Finite Group Databasebeta

← #28344531

Subgroups — #28344531

Order 13696.

380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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×#16812100C211yesmaximal, characteristic
2C2×#16812099C211yesmaximal, characteristic
3#20292569C212yesmaximal
4#20292567C211yesmaximal, characteristic
5#20292566C211yesmaximal, characteristic
6#20292561C212yesmaximal
7#20292560C212yesmaximal
8#20292558C212yesmaximal
9#20292558C211yesmaximal, characteristic
10#20292491C211yesmaximal, characteristic
11#398×C107C211yesmaximal, characteristic
12#16812100—24no—
13#16812099—24no—
14C2×C4⋊Dic107C2211yescharacteristic
15C2×C4⋊Dic107C2212yes—
16C2×C4⋊Dic107C2211yescharacteristic
17C2×Dic107⋊C4C2211yescharacteristic
18C2×Dic107⋊C4C2211yescharacteristic
19C2×Dic107⋊C4C2211yescharacteristic
20C2×Dic107⋊C4C2211yescharacteristic
21C2×Dic107⋊C4C2212yes—
22C2×Dic107⋊C4C2212yes—
23C2×Dic107⋊C4C2212yes—
24C2×C4×Dic107C2211yescharacteristic
25C107⋊#95C2211yescharacteristic
26C107⋊#95C2212yes—
27C107⋊#95C2212yes—
28C107⋊#95C2212yes—
29C107⋊#95C2212yes—
30C107⋊#95C2212yes—
31C107⋊#95C2212yes—
32C2×C4⋊C4×C107C2211yescharacteristic
33C2×C4⋊C4×C107C2211yescharacteristic
34C2×C4⋊C4×C107C2212yes—
35#95×C107C2211yescharacteristic
36#95×C107C2212yes—
37C22×Dic107C2311yescharacteristic
38C22×Dic107C2311yescharacteristic
39C22×Dic107C2312yes—
40C22×Dic107C2312yes—
41C22×Dic107C2311yescharacteristic
42C22×Dic107C2311yescharacteristic
43C4⋊Dic107—22no—
44C4⋊Dic107—22no—
45C4⋊Dic107—24no—
46Dic107⋊C4—22no—
47Dic107⋊C4—22no—
48Dic107⋊C4—22no—
49Dic107⋊C4—22no—
50Dic107⋊C4—24no—
51Dic107⋊C4—42no—
52Dic107⋊C4—42no—
53C4×Dic107D414yes—
54C22×C4×C107C2312yes—
55C22×C4×C107C2311yescharacteristic
56C22×C4×C107C2311yescharacteristic
57C22×C4×C107C2312yes—
58C22×C4×C107C2311yescharacteristic
59C4⋊C4×C107—22no—
60C4⋊C4×C107—22no—
61C4⋊C4×C107—42no—
62C23×C107C2411yescharacteristic
63C2×C4×C107—22no—
64C2×C4×C107—21no—
65C2×C4×C107—21no—
66C2×C4×C107—22no—
67C2×C4×C107—21no—
68C2×C4×C107—22no—
69C2×C4×C107—22no—
70C2×C4×C107—22no—
71C2×C4×C107—22no—
72C2×C4×C107—21no—
73C2×C4×C107—22no—
74C2×C4×C107—22no—
75C2×C4×C107C2×D412yes—
76C2×Dic107—21no—
77C2×Dic107—21no—
78C2×Dic107—22no—
79C2×Dic107—21no—
80C2×Dic107—21no—
81C2×Dic107—22no—
82C2×Dic107—21no—
83C2×Dic107—22no—
84C2×Dic107—22no—
85C2×Dic107—21no—
86C2×Dic107—22no—
87C2×Dic107—24no—
88C2×Dic107—22no—
89C2×Dic107C2×D412yes—
90C2×Dic107C2×D412yes—
91C22×C107C22×D411yescharacteristic
92C22×C107H(5,𝔽2)11yescharacteristic
93C22×C1072−1+412yes—
94C22×C1072−1+411yescharacteristic
95C22×C1072−1+412yes—
96C4×C107—22no—
97C4×C107—41no—
98C4×C107—41no—
99C4×C107—42no—
100C4×C107—42no—
101Dic107—22no—
102Dic107—22no—
103Dic107—41no—
104Dic107—42no—
105Dic107—41no—
106Dic107—42no—
107C2×C107#53611yescharacteristic
108C2×C107#53611yescharacteristic
109C2×C107#53711yescharacteristic
110C2×C107#56312yes—
111C2×C107#56412yes—
112#2822—1071nomaximal, Sylow
113C107#282211yescharacteristic, complemented, Sylow
114C2×#125—1071no—
115C2×#125—1071no—
116#400—1071no—
117#400—1071no—
118#400—1072no—
119#398—1071no—
120#398—1072no—
121#398—1072no—
122#398—1072no—
123#398D10711yescharacteristic
124#382—1071no—
125#125—2144no—
126#125—2144no—
127C2×C4⋊C4—1072no—
128C2×C4⋊C4—1072no—
129C2×C4⋊C4—1071no—
130C2×C4⋊C4—1071no—
131C2×C4⋊C4—1072no—
132C2×C4⋊C4—1071no—
133C2×C4⋊C4—1071no—
134C2×C4⋊C4—1071no—
135C2×C4⋊C4—1072no—
136C2×C4⋊C4—1071no—
137C2×C4⋊C4C2×D10711yescharacteristic
138C2×C4⋊C4C2×D10711yescharacteristic
139C2×C4⋊C4C2×D10712yes—
140C2×C42—1071no—
141#95—1072no—
142#95—1071no—
143#95—1072no—
144#95—1072no—
145#95—1072no—
146#95—1072no—
147#95—1072no—
148#95C2×D10711yescharacteristic
149#95C2×D10712yes—
150C22×C4—1071no—
151C22×C4—1071no—
152C22×C4—1072no—
153C22×C4—1071no—
154C22×C4—1072no—
155C22×C4—1071no—
156C22×C4C22×D10712yes—
157C22×C4C22×D10711yescharacteristic
158C22×C4C22×D10711yescharacteristic
159C22×C4C22×D10712yes—
160C22×C4C22×D10711yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—42no—
164C4⋊C4—4282no—
165C4⋊C4—4282no—
166C4⋊C4—2142no—
167C4⋊C4—2142no—
168C4⋊C4—2144no—
169C4⋊C4—2142no—
170C4⋊C4—2142no—
171C4⋊C4—2144no—
172C4⋊C4—2142no—
173C4⋊C4—2142no—
174C42—1074no—
175C23C23×D10711yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—1072no—
189C2×C4—1072no—
190C2×C4—2141no—
191C2×C4—2142no—
192C2×C4—2141no—
193C2×C4—2142no—
194C2×C4—2141no—
195C2×C4—2142no—
196C2×C4—2142no—
197C2×C4—2141no—
198C2×C4—2142no—
199C2×C4—2144no—
200C2×C4—2141no—
201C2×C4—2141no—
202C2×C4—2142no—
203C2×C4D4×D10712yes—
204C22C2×D4×D10711yescharacteristic
205C22#1681215411yescharacteristic
206C22#1681215612yes—
207C22#1681215611yescharacteristic
208C22#1681215712yes—
209C4—22no—
210C4—42no—
211C4—41no—
212C4—41no—
213C4—42no—
214C4—4282no—
215C4—4281no—
216C4—4282no—
217C4—4281no—
218C4—2142no—
219C4—2142no—
220C2#2029319911yescharacteristic
221C2#2029320211yescharacteristic
222C2#2029320611yescharacteristic
223C2#2029337812yes—
224C2C107⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, prime radical, cosocleC23×C107C24
Fitting#398×C107C2
hypercenter#398D107
hypocenterC107#2822
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
113. C107#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#168121002
C2×#168120992
#202925692
#202925672
#202925662
#202925612
#202925602
#202925582
#202924912
#398×C1072
#2822107