Finite Group Databasebeta

← #11863932

Subgroups — #11863932

Order 1152.

2982 conjugacy classes of subgroups; only the 337 normal subgroups are shown.

normal subgroups only

This group has 2982 conjugacy classes of subgroups — too many to draw. Only its 337 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
1C23×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2#10596262C211yesmaximal, characteristic, complemented
3C2×#64117C212yesmaximal, complemented
4C32×#407C211yesmaximal, characteristic, complemented
5#10592830C212yesmaximal, complemented
6#10592431C214yesmaximal, complemented
7#10592430C214yesmaximal, complemented
8#78637—34nomaximal
9C24×C3⋊D3—21no—
10C23×C32×C4C2211yescharacteristic
11C2×#3828C2211yescharacteristic, complemented
12C22×C4⋊(C3⋊D3)—22no—
13C22×C4⋊(C3⋊D3)—21no—
14C22×C4⋊(C3⋊D3)—28no—
15C22×C4⋊(C3⋊D3)C2214yes—
16C22×C4⋊(C3⋊D3)C2212yes—
17C2×C32×M16C2212yescomplemented
18#64162—21no—
19#64139C2212yescomplemented
20#64138—21no—
21C4×#638—22no—
22#64135C2211yescharacteristic, complemented
23#64133C2212yescomplemented
24#64117—28no—
25C2×#3745C2214yescomplemented
26C2×#3744C2214yescomplemented
27C32×C22⋊C8C2214yescomplemented
28#63648C2218yescomplemented
29C23×D12—34no—
30#5791—34no—
31C2×#908—38no—
32C3×#407D314yescomplemented
33#5131—38no—
34#4732—316no—
35#4731—316no—
36C24×C32D411yescharacteristic
37C23×C3⋊D3—28no—
38C23×C3⋊D3—24no—
39C23×C3⋊D3—22no—
40C23×C3⋊D3—48no—
41C22×C32×C4—24no—
42C22×C32×C4D412yes—
43C22×C32×C4D411yescharacteristic
44C22×C32×C4C2312yes—
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C2×#638—22no—
48#3828—24no—
49C2×C4⋊(C3⋊D3)—28no—
50C2×C4⋊(C3⋊D3)—216no—
51C2×C4⋊(C3⋊D3)—24no—
52C2×C4⋊(C3⋊D3)—22no—
53C2×C4⋊(C3⋊D3)—24no—
54C2×C4⋊(C3⋊D3)—216no—
55C2×C4⋊(C3⋊D3)D418yescomplemented
56C2×C4⋊(C3⋊D3)C2314yes—
57C2×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
58C2×C4×C3⋊D3—21no—
59C2×#634C2311yescharacteristic, complemented
60C32×M16—24no—
61C2×C32×C8C2314yescomplemented
62#3757—22no—
63#3757—21no—
64#3752—22no—
65C4⋊(C3⋊Dic3)C2312yescomplemented
66#3750—22no—
67C4×C3⋊Dic3—21no—
68#3745—28no—
69#3744—28no—
70#3003—91noSylow
71C24×D3—64no—
72C23×C3×C4C2×D314yes—
73C2×#235—34no—
74C22×D12—38no—
75C22×D12—316no—
76C22×D12—632no—
77C22×D12—68no—
78C22×D12—64no—
79C2×C3×M16C2×D318yescomplemented
80#953—64no—
81#930—38no—
82#929—64no—
83C4×#67—68no—
84#926—34no—
85#924—38no—
86#908—632no—
87C2×D24—316no—
88C2×#204—316no—
89C3×C22⋊C8C2×D3116yescomplemented
90#821—332no—
91C23×C32—22no—
92C23×C32—24no—
93C23×C32C2×D411yescharacteristic
94C23×C32C2×D412yes—
95C22×C3⋊D3—216no—
96C22×C3⋊D3—28no—
97C22×C3⋊D3—24no—
98C22×C3⋊D3—21no—
99C22×C3⋊D3—432no—
100C22×C3⋊D3—48no—
101C22×C3⋊D3—48no—
102C22×C3⋊D3—48no—
103C2×C32×C4—22no—
104C2×C32×C4—24no—
105C2×C32×C4—24no—
106C2×C32×C4C2×D412yes—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D414yes—
109C2×C32×C4C2411yescharacteristic
110#638—42no—
111#638—44no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—21no—
114C4⋊(C3⋊D3)—216no—
115C4⋊(C3⋊D3)—28no—
116C4⋊(C3⋊D3)—24no—
117C4⋊(C3⋊D3)—22no—
118C4⋊(C3⋊D3)C2×D418yes—
119C4×C3⋊D3—42no—
120#634—22no—
121C32×C8—24no—
122C23×D4—91no—
123C2×AGL(1,ℤ/8)—92no—
124#525—91no—
125#450—94no—
126#447—94no—
127#418—92no—
128#407C3⋊D311yescharacteristic, complemented
129C24×C3D1214yes—
130C23×D3—632no—
131C23×D3—616no—
132C23×D3—68no—
133C23×D3—1232no—
134C22×C3×C4—216no—
135C22×C3×C4D1218yes—
136C22×C3×C4D1214yes—
137C22×C3×C4C22×D318yes—
138C22×C3×C4C22×D314yes—
139C2×#67—68no—
140C2×#67—64no—
141#235—616no—
142C2×D12—332no—
143C2×D12—316no—
144C2×D12—34no—
145C2×D12—664no—
146C2×D12—632no—
147C2×D12—664no—
148C2×D12—616no—
149C2×D12—68no—
150C2×D12—616no—
151C2×C4×D3—64no—
152C2×Dic6—34no—
153C3×M16—216no—
154C2×C3×C8C22×D3116yescomplemented
155#217—68no—
156#217—64no—
157(C2×D3)⋊C4—68no—
158C4⋊Dic3—38no—
159Dic3⋊C4—68no—
160C4×Dic3—64no—
161D24—632no—
162#204—632no—
163C22×C32—28no—
164C22×C32—22no—
165C22×C32—22no—
166C22×C32—22no—
167C22×C32#12012yes—
168C22×C32AGL(1,ℤ/8)14yescomplemented
169C22×C32C22×D411yescharacteristic
170C2×C3⋊D3—28no—
171C2×C3⋊D3—416no—
172C2×C3⋊D3—432no—
173C2×C3⋊D3—48no—
174C2×C3⋊D3—41no—
175C2×C3⋊D3—42no—
176C32×C4—22no—
177C32×C4#12012yes—
178C32×C4C22×D412yes—
179C3⋊Dic3—41no—
180C3⋊Dic3—42no—
181C25—181no—
182C2×#41—91no—
183C22×D4—92no—
184C22×D4—94no—
185C22×D4—188no—
186C22×D4—182no—
187C22×D4—181no—
188C23×C4C2×C3⋊D311yescharacteristic
189AGL(1,ℤ/8)—188no—
190C2×SD16—94no—
191C2×D8—94no—
192C2×M16C2×C3⋊D312yescomplemented
193#123—181no—
194C22⋊Q8—92no—
195#121—92no—
196#120—181no—
197C4×D4—182no—
198#117—91no—
199#102—98no—
200C22⋊C8C2×C3⋊D314yescomplemented
201C23×C3—28no—
202C23×C3—216no—
203C23×C3C2×D1214yes—
204C23×C3C2×D1218yes—
205C22×D3—664no—
206C22×D3—632no—
207C22×D3—616no—
208C22×D3—64no—
209C22×D3—12128no—
210C22×D3—1232no—
211C22×D3—1232no—
212C22×D3—1232no—
213C2×C3×C4—28no—
214C2×C3×C4—216no—
215C2×C3×C4—216no—
216C2×C3×C4C2×D1218yes—
217C2×C3×C4C2×D1214yes—
218C2×C3×C4D3×D4116yes—
219C2×C3×C4C23×D314yes—
220#67—128no—
221#67—1216no—
222C2×Dic3—68no—
223C2×Dic3—64no—
224D12—332no—
225D12—664no—
226D12—632no—
227D12—616no—
228D12—68no—
229C4×D3—128no—
230Dic6—68no—
231C3×C8—216no—
232C2×C32—22no—
233C2×C32—24no—
234C2×C32C2×#12011yescharacteristic
235C2×C32C2×AGL(1,ℤ/8)12yes—
236C3⋊D3—48no—
237C3⋊D3—81no—
238C24—188no—
239C24—184no—
240C24—182no—
241C24—368no—
242C24C4⋊(C3⋊D3)11yescharacteristic
243#41—184no—
244C2×Q8—91no—
245C2×D4—94no—
246C2×D4—91no—
247C2×D4—98no—
248C2×D4—1816no—
249C2×D4—188no—
250C2×D4—1816no—
251C2×D4—182no—
252C2×D4—181no—
253C2×D4—184no—
254C2×D4—182no—
255C2×D4—184no—
256C22×C4—24no—
257C22×C4—181no—
258C22×C4C4⋊(C3⋊D3)12yes—
259C22×C4C4⋊(C3⋊D3)11yescharacteristic
260C22×C4C22×C3⋊D312yes—
261C22×C4C22×C3⋊D311yescharacteristic
262SD16—188no—
263D8—188no—
264M16—24no—
265C2×C8C22×C3⋊D314yescomplemented
266C4⋊C4—92no—
267C4⋊C4—182no—
268C22⋊C4—181no—
269C22⋊C4—182no—
270C22⋊C4—182no—
271C42—181no—
272C22×C3—232no—
273C22×C3—28no—
274C22×C3—28no—
275C22×C3—28no—
276C22×C3#88218yes—
277C22×C3#908116yescomplemented
278C22×C3C22×D1214yes—
279C2×D3—632no—
280C2×D3—1264no—
281C2×D3—12128no—
282C2×D3—1232no—
283C2×D3—124no—
284C2×D3—128no—
285C3×C4—28no—
286C3×C4#88218yes—
287C3×C4C2×D3×D418yes—
288Dic3—124no—
289Dic3—128no—
290C32#300311yescharacteristic, complemented, Sylow
291C23—22no—
292C23—24no—
293C23—1816no—
294C23—188no—
295C23—184no—
296C23—181no—
297C23—3632no—
298C23—368no—
299C23—368no—
300C23—368no—
301C23C2×C4⋊(C3⋊D3)11yescharacteristic
302C23C2×C4⋊(C3⋊D3)12yes—
303Q8—182no—
304D4—98no—
305D4—1816no—
306D4—188no—
307D4—184no—
308D4—182no—
309D4—362no—
310D4—364no—
311C2×C4—22no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—182no—
315C2×C4—181no—
316C2×C4—362no—
317C2×C4C2×C4⋊(C3⋊D3)12yes—
318C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
319C2×C4D4×C3⋊D314yes—
320C2×C4C23×C3⋊D311yescharacteristic
321C8—24no—
322C2×C3—28no—
323C2×C3—216no—
324C2×C3C2×#88214yes—
325C2×C3C2×#90818yes—
326D3—1232no—
327D3—244no—
328C22—28no—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—188no—
333C22—3616no—
334C22—3632no—
335C22—368no—
336C22—361no—
337C22—362no—
338C22#6409112yes—
339C22#6411714yescomplemented
340C22C22×C4⋊(C3⋊D3)11yescharacteristic
341C4—22no—
342C4—361no—
343C4—362no—
344C4#6409112yes—
345C4C2×D4×C3⋊D312yes—
346C3#7863714yescomplemented
347C2—22no—
348C2—24no—
349C2—368no—
350C2—721no—
351C2C2×#6409111yescharacteristic
352C2C2×#6411712yes—
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#407C2
socleC22×C32C22×D4
hypercenter#407C3⋊D3
hypocenterC32#3003
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C23×C4⋊(C3⋊D3)C2semidirect
2. #10596262C2semidirect
3. C2×#64117C2semidirect
4. C32×#407C2semidirect
5. #10592830C2semidirect
6. #10592431C2semidirect
7. #10592430C2semidirect
11. C2×#3828C22semidirect
17. C2×C32×M16C22semidirect
19. #64139C22semidirect
22. #64135C22semidirect
23. #64133C22semidirect
25. C2×#3745C22semidirect
26. C2×#3744C22semidirect
27. C32×C22⋊C8C22semidirect
28. #63648C22semidirect
32. C3×#407D3semidirect
55. C2×C4⋊(C3⋊D3)D4semidirect
57. C2×C4⋊(C3⋊D3)C23semidirect
59. C2×#634C23semidirect
61. C2×C32×C8C23semidirect
65. C4⋊(C3⋊Dic3)C23semidirect
79. C2×C3×M16C2×D3semidirect
89. C3×C22⋊C8C2×D3semidirect
128. #407C3⋊D3semidirect
154. C2×C3×C8C22×D3semidirect
168. C22×C32AGL(1,ℤ/8)semidirect
192. C2×M16C2×C3⋊D3semidirect
200. C22⋊C8C2×C3⋊D3semidirect
265. C2×C8C22×C3⋊D3semidirect
277. C22×C3#908semidirect
290. C32#3003semidirect
339. C22#64117semidirect
346. C3#78637semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊(C3⋊D3)2
#105962622
C2×#641172
C32×#4072
#105928302
#105924312
#105924302
#786373