Finite Group Databasebeta

← #28378497

Subgroups — #28378497

Order 13952.

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

normal subgroups only

This group has 216 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#20296048C211yesmaximal, characteristic, complemented
2C4×#13182039C211yesmaximal, characteristic, complemented
3#20295883C212yesmaximal, complemented
4#20295881C212yesmaximal, complemented
5#20295558C211yesmaximal, characteristic
6C2×#13182039—21no—
7C4⋊#11724786—21no—
8#16812756—21no—
9#16812754C2212yes—
10#16812754C2212yes—
11C4×#11724786—21no—
12#16812692—21no—
13#16812690C2211yescharacteristic
14#16812686C2211yescharacteristic
15#16812681—21no—
16#16812679C411yescharacteristic
17#16812670C411yescharacteristic
18C4×Dic218C411yescharacteristic
19C4×C22⋊D109—21no—
20#16812658—21no—
21C42×D109C2211yescharacteristic
22C4×D4×C109C411yescharacteristic
23#13182039—24no—
24C2×#11724786—22no—
25C2×#11724786—22no—
26C2×Dic218C2×C411yescharacteristic
27C2×C22⋊D109—21no—
28C2×C4×D109C2×C411yescharacteristic
29C2×C4×D109D411yescharacteristic
30C2×C4×D109D411yescharacteristic
31C4⋊Dic109—21no—
32C4⋊Dic109—21no—
33C4⋊Dic109C2×C411yescharacteristic
34#13182008—21no—
35#13182008—21no—
36C22⋊Dic109—21no—
37C22⋊Dic109—21no—
38C22⋊Dic109—21no—
39#13182006—21no—
40C4×Dic109—21no—
41C4×Dic109D411yescharacteristic
42C4×Dic109D411yescharacteristic
43C4×Dic109C2311yescharacteristic
44C2×D4×C109C2×C411yescharacteristic
45C22×C4×C109—21no—
46C4⋊C4×C109C2×C411yescharacteristic
47C22⋊C4×C109—21no—
48C42×C109C2×C411yescharacteristic
49C23×C109—21no—
50C22×D109C22⋊C411yescharacteristic
51D4×C109—41no—
52C2×C4×C109—21no—
53C2×C4×C109—42no—
54C2×C4×C109C22⋊C411yescharacteristic
55C2×C4×C109C22⋊C411yescharacteristic
56C2×C4×C109C22×C411yescharacteristic
57C22⋊D109—42no—
58C2×Dic109—21no—
59C2×Dic109—21no—
60C2×Dic109C22⋊C411yescharacteristic
61C2×Dic109C2×D411yescharacteristic
62C2×Dic109C2×D411yescharacteristic
63C4×D109—22no—
64C4×D109—41no—
65C4×D109—41no—
66Dic218—41no—
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—21no—
76C4×C109—21no—
77C4×C109—21no—
78C4×C109—41no—
79C4×C109#10412yes—
80Dic109—21no—
81Dic109—21no—
82Dic109—21no—
83Dic109—41no—
84Dic109—41no—
85C2×C109—81no—
86C2×C109#41311yescharacteristic
87C2×C109C2×#10411yescharacteristic
88C2×C109#42111yescharacteristic
89D109—41no—
90#1529—1091nomaximal, Sylow
91C109#152911yescharacteristic, complemented, Sylow
92#529—1091no—
93#432—1091no—
94C4×M16—1091no—
95#330—1092no—
96#329—1092no—
97C2×M16—2181no—
98#126—2181no—
99#125—1091no—
100#124—1091no—
101#123—2181no—
102C22⋊Q8—1091no—
103#121—1091no—
104C4×Q8—1091no—
105C4×D4—2181no—
106C4×D4#8913711yescharacteristic
107#117—2181no—
108C2×C42—1091no—
109C4⋊C8—2181no—
110C22⋊C8—2181no—
111#97—1092no—
112#97—1092no—
113C4×C8—2181no—
114C2×Q8—1091no—
115C2×D4—2181no—
116C2×D4C2×#8913711yescharacteristic
117C22×C4—21no—
118C22×C4—1091no—
119C22×C4—1091no—
120C22×C4—1091no—
121M16—2184no—
122C2×C8—2182no—
123C2×C8—2182no—
124C4⋊C4—1091no—
125C4⋊C4—2181no—
126C4⋊C4—2181no—
127C4⋊C4—2181no—
128C4⋊C4—2181no—
129C4⋊C4C2×#8913711yescharacteristic
130C22⋊C4—21no—
131C22⋊C4—2181no—
132C22⋊C4—2181no—
133C22⋊C4—2181no—
134C22⋊C4—2181no—
135C42—1091no—
136C42—1091no—
137C42—1091no—
138C42—2181no—
139C42C2×#8913711yescharacteristic
140C23—21no—
141C23—1091no—
142Q8—4361no—
143D4—41no—
144D4—4362no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—1091no—
148C2×C4—1091no—
149C2×C4—1091no—
150C2×C4—4361no—
151C2×C4—4361no—
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—2181no—
164C22—2181no—
165C22—2181no—
166C22C2×C22⋊#8913711yescharacteristic
167C4—21no—
168C4—21no—
169C4—41no—
170C4—4361no—
171C4—4361no—
172C4—2181no—
173C4—2181no—
174C4—2181no—
175C4#1681276312yes—
176C2—81no—
177C2—4361no—
178C2#2029601211yescharacteristic
179C2C2×#1681276311yescharacteristic
180C2#2029602311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC4×D4×C109C4
socleC22×C109C2×C22⋊C4
prime radical#16812670C4
cosocleC4×Dic109C23
hypercenterC4×D4#89137
hypocenterC109#1529
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #20296048C2semidirect
2. C4×#13182039C2semidirect
3. #20295883C2semidirect
4. #20295881C2semidirect
91. C109#1529semidirect

Maximal subgroups

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

subgroupindex
#202960482
C4×#131820392
#202958832
#202958812
#202955582
#1529109