Finite Group Databasebeta

← #11772596

Subgroups — #11772596

Order 1152.

696 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 157 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×C32×#99C211yesmaximal, characteristic
2#10592920C211yesmaximal, characteristic
3C2×#63661C211yesmaximal, characteristic
4#67695—34nomaximal
5C22×C32×D4C2211yescharacteristic
6C2×C32×C22⋊C4—21no—
7C2×#3757—21no—
8C2×#3757—21no—
9C2×#3757—21no—
10C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
11C2×C4×C3⋊Dic3C411yescharacteristic, complemented
12C32×#99—21no—
13C32×#99C412yescomplemented
14#63661—21no—
15#63661C412yescomplemented
16C2×C3×#99D314yes—
17#5221—34no—
18C2×#834—34no—
19C24×C32D411yescharacteristic
20C24×C32D411yescharacteristic
21C2×C32×D4—41no—
22C2×C32×D4—41no—
23C2×C32×D4C2×C411yescharacteristic
24C2×C32×D4C2×C411yescharacteristic
25C2×C32×D4D411yescharacteristic
26C2×C32×D4Q811yescharacteristic
27C22×C32×C4—41no—
28C22×C32×C4C2×C411yescharacteristic
29C22×C3⋊Dic3—21no—
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3—41no—
32C32×C22⋊C4—22no—
33C32×C22⋊C4—41no—
34#3757—22no—
35#3757—42no—
36#3757—42no—
37#3757—41no—
38C4⋊(C3⋊Dic3)—41no—
39C4×C3⋊Dic3—41no—
40#1393—91noSylow
41C22×C3×D4C2×D314yes—
42C2×C3×C22⋊C4—24no—
43C2×#217—64no—
44C2×#217—64no—
45C2×#217—64no—
46C2×C4⋊Dic3—34no—
47C2×C4×Dic3—34no—
48C3×#99—24no—
49C3×#99Dic318yescomplemented
50#834—38no—
51#834—64no—
52C23×C32—21no—
53C23×C32—21no—
54C23×C32—21no—
55C23×C32—21no—
56C23×C32—41no—
57C23×C32—41no—
58C23×C32—41no—
59C23×C32—41no—
60C23×C32C22⋊C411yescharacteristic
61C23×C32C22⋊C411yescharacteristic
62C23×C32C22⋊C411yescharacteristic
63C23×C32C4⋊C411yescharacteristic
64C23×C32C4⋊C411yescharacteristic
65C32×D4—41no—
66C32×D4—41no—
67C32×D4—41no—
68C32×D4—41no—
69C2×C32×C4—21no—
70C2×C32×C4—21no—
71C2×C32×C4—42no—
72C2×C32×C4—81no—
73C2×C32×C4—81no—
74C2×C32×C4C4211yescharacteristic
75C2×C32×C4C4⋊C411yescharacteristic
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3—41no—
78C2×C3⋊Dic3—41no—
79C2×C3⋊Dic3—42no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3—41no—
83C2×C3⋊Dic3—81no—
84C2×C3⋊Dic3—81no—
85C2×#99—91no—
86C2×#99C3⋊D311yescharacteristic
87#390—91no—
88C24×C3D1214yes—
89C24×C3#6714yes—
90C2×C3×D4—44no—
91C2×C3×D4—44no—
92C2×C3×D4Dic614yes—
93C2×C3×D4C4×D314yes—
94C2×C3×D4C2×Dic314yes—
95C2×C3×D4#6714yes—
96C22×C3×C4—44no—
97C22×C3×C4C4×D314yes—
98C22×Dic3—64no—
99C22×Dic3—64no—
100C22×Dic3—124no—
101C3×C22⋊C4—28no—
102C3×C22⋊C4—44no—
103#217—68no—
104#217—128no—
105#217—128no—
106#217—124no—
107C4⋊Dic3—124no—
108C4×Dic3—124no—
109C22×C32—21no—
110C22×C32—21no—
111C22×C32—21no—
112C22×C32—21no—
113C22×C32—21no—
114C22×C32—21no—
115C22×C32—41no—
116C22×C32—41no—
117C22×C32—41no—
118C22×C32—41no—
119C22×C32—41no—
120C22×C32—41no—
121C22×C32—41no—
122C22×C32—41no—
123C22×C32—81no—
124C22×C32—81no—
125C22×C32#9511yescharacteristic
126C22×C32#9911yescharacteristic
127C22×C32#9911yescharacteristic
128C32×C4—21no—
129C32×C4—21no—
130C32×C4—82no—
131C3⋊Dic3—42no—
132C3⋊Dic3—82no—
133C3⋊Dic3—81no—
134C22×D4C2×C3⋊D311yescharacteristic
135C2×C4⋊C4—91no—
136C2×C22⋊C4—21no—
137C2×C22⋊C4—181no—
138C2×C22⋊C4—181no—
139C2×C22⋊C4—181no—
140C2×C42—91no—
141#99—21no—
142#99—92no—
143#99—181no—
144#99C3⋊Dic312yescomplemented
145C23×C3—24no—
146C23×C3—24no—
147C23×C3—24no—
148C23×C3—24no—
149C23×C3—44no—
150C23×C3—44no—
151C23×C3—44no—
152C23×C3—44no—
153C23×C3Dic3⋊C414yes—
154C23×C3C4⋊Dic314yes—
155C23×C3(C2×D3)⋊C414yes—
156C23×C3(C2×D3)⋊C414yes—
157C23×C3#21714yes—
158C3×D4—44no—
159C3×D4—44no—
160C3×D4—44no—
161C3×D4—44no—
162C2×C3×C4—24no—
163C2×C3×C4—24no—
164C2×C3×C4—48no—
165C2×C3×C4—84no—
166C2×C3×C4—84no—
167C2×C3×C4C4×Dic314yes—
168C2×C3×C4Dic3⋊C414yes—
169C2×Dic3—68no—
170C2×Dic3—124no—
171C2×Dic3—124no—
172C2×Dic3—128no—
173C2×Dic3—124no—
174C2×Dic3—124no—
175C2×Dic3—124no—
176C2×Dic3—244no—
177C2×Dic3—244no—
178C2×C32—21no—
179C2×C32—21no—
180C2×C32—41no—
181C2×C32—41no—
182C2×C32—41no—
183C2×C32—41no—
184C2×C32#34211yescharacteristic
185C2×C32#35311yescharacteristic
186C2×C32#35411yescharacteristic
187C24C4⋊(C3⋊D3)11yescharacteristic
188C24#63811yescharacteristic
189C2×D4—41no—
190C2×D4—41no—
191C2×D4#63411yescharacteristic
192C2×D4C4×C3⋊D311yescharacteristic
193C2×D4C2×C3⋊Dic311yescharacteristic
194C2×D4#63811yescharacteristic
195C22×C4—41no—
196C22×C4—181no—
197C22×C4—181no—
198C22×C4—361no—
199C22×C4C4×C3⋊D311yescharacteristic
200C4⋊C4—361no—
201C22⋊C4—22no—
202C22⋊C4—41no—
203C22⋊C4—182no—
204C22⋊C4—362no—
205C22⋊C4—362no—
206C22⋊C4—361no—
207C42—361no—
208C22×C3—24no—
209C22×C3—24no—
210C22×C3—24no—
211C22×C3—24no—
212C22×C3—24no—
213C22×C3—24no—
214C22×C3—44no—
215C22×C3—44no—
216C22×C3—44no—
217C22×C3—44no—
218C22×C3—44no—
219C22×C3—44no—
220C22×C3—44no—
221C22×C3—44no—
222C22×C3—84no—
223C22×C3—84no—
224C22×C3#80614yes—
225C22×C3#80614yes—
226C22×C3C3⋊#9514yes—
227C3×C4—24no—
228C3×C4—24no—
229C3×C4—88no—
230Dic3—128no—
231Dic3—248no—
232Dic3—244no—
233C32#139311yescharacteristic, complemented, Sylow
234C23—21no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—41no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23#375011yescharacteristic
243C23C4⋊(C3⋊Dic3)11yescharacteristic
244C23#375211yescharacteristic
245C23#375211yescharacteristic
246C23#375711yescharacteristic
247D4—41no—
248D4—41no—
249D4—41no—
250D4—41no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—42no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—182no—
257C2×C4—361no—
258C2×C4—361no—
259C2×C4—362no—
260C2×C4—361no—
261C2×C4—361no—
262C2×C4—361no—
263C2×C4—721no—
264C2×C4—721no—
265C2×C4C4×C3⋊Dic311yescharacteristic
266C2×C4#375011yescharacteristic
267C2×C3—24no—
268C2×C3—24no—
269C2×C3—44no—
270C2×C3—44no—
271C2×C3—44no—
272C2×C3—44no—
273C2×C3#447314yes—
274C2×C3#447414yes—
275C2×C3#452714yes—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—81no—
291C22—81no—
292C22#6363311yescharacteristic
293C22#6363311yescharacteristic
294C22#6365811yescharacteristic
295C4—21no—
296C4—21no—
297C4—82no—
298C4—362no—
299C4—722no—
300C4—721no—
301C3#6769514yescomplemented
302C2—21no—
303C2—21no—
304C2—41no—
305C2—41no—
306C2—41no—
307C2—41no—
308C2#1058933911yescharacteristic
309C2#1058934011yescharacteristic
310C2#1058939311yescharacteristic
subgroupG/H
centerC22#63633
commutatorC2×C32×C4C42
FrattiniC22×D4C2×C3⋊D3
FittingC2×C32×#99C2
socleC22×C32#99
prime radical, cosocleC22×C32×D4C22
hypercenterC2×#99C3⋊D3
hypocenterC32#1393
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
10. C2×C4⋊(C3⋊Dic3)C4semidirect
11. C2×C4×C3⋊Dic3C4semidirect
13. C32×#99C4semidirect
15. #63661C4semidirect
49. C3×#99Dic3semidirect
144. #99C3⋊Dic3semidirect
233. C32#1393semidirect
301. C3#67695semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#992
#105929202
C2×#636612
#676953