Finite Group Databasebeta

← #11795365

Subgroups — #11795365

Order 1152.

539 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 539 conjugacy classes of subgroups — too many to draw. Only its 110 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#10592825C211yesmaximal, characteristic
2C3×#5125C211yesmaximal, characteristic, complemented
3#10591141C212yesmaximal, complemented
4#10591074C212yesmaximal
5C3×C3⋊#338C211yesmaximal, characteristic, complemented
6#70729—31nomaximal
7#68721—31nomaximal
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C32×M16C2211yescharacteristic
10C2×#3748C2211yescharacteristic
11C2×C3×#208C2212yes—
12C2×C3×#208C2212yes—
13#63647—22no—
14C3×#819—22no—
15#63577—24no—
16#63557—24no—
17C3×#430—31no—
18#5126—31no—
19#5126—31no—
20#5126—32no—
21#5126—32no—
22#5126—61no—
23#5125—32no—
24#5125D311yescharacteristic, complemented
25#5124—32no—
26C3×#338—31no—
27C3⋊#338D311yescharacteristic, complemented
28C23×C3⋊D3Q811yescharacteristic
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3Q811yescharacteristic
31C2×C4×C3⋊D3—21no—
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3—22no—
35C32×M16—22no—
36C2×C32×C8D412yes—
37#3748—22no—
38C2×C3⋊(C3⋊C8)—21no—
39C3×#208—22no—
40C3×#208—22no—
41C3×#208—22no—
42C3×#208—22no—
43C2×C3×C3⋊C8—22no—
44C2×C3×C3⋊C8D414yes—
45#2091—91noSylow
46C22×C4×D3—31no—
47C22×C4×D3—31no—
48C22×C4×D3—61no—
49C2×C3×M16—21no—
50C2×C3×M16—32no—
51C2×C3×M16—32no—
52C2×C3×M16C2×D311yescharacteristic
53C2×C3×M16C2×D311yescharacteristic
54C2×#208—31no—
55C2×#208—31no—
56C2×#208—61no—
57C2×#208C2×D312yes—
58C2×#208C2×D312yes—
59C3×#108—62no—
60#822—64no—
61(C2×D3)⋊C8—64no—
62(C2×D3)⋊C8—64no—
63(C2×D3)⋊C8—62no—
64(C2×D3)⋊C8—62no—
65(C2×D3)⋊C8—64no—
66#819—22no—
67#819—64no—
68C23×C32C2×Q811yescharacteristic
69C22×C3⋊D3—21no—
70C22×C3⋊D3—22no—
71C22×C3⋊D3—42no—
72C2×C32×C4C2×D412yes—
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4#4112yes—
75C2×C32×C4#4111yescharacteristic
76C2×C3⋊Dic3—21no—
77C2×C3⋊Dic3—22no—
78C4×C3⋊D3—42no—
79C4×C3⋊D3—41no—
80C4×C3⋊D3—41no—
81C32×C8—22no—
82C3⋊(C3⋊C8)—41no—
83C3×C3⋊C8—24no—
84C3×C3⋊C8—42no—
85#430—31no—
86#430—92no—
87#407—92no—
88#407—91no—
89#338—31no—
90C23×D3—31no—
91C23×D3—31no—
92C23×D3—61no—
93C22×C3×C4—21no—
94C22×C3×C4C22×D311yescharacteristic
95C22×C3×C4C22×D311yescharacteristic
96C22×Dic3—31no—
97C22×Dic3—31no—
98C22×Dic3—61no—
99C2×C4×D3—62no—
100C2×C4×D3—62no—
101C2×C4×D3—62no—
102C2×C4×D3—61no—
103C2×C4×D3—62no—
104C2×C4×D3—62no—
105C2×C4×D3—61no—
106C2×C4×D3—62no—
107C2×C4×D3—61no—
108C2×C4×D3—61no—
109C2×C4×D3—122no—
110C2×C4×D3—122no—
111C3×M16—22no—
112C3×M16—22no—
113C3×M16—42no—
114C3×M16—62no—
115C3×M16—62no—
116C3×M16—62no—
117C3×M16—62no—
118C2×C3×C8—22no—
119C2×C3×C8—34no—
120C2×C3×C8—62no—
121C2×C3×C8D1212yes—
122C2×C3×C8#6712yes—
123#208—22no—
124#208—22no—
125#208—22no—
126#208—22no—
127#208—62no—
128#208—62no—
129#208—122no—
130C2×C3⋊C8—22no—
131C2×C3⋊C8—62no—
132C2×C3⋊C8—61no—
133C2×C3⋊C8—61no—
134C2×C3⋊C8D1214yes—
135C22×C32—41no—
136C22×C32C22⋊Q812yes—
137C22×C32C22⋊Q811yescharacteristic
138C2×C3⋊D3—22no—
139C2×C3⋊D3—24no—
140C2×C3⋊D3—41no—
141C2×C3⋊D3—42no—
142C2×C3⋊D3—41no—
143C32×C4#12312yes—
144C32×C4#12311yescharacteristic
145C32×C4#12711yescharacteristic
146C3⋊Dic3—41no—
147C23×C4—91no—
148C2×M16—32no—
149C2×M16—32no—
150C2×M16—91no—
151C2×M16D3211yescharacteristic
152#108—62no—
153#108—184no—
154C22⋊C8—184no—
155C22⋊C8—182no—
156C23×C3—21no—
157C23×C3D3×Q811yescharacteristic
158C23×C3D3×Q811yescharacteristic
159C22×D3—62no—
160C22×D3—62no—
161C22×D3—61no—
162C22×D3—62no—
163C22×D3—61no—
164C22×D3—122no—
165C22×D3—122no—
166C22×D3—122no—
167C22×D3—124no—
168C2×C3×C4—21no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—21no—
172C2×C3×C4C2×D1212yes—
173C2×C3×C4C2×D1211yescharacteristic
174C2×C3×C4#23512yes—
175C2×C3×C4D3×D412yes—
176C2×C3×C4#23711yescharacteristic
177C2×C3×C4#23712yes—
178C2×C3×C4#23911yescharacteristic
179C2×C3×C4C2×#6711yescharacteristic
180C2×Dic3—62no—
181C2×Dic3—62no—
182C2×Dic3—61no—
183C2×Dic3—62no—
184C2×Dic3—61no—
185C2×Dic3—122no—
186C4×D3—124no—
187C4×D3—122no—
188C4×D3—122no—
189C4×D3—121no—
190C4×D3—122no—
191C4×D3—121no—
192C4×D3—122no—
193C4×D3—121no—
194C4×D3—121no—
195C3×C8—22no—
196C3×C8—22no—
197C3×C8—42no—
198C3×C8—64no—
199C3×C8—122no—
200C3⋊C8—24no—
201C3⋊C8—42no—
202C3⋊C8—122no—
203C3⋊C8—121no—
204C3⋊C8—121no—
205C2×C32—21no—
206C2×C32—22no—
207C2×C32#39911yescharacteristic
208C3⋊D3—42no—
209C24—91no—
210C22×C4—91no—
211C22×C4—181no—
212C22×C4—182no—
213C22×C4—182no—
214C22×C4—181no—
215C22×C4C2×D3211yescharacteristic
216M16—22no—
217M16—62no—
218M16—62no—
219M16—62no—
220M16—62no—
221M16—182no—
222C2×C8—34no—
223C2×C8—62no—
224C2×C8—181no—
225C2×C8#62612yes—
226C22×C3—21no—
227C22×C3—22no—
228C22×C3—41no—
229C22×C3—41no—
230C22×C3—42no—
231C22×C3#89612yes—
232C22×C3#89711yescharacteristic
233C22×C3#89712yes—
234C22×C3#94611yescharacteristic
235C2×D3—64no—
236C2×D3—62no—
237C2×D3—62no—
238C2×D3—64no—
239C2×D3—64no—
240C2×D3—124no—
241C2×D3—122no—
242C2×D3—122no—
243C2×D3—122no—
244C2×D3—121no—
245C2×D3—121no—
246C2×D3—122no—
247C2×D3—124no—
248C2×D3—121no—
249C2×D3—121no—
250C3×C4—22no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4#87411yescharacteristic
254C3×C4#88612yes—
255C3×C4#88611yescharacteristic
256C3×C4#89412yes—
257C3×C4#92911yescharacteristic
258C3×C4#94011yescharacteristic
259Dic3—122no—
260Dic3—121no—
261Dic3—121no—
262C32#209111yescharacteristic, complemented, Sylow
263C23—181no—
264C23—182no—
265C23—362no—
266C23#379711yescharacteristic
267C2×C4—181no—
268C2×C4—182no—
269C2×C4—362no—
270C2×C4—361no—
271C2×C4—361no—
272C2×C4#379611yescharacteristic
273C2×C4D3×D1212yes—
274C2×C4#380412yes—
275C2×C4C2×#62611yescharacteristic
276C8—22no—
277C8—64no—
278C8—122no—
279C8—361no—
280C2×C3—22no—
281C2×C3—22no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—22no—
285C2×C3—21no—
286C2×C3—42no—
287C2×C3#467711yescharacteristic
288C2×C3#499311yescharacteristic
289D3—124no—
290D3—122no—
291D3—122no—
292C22—41no—
293C22—182no—
294C22—184no—
295C22—361no—
296C22—362no—
297C22—361no—
298C22#6387111yescharacteristic
299C22#6389512yes—
300C4—361no—
301C4#6389012yes—
302C4#6391111yescharacteristic
303C4#6396611yescharacteristic
304C3—21no—
305C3#6872111yescharacteristic, complemented
306C3#7072911yescharacteristic, complemented
307C2—21no—
308C2—22no—
309C2—362no—
310C2#1059135011yescharacteristic
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
2. C3×#5125C2semidirect
3. #10591141C2semidirect
5. C3×C3⋊#338C2semidirect
24. #5125D3semidirect
27. C3⋊#338D3semidirect
262. C32#2091semidirect
305. C3#68721semidirect
306. C3#70729semidirect

Maximal subgroups

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

subgroupindex
#105928252
C3×#51252
#105911412
#105910742
C3×C3⋊#3382
#707293
#687213