Finite Group Databasebeta

← #28346982

Subgroups — #28346982

Order 13696.

348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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#20293183C211yesmaximal, characteristic
2#20293182C211yesmaximal, characteristic
3#20293037C211yesmaximal, characteristic, complemented
4#20293036C211yesmaximal, characteristic, complemented
5#20293035C212yesmaximal, complemented
6#20293034C212yesmaximal, complemented
7#20293033C211yesmaximal, characteristic, complemented
8#20292664C212yesmaximal
9#20292662C212yesmaximal
10#97×D107C211yesmaximal, characteristic
11#501×C107C211yesmaximal, characteristic, complemented
12C2×C8×D107C2212yes—
13#16812109C2211yescharacteristic
14#16812108C2211yescharacteristic
15#16812108C2211yescharacteristic
16#16812101C2211yescharacteristic
17#16812100C2212yes—
18#16812089—21no—
19#16812087—21no—
20#16812087—21no—
21#16812085—21no—
22Q8×Dic107—21no—
23#16812074—21no—
24#16812074—21no—
25#16812074—21no—
26#16812067C2211yescharacteristic
27#16812067C2212yes—
28#16812067C2211yescharacteristic
29C42×D107C2211yescharacteristic
30#16812043C2212yes—
31#16812042C2212yes—
32#16812042C2212yes—
33#16812041C2212yes—
34#16812040C2212yes—
35#16812040C2212yes—
36#16812020C2211yescharacteristic
37#16812019C2212yes—
38C4⋊Q8×C107C2211yescharacteristic
39#125×C107C2211yescharacteristic
40#107×C107C2212yes—
41#106×C107C2212yes—
42#97×C107C2211yescharacteristic
43C2×Dic214—21no—
44C2×Dic214—21no—
45C2×Dic214—21no—
46C2×C4×D107D411yescharacteristic
47C2×C4×D107D411yescharacteristic
48C2×C4×D107C2311yescharacteristic
49C2×C107⋊C8C2312yes—
50C8×D107Q818yescomplemented
51C4⋊Dic107—21no—
52C4⋊Dic107—22no—
53C4⋊Dic107C2311yescharacteristic
54C4⋊Dic107C2312yes—
55C4⋊Dic107C2311yescharacteristic
56Dic107⋊C4—21no—
57Dic107⋊C4—21no—
58Dic107⋊C4—22no—
59Dic107⋊C4—21no—
60Dic107⋊C4—21no—
61(C2×D107)⋊C4—22no—
62(C2×D107)⋊C4—21no—
63(C2×D107)⋊C4—21no—
64C4×Dic107—21no—
65C4×Dic107—21no—
66C4×Dic107—22no—
67C4×Dic107D411yescharacteristic
68C4×Dic107D411yescharacteristic
69C4×Dic107C2311yescharacteristic
70C2×Q8×C107—21no—
71C2×C8×C107C2312yes—
72C4⋊C4×C107—21no—
73C4⋊C4×C107—21no—
74C4⋊C4×C107—21no—
75C4⋊C4×C107C2311yescharacteristic
76C4⋊C4×C107C2312yes—
77C4⋊C4×C107C2311yescharacteristic
78C42×C107C2311yescharacteristic
79C22×D107C2×D411yescharacteristic
80Q8×C107—42no—
81C2×C4×C107—21no—
82C2×C4×C107—21no—
83C2×C4×C107—22no—
84C2×C4×C107C2×D411yescharacteristic
85C2×C4×C107C2×D411yescharacteristic
86C2×C4×C107C2411yescharacteristic
87C2×Dic107—21no—
88C2×Dic107—21no—
89C2×Dic107—22no—
90C2×Dic107C2×D411yescharacteristic
91C2×Dic107C2×D411yescharacteristic
92C2×Dic107C2×D411yescharacteristic
93C4×D107—41no—
94C4×D107—41no—
95C4×D107C2×Q814yes—
96Dic214—42no—
97Dic214—42no—
98Dic214—42no—
99C8×C107C2×Q814yes—
100C107⋊C8C2×Q814yes—
101C22×C107C22×D411yescharacteristic
102C2×D107—21no—
103C2×D107—21no—
104C2×D107C4⋊Q812yes—
105C4×C107—21no—
106C4×C107—21no—
107C4×C107—41no—
108C4×C107—41no—
109C4×C107—42no—
110C4×C107C22×Q812yes—
111Dic107—21no—
112Dic107—21no—
113Dic107—41no—
114Dic107—41no—
115Dic107—42no—
116Dic107C4⋊Q812yes—
117C2×C107C2×C4⋊Q811yescharacteristic
118C2×C107#57511yescharacteristic
119C2×C107#57511yescharacteristic
120D107—22no—
121#3162—1071nomaximal, Sylow
122C107#316211yescharacteristic, complemented, Sylow
123#533—1071no—
124#533—1071no—
125#501—1071no—
126#501—1071no—
127#501—1072no—
128#501—1072no—
129#501—1071no—
130#501D10711yescharacteristic, complemented
131#427—1072no—
132#427—1072no—
133C2×#97—1071no—
134C22×C8—1072no—
135C4⋊Q8—1071no—
136C4⋊Q8—1071no—
137C4⋊Q8—1071no—
138C4⋊Q8C2×D10711yescharacteristic
139#125—1072no—
140#125—1071no—
141#125C2×D10711yescharacteristic
142C22⋊Q8—2141no—
143C22⋊Q8—2141no—
144C22⋊Q8—2141no—
145C22⋊Q8—2141no—
146C4×Q8—2141no—
147C4×Q8—2141no—
148C4×Q8—2141no—
149C4×Q8—2141no—
150#117—1071no—
151#117—1072no—
152#117—1071no—
153C2×C42—1071no—
154#107—1072no—
155#107—1072no—
156#107—1072no—
157#107C2×D10712yes—
158#106—1072no—
159#106—1072no—
160#106—1072no—
161#106C2×D10712yes—
162#97—1072no—
163#97—1071no—
164#97C2×D10711yescharacteristic
165C2×Q8—21no—
166C2×Q8—2141no—
167C2×Q8—2141no—
168C2×Q8—2141no—
169C22×C4—1071no—
170C22×C4—1071no—
171C22×C4—1071no—
172C2×C8—1072no—
173C2×C8—1078no—
174C2×C8C22×D10712yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—1071no—
179C4⋊C4—1072no—
180C4⋊C4—1071no—
181C4⋊C4—2142no—
182C4⋊C4—2142no—
183C4⋊C4—2141no—
184C4⋊C4—2141no—
185C4⋊C4—2141no—
186C4⋊C4—2141no—
187C4⋊C4—2141no—
188C4⋊C4C22×D10711yescharacteristic
189C4⋊C4C22×D10712yes—
190C4⋊C4C22×D10711yescharacteristic
191C22⋊C4—2141no—
192C22⋊C4—2141no—
193C22⋊C4—2142no—
194C42—1071no—
195C42—1071no—
196C42—1071no—
197C42—2141no—
198C42—2141no—
199C42—2142no—
200C42C22×D10711yescharacteristic
201C23—1071no—
202Q8—42no—
203Q8—4282no—
204Q8—4282no—
205Q8—4282no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—1071no—
210C2×C4—1074no—
211C2×C4—1071no—
212C2×C4—1071no—
213C2×C4—4281no—
214C2×C4—4281no—
215C2×C4—2141no—
216C2×C4—2142no—
217C2×C4—2141no—
218C2×C4D4×D10711yescharacteristic
219C2×C4D4×D10711yescharacteristic
220C2×C4C23×D10711yescharacteristic
221C8—1074no—
222C8Q8×D10714yes—
223C22—1072no—
224C22—2141no—
225C22—2141no—
226C22C2×D4×D10711yescharacteristic
227C4—21no—
228C4—21no—
229C4—42no—
230C4—41no—
231C4—41no—
232C4—1072no—
233C4—4281no—
234C4—4282no—
235C4—4281no—
236C4—2141no—
237C4—2141no—
238C4C2×Q8×D10712yes—
239C2—2142no—
240C2C4⋊Q8×D10711yescharacteristic
241C2#2029342311yescharacteristic
242C2#2029342611yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#501×C107C2
socleC22×C107C22×D4
prime radicalC22×D107C2×D4
hypercenter#501D107
hypocenterC107#3162
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #20293037C2semidirect
4. #20293036C2semidirect
5. #20293035C2semidirect
6. #20293034C2semidirect
7. #20293033C2semidirect
11. #501×C107C2semidirect
50. C8×D107Q8semidirect
122. C107#3162semidirect
130. #501D107semidirect

Maximal subgroups

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

subgroupindex
#202931832
#202931822
#202930372
#202930362
#202930352
#202930342
#202930332
#202926642
#202926622
#97×D1072
#501×C1072
#3162107