Finite Group Databasebeta

← C2×#10593429 #11866987

Subgroups — C2×#10593429 #11866987

Order 1152.

1022 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 127 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×#3788C211yesmaximal, characteristic, complemented
2C22×#3774C211yesmaximal, characteristic, complemented
3C2×#63912C212yesmaximal, complemented
4C2×#63742C211yesmaximal, characteristic, complemented
5C2×#63739C212yesmaximal, complemented
6#10593429C218yesmaximal, direct product factor
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#626—22no—
9C22×#625C2212yes—
10C22×#622C2211yescharacteristic
11C22×#622C2211yescharacteristic
12C2×#3788—24no—
13C2×#3788C2214yescomplemented
14C2×#3774—24no—
15C2×#3774C2214yescomplemented
16C2×C3×(C2×D3)⋊C4—22no—
17C2×#3724C2212yes—
18#63912—24no—
19#63912C2218yescomplemented
20#63742C2214yescomplemented
21#63739C2218yescomplemented
22C2×#884—62no—
23C23×C3⋊D3D411yescharacteristic
24C23×C3×D3—22no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3C2311yescharacteristic
27C2×C4×C3⋊D3—22no—
28C2×C4×C3⋊D3—22no—
29C2×C4×C3⋊D3D412yes—
30C2×C4×C3⋊D3C2312yes—
31C22×C3×Dic3—22no—
32C2×#626—28no—
33C2×#626—48no—
34C2×#625—24no—
35C2×#625—24no—
36C2×#625—22no—
37C2×#625C2314yes—
38C2×#622—22no—
39C2×#622D414yescomplemented
40C2×#622C2312yes—
41C2×#622C2312yes—
42#3788—28no—
43#3774—28no—
44C3×(C2×D3)⋊C4—28no—
45#3724—22no—
46#3724C2314yes—
47C2×#469—91nomaximal, Sylow
48C22×#67—62no—
49C22×#67—62no—
50C22×D12—62no—
51C22×C4×D3—62no—
52C2×C3×C22⋊C4—62no—
53C2×(C2×D3)⋊C4—22no—
54C2×Dic3⋊C4—62no—
55#884—68no—
56#884—68no—
57C23×C32C2×D411yescharacteristic
58C22×C3⋊D3—24no—
59C22×C3⋊D3—22no—
60C22×C3⋊D3C2×D412yes—
61C22×C3×D3—24no—
62C22×C3×D3—44no—
63C22×C3×D3—44no—
64C22×C3×D3—44no—
65C2×C32×C4—22no—
66C2×C32×C4C2×D412yes—
67C2×C3⋊Dic3C2×D411yescharacteristic
68C2×C3⋊Dic3C2×D412yes—
69C2×C3⋊Dic3#4112yes—
70C2×C3⋊Dic3C2411yescharacteristic
71C4×C3⋊D3—24no—
72C4×C3⋊D3—22no—
73C4×C3⋊D3—22no—
74C2×C3×Dic3—24no—
75C2×C3×Dic3—44no—
76#626—416no—
77#625—24no—
78#625—24no—
79#625—44no—
80#622—22no—
81#622C2×D414yescomplemented
82C22×D8—91no—
83C22×M16—91no—
84C2×#121—92no—
85#469—98no—
86C2×#106—91no—
87C2×#102—92no—
88C24×C3—62no—
89C23×D3—22no—
90C23×D3—62no—
91C22×C3×C4—22no—
92C22×C3×C4—62no—
93C2×#67—64no—
94C2×#67—68no—
95C2×#67—64no—
96C2×#67—124no—
97C2×#67—124no—
98C2×#67—128no—
99C22×Dic3—22no—
100C22×Dic3—62no—
101C2×D12—68no—
102C2×D12—128no—
103C2×C4×D3—64no—
104C2×C4×D3—64no—
105C2×C4×D3—124no—
106C2×C4×D3—124no—
107C3×C22⋊C4—68no—
108(C2×D3)⋊C4—28no—
109Dic3⋊C4—64no—
110Dic3⋊C4—64no—
111C22×C32#12112yes—
112C22×C32AGL(1,ℤ/8)14yes—
113C22×C32C22×D411yescharacteristic
114C2×C3⋊D3—24no—
115C2×C3⋊D3—22no—
116C2×C3⋊D3—44no—
117C2×C3×D3—44no—
118C2×C3×D3—44no—
119C2×C3×D3—44no—
120C2×C3×D3—88no—
121C32×C4—22no—
122C3⋊Dic3#12112yes—
123C3⋊Dic3C22×D411yescharacteristic
124C3⋊Dic3C2×#4111yescharacteristic
125C3×Dic3—44no—
126C22×D4—92no—
127C22×D4—182no—
128C23×C4—91no—
129C2×D8—94no—
130C2×D8—184no—
131C2×M16—94no—
132C2×M16—184no—
133C22×C8—91no—
134C22×C8—91no—
135#121—98no—
136#121—184no—
137C2×C4⋊C4—92no—
138C2×C22⋊C4—62no—
139#106—94no—
140#102—98no—
141C23×C3—22no—
142C23×C3—64no—
143C23×C3—124no—
144C23×C3—124no—
145C23×C3—124no—
146C22×D3—24no—
147C22×D3—44no—
148C22×D3—44no—
149C22×D3—44no—
150C22×D3—64no—
151C22×D3—68no—
152C22×D3—124no—
153C22×D3—124no—
154C2×C3×C4—24no—
155C2×C3×C4—44no—
156C2×C3×C4—64no—
157C2×C3×C4—124no—
158#67—124no—
159#67—124no—
160#67—1216no—
161#67—128no—
162C2×Dic3—24no—
163C2×Dic3—44no—
164C2×Dic3—62no—
165C2×Dic3—64no—
166C2×Dic3—64no—
167C2×Dic3—62no—
168D12—1216no—
169C4×D3—124no—
170C4×D3—128no—
171C4×D3—124no—
172C2×C32#46914yescomplemented
173C2×C32C2×#12111yescharacteristic
174C2×C32C2×AGL(1,ℤ/8)12yes—
175C3⋊D3—42no—
176C3×D3—84no—
177C24—62no—
178C24—91no—
179C2×D4—94no—
180C2×D4—188no—
181C2×D4—184no—
182C2×D4—184no—
183C2×D4—182no—
184C2×D4—368no—
185C22×C4—62no—
186C22×C4—91no—
187C22×C4—92no—
188C22×C4—92no—
189C22×C4—182no—
190C22×C4—182no—
191C22×C4GO+(4,𝔽2)11yescharacteristic
192D8—188no—
193M16—188no—
194C2×C8—92no—
195C2×C8—94no—
196C2×C8—92no—
197C2×C8—182no—
198C4⋊C4—94no—
199C4⋊C4—182no—
200C22⋊C4—68no—
201C22×C3—22no—
202C22×C3—24no—
203C22×C3—24no—
204C22×C3—24no—
205C22×C3—124no—
206C22×C3—124no—
207C22×C3—124no—
208C22×C3—248no—
209C2×D3—44no—
210C2×D3—44no—
211C2×D3—44no—
212C2×D3—68no—
213C2×D3—88no—
214C2×D3—124no—
215C2×D3—124no—
216C2×D3—1216no—
217C3×C4—44no—
218C3×C4—124no—
219Dic3—44no—
220Dic3—64no—
221Dic3—62no—
222Dic3—62no—
223C32C2×#46911yescharacteristic, complemented, Sylow
224C23—64no—
225C23—92no—
226C23—124no—
227C23—124no—
228C23—124no—
229C23—184no—
230C23—182no—
231C23C2×GO+(4,𝔽2)11yescharacteristic
232D4—184no—
233D4—184no—
234D4—364no—
235D4—3616no—
236C2×C4—22no—
237C2×C4—64no—
238C2×C4—91no—
239C2×C4—91no—
240C2×C4—92no—
241C2×C4—92no—
242C2×C4—124no—
243C2×C4—182no—
244C2×C4—182no—
245C2×C4—184no—
246C2×C4C2×GO+(4,𝔽2)12yes—
247C8—94no—
248C8—182no—
249C2×C3—22no—
250C2×C3—22no—
251C2×C3—28no—
252C2×C3—22no—
253C2×C3—244no—
254D3—84no—
255D3—128no—
256C22—124no—
257C22—124no—
258C22—124no—
259C22—184no—
260C22—182no—
261C22—248no—
262C22—364no—
263C22#6422414yes—
264C22#6424212yes—
265C22C22×GO+(4,𝔽2)11yescharacteristic
266C4—22no—
267C4—91no—
268C4—91no—
269C4—92no—
270C4—124no—
271C3—22no—
272C2—244no—
273C2—362no—
274C2#1059342914yesdirect product factor
275C2C2×#6422412yes—
276C2C2×#6424211yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#469
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×#3788C2semidirect
2. C22×#3774C2semidirect
3. C2×#63912C2semidirect
4. C2×#63742C2semidirect
5. C2×#63739C2semidirect
6. #10593429C2direct (N × H)
13. C2×#3788C22semidirect
15. C2×#3774C22semidirect
19. #63912C22semidirect
20. #63742C22semidirect
21. #63739C22semidirect
39. C2×#622D4semidirect
81. #622C2×D4semidirect
172. C2×C32#469semidirect
223. C32C2×#469semidirect
274. C2#10593429direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37882
C22×#37742
C2×#639122
C2×#637422
C2×#637392
#105934292
C2×#4699