Finite Group Databasebeta

← #28378551

Subgroups — #28378551

Order 13952.

252 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 62 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
2C2×#16812766C211yesmaximal, characteristic, complemented
3#20295886C212yesmaximal, complemented
4#20295884C212yesmaximal, complemented
5#20295572C211yesmaximal, characteristic
6C22×#11724786—21no—
7#16812766—21no—
8#16812766C2212yes—
9#16812766C2212yes—
10C22⋊#11724786—21no—
11#16812754—21no—
12C2×#13182029C411yescharacteristic
13#16812697C2211yescharacteristic
14#16812695C2211yescharacteristic
15#16812688C411yescharacteristic
16#16812686C411yescharacteristic
17#16812671—21no—
18#16812671—21no—
19C4×C22⋊D109—21no—
20C4×C22⋊D109—21no—
21C2×C4×Dic109C2211yescharacteristic
22C2×#41×C109C411yescharacteristic
23C2×#11724786—22no—
24C2×#11724786—22no—
25C2×#11724786—42no—
26#13182029—42no—
27C2×Dic218C2×C411yescharacteristic
28C2×D436C2×C411yescharacteristic
29C2×C22⋊D109—21no—
30C2×C22⋊D109—21no—
31C2×C22⋊D109—21no—
32C22×Dic109D411yescharacteristic
33C22×Dic109D411yescharacteristic
34C2×C4×D109—21no—
35#13182008—21no—
36#13182008—21no—
37C22⋊Dic109—21no—
38C22⋊Dic109—21no—
39#13182006—21no—
40#13182006—21no—
41C4×Dic109C2×C411yescharacteristic
42C4×Dic109D411yescharacteristic
43C4×Dic109D411yescharacteristic
44C4×Dic109C2311yescharacteristic
45#41×C109—42no—
46C2×Q8×C109C2×C411yescharacteristic
47C2×D4×C109—21no—
48C2×D4×C109C2×C411yescharacteristic
49C22×C4×C109—21no—
50C22×C4×C109C2×C411yescharacteristic
51C23×C109—21no—
52C23×C109C22⋊C411yescharacteristic
53C22×D109—21no—
54Q8×C109—41no—
55D4×C109—41no—
56D4×C109—42no—
57C2×C4×C109—22no—
58C2×C4×C109—21no—
59C2×C4×C109—42no—
60C2×C4×C109C22⋊C411yescharacteristic
61C2×C4×C109C22×C411yescharacteristic
62C22⋊D109—42no—
63C22⋊D109—42no—
64C22⋊D109—41no—
65C22⋊D109—41no—
66C2×Dic109—22no—
67C2×Dic109—21no—
68C2×Dic109—21no—
69C2×Dic109—21no—
70C2×Dic109C22⋊C411yescharacteristic
71C2×Dic109C22⋊C411yescharacteristic
72C2×Dic109C2×D411yescharacteristic
73C2×Dic109C2×D411yescharacteristic
74D436—41no—
75C4×D109—42no—
76Dic218—41no—
77#11724786—42no—
78#11724786—42no—
79C22×C109—21no—
80C22×C109—21no—
81C22×C109—41no—
82C22×C109—41no—
83C22×C109—41no—
84C22×C109#10012yes—
85C22×C109C2×C22⋊C411yescharacteristic
86C2×D109—41no—
87C2×D109—41no—
88C2×D109—41no—
89C4×C109—21no—
90C4×C109—21no—
91C4×C109—41no—
92Dic109—21no—
93Dic109—21no—
94Dic109—41no—
95Dic109#13512yes—
96Dic109AGL(1,ℤ/8)11yescharacteristic
97Dic109#13711yescharacteristic
98C2×C109—22no—
99C2×C109—81no—
100C2×C109C2×#10011yescharacteristic
101C2×C109#41611yescharacteristic
102C2×C109#41711yescharacteristic
103D109—81no—
104#1551—1091nomaximal, Sylow
105C109#155111yescharacteristic, complemented, Sylow
106#532—1091no—
107#432—1091no—
108C2×C4⋊C8—1091no—
109#333—1092no—
110#331—1092no—
111C2×#41—1091no—
112C2×#41#8913711yescharacteristic
113C22×C8—2181no—
114C4⋊Q8—1091no—
115#127—1091no—
116#124—1091no—
117#124—1091no—
118#121—2181no—
119#121—2181no—
120C4×D4—2181no—
121C4×D4—2181no—
122C2×C42—1091no—
123C4⋊C8—1092no—
124C4⋊C8—1092no—
125C4⋊C8—2181no—
126C22⋊C8—2181no—
127#97—2181no—
128#41—42no—
129#41—4362no—
130C2×Q8—1091no—
131C2×Q8C2×#8913711yescharacteristic
132C2×D4—21no—
133C2×D4—1091no—
134C2×D4—2181no—
135C2×D4—2181no—
136C2×D4—2181no—
137C2×D4C2×#8913711yescharacteristic
138C22×C4—21no—
139C22×C4—1091no—
140C22×C4—1091no—
141C22×C4—2181no—
142C22×C4C2×#8913711yescharacteristic
143C2×C8—4362no—
144C2×C8—2182no—
145C2×C8—2182no—
146C4⋊C4—2181no—
147C4⋊C4—2181no—
148C22⋊C4—2181no—
149C22⋊C4—2181no—
150C22⋊C4—2181no—
151C22⋊C4—2181no—
152C42—1091no—
153C42—1091no—
154C42—1091no—
155C42—1091no—
156C23—21no—
157C23—2181no—
158C23C22⋊#8913711yescharacteristic
159Q8—41no—
160Q8—4361no—
161D4—41no—
162D4—42no—
163D4—4361no—
164D4—4362no—
165D4—4361no—
166D4—4361no—
167D4—4362no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—1091no—
172C2×C4—1091no—
173C2×C4—1091no—
174C2×C4—1091no—
175C2×C4—4362no—
176C2×C4—2181no—
177C2×C4—2182no—
178C2×C4—2181no—
179C2×C4—2181no—
180C2×C4C22⋊#8913711yescharacteristic
181C2×C4C22×#8913711yescharacteristic
182C8—4362no—
183C8—4362no—
184C22—21no—
185C22—21no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—4361no—
190C22—4361no—
191C22—4361no—
192C22#1681275912yes—
193C22C2×C22⋊#8913711yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—1092no—
198C4—1091no—
199C4—1091no—
200C4—4361no—
201C4—2181no—
202C4—2181no—
203C2—22no—
204C2—81no—
205C2—8721no—
206C2C2×#1681275911yescharacteristic
207C2#2029601611yescharacteristic
208C2#2029601711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC2×#41×C109C4
socleC22×C109C2×C22⋊C4
prime radical#20295572C2
cosocleC4×Dic109C23
hypercenterC2×#41#89137
hypocenterC109#1551
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #20296046C2semidirect
2. C2×#16812766C2semidirect
3. #20295886C2semidirect
4. #20295884C2semidirect
105. C109#1551semidirect

Maximal subgroups

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

subgroupindex
#202960462
C2×#168127662
#202958862
#202958842
#202955722
#1551109