Finite Group Databasebeta

← #11802779

Subgroups — #11802779

Order 1152.

1681 conjugacy classes of subgroups; only the 276 normal subgroups are shown.

normal subgroups only

This group has 1681 conjugacy classes of subgroups — too many to draw. Only its 276 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
1C22×#3752C211yesmaximal, characteristic
2C3×C4×#217C212yesmaximal, complemented
3#10591720C212yesmaximal, complemented
4#10591714C212yesmaximal
5#10591202C218yesmaximal, complemented
6#73567—32nomaximal
7C24×C3⋊D3C2211yescharacteristic
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C2×#3752C418yescomplemented
11C2×#3752C2214yes—
12C2×C3×#217C2214yes—
13C2×C3×C4×Dic3C2214yescomplemented
14C2×#3724C2214yescomplemented
15C2×#3722C2214yes—
16C2×#3722C2214yes—
17C3×C3⋊#95C2214yescomplemented
18#63579C2214yescomplemented
19C22×(C2×D3)⋊C4—32no—
20C22×(C2×D3)⋊C4—61no—
21C3×C4×C22⋊C4—32no—
22C4×#217D312yescomplemented
23#4955—34no—
24#4942—34no—
25#4940—38no—
26#4669—38no—
27C24×C32C2311yescharacteristic
28C23×C3⋊D3—24no—
29C23×C3⋊D3—42no—
30C23×C3⋊D3—42no—
31C23×C3⋊D3C2×C414yes—
32C23×C3⋊D3C2312yes—
33C22×C32×C4—42no—
34C22×C32×C4C2×C414yes—
35C22×C32×C4C2312yes—
36C22×C3⋊Dic3—42no—
37C22×C3⋊Dic3C2×C414yes—
38C22×C3⋊Dic3C2312yes—
39C22×C3×Dic3C2318yes—
40#3752C2×C4116yes—
41C3×#217—28no—
42C3×C4×Dic3—44no—
43#3724—44no—
44#3722—44no—
45#3722—44no—
46#2312—91noSylow
47C24×D3—32no—
48C24×D3—61no—
49C23×C3×C4—21no—
50C23×C3×C4C2×D312yes—
51C23×Dic3—32no—
52C23×Dic3—61no—
53C2×C3×C22⋊C4—34no—
54C2×C3×C42—34no—
55C2×#217C2×D314yes—
56C2×(C2×D3)⋊C4—316no—
57C2×(C2×D3)⋊C4—34no—
58C2×(C2×D3)⋊C4—34no—
59C2×(C2×D3)⋊C4—38no—
60C2×(C2×D3)⋊C4—38no—
61C2×(C2×D3)⋊C4—68no—
62C2×(C2×D3)⋊C4—64no—
63C2×Dic3⋊C4—38no—
64C2×C4×Dic3C2×D314yescomplemented
65C3×#95—34no—
66C3⋊#95—38no—
67C3⋊#95C2×D314yescomplemented
68C23×C32—22no—
69C23×C32—22no—
70C23×C32C22×C412yes—
71C23×C32#4114yes—
72C23×C32C2411yescharacteristic
73C22×C3⋊D3—28no—
74C22×C3⋊D3—24no—
75C22×C3⋊D3—24no—
76C22×C3⋊D3—24no—
77C22×C3⋊D3—44no—
78C22×C3⋊D3—44no—
79C22×C3⋊D3—416no—
80C22×C3⋊D3C22×C414yes—
81C2×C32×C4—24no—
82C2×C32×C4—44no—
83C2×C32×C4C22×C414yes—
84C2×C3⋊Dic3—24no—
85C2×C3⋊Dic3—44no—
86C2×C3⋊Dic3C22×C414yes—
87C2×C3×Dic3—28no—
88C2×C3×Dic3—28no—
89C2×C3×Dic3—28no—
90C22×C22⋊C4—91no—
91#388—98no—
92#380—92no—
93#379—92no—
94C4×C22⋊C4—32no—
95C24×C3—21no—
96C24×C3C22×D312yes—
97C23×D3—34no—
98C23×D3—38no—
99C23×D3—64no—
100C23×D3—62no—
101C23×D3—68no—
102C23×D3—68no—
103C23×D3—124no—
104C23×D3—124no—
105C23×D3—124no—
106C23×D3—124no—
107C22×C3×C4—24no—
108C22×C3×C4—22no—
109C22×C3×C4—38no—
110C22×C3×C4—44no—
111C22×C3×C4—44no—
112C22×C3×C4C4×D318yes—
113C22×C3×C4C22×D312yes—
114C22×C3×C4C22×D312yes—
115C22×Dic3—34no—
116C22×Dic3—38no—
117C22×Dic3—64no—
118C22×Dic3—62no—
119C22×Dic3—124no—
120C22×Dic3—124no—
121C22×Dic3C22×D318yes—
122C3×C22⋊C4—68no—
123C3×C42—124no—
124#217—28no—
125(C2×D3)⋊C4—316no—
126(C2×D3)⋊C4—316no—
127(C2×D3)⋊C4—616no—
128(C2×D3)⋊C4—128no—
129(C2×D3)⋊C4—128no—
130Dic3⋊C4—128no—
131C4×Dic3—44no—
132C22×C32—22no—
133C22×C32—22no—
134C22×C32—28no—
135C22×C32#11714yes—
136C22×C32C23×C411yescharacteristic
137C22×C32C2×#4112yes—
138C22×C32H(5,𝔽2)12yes—
139C22×C32H(5,𝔽2)12yes—
140C2×C3⋊D3—24no—
141C2×C3⋊D3—24no—
142C2×C3⋊D3—24no—
143C2×C3⋊D3—416no—
144C2×C3⋊D3—48no—
145C32×C4—24no—
146C3⋊Dic3—24no—
147C3×Dic3—48no—
148C25—91no—
149C23×C4—91no—
150C23×C4D3211yescharacteristic
151C2×C4⋊C4—94no—
152C2×C22⋊C4—34no—
153C2×C22⋊C4—98no—
154C2×C22⋊C4—94no—
155C2×C22⋊C4—94no—
156C2×C22⋊C4—94no—
157C2×C42—34no—
158#95—34no—
159#95—94no—
160C23×C3—24no—
161C23×C3—24no—
162C23×C3—24no—
163C23×C3—24no—
164C23×C3—21no—
165C23×C3—24no—
166C23×C3—22no—
167C23×C3C2×C4×D314yes—
168C23×C3#23518yes—
169C23×C3C23×D312yes—
170C22×D3—38no—
171C22×D3—64no—
172C22×D3—68no—
173C22×D3—616no—
174C22×D3—616no—
175C22×D3—68no—
176C22×D3—68no—
177C22×D3—68no—
178C22×D3—124no—
179C22×D3—124no—
180C22×D3—128no—
181C22×D3—128no—
182C22×D3—128no—
183C22×D3—128no—
184C22×D3—1232no—
185C22×D3—1232no—
186C2×C3×C4—24no—
187C2×C3×C4—24no—
188C2×C3×C4—24no—
189C2×C3×C4—44no—
190C2×C3×C4—48no—
191C2×C3×C4—48no—
192C2×C3×C4—68no—
193C2×C3×C4—68no—
194C2×C3×C4—68no—
195C2×C3×C4C2×C4×D314yes—
196C2×C3×C4C2×C4×D314yes—
197C2×Dic3—28no—
198C2×Dic3—28no—
199C2×Dic3—28no—
200C2×Dic3—38no—
201C2×Dic3—64no—
202C2×Dic3—68no—
203C2×Dic3—124no—
204C2×Dic3—128no—
205C2×Dic3—128no—
206C2×C32—24no—
207C2×C32C2×#11711yescharacteristic
208C2×C32#51811yescharacteristic
209C2×C32#51811yescharacteristic
210C2×C32#53814yes—
211C3⋊D3—44no—
212C24—92no—
213C24—94no—
214C24—184no—
215C24—362no—
216C24—362no—
217C24C2×D3211yescharacteristic
218C22×C4—38no—
219C22×C4—42no—
220C22×C4—92no—
221C22×C4—94no—
222C22×C4—362no—
223C22×C4#62414yes—
224C22×C4C2×D3212yes—
225C4⋊C4—364no—
226C22⋊C4—68no—
227C22⋊C4—916no—
228C22⋊C4—364no—
229C22⋊C4—364no—
230C42—124no—
231C22×C3—24no—
232C22×C3—24no—
233C22×C3—216no—
234C22×C3—24no—
235C22×C3—24no—
236C22×C3—216no—
237C22×C3—22no—
238C22×C3—22no—
239C22×C3—21no—
240C22×C3—22no—
241C22×C3—24no—
242C22×C3#87218yes—
243C22×C3C22×C4×D312yes—
244C22×C3C2×#23514yes—
245C22×C3#100414yes—
246C22×C3#100914yes—
247C2×D3—68no—
248C2×D3—68no—
249C2×D3—68no—
250C2×D3—68no—
251C2×D3—124no—
252C2×D3—124no—
253C2×D3—1232no—
254C2×D3—1232no—
255C2×D3—1216no—
256C2×D3—1216no—
257C3×C4—24no—
258C3×C4—24no—
259C3×C4—44no—
260C3×C4—128no—
261Dic3—48no—
262Dic3—68no—
263Dic3—124no—
264C32#231211yescharacteristic, complemented, Sylow
265C23—22no—
266C23—22no—
267C23—94no—
268C23—184no—
269C23—184no—
270C23—184no—
271C23—188no—
272C23—364no—
273C23—364no—
274C23—3616no—
275C23#379814yes—
276C23C2×#62412yes—
277C23C22×D3211yescharacteristic
278C2×C4—24no—
279C2×C4—44no—
280C2×C4—68no—
281C2×C4—68no—
282C2×C4—68no—
283C2×C4—94no—
284C2×C4—184no—
285C2×C4—364no—
286C2×C4C2×#62414yes—
287C2×C3—28no—
288C2×C3—28no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—24no—
293C2×C3C2×#87212yes—
294C2×C3#548612yes—
295C2×C3#552112yes—
296C2×C3#556018yes—
297D3—128no—
298D3—128no—
299C22—22no—
300C22—22no—
301C22—28no—
302C22—184no—
303C22—184no—
304C22—184no—
305C22—3616no—
306C22—368no—
307C22#6387414yes—
308C22C2×#379812yes—
309C22#6430812yes—
310C22C22×#62411yescharacteristic
311C22#6433012yes—
312C4—24no—
313C4—128no—
314C4—184no—
315C3—21no—
316C3#7356712yescomplemented
317C2—24no—
318C2—364no—
319C2C2×#6387411yescharacteristic
320C2#1059499611yescharacteristic
321C2#1059503914yes—
322C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C3⋊D3C22
hypercenterC23×C4D32
hypocenterC32#2312
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×#217C2semidirect
3. #10591720C2semidirect
5. #10591202C2semidirect
10. C2×#3752C4semidirect
13. C2×C3×C4×Dic3C22semidirect
14. C2×#3724C22semidirect
17. C3×C3⋊#95C22semidirect
18. #63579C22semidirect
22. C4×#217D3semidirect
64. C2×C4×Dic3C2×D3semidirect
67. C3⋊#95C2×D3semidirect
264. C32#2312semidirect
316. C3#73567semidirect

Maximal subgroups

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

subgroupindex
C22×#37522
C3×C4×#2172
#105917202
#105917142
#105912022
#735673