Finite Group Databasebeta

← #28378358

Subgroups — #28378358

Order 13952.

312 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 76 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#20296045C211yesmaximal, characteristic, complemented
2#20296030C211yesmaximal, characteristic, complemented
3#20295874C212yesmaximal, complemented
4D4⋊#11724786C212yesmaximal, complemented
5C4×D4×D109C211yesmaximal, characteristic
6C2×#13182039—21no—
7C4⋊#11724786—21no—
8C4⋊#11724786—21no—
9C4⋊#11724786C2212yescomplemented
10#16812756—21no—
11C4×#11724786C2212yescomplemented
12C2×D4×D109C411yescharacteristic
13C22×C4×D109—21no—
14C4×D436C411yescharacteristic
15D4×Dic109C2211yescharacteristic
16#16812661C2211yescharacteristic
17C4×C22⋊D109—21no—
18#16812659—21no—
19C4⋊C4×D109C411yescharacteristic
20C22⋊C4×D109—21no—
21C42×D109C2211yescharacteristic
22C4×D4×C109C411yescharacteristic
23#13182039—42no—
24C2×#11724786—22no—
25C2×#11724786—22no—
26C23×D109—21no—
27C2×D436C2×C411yescharacteristic
28C2×C22⋊D109—21no—
29D4×D109—22no—
30D4×D109—22no—
31C22×Dic109—21no—
32C2×C4×D109—21no—
33C2×C4×D109—21no—
34C2×C4×D109—21no—
35C2×C4×D109—42no—
36C2×C4×D109—42no—
37C2×C4×D109C2×C411yescharacteristic
38C2×C4×D109D411yescharacteristic
39C2×C4×D109D411yescharacteristic
40C4⋊Dic109C2×C411yescharacteristic
41#13182008—21no—
42C22⋊Dic109—21no—
43#13182006—21no—
44#13182006—21no—
45C4×Dic109D411yescharacteristic
46C4×Dic109D411yescharacteristic
47C4×Dic109C2311yescharacteristic
48C2×D4×C109C2×C411yescharacteristic
49C22×C4×C109—21no—
50C4⋊C4×C109C2×C411yescharacteristic
51C22⋊C4×C109—21no—
52C42×C109C2×C411yescharacteristic
53C23×C109—21no—
54C22×D109—24no—
55C22×D109—21no—
56C22×D109—42no—
57C22×D109—42no—
58C22×D109C22⋊C411yescharacteristic
59D4×C109—21no—
60D4×C109M1612yescomplemented
61C2×C4×C109—21no—
62C2×C4×C109—42no—
63C2×C4×C109C22⋊C411yescharacteristic
64C2×C4×C109C22⋊C411yescharacteristic
65C2×C4×C109C22×C411yescharacteristic
66C22⋊D109—24no—
67C2×Dic109—21no—
68C2×Dic109—41no—
69C2×Dic109—41no—
70C2×Dic109C22⋊C411yescharacteristic
71C2×Dic109C2×D411yescharacteristic
72C2×Dic109C2×D411yescharacteristic
73D436—21no—
74D436M1612yescomplemented
75C4×D109—21no—
76C4×D109—21no—
77C4×D109—41no—
78C4×D109—42no—
79C4×D109—42no—
80C4×D109—41no—
81C4×D109—41no—
82C4×D109D812yes—
83C4×D109SD1612yes—
84#11724786—42no—
85#11724786—42no—
86C22×C109—22no—
87C22×C109—41no—
88C22×C109—41no—
89C22×C109C2×C22⋊C411yescharacteristic
90C2×D109—21no—
91C2×D109—21no—
92C2×D109—22no—
93C2×D109—48no—
94C2×D109—41no—
95C2×D109—41no—
96C2×D109#10212yes—
97C4×C109—21no—
98C4×C109—41no—
99C4×C109#10212yes—
100C4×C109C2×M1611yescharacteristic
101C4×C109C2×M1611yescharacteristic
102Dic109—21no—
103Dic109—21no—
104Dic109—41no—
105Dic109C2×D811yescharacteristic
106Dic109C2×SD1611yescharacteristic
107C2×C109—42no—
108C2×C109#40711yescharacteristic
109C2×C109C2×#10211yescharacteristic
110C2×C109#42111yescharacteristic
111D109—22no—
112D109—42no—
113#1486—1091nomaximal, Sylow
114C109#148611yescharacteristic, complemented, Sylow
115C2×C4×D4—1091no—
116#431—1091no—
117#423—1091no—
118D4⋊C8—1092no—
119D4⋊C8—1092no—
120C22×D4—1091no—
121C23×C4—2181no—
122C2×M16—2181no—
123C4×D4—1091no—
124C4×D4—1091no—
125C4×D4—1091no—
126C4×D4—2181no—
127C4×D4—2181no—
128C4×D4#8913711yescharacteristic
129C2×C4⋊C4—1091no—
130C2×C22⋊C4—2181no—
131C2×C42—1091no—
132C4⋊C8—1092no—
133C4⋊C8—2181no—
134C4⋊C8—2181no—
135C22⋊C8—2181no—
136C4×C8—1092no—
137C24—2181no—
138C2×D4—1091no—
139C2×D4—2181no—
140C2×D4—2182no—
141C2×D4—2182no—
142C2×D4C2×#8913711yescharacteristic
143C22×C4—21no—
144C22×C4—1091no—
145C22×C4—1091no—
146C22×C4—1091no—
147C22×C4—4362no—
148C22×C4—4362no—
149C22×C4—2181no—
150C22×C4—2181no—
151C22×C4—2181no—
152C22×C4—2181no—
153M16—4362no—
154C2×C8—2182no—
155C2×C8—2182no—
156C4⋊C4—1091no—
157C4⋊C4—2181no—
158C4⋊C4C2×#8913711yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—2181no—
161C22⋊C4—2181no—
162C22⋊C4—2181no—
163C42—1091no—
164C42—1091no—
165C42—1091no—
166C42C2×#8913711yescharacteristic
167C23—21no—
168C23—1091no—
169C23—4362no—
170C23—4362no—
171C23—2184no—
172C23—2181no—
173D4—21no—
174D4—1092no—
175D4—2184no—
176D4—2181no—
177D4#1318203912yescomplemented
178C2×C4—21no—
179C2×C4—42no—
180C2×C4—1091no—
181C2×C4—1092no—
182C2×C4—1092no—
183C2×C4—1091no—
184C2×C4—1091no—
185C2×C4—4361no—
186C2×C4—4361no—
187C2×C4—4361no—
188C2×C4—4362no—
189C2×C4—4361no—
190C2×C4—4361no—
191C2×C4—4362no—
192C2×C4—2181no—
193C2×C4—2181no—
194C2×C4—2181no—
195C2×C4C22⋊#8913711yescharacteristic
196C2×C4C22⋊#8913711yescharacteristic
197C2×C4C22×#8913711yescharacteristic
198C8—4362no—
199C8—4362no—
200C22—22no—
201C22—41no—
202C22—41no—
203C22—1092no—
204C22—4368no—
205C22—4361no—
206C22—4361no—
207C22—2182no—
208C22—2181no—
209C22—2181no—
210C22C2×C22⋊#8913711yescharacteristic
211C4—21no—
212C4—41no—
213C4—1091no—
214C4—1091no—
215C4—4361no—
216C4—2181no—
217C4—2181no—
218C4#1681276112yes—
219C4D109⋊M1611yescharacteristic
220C4C2×#1318203911yescharacteristic
221C2—42no—
222C2—4362no—
223C2—2182no—
224C2#2029599711yescharacteristic
225C2C2×#1681276111yescharacteristic
226C2#2029602311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC4×D4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC2×D4×D109C4
cosocleC4×Dic109C23
hypercenterC4×D4#89137
hypocenterC109#1486
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #20296045C2semidirect
2. #20296030C2semidirect
3. #20295874C2semidirect
4. D4⋊#11724786C2semidirect
9. C4⋊#11724786C22semidirect
11. C4×#11724786C22semidirect
60. D4×C109M16semidirect
74. D436M16semidirect
114. C109#1486semidirect
177. D4#13182039semidirect

Maximal subgroups

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

subgroupindex
#202960452
#202960302
#202958742
D4⋊#117247862
C4×D4×D1092
#1486109