Finite Group Databasebeta

← C2×#10592371 #11808146

Subgroups — C2×#10592371 #11808146

Order 1152.

3756 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C22×#3752C212yesmaximal, complemented
3C22×#3752C212yesmaximal, complemented
4C22×#3750C211yesmaximal, characteristic, complemented
5C2×C32×#95C211yesmaximal, characteristic, complemented
6#10592371C218yesmaximal, direct product factor
7C2×#4672—34nomaximal
8C24×C3⋊D3C2212yes—
9C23×C32×C4C2212yes—
10C23×C32×C4C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C22×C4⋊(C3⋊D3)—24no—
14C22×C4⋊(C3⋊D3)—28no—
15C22×C4⋊(C3⋊D3)C2214yes—
16C2×#3752—28no—
17C2×#3752—28no—
18C2×#3752C2218yescomplemented
19C2×#3752C2218yescomplemented
20C2×#3750—24no—
21C2×#3750C2214yescomplemented
22C32×#95C2214yescomplemented
23C23×D12—34no—
24C22×(C2×D3)⋊C4—38no—
25C22×(C2×D3)⋊C4—38no—
26C22×Dic3⋊C4—34no—
27C2×C3×#95D314yescomplemented
28#4672—332no—
29C24×C32C2311yescharacteristic
30C23×C3⋊D3—24no—
31C23×C3⋊D3—24no—
32C23×C3⋊D3—24no—
33C23×C3⋊D3—24no—
34C23×C3⋊D3—24no—
35C23×C3⋊D3—24no—
36C23×C3⋊D3D418yes—
37C23×C3⋊D3C2314yes—
38C22×C32×C4—24no—
39C22×C32×C4—24no—
40C22×C32×C4—24no—
41C22×C32×C4—24no—
42C22×C32×C4D414yes—
43C22×C32×C4C2314yes—
44C22×C32×C4C2312yes—
45C22×C3⋊Dic3—22no—
46C22×C3⋊Dic3—22no—
47C22×C3⋊Dic3—22no—
48C22×C3⋊Dic3—24no—
49C22×C3⋊Dic3D414yescomplemented
50C22×C3⋊Dic3C2312yes—
51C22×C3⋊Dic3C2312yes—
52C2×C4⋊(C3⋊D3)—232no—
53C2×C4⋊(C3⋊D3)—216no—
54C2×C4⋊(C3⋊D3)—28no—
55#3752—216no—
56#3752—216no—
57#3750—28no—
58C2×#394—91noSylow
59C24×D3—38no—
60C23×C3×C4C2×D318yes—
61C23×C3×C4C2×D314yes—
62C23×Dic3—34no—
63C23×Dic3—34no—
64C22×D12—316no—
65C22×D12—632no—
66C22×D12—616no—
67C2×(C2×D3)⋊C4—332no—
68C2×(C2×D3)⋊C4—332no—
69C2×(C2×D3)⋊C4—632no—
70C2×(C2×D3)⋊C4—632no—
71C2×Dic3⋊C4—316no—
72C2×Dic3⋊C4—616no—
73C3×#95C2×D3116yescomplemented
74C23×C32C2×D412yes—
75C23×C32C2×D414yes—
76C23×C32C2×D412yes—
77C23×C32#4114yes—
78C23×C32#4112yes—
79C23×C32C2411yescharacteristic
80C22×C3⋊D3—216no—
81C22×C3⋊D3—216no—
82C22×C3⋊D3—216no—
83C22×C3⋊D3—24no—
84C22×C3⋊D3—24no—
85C22×C3⋊D3—24no—
86C22×C3⋊D3—24no—
87C22×C3⋊D3—24no—
88C22×C3⋊D3—24no—
89C22×C3⋊D3—48no—
90C22×C3⋊D3—48no—
91C22×C3⋊D3—48no—
92C22×C3⋊D3—48no—
93C22×C3⋊D3C2×D418yes—
94C2×C32×C4—28no—
95C2×C32×C4—24no—
96C2×C32×C4—24no—
97C2×C32×C4—24no—
98C2×C32×C4—24no—
99C2×C32×C4—48no—
100C2×C32×C4C2×D414yes—
101C2×C3⋊Dic3—28no—
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—24no—
106C2×C3⋊Dic3—44no—
107C2×C3⋊Dic3C2×D414yescomplemented
108C4⋊(C3⋊D3)—232no—
109C23×D4—91no—
110C22×C4⋊C4—91no—
111C22×C22⋊C4—92no—
112C22×C22⋊C4—92no—
113#394—98no—
114C2×#95C3⋊D311yescharacteristic, complemented
115C24×C3C22×D314yes—
116C23×D3—332no—
117C23×D3—316no—
118C23×D3—616no—
119C23×D3—616no—
120C23×D3—616no—
121C23×D3—616no—
122C23×D3—616no—
123C23×D3—616no—
124C22×C3×C4—216no—
125C22×C3×C4—216no—
126C22×C3×C4—216no—
127C22×C3×C4—216no—
128C22×C3×C4D12116yes—
129C22×C3×C4C22×D3116yes—
130C22×C3×C4C22×D318yes—
131C22×Dic3—316no—
132C22×Dic3—38no—
133C22×Dic3—38no—
134C22×Dic3—68no—
135C22×Dic3—68no—
136C22×Dic3—68no—
137C22×Dic3—616no—
138C2×D12—664no—
139C2×D12—6128no—
140C2×D12—632no—
141(C2×D3)⋊C4—664no—
142(C2×D3)⋊C4—664no—
143Dic3⋊C4—632no—
144C22×C32#12014yes—
145C22×C32#12118yes—
146C22×C32#12114yes—
147C22×C32#12318yes—
148C22×C32#12414yes—
149C22×C32C22×D411yescharacteristic
150C22×C32C22×D412yes—
151C22×C32C22×D411yescharacteristic
152C22×C32C2×#4112yes—
153C22×C32C2×#4111yescharacteristic
154C2×C3⋊D3—28no—
155C2×C3⋊D3—28no—
156C2×C3⋊D3—28no—
157C2×C3⋊D3—44no—
158C2×C3⋊D3—44no—
159C2×C3⋊D3—44no—
160C2×C3⋊D3—44no—
161C2×C3⋊D3—432no—
162C32×C4—24no—
163C32×C4—44no—
164C3⋊Dic3—24no—
165C3⋊Dic3—42no—
166C25—92no—
167C22×D4—94no—
168C22×D4—188no—
169C22×D4—184no—
170C23×C4—91no—
171C23×C4—91no—
172C23×C4C2×C3⋊D312yes—
173C23×C4C2×C3⋊D311yescharacteristic
174C2×C4⋊C4—94no—
175C2×C4⋊C4—184no—
176C2×C22⋊C4—98no—
177C2×C22⋊C4—98no—
178C2×C22⋊C4—188no—
179C2×C22⋊C4—188no—
180#95C2×C3⋊D314yescomplemented
181C23×C3C2×D1218yes—
182C23×C3#235116yes—
183C23×C3D3×D4116yes—
184C23×C3D3×D418yes—
185C23×C3#23918yes—
186C23×C3C23×D314yes—
187C22×D3—332no—
188C22×D3—664no—
189C22×D3—664no—
190C22×D3—664no—
191C22×D3—616no—
192C22×D3—616no—
193C22×D3—616no—
194C22×D3—616no—
195C22×D3—616no—
196C22×D3—616no—
197C22×D3—1232no—
198C22×D3—1232no—
199C22×D3—1232no—
200C22×D3—1232no—
201C2×C3×C4—232no—
202C2×C3×C4—216no—
203C2×C3×C4—216no—
204C2×C3×C4—216no—
205C2×C3×C4—216no—
206C2×C3×C4—432no—
207C2×C3×C4C2×D12116yes—
208C2×Dic3—316no—
209C2×Dic3—632no—
210C2×Dic3—68no—
211C2×Dic3—68no—
212C2×Dic3—68no—
213C2×Dic3—616no—
214C2×Dic3—1216no—
215D12—6128no—
216C2×C32#39418yescomplemented
217C2×C32C2×#12011yescharacteristic
218C2×C32C2×#12112yes—
219C2×C32C2×#12111yescharacteristic
220C2×C32C2×#12312yes—
221C2×C32C2×#12411yescharacteristic
222C3⋊D3—48no—
223C24—94no—
224C24—98no—
225C24—184no—
226C24—184no—
227C24—184no—
228C24—184no—
229C24—184no—
230C24—184no—
231C24C22×C3⋊D311yescharacteristic
232C2×D4—1816no—
233C2×D4—1832no—
234C2×D4—188no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—92no—
240C22×C4—94no—
241C22×C4—92no—
242C22×C4—182no—
243C22×C4—182no—
244C22×C4—182no—
245C22×C4—184no—
246C22×C4C4⋊(C3⋊D3)14yes—
247C22×C4C22×C3⋊D314yes—
248C22×C4C22×C3⋊D312yes—
249C4⋊C4—188no—
250C22⋊C4—1816no—
251C22⋊C4—1816no—
252C22×C3#875116yes—
253C22×C3#882116yes—
254C22×C3#884132yes—
255C22×C3#894132yes—
256C22×C3#895116yes—
257C22×C3C22×D1214yes—
258C22×C3C2×#23518yes—
259C22×C3C2×D3×D418yes—
260C22×C3C2×D3×D414yes—
261C22×C3C2×#23914yes—
262C2×D3—632no—
263C2×D3—632no—
264C2×D3—632no—
265C2×D3—12128no—
266C2×D3—1216no—
267C2×D3—1216no—
268C2×D3—1216no—
269C2×D3—1216no—
270C3×C4—216no—
271C3×C4—416no—
272Dic3—616no—
273Dic3—128no—
274C32C2×#39411yescharacteristic, complemented, Sylow
275C23—98no—
276C23—1816no—
277C23—1816no—
278C23—184no—
279C23—184no—
280C23—184no—
281C23—1816no—
282C23—184no—
283C23—184no—
284C23—184no—
285C23—368no—
286C23—368no—
287C23—368no—
288C23—368no—
289C23C2×C4⋊(C3⋊D3)12yes—
290C23#382814yes—
291C23D4×C3⋊D314yes—
292C23D4×C3⋊D312yes—
293C23#383212yes—
294C23C23×C3⋊D311yescharacteristic
295D4—1832no—
296C2×C4—28no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—48no—
302C2×C4—94no—
303C2×C4—182no—
304C2×C4—188no—
305C2×C4—182no—
306C2×C4—182no—
307C2×C4—184no—
308C2×C4—364no—
309C2×C4C2×C4⋊(C3⋊D3)14yes—
310C2×C3#4672132yescomplemented
311C2×C3C2×#87514yes—
312C2×C3C2×#88214yes—
313C2×C3C2×#88418yes—
314C2×C3C2×#89418yes—
315C2×C3C2×#89514yes—
316D3—1232no—
317C22—188no—
318C22—188no—
319C22—188no—
320C22—364no—
321C22—3632no—
322C22—364no—
323C22—364no—
324C22—364no—
325C22#6408414yes—
326C22#6409114yes—
327C22#6409318yes—
328C22#6410318yes—
329C22#6410414yes—
330C22C22×C4⋊(C3⋊D3)11yescharacteristic
331C22C2×#382812yes—
332C22C2×D4×C3⋊D312yes—
333C22C2×D4×C3⋊D311yescharacteristic
334C22C2×#383211yescharacteristic
335C4—24no—
336C4—44no—
337C4—184no—
338C4—362no—
339C3C2×#467214yescomplemented
340C2—368no—
341C2#1059237118yesdirect product factor
342C2C2×#6408411yescharacteristic
343C2C2×#6409111yescharacteristic
344C2C2×#6409312yes—
345C2C2×#6410312yes—
346C2C2×#6410411yescharacteristic
subgroupG/H
centerC24C22×C3⋊D3
commutator, cosocleC23×C32C24
FrattiniC23C23×C3⋊D3
FittingC2×C32×#95C2
socleC24×C32C23
prime radicalC23×C4⋊(C3⋊D3)C2
hypercenterC2×#95C3⋊D3
hypocenterC32C2×#394
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
2. C22×#3752C2semidirect
3. C22×#3752C2semidirect
4. C22×#3750C2semidirect
5. C2×C32×#95C2semidirect
6. #10592371C2direct (N × H)
18. C2×#3752C22semidirect
19. C2×#3752C22semidirect
21. C2×#3750C22semidirect
22. C32×#95C22semidirect
27. C2×C3×#95D3semidirect
49. C22×C3⋊Dic3D4semidirect
73. C3×#95C2×D3semidirect
107. C2×C3⋊Dic3C2×D4semidirect
114. C2×#95C3⋊D3semidirect
180. #95C2×C3⋊D3semidirect
216. C2×C32#394semidirect
274. C32C2×#394semidirect
310. C2×C3#4672semidirect
339. C3C2×#4672semidirect
341. C2#10592371direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊(C3⋊D3)2
C22×#37522
C22×#37502
C2×C32×#952
#105923712
C2×#46723