Finite Group Databasebeta

← C2×#5753⋊C3 #11923313

Subgroups — C2×#5753⋊C3 #11923313

Order 1152.

705 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 705 conjugacy classes of subgroups — too many to draw. Only its 87 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×#1010⋊C3C212yesmaximal, complemented
2C2×C3×#131⋊C3C211yesmaximal, characteristic, complemented
3#5753⋊C3C214yesmaximal, direct product factor
4C2×#5753C311yesmaximal, characteristic, complemented
5C2×#578⋊C3—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7#1010⋊C3—22no—
8#1010⋊C3C2214yescomplemented
9C2×D3×SL(2,𝔽3)—22no—
10C2×C3×D24—41nomaximal
11C3×#131⋊C3C2212yescomplemented
12C2×#1010C2×C312yescomplemented
13C2×2−1+4⋊C3—32no—
14C2×C3×#131C2×C311yescharacteristic, complemented
15#5753—34no—
16#5753C2×C314yescomplemented
17C2×#909—32no—
18C22×Dic12—31no—
19C2×#904—31no—
20#578⋊C3—34no—
21C2×#131⋊C3—21no—
22C2×#131⋊C3D311yescharacteristic, complemented
23C2×C3×D12—42no—
24C3×#41⋊C3D411yescharacteristic
25C3×#41⋊C3C2311yescharacteristic
26C2×C3×SL(2,𝔽3)D411yescharacteristic
27D3×SL(2,𝔽3)—24no—
28C2×C32×C8—41no—
29C3×D24—44no—
30C2×#578—31noSylow
31C2×C3×#41C22×C311yescharacteristic
32#1010—22no—
33#1010—34no—
34#1010—62no—
35#1010C22×C314yescomplemented
36C2×D3×Q8—22no—
37C2×#237—62no—
38C2×#235—32no—
39C22×Dic6—32no—
402−1+4⋊C3—34no—
412−1+4⋊C3—62no—
42C2×#41⋊C3—21no—
43C2×#41⋊C3C2×D311yescharacteristic
44C22×SL(2,𝔽3)—62no—
45C2×C3×D8—121no—
46C3×#131—32no—
47C3×#131C22×C312yescomplemented
48C2×C3×M16—31no—
49C22×C3×C8—31no—
50#909—38no—
51#909—38no—
52C2×Dic12—32no—
53C2×Dic12—34no—
54C2×Dic12—31no—
55C2×Dic12—34no—
56#904—34no—
57#904—34no—
58C2×D24A411yescharacteristic
59C2×#204—32no—
60#131⋊C3—22no—
61#131⋊C3C2×D312yescomplemented
62C22×C3×D3—82no—
63C2×C32×C4—41no—
64C3×D12—44no—
65C3×D12—82no—
66C3×SL(2,𝔽3)C2×D411yescharacteristic
67C32×C8—42no—
68C2×2−1+4—32no—
69#578—34no—
70#578—94no—
71C2×#137—92no—
72C2×#135—91no—
73C22×Q16—91no—
74C2×#131C3×D311yescharacteristic, complemented
75C3×#41—31no—
76C3×#41—31no—
77C3×#41C3×D411yescharacteristic
78C3×#41C23×C311yescharacteristic
79C2×C3×Q8C3×D411yescharacteristic
80C2×C3×D4—31no—
81C2×C3×D4—122no—
82C22×C3×C4—31no—
83C2×#67—62no—
84C22×Dic3—62no—
85D3×Q8—24no—
86D3×Q8—64no—
87#237—68no—
88#237—64no—
89#237—64no—
90#235—34no—
91#235—34no—
92#235—62no—
93#235—62no—
94C2×D12C2×A412yes—
95C2×C4×D3—62no—
96C2×Dic6—34no—
97C2×Dic6—32no—
98C2×Dic6—34no—
99C2×Dic6—62no—
100C2×Dic6—62no—
101C2×Dic6—62no—
102#41⋊C3—21no—
103#41⋊C3—21no—
104#41⋊C3D1211yescharacteristic
105#41⋊C3C22×D311yescharacteristic
106C2×SL(2,𝔽3)—21no—
107C2×SL(2,𝔽3)—64no—
108C2×SL(2,𝔽3)D1211yescharacteristic
109C3×D8—124no—
110C3×M16—32no—
111C3×M16—32no—
112C2×C3×C8—31no—
113C2×C3×C8—32no—
114C2×C3×C8—32no—
115C2×C3×C8—41no—
116C2×C3×C8—81no—
117C2×C3×C8C2×A411yescharacteristic
118Dic12—38no—
119Dic12—34no—
120D24C2×A414yes—
121#204—38no—
122C22×C32—41no—
123C2×C3×D3—84no—
124C2×C3×D3—164no—
125C32×C4—41no—
126C32×C4—41no—
1272−1+4—34no—
1282−1+4—62no—
1292−1+4—94no—
1302−1+4—182no—
131C2×#41—92no—
132C2×#41—182no—
133C2×#41C2×C3×D311yescharacteristic
134C22×Q8—62no—
135C22×Q8—92no—
136#137—98no—
137#137—98no—
138#135—94no—
139#135—94no—
140C2×Q16—92no—
141C2×Q16—94no—
142C2×Q16—94no—
143C2×Q16—91no—
144C2×SD16—92no—
145C2×D8—31no—
146#131—32no—
147#131C2×C3×D312yescomplemented
148C2×M16—31no—
149C22×C8—31no—
150C23×C3—31no—
151C23×C3—242no—
152C22×D3—22no—
153C3×Q8—31no—
154C3×Q8C2×C3×D411yescharacteristic
155C3×D4—31no—
156C3×D4—31no—
157C3×D4—32no—
158C3×D4—124no—
159C3×D4—242no—
160C2×C3×C4—31no—
161C2×C3×C4—31no—
162C2×C3×C4—31no—
163C2×C3×C4—31no—
164C2×C3×C4—31no—
165C2×C3×C4—41no—
166C2×C3×C4—81no—
167C2×C3×C4C22×A411yescharacteristic
168#67—64no—
169#67—64no—
170C2×Dic3—64no—
171C2×Dic3—62no—
172C2×Dic3—64no—
173D12—22no—
174D12C22×A414yes—
175C4×D3—64no—
176C4×D3—64no—
177Dic6—34no—
178Dic6—64no—
179Dic6—62no—
180Dic6—64no—
181SL(2,𝔽3)—21no—
182SL(2,𝔽3)C2×D1211yescharacteristic
183C3×C8—32no—
184C3×C8—42no—
185C3×C8—82no—
186C3×C8C22×A412yes—
187C2×C32—41no—
188C2×C32—42no—
189C3×D3—164no—
190#41—31no—
191#41—31no—
192#41—94no—
193#41—94no—
194#41—182no—
195#41—182no—
196#41—188no—
197#41—184no—
198#41—184no—
199#41C3×D1211yescharacteristic
200#41C22×C3×D311yescharacteristic
201C2×Q8—64no—
202C2×Q8—94no—
203C2×Q8—94no—
204C2×Q8—92no—
205C2×Q8—182no—
206C2×Q8—182no—
207C2×Q8—182no—
208C2×Q8—184no—
209C2×Q8C3×D1211yescharacteristic
210C2×D4—31no—
211C2×D4—32no—
212C2×D4—182no—
213C22×C4—31no—
214C22×C4—182no—
215C22×C4—182no—
216Q16—98no—
217Q16—94no—
218SD16—98no—
219D8—34no—
220M16—32no—
221M16—32no—
222C2×C8—31no—
223C2×C8—32no—
224C2×C8—32no—
225C2×C8D3×A411yescharacteristic
226C22×C3—31no—
227C22×C3—31no—
228C22×C3—41no—
229C22×C3—62no—
230C22×C3—81no—
231C22×C3—244no—
232C22×C3—484no—
233C22×C3D4×A411yescharacteristic
234C2×D3—24no—
235C2×D3—44no—
236C3×C4—31no—
237C3×C4—31no—
238C3×C4—41no—
239C3×C4—41no—
240C3×C4—81no—
241C3×C4—81no—
242C3×C4D4×A411yescharacteristic
243C3×C4C23×A411yescharacteristic
244Dic3—64no—
245C32—41noSylow
246C23—31no—
247C23—62no—
248Q8—31no—
249Q8—94no—
250Q8—184no—
251Q8—184no—
252Q8—182no—
253Q8C2×C3×D1211yescharacteristic
254D4—31no—
255D4—31no—
256D4—32no—
257D4—34no—
258D4—62no—
259D4—184no—
260D4—184no—
261C2×C4—31no—
262C2×C4—31no—
263C2×C4—31no—
264C2×C4—31no—
265C2×C4—31no—
266C2×C4—184no—
267C2×C4—184no—
268C2×C4—184no—
269C2×C4—182no—
270C2×C4—184no—
271C2×C4C2×D3×A411yescharacteristic
272C8—32no—
273C8C2×D3×A412yes—
274C2×C3—41no—
275C2×C3—42no—
276C2×C3—61no—
277C2×C3—61no—
278C2×C3—81no—
279C2×C3—82no—
280C2×C3—484no—
281C2×C3#578⋊C312yescomplemented
282C2×C3C2×D4×A411yescharacteristic
283D3—44no—
284C22—31no—
285C22—31no—
286C22—62no—
287C22—64no—
288C22—124no—
289C22A4×D1211yescharacteristic
290C4—31no—
291C4—31no—
292C4—184no—
293C4A4×D1211yescharacteristic
294C4C22×D3×A411yescharacteristic
295C3—41no—
296C3—81no—
297C3C2×#578⋊C311yescharacteristic, complemented
298C2—61no—
299C2—61no—
300C2—124no—
301C2#5753⋊C312yesdirect product factor
302C2C2×A4×D1211yescharacteristic
subgroupG/H
centerC22A4×D12
commutator, cosocleC3×#41C23×C3
FrattiniC4C22×D3×A4
FittingC2×C3×#131C2×C3
socleC22×C3D4×A4
hypercenterC2×C8D3×A4
hypocenterC3×Q8C2×C3×D4
LCSG ▷ C3×#41 ▷ C3×Q8
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. C2×#1010⋊C3C2semidirect
2. C2×C3×#131⋊C3C2semidirect
3. #5753⋊C3C2direct (N × H)
4. C2×#5753C3semidirect
8. #1010⋊C3C22semidirect
11. C3×#131⋊C3C22semidirect
12. C2×#1010C2×C3semidirect
14. C2×C3×#131C2×C3semidirect
16. #5753C2×C3semidirect
22. C2×#131⋊C3D3semidirect
35. #1010C22×C3semidirect
47. C3×#131C22×C3semidirect
61. #131⋊C3C2×D3semidirect
74. C2×#131C3×D3semidirect
147. #131C2×C3×D3semidirect
281. C2×C3#578⋊C3semidirect
297. C3C2×#578⋊C3semidirect
301. C2#5753⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#1010⋊C32
C2×C3×#131⋊C32
#5753⋊C32
C2×#57533
C2×#578⋊C33
C2×C3×D244