Finite Group Databasebeta

← #11874309

Subgroups — #11874309

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C212yesmaximal, complemented
2#10595032C212yesmaximal, complemented
3C2×#63822C212yesmaximal, complemented
4C2×C8×C3⋊Dic3C211yesmaximal, characteristic, complemented
5#10590905C211yesmaximal, characteristic, complemented
6#10590886C211yesmaximal, characteristic, complemented
7#10590884C212yesmaximal, complemented
8#10590869C212yesmaximal, complemented
9#10590867C212yesmaximal, complemented
10#83903—32nomaximal
11C2×C3×#235C2214yes—
12C22×C32×C8C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×Dic12C2212yes—
16C3×#904—28no—
17C2×C3×D24C2212yes—
18C2×C3×#204C2214yes—
19#63980—24no—
20#63914C2212yes—
21C4×#625—24no—
22#63873C2212yes—
23#63863C2214yes—
24C2×#3718C2212yes—
25C2×#3715C2214yes—
26#63822—28no—
27C2×#3713C2212yes—
28C8×C3⋊Dic3C2211yescharacteristic
29C8×C3⋊Dic3C2211yescharacteristic
30C8×C3⋊Dic3C2211yescharacteristic
31C8×C3⋊Dic3C2211yescharacteristic
32C2×C3×#135—32no—
33#5832—34no—
34C2×#950—34no—
35C2×#904D312yescomplemented
36#5191—32no—
37#5183—32no—
38#5175—34no—
39#5168—34no—
40#5155—32no—
41#5151—32no—
42C2×C8×Dic3—32no—
43C2×C8×Dic3—61no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3D412yes—
46C2×C3×#67—24no—
47C3×#235—28no—
48C3×#235—28no—
49C2×C3×D12C2314yes—
50C2×C3×C4×D3—24no—
51C2×C3×Dic6C2314yes—
52C2×#625—24no—
53C2×C32×C8D414yescomplemented
54C2×C32×C8C2311yescharacteristic
55C2×C32×C8C2311yescharacteristic
56C4×C3⋊Dic3D412yes—
57C4×C3⋊Dic3C2311yescharacteristic
58C4×C3⋊Dic3C2311yescharacteristic
59C2×C3⋊(C3⋊C8)D414yescomplemented
60C2×C3⋊(C3⋊C8)C2311yescharacteristic
61C2×C3⋊(C3⋊C8)C2311yescharacteristic
62C3×Dic12—24no—
63C3×D24—24no—
64C3×#204—28no—
65#3724—24no—
66(C2×D3)⋊Dic3—28no—
67#3718—24no—
68#3715—28no—
69#3713—24no—
70#3147—91noSylow
71C2×C3×#41—34no—
72C2×#235C2×D314yes—
73C3×#135—68no—
74C2×C3×Q16—32no—
75C2×C3×SD16—34no—
76C2×C3×D8—32no—
77C22×C3×C8—21no—
78C22×C3×C8C2×D312yes—
79#950—616no—
80#947—34no—
81#944—34no—
82C2×#216—34no—
83C2×#215—34no—
84#940—34no—
85#939—68no—
86#936—34no—
87C2×#214—34no—
88C2×#213—34no—
89C4×#67—68no—
90C2×C4×Dic3—32no—
91C2×C4×Dic3—61no—
92C22×C3⋊C8—32no—
93C22×C3⋊C8—61no—
94C2×Dic12C2×D312yes—
95#904—28no—
96C2×D24C2×D312yes—
97C2×#204C2×D314yes—
98C8×Dic3—32no—
99C8×Dic3—32no—
100C8×Dic3—32no—
101C8×Dic3—32no—
102C8×Dic3—61no—
103C8×Dic3—61no—
104C8×Dic3—61no—
105C8×Dic3—61no—
106C23×C32C2×D411yescharacteristic
107C22×C3×D3—24no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D412yes—
110C2×C32×C4C2×D412yes—
111C2×C32×C4C2411yescharacteristic
112C2×C3⋊Dic3—24no—
113C2×C3⋊Dic3C2×D412yes—
114C2×C3⋊Dic3C2×D412yes—
115C3×#67—48no—
116C2×C3×Dic3—24no—
117C3×D12—24no—
118C3×D12—24no—
119C3×C4×D3—48no—
120C3×Dic6—24no—
121C3×Dic6—24no—
122#625—48no—
123C32×C8C2×D412yes—
124C32×C8C2×D412yes—
125C3⋊(C3⋊C8)C2×D412yes—
126C3⋊(C3⋊C8)C2×D412yes—
127C2×#135—32no—
128C2×#135—92no—
129#532—92no—
130#495—92no—
131#495—92no—
132#494—91no—
133#493—91no—
134#492—92no—
135C2×C4×C8—91no—
136C3×#41—68no—
137C3×#41—68no—
138C2×C3×Q8—34no—
139C2×C3×D4—34no—
140C2×C3×D4—64no—
141C22×C3×C4—21no—
142C22×C3×C4—64no—
143C22×C3×C4C22×D312yes—
144C2×#67—24no—
145C2×#67—68no—
146C22×Dic3—34no—
147C22×Dic3—62no—
148#235—28no—
149#235—28no—
150C2×D12C22×D314yes—
151C2×C4×D3—24no—
152C2×Dic6C22×D314yes—
153C3×Q16—64no—
154C3×SD16—68no—
155C3×D8—64no—
156C2×C3×C8—24no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8#6718yescomplemented
160C2×C3×C8C22×D312yes—
161C2×C3×C8C22×D312yes—
162#217—68no—
163#216—68no—
164#215—68no—
165#214—68no—
166#213—68no—
167(C2×D3)⋊C4—68no—
168Dic3⋊C4—68no—
169C4×Dic3—34no—
170C4×Dic3—32no—
171C4×Dic3—32no—
172C4×Dic3—61no—
173C4×Dic3—61no—
174C4×Dic3—62no—
175C2×C3⋊C8—38no—
176C2×C3⋊C8—32no—
177C2×C3⋊C8—32no—
178C2×C3⋊C8—61no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8—64no—
181Dic12—24no—
182D24—24no—
183#204—28no—
184C22×C32—22no—
185C22×C32#12712yes—
186C22×C32C22×D411yescharacteristic
187C2×C3×D3—44no—
188C2×C3×D3—48no—
189C32×C4#12712yes—
190C32×C4C22×D411yescharacteristic
191C32×C4C22×D411yescharacteristic
192C3⋊Dic3—22no—
193C3⋊Dic3#13514yescomplemented
194C3×Dic3—44no—
195C2×#41—34no—
196#135—68no—
197#135—188no—
198C2×Q16—32no—
199C2×Q16—92no—
200C2×SD16—34no—
201C2×SD16—94no—
202C2×D8—32no—
203C2×D8—92no—
204C22×C8—91no—
205C22×C8D3211yescharacteristic
206C4⋊Q8—92no—
207#127—92no—
208#124—94no—
209#121—184no—
210C4×D4—184no—
211C2×C42—91no—
212C4×C8—91no—
213C4×C8—91no—
214C4×C8—91no—
215C4×C8—91no—
216C23×C3—21no—
217C23×C3—64no—
218C23×C3D3×D412yes—
219C22×D3—24no—
220C3×Q8—64no—
221C3×Q8—64no—
222C3×D4—64no—
223C3×D4—64no—
224C3×D4—128no—
225C2×C3×C4—21no—
226C2×C3×C4—22no—
227C2×C3×C4—21no—
228C2×C3×C4—22no—
229C2×C3×C4—64no—
230C2×C3×C4—128no—
231C2×C3×C4D3×D414yes—
232C2×C3×C4D3×D412yes—
233C2×C3×C4C2×#6714yes—
234C2×C3×C4C23×D312yes—
235#67—48no—
236#67—1216no—
237C2×Dic3—24no—
238C2×Dic3—34no—
239C2×Dic3—34no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—68no—
243C2×Dic3—68no—
244D12—24no—
245D12—24no—
246C4×D3—48no—
247Dic6—24no—
248Dic6—24no—
249C3×C8—22no—
250C3×C8—22no—
251C3×C8C2×#6714yes—
252C3×C8C2×#6714yes—
253C3⋊C8—34no—
254C3⋊C8—34no—
255C3⋊C8—62no—
256C3⋊C8—62no—
257C2×C32—22no—
258C2×C32C2×#12711yescharacteristic
259C2×C32C2×#13512yes—
260C3×D3—84no—
261#41—68no—
262#41—68no—
263C2×Q8—34no—
264C2×D4—34no—
265C2×D4—64no—
266C2×D4—184no—
267C22×C4—64no—
268C22×C4—92no—
269C22×C4C2×D3211yescharacteristic
270Q16—64no—
271Q16—184no—
272SD16—68no—
273SD16—188no—
274D8—64no—
275D8—184no—
276C2×C8—91no—
277C2×C8—91no—
278C2×C8—94no—
279C2×C8#62514yescomplemented
280C2×C8C2×D3211yescharacteristic
281C2×C8C2×D3211yescharacteristic
282C4⋊C4—184no—
283C22⋊C4—188no—
284C42—91no—
285C42—91no—
286C42—92no—
287C22×C3—24no—
288C22×C3—24no—
289C22×C3—21no—
290C22×C3—22no—
291C22×C3—128no—
292C22×C3—124no—
293C22×C3#94014yes—
294C22×C3C2×D3×D412yes—
295C2×D3—48no—
296C2×D3—44no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—22no—
300C3×C4—124no—
301C3×C4#94014yes—
302C3×C4C2×D3×D412yes—
303C3×C4C22×#6712yes—
304Dic3—38no—
305Dic3—44no—
306Dic3—64no—
307Dic3—64no—
308Dic3—64no—
309C32#314711yescharacteristic, complemented, Sylow
310C23—64no—
311C23#380211yescharacteristic
312Q8—64no—
313Q8—64no—
314D4—64no—
315D4—64no—
316D4—128no—
317D4—368no—
318C2×C4—64no—
319C2×C4—92no—
320C2×C4—92no—
321C2×C4—128no—
322C2×C4—184no—
323C2×C4#380212yes—
324C2×C4#380211yescharacteristic
325C2×C4C2×#62512yes—
326C2×C4C22×D3211yescharacteristic
327C8—92no—
328C8—92no—
329C8C2×#62512yes—
330C8C2×#62512yes—
331C2×C3—24no—
332C2×C3—24no—
333C2×C3—22no—
334C2×C3—21no—
335C2×C3—244no—
336C2×C3D3×#13514yes—
337C2×C3C2×#94012yes—
338D3—84no—
339C22—22no—
340C22—128no—
341C22—124no—
342C22#6391412yes—
343C22C2×#380211yescharacteristic
344C4—94no—
345C4—124no—
346C4—182no—
347C4#6391412yes—
348C4C2×#380211yescharacteristic
349C4C22×#62511yescharacteristic
350C3—21no—
351C3#8390312yescomplemented
352C2—22no—
353C2—244no—
354C2#1059468412yes—
355C2C2×#6391411yescharacteristic
subgroupG/H
centerC2×C4#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3147
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#904C2semidirect
2. #10595032C2semidirect
3. C2×#63822C2semidirect
4. C2×C8×C3⋊Dic3C2semidirect
5. #10590905C2semidirect
6. #10590886C2semidirect
7. #10590884C2semidirect
8. #10590869C2semidirect
9. #10590867C2semidirect
35. C2×#904D3semidirect
53. C2×C32×C8D4semidirect
59. C2×C3⋊(C3⋊C8)D4semidirect
159. C2×C3×C8#67semidirect
193. C3⋊Dic3#135semidirect
279. C2×C8#625semidirect
309. C32#3147semidirect
351. C3#83903semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9042
#105950322
C2×#638222
C2×C8×C3⋊Dic32
#105909052
#105908862
#105908842
#105908692
#105908672
#839033