Finite Group Databasebeta

← #28336563

Subgroups — #28336563

Order 13696.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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#20293095C211yesmaximal, characteristic
2#20292609C211yesmaximal, characteristic
3#20292600C211yesmaximal, characteristic
4#20292388C211yesmaximal, characteristic, complemented
5#20292386C211yesmaximal, characteristic, complemented
6#20292383C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C107C211yesmaximal, characteristic, complemented
8C2×#13133818C2211yescharacteristic
9C2×#13133802C2211yescharacteristic
10#16812074—21no—
11#16812071—21no—
12(C22⋊D107)⋊C4—22no—
13#16812068C2211yescharacteristic
14#16812066C412yescomplemented
15C2×C4×Dic107C2211yescharacteristic
16C42×D107C412yescomplemented
17#16812027—21no—
18#16812025—21no—
19#16812023—22no—
20C2×M16×C107C2211yescharacteristic
21#117×C107C2211yescharacteristic
22#117×C107C2211yescharacteristic
23#13133818—21no—
24#13133818—21no—
25#13133818—21no—
26#13133818—21no—
27C2×Dic214D411yescharacteristic
28C2×D428D411yescharacteristic
29C2×C22⋊D107D412yes—
30C22×Dic107—21no—
31C2×C4×D107—22no—
32C2×C4×D107C2×C412yes—
33#13133802—21no—
34#13133802—21no—
35C2×C107⋊C8—21no—
36C4⋊Dic107—21no—
37Dic107⋊C4—22no—
38C22⋊Dic107—21no—
39(C2×D107)⋊C4—22no—
40C4×Dic107—21no—
41C4×Dic107—22no—
42C4×Dic107—21no—
43C4×Dic107C2×C411yescharacteristic
44C4×Dic107C2×C411yescharacteristic
45C22×C4×C107C2311yescharacteristic
46M16×C107—21no—
47M16×C107—21no—
48C2×C8×C107—21no—
49C4⋊C4×C107—21no—
50C4⋊C4×C107—21no—
51C22⋊C4×C107—21no—
52C22⋊C4×C107—21no—
53C42×C107—21no—
54C42×C107C2×C412yes—
55C23×C107C2×D411yescharacteristic
56C22×D107C22⋊C412yes—
57C2×C4×C107—22no—
58C2×C4×C107—41no—
59C2×C4×C107C22×C411yescharacteristic
60C2×C4×C107C2×D411yescharacteristic
61C2×C4×C107#4111yescharacteristic
62C2×C4×C107#4111yescharacteristic
63C2×C4×C107#4111yescharacteristic
64C2×C4×C107#4111yescharacteristic
65C22⋊D107—22no—
66C22⋊D107—22no—
67C2×Dic107—21no—
68C2×Dic107—21no—
69C2×Dic107—42no—
70C2×Dic107—41no—
71C2×Dic107C22⋊C412yes—
72D428—21no—
73D428—21no—
74C4×D107—22no—
75C4×D107—22no—
76C4×D107—44no—
77Dic214—21no—
78Dic214—21no—
79C8×C107—41no—
80C107⋊C8—41no—
81C22×C107—41no—
82C22×C107C2×C22⋊C411yescharacteristic
83C22×C107#12311yescharacteristic
84C22×C107#12311yescharacteristic
85C2×D107—22no—
86C2×D107—42no—
87C4×C107—42no—
88C4×C107—81no—
89C4×C107#11711yescharacteristic
90C4×C107#11711yescharacteristic
91C4×C107#12311yescharacteristic
92C4×C107#12311yescharacteristic
93Dic107—22no—
94Dic107—22no—
95Dic107—41no—
96Dic107—81no—
97C2×C107—21no—
98C2×C107—21no—
99C2×C107—21no—
100C2×C107#38111yescharacteristic
101D107—42no—
102#1827—1071nomaximal, Sylow
103C107#182711yescharacteristic, complemented, Sylow
104C4×#41—1071no—
105#413—1071no—
106#410—1071no—
107#339—1071no—
108#339—1071no—
109H(3,ℤ/4)—1071no—
110H(3,ℤ/4)D10711yescharacteristic, complemented
111C2×#41—1071no—
112C2×M16—1071no—
113C2×M16C2×D10711yescharacteristic
114C4×Q8—2141no—
115C4×D4—2142no—
116C4×D4—2141no—
117#117—1072no—
118#117—1071no—
119#117C2×D10711yescharacteristic
120#117C2×D10711yescharacteristic
121C2×C42—1071no—
122C2×C42—1072no—
123#101—2141no—
124#100—2141no—
125#99—2142no—
126#41—2141no—
127#41—2141no—
128#41—2141no—
129#41—2141no—
130C2×Q8—1071no—
131C2×D4—1072no—
132C2×D4—1071no—
133C22×C4—1072no—
134C22×C4—2142no—
135C22×C4—2141no—
136C22×C4C22×D10711yescharacteristic
137M16—21no—
138M16—21no—
139M16—2141no—
140M16—2141no—
141C2×C8—21no—
142C2×C8—2141no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—2142no—
146C4⋊C4—2141no—
147C22⋊C4—21no—
148C22⋊C4—21no—
149C22⋊C4—2142no—
150C22⋊C4—2141no—
151C42—21no—
152C42—1071no—
153C42—1071no—
154C42—2142no—
155C42—2141no—
156C42—2141no—
157C42C4×D10712yes—
158C23—1072no—
159C23D4×D10711yescharacteristic
160Q8—2141no—
161Q8—2141no—
162D4—2142no—
163D4—2142no—
164D4—2141no—
165D4—2141no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—1072no—
169C2×C4—4284no—
170C2×C4—4281no—
171C2×C4—4282no—
172C2×C4—2141no—
173C2×C4—2141no—
174C2×C4—2142no—
175C2×C4—2142no—
176C2×C4C2×C4×D10711yescharacteristic
177C2×C4D4×D10711yescharacteristic
178C2×C4#1313381711yescharacteristic
179C2×C4#1313381811yescharacteristic
180C2×C4#1313381811yescharacteristic
181C2×C4#1313381911yescharacteristic
182C8—41no—
183C8—4281no—
184C22—41no—
185C22—4282no—
186C22—2142no—
187C22C22⋊C4×D10711yescharacteristic
188C22#1681209111yescharacteristic
189C22#1681209411yescharacteristic
190C4—42no—
191C4—81no—
192C4—8561no—
193C4—4281no—
194C4—2142no—
195C4—2142no—
196C4#1681206611yescharacteristic
197C4#1681206711yescharacteristic
198C4#1681209111yescharacteristic
199C4#1681209411yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—4282no—
204C2#2029248911yescharacteristic
subgroupG/H
centerC4#16812066
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
FittingH(3,ℤ/4)×C107C2
socleC2×C107#381
prime radicalC2×#13133818C22
cosocleC22×C4×C107C23
hypercenterH(3,ℤ/4)D107
hypocenterC107#1827
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C4 ◁ #117 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #20292388C2semidirect
5. #20292386C2semidirect
6. #20292383C2semidirect
7. H(3,ℤ/4)×C107C2semidirect
14. #16812066C4semidirect
16. C42×D107C4semidirect
103. C107#1827semidirect
110. 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
#202930952
#202926092
#202926002
#202923882
#202923862
#202923832
H(3,ℤ/4)×C1072
#1827107