Finite Group Databasebeta

← C2×#10592513 #11869481

Subgroups — C2×#10592513 #11869481

Order 1152.

1248 conjugacy classes of subgroups.

The subgroup lattice has 321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64155C211yesmaximal, characteristic
2C2×#64101C211yesmaximal, characteristic
3C2×C32×#103C211yesmaximal, characteristic, complemented
4C2×#63662C211yesmaximal, characteristic, complemented
5C2×#63647C211yesmaximal, characteristic
6C2×#63645C211yesmaximal, characteristic, complemented
7C2×#63635C211yesmaximal, characteristic, complemented
8#10592513C218yesmaximal, direct product factor
9C2×#4814—34nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14#64155—22no—
15#64155C2214yes—
16C2×#3752—21no—
17C2×#3752—21no—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×#3750—21no—
21C2×C4×C3⋊Dic3—21no—
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23#64101—22no—
24#64101C2214yes—
25C32×#103C2214yescomplemented
26#63662C2214yescomplemented
27#63647C2214yes—
28#63645C2214yescomplemented
29#63635C2214yescomplemented
30C2×#946—34no—
31C2×#892—34no—
32C2×C3×#103D314yescomplemented
33C2×#835—34no—
34C2×(C2×D3)⋊C8—34no—
35C2×#818—34no—
36C2×#808—34no—
37#4814—332no—
38C23×C3⋊D3D411yescharacteristic
39C2×C32×Q8—21no—
40C2×C32×Q8—22no—
41C2×C32×Q8—22no—
42C2×C32×Q8C2312yes—
43C22×C32×C4—21no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4×C3⋊D3—22no—
50C2×C4×C3⋊D3—22no—
51C2×C4×C3⋊D3D412yes—
52C2×C4×C3⋊D3C2312yes—
53C2×C32×C8—22no—
54C2×C32×C8C2312yes—
55C32×C4⋊C4—21no—
56C32×C4⋊C4C2312yes—
57#3752—24no—
58#3752—24no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)C2312yes—
62C4⋊(C3⋊Dic3)C2312yes—
63#3750—24no—
64C4×C3⋊Dic3—24no—
65C2×C3⋊(C3⋊C8)—22no—
66C2×C3⋊(C3⋊C8)C2312yes—
67C2×#485—91noSylow
68C22×C3×Q8C2×D314yes—
69C22×C4×D3—34no—
70C22×C3×C8C2×D314yes—
71C2×C3×C4⋊C4C2×D314yes—
72#946—316no—
73#946—68no—
74C2×(C2×D3)⋊C4—64no—
75C2×(C2×D3)⋊C4—64no—
76C2×C4⋊Dic3—34no—
77C2×C4⋊Dic3—34no—
78C2×Dic3⋊C4—64no—
79C2×C4×Dic3—64no—
80C22×C3⋊C8—34no—
81#892—316no—
82#892—68no—
83C3×#103C2×D3116yescomplemented
84#835—316no—
85(C2×D3)⋊C8—316no—
86#818—316no—
87#808—316no—
88C23×C32C2×D411yescharacteristic
89C22×C3⋊D3—22no—
90C22×C3⋊D3—22no—
91C22×C3⋊D3—22no—
92C22×C3⋊D3C2×D412yes—
93C32×Q8—22no—
94C32×Q8—22no—
95C32×Q8—42no—
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4—42no—
99C2×C32×C4—42no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4112yes—
102C2×C32×C4#4112yes—
103C2×C32×C4C2411yescharacteristic
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3—42no—
108C2×C3⋊Dic3—42no—
109C2×C3⋊Dic3C2×D412yes—
110C4×C3⋊D3—24no—
111C4×C3⋊D3—22no—
112C4×C3⋊D3—22no—
113C32×C8—22no—
114C3⋊(C3⋊C8)—22no—
115C2×C22⋊Q8—91no—
116C2×#117—91no—
117#485—98no—
118C2×#107—91no—
119C2×#106—91no—
120C2×#103—91no—
121C2×#103C3⋊D311yescharacteristic, complemented
122C2×C22⋊C8—91no—
123C23×D3—34no—
124C2×C3×Q8—24no—
125C2×C3×Q8—28no—
126C2×C3×Q8—28no—
127C2×C3×Q8C22×D318yes—
128C22×C3×C4—24no—
129C22×C3×C4—24no—
130C22×C3×C4C22×D314yes—
131C22×Dic3—34no—
132C22×Dic3—64no—
133C22×Dic3—64no—
134C2×C4×D3—38no—
135C2×C4×D3—38no—
136C2×C4×D3—68no—
137C2×C4×D3—68no—
138C2×C3×C8—28no—
139C2×C3×C8C22×D318yes—
140C3×C4⋊C4—24no—
141C3×C4⋊C4C22×D318yes—
142(C2×D3)⋊C4—616no—
143(C2×D3)⋊C4—616no—
144C4⋊Dic3—38no—
145C4⋊Dic3—38no—
146C4⋊Dic3—64no—
147C4⋊Dic3—64no—
148Dic3⋊C4—616no—
149C4×Dic3—616no—
150C2×C3⋊C8—38no—
151C2×C3⋊C8—68no—
152C22×C32#12312yes—
153C22×C32#13512yes—
154C22×C32#13712yes—
155C22×C32C22×D411yescharacteristic
156C2×C3⋊D3—22no—
157C2×C3⋊D3—22no—
158C2×C3⋊D3—22no—
159C2×C3⋊D3—44no—
160C32×C4—42no—
161C32×C4—42no—
162C32×C4#12312yes—
163C32×C4C2×#4111yescharacteristic
164C32×C4C2×#4111yescharacteristic
165C3⋊Dic3—22no—
166C3⋊Dic3—42no—
167C3⋊Dic3—42no—
168C22×Q8C2×C3⋊D311yescharacteristic
169C23×C4—91no—
170C22×C8—91no—
171C22×C8C2×C3⋊D311yescharacteristic
172C22⋊Q8—94no—
173C22⋊Q8—182no—
174#117—94no—
175#117—182no—
176C2×C4⋊C4—91no—
177C2×C4⋊C4—91no—
178C2×C4⋊C4—181no—
179C2×C4⋊C4C2×C3⋊D311yescharacteristic
180C2×C22⋊C4—181no—
181C2×C22⋊C4—181no—
182C2×C42—181no—
183#107—94no—
184#106—94no—
185#103—94no—
186#103C2×C3⋊D314yescomplemented
187C22⋊C8—94no—
188C23×C3D3×D414yes—
189C22×D3—38no—
190C22×D3—68no—
191C22×D3—68no—
192C22×D3—68no—
193C3×Q8—28no—
194C3×Q8—28no—
195C3×Q8—48no—
196C2×C3×C4—28no—
197C2×C3×C4—28no—
198C2×C3×C4—48no—
199C2×C3×C4—48no—
200C2×C3×C4#23518yes—
201C2×C3×C4D3×D414yes—
202C2×C3×C4#23718yes—
203C2×C3×C4C23×D314yes—
204C2×Dic3—38no—
205C2×Dic3—68no—
206C2×Dic3—68no—
207C2×Dic3—68no—
208C2×Dic3—128no—
209C2×Dic3—128no—
210C4×D3—616no—
211C4×D3—68no—
212C4×D3—68no—
213C3×C8—28no—
214C3⋊C8—68no—
215C2×C32#48514yescomplemented
216C2×C32C2×#12311yescharacteristic
217C2×C32C2×#13511yescharacteristic
218C2×C32C2×#13711yescharacteristic
219C3⋊D3—42no—
220C24—91no—
221C2×Q8—21no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8C22×C3⋊D312yes—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—91no—
228C22×C4—92no—
229C22×C4—92no—
230C22×C4—182no—
231C22×C4—182no—
232C22×C4—181no—
233C22×C4—181no—
234C22×C4C22×C3⋊D311yescharacteristic
235C2×C8—22no—
236C2×C8—92no—
237C2×C8—182no—
238C2×C8C22×C3⋊D312yes—
239C4⋊C4—21no—
240C4⋊C4—92no—
241C4⋊C4—92no—
242C4⋊C4—184no—
243C4⋊C4—181no—
244C4⋊C4—181no—
245C4⋊C4C22×C3⋊D312yes—
246C22⋊C4—184no—
247C22⋊C4—184no—
248C42—184no—
249C22×C3#88318yes—
250C22×C3#91518yes—
251C22×C3#91918yes—
252C22×C3C2×D3×D414yes—
253C2×D3—68no—
254C2×D3—68no—
255C2×D3—68no—
256C2×D3—1216no—
257C3×C4—48no—
258C3×C4—48no—
259C3×C4#88318yes—
260C3×C4C2×#23514yes—
261C3×C4C2×#23714yes—
262Dic3—68no—
263Dic3—128no—
264Dic3—128no—
265C32C2×#48511yescharacteristic, complemented, Sylow
266C23—92no—
267C23—182no—
268C23—182no—
269C23—182no—
270C23D4×C3⋊D311yescharacteristic
271Q8—22no—
272Q8—22no—
273Q8—42no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—92no—
279C2×C4—182no—
280C2×C4—184no—
281C2×C4—182no—
282C2×C4—182no—
283C2×C4—182no—
284C2×C4—182no—
285C2×C4—362no—
286C2×C4—362no—
287C2×C4#382812yes—
288C2×C4D4×C3⋊D311yescharacteristic
289C2×C4#383012yes—
290C2×C4C23×C3⋊D311yescharacteristic
291C8—22no—
292C8—182no—
293C2×C3#4814116yescomplemented
294C2×C3C2×#88314yes—
295C2×C3C2×#91514yes—
296C2×C3C2×#91914yes—
297D3—128no—
298C22—182no—
299C22—182no—
300C22—182no—
301C22—364no—
302C22#6409212yes—
303C22#6412412yes—
304C22#6412812yes—
305C22C2×D4×C3⋊D311yescharacteristic
306C4—42no—
307C4—42no—
308C4—182no—
309C4—362no—
310C4—362no—
311C4#6409212yes—
312C4C2×#382811yescharacteristic
313C4C2×#383011yescharacteristic
314C3C2×#481414yescomplemented
315C2—362no—
316C2#1059251314yesdirect product factor
317C2C2×#6409211yescharacteristic
318C2C2×#6412411yescharacteristic
319C2C2×#6412811yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC2×#103C3⋊D3
hypocenterC32C2×#485
LCSG ▷ C2×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
3. C2×C32×#103C2semidirect
4. C2×#63662C2semidirect
6. C2×#63645C2semidirect
7. C2×#63635C2semidirect
8. #10592513C2direct (N × H)
25. C32×#103C22semidirect
26. #63662C22semidirect
28. #63645C22semidirect
29. #63635C22semidirect
32. C2×C3×#103D3semidirect
83. C3×#103C2×D3semidirect
121. C2×#103C3⋊D3semidirect
186. #103C2×C3⋊D3semidirect
215. C2×C32#485semidirect
265. C32C2×#485semidirect
293. C2×C3#4814semidirect
314. C3C2×#4814semidirect
316. C2#10592513direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641552
C2×#641012
C2×C32×#1032
C2×#636622
C2×#636472
C2×#636452
C2×#636352
#105925132
C2×#48143