Finite Group Databasebeta

← D4⋊C8×D101 #27169503

Subgroups — D4⋊C8×D101 #27169503

Order 12928.

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×D101C211yesmaximal, characteristic
2C4⋊C8×D101C211yesmaximal, characteristic, complemented
3C4×C8×D101C211yesmaximal, characteristic, complemented
4#20264906C211yesmaximal, characteristic, complemented
5D4⋊#11717579C211yesmaximal, characteristic, complemented
6#20264904C211yesmaximal, characteristic, complemented
7D4⋊C8×C101C211yesmaximal, characteristic, complemented
8C2×D4×D101C411yescharacteristic
9C22×C4×D101—21no—
10C2×C8×D101—21no—
11C2×C8×D101—21no—
12C4×D404C2211yescharacteristic
13D4×Dic101C411yescharacteristic
14#15692217C411yescharacteristic
15C4×C22⋊D101—21no—
16#15692215—21no—
17C4⋊C4×D101C411yescharacteristic
18C22⋊C4×D101—21no—
19C42×D101C2211yescharacteristic
20C4⋊#11717579C2211yescharacteristic, complemented
21#15692184—21no—
22C4×#11717579C2211yescharacteristic, complemented
23C8×Dic101—21no—
24C4×D4×C101C2211yescharacteristic
25C4⋊C8×C101C2211yescharacteristic, complemented
26C4×C8×C101C2211yescharacteristic, complemented
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
41C2×#11717579—21no—
42C2×#11717579—21no—
43C8×D101—24no—
44C8×D101—42no—
45C4⋊Dic101C2×C411yescharacteristic
46#13108053—21no—
47C22⋊Dic101—21no—
48#13108051—21no—
49#13108051—21no—
50C4×Dic101C2×C411yescharacteristic
51C4×Dic101D411yescharacteristic
52C4×Dic101D411yescharacteristic
53C2×D4×C101C2×C411yescharacteristic
54C22×C4×C101—21no—
55C2×C8×C101—21no—
56C2×C8×C101—21no—
57C4⋊C4×C101C2×C411yescharacteristic
58C22⋊C4×C101—21no—
59C42×C101C2311yescharacteristic
60C23×C101—21no—
61C22×D101—21no—
62C22×D101—24no—
63C22×D101—42no—
64C22×D101—42no—
65C22×D101C22⋊C411yescharacteristic
66D4×C101—21no—
67D4×C101C2×C812yescomplemented
68C2×C4×C101—21no—
69C2×C4×C101—41no—
70C2×C4×C101—41no—
71C2×C4×C101C22×C411yescharacteristic
72C2×C4×C101C2×D411yescharacteristic
73C2×C4×C101C2×D411yescharacteristic
74C22⋊D101—24no—
75C2×Dic101—21no—
76C2×Dic101—42no—
77C2×Dic101C22⋊C411yescharacteristic
78C2×Dic101C22⋊C411yescharacteristic
79C2×Dic101C22⋊C411yescharacteristic
80D404—21no—
81D404C2×C812yescomplemented
82C4×D101—22no—
83C4×D101—42no—
84C4×D101—41no—
85C4×D101—41no—
86C4×D101—42no—
87C4×D101C2×C812yes—
88C4×D101M1612yes—
89C4×D101D812yes—
90C4×D101SD1612yes—
91C8×C101—22no—
92C8×C101—41no—
93#11717579—22no—
94#11717579—41no—
95C22×C101—22no—
96C22×C101—41no—
97C22×C101—41no—
98C22×C101C2×C22⋊C411yescharacteristic
99C2×D101—22no—
100C2×D101—41no—
101C2×D101—41no—
102C2×D101—48no—
103C2×D101C22⋊C812yes—
104C2×D101#10212yes—
105C2×D101#10412yes—
106C4×C101—21no—
107C4×C101—41no—
108C4×C101C22×C811yescharacteristic
109C4×C101C2×M1611yescharacteristic
110C4×C101C2×D811yescharacteristic
111C4×C101C2×SD1611yescharacteristic
112Dic101—21no—
113Dic101—41no—
114Dic101C22⋊C812yes—
115Dic101#10212yes—
116C2×C101—42no—
117C2×C101C2×C22⋊C811yescharacteristic
118C2×C101C2×#10211yescharacteristic
119C2×C101C2×#10411yescharacteristic
120D101—42no—
121D101D4⋊C814yesdirect product factor
122C2×D4⋊C8—1011nomaximal, Sylow
123C101C2×D4⋊C811yescharacteristic, complemented, Sylow
124C2×C4×D4—1011no—
125C2×C4⋊C8—1011no—
126C2×C4×C8—1011no—
127D4⋊C8—1011no—
128D4⋊C8—1011no—
129D4⋊C8—1011no—
130D4⋊C8D10111yescharacteristic, direct product factor
131C22×D4—1011no—
132C23×C4—2021no—
133C22×C8—2021no—
134C22×C8—2021no—
135C4×D4—1011no—
136C4×D4—1011no—
137C4×D4—1011no—
138C4×D4—2021no—
139C4×D4—2021no—
140C4×D4C2×D10111yescharacteristic
141C2×C4⋊C4—1011no—
142C2×C22⋊C4—2021no—
143C2×C42—1011no—
144C4⋊C8—1011no—
145C4⋊C8—2021no—
146C4⋊C8C2×D10111yescharacteristic, complemented
147C4×C8—1011no—
148C4×C8—2021no—
149C4×C8C2×D10111yescharacteristic, complemented
150C24—2021no—
151C2×D4—1014no—
152C2×D4—1011no—
153C2×D4—2022no—
154C2×D4—2021no—
155C2×D4C4×D10111yescharacteristic
156C22×C4—21no—
157C22×C4—1011no—
158C22×C4—1011no—
159C22×C4—1011no—
160C22×C4—4042no—
161C22×C4—4042no—
162C22×C4—2021no—
163C22×C4—2021no—
164C22×C4—2021no—
165C22×C4—2021no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—4042no—
169C2×C8—2024no—
170C2×C8—2021no—
171C2×C8—2021no—
172C4⋊C4—1011no—
173C4⋊C4—2021no—
174C4⋊C4C4×D10111yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—2021no—
177C22⋊C4—2021no—
178C22⋊C4—2021no—
179C42—1011no—
180C42—1011no—
181C42—1011no—
182C42C22×D10111yescharacteristic
183C23—21no—
184C23—1011no—
185C23—4042no—
186C23—4042no—
187C23—2024no—
188C23—2021no—
189D4—21no—
190D4—1012no—
191D4—2024no—
192D4—2021no—
193D4C8×D10112yescomplemented
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—1011no—
198C2×C4—1011no—
199C2×C4—1012no—
200C2×C4—1012no—
201C2×C4—1012no—
202C2×C4—1012no—
203C2×C4—1011no—
204C2×C4—4042no—
205C2×C4—4042no—
206C2×C4—4042no—
207C2×C4—4041no—
208C2×C4—4041no—
209C2×C4—2022no—
210C2×C4—2021no—
211C2×C4C2×C4×D10111yescharacteristic
212C2×C4D4×D10111yescharacteristic
213C2×C4D4×D10111yescharacteristic
214C8—22no—
215C8—41no—
216C8—4041no—
217C8—2022no—
218C22—22no—
219C22—41no—
220C22—41no—
221C22—1012no—
222C22—1012no—
223C22—1012no—
224C22—4048no—
225C22—4041no—
226C22—4041no—
227C22—2022no—
228C22C22⋊C4×D10111yescharacteristic
229C4—21no—
230C4—41no—
231C4—1012no—
232C4—1012no—
233C4—4041no—
234C4—2021no—
235C4C2×C8×D10111yescharacteristic
236C4M16×D10111yescharacteristic
237C4D8×D10111yescharacteristic
238C4SD16×D10111yescharacteristic
239C2—42no—
240C2—1014no—
241C2—4042no—
242C2C22⋊C8×D10111yescharacteristic
243C2#102×D10111yescharacteristic
244C2#104×D10111yescharacteristic
subgroupG/H
centerC2×C4D4×D101
commutatorC4×C101C22×C8
FrattiniC42C22×D101
FittingD4⋊C8×C101C2
socleC22×C101C2×C22⋊C4
prime radicalC2×D4×D101C4
cosocleC42×C101C23
hypercenterD4⋊C8D101
hypocenterC101C2×D4⋊C8
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4⋊C8×D101C2semidirect
3. C4×C8×D101C2semidirect
4. #20264906C2semidirect
5. D4⋊#11717579C2semidirect
6. #20264904C2semidirect
7. D4⋊C8×C101C2semidirect
20. C4⋊#11717579C22semidirect
22. C4×#11717579C22semidirect
25. C4⋊C8×C101C22semidirect
26. C4×C8×C101C22semidirect
31. D4×D101C8semidirect
67. D4×C101C2×C8semidirect
81. D404C2×C8semidirect
121. D101D4⋊C8direct (N × H)
123. C101C2×D4⋊C8semidirect
130. D4⋊C8D101direct (N × H)
146. C4⋊C8C2×D101semidirect
149. C4×C8C2×D101semidirect
193. D4C8×D101semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D1012
C4⋊C8×D1012
C4×C8×D1012
#202649062
D4⋊#117175792
#202649042
D4⋊C8×C1012
C2×D4⋊C8101