Finite Group Databasebeta

← #11797979

Subgroups — #11797979

Order 1152.

374 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 86 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#10592851C211yesmaximal, characteristic, complemented
2C3×#5147C211yesmaximal, characteristic
3#10590920C211yesmaximal, characteristic, complemented
4C3×#4563C211yesmaximal, characteristic, complemented
5#10589137C211yesmaximal, characteristic, complemented
6#10589124C211yesmaximal, characteristic, complemented
7#10589106C211yesmaximal, characteristic, complemented
8#71515—31nomaximal
9#69254—31nomaximal
10C2×C32×D8C2211yescharacteristic
11D4×C3⋊Dic3—21no—
12C3×#904C2211yescharacteristic
13#63815—21no—
14#63659—21no—
15#63644C2211yescharacteristic
16#63642C2211yescharacteristic
17C3×#827C412yescomplemented
18C3×#826C412yescomplemented
19C3×#819C2211yescharacteristic
20C3×#812C2211yescharacteristic
21C3×#812C2211yescharacteristic
22#63568—21no—
23C3×#509—31no—
24#5197—31no—
25#5152—31no—
26#5152—31no—
27#5152—61no—
28#5147D311yescharacteristic
29#4894—31no—
30C3×#361—31no—
31#4566—31no—
32#4563D311yescharacteristic, complemented
33#4518—31no—
34#4513—31no—
35#4512—31no—
36#4512—31no—
37#4494—31no—
38C2×C32×D4—21no—
39C22×C3⋊Dic3—41no—
40C3×#235—21no—
41C32×D8—21no—
42C32×D8C2×C412yes—
43C2×C32×C8C2311yescharacteristic
44#3757—41no—
45C4⋊(C3⋊Dic3)—21no—
46C4×C3⋊Dic3D411yescharacteristic
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48C3×#208—21no—
49C3×Dic12C2×C411yescharacteristic, complemented
50C3×D24C2×C411yescharacteristic, complemented
51C3×#204—21no—
52#3711—41no—
53D3×C3⋊C8—41no—
54C3×C3⋊C16—21no—
55C3×C3⋊C16C2×C412yescomplemented
56AGL(1,ℤ/16)—91noSylow
57C3×#135—31no—
58C2×C3×D8—21no—
59C2×C3×D8C2×D311yescharacteristic
60C2×C3×D8C2×D311yescharacteristic
61#948—61no—
62D4×Dic3—61no—
63D4×Dic3—61no—
64D4×Dic3—62no—
65#907—61no—
66#904C2×D311yescharacteristic
67C3×SD32—32no—
68C3×D16—32no—
69C3×M32—31no—
70C3×M32—31no—
71C3×#108—31no—
72#837—61no—
73#832—61no—
74#832—61no—
75#832—62no—
76#827Dic312yescomplemented
77#826Dic312yescomplemented
78#825—61no—
79#819C2×D311yescharacteristic
80#817—31no—
81#817—31no—
82#817—61no—
83#815—31no—
84#815—31no—
85#815—61no—
86#812C2×D311yescharacteristic
87#812C2×D311yescharacteristic
88C23×C32—41no—
89C32×D4—22no—
90C32×D4—41no—
91C2×C32×C4C2×D411yescharacteristic
92C2×C3⋊Dic3—21no—
93C2×C3⋊Dic3—41no—
94C2×C3⋊Dic3—82no—
95C3×#67—41no—
96C3×D12—21no—
97C3×C4×D3—41no—
98C3×Dic6—21no—
99C32×C8C22×C411yescharacteristic
100C32×C8#4111yescharacteristic
101C3⋊(C3⋊C8)—21no—
102C3×C3⋊C8—41no—
103#509—31no—
104#444—91no—
105#442—91no—
106#365—91no—
107#361—31no—
108#360—91no—
109#347—91no—
110C3×#41—61no—
111C2×C3×D4—22no—
112C2×C3×D4—21no—
113C2×C3×D4—21no—
114C22×Dic3—122no—
115C22×Dic3—121no—
116C22×Dic3—121no—
117#235—21no—
118C3×Q16—31no—
119C3×SD16—61no—
120C3×D8—22no—
121C3×D8—21no—
122C3×D8—21no—
123C3×D8—22no—
124C3×D8—31no—
125C3×D8C4×D312yes—
126C3×D8C2×Dic312yes—
127C3×M16—61no—
128C2×C3×C8—21no—
129C2×C3×C8C22×D311yescharacteristic
130C2×C3×C8C22×D311yescharacteristic
131#217—122no—
132#217—121no—
133#217—121no—
134C4⋊Dic3—62no—
135C4⋊Dic3—61no—
136C4⋊Dic3—61no—
137C4×Dic3—31no—
138C4×Dic3—31no—
139C4×Dic3—61no—
140#208—21no—
141#208—121no—
142C2×C3⋊C8—31no—
143C2×C3⋊C8—31no—
144C2×C3⋊C8—61no—
145C2×C3⋊C8—121no—
146Dic12C2×Dic311yescharacteristic, complemented
147D24C2×Dic311yescharacteristic, complemented
148#204—21no—
149ΓL(1,𝔽25)—121no—
150D3×C8—121no—
151C3×C16—32no—
152C3×C16—61no—
153C3⋊C16—21no—
154C3⋊C16C2×Dic312yescomplemented
155C22×C32—42no—
156C22×C32—81no—
157C22×C32—81no—
158C22×C32AGL(1,ℤ/8)11yescharacteristic
159C2×C3×D3—41no—
160C32×C4C4×D411yescharacteristic
161C32×C4AGL(1,ℤ/8)11yescharacteristic
162C3⋊Dic3—41no—
163C3⋊Dic3—81no—
164C3×Dic3—41no—
165#135—31no—
166C2×D8D3211yescharacteristic
167#131—181no—
168C4×D4—181no—
169SD32—32no—
170D16—32no—
171M32—31no—
172M32—31no—
173#108—31no—
174#106—91no—
175#104—181no—
176#102—181no—
177#97—91no—
178C23×C3—42no—
179C23×C3—41no—
180C23×C3—41no—
181C3×Q8—61no—
182C3×D4—24no—
183C3×D4—22no—
184C3×D4—22no—
185C3×D4—42no—
186C3×D4—41no—
187C3×D4—41no—
188C3×D4—61no—
189C3×D4—121no—
190C2×C3×C4—21no—
191C2×C3×C4—121no—
192C2×C3×C4D3×D411yescharacteristic
193C2×C3×C4D3×D411yescharacteristic
194#67—41no—
195C2×Dic3—62no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—122no—
199C2×Dic3—121no—
200C2×Dic3—121no—
201C2×Dic3—244no—
202C2×Dic3—242no—
203C2×Dic3—242no—
204D12—21no—
205C4×D3—41no—
206Dic6—21no—
207C3×C8—21no—
208C3×C8—21no—
209C3×C8—121no—
210C3×C8C2×C4×D311yescharacteristic
211C3×C8#23711yescharacteristic
212C3×C8#23711yescharacteristic
213C3×C8C22×Dic311yescharacteristic
214C3⋊C8—41no—
215C3⋊C8—61no—
216C3⋊C8—61no—
217C3⋊C8—121no—
218C2×C32—21no—
219C2×C32—82no—
220C2×C32#44211yescharacteristic
221C3×D3—81no—
222#41—61no—
223C2×D4—21no—
224C22×C4—361no—
225Q16—31no—
226SD16—61no—
227D8—21no—
228D8—31no—
229D8D3×Dic312yes—
230M16—61no—
231M16—361no—
232C2×C8—91no—
233C2×C8—361no—
234C2×C8C2×D3211yescharacteristic
235C4⋊C4—181no—
236C22⋊C4—361no—
237C42—91no—
238C16—32no—
239C16—61no—
240C22×C3—21no—
241C22×C3—44no—
242C22×C3—42no—
243C22×C3—42no—
244C22×C3—82no—
245C22×C3—81no—
246C22×C3—81no—
247C22×C3—82no—
248C22×C3—81no—
249C22×C3—81no—
250C22×C3—121no—
251C22×C3#91111yescharacteristic
252C22×C3#91411yescharacteristic
253C2×D3—41no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—121no—
257C3×C4#67⋊C411yescharacteristic
258C3×C4#91111yescharacteristic
259C3×C4#91111yescharacteristic
260C3×C4D4×Dic311yescharacteristic
261Dic3—41no—
262Dic3—122no—
263Dic3—121no—
264Dic3—121no—
265Dic3—242no—
266Dic3—241no—
267Dic3—241no—
268C32AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
269C23—41no—
270Q8—61no—
271D4—22no—
272D4—41no—
273D4—61no—
274D4—121no—
275C2×C4—121no—
276C2×C4—181no—
277C2×C4—361no—
278C2×C4—722no—
279C2×C4#381111yescharacteristic
280C8—121no—
281C8—181no—
282C8C2×D3×Dic311yescharacteristic
283C8#380511yescharacteristic
284C2×C3—22no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—84no—
289C2×C3—82no—
290C2×C3—82no—
291C2×C3—241no—
292C2×C3#478511yescharacteristic
293C2×C3#515211yescharacteristic
294D3—81no—
295C22—42no—
296C22—81no—
297C22—81no—
298C22—121no—
299C22#6393711yescharacteristic
300C4—121no—
301C4—361no—
302C4—721no—
303C4#6392711yescharacteristic
304C4#67⋊Dic311yescharacteristic
305C3—21no—
306C3#6925411yescharacteristic, complemented
307C3#7151511yescharacteristic, complemented
308C2—21no—
309C2—82no—
310C2—241no—
311C2#1059143611yescharacteristic
subgroupG/H
centerC2#10591436
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC2×C32×D8C22
socleC2×C32#442
prime radicalC3×#5147C2
cosocleC2×C32×C8C23
hypercenterC2×D8D32
hypocenterC32AGL(1,ℤ/16)
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10592851C2semidirect
3. #10590920C2semidirect
4. C3×#4563C2semidirect
5. #10589137C2semidirect
6. #10589124C2semidirect
7. #10589106C2semidirect
17. C3×#827C4semidirect
18. C3×#826C4semidirect
32. #4563D3semidirect
49. C3×Dic12C2×C4semidirect
50. C3×D24C2×C4semidirect
55. C3×C3⋊C16C2×C4semidirect
76. #827Dic3semidirect
77. #826Dic3semidirect
146. Dic12C2×Dic3semidirect
147. D24C2×Dic3semidirect
154. C3⋊C16C2×Dic3semidirect
268. C32AGL(1,ℤ/16)semidirect
306. C3#69254semidirect
307. C3#71515semidirect

Maximal subgroups

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

subgroupindex
#105928512
C3×#51472
#105909202
C3×#45632
#105891372
#105891242
#105891062
#715153
#692543