Finite Group Databasebeta

← #28346112

Subgroups — #28346112

Order 13696.

460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16812115C211yesmaximal, characteristic
2#20293201C212yesmaximal
3#20292882C214yesmaximal, complemented
4#20292865C214yesmaximal, complemented
5#20292665C211yesmaximal, characteristic, complemented
6#20292636C212yesmaximal, complemented
7C22×Q16×C107C211yesmaximal, characteristic, complemented
8C2×#13133818C2211yescharacteristic
9#16812115—24no—
10C2×#13133802C2211yescharacteristic
11C2×#13133801C2212yes—
12C2×C8×D107C2212yes—
13#16812107—22no—
14#16812098—22no—
15#16812092—24no—
16#16812085C2218yes—
17#16812068C2212yes—
18#16812043C2212yes—
19#16812041C2212yes—
20#16812033C2218yes—
21C22×Q8×C107C2212yes—
22C2×Q16×C107—24no—
23C2×Q16×C107C2212yes—
24C2×Q16×C107C2212yes—
25C22×C8×C107C2211yescharacteristic
26#13133818—22no—
27#13133818—22no—
28C2×Dic214D411yescharacteristic
29C2×D428D411yescharacteristic
30C2×C22⋊D107D412yes—
31C2×C4×D107C2312yes—
32#13133802—22no—
33#13133801—24no—
34C2×C107⋊C8C2312yes—
35C8×D107—24no—
36C4⋊Dic107C2314yes—
37Dic107⋊C4—28no—
38C22⋊Dic107—22no—
39(C2×D107)⋊C4—28no—
40C4×Dic107—22no—
41C2×Q8×C107—22no—
42C2×Q8×C107—24no—
43C2×Q8×C107—24no—
44C2×Q8×C107C2314yes—
45C22×C4×C107—22no—
46C22×C4×C107C2311yescharacteristic
47Q16×C107—24no—
48Q16×C107—24no—
49C2×C8×C107D414yes—
50C2×C8×C107C2311yescharacteristic
51C2×C8×C107C2311yescharacteristic
52C23×C107C2×D411yescharacteristic
53C22×D107C2×D412yes—
54Q8×C107—24no—
55Q8×C107—24no—
56Q8×C107—44no—
57C2×C4×C107—24no—
58C2×C4×C107—44no—
59C2×C4×C107C2×D411yescharacteristic
60C2×C4×C107C2×D412yes—
61C2×C4×C107#4112yes—
62C2×C4×C107C2411yescharacteristic
63C22⋊D107—24no—
64C2×Dic107—24no—
65C2×Dic107C2×D412yes—
66D428—22no—
67C4×D107—22no—
68C4×D107—22no—
69Dic214—22no—
70C8×C107C2×D412yes—
71C8×C107C2×D412yes—
72C107⋊C8—22no—
73C22×C107—22no—
74C22×C107#12112yes—
75C22×C107C22×D411yescharacteristic
76C2×D107—22no—
77C2×D107—24no—
78C4×C107—44no—
79C4×C107#12112yes—
80C4×C107C22×D411yescharacteristic
81C4×C107C2×#4111yescharacteristic
82Dic107—22no—
83Dic107—44no—
84C2×C107—22no—
85C2×C107C2×#12111yescharacteristic
86C2×C107#57812yes—
87D107—42no—
88#3059—1071nomaximal, Sylow
89C107#305911yescharacteristic, complemented, Sylow
90C22×Q16D10711yescharacteristic, complemented
91C2×#131—1071no—
92#536—1072no—
93#470—1074no—
94#467—1074no—
95#427—1071no—
96#419—1072no—
97C2×#41—1071no—
98C22×Q8C2×D10712yes—
99C2×Q16—24no—
100C2×Q16C2×D10712yes—
101C2×Q16C2×D10712yes—
102#131—2144no—
103C2×M16—1071no—
104C2×M16—1072no—
105C22×C8—1072no—
106C22×C8C2×D10711yescharacteristic
107C4⋊Q8—2142no—
108#124—2142no—
109#123—2144no—
110C22⋊Q8—1078no—
111#117—1072no—
112#107—1072no—
113#106—1072no—
114#103—1078no—
115#41—2142no—
116#41—2142no—
117C2×Q8—22no—
118C2×Q8—24no—
119C2×Q8—24no—
120C2×Q8—1071no—
121C2×Q8C22×D10714yes—
122C2×D4—1072no—
123C2×D4—1071no—
124C22×C4—22no—
125C22×C4—1072no—
126C22×C4C22×D10711yescharacteristic
127Q16—24no—
128Q16—24no—
129M16—2142no—
130M16—2144no—
131C2×C8—1072no—
132C2×C8—2144no—
133C2×C8C22⋊D10714yes—
134C2×C8C22×D10711yescharacteristic
135C2×C8C22×D10711yescharacteristic
136C4⋊C4—1074no—
137C4⋊C4—2148no—
138C22⋊C4—2148no—
139C22⋊C4—2142no—
140C42—2142no—
141C23—1072no—
142C23D4×D10711yescharacteristic
143Q8—24no—
144Q8—24no—
145Q8—44no—
146Q8—2142no—
147D4—2144no—
148D4—2142no—
149C2×C4—24no—
150C2×C4—44no—
151C2×C4—1072no—
152C2×C4—2144no—
153C2×C4—2142no—
154C2×C4—2142no—
155C2×C4D4×D10711yescharacteristic
156C2×C4C2×C22⋊D10712yes—
157C2×C4#1313381712yes—
158C2×C4C23×D10711yescharacteristic
159C8—2142no—
160C8C2×C22⋊D10712yes—
161C8C2×C22⋊D10712yes—
162C22—22no—
163C22—2144no—
164C22—2142no—
165C22#1681208012yes—
166C22C2×D4×D10711yescharacteristic
167C4—44no—
168C4—4284no—
169C4—2142no—
170C4#1681208012yes—
171C4C22×C22⋊D10711yescharacteristic
172C4C2×#1313381711yescharacteristic
173C2—22no—
174C2—4282no—
175C2C2×#1681208011yescharacteristic
176C2#2029344012yes—
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC22×Q16×C107C2
socleC22×C107C22×D4
prime radicalC2×#13133818C22
hypercenterC22×Q16D107
hypocenterC107#3059
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
3. #20292882C2semidirect
4. #20292865C2semidirect
5. #20292665C2semidirect
6. #20292636C2semidirect
7. C22×Q16×C107C2semidirect
89. C107#3059semidirect
90. C22×Q16D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168121152
#202932012
#202928822
#202928652
#202926652
#202926362
C22×Q16×C1072
#3059107