Finite Group Databasebeta

← #28378564

Subgroups — #28378564

Order 13952.

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

normal subgroups only

This group has 246 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#20296046C211yesmaximal, characteristic, complemented
2#20296029C211yesmaximal, characteristic, complemented
3#20295885C212yesmaximal, complemented
4#20295884C212yesmaximal, complemented
5#20295571C211yesmaximal, characteristic
6C2×#13182038—21no—
7#16812766C2212yes—
8#16812766C2212yes—
9C4⋊#11724786—21no—
10C22⋊#11724786—21no—
11#16812754—21no—
12C2×#13182028—21no—
13#16812698C2211yescharacteristic
14#16812695C2211yescharacteristic
15#16812685—21no—
16#16812673C411yescharacteristic
17#16812671—21no—
18D4×Dic109C411yescharacteristic
19#16812661C411yescharacteristic
20#16812659—21no—
21C2×C4×Dic109C2211yescharacteristic
22#121×C109C411yescharacteristic
23#13182038—42no—
24C2×#11724786—22no—
25C2×#11724786—22no—
26#13182028—44no—
27C2×Dic218—21no—
28C2×D436C2×C411yescharacteristic
29C2×C22⋊D109—21no—
30C2×C22⋊D109—21no—
31C2×C22⋊D109—21no—
32C22×Dic109—21no—
33C22×Dic109D411yescharacteristic
34C22×Dic109D411yescharacteristic
35C2×C4×D109—21no—
36C4⋊Dic109C2×C411yescharacteristic
37#13182008—21no—
38C22⋊Dic109—21no—
39#13182006—21no—
40#13182006—21no—
41C4×Dic109C2×C411yescharacteristic
42C4×Dic109D411yescharacteristic
43C4×Dic109D411yescharacteristic
44C4×Dic109C2311yescharacteristic
45C2×D4×C109—21no—
46C2×D4×C109C2×C411yescharacteristic
47C22×C4×C109C2×C411yescharacteristic
48C4⋊C4×C109C2×C411yescharacteristic
49C22⋊C4×C109—21no—
50C23×C109—21no—
51C23×C109C22⋊C411yescharacteristic
52C22×D109—21no—
53D4×C109—41no—
54D4×C109—42no—
55C2×C4×C109—21no—
56C2×C4×C109—41no—
57C2×C4×C109C22⋊C411yescharacteristic
58C2×C4×C109C22×C411yescharacteristic
59C22⋊D109—42no—
60C22⋊D109—41no—
61C22⋊D109—42no—
62C22⋊D109—41no—
63C2×Dic109—22no—
64C2×Dic109—21no—
65C2×Dic109—21no—
66C2×Dic109—21no—
67C2×Dic109—42no—
68C2×Dic109C22⋊C411yescharacteristic
69C2×Dic109C22⋊C411yescharacteristic
70C2×Dic109C2×D411yescharacteristic
71C2×Dic109C2×D411yescharacteristic
72D436—41no—
73C4×D109—42no—
74Dic218—42no—
75#11724786—42no—
76#11724786—42no—
77C22×C109—21no—
78C22×C109—21no—
79C22×C109—21no—
80C22×C109—41no—
81C22×C109—41no—
82C22×C109—41no—
83C22×C109C2×C22⋊C411yescharacteristic
84C2×D109—41no—
85C2×D109—41no—
86C2×D109—41no—
87C4×C109—21no—
88C4×C109—21no—
89C4×C109—41no—
90Dic109—21no—
91Dic109—21no—
92Dic109—41no—
93Dic109AGL(1,ℤ/8)11yescharacteristic
94Dic109AGL(1,ℤ/8)12yes—
95Dic109#13711yescharacteristic
96C2×C109—41no—
97C2×C109—81no—
98C2×C109#41311yescharacteristic
99C2×C109#41711yescharacteristic
100C2×C109#41811yescharacteristic
101D109—81no—
102#1557—1091nomaximal, Sylow
103C109#155711yescharacteristic, complemented, Sylow
104#532—1091no—
105#432—1091no—
106#423—1091no—
107#332—1092no—
108#331—1092no—
109C2×#41—2181no—
110C2×M16—2181no—
111C4⋊Q8—1091no—
112#127—1091no—
113#124—2181no—
114#121—1091no—
115#121—2181no—
116#121#8913711yescharacteristic
117C4×D4—1091no—
118C4×D4—1091no—
119C4×D4—2181no—
120C2×C42—1091no—
121C4⋊C8—1092no—
122C4⋊C8—1092no—
123C4⋊C8—2181no—
124C22⋊C8—2181no—
125#97—2181no—
126#41—4364no—
127C2×Q8—2181no—
128C2×D4—21no—
129C2×D4—1091no—
130C2×D4—2181no—
131C2×D4—2181no—
132C2×D4—2181no—
133C2×D4C2×#8913711yescharacteristic
134C22×C4—1091no—
135C22×C4—1091no—
136C22×C4—2181no—
137C22×C4—2181no—
138C22×C4C2×#8913711yescharacteristic
139M16—4362no—
140C2×C8—2182no—
141C2×C8—2182no—
142C4⋊C4—1091no—
143C4⋊C4—2181no—
144C4⋊C4C2×#8913711yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—2181no—
147C22⋊C4—2181no—
148C22⋊C4—2181no—
149C42—1091no—
150C42—1091no—
151C42—1091no—
152C42—1091no—
153C23—21no—
154C23—2181no—
155C23C22⋊#8913711yescharacteristic
156Q8—4362no—
157D4—41no—
158D4—42no—
159D4—4361no—
160D4—4362no—
161D4—4361no—
162D4—4361no—
163D4—4362no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—1091no—
167C2×C4—1091no—
168C2×C4—1091no—
169C2×C4—1091no—
170C2×C4—4362no—
171C2×C4—4362no—
172C2×C4—2181no—
173C2×C4—2182no—
174C2×C4—2181no—
175C2×C4—2181no—
176C2×C4C22⋊#8913711yescharacteristic
177C2×C4C22×#8913711yescharacteristic
178C8—4362no—
179C8—4362no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—41no—
184C22—41no—
185C22—41no—
186C22—4361no—
187C22—4361no—
188C22—4361no—
189C22C2×C22⋊#8913711yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—1091no—
194C4—1091no—
195C4—1092no—
196C4—4361no—
197C4—2181no—
198C4—2181no—
199C2—41no—
200C2—81no—
201C2—8721no—
202C2#2029601311yescharacteristic
203C2#2029601711yescharacteristic
204C2#2029601811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#121×C109C4
socleC22×C109C2×C22⋊C4
prime radical#20295571C2
cosocleC4×Dic109C23
hypercenter#121#89137
hypocenterC109#1557
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #20296046C2semidirect
2. #20296029C2semidirect
3. #20295885C2semidirect
4. #20295884C2semidirect
103. C109#1557semidirect

Maximal subgroups

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

subgroupindex
#202960462
#202960292
#202958852
#202958842
#202955712
#1557109