Finite Group Databasebeta

← #28335069

Subgroups — #28335069

Order 13696.

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

normal subgroups only

This group has 216 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
1#20293161C211yesmaximal, characteristic
2C4×#13133802C211yesmaximal, characteristic, complemented
3#20292368C212yesmaximal, complemented
4#20292366C212yesmaximal, complemented
5#432×C107C211yesmaximal, characteristic, complemented
6C2×#13133802—21no—
7#16812103—21no—
8#16812101C2211yescharacteristic
9#16812097C2211yescharacteristic
10#16812092—21no—
11#16812088C411yescharacteristic
12#16812083C411yescharacteristic
13C4×Dic214C411yescharacteristic
14C4×D428C411yescharacteristic
15C4×C22⋊D107—21no—
16#16812066—21no—
17#16812020C2212yes—
18C4×C107⋊C8—21no—
19C2×C42×C107C2211yescharacteristic
20C4⋊C8×C107—21no—
21C22⋊C8×C107—21no—
22#97×C107C2212yes—
23C2×Dic214C2×C411yescharacteristic
24C2×D428C2×C411yescharacteristic
25C2×C22⋊D107—21no—
26C2×C4×D107—21no—
27#13133802—24no—
28C2×C107⋊C8—22no—
29C4⋊Dic107C2×C411yescharacteristic
30C4⋊Dic107C2×C411yescharacteristic
31Dic107⋊C4—21no—
32Dic107⋊C4—21no—
33Dic107⋊C4—21no—
34Dic107⋊C4—21no—
35C22⋊Dic107—21no—
36(C2×D107)⋊C4—21no—
37(C2×D107)⋊C4—21no—
38(C2×D107)⋊C4—21no—
39(C2×D107)⋊C4—21no—
40C4×Dic107—21no—
41C22×C4×C107C2×C411yescharacteristic
42C22×C4×C107D411yescharacteristic
43C22×C4×C107D411yescharacteristic
44C2×C8×C107—22no—
45C42×C107C2×C411yescharacteristic
46C42×C107D411yescharacteristic
47C42×C107D411yescharacteristic
48C42×C107C2311yescharacteristic
49C23×C107C22⋊C411yescharacteristic
50C22×D107—21no—
51C2×C4×C107—22no—
52C2×C4×C107—41no—
53C2×C4×C107—41no—
54C2×C4×C107C22⋊C411yescharacteristic
55C2×C4×C107C22⋊C411yescharacteristic
56C2×C4×C107C22⋊C411yescharacteristic
57C2×C4×C107C22×C411yescharacteristic
58C2×C4×C107C2×D411yescharacteristic
59C2×C4×C107C2×D411yescharacteristic
60C22⋊D107—42no—
61C2×Dic107—21no—
62C2×Dic107—21no—
63C2×Dic107—21no—
64D428—41no—
65C4×D107—42no—
66Dic214—41no—
67C8×C107—42no—
68C107⋊C8—24no—
69C22×C107—21no—
70C22×C107—21no—
71C22×C107—21no—
72C22×C107C2×C22⋊C411yescharacteristic
73C2×D107—41no—
74C2×D107—41no—
75C2×D107—41no—
76C4×C107—21no—
77C4×C107—21no—
78C4×C107—21no—
79C4×C107—21no—
80C4×C107—21no—
81C4×C107#10412yes—
82Dic107—41no—
83Dic107—41no—
84Dic107—41no—
85C2×C107—41no—
86C2×C107#41311yescharacteristic
87C2×C107C2×#10411yescharacteristic
88C2×C107#42111yescharacteristic
89D107—81no—
90#1529—1071nomaximal, Sylow
91C107#152911yescharacteristic, complemented, Sylow
92#529—1071no—
93#432D10711yescharacteristic, complemented
94C4×M16—1071no—
95#330—1072no—
96#329—1072no—
97C2×M16—2141no—
98#126—2141no—
99#125—1071no—
100#124—1071no—
101#123—2141no—
102C22⋊Q8—1071no—
103#121—1071no—
104C4×Q8—1071no—
105C4×D4—1071no—
106C4×D4—2141no—
107#117—2141no—
108C2×C42C2×D10711yescharacteristic
109C4⋊C8—21no—
110C22⋊C8—21no—
111#97—1072no—
112#97C2×D10712yes—
113C4×C8—2141no—
114C2×Q8—1071no—
115C2×D4—1071no—
116C2×D4—2141no—
117C22×C4—2141no—
118C22×C4C4×D10711yescharacteristic
119C22×C4D42811yescharacteristic
120C22×C4C22⋊D10711yescharacteristic
121M16—2144no—
122C2×C8—22no—
123C2×C8—2142no—
124C4⋊C4—1071no—
125C4⋊C4—1071no—
126C4⋊C4—2141no—
127C4⋊C4—2141no—
128C4⋊C4—2141no—
129C4⋊C4—2141no—
130C22⋊C4—2141no—
131C22⋊C4—2141no—
132C22⋊C4—2141no—
133C22⋊C4—2141no—
134C22⋊C4—2141no—
135C42—2141no—
136C42C4×D10711yescharacteristic
137C42D42811yescharacteristic
138C42C22⋊D10711yescharacteristic
139C42C22×D10711yescharacteristic
140C23—2141no—
141C23(C2×D107)⋊C411yescharacteristic
142Q8—4281no—
143D4—4281no—
144D4—4282no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—4282no—
149C2×C4—2141no—
150C2×C4—2141no—
151C2×C4—2141no—
152C2×C4(C2×D107)⋊C411yescharacteristic
153C2×C4(C2×D107)⋊C411yescharacteristic
154C2×C4(C2×D107)⋊C411yescharacteristic
155C2×C4C2×C4×D10711yescharacteristic
156C2×C4C2×C22⋊D10711yescharacteristic
157C2×C4C2×D42811yescharacteristic
158C8—42no—
159C8—2144no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—4281no—
164C22—4281no—
165C22—4281no—
166C22C2×(C2×D107)⋊C411yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—4281no—
173C4—4281no—
174C4—4281no—
175C4#1681203512yes—
176C2—41no—
177C2—8561no—
178C2#2029260911yescharacteristic
179C2C2×#1681203511yescharacteristic
180C2#2029264511yescharacteristic
subgroupG/H
centerC22C2×(C2×D107)⋊C4
commutatorC2×C4×C107C22×C4
FrattiniC42C22×D107
Fitting#432×C107C2
socleC22×C107C2×C22⋊C4
prime radical#16812083C4
cosocleC42×C107C23
hypercenter#432D107
hypocenterC107#1529
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C4×#13133802C2semidirect
3. #20292368C2semidirect
4. #20292366C2semidirect
5. #432×C107C2semidirect
91. C107#1529semidirect
93. #432D107semidirect

Maximal subgroups

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

subgroupindex
#202931612
C4×#131338022
#202923682
#202923662
#432×C1072
#1529107