Finite Group Databasebeta

← #11802783

Subgroups — #11802783

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×#5212C212yesmaximal, complemented
3#10591714C212yesmaximal
4#10591705C212yesmaximal, complemented
5#10591266C218yesmaximal, complemented
6#74004—32nomaximal
7C24×C3⋊D3C2211yescharacteristic
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C2×#3752C418yescomplemented
11C2×#3752C2214yes—
12C2×C3×#217C2214yes—
13C2×C3×C4⋊Dic3C2214yescomplemented
14C2×#3722C2214yes—
15C2×#3722C2214yes—
16C2×Dic32C2214yescomplemented
17C3×C3⋊#95C2214yescomplemented
18#63579C2214yescomplemented
19C22×(C2×D3)⋊C4—32no—
20C22×(C2×D3)⋊C4—61no—
21C3×#380—32no—
22#5212D312yescomplemented
23#4990—38no—
24#4955—34no—
25Dic3×C22⋊C4—34no—
26#4670—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#3722—44no—
44#3722—44no—
45Dic32—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×C4⋊C4—34no—
54C2×C3×C22⋊C4—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×C4⋊Dic3C2×D314yescomplemented
64C2×C4×Dic3—38no—
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—32no—
93#379—92no—
94C4×C22⋊C4—92no—
95C24×C3—21no—
96C24×C3C22×D312yes—
97C23×D3—34no—
98C23×D3—38no—
99C23×D3—64no—
100C23×D3—62no—
101C23×D3—68no—
102C23×D3—64no—
103C23×D3—64no—
104C23×D3—124no—
105C23×D3—124no—
106C23×D3—124no—
107C23×D3—124no—
108C22×C3×C4—24no—
109C22×C3×C4—22no—
110C22×C3×C4—38no—
111C22×C3×C4—44no—
112C22×C3×C4—44no—
113C22×C3×C4C4×D318yes—
114C22×C3×C4C22×D312yes—
115C22×C3×C4C22×D312yes—
116C22×Dic3—34no—
117C22×Dic3—38no—
118C22×Dic3—64no—
119C22×Dic3—62no—
120C22×Dic3—124no—
121C22×Dic3—124no—
122C22×Dic3C22×D318yes—
123C3×C4⋊C4—124no—
124C3×C22⋊C4—68no—
125#217—28no—
126(C2×D3)⋊C4—316no—
127(C2×D3)⋊C4—316no—
128(C2×D3)⋊C4—616no—
129(C2×D3)⋊C4—128no—
130(C2×D3)⋊C4—128no—
131C4⋊Dic3—44no—
132C4×Dic3—128no—
133C22×C32—22no—
134C22×C32—22no—
135C22×C32—28no—
136C22×C32#11714yes—
137C22×C32C23×C411yescharacteristic
138C22×C32C2×#4112yes—
139C22×C32H(5,𝔽2)12yes—
140C22×C32H(5,𝔽2)12yes—
141C2×C3⋊D3—24no—
142C2×C3⋊D3—24no—
143C2×C3⋊D3—24no—
144C2×C3⋊D3—416no—
145C2×C3⋊D3—48no—
146C32×C4—24no—
147C3⋊Dic3—24no—
148C3×Dic3—48no—
149C25—91no—
150C23×C4—91no—
151C23×C4D3211yescharacteristic
152C2×C4⋊C4—34no—
153C2×C22⋊C4—34no—
154C2×C22⋊C4—98no—
155C2×C22⋊C4—94no—
156C2×C22⋊C4—94no—
157C2×C22⋊C4—94no—
158C2×C42—94no—
159#95—34no—
160#95—94no—
161C23×C3—24no—
162C23×C3—24no—
163C23×C3—24no—
164C23×C3—24no—
165C23×C3—21no—
166C23×C3—24no—
167C23×C3—22no—
168C23×C3C2×C4×D314yes—
169C23×C3#23714yes—
170C23×C3#23914yes—
171C23×C3C23×D312yes—
172C22×D3—38no—
173C22×D3—64no—
174C22×D3—68no—
175C22×D3—616no—
176C22×D3—616no—
177C22×D3—64no—
178C22×D3—68no—
179C22×D3—64no—
180C22×D3—68no—
181C22×D3—124no—
182C22×D3—124no—
183C22×D3—128no—
184C22×D3—128no—
185C22×D3—128no—
186C22×D3—128no—
187C22×D3—1232no—
188C22×D3—1216no—
189C22×D3—1216no—
190C2×C3×C4—24no—
191C2×C3×C4—24no—
192C2×C3×C4—24no—
193C2×C3×C4—44no—
194C2×C3×C4—48no—
195C2×C3×C4—48no—
196C2×C3×C4—68no—
197C2×C3×C4—68no—
198C2×C3×C4—68no—
199C2×C3×C4C2×C4×D314yes—
200C2×C3×C4C2×C4×D314yes—
201C2×Dic3—28no—
202C2×Dic3—28no—
203C2×Dic3—28no—
204C2×Dic3—38no—
205C2×Dic3—64no—
206C2×Dic3—68no—
207C2×Dic3—124no—
208C2×Dic3—128no—
209C2×Dic3—128no—
210C2×C32—24no—
211C2×C32C2×#11711yescharacteristic
212C2×C32#51811yescharacteristic
213C2×C32#51811yescharacteristic
214C2×C32#53814yes—
215C3⋊D3—44no—
216C24—92no—
217C24—94no—
218C24—184no—
219C24—362no—
220C24—362no—
221C24C2×D3211yescharacteristic
222C22×C4—38no—
223C22×C4—42no—
224C22×C4—92no—
225C22×C4—94no—
226C22×C4—362no—
227C22×C4#62414yes—
228C22×C4C2×D3212yes—
229C4⋊C4—124no—
230C22⋊C4—68no—
231C22⋊C4—916no—
232C22⋊C4—364no—
233C22⋊C4—364no—
234C42—364no—
235C22×C3—24no—
236C22×C3—24no—
237C22×C3—216no—
238C22×C3—28no—
239C22×C3—24no—
240C22×C3—24no—
241C22×C3—28no—
242C22×C3—22no—
243C22×C3—22no—
244C22×C3—21no—
245C22×C3—22no—
246C22×C3—24no—
247C22×C3#89218yes—
248C22×C3C22×C4×D312yes—
249C22×C3C2×#23712yes—
250C22×C3#100414yes—
251C22×C3C2×#23912yes—
252C22×C3#100914yes—
253C2×D3—68no—
254C2×D3—68no—
255C2×D3—68no—
256C2×D3—68no—
257C2×D3—124no—
258C2×D3—124no—
259C2×D3—1232no—
260C2×D3—1232no—
261C2×D3—1216no—
262C2×D3—128no—
263C2×D3—128no—
264C3×C4—24no—
265C3×C4—24no—
266C3×C4—44no—
267C3×C4—128no—
268Dic3—48no—
269Dic3—68no—
270Dic3—124no—
271C32#231211yescharacteristic, complemented, Sylow
272C23—22no—
273C23—22no—
274C23—94no—
275C23—184no—
276C23—184no—
277C23—184no—
278C23—188no—
279C23—364no—
280C23—364no—
281C23—3616no—
282C23#379614yes—
283C23C2×#62412yes—
284C23C22×D3211yescharacteristic
285C2×C4—24no—
286C2×C4—44no—
287C2×C4—68no—
288C2×C4—68no—
289C2×C4—68no—
290C2×C4—94no—
291C2×C4—184no—
292C2×C4—364no—
293C2×C4C2×#62414yes—
294C2×C3—28no—
295C2×C3—28no—
296C2×C3—21no—
297C2×C3—24no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3#548612yes—
301C2×C3C2×#89212yes—
302C2×C3#552112yes—
303C2×C3#561714yes—
304C2×C3#564414yes—
305D3—128no—
306D3—128no—
307C22—28no—
308C22—22no—
309C22—22no—
310C22—184no—
311C22—184no—
312C22—184no—
313C22—3616no—
314C22—368no—
315C22#6384914yes—
316C22C2×#379612yes—
317C22#6430812yes—
318C22C22×#62411yescharacteristic
319C22#6433012yes—
320C4—24no—
321C4—128no—
322C4—184no—
323C3—21no—
324C3#7400412yescomplemented
325C2—24no—
326C2—364no—
327C2C2×#6384911yescharacteristic
328C2#1059497914yes—
329C2#1059499611yescharacteristic
330C2#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×#5212C2semidirect
4. #10591705C2semidirect
5. #10591266C2semidirect
10. C2×#3752C4semidirect
13. C2×C3×C4⋊Dic3C22semidirect
16. C2×Dic32C22semidirect
17. C3×C3⋊#95C22semidirect
18. #63579C22semidirect
22. #5212D3semidirect
63. C2×C4⋊Dic3C2×D3semidirect
67. C3⋊#95C2×D3semidirect
271. C32#2312semidirect
324. C3#74004semidirect

Maximal subgroups

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

subgroupindex
C22×#37522
C3×#52122
#105917142
#105917052
#105912662
#740043