Finite Group Databasebeta

← #11873578

Subgroups — #11873578

Order 1152.

1049 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 1049 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#10594008C211yesmaximal, characteristic
2#10593948C211yesmaximal, characteristic, complemented
3C3⋊D3×#97C211yesmaximal, characteristic, complemented
4C3×#4713C212yesmaximal, complemented
5#10590940C214yesmaximal, complemented
6#10590888C214yesmaximal, complemented
7#10590279C212yesmaximal, complemented
8D3×#490—32nomaximal
9C2×#3802—22no—
10C2×#3802C2212yes—
11C2×C8×C3⋊D3C2212yes—
12C42×C3⋊D3C2211yescharacteristic
13C3×#874C2212yes—
14C3×#870C2212yescomplemented
15#63914—22no—
16#63914C2212yes—
17#63900C2212yes—
18#63883—22no—
19#63872C2212yescomplemented
20#63870—22no—
21C32×#97C2211yescharacteristic, complemented
22#63642C2212yescomplemented
23#63630C2211yescharacteristic, complemented
24C3×#821C2218yescomplemented
25#63562C2218yescomplemented
26D3×#127—32no—
27D3×#125—32no—
28C3×#490—32no—
29#5071—32no—
30#5067—32no—
31D3×#102—38no—
32#4764—38no—
33#4713D312yescomplemented
34D3×#97—32no—
35D3×#97—61no—
36C22×D32—22no—
37C2×C4×C3⋊D3D412yes—
38C2×C4×C3⋊D3C2311yescharacteristic
39C2×C3×D12—24no—
40C2×C3×D12C2314yes—
41C2×#625—24no—
42C2×#625—22no—
43C2×#624—22no—
44#3802—28no—
45#3802—48no—
46C2×C32×C8C2312yes—
47C32×C42C2311yescharacteristic
48C4×C3⋊Dic3D412yes—
49C4×C3⋊Dic3C2311yescharacteristic
50C2×C3⋊(C3⋊C8)C2312yes—
51C8×C3⋊D3—24no—
52C3×C4⋊Dic3C2314yes—
53C3×Dic3⋊C4—24no—
54#3724—22no—
55Dic3⋊Dic3—24no—
56C2×#490—91noSylow
57C2×D3×D4—34no—
58C2×D3×D4—64no—
59C3×#127—32no—
60C3×#125—32no—
61#940—34no—
62#940—64no—
63C2×D3×C8—34no—
64C2×D3×C8—62no—
65D3×C4⋊C4—34no—
66D3×C4⋊C4—64no—
67#890—34no—
68#889—64no—
69#874C2×D312yes—
70C42×D3—32no—
71C42×D3—61no—
72#870C2×D312yescomplemented
73C3×#102—38no—
74C3×#97—21no—
75C3×#97C2×D312yescomplemented
76#832—38no—
77#821C2×D318yescomplemented
78#815—34no—
79#815—62no—
80#809—38no—
81#803—32no—
82#803—61no—
83C22×C3⋊D3C2×D411yescharacteristic
84C22×C3×D3—24no—
85C2×D32—44no—
86C2×D32—48no—
87C2×C32×C4C2×D412yes—
88C2×C32×C4C2411yescharacteristic
89C2×C3⋊Dic3C2×D412yes—
90C2×C3⋊Dic3C2×D411yescharacteristic
91C4×C3⋊D3—24no—
92C4×C3⋊D3#4114yes—
93C2×C3×Dic3—24no—
94C3×D12—28no—
95C3×D12—48no—
96#625—48no—
97#625—44no—
98#624—44no—
99C32×C8—22no—
100C3⋊(C3⋊C8)—22no—
101C2×#127—91no—
102C2×#125—91no—
103#490—32no—
104#490—94no—
105#490—92no—
106C2×#102—94no—
107C2×#97—91no—
108C23×D3—64no—
109C2×C3×D4—34no—
110C2×C3×D4—64no—
111C2×#67—68no—
112C2×#67—64no—
113D3×D4—616no—
114D3×D4—1216no—
115C2×D12—24no—
116C2×D12C22×D314yes—
117C2×C4×D3—32no—
118C2×C4×D3—34no—
119C2×C4×D3—61no—
120C2×C4×D3—62no—
121C2×C4×D3—64no—
122C2×C3×C8—22no—
123C2×C3×C8C22×D314yes—
124C3×C4⋊C4—34no—
125C3×C4⋊C4—64no—
126C3×C42—21no—
127C3×C42C22×D312yes—
128C4⋊Dic3—64no—
129C4⋊Dic3C22×D314yes—
130Dic3⋊C4—24no—
131Dic3⋊C4—64no—
132Dic3⋊C4—64no—
133C4×Dic3—34no—
134C4×Dic3—32no—
135C4×Dic3—61no—
136C4×Dic3—62no—
137C2×C3⋊C8—34no—
138C2×C3⋊C8—62no—
139D3×C8—68no—
140D3×C8—68no—
141C22×C32C22×D411yescharacteristic
142C2×C3⋊D3#12412yes—
143C2×C3⋊D3AGL(1,ℤ/8)14yes—
144C2×C3×D3—44no—
145C2×C3×D3—48no—
146D32—88no—
147C32×C4—22no—
148C32×C4C2×#4112yes—
149C3⋊Dic3—22no—
150C3⋊Dic3#12412yes—
151C3×Dic3—44no—
152C22×D4—92no—
153C22×D4—182no—
154C22×C8—92no—
155#127—32no—
156#127—92no—
157#127—182no—
158#125—32no—
159#125—92no—
160#125—182no—
161C2×C4⋊C4—92no—
162C2×C4⋊C4—182no—
163C2×C42—91no—
164#102—38no—
165#102—98no—
166#97—92no—
167#97—91no—
168#97D3211yescharacteristic, complemented
169C23×C3—64no—
170C22×D3—24no—
171C22×D3—32no—
172C22×D3—61no—
173C22×D3—128no—
174C22×D3—1216no—
175C3×D4—68no—
176C3×D4—128no—
177C2×C3×C4—21no—
178C2×C3×C4—22no—
179C2×C3×C4—64no—
180C2×C3×C4D3×D414yes—
181C2×C3×C4C23×D312yes—
182#67—128no—
183#67—1216no—
184C2×Dic3—24no—
185C2×Dic3—32no—
186C2×Dic3—34no—
187C2×Dic3—61no—
188C2×Dic3—62no—
189D12—28no—
190D12—48no—
191C4×D3—38no—
192C4×D3—64no—
193C4×D3—68no—
194C4×D3—124no—
195C4×D3—128no—
196C3×C8—24no—
197C3×C8—24no—
198C3⋊C8—64no—
199C3⋊C8—64no—
200C2×C32C2×#12411yescharacteristic
201C2×C32C2×AGL(1,ℤ/8)12yes—
202C3⋊D3#49014yescomplemented
203C3×D3—84no—
204C24—182no—
205C2×D4—34no—
206C2×D4—64no—
207C2×D4—188no—
208C2×D4—184no—
209C2×D4—182no—
210C2×D4—368no—
211C22×C4—91no—
212C22×C4—92no—
213C22×C4—182no—
214C2×C8—92no—
215C2×C8—184no—
216C2×C8C2×D3212yes—
217C4⋊C4—34no—
218C4⋊C4—64no—
219C4⋊C4—182no—
220C4⋊C4—184no—
221C42—91no—
222C42—92no—
223C42C2×D3211yescharacteristic
224C22×C3—21no—
225C22×C3—124no—
226C22×C3—128no—
227C22×C3C2×D3×D412yes—
228C2×D3—34no—
229C2×D3—38no—
230C2×D3—44no—
231C2×D3—48no—
232C2×D3—62no—
233C2×D3—64no—
234C2×D3—2416no—
235C3×C4—24no—
236C3×C4—22no—
237C3×C4—42no—
238C3×C4—124no—
239C3×C4D3×#4114yes—
240Dic3—34no—
241Dic3—44no—
242Dic3—62no—
243Dic3—64no—
244Dic3—122no—
245C32C2×#49011yescharacteristic, complemented, Sylow
246C23—64no—
247C23—91no—
248C23—364no—
249C23—368no—
250D4—68no—
251D4—128no—
252D4—364no—
253D4—368no—
254C2×C4—64no—
255C2×C4—91no—
256C2×C4—94no—
257C2×C4—92no—
258C2×C4—184no—
259C2×C4—364no—
260C2×C4#380212yes—
261C2×C4C22×D3211yescharacteristic
262C8—22no—
263C8—182no—
264C2×C3—22no—
265C2×C3—21no—
266C2×C3—244no—
267C2×C3D3×#12412yes—
268C2×C3D3×AGL(1,ℤ/8)14yes—
269D3—38no—
270D3—64no—
271D3—84no—
272C22—94no—
273C22—92no—
274C22—128no—
275C22—124no—
276C22—728no—
277C22C2×#380211yescharacteristic
278C4—22no—
279C4—92no—
280C4—124no—
281C4—182no—
282C4#6430612yes—
283C3—21no—
284C3D3×#49012yescomplemented
285C2—94no—
286C2—244no—
287C2#1059400911yescharacteristic
288C2#1059471612yes—
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radical#10594008C2
hypercenter#97D32
hypocenterC32C2×#490
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #10593948C2semidirect
3. C3⋊D3×#97C2semidirect
4. C3×#4713C2semidirect
5. #10590940C2semidirect
6. #10590888C2semidirect
7. #10590279C2semidirect
14. C3×#870C22semidirect
19. #63872C22semidirect
21. C32×#97C22semidirect
22. #63642C22semidirect
23. #63630C22semidirect
24. C3×#821C22semidirect
25. #63562C22semidirect
33. #4713D3semidirect
72. #870C2×D3semidirect
75. C3×#97C2×D3semidirect
77. #821C2×D3semidirect
168. #97D32semidirect
202. C3⋊D3#490semidirect
245. C32C2×#490semidirect
284. C3D3×#490semidirect

Maximal subgroups

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

subgroupindex
#105940082
#105939482
C3⋊D3×#972
C3×#47132
#105909402
#105908882
#105902792
D3×#4903