Finite Group Databasebeta

← #28346753

Subgroups — #28346753

Order 13696.

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

normal subgroups only

This group has 382 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#20293232C211yesmaximal, characteristic
2#20293104C211yesmaximal, characteristic, complemented
3#20292952C212yesmaximal, complemented
4#20292935C212yesmaximal, complemented
5#20292828C212yesmaximal, complemented
6#20292768C212yesmaximal, complemented
7#20292729C212yesmaximal, complemented
8C4×#13133807C212yesmaximal, complemented
9#433×C107C211yesmaximal, characteristic, complemented
10C22×Dic214C2211yescharacteristic
11C2×#13133807C2212yes—
12C2×#13133807C2212yes—
13#16812106C2211yescharacteristic
14#16812101C2211yescharacteristic
15#16812094—22no—
16#16812083C2212yes—
17#16812082—22no—
18C4×Dic214C2212yes—
19C4×Dic214C2212yes—
20#16812074—22no—
21C4×D428C2212yes—
22#16812068C2211yescharacteristic
23#16812065—22no—
24#16812043C2212yes—
25#16812041C2212yes—
26#16812034C2212yes—
27#16812034C2212yes—
28#16812031C2212yes—
29#16812031C2212yes—
30#117×C107C2211yescharacteristic
31C4⋊C8×C107C2212yes—
32C22⋊C8×C107C2212yes—
33#97×C107C2211yescharacteristic
34C4×C8×C107C2211yescharacteristic
35C2×Dic214—21no—
36C2×Dic214—24no—
37C2×Dic214C2312yes—
38C2×D428—22no—
39C2×D428C2312yes—
40C2×C22⋊D107—22no—
41C22×Dic107—21no—
42C2×C4×D107—22no—
43#13133807—24no—
44#13133807—24no—
45C4⋊Dic107C2312yes—
46C4⋊Dic107C2312yes—
47Dic107⋊C4—22no—
48Dic107⋊C4—22no—
49Dic107⋊C4—22no—
50C22⋊Dic107—21no—
51(C2×D107)⋊C4—22no—
52(C2×D107)⋊C4—22no—
53C4×Dic107—22no—
54C4×Dic107—22no—
55C4×Dic107—21no—
56C22×C4×C107C2311yescharacteristic
57C2×C8×C107C2312yes—
58C2×C8×C107C2312yes—
59C4⋊C4×C107D412yes—
60C22⋊C4×C107D412yes—
61C42×C107C2311yescharacteristic
62C42×C107C2311yescharacteristic
63C23×C107C2×D411yescharacteristic
64C22×D107—22no—
65C2×C4×C107—22no—
66C2×C4×C107C2×D412yes—
67C2×C4×C107C2×D412yes—
68C2×C4×C107C2×D411yescharacteristic
69C2×C4×C107C2411yescharacteristic
70C22⋊D107—82no—
71C2×Dic107—24no—
72C2×Dic107—22no—
73C2×Dic107—22no—
74C2×Dic107—22no—
75D428—22no—
76D428—22no—
77D428—82no—
78C4×D107—82no—
79Dic214—24no—
80Dic214—22no—
81Dic214#4114yes—
82C8×C107—22no—
83C8×C107—22no—
84C22×C107—21no—
85C22×C107—22no—
86C22×C107C22×D411yescharacteristic
87C2×D107—42no—
88C2×D107—42no—
89C2×D107—42no—
90C4×C107—21no—
91C4×C107—22no—
92C4×C107—22no—
93C4×C107C2×#4112yes—
94Dic107—24no—
95Dic107—42no—
96Dic107—42no—
97C2×C107—41no—
98C2×C107#52511yescharacteristic
99C2×C107#57712yes—
100D107—82no—
101#3126—1071nomaximal, Sylow
102C107#312611yescharacteristic, complemented, Sylow
103#540—1071no—
104#519—1071no—
105#482—1072no—
106#479—1072no—
107#460—1072no—
108#448—1072no—
109#440—1072no—
110C4×SD16—1072no—
111#433D10711yescharacteristic, complemented
112C22×Q8—1071no—
113C2×SD16—1072no—
114C2×SD16—1072no—
115#127—1071no—
116#125—1071no—
117#123—2142no—
118#121—1072no—
119#121—2142no—
120C4×Q8—1072no—
121C4×Q8—1072no—
122C4×Q8—2142no—
123C4×D4—1072no—
124#117—1071no—
125#117—2142no—
126#117C2×D10711yescharacteristic
127#107—1072no—
128#106—1072no—
129C4⋊C8C2×D10712yes—
130#103—1072no—
131#103—1072no—
132#102—1072no—
133#102—1072no—
134C22⋊C8C2×D10712yes—
135#97C2×D10711yescharacteristic
136C4×C8C2×D10711yescharacteristic
137C2×Q8—1072no—
138C2×Q8—2144no—
139C2×Q8—2141no—
140C2×D4—1072no—
141C2×D4—2142no—
142C2×D4—2142no—
143C22×C4—2142no—
144C22×C4—2141no—
145C22×C4C22×D10711yescharacteristic
146SD16—2144no—
147SD16—2144no—
148C2×C8C22×D10712yes—
149C2×C8C22×D10712yes—
150C4⋊C4—1072no—
151C4⋊C4—1072no—
152C4⋊C4—2142no—
153C4⋊C4—2142no—
154C4⋊C4—2142no—
155C4⋊C4D42812yes—
156C22⋊C4—2141no—
157C22⋊C4—2142no—
158C22⋊C4—2142no—
159C22⋊C4D42812yes—
160C42—2141no—
161C42—2142no—
162C42—2142no—
163C42C22×D10711yescharacteristic
164C42C22×D10711yescharacteristic
165C23—2142no—
166C23C2×D42811yescharacteristic
167Q8—1074no—
168Q8—2144no—
169Q8—2142no—
170D4—8562no—
171D4—8562no—
172D4—2142no—
173D4—2142no—
174C2×C4—22no—
175C2×C4—8562no—
176C2×C4—2142no—
177C2×C4—2142no—
178C2×C4—2144no—
179C2×C4—2142no—
180C2×C4C2×D42812yes—
181C2×C4C2×D42812yes—
182C2×C4C2×D42811yescharacteristic
183C2×C4C23×D10711yescharacteristic
184C8—22no—
185C8—22no—
186C22—21no—
187C22—22no—
188C22—4282no—
189C22—4282no—
190C22—4282no—
191C22C22×D42811yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—4282no—
196C4—4282no—
197C4—2144no—
198C4#41×D10712yes—
199C2—41no—
200C2—8562no—
201C2#2029313911yescharacteristic
202C2#2029343912yes—
subgroupG/H
centerC22C22×D428
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#433×C107C2
socleC22×C107C22×D4
prime radical#20293232C2
hypercenter#433D107
hypocenterC107#3126
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
2. #20293104C2semidirect
3. #20292952C2semidirect
4. #20292935C2semidirect
5. #20292828C2semidirect
6. #20292768C2semidirect
7. #20292729C2semidirect
8. C4×#13133807C2semidirect
9. #433×C107C2semidirect
102. C107#3126semidirect
111. #433D107semidirect

Maximal subgroups

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

subgroupindex
#202932322
#202931042
#202929522
#202929352
#202928282
#202927682
#202927292
C4×#131338072
#433×C1072
#3126107