Finite Group Databasebeta

← C2×#10592457 #11859873

Subgroups — C2×#10592457 #11859873

Order 1152.

1656 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×D4×C3⋊Dic3C211yesmaximal, characteristic
2C22×#3754C211yesmaximal, characteristic
3C2×#64096C211yesmaximal, characteristic, complemented
4C2×C32×#102C211yesmaximal, characteristic
5C2×#63643C211yesmaximal, characteristic, complemented
6C2×C8×C3⋊Dic3C211yesmaximal, characteristic, complemented
7C2×#63635C211yesmaximal, characteristic, complemented
8#10592457C218yesmaximal, direct product factor
9C2×#4758—34nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C3⋊Dic3—21no—
12C22×#634C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×#3757—21no—
16D4×C3⋊Dic3—22no—
17D4×C3⋊Dic3C2214yes—
18C2×#3754C418yescomplemented
19C2×#3754C2214yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×#3750—21no—
22C2×C4×C3⋊Dic3—21no—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25#64096—22no—
26#64096C2214yescomplemented
27C32×#102C2214yes—
28#63643C2214yescomplemented
29C8×C3⋊Dic3C2214yescomplemented
30#63635C2214yescomplemented
31C2×D4×Dic3—34no—
32C22×#214—34no—
33C2×#887—34no—
34C2×C3×#102D314yes—
35C2×#816—34no—
36C2×C8×Dic3—34no—
37C2×#808—34no—
38#4758—332no—
39C24×C32—21no—
40C2×C32×D4—21no—
41C2×C32×D4—22no—
42C2×C32×D4C2×C414yes—
43C2×C32×D4C2312yes—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—24no—
49C22×C3⋊Dic3—44no—
50C22×C3⋊Dic3D411yescharacteristic
51C22×C3⋊Dic3D411yescharacteristic
52C2×#634—21no—
53C2×#634—22no—
54C2×#634C2×C414yescomplemented
55C2×#634C2312yes—
56C2×C32×C8—22no—
57C2×C32×C8C2312yes—
58C32×C4⋊C4—21no—
59C32×C4⋊C4C2312yes—
60#3757—24no—
61#3754C2×C4116yescomplemented
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)C2312yes—
64#3750—24no—
65C4×C3⋊Dic3—24no—
66C4×C3⋊Dic3D412yes—
67C4×C3⋊Dic3C2312yes—
68C2×C3⋊(C3⋊C8)C2×C414yescomplemented
69C2×C3⋊(C3⋊C8)C2312yes—
70C2×C4×SD16—91noSylow
71C22×C3×D4C2×D314yes—
72C23×Dic3—64no—
73C22×Dic6—34no—
74C22×C3×C8C2×D314yes—
75C2×C3×C4⋊C4C2×D314yes—
76C2×#217—64no—
77D4×Dic3—316no—
78D4×Dic3—68no—
79C2×#214—332no—
80C2×#214—316no—
81C2×C4⋊Dic3—34no—
82C2×Dic3⋊C4—64no—
83C2×C4×Dic3—34no—
84C2×C4×Dic3—64no—
85C22×C3⋊C8—34no—
86#887—316no—
87#887—68no—
88C3×#102C2×D3116yes—
89#816—316no—
90C8×Dic3—316no—
91#808—316no—
92C23×C32—24no—
93C23×C32—22no—
94C23×C32—42no—
95C23×C32—42no—
96C23×C32C2×D411yescharacteristic
97C32×D4—24no—
98C32×D4—22no—
99C32×D4C22×C414yes—
100C2×C32×C4—22no—
101C2×C32×C4—42no—
102C2×C32×C4C22×C412yes—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4#4112yes—
105C2×C32×C4C2411yescharacteristic
106C2×C3⋊Dic3—24no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—42no—
111C2×C3⋊Dic3—48no—
112C2×C3⋊Dic3SD1614yescomplemented
113C2×C3⋊Dic3C2×D412yes—
114C2×C3⋊Dic3C2×D412yes—
115#634—24no—
116#634—22no—
117#634C22×C414yescomplemented
118C32×C8—22no—
119C3⋊(C3⋊C8)C22×C414yescomplemented
120C22×SD16—91no—
121C2×C4×Q8—91no—
122C2×C4×D4—91no—
123C4×SD16—98no—
124C2×#106—91no—
125C2×#103—91no—
126C2×#102C3⋊D311yescharacteristic
127C2×C4×C8—91no—
128C24×C3—24no—
129C2×C3×D4—24no—
130C2×C3×D4—28no—
131C2×C3×D4C4×D3116yes—
132C2×C3×D4C22×D318yes—
133C22×C3×C4—24no—
134C22×C3×C4C22×D314yes—
135C22×Dic3—34no—
136C22×Dic3—34no—
137C22×Dic3—616no—
138C22×Dic3—64no—
139C22×Dic3—64no—
140C22×Dic3—1216no—
141C2×Dic6—316no—
142C2×Dic6—38no—
143C2×Dic6—64no—
144C2×Dic6—68no—
145C2×C3×C8—28no—
146C2×C3×C8C22×D318yes—
147C3×C4⋊C4—24no—
148C3×C4⋊C4C22×D318yes—
149#217—616no—
150#214—364no—
151C4⋊Dic3—38no—
152C4⋊Dic3—64no—
153Dic3⋊C4—616no—
154C4×Dic3—38no—
155C4×Dic3—38no—
156C4×Dic3—616no—
157C2×C3⋊C8—316no—
158C2×C3⋊C8—38no—
159C22×C32—24no—
160C22×C32—42no—
161C22×C32—42no—
162C22×C32—48no—
163C22×C32C4×D412yes—
164C22×C32C2×SD1612yes—
165C22×C32#13512yes—
166C22×C32C22×D411yescharacteristic
167C32×C4—42no—
168C32×C4C4×D412yes—
169C32×C4C23×C411yescharacteristic
170C32×C4C2×#4111yescharacteristic
171C3⋊Dic3—24no—
172C3⋊Dic3—22no—
173C3⋊Dic3—42no—
174C3⋊Dic3C2×SD1614yescomplemented
175C22×Q8—91no—
176C22×D4C2×C3⋊D311yescharacteristic
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#106—94no—
193#103—94no—
194#102C2×C3⋊D314yes—
195C4×C8—94no—
196C23×C3—216no—
197C23×C3—28no—
198C23×C3—48no—
199C23×C3—48no—
200C23×C3D3×D414yes—
201C3×D4—216no—
202C3×D4—28no—
203C3×D4C2×C4×D3116yes—
204C2×C3×C4—28no—
205C2×C3×C4—48no—
206C2×C3×C4C2×C4×D318yes—
207C2×C3×C4D3×D414yes—
208C2×C3×C4#23718yes—
209C2×C3×C4C23×D314yes—
210C2×Dic3—316no—
211C2×Dic3—38no—
212C2×Dic3—38no—
213C2×Dic3—616no—
214C2×Dic3—68no—
215C2×Dic3—68no—
216C2×Dic3—68no—
217C2×Dic3—1232no—
218C2×Dic3—128no—
219Dic6—316no—
220Dic6—616no—
221Dic6—68no—
222C3×C8—28no—
223C3⋊C8—316no—
224C2×C32—44no—
225C2×C32C4×SD1614yescomplemented
226C2×C32C2×C4×D411yescharacteristic
227C2×C32C22×SD1611yescharacteristic
228C2×C32C2×#13511yescharacteristic
229C24—21no—
230C2×Q8—92no—
231C2×Q8—94no—
232C2×Q8—181no—
233C2×Q8—182no—
234C2×D4—21no—
235C2×D4—22no—
236C2×D4C4×C3⋊D314yes—
237C2×D4C22×C3⋊D312yes—
238C22×C4—21no—
239C22×C4—91no—
240C22×C4—91no—
241C22×C4—184no—
242C22×C4—181no—
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—216no—
261C22×C3—48no—
262C22×C3—48no—
263C22×C3—432no—
264C22×C3#67⋊C418yes—
265C22×C3#91218yes—
266C22×C3D3×SD1618yes—
267C22×C3C2×D3×D414yes—
268C3×C4—48no—
269C3×C4#67⋊C418yes—
270C3×C4C22×C4×D314yes—
271C3×C4C2×#23714yes—
272Dic3—316no—
273Dic3—616no—
274Dic3—68no—
275Dic3—128no—
276C32C2×C4×SD1611yescharacteristic, complemented, Sylow
277C23—24no—
278C23—22no—
279C23—42no—
280C23—42no—
281C23D4×C3⋊D311yescharacteristic
282Q8—94no—
283Q8—184no—
284Q8—182no—
285D4—24no—
286D4—22no—
287D4C2×C4×C3⋊D314yes—
288C2×C4—22no—
289C2×C4—42no—
290C2×C4—92no—
291C2×C4—94no—
292C2×C4—92no—
293C2×C4—184no—
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—416no—
306C2×C3#4758116yescomplemented
307C2×C3C2×#67⋊C414yes—
308C2×C3C2×#91214yes—
309C2×C3C2×D3×SD1614yes—
310C22—24no—
311C22—42no—
312C22—42no—
313C22—48no—
314C22#6409012yes—
315C22#6412112yes—
316C22SD16×C3⋊D312yes—
317C22C2×D4×C3⋊D311yescharacteristic
318C4—42no—
319C4—94no—
320C4—184no—
321C4—182no—
322C4—362no—
323C4#6409012yes—
324C4C22×C4×C3⋊D311yescharacteristic
325C4C2×#383011yescharacteristic
326C3C2×#475814yescomplemented
327C2—44no—
328C2#1059245714yesdirect product factor
329C2C2×#6409011yescharacteristic
330C2C2×#6412111yescharacteristic
331C2C2×SD16×C3⋊D311yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
cosocleC2×C32×C4C24
hypercenterC2×#102C3⋊D3
hypocenterC32C2×C4×SD16
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
3. C2×#64096C2semidirect
5. C2×#63643C2semidirect
6. C2×C8×C3⋊Dic3C2semidirect
7. C2×#63635C2semidirect
8. #10592457C2direct (N × H)
18. C2×#3754C4semidirect
26. #64096C22semidirect
28. #63643C22semidirect
29. C8×C3⋊Dic3C22semidirect
30. #63635C22semidirect
54. C2×#634C2×C4semidirect
61. #3754C2×C4semidirect
68. C2×C3⋊(C3⋊C8)C2×C4semidirect
112. C2×C3⋊Dic3SD16semidirect
117. #634C22×C4semidirect
119. C3⋊(C3⋊C8)C22×C4semidirect
174. C3⋊Dic3C2×SD16semidirect
225. C2×C32C4×SD16semidirect
276. C32C2×C4×SD16semidirect
306. C2×C3#4758semidirect
326. C3C2×#4758semidirect
328. C2#10592457direct (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×#37542
C2×#640962
C2×C32×#1022
C2×#636432
C2×C8×C3⋊Dic32
C2×#636352
#105924572
C2×#47583