Finite Group Databasebeta

← #28349120

Subgroups — #28349120

Order 13696.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#20293362C211yesmaximal, characteristic, complemented
2#20293338C211yesmaximal, characteristic, complemented
3#20292983C212yesmaximal, complemented
4#20292975C211yesmaximal, characteristic, complemented
5#20292930C212yesmaximal, complemented
6#20292845C212yesmaximal, complemented
7#20292823C211yesmaximal, characteristic
8#20292751C211yesmaximal, characteristic, complemented
9C4×#13133805C211yesmaximal, characteristic, complemented
10#20292709C212yesmaximal, complemented
11#477×C107C211yesmaximal, characteristic, complemented
12C2×#13133805C2211yescharacteristic
13C2×D856C2212yes—
14#16812106C2211yescharacteristic
15#16812100C2212yes—
16#16812098C2212yes—
17#16812097—21no—
18#16812094—22no—
19#16812089—21no—
20#16812085—22no—
21C4×Dic214C2211yescharacteristic
22C4×D428—21no—
23C4×D428C2211yescharacteristic
24#16812071C2212yes—
25#16812071C2212yes—
26C4⋊C4×D107—21no—
27#16812040C2211yescharacteristic
28Dic107⋊C8C2212yes—
29#16812033C2211yescharacteristic
30#16812031C2212yes—
31#16812029C2212yes—
32#16812029C2211yescharacteristic
33#16812029C2212yes—
34C4×C107⋊C8C2211yescharacteristic
35C8×Dic107C2212yes—
36C4⋊Q8×C107C2211yescharacteristic
37C4×Q8×C107C2211yescharacteristic
38#107×C107C2212yes—
39C4⋊C8×C107C2211yescharacteristic
40#103×C107C2212yes—
41C2×Dic214D411yescharacteristic
42C2×D428—21no—
43C2×D428—21no—
44C2×D428C2312yes—
45C2×D428C2311yescharacteristic
46C2×C4×D107—21no—
47C2×C4×D107—22no—
48C2×C4×D107—22no—
49#13133805—22no—
50D856—24no—
51C2×C107⋊C8C2311yescharacteristic
52C2×C107⋊C8C2311yescharacteristic
53C4⋊Dic107—22no—
54C4⋊Dic107D411yescharacteristic
55C4⋊Dic107C2311yescharacteristic
56Dic107⋊C4—22no—
57Dic107⋊C4D412yes—
58(C2×D107)⋊C4—21no—
59(C2×D107)⋊C4—22no—
60(C2×D107)⋊C4—22no—
61(C2×D107)⋊C4—22no—
62(C2×D107)⋊C4—22no—
63C4×Dic107C2312yes—
64C2×Q8×C107—21no—
65C2×Q8×C107C2311yescharacteristic
66C2×C8×C107C2312yes—
67C4⋊C4×C107—21no—
68C4⋊C4×C107—21no—
69C4⋊C4×C107C2311yescharacteristic
70C4⋊C4×C107C2312yes—
71C42×C107—21no—
72C42×C107C2311yescharacteristic
73C22×D107—21no—
74C22×D107—22no—
75Q8×C107—21no—
76Q8×C107—21no—
77Q8×C107—81no—
78C2×C4×C107—21no—
79C2×C4×C107—21no—
80C2×C4×C107—22no—
81C2×C4×C107C2×D411yescharacteristic
82C2×C4×C107C2×D411yescharacteristic
83C2×C4×C107C2411yescharacteristic
84C2×Dic107—21no—
85C2×Dic107C2×D412yes—
86C2×Dic107C2×D412yes—
87D428—22no—
88D428—21no—
89D428—22no—
90D428—42no—
91D428—81no—
92D428#4112yes—
93C4×D107—42no—
94C4×D107—82no—
95C4×D107—82no—
96Dic214—22no—
97C8×C107—22no—
98C107⋊C8—21no—
99C107⋊C8—21no—
100C22×C107C22×D411yescharacteristic
101C2×D107—22no—
102C2×D107—41no—
103C2×D107—41no—
104C2×D107—42no—
105C2×D107—42no—
106C2×D107—42no—
107C4×C107—21no—
108C4×C107—41no—
109C4×C107—41no—
110C4×C107—42no—
111C4×C107#13512yes—
112C4×C107C2×#4111yescharacteristic
113C4×C1072−1+411yescharacteristic
114Dic107—22no—
115Dic107—22no—
116Dic107—41no—
117C2×C107#54811yescharacteristic
118C2×C107C2×#13511yescharacteristic
119C2×C107#57611yescharacteristic
120D107—42no—
121D107—82no—
122#3361—1071nomaximal, Sylow
123C107#336111yescharacteristic, complemented, Sylow
124#559—1071no—
125#554—1071no—
126#488—1072no—
127#486—1071no—
128#478—1072no—
129#477D10711yescharacteristic, complemented
130#463—1072no—
131#459—1071no—
132C8×Q8—1071no—
133C4×SD16—1071no—
134C4×D8—1072no—
135C2×SD16—1071no—
136C2×D8—1072no—
137C4⋊Q8C2×D10711yescharacteristic
138#127—1071no—
139#125—1072no—
140#124—1072no—
141#124—2141no—
142#123—2142no—
143C22⋊Q8—2141no—
144C22⋊Q8—2142no—
145C4×Q8—1071no—
146C4×Q8C2×D10711yescharacteristic
147C4×D4—1072no—
148C4×D4—1072no—
149C4×D4—1071no—
150C4×D4—2141no—
151C2×C4⋊C4—2141no—
152#107C2×D10712yes—
153#106—1071no—
154C4⋊C8—1072no—
155C4⋊C8C2×D10711yescharacteristic
156#103—1071no—
157#103C2×D10712yes—
158#102—1072no—
159#102—1071no—
160#102—1072no—
161#102—1072no—
162C4×C8—1072no—
163C4×C8—1071no—
164C2×Q8—21no—
165C2×Q8—1071no—
166C2×Q8C22×D10711yescharacteristic
167C2×D4—1071no—
168C2×D4—1072no—
169C2×D4—2141no—
170C2×D4—2141no—
171C22×C4—2142no—
172C22×C4—2142no—
173C22×C4—2141no—
174SD16—2142no—
175D8—2144no—
176C2×C8—1071no—
177C2×C8—1071no—
178C2×C8C22×D10712yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—1071no—
182C4⋊C4—1072no—
183C4⋊C4—1071no—
184C4⋊C4—2142no—
185C4⋊C4—2142no—
186C4⋊C4C22×D10712yes—
187C4⋊C4C22×D10711yescharacteristic
188C22⋊C4—2142no—
189C22⋊C4—2142no—
190C22⋊C4—2142no—
191C22⋊C4—2142no—
192C22⋊C4—2141no—
193C42—21no—
194C42—1072no—
195C42C22×D10711yescharacteristic
196C23—2142no—
197C23—2141no—
198Q8—21no—
199Q8—21no—
200Q8—81no—
201Q8—2142no—
202D4—8561no—
203D4—1072no—
204D4—4282no—
205D4—2142no—
206D4—2142no—
207D4—2141no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—8562no—
212C2×C4—8562no—
213C2×C4—1072no—
214C2×C4—1072no—
215C2×C4—4282no—
216C2×C4—2141no—
217C2×C4D4×D10711yescharacteristic
218C2×C4D4×D10711yescharacteristic
219C2×C4C23×D10711yescharacteristic
220C8—22no—
221C8—2141no—
222C8—2141no—
223C22—4282no—
224C22—4282no—
225C22—4282no—
226C22—4281no—
227C22—4281no—
228C22—2142no—
229C22C2×D4×D10711yescharacteristic
230C4—21no—
231C4—41no—
232C4—42no—
233C4—41no—
234C4—4281no—
235C4—2142no—
236C4—2142no—
237C4#1681213212yes—
238C4#41×D10711yescharacteristic
239C4#1681215711yescharacteristic
240C2—8562no—
241C2—4282no—
242C2#2029328711yescharacteristic
243C2C2×#1681213211yescharacteristic
244C2#2029343111yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#477×C107C2
socleC22×C107C22×D4
prime radical#20292823C2
hypercenter#477D107
hypocenterC107#3361
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #20293362C2semidirect
2. #20293338C2semidirect
3. #20292983C2semidirect
4. #20292975C2semidirect
5. #20292930C2semidirect
6. #20292845C2semidirect
8. #20292751C2semidirect
9. C4×#13133805C2semidirect
10. #20292709C2semidirect
11. #477×C107C2semidirect
123. C107#3361semidirect
129. #477D107semidirect

Maximal subgroups

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

subgroupindex
#202933622
#202933382
#202929832
#202929752
#202929302
#202928452
#202928232
#202927512
C4×#131338052
#202927092
#477×C1072
#3361107