Finite Group Databasebeta

← #11860703

Subgroups — #11860703

Order 1152.

1121 conjugacy classes of subgroups; only the 244 normal subgroups are shown.

normal subgroups only

This group has 1121 conjugacy classes of subgroups — too many to draw. Only its 244 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#10594982C212yesmaximal, complemented
2C22×#3713C211yesmaximal, characteristic
3#10592821C211yesmaximal, characteristic, complemented
4C3×#5131C212yesmaximal, complemented
5#10591138C211yesmaximal, characteristic, complemented
6#10590741C214yesmaximal, complemented
7#10590740C214yesmaximal, complemented
8#78915—32nomaximal
9C22×C3×D12C2212yes—
10C2×C32×M16C2211yescharacteristic
11#64135C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×#926C2212yes—
14D3×#217—24no—
15#63898C2218yescomplemented
16Dic3×D12—24no—
17C2×#3713C418yescomplemented
18C2×#3713C2212yes—
19C2×#3713C2212yes—
20#63642C2212yescomplemented
21C8×C3⋊Dic3C2212yescomplemented
22C3×#821C2218yescomplemented
23#63576C2212yescomplemented
24#63574C2212yescomplemented
25#5798—32no—
26C22×#213—32no—
27#5521—32no—
28C3×#418—32no—
29#5131D312yescomplemented
30#5122—32no—
31#5122—61no—
32#4998—32no—
33#4785—38no—
34#4756—38no—
35C23×C3×D3—22no—
36C22×C32×C4C2311yescharacteristic
37C2×C3×D12—22no—
38C2×C3×D12—24no—
39C2×C3×D12C2×C418yescomplemented
40C2×C3×D12C2314yes—
41C2×D3×Dic3—28no—
42C32×M16—22no—
43C2×C32×C8C2312yes—
44#3757D412yes—
45C4⋊(C3⋊Dic3)D412yes—
46C4×C3⋊Dic3C2312yes—
47C2×C3⋊(C3⋊C8)C2×C414yescomplemented
48C2×C3⋊(C3⋊C8)C2311yescharacteristic
49C2×C3⋊(C3⋊C8)C2311yescharacteristic
50C3×#217—22no—
51C3×C4⋊Dic3C2314yes—
52C3×C4×Dic3—22no—
53(C2×D3)⋊Dic3—28no—
54#3713C2×C418yescomplemented
55#3713C2×C418yescomplemented
56#2948—91noSylow
57C22×C3×D4—32no—
58C22×D12C2×D312yes—
59C2×C3×M16—21no—
60C2×C3×M16C2×D312yes—
61C3×#117—32no—
62C2×#217—64no—
63D4×Dic3—38no—
64D4×Dic3—64no—
65C2×#213—316no—
66C2×#213—34no—
67C2×#213—34no—
68#926—32no—
69#926—61no—
70#926C2×D312yes—
71C22×C3⋊C8—32no—
72C22×C3⋊C8—61no—
73#893—38no—
74D3×C22⋊C4—64no—
75C4×D12—64no—
76C3×#102—38no—
77#821C2×D318yescomplemented
78#815—34no—
79#815—62no—
80C8×Dic3—34no—
81C8×Dic3—62no—
82#808—34no—
83#807—34no—
84C23×C32C2×D411yescharacteristic
85C22×C3×D3—24no—
86C22×C3×D3—28no—
87C22×C3×D3—84no—
88C2×C32×C4C22×C412yes—
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4#4112yes—
91C2×C32×C4C2411yescharacteristic
92C2×C3⋊Dic3C2×D414yes—
93C2×C3×Dic3—24no—
94C3×D12—28no—
95C3×D12—24no—
96C3×D12C22×C418yes—
97D3×Dic3—88no—
98C32×C8—22no—
99C3⋊(C3⋊C8)C22×C412yes—
100C3⋊(C3⋊C8)C22×C412yes—
101C22×D8—91no—
102#518—92no—
103#442—94no—
104C4×D8—94no—
105#427—91no—
106#418—32no—
107#405—91no—
108C24×C3—62no—
109C23×D3—22no—
110C2×C3×D4—38no—
111C2×C3×D4—34no—
112C2×C3×D4—62no—
113C2×C3×D4—64no—
114C22×C3×C4—21no—
115C22×C3×C4C22×D312yes—
116C22×Dic3—68no—
117C2×D12—22no—
118C2×D12—24no—
119C2×D12C4×D318yescomplemented
120C2×D12C22×D314yes—
121C2×C4×D3—68no—
122C3×M16—24no—
123C3×M16—24no—
124C2×C3×C8—22no—
125C2×C3×C8C22×D314yes—
126C3×C4⋊C4—34no—
127C3×C22⋊C4—62no—
128C3×C42—62no—
129#217—22no—
130#217—34no—
131#217—62no—
132#217—68no—
133#213—316no—
134#213—316no—
135(C2×D3)⋊C4—68no—
136C4⋊Dic3—34no—
137C4⋊Dic3—62no—
138C4⋊Dic3C22×D314yes—
139C4×Dic3—22no—
140C4×Dic3—34no—
141C4×Dic3—62no—
142C2×C3⋊C8—38no—
143C2×C3⋊C8—32no—
144C2×C3⋊C8—32no—
145C2×C3⋊C8—61no—
146C2×C3⋊C8—61no—
147C2×C3⋊C8—64no—
148C22×C32—22no—
149C22×C32C4×D412yes—
150C22×C32C22×D411yescharacteristic
151C2×C3×D3—28no—
152C2×C3×D3—48no—
153C2×C3×D3—88no—
154C32×C4C4×D412yes—
155C32×C4C23×C411yescharacteristic
156C32×C4C2×#4111yescharacteristic
157C3⋊Dic3—24no—
158C3×Dic3—44no—
159C22×D4—32no—
160C2×D8—98no—
161C2×D8—92no—
162C2×D8—92no—
163C2×M16D3211yescharacteristic
164C22×C8—91no—
165C4×D4—98no—
166C4×D4—184no—
167#117—32no—
168#117—91no—
169C2×C22⋊C4—184no—
170#107—92no—
171#106—92no—
172#102—38no—
173#97—92no—
174C4×C8—92no—
175C23×C3—21no—
176C23×C3—64no—
177C23×C3—68no—
178C23×C3—244no—
179C23×C3D3×D412yes—
180C22×D3—24no—
181C22×D3—28no—
182C22×D3—84no—
183C3×D4—38no—
184C3×D4—68no—
185C3×D4—64no—
186C2×C3×C4—21no—
187C2×C3×C4—22no—
188C2×C3×C4—21no—
189C2×C3×C4—22no—
190C2×C3×C4—64no—
191C2×C3×C4C2×C4×D314yes—
192C2×C3×C4D3×D412yes—
193C2×C3×C4#23714yes—
194C2×C3×C4C23×D312yes—
195C2×Dic3—24no—
196C2×Dic3—38no—
197C2×Dic3—64no—
198C2×Dic3—248no—
199D12—28no—
200D12—24no—
201D12C2×C4×D318yes—
202C4×D3—248no—
203C3×C8—24no—
204C3×C8—24no—
205C3⋊C8—34no—
206C3⋊C8—34no—
207C3⋊C8—62no—
208C3⋊C8—62no—
209C2×C32—22no—
210C2×C32C2×C4×D411yescharacteristic
211C2×C32#57612yes—
212C3×D3—48no—
213C24—62no—
214C2×D4—34no—
215C2×D4—38no—
216C2×D4—62no—
217C2×D4—64no—
218C22×C4—188no—
219C22×C4C2×D3211yescharacteristic
220D8—98no—
221D8—98no—
222M16—22no—
223C2×C8—91no—
224C2×C8—91no—
225C2×C8—94no—
226C2×C8C2×D3212yes—
227C4⋊C4—34no—
228C4⋊C4—92no—
229C22⋊C4—62no—
230C22⋊C4—92no—
231C22⋊C4—188no—
232C42—62no—
233C42—92no—
234C22×C3—24no—
235C22×C3—21no—
236C22×C3—22no—
237C22×C3—42no—
238C22×C3—68no—
239C22×C3—128no—
240C22×C3—248no—
241C22×C3#67⋊C414yes—
242C22×C3C2×D3×D412yes—
243C2×D3—28no—
244C2×D3—48no—
245C2×D3—88no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—22no—
249C3×C4—124no—
250C3×C4#67⋊C414yes—
251C3×C4C22×C4×D312yes—
252C3×C4C2×#23712yes—
253Dic3—44no—
254Dic3—68no—
255Dic3—124no—
256C32#294811yescharacteristic, complemented, Sylow
257C23—64no—
258C23—68no—
259C23—244no—
260C23#380211yescharacteristic
261D4—38no—
262D4—64no—
263D4—68no—
264C2×C4—64no—
265C2×C4—94no—
266C2×C4—728no—
267C2×C4C4×D3212yes—
268C2×C4#380211yescharacteristic
269C2×C4#380512yes—
270C2×C4C22×D3211yescharacteristic
271C8—22no—
272C8—92no—
273C8—92no—
274C2×C3—24no—
275C2×C3—22no—
276C2×C3—21no—
277C2×C3—42no—
278C2×C3—128no—
279C2×C3C2×#67⋊C412yes—
280C2×C3#577414yes—
281D3—48no—
282C22—22no—
283C22—68no—
284C22—128no—
285C22—248no—
286C22#6390212yes—
287C22C2×#380211yescharacteristic
288C4—124no—
289C4—184no—
290C4#6390212yes—
291C4C2×C4×D3211yescharacteristic
292C4C2×#380511yescharacteristic
293C3—21no—
294C3#7891512yescomplemented
295C2—22no—
296C2—128no—
297C2#1059472012yes—
298C2C2×#6390211yescharacteristic
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC22×#3713C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10594982C2semidirect
3. #10592821C2semidirect
4. C3×#5131C2semidirect
5. #10591138C2semidirect
6. #10590741C2semidirect
7. #10590740C2semidirect
15. #63898C22semidirect
17. C2×#3713C4semidirect
20. #63642C22semidirect
21. C8×C3⋊Dic3C22semidirect
22. C3×#821C22semidirect
23. #63576C22semidirect
24. #63574C22semidirect
29. #5131D3semidirect
39. C2×C3×D12C2×C4semidirect
47. C2×C3⋊(C3⋊C8)C2×C4semidirect
54. #3713C2×C4semidirect
55. #3713C2×C4semidirect
77. #821C2×D3semidirect
119. C2×D12C4×D3semidirect
256. C32#2948semidirect
294. C3#78915semidirect

Maximal subgroups

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

subgroupindex
#105949822
C22×#37132
#105928212
C3×#51312
#105911382
#105907412
#105907402
#789153