Finite Group Databasebeta

← #11801967

Subgroups — #11801967

Order 1152.

1213 conjugacy classes of subgroups; only the 292 normal subgroups are shown.

normal subgroups only

This group has 1213 conjugacy classes of subgroups — too many to draw. Only its 292 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×#64135C211yesmaximal, characteristic
2C3×C4×#217C212yesmaximal
3#10591703C214yesmaximal
4C4×#3724C212yesmaximal, complemented
5#10591271C214yesmaximal, complemented
6C4×Dic32C211yesmaximal, characteristic, complemented
7#10591222C211yesmaximal, characteristic, complemented
8#73440—32nomaximal
9C23×C32×C4C2211yescharacteristic
10C2×#3757C2212yes—
11#64135C418yescomplemented
12C2×C4⋊(C3⋊Dic3)C2212yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×#217C2214yes—
16C2×C3×C4×Dic3C2212yes—
17C2×C3×C4×Dic3C2212yes—
18C2×#3724C2214yes—
19C2×Dic32C2214yes—
20C3×C3⋊#95C2214yes—
21#63579C2214yes—
22#63579C2214yes—
23C2×#926—32no—
24C2×#926—61no—
25C3×C4×C22⋊C4—32no—
26C4×#217D312yes—
27#4945—34no—
28#4944—34no—
29#4932—32no—
30C4×Dic3⋊C4—32no—
31C4×Dic3⋊C4—32no—
32C42×Dic3—32no—
33#4654—34no—
34#4653—34no—
35C24×C32C2311yescharacteristic
36C22×C32×C4—24no—
37C22×C32×C4C2×C414yes—
38C22×C32×C4C2311yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3C2312yes—
41C22×C3⋊Dic3C2312yes—
42C22×C3×Dic3C2314yes—
43C22×C3×Dic3C2314yes—
44#3757C2×C418yes—
45C4⋊(C3⋊Dic3)C2×C418yes—
46C4×C3⋊Dic3C2×C414yes—
47C4×C3⋊Dic3C2×C414yes—
48C3×#217—28no—
49C3×C4×Dic3—24no—
50C3×C4×Dic3—24no—
51#3724—28no—
52Dic32—28no—
53#2298—91noSylow
54C23×C3×C4—21no—
55C23×C3×C4C2×D312yes—
56C2×C3×C22⋊C4—34no—
57C2×C3×C42—32no—
58C2×C3×C42—32no—
59C2×#217—32no—
60C2×#217—32no—
61C2×#217—62no—
62C2×#217C2×D314yes—
63#926—316no—
64#926—68no—
65C2×C4⋊Dic3—32no—
66C2×C4⋊Dic3—32no—
67C2×C4⋊Dic3—62no—
68C2×Dic3⋊C4—34no—
69C2×Dic3⋊C4—34no—
70C2×C4×Dic3—32no—
71C2×C4×Dic3—32no—
72C2×C4×Dic3—34no—
73C2×C4×Dic3—34no—
74C2×C4×Dic3—61no—
75C2×C4×Dic3—61no—
76C2×C4×Dic3C2×D312yes—
77C2×C4×Dic3C2×D312yes—
78C3×#95—34no—
79C3⋊#95—34no—
80C3⋊#95—34no—
81C3⋊#95—34no—
82C3⋊#95—34no—
83C3⋊#95C2×D314yes—
84C23×C32—22no—
85C23×C32—24no—
86C23×C32C22×C412yes—
87C23×C32C2411yescharacteristic
88C2×C32×C4—22no—
89C2×C32×C4—28no—
90C2×C32×C4C22×C412yes—
91C2×C32×C4C22×C412yes—
92C2×C32×C4#4114yes—
93C2×C3⋊Dic3—24no—
94C2×C3⋊Dic3—24no—
95C2×C3⋊Dic3C22×C414yes—
96C2×C3⋊Dic3C22×C414yes—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—24no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—24no—
101C2×C3×Dic3—24no—
102C2×C3×Dic3#4118yes—
103C2×#117—91no—
104#388—94no—
105#387—94no—
106C4×C4⋊C4—92no—
107C4×C22⋊C4—32no—
108#376—91no—
109C43—91no—
110C24×C3—21no—
111C24×C3C22×D312yes—
112C22×C3×C4—28no—
113C22×C3×C4—24no—
114C22×C3×C4—24no—
115C22×C3×C4—24no—
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4—34no—
119C22×C3×C4—34no—
120C22×C3×C4C4×D318yes—
121C22×C3×C4C22×D312yes—
122C22×C3×C4C22×D312yes—
123C22×Dic3—32no—
124C22×Dic3—32no—
125C22×Dic3—32no—
126C22×Dic3—32no—
127C22×Dic3—62no—
128C22×Dic3—62no—
129C22×Dic3C22×D314yes—
130C22×Dic3C22×D314yes—
131C3×C22⋊C4—68no—
132C3×C42—64no—
133C3×C42—64no—
134#217—28no—
135#217—38no—
136#217—38no—
137#217—68no—
138C4⋊Dic3—38no—
139C4⋊Dic3—38no—
140C4⋊Dic3—68no—
141Dic3⋊C4—68no—
142Dic3⋊C4—68no—
143C4×Dic3—24no—
144C4×Dic3—24no—
145C4×Dic3—38no—
146C4×Dic3—38no—
147C4×Dic3—64no—
148C4×Dic3—64no—
149C4×Dic3—68no—
150C4×Dic3—68no—
151C22×C32—22no—
152C22×C32—24no—
153C22×C32—44no—
154C22×C32C23×C411yescharacteristic
155C22×C32C2×#4114yes—
156C22×C32C2×#4112yes—
157C32×C4—22no—
158C32×C4#11714yes—
159C3⋊Dic3—24no—
160C3⋊Dic3—24no—
161C3×Dic3—28no—
162C3×Dic3—44no—
163C23×C4D3211yescharacteristic
164#117—98no—
165C2×C4⋊C4—92no—
166C2×C4⋊C4—94no—
167C2×C22⋊C4—34no—
168C2×C22⋊C4—92no—
169C2×C42—32no—
170C2×C42—32no—
171C2×C42—91no—
172C2×C42—91no—
173C2×C42—94no—
174#95—34no—
175#95—94no—
176#95—94no—
177C23×C3—24no—
178C23×C3—24no—
179C23×C3—22no—
180C23×C3—22no—
181C23×C3—24no—
182C23×C3—21no—
183C23×C3—22no—
184C23×C3—44no—
185C23×C3C2×C4×D314yes—
186C23×C3C23×D312yes—
187C2×C3×C4—24no—
188C2×C3×C4—216no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—216no—
192C2×C3×C4—24no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—38no—
196C2×C3×C4—64no—
197C2×C3×C4—64no—
198C2×C3×C4—64no—
199C2×C3×C4—64no—
200C2×C3×C4—64no—
201C2×C3×C4C2×C4×D314yes—
202C2×C3×C4C2×C4×D314yes—
203C2×C3×C4#23714yes—
204C2×C3×C4#23714yes—
205C2×Dic3—24no—
206C2×Dic3—24no—
207C2×Dic3—24no—
208C2×Dic3—24no—
209C2×Dic3—24no—
210C2×Dic3—34no—
211C2×Dic3—34no—
212C2×Dic3—34no—
213C2×Dic3—34no—
214C2×Dic3—64no—
215C2×Dic3—64no—
216C2×Dic3—64no—
217C2×Dic3—64no—
218C2×Dic3—64no—
219C2×Dic3—64no—
220C2×Dic3—124no—
221C2×Dic3—124no—
222C2×Dic3#23518yes—
223C2×C32—42no—
224C2×C32C2×#11711yescharacteristic
225C2×C32C4×#4112yes—
226C2×C32#52914yes—
227C24C2×D3211yescharacteristic
228C22×C4—24no—
229C22×C4—34no—
230C22×C4—34no—
231C22×C4—92no—
232C22×C4—92no—
233C22×C4#62414yes—
234C22×C4C2×D3211yescharacteristic
235C22×C4C2×D3211yescharacteristic
236C4⋊C4—98no—
237C4⋊C4—188no—
238C22⋊C4—68no—
239C22⋊C4—98no—
240C42—64no—
241C42—64no—
242C42—94no—
243C42—94no—
244C42—188no—
245C22×C3—24no—
246C22×C3—24no—
247C22×C3—24no—
248C22×C3—24no—
249C22×C3—24no—
250C22×C3—22no—
251C22×C3—21no—
252C22×C3—44no—
253C22×C3—48no—
254C22×C3—44no—
255C22×C3—44no—
256C22×C3C22×C4×D312yes—
257C22×C3C2×#23514yes—
258C22×C3C2×#23712yes—
259C22×C3C2×#23712yes—
260C22×C3D3×#4114yes—
261C3×C4—24no—
262C3×C4—24no—
263C3×C4—24no—
264C3×C4—68no—
265C3×C4—124no—
266C3×C4#87718yes—
267Dic3—28no—
268Dic3—44no—
269Dic3—64no—
270Dic3—64no—
271Dic3—64no—
272Dic3—64no—
273Dic3—124no—
274Dic3—124no—
275C32#229811yescharacteristic, complemented, Sylow
276C23—24no—
277C23—22no—
278C23C2×#62412yes—
279C23C22×D3211yescharacteristic
280C2×C4—22no—
281C2×C4—28no—
282C2×C4—38no—
283C2×C4—64no—
284C2×C4—64no—
285C2×C4—64no—
286C2×C4—64no—
287C2×C4—64no—
288C2×C4—94no—
289C2×C4—94no—
290C2×C4—184no—
291C2×C4—184no—
292C2×C4#380514yes—
293C2×C4C2×#62412yes—
294C2×C4C2×#62412yes—
295C2×C3—24no—
296C2×C3—22no—
297C2×C3—21no—
298C2×C3—44no—
299C2×C3—44no—
300C2×C3C4×#23512yes—
301C2×C3C2×#87712yes—
302C2×C3#552212yes—
303C2×C3#553814yes—
304C2×C3#555714yes—
305C22—24no—
306C22—22no—
307C22—44no—
308C22D3×#23514yes—
309C22C2×#380512yes—
310C22C22×#62411yescharacteristic
311C4—22no—
312C4—68no—
313C4—124no—
314C4—184no—
315C4—184no—
316C4#6395714yes—
317C3—21no—
318C3#7344012yescomplemented
319C2—42no—
320C2#1059493414yes—
321C2#1059495412yes—
322C2C2×#6395711yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2298
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C4×#3724C2semidirect
5. #10591271C2semidirect
6. C4×Dic32C2semidirect
7. #10591222C2semidirect
11. #64135C4semidirect
275. C32#2298semidirect
318. C3#73440semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C3×C4×#2172
#105917032
C4×#37242
#105912712
C4×Dic322
#105912222
#734403