Finite Group Databasebeta

← #11782951

Subgroups — #11782951

Order 1152.

455 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 455 conjugacy classes of subgroups — too many to draw. Only its 108 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#10592393C211yesmaximal, characteristic
2C3×#4682C211yesmaximal, characteristic, complemented
3#10590386C211yesmaximal, characteristic, complemented
4#10590373C211yesmaximal, characteristic
5#10590311C211yesmaximal, characteristic, complemented
6#10590281C211yesmaximal, characteristic
7C3×#4454C211yesmaximal, characteristic, complemented
8#71366—31nomaximal
9#68098—31nomaximal
10#64083C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3719—22no—
15C2×#3717—22no—
16C32×C4×C8C2211yescharacteristic
17#63648—22no—
18C3×#818—22no—
19C3×C4×C3⋊C8C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63575—22no—
22#63564—22no—
23C3×#500—31no—
24#5092—31no—
25#5088—31no—
26#5085—31no—
27#5078—31no—
28#4699—31no—
29#4694—31no—
30#4694—31no—
31#4694—31no—
32#4694—61no—
33#4693—31no—
34#4682—31no—
35#4682D311yescharacteristic, 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—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8D412yes—
53C2×C3×C3⋊C8D412yes—
54#3719—44no—
55#3717—44no—
56#1722—91noSylow
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8—31no—
59C2×#216—62no—
60C2×#215—62no—
61C2×Dic12—62no—
62C2×#204—62no—
63#874—31no—
64#874—31no—
65#874—61no—
66#869—31no—
67#869—31no—
68#869—61no—
69#869C2×D311yescharacteristic
70#869C2×D311yescharacteristic
71C3×#107—62no—
72C3×C4×C8—21no—
73C3×C4×C8—31no—
74C3×C4×C8—31no—
75C3×C4×C8C2×D311yescharacteristic
76C3×C4×C8C2×D311yescharacteristic
77#821—62no—
78#821—64no—
79#821—62no—
80#821—62no—
81#818—22no—
82#818—62no—
83#809—62no—
84#807—62no—
85C4×C3⋊C8C2×D311yescharacteristic
86C4×C3⋊C8C2×D311yescharacteristic
87C22×C3⋊D3—41no—
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C3⋊Dic3—41no—
92C4⋊(C3⋊D3)—42no—
93C4⋊(C3⋊D3)—42no—
94C4⋊(C3⋊D3)—42no—
95#634—42no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98C3×Dic6—42no—
99C3×Dic6—42no—
100C32×C8—22no—
101C3×C3⋊C8—22no—
102C3×C3⋊C8D814yes—
103#500—31no—
104#500—91no—
105#494—91no—
106#492—91no—
107#486—91no—
108#486—91no—
109#322—31no—
110C2×C3×Q8—61no—
111C2×C3×Q8—61no—
112C2×D12—62no—
113C2×D12—61no—
114C2×D12—61no—
115C2×D12—61no—
116C2×D12—61no—
117C2×D12—61no—
118C2×D12—61no—
119C2×D12—121no—
120C2×D12—121no—
121C2×Dic6—21no—
122C2×Dic6—21no—
123C2×Dic6—61no—
124C2×Dic6—61no—
125C2×Dic6—121no—
126C2×C3×C8—22no—
127C2×C3×C8—32no—
128C2×C3×C8—32no—
129C2×C3×C8D1212yes—
130C2×C3×C8#6712yes—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C42—21no—
136C3×C42C22×D311yescharacteristic
137C3×C42C22×D311yescharacteristic
138#216—124no—
139#215—124no—
140C4⋊Dic3—21no—
141C4⋊Dic3—21no—
142C4⋊Dic3—21no—
143C4⋊Dic3—21no—
144C4⋊Dic3—62no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—61no—
148C4⋊Dic3—61no—
149C4⋊Dic3—121no—
150C2×C3⋊C8D1212yes—
151C2×C3⋊C8D1212yes—
152Dic12—124no—
153#204—124no—
154C22×C32#12711yescharacteristic
155C2×C3⋊D3—81no—
156C2×C3⋊D3—81no—
157C2×C3⋊D3—81no—
158C32×C4C2×D812yes—
159C32×C4#13712yes—
160C32×C4#13712yes—
161C3⋊Dic3—81no—
162C3×Dic3—81no—
163C3×Dic3—81no—
164C2×Q16—182no—
165C2×SD16—182no—
166C4⋊Q8—31no—
167C4⋊Q8—31no—
168C4⋊Q8—91no—
169#127—91no—
170#107—62no—
171#107—182no—
172#102—182no—
173#102—182no—
174C4×C8—31no—
175C4×C8—31no—
176C4×C8D3211yescharacteristic
177C22×D3—122no—
178C22×D3—121no—
179C22×D3—121no—
180C3×Q8—122no—
181C3×Q8—122no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—121no—
186C2×C3×C4—121no—
187C2×C3×C4C2×D1211yescharacteristic
188C2×C3×C4C2×D1211yescharacteristic
189C2×C3×C4C2×D1211yescharacteristic
190C2×C3×C4D3×D411yescharacteristic
191C2×C3×C4D3×D411yescharacteristic
192C2×C3×C4C2×#6711yescharacteristic
193C2×Dic3—41no—
194C2×Dic3—41no—
195C2×Dic3—122no—
196C2×Dic3—121no—
197C2×Dic3—121no—
198D12—124no—
199D12—122no—
200D12—122no—
201D12—122no—
202D12—122no—
203D12—122no—
204D12—122no—
205D12—242no—
206D12—242no—
207Dic6—42no—
208Dic6—42no—
209Dic6—122no—
210Dic6—122no—
211Dic6—242no—
212C3×C8—22no—
213C3×C8—22no—
214C3×C8—34no—
215C3×C8—42no—
216C3×C8—62no—
217C3⋊C8—22no—
218C3⋊C8D2414yes—
219C2×C32#49311yescharacteristic
220C2×C32#49711yescharacteristic
221C2×C32#49711yescharacteristic
222C3⋊D3—161no—
223C2×Q8—61no—
224C2×Q8—61no—
225C2×Q8—181no—
226C2×D4—181no—
227C2×D4—181no—
228C2×D4—181no—
229Q16—364no—
230SD16—364no—
231C2×C8—32no—
232C2×C8—32no—
233C2×C8#62612yes—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4—181no—
239C4⋊C4—181no—
240C42C2×D3211yescharacteristic
241C22×C3—21no—
242C22×C3#87411yescharacteristic
243C22×C3#94011yescharacteristic
244C2×D3—242no—
245C2×D3—242no—
246C2×D3—242no—
247C2×D3—241no—
248C2×D3—241no—
249C2×D3—241no—
250C2×D3—241no—
251C2×D3—241no—
252C2×D3—241no—
253C3×C4—22no—
254C3×C4—22no—
255C3×C4—22no—
256C3×C4—241no—
257C3×C4—241no—
258C3×C4C2×D2412yes—
259C3×C4#90912yes—
260C3×C4#90912yes—
261C3×C4D3×D812yes—
262C3×C4#91812yes—
263C3×C4#94212yes—
264Dic3—81no—
265Dic3—81no—
266Dic3—242no—
267Dic3—241no—
268Dic3—241no—
269C32#172211yescharacteristic, complemented, Sylow
270C23—361no—
271Q8—122no—
272Q8—122no—
273Q8—362no—
274D4—362no—
275D4—362no—
276D4—362no—
277C2×C4—121no—
278C2×C4—121no—
279C2×C4—361no—
280C2×C4D3×D1211yescharacteristic
281C2×C4D3×D1211yescharacteristic
282C2×C4C2×#62611yescharacteristic
283C8—22no—
284C8—34no—
285C8—62no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3#469511yescharacteristic
290C2×C3#471511yescharacteristic
291C2×C3#471511yescharacteristic
292C2×C3#508611yescharacteristic
293C2×C3#515111yescharacteristic
294C2×C3#519011yescharacteristic
295D3—482no—
296D3—481no—
297D3—481no—
298C22—721no—
299C22—721no—
300C22—721no—
301C22#6391111yescharacteristic
302C4—241no—
303C4—241no—
304C4—721no—
305C4D3×D2412yes—
306C4#6380112yes—
307C4#6383312yes—
308C3—21no—
309C3#6809811yescharacteristic, complemented
310C3#7136611yescharacteristic, complemented
311C2—1441no—
312C2#1059037411yescharacteristic
313C2#1059088011yescharacteristic
314C2#1059089911yescharacteristic
subgroupG/H
centerC22#63911
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#127
prime radical#64083C22
hypercenterC4×C8D32
hypocenterC32#1722
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×#4682C2semidirect
3. #10590386C2semidirect
5. #10590311C2semidirect
7. C3×#4454C2semidirect
35. #4682D3semidirect
37. #4454D3semidirect
269. C32#1722semidirect
309. C3#68098semidirect
310. C3#71366semidirect

Maximal subgroups

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

subgroupindex
#105923932
C3×#46822
#105903862
#105903732
#105903112
#105902812
C3×#44542
#713663
#680983