Finite Group Databasebeta

← #28346756

Subgroups — #28346756

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#20293104C211yesmaximal, characteristic
2#20292965C212yesmaximal
3#20292931C212yesmaximal, complemented
4#20292834C212yesmaximal, complemented
5#20292782C212yesmaximal
6#20292732C212yesmaximal, complemented
7C4×#13133808C212yesmaximal, complemented
8#20292688C211yesmaximal, characteristic
9#541×C107C211yesmaximal, characteristic
10C22×Dic214C2211yescharacteristic
11C2×#13133808C2212yes—
12C2×#13133808C2212yes—
13C4×Dic214C2212yes—
14C4×Dic214C2212yes—
15#16812074—22no—
16#16812068C2211yescharacteristic
17#16812065—22no—
18#16812042C2212yes—
19#16812040C2212yes—
20C4⋊(C107⋊C8)C2212yes—
21#16812033C2212yes—
22#16812033C2212yes—
23#16812032C2212yes—
24#16812032C2212yes—
25C22⋊(C107⋊C8)C2212yes—
26#16812020C2211yescharacteristic
27C4×C107⋊C8C2211yescharacteristic
28C4⋊Q8×C107C2211yescharacteristic
29#126×C107—22no—
30#125×C107—22no—
31#125×C107C2211yescharacteristic
32C22⋊Q8×C107C2212yes—
33C4×Q8×C107C2212yes—
34#117×C107C2211yescharacteristic
35C2×Dic214—21no—
36C2×Dic214—24no—
37C2×Dic214C2312yes—
38C22×Dic107—21no—
39#13133808—24no—
40#13133808—24no—
41C2×C107⋊C8C2312yes—
42C2×C107⋊C8C2312yes—
43C4⋊Dic107C2312yes—
44Dic107⋊C4—22no—
45Dic107⋊C4—22no—
46C22⋊Dic107—21no—
47C4×Dic107—22no—
48C4×Dic107—22no—
49C4×Dic107—21no—
50C2×Q8×C107C2312yes—
51C22×C4×C107C2311yescharacteristic
52C4⋊C4×C107—22no—
53C4⋊C4×C107—22no—
54C4⋊C4×C107—22no—
55C4⋊C4×C107—22no—
56C4⋊C4×C107D412yes—
57C4⋊C4×C107C2312yes—
58C22⋊C4×C107—22no—
59C22⋊C4×C107D412yes—
60C42×C107—22no—
61C42×C107C2311yescharacteristic
62C42×C107C2311yescharacteristic
63C23×C107C2×D411yescharacteristic
64Q8×C107—22no—
65Q8×C107—22no—
66C2×C4×C107—22no—
67C2×C4×C107—22no—
68C2×C4×C107—22no—
69C2×C4×C107C2×D412yes—
70C2×C4×C107C2×D412yes—
71C2×C4×C107C2×D411yescharacteristic
72C2×C4×C107C2411yescharacteristic
73C2×Dic107—24no—
74C2×Dic107—22no—
75C2×Dic107—22no—
76Dic214—24no—
77Dic214—22no—
78Dic214#4114yes—
79C107⋊C8—22no—
80C107⋊C8—22no—
81C22×C107—21no—
82C22×C107—22no—
83C22×C107C22×D411yescharacteristic
84C4×C107—21no—
85C4×C107—22no—
86C4×C107—22no—
87C4×C107—42no—
88C4×C107—42no—
89C4×C107C2×#4112yes—
90Dic107—24no—
91Dic107—42no—
92C2×C107—41no—
93C2×C107#52511yescharacteristic
94C2×C107#57812yes—
95#3127—1071nomaximal, Sylow
96C107#312711yescharacteristic, complemented, Sylow
97#541D10711yescharacteristic
98#519—1071no—
99#485—1072no—
100#479—1072no—
101#462—1072no—
102#451—1072no—
103#441—1072no—
104C4×Q16—1072no—
105#433—1071no—
106C22×Q8—1071no—
107C2×Q16—1072no—
108C2×Q16—1072no—
109C4⋊Q8C2×D10711yescharacteristic
110#126—22no—
111#125—22no—
112#125C2×D10711yescharacteristic
113C22⋊Q8C2×D10712yes—
114C4×Q8—1072no—
115C4×Q8—1072no—
116C4×Q8—2142no—
117C4×Q8C2×D10712yes—
118#117—1071no—
119#117—2142no—
120#117C2×D10711yescharacteristic
121#107—1072no—
122#106—1072no—
123C4⋊C8—1072no—
124#103—1072no—
125#103—1072no—
126#103—1072no—
127#103—1072no—
128C22⋊C8—1072no—
129#97—1071no—
130C4×C8—1071no—
131C2×Q8—1072no—
132C2×Q8—2144no—
133C2×Q8—2141no—
134C2×Q8C22×D10712yes—
135C22×C4—2141no—
136C22×C4C22×D10711yescharacteristic
137Q16—2144no—
138Q16—2144no—
139C2×C8—1072no—
140C2×C8—1072no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—22no—
144C4⋊C4—22no—
145C4⋊C4—1072no—
146C4⋊C4—2142no—
147C4⋊C4—2142no—
148C4⋊C4C22⋊D10712yes—
149C4⋊C4C22×D10712yes—
150C22⋊C4—22no—
151C22⋊C4—2141no—
152C22⋊C4C22⋊D10712yes—
153C42—22no—
154C42—2141no—
155C42—2142no—
156C42—2142no—
157C42C22×D10711yescharacteristic
158C42C22×D10711yescharacteristic
159C23C2×C22⋊D10711yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—1074no—
163Q8—2144no—
164Q8—2142no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—2142no—
169C2×C4—2144no—
170C2×C4—2142no—
171C2×C4C2×C22⋊D10712yes—
172C2×C4C2×C22⋊D10712yes—
173C2×C4C2×C22⋊D10711yescharacteristic
174C2×C4C23×D10711yescharacteristic
175C8—2142no—
176C8—2142no—
177C22—21no—
178C22—22no—
179C22C22×C22⋊D10711yescharacteristic
180C4—21no—
181C4—22no—
182C4—22no—
183C4—42no—
184C4—42no—
185C4—4282no—
186C4—2144no—
187C4#41×D10712yes—
188C2—41no—
189C2#2029313411yescharacteristic
190C2#2029344212yes—
subgroupG/H
centerC22C22×C22⋊D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#541×C107C2
socleC22×C107C22×D4
prime radicalC23×C107C2×D4
hypercenter#541D107
hypocenterC107#3127
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
3. #20292931C2semidirect
4. #20292834C2semidirect
6. #20292732C2semidirect
7. C4×#13133808C2semidirect
96. C107#3127semidirect

Maximal subgroups

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

subgroupindex
#202931042
#202929652
#202929312
#202928342
#202927822
#202927322
C4×#131338082
#202926882
#541×C1072
#3127107