Finite Group Databasebeta

← #11799044

Subgroups — #11799044

Order 1152.

349 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 349 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C2×C3×Dic24C211yesmaximal, characteristic, complemented
2#10590865C211yesmaximal, characteristic
3Dic3×Dic12C211yesmaximal, characteristic, complemented
4C2×#63549C211yesmaximal, characteristic
5#10589375C211yesmaximal, characteristic
6C3×Dic3⋊C16C211yesmaximal, characteristic, complemented
7#10589118C211yesmaximal, characteristic, complemented
8#71498—31nomaximal
9#69294—31nomaximal
10C2×#3745C2211yescharacteristic
11C2×C3×Dic12C2211yescharacteristic
12C2×C3×Dic12C2211yescharacteristic
13#63864—21no—
14Dic3×Dic6—21no—
15C2×#3717—21no—
16C2×C32×C16C2211yescharacteristic
17#63645C2211yescharacteristic
18C3×C8×Dic3C2211yescharacteristic
19C2×C3×C3⋊C16C2211yescharacteristic
20C3×Dic24—22no—
21#63566—21no—
22#63549—22no—
23C2×C3×Q32—31no—
24#5191—31no—
25Dic3×Q16—31no—
26C2×#828—31no—
27C2×Dic24D311yescharacteristic, complemented
28C2×#800—31no—
29C4×Dic12—31no—
30#4696—31no—
31C3×C4⋊C16—31no—
32#4564—31no—
33#4509—31no—
34#4509—31no—
35#4509—61no—
36#4503—31no—
37Dic3⋊C16D311yescharacteristic, complemented
38C2×C4⋊(C3⋊D3)—21no—
39C2×C3×Dic6—21no—
40C2×C3×Dic6—21no—
41C2×C32×C8C2311yescharacteristic
42C4⋊(C3⋊Dic3)—21no—
43#3745—21no—
44#3745—21no—
45C3×C4×Dic3D411yescharacteristic
46C2×C3×C3⋊C8D411yescharacteristic
47C3×Dic12—21no—
48C3×Dic12—21no—
49C3×Dic12—21no—
50C3×Dic12D412yes—
51Dic3⋊Dic3—41no—
52#3722—41no—
53#3722—41no—
54Dic32—41no—
55#3717—42no—
56C32×C16—21no—
57C3×C3⋊C16—21no—
58#2211—91noSylow
59C2×C3×Q16—31no—
60C2×C3×Q16—31no—
61#947—61no—
62Q8×Dic3—61no—
63C2×#215—61no—
64C2×Dic12C2×D311yescharacteristic
65C2×Dic12C2×D311yescharacteristic
66C2×D24—31no—
67C2×D24—31no—
68C2×D24—61no—
69C2×#204—61no—
70#875—61no—
71C4×Dic6—61no—
72C3×Q32—62no—
73C2×C3×C16—21no—
74C2×C3×C16—31no—
75C2×C3×C16C2×D311yescharacteristic
76C2×C3×C16C2×D311yescharacteristic
77C3×C4×C8—31no—
78#835—61no—
79#828—62no—
80#818—31no—
81#818—31no—
82#818—61no—
83#816—61no—
84C8×Dic3C2×D311yescharacteristic
85C2×C3⋊C16C2×D311yescharacteristic
86Dic24—22no—
87#800—62no—
88C22×C3⋊D3—41no—
89C2×C32×C4C2×D411yescharacteristic
90C2×C3⋊Dic3—41no—
91C4⋊(C3⋊D3)—41no—
92C4⋊(C3⋊D3)—41no—
93C2×C3×Dic3—41no—
94C2×C3×Dic3—41no—
95C2×C3×Dic3D811yescharacteristic
96C2×C3×Dic3D811yescharacteristic
97C3×Dic6—22no—
98C3×Dic6—41no—
99C3×Dic6—41no—
100C3×Dic6—41no—
101C32×C8C2×D411yescharacteristic
102C32×C8#4111yescharacteristic
103C3×C3⋊C8—21no—
104C2×Q32—31no—
105C2×SD32—91no—
106#495—91no—
107C4×Q16—91no—
108C4⋊C16—31no—
109#358—91no—
110#357—91no—
111C2×C3×Q8—61no—
112C2×C3×Q8—61no—
113C2×D12—61no—
114C2×D12—61no—
115C2×D12—121no—
116C2×Dic6—21no—
117C2×Dic6—21no—
118C3×Q16—32no—
119C3×Q16—61no—
120C3×Q16—61no—
121C3×Q16—61no—
122C2×C3×C8—21no—
123C2×C3×C8—31no—
124C2×C3×C8C22×D311yescharacteristic
125C2×C3×C8C22×D311yescharacteristic
126C3×C42—31no—
127#215—122no—
128(C2×D3)⋊C4—121no—
129(C2×D3)⋊C4—121no—
130(C2×D3)⋊C4—121no—
131(C2×D3)⋊C4—121no—
132C4⋊Dic3—61no—
133C4⋊Dic3—61no—
134C4⋊Dic3—121no—
135C4⋊Dic3—121no—
136Dic3⋊C4—121no—
137C4×Dic3—121no—
138C4×Dic3—121no—
139C4×Dic3D1211yescharacteristic
140C2×C3⋊C8D1211yescharacteristic
141Dic12—21no—
142Dic12—21no—
143Dic12—21no—
144Dic12#6712yes—
145D24—62no—
146D24—61no—
147D24—61no—
148D24—61no—
149D24—61no—
150D24—121no—
151#204—122no—
152C3×C16—21no—
153C3×C16—21no—
154C3×C16—41no—
155C3×C16—61no—
156C3⋊C16—21no—
157C22×C32C2×D811yescharacteristic
158C2×C3⋊D3—81no—
159C2×C3⋊D3—81no—
160C2×C3⋊D3—81no—
161C32×C4#12111yescharacteristic
162C32×C4AGL(1,ℤ/8)11yescharacteristic
163C3⋊Dic3—81no—
164C3×Dic3—21no—
165C3×Dic3—21no—
166C3×Dic3—42no—
167C3×Dic3—81no—
168C2×Q16—31no—
169C2×Q16—31no—
170C2×SD16—181no—
171C2×D8—91no—
172#124—181no—
173C4×Q8—181no—
174Q32—62no—
175SD32—182no—
176C2×C16—31no—
177C2×C16D3211yescharacteristic
178#107—91no—
179#103—181no—
180C4×C8—31no—
181C22×D3—121no—
182C22×D3—121no—
183C22×D3—241no—
184C3×Q8—62no—
185C3×Q8—121no—
186C3×Q8—121no—
187C3×Q8—121no—
188C2×C3×C4—21no—
189C2×C3×C4—31no—
190C2×C3×C4—31no—
191C2×C3×C4—121no—
192C2×C3×C4—121no—
193C2×C3×C4C2×D1211yescharacteristic
194C2×C3×C4D3×D411yescharacteristic
195C2×Dic3—41no—
196C2×Dic3—41no—
197C2×Dic3—121no—
198C2×Dic3—121no—
199C2×Dic3—241no—
200C2×Dic3D2411yescharacteristic
201C2×Dic3D2411yescharacteristic
202D12—122no—
203D12—121no—
204D12—121no—
205D12—121no—
206D12—121no—
207D12—241no—
208Dic6—22no—
209Dic6—41no—
210Dic6—41no—
211Dic6—41no—
212C3×C8—21no—
213C3×C8—21no—
214C3×C8—61no—
215C3×C8D3×D411yescharacteristic
216C3×C8#23711yescharacteristic
217C3×C8#23911yescharacteristic
218C3×C8C2×#6711yescharacteristic
219C3⋊C8—21no—
220C2×C32#45911yescharacteristic
221C2×C32#50811yescharacteristic
222C2×C32#51011yescharacteristic
223C3⋊D3—161no—
224C2×Q8—61no—
225C2×Q8—61no—
226C2×D4—181no—
227Q16—32no—
228Q16—61no—
229Q16—61no—
230Q16—61no—
231SD16—362no—
232D8—181no—
233D8—181no—
234C2×C8—31no—
235C2×C8C2×D3211yescharacteristic
236C4⋊C4—181no—
237C4⋊C4—361no—
238C22⋊C4—361no—
239C22⋊C4—361no—
240C42—31no—
241C42—361no—
242C16—21no—
243C16—61no—
244C22×C3—21no—
245C22×C3C2×D2411yescharacteristic
246C22×C3D3×D811yescharacteristic
247C2×D3—242no—
248C2×D3—241no—
249C2×D3—241no—
250C2×D3—241no—
251C2×D3—241no—
252C2×D3—241no—
253C2×D3—241no—
254C2×D3—481no—
255C2×D3—481no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—61no—
259C3×C4—61no—
260C3×C4—122no—
261C3×C4—241no—
262C3×C4#89511yescharacteristic
263C3×C4#90811yescharacteristic
264C3×C4#91111yescharacteristic
265C3×C4#93911yescharacteristic
266Dic3—21no—
267Dic3—21no—
268Dic3—42no—
269Dic3—81no—
270Dic3—241no—
271Dic3—241no—
272Dic3—481no—
273C32#221111yescharacteristic, complemented, Sylow
274C23—361no—
275Q8—62no—
276Q8—121no—
277Q8—121no—
278Q8—121no—
279D4—361no—
280D4—361no—
281C2×C4—31no—
282C2×C4—31no—
283C2×C4—121no—
284C2×C4—121no—
285C2×C4—361no—
286C2×C4D3×D1211yescharacteristic
287C8—61no—
288C8#379611yescharacteristic
289C8D3×#6711yescharacteristic
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3#484311yescharacteristic
294C2×C3#490411yescharacteristic
295C2×C3#490911yescharacteristic
296C2×C3#491811yescharacteristic
297C2×C3#491911yescharacteristic
298C2×C3#515011yescharacteristic
299D3—482no—
300D3—481no—
301D3—481no—
302C22—721no—
303C22—721no—
304C22—721no—
305C22D3×D2411yescharacteristic
306C4—61no—
307C4—61no—
308C4—122no—
309C4—241no—
310C4—721no—
311C4#6379511yescharacteristic
312C4#6388611yescharacteristic
313C3—21no—
314C3#6929411yescharacteristic, complemented
315C3#7149811yescharacteristic, complemented
316C2—1441no—
317C2#1059023811yescharacteristic
318C2#1059024311yescharacteristic
319C2#1059075311yescharacteristic
subgroupG/H
centerC22D3×D24
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×C16C22
socleC22×C32C2×D8
prime radicalC2×#3745C22
hypercenterC2×C16D32
hypocenterC32#2211
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
1. C2×C3×Dic24C2semidirect
3. Dic3×Dic12C2semidirect
6. C3×Dic3⋊C16C2semidirect
7. #10589118C2semidirect
27. C2×Dic24D3semidirect
37. Dic3⋊C16D3semidirect
273. C32#2211semidirect
314. C3#69294semidirect
315. C3#71498semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Dic242
#105908652
Dic3×Dic122
C2×#635492
#105893752
C3×Dic3⋊C162
#105891182
#714983
#692943