Finite Group Databasebeta

← #11799859

Subgroups — #11799859

Order 1152.

307 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 307 conjugacy classes of subgroups — too many to draw. Only its 76 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#10590831C211yesmaximal, characteristic
2#10590707C211yesmaximal, characteristic, complemented
3#10589370C211yesmaximal, characteristic, complemented
4C3×#4509C211yesmaximal, characteristic, complemented
5C3×(C2×D3)⋊C16C211yesmaximal, characteristic, complemented
6#10589141C211yesmaximal, characteristic, complemented
7#10589115C211yesmaximal, characteristic, complemented
8#69201—31nomaximal
9#69097—31nomaximal
10C2×C3×D24C2211yescharacteristic
11C2×C3×D3×C8C2211yescharacteristic
12#63908—21no—
13#63841—21no—
14C2×C32×C16C2211yescharacteristic
15#63645C2211yescharacteristic
16#63645C2211yescharacteristic
17C3×#818C2211yescharacteristic
18C2×C3×C3⋊C16C2211yescharacteristic
19#63573—21no—
20#63563—21no—
21#5157—31no—
22#5115—31no—
23#5106—31no—
24#4880—31no—
25C3×#357—31no—
26C3×C22⋊C16—31no—
27#4562—31no—
28#4509—31no—
29#4509D311yescharacteristic, complemented
30(C2×D3)⋊C16D311yescharacteristic, complemented
31#4505—31no—
32#4504—31no—
33#4504—31no—
34#4504—61no—
35#4490—31no—
36C2×C3×D12—21no—
37C2×C3×C4×D3D411yescharacteristic
38C2×#625—41no—
39C2×C32×C8C2311yescharacteristic
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)—21no—
42C3×C4⋊Dic3—21no—
43C2×C3×C3⋊C8D411yescharacteristic
44C3×D24—21no—
45C3×D24—21no—
46C3×D3×C8—21no—
47C3×D3×C8—21no—
48(C2×D3)⋊Dic3—41no—
49(C2×D3)⋊Dic3—41no—
50Dic32—41no—
51C32×C16—21no—
52C3×C3⋊C16—21no—
53#2234—91noSylow
54C2×C3×D8—31no—
55C22×C3×C8—31no—
56#938—61no—
57#930—61no—
58#926—61no—
59C2×D24C2×D311yescharacteristic
60C2×D3×C8C2×D311yescharacteristic
61#892—61no—
62C2×C3×C16—21no—
63C2×C3×C16—31no—
64C2×C3×C16C2×D311yescharacteristic
65C2×C3×C16C2×D311yescharacteristic
66C3×#107—31no—
67#832—61no—
68#821—61no—
69#818—31no—
70#818—31no—
71#818—31no—
72#818—31no—
73#818—61no—
74#818—61no—
75#818C2×D311yescharacteristic
76#817—61no—
77C2×C3⋊C16C2×D311yescharacteristic
78#808—61no—
79C22×C3×D3—41no—
80C22×C3×D3D811yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3—41no—
83C2×C3⋊Dic3—41no—
84C2×C3×Dic3—41no—
85C2×C3×Dic3D811yescharacteristic
86C3×D12—41no—
87C3×D12—41no—
88C3×C4×D3—21no—
89C3×C4×D3—21no—
90#625—82no—
91C32×C8#4111yescharacteristic
92C32×C8#4111yescharacteristic
93C3×C3⋊C8—21no—
94#466—91no—
95#427—91no—
96#367—91no—
97#366—91no—
98#357—31no—
99#357—91no—
100C22⋊C16—31no—
101C2×C3×D4—61no—
102C22×C3×C4—31no—
103C2×#67—121no—
104C2×#67—121no—
105C2×D12—21no—
106C2×C4×D3D1211yescharacteristic
107C3×D8—61no—
108C3×D8—61no—
109C2×C3×C8—21no—
110C2×C3×C8—31no—
111C2×C3×C8—61no—
112C2×C3×C8—61no—
113C2×C3×C8C22×D311yescharacteristic
114C2×C3×C8C22×D311yescharacteristic
115C3×C4⋊C4—61no—
116#217—121no—
117#217—121no—
118(C2×D3)⋊C4—121no—
119(C2×D3)⋊C4—121no—
120C4⋊Dic3—21no—
121C4⋊Dic3—61no—
122C4⋊Dic3—61no—
123C4⋊Dic3—61no—
124C4⋊Dic3—61no—
125C4⋊Dic3—121no—
126C4⋊Dic3—121no—
127C4×Dic3—121no—
128C4×Dic3—121no—
129C2×C3⋊C8D1211yescharacteristic
130D24—21no—
131D24—21no—
132D3×C8—21no—
133D3×C8—21no—
134C3×C16—22no—
135C3×C16—21no—
136C3×C16—21no—
137C3×C16—61no—
138C3⋊C16—21no—
139C22×C32C2×D811yescharacteristic
140C2×C3×D3—21no—
141C2×C3×D3—21no—
142C2×C3×D3—21no—
143C2×C3×D3—81no—
144C2×C3×D3—81no—
145C2×C3×D3—81no—
146C32×C4#12311yescharacteristic
147C32×C4#13711yescharacteristic
148C3⋊Dic3—81no—
149C3⋊Dic3—81no—
150C3×Dic3—21no—
151C3×Dic3—81no—
152C2×D8—31no—
153C22×C8—31no—
154#121—181no—
155#117—181no—
156C2×C16—31no—
157C2×C16D3211yescharacteristic
158#107—31no—
159#107—91no—
160#107—91no—
161#106—181no—
162#102—181no—
163C23×C3—31no—
164C23×C3—121no—
165C22×D3—41no—
166C22×D3D2411yescharacteristic
167C3×D4—121no—
168C3×D4—121no—
169C2×C3×C4—21no—
170C2×C3×C4—31no—
171C2×C3×C4—61no—
172C2×C3×C4—61no—
173C2×C3×C4—121no—
174C2×C3×C4C2×D1211yescharacteristic
175C2×C3×C4D3×D411yescharacteristic
176#67—242no—
177#67—242no—
178C2×Dic3—41no—
179C2×Dic3—121no—
180C2×Dic3—121no—
181C2×Dic3—121no—
182C2×Dic3—121no—
183C2×Dic3—241no—
184C2×Dic3—241no—
185C2×Dic3D2411yescharacteristic
186D12—41no—
187D12—41no—
188C4×D3—21no—
189C4×D3—21no—
190C3×C8—21no—
191C3×C8—21no—
192C3×C8—61no—
193C3×C8#23511yescharacteristic
194C3×C8#23711yescharacteristic
195C3×C8#23711yescharacteristic
196C3×C8#23711yescharacteristic
197C3⋊C8—21no—
198C2×C32#48011yescharacteristic
199C2×C32#50811yescharacteristic
200C2×C32#50911yescharacteristic
201C3×D3—41no—
202C3×D3—161no—
203C2×D4—61no—
204C2×D4—361no—
205C22×C4—31no—
206D8—61no—
207D8—61no—
208C2×C8—31no—
209C2×C8—61no—
210C2×C8—61no—
211C2×C8C2×D3211yescharacteristic
212C4⋊C4—61no—
213C4⋊C4—181no—
214C4⋊C4—181no—
215C22⋊C4—361no—
216C22⋊C4—361no—
217C42—361no—
218C16—21no—
219C16—61no—
220C22×C3—21no—
221C22×C3—61no—
222C22×C3—61no—
223C22×C3—61no—
224C22×C3—241no—
225C22×C3—241no—
226C22×C3—241no—
227C22×C3C2×D2411yescharacteristic
228C22×C3D3×D811yescharacteristic
229C2×D3—21no—
230C2×D3—21no—
231C2×D3—21no—
232C2×D3—81no—
233C2×D3—81no—
234C2×D3—81no—
235C3×C4—21no—
236C3×C4—21no—
237C3×C4—61no—
238C3×C4—241no—
239C3×C4#88311yescharacteristic
240C3×C4#88611yescharacteristic
241C3×C4#90911yescharacteristic
242C3×C4#91511yescharacteristic
243Dic3—21no—
244Dic3—81no—
245Dic3—241no—
246Dic3—241no—
247Dic3—241no—
248Dic3—241no—
249Dic3—481no—
250Dic3—481no—
251C32#223411yescharacteristic, complemented, Sylow
252C23—31no—
253C23—121no—
254D4—121no—
255D4—121no—
256D4—722no—
257C2×C4—31no—
258C2×C4—61no—
259C2×C4—61no—
260C2×C4—121no—
261C2×C4—361no—
262C2×C4—361no—
263C2×C4D3×D1211yescharacteristic
264C8—61no—
265C8#379511yescharacteristic
266C8#380511yescharacteristic
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—121no—
271C2×C3—481no—
272C2×C3#473611yescharacteristic
273C2×C3#477411yescharacteristic
274C2×C3#490411yescharacteristic
275C2×C3#490811yescharacteristic
276C2×C3#491211yescharacteristic
277C2×C3#491411yescharacteristic
278D3—41no—
279D3—161no—
280C22—61no—
281C22—61no—
282C22—61no—
283C22—241no—
284C22—241no—
285C22—241no—
286C22D3×D2411yescharacteristic
287C4—61no—
288C4—241no—
289C4—721no—
290C4—721no—
291C4#6380011yescharacteristic
292C4#6389111yescharacteristic
293C3—21no—
294C3#6909711yescharacteristic, complemented
295C3#6920111yescharacteristic, complemented
296C2—121no—
297C2—481no—
298C2#1059023311yescharacteristic
299C2#1059024111yescharacteristic
300C2#1059068011yescharacteristic
subgroupG/H
centerC22D3×D24
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×C16C22
socleC22×C32C2×D8
prime radical#10590831C2
hypercenterC2×C16D32
hypocenterC32#2234
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
2. #10590707C2semidirect
3. #10589370C2semidirect
4. C3×#4509C2semidirect
5. C3×(C2×D3)⋊C16C2semidirect
6. #10589141C2semidirect
7. #10589115C2semidirect
29. #4509D3semidirect
30. (C2×D3)⋊C16D3semidirect
251. C32#2234semidirect
294. C3#69097semidirect
295. C3#69201semidirect

Maximal subgroups

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

subgroupindex
#105908312
#105907072
#105893702
C3×#45092
C3×(C2×D3)⋊C162
#105891412
#105891152
#692013
#690973