Finite Group Databasebeta

← #20293443

Subgroups — #20293443

Order 6848.

248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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#16812157C211yesmaximal, characteristic, complemented
2#16812156C211yesmaximal, characteristic, complemented
3#16812142C211yesmaximal, characteristic, complemented
4#16812141C212yesmaximal, complemented
5#16812138C212yesmaximal, complemented
6#16812130C212yesmaximal, complemented
7#16812129C211yesmaximal, characteristic, complemented
8C2×#13133808C211yesmaximal, characteristic, complemented
9Q16×D107C212yesmaximal, complemented
10#16812117C211yesmaximal, characteristic, complemented
11#137×C107C211yesmaximal, characteristic, complemented
12#13133819—21no—
13#13133819C2212yes—
14#13133818—22no—
15#13133818—21no—
16#13133818C2211yescharacteristic
17#13133818C2211yescharacteristic
18#13133817—22no—
19#13133817C2212yes—
20C2×Dic214—21no—
21C2×Dic214C2211yescharacteristic
22Q8×D107—21no—
23Q8×D107C2212yes—
24Q8×D107C2212yes—
25Dic428C2212yes—
26#13133808C2211yescharacteristic
27#13133808C2212yes—
28#13133808C2212yes—
29#13133807C2212yes—
30#13133806C2211yescharacteristic
31#13133805C2211yescharacteristic
32#13133803C2211yescharacteristic
33#13133801C2212yes—
34C2×C107⋊C8C2211yescharacteristic
35C8×D107C2212yes—
36#41×C107C2211yescharacteristic
37C2×Q8×C107C2211yescharacteristic
38Q16×C107C2212yes—
39SD16×C107C2212yes—
40M16×C107C2211yescharacteristic
41Q8×C107—21no—
42Q8×C107C2312yes—
43Q8×C107C2311yescharacteristic
44D4×C107—21no—
45D4×C107C2311yescharacteristic
46C2×C4×C107—21no—
47C2×C4×C107—21no—
48C2×C4×C107C2311yescharacteristic
49C22⋊D107—21no—
50C22⋊D107—22no—
51C22⋊D107D412yes—
52C2×Dic107—21no—
53C2×Dic107—22no—
54D428—22no—
55D428D411yescharacteristic
56D428C2311yescharacteristic
57C4×D107—22no—
58C4×D107—22no—
59C4×D107—21no—
60C4×D107—22no—
61C4×D107C2312yes—
62Dic214—21no—
63Dic214—22no—
64Dic214—22no—
65Dic214D411yescharacteristic
66Dic214C2311yescharacteristic
67Dic214C2312yes—
68C8×C107C2312yes—
69C107⋊C8C2311yescharacteristic
70C107⋊C8C2311yescharacteristic
71C22×C107—21no—
72C22×C107C2×D411yescharacteristic
73C2×D107—21no—
74C2×D107C2×D412yes—
75C4×C107—21no—
76C4×C107—22no—
77C4×C107C2×D411yescharacteristic
78C4×C107C2411yescharacteristic
79Dic107—21no—
80Dic107—22no—
81Dic107C2×D412yes—
82C2×C107—21no—
83C2×C107—41no—
84C2×C107C22×D411yescharacteristic
85D107—22no—
86D107—41no—
87C107#57811yescharacteristic, complemented, Sylow
88#578—1071nomaximal, Sylow
892−1+4—1071no—
902−1+4—1071no—
91#137—1072no—
92#137—1072no—
93#137—1071no—
94#137D10711yescharacteristic, complemented
95#135—1071no—
96#135—1072no—
97C2×Q16—1071no—
98C2×Q16—1072no—
99#131—1071no—
100#41—1071no—
101#41—1072no—
102#41—1072no—
103#41—1071no—
104#41—2142no—
105#41—2141no—
106#41—2142no—
107#41—2141no—
108#41C2×D10711yescharacteristic
109C2×Q8—1072no—
110C2×Q8—1072no—
111C2×Q8—1071no—
112C2×Q8—2141no—
113C2×Q8—2141no—
114C2×Q8C2×D10711yescharacteristic
115Q16—1071no—
116Q16—1072no—
117Q16—1072no—
118Q16—1072no—
119Q16C2×D10712yes—
120SD16—1071no—
121SD16—1071no—
122SD16—1072no—
123SD16C2×D10712yes—
124D8—1071no—
125M16—1072no—
126M16C2×D10711yescharacteristic
127C2×C8—1071no—
128C2×C8—1072no—
129Q8—21no—
130Q8—1071no—
131Q8—1071no—
132Q8—1072no—
133Q8—2142no—
134Q8—2142no—
135Q8—2141no—
136Q8C22×D10711yescharacteristic
137Q8C22×D10712yes—
138D4—21no—
139D4—1072no—
140D4—1071no—
141D4—1071no—
142D4—2142no—
143D4—2142no—
144D4—2141no—
145D4C22×D10711yescharacteristic
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—1072no—
149C2×C4—2142no—
150C2×C4—2142no—
151C2×C4—2142no—
152C2×C4—2142no—
153C2×C4—2141no—
154C2×C4—2141no—
155C2×C4C22×D10711yescharacteristic
156C8—1071no—
157C8—1071no—
158C8C22×D10712yes—
159C22—21no—
160C22—1072no—
161C22—2141no—
162C22D4×D10711yescharacteristic
163C4—21no—
164C4—22no—
165C4—1072no—
166C4—2141no—
167C4—2142no—
168C4D4×D10711yescharacteristic
169C4C23×D10711yescharacteristic
170C2—21no—
171C2—41no—
172C2—4281no—
173C2—2142no—
174C2C2×D4×D10711yescharacteristic
subgroupG/H
centerC2C2×D4×D107
commutatorC4×C107C24
FrattiniC4C23×D107
Fitting#137×C107C2
socleC2×C107C22×D4
hypercenter#137D107
hypocenterC107#578
LCSG ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. #16812157C2semidirect
2. #16812156C2semidirect
3. #16812142C2semidirect
4. #16812141C2semidirect
5. #16812138C2semidirect
6. #16812130C2semidirect
7. #16812129C2semidirect
8. C2×#13133808C2semidirect
9. Q16×D107C2semidirect
10. #16812117C2semidirect
11. #137×C107C2semidirect
87. C107#578semidirect
94. #137D107semidirect