Finite Group Databasebeta

← #11874156

Subgroups — #11874156

Order 1152.

1393 conjugacy classes of subgroups; only the 220 normal subgroups are shown.

normal subgroups only

This group has 1393 conjugacy classes of subgroups — too many to draw. Only its 220 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
1C2×#63796C214yesmaximal, complemented
2#10594008C211yesmaximal, characteristic
3#10593909C211yesmaximal, characteristic, complemented
4C4×C8×C3⋊D3C211yesmaximal, characteristic, complemented
5C3×#4693C212yesmaximal, complemented
6#10590884C214yesmaximal, complemented
7#10590375C212yesmaximal, complemented
8D3×#492—32nomaximal
9C2×#3802—22no—
10C2×#3802C2212yes—
11C2×#3797C2212yes—
12C2×C8×C3⋊D3C2212yes—
13C42×C3⋊D3C2211yescharacteristic
14C2×C3×#204C2218yescomplemented
15C3×#874C2212yes—
16C3×#869C2212yescomplemented
17#63919—22no—
18#63914—22no—
19#63914C2212yes—
20#63900—22no—
21#63873C2212yescomplemented
22C2×#3715C2218yescomplemented
23#63796—216no—
24C32×C4×C8C2211yescharacteristic, complemented
25C8×C3⋊Dic3C2212yescomplemented
26C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
27C2×D3×SD16—38no—
28D3×C4⋊Q8—32no—
29D3×#127—32no—
30C3×#492—32no—
31#5175—38no—
32#5085—32no—
33#5076—32no—
34#4693D312yescomplemented
35C4×D3×C8—32no—
36C4×D3×C8—61no—
37C22×D32—22no—
38C2×C4×C3⋊D3D412yes—
39C2×C4×C3⋊D3C2311yescharacteristic
40C2×C3×D12—24no—
41C2×C3×D12C2314yes—
42C2×C3×Dic6C2314yes—
43C2×#627—22no—
44C2×#625—24no—
45C2×#625—22no—
46C2×#624—22no—
47#3802—28no—
48#3802—48no—
49#3797—28no—
50C2×C32×C8C2312yes—
51C32×C42C2311yescharacteristic
52C4×C3⋊Dic3D412yes—
53C4×C3⋊Dic3C2311yescharacteristic
54C2×C3⋊(C3⋊C8)C2312yes—
55C8×C3⋊D3D418yescomplemented
56C3×C4⋊Dic3—24no—
57C3×#204—216no—
58#3724—24no—
59#3715—216no—
60C2×#492—91noSylow
61C2×D3×Q8—34no—
62C2×D3×D4—34no—
63C2×D3×D4—64no—
64C2×C3×SD16—38no—
65C3×C4⋊Q8—32no—
66C3×#127—32no—
67#944—34no—
68C2×#215—38no—
69#940—34no—
70#940—64no—
71C2×#214—38no—
72D3×SD16—632no—
73C2×#204C2×D318yescomplemented
74C2×D3×C8—34no—
75C2×D3×C8—62no—
76D3×C4⋊C4—64no—
77#888—64no—
78#874C2×D312yes—
79C42×D3—32no—
80C42×D3—61no—
81#869C2×D312yescomplemented
82C3×C4×C8—21no—
83C3×C4×C8C2×D312yescomplemented
84C8×Dic3—34no—
85C8×Dic3—62no—
86C4×C3⋊C8—32no—
87C4×C3⋊C8—61no—
88C22×C3⋊D3C2×D411yescharacteristic
89C22×C3×D3—24no—
90C2×D32—44no—
91C2×D32—48no—
92C2×C32×C4C2×D412yes—
93C2×C32×C4C2411yescharacteristic
94C2×C3⋊Dic3C2×D411yescharacteristic
95C2×C3⋊Dic3C2×D412yes—
96C4×C3⋊D3SD1618yescomplemented
97C4×C3⋊D3C2×D414yes—
98C2×C3×Dic3—24no—
99C3×D12—28no—
100C3×D12—48no—
101C3×Dic6—28no—
102#627—44no—
103#625—44no—
104#625—48no—
105#624—44no—
106C32×C8C2×D414yescomplemented
107C3⋊(C3⋊C8)C2×D414yescomplemented
108C22×SD16—94no—
109C2×C4⋊Q8—91no—
110C2×#127—91no—
111#492—32no—
112#492—92no—
113#492—94no—
114C2×C4×C8—91no—
115C23×D3—64no—
116C2×C3×Q8—34no—
117C2×C3×D4—34no—
118C2×C3×D4—64no—
119C2×#67—68no—
120C2×#67—64no—
121D3×Q8—616no—
122D3×D4—616no—
123D3×D4—1216no—
124C2×D12—24no—
125C2×D12C22×D314yes—
126C2×C4×D3—34no—
127C2×C4×D3—32no—
128C2×C4×D3—61no—
129C2×C4×D3—62no—
130C2×C4×D3—64no—
131C2×Dic6—64no—
132C2×Dic6C22×D314yes—
133C3×SD16—616no—
134C2×C3×C8—22no—
135C2×C3×C8C22×D314yes—
136C3×C4⋊C4—64no—
137C3×C42—21no—
138C3×C42C22×D312yes—
139#215—616no—
140#214—616no—
141C4⋊Dic3—24no—
142Dic3⋊C4—68no—
143C4×Dic3—34no—
144C4×Dic3—32no—
145C4×Dic3—61no—
146C4×Dic3—62no—
147C2×C3⋊C8—34no—
148C2×C3⋊C8—62no—
149#204—216no—
150D3×C8—316no—
151D3×C8—68no—
152C22×C32C22×D411yescharacteristic
153C2×C3⋊D3#12712yes—
154C2×C3⋊D3C2×SD1614yes—
155C2×C3×D3—44no—
156C2×C3×D3—48no—
157D32—88no—
158C32×C4C2×SD1614yescomplemented
159C32×C4C22×D412yes—
160C3⋊Dic3#12712yes—
161C3⋊Dic3C2×SD1614yescomplemented
162C3×Dic3—44no—
163C22×Q8—92no—
164C22×D4—92no—
165C22×D4—182no—
166C2×SD16—38no—
167C2×SD16—98no—
168C2×SD16—1816no—
169C22×C8—92no—
170C4⋊Q8—32no—
171C4⋊Q8—92no—
172C4⋊Q8—182no—
173#127—32no—
174#127—92no—
175#127—182no—
176C2×C4⋊C4—182no—
177C2×C42—91no—
178C4×C8—92no—
179C4×C8—91no—
180C4×C8D3211yescharacteristic, complemented
181C23×C3—64no—
182C22×D3—24no—
183C22×D3—32no—
184C22×D3—61no—
185C22×D3—128no—
186C22×D3—1216no—
187C3×Q8—68no—
188C3×D4—68no—
189C3×D4—128no—
190C2×C3×C4—21no—
191C2×C3×C4—22no—
192C2×C3×C4—64no—
193C2×C3×C4D3×D414yes—
194C2×C3×C4C23×D312yes—
195#67—128no—
196#67—1216no—
197C2×Dic3—24no—
198C2×Dic3—34no—
199C2×Dic3—32no—
200C2×Dic3—62no—
201C2×Dic3—61no—
202D12—28no—
203D12—48no—
204C4×D3—316no—
205C4×D3—38no—
206C4×D3—68no—
207C4×D3—64no—
208C4×D3—128no—
209Dic6—28no—
210Dic6—128no—
211C3×C8—24no—
212C3×C8D3×D418yescomplemented
213C3⋊C8—38no—
214C3⋊C8—64no—
215C2×C32C2×#12711yescharacteristic
216C2×C32C22×SD1612yes—
217C3⋊D3#49214yescomplemented
218C3×D3—84no—
219C24—182no—
220C2×Q8—34no—
221C2×Q8—182no—
222C2×Q8—188no—
223C2×D4—34no—
224C2×D4—64no—
225C2×D4—188no—
226C2×D4—184no—
227C2×D4—182no—
228C2×D4—368no—
229C22×C4—91no—
230C22×C4—92no—
231C22×C4—182no—
232SD16—616no—
233SD16—1816no—
234C2×C8—92no—
235C2×C8—98no—
236C2×C8C2×D3212yes—
237C4⋊C4—64no—
238C4⋊C4—184no—
239C42—91no—
240C42—92no—
241C42C2×D3211yescharacteristic
242C22×C3—21no—
243C22×C3—124no—
244C22×C3—128no—
245C22×C3C2×D3×D412yes—
246C2×D3—34no—
247C2×D3—38no—
248C2×D3—44no—
249C2×D3—48no—
250C2×D3—62no—
251C2×D3—64no—
252C2×D3—2416no—
253C3×C4—22no—
254C3×C4—24no—
255C3×C4—124no—
256C3×C4D3×SD1618yescomplemented
257C3×C4C2×D3×D414yes—
258Dic3—34no—
259Dic3—38no—
260Dic3—44no—
261Dic3—62no—
262Dic3—64no—
263C32C2×#49211yescharacteristic, complemented, Sylow
264C23—64no—
265C23—91no—
266C23—364no—
267C23—368no—
268Q8—68no—
269Q8—364no—
270D4—68no—
271D4—128no—
272D4—364no—
273D4—368no—
274C2×C4—64no—
275C2×C4—92no—
276C2×C4—91no—
277C2×C4—94no—
278C2×C4—98no—
279C2×C4—364no—
280C2×C4#380212yes—
281C2×C4C22×D3211yescharacteristic
282C8—94no—
283C8#380214yescomplemented
284C2×C3—22no—
285C2×C3—21no—
286C2×C3—244no—
287C2×C3D3×#12712yes—
288C2×C3C2×D3×SD1614yes—
289D3—38no—
290D3—64no—
291D3—84no—
292C22—94no—
293C22—92no—
294C22—128no—
295C22—124no—
296C22—728no—
297C22C2×#380211yescharacteristic
298C4—94no—
299C4—92no—
300C4—124no—
301C4#6379614yescomplemented
302C4C2×#380212yes—
303C3—21no—
304C3D3×#49212yescomplemented
305C2—94no—
306C2—244no—
307C2#1059400811yescharacteristic
308C2C2×#6379612yes—
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10594008C2
hypercenterC4×C8D32
hypocenterC32C2×#492
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
1. C2×#63796C2semidirect
3. #10593909C2semidirect
4. C4×C8×C3⋊D3C2semidirect
5. C3×#4693C2semidirect
6. #10590884C2semidirect
7. #10590375C2semidirect
14. C2×C3×#204C22semidirect
16. C3×#869C22semidirect
21. #63873C22semidirect
22. C2×#3715C22semidirect
24. C32×C4×C8C22semidirect
25. C8×C3⋊Dic3C22semidirect
26. C4×C3⋊(C3⋊C8)C22semidirect
34. #4693D3semidirect
55. C8×C3⋊D3D4semidirect
73. C2×#204C2×D3semidirect
81. #869C2×D3semidirect
83. C3×C4×C8C2×D3semidirect
96. C4×C3⋊D3SD16semidirect
106. C32×C8C2×D4semidirect
107. C3⋊(C3⋊C8)C2×D4semidirect
158. C32×C4C2×SD16semidirect
161. C3⋊Dic3C2×SD16semidirect
180. C4×C8D32semidirect
212. C3×C8D3×D4semidirect
217. C3⋊D3#492semidirect
256. C3×C4D3×SD16semidirect
263. C32C2×#492semidirect
283. C8#3802semidirect
301. C4#63796semidirect
304. C3D3×#492semidirect

Maximal subgroups

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

subgroupindex
C2×#637962
#105940082
#105939092
C4×C8×C3⋊D32
C3×#46932
#105908842
#105903752
D3×#4923