Finite Group Databasebeta

← #28344286

Subgroups — #28344286

Order 13696.

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

normal subgroups only

This group has 344 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#20292569C212yesmaximal
2#20292569C212yesmaximal
3#20292557C211yesmaximal, characteristic
4#20292514C212yesmaximal
5#20292514C212yesmaximal
6#20292512C212yesmaximal
7#20292508C212yesmaximal
8#20292496C211yesmaximal, characteristic
9#400×C107C211yesmaximal, characteristic
10C2×C4⋊Dic107C2212yes—
11C2×C4⋊Dic107C2211yescharacteristic
12C2×C4⋊Dic107C2211yescharacteristic
13C2×Dic107⋊C4C2212yes—
14C2×Dic107⋊C4C2212yes—
15C2×Dic107⋊C4C2212yes—
16C2×C4×Dic107C2211yescharacteristic
17C2×C4×Dic107C2212yes—
18C107⋊#95C2212yes—
19C107⋊#95C2212yes—
20C107⋊#95C2212yes—
21C107⋊#95C2212yes—
22C107⋊#95C2212yes—
23C107⋊#95C2212yes—
24C107⋊#95C2212yes—
25C107⋊#95C2211yescharacteristic
26C2×C4⋊C4×C107C2211yescharacteristic
27C2×C4⋊C4×C107C2211yescharacteristic
28#95×C107C2212yes—
29#95×C107C2212yes—
30#95×C107C2211yescharacteristic
31C22×Dic107C2312yes—
32C22×Dic107C2312yes—
33C22×Dic107C2312yes—
34C22×Dic107C2312yes—
35C4⋊Dic107—24no—
36C4⋊Dic107—41no—
37C4⋊Dic107—41no—
38Dic107⋊C4—24no—
39Dic107⋊C4—24no—
40Dic107⋊C4—24no—
41C4×Dic107—22no—
42C4×Dic107—42no—
43C22×C4×C107C2312yes—
44C22×C4×C107C2311yescharacteristic
45C22×C4×C107C2311yescharacteristic
46C22×C4×C107C2312yes—
47C22×C4×C107C2311yescharacteristic
48C4⋊C4×C107—41no—
49C4⋊C4×C107—41no—
50C23×C107C2411yescharacteristic
51C2×C4×C107—21no—
52C2×C4×C107—21no—
53C2×C4×C107—22no—
54C2×C4×C107—22no—
55C2×C4×C107—22no—
56C2×C4×C107—21no—
57C2×C4×C107—22no—
58C2×C4×C107—21no—
59C2×C4×C107—22no—
60C2×C4×C107—22no—
61C2×C4×C107—24no—
62C2×C4×C107#4112yes—
63C2×Dic107—22no—
64C2×Dic107—22no—
65C2×Dic107—22no—
66C2×Dic107—22no—
67C2×Dic107—22no—
68C2×Dic107—22no—
69C2×Dic107—22no—
70C2×Dic107—22no—
71C2×Dic107—22no—
72C2×Dic107—22no—
73C2×Dic107—22no—
74C2×Dic107#4114yes—
75C22×C107C2×#4112yes—
76C22×C107C2×#4111yescharacteristic
77C22×C107H(5,𝔽2)11yescharacteristic
78C22×C1072−1+411yescharacteristic
79C22×C1072−1+412yes—
80C4×C107—22no—
81C4×C107—42no—
82C4×C107—41no—
83C4×C107—41no—
84C4×C107—42no—
85Dic107—24no—
86Dic107—42no—
87Dic107—42no—
88Dic107—42no—
89C2×C107#53911yescharacteristic
90C2×C107#54112yes—
91C2×C107#55212yes—
92C2×C107#55911yescharacteristic
93C2×C107#56311yescharacteristic
94#2794—1071nomaximal, Sylow
95C107#279411yescharacteristic, complemented, Sylow
96#400—1072no—
97#400—1072no—
98#400D10711yescharacteristic
99#398—1071no—
100#387—1072no—
101#387—1072no—
102#387—1072no—
103#387—1072no—
104#384—1071no—
105C2×C4⋊C4—1071no—
106C2×C4⋊C4—1071no—
107C2×C4⋊C4—1072no—
108C2×C4⋊C4—1072no—
109C2×C4⋊C4—1072no—
110C2×C4⋊C4—1072no—
111C2×C4⋊C4C2×D10711yescharacteristic
112C2×C4⋊C4C2×D10711yescharacteristic
113C2×C42—1072no—
114C2×C42—1071no—
115#95—1072no—
116#95—1072no—
117#95—1072no—
118#95—1072no—
119#95—1072no—
120#95—1072no—
121#95—1072no—
122#95—1071no—
123#95C2×D10712yes—
124#95C2×D10712yes—
125#95C2×D10711yescharacteristic
126C22×C4—1072no—
127C22×C4—1072no—
128C22×C4—1072no—
129C22×C4—1072no—
130C22×C4C22×D10712yes—
131C22×C4C22×D10712yes—
132C22×C4C22×D10711yescharacteristic
133C22×C4C22×D10711yescharacteristic
134C22×C4C22×D10711yescharacteristic
135C4⋊C4—41no—
136C4⋊C4—41no—
137C4⋊C4—4281no—
138C4⋊C4—4281no—
139C4⋊C4—2144no—
140C4⋊C4—2144no—
141C4⋊C4—2144no—
142C4⋊C4—2144no—
143C42—4282no—
144C42—2142no—
145C23C23×D10711yescharacteristic
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—24no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—1074no—
158C2×C4—2142no—
159C2×C4—2142no—
160C2×C4—2142no—
161C2×C4—2142no—
162C2×C4—2142no—
163C2×C4—2142no—
164C2×C4—2142no—
165C2×C4—2142no—
166C2×C4—2142no—
167C2×C4—2142no—
168C2×C4—2142no—
169C2×C4#1313381912yes—
170C22#41×D10712yes—
171C22C2×#1313381911yescharacteristic
172C22#1681215411yescharacteristic
173C22#1681215612yes—
174C22#1681215611yescharacteristic
175C4—22no—
176C4—42no—
177C4—42no—
178C4—41no—
179C4—41no—
180C4—4282no—
181C4—4282no—
182C4—4282no—
183C4—2144no—
184C2#2029322611yescharacteristic
185C2#2029323412yes—
186C2#2029331512yes—
187C2#2029336111yescharacteristic
188C2#2029337711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, prime radical, cosocleC23×C107C24
Fitting#400×C107C2
hypercenter#400D107
hypocenterC107#2794
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
95. C107#2794semidirect

Maximal subgroups

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

subgroupindex
#202925692
#202925572
#202925142
#202925122
#202925082
#202924962
#400×C1072
#2794107