Finite Group Databasebeta

← #11898270

Subgroups — #11898270

Order 1152.

1076 conjugacy classes of subgroups.

The subgroup lattice has 377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596048C211yesmaximal, characteristic, complemented
2C3×#5577C211yesmaximal, characteristic, complemented
3C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4#10590355C213yesmaximal, complemented
5#10590350C213yesmaximal, complemented
6#10590349C213yesmaximal, complemented
7C4×#3714C213yesmaximal, complemented
8#83582—31nomaximal
9#79910—31nomaximal
10C2×#3832—21no—
11C2×C3×#239—21no—
12C32×C4×Q8C2211yescharacteristic
13#64104—23no—
14#64083C2213yes—
15C4×C4⋊(C3⋊D3)C2213yes—
16C3×#895—23no—
17C3×#874C2213yes—
18C3×C4×D12C2213yes—
19C2×#3714C2213yes—
20C2×#3714C2216yes—
21C3×C4⋊(C3⋊C8)C2213yes—
22C3×C4×C3⋊C8C2213yes—
23#63575C2211yescharacteristic
24#63564C2213yes—
25#63563C2213yes—
26C3×#550—31no—
27#5577—31no—
28#5577—31no—
29#5577—61no—
30#5577D311yescharacteristic, complemented
31C3×C8×Q8—31no—
32#5073—33no—
33#5072—33no—
34Q8×C3⋊C8D311yescharacteristic, complemented
35#5015—33no—
36C4×#213—33no—
37#4843—33no—
38#4843—33no—
39#4695—33no—
40C4×D24—33no—
41C2×C32×Q8D411yescharacteristic
42#3832—44no—
43C2×C4⋊(C3⋊D3)—23no—
44C2×C4⋊(C3⋊D3)—23no—
45C2×C4⋊(C3⋊D3)C2313yes—
46C2×C4×C3⋊D3—23no—
47C3×#239—44no—
48C2×C3×D12—23no—
49C2×C3×D12—23no—
50C2×C3×D12C2313yes—
51C2×C3×C4×D3—23no—
52C32×C4⋊C4D413yes—
53C32×C42C2313yes—
54#3752—23no—
55C4⋊(C3⋊Dic3)C2311yescharacteristic
56C3×(C2×D3)⋊C4—23no—
57C3×C4⋊Dic3C2311yescharacteristic
58C2×C3×C3⋊C8C2313yes—
59C2×C3×C3⋊C8C2311yescharacteristic
60#3714—26no—
61#3714—46no—
62#3391—91noSylow
63C2×C3×#41—61no—
64C2×#239—21no—
65C2×#239—62no—
66C2×#239—61no—
67C2×#239—61no—
68C3×#127—33no—
69C3×#121—63no—
70C3×C4×Q8—21no—
71C3×C4×Q8C2×D311yescharacteristic
72C3×C4×Q8C2×D311yescharacteristic
73C3×C4×D4—33no—
74C2×#213—33no—
75C2×#213—36no—
76C2×D24—33no—
77C2×D24—36no—
78#895—23no—
79#895—66no—
80#895—63no—
81#895—63no—
82#874—33no—
83#874—33no—
84#874—63no—
85#874C2×D313yes—
86C4×D12—33no—
87C4×D12—33no—
88C4×D12—63no—
89C4×D12C2×D313yes—
90C3×C4⋊C8—33no—
91C3×C4×C8—33no—
92#832—33no—
93#821—33no—
94#821—33no—
95#818—31no—
96#809—33no—
97#807—31no—
98C4⋊(C3⋊C8)C2×D313yes—
99C4×C3⋊C8C2×D313yes—
100C22×C3⋊D3—23no—
101C22×C3×D3—23no—
102C32×Q8D814yescomplemented
103C2×C32×C4C2×D413yes—
104C2×C32×C4C2×D413yes—
105C2×C32×C4C2411yescharacteristic
106C2×C3⋊Dic3—21no—
107C4⋊(C3⋊D3)—23no—
108C4⋊(C3⋊D3)—23no—
109C4⋊(C3⋊D3)—46no—
110C4⋊(C3⋊D3)—83no—
111C4×C3⋊D3—46no—
112C2×C3×Dic3—21no—
113C3×D12—23no—
114C3×D12—23no—
115C3×D12—46no—
116C3×D12—83no—
117C3×C4×D3—46no—
118C3×C3⋊C8—23no—
119C3×C3⋊C8#4112yescomplemented
120#550—31no—
121#550—91no—
122#493—93no—
123#459—93no—
124#459—93no—
125C8×Q8—31no—
126C4×D8—93no—
127C3×#41—124no—
128C2×C3×Q8—21no—
129C2×C3×Q8D1211yescharacteristic
130C2×C3×Q8#6711yescharacteristic
131C2×C3×D4—33no—
132C2×C3×D4—63no—
133C2×C3×D4—63no—
134C22×C3×C4—63no—
135#239—44no—
136#239—128no—
137#239—124no—
138#239—124no—
139C2×D12—23no—
140C2×D12—23no—
141C2×D12—33no—
142C2×D12—33no—
143C2×D12—63no—
144C2×D12—66no—
145C2×D12—63no—
146C2×D12—63no—
147C2×D12—66no—
148C2×D12—63no—
149C2×D12—63no—
150C2×D12C22×D313yes—
151C2×C4×D3—23no—
152C2×C4×D3—66no—
153C2×C4×D3—63no—
154C2×C4×D3—63no—
155C2×C3×C8—31no—
156C2×C3×C8—33no—
157C3×C4⋊C4—23no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4D1213yes—
160C3×C4⋊C4#6713yes—
161C3×C22⋊C4—63no—
162C3×C42—23no—
163C3×C42C22×D313yes—
164C3×C42C22×D313yes—
165#213—66no—
166#213—126no—
167(C2×D3)⋊C4—23no—
168(C2×D3)⋊C4—66no—
169(C2×D3)⋊C4—63no—
170(C2×D3)⋊C4—63no—
171C4⋊Dic3—31no—
172C4⋊Dic3—31no—
173C4⋊Dic3—61no—
174C4⋊Dic3C22×D311yescharacteristic
175C2×C3⋊C8C22×D313yes—
176C2×C3⋊C8C22×D311yescharacteristic
177D24—66no—
178D24—126no—
179C22×C32C22×D411yescharacteristic
180C2×C3⋊D3—43no—
181C2×C3⋊D3—43no—
182C2×C3⋊D3—43no—
183C2×C3×D3—43no—
184C2×C3×D3—43no—
185C2×C3×D3—43no—
186C32×C4—23no—
187C32×C4C2×D816yes—
188C32×C4C2×#4111yescharacteristic
189C32×C4H(5,𝔽2)11yescharacteristic
190C3⋊Dic3—41no—
191C3×Dic3—41no—
192C2×#41—61no—
193C2×#41—181no—
194C2×D8—93no—
195C2×D8—96no—
196#127—33no—
197#127—93no—
198#121—63no—
199#121—183no—
200C4×Q8D3211yescharacteristic
201C4×D4—33no—
202C4×D4—93no—
203#107—91no—
204C4⋊C8—33no—
205#102—93no—
206#102—93no—
207C4×C8—33no—
208C23×C3—63no—
209C22×D3—23no—
210C22×D3—66no—
211C22×D3—63no—
212C22×D3—63no—
213C3×Q8—24no—
214C3×Q8D2414yescomplemented
215C3×Q8#21314yescomplemented
216C3×D4—63no—
217C3×D4—63no—
218C3×D4—126no—
219C3×D4—243no—
220C2×C3×C4—21no—
221C2×C3×C4—23no—
222C2×C3×C4—23no—
223C2×C3×C4—61no—
224C2×C3×C4—126no—
225C2×C3×C4C2×D1213yes—
226C2×C3×C4C2×D1213yes—
227C2×C3×C4C2×#6713yes—
228C2×C3×C4C2×#6713yes—
229C2×C3×C4C23×D311yescharacteristic
230C2×C3×C4C23×D311yescharacteristic
231C2×Dic3—21no—
232C2×Dic3—62no—
233C2×Dic3—61no—
234C2×Dic3—61no—
235D12—23no—
236D12—23no—
237D12—46no—
238D12—63no—
239D12—63no—
240D12—63no—
241D12—63no—
242D12—83no—
243D12—123no—
244D12—123no—
245D12—1212no—
246D12—126no—
247D12—126no—
248D12—243no—
249D12—243no—
250D12—246no—
251C4×D3—46no—
252C4×D3—1212no—
253C4×D3—126no—
254C4×D3—126no—
255C3×C8—32no—
256C3×C8—63no—
257C3⋊C8—23no—
258C3⋊C8#23912yescomplemented
259C2×C32#55011yescharacteristic
260C2×C32C22×D811yescharacteristic
261C2×C32#57611yescharacteristic
262C3⋊D3—83no—
263C3×D3—83no—
264#41—124no—
265#41—364no—
266C2×Q8#62611yescharacteristic
267C2×D4—33no—
268C2×D4—63no—
269C2×D4—63no—
270C2×D4—93no—
271C2×D4—183no—
272C2×D4—183no—
273C22×C4—63no—
274C22×C4—183no—
275D8—186no—
276D8—366no—
277C2×C8—31no—
278C2×C8—33no—
279C4⋊C4—31no—
280C4⋊C4—91no—
281C4⋊C4#62613yes—
282C22⋊C4—63no—
283C22⋊C4—183no—
284C42C2×D3213yes—
285C22×C3—21no—
286C22×C3—123no—
287C22×C3—123no—
288C22×C3—123no—
289C22×C3C22×D1211yescharacteristic
290C22×C3C22×#6711yescharacteristic
291C2×D3—43no—
292C2×D3—43no—
293C2×D3—43no—
294C2×D3—126no—
295C2×D3—126no—
296C2×D3—126no—
297C2×D3—123no—
298C2×D3—123no—
299C2×D3—123no—
300C2×D3—123no—
301C2×D3—123no—
302C2×D3—123no—
303C3×C4—23no—
304C3×C4—23no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—26no—
308C3×C4—43no—
309C3×C4—121no—
310C3×C4C2×D2416yes—
311C3×C4C2×#21316yes—
312C3×C4C2×#23911yescharacteristic
313C3×C4D3×#4111yescharacteristic
314C3×C4#100911yescharacteristic
315C3×C4#100911yescharacteristic
316Dic3—41no—
317Dic3—122no—
318Dic3—121no—
319Dic3—121no—
320C32#339111yescharacteristic, complemented, Sylow
321C23—63no—
322C23—183no—
323Q8#371414yescomplemented
324D4—63no—
325D4—63no—
326D4—126no—
327D4—183no—
328D4—183no—
329D4—243no—
330D4—366no—
331D4—723no—
332C2×C4—61no—
333C2×C4—126no—
334C2×C4—181no—
335C2×C4—366no—
336C2×C4C2×#62613yes—
337C2×C4C2×#62613yes—
338C2×C4C22×D3211yescharacteristic
339C8—32no—
340C8—63no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—243no—
345C2×C3#557711yescharacteristic
346C2×C3C22×D2411yescharacteristic
347C2×C3#575211yescharacteristic
348C2×C3C22×#21311yescharacteristic
349C2×C3#583411yescharacteristic
350C2×C3#583511yescharacteristic
351D3—83no—
352D3—246no—
353D3—243no—
354D3—243no—
355C22—123no—
356C22—123no—
357C22—123no—
358C22—363no—
359C22—363no—
360C22—363no—
361C22C22×#62611yescharacteristic
362C4—23no—
363C4—121no—
364C4—361no—
365C4C2×#371416yes—
366C4D3×#23911yescharacteristic
367C4#6432011yescharacteristic
368C3—21no—
369C3#7991011yescharacteristic, complemented
370C3#8358211yescharacteristic, complemented
371C2—243no—
372C2—723no—
373C2C22×#371411yescharacteristic
374C2#1059541011yescharacteristic
375C2#1059544911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
hypercenterC4×Q8D32
hypocenterC32#3391
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596048C2semidirect
2. C3×#5577C2semidirect
3. C3×Q8×C3⋊C8C2semidirect
4. #10590355C2semidirect
5. #10590350C2semidirect
6. #10590349C2semidirect
7. C4×#3714C2semidirect
30. #5577D3semidirect
34. Q8×C3⋊C8D3semidirect
102. C32×Q8D8semidirect
119. C3×C3⋊C8#41semidirect
214. C3×Q8D24semidirect
215. C3×Q8#213semidirect
258. C3⋊C8#239semidirect
320. C32#3391semidirect
323. Q8#3714semidirect
369. C3#79910semidirect
370. C3#83582semidirect

Maximal subgroups

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

subgroupindex
#105960482
C3×#55772
C3×Q8×C3⋊C82
#105903552
#105903502
#105903492
C4×#37142
#835823
#799103