Finite Group Databasebeta

← #11778801

Subgroups — #11778801

Order 1152.

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

normal subgroups only

This group has 606 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×#484C211yesmaximal, characteristic
3#10592684C211yesmaximal, characteristic
4#10592669C211yesmaximal, characteristic
5#10589404C211yesmaximal, characteristic
6#10589335C211yesmaximal, characteristic
7#10589333C211yesmaximal, characteristic
8#71179—34nomaximal
9C32×C22⋊Q8C2211yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11#64153—21no—
12#64133C2211yescharacteristic
13C2×#3750C2211yescharacteristic
14#64098—21no—
15#64098—21no—
16#64097—21no—
17#64087—21no—
18#64086—21no—
19C32×#107—21no—
20C32×#103—21no—
21C32×C22⋊C8C2211yescharacteristic
22#63658—21no—
23#63658—21no—
24#63658C2211yescharacteristic
25#63657C2211yescharacteristic
26#63637—21no—
27#63634—21no—
28#5623—34no—
29C3×#484D314yes—
30#4985—34no—
31#4970—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—
59C4×C3⋊Dic3—21no—
60C4×C3⋊Dic3—21no—
61C2×C3⋊(C3⋊C8)—21no—
62#1617—91noSylow
63C3×C22⋊Q8C2×D314yes—
64C2×C3×C4⋊C4C2×D314yes—
65#944—64no—
66#924—34no—
67C2×Dic3⋊C4—34no—
68#889—64no—
69#889—64no—
70#888—64no—
71#878—64no—
72#877—64no—
73C3×#107—24no—
74C3×#103—24no—
75C3×C22⋊C8C2×D314yes—
76C3⋊#95—34no—
77C3⋊#95—64no—
78C3⋊#95—64no—
79#830—34no—
80#810—64no—
81#807—64no—
82C23×C32C2×D411yescharacteristic
83C32×Q8—41no—
84C2×C32×C4—21no—
85C2×C32×C4—21no—
86C2×C32×C4—41no—
87C2×C32×C4—42no—
88C2×C32×C4—41no—
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C3⋊Dic3—21no—
92C2×C3⋊Dic3—21no—
93C2×C3⋊Dic3—21no—
94C2×C3⋊Dic3—21no—
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—41no—
97C2×C3⋊Dic3—41no—
98C2×C3⋊Dic3—41no—
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3Q1612yes—
101#634—41no—
102#634—81no—
103C32×C8—41no—
104C3⋊(C3⋊C8)—41no—
105#544—91no—
106#484—91no—
107#484C3⋊D311yescharacteristic
108#400—91no—
109#328—91no—
110#328—91no—
111#324—91no—
112C2×C3×Q8#6714yes—
113C22×C3×C4—24no—
114C22×C3×C4C22×D314yes—
115C22×Dic3—34no—
116C22×Dic3—34no—
117C22×Dic3—64no—
118C2×Dic6—34no—
119C2×Dic6—64no—
120C2×C3×C8—24no—
121C3×C4⋊C4—24no—
122C3×C4⋊C4—24no—
123C3×C4⋊C4—24no—
124C3×C4⋊C4#6714yes—
125C3×C22⋊C4—24no—
126#217—64no—
127C4⋊Dic3—34no—
128C4⋊Dic3—64no—
129Dic3⋊C4—64no—
130Dic3⋊C4—64no—
131Dic3⋊C4—64no—
132Dic3⋊C4—64no—
133Dic3⋊C4—64no—
134Dic3⋊C4—64no—
135Dic3⋊C4—64no—
136C4×Dic3—64no—
137C4×Dic3—64no—
138C2×C3⋊C8—64no—
139C22×C32—21no—
140C22×C32—21no—
141C22×C32#12011yescharacteristic
142C22×C32C2×Q1611yescharacteristic
143C22×C32#13711yescharacteristic
144C32×C4—21no—
145C32×C4—21no—
146C32×C4—41no—
147C32×C4—41no—
148C32×C4—81no—
149C3⋊Dic3—22no—
150C3⋊Dic3—41no—
151C3⋊Dic3—41no—
152C3⋊Dic3—41no—
153C3⋊Dic3—81no—
154C4⋊Q8—181no—
155C4⋊Q8—181no—
156#125—181no—
157#125—181no—
158C22⋊Q8—91no—
159C22⋊Q8—181no—
160C22⋊Q8C2×C3⋊D311yescharacteristic
161#117—181no—
162C2×C4⋊C4—91no—
163C2×C4⋊C4C2×C3⋊D311yescharacteristic
164#107—21no—
165#107—181no—
166#103—21no—
167#103—181no—
168C22⋊C8—91no—
169C22⋊C8C2×C3⋊D311yescharacteristic
170#95—91no—
171#95—181no—
172#95—181no—
173C23×C3D3×D414yes—
174C3×Q8—44no—
175C2×C3×C4—24no—
176C2×C3×C4—24no—
177C2×C3×C4—44no—
178C2×C3×C4—48no—
179C2×C3×C4—44no—
180C2×C3×C4D3×D414yes—
181C2×C3×C4C2×#6714yes—
182C2×Dic3—38no—
183C2×Dic3—64no—
184C2×Dic3—64no—
185C2×Dic3—64no—
186C2×Dic3—64no—
187C2×Dic3—64no—
188C2×Dic3—124no—
189C2×Dic3—124no—
190C2×Dic3—124no—
191C2×Dic3—124no—
192Dic6—124no—
193Dic6—244no—
194C3×C8—44no—
195C3⋊C8—124no—
196C2×C32—21no—
197C2×C32—21no—
198C2×C32#45111yescharacteristic
199C2×C32#45411yescharacteristic
200C2×C32#45811yescharacteristic
201C2×Q8—91no—
202C2×Q8—181no—
203C2×Q8#63811yescharacteristic
204C22×C4—21no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—181no—
208C22×C4C22×C3⋊D311yescharacteristic
209C2×C8—21no—
210C2×C8—181no—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C4⋊C4—21no—
214C4⋊C4—91no—
215C4⋊C4—181no—
216C4⋊C4—181no—
217C4⋊C4—181no—
218C4⋊C4—181no—
219C4⋊C4—181no—
220C4⋊C4—181no—
221C4⋊C4—181no—
222C4⋊C4—181no—
223C4⋊C4#63811yescharacteristic
224C22⋊C4—21no—
225C22⋊C4—181no—
226C42—181no—
227C42—181no—
228C22×C3—24no—
229C22×C3—24no—
230C22×C3D3×Q1614yes—
231C22×C3#91814yes—
232C22×C3#93714yes—
233C3×C4—24no—
234C3×C4—24no—
235C3×C4—44no—
236C3×C4—44no—
237C3×C4—84no—
238Dic3—68no—
239Dic3—124no—
240Dic3—124no—
241Dic3—124no—
242Dic3—244no—
243C32#161711yescharacteristic, complemented, Sylow
244C23D4×C3⋊D311yescharacteristic
245Q8—41no—
246Q8—361no—
247Q8—721no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—92no—
254C2×C4—181no—
255C2×C4—181no—
256C2×C4—181no—
257C2×C4—181no—
258C2×C4—181no—
259C2×C4—361no—
260C2×C4—361no—
261C2×C4—361no—
262C2×C4—361no—
263C2×C4D4×C3⋊D311yescharacteristic
264C2×C4C2×#63811yescharacteristic
265C8—41no—
266C8—361no—
267C2×C3—24no—
268C2×C3—24no—
269C2×C3#505314yes—
270C2×C3#518614yes—
271C2×C3#520114yes—
272C22—21no—
273C22—21no—
274C22Q16×C3⋊D311yescharacteristic
275C22#6412711yescharacteristic
276C22#6414611yescharacteristic
277C4—21no—
278C4—21no—
279C4—41no—
280C4—41no—
281C4—81no—
282C4—182no—
283C4—361no—
284C4—361no—
285C4—361no—
286C4—721no—
287C3#7117914yescomplemented
288C2—21no—
289C2—21no—
290C2#1059275211yescharacteristic
291C2#1059288511yescharacteristic
292C2#1059290011yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#484C2
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenter#484C3⋊D3
hypocenterC32#1617
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
243. C32#1617semidirect
287. C3#71179semidirect

Maximal subgroups

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

subgroupindex
#105960942
C32×#4842
#105926842
#105926692
#105894042
#105893352
#105893332
#711793