Finite Group Databasebeta

← #11782644

Subgroups — #11782644

Order 1152.

445 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 445 conjugacy classes of subgroups — too many to draw. Only its 98 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#10592777C211yesmaximal, characteristic, complemented
2C3×#5085C211yesmaximal, characteristic
3C3×#5080C211yesmaximal, characteristic, complemented
4#10590375C211yesmaximal, characteristic
5#10590288C211yesmaximal, characteristic, complemented
6#10590273C211yesmaximal, characteristic
7#10589079C211yesmaximal, characteristic, complemented
8#71335—31nomaximal
9#71257—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×#215—22no—
13C3×#874C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C2×#3715—22no—
16#63634—22no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#808—22no—
19C3×C4×C3⋊C8C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63567—22no—
22#63563—22no—
23C3×#498—31no—
24C3×#492—31no—
25#5093—31no—
26#5085—31no—
27#5085D311yescharacteristic
28#5080D311yescharacteristic, complemented
29#5078—31no—
30#5078—31no—
31#5078—61no—
32#5076—31no—
33#5070—31no—
34#4694—31no—
35#4681—31no—
36#4454—31no—
37#4454—31no—
38C2×C32×Q8—21no—
39C2×#634—21no—
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×Dic6—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C2×C3⋊(C3⋊C8)D412yes—
50C3×#215—44no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8D412yes—
54C2×C3×C3⋊C8D412yes—
55#3715—44no—
56#1714—91noSylow
57C2×C3×SD16—62no—
58C3×C4⋊Q8—21no—
59C3×C4⋊Q8—31no—
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×#127—31no—
63C2×#215—22no—
64C2×#215—62no—
65C2×#214—62no—
66#874C2×D311yescharacteristic
67#869—31no—
68#869—31no—
69#869—61no—
70#869C2×D311yescharacteristic
71C3×#106—62no—
72C3×C4×C8—31no—
73C3×C4×C8—31no—
74#832—62no—
75#821—62no—
76#816—62no—
77#810—62no—
78#808—22no—
79#807—62no—
80#807—62no—
81#807—64no—
82C4×C3⋊C8—31no—
83C4×C3⋊C8—31no—
84C4×C3⋊C8—61no—
85C4×C3⋊C8C2×D311yescharacteristic
86C4×C3⋊C8C2×D311yescharacteristic
87C22×C3×D3—41no—
88C32×Q8—42no—
89C2×C32×C4—41no—
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C3⋊Dic3—41no—
94#634—42no—
95C2×C3×Dic3—41no—
96C3×D12—42no—
97C3×D12—42no—
98C3×D12—42no—
99C3×Dic6—42no—
100C3⋊(C3⋊C8)SD1614yescomplemented
101C3×C3⋊C8—22no—
102C3×C3⋊C8—22no—
103#500—91no—
104#498—31no—
105#492—31no—
106#492—91no—
107#487—91no—
108#486—91no—
109#322—91no—
110C2×C3×Q8—21no—
111C2×C3×Q8—21no—
112C2×C3×Q8—41no—
113C2×C3×Q8—61no—
114C2×C3×D4—61no—
115C2×C3×D4—61no—
116C2×C3×D4—61no—
117C2×D12—21no—
118C2×D12—21no—
119C2×D12—21no—
120C2×Dic6—21no—
121C2×Dic6—61no—
122C2×Dic6—61no—
123C2×Dic6—121no—
124C3×SD16—124no—
125C2×C3×C8—32no—
126C2×C3×C8—32no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—41no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C42—21no—
136C3×C42C22×D311yescharacteristic
137C3×C42C22×D311yescharacteristic
138#215—44no—
139#215—124no—
140#214—124no—
141C4⋊Dic3—21no—
142C4⋊Dic3—21no—
143C4⋊Dic3—62no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—61no—
148C4⋊Dic3—121no—
149C2×C3⋊C8—32no—
150C2×C3⋊C8—32no—
151C2×C3⋊C8—62no—
152C2×C3⋊C8#6712yes—
153C2×C3⋊C8#6712yes—
154C22×C32#12711yescharacteristic
155C2×C3×D3—81no—
156C2×C3×D3—81no—
157C2×C3×D3—81no—
158C32×C4—81no—
159C32×C4C2×SD1612yes—
160C32×C4AGL(1,ℤ/8)12yes—
161C32×C4#13712yes—
162C3⋊Dic3—81no—
163C3×Dic3—81no—
164C2×SD16—62no—
165C2×SD16—182no—
166C4⋊Q8—31no—
167C4⋊Q8—91no—
168C4⋊Q8D3211yescharacteristic
169#127—31no—
170#107—182no—
171#106—62no—
172#103—182no—
173#102—182no—
174C4×C8—31no—
175C4×C8—31no—
176C4×C8—91no—
177C23×C3—121no—
178C22×D3—41no—
179C3×Q8—42no—
180C3×Q8—42no—
181C3×Q8—82no—
182C3×Q8—122no—
183C3×D4—122no—
184C3×D4—122no—
185C3×D4—122no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—42no—
190C2×C3×C4—41no—
191C2×C3×C4—41no—
192C2×C3×C4—121no—
193C2×C3×C4D3×D411yescharacteristic
194C2×C3×C4D3×D411yescharacteristic
195C2×C3×C4D3×D411yescharacteristic
196C2×C3×C4D3×D411yescharacteristic
197C2×C3×C4C2×#6711yescharacteristic
198C2×C3×C4C2×#6711yescharacteristic
199C2×Dic3—41no—
200C2×Dic3—122no—
201C2×Dic3—121no—
202C2×Dic3—121no—
203D12—42no—
204D12—42no—
205D12—42no—
206Dic6—42no—
207Dic6—122no—
208Dic6—122no—
209Dic6—242no—
210C3×C8—62no—
211C3×C8—62no—
212C3⋊C8—22no—
213C3⋊C8—22no—
214C3⋊C8—34no—
215C3⋊C8—34no—
216C3⋊C8—64no—
217C2×C32#49211yescharacteristic
218C2×C32#49611yescharacteristic
219C2×C32#49711yescharacteristic
220C3×D3—161no—
221C2×Q8—21no—
222C2×Q8—61no—
223C2×Q8—181no—
224C2×D4—61no—
225C2×D4—61no—
226C2×D4—61no—
227SD16—124no—
228SD16—364no—
229C2×C8—32no—
230C2×C8—32no—
231C2×C8—92no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—181no—
237C4⋊C4—181no—
238C42C2×D3211yescharacteristic
239C22×C3—21no—
240C22×C3—241no—
241C22×C3—241no—
242C22×C3—241no—
243C22×C3#94011yescharacteristic
244C22×C3#94011yescharacteristic
245C2×D3—81no—
246C2×D3—81no—
247C2×D3—81no—
248C3×C4—22no—
249C3×C4—22no—
250C3×C4—22no—
251C3×C4—82no—
252C3×C4—81no—
253C3×C4—81no—
254C3×C4—241no—
255C3×C4D3×SD1612yes—
256C3×C4D3×SD1612yes—
257C3×C4#91412yes—
258C3×C4#91512yes—
259C3×C4#93212yes—
260C3×C4#94212yes—
261Dic3—81no—
262Dic3—242no—
263Dic3—241no—
264Dic3—241no—
265C32#171411yescharacteristic, complemented, Sylow
266C23—121no—
267Q8—42no—
268Q8—122no—
269Q8—362no—
270D4—122no—
271D4—122no—
272D4—122no—
273C2×C4—41no—
274C2×C4—121no—
275C2×C4—361no—
276C2×C4D3×#6711yescharacteristic
277C2×C4D3×#6711yescharacteristic
278C2×C4#381111yescharacteristic
279C8—62no—
280C8—62no—
281C8—94no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—481no—
286C2×C3#507411yescharacteristic
287C2×C3#508611yescharacteristic
288C2×C3#516711yescharacteristic
289C2×C3#517511yescharacteristic
290C2×C3#517511yescharacteristic
291C2×C3#517611yescharacteristic
292D3—161no—
293C22—241no—
294C22—241no—
295C22—241no—
296C22#6397911yescharacteristic
297C4—81no—
298C4—241no—
299C4—721no—
300C4#6393412yes—
301C4#6394012yes—
302C4#6394612yes—
303C3—21no—
304C3#7125711yescharacteristic, complemented
305C3#7133511yescharacteristic, complemented
306C2—481no—
307C2#1059147211yescharacteristic
308C2#1059160511yescharacteristic
309C2#1059162011yescharacteristic
subgroupG/H
centerC22#63979
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#127
prime radicalC3×#874C22
hypercenterC4⋊Q8D32
hypocenterC32#1714
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
1. #10592777C2semidirect
3. C3×#5080C2semidirect
5. #10590288C2semidirect
7. #10589079C2semidirect
28. #5080D3semidirect
100. C3⋊(C3⋊C8)SD16semidirect
265. C32#1714semidirect
304. C3#71257semidirect
305. C3#71335semidirect

Maximal subgroups

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

subgroupindex
#105927772
C3×#50852
C3×#50802
#105903752
#105902882
#105902732
#105890792
#713353
#712573