Finite Group Databasebeta

← C2×#1635 #18487

Subgroups — C2×#1635 #18487

Order 256.

603 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 603 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×#547C211yesmaximal, characteristic
2C2×#487C211yesmaximal, characteristic, complemented
3C2×#476C211yesmaximal, characteristic, complemented
4C2×#476C211yesmaximal, characteristic, complemented
5#1635C218yesmaximal, direct product factor
6C2×#332C211yesmaximal, characteristic, complemented
7C2×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×D4⋊C8C211yesmaximal, characteristic, complemented
9C22×#41—21no—
10#547—22no—
11#547—22no—
12#547—22no—
13#547C2214yes—
14C2×C4⋊Q8C2211yescharacteristic
15C2×C4⋊Q8C2211yescharacteristic
16C2×#123—22no—
17C2×C22⋊Q8—21no—
18C2×#121—21no—
19C2×C4×D4C2211yescharacteristic
20C2×C4×D4C2211yescharacteristic
21C22×C4⋊C4—21no—
22#487—22no—
23#487C2214yescomplemented
24#476—22no—
25#476—22no—
26#476C2214yescomplemented
27#476C2214yescomplemented
28C2×#106—21no—
29C2×#106—21no—
30C2×C4⋊C8C2211yescharacteristic
31C2×C4⋊C8C2211yescharacteristic
32C2×#103—22no—
33C2×#102—21no—
34C2×#102—21no—
35C2×C4×C8C2211yescharacteristic
36#332C2214yescomplemented
37D4⋊C8C2214yescomplemented
38D4⋊C8C2214yescomplemented
39C2×#41—24no—
40C2×#41—24no—
41C2×#41—44no—
42C2×#41—44no—
43C22×Q8—21no—
44C22×Q8—21no—
45C22×D4—22no—
46C22×D4D411yescharacteristic
47C22×D4D411yescharacteristic
48C23×C4—22no—
49C23×C4—21no—
50C23×C4—21no—
51C22×C8—21no—
52C22×C8—21no—
53C22×C8—21no—
54C4⋊Q8—21no—
55C4⋊Q8—21no—
56C4⋊Q8—21no—
57C4⋊Q8—21no—
58C4⋊Q8—21no—
59C4⋊Q8D412yes—
60C4⋊Q8C2312yes—
61C4⋊Q8C2312yes—
62#123—28no—
63#123—28no—
64C22⋊Q8—24no—
65C22⋊Q8—24no—
66#121—24no—
67#121—24no—
68C4×D4—21no—
69C4×D4—21no—
70C4×D4—21no—
71C4×D4—21no—
72C4×D4D412yes—
73C4×D4D412yes—
74C4×D4C2312yes—
75C4×D4C2312yes—
76C2×C4⋊C4—22no—
77C2×C4⋊C4—24no—
78C2×C4⋊C4—21no—
79C2×C4⋊C4—24no—
80C2×C4⋊C4—21no—
81C2×C4⋊C4—21no—
82C2×C4⋊C4D411yescharacteristic
83C2×C4⋊C4D411yescharacteristic
84C2×C4⋊C4D412yes—
85C2×C22⋊C4—22no—
86C2×C22⋊C4—21no—
87C2×C22⋊C4—21no—
88C2×C42C2311yescharacteristic
89#106—24no—
90#106—24no—
91C4⋊C8—21no—
92C4⋊C8—21no—
93C4⋊C8C2312yes—
94C4⋊C8C2312yes—
95#103—28no—
96#102—24no—
97#102—24no—
98C4×C8—21no—
99C4×C8C2312yes—
100C24—21no—
101C24—21no—
102#41—48no—
103#41—416no—
104#41—48no—
105C2×Q8—22no—
106C2×Q8—22no—
107C2×Q8—22no—
108C2×Q8—44no—
109C2×Q8—41no—
110C2×Q8—42no—
111C2×Q8—42no—
112C2×D4—28no—
113C2×D4—21no—
114C2×D4—21no—
115C2×D4—22no—
116C2×D4—22no—
117C2×D4—22no—
118C2×D4—48no—
119C2×D4SD1614yes—
120C2×D4C2×D412yes—
121C2×D4C2×D412yes—
122C22×C4—28no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—22no—
126C22×C4—22no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—48no—
131C22×C4—42no—
132C22×C4—42no—
133C22×C4—42no—
134C22×C4—42no—
135C22×C4—41no—
136C22×C4C2×D411yescharacteristic
137C22×C4C2×D411yescharacteristic
138C22×C4C2×D411yescharacteristic
139C2×C8—22no—
140C2×C8—22no—
141C2×C8—22no—
142C2×C8—42no—
143C2×C8—42no—
144C2×C8—42no—
145C4⋊C4—28no—
146C4⋊C4—21no—
147C4⋊C4—22no—
148C4⋊C4—21no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—41no—
154C4⋊C4—41no—
155C4⋊C4C2×D414yes—
156C4⋊C4C2×D412yes—
157C4⋊C4C2×D412yes—
158C22⋊C4—28no—
159C22⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—22no—
162C22⋊C4—22no—
163C42C2×D411yescharacteristic
164C42C2×D411yescharacteristic
165C42C2×D411yescharacteristic
166C42C2411yescharacteristic
167C23—22no—
168C23—24no—
169C23—22no—
170C23—42no—
171C23—42no—
172C23—42no—
173C23—42no—
174C23—42no—
175C23#12011yescharacteristic
176Q8—44no—
177Q8—42no—
178Q8—42no—
179Q8—44no—
180Q8—82no—
181D4—22no—
182D4—22no—
183D4—22no—
184D4—24no—
185D4—416no—
186D4—42no—
187D4C2×SD1614yes—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—24no—
192C2×C4—416no—
193C2×C4—42no—
194C2×C4—44no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—44no—
201C2×C4—44no—
202C2×C4—42no—
203C2×C4—82no—
204C2×C4#12011yescharacteristic
205C2×C4#12011yescharacteristic
206C2×C4#12011yescharacteristic
207C2×C4C2×SD1612yes—
208C2×C4#13512yes—
209C2×C4AGL(1,ℤ/8)12yes—
210C2×C4#13712yes—
211C2×C4C22×D411yescharacteristic
212C2×C4C22×D411yescharacteristic
213C2×C4C22×D411yescharacteristic
214C8—42no—
215C8—42no—
216C8—42no—
217C22—24no—
218C22—48no—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—84no—
225C22#45012yes—
226C22#45212yes—
227C22#45412yes—
228C22C2×#12011yescharacteristic
229C4—21no—
230C4—21no—
231C4—42no—
232C4—44no—
233C4—42no—
234C4—82no—
235C4#45012yes—
236C4#45212yes—
237C4C22×SD1611yescharacteristic
238C4C2×#13511yescharacteristic
239C4C2×AGL(1,ℤ/8)11yescharacteristic
240C4C2×#13711yescharacteristic
241C2—44no—
242C2—82no—
243C2#163514yesdirect product factor
244C2C2×#45011yescharacteristic
245C2C2×#45211yescharacteristic
246C2C2×#45411yescharacteristic
subgroupG/H
center, socleC23#120
commutator, Frattini, cosocleC42C24
prime radicalC2×#547C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#487C2semidirect
3. C2×#476C2semidirect
4. C2×#476C2semidirect
5. #1635C2direct (N × H)
6. C2×#332C2semidirect
7. C2×D4⋊C8C2semidirect
8. C2×D4⋊C8C2semidirect
23. #487C22semidirect
26. #476C22semidirect
27. #476C22semidirect
36. #332C22semidirect
37. D4⋊C8C22semidirect
38. D4⋊C8C22semidirect
243. C2#1635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#5472
C2×#4872
C2×#4762
#16352
C2×#3322
C2×D4⋊C82