Finite Group Databasebeta

← #11878818

Subgroups — #11878818

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×#492C211yesmaximal, characteristic, complemented
4#10592868C214yesmaximal, complemented
5#10592862C214yesmaximal, complemented
6#10592784C211yesmaximal, characteristic, complemented
7#10592769C211yesmaximal, characteristic, complemented
8#10592393C211yesmaximal, characteristic, complemented
9#10592384C211yesmaximal, characteristic, complemented
10#81766—34nomaximal
11C2×D4×C3⋊D3—21no—
12C2×D4×C3⋊D3—21no—
13C2×D4×C3⋊D3C2212yes—
14C2×C32×SD16C2214yescomplemented
15C32×C4⋊Q8C2211yescharacteristic, complemented
16C32×#127C2211yescharacteristic
17#64155C2212yes—
18Q8×C3⋊Dic3C2212yescomplemented
19C2×#3755C2214yescomplemented
20#64149—21no—
21#64149—21no—
22#64149C2212yes—
23#64106—21no—
24#64101—21no—
25#64099—21no—
26#64096—21no—
27#64083C2211yescharacteristic
28C42×C3⋊D3C2211yescharacteristic
29#64078C2211yescharacteristic, complemented
30C32×C4×C8C2211yescharacteristic, complemented
31#63659C2214yescomplemented
32#63648C2214yescomplemented
33#63647C2212yes—
34#63641C2212yescomplemented
35C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
36#5728—34no—
37D3×#127—34no—
38C3×#492D314yescomplemented
39#5169—316no—
40#5163—316no—
41#5085—34no—
42#5070—34no—
43#4694—34no—
44#4685—34no—
45C23×C3⋊D3—22no—
46C2×C32×Q8C2312yes—
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×#634—21no—
63C32×SD16—44no—
64C2×C32×C8C2312yes—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C32×C42C2311yescharacteristic
68#3755—44no—
69#3752—22no—
70C4⋊(C3⋊Dic3)—21no—
71C4⋊(C3⋊Dic3)—22no—
72C4⋊(C3⋊Dic3)C2312yes—
73#3750—22no—
74C4×C3⋊Dic3—22no—
75C4×C3⋊Dic3D411yescharacteristic
76C4×C3⋊Dic3D411yescharacteristic
77C4×C3⋊Dic3C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2312yes—
79#3208—91noSylow
80C2×D3×D4—38no—
81C2×D3×D4—64no—
82C2×D3×D4—64no—
83C2×C3×SD16C2×D3116yescomplemented
84C3×C4⋊Q8C2×D314yescomplemented
85C3×#127C2×D314yes—
86#946—38no—
87Q8×Dic3—38no—
88C2×#215—316no—
89#940—38no—
90#940—64no—
91#940—64no—
92#897—64no—
93#892—64no—
94#890—64no—
95#887—64no—
96#874—34no—
97C42×D3—34no—
98#869—34no—
99C3×C4×C8C2×D314yescomplemented
100#832—316no—
101#821—316no—
102(C2×D3)⋊C8—38no—
103Dic3⋊C8—38no—
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—24no—
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—42no—
133C32×C8—22no—
134C3⋊(C3⋊C8)—22no—
135#533—91no—
136C2×#127—91no—
137#492—91no—
138#492C3⋊D311yescharacteristic, complemented
139#486—91no—
140#486—91no—
141#460—94no—
142#450—94no—
143#431—91no—
144C23×D3—68no—
145C2×C3×Q8C22×D318yes—
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—64no—
162C3×SD16—416no—
163C2×C3×C8C22×D318yes—
164C3×C4⋊C4—24no—
165C3×C4⋊C4—24no—
166C3×C42C22×D314yes—
167#215—1216no—
168(C2×D3)⋊C4—68no—
169C4⋊Dic3—38no—
170C4⋊Dic3—68no—
171C4⋊Dic3—64no—
172Dic3⋊C4—68no—
173C4×Dic3—34no—
174C4×Dic3—34no—
175C4×Dic3—34no—
176C4×Dic3—68no—
177C2×C3⋊C8—38no—
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×SD16C2×C3⋊D314yescomplemented
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#102—94no—
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—216no—
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—128no—
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—181no—
260C2×Q8C22×C3⋊D312yes—
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—44no—
277SD16—364no—
278C2×C8—92no—
279C2×C8C22×C3⋊D312yes—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—92no—
283C4⋊C4—182no—
284C4⋊C4—182no—
285C4⋊C4—181no—
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×C4D3×SD1618yes—
305C3×C4#91418yes—
306C3×C4#100418yes—
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—24no—
319Q8—362no—
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#571514yes—
344C2×C3C2×D3×SD1614yes—
345C2×C3C2×#91414yes—
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—
364C4SD16×C3⋊D312yes—
365C4#6412312yes—
366C4#6436112yes—
367C3#8176614yescomplemented
368C2—82no—
369C2—182no—
370C2—722no—
371C2#1059618611yescharacteristic
372C2C2×SD16×C3⋊D311yescharacteristic
373C2C2×#6412311yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#492C2
socleC22×C32C22×D4
prime radicalC3⋊D3×#127C2
hypercenter#492C3⋊D3
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
3. C32×#492C2semidirect
4. #10592868C2semidirect
5. #10592862C2semidirect
6. #10592784C2semidirect
7. #10592769C2semidirect
8. #10592393C2semidirect
9. #10592384C2semidirect
14. C2×C32×SD16C22semidirect
15. C32×C4⋊Q8C22semidirect
18. Q8×C3⋊Dic3C22semidirect
19. C2×#3755C22semidirect
29. #64078C22semidirect
30. C32×C4×C8C22semidirect
31. #63659C22semidirect
32. #63648C22semidirect
34. #63641C22semidirect
35. C4×C3⋊(C3⋊C8)C22semidirect
38. C3×#492D3semidirect
83. C2×C3×SD16C2×D3semidirect
84. C3×C4⋊Q8C2×D3semidirect
99. C3×C4×C8C2×D3semidirect
131. C4×C3⋊D3SD16semidirect
138. #492C3⋊D3semidirect
201. C2×SD16C2×C3⋊D3semidirect
203. C4⋊Q8C2×C3⋊D3semidirect
221. C4×C8C2×C3⋊D3semidirect
311. C32#3208semidirect
367. C3#81766semidirect

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×#4922
#105928682
#105928622
#105927842
#105927692
#105923932
#105923842
#817663