Finite Group Databasebeta

← D4⋊C8×D97 #27140107

Subgroups — D4⋊C8×D97 #27140107

Order 12416.

344 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 97 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×D97C211yesmaximal, characteristic
2C4⋊C8×D97C211yesmaximal, characteristic, complemented
3C4×C8×D97C211yesmaximal, characteristic, complemented
4#20260464C211yesmaximal, characteristic, complemented
5D4⋊#11715895C211yesmaximal, characteristic, complemented
6#20260462C211yesmaximal, characteristic, complemented
7D4⋊C8×C97C211yesmaximal, characteristic, complemented
8C2×D4×D97C411yescharacteristic
9C22×C4×D97—21no—
10C2×C8×D97—21no—
11C2×C8×D97—21no—
12C4×D388C2211yescharacteristic
13D4×Dic97C411yescharacteristic
14#15690772C411yescharacteristic
15C4×C22⋊D97—21no—
16#15690770—21no—
17C4⋊C4×D97C411yescharacteristic
18C22⋊C4×D97—21no—
19C42×D97C2211yescharacteristic
20C4⋊#11715895C2211yescharacteristic, complemented
21#15690739—21no—
22C4×#11715895C2211yescharacteristic, complemented
23C8×Dic97—21no—
24C4×D4×C97C2211yescharacteristic
25C4⋊C8×C97C2211yescharacteristic, complemented
26C4×C8×C97C2211yescharacteristic, complemented
27C23×D97—21no—
28C2×D388C2×C411yescharacteristic
29C2×C22⋊D97—21no—
30D4×D97—22no—
31D4×D97C814yescomplemented
32C22×Dic97—21no—
33C2×C4×D97—21no—
34C2×C4×D97—21no—
35C2×C4×D97—21no—
36C2×C4×D97—42no—
37C2×C4×D97—42no—
38C2×C4×D97C2×C411yescharacteristic
39C2×C4×D97D411yescharacteristic
40C2×C4×D97D411yescharacteristic
41C2×#11715895—21no—
42C2×#11715895—21no—
43C8×D97—24no—
44C8×D97—42no—
45C4⋊Dic97C2×C411yescharacteristic
46#13095490—21no—
47C22⋊Dic97—21no—
48#13095488—21no—
49#13095488—21no—
50C4×Dic97C2×C411yescharacteristic
51C4×Dic97D411yescharacteristic
52C4×Dic97D411yescharacteristic
53C2×D4×C97C2×C411yescharacteristic
54C22×C4×C97—21no—
55C2×C8×C97—21no—
56C2×C8×C97—21no—
57C4⋊C4×C97C2×C411yescharacteristic
58C22⋊C4×C97—21no—
59C42×C97C2311yescharacteristic
60C23×C97—21no—
61C22×D97—21no—
62C22×D97—24no—
63C22×D97—42no—
64C22×D97—42no—
65C22×D97C22⋊C411yescharacteristic
66D4×C97—21no—
67D4×C97C2×C812yescomplemented
68C2×C4×C97—21no—
69C2×C4×C97—41no—
70C2×C4×C97—41no—
71C2×C4×C97C22×C411yescharacteristic
72C2×C4×C97C2×D411yescharacteristic
73C2×C4×C97C2×D411yescharacteristic
74C22⋊D97—24no—
75C2×Dic97—21no—
76C2×Dic97—42no—
77C2×Dic97C22⋊C411yescharacteristic
78C2×Dic97C22⋊C411yescharacteristic
79C2×Dic97C22⋊C411yescharacteristic
80D388—21no—
81D388C2×C812yescomplemented
82C4×D97—22no—
83C4×D97—42no—
84C4×D97—41no—
85C4×D97—41no—
86C4×D97—42no—
87C4×D97C2×C812yes—
88C4×D97M1612yes—
89C4×D97D812yes—
90C4×D97SD1612yes—
91C8×C97—22no—
92C8×C97—41no—
93#11715895—22no—
94#11715895—41no—
95C22×C97—22no—
96C22×C97—41no—
97C22×C97—41no—
98C22×C97C2×C22⋊C411yescharacteristic
99C2×D97—22no—
100C2×D97—41no—
101C2×D97—41no—
102C2×D97—48no—
103C2×D97C22⋊C812yes—
104C2×D97#10212yes—
105C2×D97#10412yes—
106C4×C97—21no—
107C4×C97—41no—
108C4×C97C22×C811yescharacteristic
109C4×C97C2×M1611yescharacteristic
110C4×C97C2×D811yescharacteristic
111C4×C97C2×SD1611yescharacteristic
112Dic97—21no—
113Dic97—41no—
114Dic97C22⋊C812yes—
115Dic97#10212yes—
116C2×C97—42no—
117C2×C97C2×C22⋊C811yescharacteristic
118C2×C97C2×#10211yescharacteristic
119C2×C97C2×#10411yescharacteristic
120D97—42no—
121D97D4⋊C814yesdirect product factor
122C2×D4⋊C8—971nomaximal, Sylow
123C97C2×D4⋊C811yescharacteristic, complemented, Sylow
124C2×C4×D4—971no—
125C2×C4⋊C8—971no—
126C2×C4×C8—971no—
127D4⋊C8—971no—
128D4⋊C8—971no—
129D4⋊C8—971no—
130D4⋊C8D9711yescharacteristic, direct product factor
131C22×D4—971no—
132C23×C4—1941no—
133C22×C8—1941no—
134C22×C8—1941no—
135C4×D4—971no—
136C4×D4—971no—
137C4×D4—971no—
138C4×D4—1941no—
139C4×D4—1941no—
140C4×D4C2×D9711yescharacteristic
141C2×C4⋊C4—971no—
142C2×C22⋊C4—1941no—
143C2×C42—971no—
144C4⋊C8—971no—
145C4⋊C8—1941no—
146C4⋊C8C2×D9711yescharacteristic, complemented
147C4×C8—971no—
148C4×C8—1941no—
149C4×C8C2×D9711yescharacteristic, complemented
150C24—1941no—
151C2×D4—974no—
152C2×D4—971no—
153C2×D4—1942no—
154C2×D4—1941no—
155C2×D4C4×D9711yescharacteristic
156C22×C4—21no—
157C22×C4—971no—
158C22×C4—971no—
159C22×C4—971no—
160C22×C4—3882no—
161C22×C4—3882no—
162C22×C4—1941no—
163C22×C4—1941no—
164C22×C4—1941no—
165C22×C4—1941no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—3882no—
169C2×C8—1944no—
170C2×C8—1941no—
171C2×C8—1941no—
172C4⋊C4—971no—
173C4⋊C4—1941no—
174C4⋊C4C4×D9711yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—1941no—
177C22⋊C4—1941no—
178C22⋊C4—1941no—
179C42—971no—
180C42—971no—
181C42—971no—
182C42C22×D9711yescharacteristic
183C23—21no—
184C23—971no—
185C23—3882no—
186C23—3882no—
187C23—1944no—
188C23—1941no—
189D4—21no—
190D4—972no—
191D4—1944no—
192D4—1941no—
193D4C8×D9712yescomplemented
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—971no—
198C2×C4—971no—
199C2×C4—972no—
200C2×C4—972no—
201C2×C4—972no—
202C2×C4—972no—
203C2×C4—971no—
204C2×C4—3882no—
205C2×C4—3882no—
206C2×C4—3882no—
207C2×C4—3881no—
208C2×C4—3881no—
209C2×C4—1942no—
210C2×C4—1941no—
211C2×C4C2×C4×D9711yescharacteristic
212C2×C4D4×D9711yescharacteristic
213C2×C4D4×D9711yescharacteristic
214C8—22no—
215C8—41no—
216C8—3881no—
217C8—1942no—
218C22—22no—
219C22—41no—
220C22—41no—
221C22—972no—
222C22—972no—
223C22—972no—
224C22—3888no—
225C22—3881no—
226C22—3881no—
227C22—1942no—
228C22C22⋊C4×D9711yescharacteristic
229C4—21no—
230C4—41no—
231C4—972no—
232C4—972no—
233C4—3881no—
234C4—1941no—
235C4C2×C8×D9711yescharacteristic
236C4M16×D9711yescharacteristic
237C4D8×D9711yescharacteristic
238C4SD16×D9711yescharacteristic
239C2—42no—
240C2—974no—
241C2—3882no—
242C2C22⋊C8×D9711yescharacteristic
243C2#102×D9711yescharacteristic
244C2#104×D9711yescharacteristic
subgroupG/H
centerC2×C4D4×D97
commutatorC4×C97C22×C8
FrattiniC42C22×D97
FittingD4⋊C8×C97C2
socleC22×C97C2×C22⋊C4
prime radicalC2×D4×D97C4
cosocleC42×C97C23
hypercenterD4⋊C8D97
hypocenterC97C2×D4⋊C8
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4⋊C8×D97C2semidirect
3. C4×C8×D97C2semidirect
4. #20260464C2semidirect
5. D4⋊#11715895C2semidirect
6. #20260462C2semidirect
7. D4⋊C8×C97C2semidirect
20. C4⋊#11715895C22semidirect
22. C4×#11715895C22semidirect
25. C4⋊C8×C97C22semidirect
26. C4×C8×C97C22semidirect
31. D4×D97C8semidirect
67. D4×C97C2×C8semidirect
81. D388C2×C8semidirect
121. D97D4⋊C8direct (N × H)
123. C97C2×D4⋊C8semidirect
130. D4⋊C8D97direct (N × H)
146. C4⋊C8C2×D97semidirect
149. C4×C8C2×D97semidirect
193. D4C8×D97semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D972
C4⋊C8×D972
C4×C8×D972
#202604642
D4⋊#117158952
#202604622
D4⋊C8×C972
C2×D4⋊C897