Finite Group Databasebeta

← C2×#10592747 #11866677

Subgroups — C2×#10592747 #11866677

Order 1152.

1692 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×#3755C211yesmaximal, characteristic, complemented
3C2×#64139C211yesmaximal, characteristic
4C23×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5C2×#63662C211yesmaximal, characteristic, complemented
6#10592747C218yesmaximal, direct product factor
7C2×#63636C211yesmaximal, characteristic, complemented
8C2×#63635C211yesmaximal, characteristic, complemented
9C2×#5048—34nomaximal
10C22×C32×Q8C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C22×#638—21no—
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C32×C22⋊Q8—22no—
15C32×C22⋊Q8C2214yescomplemented
16C2×C32×C4⋊C4—21no—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C32×C22⋊C4—21no—
19C2×#3755—24no—
20C2×#3755C2214yescomplemented
21#64139—22no—
22#64139C2214yes—
23C2×#3752—21no—
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C22×C3⋊(C3⋊C8)—24no—
26C22×C3⋊(C3⋊C8)C2211yescharacteristic
27C22×C3⋊(C3⋊C8)C2211yescharacteristic
28C22×C3⋊(C3⋊C8)C2214yescomplemented
29#63662C2214yescomplemented
30#63636C2214yescomplemented
31#63635C2214yescomplemented
32C2×C3×C22⋊Q8D314yescomplemented
33C22×#215—34no—
34C2×#930—34no—
35C23×C3⋊C8—34no—
36C2×#835—34no—
37#5048—332no—
38C2×#809—34no—
39C2×#808—34no—
40C24×C32D411yescharacteristic
41C23×C3⋊D3—21no—
42C2×C32×Q8—21no—
43C2×C32×Q8—22no—
44C2×C32×Q8—22no—
45C2×C32×Q8C2312yes—
46C22×C32×C4—22no—
47C22×C32×C4—22no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4D411yescharacteristic
51C22×C32×C4D412yes—
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C2×#638—24no—
55C2×#638—44no—
56C22×C3⋊Dic3—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C32×C4⋊C4—24no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4C2312yes—
64C32×C22⋊C4—24no—
65#3755—28no—
66#3752—24no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)C2312yes—
69C2×C3⋊(C3⋊C8)—22no—
70C2×C3⋊(C3⋊C8)—28no—
71C2×C3⋊(C3⋊C8)D414yescomplemented
72C2×C3⋊(C3⋊C8)C2312yes—
73C2×C3⋊(C3⋊C8)C2312yes—
74C2×#465—91noSylow
75C22×C3×Q8C2×D314yes—
76C23×C3×C4C2×D314yes—
77C22×#67—64no—
78C22×D12—34no—
79C3×C22⋊Q8—28no—
80C3×C22⋊Q8C2×D3116yescomplemented
81C2×C3×C4⋊C4—24no—
82C2×C3×C4⋊C4C2×D314yes—
83C2×C3×C22⋊C4—24no—
84C2×#215—316no—
85C2×#215—616no—
86#930—316no—
87#930—68no—
88C2×(C2×D3)⋊C4—64no—
89C2×C4⋊Dic3—34no—
90C22×C3⋊C8—34no—
91C22×C3⋊C8—34no—
92C22×C3⋊C8—316no—
93C22×C3⋊C8—616no—
94#835—316no—
95#809—316no—
96#808—316no—
97C23×C32—22no—
98C23×C32—22no—
99C23×C32SD1614yescomplemented
100C23×C32C2×D412yes—
101C23×C32C2×D411yescharacteristic
102C22×C3⋊D3—22no—
103C22×C3⋊D3—42no—
104C22×C3⋊D3—42no—
105C22×C3⋊D3—42no—
106C32×Q8—22no—
107C32×Q8—22no—
108C32×Q8—42no—
109C2×C32×C4—22no—
110C2×C32×C4—24no—
111C2×C32×C4—22no—
112C2×C32×C4—22no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—42no—
116C2×C32×C4—42no—
117C2×C32×C4C2×D412yes—
118C2×C32×C4C2×D412yes—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4#4112yes—
121C2×C32×C4C2411yescharacteristic
122#638—48no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—42no—
125C4⋊(C3⋊D3)—22no—
126C4⋊(C3⋊D3)—22no—
127C4⋊(C3⋊D3)—42no—
128C3⋊(C3⋊C8)—22no—
129C3⋊(C3⋊C8)C2×D414yescomplemented
130C22×SD16—91no—
131C23×C8—91no—
132C2×C22⋊Q8C3⋊D311yescharacteristic, complemented
133C2×#121—91no—
134#465—98no—
135C2×#106—91no—
136C2×#103—91no—
137C2×#102—91no—
138C24×C3#6714yes—
139C23×D3—64no—
140C2×C3×Q8—24no—
141C2×C3×Q8—28no—
142C2×C3×Q8—28no—
143C2×C3×Q8C22×D318yes—
144C22×C3×C4—28no—
145C22×C3×C4—28no—
146C22×C3×C4—24no—
147C22×C3×C4—24no—
148C22×C3×C4#6714yes—
149C22×C3×C4#6718yes—
150C22×C3×C4C22×D318yes—
151C22×C3×C4C22×D314yes—
152C2×#67—616no—
153C2×#67—1216no—
154C22×Dic3—64no—
155C2×D12—38no—
156C2×D12—68no—
157C2×D12—68no—
158C2×D12—64no—
159C3×C4⋊C4—216no—
160C3×C4⋊C4—24no—
161C3×C4⋊C4C22×D318yes—
162C3×C22⋊C4—216no—
163#215—632no—
164(C2×D3)⋊C4—616no—
165C4⋊Dic3—38no—
166C4⋊Dic3—64no—
167C2×C3⋊C8—316no—
168C2×C3⋊C8—38no—
169C2×C3⋊C8—38no—
170C2×C3⋊C8—632no—
171C2×C3⋊C8—68no—
172C22×C32—22no—
173C22×C32—22no—
174C22×C32—28no—
175C22×C32#12112yes—
176C22×C32C2×SD1612yes—
177C22×C32C2×SD1614yescomplemented
178C22×C32#13512yes—
179C22×C32C22×D411yescharacteristic
180C2×C3⋊D3—42no—
181C2×C3⋊D3—42no—
182C2×C3⋊D3—42no—
183C2×C3⋊D3—84no—
184C32×C4—22no—
185C32×C4—42no—
186C32×C4—42no—
187C32×C4#12112yes—
188C32×C4C22×D411yescharacteristic
189C32×C4C2×#4111yescharacteristic
190C3⋊Dic3—42no—
191C22×Q8C2×C3⋊D311yescharacteristic
192C22×D4—91no—
193C22×D4—181no—
194C23×C4C2×C3⋊D311yescharacteristic
195C2×SD16—94no—
196C2×SD16—184no—
197C22×C8—91no—
198C22×C8—91no—
199C22×C8—94no—
200C22×C8—184no—
201C22⋊Q8—22no—
202C22⋊Q8C2×C3⋊D314yescomplemented
203#121—94no—
204#121—182no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—91no—
207C2×C4⋊C4C2×C3⋊D311yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—181no—
210#106—94no—
211#103—94no—
212#102—94no—
213C23×C3—28no—
214C23×C3—28no—
215C23×C3#215116yescomplemented
216C23×C3C2×#6718yes—
217C23×C3C2×#6714yes—
218C22×D3—68no—
219C22×D3—128no—
220C22×D3—128no—
221C22×D3—128no—
222C3×Q8—28no—
223C3×Q8—28no—
224C3×Q8—48no—
225C2×C3×C4—28no—
226C2×C3×C4—216no—
227C2×C3×C4—28no—
228C2×C3×C4—28no—
229C2×C3×C4—28no—
230C2×C3×C4—28no—
231C2×C3×C4—48no—
232C2×C3×C4—48no—
233C2×C3×C4D3×D418yes—
234C2×C3×C4#23718yes—
235C2×C3×C4C2×#6718yes—
236C2×C3×C4C2×#6714yes—
237C2×C3×C4C23×D314yes—
238#67—1232no—
239C2×Dic3—68no—
240C2×Dic3—128no—
241D12—68no—
242D12—68no—
243D12—128no—
244C3⋊C8—316no—
245C3⋊C8—68no—
246C2×C32—24no—
247C2×C32#46514yescomplemented
248C2×C32C2×#12111yescharacteristic
249C2×C32C22×SD1611yescharacteristic
250C2×C32C2×#13511yescharacteristic
251C3⋊D3—82no—
252C24—181no—
253C24#63811yescharacteristic
254C2×Q8—21no—
255C2×Q8—22no—
256C2×Q8—22no—
257C2×Q8C22×C3⋊D312yes—
258C2×D4—92no—
259C2×D4—184no—
260C2×D4—182no—
261C2×D4—182no—
262C2×D4—181no—
263C2×D4—364no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—181no—
269C22×C4#63812yes—
270C22×C4#63811yescharacteristic
271C22×C4C22×C3⋊D312yes—
272C22×C4C22×C3⋊D311yescharacteristic
273SD16—188no—
274C2×C8—92no—
275C2×C8—94no—
276C2×C8—92no—
277C2×C8—188no—
278C2×C8—182no—
279C4⋊C4—24no—
280C4⋊C4—21no—
281C4⋊C4—92no—
282C4⋊C4—181no—
283C4⋊C4C22×C3⋊D312yes—
284C22⋊C4—24no—
285C22⋊C4—184no—
286C22×C3—28no—
287C22×C3—232no—
288C22×C3—28no—
289C22×C3#93918yes—
290C22×C3C2×#21518yes—
291C22×C3C2×#215116yescomplemented
292C22×C3#95018yes—
293C22×C3C22×#6714yes—
294C2×D3—128no—
295C2×D3—128no—
296C2×D3—128no—
297C2×D3—2416no—
298C3×C4—28no—
299C3×C4—48no—
300C3×C4—48no—
301C3×C4#93918yes—
302C3×C4C2×D3×D414yes—
303C3×C4C2×#23714yes—
304Dic3—128no—
305C32C2×#46511yescharacteristic, complemented, Sylow
306C23—22no—
307C23—22no—
308C23—182no—
309C23—362no—
310C23—362no—
311C23—362no—
312C23#375514yescomplemented
313C23C2×#63812yes—
314C23C2×#63811yescharacteristic
315Q8—22no—
316Q8—22no—
317Q8—42no—
318D4—182no—
319D4—182no—
320D4—368no—
321D4—362no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—182no—
331C2×C4—362no—
332C2×C4D4×C3⋊D312yes—
333C2×C4#383012yes—
334C2×C4C2×#63812yes—
335C2×C4C2×#63811yescharacteristic
336C2×C4C23×C3⋊D311yescharacteristic
337C8—94no—
338C8—182no—
339C2×C3—216no—
340C2×C3#5048116yescomplemented
341C2×C3C2×#93914yes—
342C2×C3C22×#21514yes—
343C2×C3C2×#95014yes—
344D3—248no—
345C22—22no—
346C22—22no—
347C22—28no—
348C22—362no—
349C22—362no—
350C22—362no—
351C22—724no—
352C22#6414812yes—
353C22C2×#375512yes—
354C22C2×#375514yescomplemented
355C22#6415912yes—
356C22C22×#63811yescharacteristic
357C4—22no—
358C4—42no—
359C4—42no—
360C4—362no—
361C4#6414812yes—
362C4C2×D4×C3⋊D311yescharacteristic
363C4C2×#383011yescharacteristic
364C3C2×#504814yescomplemented
365C2—24no—
366C2—722no—
367C2#1059274714yesdirect product factor
368C2C2×#6414811yescharacteristic
369C2C22×#375511yescharacteristic
370C2C2×#6415911yescharacteristic
subgroupG/H
centerC23C2×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C2×D4
prime radicalC2×#64139C2
hypercenterC2×C22⋊Q8C3⋊D3
hypocenterC32C2×#465
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C22⋊Q8C2semidirect
2. C22×#3755C2semidirect
4. C23×C3⋊(C3⋊C8)C2semidirect
5. C2×#63662C2semidirect
6. #10592747C2direct (N × H)
7. C2×#63636C2semidirect
8. C2×#63635C2semidirect
15. C32×C22⋊Q8C22semidirect
20. C2×#3755C22semidirect
28. C22×C3⋊(C3⋊C8)C22semidirect
29. #63662C22semidirect
30. #63636C22semidirect
31. #63635C22semidirect
32. C2×C3×C22⋊Q8D3semidirect
71. C2×C3⋊(C3⋊C8)D4semidirect
80. C3×C22⋊Q8C2×D3semidirect
99. C23×C32SD16semidirect
129. C3⋊(C3⋊C8)C2×D4semidirect
132. C2×C22⋊Q8C3⋊D3semidirect
177. C22×C32C2×SD16semidirect
202. C22⋊Q8C2×C3⋊D3semidirect
215. C23×C3#215semidirect
247. C2×C32#465semidirect
291. C22×C3C2×#215semidirect
305. C32C2×#465semidirect
312. C23#3755semidirect
340. C2×C3#5048semidirect
354. C22C2×#3755semidirect
364. C3C2×#5048semidirect
367. C2#10592747direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
C22×#37552
C2×#641392
C23×C3⋊(C3⋊C8)2
C2×#636622
#105927472
C2×#636362
C2×#636352
C2×#50483