Finite Group Databasebeta

← #11799462

Subgroups — #11799462

Order 1152.

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

normal subgroups only

This group has 308 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
1C2×C3×#800C211yesmaximal, characteristic, complemented
2C3×#4901C211yesmaximal, characteristic, complemented
3#10590930C211yesmaximal, characteristic, complemented
4#10590926C211yesmaximal, characteristic
5#10589372C211yesmaximal, characteristic, complemented
6#10589130C211yesmaximal, characteristic, complemented
7#10589127C211yesmaximal, characteristic, complemented
8#71491—31nomaximal
9#71455—31nomaximal
10C2×C3×Dic12C2211yescharacteristic
11C2×C3×D24C2211yescharacteristic
12C3×#901C2211yescharacteristic
13#63827—21no—
14#63823—21no—
15C2×C32×C16C2211yescharacteristic
16#63646C2211yescharacteristic
17#63646C2211yescharacteristic
18C3×#812C2211yescharacteristic
19C3×#800—21no—
20C3×#800—21no—
21C3×#798—21no—
22C3×D3×C16—21no—
23#63560—21no—
24#63558—21no—
25C2×C3×SD32—31no—
26C3×#504—31no—
27#5192—31no—
28#5160—31no—
29#5143—31no—
30#5142—31no—
31C2×#800D311yescharacteristic, complemented
32#4901D311yescharacteristic, complemented
33#4565—31no—
34#4563—31no—
35#4517—31no—
36#4516—31no—
37#4506—31no—
38#4506—31no—
39#4506—61no—
40C3×#235D411yescharacteristic
41C2×C3×D12—21no—
42C2×C3×Dic6—21no—
43C2×C32×C8C2311yescharacteristic
44#3748—21no—
45#3748—21no—
46C3×#208D411yescharacteristic
47C3×Dic12—21no—
48C3×Dic12—21no—
49C3×D24—21no—
50C3×D24—21no—
51C3×ΓL(1,𝔽25)—21no—
52C3×D3×C8—21no—
53#3718—41no—
54#3715—41no—
55#3715—41no—
56#3713—41no—
57C32×C16D411yescharacteristic
58C32×C16D411yescharacteristic
59C3×C3⋊C16—21no—
60#2223—91noSylow
61C2×C3×Q16—31no—
62C2×C3×D8—31no—
63C3×#131—31no—
64#951—61no—
65#949—61no—
66#942—61no—
67#932—61no—
68C2×Dic12C2×D311yescharacteristic
69C2×D24C2×D311yescharacteristic
70#901C2×D311yescharacteristic
71C3×SD32—61no—
72C3×SD32—61no—
73C3×M32—31no—
74C3×M32—61no—
75C2×C3×C16—21no—
76C2×C3×C16—61no—
77C2×C3×C16C2×D311yescharacteristic
78C2×C3×C16C2×D311yescharacteristic
79#836—61no—
80#833—61no—
81#824—61no—
82#823—61no—
83#819—31no—
84#819—31no—
85#819—31no—
86#819—31no—
87#819—61no—
88#819—61no—
89#812C2×D311yescharacteristic
90#800—21no—
91#800—21no—
92#798—21no—
93D3×C16—21no—
94C22×C3×D3—41no—
95C2×C32×C4C2×D411yescharacteristic
96C3×#67—21no—
97C2×C3×Dic3—41no—
98C3×D12—41no—
99C3×D12—41no—
100C3×D12D811yescharacteristic
101C3×C4×D3—21no—
102C3×Dic6—41no—
103C3×Dic6—41no—
104C3×Dic6D811yescharacteristic
105C32×C8C2×D411yescharacteristic
106C32×C8#4111yescharacteristic
107C3⋊(C3⋊C8)—41no—
108C3⋊(C3⋊C8)—41no—
109C3×C3⋊C8—21no—
110C2×SD32—31no—
111#504—31no—
112#473—91no—
113#472—91no—
114#368—91no—
115#362—91no—
116#361—91no—
117C3×#41—31no—
118C2×C3×Q8—61no—
119C2×C3×D4—61no—
120#235D1211yescharacteristic
121C2×D12—21no—
122C2×Dic6—21no—
123C3×Q16—61no—
124C3×Q16—61no—
125C3×D8—61no—
126C3×D8—61no—
127C3×M16—31no—
128C3×M16—61no—
129C2×C3×C8—21no—
130C2×C3×C8—61no—
131C2×C3×C8C22×D311yescharacteristic
132C2×C3×C8C22×D311yescharacteristic
133#216—121no—
134#216—121no—
135#215—121no—
136#215—121no—
137#214—121no—
138#214—121no—
139#213—121no—
140#213—121no—
141#208—61no—
142#208—61no—
143#208—61no—
144#208—61no—
145#208—121no—
146#208—121no—
147#208D1211yescharacteristic
148Dic12—21no—
149Dic12—21no—
150D24—21no—
151D24—21no—
152ΓL(1,𝔽25)—21no—
153D3×C8—21no—
154C3×C16—21no—
155C3×C16—21no—
156C3×C16—61no—
157C3×C16#6711yescharacteristic
158C3×C16#6711yescharacteristic
159C3×C16#6711yescharacteristic
160C3×C16#6711yescharacteristic
161C3⋊C16—21no—
162C22×C32#13511yescharacteristic
163C2×C3×D3—21no—
164C2×C3×D3—81no—
165C2×C3×D3—161no—
166C32×C4#12111yescharacteristic
167C32×C4C2×D811yescharacteristic
168C3×Dic3—21no—
169C3×Dic3—81no—
170#137—181no—
171AGL(1,ℤ/8)—181no—
172C2×Q16—31no—
173C2×D8—31no—
174#131—31no—
175SD32—61no—
176SD32—61no—
177M32—31no—
178M32—61no—
179C2×C16—61no—
180C2×C16D3211yescharacteristic
181#108—91no—
182#108—91no—
183#101—181no—
184#100—181no—
185C23×C3—121no—
186C22×D3—41no—
187C3×Q8—31no—
188C3×Q8—121no—
189C3×Q8—121no—
190C3×D4—31no—
191C3×D4—61no—
192C3×D4—121no—
193C3×D4—121no—
194C2×C3×C4—21no—
195C2×C3×C4—61no—
196C2×C3×C4—121no—
197C2×C3×C4C2×D1211yescharacteristic
198C2×C3×C4D3×D411yescharacteristic
199#67—21no—
200C2×Dic3—41no—
201D12—41no—
202D12—41no—
203D12D2411yescharacteristic
204C4×D3—21no—
205Dic6—41no—
206Dic6—41no—
207Dic6D2411yescharacteristic
208C3×C8—21no—
209C3×C8—21no—
210C3×C8—61no—
211C3×C8#23511yescharacteristic
212C3×C8#23711yescharacteristic
213C3×C8C2×#6711yescharacteristic
214C3×C8C2×#6711yescharacteristic
215C3⋊C8—21no—
216C3⋊C8—121no—
217C3⋊C8—121no—
218C3⋊C8—121no—
219C3⋊C8—121no—
220C3⋊C8—241no—
221C3⋊C8—241no—
222C2×C32—21no—
223C2×C32#46611yescharacteristic
224C3×D3—41no—
225C3×D3—161no—
226#41—31no—
227C2×Q8—61no—
228C2×D4—61no—
229Q16—61no—
230Q16—61no—
231Q16—361no—
232SD16—361no—
233SD16—361no—
234D8—61no—
235D8—61no—
236D8—361no—
237M16—31no—
238M16—61no—
239M16—181no—
240M16—181no—
241C2×C8—61no—
242C2×C8C2×D3211yescharacteristic
243C16—61no—
244C16#62511yescharacteristic
245C16#62511yescharacteristic
246C22×C3—21no—
247C22×C3—61no—
248C22×C3—241no—
249C22×C3—481no—
250C22×C3#90411yescharacteristic
251C22×C3#91211yescharacteristic
252C2×D3—21no—
253C2×D3—81no—
254C2×D3—161no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—61no—
258C3×C4—241no—
259C3×C4C2×D2411yescharacteristic
260C3×C4D3×D811yescharacteristic
261C3×C4#93011yescharacteristic
262C3×C4#93811yescharacteristic
263Dic3—21no—
264Dic3—81no—
265C32#222311yescharacteristic, complemented, Sylow
266C23—121no—
267Q8—31no—
268Q8—121no—
269Q8—121no—
270D4—31no—
271D4—61no—
272D4—121no—
273D4—121no—
274C2×C4—61no—
275C2×C4—121no—
276C2×C4D3×D1211yescharacteristic
277C8—61no—
278C8—361no—
279C8—361no—
280C8#379511yescharacteristic
281C8C2×#62511yescharacteristic
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—41no—
286C2×C3—121no—
287C2×C3—481no—
288C2×C3#511511yescharacteristic
289C2×C3#515711yescharacteristic
290D3—41no—
291D3—161no—
292C22—61no—
293C22—241no—
294C22—481no—
295C22#6380711yescharacteristic
296C4—61no—
297C4—241no—
298C4D3×D2411yescharacteristic
299C4#6390811yescharacteristic
300C3—21no—
301C3#7145511yescharacteristic, complemented
302C3#7149111yescharacteristic, complemented
303C2—21no—
304C2—121no—
305C2—481no—
306C2#1059083111yescharacteristic
subgroupG/H
centerC2#10590831
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×C16C22
socleC2×C32#466
prime radical#10590926C2
hypercenterC2×C16D32
hypocenterC32#2223
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#800C2semidirect
2. C3×#4901C2semidirect
3. #10590930C2semidirect
5. #10589372C2semidirect
6. #10589130C2semidirect
7. #10589127C2semidirect
31. C2×#800D3semidirect
32. #4901D3semidirect
265. C32#2223semidirect
301. C3#71455semidirect
302. C3#71491semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8002
C3×#49012
#105909302
#105909262
#105893722
#105891302
#105891272
#714913
#714553