Finite Group Databasebeta

← #34088397

Subgroups — #34088397

Order 19648.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C2×#19096825C211yesmaximal, characteristic, complemented
2C22×C4×D307C211yesmaximal, characteristic, complemented
3#23754242C212yesmaximal, complemented
4#23754240C211yesmaximal, characteristic, complemented
5#23754239C211yesmaximal, characteristic, complemented
6#23754231C211yesmaximal, characteristic, complemented
7#23754228C212yesmaximal, complemented
8D4×Dic307C212yesmaximal, complemented
9(C22⋊D307)⋊C4C212yesmaximal, complemented
10#23754218C211yesmaximal, characteristic, complemented
11#121×C307C211yesmaximal, characteristic, complemented
12C23×D307C2211yescharacteristic
13#19096825—24no—
14C2×Dic614C2211yescharacteristic, complemented
15C2×C22⋊D307C2212yes—
16C2×C22⋊D307C2212yes—
17C22×Dic307C2211yescharacteristic
18C22×Dic307C2212yescomplemented
19C2×C4×D307—24no—
20C2×C4×D307C2211yescharacteristic
21C2×C4×D307C2211yescharacteristic
22C2×C4×D307C2211yescharacteristic
23C2×C4×D307C2211yescharacteristic
24C4⋊Dic307C2212yescomplemented
25C4⋊Dic307C2211yescharacteristic, complemented
26Dic307⋊C4C2212yescomplemented
27C22⋊Dic307C2212yes—
28C22⋊Dic307C2212yescomplemented
29(C2×D307)⋊C4C2212yes—
30(C2×D307)⋊C4C2212yes—
31C4×Dic307C2212yescomplemented
32C2×D4×C307C2212yes—
33C2×D4×C307C2211yescharacteristic, complemented
34C22×C4×C307C2211yescharacteristic
35C4⋊C4×C307C2211yescharacteristic, complemented
36C22⋊C4×C307C2212yescomplemented
37C22×D307—22no—
38C22×D307—22no—
39C22×D307—22no—
40C22×D307C2311yescharacteristic
41C22×D307C2311yescharacteristic
42Dic614—22no—
43C22⋊D307—24no—
44C22⋊D307—24no—
45C2×Dic307—22no—
46C2×Dic307—24no—
47C2×Dic307C2312yes—
48C2×Dic307C2312yes—
49C2×Dic307C2311yescharacteristic
50C2×Dic307C2311yescharacteristic
51C4×D307—22no—
52C4×D307—22no—
53C4×D307—22no—
54C4×D307D414yescomplemented
55C23×C307C2312yes—
56C23×C307C2311yescharacteristic
57D4×C307—24no—
58D4×C307—22no—
59C2×C4×C307—22no—
60C2×C4×C307C2311yescharacteristic
61C2×C4×C307C2312yes—
62C2×C4×C307C2311yescharacteristic
63C22×C307—21no—
64C22×C307—21no—
65C22×C307—22no—
66C22×C307—22no—
67C22×C307—22no—
68C22×C307#4112yescomplemented
69C22×C307C2411yescharacteristic
70C2×D307—28no—
71C2×D307—21no—
72C2×D307—21no—
73C2×D307—21no—
74C2×D307—21no—
75C2×D307C2×D412yes—
76C2×D307#4112yescomplemented
77C4×C307—21no—
78C4×C307—22no—
79C4×C307C2×D412yes—
80Dic307—21no—
81Dic307—22no—
82Dic307—22no—
83Dic307C2×D412yes—
84C2×C307—22no—
85C2×C307—42no—
86C2×C307C22×D411yescharacteristic
87C2×C307C2×#4111yescharacteristic
88C2×C307C2×#4111yescharacteristic
89D307—22no—
90D307—22no—
91C307#52511yescharacteristic, complemented, Sylow
92#525—3071nomaximal, Sylow
93C2×#41—3071no—
94C23×C4—3071no—
95#123—3072no—
96C22⋊Q8—3071no—
97C22⋊Q8—3071no—
98#121—3071no—
99#121D30711yescharacteristic, complemented
100#120—3072no—
101C4×D4—3072no—
102C4×D4—3072no—
103#117—3071no—
104C24—3071no—
105#41—6144no—
106C2×Q8—3071no—
107C2×D4—3072no—
108C2×D4—3072no—
109C2×D4C2×D30712yes—
110C2×D4C2×D30711yescharacteristic, complemented
111C22×C4—3071no—
112C22×C4—3071no—
113C22×C4—3072no—
114C22×C4—3071no—
115C22×C4—3071no—
116C22×C4—3071no—
117C22×C4—6144no—
118C22×C4C2×D30711yescharacteristic
119C4⋊C4—3071no—
120C4⋊C4—3072no—
121C4⋊C4—3072no—
122C4⋊C4C2×D30711yescharacteristic, complemented
123C22⋊C4—3072no—
124C22⋊C4—3072no—
125C22⋊C4—3072no—
126C22⋊C4—3072no—
127C22⋊C4C2×D30712yescomplemented
128C42—3072no—
129C23—3071no—
130C23—3071no—
131C23—6142no—
132C23—6142no—
133C23—6142no—
134C23C22×D30712yes—
135C23C22×D30711yescharacteristic
136Q8—6142no—
137D4—24no—
138D4—22no—
139D4—6144no—
140D4—6144no—
141C2×C4—22no—
142C2×C4—3071no—
143C2×C4—3074no—
144C2×C4—3072no—
145C2×C4—3071no—
146C2×C4—3072no—
147C2×C4—6142no—
148C2×C4—6142no—
149C2×C4—6142no—
150C2×C4—6144no—
151C2×C4—6142no—
152C2×C4C22×D30712yes—
153C2×C4C22×D30711yescharacteristic
154C2×C4C22×D30711yescharacteristic
155C22—21no—
156C22—21no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—3072no—
161C22—3072no—
162C22—6148no—
163C22—6141no—
164C22—6141no—
165C22—6141no—
166C22—6141no—
167C22#1909682512yescomplemented
168C22C23×D30711yescharacteristic
169C4—21no—
170C4—22no—
171C4—3072no—
172C4—6141no—
173C4—6142no—
174C4—6142no—
175C4D4×D30712yes—
176C2—22no—
177C2—42no—
178C2—6142no—
179C2—6142no—
180C2C2×D4×D30711yescharacteristic
181C2#41×D30711yescharacteristic
182C2C2×#1909682511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D307
commutator, socle, cosocleC22×C307C24
Fitting#121×C307C2
hypercenter#121D307
hypocenterC307#525
LCSG ▷ C22×C307 ▷ C307
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#19096825C2semidirect
2. C22×C4×D307C2semidirect
3. #23754242C2semidirect
4. #23754240C2semidirect
5. #23754239C2semidirect
6. #23754231C2semidirect
7. #23754228C2semidirect
8. D4×Dic307C2semidirect
9. (C22⋊D307)⋊C4C2semidirect
10. #23754218C2semidirect
11. #121×C307C2semidirect
14. C2×Dic614C22semidirect
18. C22×Dic307C22semidirect
24. C4⋊Dic307C22semidirect
25. C4⋊Dic307C22semidirect
26. Dic307⋊C4C22semidirect
28. C22⋊Dic307C22semidirect
31. C4×Dic307C22semidirect
33. C2×D4×C307C22semidirect
35. C4⋊C4×C307C22semidirect
36. C22⋊C4×C307C22semidirect
54. C4×D307D4semidirect
68. C22×C307#41semidirect
76. C2×D307#41semidirect
91. C307#525semidirect
99. #121D307semidirect
110. C2×D4C2×D307semidirect
122. C4⋊C4C2×D307semidirect
127. C22⋊C4C2×D307semidirect
167. C22#19096825semidirect

Maximal subgroups

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

subgroupindex
C2×#190968252
C22×C4×D3072
#237542422
#237542402
#237542392
#237542312
#237542282
D4×Dic3072
(C22⋊D307)⋊C42
#237542182
#121×C3072
#525307