Finite Group Databasebeta

← #11799461

Subgroups — #11799461

Order 1152.

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

normal subgroups only

This group has 330 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
1#10592600C211yesmaximal, characteristic, complemented
2C2×C3×#800C211yesmaximal, characteristic, complemented
3#10590933C211yesmaximal, characteristic, complemented
4#10590929C211yesmaximal, characteristic
5C3×#4506C211yesmaximal, characteristic, complemented
6#10589129C211yesmaximal, characteristic, complemented
7#10589126C211yesmaximal, characteristic, complemented
8#71491—31nomaximal
9#69363—31nomaximal
10#64110C2211yescharacteristic
11C2×C3×Dic12C2211yescharacteristic
12C2×C3×D24C2211yescharacteristic
13#63833—21no—
14#63830—21no—
15C2×C32×C16C2211yescharacteristic
16#63639C2211yescharacteristic
17#63625—21no—
18C16×C3⋊D3—21no—
19C3×#819C2211yescharacteristic
20C3×#819C2211yescharacteristic
21C3×#800—21no—
22C3×#800—21no—
23#63560—21no—
24#63558—21no—
25C2×C3×SD32—31no—
26#5192—31no—
27#5160—31no—
28C2×#800D311yescharacteristic, complemented
29#4901—31no—
30#4901—31no—
31#4901—61no—
32#4897—31no—
33#4896—31no—
34C3×#368—31no—
35#4565—31no—
36#4563—31no—
37#4506D311yescharacteristic, complemented
38#4496—31no—
39#4495—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×C16D411yescharacteristic
58C32×C16D411yescharacteristic
59C3⋊(C3⋊C16)—21no—
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×SD32—61no—
73C3×SD32—61no—
74C2×C3×C16—21no—
75C2×C3×C16C2×D311yescharacteristic
76C2×C3×C16C2×D311yescharacteristic
77C3×#108—31no—
78C3×#108—31no—
79#836—61no—
80#833—61no—
81#824—61no—
82#823—61no—
83#819C2×D311yescharacteristic
84#819C2×D311yescharacteristic
85#812—31no—
86#812—31no—
87#812—61no—
88#800—21no—
89#800—21no—
90#798—62no—
91#798—61no—
92#798—61no—
93D3×C16—62no—
94D3×C16—61no—
95D3×C16—61no—
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—31no—
113#504—91no—
114#473—91no—
115#472—91no—
116#368—31no—
117#362—91no—
118#361—91no—
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—21no—
159C3×C16—21no—
160C3×C16D1211yescharacteristic
161C3×C16D1211yescharacteristic
162C3×C16#6711yescharacteristic
163C3×C16#6711yescharacteristic
164C3⋊C16—62no—
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—61no—
181SD32—61no—
182M32—91no—
183M32—181no—
184C2×C16—181no—
185C2×C16D3211yescharacteristic
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×C8C2×D1211yescharacteristic
222C3×C8#23711yescharacteristic
223C3×C8#23911yescharacteristic
224C3×C8C2×#6711yescharacteristic
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—181no—
252C16#62611yescharacteristic
253C16#62611yescharacteristic
254C22×C3—21no—
255C22×C3—241no—
256C22×C3—481no—
257C22×C3#91211yescharacteristic
258C22×C3#91911yescharacteristic
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#89511yescharacteristic
268C3×C4D3×D811yescharacteristic
269C3×C4D3×D811yescharacteristic
270C3×C4#93811yescharacteristic
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#379611yescharacteristic
291C8C2×#62611yescharacteristic
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—41no—
296C2×C3—481no—
297C2×C3#488311yescharacteristic
298C2×C3#515711yescharacteristic
299D3—122no—
300D3—121no—
301D3—121no—
302D3—161no—
303C22—181no—
304C22—241no—
305C22—481no—
306C22#6381011yescharacteristic
307C4—181no—
308C4—241no—
309C4#6379711yescharacteristic
310C4#6391611yescharacteristic
311C3—21no—
312C3#6936311yescharacteristic, complemented
313C3#7149111yescharacteristic, complemented
314C2—21no—
315C2—361no—
316C2—481no—
317C2#1059084411yescharacteristic
subgroupG/H
centerC2#10590844
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×C16C22
socleC2×C32#466
prime radical#10590929C2
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. #10592600C2semidirect
2. C2×C3×#800C2semidirect
3. #10590933C2semidirect
5. C3×#4506C2semidirect
6. #10589129C2semidirect
7. #10589126C2semidirect
28. C2×#800D3semidirect
37. #4506D3semidirect
275. C32#2223semidirect
312. C3#69363semidirect
313. C3#71491semidirect

Maximal subgroups

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

subgroupindex
#105926002
C2×C3×#8002
#105909332
#105909292
C3×#45062
#105891292
#105891262
#714913
#693633