Finite Group Databasebeta

← #28344836

Subgroups — #28344836

Order 13696.

504 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 177 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×#16812108C211yesmaximal, characteristic
2C2×#16812107C211yesmaximal, characteristic
3#20292534C211yesmaximal, characteristic
4#20292533C211yesmaximal, characteristic
5#20292532C211yesmaximal, characteristic
6#20292531C214yesmaximal
7#20292491C214yesmaximal
8C42×Dic107C211yesmaximal, characteristic
9#391×C107C211yesmaximal, characteristic
10C22×Dic214C2211yescharacteristic
11C22×Dic214C2212yes—
12#16812108—24no—
13#16812107—24no—
14C2×C4⋊Dic107C2211yescharacteristic
15C2×Dic107⋊C4C2212yes—
16C2×Dic107⋊C4C2212yes—
17C2×Dic107⋊C4C2212yes—
18C2×C4×Dic107C2212yes—
19C2×C4×Dic107C2211yescharacteristic
20C2×C4×Dic107C2211yescharacteristic
21C2×C4×Dic107C2212yes—
22C107⋊#95C2214yes—
23C107⋊#95C2214yes—
24C107⋊#95C2214yes—
25C22×Q8×C107C2211yescharacteristic
26C2×C4⋊C4×C107C2211yescharacteristic
27C2×C42×C107C2211yescharacteristic
28#95×C107C2214yes—
29C2×Dic214—22no—
30C2×Dic214—22no—
31C2×Dic214—22no—
32C2×Dic214—24no—
33C2×Dic214—28no—
34C22×Dic107C2312yes—
35C22×Dic107C2312yes—
36C22×Dic107C2312yes—
37C22×Dic107C2311yescharacteristic
38C22×Dic107C2311yescharacteristic
39C4⋊Dic107—22no—
40Dic107⋊C4—24no—
41Dic107⋊C4—24no—
42Dic107⋊C4—24no—
43C4×Dic107—22no—
44C4×Dic107—24no—
45C4×Dic107D414yes—
46C4×Dic107Q818yescomplemented
47C2×Q8×C107—22no—
48C2×Q8×C107—22no—
49C2×Q8×C107—22no—
50C22×C4×C107C2312yes—
51C22×C4×C107C2312yes—
52C22×C4×C107C2312yes—
53C22×C4×C107C2311yescharacteristic
54C4⋊C4×C107—22no—
55C42×C107—22no—
56C23×C107C2411yescharacteristic
57Q8×C107—44no—
58C2×C4×C107—22no—
59C2×C4×C107—22no—
60C2×C4×C107—22no—
61C2×C4×C107—22no—
62C2×C4×C107—22no—
63C2×C4×C107—22no—
64C2×C4×C107—24no—
65C2×C4×C107C2×D412yes—
66C2×C4×C107C2×Q814yes—
67C2×C4×C107#4112yes—
68C2×C4×C107#4112yes—
69C2×Dic107—22no—
70C2×Dic107—22no—
71C2×Dic107—22no—
72C2×Dic107—22no—
73C2×Dic107—24no—
74C2×Dic107—22no—
75C2×Dic107—22no—
76C2×Dic107C2×D412yes—
77C2×Dic107C2×D412yes—
78C2×Dic107C2×Q814yes—
79C2×Dic107C2×Q814yes—
80C2×Dic107#4114yes—
81Dic214—44no—
82Dic214—48no—
83C22×C107C22×D411yescharacteristic
84C22×C107C22×Q812yes—
85C22×C107C2×#4112yes—
86C22×C107C2×#4111yescharacteristic
87C22×C107C2×#4111yescharacteristic
88C4×C107—24no—
89C4×C107—42no—
90C4×C107—42no—
91C4×C107#12414yes—
92Dic107—24no—
93Dic107—42no—
94Dic107—42no—
95Dic107#12414yes—
96Dic107C4⋊Q814yes—
97C2×C107C2×#12411yescharacteristic
98C2×C107C2×#12411yescharacteristic
99C2×C107C2×C4⋊Q811yescharacteristic
100C2×C107#53312yes—
101C2×C107#53312yes—
102#2862—1071nomaximal, Sylow
103C107#286211yescharacteristic, complemented, Sylow
104C2×C4⋊Q8—1071no—
105C2×C4⋊Q8—1071no—
106#391—1071no—
107#391—1071no—
108#391—1071no—
109#391—1074no—
110#391D10711yescharacteristic
111#382—1074no—
112C43—1071no—
113C22×Q8—1072no—
114C22×Q8—1071no—
115C22×Q8C2×D10711yescharacteristic
116C4⋊Q8—2144no—
117C4⋊Q8—2144no—
118C2×C4⋊C4—1072no—
119C2×C4⋊C4—1072no—
120C2×C4⋊C4—1072no—
121C2×C4⋊C4—1071no—
122C2×C4⋊C4C2×D10711yescharacteristic
123C2×C42—1071no—
124C2×C42—1072no—
125C2×C42—1072no—
126C2×C42—1071no—
127C2×C42C2×D10711yescharacteristic
128#95—1074no—
129#95—1074no—
130#95—1074no—
131#95C2×D10714yes—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—2144no—
136C2×Q8—2148no—
137C2×Q8—2142no—
138C2×Q8—2142no—
139C2×Q8—2142no—
140C22×C4—1071no—
141C22×C4—1071no—
142C22×C4—1072no—
143C22×C4—1072no—
144C22×C4—1072no—
145C22×C4C22×D10712yes—
146C22×C4C22×D10712yes—
147C22×C4C22×D10712yes—
148C22×C4C22×D10711yescharacteristic
149C4⋊C4—22no—
150C4⋊C4—2144no—
151C4⋊C4—2144no—
152C4⋊C4—2144no—
153C4⋊C4—2142no—
154C42—22no—
155C42—1074no—
156C42—1078no—
157C42—2144no—
158C42—2142no—
159C23C23×D10711yescharacteristic
160Q8—44no—
161Q8—4288no—
162Q8—4284no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—1072no—
171C2×C4—1072no—
172C2×C4—1074no—
173C2×C4—1074no—
174C2×C4—1074no—
175C2×C4—2142no—
176C2×C4—2142no—
177C2×C4—2144no—
178C2×C4—2142no—
179C2×C4—2142no—
180C2×C4—2142no—
181C2×C4—2142no—
182C2×C4D4×D10712yes—
183C2×C4Q8×D10714yes—
184C2×C4#1313381712yes—
185C2×C4#1313381812yes—
186C22C2×D4×D10711yescharacteristic
187C22C2×Q8×D10712yes—
188C22#41×D10712yes—
189C22C2×#1313381711yescharacteristic
190C22C2×#1313381811yescharacteristic
191C4—24no—
192C4—42no—
193C4—42no—
194C4—1074no—
195C4—1074no—
196C4—4282no—
197C4—4282no—
198C4—2144no—
199C4#1681209514yes—
200C2#124×D10711yescharacteristic
201C2C2×#1681209511yescharacteristic
202C2C4⋊Q8×D10711yescharacteristic
203C2#2029317912yes—
204C2#2029318112yes—
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, prime radical, cosocleC23×C107C24
Fitting#391×C107C2
hypercenter#391D107
hypocenterC107#2862
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
46. C4×Dic107Q8semidirect
103. C107#2862semidirect

Maximal subgroups

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

subgroupindex
C2×#168121082
C2×#168121072
#202925342
#202925332
#202925322
#202925312
#202924912
C42×Dic1072
#391×C1072
#2862107