Finite Group Databasebeta

← #11782843

Subgroups — #11782843

Order 1152.

443 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 443 conjugacy classes of subgroups — too many to draw. Only its 94 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#10592784C211yesmaximal, characteristic
2C3×#5093C211yesmaximal, characteristic, complemented
3C3×#5078C211yesmaximal, characteristic, complemented
4#10590290C211yesmaximal, characteristic, complemented
5#10590281C211yesmaximal, characteristic
6#10590281C211yesmaximal, characteristic
7#10589078C211yesmaximal, characteristic, complemented
8#71365—31nomaximal
9#71224—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3755—22no—
12#64083C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#810—22no—
17C3×#807—22no—
18C3×C4×C3⋊C8C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63565—22no—
21#63564—22no—
22#63564—22no—
23C3×#500—31no—
24C3×#487—31no—
25#5093—31no—
26#5093D311yescharacteristic, complemented
27#5088—31no—
28#5088—31no—
29#5085—31no—
30#5085—31no—
31#5085—61no—
32#5079—31no—
33#5078D311yescharacteristic, complemented
34#4694—31no—
35#4694—31no—
36#4455—31no—
37#4454—31no—
38C2×C32×Q8—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C42C2311yescharacteristic
47#3755—44no—
48C2×C3⋊(C3⋊C8)D412yes—
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—21no—
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8—31no—
59C3×C4⋊Q8C2×D311yescharacteristic
60C3×C4⋊Q8C2×D311yescharacteristic
61C2×#215—62no—
62C2×#215—62no—
63C2×#215—64no—
64#874—31no—
65#874—31no—
66#874—61no—
67#869C2×D311yescharacteristic
68#869C2×D311yescharacteristic
69C3×#107—62no—
70C3×#103—62no—
71C3×C4×C8—31no—
72C3×C4×C8—31no—
73#835—62no—
74#821—62no—
75#821—62no—
76#810—22no—
77#810—62no—
78#809—62no—
79#809—62no—
80#807—22no—
81C4×C3⋊C8—31no—
82C4×C3⋊C8—31no—
83C4×C3⋊C8—61no—
84C4×C3⋊C8C2×D311yescharacteristic
85C4×C3⋊C8C2×D311yescharacteristic
86C22×C3⋊D3—41no—
87C32×Q8—42no—
88C2×C32×C4—41no—
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C4⋊(C3⋊D3)—42no—
93C4⋊(C3⋊D3)—42no—
94C4⋊(C3⋊D3)—42no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—41no—
97C3×Dic6—42no—
98C3×Dic6—42no—
99C3⋊(C3⋊C8)—22no—
100C3×C3⋊C8—22no—
101C3×C3⋊C8—22no—
102#500—31no—
103#492—91no—
104#487—31no—
105#487—91no—
106#486—91no—
107#486—91no—
108#322—91no—
109C2×C3×Q8—22no—
110C2×C3×Q8—21no—
111C2×C3×Q8—21no—
112C2×C3×Q8—61no—
113C2×C3×Q8—61no—
114C2×D12—62no—
115C2×D12—61no—
116C2×D12—61no—
117C2×D12—61no—
118C2×D12—61no—
119C2×D12—61no—
120C2×D12—61no—
121C2×D12—121no—
122C2×D12—121no—
123C2×Dic6—21no—
124C2×Dic6—21no—
125C2×C3×C8—32no—
126C2×C3×C8—32no—
127C3×C4⋊C4—21no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—41no—
132C3×C4⋊C4—41no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—61no—
137C3×C42—21no—
138C3×C42C22×D311yescharacteristic
139C3×C42C22×D311yescharacteristic
140#215—128no—
141#215—124no—
142#215—124no—
143C4⋊Dic3—21no—
144C4⋊Dic3—21no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C2×C3⋊C8—32no—
148C2×C3⋊C8—32no—
149C2×C3⋊C8—62no—
150C2×C3⋊C8#6712yes—
151C2×C3⋊C8#6712yes—
152C22×C32#12711yescharacteristic
153C2×C3⋊D3—81no—
154C2×C3⋊D3—81no—
155C2×C3⋊D3—81no—
156C32×C4—81no—
157C32×C4#13512yes—
158C32×C4AGL(1,ℤ/8)12yes—
159C32×C4#13712yes—
160C3×Dic3—81no—
161C3×Dic3—81no—
162C2×SD16—182no—
163C4⋊Q8—31no—
164C4⋊Q8—31no—
165C4⋊Q8D3211yescharacteristic
166#127—91no—
167#107—62no—
168#103—62no—
169#103—182no—
170#102—182no—
171#102—182no—
172C4×C8—31no—
173C4×C8—31no—
174C4×C8—91no—
175C22×D3—122no—
176C22×D3—121no—
177C22×D3—121no—
178C3×Q8—44no—
179C3×Q8—42no—
180C3×Q8—42no—
181C3×Q8—122no—
182C3×Q8—122no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—42no—
187C2×C3×C4—41no—
188C2×C3×C4—41no—
189C2×C3×C4—121no—
190C2×C3×C4—121no—
191C2×C3×C4D3×D411yescharacteristic
192C2×C3×C4D3×D411yescharacteristic
193C2×C3×C4D3×D411yescharacteristic
194C2×C3×C4D3×D411yescharacteristic
195C2×C3×C4C2×#6711yescharacteristic
196C2×C3×C4C2×#6711yescharacteristic
197C2×Dic3—41no—
198C2×Dic3—41no—
199D12—124no—
200D12—122no—
201D12—122no—
202D12—122no—
203D12—122no—
204D12—122no—
205D12—122no—
206D12—242no—
207D12—242no—
208Dic6—42no—
209Dic6—42no—
210C3×C8—62no—
211C3×C8—62no—
212C3⋊C8—22no—
213C3⋊C8—22no—
214C3⋊C8—64no—
215C3⋊C8—62no—
216C3⋊C8—62no—
217C2×C32#49511yescharacteristic
218C2×C32#49611yescharacteristic
219C2×C32#49711yescharacteristic
220C3⋊D3—161no—
221C2×Q8—21no—
222C2×Q8—61no—
223C2×Q8—61no—
224C2×D4—181no—
225C2×D4—181no—
226C2×D4—181no—
227SD16—364no—
228C2×C8—32no—
229C2×C8—32no—
230C2×C8—92no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C42C2×D3211yescharacteristic
238C22×C3—21no—
239C22×C3#94011yescharacteristic
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—82no—
254C3×C4—81no—
255C3×C4—81no—
256C3×C4—241no—
257C3×C4—241no—
258C3×C4#91112yes—
259C3×C4#91412yes—
260C3×C4#91812yes—
261C3×C4#91912yes—
262C3×C4#94212yes—
263C3×C4#95012yes—
264Dic3—81no—
265Dic3—81no—
266C32#171911yescharacteristic, complemented, Sylow
267C23—361no—
268Q8—42no—
269Q8—122no—
270Q8—122no—
271D4—362no—
272D4—362no—
273D4—362no—
274C2×C4—41no—
275C2×C4—121no—
276C2×C4—121no—
277C2×C4D3×#6711yescharacteristic
278C2×C4D3×#6711yescharacteristic
279C2×C4#381111yescharacteristic
280C8—62no—
281C8—62no—
282C8—182no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3#505911yescharacteristic
287C2×C3#508611yescharacteristic
288C2×C3#515411yescharacteristic
289C2×C3#517611yescharacteristic
290C2×C3#519011yescharacteristic
291C2×C3#519111yescharacteristic
292D3—482no—
293D3—481no—
294D3—481no—
295C22—721no—
296C22—721no—
297C22—721no—
298C22#6397911yescharacteristic
299C4—81no—
300C4—241no—
301C4—241no—
302C4#6393712yes—
303C4#6394812yes—
304C4#6394912yes—
305C3—21no—
306C3#7122411yescharacteristic, complemented
307C3#7136511yescharacteristic, complemented
308C2—1441no—
309C2#1059147511yescharacteristic
310C2#1059160811yescharacteristic
311C2#1059160911yescharacteristic
subgroupG/H
centerC22#63979
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#127
prime radical#64083C22
hypercenterC4⋊Q8D32
hypocenterC32#1719
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5093C2semidirect
3. C3×#5078C2semidirect
4. #10590290C2semidirect
7. #10589078C2semidirect
26. #5093D3semidirect
33. #5078D3semidirect
266. C32#1719semidirect
306. C3#71224semidirect
307. C3#71365semidirect

Maximal subgroups

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

subgroupindex
#105927842
C3×#50932
C3×#50782
#105902902
#105902812
#105890782
#713653
#712243