Finite Group Databasebeta

← C2×#10593423 #11866765

Subgroups — C2×#10593423 #11866765

Order 1152.

1042 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 1042 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×#3787C211yesmaximal, characteristic, complemented
2C22×#3774C211yesmaximal, characteristic, complemented
3C2×#63912C212yesmaximal, complemented
4C2×#63743C211yesmaximal, characteristic, complemented
5C2×#63739C212yesmaximal, complemented
6#10593423C218yesmaximal, direct product factor
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#626—22no—
9C22×#625C2212yes—
10C22×#622C2211yescharacteristic
11C22×#622C2211yescharacteristic
12C2×#3787—24no—
13C2×#3787C2214yescomplemented
14C2×#3774—24no—
15C2×#3774C2214yescomplemented
16C2×C3×(C2×D3)⋊C4—22no—
17C2×#3724C2212yes—
18#63912—24no—
19#63912C2218yescomplemented
20#63743C2214yescomplemented
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#3787—28no—
43#3774—28no—
44C3×(C2×D3)⋊C4—28no—
45#3724—22no—
46#3724C2314yes—
47C2×#466—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—22no—
59C22×C3⋊D3—22no—
60C22×C3⋊D3D814yescomplemented
61C22×C3⋊D3C2×D412yes—
62C22×C3×D3—24no—
63C22×C3×D3—44no—
64C22×C3×D3—44no—
65C22×C3×D3—44no—
66C2×C32×C4—22no—
67C2×C32×C4C2×D412yes—
68C2×C3⋊Dic3C2×D411yescharacteristic
69C2×C3⋊Dic3C2×D412yes—
70C2×C3⋊Dic3#4112yes—
71C2×C3⋊Dic3C2411yescharacteristic
72C4×C3⋊D3—24no—
73C4×C3⋊D3—22no—
74C4×C3⋊D3—22no—
75C2×C3×Dic3—24no—
76C2×C3×Dic3—44no—
77#626—416no—
78#625—24no—
79#625—24no—
80#625—44no—
81#622—22no—
82#622C2×D414yescomplemented
83C22×D8—91no—
84C23×C8—91no—
85C2×#121—92no—
86#466—98no—
87C2×#107—91no—
88C2×#102—92no—
89C24×C3—62no—
90C23×D3—22no—
91C23×D3—62no—
92C22×C3×C4—22no—
93C22×C3×C4—62no—
94C2×#67—64no—
95C2×#67—68no—
96C2×#67—64no—
97C2×#67—124no—
98C2×#67—124no—
99C2×#67—128no—
100C22×Dic3—22no—
101C22×Dic3—62no—
102C2×D12—68no—
103C2×D12—128no—
104C2×C4×D3—64no—
105C2×C4×D3—64no—
106C2×C4×D3—124no—
107C2×C4×D3—124no—
108C3×C22⋊C4—68no—
109(C2×D3)⋊C4—28no—
110Dic3⋊C4—64no—
111Dic3⋊C4—64no—
112C22×C32#12112yes—
113C22×C32C2×D812yes—
114C22×C32#13512yes—
115C22×C32C22×D411yescharacteristic
116C2×C3⋊D3—22no—
117C2×C3⋊D3—22no—
118C2×C3⋊D3—28no—
119C2×C3⋊D3C2×D814yescomplemented
120C2×C3×D3—44no—
121C2×C3×D3—44no—
122C2×C3×D3—44no—
123C2×C3×D3—88no—
124C32×C4—22no—
125C3⋊Dic3#12112yes—
126C3⋊Dic3C22×D411yescharacteristic
127C3⋊Dic3C2×#4111yescharacteristic
128C3×Dic3—44no—
129C22×D4—92no—
130C22×D4—182no—
131C23×C4—91no—
132C2×D8—94no—
133C2×D8—184no—
134C22×C8—91no—
135C22×C8—94no—
136C22×C8—91no—
137C22×C8—184no—
138#121—98no—
139#121—184no—
140C2×C4⋊C4—92no—
141C2×C22⋊C4—62no—
142#107—94no—
143#102—98no—
144C23×C3—22no—
145C23×C3—64no—
146C23×C3—124no—
147C23×C3—124no—
148C23×C3—124no—
149C22×D3—24no—
150C22×D3—44no—
151C22×D3—44no—
152C22×D3—44no—
153C22×D3—68no—
154C22×D3—64no—
155C22×D3—124no—
156C22×D3—124no—
157C2×C3×C4—24no—
158C2×C3×C4—44no—
159C2×C3×C4—64no—
160C2×C3×C4—124no—
161#67—124no—
162#67—124no—
163#67—1216no—
164#67—128no—
165C2×Dic3—24no—
166C2×Dic3—44no—
167C2×Dic3—62no—
168C2×Dic3—64no—
169C2×Dic3—64no—
170C2×Dic3—62no—
171D12—1216no—
172C4×D3—124no—
173C4×D3—128no—
174C4×D3—124no—
175C2×C32#46614yescomplemented
176C2×C32C2×#12111yescharacteristic
177C2×C32C22×D811yescharacteristic
178C2×C32C2×#13511yescharacteristic
179C3⋊D3—24no—
180C3×D3—84no—
181C24—62no—
182C24—91no—
183C2×D4—94no—
184C2×D4—188no—
185C2×D4—184no—
186C2×D4—184no—
187C2×D4—182no—
188C2×D4—368no—
189C22×C4—62no—
190C22×C4—91no—
191C22×C4—92no—
192C22×C4—92no—
193C22×C4—182no—
194C22×C4—182no—
195C22×C4GO+(4,𝔽2)11yescharacteristic
196D8—188no—
197C2×C8—92no—
198C2×C8—94no—
199C2×C8—92no—
200C2×C8—188no—
201C2×C8—182no—
202C4⋊C4—94no—
203C4⋊C4—182no—
204C22⋊C4—68no—
205C22×C3—22no—
206C22×C3—24no—
207C22×C3—24no—
208C22×C3—24no—
209C22×C3—124no—
210C22×C3—124no—
211C22×C3—124no—
212C22×C3—248no—
213C2×D3—44no—
214C2×D3—44no—
215C2×D3—44no—
216C2×D3—68no—
217C2×D3—88no—
218C2×D3—124no—
219C2×D3—1216no—
220C2×D3—124no—
221C3×C4—44no—
222C3×C4—124no—
223Dic3—44no—
224Dic3—64no—
225Dic3—62no—
226Dic3—62no—
227C32C2×#46611yescharacteristic, complemented, Sylow
228C23—64no—
229C23—92no—
230C23—94no—
231C23—124no—
232C23—124no—
233C23—124no—
234C23—182no—
235C23—182no—
236C23C2×GO+(4,𝔽2)11yescharacteristic
237D4—184no—
238D4—184no—
239D4—364no—
240D4—3616no—
241C2×C4—22no—
242C2×C4—64no—
243C2×C4—91no—
244C2×C4—91no—
245C2×C4—92no—
246C2×C4—92no—
247C2×C4—124no—
248C2×C4—182no—
249C2×C4—182no—
250C2×C4—184no—
251C2×C4C2×GO+(4,𝔽2)12yes—
252C8—94no—
253C8—182no—
254C2×C3—28no—
255C2×C3—22no—
256C2×C3—22no—
257C2×C3—22no—
258C2×C3—244no—
259D3—84no—
260D3—128no—
261C22—94no—
262C22—124no—
263C22—124no—
264C22—124no—
265C22—188no—
266C22—182no—
267C22—182no—
268C22—248no—
269C22#6422312yes—
270C22#6422512yes—
271C22#6424212yes—
272C22C22×GO+(4,𝔽2)11yescharacteristic
273C4—22no—
274C4—91no—
275C4—91no—
276C4—92no—
277C4—124no—
278C3—22no—
279C2—184no—
280C2—244no—
281C2#1059342314yesdirect product factor
282C2C2×#6422311yescharacteristic
283C2C2×#6422511yescharacteristic
284C2C2×#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×#466
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×#3787C2semidirect
2. C22×#3774C2semidirect
3. C2×#63912C2semidirect
4. C2×#63743C2semidirect
5. C2×#63739C2semidirect
6. #10593423C2direct (N × H)
13. C2×#3787C22semidirect
15. C2×#3774C22semidirect
19. #63912C22semidirect
20. #63743C22semidirect
21. #63739C22semidirect
39. C2×#622D4semidirect
60. C22×C3⋊D3D8semidirect
82. #622C2×D4semidirect
119. C2×C3⋊D3C2×D8semidirect
175. C2×C32#466semidirect
227. C32C2×#466semidirect
281. C2#10593423direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37872
C22×#37742
C2×#639122
C2×#637432
C2×#637392
#105934232
C2×#4669