—
179C2×C4—3881no—
180C2×C4—3881no—
181C2×C4—1942no—
182C2×C4—1942no—
183C2×C4C22×D9711yescharacteristic
184C2×C4C22×D9711yescharacteristic
185C2×C4C22×D9711yescharacteristic
186C2×C4C22×D9711yescharacteristic
187C2×C4C22×D9711yescharacteristic
188C2×C4C22×D9711yescharacteristic
189C22—21no—
190C22—21no—
191C22—972no—
192C22—3884no—
193C22—1941no—
194C22—1941no—
195C22—1941no—
196C22—1941no—
197C22—1941no—
198C22—1941no—
199C22—1941no—
200C22—1941no—
201C22#1309551212yes—
202C22C23×D9711yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—1941no—
210C4—1941no—
211C4—1941no—
212C4—1941no—
213C4—1941no—
214C2—22no—
215C2—3881no—
216C2—3881no—
217C2—1942no—
218C2#41×D9711yescharacteristic
219C2C2×#1309551211yescharacteristic
220C2#1569085511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D97
commutator, socleC22×C97C24
FittingC22⋊Q8×C97C2
hypercenterC22⋊Q8D97
hypocenterC97#551
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #15690805C2semidirect
2. #15690805C2semidirect
3. #15690799C2semidirect
4. #15690795C2semidirect
5. #15690795C2semidirect
6. #15690794C2semidirect
7. #15690786C2semidirect
9. #15690772C2semidirect
10. C4×C22⋊D97C2semidirect
11. #15690768C2semidirect
12. #15690766C2semidirect
13. C2×#13095488C2semidirect
14. C22⋊C4×D97C2semidirect
15. C22⋊Q8×C97C2semidirect
23. C2×C4×D97C22semidirect
24. C4⋊Dic97C22semidirect
25. C4⋊Dic97C22semidirect
26. #13095490C22semidirect
27. #13095490C22semidirect
28. #13095490C22semidirect
38. #13095488C22semidirect
39. #13095488C22semidirect
40. #13095488C22semidirect
41. C4×Dic97C22semidirect
42. C4×Dic97C22semidirect
43. C4×Dic97C22semidirect
44. C2×Q8×C97C22semidirect
46. C4⋊C4×C97C22semidirect
47. C4⋊C4×C97C22semidirect
48. C4⋊C4×C97C22semidirect
110. C97#551semidirect
119. C22⋊Q8D97semidirect
128. C2×Q8C2×D97semidirect
142. C4⋊C4C2×D97semidirect
143. C4⋊C4C2×D97semidirect
144. C4⋊C4C2×D97semidirect