Finite Group Databasebeta

← D101⋊(D4⋊C8) #27186418

Subgroups — D101⋊(D4⋊C8) #27186418

Order 12928.

344 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 94 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
1D101⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C4×D101⋊C8C211yesmaximal, characteristic, complemented
3#20266025C212yesmaximal, complemented
4D4⋊#11717581C212yesmaximal, complemented
5C4×D4×D101C211yesmaximal, characteristic
6C2×D101⋊C8—21no—
7C2×D101⋊C8—21no—
8#15692322—21no—
9C4⋊#11717581C2212yescomplemented
10C4×#11717581—21no—
11C4×#11717581C2212yescomplemented
12C2×D4×D101C411yescharacteristic
13C22×C4×D101—21no—
14C4×D404C411yescharacteristic
15D4×Dic101C2211yescharacteristic
16#15692217C2211yescharacteristic
17C4×C22⋊D101—21no—
18#15692215—21no—
19C4⋊C4×D101C411yescharacteristic
20C22⋊C4×D101—21no—
21C42×D101C2211yescharacteristic
22C4×D4×C101C411yescharacteristic
23D101⋊C8—24no—
24D101⋊C8—42no—
25C2×#11717581—22no—
26C2×#11717581—22no—
27C23×D101—21no—
28C2×D404C2×C411yescharacteristic
29C2×C22⋊D101—21no—
30D4×D101—22no—
31D4×D101C814yescomplemented
32C22×Dic101—21no—
33C2×C4×D101—21no—
34C2×C4×D101—21no—
35C2×C4×D101—21no—
36C2×C4×D101—42no—
37C2×C4×D101—42no—
38C2×C4×D101C2×C411yescharacteristic
39C2×C4×D101D411yescharacteristic
40C2×C4×D101D411yescharacteristic
41C4⋊Dic101C2×C411yescharacteristic
42#13108053—21no—
43C22⋊Dic101—21no—
44#13108051—21no—
45#13108051—21no—
46C4×Dic101D411yescharacteristic
47C4×Dic101D411yescharacteristic
48C4×Dic101C2311yescharacteristic
49C2×D4×C101C2×C411yescharacteristic
50C22×C4×C101—21no—
51C4⋊C4×C101C2×C411yescharacteristic
52C22⋊C4×C101—21no—
53C42×C101C2×C411yescharacteristic
54C23×C101—21no—
55C22×D101—21no—
56C22×D101—24no—
57C22×D101—42no—
58C22×D101—42no—
59C22×D101C22⋊C411yescharacteristic
60D4×C101—21no—
61D4×C101C2×C812yescomplemented
62C2×C4×C101—21no—
63C2×C4×C101—42no—
64C2×C4×C101C22⋊C411yescharacteristic
65C2×C4×C101C22⋊C411yescharacteristic
66C2×C4×C101C22×C411yescharacteristic
67C22⋊D101—24no—
68C2×Dic101—21no—
69C2×Dic101—41no—
70C2×Dic101—41no—
71C2×Dic101C22⋊C411yescharacteristic
72C2×Dic101C2×D411yescharacteristic
73C2×Dic101C2×D411yescharacteristic
74D404—21no—
75D404C2×C812yescomplemented
76C4×D101—22no—
77C4×D101—42no—
78C4×D101—42no—
79C4×D101—41no—
80C4×D101—41no—
81C4×D101C2×C812yes—
82C4×D101M1612yes—
83C4×D101D812yes—
84C4×D101SD1612yes—
85#11717581—24no—
86#11717581—42no—
87C22×C101—22no—
88C22×C101—41no—
89C22×C101—41no—
90C22×C101C2×C22⋊C411yescharacteristic
91C2×D101—22no—
92C2×D101—41no—
93C2×D101—41no—
94C2×D101—48no—
95C2×D101C22⋊C812yes—
96C2×D101#10212yes—
97C2×D101#10412yes—
98C4×C101—21no—
99C4×C101—41no—
100C4×C101#10212yes—
101C4×C101C22×C811yescharacteristic
102C4×C101C2×M1611yescharacteristic
103Dic101—21no—
104Dic101—41no—
105Dic101C22⋊C812yes—
106Dic101C2×D811yescharacteristic
107Dic101C2×SD1611yescharacteristic
108C2×C101—42no—
109C2×C101C2×C22⋊C811yescharacteristic
110C2×C101C2×#10211yescharacteristic
111C2×C101C2×#10411yescharacteristic
112D101—42no—
113D101D4⋊C814yescomplemented
114C2×D4⋊C8—1011nomaximal, Sylow
115C101C2×D4⋊C811yescharacteristic, complemented, Sylow
116C2×C4×D4—1011no—
117C2×C4⋊C8—1011no—
118C2×C4×C8—1011no—
119D4⋊C8—1012no—
120D4⋊C8—1012no—
121C22×D4—1011no—
122C23×C4—2021no—
123C22×C8—2021no—
124C22×C8—2021no—
125C4×D4—1011no—
126C4×D4—1011no—
127C4×D4—1011no—
128C4×D4—2021no—
129C4×D4—2021no—
130C4×D4#8793811yescharacteristic
131C2×C4⋊C4—1011no—
132C2×C22⋊C4—2021no—
133C2×C42—1011no—
134C4⋊C8—1012no—
135C4⋊C8—2021no—
136C4×C8—1012no—
137C4×C8—2021no—
138C24—2021no—
139C2×D4—1014no—
140C2×D4—1011no—
141C2×D4—2022no—
142C2×D4—2021no—
143C2×D4C2×#8793811yescharacteristic
144C22×C4—21no—
145C22×C4—1011no—
146C22×C4—1011no—
147C22×C4—1011no—
148C22×C4—4042no—
149C22×C4—4042no—
150C22×C4—2021no—
151C22×C4—2021no—
152C22×C4—2021no—
153C22×C4—2021no—
154C2×C8—4042no—
155C2×C8—2022no—
156C2×C8—2022no—
157C2×C8—2024no—
158C4⋊C4—1011no—
159C4⋊C4—2021no—
160C4⋊C4C2×#8793811yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—2021no—
163C22⋊C4—2021no—
164C22⋊C4—2021no—
165C42—1011no—
166C42—1011no—
167C42—1011no—
168C42C2×#8793811yescharacteristic
169C23—21no—
170C23—1011no—
171C23—4042no—
172C23—4042no—
173C23—2024no—
174C23—2021no—
175D4—21no—
176D4—1012no—
177D4—2024no—
178D4—2021no—
179D4D101⋊C812yescomplemented
180C2×C4—21no—
181C2×C4—42no—
182C2×C4—1011no—
183C2×C4—1011no—
184C2×C4—1012no—
185C2×C4—1012no—
186C2×C4—1012no—
187C2×C4—1012no—
188C2×C4—1011no—
189C2×C4—4041no—
190C2×C4—4041no—
191C2×C4—4042no—
192C2×C4—4041no—
193C2×C4—4041no—
194C2×C4—4042no—
195C2×C4—2022no—
196C2×C4—2021no—
197C2×C4C22⋊#8793811yescharacteristic
198C2×C4C22⋊#8793811yescharacteristic
199C2×C4C22×#8793811yescharacteristic
200C8—4042no—
201C8—2024no—
202C22—22no—
203C22—41no—
204C22—41no—
205C22—1012no—
206C22—1012no—
207C22—1012no—
208C22—4048no—
209C22—4041no—
210C22—4041no—
211C22—2022no—
212C22C2×C22⋊#8793811yescharacteristic
213C4—21no—
214C4—41no—
215C4—1012no—
216C4—1011no—
217C4—1011no—
218C4—4041no—
219C4—2021no—
220C4#1569231712yes—
221C4C2×D101⋊C811yescharacteristic
222C4D101⋊M1611yescharacteristic
223C2—42no—
224C2—1014no—
225C2—4042no—
226C2D101⋊(C22⋊C8)11yescharacteristic
227C2C2×#1569231711yescharacteristic
228C2D101⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#87938
commutatorC4×C101C22×C8
FrattiniC2×C4C22×#87938
FittingC4×D4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC2×D4×D101C4
cosocleC4×Dic101C23
hypercenterC4×D4#87938
hypocenterC101C2×D4⋊C8
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D101⋊(C4⋊C8)C2semidirect
2. C4×D101⋊C8C2semidirect
3. #20266025C2semidirect
4. D4⋊#11717581C2semidirect
9. C4⋊#11717581C22semidirect
11. C4×#11717581C22semidirect
31. D4×D101C8semidirect
61. D4×C101C2×C8semidirect
75. D404C2×C8semidirect
113. D101D4⋊C8semidirect
115. C101C2×D4⋊C8semidirect
179. D4D101⋊C8semidirect

Maximal subgroups

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

subgroupindex
D101⋊(C4⋊C8)2
C4×D101⋊C82
#202660252
D4⋊#117175812
C4×D4×D1012
C2×D4⋊C8101