Finite Group Databasebeta

← #11793992

Subgroups — #11793992

Order 1152.

585 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 585 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C3×#5748C211yesmaximal, characteristic
2#10592818C211yesmaximal, characteristic, complemented
3#10591231C212yesmaximal, complemented
4#10591083C212yesmaximal, complemented
5C3×#4557C211yesmaximal, characteristic, complemented
6#72115—31nomaximal
7#68698—31nomaximal
8C2×C3×#235C2212yes—
9C2×C32×M16C2211yescharacteristic
10#64135C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C3×#926C2212yes—
13C3×#909—22no—
14C3×#908—22no—
15C3×#904—22no—
16#63641—22no—
17#63580—24no—
18#63565—22no—
19#63562—22no—
20C3×#575—31no—
21#5748D311yescharacteristic
22#5240—32no—
23#5233—32no—
24#5119—31no—
25#5119—31no—
26#5119—61no—
27#5006—32no—
28#5002—32no—
29C3×H(3,ℤ/4)—31no—
30#4557D311yescharacteristic, complemented
31C22×C32×C4C2311yescharacteristic
32C2×C3×#67—22no—
33C3×#235—22no—
34C3×#235—22no—
35C3×#235—22no—
36C3×#235—22no—
37C2×C3×D12D412yes—
38C2×C3×C4×D3—22no—
39C2×C3×Dic6D412yes—
40C32×M16—22no—
41C2×C32×C8D412yes—
42#3757D412yes—
43C4⋊(C3⋊Dic3)—21no—
44C4×C3⋊Dic3—21no—
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)—22no—
47C3×#217—22no—
48C3×C4⋊Dic3—22no—
49C3×C4×Dic3—22no—
50C3×Dic12—22no—
51C3×D24—22no—
52C3×#204—24no—
53#2053—91noSylow
54C2×C3×#41—32no—
55C2×#235C2×D312yes—
56C3×#137—62no—
57C3×AGL(1,ℤ/8)—62no—
58C3×#135—62no—
59C2×C3×M16—21no—
60C2×C3×M16C2×D311yescharacteristic
61C2×C3×M16C2×D311yescharacteristic
62C3×#117—32no—
63#926—31no—
64#926—31no—
65#926—61no—
66#926C2×D312yes—
67C22×C3⋊C8—31no—
68C22×C3⋊C8—31no—
69C22×C3⋊C8—61no—
70#909—22no—
71#908—22no—
72#904—22no—
73#835—62no—
74#834—64no—
75#832—62no—
76Dic3⋊C8—64no—
77Dic3⋊C8—62no—
78Dic3⋊C8—62no—
79#810—62no—
80#809—62no—
81#806—64no—
82C23×C32C2×D411yescharacteristic
83C22×C3×D3—22no—
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4C2×D412yes—
86C2×C32×C4#4112yes—
87C2×C32×C4#4111yescharacteristic
88C2×C3⋊Dic3—22no—
89C3×#67—42no—
90C3×#67—42no—
91C2×C3×Dic3—22no—
92C2×C3×Dic3—42no—
93C3×D12—22no—
94C3×D12—22no—
95C3×C4×D3—42no—
96C3×C4×D3—42no—
97C3×Dic6—22no—
98C3×Dic6—22no—
99C32×C8—22no—
100C3⋊(C3⋊C8)—41no—
101#575—31no—
102#424—91no—
103#416—92no—
104#410—92no—
105H(3,ℤ/4)—31no—
106C3×#41—62no—
107C3×#41—62no—
108C3×#41—62no—
109C3×#41—62no—
110C2×C3×Q8—32no—
111C2×C3×D4—32no—
112C2×C3×D4—62no—
113C22×C3×C4—21no—
114C22×C3×C4—62no—
115C22×C3×C4C22×D311yescharacteristic
116C22×C3×C4C22×D311yescharacteristic
117C2×#67—22no—
118#235—22no—
119#235—22no—
120#235—22no—
121#235—22no—
122C2×D12#6712yes—
123C2×C4×D3—22no—
124C2×Dic6#6712yes—
125C3×Q16—62no—
126C3×SD16—64no—
127C3×D8—62no—
128C3×M16—22no—
129C3×M16—22no—
130C3×M16—42no—
131C2×C3×C8—22no—
132C2×C3×C8D1212yes—
133C2×C3×C8#6712yes—
134C3×C4⋊C4—62no—
135C3×C22⋊C4—62no—
136C3×C42—62no—
137#217—22no—
138#217—32no—
139#217—32no—
140#217—62no—
141C4⋊Dic3—22no—
142C4⋊Dic3—62no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4×Dic3—22no—
146C4×Dic3—62no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C2×C3⋊C8—62no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—62no—
152C2×C3⋊C8—62no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—122no—
155Dic12—22no—
156D24—22no—
157#204—24no—
158C22×C32—41no—
159C22×C32#12112yes—
160C22×C32#12111yescharacteristic
161C2×C3×D3—42no—
162C2×C3×D3—82no—
163C32×C4#12011yescharacteristic
164C32×C4#12312yes—
165C32×C4#12411yescharacteristic
166C3⋊Dic3—42no—
167C3×Dic3—42no—
168C3×Dic3—82no—
169C2×#41—32no—
170#137—62no—
171AGL(1,ℤ/8)—62no—
172#135—62no—
173C2×M16D3211yescharacteristic
174C22×C8—91no—
175#117—32no—
176#117—91no—
177C4⋊C8—182no—
178#103—182no—
179#102—182no—
180#99—184no—
181C23×C3—21no—
182C23×C3—62no—
183C23×C3D3×D411yescharacteristic
184C23×C3D3×D411yescharacteristic
185C22×D3—22no—
186C3×Q8—62no—
187C3×Q8—62no—
188C3×D4—62no—
189C3×D4—62no—
190C3×D4—122no—
191C3×D4—122no—
192C2×C3×C4—22no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—22no—
196C2×C3×C4—62no—
197C2×C3×C4—122no—
198C2×C3×C4—122no—
199C2×C3×C4—122no—
200C2×C3×C4C2×D1211yescharacteristic
201C2×C3×C4#23512yes—
202C2×C3×C4D3×D412yes—
203C2×C3×C4#23712yes—
204C2×C3×C4#23711yescharacteristic
205C2×C3×C4#23911yescharacteristic
206C2×C3×C4C2×#6711yescharacteristic
207C2×C3×C4C2×#6712yes—
208#67—42no—
209#67—42no—
210C2×Dic3—22no—
211C2×Dic3—42no—
212C2×Dic3—64no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215D12—22no—
216D12—22no—
217C4×D3—42no—
218C4×D3—42no—
219Dic6—22no—
220Dic6—22no—
221C3×C8—22no—
222C3×C8—22no—
223C3×C8—42no—
224C3⋊C8—122no—
225C3⋊C8—121no—
226C3⋊C8—121no—
227C2×C32—21no—
228C2×C32—22no—
229C2×C32#39411yescharacteristic
230C3×D3—82no—
231#41—62no—
232#41—62no—
233#41—62no—
234#41—62no—
235C2×Q8—32no—
236C2×D4—32no—
237C2×D4—62no—
238C22×C4—62no—
239C22×C4C2×D3211yescharacteristic
240Q16—62no—
241SD16—64no—
242D8—62no—
243M16—22no—
244C2×C8—181no—
245C2×C8—182no—
246C2×C8#62612yes—
247C4⋊C4—62no—
248C4⋊C4—181no—
249C22⋊C4—62no—
250C22⋊C4—92no—
251C42—62no—
252C42—181no—
253C22×C3—22no—
254C22×C3—21no—
255C22×C3—41no—
256C22×C3—41no—
257C22×C3—42no—
258C22×C3—122no—
259C22×C3—242no—
260C22×C3#88412yes—
261C22×C3#89511yescharacteristic
262C22×C3#93811yescharacteristic
263C22×C3#93912yes—
264C2×D3—42no—
265C2×D3—82no—
266C3×C4—21no—
267C3×C4—22no—
268C3×C4—21no—
269C3×C4—122no—
270C3×C4—242no—
271C3×C4#87511yescharacteristic
272C3×C4#88211yescharacteristic
273C3×C4#89412yes—
274C3×C4#93512yes—
275C3×C4#93611yescharacteristic
276C3×C4#95311yescharacteristic
277Dic3—42no—
278Dic3—82no—
279Dic3—124no—
280Dic3—122no—
281Dic3—122no—
282C32#205311yescharacteristic, complemented, Sylow
283C23—62no—
284C23#380211yescharacteristic
285Q8—62no—
286Q8—62no—
287D4—62no—
288D4—62no—
289D4—122no—
290D4—122no—
291C2×C4—62no—
292C2×C4—122no—
293C2×C4—122no—
294C2×C4—122no—
295C2×C4—182no—
296C2×C4#379512yes—
297C2×C4#379611yescharacteristic
298C2×C4C2×#62611yescharacteristic
299C2×C4D3×#6712yes—
300C8—22no—
301C8—361no—
302C2×C3—22no—
303C2×C3—22no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—22no—
307C2×C3—21no—
308C2×C3—42no—
309C2×C3—242no—
310C2×C3#467211yescharacteristic
311C2×C3#522211yescharacteristic
312D3—82no—
313C22—41no—
314C22—122no—
315C22—242no—
316C22#6388512yes—
317C22#6391611yescharacteristic
318C4—122no—
319C4—242no—
320C4—362no—
321C4#6386011yescharacteristic
322C4#6388412yes—
323C4#6397711yescharacteristic
324C3—21no—
325C3#6869811yescharacteristic, complemented
326C3#7211511yescharacteristic, complemented
327C2—22no—
328C2—21no—
329C2—242no—
330C2#1059130211yescharacteristic
subgroupG/H
centerC4#63860
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#394
prime radicalC3×#5748C2
hypercenterC2×M16D32
hypocenterC32#2053
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10592818C2semidirect
3. #10591231C2semidirect
4. #10591083C2semidirect
5. C3×#4557C2semidirect
30. #4557D3semidirect
282. C32#2053semidirect
325. C3#68698semidirect
326. C3#72115semidirect

Maximal subgroups

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

subgroupindex
C3×#57482
#105928182
#105912312
#105910832
C3×#45572
#721153
#686983