Finite Group Databasebeta

← #11803879

Subgroups — #11803879

Order 1152.

1569 conjugacy classes of subgroups; only the 276 normal subgroups are shown.

normal subgroups only

This group has 1569 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
1C2×#63914C211yesmaximal, characteristic
2C2×#63898C212yesmaximal, complemented
3#10592631C211yesmaximal, characteristic, complemented
4C3×#4939C212yesmaximal, complemented
5#10591363C218yesmaximal, complemented
6#10591230C211yesmaximal, characteristic, complemented
7#76298—32nomaximal
8C22×C3×D12C2212yes—
9C22×#625C2214yes—
10C22×D3×Dic3C2214yes—
11C2×C32×C42C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4C2218yes—
15C2×C3×C4⋊Dic3C2212yes—
16C2×(C2×D3)⋊Dic3C2214yes—
17#63914C418yescomplemented
18#63898—28no—
19#63658C2214yes—
20#63579C2214yes—
21C2×#940—32no—
22C2×D4×Dic3—32no—
23C2×#893—32no—
24C3×#390—32no—
25#4977—32no—
26#4958—38no—
27#4956—38no—
28#4939D312yescomplemented
29#4932—32no—
30#4932—61no—
31C23×C3×D3C2314yes—
32C22×C32×C4C2312yes—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3C2312yes—
35C22×C3⋊Dic3C2312yes—
36C22×C3×Dic3C2314yes—
37C2×C3×D12—24no—
38C2×C3×D12—24no—
39C2×C3×D12C2×C418yescomplemented
40C2×#625—48no—
41C2×#625C2×C4116yescomplemented
42C2×D3×Dic3—28no—
43C2×D3×Dic3—48no—
44C32×C42—22no—
45C4×C3⋊Dic3C2×C414yescomplemented
46C4×C3⋊Dic3D414yescomplemented
47C3×(C2×D3)⋊C4—48no—
48C3×C4⋊Dic3—24no—
49(C2×D3)⋊Dic3—28no—
50#2328—91noSylow
51C22×C3×D4—32no—
52C22×#67—38no—
53C23×Dic3—34no—
54C22×D12C2×D312yes—
55C22×C4×D3—34no—
56C2×C3×C4⋊C4—32no—
57C2×C3×C22⋊C4—38no—
58C2×C3×C42—21no—
59C2×C3×C42C2×D312yes—
60C2×#217—34no—
61#940—316no—
62D4×Dic3—68no—
63C2×(C2×D3)⋊C4—34no—
64C2×(C2×D3)⋊C4C2×D318yes—
65C2×C4⋊Dic3C2×D312yes—
66C2×C4×Dic3—32no—
67C2×C4×Dic3—32no—
68C2×C4×Dic3—61no—
69C2×C4×Dic3—61no—
70#893—68no—
71C3⋊#95—34no—
72C3⋊#95—34no—
73C3⋊#95—38no—
74C3⋊#95—64no—
75C23×C32C2411yescharacteristic
76C22×C3×D3—24no—
77C22×C3×D3—24no—
78C22×C3×D3—28no—
79C22×C3×D3—28no—
80C22×C3×D3C22×C418yes—
81C2×C32×C4—22no—
82C2×C32×C4—24no—
83C2×C32×C4C22×C412yes—
84C2×C32×C4C2×D412yes—
85C2×C32×C4#4112yes—
86C2×C3⋊Dic3—24no—
87C2×C3⋊Dic3—24no—
88C2×C3⋊Dic3C22×C414yes—
89C2×C3⋊Dic3C2×D414yes—
90C2×C3×Dic3—24no—
91C2×C3×Dic3—28no—
92C3×D12—216no—
93#625—416no—
94D3×Dic3—416no—
95C2×#127—91no—
96C2×C4×D4—92no—
97#390—32no—
98#386—98no—
99#382—91no—
100#376—91no—
101C24×C3—34no—
102C23×D3C22×D314yes—
103C2×C3×D4—38no—
104C2×C3×D4—64no—
105C2×C3×D4—64no—
106C22×C3×C4—21no—
107C22×C3×C4—22no—
108C22×C3×C4—34no—
109C22×C3×C4C22×D314yes—
110C22×C3×C4C22×D312yes—
111C2×#67—332no—
112C2×#67—128no—
113C2×#67—128no—
114C22×Dic3—34no—
115C22×Dic3—32no—
116C22×Dic3—32no—
117C22×Dic3—62no—
118C22×Dic3—62no—
119C22×Dic3—68no—
120C22×Dic3—128no—
121C22×Dic3C22×D314yes—
122C2×D12—24no—
123C2×D12—24no—
124C2×D12C4×D318yescomplemented
125C2×C4×D3—68no—
126C2×C4×D3—128no—
127C3×C4⋊C4—64no—
128C3×C22⋊C4—128no—
129C3×C42—24no—
130C3×C42—24no—
131#217—68no—
132(C2×D3)⋊C4—48no—
133(C2×D3)⋊C4—68no—
134C4⋊Dic3—24no—
135C4×Dic3—38no—
136C4×Dic3—38no—
137C4×Dic3—64no—
138C4×Dic3—64no—
139C22×C32C23×C411yescharacteristic
140C22×C32C22×D411yescharacteristic
141C22×C32C2×#4111yescharacteristic
142C22×C32H(5,𝔽2)14yes—
143C2×C3×D3—28no—
144C2×C3×D3—216no—
145C2×C3×D3—44no—
146C2×C3×D3—44no—
147C2×C3×D3—48no—
148C32×C4—42no—
149C32×C4C4×D414yes—
150C3⋊Dic3—24no—
151C3⋊Dic3—24no—
152C3×Dic3—44no—
153C22×D4—32no—
154C22×D4—94no—
155C23×C4—94no—
156#127—98no—
157C4×D4—188no—
158C2×C4⋊C4—32no—
159C2×C22⋊C4—38no—
160C2×C22⋊C4—94no—
161C2×C42—91no—
162C2×C42—91no—
163C2×C42D3211yescharacteristic
164#95—94no—
165#95—94no—
166C23×C3—21no—
167C23×C3—38no—
168C23×C3—64no—
169C23×C3—64no—
170C23×C3—68no—
171C23×C3—68no—
172C23×C3C23×D312yes—
173C22×D3—24no—
174C22×D3—24no—
175C22×D3—28no—
176C22×D3—28no—
177C22×D3C2×C4×D318yes—
178C3×D4—616no—
179C2×C3×C4—24no—
180C2×C3×C4—24no—
181C2×C3×C4—24no—
182C2×C3×C4—24no—
183C2×C3×C4—22no—
184C2×C3×C4—22no—
185C2×C3×C4—22no—
186C2×C3×C4—44no—
187C2×C3×C4—64no—
188C2×C3×C4—68no—
189C2×C3×C4C2×C4×D314yes—
190C2×C3×C4D3×D414yes—
191C2×C3×C4#23714yes—
192#67—1232no—
193C2×Dic3—24no—
194C2×Dic3—28no—
195C2×Dic3—38no—
196C2×Dic3—34no—
197C2×Dic3—34no—
198C2×Dic3—64no—
199C2×Dic3—64no—
200C2×Dic3—64no—
201C2×Dic3—64no—
202C2×Dic3—64no—
203C2×Dic3—64no—
204C2×Dic3—124no—
205C2×Dic3—124no—
206C2×Dic3—1216no—
207D12—216no—
208C4×D3—1216no—
209C2×C32C2×C4×D411yescharacteristic
210C2×C32#51812yes—
211C2×C32#53512yes—
212C2×C32#54012yes—
213C3×D3—48no—
214C24—34no—
215C2×D4—38no—
216C2×D4—64no—
217C2×D4—64no—
218C2×D4—916no—
219C2×D4—368no—
220C22×C4—34no—
221C22×C4—92no—
222C22×C4—92no—
223C22×C4—188no—
224C22×C4—368no—
225C22×C4C2×D3212yes—
226C22×C4C2×D3211yescharacteristic
227C4⋊C4—64no—
228C22⋊C4—128no—
229C22⋊C4—188no—
230C42—22no—
231C42—94no—
232C42—94no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—24no—
236C22×C3—21no—
237C22×C3—68no—
238C22×C3—616no—
239C22×C3—124no—
240C22×C3—124no—
241C22×C3—128no—
242C22×C3C22×C4×D312yes—
243C22×C3C2×D3×D412yes—
244C22×C3C2×#23712yes—
245C22×C3#100414yes—
246C22×C3#100914yes—
247C2×D3—28no—
248C2×D3—216no—
249C2×D3—44no—
250C2×D3—44no—
251C2×D3—48no—
252C3×C4—24no—
253C3×C4—44no—
254C3×C4—44no—
255C3×C4—124no—
256C3×C4#67⋊C418yes—
257Dic3—44no—
258Dic3—64no—
259Dic3—64no—
260Dic3—68no—
261Dic3—124no—
262Dic3—124no—
263C32#232811yescharacteristic, complemented, Sylow
264C23—38no—
265C23—64no—
266C23—68no—
267C23—68no—
268C23—64no—
269C23C22×D3211yescharacteristic
270D4—616no—
271D4—3616no—
272C2×C4—24no—
273C2×C4—22no—
274C2×C4—64no—
275C2×C4—68no—
276C2×C4—94no—
277C2×C4—94no—
278C2×C4—184no—
279C2×C4—184no—
280C2×C4—3616no—
281C2×C4C4×D3212yes—
282C2×C4#380212yes—
283C2×C4#380512yes—
284C2×C3—21no—
285C2×C3—22no—
286C2×C3—22no—
287C2×C3—22no—
288C2×C3—128no—
289C2×C3C2×#67⋊C412yes—
290C2×C3#554514yes—
291C2×C3#561914yes—
292C2×C3#567412yes—
293C2×C3#571512yes—
294D3—48no—
295C22—68no—
296C22—616no—
297C22—124no—
298C22—124no—
299C22—128no—
300C22C2×C4×D3211yescharacteristic
301C22C2×#380211yescharacteristic
302C22#6430714yes—
303C22C2×#380511yescharacteristic
304C4—42no—
305C4—124no—
306C4—184no—
307C4—184no—
308C4#6390214yes—
309C3—21no—
310C3#7629812yescomplemented
311C2—128no—
312C2#1059399612yes—
313C2#1059401012yes—
314C2C2×#6390211yescharacteristic
315C2#1059504112yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC2×#63914C2
hypercenterC2×C42D32
hypocenterC32#2328
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#63898C2semidirect
3. #10592631C2semidirect
4. C3×#4939C2semidirect
5. #10591363C2semidirect
6. #10591230C2semidirect
17. #63914C4semidirect
28. #4939D3semidirect
39. C2×C3×D12C2×C4semidirect
41. C2×#625C2×C4semidirect
45. C4×C3⋊Dic3C2×C4semidirect
46. C4×C3⋊Dic3D4semidirect
124. C2×D12C4×D3semidirect
263. C32#2328semidirect
310. C3#76298semidirect

Maximal subgroups

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

subgroupindex
C2×#639142
C2×#638982
#105926312
C3×#49392
#105913632
#105912302
#762983