Finite Group Databasebeta

← #28335037

Subgroups — #28335037

Order 13696.

218 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 61 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#20293163C211yesmaximal, characteristic
2#20292677C211yesmaximal, characteristic, complemented
3#20292494C211yesmaximal, characteristic, complemented
4#20292364C211yesmaximal, characteristic, complemented
5#20292362C211yesmaximal, characteristic
6#20292360C211yesmaximal, characteristic
7#328×C107C211yesmaximal, characteristic, complemented
8#16812104—21no—
9#16812100C411yescharacteristic, complemented
10#16812098C411yescharacteristic, complemented
11#16812093—21no—
12#16812083C2211yescharacteristic
13Q8×Dic107C411yescharacteristic, complemented
14#16812071C411yescharacteristic, complemented
15(C22⋊D107)⋊C4—21no—
16#16812067—21no—
17C2×C4×Dic107C2211yescharacteristic
18Dic107⋊C8—21no—
19C22⋊(C107⋊C8)C2211yescharacteristic
20C8×Dic107—21no—
21C107⋊#95—21no—
22C107⋊#95—21no—
23C107⋊#95C2211yescharacteristic
24C22⋊Q8×C107C2211yescharacteristic
25C22⋊C8×C107C2211yescharacteristic
26#95×C107C2211yescharacteristic
27C2×D428C2×C411yescharacteristic
28C2×C22⋊D107—21no—
29C22×Dic107—21no—
30C22×Dic107D411yescharacteristic
31C22×Dic107D411yescharacteristic
32C2×C4×D107—21no—
33C2×C107⋊C8—21no—
34C4⋊Dic107—21no—
35C4⋊Dic107—21no—
36C4⋊Dic107C2×C411yescharacteristic
37Dic107⋊C4—21no—
38(C2×D107)⋊C4—21no—
39(C2×D107)⋊C4—21no—
40(C2×D107)⋊C4—21no—
41(C2×D107)⋊C4—21no—
42C4×Dic107—21no—
43C4×Dic107C2×C411yescharacteristic
44C4×Dic107C2×C411yescharacteristic
45C4×Dic107D411yescharacteristic
46C4×Dic107D411yescharacteristic
47C2×Q8×C107C2×C411yescharacteristic
48C22×C4×C107—21no—
49C22×C4×C107C2311yescharacteristic
50C2×C8×C107—21no—
51C4⋊C4×C107—21no—
52C4⋊C4×C107C2×C411yescharacteristic
53C22⋊C4×C107—21no—
54C23×C107C2×D411yescharacteristic
55C22×D107—21no—
56Q8×C107—41no—
57C2×C4×C107—21no—
58C2×C4×C107—21no—
59C2×C4×C107—41no—
60C2×C4×C107—41no—
61C2×C4×C107—41no—
62C2×C4×C107—41no—
63C2×C4×C107C22×C411yescharacteristic
64C2×C4×C107C2×D411yescharacteristic
65C22⋊D107—41no—
66C22⋊D107—41no—
67C2×Dic107—21no—
68C2×Dic107—21no—
69C2×Dic107—21no—
70C2×Dic107—41no—
71C2×Dic107—41no—
72C2×Dic107—41no—
73C2×Dic107—41no—
74C2×Dic107C22⋊C411yescharacteristic
75C2×Dic107C22⋊C411yescharacteristic
76C2×Dic107C22⋊C411yescharacteristic
77C2×Dic107C22⋊C411yescharacteristic
78D428—41no—
79C4×D107—42no—
80C8×C107—41no—
81C107⋊C8—41no—
82C22×C107—21no—
83C22×C107—21no—
84C22×C107C2×C22⋊C411yescharacteristic
85C22×C107#13511yescharacteristic
86C22×C107#13511yescharacteristic
87C2×D107—41no—
88C2×D107—41no—
89C2×D107—41no—
90C4×C107—21no—
91C4×C107—21no—
92C4×C107—41no—
93C4×C107—41no—
94C4×C107—81no—
95Dic107—21no—
96Dic107—21no—
97Dic107—21no—
98Dic107—21no—
99Dic107—41no—
100Dic107—81no—
101C2×C107—21no—
102C2×C107—21no—
103C2×C107#41011yescharacteristic
104C2×C107#41611yescharacteristic
105C2×C107#42111yescharacteristic
106D107—81no—
107#1521—1071nomaximal, Sylow
108C107#152111yescharacteristic, complemented, Sylow
109#529—1071no—
110#431—1071no—
111#383—1071no—
112#328—1071no—
113#328D10711yescharacteristic, complemented
114#327—1071no—
115#327—1071no—
116#126—2141no—
117#125—1071no—
118#124—1071no—
119#123—2141no—
120C22⋊Q8C2×D10711yescharacteristic
121#121—1071no—
122C4×Q8—1071no—
123C4×D4—1071no—
124C4×D4—2141no—
125#117—2141no—
126C2×C42—1071no—
127C4⋊C8—2141no—
128C22⋊C8—1071no—
129C22⋊C8C2×D10711yescharacteristic
130C4×C8—2141no—
131#95—1071no—
132#95—2141no—
133#95—2141no—
134#95C2×D10711yescharacteristic
135C2×Q8C4×D10711yescharacteristic
136C2×D4—1071no—
137C2×D4—2141no—
138C22×C4—21no—
139C22×C4—1071no—
140C22×C4—1071no—
141C22×C4—2141no—
142C22×C4—2141no—
143C22×C4C22×D10711yescharacteristic
144C2×C8—21no—
145C2×C8—2141no—
146C4⋊C4—21no—
147C4⋊C4—1071no—
148C4⋊C4—2141no—
149C4⋊C4—2141no—
150C4⋊C4—2141no—
151C4⋊C4C4×D10711yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—2141no—
154C22⋊C4—2141no—
155C22⋊C4—2141no—
156C22⋊C4—2141no—
157C42—1071no—
158C42—1071no—
159C42—1071no—
160C42—1071no—
161C42—2141no—
162C23—2141no—
163C23D4×D10711yescharacteristic
164Q8—41no—
165D4—4281no—
166D4—4281no—
167D4—4281no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—1071no—
175C2×C4—1071no—
176C2×C4—1071no—
177C2×C4—1071no—
178C2×C4—4282no—
179C2×C4—4281no—
180C2×C4—4281no—
181C2×C4—4281no—
182C2×C4—4281no—
183C2×C4—2141no—
184C2×C4—2141no—
185C2×C4—2141no—
186C2×C4C2×C4×D10711yescharacteristic
187C2×C4D4×D10711yescharacteristic
188C8—41no—
189C8—4281no—
190C22—21no—
191C22—21no—
192C22—4281no—
193C22—4281no—
194C22—4281no—
195C22C22⋊C4×D10711yescharacteristic
196C22#1681213011yescharacteristic
197C22#1681213211yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—8561no—
204C4—4281no—
205C4—2141no—
206C4—2141no—
207C4—2141no—
208C4—2141no—
209C2—21no—
210C2—21no—
211C2—8561no—
212C2#2029259911yescharacteristic
213C2#2029262211yescharacteristic
214C2#2029264211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#328×C107C2
socleC22×C107C2×C22⋊C4
prime radical#16812083C22
cosocleC22×C4×C107C23
hypercenter#328D107
hypocenterC107#1521
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #20292677C2semidirect
3. #20292494C2semidirect
4. #20292364C2semidirect
7. #328×C107C2semidirect
9. #16812100C4semidirect
10. #16812098C4semidirect
13. Q8×Dic107C4semidirect
14. #16812071C4semidirect
108. C107#1521semidirect
113. #328D107semidirect

Maximal subgroups

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

subgroupindex
#202931632
#202926772
#202924942
#202923642
#202923622
#202923602
#328×C1072
#1521107