Finite Group Databasebeta

← D4×D88 #13080293

Subgroups — D4×D88 #13080293

Order 1408.

620 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×D88C212yesmaximal, complemented
2D4×D44C212yesmaximal, complemented
3C8×D4×C11C211yesmaximal, characteristic, complemented
4#10622728C212yesmaximal, complemented
5#10622456C212yesmaximal, complemented
6#10622345C214yesmaximal, complemented
7#10622308C211yesmaximal, characteristic, complemented
8C4×D88C211yesmaximal, characteristic, complemented
9C2×D4×D11—22no—
10C22×D44C2214yescomplemented
11C22×C8×C11C2212yescomplemented
12C4×D4×C11C2211yescharacteristic
13#66983C2214yescomplemented
14C2×D88—28no—
15C2×D88C2211yescharacteristic
16C2×D88C2212yescomplemented
17C2×D88C2214yescomplemented
18C2×D88C2212yescomplemented
19#66948—22no—
20#66935—24no—
21#66927C2212yescomplemented
22C4×D44C2212yescomplemented
23C11×C4⋊C8C2211yescharacteristic, complemented
24C11×C22⋊C8C2212yescomplemented
25C4×C8×C11C2211yescharacteristic, complemented
26#66885C2214yescomplemented
27#66885C2212yescomplemented
28#66882C2211yescharacteristic, complemented
29C23×D11—24no—
30C2×D4×C11D411yescharacteristic
31C22×C4×C11C2312yes—
32C2×C22⋊D11—24no—
33D4×D11—48no—
34C2×D44—28no—
35C2×D44—22no—
36C2×D44—24no—
37C2×D44—22no—
38C2×D44—44no—
39C2×D44C2314yes—
40C2×D44C2312yes—
41C2×C4×D11—22no—
42C2×C8×C11—24no—
43C2×C8×C11C2311yescharacteristic
44C2×C8×C11C2312yes—
45C2×C8×C11C2311yescharacteristic
46C11×C4⋊C4D411yescharacteristic
47C11×C22⋊C4D412yes—
48C42×C11C2311yescharacteristic
49(C2×D11)⋊C4—22no—
50(C2×D11)⋊C4—24no—
51C4⋊Dic11C2312yes—
52D88—28no—
53D88—24no—
54D88—42no—
55D88D414yesdirect product factor
56D4×D8—111nomaximal, Sylow
57C23×C11C2×D412yes—
58C22×D11—22no—
59C22×D11—24no—
60C22×D11—48no—
61C22×D11—48no—
62C22×D11—84no—
63D4×C11D814yescomplemented
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11C2×D411yescharacteristic
67C2×C4×C11C2×D412yes—
68C2×C4×C11C2×D411yescharacteristic
69C2×C4×C11C2411yescharacteristic
70C22⋊D11—48no—
71C2×Dic11—22no—
72D44—24no—
73D44—22no—
74D44—24no—
75D44—48no—
76D44—44no—
77D44—82no—
78D44C2×D414yescomplemented
79C4×D11—44no—
80C8×C11—22no—
81C8×C11—21no—
82C8×C11C2×D412yescomplemented
83C22×D8—112no—
84D42—112no—
85#493—111no—
86#466—112no—
87#459—112no—
88#447—114no—
89C4×D8—111no—
90C8×D4D1111yescharacteristic, complemented
91C22×C11—22no—
92C22×C11—22no—
93C22×C11C2×D814yescomplemented
94C22×C11C22×D411yescharacteristic
95C2×D11—24no—
96C2×D11—42no—
97C2×D11—42no—
98C2×D11—44no—
99C2×D11—44no—
100C2×D11—44no—
101C2×D11—816no—
102C4×C11—22no—
103C4×C11—21no—
104C4×C11C2×D812yescomplemented
105C4×C11C22×D411yescharacteristic
106C4×C11H(5,𝔽2)11yescharacteristic
107Dic11—42no—
108C22×D4—114no—
109C22×D4—222no—
110C2×D8—111no—
111C2×D8—114no—
112C2×D8—112no—
113C2×D8—112no—
114C2×D8—228no—
115C22×C8C2×D1112yescomplemented
116#127—112no—
117#121—114no—
118#121—222no—
119#120—224no—
120C4×D4—112no—
121C4×D4C2×D1111yescharacteristic
122#107—111no—
123C4⋊C8C2×D1111yescharacteristic, complemented
124#102—112no—
125#102—114no—
126C22⋊C8C2×D1112yescomplemented
127C4×C8C2×D1111yescharacteristic, complemented
128C2×C11—24no—
129C2×C11D4211yescharacteristic
130C2×C11C22×D811yescharacteristic
131C2×C11#57611yescharacteristic
132D11—44no—
133D11—84no—
134C24—224no—
135C2×D4—112no—
136C2×D4—114no—
137C2×D4—228no—
138C2×D4—224no—
139C2×D4—224no—
140C2×D4—222no—
141C2×D4—222no—
142C2×D4—444no—
143C2×D4—448no—
144C2×D4D4411yescharacteristic
145C22×C4—222no—
146C22×C4C22×D1112yes—
147D8—114no—
148D8—228no—
149D8—224no—
150D8—442no—
151C2×C8—24no—
152C2×C8C22×D1111yescharacteristic
153C2×C8C22×D1112yes—
154C2×C8C22×D1111yescharacteristic
155C4⋊C4—112no—
156C4⋊C4D4411yescharacteristic
157C22⋊C4—222no—
158C22⋊C4—224no—
159C22⋊C4D4412yes—
160C42C22×D1111yescharacteristic
161C11D4×D811yescharacteristic, complemented, Sylow
162C23—222no—
163C23—224no—
164C23—448no—
165C23—448no—
166C23—884no—
167C23C2×D4412yes—
168D4—114no—
169D4—224no—
170D4—222no—
171D4—224no—
172D4—448no—
173D4—448no—
174D4—444no—
175D4—882no—
176D4D8814yesdirect product factor
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—222no—
180C2×C4—444no—
181C2×C4C2×D4411yescharacteristic
182C2×C4C2×D4412yes—
183C2×C4C2×D4411yescharacteristic
184C2×C4C23×D1111yescharacteristic
185C8—22no—
186C8—21no—
187C8D4×D1112yescomplemented
188C22—22no—
189C22—22no—
190C22—224no—
191C22—442no—
192C22—442no—
193C22—444no—
194C22—444no—
195C22—444no—
196C22—8816no—
197C22C2×D8814yescomplemented
198C22C22×D4411yescharacteristic
199C4—21no—
200C4—22no—
201C4—442no—
202C4C2×D8812yescomplemented
203C4C2×D4×D1111yescharacteristic
204C4#6704211yescharacteristic
205C2—24no—
206C2—444no—
207C2—884no—
208C2D4×D4411yescharacteristic
209C2C22×D8811yescharacteristic
210C2#1062328311yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC8×D4×C11C2
socleC22×C11C22×D4
hypercenterC8×D4D11
hypocenterC11D4×D8
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×D88C2semidirect
2. D4×D44C2semidirect
3. C8×D4×C11C2semidirect
4. #10622728C2semidirect
5. #10622456C2semidirect
6. #10622345C2semidirect
7. #10622308C2semidirect
8. C4×D88C2semidirect
10. C22×D44C22semidirect
11. C22×C8×C11C22semidirect
13. #66983C22semidirect
16. C2×D88C22semidirect
17. C2×D88C22semidirect
18. C2×D88C22semidirect
21. #66927C22semidirect
22. C4×D44C22semidirect
23. C11×C4⋊C8C22semidirect
24. C11×C22⋊C8C22semidirect
25. C4×C8×C11C22semidirect
26. #66885C22semidirect
27. #66885C22semidirect
28. #66882C22semidirect
55. D88D4direct (N × H)
63. D4×C11D8semidirect
78. D44C2×D4semidirect
82. C8×C11C2×D4semidirect
90. C8×D4D11semidirect
93. C22×C11C2×D8semidirect
104. C4×C11C2×D8semidirect
115. C22×C8C2×D11semidirect
123. C4⋊C8C2×D11semidirect
126. C22⋊C8C2×D11semidirect
127. C4×C8C2×D11semidirect
161. C11D4×D8semidirect
176. D4D88direct (N × H)
187. C8D4×D11semidirect
197. C22C2×D88semidirect
202. C4C2×D88semidirect

Maximal subgroups

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

subgroupindex
C22×D882
D4×D442
C8×D4×C112
#106227282
#106224562
#106223452
#106223082
C4×D882
D4×D811