Finite Group Databasebeta

← C2×#10592702 #11869422

Subgroups — C2×#10592702 #11869422

Order 1152.

1404 conjugacy classes of subgroups.

The subgroup lattice has 345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic, complemented
2C2×#64139C211yesmaximal, characteristic
3C2×#63657C211yesmaximal, characteristic, complemented
4#10592702C218yesmaximal, direct product factor
5C2×#63636C211yesmaximal, characteristic, complemented
6C2×#63636C211yesmaximal, characteristic, complemented
7C2×#63635C211yesmaximal, characteristic, complemented
8C2×#63634C211yesmaximal, characteristic, complemented
9C2×#5003—34nomaximal
10C23×C32×C4C2211yescharacteristic
11C22×#638—21no—
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C32×#117—22no—
14C32×#117C2214yescomplemented
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C22⋊C4—21no—
18C2×C32×C42—21no—
19#64139—22no—
20#64139C2214yes—
21C2×#3752—21no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25#63657C2214yescomplemented
26#63636C2214yescomplemented
27#63636C2214yescomplemented
28#63635C2214yescomplemented
29#63634C2214yescomplemented
30C2×C3×#117D314yescomplemented
31C2×#930—34no—
32C2×#830—34no—
33#5003—332no—
34C2×#809—34no—
35C2×#809—34no—
36C2×#808—34no—
37C2×#807—34no—
38C24×C32D411yescharacteristic
39C23×C3⋊D3—21no—
40C22×C32×C4—22no—
41C22×C32×C4—22no—
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D412yes—
46C22×C32×C4C2312yes—
47C22×C32×C4C2311yescharacteristic
48C2×#638—24no—
49C2×#638—44no—
50C22×C3⋊Dic3—21no—
51C2×C4⋊(C3⋊D3)—22no—
52C2×C4⋊(C3⋊D3)—22no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)C2312yes—
55C32×C4⋊C4—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4C2312yes—
58C32×C4⋊C4C2312yes—
59C32×C22⋊C4—24no—
60C32×C42—24no—
61#3752—24no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)C2312yes—
64C2×C3⋊(C3⋊C8)—22no—
65C2×C3⋊(C3⋊C8)—22no—
66C2×C3⋊(C3⋊C8)C2312yes—
67C2×C3⋊(C3⋊C8)C2312yes—
68C2×#482—91noSylow
69C23×C3×C4C2×D314yes—
70C22×#67—64no—
71C22×D12—34no—
72C3×#117—28no—
73C3×#117C2×D3116yescomplemented
74C2×C3×C4⋊C4C2×D314yes—
75C2×C3×C4⋊C4C2×D314yes—
76C2×C3×C22⋊C4—24no—
77C2×C3×C42—24no—
78#930—316no—
79#930—68no—
80C2×(C2×D3)⋊C4—64no—
81C2×C4⋊Dic3—34no—
82C22×C3⋊C8—34no—
83C22×C3⋊C8—34no—
84#830—316no—
85#809—316no—
86#809—316no—
87#808—316no—
88#807—316no—
89C23×C32—22no—
90C23×C32—22no—
91C23×C32—22no—
92C23×C32C2×D412yes—
93C23×C32C2×D411yescharacteristic
94C22×C3⋊D3—22no—
95C22×C3⋊D3—42no—
96C22×C3⋊D3—42no—
97C22×C3⋊D3—42no—
98C2×C32×C4—22no—
99C2×C32×C4—24no—
100C2×C32×C4—22no—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—42no—
105C2×C32×C4—42no—
106C2×C32×C4C2×D412yes—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4#4112yes—
109C2×C32×C4#4112yes—
110C2×C32×C4C2411yescharacteristic
111#638—48no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—42no—
114C4⋊(C3⋊D3)—22no—
115C4⋊(C3⋊D3)—22no—
116C4⋊(C3⋊D3)—42no—
117C3⋊(C3⋊C8)—22no—
118C3⋊(C3⋊C8)—22no—
119C2×#121—91no—
120C2×#117C3⋊D311yescharacteristic, complemented
121#482—98no—
122C2×#107—91no—
123C2×#106—91no—
124C2×#102—91no—
125C2×#102—91no—
126C2×C22⋊C8—91no—
127C24×C3#6714yes—
128C23×D3—64no—
129C22×C3×C4—28no—
130C22×C3×C4—28no—
131C22×C3×C4—24no—
132C22×C3×C4—24no—
133C22×C3×C4#6714yes—
134C22×C3×C4#6718yes—
135C22×C3×C4C22×D318yes—
136C22×C3×C4C22×D314yes—
137C2×#67—616no—
138C2×#67—1216no—
139C22×Dic3—64no—
140C2×D12—38no—
141C2×D12—68no—
142C2×D12—68no—
143C2×D12—64no—
144C3×C4⋊C4—24no—
145C3×C4⋊C4—24no—
146C3×C4⋊C4C22×D318yes—
147C3×C4⋊C4C22×D318yes—
148C3×C22⋊C4—216no—
149C3×C42—216no—
150(C2×D3)⋊C4—616no—
151C4⋊Dic3—38no—
152C4⋊Dic3—64no—
153C2×C3⋊C8—38no—
154C2×C3⋊C8—38no—
155C2×C3⋊C8—68no—
156C2×C3⋊C8—68no—
157C22×C32—22no—
158C22×C32—22no—
159C22×C32—22no—
160C22×C32—44no—
161C22×C32#12312yes—
162C22×C32#13512yes—
163C22×C32AGL(1,ℤ/8)12yes—
164C22×C32C22×D411yescharacteristic
165C2×C3⋊D3—42no—
166C2×C3⋊D3—42no—
167C2×C3⋊D3—42no—
168C2×C3⋊D3—84no—
169C32×C4—22no—
170C32×C4—42no—
171C32×C4—42no—
172C32×C4#12312yes—
173C32×C4C2×#4111yescharacteristic
174C32×C4C2×#4111yescharacteristic
175C3⋊Dic3—42no—
176C22×D4—91no—
177C22×D4—181no—
178C23×C4C2×C3⋊D311yescharacteristic
179C22×C8—91no—
180C22×C8—91no—
181#121—94no—
182#121—182no—
183#117—22no—
184#117C2×C3⋊D314yescomplemented
185C2×C4⋊C4—91no—
186C2×C4⋊C4C2×C3⋊D311yescharacteristic
187C2×C4⋊C4C2×C3⋊D311yescharacteristic
188C2×C22⋊C4—21no—
189C2×C22⋊C4—181no—
190C2×C42—21no—
191#107—94no—
192#106—94no—
193#102—94no—
194#102—94no—
195C22⋊C8—94no—
196C23×C3—28no—
197C23×C3—28no—
198C23×C3—28no—
199C23×C3C2×#6718yes—
200C23×C3C2×#6714yes—
201C22×D3—68no—
202C22×D3—128no—
203C22×D3—128no—
204C22×D3—128no—
205C2×C3×C4—28no—
206C2×C3×C4—216no—
207C2×C3×C4—28no—
208C2×C3×C4—28no—
209C2×C3×C4—28no—
210C2×C3×C4—28no—
211C2×C3×C4—48no—
212C2×C3×C4—48no—
213C2×C3×C4#23518yes—
214C2×C3×C4#23518yes—
215C2×C3×C4C2×#6718yes—
216C2×C3×C4C2×#6714yes—
217C2×C3×C4C23×D314yes—
218#67—1232no—
219C2×Dic3—68no—
220C2×Dic3—128no—
221D12—68no—
222D12—68no—
223D12—128no—
224C3⋊C8—68no—
225C3⋊C8—68no—
226C2×C32—42no—
227C2×C32#48214yescomplemented
228C2×C32C2×#12311yescharacteristic
229C2×C32C2×#13511yescharacteristic
230C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
231C3⋊D3—82no—
232C24—181no—
233C24#63811yescharacteristic
234C2×D4—92no—
235C2×D4—184no—
236C2×D4—182no—
237C2×D4—182no—
238C2×D4—181no—
239C2×D4—364no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—181no—
245C22×C4#63812yes—
246C22×C4#63811yescharacteristic
247C22×C4C22×C3⋊D312yes—
248C22×C4C22×C3⋊D311yescharacteristic
249C2×C8—92no—
250C2×C8—92no—
251C2×C8—182no—
252C2×C8—182no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—92no—
256C4⋊C4—181no—
257C4⋊C4C22×C3⋊D312yes—
258C4⋊C4C22×C3⋊D312yes—
259C22⋊C4—24no—
260C22⋊C4—184no—
261C42—24no—
262C22×C3—28no—
263C22×C3—28no—
264C22×C3—28no—
265C22×C3—416no—
266C22×C3#92918yes—
267C22×C3#94918yes—
268C22×C3#95018yes—
269C22×C3C22×#6714yes—
270C2×D3—128no—
271C2×D3—128no—
272C2×D3—128no—
273C2×D3—2416no—
274C3×C4—28no—
275C3×C4—48no—
276C3×C4—48no—
277C3×C4#92918yes—
278C3×C4C2×#23514yes—
279C3×C4C2×#23514yes—
280Dic3—128no—
281C32C2×#48211yescharacteristic, complemented, Sylow
282C23—22no—
283C23—22no—
284C23—22no—
285C23—182no—
286C23—362no—
287C23—362no—
288C23—362no—
289C23C2×#63812yes—
290C23C2×#63811yescharacteristic
291D4—182no—
292D4—182no—
293D4—368no—
294D4—362no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—24no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—182no—
304C2×C4—362no—
305C2×C4#382812yes—
306C2×C4#382812yes—
307C2×C4C2×#63812yes—
308C2×C4C2×#63811yescharacteristic
309C2×C4C23×C3⋊D311yescharacteristic
310C8—182no—
311C8—182no—
312C2×C3—48no—
313C2×C3#5003116yescomplemented
314C2×C3C2×#92914yes—
315C2×C3C2×#94914yes—
316C2×C3C2×#95014yes—
317D3—248no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—44no—
322C22—362no—
323C22—362no—
324C22—362no—
325C22—724no—
326C22#6413812yes—
327C22#6415812yes—
328C22#6415912yes—
329C22C22×#63811yescharacteristic
330C4—22no—
331C4—42no—
332C4—42no—
333C4—362no—
334C4#6413812yes—
335C4C2×#382811yescharacteristic
336C4C2×#382811yescharacteristic
337C3C2×#500314yescomplemented
338C2—42no—
339C2—722no—
340C2#1059270214yesdirect product factor
341C2C2×#6413811yescharacteristic
342C2C2×#6415811yescharacteristic
343C2C2×#6415911yescharacteristic
subgroupG/H
centerC23C2×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#117C2
socleC23×C32C2×D4
prime radicalC2×#64139C2
hypercenterC2×#117C3⋊D3
hypocenterC32C2×#482
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C32×#117C2semidirect
3. C2×#63657C2semidirect
4. #10592702C2direct (N × H)
5. C2×#63636C2semidirect
6. C2×#63636C2semidirect
7. C2×#63635C2semidirect
8. C2×#63634C2semidirect
14. C32×#117C22semidirect
25. #63657C22semidirect
26. #63636C22semidirect
27. #63636C22semidirect
28. #63635C22semidirect
29. #63634C22semidirect
30. C2×C3×#117D3semidirect
73. C3×#117C2×D3semidirect
120. C2×#117C3⋊D3semidirect
184. #117C2×C3⋊D3semidirect
227. C2×C32#482semidirect
281. C32C2×#482semidirect
313. C2×C3#5003semidirect
337. C3C2×#5003semidirect
340. C2#10592702direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C2×#641392
C2×#636572
#105927022
C2×#636362
C2×#636352
C2×#636342
C2×#50033