Finite Group Databasebeta

← #11783623

Subgroups — #11783623

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic
2C2×C3×#830C212yesmaximal
3C2×#63555C211yesmaximal, characteristic, complemented
4C2×#63553C211yesmaximal, characteristic, complemented
5#10589156C212yesmaximal, complemented
6#69907—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C2×#3757C412yes—
9#64135—22no—
10#64135—22no—
11C2×C4⋊(C3⋊Dic3)C412yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊C8C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C3×#830C418yescomplemented
17#63555—22no—
18#63553—22no—
19C2×#926—32no—
20C2×#926—61no—
21C2×C3×C22⋊C8—32no—
22C2×#830D312yes—
23C2×#815—32no—
24C2×C8×Dic3—32no—
25#4550—32no—
26#4550—32no—
27C24×C32C2×C411yescharacteristic
28C22×C32×C4—21no—
29C22×C32×C4—21no—
30C22×C32×C4—22no—
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4C2×C414yes—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3C2×C412yes—
35C22×C3⋊Dic3C2×C412yes—
36#3757—24no—
37C4⋊(C3⋊Dic3)—24no—
38C4×C3⋊Dic3—21no—
39C4×C3⋊Dic3—21no—
40C4×C3⋊Dic3D412yes—
41C4×C3⋊Dic3D412yes—
42C2×C3×C3⋊C8—22no—
43C2×C3×C3⋊C8—22no—
44C2×C3×C3⋊C8—22no—
45C2×C3×C3⋊C8—22no—
46C2×C3×C3⋊C8C2×C414yes—
47C2×C3×C3⋊C8C2×C414yes—
48#1750—91noSylow
49C23×C3×C4—21no—
50C23×C3×C4C2×D312yes—
51C22×C3×C8—32no—
52C22×C3×C8—32no—
53C2×#217—34no—
54C2×#217—62no—
55#926—64no—
56#926—64no—
57#926—64no—
58#926—64no—
59C2×C4⋊Dic3—34no—
60C2×C4⋊Dic3—62no—
61C2×C4×Dic3—32no—
62C2×C4×Dic3—32no—
63C2×C4×Dic3—61no—
64C2×C4×Dic3—61no—
65C22×C3⋊C8C2×D312yes—
66C22×C3⋊C8C2×D312yes—
67C3×C22⋊C8—38no—
68#830Dic318yescomplemented
69#815—64no—
70C8×Dic3—64no—
71C23×C32—21no—
72C23×C32—21no—
73C23×C32—24no—
74C23×C32C4212yes—
75C23×C32C22×C411yescharacteristic
76C2×C32×C4—21no—
77C2×C32×C4—21no—
78C2×C32×C4—24no—
79C2×C32×C4—24no—
80C2×C32×C4C4212yes—
81C2×C32×C4C22×C412yes—
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4#4112yes—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—24no—
87C2×C3⋊Dic3—24no—
88C2×C3⋊Dic3C22⋊C414yes—
89C3×C3⋊C8—24no—
90C3×C3⋊C8—24no—
91C2×#117—91no—
92C2×C22⋊C8—32no—
93C2×#97—91no—
94C2×C4×C8—91no—
95#336—92no—
96C24×C3—21no—
97C24×C3C4×D312yes—
98C22×C3×C4—22no—
99C22×C3×C4—22no—
100C22×C3×C4—24no—
101C22×C3×C4—22no—
102C22×C3×C4—22no—
103C22×C3×C4—22no—
104C22×C3×C4—22no—
105C22×C3×C4—24no—
106C22×C3×C4—21no—
107C22×C3×C4—21no—
108C22×C3×C4C4×D314yes—
109C22×C3×C4C4×D312yes—
110C22×C3×C4C2×Dic314yes—
111C22×C3×C4C22×D312yes—
112C22×Dic3—34no—
113C22×Dic3—34no—
114C22×Dic3—62no—
115C22×Dic3—62no—
116C2×C3×C8—34no—
117C2×C3×C8—34no—
118C2×C3×C8—62no—
119C2×C3×C8—62no—
120C2×C3×C8—62no—
121C2×C3×C8—62no—
122#217—68no—
123#217—68no—
124C4⋊Dic3—68no—
125C4⋊Dic3—68no—
126C4×Dic3—34no—
127C4×Dic3—34no—
128C4×Dic3—62no—
129C4×Dic3—62no—
130C4×Dic3—62no—
131C4×Dic3—62no—
132C4×Dic3—62no—
133C4×Dic3—62no—
134C2×C3⋊C8—22no—
135C2×C3⋊C8—22no—
136C2×C3⋊C8—22no—
137C2×C3⋊C8—22no—
138C2×C3⋊C8C2×Dic314yes—
139C2×C3⋊C8C2×Dic314yes—
140C22×C32—22no—
141C22×C32—24no—
142C22×C32—42no—
143C22×C32—42no—
144C22×C32C2×C4211yescharacteristic
145C22×C32C2×C22⋊C411yescharacteristic
146C22×C32#11711yescharacteristic
147C22×C32#13114yes—
148C32×C4—22no—
149C32×C4C4×D412yes—
150C32×C4C4×D412yes—
151C3⋊Dic3—24no—
152C3⋊Dic3—42no—
153C23×C4D3211yescharacteristic
154C22×C8—32no—
155C22×C8—32no—
156#117—182no—
157#117—182no—
158C2×C4⋊C4—92no—
159C2×C22⋊C4—92no—
160C2×C42—91no—
161C2×C42—91no—
162C22⋊C8—38no—
163#97—182no—
164C4×C8—182no—
165C23×C3—22no—
166C23×C3—22no—
167C23×C3—22no—
168C23×C3—22no—
169C23×C3—24no—
170C23×C3—24no—
171C23×C3—22no—
172C23×C3—21no—
173C23×C3—44no—
174C23×C3C4×Dic314yes—
175C23×C3C2×C4×D312yes—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—28no—
179C2×C3×C4—28no—
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—24no—
183C2×C3×C4—24no—
184C2×C3×C4—24no—
185C2×C3×C4—24no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4C4×Dic314yes—
192C2×C3×C4C2×C4×D312yes—
193C2×C3×C4D3×D412yes—
194C2×C3×C4D3×D412yes—
195C2×C3×C4#23712yes—
196C2×C3×C4#23712yes—
197C2×C3×C4C22×Dic312yes—
198C2×Dic3—38no—
199C2×Dic3—64no—
200C2×Dic3—64no—
201C2×Dic3—64no—
202C2×Dic3—64no—
203C2×Dic3—64no—
204C2×Dic3—64no—
205C2×Dic3—64no—
206C2×Dic3—124no—
207C2×Dic3—124no—
208C3×C8—64no—
209C3×C8—64no—
210C3⋊C8—24no—
211C3⋊C8—24no—
212C2×C32—42no—
213C2×C32C4×C22⋊C411yescharacteristic
214C2×C32#40512yes—
215C2×C32#40812yes—
216C2×C32#43312yes—
217C24#62411yescharacteristic
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—92no—
222C22×C4—92no—
223C22×C4D3×Dic314yes—
224C22×C4#62411yescharacteristic
225C22×C4C2×D3211yescharacteristic
226C2×C8—34no—
227C2×C8—34no—
228C2×C8—62no—
229C2×C8—62no—
230C2×C8—62no—
231C2×C8—62no—
232C4⋊C4—184no—
233C22⋊C4—184no—
234C42—92no—
235C42—92no—
236C42—181no—
237C42—181no—
238C22×C3—24no—
239C22×C3—24no—
240C22×C3—24no—
241C22×C3—24no—
242C22×C3—24no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—44no—
247C22×C3—44no—
248C22×C3—44no—
249C22×C3—44no—
250C22×C3—44no—
251C22×C3#87712yes—
252C22×C3D3×C22⋊C412yes—
253C22×C3#90114yes—
254C22×C3#90714yes—
255C22×C3C2×C4×Dic312yes—
256C3×C4—24no—
257C3×C4—24no—
258C3×C4—22no—
259C3×C4—22no—
260C3×C4#67⋊C412yes—
261C3×C4#67⋊C412yes—
262C3×C4D4×Dic312yes—
263C3×C4D4×Dic312yes—
264Dic3—68no—
265Dic3—124no—
266Dic3—124no—
267Dic3—124no—
268C32#175011yescharacteristic, complemented, Sylow
269C23—24no—
270C23—21no—
271C23—21no—
272C23Dic3212yes—
273C23C2×#62411yescharacteristic
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—94no—
279C2×C4—184no—
280C2×C4—184no—
281C2×C4—182no—
282C2×C4Dic3212yes—
283C2×C4C2×D3×Dic312yes—
284C2×C4#380512yes—
285C2×C4#381111yescharacteristic
286C2×C4#381111yescharacteristic
287C8—64no—
288C8—64no—
289C2×C3—22no—
290C2×C3—22no—
291C2×C3—22no—
292C2×C3—21no—
293C2×C3—44no—
294C2×C3—44no—
295C2×C3#472014yes—
296C2×C3#472714yes—
297C2×C3Dic3×C22⋊C412yes—
298C2×C3#510112yes—
299C2×C3#512212yes—
300C22—24no—
301C22—22no—
302C22—42no—
303C22—42no—
304C22#6381714yes—
305C22C2×Dic3211yescharacteristic
306C22#6395711yescharacteristic
307C22#6397411yescharacteristic
308C4—22no—
309C4—184no—
310C4—362no—
311C4#67⋊Dic312yes—
312C4#67⋊Dic312yes—
313C3—21no—
314C3#6990712yescomplemented
315C2—42no—
316C2#1059105912yes—
317C2#1059106212yes—
318C2#1059115312yes—
319C2#1059170511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C2×C42
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1750
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C2×#63555C2semidirect
4. C2×#63553C2semidirect
5. #10589156C2semidirect
16. C3×#830C4semidirect
68. #830Dic3semidirect
268. C32#1750semidirect
314. C3#69907semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C2×C3×#8302
C2×#635552
C2×#635532
#105891562
#699073