Finite Group Databasebeta

← #28378465

Subgroups — #28378465

Order 13952.

220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 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#20296045C211yesmaximal, characteristic
2#20295970C211yesmaximal, characteristic
3#20295880C212yesmaximal
4#20295879C212yesmaximal
5#20295580C211yesmaximal, characteristic
6C2×C4⋊#89137—21no—
7C4⋊#11724786—21no—
8#16812756C2212yes—
9C4×#11724786—21no—
10(C2×#89137)⋊C4—21no—
11(C2×#89137)⋊C4C2212yes—
12#16812698C411yescharacteristic, complemented
13#16812697C411yescharacteristic, complemented
14#16812689—21no—
15#16812679C2211yescharacteristic
16#16812677—21no—
17#16812675C2211yescharacteristic
18C4×Dic218—21no—
19C4×Dic218C411yescharacteristic, complemented
20#16812656—21no—
21C42×D109C2211yescharacteristic
22C4×Q8×C109C411yescharacteristic, complemented
23C22×#89137—22no—
24C2×#11724786—22no—
25C4⋊#89137—42no—
26C2×Dic218—21no—
27C2×Dic218C2×C411yescharacteristic
28C2×C4×D109D411yescharacteristic
29C2×C4×D109D411yescharacteristic
30C2×C4×D109C2311yescharacteristic
31C4⋊Dic109—21no—
32C4⋊Dic109C2×C411yescharacteristic
33#13182008—21no—
34#13182008—21no—
35#13182008—21no—
36#13182008—21no—
37#13182008—21no—
38#13182006—21no—
39#13182006—21no—
40C4×Dic109—21no—
41C4×Dic109C2×C411yescharacteristic
42C4×Dic109D411yescharacteristic
43C4×Dic109D411yescharacteristic
44C2×Q8×C109C2×C411yescharacteristic
45C4⋊C4×C109—21no—
46C4⋊C4×C109C2×C411yescharacteristic
47C42×C109—21no—
48C42×C109C2×C411yescharacteristic
49C22×D109C2×D411yescharacteristic
50C2×#89137—42no—
51C2×#89137—42no—
52C2×#89137—42no—
53Q8×C109—41no—
54C2×C4×C109—21no—
55C2×C4×C109—21no—
56C2×C4×C109C22⋊C411yescharacteristic
57C2×C4×C109C22⋊C411yescharacteristic
58C2×C4×C109C22×C411yescharacteristic
59C2×Dic109—21no—
60C2×Dic109—21no—
61C2×Dic109C22⋊C411yescharacteristic
62C2×Dic109C22⋊C411yescharacteristic
63C2×Dic109C2×D411yescharacteristic
64C4×D109—41no—
65C4×D109—41no—
66C4×D109SD1612yes—
67C4×D109Q1612yes—
68Dic218—42no—
69Dic218—41no—
70#11724786—42no—
71C22×C109C2×C22⋊C411yescharacteristic
72C2×D109—21no—
73C2×D109—21no—
74C2×D109C2×SD1611yescharacteristic
75C2×D109C2×Q1611yescharacteristic
76#89137—82no—
77C4×C109—21no—
78C4×C109—21no—
79C4×C109—41no—
80C4×C109—41no—
81C4×C109#10312yes—
82Dic109—21no—
83Dic109—21no—
84Dic109—41no—
85Dic109—41no—
86Dic109#10312yes—
87C2×C109#41011yescharacteristic
88C2×C109C2×#10311yescharacteristic
89C2×C109#42111yescharacteristic
90D109—21no—
91D109—21no—
92#1518—1091nomaximal, Sylow
93C109#151811yescharacteristic, complemented, Sylow
94#533—1091no—
95#431—1091no—
96#382—1091no—
97#328—1092no—
98#328—1092no—
99C4⋊Q8—1091no—
100C4⋊Q8—1091no—
101#125—2181no—
102C22⋊Q8—1091no—
103C22⋊Q8—1091no—
104C22⋊Q8—2181no—
105C4×Q8—1091no—
106C4×Q8—2181no—
107C4×Q8#8913711yescharacteristic, complemented
108#117—2181no—
109C2×C4⋊C4—2181no—
110C2×C42—1091no—
111C4⋊C8—2181no—
112C22⋊C8—1092no—
113C4×C8—2181no—
114#95—1092no—
115#95—2181no—
116C2×Q8—1091no—
117C2×Q8—2181no—
118C2×Q8C2×#8913711yescharacteristic
119C22×C4—1091no—
120C22×C4—1091no—
121C22×C4—1091no—
122C22×C4—2182no—
123C2×C8—2182no—
124C4⋊C4—21no—
125C4⋊C4—1091no—
126C4⋊C4—4362no—
127C4⋊C4—2181no—
128C4⋊C4—2181no—
129C4⋊C4—2181no—
130C4⋊C4—2181no—
131C4⋊C4—2181no—
132C4⋊C4—2181no—
133C4⋊C4C2×#8913711yescharacteristic
134C22⋊C4—2181no—
135C22⋊C4—2181no—
136C42—21no—
137C42—1091no—
138C42—1091no—
139C42—1091no—
140C42—2181no—
141C42C2×#8913711yescharacteristic
142C23—1091no—
143Q8—41no—
144Q8—4361no—
145Q8—4362no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—1091no—
149C2×C4—1092no—
150C2×C4—1092no—
151C2×C4—1091no—
152C2×C4—1091no—
153C2×C4—4361no—
154C2×C4—4361no—
155C2×C4—4362no—
156C2×C4—4362no—
157C2×C4—4362no—
158C2×C4—2181no—
159C2×C4—2181no—
160C2×C4C22⋊#8913711yescharacteristic
161C2×C4C22⋊#8913711yescharacteristic
162C2×C4C22×#8913711yescharacteristic
163C8—4362no—
164C22—1091no—
165C22—1091no—
166C22—2181no—
167C22—2181no—
168C22C2×C22⋊#8913711yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—8722no—
174C4—1092no—
175C4—4361no—
176C4—4361no—
177C4—2181no—
178C4—2181no—
179C4#1681276212yes—
180C2—2181no—
181C2—2181no—
182C2#2029600511yescharacteristic
183C2C2×#1681276211yescharacteristic
184C2#2029602311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC4×Q8×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC22×D109C2×D4
cosocleC2×C4×D109C23
hypercenterC4×Q8#89137
hypocenterC109#1518
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
12. #16812698C4semidirect
13. #16812697C4semidirect
19. C4×Dic218C4semidirect
22. C4×Q8×C109C4semidirect
93. C109#1518semidirect
107. C4×Q8#89137semidirect

Maximal subgroups

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

subgroupindex
#202960452
#202959702
#202958802
#202958792
#202955802
#1518109