Finite Group Databasebeta

← C2×#10592436 #11869425

Subgroups — C2×#10592436 #11869425

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×#64139C211yesmaximal, characteristic
2C2×#64135C211yesmaximal, characteristic, complemented
3C2×C32×C22⋊C8C211yesmaximal, characteristic, complemented
4C2×#63648C211yesmaximal, characteristic, complemented
5C2×#63648C211yesmaximal, characteristic, complemented
6C2×#63645C211yesmaximal, characteristic, complemented
7C2×#63644C211yesmaximal, characteristic, complemented
8#10592436C218yesmaximal, direct product factor
9C2×#4737—34nomaximal
10C23×C32×C4C2211yescharacteristic
11C22×#638—21no—
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×#3757—21no—
16#64139—22no—
17#64139C2214yes—
18C2×#3752—21no—
19#64135—22no—
20#64135C2214yescomplemented
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4×C3⋊Dic3—21no—
25C32×C22⋊C8C2214yescomplemented
26#63648C2214yescomplemented
27#63648C2214yescomplemented
28#63645C2214yescomplemented
29#63644C2214yescomplemented
30C2×#930—34no—
31C2×#926—34no—
32C2×C3×C22⋊C8D314yescomplemented
33C2×#821—34no—
34C2×#821—34no—
35C2×#818—34no—
36C2×#817—34no—
37#4737—332no—
38C24×C32D411yescharacteristic
39C23×C3⋊D3—21no—
40C22×C32×C4—22no—
41C22×C32×C4—22no—
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D412yes—
44C22×C32×C4C2312yes—
45C22×C32×C4C2311yescharacteristic
46C2×#638—24no—
47C2×#638—44no—
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3—21no—
50C22×C3⋊Dic3—21no—
51C2×C4⋊(C3⋊D3)—22no—
52C2×C4⋊(C3⋊D3)—22no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)C2312yes—
55C2×C32×C8—22no—
56C2×C32×C8—22no—
57C2×C32×C8C2312yes—
58C2×C32×C8C2312yes—
59#3757—24no—
60#3752—24no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)C2312yes—
65C4⋊(C3⋊Dic3)C2312yes—
66C4⋊(C3⋊Dic3)C2312yes—
67C4×C3⋊Dic3—24no—
68C2×#482—91noSylow
69C23×C3×C4C2×D314yes—
70C22×#67—64no—
71C22×D12—34no—
72C22×C3×C8C2×D314yes—
73C22×C3×C8C2×D314yes—
74C2×#217—64no—
75#930—316no—
76#930—68no—
77C2×(C2×D3)⋊C4—64no—
78#926—316no—
79#926—68no—
80C2×C4⋊Dic3—34no—
81C2×C4⋊Dic3—34no—
82C2×C4⋊Dic3—34no—
83C2×C4×Dic3—64no—
84C3×C22⋊C8C2×D3116yescomplemented
85#821—316no—
86#821—316no—
87#818—316no—
88#817—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×C4C2×D412yes—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4#4112yes—
105C2×C32×C4#4112yes—
106C2×C32×C4C2411yescharacteristic
107#638—48no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—42no—
112C2×C3⋊Dic3—42no—
113C2×C3⋊Dic3—42no—
114C4⋊(C3⋊D3)—22no—
115C4⋊(C3⋊D3)—22no—
116C4⋊(C3⋊D3)—42no—
117C32×C8—22no—
118C32×C8—22no—
119C2×#121—91no—
120C2×#117—91no—
121#482—98no—
122C2×#107—91no—
123C2×#106—91no—
124C2×#102—91no—
125C2×#102—91no—
126C2×C22⋊C8C3⋊D311yescharacteristic, complemented
127C24×C3D1214yes—
128C23×D3—64no—
129C22×C3×C4—28no—
130C22×C3×C4—28no—
131C22×C3×C4D1214yes—
132C22×C3×C4D1218yes—
133C22×C3×C4C22×D318yes—
134C22×C3×C4C22×D314yes—
135C2×#67—616no—
136C2×#67—1216no—
137C22×Dic3—64no—
138C22×Dic3—64no—
139C22×Dic3—64no—
140C2×D12—38no—
141C2×D12—68no—
142C2×D12—68no—
143C2×D12—64no—
144C2×C3×C8—28no—
145C2×C3×C8—28no—
146C2×C3×C8C22×D318yes—
147C2×C3×C8C22×D318yes—
148#217—616no—
149(C2×D3)⋊C4—616no—
150C4⋊Dic3—38no—
151C4⋊Dic3—38no—
152C4⋊Dic3—38no—
153C4⋊Dic3—64no—
154C4⋊Dic3—64no—
155C4⋊Dic3—64no—
156C4×Dic3—616no—
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#12312yes—
171C32×C4C2×#4111yescharacteristic
172C32×C4C2×#4111yescharacteristic
173C3⋊Dic3—42no—
174C3⋊Dic3—42no—
175C3⋊Dic3—42no—
176C22×D4—91no—
177C22×D4—181no—
178C23×C4C2×C3⋊D311yescharacteristic
179C22×C8C2×C3⋊D311yescharacteristic
180C22×C8C2×C3⋊D311yescharacteristic
181#121—94no—
182#121—182no—
183#117—94no—
184#117—182no—
185C2×C4⋊C4—91no—
186C2×C4⋊C4—91no—
187C2×C4⋊C4—91no—
188C2×C22⋊C4—181no—
189C2×C22⋊C4—181no—
190C2×C42—181no—
191#107—94no—
192#106—94no—
193#102—94no—
194#102—94no—
195C22⋊C8C2×C3⋊D314yescomplemented
196C23×C3—28no—
197C23×C3—28no—
198C23×C3—28no—
199C23×C3C2×D1218yes—
200C23×C3C2×D1214yes—
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×C4C2×D1218yes—
210C2×C3×C4C2×D1214yes—
211C2×C3×C4#23718yes—
212C2×C3×C4#23718yes—
213C2×C3×C4C23×D314yes—
214#67—1232no—
215C2×Dic3—68no—
216C2×Dic3—68no—
217C2×Dic3—68no—
218C2×Dic3—128no—
219C2×Dic3—128no—
220C2×Dic3—128no—
221D12—68no—
222D12—68no—
223D12—128no—
224C3×C8—28no—
225C3×C8—28no—
226C2×C32—42no—
227C2×C32#48214yescomplemented
228C2×C32C2×#12311yescharacteristic
229C2×C32C2×#13511yescharacteristic
230C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
231C3⋊D3—82no—
232C24—181no—
233C24C4⋊(C3⋊D3)11yescharacteristic
234C2×D4—92no—
235C2×D4—184no—
236C2×D4—181no—
237C2×D4—182no—
238C2×D4—182no—
239C2×D4—364no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—181no—
243C22×C4—181no—
244C22×C4—181no—
245C22×C4C4⋊(C3⋊D3)12yes—
246C22×C4C4⋊(C3⋊D3)11yescharacteristic
247C22×C4C22×C3⋊D312yes—
248C22×C4C22×C3⋊D311yescharacteristic
249C2×C8—22no—
250C2×C8—22no—
251C2×C8C22×C3⋊D312yes—
252C2×C8C22×C3⋊D312yes—
253C4⋊C4—92no—
254C4⋊C4—92no—
255C4⋊C4—92no—
256C4⋊C4—181no—
257C4⋊C4—181no—
258C4⋊C4—181no—
259C22⋊C4—184no—
260C22⋊C4—184no—
261C42—184no—
262C22×C3—28no—
263C22×C3—28no—
264C22×C3—28no—
265C22×C3—416no—
266C22×C3#88618yes—
267C22×C3#90418yes—
268C22×C3#90818yes—
269C22×C3C22×D1214yes—
270C2×D3—128no—
271C2×D3—128no—
272C2×D3—128no—
273C2×D3—2416no—
274C3×C4—28no—
275C3×C4#88618yes—
276C3×C4C2×#23714yes—
277C3×C4C2×#23714yes—
278Dic3—128no—
279Dic3—128no—
280Dic3—128no—
281C32C2×#48211yescharacteristic, complemented, Sylow
282C23—22no—
283C23—22no—
284C23—22no—
285C23—182no—
286C23—362no—
287C23—362no—
288C23—362no—
289C23C2×C4⋊(C3⋊D3)12yes—
290C23C2×C4⋊(C3⋊D3)11yescharacteristic
291D4—182no—
292D4—182no—
293D4—368no—
294D4—362no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—182no—
300C2×C4—182no—
301C2×C4—182no—
302C2×C4—362no—
303C2×C4—362no—
304C2×C4—362no—
305C2×C4C2×C4⋊(C3⋊D3)12yes—
306C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
307C2×C4#383012yes—
308C2×C4#383012yes—
309C2×C4C23×C3⋊D311yescharacteristic
310C8—22no—
311C8—22no—
312C2×C3—48no—
313C2×C3#4737116yescomplemented
314C2×C3C2×#88614yes—
315C2×C3C2×#90414yes—
316C2×C3C2×#90814yes—
317D3—248no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—44no—
322C22—362no—
323C22—362no—
324C22—362no—
325C22—724no—
326C22#6409512yes—
327C22#6411312yes—
328C22#6411712yes—
329C22C22×C4⋊(C3⋊D3)11yescharacteristic
330C4—22no—
331C4—362no—
332C4—362no—
333C4—362no—
334C4#6409512yes—
335C4C2×#383011yescharacteristic
336C4C2×#383011yescharacteristic
337C3C2×#473714yescomplemented
338C2—42no—
339C2—722no—
340C2#1059243614yesdirect product factor
341C2C2×#6409511yescharacteristic
342C2C2×#6411311yescharacteristic
343C2C2×#6411711yescharacteristic
subgroupG/H
centerC23C2×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×C22⋊C8C2
socleC23×C32C2×D4
prime radicalC2×#64139C2
hypercenterC2×C22⋊C8C3⋊D3
hypocenterC32C2×#482
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#64135C2semidirect
3. C2×C32×C22⋊C8C2semidirect
4. C2×#63648C2semidirect
5. C2×#63648C2semidirect
6. C2×#63645C2semidirect
7. C2×#63644C2semidirect
8. #10592436C2direct (N × H)
20. #64135C22semidirect
25. C32×C22⋊C8C22semidirect
26. #63648C22semidirect
27. #63648C22semidirect
28. #63645C22semidirect
29. #63644C22semidirect
32. C2×C3×C22⋊C8D3semidirect
84. C3×C22⋊C8C2×D3semidirect
126. C2×C22⋊C8C3⋊D3semidirect
195. C22⋊C8C2×C3⋊D3semidirect
227. C2×C32#482semidirect
281. C32C2×#482semidirect
313. C2×C3#4737semidirect
337. C3C2×#4737semidirect
340. C2#10592436direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641392
C2×#641352
C2×C32×C22⋊C82
C2×#636482
C2×#636452
C2×#636442
#105924362
C2×#47373