Finite Group Databasebeta

← #11801151

Subgroups — #11801151

Order 1152.

1385 conjugacy classes of subgroups.

The subgroup lattice has 343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊Dic3C211yesmaximal, characteristic
2C3×#5211C212yesmaximal
3#10591720C212yesmaximal
4#10591705C212yesmaximal
5#10591360C212yesmaximal, complemented
6#10591257C212yesmaximal, complemented
7#10591252C212yesmaximal, complemented
8#10591229C212yesmaximal, complemented
9#74051—32nomaximal
10C23×C32×C4C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C2×C4×C3⋊Dic3C418yescomplemented
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×#217C2214yes—
19C2×#3724C2214yes—
20C2×Dic32C2214yes—
21C3×C3⋊#95C2214yes—
22C3×C3⋊#95C2214yes—
23#63579C2214yes—
24#63579C2214yes—
25C22×C4×Dic3—32no—
26C22×C4×Dic3—61no—
27C3×#381—32no—
28#5211D312yes—
29#4942—34no—
30Dic3×C22⋊C4—34no—
31#4651—34no—
32#4650—34no—
33#4649—34no—
34#4648—34no—
35C24×C32C2311yescharacteristic
36C22×C32×C4—24no—
37C22×C32×C4C2×C414yes—
38C22×C32×C4C2311yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3—24no—
41C22×C3⋊Dic3—24no—
42C22×C3⋊Dic3C2×C414yes—
43C22×C3⋊Dic3C2×C414yes—
44C22×C3⋊Dic3C2311yescharacteristic
45C22×C3⋊Dic3C2311yescharacteristic
46C22×C3⋊Dic3C2311yescharacteristic
47C22×C3⋊Dic3C2311yescharacteristic
48C22×C3×Dic3C2318yes—
49C4×C3⋊Dic3C2×C414yes—
50C4×C3⋊Dic3C2×C414yes—
51C4×C3⋊Dic3C2×C414yes—
52C4×C3⋊Dic3C2×C414yes—
53C3×#217—28no—
54#3724—28no—
55Dic32—28no—
56#2283—91noSylow
57C23×C3×C4—21no—
58C23×C3×C4C2×D312yes—
59C23×Dic3—32no—
60C23×Dic3—32no—
61C23×Dic3—61no—
62C23×Dic3—61no—
63C2×C3×C22⋊C4—34no—
64C2×#217C2×D314yes—
65C2×Dic3⋊C4—38no—
66C2×C4×Dic3—316no—
67C2×C4×Dic3—32no—
68C2×C4×Dic3—32no—
69C2×C4×Dic3—32no—
70C2×C4×Dic3—32no—
71C2×C4×Dic3—38no—
72C2×C4×Dic3—68no—
73C2×C4×Dic3—61no—
74C2×C4×Dic3—61no—
75C2×C4×Dic3—61no—
76C2×C4×Dic3—61no—
77C3×#95—34no—
78C3×#95—34no—
79C3⋊#95—38no—
80C3⋊#95—38no—
81C3⋊#95C2×D314yes—
82C3⋊#95C2×D314yes—
83C23×C32—22no—
84C23×C32—22no—
85C23×C32C22×C412yes—
86C23×C32#4114yes—
87C23×C32C2411yescharacteristic
88C2×C32×C4—28no—
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4C22×C412yes—
92C2×C32×C4C22×C412yes—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—28no—
96C2×C3⋊Dic3—28no—
97C2×C3⋊Dic3C22×C412yes—
98C2×C3⋊Dic3C22×C412yes—
99C2×C3⋊Dic3C22×C412yes—
100C2×C3⋊Dic3C22×C412yes—
101C2×C3⋊Dic3#4114yes—
102C2×C3⋊Dic3#4114yes—
103C2×C3×Dic3—28no—
104C2×C3×Dic3—28no—
105C2×C3×Dic3—28no—
106C22×C42—91no—
107#383—92no—
108#382—92no—
109#381—32no—
110#380—92no—
111C4×C4⋊C4—92no—
112C4×C22⋊C4—92no—
113#376—92no—
114C24×C3—21no—
115C24×C3C22×D312yes—
116C22×C3×C4—28no—
117C22×C3×C4—28no—
118C22×C3×C4—24no—
119C22×C3×C4—21no—
120C22×C3×C4—21no—
121C22×C3×C4—38no—
122C22×C3×C4C4×D318yes—
123C22×C3×C4C22×D312yes—
124C22×C3×C4C22×D312yes—
125C22×Dic3—32no—
126C22×Dic3—32no—
127C22×Dic3—38no—
128C22×Dic3—38no—
129C22×Dic3—32no—
130C22×Dic3—32no—
131C22×Dic3—64no—
132C22×Dic3—64no—
133C22×Dic3—61no—
134C22×Dic3—61no—
135C22×Dic3—61no—
136C22×Dic3—61no—
137C22×Dic3—68no—
138C22×Dic3—68no—
139C22×Dic3—68no—
140C22×Dic3—68no—
141C22×Dic3C22×D318yes—
142C3×C22⋊C4—68no—
143#217—28no—
144Dic3⋊C4—616no—
145C4×Dic3—38no—
146C4×Dic3—38no—
147C4×Dic3—38no—
148C4×Dic3—38no—
149C4×Dic3—64no—
150C4×Dic3—64no—
151C4×Dic3—64no—
152C4×Dic3—64no—
153C4×Dic3—616no—
154C22×C32—22no—
155C22×C32—22no—
156C22×C32—28no—
157C22×C32#11714yes—
158C22×C32C23×C411yescharacteristic
159C22×C32C2×#4112yes—
160C22×C32C2×#4112yes—
161C22×C32C2×#4112yes—
162C32×C4—22no—
163C32×C4—22no—
164C3⋊Dic3—22no—
165C3⋊Dic3—22no—
166C3⋊Dic3#11714yes—
167C3⋊Dic3#11714yes—
168C3×Dic3—48no—
169C23×C4—91no—
170C23×C4—91no—
171C23×C4D3211yescharacteristic
172C2×C4⋊C4—94no—
173C2×C22⋊C4—34no—
174C2×C42—98no—
175C2×C42—91no—
176C2×C42—91no—
177C2×C42—91no—
178C2×C42—91no—
179C2×C42—94no—
180#95—34no—
181#95—34no—
182#95—94no—
183#95—94no—
184C23×C3—24no—
185C23×C3—24no—
186C23×C3—24no—
187C23×C3—24no—
188C23×C3—21no—
189C23×C3—24no—
190C23×C3—22no—
191C23×C3C2×C4×D314yes—
192C23×C3#23718yes—
193C23×C3C23×D312yes—
194C2×C3×C4—24no—
195C2×C3×C4—24no—
196C2×C3×C4—216no—
197C2×C3×C4—216no—
198C2×C3×C4—24no—
199C2×C3×C4—24no—
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—68no—
203C2×C3×C4—68no—
204C2×C3×C4—68no—
205C2×C3×C4C2×C4×D314yes—
206C2×C3×C4C2×C4×D314yes—
207C2×Dic3—28no—
208C2×Dic3—28no—
209C2×Dic3—28no—
210C2×Dic3—34no—
211C2×Dic3—34no—
212C2×Dic3—38no—
213C2×Dic3—38no—
214C2×Dic3—34no—
215C2×Dic3—34no—
216C2×Dic3—62no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—64no—
221C2×Dic3—64no—
222C2×Dic3—616no—
223C2×Dic3—616no—
224C2×Dic3—616no—
225C2×Dic3—616no—
226C2×Dic3—64no—
227C2×Dic3—64no—
228C2×Dic3—64no—
229C2×Dic3—64no—
230C2×C32—24no—
231C2×C32C2×#11711yescharacteristic
232C2×C32C2×#11711yescharacteristic
233C2×C32C2×#11711yescharacteristic
234C2×C32#52914yes—
235C24C2×D3211yescharacteristic
236C22×C4—24no—
237C22×C4—38no—
238C22×C4—91no—
239C22×C4—91no—
240C22×C4—91no—
241C22×C4—91no—
242C22×C4—94no—
243C22×C4—94no—
244C22×C4—184no—
245C22×C4—184no—
246C22×C4#62414yes—
247C22×C4C2×D3211yescharacteristic
248C22×C4C2×D3211yescharacteristic
249C4⋊C4—188no—
250C22⋊C4—68no—
251C42—94no—
252C42—94no—
253C42—94no—
254C42—94no—
255C42—188no—
256C22×C3—24no—
257C22×C3—24no—
258C22×C3—216no—
259C22×C3—216no—
260C22×C3—24no—
261C22×C3—24no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3—21no—
266C22×C3—24no—
267C22×C3#87718yes—
268C22×C3C22×C4×D312yes—
269C22×C3C2×#23714yes—
270C22×C3D3×#4114yes—
271C22×C3D3×#4114yes—
272C3×C4—24no—
273C3×C4—24no—
274C3×C4—24no—
275C3×C4—24no—
276C3×C4—128no—
277Dic3—38no—
278Dic3—38no—
279Dic3—48no—
280Dic3—64no—
281Dic3—64no—
282Dic3—64no—
283Dic3—64no—
284Dic3—64no—
285Dic3—64no—
286C32#228311yescharacteristic, complemented, Sylow
287C23—22no—
288C23—22no—
289C23#380514yes—
290C23C2×#62412yes—
291C23C22×D3211yescharacteristic
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—28no—
295C2×C4—68no—
296C2×C4—68no—
297C2×C4—68no—
298C2×C4—94no—
299C2×C4—94no—
300C2×C4—92no—
301C2×C4—92no—
302C2×C4—92no—
303C2×C4—92no—
304C2×C4—188no—
305C2×C4—188no—
306C2×C4—182no—
307C2×C4—182no—
308C2×C4C2×#62412yes—
309C2×C4C2×#62412yes—
310C2×C3—28no—
311C2×C3—28no—
312C2×C3—24no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3C2×#87712yes—
317C2×C3D3×#11712yes—
318C2×C3D3×#11712yes—
319C2×C3#564918yes—
320C22—28no—
321C22—22no—
322C22—22no—
323C22#6395714yes—
324C22#6430612yes—
325C22#6430612yes—
326C22C2×#380512yes—
327C22C22×#62411yescharacteristic
328C4—22no—
329C4—22no—
330C4—94no—
331C4—94no—
332C4—128no—
333C4—182no—
334C4—182no—
335C3—21no—
336C3#7405112yescomplemented
337C2—24no—
338C2#1059496314yes—
339C2#1059496911yescharacteristic
340C2#1059496911yescharacteristic
341C2C2×#6395711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2283
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
5. #10591360C2semidirect
6. #10591257C2semidirect
7. #10591252C2semidirect
8. #10591229C2semidirect
13. C2×C4×C3⋊Dic3C4semidirect
286. C32#2283semidirect
336. C3#74051semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊Dic32
C3×#52112
#105917202
#105917052
#105913602
#105912572
#105912522
#105912292
#740513