Finite Group Databasebeta

← C2×#10593636 #11922988

Subgroups — C2×#10593636 #11922988

Order 1152.

822 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 99 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×C4⋊(C3⋊S4)C212yesmaximal, complemented
2C2×C3×C8×A4C211yesmaximal, characteristic, complemented
3#10593636C214yesmaximal, direct product factor
4C2×#5402—33nomaximal
5C2×#5115—31nomaximal
6C22×C3⋊S4—22no—
7C2×C3×C4×A4C2211yescharacteristic
8C4⋊(C3⋊S4)—22no—
9C4⋊(C3⋊S4)C2214yescomplemented
10C2×#3745—41nomaximal
11C3×C8×A4C2212yescomplemented
12C2×C4⋊S4—36no—
13C23×C3×C8D311yescharacteristic, complemented
14C2×#930—32no—
15C22×D24—31no—
16C2×C8×A4D313yescomplemented
17#5402—312no—
18#5115—34no—
19#5115—34no—
20C2×#821—32no—
21C2×#818—31no—
22C22×C3×A4D411yescharacteristic
23C2×C3⋊S4—24no—
24C2×C3⋊S4—44no—
25C2×C4⋊(C3⋊D3)—42no—
26C3×C4×A4D411yescharacteristic
27C3×C4×A4C2311yescharacteristic
28C2×C32×C8—41no—
29#3745—44no—
30C2×#466—91noSylow
31C22×S4—66no—
32C23×C3×C4C2×D311yescharacteristic
33C22×#67—62no—
34C22×D12—32no—
35C2×C4×A4C2×D313yes—
36C4⋊S4—312no—
37C4⋊S4—66no—
38C22×C3×C8—31no—
39C22×C3×C8—31no—
40C22×C3×C8—32no—
41C22×C3×C8C2×D312yescomplemented
42#930—34no—
43#930—34no—
44#930—62no—
45#930—62no—
46C2×(C2×D3)⋊C4—62no—
47C2×C4⋊Dic3—32no—
48C2×D24—34no—
49C2×D24—61no—
50C2×D24—62no—
51C2×D24—61no—
52C2×D24—123no—
53C8×A4C2×D316yescomplemented
54#821—38no—
55#818—34no—
56C22×C3⋊D3—82no—
57C2×C3×A4D812yescomplemented
58C2×C3×A4C2×D411yescharacteristic
59C3⋊S4—44no—
60C2×C32×C4—41no—
61C4⋊(C3⋊D3)—44no—
62C4⋊(C3⋊D3)—82no—
63C32×C8—42no—
64C22×D8—91no—
65C23×C8C3⋊D311yescharacteristic, complemented
66C2×#121—92no—
67#466—94no—
68#466—94no—
69C2×#107—91no—
70C2×#102—92no—
71C24×C3D1211yescharacteristic
72C23×D3—62no—
73C22×A4D1213yes—
74C2×S4—612no—
75C2×S4—1212no—
76C22×C3×C4—31no—
77C22×C3×C4—31no—
78C22×C3×C4—31no—
79C22×C3×C4—31no—
80C22×C3×C4D1211yescharacteristic
81C22×C3×C4C22×D311yescharacteristic
82C2×#67—64no—
83C2×#67—64no—
84C2×#67—124no—
85C2×#67—124no—
86C22×Dic3—62no—
87C2×D12—34no—
88C2×D12—62no—
89C2×D12—62no—
90C2×D12—62no—
91C2×D12—62no—
92C2×D12—62no—
93C2×D12—126no—
94C4×A4D1213yes—
95C4×A4C22×D313yes—
96C2×C3×C8—31no—
97C2×C3×C8—32no—
98C2×C3×C8—32no—
99C2×C3×C8—32no—
100C2×C3×C8—43no—
101C2×C3×C8—61no—
102C2×C3×C8S411yescharacteristic, complemented
103(C2×D3)⋊C4—64no—
104(C2×D3)⋊C4—64no—
105C4⋊Dic3—34no—
106C4⋊Dic3—62no—
107D24—64no—
108D24—64no—
109D24—1212no—
110C22×C32—41no—
111C2×C3⋊D3—84no—
112C2×C3⋊D3—164no—
113C3×A4C2×D811yescharacteristic, complemented
114C32×C4—41no—
115C32×C4—41no—
116C22×D4—92no—
117C22×D4—182no—
118C23×C4C2×C3⋊D311yescharacteristic
119C2×D8—94no—
120C2×D8—181no—
121C2×D8—182no—
122C2×D8—181no—
123C22×C8—31no—
124C22×C8—31no—
125C22×C8—32no—
126C22×C8C2×C3⋊D312yescomplemented
127#121—94no—
128#121—94no—
129#121—182no—
130#121—182no—
131C2×C4⋊C4—92no—
132C2×C22⋊C4—182no—
133#107—94no—
134#102—98no—
135C23×C3—31no—
136C23×C3—31no—
137C23×C3—32no—
138C23×C3D2412yescomplemented
139C23×C3C2×D1211yescharacteristic
140C22×D3—64no—
141C22×D3—122no—
142C22×D3—124no—
143C22×D3—124no—
144C22×D3—122no—
145C22×D3—246no—
146C2×A4D2416yescomplemented
147C2×A4C2×D1213yes—
148S4—1212no—
149C2×C3×C4—31no—
150C2×C3×C4—31no—
151C2×C3×C4—31no—
152C2×C3×C4—31no—
153C2×C3×C4—31no—
154C2×C3×C4—31no—
155C2×C3×C4—31no—
156C2×C3×C4—43no—
157C2×C3×C4—61no—
158C2×C3×C4C2×S411yescharacteristic
159#67—128no—
160#67—124no—
161#67—124no—
162C2×Dic3—64no—
163C2×Dic3—124no—
164D12—64no—
165D12—64no—
166D12—1212no—
167D12—122no—
168D12—122no—
169D12—246no—
170C3×C8—32no—
171C3×C8—46no—
172C3×C8C2×S412yescomplemented
173C2×C32—41no—
174C2×C32—42no—
175C3⋊D3—164no—
176C24—182no—
177C24C4⋊(C3⋊D3)11yescharacteristic
178C2×D4—94no—
179C2×D4—182no—
180C2×D4—182no—
181C2×D4—182no—
182C2×D4—182no—
183C2×D4—184no—
184C2×D4—184no—
185C2×D4—182no—
186C2×D4—364no—
187C2×D4—364no—
188C22×C4—31no—
189C22×C4—31no—
190C22×C4—31no—
191C22×C4—31no—
192C22×C4—182no—
193C22×C4C4⋊(C3⋊D3)11yescharacteristic
194C22×C4C22×C3⋊D311yescharacteristic
195D8—184no—
196D8—184no—
197C2×C8—31no—
198C2×C8—32no—
199C2×C8—32no—
200C2×C8—32no—
201C2×C8—61no—
202C2×C8C3⋊S411yescharacteristic, complemented
203C4⋊C4—94no—
204C4⋊C4—182no—
205C22⋊C4—184no—
206C22⋊C4—184no—
207C22×C3—32no—
208C22×C3—31no—
209C22×C3—31no—
210C22×C3—31no—
211C22×C3—32no—
212C22×C3—32no—
213C22×C3—43no—
214C22×C3—61no—
215C22×C3C2×D2411yescharacteristic, complemented
216C22×C3C4⋊S411yescharacteristic
217C2×D3—124no—
218C2×D3—124no—
219C2×D3—124no—
220C2×D3—2412no—
221C2×D3—244no—
222C2×D3—244no—
223C2×D3—4812no—
224A4C2×D2413yescomplemented
225C3×C4—31no—
226C3×C4—31no—
227C3×C4—43no—
228C3×C4—43no—
229C3×C4C4⋊S411yescharacteristic
230C3×C4C22×S411yescharacteristic
231Dic3—124no—
232C32—41noSylow
233C23—31no—
234C23—31no—
235C23—32no—
236C23—184no—
237C23—362no—
238C23—364no—
239C23—364no—
240C23—362no—
241C23#374512yescomplemented
242C23C2×C4⋊(C3⋊D3)11yescharacteristic
243D4—184no—
244D4—184no—
245D4—362no—
246D4—368no—
247D4—364no—
248D4—364no—
249D4—362no—
250C2×C4—31no—
251C2×C4—31no—
252C2×C4—31no—
253C2×C4—31no—
254C2×C4—31no—
255C2×C4—31no—
256C2×C4—31no—
257C2×C4—61no—
258C2×C4—184no—
259C2×C4—364no—
260C2×C4C2×C3⋊S411yescharacteristic
261C8—32no—
262C8C2×C3⋊S412yescomplemented
263C2×C3—31no—
264C2×C3—31no—
265C2×C3—32no—
266C2×C3—46no—
267C2×C3—43no—
268C2×C3#540212yescomplemented
269C2×C3C2×C4⋊S411yescharacteristic
270D3—244no—
271D3—4812no—
272C22—32no—
273C22—31no—
274C22—32no—
275C22—32no—
276C22—31no—
277C22—31no—
278C22—61no—
279C22—364no—
280C22—364no—
281C22—364no—
282C22—724no—
283C22—724no—
284C22C2×#374511yescharacteristic, complemented
285C22C4⋊(C3⋊S4)11yescharacteristic
286C4—31no—
287C4—31no—
288C4—364no—
289C4C4⋊(C3⋊S4)11yescharacteristic
290C4C22×C3⋊S411yescharacteristic
291C3—43no—
292C3C2×#540211yescharacteristic, complemented
293C2—31no—
294C2—31no—
295C2—32no—
296C2—724no—
297C2#1059363612yesdirect product factor
298C2C2×C4⋊(C3⋊S4)11yescharacteristic
subgroupG/H
centerC22C4⋊(C3⋊S4)
commutator, cosocleC3×C4×A4C23
FrattiniC4C22×C3⋊S4
FittingC23×C3×C8D3
socleC24×C3D12
hypercenterC2×C8C3⋊S4
hypocenterC3×A4C2×D8
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊(C3⋊S4)C2semidirect
2. C2×C3×C8×A4C2semidirect
3. #10593636C2direct (N × H)
9. C4⋊(C3⋊S4)C22semidirect
11. C3×C8×A4C22semidirect
13. C23×C3×C8D3semidirect
16. C2×C8×A4D3semidirect
41. C22×C3×C8C2×D3semidirect
53. C8×A4C2×D3semidirect
57. C2×C3×A4D8semidirect
65. C23×C8C3⋊D3semidirect
102. C2×C3×C8S4semidirect
113. C3×A4C2×D8semidirect
126. C22×C8C2×C3⋊D3semidirect
138. C23×C3D24semidirect
146. C2×A4D24semidirect
172. C3×C8C2×S4semidirect
202. C2×C8C3⋊S4semidirect
215. C22×C3C2×D24semidirect
224. A4C2×D24semidirect
241. C23#3745semidirect
262. C8C2×C3⋊S4semidirect
268. C2×C3#5402semidirect
284. C22C2×#3745semidirect
292. C3C2×#5402semidirect
297. C2#10593636direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊(C3⋊S4)2
C2×C3×C8×A42
#105936362
C2×#54023
C2×#51153
C2×#37454