Finite Group Databasebeta

← #11799858

Subgroups — #11799858

Order 1152.

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

normal subgroups only

This group has 317 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#10590832C211yesmaximal, characteristic
2#10590707C211yesmaximal, characteristic, complemented
3#10589375C211yesmaximal, characteristic, complemented
4C3×(C2×D3)⋊C16C211yesmaximal, characteristic, complemented
5C3×#4504C211yesmaximal, characteristic, complemented
6#10589141C211yesmaximal, characteristic, complemented
7#10589116C211yesmaximal, characteristic, complemented
8#69323—31nomaximal
9#69097—31nomaximal
10C2×#3745C2211yescharacteristic
11C2×C3×D3×C8C2211yescharacteristic
12#63909—21no—
13#63841—21no—
14C2×C32×C16C2211yescharacteristic
15#63645C2211yescharacteristic
16C3×#818C2211yescharacteristic
17C3×#818C2211yescharacteristic
18C2×C3×C3⋊C16C2211yescharacteristic
19#63573—21no—
20#63564—21no—
21#5115—31no—
22#5106—31no—
23#4883—31no—
24#4880—31no—
25C3×#366—31no—
26C3×C22⋊C16—31no—
27#4509—31no—
28#4509—31no—
29#4509—31no—
30#4509—61no—
31(C2×D3)⋊C16D311yescharacteristic, complemented
32#4505—31no—
33#4504D311yescharacteristic, complemented
34#4491—31no—
35#4490—31no—
36C2×C4⋊(C3⋊D3)—21no—
37C2×C3×C4×D3D411yescharacteristic
38C2×#626—41no—
39C2×C32×C8C2311yescharacteristic
40C4⋊(C3⋊Dic3)—21no—
41#3745—21no—
42#3745—21no—
43C3×C4⋊Dic3—21no—
44C3×C4⋊Dic3—21no—
45C2×C3×C3⋊C8D411yescharacteristic
46C3×D3×C8—21no—
47C3×D3×C8—21no—
48#3722—41no—
49(C2×D3)⋊Dic3—41no—
50Dic32—41no—
51C32×C16—21no—
52C3×C3⋊C16—21no—
53#2234—91noSylow
54C22×C3×C8—31no—
55#930—61no—
56#926—61no—
57C2×D24—31no—
58C2×D24—31no—
59C2×D24—61no—
60C2×D3×C8C2×D311yescharacteristic
61#895—61no—
62#892—61no—
63C2×C3×C16—21no—
64C2×C3×C16—31no—
65C2×C3×C16C2×D311yescharacteristic
66C2×C3×C16C2×D311yescharacteristic
67C3×#107—31no—
68C3×#107—31no—
69#821—61no—
70#818—31no—
71#818—31no—
72#818—61no—
73#818C2×D311yescharacteristic
74#818C2×D311yescharacteristic
75#817—61no—
76C2×C3⋊C16C2×D311yescharacteristic
77#809—61no—
78#808—61no—
79C22×C3⋊D3—41no—
80C22×C3×D3D811yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3—41no—
83C4⋊(C3⋊D3)—41no—
84C4⋊(C3⋊D3)—41no—
85C2×C3×Dic3—41no—
86C2×C3×Dic3—41no—
87C2×C3×Dic3D811yescharacteristic
88C3×C4×D3—21no—
89C3×C4×D3—21no—
90#626—82no—
91C32×C8#4111yescharacteristic
92C32×C8#4111yescharacteristic
93C3×C3⋊C8—21no—
94#466—91no—
95#427—91no—
96#367—91no—
97#366—31no—
98#357—91no—
99#357—91no—
100C22⋊C16—31no—
101C22×C3×C4—31no—
102C2×#67—121no—
103C2×D12—61no—
104C2×D12—61no—
105C2×D12—121no—
106C2×D12—121no—
107C2×C4×D3D1211yescharacteristic
108C2×C3×C8—21no—
109C2×C3×C8—31no—
110C2×C3×C8—61no—
111C2×C3×C8—61no—
112C2×C3×C8C22×D311yescharacteristic
113C2×C3×C8C22×D311yescharacteristic
114C3×C4⋊C4—61no—
115C3×C4⋊C4—61no—
116#217—121no—
117(C2×D3)⋊C4—121no—
118(C2×D3)⋊C4—121no—
119(C2×D3)⋊C4—121no—
120C4⋊Dic3—21no—
121C4⋊Dic3—21no—
122C4⋊Dic3—61no—
123C4⋊Dic3—61no—
124C4⋊Dic3—121no—
125C4×Dic3—121no—
126C4×Dic3—121no—
127C2×C3⋊C8D1211yescharacteristic
128D24—62no—
129D24—61no—
130D24—61no—
131D24—61no—
132D24—61no—
133D24—121no—
134D3×C8—21no—
135D3×C8—21no—
136C3×C16—21no—
137C3×C16—21no—
138C3×C16—41no—
139C3×C16—61no—
140C3⋊C16—21no—
141C22×C32C2×D811yescharacteristic
142C2×C3⋊D3—81no—
143C2×C3⋊D3—81no—
144C2×C3⋊D3—81no—
145C2×C3×D3—21no—
146C2×C3×D3—21no—
147C2×C3×D3—21no—
148C32×C4#12311yescharacteristic
149C32×C4#13711yescharacteristic
150C3⋊Dic3—81no—
151C3×Dic3—21no—
152C3×Dic3—81no—
153C3×Dic3—81no—
154C2×D8—91no—
155C22×C8—31no—
156#121—181no—
157#117—181no—
158C2×C16—31no—
159C2×C16D3211yescharacteristic
160#107—31no—
161#107—31no—
162#107—91no—
163#106—181no—
164#102—181no—
165C23×C3—31no—
166C22×D3—121no—
167C22×D3—121no—
168C22×D3—241no—
169C22×D3D2411yescharacteristic
170C2×C3×C4—21no—
171C2×C3×C4—31no—
172C2×C3×C4—61no—
173C2×C3×C4—61no—
174C2×C3×C4—121no—
175C2×C3×C4—121no—
176C2×C3×C4C2×D1211yescharacteristic
177C2×C3×C4D3×D411yescharacteristic
178#67—242no—
179C2×Dic3—41no—
180C2×Dic3—41no—
181C2×Dic3—121no—
182C2×Dic3—121no—
183C2×Dic3—241no—
184C2×Dic3D2411yescharacteristic
185D12—122no—
186D12—121no—
187D12—121no—
188D12—121no—
189D12—121no—
190D12—241no—
191D12—242no—
192C4×D3—21no—
193C4×D3—21no—
194C3×C8—21no—
195C3×C8—21no—
196C3×C8—61no—
197C3×C8#23511yescharacteristic
198C3×C8#23711yescharacteristic
199C3×C8#23711yescharacteristic
200C3×C8#23911yescharacteristic
201C3⋊C8—21no—
202C2×C32#48011yescharacteristic
203C2×C32#50811yescharacteristic
204C2×C32#50911yescharacteristic
205C3⋊D3—161no—
206C3×D3—41no—
207C2×D4—181no—
208C2×D4—361no—
209C22×C4—31no—
210D8—181no—
211D8—181no—
212C2×C8—31no—
213C2×C8—61no—
214C2×C8—61no—
215C2×C8C2×D3211yescharacteristic
216C4⋊C4—61no—
217C4⋊C4—61no—
218C4⋊C4—181no—
219C22⋊C4—361no—
220C22⋊C4—361no—
221C42—361no—
222C16—21no—
223C16—61no—
224C22×C3—21no—
225C22×C3—61no—
226C22×C3—61no—
227C22×C3—61no—
228C22×C3C2×D2411yescharacteristic
229C22×C3D3×D811yescharacteristic
230C2×D3—21no—
231C2×D3—21no—
232C2×D3—21no—
233C2×D3—242no—
234C2×D3—241no—
235C2×D3—241no—
236C2×D3—241no—
237C2×D3—241no—
238C2×D3—241no—
239C2×D3—241no—
240C2×D3—481no—
241C2×D3—481no—
242C3×C4—21no—
243C3×C4—21no—
244C3×C4—61no—
245C3×C4—241no—
246C3×C4—241no—
247C3×C4#88611yescharacteristic
248C3×C4#89411yescharacteristic
249C3×C4#90911yescharacteristic
250C3×C4#91811yescharacteristic
251Dic3—21no—
252Dic3—81no—
253Dic3—81no—
254Dic3—241no—
255Dic3—241no—
256Dic3—481no—
257C32#223411yescharacteristic, complemented, Sylow
258C23—31no—
259C23—361no—
260D4—361no—
261D4—361no—
262D4—722no—
263C2×C4—31no—
264C2×C4—61no—
265C2×C4—61no—
266C2×C4—121no—
267C2×C4—121no—
268C2×C4—361no—
269C2×C4D3×D1211yescharacteristic
270C8—61no—
271C8#379611yescharacteristic
272C8#380411yescharacteristic
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—121no—
277C2×C3#473611yescharacteristic
278C2×C3#488211yescharacteristic
279C2×C3#490411yescharacteristic
280C2×C3#490811yescharacteristic
281C2×C3#491111yescharacteristic
282C2×C3#491911yescharacteristic
283D3—41no—
284D3—482no—
285D3—481no—
286D3—481no—
287C22—61no—
288C22—61no—
289C22—61no—
290C22—721no—
291C22—721no—
292C22—721no—
293C22D3×D2411yescharacteristic
294C4—61no—
295C4—241no—
296C4—241no—
297C4—721no—
298C4#6380111yescharacteristic
299C4#6389011yescharacteristic
300C3—21no—
301C3#6909711yescharacteristic, complemented
302C3#6932311yescharacteristic, complemented
303C2—121no—
304C2—1441no—
305C2#1059023211yescharacteristic
306C2#1059024311yescharacteristic
307C2#1059067911yescharacteristic
subgroupG/H
centerC22D3×D24
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×C16C22
socleC22×C32C2×D8
prime radical#10590832C2
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. #10589375C2semidirect
4. C3×(C2×D3)⋊C16C2semidirect
5. C3×#4504C2semidirect
6. #10589141C2semidirect
7. #10589116C2semidirect
31. (C2×D3)⋊C16D3semidirect
33. #4504D3semidirect
257. C32#2234semidirect
301. C3#69097semidirect
302. C3#69323semidirect

Maximal subgroups

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

subgroupindex
#105908322
#105907072
#105893752
C3×(C2×D3)⋊C162
C3×#45042
#105891412
#105891162
#693233
#690973