Finite Group Databasebeta

← #28344446

Subgroups — #28344446

Order 13696.

368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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#20292569C212yesmaximal
2#20292558C212yesmaximal
3#20292557C212yesmaximal
4#20292533C211yesmaximal, characteristic
5#20292531C212yesmaximal
6#20292525C211yesmaximal, characteristic
7#20292513C212yesmaximal
8#20292508C212yesmaximal
9#389×C107C211yesmaximal, characteristic
10C22×Dic214C2211yescharacteristic
11C2×C4⋊Dic107C2211yescharacteristic
12C2×C4⋊Dic107C2211yescharacteristic
13C2×C4⋊Dic107C2211yescharacteristic
14C2×Dic107⋊C4C2212yes—
15C2×Dic107⋊C4C2212yes—
16C2×Dic107⋊C4C2212yes—
17C2×C4×Dic107C2212yes—
18C107⋊#95C2212yes—
19C107⋊#95C2212yes—
20C107⋊#95C2212yes—
21C107⋊#95C2212yes—
22C107⋊#95C2212yes—
23C107⋊#95C2212yes—
24C107⋊#95C2212yes—
25C107⋊#95C2212yes—
26C2×C4⋊C4×C107C2212yes—
27C2×C4⋊C4×C107C2211yescharacteristic
28C2×C4⋊C4×C107C2211yescharacteristic
29C2×C42×C107C2211yescharacteristic
30#95×C107C2212yes—
31C2×Dic214—41no—
32C2×Dic214—41no—
33C2×Dic214Q814yes—
34C22×Dic107C2312yes—
35C22×Dic107C2312yes—
36C22×Dic107C2312yes—
37C22×Dic107C2312yes—
38C4⋊Dic107—22no—
39C4⋊Dic107—41no—
40C4⋊Dic107—41no—
41Dic107⋊C4—24no—
42Dic107⋊C4—42no—
43Dic107⋊C4—42no—
44C4×Dic107—42no—
45C22×C4×C107C2312yes—
46C22×C4×C107C2312yes—
47C22×C4×C107C2311yescharacteristic
48C22×C4×C107C2311yescharacteristic
49C22×C4×C107C2311yescharacteristic
50C4⋊C4×C107—24no—
51C4⋊C4×C107—22no—
52C4⋊C4×C107—41no—
53C42×C107—41no—
54C23×C107C2411yescharacteristic
55C2×C4×C107—21no—
56C2×C4×C107—21no—
57C2×C4×C107—21no—
58C2×C4×C107—21no—
59C2×C4×C107—21no—
60C2×C4×C107—21no—
61C2×C4×C107—22no—
62C2×C4×C107—22no—
63C2×C4×C107—22no—
64C2×C4×C107—22no—
65C2×C4×C107—22no—
66C2×C4×C107—22no—
67C2×C4×C107C2×Q812yes—
68C2×C4×C107#4112yes—
69C2×C4×C107#4112yes—
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×Dic107—22no—
80C2×Dic107—22no—
81C2×Dic107C2×Q814yes—
82Dic214—44no—
83C22×C107C22×Q811yescharacteristic
84C22×C107C2×#4111yescharacteristic
85C22×C107C2×#4111yescharacteristic
86C22×C107H(5,𝔽2)11yescharacteristic
87C22×C107H(5,𝔽2)11yescharacteristic
88C22×C1072−1+411yescharacteristic
89C22×C1072−1+411yescharacteristic
90C4×C107—22no—
91C4×C107—22no—
92C4×C107—22no—
93C4×C107—42no—
94C4×C107—42no—
95Dic107—24no—
96Dic107—42no—
97Dic107—42no—
98Dic107—42no—
99C2×C107#53911yescharacteristic
100C2×C107#53911yescharacteristic
101C2×C107#54311yescharacteristic
102C2×C107#55511yescharacteristic
103C2×C107#55711yescharacteristic
104C2×C107#55711yescharacteristic
105C2×C107#56311yescharacteristic
106#2809—1071nomaximal, Sylow
107C107#280911yescharacteristic, complemented, Sylow
108#400—1072no—
109#398—1072no—
110#398—1072no—
111#391—1071no—
112#391—1072no—
113#389—1071no—
114#389D10711yescharacteristic
115#387—1072no—
116#387—1072no—
117C22×Q8—1071no—
118C2×C4⋊C4—1072no—
119C2×C4⋊C4—1072no—
120C2×C4⋊C4—1071no—
121C2×C4⋊C4—1071no—
122C2×C4⋊C4—1072no—
123C2×C4⋊C4—1071no—
124C2×C4⋊C4C2×D10712yes—
125C2×C4⋊C4C2×D10711yescharacteristic
126C2×C4⋊C4C2×D10711yescharacteristic
127C2×C42—1072no—
128C2×C42C2×D10711yescharacteristic
129#95—1072no—
130#95—1072no—
131#95—1072no—
132#95—1072no—
133#95—1072no—
134#95—1072no—
135#95—1072no—
136#95—1072no—
137#95C2×D10712yes—
138C2×Q8—1074no—
139C2×Q8—4281no—
140C2×Q8—4281no—
141C22×C4—1072no—
142C22×C4—1072no—
143C22×C4—1072no—
144C22×C4—1072no—
145C22×C4C22×D10712yes—
146C22×C4C22×D10712yes—
147C22×C4C22×D10711yescharacteristic
148C22×C4C22×D10711yescharacteristic
149C22×C4C22×D10711yescharacteristic
150C4⋊C4—24no—
151C4⋊C4—22no—
152C4⋊C4—41no—
153C4⋊C4—4282no—
154C4⋊C4—4282no—
155C4⋊C4—4281no—
156C4⋊C4—4281no—
157C4⋊C4—2142no—
158C4⋊C4—2144no—
159C42—41no—
160C42—4282no—
161C23C23×D10711yescharacteristic
162Q8—4284no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—1074no—
176C2×C4—2142no—
177C2×C4—2142no—
178C2×C4—2142no—
179C2×C4—2142no—
180C2×C4—2142no—
181C2×C4—2142no—
182C2×C4—2142no—
183C2×C4—2142no—
184C2×C4—2142no—
185C2×C4—2142no—
186C2×C4—2142no—
187C2×C4Q8×D10712yes—
188C2×C4#1313381712yes—
189C2×C4#1313381812yes—
190C22C2×Q8×D10711yescharacteristic
191C22C2×#1313381711yescharacteristic
192C22C2×#1313381811yescharacteristic
193C22#1681215411yescharacteristic
194C22#1681215511yescharacteristic
195C22#1681215611yescharacteristic
196C22#1681215711yescharacteristic
197C4—22no—
198C4—22no—
199C4—22no—
200C4—42no—
201C4—42no—
202C4—4282no—
203C4—4282no—
204C4—4282no—
205C4—2144no—
206C2#2029322211yescharacteristic
207C2#2029322411yescharacteristic
208C2#2029325211yescharacteristic
209C2#2029334211yescharacteristic
210C2#2029335211yescharacteristic
211C2#2029335511yescharacteristic
212C2#2029338111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, prime radical, cosocleC23×C107C24
Fitting#389×C107C2
hypercenter#389D107
hypocenterC107#2809
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
107. C107#2809semidirect

Maximal subgroups

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

subgroupindex
#202925692
#202925582
#202925572
#202925332
#202925312
#202925252
#202925132
#202925082
#389×C1072
#2809107