Finite Group Databasebeta

← #28344168

Subgroups — #28344168

Order 13696.

428 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 121 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#20292547C211yesmaximal, characteristic, complemented
2#20292541C212yesmaximal
3#20292539C212yesmaximal, complemented
4#20292521C212yesmaximal, complemented
5#20292520C212yesmaximal, complemented
6#20292515C212yesmaximal, complemented
7#20292492C211yesmaximal, characteristic, complemented
8#20292491C212yesmaximal, complemented
9#394×C107C211yesmaximal, characteristic
10C22×Dic214C2211yescharacteristic
11C2×C4⋊Dic107C2211yescharacteristic
12C2×Dic107⋊C4C2212yes—
13C2×Dic107⋊C4C2212yes—
14C2×C22⋊Dic107C2212yes—
15C2×C22⋊Dic107C2212yes—
16C2×C22⋊Dic107C2212yes—
17C2×C22⋊Dic107C2212yes—
18C2×C4×Dic107C2212yes—
19C2×C4×Dic107C2211yescharacteristic
20C107⋊#95C2212yes—
21C107⋊#95C2212yes—
22C107⋊#95C2212yes—
23C107⋊#95C2212yes—
24C107⋊#95C2212yes—
25C107⋊#95C2211yescharacteristic
26C22×D4×C107C2211yescharacteristic
27C2×C4⋊C4×C107C2211yescharacteristic
28C2×C22⋊C4×C107C2212yes—
29C2×C22⋊C4×C107C2212yes—
30#95×C107C2211yescharacteristic
31C2×Dic214—41no—
32C2×Dic214—42no—
33C22×Dic107C2312yes—
34C22×Dic107C2312yes—
35C22×Dic107C2312yes—
36C22×Dic107C2312yes—
37C4⋊Dic107—41no—
38Dic107⋊C4—42no—
39Dic107⋊C4—42no—
40C22⋊Dic107—24no—
41C22⋊Dic107—24no—
42C22⋊Dic107—42no—
43C22⋊Dic107—42no—
44C4×Dic107—22no—
45C4×Dic107—24no—
46C24×C107C2312yes—
47C2×D4×C107—41no—
48C2×D4×C107—42no—
49C22×C4×C107C2312yes—
50C22×C4×C107C2311yescharacteristic
51C22×C4×C107C2311yescharacteristic
52C22×C4×C107C2311yescharacteristic
53C4⋊C4×C107—41no—
54C22⋊C4×C107—24no—
55C22⋊C4×C107—42no—
56C23×C107—22no—
57C23×C107—22no—
58C23×C107—22no—
59C23×C107—22no—
60C23×C107—22no—
61C23×C107—22no—
62C23×C107—22no—
63C23×C107C2411yescharacteristic
64D4×C107—44no—
65C2×C4×C107—21no—
66C2×C4×C107—21no—
67C2×C4×C107—22no—
68C2×C4×C107—22no—
69C2×C4×C107—22no—
70C2×C4×C107—22no—
71C2×C4×C107—21no—
72C2×C4×C107—21no—
73C2×C4×C107—22no—
74C2×C4×C107#4112yes—
75C2×Dic107—22no—
76C2×Dic107—22no—
77C2×Dic107—22no—
78C2×Dic107—22no—
79C2×Dic107—22no—
80C2×Dic107—22no—
81C2×Dic107—22no—
82C2×Dic107—22no—
83C2×Dic107—22no—
84C2×Dic107—22no—
85C2×Dic107—22no—
86C2×Dic107#4114yes—
87Dic214—44no—
88C22×C107—42no—
89C22×C107—42no—
90C22×C107—42no—
91C22×C107—42no—
92C22×C107—42no—
93C22×C107—42no—
94C22×C107—42no—
95C22×C107C2×#4112yes—
96C22×C107C2×#4111yescharacteristic
97C22×C107H(5,𝔽2)12yes—
98C22×C107H(5,𝔽2)11yescharacteristic
99C22×C1072−1+411yescharacteristic
100C4×C107—22no—
101C4×C107—42no—
102C4×C107—41no—
103C4×C107—41no—
104Dic107—24no—
105Dic107—42no—
106Dic107—42no—
107Dic107—42no—
108C2×C107—82no—
109C2×C107#53912yes—
110C2×C107#53911yescharacteristic
111C2×C107#55511yescharacteristic
112C2×C107#55512yes—
113C2×C107H(3,𝔽4)11yescharacteristic
114#2785—1071nomaximal, Sylow
115C107#278511yescharacteristic, complemented, Sylow
116#395—1071no—
117#394—1072no—
118#394D10711yescharacteristic
119#393—1072no—
120#388—1072no—
121#388—1072no—
122#388—1072no—
123#382—1071no—
124#382—1072no—
125C22×Q8—1071no—
126C22×D4C2×D10711yescharacteristic
127C2×C4⋊C4—1072no—
128C2×C4⋊C4—1072no—
129C2×C4⋊C4—1071no—
130C2×C4⋊C4C2×D10711yescharacteristic
131C2×C22⋊C4—1072no—
132C2×C22⋊C4—1072no—
133C2×C22⋊C4—1072no—
134C2×C22⋊C4—1072no—
135C2×C22⋊C4C2×D10712yes—
136C2×C22⋊C4C2×D10712yes—
137C2×C42—1072no—
138C2×C42—1071no—
139#95—1072no—
140#95—1072no—
141#95—1072no—
142#95—1072no—
143#95—1071no—
144#95—1072no—
145#95C2×D10711yescharacteristic
146C24C22×D10712yes—
147C2×Q8—4282no—
148C2×Q8—4281no—
149C2×D4—41no—
150C2×D4—42no—
151C22×C4—1072no—
152C22×C4—1072no—
153C22×C4—1072no—
154C22×C4—1072no—
155C22×C4C22×D10711yescharacteristic
156C22×C4C22×D10712yes—
157C22×C4C22×D10711yescharacteristic
158C22×C4C22×D10711yescharacteristic
159C4⋊C4—41no—
160C4⋊C4—4282no—
161C4⋊C4—4282no—
162C4⋊C4—4281no—
163C22⋊C4—24no—
164C22⋊C4—42no—
165C22⋊C4—4282no—
166C22⋊C4—4282no—
167C22⋊C4—2144no—
168C22⋊C4—2144no—
169C42—2144no—
170C42—2142no—
171C23—22no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23C23×D10711yescharacteristic
179Q8—4284no—
180D4—44no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—1074no—
191C2×C4—2142no—
192C2×C4—2142no—
193C2×C4—2142no—
194C2×C4—2142no—
195C2×C4—2142no—
196C2×C4—2142no—
197C2×C4—2142no—
198C2×C4—2142no—
199C2×C4—2142no—
200C2×C4—2142no—
201C2×C4—2142no—
202C2×C4#1313381712yes—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22#41×D10712yes—
211C22C2×#1313381711yescharacteristic
212C22#1681215412yes—
213C22#1681215411yescharacteristic
214C22#1681215611yescharacteristic
215C4—22no—
216C4—42no—
217C4—41no—
218C4—41no—
219C4—4282no—
220C4—4282no—
221C4—4282no—
222C4—2144no—
223C2—82no—
224C2#2029322012yes—
225C2#2029322211yescharacteristic
226C2#2029333911yescharacteristic
227C2#2029334112yes—
228C2#2029337011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#394×C107C2
prime radicalC22×D4×C107C22
hypercenter#394D107
hypocenterC107#2785
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #20292547C2semidirect
3. #20292539C2semidirect
4. #20292521C2semidirect
5. #20292520C2semidirect
6. #20292515C2semidirect
7. #20292492C2semidirect
8. #20292491C2semidirect
115. C107#2785semidirect

Maximal subgroups

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

subgroupindex
#202925472
#202925412
#202925392
#202925212
#202925202
#202925152
#202924922
#202924912
#394×C1072
#2785107