Finite Group Databasebeta

← #11788167

Subgroups — #11788167

Order 1152.

1326 conjugacy classes of subgroups; only the 285 normal subgroups are shown.

normal subgroups only

This group has 1326 conjugacy classes of subgroups — too many to draw. Only its 285 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
1C32×#525C211yesmaximal, characteristic
2C22×C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#63664C212yesmaximal, complemented
4#10592906C211yesmaximal, characteristic, complemented
5#10589398C212yesmaximal, complemented
6#71711—34nomaximal
7C2×C32×#41C2211yescharacteristic
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3—21no—
10C32×#123—21no—
11C32×C22⋊Q8C412yescomplemented
12C32×#121C412yescomplemented
13C32×#120—21no—
14C32×C4×D4—22no—
15C32×#117C2211yescharacteristic
16C2×C4×C3⋊Dic3—21no—
17C2×C4×C3⋊Dic3—24no—
18C2×C4×C3⋊Dic3C2212yes—
19C2×#3748C2212yes—
20#63664—24no—
21#63657—22no—
22C3×#525D314yes—
23C22×C4×Dic3—34no—
24C2×#837—38no—
25#5207—34no—
26#4532—38no—
27C24×C32D411yescharacteristic
28C32×#41—22no—
29C32×#41—22no—
30C2×C32×Q8C2×C411yescharacteristic, complemented
31C2×C32×D4—22no—
32C2×C32×D4—21no—
33C2×C32×D4C2×C411yescharacteristic, complemented
34C22×C32×C4—22no—
35C22×C32×C4—22no—
36C22×C32×C4—21no—
37C22×C32×C4C2×C412yes—
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D412yes—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—28no—
42C22×C3⋊Dic3—24no—
43C22×C3⋊Dic3—22no—
44C32×C4⋊C4—22no—
45C32×C4⋊C4C2×C412yescomplemented
46C32×C22⋊C4—22no—
47C32×C22⋊C4—21no—
48C32×C22⋊C4—22no—
49C32×C42—21no—
50C4×C3⋊Dic3—24no—
51C4×C3⋊Dic3—22no—
52C4×C3⋊Dic3D414yescomplemented
53#3748—22no—
54#3748—22no—
55C2×C3⋊(C3⋊C8)—22no—
56#1896—91noSylow
57C2×C3×#41C2×D314yes—
58C23×C3×C4C2×D314yes—
59C23×Dic3—64no—
60C3×#123—24no—
61C3×C22⋊Q8Dic318yescomplemented
62C3×#121Dic318yescomplemented
63C3×#120—24no—
64C3×C4×D4—28no—
65C3×#117C2×D314yes—
66C2×C4×Dic3—38no—
67C2×C4×Dic3—616no—
68C2×C4×Dic3—64no—
69C2×#208—38no—
70#837—616no—
71#830—68no—
72C23×C32—24no—
73C23×C32—21no—
74C23×C32—21no—
75C23×C32—21no—
76C23×C32C22⋊C412yes—
77C23×C32C2×D411yescharacteristic
78C32×Q8—22no—
79C32×D4—22no—
80C32×D4—44no—
81C32×D4—41no—
82C32×D4—41no—
83C2×C32×C4—21no—
84C2×C32×C4—21no—
85C2×C32×C4—24no—
86C2×C32×C4—24no—
87C2×C32×C4—22no—
88C2×C32×C4—21no—
89C2×C32×C4—42no—
90C2×C32×C4C22⋊C412yes—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D412yes—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4#4112yes—
95C2×C3⋊Dic3—216no—
96C2×C3⋊Dic3—28no—
97C2×C3⋊Dic3—24no—
98C3⋊(C3⋊C8)—42no—
99#525C3⋊D311yescharacteristic
100C22×C42—91no—
101C2×#104—92no—
102#407—91no—
103#339—92no—
104C24×C3#6714yes—
105C3×#41—28no—
106C3×#41—28no—
107C2×C3×Q8C2×Dic314yescomplemented
108C2×C3×D4—28no—
109C2×C3×D4—24no—
110C2×C3×D4C2×Dic314yescomplemented
111C22×C3×C4—28no—
112C22×C3×C4—28no—
113C22×C3×C4—24no—
114C22×C3×C4C2×Dic318yes—
115C22×C3×C4#6714yes—
116C22×C3×C4#6718yes—
117C22×C3×C4C22×D314yes—
118C22×Dic3—616no—
119C22×Dic3—632no—
120C22×Dic3—68no—
121C3×C4⋊C4—28no—
122C3×C4⋊C4C2×Dic318yescomplemented
123C3×C22⋊C4—28no—
124C3×C22⋊C4—24no—
125C3×C22⋊C4—28no—
126C3×C42—24no—
127C4×Dic3—316no—
128C4×Dic3—616no—
129C4×Dic3—68no—
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—41no—
139C22×C32—42no—
140C22×C32#10414yescomplemented
141C22×C32C2×C22⋊C411yescharacteristic
142C22×C32#12011yescharacteristic
143C22×C32#12311yescharacteristic
144C32×C4—22no—
145C32×C4—41no—
146C32×C4—42no—
147C32×C4C4×D412yes—
148C32×C4#12112yes—
149C3⋊Dic3—28no—
150C2×#41C2×C3⋊D311yescharacteristic
151C23×C4—181no—
152C23×C4C2×C3⋊D311yescharacteristic
153C2×M16—92no—
154#123—21no—
155C22⋊Q8C3⋊Dic312yescomplemented
156#121C3⋊Dic312yescomplemented
157#120—21no—
158C4×D4—22no—
159#117C2×C3⋊D311yescharacteristic
160C2×C42—92no—
161C2×C42—184no—
162C2×C42—181no—
163#104—184no—
164C22⋊C8—182no—
165C23×C3—216no—
166C23×C3—24no—
167C23×C3—24no—
168C23×C3—24no—
169C23×C3#21718yes—
170C23×C3C2×#6714yes—
171C3×Q8—28no—
172C3×D4—28no—
173C3×D4—416no—
174C3×D4—44no—
175C3×D4—44no—
176C2×C3×C4—24no—
177C2×C3×C4—24no—
178C2×C3×C4—216no—
179C2×C3×C4—216no—
180C2×C3×C4—28no—
181C2×C3×C4—24no—
182C2×C3×C4—48no—
183C2×C3×C4#21718yes—
184C2×C3×C4D3×D418yes—
185C2×C3×C4#23718yes—
186C2×C3×C4C22×Dic314yes—
187C2×C3×C4C2×#6714yes—
188C2×Dic3—664no—
189C2×Dic3—632no—
190C2×Dic3—616no—
191C3⋊C8—128no—
192C2×C32—21no—
193C2×C32—24no—
194C2×C32—21no—
195C2×C32—81no—
196C2×C32#38611yescharacteristic
197C2×C32C2×#10412yes—
198C24#63811yescharacteristic
199#41—22no—
200#41—22no—
201C2×Q8C2×C3⋊Dic311yescharacteristic, complemented
202C2×D4—22no—
203C2×D4—21no—
204C2×D4C2×C3⋊Dic311yescharacteristic, complemented
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—184no—
209C22×C4—188no—
210C22×C4—182no—
211C22×C4C2×C3⋊Dic312yes—
212C22×C4#63811yescharacteristic
213C22×C4#63812yes—
214C22×C4C22×C3⋊D311yescharacteristic
215M16—182no—
216M16—182no—
217C2×C8—182no—
218C4⋊C4—22no—
219C4⋊C4C2×C3⋊Dic312yescomplemented
220C22⋊C4—22no—
221C22⋊C4—21no—
222C22⋊C4—22no—
223C42—21no—
224C42—94no—
225C42—184no—
226C42—182no—
227C22×C3—216no—
228C22×C3—216no—
229C22×C3—28no—
230C22×C3—28no—
231C22×C3—28no—
232C22×C3—44no—
233C22×C3—48no—
234C22×C3#837116yescomplemented
235C22×C3#93514yes—
236C22×C3#93714yes—
237C22×C3C2×#21714yes—
238C3×C4—28no—
239C3×C4—44no—
240C3×C4—48no—
241C3×C4D4×Dic318yes—
242C3×C4#93918yes—
243Dic3—632no—
244C32#189611yescharacteristic, complemented, Sylow
245C23—21no—
246C23—21no—
247C23—24no—
248C23—21no—
249C23#375712yes—
250C23C2×#63811yescharacteristic
251Q8—22no—
252D4—22no—
253D4—41no—
254D4—41no—
255D4—44no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—24no—
259C2×C4—24no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—1816no—
264C2×C4—188no—
265C2×C4—184no—
266C2×C4#375712yes—
267C2×C4D4×C3⋊D312yes—
268C2×C4#383012yes—
269C2×C4C22×C3⋊Dic311yescharacteristic
270C2×C4C2×#63811yescharacteristic
271C8—362no—
272C2×C3—24no—
273C2×C3—216no—
274C2×C3—24no—
275C2×C3—84no—
276C2×C3#522014yes—
277C2×C3C2×#83718yes—
278C22—24no—
279C22—24no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—41no—
284C22—42no—
285C22#6366414yescomplemented
286C22#6414411yescharacteristic
287C22#6414611yescharacteristic
288C22C2×#375711yescharacteristic
289C4—22no—
290C4—41no—
291C4—42no—
292C4—188no—
293C4D4×C3⋊Dic312yes—
294C4#6414812yes—
295C3#7171114yescomplemented
296C2—21no—
297C2—21no—
298C2—24no—
299C2—81no—
300C2#1059291911yescharacteristic
301C2C2×#6366412yes—
subgroupG/H
centerC2×C4C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
Fitting, prime radicalC32×#525C2
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenter#525C3⋊D3
hypocenterC32#1896
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
2. C22×C4×C3⋊Dic3C2semidirect
3. C2×#63664C2semidirect
4. #10592906C2semidirect
5. #10589398C2semidirect
11. C32×C22⋊Q8C4semidirect
12. C32×#121C4semidirect
30. C2×C32×Q8C2×C4semidirect
33. C2×C32×D4C2×C4semidirect
45. C32×C4⋊C4C2×C4semidirect
52. C4×C3⋊Dic3D4semidirect
61. C3×C22⋊Q8Dic3semidirect
62. C3×#121Dic3semidirect
107. C2×C3×Q8C2×Dic3semidirect
110. C2×C3×D4C2×Dic3semidirect
122. C3×C4⋊C4C2×Dic3semidirect
140. C22×C32#104semidirect
155. C22⋊Q8C3⋊Dic3semidirect
156. #121C3⋊Dic3semidirect
201. C2×Q8C2×C3⋊Dic3semidirect
204. C2×D4C2×C3⋊Dic3semidirect
219. C4⋊C4C2×C3⋊Dic3semidirect
234. C22×C3#837semidirect
244. C32#1896semidirect
285. C22#63664semidirect
295. C3#71711semidirect

Maximal subgroups

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

subgroupindex
C32×#5252
C22×C4×C3⋊Dic32
C2×#636642
#105929062
#105893982
#717113