Finite Group Databasebeta

← #11882236

Subgroups — #11882236

Order 1152.

1176 conjugacy classes of subgroups.

The subgroup lattice has 339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic
2#10595941C211yesmaximal, characteristic, complemented
3C2×C32×C4⋊C8C211yesmaximal, characteristic, complemented
4#10592813C214yesmaximal, complemented
5#10592550C212yesmaximal, complemented
6#10592547C212yesmaximal, complemented
7#10592541C212yesmaximal, complemented
8#10592540C212yesmaximal, complemented
9#79027—34nomaximal
10C2×#3828—21no—
11C22×C32×C8C2212yes—
12C2×C32×C42C2211yescharacteristic
13#64139—21no—
14#64139C2212yes—
15#64135—21no—
16#64133—21no—
17#64133C2212yes—
18C2×#3744C2214yes—
19#64084—21no—
20#64083C2211yescharacteristic
21C4×C4⋊(C3⋊D3)—21no—
22C4×C4⋊(C3⋊D3)C2212yes—
23#64079—21no—
24#64078C2211yescharacteristic
25#64078C2211yescharacteristic
26#64078C2211yescharacteristic
27C4×#634—21no—
28C4×#634C2212yes—
29C32×C4⋊C8C2212yes—
30C32×C4⋊C8C2212yes—
31#63648C2214yes—
32#63644C2214yes—
33#63643C2214yes—
34#5477—34no—
35#5470—34no—
36C2×C3×C4⋊C8D314yescomplemented
37#5114—316no—
38#4851—38no—
39#4848—38no—
40#4842—38no—
41#4841—38no—
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C2×#638—22no—
46#3828—44no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)C2312yes—
50C2×C4×C3⋊D3—22no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634C2312yes—
54C2×C32×C8—42no—
55C2×C32×C8C2314yes—
56C32×C42D411yescharacteristic
57C32×C42D411yescharacteristic
58C32×C42C2311yescharacteristic
59C32×C42C2311yescharacteristic
60#3757—22no—
61#3752—22no—
62#3752—22no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)C2312yes—
68C4⋊(C3⋊Dic3)C2312yes—
69#3750—22no—
70#3750—22no—
71C4×C3⋊Dic3—22no—
72#3744—44no—
73#3246—91noSylow
74C2×#235—64no—
75C22×C3×C8C2×D318yes—
76C2×C3×C42C2×D314yes—
77#930—38no—
78#930—64no—
79#926—64no—
80#924—38no—
81#924—64no—
82C2×#204—316no—
83#875—64no—
84#874—34no—
85C4×D12—38no—
86C4×D12—64no—
87#870—64no—
88#869—34no—
89#869—34no—
90#869—34no—
91C4×Dic6—38no—
92C4×Dic6—64no—
93C3×C4⋊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—21no—
101C2×C32×C4—21no—
102C2×C32×C4—41no—
103C2×C32×C4SD1614yescomplemented
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2411yescharacteristic
110#638—44no—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—22no—
114C4⋊(C3⋊D3)—22no—
115C4⋊(C3⋊D3)—22no—
116C4⋊(C3⋊D3)—42no—
117C4⋊(C3⋊D3)—42no—
118C4×C3⋊D3—44no—
119#634—22no—
120#634—22no—
121#634—42no—
122#634—42no—
123C32×C8—24no—
124#533—91no—
125#532—91no—
126#476—92no—
127#475—92no—
128#465—94no—
129#461—92no—
130#460—92no—
131C2×C4⋊C8C3⋊D311yescharacteristic, complemented
132C22×C3×C4D1214yes—
133C22×C3×C4D1214yes—
134C22×C3×C4C22×D314yes—
135C2×#67—68no—
136#235—1216no—
137C2×D12—38no—
138C2×D12—64no—
139C2×D12—64no—
140C2×C4×D3—68no—
141C2×Dic6—38no—
142C2×Dic6—64no—
143C2×Dic6—64no—
144C2×C3×C8—48no—
145C2×C3×C8C22×D3116yes—
146C3×C42D1214yes—
147C3×C42D1214yes—
148C3×C42C22×D314yes—
149C3×C42C22×D314yes—
150#217—68no—
151(C2×D3)⋊C4—68no—
152(C2×D3)⋊C4—68no—
153C4⋊Dic3—38no—
154C4⋊Dic3—38no—
155C4⋊Dic3—64no—
156C4⋊Dic3—64no—
157C4⋊Dic3—64no—
158C4⋊Dic3—64no—
159Dic3⋊C4—68no—
160Dic3⋊C4—68no—
161C4×Dic3—68no—
162#204—1216no—
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×C4H(5,𝔽2)11yescharacteristic
176C32×C42−1+411yescharacteristic
177C3⋊Dic3—42no—
178C3⋊Dic3—42no—
179C3⋊Dic3—42no—
180C2×#41—181no—
181C2×SD16—94no—
182C22×C8C2×C3⋊D312yes—
183C4⋊Q8—91no—
184C4⋊Q8—91no—
185C4⋊Q8—91no—
186#127—91no—
187#125—181no—
188#124—181no—
189C22⋊Q8—92no—
190C22⋊Q8—181no—
191#121—92no—
192#121—181no—
193C4×Q8—92no—
194C4×Q8—181no—
195C4×D4—92no—
196C4×D4—181no—
197#117—181no—
198C2×C42C2×C3⋊D311yescharacteristic
199#106—94no—
200C4⋊C8C2×C3⋊D312yes—
201C4⋊C8C2×C3⋊D312yes—
202#103—94no—
203#102—94no—
204C23×C3C2×D1214yes—
205C22×D3—68no—
206C2×C3×C4—24no—
207C2×C3×C4—24no—
208C2×C3×C4—44no—
209C2×C3×C4#204116yescomplemented
210C2×C3×C4C2×D1214yes—
211C2×C3×C4C2×D1214yes—
212C2×C3×C4C2×D1214yes—
213C2×C3×C4C2×D1214yes—
214C2×C3×C4C2×D1214yes—
215C2×C3×C4C23×D314yes—
216#67—1216no—
217C2×Dic3—68no—
218C2×Dic3—68no—
219C2×Dic3—68no—
220D12—68no—
221D12—68no—
222D12—128no—
223D12—128no—
224C4×D3—1216no—
225Dic6—68no—
226Dic6—68no—
227Dic6—128no—
228Dic6—128no—
229C3×C8—216no—
230C2×C32—22no—
231C2×C32#53711yescharacteristic
232C2×C32C22×SD1611yescharacteristic
233C2×C32#57511yescharacteristic
234C3⋊D3—82no—
235#41—364no—
236C2×Q8—92no—
237C2×Q8—181no—
238C2×Q8—181no—
239C2×D4—92no—
240C2×D4—182no—
241C2×D4—181no—
242C2×D4—181no—
243C22×C4—182no—
244C22×C4C4⋊(C3⋊D3)11yescharacteristic
245C22×C4C4⋊(C3⋊D3)11yescharacteristic
246C22×C4C22×C3⋊D311yescharacteristic
247SD16—364no—
248C2×C8—42no—
249C2×C8C22×C3⋊D314yes—
250C4⋊C4—92no—
251C4⋊C4—92no—
252C4⋊C4—181no—
253C4⋊C4—181no—
254C4⋊C4—181no—
255C4⋊C4—182no—
256C4⋊C4—182no—
257C4⋊C4—181no—
258C22⋊C4—182no—
259C22⋊C4—182no—
260C22⋊C4—182no—
261C42—182no—
262C42C4⋊(C3⋊D3)11yescharacteristic
263C42C4⋊(C3⋊D3)11yescharacteristic
264C42C22×C3⋊D311yescharacteristic
265C42C22×C3⋊D311yescharacteristic
266C22×C3—24no—
267C22×C3—24no—
268C22×C3C2×#20418yes—
269C22×C3C22×D1214yes—
270C2×D3—128no—
271C2×D3—128no—
272C2×D3—128no—
273C3×C4—24no—
274C3×C4—24no—
275C3×C4—24no—
276C3×C4C2×#20418yes—
277C3×C4C2×#20418yes—
278C3×C4#100414yes—
279C3×C4#100714yes—
280Dic3—128no—
281Dic3—128no—
282Dic3—128no—
283C32#324611yescharacteristic, complemented, Sylow
284C23—182no—
285C23C2×C4⋊(C3⋊D3)11yescharacteristic
286Q8—182no—
287Q8—182no—
288Q8—362no—
289Q8—362no—
290D4—182no—
291D4—182no—
292D4—362no—
293D4—364no—
294D4—362no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—182no—
299C2×C4—182no—
300C2×C4—182no—
301C2×C4—364no—
302C2×C4#374414yescomplemented
303C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
304C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
305C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
306C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
307C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
308C2×C4C23×C3⋊D311yescharacteristic
309C8—24no—
310C2×C3—28no—
311C2×C3#551014yes—
312C2×C3C22×#20414yes—
313C2×C3#574814yes—
314D3—248no—
315C22—21no—
316C22—21no—
317C22—362no—
318C22—362no—
319C22—362no—
320C22C2×#374412yes—
321C22C22×C4⋊(C3⋊D3)11yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—362no—
326C4—362no—
327C4—362no—
328C4C2×#374412yes—
329C4C2×#374412yes—
330C4#6436111yescharacteristic
331C4#6436411yescharacteristic
332C3#7902714yescomplemented
333C2—22no—
334C2—722no—
335C2#1059598111yescharacteristic
336C2C22×#374411yescharacteristic
337C2#1059621911yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×C4⋊C8C2
socleC22×C32C22×D4
prime radical#10595948C2
hypercenterC2×C4⋊C8C3⋊D3
hypocenterC32#3246
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10595941C2semidirect
3. C2×C32×C4⋊C8C2semidirect
4. #10592813C2semidirect
5. #10592550C2semidirect
6. #10592547C2semidirect
7. #10592541C2semidirect
8. #10592540C2semidirect
36. C2×C3×C4⋊C8D3semidirect
103. C2×C32×C4SD16semidirect
131. C2×C4⋊C8C3⋊D3semidirect
209. C2×C3×C4#204semidirect
283. C32#3246semidirect
302. C2×C4#3744semidirect
332. C3#79027semidirect

Maximal subgroups

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

subgroupindex
#105959482
#105959412
C2×C32×C4⋊C82
#105928132
#105925502
#105925472
#105925412
#105925402
#790273