Finite Group Databasebeta

← #11795366

Subgroups — #11795366

Order 1152.

487 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 487 conjugacy classes of subgroups — too many to draw. Only its 108 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×#5126C211yesmaximal, characteristic
2C3×#5125C211yesmaximal, characteristic, complemented
3#10591143C212yesmaximal, complemented
4#10591069C212yesmaximal
5#10589426C211yesmaximal, characteristic, complemented
6#70729—31nomaximal
7#69987—31nomaximal
8C22×C3×C4×D3C2211yescharacteristic
9C2×C32×M16C2211yescharacteristic
10C2×#3748C2212yes—
11C2×C3×#208C2212yes—
12C2×C3×#208C2211yescharacteristic
13C3×(C2×D3)⋊C8—22no—
14C3×#819—22no—
15#63578—24no—
16(C2×D3)⋊(C3⋊C8)—24no—
17C3×#430—31no—
18C3×#407—31no—
19#5207—32no—
20#5126—32no—
21#5126D311yescharacteristic
22#5125D311yescharacteristic, complemented
23#5124—32no—
24#5124—32no—
25C3⋊#338—31no—
26C3⋊#338—31no—
27C3⋊#338—61no—
28C23×C3×D3Q811yescharacteristic
29C22×C32×C4C2311yescharacteristic
30C22×C3×Dic3Q811yescharacteristic
31C2×C3×C4×D3—22no—
32C2×C3×C4×D3—21no—
33C2×C3×C4×D3—22no—
34C2×C3×C4×D3—21no—
35C32×M16—22no—
36C2×C32×C8D412yes—
37#3748—22no—
38#3748—22no—
39C2×C3⋊(C3⋊C8)D414yes—
40C3×#208—22no—
41C3×#208—22no—
42C3×#208—22no—
43C2×C3×C3⋊C8—22no—
44C2×C3×C3⋊C8—21no—
45#2091—91noSylow
46C23×C3×C4—31no—
47C22×C4×D3C2×D311yescharacteristic
48C2×C3×M16—21no—
49C2×C3×M16—31no—
50C2×C3×M16—32no—
51C2×C3×M16C2×D311yescharacteristic
52C2×C3×M16C2×D311yescharacteristic
53C2×#208—32no—
54C2×#208—32no—
55C2×#208—62no—
56C2×#208C2×D311yescharacteristic
57C2×#208C2×D312yes—
58C3×#108—62no—
59C3×C22⋊C8—62no—
60#830—64no—
61#822—64no—
62#822—64no—
63(C2×D3)⋊C8—22no—
64(C2×D3)⋊C8—64no—
65#819—22no—
66C23×C32C2×Q811yescharacteristic
67C22×C3×D3—22no—
68C22×C3×D3—21no—
69C22×C3×D3—42no—
70C2×C32×C4C2×D412yes—
71C2×C32×C4C2×D411yescharacteristic
72C2×C32×C4#4112yes—
73C2×C32×C4#4111yescharacteristic
74C2×C3×Dic3—22no—
75C2×C3×Dic3—21no—
76C3×C4×D3—42no—
77C3×C4×D3—41no—
78C3×C4×D3—41no—
79C32×C8—22no—
80C3⋊(C3⋊C8)—24no—
81C3×C3⋊C8—42no—
82C3×C3⋊C8—41no—
83#430—31no—
84#430—92no—
85#407—31no—
86#407—92no—
87#338—91no—
88C24×C3—31no—
89C23×D3Dic611yescharacteristic
90C22×C3×C4—21no—
91C22×C3×C4—31no—
92C22×C3×C4—62no—
93C22×C3×C4—62no—
94C22×C3×C4—61no—
95C22×C3×C4—61no—
96C22×C3×C4C22×D311yescharacteristic
97C22×C3×C4C22×D311yescharacteristic
98C22×Dic3Dic611yescharacteristic
99C2×C4×D3—21no—
100C2×C4×D3—22no—
101C2×C4×D3—22no—
102C2×C4×D3—21no—
103C3×M16—22no—
104C3×M16—22no—
105C3×M16—42no—
106C3×M16—62no—
107C3×M16—62no—
108C3×M16—62no—
109C2×C3×C8—22no—
110C2×C3×C8—62no—
111C2×C3×C8—61no—
112C2×C3×C8#6712yes—
113C2×C3×C8#6712yes—
114#208—22no—
115#208—22no—
116#208—22no—
117#208—62no—
118#208—62no—
119#208—62no—
120#208—62no—
121#208—122no—
122#208—122no—
123C2×C3⋊C8—22no—
124C2×C3⋊C8—21no—
125C2×C3⋊C8—34no—
126C2×C3⋊C8—34no—
127C2×C3⋊C8—64no—
128C22×C32—41no—
129C22×C32C22⋊Q812yes—
130C22×C32C22⋊Q811yescharacteristic
131C2×C3×D3—24no—
132C2×C3×D3—22no—
133C2×C3×D3—42no—
134C2×C3×D3—41no—
135C2×C3×D3—41no—
136C32×C4#12312yes—
137C32×C4#12311yescharacteristic
138C32×C4#12711yescharacteristic
139C3×Dic3—41no—
140C23×C4—31no—
141C2×M16—31no—
142C2×M16—32no—
143C2×M16—92no—
144C2×M16D3211yescharacteristic
145#108—62no—
146#108—184no—
147C22⋊C8—62no—
148C22⋊C8—184no—
149C23×C3—21no—
150C23×C3—62no—
151C23×C3—61no—
152C23×C3—122no—
153C23×C3C2×Dic611yescharacteristic
154C23×C3D3×Q811yescharacteristic
155C22×D3—22no—
156C22×D3—21no—
157C22×D3—42no—
158C2×C3×C4—21no—
159C2×C3×C4—22no—
160C2×C3×C4—22no—
161C2×C3×C4—21no—
162C2×C3×C4—62no—
163C2×C3×C4—61no—
164C2×C3×C4—122no—
165C2×C3×C4—121no—
166C2×C3×C4—121no—
167C2×C3×C4#23511yescharacteristic
168C2×C3×C4#23512yes—
169C2×C3×C4D3×D412yes—
170C2×C3×C4D3×D412yes—
171C2×C3×C4#23712yes—
172C2×C3×C4#23911yescharacteristic
173C2×C3×C4C2×#6711yescharacteristic
174C2×C3×C4C2×#6711yescharacteristic
175C2×Dic3—22no—
176C2×Dic3—21no—
177C4×D3—42no—
178C4×D3—41no—
179C4×D3—41no—
180C3×C8—22no—
181C3×C8—22no—
182C3×C8—42no—
183C3×C8—122no—
184C3×C8—121no—
185C3⋊C8—41no—
186C3⋊C8—42no—
187C3⋊C8—64no—
188C3⋊C8—64no—
189C3⋊C8—124no—
190C2×C32—22no—
191C2×C32—21no—
192C2×C32#39911yescharacteristic
193C3×D3—42no—
194C24—31no—
195C22×C4—31no—
196C22×C4—61no—
197C22×C4—62no—
198C22×C4—62no—
199C22×C4—61no—
200C22×C4C2×D3211yescharacteristic
201M16—22no—
202M16—62no—
203M16—62no—
204M16—62no—
205M16—182no—
206M16—182no—
207C2×C8—62no—
208C2×C8—61no—
209C2×C8—94no—
210C2×C8#62512yes—
211C22×C3—21no—
212C22×C3—22no—
213C22×C3—41no—
214C22×C3—41no—
215C22×C3—64no—
216C22×C3—62no—
217C22×C3—81no—
218C22×C3—122no—
219C22×C3—121no—
220C22×C3—121no—
221C22×C3#87812yes—
222C22×C3#89612yes—
223C22×C3#92411yescharacteristic
224C22×C3#94611yescharacteristic
225C2×D3—24no—
226C2×D3—22no—
227C2×D3—42no—
228C2×D3—41no—
229C2×D3—41no—
230C3×C4—22no—
231C3×C4—21no—
232C3×C4—21no—
233C3×C4—121no—
234C3×C4#88312yes—
235C3×C4#89412yes—
236C3×C4#92911yescharacteristic
237C3×C4#93511yescharacteristic
238C3×C4#94011yescharacteristic
239C3×C4#94011yescharacteristic
240Dic3—41no—
241C32#209111yescharacteristic, complemented, Sylow
242C23—61no—
243C23—62no—
244C23—122no—
245C23D3×Dic611yescharacteristic
246C2×C4—61no—
247C2×C4—62no—
248C2×C4—122no—
249C2×C4—121no—
250C2×C4—121no—
251C2×C4#379911yescharacteristic
252C2×C4#380212yes—
253C2×C4#380412yes—
254C2×C4C2×#62511yescharacteristic
255C8—22no—
256C8—122no—
257C8—121no—
258C8—184no—
259C2×C3—22no—
260C2×C3—21no—
261C2×C3—22no—
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—41no—
265C2×C3—42no—
266C2×C3—122no—
267C2×C3#494911yescharacteristic
268C2×C3#499311yescharacteristic
269D3—42no—
270C22—41no—
271C22—62no—
272C22—64no—
273C22—121no—
274C22—122no—
275C22—121no—
276C22#6385611yescharacteristic
277C22#6389912yes—
278C4—121no—
279C4#6385412yes—
280C4#6391411yescharacteristic
281C4#6396111yescharacteristic
282C3—21no—
283C3#6998711yescharacteristic, complemented
284C3#7072911yescharacteristic, complemented
285C2—21no—
286C2—22no—
287C2—122no—
288C2#1059132411yescharacteristic
subgroupG/H
centerC4#63914
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
2. C3×#5125C2semidirect
3. #10591143C2semidirect
5. #10589426C2semidirect
22. #5125D3semidirect
241. C32#2091semidirect
283. C3#69987semidirect
284. C3#70729semidirect

Maximal subgroups

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

subgroupindex
C3×#51262
C3×#51252
#105911432
#105910692
#105894262
#707293
#699873