Finite Group Databasebeta

← #11797968

Subgroups — #11797968

Order 1152.

329 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 329 conjugacy classes of subgroups — too many to draw. Only its 78 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×#4869C211yesmaximal, characteristic, complemented
2#10590916C211yesmaximal, characteristic, complemented
3#10590630C211yesmaximal, characteristic
4#10589353C211yesmaximal, characteristic, complemented
5C3×#4488C211yesmaximal, characteristic, complemented
6#10589127C211yesmaximal, characteristic, complemented
7#10589105C211yesmaximal, characteristic, complemented
8#70918—31nomaximal
9#69249—31nomaximal
10C3×#904C2211yescharacteristic
11C2×C3×D24C2211yescharacteristic
12C3×#893—21no—
13#63814—21no—
14C32×#106C2211yescharacteristic
15#63646C2211yescharacteristic
16#63639C2211yescharacteristic
17C3×#815C2211yescharacteristic
18C3×#812C2211yescharacteristic
19C3×#809—21no—
20#63569—21no—
21#63547C412yescomplemented
22#63545C412yescomplemented
23C3×#442—31no—
24#5197—31no—
25#5193—31no—
26#5147—31no—
27#4869D311yescharacteristic, complemented
28#4717—31no—
29C3×#360—31no—
30#4563—31no—
31#4516—31no—
32#4512—31no—
33#4488D311yescharacteristic, complemented
34#4487—31no—
35#4487—31no—
36#4487—61no—
37#4466—31no—
38C3×#235—21no—
39C2×C3×D12—21no—
40C2×C3×C4×D3—41no—
41C2×C32×C8C2311yescharacteristic
42C32×C4⋊C4—21no—
43#3748—21no—
44C3×(C2×D3)⋊C4—41no—
45C3×C4×Dic3D411yescharacteristic
46C2×C3×C3⋊C8D411yescharacteristic
47C3×Dic12C2×C411yescharacteristic, complemented
48C3×D24—21no—
49C3×D24C2×C412yes—
50C3×D24C2×C411yescharacteristic, complemented
51C3×#204—21no—
52#3711—41no—
53D3×C3⋊C8—41no—
54C3⋊(C3⋊C16)C2×C412yescomplemented
55C3×C3⋊C16—21no—
56AGL(1,ℤ/16)—91noSylow
57C3×#135—31no—
58C2×C3×D8—31no—
59C3×C4×D4—61no—
60#948—61no—
61#904C2×D311yescharacteristic
62C2×D24C2×D311yescharacteristic
63#901—61no—
64#893—21no—
65C3×M32—31no—
66C3×#106—21no—
67C3×#106C2×D311yescharacteristic
68C3×#106C2×D311yescharacteristic
69C3×#102—61no—
70C3×#97—31no—
71#837—61no—
72#828—32no—
73#827—32no—
74#826—32no—
75#826—32no—
76#819—31no—
77#819—31no—
78#819—61no—
79#815C2×D311yescharacteristic
80#812—31no—
81#812—31no—
82#812—61no—
83#812C2×D311yescharacteristic
84#809—21no—
85#805—61no—
86C22×C3×D3—41no—
87C2×C32×C4—41no—
88C2×C32×C4C2×D411yescharacteristic
89C3×#67—41no—
90C2×C3×Dic3—21no—
91C3×D12—21no—
92C3×D12—22no—
93C3×D12—41no—
94C3×C4×D3—41no—
95C3×C4×D3—82no—
96C3×Dic6—21no—
97C32×C8C22×C411yescharacteristic
98C32×C8#4111yescharacteristic
99C3⋊(C3⋊C8)—41no—
100C3×C3⋊C8—21no—
101#509—91no—
102#444—91no—
103#442—31no—
104#365—91no—
105#361—91no—
106#360—31no—
107#347—91no—
108C3×#41—61no—
109C2×C3×D4—61no—
110C22×C3×C4—121no—
111#235—21no—
112C2×D12—21no—
113C2×C4×D3—41no—
114C3×Q16—31no—
115C3×SD16—61no—
116C3×D8—31no—
117C3×D8—32no—
118C3×D8—61no—
119C2×C3×C8—21no—
120C2×C3×C8—31no—
121C2×C3×C8C22×D311yescharacteristic
122C2×C3×C8C22×D311yescharacteristic
123C3×C4⋊C4—21no—
124C3×C4⋊C4—21no—
125C3×C4⋊C4—41no—
126C3×C22⋊C4—121no—
127C3×C42—31no—
128(C2×D3)⋊C4—41no—
129C4×Dic3#6711yescharacteristic
130#208—61no—
131#208—61no—
132#208—121no—
133#208—121no—
134C2×C3⋊C8—121no—
135C2×C3⋊C8#6711yescharacteristic
136Dic12C4×D311yescharacteristic, complemented
137D24—21no—
138D24C4×D312yes—
139D24C4×D311yescharacteristic, complemented
140#204—21no—
141ΓL(1,𝔽25)—121no—
142D3×C8—121no—
143C3×C16—61no—
144C3⋊C16—21no—
145C3⋊C16—32no—
146C3⋊C16—32no—
147C3⋊C16—62no—
148C22×C32AGL(1,ℤ/8)11yescharacteristic
149C2×C3×D3—41no—
150C2×C3×D3—42no—
151C2×C3×D3—81no—
152C2×C3×D3—81no—
153C32×C4—81no—
154C32×C4C4×D411yescharacteristic
155C32×C4AGL(1,ℤ/8)11yescharacteristic
156C3×Dic3—41no—
157C3×Dic3—41no—
158#135—31no—
159C2×D8—31no—
160#131—181no—
161C4×D4—61no—
162SD32—92no—
163D16—92no—
164M32—31no—
165M32—91no—
166#108—91no—
167#106D3211yescharacteristic
168#104—181no—
169#102—61no—
170#97—31no—
171C23×C3—121no—
172C22×D3—41no—
173C3×Q8—61no—
174C3×D4—62no—
175C3×D4—61no—
176C3×D4—121no—
177C3×D4—121no—
178C2×C3×C4—21no—
179C2×C3×C4—41no—
180C2×C3×C4—41no—
181C2×C3×C4—61no—
182C2×C3×C4—81no—
183C2×C3×C4—121no—
184C2×C3×C4—242no—
185C2×C3×C4D3×D411yescharacteristic
186C2×C3×C4C2×#6711yescharacteristic
187#67—41no—
188C2×Dic3—21no—
189D12—21no—
190D12—22no—
191D12—41no—
192C4×D3—41no—
193C4×D3—82no—
194Dic6—21no—
195C3×C8—21no—
196C3×C8—21no—
197C3×C8—61no—
198C3×C8C2×C4×D311yescharacteristic
199C3×C8C2×C4×D311yescharacteristic
200C3×C8#23511yescharacteristic
201C3×C8#23711yescharacteristic
202C3⋊C8—21no—
203C3⋊C8—121no—
204C3⋊C8—121no—
205C3⋊C8—241no—
206C2×C32—21no—
207C2×C32#44211yescharacteristic
208C3×D3—81no—
209C3×D3—82no—
210#41—61no—
211C2×D4—61no—
212C22×C4—121no—
213Q16—31no—
214SD16—61no—
215D8—31no—
216D8—32no—
217D8—61no—
218M16—181no—
219M16—361no—
220C2×C8—31no—
221C2×C8—361no—
222C2×C8C2×D3211yescharacteristic
223C4⋊C4—21no—
224C22⋊C4—121no—
225C42—31no—
226C16—61no—
227C16—92no—
228C22×C3—21no—
229C22×C3—121no—
230C22×C3—122no—
231C22×C3—241no—
232C22×C3—241no—
233C22×C3#91111yescharacteristic
234C22×C3#93211yescharacteristic
235C2×D3—42no—
236C2×D3—41no—
237C2×D3—81no—
238C2×D3—81no—
239C3×C4—21no—
240C3×C4—21no—
241C3×C4—81no—
242C3×C4—81no—
243C3×C4—121no—
244C3×C4—121no—
245C3×C4—161no—
246C3×C4#67⋊C411yescharacteristic
247C3×C4#91411yescharacteristic
248C3×C4C4×#6711yescharacteristic
249C3×C4#94911yescharacteristic
250Dic3—41no—
251Dic3—41no—
252C32AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
253C23—121no—
254Q8—61no—
255D4—62no—
256D4—61no—
257D4—121no—
258D4—121no—
259C2×C4—41no—
260C2×C4—61no—
261C2×C4—121no—
262C2×C4—242no—
263C2×C4D3×#6711yescharacteristic
264C8—61no—
265C8—361no—
266C8#379511yescharacteristic
267C8C4×D3211yescharacteristic
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—41no—
272C2×C3—241no—
273C2×C3—242no—
274C2×C3#478511yescharacteristic
275C2×C3#501411yescharacteristic
276D3—82no—
277D3—81no—
278C22—121no—
279C22—122no—
280C22—241no—
281C22—241no—
282C22#6393211yescharacteristic
283C4—81no—
284C4—121no—
285C4—121no—
286C4#6387911yescharacteristic
287C4#6393911yescharacteristic
288C3—21no—
289C3#6924911yescharacteristic, complemented
290C3#7091811yescharacteristic, complemented
291C2—21no—
292C2—242no—
293C2—241no—
294C2#1059045511yescharacteristic
subgroupG/H
centerC2#10590455
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#106C22
socleC2×C32#442
prime radical#10590630C2
cosocleC2×C32×C8C23
hypercenter#106D32
hypocenterC32AGL(1,ℤ/16)
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
1. C3×#4869C2semidirect
2. #10590916C2semidirect
4. #10589353C2semidirect
5. C3×#4488C2semidirect
6. #10589127C2semidirect
7. #10589105C2semidirect
21. #63547C4semidirect
22. #63545C4semidirect
27. #4869D3semidirect
33. #4488D3semidirect
47. C3×Dic12C2×C4semidirect
50. C3×D24C2×C4semidirect
54. C3⋊(C3⋊C16)C2×C4semidirect
136. Dic12C4×D3semidirect
139. D24C4×D3semidirect
252. C32AGL(1,ℤ/16)semidirect
289. C3#69249semidirect
290. C3#70918semidirect

Maximal subgroups

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

subgroupindex
C3×#48692
#105909162
#105906302
#105893532
C3×#44882
#105891272
#105891052
#709183
#692493