Finite Group Databasebeta

← #28378414

Subgroups — #28378414

Order 13952.

240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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#20296044C211yesmaximal, characteristic
2C4×C4⋊#89137C211yesmaximal, characteristic
3#20295880C212yesmaximal
4#20295879C212yesmaximal
5#20295580C211yesmaximal, characteristic
6C2×C4⋊#89137—21no—
7C2×C4×#89137—21no—
8#16812766—21no—
9#16812756C2212yes—
10C4×#11724786—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—24no—
26C4×#89137—42no—
27C2×Dic218—21no—
28C2×Dic218C2×C411yescharacteristic
29C2×C4×D109D411yescharacteristic
30C2×C4×D109D411yescharacteristic
31C2×C4×D109C2311yescharacteristic
32C4⋊Dic109—21no—
33C4⋊Dic109C2×C411yescharacteristic
34#13182008—21no—
35#13182008—21no—
36#13182008—21no—
37#13182008—21no—
38#13182008—21no—
39#13182006—21no—
40#13182006—21no—
41C4×Dic109—21no—
42C4×Dic109C2×C411yescharacteristic
43C4×Dic109D411yescharacteristic
44C4×Dic109D411yescharacteristic
45C2×Q8×C109C2×C411yescharacteristic
46C4⋊C4×C109—21no—
47C4⋊C4×C109C2×C411yescharacteristic
48C42×C109—21no—
49C42×C109C2×C411yescharacteristic
50C22×D109C2×D411yescharacteristic
51C2×#89137—24no—
52C2×#89137—42no—
53C2×#89137—42no—
54Q8×C109—41no—
55C2×C4×C109—21no—
56C2×C4×C109—21no—
57C2×C4×C109C22⋊C411yescharacteristic
58C2×C4×C109C22⋊C411yescharacteristic
59C2×C4×C109C22×C411yescharacteristic
60C2×Dic109—21no—
61C2×Dic109—21no—
62C2×Dic109C22⋊C411yescharacteristic
63C2×Dic109C22⋊C411yescharacteristic
64C2×Dic109C2×D411yescharacteristic
65C4×D109—22no—
66C4×D109—41no—
67C4×D109SD1612yes—
68C4×D109Q1612yes—
69Dic218—42no—
70Dic218—41no—
71#11724786—42no—
72C22×C109C2×C22⋊C411yescharacteristic
73C2×D109—21no—
74C2×D109—21no—
75C2×D109C2×SD1611yescharacteristic
76C2×D109C2×Q1611yescharacteristic
77#89137—44no—
78C4×C109—21no—
79C4×C109—21no—
80C4×C109—41no—
81C4×C109—41no—
82C4×C109#10312yes—
83Dic109—21no—
84Dic109—41no—
85Dic109—41no—
86Dic109#10312yes—
87Dic109#10412yes—
88C2×C109#41011yescharacteristic
89C2×C109C2×#10311yescharacteristic
90C2×C109C2×#10411yescharacteristic
91D109—21no—
92D109—21no—
93#1503—1091nomaximal, Sylow
94C109#150311yescharacteristic, complemented, Sylow
95#533—1091no—
96#431—1091no—
97C4×C4⋊C4—1091no—
98#328—1092no—
99#328—1092no—
100C4⋊Q8—1091no—
101C4⋊Q8—1091no—
102#125—2181no—
103C22⋊Q8—1091no—
104C22⋊Q8—1091no—
105C22⋊Q8—2181no—
106C4×Q8—1091no—
107C4×Q8—2181no—
108C4×Q8#8913711yescharacteristic, complemented
109#117—2181no—
110C2×C4⋊C4—2181no—
111C2×C42—1091no—
112C2×C42—2181no—
113C4⋊C8—2181no—
114C22⋊C8—1092no—
115C4×C8—2181no—
116#95—1092no—
117C2×Q8—1091no—
118C2×Q8—2181no—
119C2×Q8C2×#8913711yescharacteristic
120C22×C4—1091no—
121C22×C4—1091no—
122C22×C4—1091no—
123C22×C4—2182no—
124C2×C8—2182no—
125C4⋊C4—21no—
126C4⋊C4—1091no—
127C4⋊C4—2181no—
128C4⋊C4—2181no—
129C4⋊C4—2181no—
130C4⋊C4—2181no—
131C4⋊C4—2181no—
132C4⋊C4—2184no—
133C4⋊C4—2181no—
134C4⋊C4C2×#8913711yescharacteristic
135C22⋊C4—2181no—
136C22⋊C4—2181no—
137C42—21no—
138C42—1091no—
139C42—1091no—
140C42—1091no—
141C42—4362no—
142C42—2181no—
143C42C2×#8913711yescharacteristic
144C23—1091no—
145Q8—41no—
146Q8—4361no—
147Q8—4362no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—1091no—
151C2×C4—1091no—
152C2×C4—1092no—
153C2×C4—1092no—
154C2×C4—1091no—
155C2×C4—4361no—
156C2×C4—4362no—
157C2×C4—4362no—
158C2×C4—2182no—
159C2×C4—2184no—
160C2×C4—2181no—
161C2×C4—2181no—
162C2×C4C22⋊#8913711yescharacteristic
163C2×C4C22⋊#8913711yescharacteristic
164C2×C4C22×#8913711yescharacteristic
165C8—4362no—
166C22—1091no—
167C22—1091no—
168C22—2181no—
169C22—2181no—
170C22C2×C22⋊#8913711yescharacteristic
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—1092no—
176C4—1092no—
177C4—4364no—
178C4—4361no—
179C4—4361no—
180C4—2181no—
181C4#1681276212yes—
182C2—2181no—
183C2—2181no—
184C2#2029600511yescharacteristic
185C2C2×#1681276211yescharacteristic
186C2D109⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#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#1503
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ 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
94. C109#1503semidirect
108. C4×Q8#89137semidirect

Maximal subgroups

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

subgroupindex
#202960442
C4×C4⋊#891372
#202958802
#202958792
#202955802
#1503109