Finite Group Databasebeta

← C2×#10593520 #11866764

Subgroups — C2×#10593520 #11866764

Order 1152.

1042 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 1042 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
1C23×#622C211yesmaximal, characteristic, complemented
2C22×#3774C211yesmaximal, characteristic, complemented
3C2×#63980C212yesmaximal, complemented
4#10593520C218yesmaximal, direct product factor
5C2×#63743C211yesmaximal, characteristic, complemented
6C2×#63739C212yesmaximal, complemented
7C23×C3⋊Dic3C2211yescharacteristic
8C22×C3×#67—22no—
9C22×#625C2212yes—
10C22×#622—24no—
11C22×#622C2211yescharacteristic
12C22×#622C2211yescharacteristic
13C22×#622C2214yescomplemented
14C2×#3774—24no—
15C2×#3774C2214yescomplemented
16#63980—24no—
17#63980C2218yescomplemented
18C2×#3724C2212yes—
19C2×(C2×D3)⋊Dic3—22no—
20#63743C2214yescomplemented
21#63739C2218yescomplemented
22C2×#939—62no—
23C24×C32D411yescharacteristic
24C23×C3×D3—22no—
25C22×C3⋊Dic3—22no—
26C22×C3⋊Dic3—22no—
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3D412yes—
29C22×C3⋊Dic3C2312yes—
30C22×C3⋊Dic3C2311yescharacteristic
31C2×C3×#67—28no—
32C2×C3×#67—48no—
33C22×C3×Dic3—22no—
34C2×#625—24no—
35C2×#625—24no—
36C2×#625—22no—
37C2×#625C2314yes—
38C2×#622—22no—
39C2×#622—28no—
40C2×#622D414yescomplemented
41C2×#622C2312yes—
42C2×#622C2312yes—
43#3774—28no—
44#3724—22no—
45#3724C2314yes—
46(C2×D3)⋊Dic3—28no—
47C2×#466—91nomaximal, Sylow
48C22×C3×D4—62no—
49C22×#67—22no—
50C22×#67—62no—
51C23×Dic3—62no—
52C2×#217—62no—
53#939—68no—
54#939—68no—
55C2×(C2×D3)⋊C4—62no—
56C2×Dic3⋊C4—62no—
57C23×C32—22no—
58C23×C32—22no—
59C23×C32D814yescomplemented
60C23×C32C2×D412yes—
61C23×C32C2×D411yescharacteristic
62C22×C3×D3—24no—
63C22×C3×D3—44no—
64C22×C3×D3—44no—
65C22×C3×D3—44no—
66C2×C3⋊Dic3—22no—
67C2×C3⋊Dic3—24no—
68C2×C3⋊Dic3—22no—
69C2×C3⋊Dic3—22no—
70C2×C3⋊Dic3C2×D412yes—
71C2×C3⋊Dic3C2×D411yescharacteristic
72C2×C3⋊Dic3C2×D412yes—
73C2×C3⋊Dic3#4112yes—
74C2×C3⋊Dic3C2411yescharacteristic
75C3×#67—416no—
76C2×C3×Dic3—24no—
77C2×C3×Dic3—44no—
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—22no—
90C24×C3—62no—
91C23×D3—22no—
92C2×C3×D4—68no—
93C2×C3×D4—128no—
94C22×C3×C4—62no—
95C2×#67—28no—
96C2×#67—48no—
97C2×#67—64no—
98C2×#67—64no—
99C2×#67—124no—
100C2×#67—124no—
101C22×Dic3—22no—
102C22×Dic3—62no—
103C22×Dic3—62no—
104C22×Dic3—64no—
105C22×Dic3—64no—
106C22×Dic3—124no—
107C22×Dic3—124no—
108#217—68no—
109(C2×D3)⋊C4—68no—
110Dic3⋊C4—64no—
111Dic3⋊C4—64no—
112C22×C32—22no—
113C22×C32—22no—
114C22×C32—28no—
115C22×C32#12112yes—
116C22×C32C2×D812yes—
117C22×C32C2×D814yescomplemented
118C22×C32#13512yes—
119C22×C32C22×D411yescharacteristic
120C2×C3×D3—44no—
121C2×C3×D3—44no—
122C2×C3×D3—44no—
123C2×C3×D3—88no—
124C3⋊Dic3—22no—
125C3⋊Dic3#12112yes—
126C3⋊Dic3C22×D411yescharacteristic
127C3⋊Dic3C2×#4111yescharacteristic
128C3×Dic3—44no—
129C22×D4—62no—
130C22×D4—92no—
131C23×C4—91no—
132C2×D8—94no—
133C2×D8—184no—
134C22×C8—91no—
135C22×C8—91no—
136C22×C8—94no—
137C22×C8—184no—
138#121—98no—
139#121—184no—
140C2×C4⋊C4—92no—
141C2×C22⋊C4—182no—
142#107—94no—
143#102—98no—
144C23×C3—24no—
145C23×C3—22no—
146C23×C3—28no—
147C23×C3—44no—
148C23×C3—44no—
149C23×C3—64no—
150C23×C3—124no—
151C23×C3—124no—
152C23×C3—124no—
153C22×D3—24no—
154C22×D3—44no—
155C22×D3—44no—
156C22×D3—44no—
157C3×D4—1216no—
158C2×C3×C4—64no—
159C2×C3×C4—124no—
160#67—416no—
161#67—124no—
162#67—124no—
163#67—128no—
164C2×Dic3—24no—
165C2×Dic3—44no—
166C2×Dic3—62no—
167C2×Dic3—64no—
168C2×Dic3—64no—
169C2×Dic3—62no—
170C2×Dic3—64no—
171C2×Dic3—124no—
172C2×Dic3—128no—
173C2×Dic3—124no—
174C2×Dic3—124no—
175C2×C32—24no—
176C2×C32#46614yescomplemented
177C2×C32C2×#12111yescharacteristic
178C2×C32C22×D811yescharacteristic
179C2×C32C2×#13511yescharacteristic
180C3×D3—84no—
181C24—62no—
182C24GO+(4,𝔽2)11yescharacteristic
183C2×D4—68no—
184C2×D4—94no—
185C2×D4—128no—
186C2×D4—184no—
187C2×D4—184no—
188C2×D4—182no—
189C22×C4—62no—
190C22×C4—91no—
191C22×C4—92no—
192C22×C4—92no—
193C22×C4—91no—
194C22×C4—182no—
195C22×C4—182no—
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—188no—
205C22×C3—22no—
206C22×C3—24no—
207C22×C3—28no—
208C22×C3—24no—
209C22×C3—24no—
210C22×C3—44no—
211C22×C3—44no—
212C22×C3—416no—
213C22×C3—124no—
214C22×C3—124no—
215C22×C3—124no—
216C22×C3—248no—
217C2×D3—44no—
218C2×D3—44no—
219C2×D3—44no—
220C2×D3—88no—
221C3×C4—124no—
222Dic3—44no—
223Dic3—64no—
224Dic3—62no—
225Dic3—62no—
226Dic3—124no—
227C32C2×#46611yescharacteristic, complemented, Sylow
228C23—22no—
229C23—22no—
230C23—64no—
231C23—124no—
232C23—124no—
233C23—124no—
234C23#377414yescomplemented
235C23C2×GO+(4,𝔽2)12yes—
236C23C2×GO+(4,𝔽2)11yescharacteristic
237D4—1216no—
238D4—184no—
239D4—184no—
240D4—364no—
241C2×C4—64no—
242C2×C4—91no—
243C2×C4—91no—
244C2×C4—92no—
245C2×C4—92no—
246C2×C4—92no—
247C2×C4—124no—
248C2×C4—182no—
249C2×C4—182no—
250C2×C4—184no—
251C2×C4—182no—
252C8—94no—
253C8—182no—
254C2×C3—22no—
255C2×C3—22no—
256C2×C3—22no—
257C2×C3—28no—
258C2×C3—48no—
259C2×C3—244no—
260D3—84no—
261C22—22no—
262C22—22no—
263C22—28no—
264C22—124no—
265C22—124no—
266C22—124no—
267C22—248no—
268C22C2×#377412yes—
269C22C2×#377414yescomplemented
270C22#6423712yes—
271C22#6424212yes—
272C22C22×GO+(4,𝔽2)11yescharacteristic
273C4—91no—
274C4—91no—
275C4—92no—
276C4—124no—
277C4—182no—
278C3—22no—
279C2—24no—
280C2—244no—
281C2#1059352014yesdirect product factor
282C2C22×#377411yescharacteristic
283C2C2×#6423711yescharacteristic
284C2C2×#6424211yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC24×C32D4
socleC23×C32C2×D4
hypercenterC24GO+(4,𝔽2)
hypocenterC32C2×#466
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C23×#622C2semidirect
2. C22×#3774C2semidirect
3. C2×#63980C2semidirect
4. #10593520C2direct (N × H)
5. C2×#63743C2semidirect
6. C2×#63739C2semidirect
13. C22×#622C22semidirect
15. C2×#3774C22semidirect
17. #63980C22semidirect
20. #63743C22semidirect
21. #63739C22semidirect
40. C2×#622D4semidirect
59. C23×C32D8semidirect
82. #622C2×D4semidirect
117. C22×C32C2×D8semidirect
176. C2×C32#466semidirect
227. C32C2×#466semidirect
234. C23#3774semidirect
269. C22C2×#3774semidirect
281. C2#10593520direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6222
C22×#37742
C2×#639802
#105935202
C2×#637432
C2×#637392
C2×#4669