Finite Group Databasebeta

← #11799473

Subgroups — #11799473

Order 1152.

330 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 66 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#10592606C211yesmaximal, characteristic, complemented
2#10590933C211yesmaximal, characteristic, complemented
3#10590929C211yesmaximal, characteristic
4C2×#63547C211yesmaximal, characteristic, complemented
5C3×#4517C211yesmaximal, characteristic, complemented
6C3×#4516C211yesmaximal, characteristic, complemented
7#10589144C211yesmaximal, characteristic, complemented
8#69271—31nomaximal
9#69261—31nomaximal
10#64110C2211yescharacteristic
11C2×C3×Dic12C2211yescharacteristic
12C2×C3×D24C2211yescharacteristic
13#63833—21no—
14#63830—21no—
15C32×M32C2211yescharacteristic
16C2×C3⋊(C3⋊C16)C2211yescharacteristic
17#63625—21no—
18C16×C3⋊D3—21no—
19C3×#819C2211yescharacteristic
20C3×#819C2211yescharacteristic
21#63560—21no—
22#63558—21no—
23#63547—21no—
24#63547—21no—
25#5192—31no—
26C2×#828—31no—
27#5160—31no—
28C2×#827—31no—
29#4907—31no—
30#4907—31no—
31#4907—61no—
32#4897—31no—
33#4896—31no—
34C3×#362—31no—
35C3×#361—31no—
36#4517D311yescharacteristic, complemented
37#4516D311yescharacteristic, complemented
38#4493—31no—
39#4493—31no—
40#3828D411yescharacteristic
41C2×C3×D12—21no—
42C2×C3×Dic6—21no—
43C2×C32×C8C2311yescharacteristic
44#3748D411yescharacteristic
45#3743—21no—
46C8×C3⋊D3—21no—
47C3×#208—21no—
48C3×#208—21no—
49C3×Dic12—21no—
50C3×Dic12—21no—
51C3×D24—21no—
52C3×D24—21no—
53#3719—41no—
54#3717—41no—
55#3716—41no—
56#3714—41no—
57C32×C16—21no—
58C3⋊(C3⋊C16)D411yescharacteristic
59C3⋊(C3⋊C16)D411yescharacteristic
60#2223—91noSylow
61C2×C3×Q16—31no—
62C2×C3×D8—31no—
63#942—61no—
64#932—61no—
65#909—61no—
66#908—61no—
67C2×Dic12C2×D311yescharacteristic
68C2×D24C2×D311yescharacteristic
69#901—31no—
70#901—31no—
71#901—61no—
72C3×M32—21no—
73C3×M32C2×D311yescharacteristic
74C3×M32C2×D311yescharacteristic
75C3×#108—31no—
76C3×#108—31no—
77#836—61no—
78#833—61no—
79#828—61no—
80#828—61no—
81#827—61no—
82#827—61no—
83#824—61no—
84#823—61no—
85#819C2×D311yescharacteristic
86#819C2×D311yescharacteristic
87C2×C3⋊C16—31no—
88C2×C3⋊C16—31no—
89C2×C3⋊C16—61no—
90#798—61no—
91#798—61no—
92#798—62no—
93D3×C16—61no—
94D3×C16—61no—
95D3×C16—62no—
96C22×C3×D3—41no—
97C2×C32×C4C2×D411yescharacteristic
98#638—21no—
99C4⋊(C3⋊D3)D811yescharacteristic
100C4×C3⋊D3—21no—
101#634D811yescharacteristic
102C2×C3×Dic3—41no—
103C3×D12—41no—
104C3×D12—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C32×C8C2×D411yescharacteristic
108C32×C8#4111yescharacteristic
109C3⋊(C3⋊C8)—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112C2×SD32—91no—
113#504—91no—
114#473—91no—
115#472—91no—
116#368—91no—
117#362—31no—
118#361—31no—
119C2×C3×Q8—61no—
120C2×C3×D4—61no—
121#235—31no—
122#235—31no—
123#235—61no—
124C2×D12—21no—
125C2×Dic6—21no—
126C3×Q16—61no—
127C3×Q16—61no—
128C3×D8—61no—
129C3×D8—61no—
130C3×M16—61no—
131C3×M16—61no—
132C2×C3×C8—21no—
133C2×C3×C8C22×D311yescharacteristic
134C2×C3×C8C22×D311yescharacteristic
135#216—121no—
136#215—121no—
137#214—121no—
138#213—121no—
139#208—21no—
140#208—21no—
141#208—31no—
142#208—31no—
143#208—61no—
144Dic12—21no—
145Dic12—21no—
146Dic12—121no—
147D24—21no—
148D24—21no—
149D24—121no—
150#204—121no—
151#204—121no—
152ΓL(1,𝔽25)—62no—
153ΓL(1,𝔽25)—61no—
154ΓL(1,𝔽25)—61no—
155D3×C8—62no—
156D3×C8—61no—
157D3×C8—61no—
158C3×C16—22no—
159C3×C16—21no—
160C3×C16—21no—
161C3⋊C16—31no—
162C3⋊C16—31no—
163C3⋊C16—31no—
164C3⋊C16—31no—
165C3⋊C16—61no—
166C3⋊C16—61no—
167C22×C32#13511yescharacteristic
168C2×C3⋊D3—21no—
169C2×C3×D3—81no—
170C2×C3×D3—161no—
171C32×C4#12111yescharacteristic
172C32×C4C2×D811yescharacteristic
173C3⋊Dic3—21no—
174C3×Dic3—81no—
175#137—181no—
176AGL(1,ℤ/8)—181no—
177C2×Q16—31no—
178C2×D8—31no—
179#131—91no—
180SD32—181no—
181SD32—181no—
182M32—181no—
183M32D3211yescharacteristic
184C2×C16—91no—
185C2×C16—181no—
186#108—31no—
187#108—31no—
188#101—181no—
189#100—181no—
190C23×C3—121no—
191C22×D3—41no—
192C3×Q8—121no—
193C3×Q8—121no—
194C3×D4—121no—
195C3×D4—121no—
196C2×C3×C4—21no—
197C2×C3×C4—121no—
198C2×C3×C4D3×D411yescharacteristic
199C2×C3×C4D3×D411yescharacteristic
200#67—62no—
201#67—61no—
202#67—61no—
203C2×Dic3—41no—
204D12—31no—
205D12—31no—
206D12—41no—
207D12—41no—
208D12—61no—
209C4×D3—62no—
210C4×D3—61no—
211C4×D3—61no—
212Dic6—31no—
213Dic6—31no—
214Dic6—41no—
215Dic6—41no—
216Dic6—61no—
217C3×C8—21no—
218C3×C8—21no—
219C3×C8—121no—
220C3×C8—121no—
221C3×C8#23511yescharacteristic
222C3×C8#23511yescharacteristic
223C3×C8D3×D411yescharacteristic
224C3×C8D3×D411yescharacteristic
225C3⋊C8—41no—
226C3⋊C8—41no—
227C3⋊C8—62no—
228C3⋊C8—61no—
229C3⋊C8—61no—
230C2×C32—21no—
231C2×C32#46611yescharacteristic
232C3⋊D3—41no—
233C3×D3—161no—
234#41—91no—
235C2×Q8—61no—
236C2×D4—61no—
237Q16—61no—
238Q16—61no—
239Q16—361no—
240SD16—361no—
241SD16—361no—
242D8—61no—
243D8—61no—
244D8—361no—
245M16—61no—
246M16—61no—
247M16—91no—
248M16—181no—
249C2×C8—181no—
250C2×C8C2×D3211yescharacteristic
251C16—21no—
252C16—91no—
253C16—91no—
254C22×C3—21no—
255C22×C3—241no—
256C22×C3—481no—
257C22×C3#91611yescharacteristic
258C22×C3#91611yescharacteristic
259C2×D3—62no—
260C2×D3—61no—
261C2×D3—61no—
262C2×D3—81no—
263C2×D3—161no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—241no—
267C3×C4#88411yescharacteristic
268C3×C4#88411yescharacteristic
269C3×C4D3×D811yescharacteristic
270C3×C4D3×D811yescharacteristic
271Dic3—62no—
272Dic3—61no—
273Dic3—61no—
274Dic3—81no—
275C32#222311yescharacteristic, complemented, Sylow
276C23—121no—
277Q8—91no—
278Q8—121no—
279Q8—121no—
280D4—91no—
281D4—121no—
282D4—121no—
283D4—181no—
284C2×C4—121no—
285C2×C4—181no—
286C2×C4#380211yescharacteristic
287C8—121no—
288C8—121no—
289C8—181no—
290C8#379811yescharacteristic
291C8#381111yescharacteristic
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—41no—
296C2×C3—481no—
297C2×C3#477511yescharacteristic
298C2×C3#477511yescharacteristic
299D3—122no—
300D3—121no—
301D3—121no—
302D3—161no—
303C22—181no—
304C22—241no—
305C22—481no—
306C22#6380911yescharacteristic
307C4—181no—
308C4—241no—
309C4#6379711yescharacteristic
310C4#6391211yescharacteristic
311C3—21no—
312C3#6926111yescharacteristic, complemented
313C3#6927111yescharacteristic, complemented
314C2—21no—
315C2—361no—
316C2—481no—
317C2#1059083911yescharacteristic
subgroupG/H
centerC2#10590839
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32#466
prime radical#10590929C2
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. #10592606C2semidirect
2. #10590933C2semidirect
4. C2×#63547C2semidirect
5. C3×#4517C2semidirect
6. C3×#4516C2semidirect
7. #10589144C2semidirect
36. #4517D3semidirect
37. #4516D3semidirect
275. C32#2223semidirect
312. C3#69261semidirect
313. C3#69271semidirect

Maximal subgroups

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

subgroupindex
#105926062
#105909332
#105909292
C2×#635472
C3×#45172
C3×#45162
#105891442
#692713
#692613