Finite Group Databasebeta

← #11773888

Subgroups — #11773888

Order 1152.

756 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 173 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×#64081C211yesmaximal, characteristic
2C32×#432C211yesmaximal, characteristic, complemented
3#10592625C211yesmaximal, characteristic, complemented
4#10589335C212yesmaximal, complemented
5#10589334C212yesmaximal
6#70826—34nomaximal
7C22×C4×C3⋊D3C411yescharacteristic
8C2×C32×C42C2211yescharacteristic
9C2×#3752C411yescharacteristic
10C2×#3752C2211yescharacteristic
11C2×#3750C411yescharacteristic
12C2×#3750C2211yescharacteristic
13C2×C4×C3⋊Dic3C411yescharacteristic
14#64081—21no—
15#64081—21no—
16#64081—21no—
17#64081—21no—
18C32×C4⋊C8—21no—
19C32×C22⋊C8C2212yes—
20C32×#97—21no—
21#63657C2212yes—
22C4⋊(C3⋊(C3⋊C8))—21no—
23#63630—21no—
24C2×#872—34no—
25C3×#432D314yescomplemented
26#4926—34no—
27#4469—38no—
28#4468—38no—
29C23×C3⋊D3C2×C411yescharacteristic
30C22×C32×C4C2×C411yescharacteristic
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3C2×C411yescharacteristic
34C22×C3⋊Dic3C2×C411yescharacteristic
35C22×C3⋊Dic3C2×C411yescharacteristic
36C2×C4×C3⋊D3—22no—
37C2×C4×C3⋊D3—21no—
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3—22no—
40C2×C32×C8—22no—
41C32×C42D411yescharacteristic
42C32×C42D411yescharacteristic
43C32×C42D411yescharacteristic
44C32×C42D411yescharacteristic
45#3752—21no—
46#3752—21no—
47#3752—21no—
48#3752—21no—
49#3750—21no—
50#3750—21no—
51#3750—21no—
52#3750—21no—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3—21no—
55C2×C3⋊(C3⋊C8)—22no—
56#1464—91noSylow
57C22×C4×D3—34no—
58C2×C3×C42C2×D314yes—
59C2×(C2×D3)⋊C4—34no—
60C2×(C2×D3)⋊C4—34no—
61C2×Dic3⋊C4—34no—
62C2×Dic3⋊C4—34no—
63C2×C4×Dic3—34no—
64#872—64no—
65#872—64no—
66#872—64no—
67#872—64no—
68C3×C4⋊C8—24no—
69C3×C22⋊C8C2×D318yes—
70C3×#97—24no—
71#830—38no—
72C4⋊(C3⋊C8)—64no—
73#803—64no—
74C23×C32C22×C411yescharacteristic
75C22×C3⋊D3—21no—
76C22×C3⋊D3—21no—
77C22×C3⋊D3—41no—
78C22×C3⋊D3—41no—
79C22×C3⋊D3M1612yes—
80C2×C32×C4—21no—
81C2×C32×C4—21no—
82C2×C32×C4—41no—
83C2×C32×C4—41no—
84C2×C32×C4C22⋊C411yescharacteristic
85C2×C32×C4C22⋊C411yescharacteristic
86C2×C32×C4C22⋊C411yescharacteristic
87C2×C32×C4C22⋊C411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C3⋊Dic3—21no—
91C2×C3⋊Dic3—21no—
92C2×C3⋊Dic3—21no—
93C2×C3⋊Dic3—21no—
94C2×C3⋊Dic3—41no—
95C2×C3⋊Dic3—41no—
96C2×C3⋊Dic3M1612yes—
97C4×C3⋊D3—24no—
98C4×C3⋊D3—24no—
99C32×C8—42no—
100C3⋊(C3⋊C8)—42no—
101C2×#117—91no—
102#432—91no—
103#432C3⋊D311yescharacteristic, complemented
104#324—92no—
105#323—92no—
106C23×D3—34no—
107C22×C3×C4C4×D314yes—
108C22×C3×C4C4×D314yes—
109C22×C3×C4C22×D314yes—
110C22×Dic3—34no—
111C22×Dic3—34no—
112C22×Dic3—34no—
113C2×C4×D3—68no—
114C2×C4×D3—68no—
115C2×C4×D3—64no—
116C2×C4×D3—64no—
117C2×C3×C8—28no—
118C3×C42D1214yes—
119C3×C42D1214yes—
120C3×C42#6714yes—
121C3×C42#6714yes—
122(C2×D3)⋊C4—64no—
123(C2×D3)⋊C4—64no—
124(C2×D3)⋊C4—64no—
125(C2×D3)⋊C4—64no—
126Dic3⋊C4—64no—
127Dic3⋊C4—64no—
128Dic3⋊C4—64no—
129Dic3⋊C4—64no—
130C4×Dic3—64no—
131C4×Dic3—64no—
132C2×C3⋊C8—68no—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32C2×C22⋊C411yescharacteristic
136C22×C32C2×M1611yescharacteristic
137C22×C32C2×M1611yescharacteristic
138C2×C3⋊D3—22no—
139C2×C3⋊D3—42no—
140C2×C3⋊D3—41no—
141C2×C3⋊D3—41no—
142C2×C3⋊D3—42no—
143C32×C4—21no—
144C32×C4—21no—
145C32×C4—21no—
146C32×C4—21no—
147C32×C4—21no—
148C32×C4—21no—
149C3⋊Dic3—22no—
150C3⋊Dic3—41no—
151C3⋊Dic3—41no—
152C23×C4—91no—
153#117—181no—
154#117—181no—
155#117—181no—
156#117—181no—
157C2×C4⋊C4—91no—
158C2×C4⋊C4—91no—
159C2×C22⋊C4—91no—
160C2×C22⋊C4—91no—
161C2×C42—91no—
162C2×C42C2×C3⋊D311yescharacteristic
163C4⋊C8—21no—
164C4⋊C8—181no—
165C22⋊C8—92no—
166C22⋊C8C2×C3⋊D312yes—
167#97—21no—
168#97—181no—
169C23×C3C2×C4×D314yes—
170C22×D3—38no—
171C22×D3—64no—
172C22×D3—64no—
173C22×D3—124no—
174C22×D3—124no—
175C2×C3×C4—24no—
176C2×C3×C4—24no—
177C2×C3×C4—44no—
178C2×C3×C4—44no—
179C2×C3×C4(C2×D3)⋊C414yes—
180C2×C3×C4(C2×D3)⋊C414yes—
181C2×C3×C4(C2×D3)⋊C414yes—
182C2×C3×C4(C2×D3)⋊C414yes—
183C2×C3×C4C2×D1214yes—
184C2×C3×C4C2×#6714yes—
185C2×Dic3—38no—
186C2×Dic3—64no—
187C2×Dic3—64no—
188C2×Dic3—64no—
189C2×Dic3—64no—
190C2×Dic3—124no—
191C2×Dic3—124no—
192C4×D3—616no—
193C4×D3—616no—
194C3×C8—48no—
195C3⋊C8—128no—
196C2×C32—21no—
197C2×C32—21no—
198C2×C32#40711yescharacteristic
199C2×C32#41011yescharacteristic
200C2×C32#41311yescharacteristic
201C3⋊D3—42no—
202C24—91no—
203C22×C4—91no—
204C22×C4—91no—
205C22×C4—91no—
206C22×C4—182no—
207C22×C4—182no—
208C22×C4—181no—
209C22×C4—181no—
210C22×C4C4×C3⋊D311yescharacteristic
211C22×C4C4×C3⋊D311yescharacteristic
212C22×C4C22×C3⋊D311yescharacteristic
213C2×C8—22no—
214C2×C8—182no—
215C4⋊C4—181no—
216C4⋊C4—181no—
217C4⋊C4—181no—
218C4⋊C4—181no—
219C22⋊C4—181no—
220C22⋊C4—181no—
221C22⋊C4—181no—
222C22⋊C4—181no—
223C42—181no—
224C42—181no—
225C42C4⋊(C3⋊D3)11yescharacteristic
226C42C4⋊(C3⋊D3)11yescharacteristic
227C42#63811yescharacteristic
228C42#63811yescharacteristic
229C22×C3—24no—
230C22×C3—24no—
231C22×C3D3×M1614yes—
232C22×C3D3×M1614yes—
233C22×C3C2×(C2×D3)⋊C414yes—
234C2×D3—68no—
235C2×D3—128no—
236C2×D3—124no—
237C2×D3—124no—
238C2×D3—128no—
239C3×C4—24no—
240C3×C4—24no—
241C3×C4—24no—
242C3×C4—24no—
243C3×C4—24no—
244C3×C4—24no—
245Dic3—68no—
246Dic3—124no—
247Dic3—124no—
248C32#146411yescharacteristic, complemented, Sylow
249C23—92no—
250C23—181no—
251C23—181no—
252C23—361no—
253C23—361no—
254C23C2×C4×C3⋊D311yescharacteristic
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—92no—
260C2×C4—184no—
261C2×C4—184no—
262C2×C4—181no—
263C2×C4—181no—
264C2×C4—181no—
265C2×C4—181no—
266C2×C4—361no—
267C2×C4—361no—
268C2×C4#375211yescharacteristic
269C2×C4#375211yescharacteristic
270C2×C4#375211yescharacteristic
271C2×C4#375211yescharacteristic
272C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
273C2×C4C2×#63811yescharacteristic
274C8—42no—
275C8—362no—
276C2×C3—24no—
277C2×C3—24no—
278C2×C3#500614yes—
279C2×C3#512614yes—
280C2×C3#513214yes—
281D3—128no—
282C22—21no—
283C22—21no—
284C22—182no—
285C22—362no—
286C22—362no—
287C22—361no—
288C22—361no—
289C22M16×C3⋊D311yescharacteristic
290C22M16×C3⋊D311yescharacteristic
291C22C2×#375211yescharacteristic
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—182no—
299C4—361no—
300C4—361no—
301C3#7082614yescomplemented
302C2—21no—
303C2—21no—
304C2—362no—
305C2#1059270511yescharacteristic
306C2#1059282511yescharacteristic
307C2#1059283111yescharacteristic
subgroupG/H
centerC22C2×#3752
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#432C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenter#432C3⋊D3
hypocenterC32#1464
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C32×#432C2semidirect
3. #10592625C2semidirect
4. #10589335C2semidirect
25. C3×#432D3semidirect
103. #432C3⋊D3semidirect
248. C32#1464semidirect
301. C3#70826semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C32×#4322
#105926252
#105893352
#105893342
#708263