Finite Group Databasebeta

← #28346762

Subgroups — #28346762

Order 13696.

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

normal subgroups only

This group has 358 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#20293239C211yesmaximal, characteristic
2#20293104C211yesmaximal, characteristic
3#20292969C212yesmaximal
4#20292935C212yesmaximal, complemented
5#20292838C212yesmaximal, complemented
6#20292785C212yesmaximal
7#20292735C212yesmaximal, complemented
8C4×Dic428C212yesmaximal, complemented
9#433×C107C211yesmaximal, characteristic
10C22×Dic214C2211yescharacteristic
11C2×Dic428C2212yes—
12C2×Dic428C2212yes—
13#16812109C2211yescharacteristic
14#16812102—22no—
15#16812101C2211yescharacteristic
16#16812099—22no—
17#16812088C2212yes—
18C4×Dic214C2212yes—
19C4×Dic214C2212yes—
20C4×Dic214C2212yes—
21#16812074—22no—
22#16812068C2211yescharacteristic
23#16812065—22no—
24#16812043C2212yes—
25#16812041C2212yes—
26#16812034C2212yes—
27#16812034C2212yes—
28#16812034C2212yes—
29#16812034C2212yes—
30#117×C107C2211yescharacteristic
31C4⋊C8×C107C2212yes—
32C22⋊C8×C107C2212yes—
33#97×C107C2211yescharacteristic
34C4×C8×C107C2211yescharacteristic
35C2×Dic214—21no—
36C2×Dic214—24no—
37C2×Dic214C2312yes—
38C2×Dic214C2312yes—
39C22×Dic107—21no—
40Dic428—24no—
41Dic428—24no—
42C4⋊Dic107—22no—
43C4⋊Dic107C2312yes—
44C4⋊Dic107C2312yes—
45Dic107⋊C4—22no—
46Dic107⋊C4—22no—
47Dic107⋊C4—22no—
48Dic107⋊C4—22no—
49Dic107⋊C4—22no—
50C22⋊Dic107—21no—
51C22⋊Dic107—22no—
52C4×Dic107—22no—
53C4×Dic107—22no—
54C4×Dic107—21no—
55C4×Dic107—22no—
56C22×C4×C107C2311yescharacteristic
57C2×C8×C107C2312yes—
58C2×C8×C107C2312yes—
59C4⋊C4×C107D412yes—
60C22⋊C4×C107D412yes—
61C42×C107C2311yescharacteristic
62C42×C107C2311yescharacteristic
63C23×C107C2×D411yescharacteristic
64C2×C4×C107—22no—
65C2×C4×C107C2×D412yes—
66C2×C4×C107C2×D412yes—
67C2×C4×C107C2×D411yescharacteristic
68C2×C4×C107C2411yescharacteristic
69C2×Dic107—24no—
70C2×Dic107—22no—
71C2×Dic107—22no—
72C2×Dic107—22no—
73C2×Dic107—22no—
74Dic214—24no—
75Dic214—22no—
76Dic214—22no—
77Dic214—22no—
78Dic214#4114yes—
79C8×C107—22no—
80C8×C107—22no—
81C22×C107—21no—
82C22×C107—22no—
83C22×C107C22×D411yescharacteristic
84C4×C107—21no—
85C4×C107—22no—
86C4×C107—22no—
87C4×C107C2×#4112yes—
88Dic107—24no—
89Dic107—42no—
90Dic107—42no—
91Dic107—42no—
92C2×C107—41no—
93C2×C107#52511yescharacteristic
94C2×C107#57812yes—
95#3127—1071nomaximal, Sylow
96C107#312711yescharacteristic, complemented, Sylow
97#541—1071no—
98#519—1071no—
99#485—1072no—
100#479—1072no—
101#462—1072no—
102#451—1072no—
103#441—1072no—
104C4×Q16—1072no—
105#433D10711yescharacteristic
106C22×Q8—1071no—
107C2×Q16—1072no—
108C2×Q16—1072no—
109C4⋊Q8—1071no—
110#126—2142no—
111#125—1071no—
112#125—2142no—
113C22⋊Q8—1072no—
114C4×Q8—1072no—
115C4×Q8—1072no—
116C4×Q8—1072no—
117C4×Q8—2142no—
118#117—1071no—
119#117—2142no—
120#117C2×D10711yescharacteristic
121#107—1072no—
122#106—1072no—
123C4⋊C8C2×D10712yes—
124#103—1072no—
125#103—1072no—
126#103—1072no—
127#103—1072no—
128C22⋊C8C2×D10712yes—
129#97C2×D10711yescharacteristic
130C4×C8C2×D10711yescharacteristic
131C2×Q8—1072no—
132C2×Q8—1072no—
133C2×Q8—2144no—
134C2×Q8—2141no—
135C22×C4—2141no—
136C22×C4C22×D10711yescharacteristic
137Q16—2144no—
138Q16—2144no—
139C2×C8C22×D10712yes—
140C2×C8C22×D10712yes—
141C4⋊C4—1072no—
142C4⋊C4—1072no—
143C4⋊C4—2142no—
144C4⋊C4—2142no—
145C4⋊C4—2142no—
146C4⋊C4—2142no—
147C4⋊C4—2142no—
148C4⋊C4—2142no—
149C4⋊C4D42812yes—
150C22⋊C4—2141no—
151C22⋊C4—2142no—
152C22⋊C4D42812yes—
153C42—2141no—
154C42—2142no—
155C42—2142no—
156C42—2142no—
157C42C22×D10711yescharacteristic
158C42C22×D10711yescharacteristic
159C23C2×D42811yescharacteristic
160Q8—1074no—
161Q8—2144no—
162Q8—2142no—
163Q8—2142no—
164Q8—2142no—
165C2×C4—22no—
166C2×C4—2142no—
167C2×C4—2142no—
168C2×C4—2142no—
169C2×C4—2144no—
170C2×C4—2142no—
171C2×C4C2×D42812yes—
172C2×C4C2×D42812yes—
173C2×C4C2×D42811yescharacteristic
174C2×C4C23×D10711yescharacteristic
175C8—22no—
176C8—22no—
177C22—21no—
178C22—22no—
179C22C22×D42811yescharacteristic
180C4—21no—
181C4—22no—
182C4—22no—
183C4—4282no—
184C4—4282no—
185C4—4282no—
186C4—2144no—
187C4#41×D10712yes—
188C2—41no—
189C2#2029313911yescharacteristic
190C2#2029344412yes—
subgroupG/H
centerC22C22×D428
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#433×C107C2
socleC22×C107C22×D4
prime radicalC23×C107C2×D4
hypercenter#433D107
hypocenterC107#3127
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
4. #20292935C2semidirect
5. #20292838C2semidirect
7. #20292735C2semidirect
8. C4×Dic428C2semidirect
96. C107#3127semidirect

Maximal subgroups

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

subgroupindex
#202932392
#202931042
#202929692
#202929352
#202928382
#202927852
#202927352
C4×Dic4282
#433×C1072
#3127107