Finite Group Databasebeta

← #11873442

Subgroups — #11873442

Order 1152.

905 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 905 conjugacy classes of subgroups — too many to draw. Only its 164 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#10594009C211yesmaximal, characteristic
2#10593948C211yesmaximal, characteristic, complemented
3C4×C8×C3⋊D3C211yesmaximal, characteristic, complemented
4C3×#4697C212yesmaximal, complemented
5#10590940C212yesmaximal
6#10590868C214yesmaximal, complemented
7#10590672C212yesmaximal, complemented
8#10590278C212yesmaximal, complemented
9D3×#488—32nomaximal
10C2×#3802C2211yescharacteristic
11C2×#3797C2211yescharacteristic
12C2×C8×C3⋊D3C2212yes—
13C42×C3⋊D3C2211yescharacteristic
14C3×#875C2212yes—
15C3×#870C2212yescomplemented
16#63921—22no—
17#63915—22no—
18#63900C2212yes—
19#63883—22no—
20#63872C2212yescomplemented
21#63870—22no—
22#63863C2212yes—
23C32×C4×C8C2211yescharacteristic, complemented
24C8×C3⋊Dic3C2212yescomplemented
25C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C3×#821C2214yes—
27C3×#816C2214yescomplemented
28#63565C2214yescomplemented
29#63562C2214yes—
30D3×#125—32no—
31D3×#124—32no—
32C3×#488—32no—
33#5068—32no—
34#5056—32no—
35D3×#103—34no—
36#4800—34no—
37D3×#102—34no—
38#4768—34no—
39#4697D312yescomplemented
40C4×D3×C8—32no—
41C4×D3×C8—61no—
42C22×D32—21no—
43C2×C4×C3⋊D3D412yes—
44C2×C4×C3⋊D3C2311yescharacteristic
45C2×C3×D12C2312yes—
46C2×C3×Dic6C2312yes—
47C2×#627—21no—
48C2×#625—21no—
49C2×#624—21no—
50C2×#624—22no—
51#3802—24no—
52#3797—24no—
53C2×C32×C8C2312yes—
54C32×C42C2311yescharacteristic
55C4×C3⋊Dic3D412yes—
56C4×C3⋊Dic3C2311yescharacteristic
57C2×C3⋊(C3⋊C8)C2312yes—
58C8×C3⋊D3—24no—
59C3×(C2×D3)⋊C4—24no—
60C3×C4⋊Dic3C2314yes—
61C3×Dic3⋊C4—24no—
62#3724—22no—
63Dic3⋊Dic3—24no—
64(C2×D3)⋊Dic3—24no—
65C2×#488—91noSylow
66C2×D3×Q8—32no—
67C2×D3×D4—32no—
68C3×#125—32no—
69C3×#124—32no—
70#947—32no—
71#936—32no—
72C2×D3×C8—34no—
73C2×D3×C8—62no—
74D3×C4⋊C4—34no—
75D3×C4⋊C4—64no—
76#890—34no—
77#889—64no—
78#885—64no—
79D3×C22⋊C4—64no—
80#875C2×D312yes—
81C42×D3—32no—
82C42×D3—61no—
83#870C2×D312yescomplemented
84C3×#103—34no—
85C3×#102—34no—
86C3×C4×C8—21no—
87C3×C4×C8C2×D312yescomplemented
88#835—34no—
89#832—34no—
90#821C2×D314yes—
91#816C2×D314yescomplemented
92C8×Dic3—34no—
93C8×Dic3—62no—
94#810—34no—
95#809—34no—
96C4×C3⋊C8—32no—
97C4×C3⋊C8—61no—
98C22×C3⋊D3C2×D411yescharacteristic
99C22×C3×D3—22no—
100C2×D32—42no—
101C2×D32—44no—
102C2×C32×C4C2×D412yes—
103C2×C32×C4C2411yescharacteristic
104C2×C3⋊Dic3C2×D412yes—
105C2×C3⋊Dic3C2×D411yescharacteristic
106C4×C3⋊D3—24no—
107C4×C3⋊D3#4114yes—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—24no—
110C3×D12—24no—
111C3×Dic6—24no—
112#627—42no—
113#625—42no—
114#624—42no—
115#624—44no—
116C32×C8—22no—
117C3⋊(C3⋊C8)—22no—
118C2×#125—91no—
119C2×#124—91no—
120#488—32no—
121#488—94no—
122#488—92no—
123C2×#103—92no—
124C2×#102—92no—
125C2×C4×C8—91no—
126C23×D3—62no—
127C2×C3×Q8—32no—
128C2×C3×D4—32no—
129C2×#67—62no—
130D3×Q8—68no—
131D3×D4—68no—
132C2×D12C22×D312yes—
133C2×C4×D3—32no—
134C2×C4×D3—34no—
135C2×C4×D3—61no—
136C2×C4×D3—62no—
137C2×C4×D3—62no—
138C2×C4×D3—64no—
139C2×Dic6—62no—
140C2×Dic6C22×D312yes—
141C2×C3×C8—22no—
142C2×C3×C8C22×D314yes—
143C3×C4⋊C4—34no—
144C3×C4⋊C4—64no—
145C3×C22⋊C4—64no—
146C3×C42—21no—
147C3×C42C22×D312yes—
148#217—64no—
149(C2×D3)⋊C4—24no—
150(C2×D3)⋊C4—64no—
151C4⋊Dic3—64no—
152C4⋊Dic3C22×D314yes—
153Dic3⋊C4—24no—
154Dic3⋊C4—64no—
155Dic3⋊C4—64no—
156C4×Dic3—34no—
157C4×Dic3—32no—
158C4×Dic3—61no—
159C4×Dic3—62no—
160C2×C3⋊C8—34no—
161C2×C3⋊C8—62no—
162D3×C8—68no—
163D3×C8—68no—
164C22×C32C22×D411yescharacteristic
165C2×C3⋊D3#12412yes—
166C2×C3⋊D3#13514yes—
167C2×C3×D3—42no—
168C2×C3×D3—44no—
169D32—84no—
170C32×C4—22no—
171C32×C4C2×#4112yes—
172C3⋊Dic3—22no—
173C3⋊Dic3#12412yes—
174C3×Dic3—42no—
175C3×Dic3—44no—
176C22×Q8—91no—
177C22×D4—91no—
178C22×C8—92no—
179#125—32no—
180#125—92no—
181#125—182no—
182#124—32no—
183#124—92no—
184#124—182no—
185C2×C4⋊C4—92no—
186C2×C4⋊C4—182no—
187C2×C22⋊C4—182no—
188C2×C42—91no—
189#103—34no—
190#103—94no—
191#102—34no—
192#102—94no—
193C4×C8—92no—
194C4×C8—91no—
195C4×C8D3211yescharacteristic, complemented
196C23×C3—62no—
197C22×D3—22no—
198C22×D3—32no—
199C22×D3—61no—
200C22×D3—124no—
201C22×D3—128no—
202C3×Q8—64no—
203C3×D4—64no—
204C2×C3×C4—21no—
205C2×C3×C4—22no—
206C2×C3×C4—64no—
207C2×C3×C4—62no—
208C2×C3×C4D3×D414yes—
209C2×C3×C4C23×D312yes—
210#67—124no—
211C2×Dic3—24no—
212C2×Dic3—22no—
213C2×Dic3—32no—
214C2×Dic3—34no—
215C2×Dic3—61no—
216C2×Dic3—62no—
217D12—24no—
218C4×D3—38no—
219C4×D3—64no—
220C4×D3—68no—
221C4×D3—68no—
222C4×D3—128no—
223C4×D3—124no—
224Dic6—24no—
225Dic6—124no—
226C3×C8—24no—
227C3×C8—24no—
228C3⋊C8—64no—
229C3⋊C8—64no—
230C2×C32C2×#12411yescharacteristic
231C2×C32C2×#13512yes—
232C3⋊D3#48814yescomplemented
233C3×D3—82no—
234C24—181no—
235C2×Q8—32no—
236C2×Q8—181no—
237C2×Q8—184no—
238C2×D4—32no—
239C2×D4—184no—
240C2×D4—181no—
241C22×C4—91no—
242C22×C4—92no—
243C22×C4—181no—
244C22×C4—182no—
245C2×C8—92no—
246C2×C8—184no—
247C2×C8C2×D3212yes—
248C4⋊C4—34no—
249C4⋊C4—64no—
250C4⋊C4—182no—
251C4⋊C4—184no—
252C22⋊C4—64no—
253C22⋊C4—184no—
254C42—91no—
255C42—92no—
256C42C2×D3211yescharacteristic
257C22×C3—21no—
258C22×C3—122no—
259C22×C3—124no—
260C22×C3C2×D3×D412yes—
261C2×D3—34no—
262C2×D3—38no—
263C2×D3—42no—
264C2×D3—44no—
265C2×D3—62no—
266C2×D3—64no—
267C2×D3—248no—
268C3×C4—24no—
269C3×C4—24no—
270C3×C4—22no—
271C3×C4—122no—
272C3×C4—124no—
273C3×C4D3×#4114yes—
274Dic3—34no—
275Dic3—42no—
276Dic3—44no—
277Dic3—62no—
278Dic3—64no—
279Dic3—64no—
280C32C2×#48811yescharacteristic, complemented, Sylow
281C23—62no—
282C23—91no—
283C23—362no—
284C23—364no—
285Q8—64no—
286Q8—362no—
287D4—64no—
288D4—362no—
289C2×C4—62no—
290C2×C4—64no—
291C2×C4—91no—
292C2×C4—94no—
293C2×C4—92no—
294C2×C4—184no—
295C2×C4—362no—
296C2×C4—364no—
297C2×C4#380212yes—
298C2×C4C22×D3211yescharacteristic
299C8—22no—
300C8—182no—
301C2×C3—22no—
302C2×C3—21no—
303C2×C3—242no—
304C2×C3D3×#12412yes—
305C2×C3D3×#13514yes—
306D3—38no—
307D3—64no—
308D3—82no—
309C22—94no—
310C22—92no—
311C22—124no—
312C22—122no—
313C22—724no—
314C22C2×#380211yescharacteristic
315C4—22no—
316C4—92no—
317C4—124no—
318C4—122no—
319C4—182no—
320C4#6430612yes—
321C3—21no—
322C3D3×#48812yescomplemented
323C2—94no—
324C2—242no—
325C2#1059400911yescharacteristic
326C2#1059468412yes—
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC4×C8D32
hypocenterC32C2×#488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593948C2semidirect
3. C4×C8×C3⋊D3C2semidirect
4. C3×#4697C2semidirect
6. #10590868C2semidirect
7. #10590672C2semidirect
8. #10590278C2semidirect
15. C3×#870C22semidirect
20. #63872C22semidirect
23. C32×C4×C8C22semidirect
24. C8×C3⋊Dic3C22semidirect
25. C4×C3⋊(C3⋊C8)C22semidirect
27. C3×#816C22semidirect
28. #63565C22semidirect
39. #4697D3semidirect
83. #870C2×D3semidirect
87. C3×C4×C8C2×D3semidirect
91. #816C2×D3semidirect
195. C4×C8D32semidirect
232. C3⋊D3#488semidirect
280. C32C2×#488semidirect
322. C3D3×#488semidirect

Maximal subgroups

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

subgroupindex
#105940092
#105939482
C4×C8×C3⋊D32
C3×#46972
#105909402
#105908682
#105906722
#105902782
D3×#4883