Finite Group Databasebeta

← C2×#10593424 #11874268

Subgroups — C2×#10593424 #11874268

Order 1152.

922 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 922 conjugacy classes of subgroups — too many to draw. Only its 135 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×#3776C211yesmaximal, characteristic, complemented
2C22×#3775C212yesmaximal, complemented
3C22×#3774C211yesmaximal, characteristic
4C2×#63915C212yesmaximal, complemented
5C2×C4×#622C211yesmaximal, characteristic, complemented
6#10593424C218yesmaximal, direct product factor
7C22×#627C2212yes—
8C22×#625C2212yes—
9C22×#622C2211yescharacteristic
10C22×#622C2211yescharacteristic
11C2×#3776—24no—
12C2×#3776C2214yescomplemented
13C2×#3775—28no—
14C2×#3775C2218yescomplemented
15C2×#3774—24no—
16C2×#3774C2214yes—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4—22no—
19C2×(C2×D3)⋊Dic3—22no—
20#63915—24no—
21#63915C2218yescomplemented
22C4×#622C2214yescomplemented
23C2×#885—62no—
24C23×C3×D3—22no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3C2311yescharacteristic
28C22×C3×Dic3—22no—
29C2×#627—24no—
30C2×#627—24no—
31C2×#627—22no—
32C2×#627C2314yes—
33C2×#625—24no—
34C2×#625—24no—
35C2×#625—22no—
36C2×#625C2314yes—
37C2×#622D414yes—
38C2×#622D414yes—
39C2×#622C2312yes—
40C2×#622C2312yes—
41#3776—28no—
42#3775—216no—
43#3774—28no—
44C4×C3⋊Dic3D412yes—
45C4×C3⋊Dic3C2312yes—
46C3×(C2×D3)⋊C4—28no—
47(C2×D3)⋊Dic3—28no—
48C2×#495—91nomaximal, Sylow
49C22×#67—62no—
50C22×Dic6—62no—
51C2×C3×C22⋊C4—62no—
52C2×#217—62no—
53C2×(C2×D3)⋊C4—22no—
54C2×(C2×D3)⋊C4—62no—
55C2×C4×Dic3—62no—
56#885—68no—
57#885—68no—
58C23×C32C2×D411yescharacteristic
59C22×C3×D3—24no—
60C22×C3×D3—44no—
61C22×C3×D3—44no—
62C22×C3×D3—44no—
63C2×C32×C4—22no—
64C2×C32×C4C2×D412yes—
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3C2×D412yes—
67C2×C3⋊Dic3C2×D411yescharacteristic
68C2×C3⋊Dic3C2×D412yes—
69C2×C3⋊Dic3C2×D412yes—
70C2×C3⋊Dic3C2411yescharacteristic
71C2×C3×Dic3—24no—
72C2×C3×Dic3—44no—
73#627—24no—
74#627—24no—
75#627—44no—
76#625—24no—
77#625—24no—
78#625—44no—
79#622C2×D414yes—
80#622C2×D414yes—
81C22×Q16—91no—
82C22×SD16—92no—
83C22×D8—91no—
84C2×#124—92no—
85#495—98no—
86C2×C4×C8—91no—
87C24×C3—62no—
88C23×D3—22no—
89C22×C3×C4—22no—
90C22×C3×C4—62no—
91C2×#67—64no—
92C2×#67—64no—
93C2×#67—124no—
94C2×#67—124no—
95C22×Dic3—22no—
96C22×Dic3—62no—
97C22×Dic3—62no—
98C2×Dic6—64no—
99C2×Dic6—64no—
100C2×Dic6—124no—
101C2×Dic6—124no—
102C3×C22⋊C4—68no—
103#217—68no—
104(C2×D3)⋊C4—28no—
105(C2×D3)⋊C4—68no—
106C4×Dic3—64no—
107C4×Dic3—64no—
108C22×C32#12712yes—
109C22×C32#13512yes—
110C22×C32#13512yes—
111C22×C32C22×D411yescharacteristic
112C2×C3×D3—44no—
113C2×C3×D3—44no—
114C2×C3×D3—44no—
115C2×C3×D3—88no—
116C32×C4—22no—
117C3⋊Dic3—22no—
118C3⋊Dic3#12712yes—
119C3⋊Dic3C22×D411yescharacteristic
120C3⋊Dic3C22×D411yescharacteristic
121C3×Dic3—44no—
122C22×Q8—92no—
123C22×D4—92no—
124C2×Q16—94no—
125C2×Q16—184no—
126C2×SD16—98no—
127C2×SD16—188no—
128C2×D8—94no—
129C2×D8—184no—
130C22×C8—91no—
131C22×C8—91no—
132#124—98no—
133#124—184no—
134C2×C22⋊C4—62no—
135C2×C22⋊C4—182no—
136C2×C42—91no—
137C4×C8—94no—
138C23×C3—22no—
139C23×C3—64no—
140C23×C3—124no—
141C23×C3—124no—
142C23×C3—124no—
143C22×D3—24no—
144C22×D3—44no—
145C22×D3—44no—
146C22×D3—44no—
147C2×C3×C4—24no—
148C2×C3×C4—44no—
149C2×C3×C4—64no—
150C2×C3×C4—124no—
151#67—124no—
152#67—124no—
153#67—128no—
154C2×Dic3—24no—
155C2×Dic3—44no—
156C2×Dic3—62no—
157C2×Dic3—64no—
158C2×Dic3—64no—
159C2×Dic3—62no—
160C2×Dic3—64no—
161C2×Dic3—124no—
162Dic6—124no—
163Dic6—124no—
164Dic6—128no—
165C2×C32#49514yescomplemented
166C2×C32C2×#12711yescharacteristic
167C2×C32C2×#13511yescharacteristic
168C2×C32C2×#13511yescharacteristic
169C3×D3—84no—
170C24—62no—
171C2×Q8—94no—
172C2×Q8—182no—
173C2×Q8—184no—
174C2×Q8—184no—
175C2×D4—94no—
176C2×D4—184no—
177C2×D4—184no—
178C2×D4—182no—
179C22×C4—62no—
180C22×C4—91no—
181C22×C4—91no—
182C22×C4GO+(4,𝔽2)11yescharacteristic
183Q16—188no—
184SD16—1816no—
185D8—188no—
186C2×C8—92no—
187C2×C8—92no—
188C2×C8—94no—
189C2×C8—94no—
190C22⋊C4—68no—
191C22⋊C4—188no—
192C42—92no—
193C42—92no—
194C22×C3—22no—
195C22×C3—24no—
196C22×C3—24no—
197C22×C3—24no—
198C22×C3—124no—
199C22×C3—124no—
200C22×C3—124no—
201C22×C3—248no—
202C2×D3—44no—
203C2×D3—44no—
204C2×D3—44no—
205C2×D3—88no—
206C3×C4—44no—
207C3×C4—124no—
208Dic3—44no—
209Dic3—64no—
210Dic3—62no—
211Dic3—62no—
212Dic3—124no—
213C32C2×#49511yescharacteristic, complemented, Sylow
214C23—64no—
215C23—124no—
216C23—124no—
217C23—124no—
218C23C2×GO+(4,𝔽2)11yescharacteristic
219Q8—184no—
220Q8—184no—
221Q8—364no—
222D4—184no—
223D4—184no—
224D4—364no—
225C2×C4—22no—
226C2×C4—64no—
227C2×C4—91no—
228C2×C4—91no—
229C2×C4—92no—
230C2×C4—92no—
231C2×C4—92no—
232C2×C4—124no—
233C2×C4—182no—
234C2×C4C2×GO+(4,𝔽2)12yes—
235C8—94no—
236C8—94no—
237C2×C3—28no—
238C2×C3—22no—
239C2×C3—22no—
240C2×C3—22no—
241C2×C3—244no—
242D3—84no—
243C22—124no—
244C22—124no—
245C22—124no—
246C22—248no—
247C22#6422312yes—
248C22#6423112yes—
249C22#6423712yes—
250C22C22×GO+(4,𝔽2)11yescharacteristic
251C4—22no—
252C4—91no—
253C4—91no—
254C4—92no—
255C4—124no—
256C4—182no—
257C3—22no—
258C2—244no—
259C2#1059342414yesdirect product factor
260C2C2×#6422311yescharacteristic
261C2C2×#6423111yescharacteristic
262C2C2×#6423711yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#3774C2
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#495
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3776C2semidirect
2. C22×#3775C2semidirect
4. C2×#63915C2semidirect
5. C2×C4×#622C2semidirect
6. #10593424C2direct (N × H)
12. C2×#3776C22semidirect
14. C2×#3775C22semidirect
21. #63915C22semidirect
22. C4×#622C22semidirect
165. C2×C32#495semidirect
213. C32C2×#495semidirect
259. C2#10593424direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37762
C22×#37752
C22×#37742
C2×#639152
C2×C4×#6222
#105934242
C2×#4959