Finite Group Databasebeta

← #11782836

Subgroups — #11782836

Order 1152.

443 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 443 conjugacy classes of subgroups — too many to draw. Only its 100 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#10592392C211yesmaximal, characteristic
2C3×#4681C211yesmaximal, characteristic, complemented
3#10590311C211yesmaximal, characteristic, complemented
4#10590287C211yesmaximal, characteristic, complemented
5#10590281C211yesmaximal, characteristic
6#10590281C211yesmaximal, characteristic
7C3×#4454C211yesmaximal, characteristic, complemented
8#71223—31nomaximal
9#68093—31nomaximal
10C2×#3744—22no—
11#64083C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C32×C4×C8C2211yescharacteristic
16C3×#816—22no—
17C3×C4×C3⋊C8C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19#63575—22no—
20#63566—22no—
21#63564—22no—
22#63564—22no—
23C3×#487—31no—
24#5088—31no—
25#5088—31no—
26#5079—31no—
27#5078—31no—
28#4694—31no—
29#4694—31no—
30#4693—31no—
31#4693—31no—
32#4693—61no—
33#4682—31no—
34#4681—31no—
35#4681D311yescharacteristic, complemented
36C3×#322—31no—
37#4454D311yescharacteristic, complemented
38C2×C4⋊(C3⋊D3)—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×#634—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8D412yes—
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48#3744—44no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8D412yes—
54C2×C3×C3⋊C8D412yes—
55#1719—91noSylow
56C3×C4⋊Q8—31no—
57C3×C4⋊Q8—31no—
58C2×#204—64no—
59C2×#204—62no—
60C2×#204—62no—
61#874—31no—
62#874—31no—
63#874—61no—
64#869—31no—
65#869—31no—
66#869—61no—
67#869C2×D311yescharacteristic
68#869C2×D311yescharacteristic
69C3×#103—62no—
70C3×C4×C8—21no—
71C3×C4×C8—31no—
72C3×C4×C8—31no—
73C3×C4×C8C2×D311yescharacteristic
74C3×C4×C8C2×D311yescharacteristic
75#835—62no—
76#821—62no—
77#821—62no—
78#818—62no—
79#816—22no—
80#816—62no—
81#809—62no—
82#809—62no—
83#807—62no—
84C4×C3⋊C8C2×D311yescharacteristic
85C4×C3⋊C8C2×D311yescharacteristic
86C22×C3⋊D3—41no—
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C3⋊Dic3—41no—
91C4⋊(C3⋊D3)—42no—
92C4⋊(C3⋊D3)—42no—
93C4⋊(C3⋊D3)—42no—
94#634—42no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—41no—
97C3×Dic6—42no—
98C3×Dic6—42no—
99C32×C8—22no—
100C3×C3⋊C8—22no—
101C3×C3⋊C8—22no—
102#500—91no—
103#492—91no—
104#487—31no—
105#487—91no—
106#486—91no—
107#486—91no—
108#322—31no—
109C2×C3×Q8—61no—
110C2×C3×Q8—61no—
111C2×D12—62no—
112C2×D12—61no—
113C2×D12—61no—
114C2×D12—61no—
115C2×D12—61no—
116C2×D12—61no—
117C2×D12—61no—
118C2×D12—121no—
119C2×D12—121no—
120C2×Dic6—21no—
121C2×Dic6—21no—
122C2×Dic6—62no—
123C2×Dic6—61no—
124C2×Dic6—61no—
125C2×C3×C8—22no—
126C2×C3×C8—32no—
127C2×C3×C8—32no—
128C2×C3×C8D1212yes—
129C2×C3×C8#6712yes—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C42—21no—
135C3×C42C22×D311yescharacteristic
136C3×C42C22×D311yescharacteristic
137C4⋊Dic3—21no—
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—21no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—121no—
146C4⋊Dic3—121no—
147C2×C3⋊C8D1212yes—
148C2×C3⋊C8D1212yes—
149#204—128no—
150#204—124no—
151#204—124no—
152C22×C32#12711yescharacteristic
153C2×C3⋊D3—81no—
154C2×C3⋊D3—81no—
155C2×C3⋊D3—81no—
156C32×C4#13512yes—
157C32×C4AGL(1,ℤ/8)12yes—
158C32×C4#13712yes—
159C3⋊Dic3—81no—
160C3×Dic3—81no—
161C3×Dic3—81no—
162C2×SD16—182no—
163C4⋊Q8—31no—
164C4⋊Q8—31no—
165C4⋊Q8—91no—
166#127—91no—
167#107—182no—
168#103—62no—
169#103—182no—
170#102—182no—
171#102—182no—
172C4×C8—31no—
173C4×C8—31no—
174C4×C8D3211yescharacteristic
175C22×D3—122no—
176C22×D3—121no—
177C22×D3—121no—
178C3×Q8—122no—
179C3×Q8—122no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—121no—
184C2×C3×C4—121no—
185C2×C3×C4C2×D1211yescharacteristic
186C2×C3×C4C2×D1211yescharacteristic
187C2×C3×C4C2×D1211yescharacteristic
188C2×C3×C4D3×D411yescharacteristic
189C2×C3×C4D3×D411yescharacteristic
190C2×C3×C4C2×#6711yescharacteristic
191C2×Dic3—41no—
192C2×Dic3—41no—
193C2×Dic3—122no—
194C2×Dic3—121no—
195C2×Dic3—121no—
196D12—124no—
197D12—122no—
198D12—122no—
199D12—122no—
200D12—122no—
201D12—122no—
202D12—122no—
203D12—242no—
204D12—242no—
205Dic6—42no—
206Dic6—42no—
207Dic6—124no—
208Dic6—122no—
209Dic6—122no—
210C3×C8—24no—
211C3×C8—22no—
212C3×C8—22no—
213C3×C8—62no—
214C3×C8—62no—
215C3⋊C8—22no—
216C3⋊C8—22no—
217C2×C32#49511yescharacteristic
218C2×C32#49611yescharacteristic
219C2×C32#49711yescharacteristic
220C3⋊D3—161no—
221C2×Q8—61no—
222C2×Q8—61no—
223C2×Q8—181no—
224C2×D4—181no—
225C2×D4—181no—
226C2×D4—181no—
227SD16—364no—
228C2×C8—32no—
229C2×C8—32no—
230C2×C8#62612yes—
231C4⋊C4—61no—
232C4⋊C4—61no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4—181no—
236C4⋊C4—181no—
237C42C2×D3211yescharacteristic
238C22×C3—21no—
239C22×C3#87411yescharacteristic
240C22×C3#94011yescharacteristic
241C2×D3—242no—
242C2×D3—242no—
243C2×D3—242no—
244C2×D3—241no—
245C2×D3—241no—
246C2×D3—241no—
247C2×D3—241no—
248C2×D3—241no—
249C2×D3—241no—
250C3×C4—22no—
251C3×C4—22no—
252C3×C4—22no—
253C3×C4—241no—
254C3×C4—241no—
255C3×C4#90412yes—
256C3×C4#90812yes—
257C3×C4#90912yes—
258C3×C4#91612yes—
259C3×C4#91812yes—
260C3×C4#94912yes—
261Dic3—81no—
262Dic3—81no—
263Dic3—242no—
264Dic3—241no—
265Dic3—241no—
266C32#171911yescharacteristic, complemented, Sylow
267C23—361no—
268Q8—122no—
269Q8—122no—
270Q8—362no—
271D4—362no—
272D4—362no—
273D4—362no—
274C2×C4—121no—
275C2×C4—121no—
276C2×C4—361no—
277C2×C4D3×D1211yescharacteristic
278C2×C4D3×D1211yescharacteristic
279C2×C4C2×#62611yescharacteristic
280C8—22no—
281C8—62no—
282C8—62no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3#469611yescharacteristic
287C2×C3#471211yescharacteristic
288C2×C3#471511yescharacteristic
289C2×C3#505811yescharacteristic
290C2×C3#516811yescharacteristic
291C2×C3#519011yescharacteristic
292D3—482no—
293D3—481no—
294D3—481no—
295C22—721no—
296C22—721no—
297C22—721no—
298C22#6391111yescharacteristic
299C4—241no—
300C4—241no—
301C4—721no—
302C4#6380112yes—
303C4#6380612yes—
304C4#6382512yes—
305C3—21no—
306C3#6809311yescharacteristic, complemented
307C3#7122311yescharacteristic, complemented
308C2—1441no—
309C2#1059035111yescharacteristic
310C2#1059086211yescharacteristic
311C2#1059089911yescharacteristic
subgroupG/H
centerC22#63911
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#127
prime radical#64083C22
hypercenterC4×C8D32
hypocenterC32#1719
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C3×#4681C2semidirect
3. #10590311C2semidirect
4. #10590287C2semidirect
7. C3×#4454C2semidirect
35. #4681D3semidirect
37. #4454D3semidirect
266. C32#1719semidirect
306. C3#68093semidirect
307. C3#71223semidirect

Maximal subgroups

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

subgroupindex
#105923922
C3×#46812
#105903112
#105902872
#105902812
C3×#44542
#712233
#680933