Finite Group Databasebeta

← #343×D107 #28336195

Subgroups — #343×D107 #28336195

Order 13696.

432 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 145 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×M16×D107C212yesmaximal
2C2×C4⋊C4×D107C211yesmaximal, characteristic
3#20292396C211yesmaximal, characteristic, complemented
4#20292395C212yesmaximal, complemented
5#343×C107C211yesmaximal, characteristic, complemented
6C22×C4×D107C412yes—
7C22×C4×D107C2211yescharacteristic
8C2×#13133802C2212yes—
9C2×#13133801—22no—
10M16×D107—24no—
11M16×D107C418yescomplemented
12C2×C8×D107—22no—
13C2×C4⋊Dic107C2211yescharacteristic
14C2×Dic107⋊C4C412yes—
15C4⋊C4×D107—22no—
16C4⋊C4×D107—22no—
17C2×M16×C107C2212yes—
18C2×C4⋊C4×C107C2211yescharacteristic
19C23×D107C2×C411yescharacteristic
20C22×Dic107C2×C412yes—
21C22×Dic107C2×C411yescharacteristic
22C2×C4×D107—22no—
23C2×C4×D107—22no—
24C2×C4×D107—44no—
25C2×C4×D107C2×C414yes—
26C2×C4×D107D412yes—
27C2×C4×D107D412yes—
28C2×C4×D107D412yes—
29C2×C4×D107Q812yes—
30#13133802—22no—
31#13133802C2×C414yescomplemented
32#13133801—28no—
33C2×C107⋊C8—22no—
34C8×D107—28no—
35C4⋊Dic107—22no—
36Dic107⋊C4—24no—
37C22×C4×C107C2×C412yes—
38C22×C4×C107C2311yescharacteristic
39M16×C107—22no—
40M16×C107C2×C414yescomplemented
41C2×C8×C107—22no—
42C4⋊C4×C107—22no—
43C23×C107C22×C411yescharacteristic
44C22×D107—22no—
45C22×D107—22no—
46C22×D107C4212yes—
47C22×D107C22⋊C411yescharacteristic
48C22×D107C22⋊C411yescharacteristic
49C22×D107C4⋊C412yes—
50C2×C4×C107—22no—
51C2×C4×C107—42no—
52C2×C4×C107C22×C412yes—
53C2×C4×C107C2×D411yescharacteristic
54C2×C4×C107C2×D412yes—
55C2×C4×C107C2×Q811yescharacteristic
56C2×Dic107—22no—
57C2×Dic107—42no—
58C2×Dic107C4212yes—
59C2×Dic107C22⋊C412yes—
60C2×Dic107C4⋊C412yes—
61C4×D107—44no—
62C4×D107—44no—
63C4×D107C22⋊C414yes—
64C4×D107C22⋊C414yes—
65C4×D107C4⋊C414yes—
66C4×D107C4⋊C414yes—
67C8×C107—24no—
68C107⋊C8—24no—
69C22×C107—21no—
70C22×C107—21no—
71C22×C107C2×C4211yescharacteristic
72C22×C107C2×C22⋊C411yescharacteristic
73C22×C107C2×C4⋊C411yescharacteristic
74C2×D107—21no—
75C2×D107—21no—
76C2×D107—24no—
77C2×D107—24no—
78C2×D107#9512yes—
79C2×D107#9512yes—
80C2×D107#10012yes—
81C2×D107#10112yes—
82C4×C107—42no—
83C4×C107C2×C22⋊C412yes—
84C4×C107C2×C4⋊C412yes—
85Dic107—42no—
86Dic107#9514yes—
87C2×C107—21no—
88C2×C107—21no—
89C2×C107C2×#9511yescharacteristic
90C2×C107C2×#10011yescharacteristic
91C2×C107C2×#10111yescharacteristic
92D107—22no—
93D107#34314yesdirect product factor
94C2×#343—1071nomaximal, Sylow
95C107C2×#34311yescharacteristic, complemented, Sylow
96C22×M16—1072no—
97C22×C4⋊C4—1071no—
98#343—1072no—
99#343—1071no—
100#343D10711yescharacteristic, direct product factor
101C23×C4—1071no—
102C23×C4—1072no—
103C2×M16—1072no—
104C2×M16—1078no—
105C2×M16—2142no—
106C2×M16—2144no—
107C2×M16C2×D10712yes—
108C22×C8—2142no—
109C2×C4⋊C4—1072no—
110C2×C4⋊C4—1071no—
111C2×C4⋊C4—2142no—
112C2×C4⋊C4—2142no—
113C2×C4⋊C4C2×D10711yescharacteristic
114C24—1071no—
115C22×C4—1071no—
116C22×C4—1074no—
117C22×C4—1072no—
118C22×C4—1072no—
119C22×C4—1072no—
120C22×C4—1072no—
121C22×C4—1072no—
122C22×C4—4284no—
123C22×C4—2142no—
124C22×C4—2142no—
125C22×C4C4×D10712yes—
126C22×C4C22×D10711yescharacteristic
127M16—22no—
128M16—1074no—
129M16—2148no—
130M16—2142no—
131M16C4×D10714yescomplemented
132C2×C8—22no—
133C2×C8—2148no—
134C2×C8—2142no—
135C4⋊C4—22no—
136C4⋊C4—2144no—
137C4⋊C4—2142no—
138C23—1071no—
139C23—1072no—
140C23—1071no—
141C23—1072no—
142C23—2142no—
143C23—2142no—
144C23C2×C4×D10711yescharacteristic
145C2×C4—22no—
146C2×C4—42no—
147C2×C4—1072no—
148C2×C4—1072no—
149C2×C4—1072no—
150C2×C4—1074no—
151C2×C4—1074no—
152C2×C4—1074no—
153C2×C4—1074no—
154C2×C4—4284no—
155C2×C4—4284no—
156C2×C4—4282no—
157C2×C4—2142no—
158C2×C4C2×C4×D10712yes—
159C2×C4D4×D10711yescharacteristic
160C2×C4D4×D10712yes—
161C2×C4Q8×D10711yescharacteristic
162C8—24no—
163C8—2144no—
164C22—21no—
165C22—21no—
166C22—1072no—
167C22—1072no—
168C22—1072no—
169C22—1072no—
170C22—2144no—
171C22—2144no—
172C22—2141no—
173C22—2141no—
174C22C42×D10711yescharacteristic
175C22C22⋊C4×D10711yescharacteristic
176C22C4⋊C4×D10711yescharacteristic
177C4—42no—
178C4—1074no—
179C4—4282no—
180C4C22⋊C4×D10712yes—
181C4C4⋊C4×D10712yes—
182C2—21no—
183C2—21no—
184C2—1074no—
185C2—2142no—
186C2#95×D10711yescharacteristic
187C2#100×D10711yescharacteristic
188C2#101×D10711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC22×C107C2×C42
FrattiniC22×C4C22×D107
Fitting#343×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC23×D107C2×C4
cosocleC22×C4×C107C23
hypercenter#343D107
hypocenterC107C2×#343
LCSG ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. #20292396C2semidirect
4. #20292395C2semidirect
5. #343×C107C2semidirect
11. M16×D107C4semidirect
31. #13133802C2×C4semidirect
40. M16×C107C2×C4semidirect
93. D107#343direct (N × H)
95. C107C2×#343semidirect
100. #343D107direct (N × H)
131. M16C4×D107semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D1072
C2×C4⋊C4×D1072
#202923962
#202923952
#343×C1072
C2×#343107