Finite Group Databasebeta

← C2×#10592484 #11860140

Subgroups — C2×#10592484 #11860140

Order 1152.

1824 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C22×#3753C211yesmaximal, characteristic
3C2×#64102C211yesmaximal, characteristic, complemented
4C2×C32×#102C211yesmaximal, characteristic, complemented
5C2×#63648C211yesmaximal, characteristic, complemented
6C2×#63642C211yesmaximal, characteristic, complemented
7C2×#63635C211yesmaximal, characteristic, complemented
8#10592484C218yesmaximal, direct product factor
9C2×#4785—34nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C3⋊Dic3—21no—
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C4×C3⋊D3—21no—
14C22×C32×C8C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×#3757—21no—
17D4×C3⋊Dic3—22no—
18D4×C3⋊Dic3C2214yescomplemented
19C2×#3753C418yescomplemented
20C2×#3753C2214yes—
21C2×#3752—21no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25#64102—22no—
26#64102C2214yescomplemented
27C32×#102C2214yescomplemented
28#63648C2214yescomplemented
29#63642C2214yescomplemented
30#63635C2214yescomplemented
31C2×D4×Dic3—34no—
32C22×#213—34no—
33C2×#893—34no—
34C2×C3×#102D314yescomplemented
35C2×#821—34no—
36C2×#815—34no—
37C2×#808—34no—
38#4785—332no—
39C24×C32—21no—
40C23×C3⋊D3—21no—
41C2×C32×D4—21no—
42C2×C32×D4—22no—
43C2×C32×D4C2×C414yescomplemented
44C2×C32×D4C2312yes—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—24no—
49C22×C3⋊Dic3—44no—
50C22×C3⋊Dic3D411yescharacteristic
51C22×C3⋊Dic3D411yescharacteristic
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)C2×C414yescomplemented
55C2×C4⋊(C3⋊D3)C2312yes—
56C2×C4×C3⋊D3—24no—
57C2×C4×C3⋊D3—44no—
58C2×C32×C8—22no—
59C2×C32×C8C2312yes—
60C32×C4⋊C4—21no—
61C32×C4⋊C4C2312yes—
62#3757—24no—
63#3753C2×C4116yescomplemented
64#3752—24no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)C2312yes—
67C4×C3⋊Dic3D412yes—
68C4×C3⋊Dic3C2312yes—
69C2×C3⋊(C3⋊C8)C2×C414yescomplemented
70C2×C3⋊(C3⋊C8)C2312yes—
71C2×#442—91noSylow
72C22×C3×D4C2×D314yes—
73C23×Dic3—64no—
74C22×D12—34no—
75C22×C4×D3—64no—
76C22×C3×C8C2×D314yes—
77C2×C3×C4⋊C4C2×D314yes—
78C2×#217—64no—
79D4×Dic3—316no—
80D4×Dic3—68no—
81C2×#213—332no—
82C2×#213—316no—
83C2×(C2×D3)⋊C4—64no—
84C2×C4⋊Dic3—34no—
85C2×C4×Dic3—34no—
86C22×C3⋊C8—34no—
87#893—316no—
88#893—68no—
89C3×#102C2×D3116yescomplemented
90#821—316no—
91#815—316no—
92#808—316no—
93C23×C32—24no—
94C23×C32—22no—
95C23×C32—42no—
96C23×C32—42no—
97C23×C32C2×D411yescharacteristic
98C22×C3⋊D3—24no—
99C22×C3⋊D3—22no—
100C22×C3⋊D3—42no—
101C22×C3⋊D3—42no—
102C32×D4—24no—
103C32×D4—22no—
104C32×D4C22×C414yescomplemented
105C2×C32×C4—22no—
106C2×C32×C4—42no—
107C2×C32×C4C22×C412yes—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4#4112yes—
110C2×C32×C4C2411yescharacteristic
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—48no—
115C2×C3⋊Dic3—42no—
116C2×C3⋊Dic3C2×D412yes—
117C2×C3⋊Dic3C2×D412yes—
118C4⋊(C3⋊D3)—24no—
119C4⋊(C3⋊D3)—22no—
120C4⋊(C3⋊D3)C22×C414yescomplemented
121C4×C3⋊D3—48no—
122C32×C8—22no—
123C3⋊(C3⋊C8)C22×C414yescomplemented
124C22×D8—91no—
125C2×C4×D4—91no—
126C2×C4×D4—91no—
127#442—98no—
128C2×#106—91no—
129C2×#102—91no—
130C2×#102C3⋊D311yescharacteristic, complemented
131C2×#97—91no—
132C24×C3—24no—
133C23×D3—64no—
134C2×C3×D4—24no—
135C2×C3×D4—28no—
136C2×C3×D4C4×D3116yescomplemented
137C2×C3×D4C22×D318yes—
138C22×C3×C4—24no—
139C22×C3×C4C22×D314yes—
140C22×Dic3—34no—
141C22×Dic3—34no—
142C22×Dic3—616no—
143C22×Dic3—64no—
144C22×Dic3—1216no—
145C2×D12—316no—
146C2×D12—38no—
147C2×D12—64no—
148C2×D12—68no—
149C2×C4×D3—616no—
150C2×C4×D3—1216no—
151C2×C3×C8—28no—
152C2×C3×C8C22×D318yes—
153C3×C4⋊C4—24no—
154C3×C4⋊C4C22×D318yes—
155#217—616no—
156#213—364no—
157(C2×D3)⋊C4—616no—
158C4⋊Dic3—38no—
159C4⋊Dic3—64no—
160C4×Dic3—38no—
161C4×Dic3—38no—
162C2×C3⋊C8—316no—
163C2×C3⋊C8—38no—
164C22×C32—24no—
165C22×C32—42no—
166C22×C32—42no—
167C22×C32—48no—
168C22×C32C4×D412yes—
169C22×C32AGL(1,ℤ/8)12yes—
170C22×C32AGL(1,ℤ/8)12yes—
171C22×C32C22×D411yescharacteristic
172C2×C3⋊D3—24no—
173C2×C3⋊D3—42no—
174C2×C3⋊D3—42no—
175C2×C3⋊D3—48no—
176C32×C4—42no—
177C32×C4C4×D412yes—
178C32×C4C23×C411yescharacteristic
179C32×C4C2×#4111yescharacteristic
180C3⋊Dic3—22no—
181C3⋊Dic3—22no—
182C3⋊Dic3—42no—
183C22×D4—91no—
184C22×D4C2×C3⋊D311yescharacteristic
185C23×C4—181no—
186C23×C4—181no—
187C2×D8—98no—
188C2×D8—94no—
189C22×C8—91no—
190C22×C8C2×C3⋊D311yescharacteristic
191C4×D4—94no—
192C4×D4—94no—
193C4×D4—182no—
194C4×D4—182no—
195C2×C4⋊C4—91no—
196C2×C4⋊C4C2×C3⋊D311yescharacteristic
197C2×C22⋊C4—181no—
198C2×C22⋊C4—181no—
199C2×C42—91no—
200#106—94no—
201#102—94no—
202#102C2×C3⋊D314yescomplemented
203#97—94no—
204C23×C3—216no—
205C23×C3—28no—
206C23×C3—48no—
207C23×C3—48no—
208C23×C3D3×D414yes—
209C22×D3—616no—
210C22×D3—68no—
211C22×D3—128no—
212C22×D3—128no—
213C3×D4—216no—
214C3×D4—28no—
215C3×D4C2×C4×D3116yescomplemented
216C2×C3×C4—28no—
217C2×C3×C4—48no—
218C2×C3×C4C2×C4×D318yes—
219C2×C3×C4D3×D414yes—
220C2×C3×C4#23718yes—
221C2×C3×C4C23×D314yes—
222C2×Dic3—38no—
223C2×Dic3—38no—
224C2×Dic3—68no—
225C2×Dic3—68no—
226C2×Dic3—68no—
227C2×Dic3—1232no—
228C2×Dic3—128no—
229D12—316no—
230D12—616no—
231D12—68no—
232C4×D3—1232no—
233C3×C8—28no—
234C3⋊C8—316no—
235C2×C32—44no—
236C2×C32#44214yescomplemented
237C2×C32C2×C4×D411yescharacteristic
238C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
239C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
240C3⋊D3—44no—
241C24—21no—
242C24—181no—
243C2×D4—21no—
244C2×D4—22no—
245C2×D4—92no—
246C2×D4—94no—
247C2×D4—181no—
248C2×D4—182no—
249C2×D4C4×C3⋊D314yescomplemented
250C2×D4C22×C3⋊D312yes—
251C22×C4—21no—
252C22×C4—91no—
253C22×C4—91no—
254C22×C4—184no—
255C22×C4—184no—
256C22×C4—181no—
257C22×C4—364no—
258C22×C4—364no—
259C22×C4C22×C3⋊D311yescharacteristic
260D8—916no—
261C2×C8—22no—
262C2×C8—92no—
263C2×C8—94no—
264C2×C8C22×C3⋊D312yes—
265C4⋊C4—21no—
266C4⋊C4—92no—
267C4⋊C4—181no—
268C4⋊C4C22×C3⋊D312yes—
269C22⋊C4—184no—
270C22⋊C4—184no—
271C42—92no—
272C42—92no—
273C22×C3—216no—
274C22×C3—48no—
275C22×C3—48no—
276C22×C3—432no—
277C22×C3#67⋊C418yes—
278C22×C3#91118yes—
279C22×C3#91418yes—
280C22×C3C2×D3×D414yes—
281C2×D3—616no—
282C2×D3—128no—
283C2×D3—128no—
284C2×D3—1232no—
285C3×C4—48no—
286C3×C4#67⋊C418yes—
287C3×C4C22×C4×D314yes—
288C3×C4C2×#23714yes—
289Dic3—68no—
290Dic3—68no—
291Dic3—128no—
292C32C2×#44211yescharacteristic, complemented, Sylow
293C23—24no—
294C23—22no—
295C23—42no—
296C23—42no—
297C23—184no—
298C23—182no—
299C23—362no—
300C23—362no—
301C23D4×C3⋊D311yescharacteristic
302D4—24no—
303D4—22no—
304D4—94no—
305D4—184no—
306D4—182no—
307D4C2×C4×C3⋊D314yescomplemented
308C2×C4—22no—
309C2×C4—42no—
310C2×C4—92no—
311C2×C4—92no—
312C2×C4—182no—
313C2×C4—182no—
314C2×C4—182no—
315C2×C4—368no—
316C2×C4—368no—
317C2×C4—362no—
318C2×C4C2×C4×C3⋊D312yes—
319C2×C4D4×C3⋊D311yescharacteristic
320C2×C4#383012yes—
321C2×C4C23×C3⋊D311yescharacteristic
322C8—22no—
323C8—94no—
324C2×C3—416no—
325C2×C3#4785116yescomplemented
326C2×C3C2×#67⋊C414yes—
327C2×C3C2×#91114yes—
328C2×C3C2×#91414yes—
329D3—1216no—
330C22—24no—
331C22—42no—
332C22—42no—
333C22—48no—
334C22—184no—
335C22—362no—
336C22—362no—
337C22—368no—
338C22#6409012yes—
339C22#6412012yes—
340C22#6412312yes—
341C22C2×D4×C3⋊D311yescharacteristic
342C4—42no—
343C4—182no—
344C4—182no—
345C4—362no—
346C4#6409012yes—
347C4C22×C4×C3⋊D311yescharacteristic
348C4C2×#383011yescharacteristic
349C3C2×#478514yescomplemented
350C2—44no—
351C2—364no—
352C2#1059248414yesdirect product factor
353C2C2×#6409011yescharacteristic
354C2C2×#6412011yescharacteristic
355C2C2×#6412311yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC22×#3753C2
cosocleC2×C32×C4C24
hypercenterC2×#102C3⋊D3
hypocenterC32C2×#442
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
3. C2×#64102C2semidirect
4. C2×C32×#102C2semidirect
5. C2×#63648C2semidirect
6. C2×#63642C2semidirect
7. C2×#63635C2semidirect
8. #10592484C2direct (N × H)
18. D4×C3⋊Dic3C22semidirect
19. C2×#3753C4semidirect
26. #64102C22semidirect
27. C32×#102C22semidirect
28. #63648C22semidirect
29. #63642C22semidirect
30. #63635C22semidirect
34. C2×C3×#102D3semidirect
43. C2×C32×D4C2×C4semidirect
54. C2×C4⋊(C3⋊D3)C2×C4semidirect
63. #3753C2×C4semidirect
69. C2×C3⋊(C3⋊C8)C2×C4semidirect
89. C3×#102C2×D3semidirect
104. C32×D4C22×C4semidirect
120. C4⋊(C3⋊D3)C22×C4semidirect
123. C3⋊(C3⋊C8)C22×C4semidirect
130. C2×#102C3⋊D3semidirect
136. C2×C3×D4C4×D3semidirect
202. #102C2×C3⋊D3semidirect
215. C3×D4C2×C4×D3semidirect
236. C2×C32#442semidirect
249. C2×D4C4×C3⋊D3semidirect
292. C32C2×#442semidirect
307. D4C2×C4×C3⋊D3semidirect
325. C2×C3#4785semidirect
349. C3C2×#4785semidirect
352. C2#10592484direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C22×#37532
C2×#641022
C2×C32×#1022
C2×#636482
C2×#636422
C2×#636352
#105924842
C2×#47853