Finite Group Databasebeta

← #11805953

Subgroups — #11805953

Order 1152.

1392 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic
2C32×#383C211yesmaximal, characteristic
3#10592631C211yesmaximal, characteristic
4#10592353C212yesmaximal
5#10592351C212yesmaximal
6#10592350C211yesmaximal, characteristic
7#10592349C211yesmaximal, characteristic
8#10592348C211yesmaximal, characteristic
9#10592348C212yesmaximal
10#10592347C211yesmaximal, characteristic
11#10592345C212yesmaximal
12#74264—34nomaximal
13C22×#634C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×#3750C2212yes—
17C2×#3750C2212yes—
18C2×#3750C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C2×C4×C3⋊Dic3C2212yes—
21C2×C4×C3⋊Dic3C2212yes—
22C2×C4×C3⋊Dic3C2212yes—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C4×#634C418yescomplemented
26C32×#95C2212yes—
27C32×#95C2211yescharacteristic
28C32×#95C2211yescharacteristic
29C32×#95C2212yes—
30#63658C2212yes—
31#63658C2212yes—
32#63658C2212yes—
33#63658C2211yescharacteristic
34#63658C2212yes—
35#63658C2211yescharacteristic
36#63658C2212yes—
37C2×C4×Dic6—34no—
38C3×#383D314yes—
39#4932—34no—
40#4654—38no—
41#4652—38no—
42#4651—34no—
43#4650—34no—
44#4649—34no—
45#4649—38no—
46#4648—34no—
47#4646—38no—
48C22×C32×C4C2312yes—
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3C2312yes—
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3⋊Dic3C2311yescharacteristic
57C22×C3⋊Dic3C2312yes—
58C22×C3⋊Dic3C2311yescharacteristic
59C2×#634—22no—
60C2×#634—22no—
61C2×#634C2×C414yes—
62C32×C42C2×C414yes—
63C4⋊(C3⋊Dic3)C2×C414yes—
64#3750—24no—
65#3750—24no—
66#3750C2×C414yes—
67#3750C2×C414yes—
68C4×C3⋊Dic3—24no—
69C4×C3⋊Dic3—24no—
70C4×C3⋊Dic3—24no—
71C4×C3⋊Dic3C2×C414yes—
72C4×C3⋊Dic3C2×C414yes—
73#2356—91noSylow
74C22×Dic6—34no—
75C2×C3×C42C2×D314yes—
76C2×C4⋊Dic3—34no—
77C2×Dic3⋊C4—34no—
78C2×Dic3⋊C4—34no—
79C2×Dic3⋊C4—38no—
80C2×Dic3⋊C4—38no—
81C2×C4×Dic3—34no—
82C2×C4×Dic3—34no—
83C2×C4×Dic3—38no—
84C2×C4×Dic3—38no—
85C2×C4×Dic3—38no—
86C4×Dic6—332no—
87C3×#95C2×D318yes—
88C3×#95C2×D314yes—
89C3×#95C2×D314yes—
90C3×#95C2×D318yes—
91C3⋊#95—38no—
92C3⋊#95—38no—
93C3⋊#95—38no—
94C3⋊#95—34no—
95C3⋊#95—38no—
96C3⋊#95—34no—
97C3⋊#95—38no—
98C23×C32C2411yescharacteristic
99C2×C32×C4—22no—
100C2×C32×C4—21no—
101C2×C32×C4—21no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—22no—
105C2×C32×C4—22no—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4C22×C412yes—
110C2×C32×C4C22×C412yes—
111C2×C32×C4C22×C412yes—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3C22×C412yes—
122C2×C3⋊Dic3C22×C412yes—
123C2×C3⋊Dic3C22×C412yes—
124C2×C3⋊Dic3C22×C412yes—
125C2×C3⋊Dic3#4114yes—
126C2×C3⋊Dic3#4112yes—
127C2×C3⋊Dic3#4112yes—
128#634—28no—
129C2×C4×Q8—91no—
130#391—92no—
131#387—92no—
132#387—92no—
133#383—91no—
134#383C3⋊D311yescharacteristic
135#382—91no—
136C4×C4⋊C4—91no—
137C4×C4⋊C4—92no—
138#376—91no—
139#376—91no—
140C22×C3×C4C22×D318yes—
141C22×C3×C4C22×D318yes—
142C22×C3×C4C22×D314yes—
143C22×C3×C4C22×D314yes—
144C22×C3×C4C22×D314yes—
145C22×Dic3—34no—
146C22×Dic3—34no—
147C22×Dic3—38no—
148C22×Dic3—34no—
149C22×Dic3—34no—
150C22×Dic3—38no—
151C2×Dic6—316no—
152C2×Dic6—68no—
153C2×Dic6—68no—
154C3×C42C4×D3116yes—
155C4⋊Dic3—316no—
156Dic3⋊C4—316no—
157Dic3⋊C4—316no—
158Dic3⋊C4—616no—
159Dic3⋊C4—616no—
160C4×Dic3—316no—
161C4×Dic3—316no—
162C4×Dic3—616no—
163C4×Dic3—616no—
164C4×Dic3—616no—
165C22×C32C23×C411yescharacteristic
166C22×C32C2×#4111yescharacteristic
167C22×C32C2×#4111yescharacteristic
168C22×C32C2×#4112yes—
169C22×C322−1+412yes—
170C32×C4—22no—
171C32×C4—22no—
172C32×C4—22no—
173C32×C4—42no—
174C32×C4—42no—
175C3⋊Dic3—22no—
176C3⋊Dic3—22no—
177C3⋊Dic3—22no—
178C3⋊Dic3—24no—
179C3⋊Dic3—42no—
180C3⋊Dic3#11714yes—
181C22×Q8—91no—
182C4×Q8—98no—
183C2×C4⋊C4—91no—
184C2×C4⋊C4—91no—
185C2×C4⋊C4—91no—
186C2×C4⋊C4—92no—
187C2×C4⋊C4—92no—
188C2×C42—91no—
189C2×C42—91no—
190C2×C42—92no—
191C2×C42—92no—
192C2×C42—92no—
193C2×C42C2×C3⋊D311yescharacteristic
194#95—91no—
195#95—91no—
196#95—92no—
197#95—92no—
198#95—92no—
199#95—92no—
200#95—92no—
201#95C2×C3⋊D311yescharacteristic
202#95C2×C3⋊D311yescharacteristic
203#95C2×C3⋊D312yes—
204#95C2×C3⋊D312yes—
205C23×C3C23×D314yes—
206C2×C3×C4—28no—
207C2×C3×C4—24no—
208C2×C3×C4—24no—
209C2×C3×C4—28no—
210C2×C3×C4—28no—
211C2×C3×C4—28no—
212C2×C3×C4—28no—
213C2×C3×C4—28no—
214C2×C3×C4—28no—
215C2×C3×C4—28no—
216C2×C3×C4C2×C4×D318yes—
217C2×C3×C4C2×C4×D318yes—
218C2×C3×C4C2×C4×D318yes—
219C2×Dic3—38no—
220C2×Dic3—38no—
221C2×Dic3—38no—
222C2×Dic3—38no—
223C2×Dic3—38no—
224C2×Dic3—38no—
225C2×Dic3—316no—
226C2×Dic3—68no—
227C2×Dic3—68no—
228C2×Dic3—68no—
229C2×Dic3—64no—
230C2×Dic3—64no—
231C2×Dic3—68no—
232C2×Dic3—68no—
233C2×Dic3—68no—
234C2×Dic3—68no—
235Dic6—632no—
236C2×C32C2×#11711yescharacteristic
237C2×C32C4×#4111yescharacteristic
238C2×C32#51911yescharacteristic
239C2×C32#55212yes—
240C2×C32#55612yes—
241C2×Q8—94no—
242C2×Q8—182no—
243C2×Q8—182no—
244C22×C4—91no—
245C22×C4—91no—
246C22×C4—92no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—92no—
250C22×C4C22×C3⋊D312yes—
251C22×C4C22×C3⋊D312yes—
252C22×C4C22×C3⋊D311yescharacteristic
253C22×C4C22×C3⋊D311yescharacteristic
254C22×C4C22×C3⋊D311yescharacteristic
255C4⋊C4—94no—
256C4⋊C4—94no—
257C4⋊C4—94no—
258C4⋊C4—184no—
259C4⋊C4—184no—
260C42—94no—
261C42—94no—
262C42—184no—
263C42—184no—
264C42—184no—
265C42C4×C3⋊D314yes—
266C22×C3C22×C4×D314yes—
267C22×C3D3×#4114yes—
268C22×C3D3×#4118yes—
269C22×C3D3×#4114yes—
270C22×C3#101018yes—
271C3×C4—28no—
272C3×C4—28no—
273C3×C4—28no—
274C3×C4—48no—
275C3×C4—48no—
276Dic3—316no—
277Dic3—616no—
278Dic3—68no—
279Dic3—68no—
280Dic3—68no—
281Dic3—128no—
282C32#235611yescharacteristic, complemented, Sylow
283C23C23×C3⋊D311yescharacteristic
284Q8—188no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—92no—
296C2×C4—92no—
297C2×C4—92no—
298C2×C4—92no—
299C2×C4—92no—
300C2×C4—92no—
301C2×C4—94no—
302C2×C4—182no—
303C2×C4—182no—
304C2×C4—182no—
305C2×C4—181no—
306C2×C4—181no—
307C2×C4—182no—
308C2×C4—182no—
309C2×C4—182no—
310C2×C4—182no—
311C2×C4C2×C4×C3⋊D312yes—
312C2×C4C2×C4×C3⋊D312yes—
313C2×C4C2×C4×C3⋊D312yes—
314C2×C3#551614yes—
315C2×C3D3×#11714yes—
316C2×C3#552214yes—
317C2×C3#570218yes—
318C2×C3#570818yes—
319C22C22×C4×C3⋊D311yescharacteristic
320C22#41×C3⋊D311yescharacteristic
321C22#41×C3⋊D312yes—
322C22#41×C3⋊D311yescharacteristic
323C22#6436712yes—
324C4—22no—
325C4—22no—
326C4—22no—
327C4—42no—
328C4—42no—
329C4—94no—
330C4—184no—
331C4—182no—
332C4—182no—
333C4—182no—
334C4—362no—
335C3#7426414yescomplemented
336C2#1059598711yescharacteristic
337C2C3⋊D3×#11711yescharacteristic
338C2#1059599311yescharacteristic
339C2#1059617312yes—
340C2#1059617912yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#383C2
socle, prime radical, cosocleC23×C32C24
hypercenter#383C3⋊D3
hypocenterC32#2356
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
25. C4×#634C4semidirect
282. C32#2356semidirect
335. C3#74264semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C32×#3832
#105926312
#105923532
#105923512
#105923502
#105923492
#105923482
#105923472
#105923452
#742643