Finite Group Databasebeta

← #28339755

Subgroups — #28339755

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×C4×Dic214C212yesmaximal
2#20292561C212yesmaximal
3#20292560C212yesmaximal
4#20292548C212yesmaximal
5#20292547C212yesmaximal
6C4×Dic107⋊C4C212yesmaximal
7C4×C4⋊Dic107C211yesmaximal, characteristic
8#20292473C211yesmaximal, characteristic
9C4×C4⋊C4×C107C211yesmaximal, characteristic
10C22×Dic214C2212yes—
11C4×Dic214—28no—
12C2×C4⋊Dic107C2212yes—
13C2×C4⋊Dic107C2212yes—
14C2×Dic107⋊C4C2212yes—
15C2×Dic107⋊C4C2212yes—
16C2×Dic107⋊C4C2212yes—
17C2×Dic107⋊C4C2212yes—
18C2×C4×Dic107C2212yes—
19C2×C4×Dic107C2211yescharacteristic
20C2×C4×Dic107C2211yescharacteristic
21C107⋊#95C2212yes—
22C107⋊#95C2212yes—
23C107⋊#95C2211yescharacteristic
24C107⋊#95C2211yescharacteristic
25C107⋊#95C2212yes—
26C107⋊#95C2212yes—
27C2×C4⋊C4×C107C2212yes—
28C2×C42×C107C2212yes—
29C2×C42×C107C2211yescharacteristic
30#95×C107C2211yescharacteristic
31#95×C107C2211yescharacteristic
32C2×Dic214—24no—
33C2×Dic214—24no—
34C2×Dic214—24no—
35C22×Dic107C2312yes—
36C22×Dic107C2312yes—
37C22×Dic107C2312yes—
38C22×Dic107C2312yes—
39C4⋊Dic107—24no—
40C4⋊Dic107—24no—
41Dic107⋊C4—24no—
42Dic107⋊C4—24no—
43Dic107⋊C4—24no—
44Dic107⋊C4—24no—
45C4×Dic107—24no—
46C4×Dic107D414yes—
47C4×Dic107Q814yescomplemented
48C22×C4×C107C2312yes—
49C22×C4×C107C2311yescharacteristic
50C22×C4×C107C2311yescharacteristic
51C22×C4×C107C2312yes—
52C22×C4×C107C2311yescharacteristic
53C4⋊C4×C107—24no—
54C42×C107—24no—
55C42×C107Q814yescomplemented
56C23×C107C2411yescharacteristic
57C2×C4×C107—22no—
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×C107C2×D412yes—
65C2×C4×C107C2×Q812yes—
66C2×C4×C107C2×Q812yes—
67C2×C4×C107C2×Q812yes—
68C2×C4×C107C2×Q812yes—
69C2×C4×C107#4114yes—
70C2×Dic107—22no—
71C2×Dic107—22no—
72C2×Dic107—22no—
73C2×Dic107—22no—
74C2×Dic107—22no—
75C2×Dic107—22no—
76C2×Dic107—22no—
77C2×Dic107—22no—
78C2×Dic107—22no—
79C2×Dic107C2×D414yes—
80C2×Dic107C2×Q814yes—
81C2×Dic107#4114yes—
82Dic214—216no—
83C22×C107C22×D411yescharacteristic
84C22×C107C22×Q811yescharacteristic
85C22×C107C22×Q811yescharacteristic
86C22×C107C2×#4112yes—
87C22×C107C2×#4112yes—
88C4×C107—24no—
89C4×C107—22no—
90C4×C107—22no—
91C4×C107—42no—
92C4×C107C4⋊Q814yes—
93Dic107—24no—
94Dic107—24no—
95Dic107—24no—
96Dic107—42no—
97C2×C107#52512yes—
98C2×C107C2×C4⋊Q811yescharacteristic
99C2×C107#53311yescharacteristic
100C2×C107#53312yes—
101C2×C107#53311yescharacteristic
102#2399—1071nomaximal, Sylow
103C107#239911yescharacteristic, complemented, Sylow
104C2×C4×Q8—1072no—
105#398—1072no—
106#398—1072no—
107#395—1072no—
108#395—1072no—
109C4×C4⋊C4—1071no—
110C4×C4⋊C4—1072no—
111C4×C4⋊C4D10711yescharacteristic
112#376—1071no—
113C22×Q8—1072no—
114C4×Q8—2148no—
115C2×C4⋊C4—1072no—
116C2×C4⋊C4—1072no—
117C2×C4⋊C4—1072no—
118C2×C4⋊C4—1072no—
119C2×C4⋊C4—1072no—
120C2×C4⋊C4—1072no—
121C2×C4⋊C4C2×D10712yes—
122C2×C42—1071no—
123C2×C42—1071no—
124C2×C42—1072no—
125C2×C42C2×D10712yes—
126C2×C42C2×D10711yescharacteristic
127#95—1072no—
128#95—1072no—
129#95—1072no—
130#95—1071no—
131#95—1072no—
132#95—1071no—
133#95C2×D10711yescharacteristic
134#95C2×D10711yescharacteristic
135C2×Q8—2144no—
136C2×Q8—2144no—
137C2×Q8—2144no—
138C22×C4—1072no—
139C22×C4—1072no—
140C22×C4—1072no—
141C22×C4—1072no—
142C22×C4C22×D10712yes—
143C22×C4C22×D10711yescharacteristic
144C22×C4C22×D10711yescharacteristic
145C22×C4C22×D10712yes—
146C22×C4C22×D10711yescharacteristic
147C4⋊C4—24no—
148C4⋊C4—2144no—
149C4⋊C4—2144no—
150C4⋊C4—2144no—
151C4⋊C4—2144no—
152C4⋊C4—2144no—
153C4⋊C4—2144no—
154C42—24no—
155C42—1074no—
156C42—1074no—
157C42—2144no—
158C42Dic21414yescomplemented
159C23C23×D10711yescharacteristic
160Q8—21416no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—1074no—
169C2×C4—1074no—
170C2×C4—1074no—
171C2×C4—2142no—
172C2×C4—2142no—
173C2×C4—2142no—
174C2×C4—2142no—
175C2×C4—2142no—
176C2×C4—2142no—
177C2×C4—2142no—
178C2×C4—2142no—
179C2×C4—2142no—
180C2×C4D4×D10712yes—
181C2×C4Q8×D10712yes—
182C2×C4C2×Dic21412yes—
183C2×C4C2×Dic21412yes—
184C2×C4C2×Dic21412yes—
185C2×C4#1313381814yes—
186C22C2×D4×D10711yescharacteristic
187C22C2×Q8×D10711yescharacteristic
188C22C22×Dic21411yescharacteristic
189C22#41×D10712yes—
190C22C2×#1313381812yes—
191C4—24no—
192C4—22no—
193C4—22no—
194C4—42no—
195C4—4282no—
196C4—2144no—
197C4—2144no—
198C4—2144no—
199C4#1681210814yes—
200C2#2029313612yes—
201C2C2×#1681210811yescharacteristic
202C2#2029318011yescharacteristic
203C2#2029318112yes—
204C2#2029318411yescharacteristic
subgroupG/H
centerC22×C4C22×D107
commutator, socle, prime radical, cosocleC23×C107C24
FrattiniC23C23×D107
FittingC4×C4⋊C4×C107C2
hypercenterC4×C4⋊C4D107
hypocenterC107#2399
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
47. C4×Dic107Q8semidirect
55. C42×C107Q8semidirect
103. C107#2399semidirect
158. C42Dic214semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic2142
#202925612
#202925602
#202925482
#202925472
C4×Dic107⋊C42
C4×C4⋊Dic1072
#202924732
C4×C4⋊C4×C1072
#2399107