Finite Group Databasebeta

← #28338144

Subgroups — #28338144

Order 13696.

250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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#20293173C211yesmaximal, characteristic
2#20292611C211yesmaximal, characteristic, complemented
3#20292425C212yesmaximal, complemented
4#20292423C212yesmaximal, complemented
5#413×C107C211yesmaximal, characteristic, complemented
6C2×#13133818C411yescharacteristic
7C2×#13133802—21no—
8#16812107C2211yescharacteristic
9#16812105C411yescharacteristic
10#16812098C2211yescharacteristic
11#16812096C411yescharacteristic
12#16812081—21no—
13#16812081—21no—
14C4×C22⋊D107—21no—
15C4×C22⋊D107—21no—
16C2×C4×Dic107C411yescharacteristic
17#16812028C2212yes—
18#16812026—21no—
19C2×#41×C107C2211yescharacteristic
20C2×M16×C107—21no—
21#101×C107C2212yes—
22#100×C107—21no—
23#13133818—41no—
24#13133818—41no—
25C2×Dic214C2×C411yescharacteristic
26C2×D428C2×C411yescharacteristic
27C2×C22⋊D107—21no—
28C2×C22⋊D107—21no—
29C2×C22⋊D107—21no—
30C22×Dic107—21no—
31C2×C4×D107—21no—
32#13133802—22no—
33#13133802—41no—
34C2×C107⋊C8—41no—
35Dic107⋊C4—21no—
36Dic107⋊C4—21no—
37C22⋊Dic107—21no—
38C22⋊Dic107—21no—
39(C2×D107)⋊C4—21no—
40(C2×D107)⋊C4—21no—
41C4×Dic107—21no—
42C4×Dic107C2×C411yescharacteristic
43C4×Dic107C2×C411yescharacteristic
44#41×C107—41no—
45#41×C107—41no—
46C2×Q8×C107C2311yescharacteristic
47C2×D4×C107C2×C411yescharacteristic
48C2×D4×C107D411yescharacteristic
49C2×D4×C107D411yescharacteristic
50C22×C4×C107C2×C411yescharacteristic
51C22×C4×C107D411yescharacteristic
52C22×C4×C107D411yescharacteristic
53M16×C107—22no—
54M16×C107—41no—
55C2×C8×C107—41no—
56C23×C107C22⋊C411yescharacteristic
57C23×C107C22⋊C411yescharacteristic
58C23×C107C22⋊C411yescharacteristic
59C22×D107—21no—
60Q8×C107—41no—
61D4×C107—41no—
62D4×C107—41no—
63D4×C107—41no—
64C2×C4×C107—21no—
65C2×C4×C107—21no—
66C2×C4×C107—21no—
67C2×C4×C107—21no—
68C2×C4×C107—21no—
69C2×C4×C107—21no—
70C2×C4×C107C22⋊C411yescharacteristic
71C2×C4×C107C22×C411yescharacteristic
72C2×C4×C107C2×D411yescharacteristic
73C2×C4×C107C2×D411yescharacteristic
74C22⋊D107—42no—
75C22⋊D107—42no—
76C22⋊D107—42no—
77C2×Dic107—21no—
78C2×Dic107—21no—
79C2×Dic107—21no—
80C2×Dic107—42no—
81D428—41no—
82C4×D107—41no—
83C4×D107—41no—
84Dic214—41no—
85C8×C107—42no—
86C107⋊C8—42no—
87C22×C107—21no—
88C22×C107—21no—
89C22×C107—21no—
90C22×C107—41no—
91C22×C107—41no—
92C22×C107—41no—
93C22×C107C2×C22⋊C411yescharacteristic
94C2×D107—41no—
95C2×D107—41no—
96C2×D107—41no—
97C4×C107—21no—
98C4×C107—21no—
99C4×C107—21no—
100C4×C107#9911yescharacteristic
101C4×C107#9911yescharacteristic
102Dic107—22no—
103Dic107—41no—
104Dic107—41no—
105C2×C107—21no—
106C2×C107—41no—
107C2×C107—41no—
108C2×C107—41no—
109C2×C107C2×#9911yescharacteristic
110D107—81no—
111#2132—1071nomaximal, Sylow
112C107#213211yescharacteristic, complemented, Sylow
113#532—1071no—
114#413—1071no—
115#413D10711yescharacteristic, complemented
116#356—1072no—
117#355—1072no—
118C2×#41—1071no—
119C2×#41C2×D10711yescharacteristic
120C2×M16—21no—
121C2×M16—2141no—
122C4⋊Q8—1071no—
123#127—1071no—
124#124—1071no—
125#124—1071no—
126#121—2141no—
127#121—2141no—
128C4×D4—2141no—
129C4×D4—2141no—
130C2×C42—1071no—
131#101—1072no—
132#101C2×D10712yes—
133#100—21no—
134#100—2141no—
135#41—41no—
136#41—41no—
137#41—4281no—
138#41—4281no—
139C2×Q8—1071no—
140C2×Q8C22×D10711yescharacteristic
141C2×D4—1071no—
142C2×D4—2141no—
143C2×D4—2141no—
144C2×D4—2141no—
145C2×D4C4×D10711yescharacteristic
146C2×D4D42811yescharacteristic
147C2×D4C22⋊D10711yescharacteristic
148C22×C4—2141no—
149C22×C4—2141no—
150C22×C4C4×D10711yescharacteristic
151C22×C4D42811yescharacteristic
152C22×C4C22⋊D10711yescharacteristic
153M16—22no—
154M16—41no—
155M16—4281no—
156M16—2142no—
157C2×C8—41no—
158C2×C8—4281no—
159C4⋊C4—2141no—
160C4⋊C4—2141no—
161C22⋊C4—2141no—
162C22⋊C4—2141no—
163C22⋊C4—2141no—
164C22⋊C4—2141no—
165C42—1071no—
166C42—1071no—
167C42—2141no—
168C23—2141no—
169C23(C2×D107)⋊C411yescharacteristic
170C23(C2×D107)⋊C411yescharacteristic
171C23(C2×D107)⋊C411yescharacteristic
172Q8—41no—
173Q8—4281no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—4281no—
178D4—4282no—
179D4—4282no—
180D4—4282no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—4282no—
188C2×C4—4281no—
189C2×C4—4281no—
190C2×C4—2141no—
191C2×C4—2141no—
192C2×C4—2141no—
193C2×C4(C2×D107)⋊C411yescharacteristic
194C2×C4C2×C4×D10711yescharacteristic
195C2×C4C2×C22⋊D10711yescharacteristic
196C2×C4C2×D42811yescharacteristic
197C8—42no—
198C8—4282no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—4281no—
206C22—4281no—
207C22—4281no—
208C22C2×(C2×D107)⋊C411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—4281no—
213C4—4281no—
214C4—2142no—
215C4#1681202311yescharacteristic
216C4#1681202311yescharacteristic
217C2—21no—
218C2—41no—
219C2—41no—
220C2—41no—
221C2—8561no—
222C2C2×#1681202311yescharacteristic
subgroupG/H
centerC4#16812023
commutatorC2×C4×C107C22×C4
FrattiniC2×Q8C22×D107
Fitting#413×C107C2
socleC2×C107C2×#99
prime radical#20293173C2
cosocleC2×Q8×C107C23
hypercenter#413D107
hypocenterC107#2132
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #20292611C2semidirect
3. #20292425C2semidirect
4. #20292423C2semidirect
5. #413×C107C2semidirect
112. C107#2132semidirect
115. #413D107semidirect

Maximal subgroups

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

subgroupindex
#202931732
#202926112
#202924252
#202924232
#413×C1072
#2132107