Finite Group Databasebeta

← #20293313

Subgroups — #20293313

Order 6848.

214 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 95 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#16812102C211yesmaximal, characteristic, complemented
2#16812100C211yesmaximal, characteristic, complemented
3#16812099C211yesmaximal, characteristic, complemented
4#16812099C211yesmaximal, characteristic, complemented
5#16812091C211yesmaximal, characteristic
6#16812091C211yesmaximal, characteristic
7#16812087C211yesmaximal, characteristic, complemented
8#16812086C211yesmaximal, characteristic, complemented
9C4×Dic214C211yesmaximal, characteristic, complemented
10(C22⋊D107)⋊C4C211yesmaximal, characteristic
11#16812067C211yesmaximal, characteristic, complemented
12#16812066C211yesmaximal, characteristic, complemented
13#16812065C211yesmaximal, characteristic, complemented
14C4⋊C4×D107C211yesmaximal, characteristic, complemented
15#126×C107C211yesmaximal, characteristic, complemented
16C2×Dic214C2211yescharacteristic
17C2×C22⋊D107C2211yescharacteristic
18C22×Dic107C2211yescharacteristic
19C2×C4×D107C2211yescharacteristic
20C2×C4×D107C2211yescharacteristic
21C2×C4×D107C2211yescharacteristic
22C4⋊Dic107C2211yescharacteristic
23C4⋊Dic107C2211yescharacteristic
24C4⋊Dic107C2211yescharacteristic
25C4⋊Dic107C2211yescharacteristic
26Dic107⋊C4C2211yescharacteristic
27Dic107⋊C4C2211yescharacteristic
28Dic107⋊C4C2211yescharacteristic
29Dic107⋊C4C2211yescharacteristic
30Dic107⋊C4C2211yescharacteristic
31Dic107⋊C4C2211yescharacteristic
32Dic107⋊C4C2211yescharacteristic
33Dic107⋊C4C2211yescharacteristic
34Dic107⋊C4C2211yescharacteristic
35C22⋊Dic107C2211yescharacteristic
36C22⋊Dic107C2211yescharacteristic
37(C2×D107)⋊C4C2211yescharacteristic
38(C2×D107)⋊C4C2211yescharacteristic
39(C2×D107)⋊C4C2211yescharacteristic
40C4×Dic107C2211yescharacteristic
41C4×Dic107C2211yescharacteristic
42C4×Dic107C2211yescharacteristic
43C4×Dic107C2211yescharacteristic
44C4⋊C4×C107C2211yescharacteristic
45C4⋊C4×C107C2211yescharacteristic
46C4⋊C4×C107C2211yescharacteristic
47C22⋊C4×C107C2211yescharacteristic
48C22⋊C4×C107C2211yescharacteristic
49C22⋊C4×C107C2211yescharacteristic
50C42×C107C2211yescharacteristic
51C23×C107C2311yescharacteristic
52C22×D107C2311yescharacteristic
53C2×C4×C107C2311yescharacteristic
54C2×C4×C107C2311yescharacteristic
55C2×C4×C107C2311yescharacteristic
56C2×C4×C107C2311yescharacteristic
57C2×C4×C107C2311yescharacteristic
58C2×C4×C107C2311yescharacteristic
59C22⋊D107—22no—
60C2×Dic107—22no—
61C2×Dic107C2311yescharacteristic
62C2×Dic107C2311yescharacteristic
63C2×Dic107C2311yescharacteristic
64C2×Dic107C2311yescharacteristic
65C2×Dic107C2311yescharacteristic
66C2×Dic107C2311yescharacteristic
67C2×Dic107C2311yescharacteristic
68C4×D107—22no—
69C4×D107—22no—
70C4×D107—22no—
71Dic214—22no—
72C22×C107—21no—
73C22×C107—21no—
74C22×C107—21no—
75C22×C107C2411yescharacteristic
76C2×D107—21no—
77C2×D107—21no—
78C2×D107#4112yes—
79C4×C107—21no—
80C4×C107—21no—
81C4×C107—21no—
82C4×C107—21no—
83C4×C107—21no—
84C4×C107—21no—
85Dic107—21no—
86Dic107—21no—
87Dic107—21no—
88Dic107—21no—
89Dic107—21no—
90Dic107—21no—
91Dic107#4112yes—
92C2×C107—41no—
93C2×C107C2×#4111yescharacteristic
94C2×C107C2×#4111yescharacteristic
95C2×C1072−1+411yescharacteristic
96D107—22no—
97C107#55211yescharacteristic, complemented, Sylow
98#552—1071nomaximal, Sylow
99#126—1071no—
100#126D10711yescharacteristic, complemented
101#125—1071no—
102#125—1071no—
103#125—1071no—
104#123—1071no—
105#123—1071no—
106C22⋊Q8—1071no—
107C22⋊Q8—1071no—
108C4×Q8—1071no—
109C4×D4—1071no—
110#117—1071no—
111#117—1071no—
112#117—1071no—
113C2×C4⋊C4—1071no—
114C2×Q8—1071no—
115C2×D4—1071no—
116C22×C4—1071no—
117C22×C4—1071no—
118C22×C4—1071no—
119C22×C4—1071no—
120C4⋊C4—1071no—
121C4⋊C4—1071no—
122C4⋊C4—1071no—
123C4⋊C4—1071no—
124C4⋊C4—1071no—
125C4⋊C4—1071no—
126C4⋊C4—1071no—
127C4⋊C4—1071no—
128C4⋊C4—1071no—
129C4⋊C4—1071no—
130C4⋊C4—1071no—
131C4⋊C4—1071no—
132C4⋊C4—1071no—
133C4⋊C4C2×D10711yescharacteristic
134C4⋊C4C2×D10711yescharacteristic
135C4⋊C4C2×D10711yescharacteristic
136C22⋊C4—1071no—
137C22⋊C4—1071no—
138C22⋊C4—1071no—
139C22⋊C4—1071no—
140C22⋊C4—1071no—
141C22⋊C4C2×D10711yescharacteristic
142C22⋊C4C2×D10711yescharacteristic
143C22⋊C4C2×D10711yescharacteristic
144C42—1071no—
145C42—1071no—
146C42—1071no—
147C42—1071no—
148C42C2×D10711yescharacteristic
149C23—1071no—
150C23C22×D10711yescharacteristic
151Q8—2142no—
152D4—2142no—
153C2×C4—1071no—
154C2×C4—1071no—
155C2×C4—1071no—
156C2×C4—1071no—
157C2×C4—1071no—
158C2×C4—1071no—
159C2×C4—1071no—
160C2×C4—2142no—
161C2×C4—2142no—
162C2×C4—2142no—
163C2×C4—2142no—
164C2×C4C22×D10711yescharacteristic
165C2×C4C22×D10711yescharacteristic
166C2×C4C22×D10711yescharacteristic
167C2×C4C22×D10711yescharacteristic
168C2×C4C22×D10711yescharacteristic
169C2×C4C22×D10711yescharacteristic
170C22—21no—
171C22—21no—
172C22—21no—
173C22—1072no—
174C22—2141no—
175C22—2141no—
176C22C23×D10711yescharacteristic
177C4—21no—
178C4—21no—
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—1072no—
184C4—2141no—
185C4—2141no—
186C4—2141no—
187C4—2141no—
188C4—2141no—
189C4—2141no—
190C2—41no—
191C2—2142no—
192C2#41×D10711yescharacteristic
193C2#41×D10711yescharacteristic
194C2#1681215611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D107
commutator, socleC22×C107C24
Fitting#126×C107C2
hypercenter#126D107
hypocenterC107#552
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #16812102C2semidirect
2. #16812100C2semidirect
3. #16812099C2semidirect
4. #16812099C2semidirect
7. #16812087C2semidirect
8. #16812086C2semidirect
9. C4×Dic214C2semidirect
11. #16812067C2semidirect
12. #16812066C2semidirect
13. #16812065C2semidirect
14. C4⋊C4×D107C2semidirect
15. #126×C107C2semidirect
97. C107#552semidirect
100. #126D107semidirect