Finite Group Databasebeta

← #28378485

Subgroups — #28378485

Order 13952.

234 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C4×#13182038C211yesmaximal, characteristic, complemented
2C2×#16812754C211yesmaximal, characteristic, complemented
3#20295883C212yesmaximal, complemented
4#20295882C212yesmaximal, complemented
5#20295562C211yesmaximal, characteristic
6C2×#13182038—21no—
7C22×#11724786—21no—
8#16812754—21no—
9#16812754C2212yes—
10#16812754C2212yes—
11C4×#11724786—21no—
12#16812694—21no—
13#16812690C2211yescharacteristic
14#16812688C2211yescharacteristic
15#16812683—21no—
16#16812673C411yescharacteristic
17Q8×Dic109C411yescharacteristic
18#16812661C411yescharacteristic
19#16812659—21no—
20#16812657—21no—
21C2×C4×Dic109C2211yescharacteristic
22C22⋊Q8×C109C411yescharacteristic
23#13182038—24no—
24C2×#11724786—24no—
25C2×#11724786—22no—
26C2×#11724786—22no—
27C2×D436C2×C411yescharacteristic
28C2×C22⋊D109—21no—
29C22×Dic109D411yescharacteristic
30C22×Dic109D411yescharacteristic
31C2×C4×D109—21no—
32C4⋊Dic109—21no—
33C4⋊Dic109—21no—
34C4⋊Dic109C2×C411yescharacteristic
35#13182008—21no—
36#13182006—21no—
37#13182006—21no—
38#13182006—21no—
39#13182006—21no—
40C4×Dic109—21no—
41C4×Dic109C2×C411yescharacteristic
42C4×Dic109D411yescharacteristic
43C4×Dic109D411yescharacteristic
44C4×Dic109C2311yescharacteristic
45C2×Q8×C109C2×C411yescharacteristic
46C22×C4×C109C2×C411yescharacteristic
47C4⋊C4×C109—21no—
48C4⋊C4×C109C2×C411yescharacteristic
49C22⋊C4×C109—21no—
50C23×C109C22⋊C411yescharacteristic
51C22×D109—21no—
52Q8×C109—41no—
53C2×C4×C109—21no—
54C2×C4×C109—21no—
55C2×C4×C109—41no—
56C2×C4×C109C22⋊C411yescharacteristic
57C2×C4×C109C22×C411yescharacteristic
58C22⋊D109—42no—
59C2×Dic109—22no—
60C2×Dic109—22no—
61C2×Dic109—21no—
62C2×Dic109C22⋊C411yescharacteristic
63C2×Dic109C22⋊C411yescharacteristic
64C2×Dic109C2×D411yescharacteristic
65C2×Dic109C2×D411yescharacteristic
66D436—41no—
67C4×D109—42no—
68#11724786—24no—
69#11724786—24no—
70C22×C109—21no—
71C22×C109—21no—
72C22×C109#10412yes—
73C22×C109C2×C22⋊C411yescharacteristic
74C2×D109—41no—
75C2×D109—41no—
76C2×D109—41no—
77C4×C109—21no—
78C4×C109—21no—
79C4×C109—41no—
80C4×C109—41no—
81Dic109—21no—
82Dic109—21no—
83Dic109—21no—
84Dic109—41no—
85Dic109#10412yes—
86C2×C109—22no—
87C2×C109#41311yescharacteristic
88C2×C109C2×#10411yescharacteristic
89C2×C109C2×#10411yescharacteristic
90D109—81no—
91#1524—1091nomaximal, Sylow
92C109#152411yescharacteristic, complemented, Sylow
93#529—1091no—
94C4×M16—1091no—
95C2×#97—1091no—
96#330—1092no—
97#329—1092no—
98C2×M16—2181no—
99C22×C8—2181no—
100#126—2181no—
101#125—1091no—
102#124—1091no—
103#123—2181no—
104C22⋊Q8#8913711yescharacteristic
105#121—1091no—
106C4×Q8—1091no—
107C4×D4—1091no—
108C4×D4—2181no—
109#117—2181no—
110C2×C42—1091no—
111#97—1092no—
112#97—1092no—
113#97—2181no—
114C4×C8—2181no—
115C2×Q8C2×#8913711yescharacteristic
116C2×D4—1091no—
117C2×D4—2181no—
118C22×C4—1091no—
119C22×C4—1091no—
120C22×C4—2181no—
121C22×C4C2×#8913711yescharacteristic
122M16—2184no—
123C2×C8—2182no—
124C2×C8—2182no—
125C2×C8—2184no—
126C4⋊C4—21no—
127C4⋊C4—1091no—
128C4⋊C4—2181no—
129C4⋊C4—2181no—
130C4⋊C4—2181no—
131C4⋊C4C2×#8913711yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—2181no—
134C22⋊C4—2181no—
135C22⋊C4—2181no—
136C22⋊C4—2181no—
137C42—1091no—
138C42—1091no—
139C42—1091no—
140C42—1091no—
141C42—2181no—
142C23—2181no—
143C23C22⋊#8913711yescharacteristic
144Q8—41no—
145D4—4361no—
146D4—4362no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—1091no—
151C2×C4—1091no—
152C2×C4—1091no—
153C2×C4—1091no—
154C2×C4—4362no—
155C2×C4—2182no—
156C2×C4—2181no—
157C2×C4—2182no—
158C2×C4C22⋊#8913711yescharacteristic
159C2×C4C22×#8913711yescharacteristic
160C8—2184no—
161C8—2184no—
162C22—21no—
163C22—21no—
164C22—4361no—
165C22—4361no—
166C22—4361no—
167C22#1681276412yes—
168C22C2×C22⋊#8913711yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—1092no—
174C4—4361no—
175C4—2181no—
176C4—2181no—
177C4—2181no—
178C2—22no—
179C2—8721no—
180C2#2029601311yescharacteristic
181C2D109⋊#10411yescharacteristic
182C2C2×#1681276411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC22⋊Q8×C109C4
socleC22×C109C2×C22⋊C4
prime radical#16812673C4
cosocleC4×Dic109C23
hypercenterC22⋊Q8#89137
hypocenterC109#1524
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C4×#13182038C2semidirect
2. C2×#16812754C2semidirect
3. #20295883C2semidirect
4. #20295882C2semidirect
92. C109#1524semidirect

Maximal subgroups

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

subgroupindex
C4×#131820382
C2×#168127542
#202958832
#202958822
#202955622
#1524109