Finite Group Databasebeta

← #11788164

Subgroups — #11788164

Order 1152.

1326 conjugacy classes of subgroups; only the 265 normal subgroups are shown.

normal subgroups only

This group has 1326 conjugacy classes of subgroups — too many to draw. Only its 265 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×C32×C42C211yesmaximal, characteristic, complemented
2#10596262C211yesmaximal, characteristic
3#10592906C211yesmaximal, characteristic, complemented
4C2×#63632C212yesmaximal, complemented
5#10589389C212yesmaximal, complemented
6#71532—34nomaximal
7C23×C32×C4—21no—
8C23×C32×C4C2211yescharacteristic
9C2×#3828C2211yescharacteristic
10C2×C32×C42—21no—
11C2×C32×C42—24no—
12C2×C32×C42C2212yes—
13#64162—21no—
14#64139C412yescomplemented
15#64138—21no—
16C4×#638—22no—
17#64135C2211yescharacteristic
18#64133C412yescomplemented
19C2×#3748C2212yes—
20#63657—22no—
21#63632—24no—
22C22×C3×C42D314yescomplemented
23#5791—34no—
24#5207—34no—
25C2×#805—38no—
26#4523—38no—
27C24×C32D411yescharacteristic
28C22×C32×C4—28no—
29C22×C32×C4—24no—
30C22×C32×C4—22no—
31C22×C32×C4—22no—
32C22×C32×C4—22no—
33C22×C32×C4C2×C412yes—
34C22×C32×C4D411yescharacteristic
35C22×C32×C4D412yes—
36C22×C32×C4C2311yescharacteristic
37C2×#638—22no—
38C2×#638—21no—
39#3828—22no—
40#3828—22no—
41C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
42C2×C4×C3⋊D3—21no—
43C2×#634C2×C411yescharacteristic, complemented
44C32×C42—24no—
45C32×C42—22no—
46C32×C42D414yescomplemented
47#3757—22no—
48#3757—21no—
49#3752—22no—
50C4⋊(C3⋊Dic3)C2×C412yescomplemented
51#3750—22no—
52C4×C3⋊Dic3—21no—
53#3748—22no—
54#3748—22no—
55C2×C3⋊(C3⋊C8)—22no—
56#1896—91noSylow
57C23×C3×C4—24no—
58C23×C3×C4C2×D314yes—
59C2×#235—34no—
60C2×C3×C42—24no—
61C2×C3×C42—216no—
62C2×C3×C42C2×D318yes—
63#953—64no—
64#930—38no—
65#929—64no—
66C4×#67—68no—
67#926—34no—
68#924—38no—
69C2×#208—38no—
70#830—68no—
71#805—616no—
72C23×C32—24no—
73C23×C32—21no—
74C23×C32—21no—
75C23×C32C22⋊C412yes—
76C23×C32C2×D411yescharacteristic
77C22×C3⋊D3—21no—
78C2×C32×C4—216no—
79C2×C32×C4—28no—
80C2×C32×C4—21no—
81C2×C32×C4—24no—
82C2×C32×C4—21no—
83C2×C32×C4—24no—
84C2×C32×C4—24no—
85C2×C32×C4C22⋊C412yes—
86C2×C32×C4C22×C411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D412yes—
89C2×C32×C4#4112yes—
90#638—44no—
91#638—41no—
92#638—41no—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—21no—
95C4⋊(C3⋊D3)—22no—
96C4×C3⋊D3—42no—
97#634—22no—
98C3⋊(C3⋊C8)—42no—
99#525—91no—
100C22×C42C3⋊D311yescharacteristic, complemented
101C2×#104—92no—
102#407—91no—
103#339—92no—
104C24×C3#6714yes—
105C22×C3×C4—216no—
106C22×C3×C4—232no—
107C22×C3×C4—28no—
108C22×C3×C4—28no—
109C22×C3×C4—28no—
110C22×C3×C4C4×D318yes—
111C22×C3×C4D1218yes—
112C22×C3×C4#6714yes—
113C22×C3×C4C22×D314yes—
114C2×#67—68no—
115C2×#67—64no—
116#235—68no—
117#235—68no—
118C2×D12—34no—
119C2×C4×D3—64no—
120C2×Dic6—34no—
121C3×C42—216no—
122C3×C42—28no—
123C3×C42#67116yescomplemented
124#217—68no—
125#217—64no—
126(C2×D3)⋊C4—68no—
127C4⋊Dic3—38no—
128Dic3⋊C4—68no—
129C4×Dic3—64no—
130#208—68no—
131#208—68no—
132C2×C3⋊C8—68no—
133C22×C32—24no—
134C22×C32—24no—
135C22×C32—22no—
136C22×C32—22no—
137C22×C32—22no—
138C22×C32#10414yescomplemented
139C22×C32C2×C22⋊C411yescharacteristic
140C22×C32#12011yescharacteristic
141C22×C32#12311yescharacteristic
142C2×C3⋊D3—41no—
143C2×C3⋊D3—42no—
144C32×C4—28no—
145C32×C4—22no—
146C32×C4C4×D412yes—
147C32×C4#12112yes—
148C3⋊Dic3—41no—
149C3⋊Dic3—42no—
150C2×#41—91no—
151C23×C4—21no—
152C23×C4C2×C3⋊D311yescharacteristic
153C2×M16—92no—
154#123—181no—
155C22⋊Q8—92no—
156#121—92no—
157#120—181no—
158C4×D4—182no—
159#117—91no—
160C2×C42—21no—
161C2×C42—24no—
162C2×C42C2×C3⋊D312yes—
163#104—184no—
164C22⋊C8—182no—
165C23×C3—216no—
166C23×C3—24no—
167C23×C3—24no—
168C23×C3(C2×D3)⋊C418yes—
169C23×C3C2×#6714yes—
170C22×D3—64no—
171C2×C3×C4—264no—
172C2×C3×C4—232no—
173C2×C3×C4—24no—
174C2×C3×C4—24no—
175C2×C3×C4—216no—
176C2×C3×C4—216no—
177C2×C3×C4—216no—
178C2×C3×C4(C2×D3)⋊C418yes—
179C2×C3×C4C2×C4×D314yes—
180C2×C3×C4C2×D1214yes—
181C2×C3×C4#23518yes—
182C2×C3×C4C2×#6718yes—
183#67—1216no—
184#67—124no—
185#67—124no—
186C2×Dic3—68no—
187C2×Dic3—64no—
188D12—68no—
189C4×D3—128no—
190Dic6—68no—
191C3⋊C8—128no—
192C2×C32—21no—
193C2×C32—24no—
194C2×C32—21no—
195C2×C32#38611yescharacteristic
196C2×C32C2×#10412yes—
197C3⋊D3—81no—
198C24#63811yescharacteristic
199#41—182no—
200#41—182no—
201C2×Q8—91no—
202C2×D4—91no—
203C2×D4—182no—
204C2×D4—181no—
205C22×C4—24no—
206C22×C4—28no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—181no—
211C22×C4C4×C3⋊D312yes—
212C22×C4C4⋊(C3⋊D3)12yes—
213C22×C4#63811yescharacteristic
214C22×C4C22×C3⋊D311yescharacteristic
215M16—182no—
216M16—182no—
217C2×C8—182no—
218C4⋊C4—92no—
219C4⋊C4—182no—
220C22⋊C4—182no—
221C22⋊C4—181no—
222C22⋊C4—182no—
223C42—24no—
224C42—22no—
225C42—181no—
226C42#63814yescomplemented
227C22×C3—216no—
228C22×C3—216no—
229C22×C3—28no—
230C22×C3—28no—
231C22×C3—28no—
232C22×C3#805116yescomplemented
233C22×C3C2×(C2×D3)⋊C414yes—
234C22×C3#92914yes—
235C22×C3#95314yes—
236C2×D3—128no—
237C2×D3—124no—
238C3×C4—232no—
239C3×C4—28no—
240C3×C4C4×#6718yes—
241C3×C4#93018yes—
242Dic3—128no—
243Dic3—124no—
244C32#189611yescharacteristic, complemented, Sylow
245C23—21no—
246C23—24no—
247C23—21no—
248C23—181no—
249C23#375212yes—
250C23C2×#63811yescharacteristic
251Q8—182no—
252D4—182no—
253D4—361no—
254D4—364no—
255D4—361no—
256C2×C4—216no—
257C2×C4—28no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—24no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—182no—
264C2×C4—181no—
265C2×C4—362no—
266C2×C4#375212yes—
267C2×C4C2×C4×C3⋊D311yescharacteristic
268C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
269C2×C4#382812yes—
270C2×C4C2×#63812yes—
271C8—362no—
272C2×C3—24no—
273C2×C3—216no—
274C2×C3—24no—
275C2×C3C2×#80518yes—
276C2×C3#521314yes—
277D3—244no—
278C22—24no—
279C22—24no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—362no—
284C22—361no—
285C22#6363214yescomplemented
286C22C2×#375211yescharacteristic
287C22#6413811yescharacteristic
288C22#6416211yescharacteristic
289C4—28no—
290C4—22no—
291C4—362no—
292C4—361no—
293C4C4×#63812yes—
294C4#6413912yes—
295C3#7153214yescomplemented
296C2—21no—
297C2—21no—
298C2—24no—
299C2—721no—
300C2C2×#6363212yes—
301C2#1059291211yescharacteristic
subgroupG/H
centerC2×C4C2×C4⋊(C3⋊D3)
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC22×C32×C42C2
socleC22×C32C2×C22⋊C4
prime radical#10596262C2
cosocleC22×C32×C4C23
hypercenterC22×C42C3⋊D3
hypocenterC32#1896
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. C22×C32×C42C2semidirect
3. #10592906C2semidirect
4. C2×#63632C2semidirect
5. #10589389C2semidirect
14. #64139C4semidirect
18. #64133C4semidirect
22. C22×C3×C42D3semidirect
41. C2×C4⋊(C3⋊D3)C2×C4semidirect
43. C2×#634C2×C4semidirect
46. C32×C42D4semidirect
50. C4⋊(C3⋊Dic3)C2×C4semidirect
100. C22×C42C3⋊D3semidirect
123. C3×C42#67semidirect
138. C22×C32#104semidirect
226. C42#638semidirect
232. C22×C3#805semidirect
244. C32#1896semidirect
285. C22#63632semidirect
295. C3#71532semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C422
#105962622
#105929062
C2×#636322
#105893892
#715323