Finite Group Databasebeta

← #11775165

Subgroups — #11775165

Order 1152.

684 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 131 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
1#10596093C211yesmaximal, characteristic
2#10592418C211yesmaximal, characteristic
3#10592347C211yesmaximal, characteristic
4C32×#328C211yesmaximal, characteristic
5#10589404C211yesmaximal, characteristic
6#10589333C211yesmaximal, characteristic
7#10589318C211yesmaximal, characteristic
8#68310—34nomaximal
9C32×C22⋊Q8C2211yescharacteristic
10Q8×C3⋊Dic3C411yescharacteristic, complemented
11#64153C411yescharacteristic, complemented
12#64133C2211yescharacteristic
13C2×C4×C3⋊Dic3—21no—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15#64098—21no—
16#64097C411yescharacteristic, complemented
17#64096—21no—
18#64096C411yescharacteristic, complemented
19#64087—21no—
20#64086—21no—
21C32×C22⋊C8C2211yescharacteristic
22C32×#95C2211yescharacteristic
23#63658—21no—
24#63658C2211yescharacteristic
25#63657C2211yescharacteristic
26#63642—21no—
27#63641—21no—
28#5622—34no—
29#4719—34no—
30#4648—34no—
31C3×#328D314yes—
32#4538—34no—
33#4467—34no—
34#4452—34no—
35C2×C32×Q8C2×C411yescharacteristic
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C2×#634—21no—
42C2×#634C2×C411yescharacteristic
43C2×C32×C8—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4C2×C411yescharacteristic
46C32×C22⋊C4—21no—
47#3757—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)C2×C411yescharacteristic
50#3750—21no—
51#3750—21no—
52#3750—21no—
53#3750—21no—
54#3750—21no—
55C4×C3⋊Dic3—24no—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3—21no—
58C4×C3⋊Dic3C2×C411yescharacteristic
59C4×C3⋊Dic3C2×C411yescharacteristic
60C4×C3⋊Dic3D411yescharacteristic
61C4×C3⋊Dic3D411yescharacteristic
62C2×C3⋊(C3⋊C8)—21no—
63#1506—91noSylow
64C3×C22⋊Q8C2×D314yes—
65Q8×Dic3—34no—
66#944—34no—
67#924—34no—
68C2×C4×Dic3—34no—
69C2×C4×Dic3—64no—
70#889—64no—
71#888—34no—
72#887—34no—
73#887—64no—
74#878—64no—
75#877—64no—
76C3×C22⋊C8C2×D314yes—
77C3×#95C2×D314yes—
78C3⋊#95—34no—
79C3⋊#95—64no—
80#830—34no—
81#815—64no—
82Dic3⋊C8—64no—
83C23×C32C2×D411yescharacteristic
84C32×Q8—41no—
85C2×C32×C4—22no—
86C2×C32×C4—21no—
87C2×C32×C4—21no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C3⋊Dic3—21no—
94C2×C3⋊Dic3—21no—
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3C22⋊C411yescharacteristic
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C2×C3⋊Dic3C22⋊C411yescharacteristic
104C2×C3⋊Dic3C22⋊C411yescharacteristic
105#634—42no—
106#634—41no—
107C32×C8—41no—
108C3⋊(C3⋊C8)—41no—
109#533—91no—
110#432—91no—
111#376—91no—
112#328—91no—
113#328—91no—
114#328—91no—
115#328C3⋊D311yescharacteristic
116C2×C3×Q8C4×D314yes—
117C22×C3×C4—24no—
118C22×C3×C4C22×D314yes—
119C22×Dic3—34no—
120C22×Dic3—34no—
121C22×Dic3—64no—
122C2×Dic6—34no—
123C2×Dic6—64no—
124C2×C3×C8—24no—
125C3×C4⋊C4—24no—
126C3×C4⋊C4C4×D314yes—
127C3×C22⋊C4—24no—
128#217—64no—
129C4⋊Dic3—34no—
130C4⋊Dic3—64no—
131Dic3⋊C4—64no—
132Dic3⋊C4—64no—
133Dic3⋊C4—64no—
134Dic3⋊C4—64no—
135Dic3⋊C4—64no—
136C4×Dic3—34no—
137C4×Dic3—34no—
138C4×Dic3—34no—
139C4×Dic3—34no—
140C4×Dic3—64no—
141C4×Dic3—64no—
142C4×Dic3—616no—
143C2×C3⋊C8—64no—
144C22×C32—21no—
145C22×C32—21no—
146C22×C32C2×C22⋊C411yescharacteristic
147C22×C32#13711yescharacteristic
148C22×C32#13711yescharacteristic
149C32×C4—21no—
150C32×C4—21no—
151C32×C4—42no—
152C32×C4—41no—
153C32×C4—41no—
154C3⋊Dic3—21no—
155C3⋊Dic3—21no—
156C3⋊Dic3—21no—
157C3⋊Dic3—42no—
158C3⋊Dic3—41no—
159C3⋊Dic3—41no—
160C3⋊Dic3#10412yes—
161C4⋊Q8—91no—
162C4⋊Q8—91no—
163#125—181no—
164C22⋊Q8—91no—
165C22⋊Q8—181no—
166C22⋊Q8C2×C3⋊D311yescharacteristic
167C4×Q8—91no—
168C4×Q8—91no—
169C4×Q8—181no—
170#117—181no—
171C2×C42—91no—
172C2×C42—181no—
173C4⋊C8—181no—
174C22⋊C8—91no—
175C22⋊C8C2×C3⋊D311yescharacteristic
176#97—181no—
177#95—91no—
178#95—181no—
179#95C2×C3⋊D311yescharacteristic
180C23×C3D3×D414yes—
181C3×Q8—44no—
182C2×C3×C4—28no—
183C2×C3×C4—24no—
184C2×C3×C4—24no—
185C2×C3×C4—44no—
186C2×C3×C4—44no—
187C2×C3×C4—44no—
188C2×C3×C4C2×C4×D314yes—
189C2×C3×C4D3×D414yes—
190C2×Dic3—34no—
191C2×Dic3—34no—
192C2×Dic3—34no—
193C2×Dic3—34no—
194C2×Dic3—68no—
195C2×Dic3—64no—
196C2×Dic3—64no—
197C2×Dic3—68no—
198C2×Dic3—64no—
199C2×Dic3—64no—
200C2×Dic3—124no—
201C2×Dic3—124no—
202Dic6—128no—
203Dic6—124no—
204C3×C8—44no—
205C3⋊C8—124no—
206C2×C32—21no—
207C2×C32—21no—
208C2×C32#41011yescharacteristic
209C2×C32#41911yescharacteristic
210C2×C32C2×#10411yescharacteristic
211C2×Q8—91no—
212C2×Q8—181no—
213C2×Q8C4×C3⋊D311yescharacteristic
214C22×C4—21no—
215C22×C4—91no—
216C22×C4—91no—
217C22×C4—181no—
218C22×C4C22×C3⋊D311yescharacteristic
219C2×C8—21no—
220C2×C8—181no—
221C4⋊C4—21no—
222C4⋊C4—91no—
223C4⋊C4—181no—
224C4⋊C4—181no—
225C4⋊C4—181no—
226C4⋊C4—181no—
227C4⋊C4—181no—
228C4⋊C4—181no—
229C4⋊C4C4×C3⋊D311yescharacteristic
230C22⋊C4—21no—
231C22⋊C4—181no—
232C42—91no—
233C42—91no—
234C42—91no—
235C42—91no—
236C42—181no—
237C42—181no—
238C42—184no—
239C22×C3—24no—
240C22×C3—24no—
241C22×C3D3×C22⋊C414yes—
242C22×C3#91514yes—
243C22×C3#91814yes—
244C3×C4—24no—
245C3×C4—24no—
246C3×C4—48no—
247C3×C4—44no—
248C3×C4—44no—
249Dic3—38no—
250Dic3—64no—
251Dic3—64no—
252Dic3—64no—
253Dic3—128no—
254Dic3—124no—
255Dic3—124no—
256C32#150611yescharacteristic, complemented, Sylow
257C23D4×C3⋊D311yescharacteristic
258Q8—41no—
259Q8—361no—
260Q8—362no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—91no—
268C2×C4—91no—
269C2×C4—91no—
270C2×C4—91no—
271C2×C4—182no—
272C2×C4—181no—
273C2×C4—181no—
274C2×C4—182no—
275C2×C4—181no—
276C2×C4—181no—
277C2×C4—361no—
278C2×C4—361no—
279C2×C4C2×C4×C3⋊D311yescharacteristic
280C2×C4D4×C3⋊D311yescharacteristic
281C8—41no—
282C8—361no—
283C2×C3—24no—
284C2×C3—24no—
285C2×C3#474014yes—
286C2×C3#480214yes—
287C2×C3D3×#10414yes—
288C22—21no—
289C22—21no—
290C22C22⋊C4×C3⋊D311yescharacteristic
291C22#6412411yescharacteristic
292C22#6412711yescharacteristic
293C4—21no—
294C4—21no—
295C4—42no—
296C4—41no—
297C4—41no—
298C4—92no—
299C4—181no—
300C4—181no—
301C4—181no—
302C4—362no—
303C4—361no—
304C4—361no—
305C3#6831014yescomplemented
306C2—21no—
307C2—21no—
308C2#1059243911yescharacteristic
309C2#1059250111yescharacteristic
310C2C3⋊D3×#10411yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#328C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenter#328C3⋊D3
hypocenterC32#1506
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
10. Q8×C3⋊Dic3C4semidirect
11. #64153C4semidirect
16. #64097C4semidirect
18. #64096C4semidirect
256. C32#1506semidirect
305. C3#68310semidirect

Maximal subgroups

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

subgroupindex
#105960932
#105924182
#105923472
C32×#3282
#105894042
#105893332
#105893182
#683103