Finite Group Databasebeta

← #11878833

Subgroups — #11878833

Order 1152.

1464 conjugacy classes of subgroups; only the 241 normal subgroups are shown.

normal subgroups only

This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 241 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596199C211yesmaximal, characteristic, complemented
2C3⋊D3×#127C211yesmaximal, characteristic
3C32×#486C211yesmaximal, characteristic, complemented
4#10592787C211yesmaximal, characteristic, complemented
5#10592775C211yesmaximal, characteristic, complemented
6#10592475C214yesmaximal, complemented
7#10592461C214yesmaximal, complemented
8#10592392C211yesmaximal, characteristic, complemented
9#10592384C211yesmaximal, characteristic, complemented
10#81568—34nomaximal
11C2×D4×C3⋊D3—21no—
12C2×D4×C3⋊D3—21no—
13C2×D4×C3⋊D3C2212yes—
14C32×C4⋊Q8C2211yescharacteristic, complemented
15C32×#127C2211yescharacteristic
16#64155—21no—
17Q8×C3⋊Dic3—21no—
18#64149—21no—
19#64149—21no—
20#64149C2212yes—
21C2×#3754C2214yescomplemented
22C2×#3744C2214yescomplemented
23#64106C2212yes—
24#64101—21no—
25#64099—21no—
26#64096C2212yescomplemented
27#64083C2211yescharacteristic
28C42×C3⋊D3C2211yescharacteristic
29#64078C2211yescharacteristic, complemented
30C32×#102C2214yescomplemented
31C32×C4×C8C2211yescharacteristic, complemented
32#63647C2212yes—
33#63641C2212yescomplemented
34#63636C2214yescomplemented
35C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
36#5728—34no—
37D3×#127—34no—
38C3×#486D314yescomplemented
39#5088—34no—
40#5076—34no—
41#4776—316no—
42#4762—316no—
43#4693—34no—
44#4685—34no—
45C23×C3⋊D3—22no—
46C2×C32×Q8—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4C2312yes—
50C2×#638—22no—
51C2×#638—22no—
52C2×#638—22no—
53D4×C3⋊D3—44no—
54D4×C3⋊D3—44no—
55D4×C3⋊D3—44no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C4×C3⋊D3D411yescharacteristic
60C2×C4×C3⋊D3D411yescharacteristic
61C2×C4×C3⋊D3C2311yescharacteristic
62C2×#634C2312yes—
63C2×C32×C8C2312yes—
64C32×C4⋊C4—21no—
65C32×C4⋊C4C2312yes—
66C32×C42C2311yescharacteristic
67#3754—44no—
68#3752—22no—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)—21no—
71C4⋊(C3⋊Dic3)—22no—
72#3750—22no—
73C4×C3⋊Dic3—22no—
74C4×C3⋊Dic3D411yescharacteristic
75C4×C3⋊Dic3D411yescharacteristic
76C4×C3⋊Dic3C2311yescharacteristic
77C2×C3⋊(C3⋊C8)C2312yes—
78#3744—44no—
79#3208—91noSylow
80C2×D3×D4—38no—
81C2×D3×D4—64no—
82C2×D3×D4—64no—
83C3×C4⋊Q8C2×D314yescomplemented
84C3×#127C2×D314yes—
85#946—64no—
86Q8×Dic3—64no—
87#940—38no—
88#940—64no—
89#940—64no—
90C2×#214—316no—
91C2×#204—316no—
92#897—38no—
93#892—64no—
94#890—64no—
95#887—38no—
96#874—34no—
97C42×D3—34no—
98#869—34no—
99C3×#102C2×D3116yescomplemented
100C3×C4×C8C2×D314yescomplemented
101(C2×D3)⋊C8—38no—
102Dic3⋊C8—38no—
103#809—316no—
104C4×C3⋊C8—34no—
105C23×C32—22no—
106C22×C3⋊D3—22no—
107C22×C3⋊D3—44no—
108C22×C3⋊D3—44no—
109C22×C3⋊D3—44no—
110C22×C3⋊D3C2×D411yescharacteristic
111C32×Q8—42no—
112C32×D4—24no—
113C32×D4—42no—
114C32×D4—42no—
115C2×C32×C4—22no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2411yescharacteristic
119#638—44no—
120#638—44no—
121#638—44no—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3C2×D411yescharacteristic
124C2×C3⋊Dic3C2×D411yescharacteristic
125C2×C3⋊Dic3C2×D411yescharacteristic
126C4⋊(C3⋊D3)—24no—
127C4⋊(C3⋊D3)—42no—
128C4⋊(C3⋊D3)—42no—
129C4×C3⋊D3—22no—
130C4×C3⋊D3—22no—
131C4×C3⋊D3SD1614yescomplemented
132#634—24no—
133C32×C8—22no—
134C3⋊(C3⋊C8)—22no—
135#533—91no—
136C2×#127—91no—
137#492—91no—
138#492—91no—
139#486—91no—
140#486C3⋊D311yescharacteristic, complemented
141#460—94no—
142#450—94no—
143#431—91no—
144C23×D3—68no—
145C2×C3×Q8—24no—
146C2×C3×D4—24no—
147C2×C3×D4—24no—
148C2×C3×D4C22×D318yes—
149C2×#67—68no—
150C2×#67—68no—
151C2×#67—68no—
152D3×D4—1216no—
153D3×D4—1216no—
154D3×D4—1216no—
155C2×D12—38no—
156C2×D12—64no—
157C2×D12—64no—
158C2×C4×D3—34no—
159C2×C4×D3—34no—
160C2×C4×D3—34no—
161C2×Dic6—38no—
162C2×C3×C8C22×D318yes—
163C3×C4⋊C4—24no—
164C3×C4⋊C4C22×D318yes—
165C3×C42C22×D314yes—
166#214—1216no—
167(C2×D3)⋊C4—68no—
168C4⋊Dic3—68no—
169C4⋊Dic3—64no—
170C4⋊Dic3—64no—
171Dic3⋊C4—68no—
172C4×Dic3—34no—
173C4×Dic3—34no—
174C4×Dic3—34no—
175C4×Dic3—68no—
176C2×C3⋊C8—38no—
177#204—1216no—
178C22×C32—42no—
179C22×C32—42no—
180C22×C32—42no—
181C22×C32C22×D411yescharacteristic
182C2×C3⋊D3—21no—
183C2×C3⋊D3—21no—
184C2×C3⋊D3—42no—
185C2×C3⋊D3—42no—
186C2×C3⋊D3—42no—
187C2×C3⋊D3—88no—
188C2×C3⋊D3C2×SD1612yes—
189C32×C4—42no—
190C32×C4C2×SD1612yes—
191C32×C4AGL(1,ℤ/8)12yes—
192C32×C4H(5,𝔽2)12yes—
193C3⋊Dic3—21no—
194C3⋊Dic3—21no—
195C3⋊Dic3—42no—
196C3⋊Dic3C2×SD1612yes—
197C22×D4—92no—
198C22×D4—181no—
199C22×D4—181no—
200C2×SD16—94no—
201C2×SD16—94no—
202C4⋊Q8—91no—
203C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
204#127—92no—
205#127—91no—
206#127—181no—
207#127—181no—
208#127C2×C3⋊D311yescharacteristic
209#125—181no—
210C22⋊Q8—92no—
211C22⋊Q8—181no—
212C4×Q8—92no—
213C4×Q8—181no—
214#117—181no—
215C2×C42—91no—
216C4⋊C8—92no—
217#102—94no—
218#102C2×C3⋊D314yescomplemented
219C22⋊C8—92no—
220C4×C8—91no—
221C4×C8C2×C3⋊D311yescharacteristic, complemented
222C23×C3—28no—
223C22×D3—34no—
224C22×D3—68no—
225C22×D3—1216no—
226C22×D3—1216no—
227C22×D3—1216no—
228C3×Q8—48no—
229C3×D4—216no—
230C3×D4—48no—
231C3×D4—48no—
232C2×C3×C4—28no—
233C2×C3×C4D3×D414yes—
234C2×C3×C4D3×D414yes—
235C2×C3×C4C23×D314yes—
236#67—1216no—
237#67—1216no—
238#67—1216no—
239C2×Dic3—34no—
240C2×Dic3—34no—
241C2×Dic3—34no—
242C2×Dic3—68no—
243D12—616no—
244D12—128no—
245D12—128no—
246C4×D3—316no—
247C4×D3—68no—
248C4×D3—68no—
249Dic6—616no—
250C3×C8—28no—
251C3⋊C8—68no—
252C2×C32—82no—
253C2×C32#53511yescharacteristic
254C2×C32C22×SD1611yescharacteristic
255C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
256C3⋊D3—22no—
257C3⋊D3—82no—
258C24—182no—
259C2×Q8—21no—
260C2×Q8—92no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—92no—
264C2×D4—182no—
265C2×D4—182no—
266C2×D4—182no—
267C2×D4—181no—
268C2×D4—181no—
269C2×D4—364no—
270C2×D4—364no—
271C2×D4—364no—
272C2×D4C22×C3⋊D312yes—
273C22×C4—91no—
274C22×C4—91no—
275C22×C4—91no—
276SD16—364no—
277SD16—364no—
278C2×C8—92no—
279C2×C8C22×C3⋊D312yes—
280C4⋊C4—21no—
281C4⋊C4—182no—
282C4⋊C4—182no—
283C4⋊C4—181no—
284C4⋊C4—181no—
285C4⋊C4C22×C3⋊D312yes—
286C22⋊C4—182no—
287C42—91no—
288C42—91no—
289C42—91no—
290C42—182no—
291C42C22×C3⋊D311yescharacteristic
292C22×C3—48no—
293C22×C3—48no—
294C22×C3—48no—
295C22×C3C2×D3×D414yes—
296C2×D3—38no—
297C2×D3—64no—
298C2×D3—64no—
299C2×D3—128no—
300C2×D3—128no—
301C2×D3—128no—
302C2×D3—2432no—
303C3×C4—48no—
304C3×C4#91118yes—
305C3×C4D3×SD1618yes—
306C3×C4#100918yes—
307Dic3—38no—
308Dic3—64no—
309Dic3—64no—
310Dic3—128no—
311C32#320811yescharacteristic, complemented, Sylow
312C23—22no—
313C23—91no—
314C23—182no—
315C23—364no—
316C23—364no—
317C23—364no—
318Q8—42no—
319Q8—184no—
320D4—24no—
321D4—42no—
322D4—42no—
323D4—184no—
324D4—364no—
325D4—364no—
326D4—364no—
327D4—362no—
328D4—362no—
329C2×C4—22no—
330C2×C4—91no—
331C2×C4—94no—
332C2×C4—91no—
333C2×C4—91no—
334C2×C4—182no—
335C2×C4—182no—
336C2×C4—182no—
337C2×C4D4×C3⋊D311yescharacteristic
338C2×C4D4×C3⋊D311yescharacteristic
339C2×C4C23×C3⋊D311yescharacteristic
340C8—22no—
341C8—182no—
342C2×C3—88no—
343C2×C3#567414yes—
344C2×C3C2×#91114yes—
345C2×C3C2×D3×SD1614yes—
346D3—68no—
347D3—248no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22—92no—
352C22—181no—
353C22—181no—
354C22—362no—
355C22—362no—
356C22—362no—
357C22—728no—
358C22C2×D4×C3⋊D311yescharacteristic
359C4—42no—
360C4—92no—
361C4—181no—
362C4—181no—
363C4—362no—
364C4#6412012yes—
365C4SD16×C3⋊D312yes—
366C4#6436612yes—
367C3#8156814yescomplemented
368C2—82no—
369C2—182no—
370C2—722no—
371C2#1059614511yescharacteristic
372C2C2×#6412011yescharacteristic
373C2C2×SD16×C3⋊D311yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#486C2
socleC22×C32C22×D4
prime radicalC3⋊D3×#127C2
hypercenter#486C3⋊D3
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
3. C32×#486C2semidirect
4. #10592787C2semidirect
5. #10592775C2semidirect
6. #10592475C2semidirect
7. #10592461C2semidirect
8. #10592392C2semidirect
9. #10592384C2semidirect
14. C32×C4⋊Q8C22semidirect
21. C2×#3754C22semidirect
22. C2×#3744C22semidirect
26. #64096C22semidirect
29. #64078C22semidirect
30. C32×#102C22semidirect
31. C32×C4×C8C22semidirect
33. #63641C22semidirect
34. #63636C22semidirect
35. C4×C3⋊(C3⋊C8)C22semidirect
38. C3×#486D3semidirect
83. C3×C4⋊Q8C2×D3semidirect
99. C3×#102C2×D3semidirect
100. C3×C4×C8C2×D3semidirect
131. C4×C3⋊D3SD16semidirect
140. #486C3⋊D3semidirect
203. C4⋊Q8C2×C3⋊D3semidirect
218. #102C2×C3⋊D3semidirect
221. C4×C8C2×C3⋊D3semidirect
311. C32#3208semidirect
367. C3#81568semidirect

Maximal subgroups

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

subgroupindex
#105961992
C3⋊D3×#1272
C32×#4862
#105927872
#105927752
#105924752
#105924612
#105923922
#105923842
#815683