Finite Group Databasebeta

← #28334831

Subgroups — #28334831

Order 13696.

214 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 69 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×#16812103C211yesmaximal, characteristic
2#20292680C211yesmaximal, characteristic, complemented
3#20292352C212yesmaximal, complemented
4#20292350C212yesmaximal
5#432×C107C211yesmaximal, characteristic, complemented
6#16812103—21no—
7#16812103—21no—
8#16812103—21no—
9#16812103—21no—
10C2×Dic107⋊C4C411yescharacteristic
11C2×Dic107⋊C4C411yescharacteristic
12C2×Dic107⋊C4C2211yescharacteristic
13C2×(C2×D107)⋊C4C411yescharacteristic
14C2×(C2×D107)⋊C4C411yescharacteristic
15C2×(C2×D107)⋊C4C2211yescharacteristic
16C4⋊(C107⋊C8)—21no—
17C22⋊(C107⋊C8)C2212yes—
18C4×C107⋊C8—21no—
19C2×C42×C107C2211yescharacteristic
20C4⋊C8×C107—21no—
21C22⋊C8×C107C2212yes—
22#97×C107—21no—
23C23×D107C2×C411yescharacteristic
24C22×Dic107C2×C411yescharacteristic
25C22×Dic107C2×C411yescharacteristic
26C22×Dic107C2×C411yescharacteristic
27C2×C107⋊C8—22no—
28Dic107⋊C4—21no—
29Dic107⋊C4—21no—
30Dic107⋊C4—21no—
31Dic107⋊C4—21no—
32Dic107⋊C4—21no—
33Dic107⋊C4—21no—
34(C2×D107)⋊C4—21no—
35(C2×D107)⋊C4—21no—
36(C2×D107)⋊C4—21no—
37(C2×D107)⋊C4—21no—
38(C2×D107)⋊C4—21no—
39(C2×D107)⋊C4—21no—
40C22×C4×C107C2×C411yescharacteristic
41C22×C4×C107C2×C411yescharacteristic
42C22×C4×C107C2311yescharacteristic
43C2×C8×C107—22no—
44C42×C107D411yescharacteristic
45C42×C107D411yescharacteristic
46C42×C107D411yescharacteristic
47C42×C107D411yescharacteristic
48C23×C107C22×C411yescharacteristic
49C22×D107—21no—
50C22×D107—22no—
51C22×D107—41no—
52C22×D107—41no—
53C2×C4×C107—22no—
54C2×C4×C107—41no—
55C2×C4×C107—41no—
56C2×C4×C107C22⋊C411yescharacteristic
57C2×C4×C107C22⋊C411yescharacteristic
58C2×C4×C107C22⋊C411yescharacteristic
59C2×C4×C107C22⋊C411yescharacteristic
60C2×C4×C107C2×D411yescharacteristic
61C2×C4×C107C2×D411yescharacteristic
62C2×Dic107—21no—
63C2×Dic107—21no—
64C2×Dic107—21no—
65C2×Dic107—22no—
66C2×Dic107—41no—
67C2×Dic107—41no—
68C8×C107—42no—
69C107⋊C8—42no—
70C22×C107—21no—
71C22×C107—21no—
72C22×C107C2×C22⋊C411yescharacteristic
73C22×C107#13112yes—
74C2×D107—41no—
75C2×D107—41no—
76C2×D107—41no—
77C2×D107—82no—
78C4×C107—21no—
79C4×C107—21no—
80C4×C107—21no—
81C4×C107—21no—
82C4×C107—21no—
83C4×C107—21no—
84Dic107—41no—
85Dic107—41no—
86Dic107—41no—
87C2×C107—22no—
88C2×C107#40811yescharacteristic
89C2×C107#41011yescharacteristic
90C2×C107#41311yescharacteristic
91D107—81no—
92#1473—1071nomaximal, Sylow
93C107#147311yescharacteristic, complemented, Sylow
94C2×#126—1071no—
95#432D10711yescharacteristic, complemented
96#431—1071no—
97#324—1072no—
98#323—1072no—
99#126—2141no—
100#126—2141no—
101#126—2141no—
102#126—2141no—
103C2×C4⋊C4—1071no—
104C2×C4⋊C4—1071no—
105C2×C4⋊C4—1071no—
106C2×C22⋊C4—1071no—
107C2×C22⋊C4—1071no—
108C2×C22⋊C4—1071no—
109C2×C42C2×D10711yescharacteristic
110C4⋊C8—21no—
111C4⋊C8—2141no—
112C22⋊C8—1072no—
113C22⋊C8C2×D10712yes—
114#97—21no—
115C4×C8—2141no—
116C24—1071no—
117C22×C4—1071no—
118C22×C4—1071no—
119C22×C4—1071no—
120C22×C4C4×D10711yescharacteristic
121C22×C4C4×D10711yescharacteristic
122C22×C4C22×D10711yescharacteristic
123C2×C8—22no—
124C2×C8—2142no—
125C4⋊C4—2141no—
126C4⋊C4—2141no—
127C4⋊C4—2141no—
128C4⋊C4—2141no—
129C4⋊C4—2141no—
130C4⋊C4—2141no—
131C22⋊C4—2141no—
132C22⋊C4—2141no—
133C22⋊C4—2141no—
134C22⋊C4—2141no—
135C22⋊C4—2141no—
136C22⋊C4—2141no—
137C42D42811yescharacteristic
138C42D42811yescharacteristic
139C42C22⋊D10711yescharacteristic
140C42C22⋊D10711yescharacteristic
141C23—4281no—
142C23—4281no—
143C23—2142no—
144C23—2141no—
145C23C2×C4×D10711yescharacteristic
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—4281no—
150C2×C4—4281no—
151C2×C4—2141no—
152C2×C4—2141no—
153C2×C4—2141no—
154C2×C4—2142no—
155C2×C4(C2×D107)⋊C411yescharacteristic
156C2×C4(C2×D107)⋊C411yescharacteristic
157C2×C4(C2×D107)⋊C411yescharacteristic
158C2×C4(C2×D107)⋊C411yescharacteristic
159C2×C4C2×C22⋊D10711yescharacteristic
160C2×C4C2×D42811yescharacteristic
161C8—42no—
162C8—4282no—
163C22—21no—
164C22—21no—
165C22—8562no—
166C22—4281no—
167C22—4281no—
168C22—4281no—
169C22C2×(C2×D107)⋊C411yescharacteristic
170C22#1681211712yes—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—4281no—
178C4—4281no—
179C4—4281no—
180C2—22no—
181C2—8561no—
182C2#2029259511yescharacteristic
183C2#2029260011yescharacteristic
184C2#2029260911yescharacteristic
subgroupG/H
centerC22C2×(C2×D107)⋊C4
commutatorC23×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#432×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC23×D107C2×C4
cosocleC22×C4×C107C23
hypercenter#432D107
hypocenterC107#1473
LCSG ▷ C23×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #20292680C2semidirect
3. #20292352C2semidirect
5. #432×C107C2semidirect
93. C107#1473semidirect
95. #432D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168121032
#202926802
#202923522
#202923502
#432×C1072
#1473107