Finite Group Databasebeta

← #28378425

Subgroups — #28378425

Order 13952.

228 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 58 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#20296049C211yesmaximal, characteristic
2#20295962C211yesmaximal, characteristic
3#20295880C212yesmaximal
4#20295879C212yesmaximal
5#20295580C211yesmaximal, characteristic
6C2×C4×#89137—21no—
7#16812766—21no—
8#16812756C2212yes—
9#16812754—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—24no—
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—24no—
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—22no—
65C4×D109—22no—
66C4×D109—41no—
67Dic218—42no—
68Dic218—41no—
69#11724786—42no—
70C22×C109C2×C22⋊C411yescharacteristic
71C2×D109—21no—
72C2×D109—21no—
73C2×D109#13712yes—
74#89137—44no—
75C4×C109—21no—
76C4×C109—21no—
77C4×C109—21no—
78C4×C109—41no—
79C4×C109—41no—
80Dic109—21no—
81Dic109—21no—
82Dic109—41no—
83Dic109—41no—
84Dic109#10412yes—
85C2×C109#41011yescharacteristic
86C2×C109#41911yescharacteristic
87C2×C109C2×#10411yescharacteristic
88D109—22no—
89#1506—1091nomaximal, Sylow
90C109#150611yescharacteristic, complemented, Sylow
91#533—1091no—
92#432—1091no—
93#376—1091no—
94#328—1092no—
95#328—1092no—
96C4⋊Q8—1091no—
97C4⋊Q8—1091no—
98#125—2181no—
99C22⋊Q8—1091no—
100C22⋊Q8—1091no—
101C22⋊Q8—2181no—
102C4×Q8—1091no—
103C4×Q8—2181no—
104C4×Q8#8913711yescharacteristic, complemented
105#117—2181no—
106C2×C42—1091no—
107C2×C42—2181no—
108C4⋊C8—2181no—
109C22⋊C8—1092no—
110#97—2181no—
111#95—1092no—
112#95—2181no—
113C2×Q8—1091no—
114C2×Q8—2181no—
115C2×Q8C2×#8913711yescharacteristic
116C22×C4—1091no—
117C22×C4—1091no—
118C22×C4—1091no—
119C22×C4—2182no—
120C2×C8—2182no—
121C4⋊C4—21no—
122C4⋊C4—1091no—
123C4⋊C4—2181no—
124C4⋊C4—2181no—
125C4⋊C4—2181no—
126C4⋊C4—2181no—
127C4⋊C4—2181no—
128C4⋊C4—2181no—
129C4⋊C4C2×#8913711yescharacteristic
130C22⋊C4—2181no—
131C22⋊C4—2181no—
132C42—21no—
133C42—1091no—
134C42—1091no—
135C42—1091no—
136C42—2184no—
137C42—2181no—
138C42C2×#8913711yescharacteristic
139C23—1091no—
140Q8—41no—
141Q8—4361no—
142Q8—4362no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—1091no—
146C2×C4—1091no—
147C2×C4—1091no—
148C2×C4—4361no—
149C2×C4—4362no—
150C2×C4—4362no—
151C2×C4—2182no—
152C2×C4—2182no—
153C2×C4—2184no—
154C2×C4—2181no—
155C2×C4—2181no—
156C2×C4C22⋊#8913711yescharacteristic
157C2×C4C22⋊#8913711yescharacteristic
158C2×C4C22×#8913711yescharacteristic
159C8—4362no—
160C22—1092no—
161C22—2181no—
162C22—2181no—
163C22C2×C22⋊#8913711yescharacteristic
164C4—21no—
165C4—21no—
166C4—21no—
167C4—41no—
168C4—41no—
169C4—1092no—
170C4—4364no—
171C4—4361no—
172C4—4361no—
173C4—2181no—
174C4—2181no—
175C2—2182no—
176C2#2029600511yescharacteristic
177C2#2029601911yescharacteristic
178C2D109⋊#10411yescharacteristic
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#1506
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
90. C109#1506semidirect
104. C4×Q8#89137semidirect

Maximal subgroups

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

subgroupindex
#202960492
#202959622
#202958802
#202958792
#202955802
#1506109