Finite Group Databasebeta

← #11795364

Subgroups — #11795364

Order 1152.

495 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 495 conjugacy classes of subgroups — too many to draw. Only its 112 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#10592824C211yesmaximal, characteristic, complemented
2C3×#5126C211yesmaximal, characteristic
3#10591141C212yesmaximal, complemented
4#10591069C212yesmaximal
5C3×C3⋊#338C211yesmaximal, characteristic, complemented
6#69987—31nomaximal
7#68721—31nomaximal
8C22×C3×C4×D3C2211yescharacteristic
9C2×C32×M16C2211yescharacteristic
10C2×#3748C2212yes—
11C2×C3×#208C2211yescharacteristic
12C2×C3×#208C2212yes—
13#63646—22no—
14C3×(C2×D3)⋊C8—22no—
15#63577—24no—
16(C2×D3)⋊(C3⋊C8)—24no—
17C3×#407—31no—
18#5207—32no—
19#5126—32no—
20#5126D311yescharacteristic
21#5125—31no—
22#5125—31no—
23#5125—32no—
24#5125—61no—
25#5124—32no—
26C3×#338—31no—
27C3⋊#338D311yescharacteristic, complemented
28C23×C3×D3Q811yescharacteristic
29C22×C32×C4C2311yescharacteristic
30C22×C3×Dic3Q811yescharacteristic
31C2×C3×C4×D3—22no—
32C2×C3×C4×D3—21no—
33C2×C3×C4×D3—21no—
34C2×C3×C4×D3—22no—
35C32×M16—22no—
36C2×C32×C8D412yes—
37#3748—22no—
38#3748—22no—
39C2×C3⋊(C3⋊C8)—22no—
40C3×#208—22no—
41C3×#208—22no—
42C3×#208—22no—
43C2×C3×C3⋊C8—21no—
44C2×C3×C3⋊C8D414yes—
45#2091—91noSylow
46C23×C3×C4—31no—
47C22×C4×D3C2×D311yescharacteristic
48C2×C3×M16—21no—
49C2×C3×M16—32no—
50C2×C3×M16—31no—
51C2×C3×M16C2×D311yescharacteristic
52C2×C3×M16C2×D311yescharacteristic
53C2×#208—32no—
54C2×#208—32no—
55C2×#208—62no—
56C2×#208C2×D311yescharacteristic
57C2×#208C2×D312yes—
58C3×C22⋊C8—62no—
59#830—64no—
60#822—64no—
61(C2×D3)⋊C8—22no—
62(C2×D3)⋊C8—64no—
63#819—64no—
64#819—64no—
65#819—62no—
66#819—62no—
67C23×C32C2×Q811yescharacteristic
68C22×C3×D3—22no—
69C22×C3×D3—21no—
70C22×C3×D3—42no—
71C2×C32×C4C2×D412yes—
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4#4111yescharacteristic
74C2×C32×C4#4112yes—
75C2×C3×Dic3—22no—
76C2×C3×Dic3—21no—
77C3×C4×D3—42no—
78C3×C4×D3—41no—
79C3×C4×D3—41no—
80C32×C8—22no—
81C3⋊(C3⋊C8)—42no—
82C3×C3⋊C8—24no—
83C3×C3⋊C8—41no—
84#430—92no—
85#430—91no—
86#407—31no—
87#407—92no—
88#338—31no—
89C24×C3—31no—
90C23×D3Dic611yescharacteristic
91C22×C3×C4—21no—
92C22×C3×C4—31no—
93C22×C3×C4—62no—
94C22×C3×C4—61no—
95C22×C3×C4—61no—
96C22×C3×C4—62no—
97C22×C3×C4C22×D311yescharacteristic
98C22×C3×C4C22×D311yescharacteristic
99C22×Dic3Dic611yescharacteristic
100C2×C4×D3—21no—
101C2×C4×D3—22no—
102C2×C4×D3—22no—
103C2×C4×D3—21no—
104C3×M16—24no—
105C3×M16—22no—
106C3×M16—22no—
107C3×M16—62no—
108C3×M16—62no—
109C3×M16—62no—
110C2×C3×C8—22no—
111C2×C3×C8—34no—
112C2×C3×C8—61no—
113C2×C3×C8D1212yes—
114C2×C3×C8#6712yes—
115#208—22no—
116#208—22no—
117#208—22no—
118#208—64no—
119#208—62no—
120#208—62no—
121#208—62no—
122#208—62no—
123#208—122no—
124C2×C3⋊C8—21no—
125C2×C3⋊C8—62no—
126C2×C3⋊C8—62no—
127C2×C3⋊C8—122no—
128C2×C3⋊C8D1214yes—
129C22×C32—41no—
130C22×C32C22⋊Q812yes—
131C22×C32C22⋊Q811yescharacteristic
132C2×C3×D3—24no—
133C2×C3×D3—22no—
134C2×C3×D3—42no—
135C2×C3×D3—41no—
136C2×C3×D3—41no—
137C32×C4#12312yes—
138C32×C4#12311yescharacteristic
139C32×C4#12711yescharacteristic
140C3×Dic3—41no—
141C23×C4—31no—
142C2×M16—32no—
143C2×M16—31no—
144C2×M16—92no—
145C2×M16D3211yescharacteristic
146#108—184no—
147#108—182no—
148C22⋊C8—62no—
149C22⋊C8—184no—
150C23×C3—21no—
151C23×C3—61no—
152C23×C3—62no—
153C23×C3—122no—
154C23×C3C2×Dic611yescharacteristic
155C23×C3D3×Q811yescharacteristic
156C22×D3—22no—
157C22×D3—21no—
158C22×D3—42no—
159C2×C3×C4—21no—
160C2×C3×C4—22no—
161C2×C3×C4—22no—
162C2×C3×C4—21no—
163C2×C3×C4—61no—
164C2×C3×C4—62no—
165C2×C3×C4—121no—
166C2×C3×C4—122no—
167C2×C3×C4—121no—
168C2×C3×C4C2×D1212yes—
169C2×C3×C4C2×D1211yescharacteristic
170C2×C3×C4#23511yescharacteristic
171C2×C3×C4D3×D412yes—
172C2×C3×C4#23711yescharacteristic
173C2×C3×C4#23712yes—
174C2×C3×C4#23712yes—
175C2×C3×C4C2×#6711yescharacteristic
176C2×Dic3—22no—
177C2×Dic3—21no—
178C4×D3—42no—
179C4×D3—41no—
180C4×D3—41no—
181C3×C8—24no—
182C3×C8—22no—
183C3×C8—22no—
184C3×C8—64no—
185C3×C8—121no—
186C3⋊C8—24no—
187C3⋊C8—41no—
188C3⋊C8—124no—
189C3⋊C8—122no—
190C3⋊C8—122no—
191C2×C32—22no—
192C2×C32—21no—
193C2×C32#39911yescharacteristic
194C3×D3—42no—
195C24—31no—
196C22×C4—31no—
197C22×C4—61no—
198C22×C4—62no—
199C22×C4—62no—
200C22×C4—61no—
201C22×C4C2×D3211yescharacteristic
202M16—22no—
203M16—62no—
204M16—62no—
205M16—62no—
206M16—182no—
207M16—182no—
208C2×C8—34no—
209C2×C8—61no—
210C2×C8—182no—
211C2×C8#62612yes—
212C22×C3—21no—
213C22×C3—22no—
214C22×C3—41no—
215C22×C3—41no—
216C22×C3—62no—
217C22×C3—64no—
218C22×C3—81no—
219C22×C3—121no—
220C22×C3—122no—
221C22×C3—121no—
222C22×C3#87812yes—
223C22×C3#89711yescharacteristic
224C22×C3#89712yes—
225C22×C3#92411yescharacteristic
226C2×D3—24no—
227C2×D3—22no—
228C2×D3—42no—
229C2×D3—41no—
230C2×D3—41no—
231C3×C4—22no—
232C3×C4—21no—
233C3×C4—21no—
234C3×C4—121no—
235C3×C4#87411yescharacteristic
236C3×C4#88312yes—
237C3×C4#88612yes—
238C3×C4#88611yescharacteristic
239C3×C4#93511yescharacteristic
240C3×C4#94011yescharacteristic
241Dic3—41no—
242C32#209111yescharacteristic, complemented, Sylow
243C23—61no—
244C23—62no—
245C23—122no—
246C23D3×Dic611yescharacteristic
247C2×C4—61no—
248C2×C4—62no—
249C2×C4—122no—
250C2×C4—121no—
251C2×C4—121no—
252C2×C4#379511yescharacteristic
253C2×C4D3×D1212yes—
254C2×C4#380512yes—
255C2×C4C2×#62611yescharacteristic
256C8—22no—
257C8—64no—
258C8—121no—
259C8—362no—
260C2×C3—22no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3—22no—
264C2×C3—21no—
265C2×C3—41no—
266C2×C3—42no—
267C2×C3—122no—
268C2×C3#467711yescharacteristic
269C2×C3#494911yescharacteristic
270D3—42no—
271C22—41no—
272C22—62no—
273C22—64no—
274C22—121no—
275C22—122no—
276C22—121no—
277C22#6385711yescharacteristic
278C22#6389312yes—
279C4—121no—
280C4#6389112yes—
281C4#6391111yescharacteristic
282C4#6396211yescharacteristic
283C3—21no—
284C3#6872111yescharacteristic, complemented
285C3#6998711yescharacteristic, complemented
286C2—21no—
287C2—22no—
288C2—122no—
289C2#1059131711yescharacteristic
subgroupG/H
centerC4#63911
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#399
prime radicalC23×C3×D3Q8
hypercenterC2×M16D32
hypocenterC32#2091
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10592824C2semidirect
3. #10591141C2semidirect
5. C3×C3⋊#338C2semidirect
27. C3⋊#338D3semidirect
242. C32#2091semidirect
284. C3#68721semidirect
285. C3#69987semidirect

Maximal subgroups

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

subgroupindex
#105928242
C3×#51262
#105911412
#105910692
C3×C3⋊#3382
#699873
#687213