Finite Group Databasebeta

← C2×#10592516 #11860051

Subgroups — C2×#10592516 #11860051

Order 1152.

1632 conjugacy classes of subgroups.

The subgroup lattice has 333 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C22×#3755C211yesmaximal, characteristic
3C2×#64102C211yesmaximal, characteristic
4C2×C32×#103C211yesmaximal, characteristic, complemented
5C2×#63648C211yesmaximal, characteristic
6C2×#63642C211yesmaximal, characteristic, complemented
7C2×#63634C211yesmaximal, characteristic, complemented
8#10592516C218yesmaximal, direct product factor
9C2×#4817—34nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3—21no—
13C22×C32×C8C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15Q8×C3⋊Dic3—22no—
16Q8×C3⋊Dic3C2214yescomplemented
17C2×#3755C418yescomplemented
18C2×#3755C2214yes—
19C2×#3752—21no—
20C2×C4⋊(C3⋊Dic3)—21no—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4×C3⋊Dic3—21no—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25#64102—22no—
26#64102C2214yes—
27C32×#103C2214yescomplemented
28#63648C2214yes—
29#63642C2214yescomplemented
30#63634C2214yescomplemented
31C2×Q8×Dic3—34no—
32C22×#215—34no—
33C2×#893—34no—
34C2×C3×#103D314yescomplemented
35C2×#821—34no—
36C2×#815—34no—
37C2×#807—34no—
38#4817—332no—
39C23×C3⋊D3—21no—
40C2×C32×Q8—21no—
41C2×C32×Q8—22no—
42C2×C32×Q8C2×C414yescomplemented
43C2×C32×Q8C2312yes—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D411yescharacteristic
49C22×C3⋊Dic3D411yescharacteristic
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—22no—
52C2×C4⋊(C3⋊D3)C2×C414yes—
53C2×C4⋊(C3⋊D3)C2312yes—
54C2×C4×C3⋊D3—24no—
55C2×C4×C3⋊D3—44no—
56C2×C32×C8—22no—
57C2×C32×C8C2312yes—
58C32×C4⋊C4—21no—
59C32×C4⋊C4C2312yes—
60#3755C2×C4116yescomplemented
61#3752—24no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—24no—
64C4⋊(C3⋊Dic3)C2312yes—
65C4×C3⋊Dic3—24no—
66C4×C3⋊Dic3D412yes—
67C4×C3⋊Dic3C2312yes—
68C2×C3⋊(C3⋊C8)C2×C414yescomplemented
69C2×C3⋊(C3⋊C8)C2312yes—
70C2×#440—91noSylow
71C22×C3×Q8C2×D314yes—
72C22×D12—34no—
73C22×C4×D3—64no—
74C22×C3×C8C2×D314yes—
75C2×C3×C4⋊C4C2×D314yes—
76Q8×Dic3—316no—
77Q8×Dic3—68no—
78C2×#215—332no—
79C2×#215—316no—
80C2×(C2×D3)⋊C4—64no—
81C2×C4⋊Dic3—34no—
82C2×C4⋊Dic3—64no—
83C2×C4×Dic3—34no—
84C2×C4×Dic3—64no—
85C22×C3⋊C8—34no—
86#893—316no—
87#893—68no—
88C3×#103C2×D3116yescomplemented
89#821—316no—
90#815—316no—
91#807—316no—
92C23×C32C2×D411yescharacteristic
93C22×C3⋊D3—24no—
94C22×C3⋊D3—22no—
95C22×C3⋊D3—42no—
96C22×C3⋊D3—42no—
97C32×Q8—24no—
98C32×Q8—22no—
99C32×Q8C22×C414yescomplemented
100C2×C32×C4—24no—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4—42no—
104C2×C32×C4C22×C412yes—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4#4112yes—
107C2×C32×C4C2411yescharacteristic
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—42no—
112C2×C3⋊Dic3C2×D412yes—
113C2×C3⋊Dic3C2×D412yes—
114C4⋊(C3⋊D3)—24no—
115C4⋊(C3⋊D3)—22no—
116C4⋊(C3⋊D3)C22×C414yes—
117C4×C3⋊D3—48no—
118C32×C8—22no—
119C3⋊(C3⋊C8)C22×C414yescomplemented
120C22×SD16—91no—
121C2×C4×Q8—91no—
122C2×C4×D4—91no—
123#440—98no—
124C2×#107—91no—
125C2×#103C3⋊D311yescharacteristic, complemented
126C2×#102—91no—
127C2×#97—91no—
128C23×D3—64no—
129C2×C3×Q8—24no—
130C2×C3×Q8—28no—
131C2×C3×Q8C4×D3116yescomplemented
132C2×C3×Q8C22×D318yes—
133C22×C3×C4—24no—
134C22×C3×C4—24no—
135C22×C3×C4C22×D314yes—
136C22×Dic3—34no—
137C22×Dic3—34no—
138C22×Dic3—64no—
139C2×D12—316no—
140C2×D12—38no—
141C2×D12—64no—
142C2×D12—68no—
143C2×C4×D3—616no—
144C2×C4×D3—1216no—
145C2×C3×C8—28no—
146C2×C3×C8C22×D318yes—
147C3×C4⋊C4—24no—
148C3×C4⋊C4C22×D318yes—
149#215—364no—
150(C2×D3)⋊C4—616no—
151C4⋊Dic3—38no—
152C4⋊Dic3—616no—
153C4⋊Dic3—64no—
154C4×Dic3—38no—
155C4×Dic3—38no—
156C4×Dic3—616no—
157C2×C3⋊C8—316no—
158C2×C3⋊C8—38no—
159C22×C32C4×D412yes—
160C22×C32AGL(1,ℤ/8)12yes—
161C22×C32#13712yes—
162C22×C32C22×D411yescharacteristic
163C2×C3⋊D3—24no—
164C2×C3⋊D3—42no—
165C2×C3⋊D3—42no—
166C2×C3⋊D3—48no—
167C32×C4—24no—
168C32×C4—42no—
169C32×C4C4×D412yes—
170C32×C4C23×C411yescharacteristic
171C32×C4C2×#4111yescharacteristic
172C3⋊Dic3—22no—
173C3⋊Dic3—22no—
174C3⋊Dic3—42no—
175C22×Q8C2×C3⋊D311yescharacteristic
176C22×D4—91no—
177C23×C4—181no—
178C2×SD16—98no—
179C2×SD16—94no—
180C22×C8—91no—
181C22×C8C2×C3⋊D311yescharacteristic
182C4×Q8—94no—
183C4×Q8—182no—
184C4×D4—94no—
185C4×D4—182no—
186C2×C4⋊C4—91no—
187C2×C4⋊C4—181no—
188C2×C4⋊C4C2×C3⋊D311yescharacteristic
189C2×C22⋊C4—181no—
190C2×C42—91no—
191C2×C42—181no—
192#107—94no—
193#103C2×C3⋊D314yescomplemented
194#102—94no—
195#97—94no—
196C23×C3D3×D414yes—
197C22×D3—616no—
198C22×D3—68no—
199C22×D3—128no—
200C22×D3—128no—
201C3×Q8—216no—
202C3×Q8—28no—
203C3×Q8C2×C4×D3116yescomplemented
204C2×C3×C4—216no—
205C2×C3×C4—28no—
206C2×C3×C4—28no—
207C2×C3×C4—48no—
208C2×C3×C4C2×C4×D318yes—
209C2×C3×C4D3×D414yes—
210C2×C3×C4#23718yes—
211C2×C3×C4C23×D314yes—
212C2×Dic3—38no—
213C2×Dic3—38no—
214C2×Dic3—68no—
215C2×Dic3—68no—
216C2×Dic3—68no—
217C2×Dic3—128no—
218D12—316no—
219D12—616no—
220D12—68no—
221C4×D3—1232no—
222C3×C8—28no—
223C3⋊C8—316no—
224C2×C32#44014yescomplemented
225C2×C32C2×C4×D411yescharacteristic
226C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
227C2×C32C2×#13711yescharacteristic
228C3⋊D3—44no—
229C24—181no—
230C2×Q8—21no—
231C2×Q8—22no—
232C2×Q8C4×C3⋊D314yescomplemented
233C2×Q8C22×C3⋊D312yes—
234C2×D4—92no—
235C2×D4—94no—
236C2×D4—181no—
237C2×D4—182no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—91no—
241C22×C4—91no—
242C22×C4—184no—
243C22×C4—181no—
244C22×C4—364no—
245C22×C4C22×C3⋊D311yescharacteristic
246SD16—916no—
247C2×C8—22no—
248C2×C8—92no—
249C2×C8—94no—
250C2×C8C22×C3⋊D312yes—
251C4⋊C4—21no—
252C4⋊C4—92no—
253C4⋊C4—184no—
254C4⋊C4—181no—
255C4⋊C4C22×C3⋊D312yes—
256C22⋊C4—184no—
257C42—92no—
258C42—92no—
259C42—184no—
260C22×C3#67⋊C418yes—
261C22×C3#91418yes—
262C22×C3#91818yes—
263C22×C3C2×D3×D414yes—
264C2×D3—616no—
265C2×D3—128no—
266C2×D3—128no—
267C2×D3—1232no—
268C3×C4—216no—
269C3×C4—48no—
270C3×C4#67⋊C418yes—
271C3×C4C22×C4×D314yes—
272C3×C4C2×#23714yes—
273Dic3—68no—
274Dic3—68no—
275Dic3—128no—
276C32C2×#44011yescharacteristic, complemented, Sylow
277C23—184no—
278C23—182no—
279C23—362no—
280C23—362no—
281C23D4×C3⋊D311yescharacteristic
282Q8—24no—
283Q8—22no—
284Q8C2×C4×C3⋊D314yescomplemented
285D4—94no—
286D4—184no—
287D4—182no—
288C2×C4—24no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—42no—
292C2×C4—92no—
293C2×C4—92no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4—182no—
297C2×C4—368no—
298C2×C4—362no—
299C2×C4C2×C4×C3⋊D312yes—
300C2×C4D4×C3⋊D311yescharacteristic
301C2×C4#383012yes—
302C2×C4C23×C3⋊D311yescharacteristic
303C8—22no—
304C8—94no—
305C2×C3#4817116yescomplemented
306C2×C3C2×#67⋊C414yes—
307C2×C3C2×#91414yes—
308C2×C3C2×#91814yes—
309D3—1216no—
310C22—184no—
311C22—368no—
312C22—362no—
313C22—362no—
314C22#6409012yes—
315C22#6412312yes—
316C22#6412712yes—
317C22C2×D4×C3⋊D311yescharacteristic
318C4—24no—
319C4—42no—
320C4—182no—
321C4—182no—
322C4—362no—
323C4#6409012yes—
324C4C22×C4×C3⋊D311yescharacteristic
325C4C2×#383011yescharacteristic
326C3C2×#481714yescomplemented
327C2—364no—
328C2#1059251614yesdirect product factor
329C2C2×#6409011yescharacteristic
330C2C2×#6412311yescharacteristic
331C2C2×#6412711yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC2×C32×C4C24
hypercenterC2×#103C3⋊D3
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C3⋊Dic3C2semidirect
4. C2×C32×#103C2semidirect
6. C2×#63642C2semidirect
7. C2×#63634C2semidirect
8. #10592516C2direct (N × H)
16. Q8×C3⋊Dic3C22semidirect
17. C2×#3755C4semidirect
27. C32×#103C22semidirect
29. #63642C22semidirect
30. #63634C22semidirect
34. C2×C3×#103D3semidirect
42. C2×C32×Q8C2×C4semidirect
60. #3755C2×C4semidirect
68. C2×C3⋊(C3⋊C8)C2×C4semidirect
88. C3×#103C2×D3semidirect
99. C32×Q8C22×C4semidirect
119. C3⋊(C3⋊C8)C22×C4semidirect
125. C2×#103C3⋊D3semidirect
131. C2×C3×Q8C4×D3semidirect
193. #103C2×C3⋊D3semidirect
203. C3×Q8C2×C4×D3semidirect
224. C2×C32#440semidirect
232. C2×Q8C4×C3⋊D3semidirect
276. C32C2×#440semidirect
284. Q8C2×C4×C3⋊D3semidirect
305. C2×C3#4817semidirect
326. C3C2×#4817semidirect
328. C2#10592516direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C22×#37552
C2×#641022
C2×C32×#1032
C2×#636482
C2×#636422
C2×#636342
#105925162
C2×#48173