Finite Group Databasebeta

← #28361473

Subgroups — #28361473

Order 13952.

316 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 73 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×D4×D109C211yesmaximal, characteristic
2#20295082C211yesmaximal, characteristic, complemented
3C4×#13182012C211yesmaximal, characteristic, complemented
4#20294755C211yesmaximal, characteristic, complemented
5D4⋊#11724784C211yesmaximal, characteristic, complemented
6#20294753C211yesmaximal, characteristic, complemented
7D4⋊C8×C109C211yesmaximal, characteristic, complemented
8C2×D4×D109C411yescharacteristic
9C22×C4×D109—21no—
10C2×#13182012—21no—
11C4×D436C2211yescharacteristic
12D4×Dic109C411yescharacteristic
13#16812661C411yescharacteristic
14C4×C22⋊D109—21no—
15#16812659—21no—
16C4⋊C4×D109C411yescharacteristic
17C22⋊C4×D109—21no—
18C42×D109C2211yescharacteristic
19C4⋊#11724784C2211yescharacteristic, complemented
20#16812611—21no—
21#16812609—21no—
22#16812609—21no—
23C4×#11724784C2211yescharacteristic, complemented
24C4×D4×C109C2211yescharacteristic
25C4⋊C8×C109C2211yescharacteristic, complemented
26C4×C8×C109C2211yescharacteristic, complemented
27C23×D109—21no—
28C2×D436C2×C411yescharacteristic
29C2×C22⋊D109—21no—
30D4×D109—22no—
31D4×D109—22no—
32C22×Dic109—21no—
33C2×C4×D109—21no—
34C2×C4×D109—21no—
35C2×C4×D109—21no—
36C2×C4×D109—42no—
37C2×C4×D109—42no—
38C2×C4×D109C2×C411yescharacteristic
39C2×C4×D109D411yescharacteristic
40C2×C4×D109D411yescharacteristic
41#13182012—24no—
42C2×#11724784—21no—
43C2×#11724784—21no—
44C4⋊Dic109C2×C411yescharacteristic
45#13182008—21no—
46C22⋊Dic109—21no—
47#13182006—21no—
48#13182006—21no—
49C4×Dic109C2×C411yescharacteristic
50C4×Dic109D411yescharacteristic
51C4×Dic109D411yescharacteristic
52C2×D4×C109C2×C411yescharacteristic
53C22×C4×C109—21no—
54C2×C8×C109—21no—
55C2×C8×C109—21no—
56C4⋊C4×C109C2×C411yescharacteristic
57C22⋊C4×C109—21no—
58C42×C109C2311yescharacteristic
59C23×C109—21no—
60C22×D109—24no—
61C22×D109—21no—
62C22×D109—42no—
63C22×D109—42no—
64C22×D109C22⋊C411yescharacteristic
65D4×C109—21no—
66D4×C109M1612yescomplemented
67C2×C4×C109—21no—
68C2×C4×C109—41no—
69C2×C4×C109—41no—
70C2×C4×C109C22×C411yescharacteristic
71C2×C4×C109C2×D411yescharacteristic
72C2×C4×C109C2×D411yescharacteristic
73C22⋊D109—24no—
74C2×Dic109—21no—
75C2×Dic109—42no—
76C2×Dic109C22⋊C411yescharacteristic
77C2×Dic109C22⋊C411yescharacteristic
78C2×Dic109C22⋊C411yescharacteristic
79D436—21no—
80D436M1612yescomplemented
81C4×D109—22no—
82C4×D109—21no—
83C4×D109—21no—
84C4×D109—21no—
85C4×D109—21no—
86C4×D109—42no—
87C4×D109—42no—
88C4×D109—41no—
89C4×D109—41no—
90C8×C109—22no—
91C8×C109—41no—
92#11724784—22no—
93#11724784—41no—
94C22×C109—22no—
95C22×C109—41no—
96C22×C109—41no—
97C22×C109C2×C22⋊C411yescharacteristic
98C2×D109—21no—
99C2×D109—21no—
100C2×D109—22no—
101C2×D109—48no—
102C2×D109—41no—
103C2×D109—41no—
104C2×D109#10412yes—
105C4×C109—21no—
106C4×C109—41no—
107C4×C109C2×M1611yescharacteristic
108C4×C109C2×M1611yescharacteristic
109C4×C109AGL(1,ℤ/8)11yescharacteristic
110C4×C109AGL(1,ℤ/8)11yescharacteristic
111Dic109—21no—
112Dic109—21no—
113Dic109—21no—
114Dic109—41no—
115C2×C109—42no—
116C2×C109#40711yescharacteristic
117C2×C109#41811yescharacteristic
118C2×C109C2×#10411yescharacteristic
119D109—22no—
120D109—42no—
121#1490—1091nomaximal, Sylow
122C109#149011yescharacteristic, complemented, Sylow
123C2×C4×D4—1091no—
124#432—1091no—
125C4×M16—1091no—
126D4⋊C8—1091no—
127D4⋊C8—1091no—
128D4⋊C8—1091no—
129D4⋊C8D10911yescharacteristic, complemented
130C22×D4—1091no—
131C23×C4—2181no—
132C2×M16—2181no—
133C4×D4—1091no—
134C4×D4—1091no—
135C4×D4—1091no—
136C4×D4—2181no—
137C4×D4—2181no—
138C4×D4C2×D10911yescharacteristic
139C2×C4⋊C4—1091no—
140C2×C22⋊C4—2181no—
141C2×C42—1091no—
142C4⋊C8—1091no—
143C4⋊C8C2×D10911yescharacteristic, complemented
144C22⋊C8—2181no—
145#97—2181no—
146#97—2181no—
147C4×C8—1091no—
148C4×C8C2×D10911yescharacteristic, complemented
149C24—2181no—
150C2×D4—1091no—
151C2×D4—2181no—
152C2×D4—2182no—
153C2×D4—2182no—
154C2×D4C4×D10911yescharacteristic
155C22×C4—21no—
156C22×C4—1091no—
157C22×C4—1091no—
158C22×C4—1091no—
159C22×C4—4362no—
160C22×C4—4362no—
161C22×C4—2181no—
162C22×C4—2181no—
163C22×C4—2181no—
164C22×C4—2181no—
165M16—2184no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—2181no—
169C2×C8—2181no—
170C4⋊C4—1091no—
171C4⋊C4—2181no—
172C4⋊C4C4×D10911yescharacteristic
173C22⋊C4—21no—
174C22⋊C4—2181no—
175C22⋊C4—2181no—
176C22⋊C4—2181no—
177C42—1091no—
178C42—1091no—
179C42—1091no—
180C42C22×D10911yescharacteristic
181C23—21no—
182C23—1091no—
183C23—4362no—
184C23—4362no—
185C23—2184no—
186C23—2181no—
187D4—21no—
188D4—1092no—
189D4—2184no—
190D4—2181no—
191D4#1318201212yescomplemented
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—1091no—
196C2×C4—1091no—
197C2×C4—1091no—
198C2×C4—4362no—
199C2×C4—4362no—
200C2×C4—4362no—
201C2×C4—4361no—
202C2×C4—4361no—
203C2×C4—2182no—
204C2×C4—2181no—
205C2×C4—2181no—
206C2×C4—2181no—
207C2×C4—2181no—
208C2×C4—2181no—
209C2×C4C2×C4×D10911yescharacteristic
210C2×C4D4×D10911yescharacteristic
211C2×C4D4×D10911yescharacteristic
212C8—22no—
213C8—41no—
214C8—4361no—
215C8—2182no—
216C22—22no—
217C22—41no—
218C22—41no—
219C22—1092no—
220C22—4368no—
221C22—4361no—
222C22—4361no—
223C22—2182no—
224C22—2181no—
225C22—2181no—
226C22C22⋊C4×D10911yescharacteristic
227C4—21no—
228C4—41no—
229C4—4361no—
230C4—2181no—
231C4—2181no—
232C4—2181no—
233C4M16×D10911yescharacteristic
234C4C2×#1318201211yescharacteristic
235C4#1681272311yescharacteristic
236C4#1681272611yescharacteristic
237C2—42no—
238C2—4362no—
239C2—2182no—
240C2#2029498811yescharacteristic
241C2#2029502911yescharacteristic
242C2#104×D10911yescharacteristic
subgroupG/H
centerC2×C4D4×D109
commutatorC2×C4×C109C22×C4
FrattiniC42C22×D109
FittingD4⋊C8×C109C2
socleC22×C109C2×C22⋊C4
prime radicalC2×D4×D109C4
cosocleC42×C109C23
hypercenterD4⋊C8D109
hypocenterC109#1490
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20295082C2semidirect
3. C4×#13182012C2semidirect
4. #20294755C2semidirect
5. D4⋊#11724784C2semidirect
6. #20294753C2semidirect
7. D4⋊C8×C109C2semidirect
19. C4⋊#11724784C22semidirect
23. C4×#11724784C22semidirect
25. C4⋊C8×C109C22semidirect
26. C4×C8×C109C22semidirect
66. D4×C109M16semidirect
80. D436M16semidirect
122. C109#1490semidirect
129. D4⋊C8D109semidirect
143. C4⋊C8C2×D109semidirect
148. C4×C8C2×D109semidirect
191. D4#13182012semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D1092
#202950822
C4×#131820122
#202947552
D4⋊#117247842
#202947532
D4⋊C8×C1092
#1490109