Finite Group Databasebeta

← #11799474

Subgroups — #11799474

Order 1152.

315 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 315 conjugacy classes of subgroups — too many to draw. Only its 72 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×#4907C211yesmaximal, characteristic, complemented
2#10590932C211yesmaximal, characteristic, complemented
3#10590926C211yesmaximal, characteristic
4C2×#63548C211yesmaximal, characteristic, complemented
5#10589383C211yesmaximal, characteristic, complemented
6C3×#4516C211yesmaximal, characteristic, complemented
7#10589143C211yesmaximal, characteristic, complemented
8#71455—31nomaximal
9#69261—31nomaximal
10C2×#3746C2211yescharacteristic
11C2×C3×D24C2211yescharacteristic
12C3×#901C2211yescharacteristic
13#63831—21no—
14#63823—21no—
15C32×M32C2211yescharacteristic
16#63646C2211yescharacteristic
17C3×#819C2211yescharacteristic
18C2×C3×C3⋊C16C2211yescharacteristic
19C3×#798—21no—
20C3×D3×C16—21no—
21#63561—21no—
22#63558—21no—
23#63548—21no—
24#63548—21no—
25C3×#504—31no—
26#5160—31no—
27C2×#827—31no—
28#5143—31no—
29#5142—31no—
30#4907D311yescharacteristic, complemented
31C2×#800—31no—
32#4896—31no—
33C3×#361—31no—
34#4517—31no—
35#4517—31no—
36#4517—61no—
37#4516D311yescharacteristic, complemented
38#4506—31no—
39#4493—31no—
40C2×#634—21no—
41C3×#235D411yescharacteristic
42C2×C3×D12—21no—
43C2×C32×C8C2311yescharacteristic
44#3748—21no—
45#3746—21no—
46#3746—21no—
47C3×#208—21no—
48C3×#208D411yescharacteristic
49C3×D24—21no—
50C3×D24—21no—
51C3×ΓL(1,𝔽25)—21no—
52C3×D3×C8—21no—
53#3719—41no—
54#3716—41no—
55#3715—41no—
56#3713—41no—
57C32×C16—21no—
58C3×C3⋊C16D411yescharacteristic
59C3×C3⋊C16D411yescharacteristic
60#2223—91noSylow
61C2×C3×D8—31no—
62C3×#131—31no—
63#951—61no—
64#949—61no—
65#932—61no—
66#909—61no—
67C2×Dic12—31no—
68C2×Dic12—31no—
69C2×Dic12—61no—
70C2×D24C2×D311yescharacteristic
71#901C2×D311yescharacteristic
72C3×M32—21no—
73C3×M32—61no—
74C3×M32C2×D311yescharacteristic
75C3×M32C2×D311yescharacteristic
76C2×C3×C16—31no—
77C2×C3×C16—61no—
78C3×#108—31no—
79#833—61no—
80#827—61no—
81#827—61no—
82#824—61no—
83#824—61no—
84#823—61no—
85#819—31no—
86#819—31no—
87#819—61no—
88#819C2×D311yescharacteristic
89C2×C3⋊C16C2×D311yescharacteristic
90#800—61no—
91#800—61no—
92#798—21no—
93D3×C16—21no—
94C22×C3×D3—41no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C3⋊Dic3—41no—
97#634—41no—
98#634—41no—
99C3×#67—21no—
100C3×D12—41no—
101C3×D12—41no—
102C3×D12D811yescharacteristic
103C3×C4×D3—21no—
104C3×Dic6D811yescharacteristic
105C32×C8C2×D411yescharacteristic
106C32×C8#4111yescharacteristic
107C3⋊(C3⋊C8)—41no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—41no—
110C2×SD32—91no—
111#504—31no—
112#473—91no—
113#472—91no—
114#368—91no—
115#362—91no—
116#361—31no—
117C3×#41—31no—
118C2×C3×D4—61no—
119#235D1211yescharacteristic
120C2×D12—21no—
121C2×Dic6—61no—
122C2×Dic6—61no—
123C2×Dic6—121no—
124C3×D8—61no—
125C3×D8—61no—
126C3×M16—31no—
127C3×M16—61no—
128C3×M16—61no—
129C2×C3×C8—21no—
130C2×C3×C8—61no—
131C2×C3×C8C22×D311yescharacteristic
132C2×C3×C8C22×D311yescharacteristic
133#216—121no—
134#215—121no—
135#214—121no—
136#214—121no—
137#213—121no—
138#213—121no—
139#208—21no—
140#208—61no—
141#208—61no—
142#208—121no—
143#208D1211yescharacteristic
144Dic12—62no—
145Dic12—61no—
146Dic12—61no—
147Dic12—61no—
148Dic12—61no—
149Dic12—121no—
150Dic12—121no—
151D24—21no—
152D24—21no—
153#204—121no—
154ΓL(1,𝔽25)—21no—
155D3×C8—21no—
156C3×C16—21no—
157C3×C16—21no—
158C3×C16—31no—
159C3×C16—31no—
160C3×C16—41no—
161C3⋊C16#6711yescharacteristic
162C3⋊C16#6711yescharacteristic
163C22×C32#13511yescharacteristic
164C2×C3×D3—21no—
165C2×C3×D3—81no—
166C2×C3×D3—161no—
167C32×C4#12111yescharacteristic
168C32×C4C2×D811yescharacteristic
169C3⋊Dic3—81no—
170C3×Dic3—21no—
171#137—181no—
172AGL(1,ℤ/8)—181no—
173C2×Q16—91no—
174C2×D8—31no—
175#131—31no—
176SD32—181no—
177SD32—181no—
178M32—61no—
179M32D3211yescharacteristic
180C2×C16—31no—
181C2×C16—61no—
182#108—31no—
183#108—91no—
184#101—181no—
185#100—181no—
186C23×C3—121no—
187C22×D3—41no—
188C3×Q8—31no—
189C3×D4—31no—
190C3×D4—61no—
191C3×D4—121no—
192C3×D4—121no—
193C2×C3×C4—21no—
194C2×C3×C4—61no—
195C2×C3×C4C2×D1211yescharacteristic
196C2×C3×C4D3×D411yescharacteristic
197#67—21no—
198C2×Dic3—121no—
199C2×Dic3—121no—
200C2×Dic3—241no—
201D12—41no—
202D12—41no—
203D12D2411yescharacteristic
204C4×D3—21no—
205Dic6—122no—
206Dic6—121no—
207Dic6—121no—
208Dic6—121no—
209Dic6—121no—
210Dic6—241no—
211Dic6D2411yescharacteristic
212C3×C8—21no—
213C3×C8—21no—
214C3×C8—61no—
215C3×C8—121no—
216C3×C8#23511yescharacteristic
217C3×C8#23511yescharacteristic
218C3×C8D3×D411yescharacteristic
219C3×C8C2×#6711yescharacteristic
220C3⋊C8—21no—
221C3⋊C8—41no—
222C3⋊C8—121no—
223C3⋊C8—121no—
224C3⋊C8—241no—
225C2×C32—21no—
226C2×C32#46611yescharacteristic
227C3×D3—41no—
228C3×D3—161no—
229#41—31no—
230C2×Q8—181no—
231C2×D4—61no—
232Q16—181no—
233Q16—181no—
234Q16—361no—
235SD16—361no—
236SD16—361no—
237D8—61no—
238D8—61no—
239D8—361no—
240M16—31no—
241M16—61no—
242M16—61no—
243M16—181no—
244C2×C8—61no—
245C2×C8C2×D3211yescharacteristic
246C16—21no—
247C16—31no—
248C16—31no—
249C22×C3—21no—
250C22×C3—61no—
251C22×C3—241no—
252C22×C3—481no—
253C22×C3#90411yescharacteristic
254C22×C3#91611yescharacteristic
255C2×D3—21no—
256C2×D3—81no—
257C2×D3—161no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—61no—
261C3×C4#88411yescharacteristic
262C3×C4C2×D2411yescharacteristic
263C3×C4D3×D811yescharacteristic
264C3×C4#93011yescharacteristic
265Dic3—21no—
266Dic3—242no—
267Dic3—241no—
268Dic3—241no—
269C32#222311yescharacteristic, complemented, Sylow
270C23—121no—
271Q8—31no—
272Q8—361no—
273Q8—361no—
274D4—31no—
275D4—61no—
276D4—121no—
277D4—121no—
278C2×C4—61no—
279C2×C4—361no—
280C2×C4D3×D1211yescharacteristic
281C8—61no—
282C8—121no—
283C8—361no—
284C8#379811yescharacteristic
285C8D3×#6711yescharacteristic
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—41no—
290C2×C3—121no—
291C2×C3—481no—
292C2×C3#477511yescharacteristic
293C2×C3#511511yescharacteristic
294D3—41no—
295D3—161no—
296C22—61no—
297C22—241no—
298C22—481no—
299C22#6380611yescharacteristic
300C4—61no—
301C4—721no—
302C4D3×D2411yescharacteristic
303C4#6390611yescharacteristic
304C3—21no—
305C3#6926111yescharacteristic, complemented
306C3#7145511yescharacteristic, complemented
307C2—21no—
308C2—121no—
309C2—481no—
310C2#1059082611yescharacteristic
subgroupG/H
centerC2#10590826
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32#466
prime radical#10590926C2
hypercenterM32D32
hypocenterC32#2223
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
1. C3×#4907C2semidirect
2. #10590932C2semidirect
4. C2×#63548C2semidirect
5. #10589383C2semidirect
6. C3×#4516C2semidirect
7. #10589143C2semidirect
30. #4907D3semidirect
37. #4516D3semidirect
269. C32#2223semidirect
305. C3#69261semidirect
306. C3#71455semidirect

Maximal subgroups

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

subgroupindex
C3×#49072
#105909322
#105909262
C2×#635482
#105893832
C3×#45162
#105891432
#714553
#692613