Finite Group Databasebeta

← #11802487

Subgroups — #11802487

Order 1152.

1081 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
1C2×#64079C211yesmaximal, characteristic
2C3×#4936C211yesmaximal, characteristic
3C3×C42×Dic3C211yesmaximal, characteristic
4Dic3×C4⋊Dic3C212yesmaximal
5#10591243C214yesmaximal
6#10591212C212yesmaximal
7#10591197C214yesmaximal
8#74150—31nomaximal
9C4×#870—31nomaximal
10C2×C32×C42C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2212yes—
12C2×#3750C2214yes—
13#64079C418yescomplemented
14C2×C3×C4⋊Dic3C2212yes—
15C2×C3×C4×Dic3C2212yes—
16C2×C3×C4×Dic3C2212yes—
17C2×C3×C4×Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×#3724C2214yes—
20C2×Dic32C2214yes—
21C3×C3⋊#95C2214yes—
22#63579C2214yes—
23#63579C2214yes—
24C2×#870—31no—
25C2×#870—31no—
26C2×#870—61no—
27C3×#382—31no—
28C3×C43—31no—
29Dic3×C4⋊C4—32no—
30#4972—32no—
31#4936D311yescharacteristic
32C4×C4⋊Dic3—32no—
33#4933—34no—
34C4×Dic3⋊C4—34no—
35C42×Dic3D311yescharacteristic
36#4928—32no—
37#4652—34no—
38#4649—34no—
39C22×C32×C4C2312yes—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3C2314yes—
42C22×C3×Dic3C2314yes—
43C22×C3×Dic3C2311yescharacteristic
44C22×C3×Dic3C2312yes—
45C22×C3×Dic3C2311yescharacteristic
46C32×C42C2×C414yes—
47C4⋊(C3⋊Dic3)C2×C418yes—
48#3750C2×C4116yes—
49C3×C4⋊Dic3—24no—
50C3×C4×Dic3—22no—
51C3×C4×Dic3—24no—
52C3×C4×Dic3—24no—
53C3×C4×Dic3Q814yes—
54#3724—28no—
55Dic32—28no—
56C4×#125—91noSylow
57C2×C3×C4⋊C4—32no—
58C2×C3×C42—21no—
59C2×C3×C42—31no—
60C2×C3×C42—31no—
61C2×C3×C42—32no—
62C2×C3×C42—32no—
63C2×C3×C42C2×D311yescharacteristic
64C2×C3×C42C2×D311yescharacteristic
65C2×C4⋊Dic3—32no—
66C2×C4⋊Dic3—32no—
67C2×C4⋊Dic3—62no—
68C2×C4⋊Dic3C2×D312yes—
69C2×Dic3⋊C4—34no—
70C2×Dic3⋊C4—34no—
71C2×Dic3⋊C4—34no—
72C2×Dic3⋊C4—34no—
73C2×Dic3⋊C4—64no—
74C2×C4×Dic3—34no—
75C2×C4×Dic3—34no—
76C2×C4×Dic3C2×D312yes—
77C2×C4×Dic3C2×D312yes—
78C2×C4×Dic3C2×D311yescharacteristic
79C2×C4×Dic3C2×D311yescharacteristic
80#870—38no—
81#870—38no—
82#870—68no—
83C3×#95—34no—
84C3⋊#95—34no—
85C3⋊#95—34no—
86C3⋊#95—34no—
87C3⋊#95—34no—
88C3⋊#95C2×D314yes—
89C23×C32C2411yescharacteristic
90C2×C32×C4—22no—
91C2×C32×C4—22no—
92C2×C32×C4C22×C414yes—
93C2×C32×C4C22×C412yes—
94C2×C32×C4C2×Q812yes—
95C2×C32×C4#4112yes—
96C2×C3⋊Dic3—24no—
97C2×C3⋊Dic3—24no—
98C2×C3⋊Dic3C22×C418yes—
99C2×C3×Dic3—22no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—24no—
104C2×C3×Dic3—24no—
105C2×C3×Dic3C2×Q812yes—
106C2×C3×Dic3C2×Q812yes—
107C2×C3×Dic3#4114yes—
108C2×C3×Dic3#4114yes—
109C2×#125—91no—
110#389—92no—
111#387—94no—
112#382—31no—
113C4×C4⋊C4—94no—
114C4×C4⋊C4—92no—
115C43—31no—
116C22×C3×C4—21no—
117C22×C3×C4—22no—
118C22×C3×C4—31no—
119C22×C3×C4—31no—
120C22×C3×C4—32no—
121C22×C3×C4—34no—
122C22×C3×C4C22×D312yes—
123C22×C3×C4C22×D312yes—
124C22×C3×C4C22×D311yescharacteristic
125C22×C3×C4C22×D311yescharacteristic
126C22×Dic3—34no—
127C22×Dic3—34no—
128C22×Dic3—64no—
129C22×Dic3C22×D314yes—
130C22×Dic3C22×D311yescharacteristic
131C22×Dic3C22×D312yes—
132C22×Dic3C22×D311yescharacteristic
133C3×C4⋊C4—64no—
134C3×C42—24no—
135C3×C42—34no—
136C3×C42—64no—
137C3×C42—64no—
138C3×C42—62no—
139C3×C42C4×D314yes—
140C3×C42C4×D314yes—
141C4⋊Dic3—24no—
142C4⋊Dic3—38no—
143C4⋊Dic3—38no—
144C4⋊Dic3—68no—
145Dic3⋊C4—316no—
146Dic3⋊C4—316no—
147Dic3⋊C4—616no—
148Dic3⋊C4—68no—
149Dic3⋊C4—68no—
150C4×Dic3—22no—
151C4×Dic3—24no—
152C4×Dic3—24no—
153C4×Dic3—68no—
154C4×Dic3—68no—
155C4×Dic3Dic614yes—
156C22×C32C23×C411yescharacteristic
157C22×C32C22×Q811yescharacteristic
158C22×C32C2×#4111yescharacteristic
159C22×C32C2×#4112yes—
160C22×C32C2×#4112yes—
161C32×C4—24no—
162C32×C4C4×Q814yes—
163C3⋊Dic3—28no—
164C3×Dic3—24no—
165C3×Dic3—22no—
166C3×Dic3—44no—
167C3×Dic3#12514yescomplemented
168#125—98no—
169C2×C4⋊C4—32no—
170C2×C4⋊C4—94no—
171C2×C4⋊C4—92no—
172C2×C4⋊C4—94no—
173C2×C42—31no—
174C2×C42—32no—
175C2×C42—32no—
176C2×C42—31no—
177C2×C42—94no—
178C2×C42D3211yescharacteristic
179#95—34no—
180#95—94no—
181#95—94no—
182C23×C3—21no—
183C23×C3C23×D311yescharacteristic
184C23×C3C23×D311yescharacteristic
185C2×C3×C4—22no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—24no—
193C2×C3×C4—32no—
194C2×C3×C4—34no—
195C2×C3×C4—32no—
196C2×C3×C4—34no—
197C2×C3×C4—42no—
198C2×C3×C4—42no—
199C2×C3×C4—62no—
200C2×C3×C4—62no—
201C2×C3×C4—62no—
202C2×C3×C4—64no—
203C2×C3×C4—64no—
204C2×C3×C4—64no—
205C2×C3×C4C2×Dic612yes—
206C2×C3×C4C2×C4×D314yes—
207C2×C3×C4C2×C4×D314yes—
208C2×C3×C4C2×C4×D312yes—
209C2×C3×C4C2×C4×D312yes—
210C2×C3×C4#23512yes—
211C2×C3×C4#23712yes—
212C2×C3×C4D3×Q812yes—
213C2×Dic3—22no—
214C2×Dic3—22no—
215C2×Dic3—22no—
216C2×Dic3—24no—
217C2×Dic3—24no—
218C2×Dic3—24no—
219C2×Dic3—38no—
220C2×Dic3—38no—
221C2×Dic3—68no—
222C2×Dic3—64no—
223C2×Dic3—64no—
224C2×Dic3—64no—
225C2×Dic3—64no—
226C2×Dic3—124no—
227C2×Dic3—124no—
228C2×Dic3C2×Dic612yes—
229C2×Dic3C2×Dic612yes—
230C2×Dic3#23514yes—
231C2×Dic3#23514yes—
232C2×C32C2×C4×Q811yescharacteristic
233C2×C32C4×#4112yes—
234C2×C32C2×#12511yescharacteristic
235C2×C32#52912yes—
236C2×C32#53311yescharacteristic
237C22×C4—31no—
238C22×C4—31no—
239C22×C4—32no—
240C22×C4—34no—
241C22×C4—94no—
242C22×C4C2×D3212yes—
243C22×C4C2×D3211yescharacteristic
244C4⋊C4—64no—
245C4⋊C4—916no—
246C4⋊C4—98no—
247C4⋊C4—188no—
248C42—34no—
249C42—64no—
250C42—64no—
251C42—62no—
252C42—188no—
253C42#62414yes—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—22no—
257C22×C3—22no—
258C22×C3—21no—
259C22×C3C22×Dic611yescharacteristic
260C22×C3C22×C4×D311yescharacteristic
261C22×C3C22×C4×D311yescharacteristic
262C22×C3C2×#23511yescharacteristic
263C22×C3C2×#23512yes—
264C22×C3C2×#23512yes—
265C22×C3C2×#23711yescharacteristic
266C22×C3C2×D3×Q811yescharacteristic
267C22×C3D3×#4112yes—
268C22×C3D3×#4112yes—
269C3×C4—24no—
270C3×C4—24no—
271C3×C4—24no—
272C3×C4—34no—
273C3×C4—44no—
274C3×C4—64no—
275C3×C4—62no—
276C3×C4—124no—
277C3×C4C4×Dic614yes—
278C3×C4#88714yes—
279Dic3—22no—
280Dic3—24no—
281Dic3—44no—
282Dic3—68no—
283Dic3—68no—
284Dic3—128no—
285Dic3#87014yescomplemented
286C32C4×#12511yescharacteristic, complemented, Sylow
287C23C22×D3211yescharacteristic
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—32no—
291C2×C4—34no—
292C2×C4—32no—
293C2×C4—34no—
294C2×C4—62no—
295C2×C4—62no—
296C2×C4—62no—
297C2×C4—64no—
298C2×C4—64no—
299C2×C4—64no—
300C2×C4—98no—
301C2×C4—184no—
302C2×C4—184no—
303C2×C4D3×Dic612yes—
304C2×C4#379512yes—
305C2×C4C2×#62414yes—
306C2×C4C2×#62412yes—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—22no—
311C2×C3—22no—
312C2×C3C2×C4×Dic611yescharacteristic
313C2×C3C2×#87011yescharacteristic
314C2×C3#547011yescharacteristic
315C2×C3C4×#23512yes—
316C2×C3#547912yes—
317C2×C3C2×#88711yescharacteristic
318C2×C3#552212yes—
319C2×C3#568012yes—
320C2×C3D3×#12511yescharacteristic
321C2×C3#568811yescharacteristic
322C22C2×D3×Dic611yescharacteristic
323C22C2×#379511yescharacteristic
324C22D3×#23512yes—
325C22D3×#23512yes—
326C22C22×#62411yescharacteristic
327C4—24no—
328C4—34no—
329C4—62no—
330C4—64no—
331C4—124no—
332C4—188no—
333C4#6384414yes—
334C3—21no—
335C3C4×#87011yescharacteristic, complemented
336C3#7415011yescharacteristic, complemented
337C2#1059387411yescharacteristic
338C2D3×#87011yescharacteristic
339C2#1059392112yes—
340C2C2×#6384411yescharacteristic
341C2#1059495412yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C4×#125
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
13. #64079C4semidirect
167. C3×Dic3#125semidirect
285. Dic3#870semidirect
286. C32C4×#125semidirect
335. C3C4×#870semidirect
336. C3#74150semidirect

Maximal subgroups

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

subgroupindex
C2×#640792
C3×#49362
C3×C42×Dic32
Dic3×C4⋊Dic32
#105912432
#105912122
#105911972
#741503
C4×#8703