Finite Group Databasebeta

← #28336534

Subgroups — #28336534

Order 13696.

504 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 81 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×C22⋊C4×D107C211yesmaximal, characteristic
2#20292482C212yesmaximal
3#20292394C211yesmaximal, characteristic, complemented
4#20292393C212yesmaximal, complemented
5#342×C107C211yesmaximal, characteristic, complemented
6C24×D107C2211yescharacteristic
7C22×C4×D107C412yescomplemented
8C2×C22⋊Dic107C2212yes—
9C2×C22⋊Dic107C2211yescharacteristic
10C2×(C2×D107)⋊C4—24no—
11C2×(C2×D107)⋊C4C412yescomplemented
12C22⋊C4×D107—24no—
13C2×C22⋊C4×C107C2212yes—
14C2×C22⋊C4×C107C2211yescharacteristic
15C23×D107—21no—
16C23×D107—22no—
17C23×D107—21no—
18C23×D107—44no—
19C23×D107C2×C411yescharacteristic
20C23×D107C2×C411yescharacteristic
21C23×D107D414yes—
22C22×Dic107—22no—
23C22×Dic107C2×C412yes—
24C2×C4×D107—22no—
25C2×C4×D107—22no—
26C2×C4×D107—44no—
27C22⋊Dic107—22no—
28C22⋊Dic107—22no—
29C22⋊Dic107—22no—
30(C2×D107)⋊C4—24no—
31(C2×D107)⋊C4—48no—
32C24×C107C2311yescharacteristic
33C22×C4×C107—22no—
34C22×C4×C107C2×C412yes—
35C22⋊C4×C107—22no—
36C22⋊C4×C107—22no—
37C22⋊C4×C107—22no—
38C23×C107—42no—
39C23×C107C22×C411yescharacteristic
40C23×C107C2×D412yes—
41C23×C107#4111yescharacteristic
42C23×C107#4112yes—
43C23×C107#4111yescharacteristic
44C22×D107—21no—
45C22×D107—21no—
46C22×D107—24no—
47C22×D107—21no—
48C22×D107—21no—
49C22×D107—24no—
50C22×D107—24no—
51C22×D107—28no—
52C22×D107—42no—
53C22×D107—44no—
54C22×D107—44no—
55C22×D107—48no—
56C22×D107—44no—
57C22×D107C22⋊C412yes—
58C22×D107C22⋊C412yes—
59C2×C4×C107—22no—
60C2×C4×C107—42no—
61C2×C4×C107—44no—
62C2×C4×C107—42no—
63C2×Dic107—22no—
64C2×Dic107—42no—
65C2×Dic107—44no—
66C2×Dic107—42no—
67C4×D107—44no—
68C4×D107—44no—
69C22×C107—22no—
70C22×C107—24no—
71C22×C107—41no—
72C22×C107—42no—
73C22×C107—41no—
74C22×C107C2×C22⋊C411yescharacteristic
75C22×C107#11711yescharacteristic
76C22×C107#11711yescharacteristic
77C22×C107#12312yes—
78C22×C107#12312yes—
79C2×D107—24no—
80C2×D107—24no—
81C2×D107—22no—
82C2×D107—22no—
83C2×D107—22no—
84C2×D107—24no—
85C2×D107—48no—
86C2×D107—48no—
87C2×D107—42no—
88C2×D107—42no—
89C2×D107#9914yes—
90C4×C107—42no—
91C4×C107—82no—
92Dic107—42no—
93Dic107—82no—
94C2×C107—22no—
95C2×C107—22no—
96C2×C107—21no—
97C2×C107—21no—
98C2×C107#38111yescharacteristic
99C2×C107C2×#9912yes—
100D107—24no—
101D107—42no—
102#1819—1071nomaximal, Sylow
103C107#181911yescharacteristic, complemented, Sylow
104C22×C22⋊C4—1071no—
105#379—1072no—
106#342—1072no—
107#342—1071no—
108#342D10711yescharacteristic, complemented
109C25—1071no—
110C23×C4—1072no—
111C2×C22⋊C4—1071no—
112C2×C22⋊C4—1072no—
113C2×C22⋊C4—1072no—
114C2×C22⋊C4—2144no—
115C2×C22⋊C4—2144no—
116C2×C22⋊C4C2×D10712yes—
117C2×C22⋊C4C2×D10711yescharacteristic
118C24—1071no—
119C24—1074no—
120C24—1071no—
121C24—4284no—
122C24—2141no—
123C24—2142no—
124C24—2141no—
125C24C22×D10711yescharacteristic
126C22×C4—22no—
127C22×C4—1072no—
128C22×C4—4284no—
129C22×C4—2142no—
130C22×C4—2142no—
131C22×C4—2142no—
132C22×C4C4×D10712yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—4288no—
137C22⋊C4—2144no—
138C22⋊C4—2142no—
139C22⋊C4—2142no—
140C22⋊C4—2142no—
141C23—42no—
142C23—1072no—
143C23—1072no—
144C23—4282no—
145C23—4284no—
146C23—4284no—
147C23—4288no—
148C23—4284no—
149C23—2148no—
150C23—2144no—
151C23—2141no—
152C23—2141no—
153C23—2144no—
154C23—2144no—
155C23—2141no—
156C23—2141no—
157C23C2×C4×D10711yescharacteristic
158C23D4×D10712yes—
159C23#1313381711yescharacteristic
160C23#1313381812yes—
161C23#1313381911yescharacteristic
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—44no—
165C2×C4—42no—
166C2×C4—4284no—
167C2×C4—4284no—
168C2×C4—4284no—
169C2×C4—4282no—
170C2×C4—4282no—
171C2×C4—2142no—
172C22—22no—
173C22—24no—
174C22—41no—
175C22—42no—
176C22—41no—
177C22—1074no—
178C22—4282no—
179C22—4282no—
180C22—4288no—
181C22—4288no—
182C22—2144no—
183C22—2144no—
184C22—2142no—
185C22—2144no—
186C22—2142no—
187C22—2142no—
188C22C22⋊C4×D10711yescharacteristic
189C22#1681206611yescharacteristic
190C22#1681206711yescharacteristic
191C22#1681209112yes—
192C22#1681209412yes—
193C4—42no—
194C4—82no—
195C4—8562no—
196C4—4282no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—21no—
201C2—4282no—
202C2—2144no—
203C2#2029248911yescharacteristic
204C2#99×D10712yes—
subgroupG/H
centerC22C22⋊C4×D107
commutatorC23×C107C22×C4
FrattiniC24C22×D107
Fitting#342×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC24×D107C22
cosocleC24×C107C23
hypercenter#342D107
hypocenterC107#1819
LCSG ▷ C23×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. #20292394C2semidirect
4. #20292393C2semidirect
5. #342×C107C2semidirect
7. C22×C4×D107C4semidirect
11. C2×(C2×D107)⋊C4C4semidirect
103. C107#1819semidirect
108. #342D107semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D1072
#202924822
#202923942
#202923932
#342×C1072
#1819107