Finite Group Databasebeta

← #11870713

Subgroups — #11870713

Order 1152.

1284 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic
2C2×C4×#634C211yesmaximal, characteristic, complemented
3C32×#431C211yesmaximal, characteristic, complemented
4#10592550C212yesmaximal, complemented
5#10592547C212yesmaximal, complemented
6#10592437C212yesmaximal, complemented
7#10592434C212yesmaximal, complemented
8C4×#3744C214yesmaximal, complemented
9#79309—34nomaximal
10C2×#3828—21no—
11C22×#634C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13#64139—21no—
14#64139C2212yes—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×#3750—21no—
17C2×C4×C3⋊Dic3—21no—
18C2×#3744C2214yes—
19#64084—21no—
20#64083C2211yescharacteristic
21C4×C4⋊(C3⋊D3)—21no—
22C4×C4⋊(C3⋊D3)C2212yes—
23#64078C2211yescharacteristic
24C4×#634—21no—
25C4×#634—21no—
26C4×#634C2212yes—
27C4×#634C2212yes—
28C32×C4⋊C8C2212yes—
29C32×C22⋊C8C2212yes—
30C32×C4×C8C2212yes—
31#63648C2214yes—
32#63644C2214yes—
33#63643C2214yes—
34#5477—34no—
35C2×C4×Dic6—34no—
36C3×#431D314yescomplemented
37#4851—38no—
38#4848—38no—
39#4738—38no—
40#4735—38no—
41C4×#204—316no—
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C2×#638—22no—
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3—21no—
48#3828—44no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)C2312yes—
52C2×C4×C3⋊D3—22no—
53C2×#634—21no—
54C2×#634—24no—
55C2×#634—21no—
56C2×#634C2312yes—
57C2×C32×C8C2314yes—
58C32×C42D411yescharacteristic
59C32×C42D411yescharacteristic
60C32×C42C2311yescharacteristic
61C32×C42C2311yescharacteristic
62#3752—22no—
63#3752—22no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)C2312yes—
67C4⋊(C3⋊Dic3)C2312yes—
68#3750—22no—
69#3750—22no—
70C4×C3⋊Dic3—22no—
71C4×C3⋊Dic3—22no—
72#3744—28no—
73#3103—91noSylow
74C2×#235—64no—
75C22×Dic6—34no—
76C2×C3×C42C2×D314yes—
77#930—38no—
78#930—64no—
79C2×C4⋊Dic3—34no—
80C2×Dic3⋊C4—64no—
81C2×C4×Dic3—64no—
82C2×#204—316no—
83#875—64no—
84#874—34no—
85C4×D12—38no—
86C4×D12—64no—
87#869—34no—
88C4×Dic6—38no—
89C4×Dic6—38no—
90C4×Dic6—64no—
91C4×Dic6—64no—
92C3×C4⋊C8C2×D318yes—
93C3×C22⋊C8C2×D318yes—
94C3×C4×C8C2×D318yes—
95#821—316no—
96#817—316no—
97#816—316no—
98C23×C32C2×D411yescharacteristic
99C22×C3⋊D3—22no—
100C2×C32×C4—22no—
101C2×C32×C4—41no—
102C2×C32×C4SD1614yescomplemented
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2411yescharacteristic
109#638—44no—
110C2×C3⋊Dic3—24no—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—42no—
115C4⋊(C3⋊D3)—24no—
116C4⋊(C3⋊D3)—42no—
117C4⋊(C3⋊D3)—42no—
118C4×C3⋊D3—44no—
119#634—24no—
120#634—22no—
121#634—42no—
122#634#4114yescomplemented
123C32×C8—24no—
124#532—91no—
125C2×C4×Q8—91no—
126#481—92no—
127#475—92no—
128#460—92no—
129#448—92no—
130C4×SD16—94no—
131#431C3⋊D311yescharacteristic, complemented
132C22×C3×C4D1214yes—
133C22×C3×C4D1214yes—
134C22×C3×C4C22×D314yes—
135C2×#67—68no—
136C22×Dic3—64no—
137C22×Dic3—64no—
138#235—1216no—
139C2×D12—38no—
140C2×D12—64no—
141C2×D12—64no—
142C2×C4×D3—68no—
143C2×Dic6—38no—
144C2×Dic6—616no—
145C2×Dic6—64no—
146C2×Dic6—64no—
147C2×C3×C8C22×D3116yes—
148C3×C42D1214yes—
149C3×C42D1214yes—
150C3×C42C22×D314yes—
151C3×C42C22×D314yes—
152(C2×D3)⋊C4—68no—
153(C2×D3)⋊C4—68no—
154C4⋊Dic3—38no—
155C4⋊Dic3—38no—
156C4⋊Dic3—64no—
157C4⋊Dic3—64no—
158Dic3⋊C4—68no—
159Dic3⋊C4—68no—
160C4×Dic3—68no—
161C4×Dic3—68no—
162#204—632no—
163C22×C32—21no—
164C22×C32—21no—
165C22×C32C2×SD1612yes—
166C22×C32C22×D411yescharacteristic
167C2×C3⋊D3—42no—
168C2×C3⋊D3—42no—
169C2×C3⋊D3—42no—
170C32×C4—21no—
171C32×C4—21no—
172C32×C4—21no—
173C32×C4C2×SD1612yes—
174C32×C4C2×SD1612yes—
175C32×C4C2×#4112yes—
176C3⋊Dic3—24no—
177C3⋊Dic3—42no—
178C3⋊Dic3—42no—
179C2×#41—181no—
180C22×Q8—91no—
181C2×SD16—94no—
182C4⋊Q8—91no—
183#127—91no—
184#124—181no—
185#121—92no—
186#121—181no—
187C4×Q8—92no—
188C4×Q8—92no—
189C4×Q8—181no—
190C4×Q8—181no—
191C4×D4—92no—
192C4×D4—181no—
193C2×C4⋊C4—91no—
194C2×C4⋊C4—181no—
195C2×C42—181no—
196C2×C42C2×C3⋊D311yescharacteristic
197#106—94no—
198C4⋊C8C2×C3⋊D312yes—
199#103—94no—
200#102—94no—
201C22⋊C8C2×C3⋊D312yes—
202C4×C8C2×C3⋊D312yes—
203C23×C3C2×D1214yes—
204C22×D3—68no—
205C2×C3×C4—28no—
206C2×C3×C4—44no—
207C2×C3×C4#204116yescomplemented
208C2×C3×C4C2×D1214yes—
209C2×C3×C4C2×D1214yes—
210C2×C3×C4C2×D1214yes—
211C2×C3×C4C2×D1214yes—
212C2×C3×C4C2×D1214yes—
213C2×C3×C4C23×D314yes—
214#67—1216no—
215C2×Dic3—616no—
216C2×Dic3—68no—
217C2×Dic3—68no—
218C2×Dic3—68no—
219C2×Dic3—128no—
220D12—616no—
221D12—128no—
222D12—128no—
223C4×D3—1216no—
224Dic6—316no—
225Dic6—616no—
226Dic6—68no—
227Dic6—128no—
228C3×C8—216no—
229C2×C32—22no—
230C2×C32#52511yescharacteristic
231C2×C32C22×SD1611yescharacteristic
232C2×C32#57511yescharacteristic
233C3⋊D3—82no—
234#41—364no—
235C2×Q8—92no—
236C2×Q8—184no—
237C2×Q8—181no—
238C2×Q8—181no—
239C2×D4—92no—
240C2×D4—182no—
241C2×D4—181no—
242C2×D4—181no—
243C22×C4—181no—
244C22×C4—181no—
245C22×C4—182no—
246C22×C4C4⋊(C3⋊D3)11yescharacteristic
247C22×C4C4⋊(C3⋊D3)11yescharacteristic
248C22×C4C22×C3⋊D311yescharacteristic
249SD16—188no—
250C2×C8C22×C3⋊D314yes—
251C4⋊C4—92no—
252C4⋊C4—92no—
253C4⋊C4—181no—
254C4⋊C4—182no—
255C4⋊C4—182no—
256C4⋊C4—181no—
257C22⋊C4—182no—
258C22⋊C4—182no—
259C42—182no—
260C42—182no—
261C42C4⋊(C3⋊D3)11yescharacteristic
262C42C4⋊(C3⋊D3)11yescharacteristic
263C42C22×C3⋊D311yescharacteristic
264C42C22×C3⋊D311yescharacteristic
265C22×C3—24no—
266C22×C3—24no—
267C22×C3C2×#20418yes—
268C22×C3C22×D1214yes—
269C2×D3—128no—
270C2×D3—128no—
271C2×D3—128no—
272C3×C4—24no—
273C3×C4—24no—
274C3×C4—24no—
275C3×C4C2×#20418yes—
276C3×C4C2×#20418yes—
277C3×C4D3×#4118yes—
278Dic3—616no—
279Dic3—128no—
280Dic3—128no—
281C32#310311yescharacteristic, complemented, Sylow
282C23—182no—
283C23C2×C4⋊(C3⋊D3)11yescharacteristic
284Q8—94no—
285Q8—184no—
286Q8—182no—
287Q8—362no—
288D4—184no—
289D4—362no—
290D4—364no—
291D4—362no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—184no—
295C2×C4—182no—
296C2×C4—182no—
297C2×C4—182no—
298C2×C4—362no—
299C2×C4—364no—
300C2×C4#374414yescomplemented
301C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
302C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
303C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
304C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
305C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
306C2×C4C23×C3⋊D311yescharacteristic
307C8—24no—
308C2×C3—28no—
309C2×C3#552414yes—
310C2×C3C22×#20414yes—
311C2×C3#574814yes—
312D3—248no—
313C22—21no—
314C22—21no—
315C22—362no—
316C22—362no—
317C22—362no—
318C22C2×#374412yes—
319C22C22×C4⋊(C3⋊D3)11yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—184no—
324C4—362no—
325C4—362no—
326C4C2×#374412yes—
327C4C2×#374412yes—
328C4#41×C3⋊D312yes—
329C3#7930914yescomplemented
330C2—22no—
331C2—722no—
332C2#1059599511yescharacteristic
333C2C22×#374411yescharacteristic
334C2#1059621911yescharacteristic
subgroupG/H
centerC2×C4C2×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#431C2
socleC22×C32C22×D4
prime radical#10595948C2
hypercenter#431C3⋊D3
hypocenterC32#3103
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. C2×C4×#634C2semidirect
3. C32×#431C2semidirect
4. #10592550C2semidirect
5. #10592547C2semidirect
6. #10592437C2semidirect
7. #10592434C2semidirect
8. C4×#3744C2semidirect
36. C3×#431D3semidirect
102. C2×C32×C4SD16semidirect
122. #634#41semidirect
131. #431C3⋊D3semidirect
207. C2×C3×C4#204semidirect
281. C32#3103semidirect
300. C2×C4#3744semidirect
329. C3#79309semidirect

Maximal subgroups

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

subgroupindex
#105959482
C2×C4×#6342
C32×#4312
#105925502
#105925472
#105924372
#105924342
C4×#37442
#793093