Finite Group Databasebeta

← #28336982

Subgroups — #28336982

Order 13696.

312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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#20293393C211yesmaximal, characteristic
2#20293203C211yesmaximal, characteristic
3#20292637C211yesmaximal, characteristic, complemented
4#20292635C211yesmaximal, characteristic, complemented
5#20292600C211yesmaximal, characteristic
6#20292383C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C107C211yesmaximal, characteristic, complemented
8C2×#13133818C2211yescharacteristic
9C22×Dic214C2211yescharacteristic
10#16812117—22no—
11#16812115—22no—
12C2×#13133802C2211yescharacteristic
13M16×D107—22no—
14#16812109C412yescomplemented
15#16812097C412yescomplemented
16#16812093—22no—
17#16812089—22no—
18#16812068C2211yescharacteristic
19#16812034—22no—
20#16812032—22no—
21#16812023—22no—
22C2×M16×C107C2211yescharacteristic
23#117×C107C2211yescharacteristic
24#117×C107C2211yescharacteristic
25#13133818—21no—
26#13133818—21no—
27#13133818—21no—
28#13133818—21no—
29C2×Dic214—21no—
30C2×Dic214—21no—
31C2×Dic214—21no—
32C2×Dic214—21no—
33C2×Dic214—21no—
34C2×Dic214C2×C412yes—
35C2×Dic214C2×C411yescharacteristic
36C2×D428C2×C411yescharacteristic
37C2×C22⋊D107D412yes—
38C22×Dic107—21no—
39C2×C4×D107D412yes—
40#13133802—21no—
41#13133802—21no—
42#13133801—24no—
43C2×C107⋊C8D412yes—
44C8×D107—24no—
45C4⋊Dic107—24no—
46C4⋊Dic107—21no—
47C22⋊Dic107—21no—
48(C2×D107)⋊C4—24no—
49C4×Dic107—21no—
50C22×C4×C107C2311yescharacteristic
51M16×C107—21no—
52M16×C107—21no—
53C2×C8×C107D412yes—
54C4⋊C4×C107—21no—
55C4⋊C4×C107—21no—
56C22⋊C4×C107—21no—
57C22⋊C4×C107—21no—
58C42×C107—21no—
59C42×C107C2×C412yes—
60C23×C107C2×D411yescharacteristic
61C22×D107C22⋊C412yes—
62C2×C4×C107—22no—
63C2×C4×C107—41no—
64C2×C4×C107C22×C411yescharacteristic
65C2×C4×C107C2×D411yescharacteristic
66C2×C4×C107C2×D411yescharacteristic
67C2×C4×C107C2×D411yescharacteristic
68C2×C4×C107#4111yescharacteristic
69C2×C4×C107#4111yescharacteristic
70C22⋊D107—22no—
71C22⋊D107—22no—
72C2×Dic107—22no—
73C2×Dic107—41no—
74C2×Dic107—41no—
75C2×Dic107—41no—
76C2×Dic107C22⋊C412yes—
77D428—21no—
78D428—21no—
79C4×D107—22no—
80C4×D107—22no—
81Dic214—21no—
82Dic214—21no—
83Dic214—22no—
84Dic214—22no—
85Dic214—41no—
86Dic214—41no—
87C8×C107—22no—
88C107⋊C8—22no—
89C22×C107—41no—
90C22×C107C2×C22⋊C411yescharacteristic
91C22×C107#12111yescharacteristic
92C22×C107#12111yescharacteristic
93C2×D107—22no—
94C2×D107—42no—
95C4×C107—42no—
96C4×C107—81no—
97C4×C107C4×D411yescharacteristic
98C4×C107C4×D411yescharacteristic
99C4×C107#12011yescharacteristic
100C4×C107#12311yescharacteristic
101Dic107—22no—
102Dic107—42no—
103Dic107—81no—
104C2×C107—21no—
105C2×C107—21no—
106C2×C107—21no—
107C2×C107#38611yescharacteristic
108D107—42no—
109#1909—1071nomaximal, Sylow
110C107#190911yescharacteristic, complemented, Sylow
111#568—1071no—
112#536—1071no—
113#419—1071no—
114#419—1071no—
115#410—1071no—
116H(3,ℤ/4)—1071no—
117H(3,ℤ/4)D10711yescharacteristic, complemented
118C2×#41—1071no—
119C22×Q8—1071no—
120#131—2142no—
121#131—2142no—
122C2×M16—1071no—
123C2×M16—2142no—
124C2×M16C2×D10711yescharacteristic
125C4⋊Q8—1072no—
126#124—1072no—
127#123—2142no—
128C22⋊Q8—2142no—
129#117—1071no—
130#117C2×D10711yescharacteristic
131#117C2×D10711yescharacteristic
132#103—2142no—
133#103—2142no—
134#99—2142no—
135#41—2141no—
136#41—2141no—
137#41—2141no—
138#41—2141no—
139C2×Q8—1071no—
140C2×Q8—1072no—
141C2×Q8—2141no—
142C2×Q8—2141no—
143C2×Q8—2141no—
144C2×Q8—2141no—
145C2×Q8—2141no—
146C2×D4—1072no—
147C2×D4—1071no—
148C22×C4—1072no—
149C22×C4—2141no—
150C22×C4C22×D10711yescharacteristic
151M16—21no—
152M16—21no—
153M16—2144no—
154M16—2141no—
155M16—2141no—
156C2×C8—1072no—
157C2×C8—2144no—
158C2×C8D42812yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—2144no—
162C4⋊C4—2141no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—2144no—
166C22⋊C4—2141no—
167C42—21no—
168C42—2141no—
169C42C4×D10712yes—
170C23—1072no—
171C23D4×D10711yescharacteristic
172Q8—4281no—
173Q8—4281no—
174Q8—2142no—
175Q8—2142no—
176Q8—2141no—
177Q8—2141no—
178D4—2142no—
179D4—2142no—
180D4—2141no—
181D4—2141no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—1072no—
185C2×C4—4281no—
186C2×C4—4281no—
187C2×C4—4281no—
188C2×C4—2142no—
189C2×C4—2142no—
190C2×C4—2142no—
191C2×C4C2×C4×D10711yescharacteristic
192C2×C4D4×D10711yescharacteristic
193C2×C4D4×D10711yescharacteristic
194C2×C4C2×D42811yescharacteristic
195C2×C4#1313381811yescharacteristic
196C2×C4#1313381911yescharacteristic
197C8—22no—
198C8—2142no—
199C22—41no—
200C22—4282no—
201C22—2142no—
202C22C22⋊C4×D10711yescharacteristic
203C22#1681208211yescharacteristic
204C22#1681208411yescharacteristic
205C4—42no—
206C4—81no—
207C4—8561no—
208C4—4282no—
209C4—2142no—
210C4#1681207111yescharacteristic
211C4C4×D42811yescharacteristic
212C4#1681207911yescharacteristic
213C4#1681209411yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—4282no—
218C2#2029250511yescharacteristic
subgroupG/H
centerC2#20292505
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
FittingH(3,ℤ/4)×C107C2
socleC2×C107#386
prime radicalC2×#13133818C22
cosocleC22×C4×C107C23
hypercenterH(3,ℤ/4)D107
hypocenterC107#1909
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
3. #20292637C2semidirect
4. #20292635C2semidirect
6. #20292383C2semidirect
7. H(3,ℤ/4)×C107C2semidirect
14. #16812109C4semidirect
15. #16812097C4semidirect
110. C107#1909semidirect
117. H(3,ℤ/4)D107semidirect

Maximal subgroups

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

subgroupindex
#202933932
#202932032
#202926372
#202926352
#202926002
#202923832
H(3,ℤ/4)×C1072
#1909107