Finite Group Databasebeta

← #11782889

Subgroups — #11782889

Order 1152.

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

normal subgroups only

This group has 433 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#10592791C211yesmaximal, characteristic, complemented
2C3×#5088C211yesmaximal, characteristic
3C3×#5080C211yesmaximal, characteristic, complemented
4#10590287C211yesmaximal, characteristic, complemented
5#10590277C211yesmaximal, characteristic
6#10590273C211yesmaximal, characteristic
7#10589078C211yesmaximal, characteristic, complemented
8#71340—31nomaximal
9#71192—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3756—22no—
12#64078C2211yescharacteristic
13C3×#874C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#809—22no—
17C3×#808—22no—
18C3×C4×C3⋊C8C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63566—22no—
21#63563—22no—
22#63562—22no—
23C3×#498—31no—
24C3×#486—31no—
25#5092—31no—
26#5092—31no—
27#5092—61no—
28#5088—31no—
29#5088D311yescharacteristic
30#5080D311yescharacteristic, complemented
31#5079—31no—
32#5070—31no—
33#5070—31no—
34#4694—31no—
35#4681—31no—
36#4455—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
47#3756—44no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C2×C3⋊(C3⋊C8)D412yes—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8D412yes—
54C2×C3×C3⋊C8D412yes—
55#1720—91noSylow
56C3×C4⋊Q8—21no—
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8C2×D311yescharacteristic
59C3×C4⋊Q8C2×D311yescharacteristic
60C3×#127—31no—
61C2×#216—62no—
62C2×#216—62no—
63C2×#216—64no—
64#874C2×D311yescharacteristic
65#869—31no—
66#869—31no—
67#869—61no—
68#869C2×D311yescharacteristic
69C3×#106—62no—
70C3×#102—62no—
71C3×C4×C8—31no—
72C3×C4×C8—31no—
73#835—62no—
74#832—62no—
75#832—62no—
76#821—62no—
77#816—62no—
78#809—22no—
79#809—62no—
80#808—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
92C2×C3⋊Dic3—41no—
93#634—42no—
94C2×C3×Dic3—41no—
95C3×D12—42no—
96C3×D12—42no—
97C3×D12—42no—
98C3×Dic6—42no—
99C3⋊(C3⋊C8)—22no—
100C3×C3⋊C8—22no—
101C3×C3⋊C8—22no—
102#498—31no—
103#494—91no—
104#487—91no—
105#486—31no—
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×D4—61no—
114C2×C3×D4—61no—
115C2×C3×D4—61no—
116C2×D12—21no—
117C2×D12—21no—
118C2×D12—21no—
119C2×Dic6—21no—
120C2×Dic6—62no—
121C2×Dic6—61no—
122C2×Dic6—61no—
123C2×C3×C8—32no—
124C2×C3×C8—32no—
125C3×C4⋊C4—21no—
126C3×C4⋊C4—21no—
127C3×C4⋊C4—21no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—41no—
130C3×C4⋊C4—41no—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C42—21no—
134C3×C42C22×D311yescharacteristic
135C3×C42C22×D311yescharacteristic
136#216—128no—
137#216—124no—
138#216—124no—
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⋊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×Q16—182no—
163C4⋊Q8—31no—
164C4⋊Q8—91no—
165C4⋊Q8D3211yescharacteristic
166#127—31no—
167#106—62no—
168#103—182no—
169#102—62no—
170#102—182no—
171#102—182no—
172C4×C8—31no—
173C4×C8—31no—
174C4×C8—91no—
175C23×C3—121no—
176C22×D3—41no—
177C3×Q8—44no—
178C3×Q8—42no—
179C3×Q8—42no—
180C3×Q8—122no—
181C3×D4—122no—
182C3×D4—122no—
183C3×D4—122no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—42no—
188C2×C3×C4—41no—
189C2×C3×C4—41no—
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—122no—
199C2×Dic3—121no—
200C2×Dic3—121no—
201D12—42no—
202D12—42no—
203D12—42no—
204Dic6—42no—
205Dic6—124no—
206Dic6—122no—
207Dic6—122no—
208C3×C8—62no—
209C3×C8—62no—
210C3⋊C8—22no—
211C3⋊C8—22no—
212C3⋊C8—64no—
213C3⋊C8—62no—
214C3⋊C8—62no—
215C2×C32#49511yescharacteristic
216C2×C32#49611yescharacteristic
217C2×C32#49711yescharacteristic
218C3×D3—161no—
219C2×Q8—21no—
220C2×Q8—61no—
221C2×Q8—181no—
222C2×D4—61no—
223C2×D4—61no—
224C2×D4—61no—
225Q16—364no—
226C2×C8—32no—
227C2×C8—32no—
228C2×C8—92no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—61no—
232C4⋊C4—61no—
233C4⋊C4—181no—
234C4⋊C4—181no—
235C42C2×D3211yescharacteristic
236C22×C3—21no—
237C22×C3—241no—
238C22×C3—241no—
239C22×C3—241no—
240C22×C3#94011yescharacteristic
241C22×C3#94011yescharacteristic
242C2×D3—81no—
243C2×D3—81no—
244C2×D3—81no—
245C3×C4—22no—
246C3×C4—22no—
247C3×C4—22no—
248C3×C4—82no—
249C3×C4—81no—
250C3×C4—81no—
251C3×C4—241no—
252C3×C4#91112yes—
253C3×C4#91412yes—
254C3×C4#91512yes—
255C3×C4#91612yes—
256C3×C4#94212yes—
257C3×C4#95012yes—
258Dic3—81no—
259Dic3—242no—
260Dic3—241no—
261Dic3—241no—
262C32#172011yescharacteristic, complemented, Sylow
263C23—121no—
264Q8—42no—
265Q8—122no—
266Q8—362no—
267D4—122no—
268D4—122no—
269D4—122no—
270C2×C4—41no—
271C2×C4—121no—
272C2×C4—361no—
273C2×C4D3×#6711yescharacteristic
274C2×C4D3×#6711yescharacteristic
275C2×C4#381111yescharacteristic
276C8—62no—
277C8—62no—
278C8—182no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—21no—
282C2×C3—481no—
283C2×C3#505911yescharacteristic
284C2×C3#508611yescharacteristic
285C2×C3#515411yescharacteristic
286C2×C3#516711yescharacteristic
287C2×C3#516811yescharacteristic
288C2×C3#517611yescharacteristic
289D3—161no—
290C22—241no—
291C22—241no—
292C22—241no—
293C22#6397911yescharacteristic
294C4—81no—
295C4—241no—
296C4—721no—
297C4#6393712yes—
298C4#6394612yes—
299C4#6394712yes—
300C3—21no—
301C3#7119211yescharacteristic, complemented
302C3#7134011yescharacteristic, complemented
303C2—481no—
304C2#1059147511yescharacteristic
305C2#1059160511yescharacteristic
306C2#1059160611yescharacteristic
subgroupG/H
centerC22#63979
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#127
prime radicalC3×#874C22
hypercenterC4⋊Q8D32
hypocenterC32#1720
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. #10592791C2semidirect
3. C3×#5080C2semidirect
4. #10590287C2semidirect
7. #10589078C2semidirect
30. #5080D3semidirect
262. C32#1720semidirect
301. C3#71192semidirect
302. C3#71340semidirect

Maximal subgroups

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

subgroupindex
#105927912
C3×#50882
C3×#50802
#105902872
#105902772
#105902732
#105890782
#713403
#711923