Finite Group Databasebeta

← #28361724

Subgroups — #28361724

Order 13952.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#20295574C211yesmaximal, characteristic
2#20295082C211yesmaximal, characteristic, complemented
3C4⋊C8×D109C211yesmaximal, characteristic, complemented
4#20294774C211yesmaximal, characteristic, complemented
5#20294774C211yesmaximal, characteristic, complemented
6#20294770C211yesmaximal, characteristic, complemented
7#331×C109C211yesmaximal, characteristic, complemented
8C2×#13182028C412yes—
9C2×C8×D109—21no—
10#16812699C2211yescharacteristic
11#16812686C412yes—
12#16812670—21no—
13#16812670—21no—
14D4×Dic109—21no—
15D4×Dic109—21no—
16C42×D109C2211yescharacteristic
17C4⋊#11724784C2211yescharacteristic
18C4⋊#11724784C2211yescharacteristic
19#16812628—21no—
20#16812611—21no—
21#16812609—21no—
22#127×C109C2211yescharacteristic
23C4⋊C8×C109C2211yescharacteristic
24C4⋊C8×C109C2211yescharacteristic
25#13182028—44no—
26C2×Dic218C2×C412yes—
27C2×C22⋊D109—22no—
28C22×Dic109—22no—
29C2×C4×D109C2×C411yescharacteristic
30C2×C4×D109D411yescharacteristic
31C2×C4×D109D411yescharacteristic
32C2×#11724784—21no—
33C2×#11724784—21no—
34C8×D109—42no—
35C4⋊Dic109—21no—
36C4⋊Dic109—21no—
37C22⋊Dic109—22no—
38C22⋊Dic109—22no—
39C4×Dic109C2×C411yescharacteristic
40C4×Dic109D411yescharacteristic
41C4×Dic109D411yescharacteristic
42C2×D4×C109—21no—
43C2×D4×C109—21no—
44C2×D4×C109C2×C412yes—
45C2×C8×C109—21no—
46C2×C8×C109—21no—
47C42×C109C2311yescharacteristic
48C23×C109—22no—
49C22×D109C22⋊C411yescharacteristic
50D4×C109—42no—
51D4×C109—41no—
52D4×C109—41no—
53D4×C109—41no—
54D4×C109—41no—
55C2×C4×C109C22×C411yescharacteristic
56C2×C4×C109C2×D411yescharacteristic
57C2×C4×C109C2×D411yescharacteristic
58C22⋊D109—44no—
59C2×Dic109—22no—
60C2×Dic109—44no—
61C2×Dic109C22⋊C411yescharacteristic
62C2×Dic109C22⋊C411yescharacteristic
63C2×Dic109C22⋊C411yescharacteristic
64C4×D109—22no—
65C4×D109—21no—
66C4×D109—21no—
67C4×D109—21no—
68C4×D109—21no—
69Dic218—42no—
70C8×C109—41no—
71C8×C109—41no—
72#11724784—41no—
73#11724784—41no—
74C22×C109—42no—
75C22×C109—42no—
76C22×C109—42no—
77C22×C109C2×C22⋊C411yescharacteristic
78C2×D109—21no—
79C2×D109—21no—
80C2×D109#10012yes—
81C4×C109—21no—
82C4×C109#13511yescharacteristic
83C4×C109#13511yescharacteristic
84C4×C109AGL(1,ℤ/8)11yescharacteristic
85C4×C109#13711yescharacteristic
86Dic109—21no—
87Dic109—21no—
88Dic109—21no—
89Dic109—42no—
90C2×C109—82no—
91C2×C109C2×#10011yescharacteristic
92C2×C109#41611yescharacteristic
93C2×C109#41711yescharacteristic
94D109—22no—
95#1551—1091nomaximal, Sylow
96C109#155111yescharacteristic, complemented, Sylow
97#532—1091no—
98#432—1091no—
99C2×C4⋊C8—1091no—
100#333—1091no—
101#333—1091no—
102#331—1091no—
103#331D10911yescharacteristic, complemented
104C2×#41—1092no—
105C22×C8—2181no—
106C4⋊Q8—1091no—
107#127C2×D10911yescharacteristic
108#124—1092no—
109#121—2181no—
110#121—2181no—
111C4×D4—2181no—
112C4×D4—2181no—
113C2×C42—1091no—
114C4⋊C8—1091no—
115C4⋊C8—1091no—
116C4⋊C8—2181no—
117C4⋊C8C2×D10911yescharacteristic
118C4⋊C8C2×D10911yescharacteristic
119C22⋊C8—2181no—
120#97—2181no—
121#41—4364no—
122C2×Q8—1092no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—2182no—
126C2×D4C4×D10912yes—
127C22×C4—1091no—
128C22×C4—1091no—
129C22×C4—1091no—
130C22×C4—2182no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—4362no—
134C2×C8—2181no—
135C2×C8—2181no—
136C4⋊C4—2181no—
137C4⋊C4—2181no—
138C22⋊C4—2182no—
139C22⋊C4—2182no—
140C42—1091no—
141C42—1091no—
142C42—1091no—
143C42C22×D10911yescharacteristic
144C23—22no—
145C23—1091no—
146Q8—4362no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4—4364no—
153C2×C4—1091no—
154C2×C4—1091no—
155C2×C4—1091no—
156C2×C4—4364no—
157C2×C4—2182no—
158C2×C4—2182no—
159C2×C4—2181no—
160C2×C4—2181no—
161C2×C4—2181no—
162C2×C4—2181no—
163C2×C4C2×C4×D10911yescharacteristic
164C2×C4D4×D10911yescharacteristic
165C2×C4D4×D10911yescharacteristic
166C8—41no—
167C8—41no—
168C8—4361no—
169C8—4361no—
170C22—42no—
171C22—42no—
172C22—42no—
173C22—1092no—
174C22—2181no—
175C22—2181no—
176C22C22⋊C4×D10911yescharacteristic
177C4—21no—
178C4—4362no—
179C4—2181no—
180C4—2181no—
181C4—2181no—
182C4#1681271811yescharacteristic
183C4#1681272011yescharacteristic
184C4#1681272311yescharacteristic
185C4#1681272811yescharacteristic
186C2—82no—
187C2—2182no—
188C2#100×D10911yescharacteristic
189C2#2029501911yescharacteristic
190C2#2029502411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D109
commutatorC2×C4×C109C22×C4
FrattiniC42C22×D109
Fitting#331×C109C2
socleC22×C109C2×C22⋊C4
prime radical#20295574C2
cosocleC42×C109C23
hypercenter#331D109
hypocenterC109#1551
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #20295082C2semidirect
3. C4⋊C8×D109C2semidirect
4. #20294774C2semidirect
5. #20294774C2semidirect
6. #20294770C2semidirect
7. #331×C109C2semidirect
96. C109#1551semidirect
103. #331D109semidirect

Maximal subgroups

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

subgroupindex
#202955742
#202950822
C4⋊C8×D1092
#202947742
#202947702
#331×C1092
#1551109