Finite Group Databasebeta

← C2×#10592409 #11860048

Subgroups — C2×#10592409 #11860048

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
1C22×#3744C211yesmaximal, characteristic
2C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
3C2×C4×#634C211yesmaximal, characteristic, complemented
4C2×C32×#97C211yesmaximal, characteristic, complemented
5C2×#63648C211yesmaximal, characteristic
6C2×#63645C211yesmaximal, characteristic, complemented
7C2×#63643C211yesmaximal, characteristic, complemented
8#10592409C218yesmaximal, direct product factor
9C2×#4710—34nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C4×C3⋊D3—21no—
12C22×#634C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×#3752—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#3750—21no—
20C2×C4×C3⋊Dic3—21no—
21C2×#3744C418yescomplemented
22C2×#3744C2214yes—
23C4×C4⋊(C3⋊D3)—22no—
24C4×C4⋊(C3⋊D3)C2214yes—
25C4×#634—22no—
26C4×#634C2214yescomplemented
27C32×#97C2214yescomplemented
28#63648C2214yes—
29#63645C2214yescomplemented
30#63643C2214yescomplemented
31C22×#204—34no—
32C2×C4×D12—34no—
33C2×C4×Dic6—34no—
34C2×C3×#97D314yescomplemented
35C2×#821—34no—
36C2×#818—34no—
37C2×#816—34no—
38#4710—332no—
39C23×C3⋊D3—21no—
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—22no—
48C2×C4⋊(C3⋊D3)C2×C414yes—
49C2×C4⋊(C3⋊D3)C2312yes—
50C2×C4×C3⋊D3—24no—
51C2×C4×C3⋊D3—44no—
52C2×#634—21no—
53C2×#634—22no—
54C2×#634C2×C414yescomplemented
55C2×#634C2312yes—
56C2×C32×C8—22no—
57C2×C32×C8C2×C414yescomplemented
58C2×C32×C8C2312yes—
59C2×C32×C8C2312yes—
60C32×C42D412yes—
61C32×C42C2312yes—
62#3752—24no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)C2312yes—
66C4⋊(C3⋊Dic3)C2312yes—
67#3750—24no—
68C4×C3⋊Dic3—24no—
69#3744C2×C4116yescomplemented
70C2×#440—91noSylow
71C22×D12—34no—
72C22×C4×D3—64no—
73C22×Dic6—34no—
74C22×C3×C8C2×D314yes—
75C22×C3×C8C2×D314yes—
76C2×C3×C42C2×D314yes—
77C2×(C2×D3)⋊C4—64no—
78C2×C4⋊Dic3—34no—
79C2×C4⋊Dic3—34no—
80C2×Dic3⋊C4—64no—
81C2×C4×Dic3—64no—
82C2×#204—332no—
83C2×#204—316no—
84C4×D12—316no—
85C4×D12—68no—
86C4×Dic6—316no—
87C4×Dic6—68no—
88C3×#97C2×D3116yescomplemented
89#821—316no—
90#818—316no—
91#816—316no—
92C23×C32C2×D411yescharacteristic
93C22×C3⋊D3—24no—
94C22×C3⋊D3—22no—
95C22×C3⋊D3—42no—
96C22×C3⋊D3—42no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4C22×C412yes—
100C2×C32×C4C2×D412yes—
101C2×C32×C4C2×D412yes—
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4112yes—
104C2×C32×C4C2411yescharacteristic
105C2×C3⋊Dic3—24no—
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—42no—
110C2×C3⋊Dic3—42no—
111C4⋊(C3⋊D3)—24no—
112C4⋊(C3⋊D3)—22no—
113C4⋊(C3⋊D3)C22×C414yes—
114C4×C3⋊D3—48no—
115#634—24no—
116#634—22no—
117#634C22×C414yescomplemented
118C32×C8—22no—
119C32×C8C22×C414yescomplemented
120C22×SD16—91no—
121C2×C4×Q8—91no—
122C2×C4×D4—91no—
123#440—98no—
124C2×#107—91no—
125C2×#103—91no—
126C2×#102—91no—
127C2×#97C3⋊D311yescharacteristic, complemented
128C23×D3—64no—
129C22×C3×C4D1214yes—
130C22×C3×C4D1214yes—
131C22×C3×C4C22×D314yes—
132C22×Dic3—64no—
133C22×Dic3—64no—
134C22×Dic3—64no—
135C2×D12—316no—
136C2×D12—38no—
137C2×D12—64no—
138C2×D12—68no—
139C2×C4×D3—616no—
140C2×C4×D3—1216no—
141C2×Dic6—316no—
142C2×Dic6—38no—
143C2×Dic6—64no—
144C2×Dic6—68no—
145C2×C3×C8—28no—
146C2×C3×C8C4×D3116yescomplemented
147C2×C3×C8C22×D318yes—
148C2×C3×C8C22×D318yes—
149C3×C42D1218yes—
150C3×C42C22×D318yes—
151(C2×D3)⋊C4—616no—
152C4⋊Dic3—38no—
153C4⋊Dic3—38no—
154C4⋊Dic3—64no—
155C4⋊Dic3—64no—
156Dic3⋊C4—616no—
157C4×Dic3—616no—
158#204—364no—
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—22no—
168C32×C4—22no—
169C32×C4C4×D412yes—
170C32×C4C23×C411yescharacteristic
171C32×C4C2×#4111yescharacteristic
172C3⋊Dic3—24no—
173C3⋊Dic3—42no—
174C3⋊Dic3—42no—
175C22×Q8—91no—
176C22×D4—91no—
177C23×C4—181no—
178C2×SD16—98no—
179C2×SD16—94no—
180C22×C8C2×C3⋊D311yescharacteristic
181C22×C8C2×C3⋊D311yescharacteristic
182C4×Q8—94no—
183C4×Q8—182no—
184C4×D4—94no—
185C4×D4—182no—
186C2×C4⋊C4—91no—
187C2×C4⋊C4—91no—
188C2×C4⋊C4—181no—
189C2×C22⋊C4—181no—
190C2×C42—181no—
191C2×C42C2×C3⋊D311yescharacteristic
192#107—94no—
193#103—94no—
194#102—94no—
195#97C2×C3⋊D314yescomplemented
196C23×C3C2×D1214yes—
197C22×D3—616no—
198C22×D3—68no—
199C22×D3—128no—
200C22×D3—128no—
201C2×C3×C4—28no—
202C2×C3×C4—28no—
203C2×C3×C4C2×C4×D318yes—
204C2×C3×C4C2×D1218yes—
205C2×C3×C4C2×D1218yes—
206C2×C3×C4C2×D1214yes—
207C2×C3×C4#23518yes—
208C2×C3×C4C23×D314yes—
209C2×Dic3—616no—
210C2×Dic3—68no—
211C2×Dic3—68no—
212C2×Dic3—68no—
213C2×Dic3—128no—
214C2×Dic3—128no—
215D12—316no—
216D12—616no—
217D12—68no—
218C4×D3—1232no—
219Dic6—316no—
220Dic6—616no—
221Dic6—68no—
222C3×C8—28no—
223C3×C8C2×C4×D3116yescomplemented
224C2×C32#44014yescomplemented
225C2×C32C2×C4×D411yescharacteristic
226C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
227C2×C32C2×#13711yescharacteristic
228C3⋊D3—44no—
229C24—181no—
230C2×Q8—92no—
231C2×Q8—94no—
232C2×Q8—181no—
233C2×Q8—182no—
234C2×D4—92no—
235C2×D4—94no—
236C2×D4—181no—
237C2×D4—182no—
238C22×C4—181no—
239C22×C4—181no—
240C22×C4—181no—
241C22×C4—184no—
242C22×C4—364no—
243C22×C4C4⋊(C3⋊D3)11yescharacteristic
244C22×C4C4⋊(C3⋊D3)11yescharacteristic
245C22×C4C22×C3⋊D311yescharacteristic
246SD16—916no—
247C2×C8—22no—
248C2×C8C4×C3⋊D314yescomplemented
249C2×C8C22×C3⋊D312yes—
250C2×C8C22×C3⋊D312yes—
251C4⋊C4—92no—
252C4⋊C4—92no—
253C4⋊C4—181no—
254C4⋊C4—181no—
255C4⋊C4—184no—
256C22⋊C4—184no—
257C42—184no—
258C42C4⋊(C3⋊D3)12yes—
259C42C22×C3⋊D312yes—
260C22×C3C4×D1218yes—
261C22×C3#90818yes—
262C22×C3#90918yes—
263C22×C3C22×D1214yes—
264C2×D3—616no—
265C2×D3—1232no—
266C2×D3—128no—
267C2×D3—128no—
268C3×C4—28no—
269C3×C4—28no—
270C3×C4C4×D1218yes—
271C3×C4C22×C4×D314yes—
272C3×C4C2×#23514yes—
273Dic3—616no—
274Dic3—128no—
275Dic3—128no—
276C32C2×#44011yescharacteristic, complemented, Sylow
277C23—184no—
278C23—182no—
279C23—362no—
280C23—362no—
281C23C2×C4⋊(C3⋊D3)11yescharacteristic
282Q8—94no—
283Q8—184no—
284Q8—182no—
285D4—94no—
286D4—184no—
287D4—182no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—184no—
291C2×C4—182no—
292C2×C4—182no—
293C2×C4—182no—
294C2×C4—368no—
295C2×C4—362no—
296C2×C4—362no—
297C2×C4C2×C4×C3⋊D312yes—
298C2×C4C2×C4⋊(C3⋊D3)12yes—
299C2×C4C2×C4⋊(C3⋊D3)12yes—
300C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
301C2×C4#382812yes—
302C2×C4C23×C3⋊D311yescharacteristic
303C8—22no—
304C8C2×C4×C3⋊D314yescomplemented
305C2×C3#4710116yescomplemented
306C2×C3C2×C4×D1214yes—
307C2×C3C2×#90814yes—
308C2×C3C2×#90914yes—
309D3—1216no—
310C22—184no—
311C22—362no—
312C22—362no—
313C22—368no—
314C22C4×C4⋊(C3⋊D3)12yes—
315C22#6411712yes—
316C22#6411812yes—
317C22C22×C4⋊(C3⋊D3)11yescharacteristic
318C4—22no—
319C4—22no—
320C4—184no—
321C4—362no—
322C4—362no—
323C4C4×C4⋊(C3⋊D3)12yes—
324C4C22×C4×C3⋊D311yescharacteristic
325C4C2×#382811yescharacteristic
326C3C2×#471014yescomplemented
327C2—364no—
328C2#1059240914yesdirect product factor
329C2C2×C4×C4⋊(C3⋊D3)11yescharacteristic
330C2C2×#6411711yescharacteristic
331C2C2×#6411811yescharacteristic
subgroupG/H
centerC23C2×C4⋊(C3⋊D3)
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#97C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC2×C32×C4C24
hypercenterC2×#97C3⋊D3
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
3. C2×C4×#634C2semidirect
4. C2×C32×#97C2semidirect
6. C2×#63645C2semidirect
7. C2×#63643C2semidirect
8. #10592409C2direct (N × H)
21. C2×#3744C4semidirect
26. C4×#634C22semidirect
27. C32×#97C22semidirect
29. #63645C22semidirect
30. #63643C22semidirect
34. C2×C3×#97D3semidirect
54. C2×#634C2×C4semidirect
57. C2×C32×C8C2×C4semidirect
69. #3744C2×C4semidirect
88. C3×#97C2×D3semidirect
117. #634C22×C4semidirect
119. C32×C8C22×C4semidirect
127. C2×#97C3⋊D3semidirect
146. C2×C3×C8C4×D3semidirect
195. #97C2×C3⋊D3semidirect
223. C3×C8C2×C4×D3semidirect
224. C2×C32#440semidirect
248. C2×C8C4×C3⋊D3semidirect
276. C32C2×#440semidirect
304. C8C2×C4×C3⋊D3semidirect
305. C2×C3#4710semidirect
326. C3C2×#4710semidirect
328. C2#10592409direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37442
C2×C4×C4⋊(C3⋊D3)2
C2×C4×#6342
C2×C32×#972
C2×#636482
C2×#636452
C2×#636432
#105924092
C2×#47103