Finite Group Databasebeta

← C2×#10593628 #11922875

Subgroups — C2×#10593628 #11922875

Order 1152.

840 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 105 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×C3⋊GL(2,𝔽3)C211yesmaximal, characteristic
2C2×C3×C4×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
3C2×C3⋊#859C211yesmaximal, characteristic, complemented
4#10593628C214yesmaximal, direct product factor
5C2×#5394—33nomaximal
6C2×#5026—31nomaximal
7C22×C3×SL(2,𝔽3)C2211yescharacteristic
8C2×C3⋊GL(2,𝔽3)C414yescomplemented
9C2×C3⋊GL(2,𝔽3)C2212yes—
10C2×#3752—41nomaximal
11C3×C4×SL(2,𝔽3)C2212yescomplemented
12C3⋊#859C2212yescomplemented
13C22×GL(2,𝔽3)—33no—
14C2×C3×C4×Q8D311yescharacteristic, complemented
15C22×#215—31no—
16C2×C4×D12—31no—
17C2×C4×SL(2,𝔽3)D313yescomplemented
18C2×#859—33no—
19#5394—312no—
20C2×#835—31no—
21#5026—34no—
22#5026—34no—
23C2×#809—31no—
24C2×#807—31no—
25C2×#803—31no—
26C23×C3⋊D3—41no—
27C22×C32×C4—41no—
28C22×C3⋊Dic3—41no—
29C2×C3×SL(2,𝔽3)C2×C412yescomplemented
30C2×C3×SL(2,𝔽3)C2311yescharacteristic
31C3⋊GL(2,𝔽3)C2×C414yescomplemented
32#3752—44no—
33C2×#440—91noSylow
34C22×C3×Q8C2×D311yescharacteristic
35C22×D12—31no—
36C22×C4×D3—61no—
37C22×SL(2,𝔽3)C2×D313yes—
38C2×GL(2,𝔽3)—312no—
39C2×GL(2,𝔽3)—36no—
40C3×C4×Q8—32no—
41C3×C4×Q8C2×D312yescomplemented
42C2×C3×C4⋊C4—31no—
43C2×C3×C42—31no—
44C2×#215—32no—
45C2×#215—34no—
46C2×#215—34no—
47C2×#215—32no—
48C2×(C2×D3)⋊C4—61no—
49C2×(C2×D3)⋊C4—123no—
50C2×C4⋊Dic3—31no—
51C22×C3⋊C8—31no—
52C22×C3⋊C8—31no—
53C4×D12—34no—
54C4×D12—62no—
55C4×SL(2,𝔽3)C2×D316yescomplemented
56#859—36no—
57#835—32no—
58#835—32no—
59#809—34no—
60#807—34no—
61#803—34no—
62C23×C32—41no—
63C22×C3⋊D3—44no—
64C22×C3⋊D3—42no—
65C22×C3⋊D3—82no—
66C22×C3⋊D3—82no—
67C2×C32×C4—42no—
68C2×C32×C4—82no—
69C2×C3⋊Dic3—42no—
70C2×C3⋊Dic3—82no—
71C3×SL(2,𝔽3)C22×C411yescharacteristic, complemented
72C22×SD16—91no—
73C2×C4×Q8C3⋊D311yescharacteristic, complemented
74C2×C4×D4—91no—
75#440—94no—
76#440—94no—
77C2×#107—91no—
78C2×#103—91no—
79C2×#102—91no—
80C2×#97—91no—
81C23×D3—61no—
82C23×D3—123no—
83C2×C3×Q8—31no—
84C2×C3×Q8—32no—
85C2×C3×Q8C4×D312yes—
86C2×C3×Q8C22×D311yescharacteristic
87C22×C3×C4—31no—
88C22×C3×C4—31no—
89C22×C3×C4—43no—
90C22×C3×C4S411yescharacteristic
91C22×Dic3—61no—
92C22×Dic3—123no—
93C2×D12—32no—
94C2×D12—34no—
95C2×D12—61no—
96C2×D12—62no—
97C2×C4×D3—64no—
98C2×C4×D3—124no—
99C2×SL(2,𝔽3)C4×D316yescomplemented
100C2×SL(2,𝔽3)C22×D313yes—
101GL(2,𝔽3)—312no—
102C3×C4⋊C4—32no—
103C3×C4⋊C4—61no—
104C3×C42—32no—
105C3×C42—32no—
106#215—38no—
107#215—34no—
108#215—34no—
109(C2×D3)⋊C4—64no—
110(C2×D3)⋊C4—1212no—
111C4⋊Dic3—32no—
112C4⋊Dic3—61no—
113C2×C3⋊C8—32no—
114C2×C3⋊C8—34no—
115C2×C3⋊C8—32no—
116C2×C3⋊C8—62no—
117C22×C32—42no—
118C22×C32—42no—
119C22×C32—42no—
120C22×C32—41no—
121C2×C3⋊D3—44no—
122C2×C3⋊D3—88no—
123C2×C3⋊D3—82no—
124C2×C3⋊D3—82no—
125C32×C4—82no—
126C3⋊Dic3—82no—
127C22×Q8C2×C3⋊D311yescharacteristic
128C22×D4—91no—
129C23×C4—181no—
130C2×SD16—94no—
131C2×SD16—92no—
132C2×SD16—94no—
133C2×SD16—92no—
134C22×C8—91no—
135C22×C8—91no—
136C4×Q8—32no—
137C4×Q8C2×C3⋊D312yescomplemented
138C4×D4—94no—
139C4×D4—182no—
140C2×C4⋊C4—31no—
141C2×C4⋊C4—91no—
142C2×C22⋊C4—181no—
143C2×C42—31no—
144#107—94no—
145#103—92no—
146#103—92no—
147#102—94no—
148#97—94no—
149C23×C3—43no—
150C23×C3C2×S411yescharacteristic
151C22×D3—64no—
152C22×D3—62no—
153C22×D3—126no—
154C22×D3—1212no—
155C22×D3—122no—
156C22×D3—122no—
157C22×D3—246no—
158C22×D3—246no—
159C3×Q8—32no—
160C3×Q8—31no—
161C3×Q8—61no—
162C3×Q8C2×C4×D311yescharacteristic
163C2×C3×C4—22no—
164C2×C3×C4—32no—
165C2×C3×C4—32no—
166C2×C3×C4—31no—
167C2×C3×C4—31no—
168C2×C3×C4—32no—
169C2×C3×C4—46no—
170C2×C3×C4—62no—
171C2×C3×C4—86no—
172C2×C3×C4C2×S412yes—
173C2×Dic3—62no—
174C2×Dic3—126no—
175C2×Dic3—122no—
176C2×Dic3—246no—
177D12—34no—
178D12—62no—
179D12—64no—
180C4×D3—128no—
181SL(2,𝔽3)C2×C4×D313yescomplemented
182C3⋊C8—34no—
183C3⋊C8—62no—
184C2×C32—44no—
185C2×C32—41no—
186C2×C32—41no—
187C2×C32—41no—
188C3⋊D3—84no—
189C24—181no—
190C2×Q8—31no—
191C2×Q8—32no—
192C2×Q8C4×C3⋊D312yes—
193C2×Q8C22×C3⋊D311yescharacteristic
194C2×D4—92no—
195C2×D4—94no—
196C2×D4—181no—
197C2×D4—182no—
198C22×C4—31no—
199C22×C4—31no—
200C22×C4—184no—
201C22×C4—181no—
202C22×C4—364no—
203C22×C4C3⋊S411yescharacteristic
204SD16—98no—
205SD16—94no—
206SD16—94no—
207C2×C8—92no—
208C2×C8—94no—
209C2×C8—92no—
210C2×C8—182no—
211C4⋊C4—32no—
212C4⋊C4—61no—
213C4⋊C4—92no—
214C4⋊C4—181no—
215C22⋊C4—184no—
216C42—32no—
217C42—32no—
218C22×C3—46no—
219C22×C3—46no—
220C22×C3—46no—
221C22×C3—43no—
222C22×C3C4×S412yes—
223C22×C3#98312yes—
224C22×C3#98612yes—
225C22×C3C22×S411yescharacteristic
226C2×D3—64no—
227C2×D3—1212no—
228C2×D3—128no—
229C2×D3—122no—
230C2×D3—122no—
231C2×D3—2424no—
232C2×D3—246no—
233C2×D3—246no—
234C3×C4—22no—
235C3×C4—31no—
236C3×C4—31no—
237C3×C4—32no—
238C3×C4—62no—
239C3×C4—86no—
240Dic3—122no—
241Dic3—246no—
242C32—41noSylow
243C23—184no—
244C23—182no—
245C23—362no—
246C23—362no—
247C23C2×C3⋊S411yescharacteristic
248Q8—32no—
249Q8—31no—
250Q8—61no—
251Q8C2×C4×C3⋊D311yescharacteristic
252D4—94no—
253D4—182no—
254D4—184no—
255C2×C4—22no—
256C2×C4—32no—
257C2×C4—32no—
258C2×C4—31no—
259C2×C4—31no—
260C2×C4—32no—
261C2×C4—62no—
262C2×C4—182no—
263C2×C4—368no—
264C2×C4—362no—
265C2×C4C2×C3⋊S412yes—
266C8—94no—
267C8—182no—
268C2×C3—412no—
269C2×C3—43no—
270C2×C3—43no—
271C2×C3—43no—
272C2×C3#539414yescomplemented
273C2×C3C2×C4×S411yescharacteristic
274C2×C3C2×#98311yescharacteristic
275C2×C3C2×#98611yescharacteristic
276D3—124no—
277D3—2412no—
278C22—184no—
279C22—368no—
280C22—362no—
281C22—362no—
282C22C4×C3⋊S412yes—
283C22#6426412yes—
284C22#6426712yes—
285C22C22×C3⋊S411yescharacteristic
286C4—22no—
287C4—31no—
288C4—31no—
289C4—32no—
290C4—62no—
291C4—362no—
292C3—43no—
293C3C2×#539411yescharacteristic, complemented
294C2—364no—
295C2#1059362814yesdirect product factor
296C2C2×C4×C3⋊S411yescharacteristic
297C2C2×#6426411yescharacteristic
298C2C2×#6426711yescharacteristic
subgroupG/H
centerC23C2×C3⋊S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FrattiniC22C22×C3⋊S4
FittingC2×C3×C4×Q8D3
socleC23×C3C2×S4
prime radicalC22×C3⋊GL(2,𝔽3)C2
cosocleC2×C3×SL(2,𝔽3)C23
hypercenterC22×C4C3⋊S4
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×SL(2,𝔽3)C2semidirect
3. C2×C3⋊#859C2semidirect
4. #10593628C2direct (N × H)
8. C2×C3⋊GL(2,𝔽3)C4semidirect
11. C3×C4×SL(2,𝔽3)C22semidirect
12. C3⋊#859C22semidirect
14. C2×C3×C4×Q8D3semidirect
17. C2×C4×SL(2,𝔽3)D3semidirect
29. C2×C3×SL(2,𝔽3)C2×C4semidirect
31. C3⋊GL(2,𝔽3)C2×C4semidirect
41. C3×C4×Q8C2×D3semidirect
55. C4×SL(2,𝔽3)C2×D3semidirect
71. C3×SL(2,𝔽3)C22×C4semidirect
73. C2×C4×Q8C3⋊D3semidirect
99. C2×SL(2,𝔽3)C4×D3semidirect
137. C4×Q8C2×C3⋊D3semidirect
181. SL(2,𝔽3)C2×C4×D3semidirect
272. C2×C3#5394semidirect
293. C3C2×#5394semidirect
295. C2#10593628direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3⋊GL(2,𝔽3)2
C2×C3×C4×SL(2,𝔽3)2
C2×C3⋊#8592
#105936282
C2×#53943
C2×#50263
C2×#37524