Finite Group Databasebeta

← #11778574

Subgroups — #11778574

Order 1152.

630 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 119 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#10596094C211yesmaximal, characteristic
2C32×#483C211yesmaximal, characteristic
3#10592682C211yesmaximal, characteristic
4#10592670C211yesmaximal, characteristic
5#10589404C211yesmaximal, characteristic
6#10589335C211yesmaximal, characteristic
7#10589333C211yesmaximal, characteristic
8#71175—34nomaximal
9C32×C22⋊Q8C2211yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11#64153—21no—
12#64133C2211yescharacteristic
13C2×#3750—21no—
14C2×#3750C2211yescharacteristic
15#64098—21no—
16#64098—21no—
17#64097—21no—
18#64087—21no—
19#64086—21no—
20C32×#106—21no—
21C32×#103—21no—
22C32×C22⋊C8C2211yescharacteristic
23#63658—21no—
24#63658C2211yescharacteristic
25#63657C2211yescharacteristic
26#63637—21no—
27#63635—21no—
28#5623—34no—
29C3×#483D314yes—
30#4983—34no—
31#4971—34no—
32#4538—34no—
33#4469—34no—
34#4467—34no—
35C2×C32×Q8D411yescharacteristic
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C2×#634—21no—
42C2×#634D411yescharacteristic
43C2×C32×C8—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4D411yescharacteristic
48C32×C22⋊C4—21no—
49#3757—21no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)D411yescharacteristic
52#3750—21no—
53#3750—21no—
54#3750—21no—
55#3750—21no—
56#3750—21no—
57#3750—21no—
58#3750—21no—
59#3750—42no—
60C4×C3⋊Dic3—21no—
61C4×C3⋊Dic3—21no—
62C2×C3⋊(C3⋊C8)—21no—
63#1611—91noSylow
64C3×C22⋊Q8C2×D314yes—
65C2×C3×C4⋊C4C2×D314yes—
66#944—64no—
67#924—34no—
68C2×Dic3⋊C4—34no—
69C2×Dic3⋊C4—64no—
70#889—64no—
71#889—64no—
72#888—64no—
73#878—64no—
74#877—64no—
75C3×#106—24no—
76C3×#103—24no—
77C3×C22⋊C8C2×D314yes—
78C3⋊#95—34no—
79C3⋊#95—64no—
80#830—34no—
81#810—64no—
82#808—64no—
83C23×C32C2×D411yescharacteristic
84C32×Q8—41no—
85C2×C32×C4—21no—
86C2×C32×C4—21no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C3⋊Dic3—21no—
94C2×C3⋊Dic3—21no—
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3SD1612yes—
103#634—41no—
104#634—81no—
105C32×C8—41no—
106C3⋊(C3⋊C8)—41no—
107#544—91no—
108#483—91no—
109#483C3⋊D311yescharacteristic
110#398—91no—
111#328—91no—
112#328—91no—
113#324—91no—
114C2×C3×Q8#6714yes—
115C22×C3×C4—24no—
116C22×C3×C4C22×D314yes—
117C22×Dic3—34no—
118C22×Dic3—34no—
119C22×Dic3—64no—
120C2×Dic6—34no—
121C2×Dic6—64no—
122C2×C3×C8—24no—
123C3×C4⋊C4—24no—
124C3×C4⋊C4—24no—
125C3×C4⋊C4—24no—
126C3×C4⋊C4#6714yes—
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—
136Dic3⋊C4—64no—
137Dic3⋊C4—64no—
138Dic3⋊C4—128no—
139C4×Dic3—64no—
140C4×Dic3—64no—
141C2×C3⋊C8—64no—
142C22×C32—21no—
143C22×C32—21no—
144C22×C32#12011yescharacteristic
145C22×C32C2×SD1611yescharacteristic
146C22×C32#13711yescharacteristic
147C32×C4—21no—
148C32×C4—21no—
149C32×C4—41no—
150C32×C4—41no—
151C32×C4—81no—
152C3⋊Dic3—22no—
153C3⋊Dic3—42no—
154C3⋊Dic3—41no—
155C3⋊Dic3—41no—
156C3⋊Dic3—41no—
157C4⋊Q8—181no—
158C4⋊Q8—181no—
159#125—181no—
160#125—181no—
161C22⋊Q8—91no—
162C22⋊Q8—181no—
163C22⋊Q8C2×C3⋊D311yescharacteristic
164#117—181no—
165C2×C4⋊C4—91no—
166C2×C4⋊C4—181no—
167C2×C4⋊C4C2×C3⋊D311yescharacteristic
168#106—21no—
169#106—181no—
170#103—21no—
171#103—181no—
172C22⋊C8—91no—
173C22⋊C8C2×C3⋊D311yescharacteristic
174#95—91no—
175#95—181no—
176C23×C3D3×D414yes—
177C3×Q8—44no—
178C2×C3×C4—24no—
179C2×C3×C4—24no—
180C2×C3×C4—44no—
181C2×C3×C4—44no—
182C2×C3×C4—44no—
183C2×C3×C4—44no—
184C2×C3×C4D3×D414yes—
185C2×C3×C4C2×#6714yes—
186C2×Dic3—38no—
187C2×Dic3—64no—
188C2×Dic3—64no—
189C2×Dic3—68no—
190C2×Dic3—64no—
191C2×Dic3—64no—
192C2×Dic3—64no—
193C2×Dic3—124no—
194C2×Dic3—124no—
195C2×Dic3—124no—
196Dic6—124no—
197Dic6—244no—
198C3×C8—44no—
199C3⋊C8—124no—
200C2×C32—21no—
201C2×C32—21no—
202C2×C32#44811yescharacteristic
203C2×C32#45611yescharacteristic
204C2×C32#45811yescharacteristic
205C2×Q8—91no—
206C2×Q8—181no—
207C2×Q8#63811yescharacteristic
208C22×C4—21no—
209C22×C4—91no—
210C22×C4—91no—
211C22×C4—181no—
212C22×C4C22×C3⋊D311yescharacteristic
213C2×C8—21no—
214C2×C8—181no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—91no—
219C4⋊C4—181no—
220C4⋊C4—181no—
221C4⋊C4—181no—
222C4⋊C4—181no—
223C4⋊C4—181no—
224C4⋊C4—181no—
225C4⋊C4—181no—
226C4⋊C4—181no—
227C4⋊C4—362no—
228C4⋊C4#63811yescharacteristic
229C22⋊C4—21no—
230C22⋊C4—181no—
231C42—181no—
232C42—181no—
233C22×C3—24no—
234C22×C3—24no—
235C22×C3D3×SD1614yes—
236C22×C3#91514yes—
237C22×C3#93714yes—
238C3×C4—24no—
239C3×C4—24no—
240C3×C4—44no—
241C3×C4—44no—
242C3×C4—84no—
243Dic3—68no—
244Dic3—128no—
245Dic3—124no—
246Dic3—124no—
247Dic3—124no—
248C32#161111yescharacteristic, complemented, Sylow
249C23D4×C3⋊D311yescharacteristic
250Q8—41no—
251Q8—361no—
252Q8—721no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—92no—
260C2×C4—181no—
261C2×C4—181no—
262C2×C4—182no—
263C2×C4—181no—
264C2×C4—181no—
265C2×C4—181no—
266C2×C4—361no—
267C2×C4—361no—
268C2×C4—361no—
269C2×C4D4×C3⋊D311yescharacteristic
270C2×C4C2×#63811yescharacteristic
271C8—41no—
272C8—361no—
273C2×C3—24no—
274C2×C3—24no—
275C2×C3#505314yes—
276C2×C3#517014yes—
277C2×C3#520514yes—
278C22—21no—
279C22—21no—
280C22SD16×C3⋊D311yescharacteristic
281C22#6412411yescharacteristic
282C22#6414611yescharacteristic
283C4—21no—
284C4—21no—
285C4—41no—
286C4—41no—
287C4—81no—
288C4—182no—
289C4—362no—
290C4—361no—
291C4—361no—
292C4—361no—
293C3#7117514yescomplemented
294C2—21no—
295C2—21no—
296C2#1059275211yescharacteristic
297C2#1059286911yescharacteristic
298C2#1059290411yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#483C2
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenter#483C3⋊D3
hypocenterC32#1611
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
248. C32#1611semidirect
293. C3#71175semidirect

Maximal subgroups

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

subgroupindex
#105960942
C32×#4832
#105926822
#105926702
#105894042
#105893352
#105893332
#711753