Finite Group Databasebeta

← #28378384

Subgroups — #28378384

Order 13952.

230 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 62 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#20296048C211yesmaximal, characteristic, complemented
2C4×D109⋊C8C211yesmaximal, characteristic, complemented
3Q8⋊#11724786C212yesmaximal, complemented
4D4⋊#11724786C212yesmaximal, complemented
5#20295555C211yesmaximal, characteristic
6C2×D109⋊C8—21no—
7C4⋊#11724786C2212yes—
8#16812756—21no—
9#16812754—21no—
10C4×#11724786—21no—
11C4×#11724786C2212yes—
12#16812692—21no—
13#16812691C411yescharacteristic
14#16812681—21no—
15#16812675C411yescharacteristic
16#16812670C411yescharacteristic
17Q8×Dic109C2211yescharacteristic
18D4×Dic109C2211yescharacteristic
19#16812659—21no—
20#16812655—21no—
21C42×D109C2211yescharacteristic
22#124×C109C411yescharacteristic
23D109⋊C8—24no—
24C2×#11724786—22no—
25C2×#11724786—22no—
26C2×C22⋊D109—21no—
27C22×Dic109—21no—
28C2×C4×D109C2×C411yescharacteristic
29C2×C4×D109D411yescharacteristic
30C2×C4×D109D411yescharacteristic
31C4⋊Dic109—21no—
32C4⋊Dic109C2×C411yescharacteristic
33C4⋊Dic109C2×C411yescharacteristic
34#13182008—21no—
35#13182008—21no—
36#13182008—21no—
37C22⋊Dic109—21no—
38C22⋊Dic109—21no—
39#13182006—21no—
40C4×Dic109—21no—
41C4×Dic109D411yescharacteristic
42C4×Dic109D411yescharacteristic
43C4×Dic109C2311yescharacteristic
44C2×Q8×C109C2×C411yescharacteristic
45C2×D4×C109C2×C411yescharacteristic
46C22⋊C4×C109—21no—
47C22⋊C4×C109—21no—
48C42×C109C2×C411yescharacteristic
49C23×C109—21no—
50C22×D109C22⋊C411yescharacteristic
51Q8×C109—22no—
52D4×C109—22no—
53C2×C4×C109—21no—
54C2×C4×C109C22⋊C411yescharacteristic
55C2×C4×C109C22⋊C411yescharacteristic
56C2×C4×C109C22×C411yescharacteristic
57C22⋊D109—42no—
58C2×Dic109—21no—
59C2×Dic109—21no—
60C2×Dic109—42no—
61C2×Dic109C22⋊C411yescharacteristic
62C2×Dic109C2×D411yescharacteristic
63C2×Dic109C2×D411yescharacteristic
64C4×D109—22no—
65C4×D109—22no—
66C4×D109—22no—
67#11724786—24no—
68#11724786—42no—
69C22×C109—41no—
70C22×C109—41no—
71C22×C109—41no—
72C22×C109C2×C22⋊C411yescharacteristic
73C2×D109—21no—
74C2×D109—21no—
75C2×D109#10412yes—
76C4×C109—21no—
77C4×C109—21no—
78C4×C109—41no—
79C4×C109#13112yes—
80Dic109—21no—
81Dic109—21no—
82Dic109—41no—
83Dic109—41no—
84Dic109#13512yes—
85C2×C109—81no—
86C2×C109#40811yescharacteristic
87C2×C109#41611yescharacteristic
88C2×C109C2×#10411yescharacteristic
89D109—22no—
90#1494—1091nomaximal, Sylow
91C109#149411yescharacteristic, complemented, Sylow
92#529—1091no—
93#432—1091no—
94C2×C4×C8—1091no—
95Q8⋊C8—1092no—
96D4⋊C8—1092no—
97C22×C8—2181no—
98#126—2181no—
99#125—1091no—
100#124#8913711yescharacteristic
101#123—2181no—
102C22⋊Q8—1091no—
103#121—1091no—
104C4×Q8—1091no—
105C4×D4—1091no—
106C4×D4—2181no—
107#117—2181no—
108C2×C42—1091no—
109C4⋊C8—1092no—
110C22⋊C8—2181no—
111#97—2181no—
112C4×C8—1092no—
113C4×C8—2181no—
114C2×Q8C2×#8913711yescharacteristic
115C2×D4—2181no—
116C2×D4C2×#8913711yescharacteristic
117C22×C4—1091no—
118C22×C4—1091no—
119C22×C4—1091no—
120C22×C4—2181no—
121C2×C8—2182no—
122C2×C8—2182no—
123C2×C8—2184no—
124C4⋊C4—1091no—
125C4⋊C4—1091no—
126C4⋊C4—2181no—
127C4⋊C4—2181no—
128C4⋊C4—2181no—
129C4⋊C4—2181no—
130C22⋊C4—21no—
131C22⋊C4—21no—
132C22⋊C4—2181no—
133C22⋊C4—2181no—
134C22⋊C4—2181no—
135C42—1091no—
136C42—1091no—
137C42—1091no—
138C42—2181no—
139C42C2×#8913711yescharacteristic
140C23—21no—
141C23—1091no—
142Q8—22no—
143D4—22no—
144D4—4362no—
145C2×C4—21no—
146C2×C4—1091no—
147C2×C4—1091no—
148C2×C4—1091no—
149C2×C4—4362no—
150C2×C4—2182no—
151C2×C4—2182no—
152C2×C4—2181no—
153C2×C4—2181no—
154C2×C4—2182no—
155C2×C4C22⋊#8913711yescharacteristic
156C2×C4C22⋊#8913711yescharacteristic
157C2×C4C22×#8913711yescharacteristic
158C8—4362no—
159C8—2184no—
160C22—41no—
161C22—41no—
162C22—41no—
163C22—1092no—
164C22—2181no—
165C22—2181no—
166C22C2×C22⋊#8913711yescharacteristic
167C4—21no—
168C4—21no—
169C4—41no—
170C4—1092no—
171C4—4361no—
172C4—4361no—
173C4—2181no—
174C4—2181no—
175C4#1681278612yes—
176C2—81no—
177C2—2182no—
178C2#2029600011yescharacteristic
179C2#2029601611yescharacteristic
180C2D109⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#124×C109C4
socleC22×C109C2×C22⋊C4
prime radical#16812670C4
cosocleC4×Dic109C23
hypercenter#124#89137
hypocenterC109#1494
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #20296048C2semidirect
2. C4×D109⋊C8C2semidirect
3. Q8⋊#11724786C2semidirect
4. D4⋊#11724786C2semidirect
91. C109#1494semidirect

Maximal subgroups

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

subgroupindex
#202960482
C4×D109⋊C82
Q8⋊#117247862
D4⋊#117247862
#202955552
#1494109