Finite Group Databasebeta

← #11860012

Subgroups — #11860012

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594958C212yesmaximal, complemented
2C2×#63822C211yesmaximal, characteristic
3C2×C8×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#5113C212yesmaximal, complemented
5#10591138C211yesmaximal, characteristic, complemented
6#10590790C212yesmaximal, complemented
7#10590742C214yesmaximal, complemented
8#10590740C212yesmaximal, complemented
9#78818—32nomaximal
10C2×C3×#235C2212yes—
11C22×C32×C8C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2212yes—
15#67⋊Dic3—24no—
16#63898C2214yes—
17C4×D3×Dic3—22no—
18#63855—22no—
19#63843C2214yes—
20C2×#3718C2211yescharacteristic
21C2×#3715C2212yes—
22#63822C418yescomplemented
23C2×#3713C2211yescharacteristic
24C8×C3⋊Dic3C2212yes—
25C8×C3⋊Dic3C2212yes—
26C3×#821C2214yes—
27C3×#816C2214yes—
28#63576C2212yes—
29#63574C2212yes—
30Dic3×#41—32no—
31C2×#950—32no—
32#5522—32no—
33C3×#416—32no—
34#5113D312yescomplemented
35C2×C8×Dic3—32no—
36C2×C8×Dic3—61no—
37#4998—32no—
38#4790—34no—
39#4788—34no—
40#4758—34no—
41#4756—34no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3D412yes—
44C2×C3×#67—22no—
45C3×#235—24no—
46C3×#235C2×C418yescomplemented
47C2×C3×D12C2312yes—
48C2×C3×C4×D3—22no—
49C2×C3×Dic6C2312yes—
50C2×D3×Dic3—24no—
51C2×C32×C8—22no—
52C2×C32×C8C2312yes—
53C4×C3⋊Dic3D411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3C2312yes—
56C2×C3⋊(C3⋊C8)C2×C414yescomplemented
57C2×C3⋊(C3⋊C8)C2311yescharacteristic
58C2×C3⋊(C3⋊C8)C2311yescharacteristic
59C3×#217—22no—
60C3×C4⋊Dic3C2314yes—
61C3×C4×Dic3—22no—
62Dic3⋊Dic3—24no—
63(C2×D3)⋊Dic3—24no—
64Dic32—24no—
65#3718C2×C414yescomplemented
66#3715C2×C418yescomplemented
67#3713C2×C414yescomplemented
68C4×#135—91noSylow
69C2×C3×#41—32no—
70C2×#235C2×D312yes—
71C22×C3×C8—21no—
72C22×C3×C8C2×D312yes—
73C3×#117—32no—
74#950—316no—
75Q8×Dic3—34no—
76C2×#216—32no—
77C2×#215—32no—
78D4×Dic3—34no—
79D4×Dic3—64no—
80C2×#214—32no—
81C2×#213—32no—
82#926—62no—
83#926C2×D312yes—
84C2×C4×Dic3—32no—
85C2×C4×Dic3—61no—
86C2×C4×Dic3—62no—
87C22×C3⋊C8—32no—
88C22×C3⋊C8—61no—
89#893—34no—
90#887—34no—
91#67⋊C4—64no—
92#872—62no—
93C42×D3—62no—
94C3×#103—34no—
95C3×#102—34no—
96#821C2×D314yes—
97#816C2×D314yes—
98C8×Dic3—34no—
99C8×Dic3—34no—
100C8×Dic3—62no—
101C8×Dic3—62no—
102#808—34no—
103#807—34no—
104C23×C32C2×D411yescharacteristic
105C22×C3×D3—22no—
106C2×C32×C4C22×C412yes—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4#4112yes—
109C2×C32×C4C2411yescharacteristic
110C2×C3⋊Dic3—24no—
111C2×C3⋊Dic3C2×D412yes—
112C2×C3⋊Dic3C2×D412yes—
113C3×#67—28no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—24no—
116C3×D12—22no—
117C3×D12C22×C414yes—
118C3×C4×D3—28no—
119C3×Dic6—22no—
120C3×Dic6C22×C414yes—
121D3×Dic3—48no—
122C32×C8—22no—
123C3⋊(C3⋊C8)C22×C412yes—
124C3⋊(C3⋊C8)C22×C412yes—
125C2×#135—91no—
126C4×#41—92no—
127C4×Q16—92no—
128C4×SD16—94no—
129C4×D8—92no—
130#427—91no—
131#416—32no—
132C2×C4×C8—91no—
133C3×#41—38no—
134C3×#41—64no—
135C2×C3×Q8—32no—
136C2×C3×D4—32no—
137C2×C3×D4—62no—
138C22×C3×C4—21no—
139C22×C3×C4—62no—
140C22×C3×C4C22×D312yes—
141C2×#67—22no—
142C22×Dic3—34no—
143C22×Dic3—62no—
144C22×Dic3—64no—
145#235—24no—
146#235C4×D318yescomplemented
147C2×D12C22×D312yes—
148C2×C4×D3—22no—
149C2×C4×D3—64no—
150C2×Dic6C22×D312yes—
151C2×C3×C8—24no—
152C2×C3×C8—24no—
153C2×C3×C8—22no—
154C2×C3×C8C22×D314yes—
155C3×C4⋊C4—34no—
156C3×C22⋊C4—62no—
157C3×C42—62no—
158#217—22no—
159#217—64no—
160#216—38no—
161#215—38no—
162#214—38no—
163#213—38no—
164(C2×D3)⋊C4—64no—
165C4⋊Dic3—64no—
166C4⋊Dic3C22×D314yes—
167Dic3⋊C4—64no—
168C4×Dic3—22no—
169C4×Dic3—32no—
170C4×Dic3—32no—
171C4×Dic3—34no—
172C4×Dic3—62no—
173C4×Dic3—61no—
174C4×Dic3—61no—
175C4×Dic3—64no—
176C4×Dic3—64no—
177C2×C3⋊C8—38no—
178C2×C3⋊C8—32no—
179C2×C3⋊C8—32no—
180C2×C3⋊C8—61no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—64no—
183C22×C32—22no—
184C22×C32C4×D412yes—
185C22×C32C22×D411yescharacteristic
186C2×C3×D3—24no—
187C2×C3×D3—44no—
188C32×C4C4×D412yes—
189C32×C4C23×C411yescharacteristic
190C32×C4C2×#4111yescharacteristic
191C3⋊Dic3—22no—
192C3⋊Dic3#13514yescomplemented
193C3×Dic3—24no—
194C3×Dic3—44no—
195C2×#41—32no—
196#135—98no—
197C2×Q16—91no—
198C2×SD16—92no—
199C2×D8—91no—
200C22×C8—91no—
201C22×C8D3211yescharacteristic
202C4×Q8—94no—
203C4×D4—94no—
204C4×D4—184no—
205#117—32no—
206#117—182no—
207C2×C42—91no—
208C2×C42—182no—
209#107—92no—
210#106—92no—
211#103—34no—
212#102—34no—
213C4×C8—92no—
214C4×C8—92no—
215C23×C3—21no—
216C23×C3—62no—
217C23×C3D3×D412yes—
218C22×D3—22no—
219C3×Q8—34no—
220C3×Q8—62no—
221C3×D4—34no—
222C3×D4—68no—
223C3×D4—62no—
224C2×C3×C4—21no—
225C2×C3×C4—22no—
226C2×C3×C4—21no—
227C2×C3×C4—22no—
228C2×C3×C4—62no—
229C2×C3×C4—68no—
230C2×C3×C4—64no—
231C2×C3×C4C2×C4×D314yes—
232C2×C3×C4D3×D412yes—
233C2×C3×C4#23714yes—
234C2×C3×C4C23×D312yes—
235#67—28no—
236C2×Dic3—22no—
237C2×Dic3—24no—
238C2×Dic3—34no—
239C2×Dic3—34no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—68no—
243C2×Dic3—68no—
244C2×Dic3—128no—
245D12—22no—
246D12C2×C4×D314yes—
247C4×D3—28no—
248C4×D3—128no—
249Dic6—22no—
250Dic6C2×C4×D314yes—
251C3×C8—24no—
252C3×C8—24no—
253C3⋊C8—34no—
254C3⋊C8—34no—
255C3⋊C8—62no—
256C3⋊C8—62no—
257C2×C32—22no—
258C2×C32C2×C4×D411yescharacteristic
259C2×C32C2×#13512yes—
260C3×D3—44no—
261#41—38no—
262#41—64no—
263C2×Q8—32no—
264C2×D4—32no—
265C2×D4—62no—
266C22×C4—62no—
267C22×C4—92no—
268C22×C4—184no—
269C22×C4C2×D3211yescharacteristic
270Q16—94no—
271SD16—98no—
272D8—94no—
273C2×C8—22no—
274C2×C8—91no—
275C2×C8—91no—
276C2×C8—94no—
277C2×C8C2×D3212yes—
278C4⋊C4—34no—
279C4⋊C4—184no—
280C22⋊C4—62no—
281C22⋊C4—184no—
282C42—62no—
283C42—92no—
284C42—91no—
285C42—91no—
286C42—184no—
287C22×C3—24no—
288C22×C3—24no—
289C22×C3—21no—
290C22×C3—22no—
291C22×C3—64no—
292C22×C3—124no—
293C22×C3#67⋊C414yes—
294C22×C3C2×D3×D412yes—
295C2×D3—24no—
296C2×D3—44no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—22no—
300C3×C4—64no—
301C3×C4—124no—
302C3×C4#67⋊C414yes—
303C3×C4C22×C4×D312yes—
304C3×C4C2×#23712yes—
305Dic3—24no—
306Dic3—38no—
307Dic3—44no—
308Dic3—64no—
309Dic3—64no—
310Dic3—64no—
311C32C4×#13511yescharacteristic, complemented, Sylow
312C23—62no—
313C23#380211yescharacteristic
314Q8—34no—
315Q8—62no—
316D4—34no—
317D4—68no—
318D4—62no—
319C2×C4—62no—
320C2×C4—68no—
321C2×C4—64no—
322C2×C4—92no—
323C2×C4—92no—
324C2×C4—184no—
325C2×C4—368no—
326C2×C4C4×D3212yes—
327C2×C4#380211yescharacteristic
328C2×C4#380512yes—
329C2×C4C22×D3211yescharacteristic
330C8—22no—
331C8—92no—
332C8—92no—
333C2×C3—24no—
334C2×C3—24no—
335C2×C3—22no—
336C2×C3—21no—
337C2×C3—124no—
338C2×C3C2×#67⋊C412yes—
339C2×C3D3×#13514yes—
340D3—44no—
341C22—22no—
342C22—64no—
343C22—124no—
344C22#6390212yes—
345C22C2×#380211yescharacteristic
346C4—64no—
347C4—94no—
348C4—124no—
349C4—182no—
350C4#6390212yes—
351C4C2×C4×D3211yescharacteristic
352C4C2×#380511yescharacteristic
353C3—21no—
354C3#7881812yescomplemented
355C2—22no—
356C2—124no—
357C2#1059468412yes—
358C2C2×#6390211yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC2×#63822C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C4×#135
LCSG ▷ 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. #10594958C2semidirect
3. C2×C8×C3⋊Dic3C2semidirect
4. C3×#5113C2semidirect
5. #10591138C2semidirect
6. #10590790C2semidirect
7. #10590742C2semidirect
8. #10590740C2semidirect
22. #63822C4semidirect
34. #5113D3semidirect
46. C3×#235C2×C4semidirect
56. C2×C3⋊(C3⋊C8)C2×C4semidirect
65. #3718C2×C4semidirect
66. #3715C2×C4semidirect
67. #3713C2×C4semidirect
146. #235C4×D3semidirect
192. C3⋊Dic3#135semidirect
311. C32C4×#135semidirect
354. C3#78818semidirect

Maximal subgroups

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

subgroupindex
#105949582
C2×#638222
C2×C8×C3⋊Dic32
C3×#51132
#105911382
#105907902
#105907422
#105907402
#788183