Finite Group Databasebeta

← C2×#10588649 #11857892

Subgroups — C2×#10588649 #11857892

Order 1152.

1224 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
1C22×#3697C211yesmaximal, characteristic
2C22×C9×C4⋊C4C211yesmaximal, characteristic, complemented
3C22×#3667C211yesmaximal, characteristic, complemented
4#10588649C218yesmaximal, direct product factor
5C2×#63369C212yesmaximal, complemented
6C2×#63368C212yesmaximal, complemented
7C2×#4966—31nomaximal
8C23×C4×C9—21no—
9C23×C4×C9C2211yescharacteristic
10C22×#611—21no—
11C2×#3697—24no—
12C2×#3697—22no—
13C2×#3697C418yescomplemented
14C2×#3697C2214yes—
15C22×D36C2211yescharacteristic
16C22×C4×D9—21no—
17C22×Dic18C2211yescharacteristic
18C2×C9×C4⋊C4—22no—
19C2×C9×C4⋊C4—21no—
20C2×C9×C4⋊C4C2212yes—
21C2×C9×C4⋊C4C2214yescomplemented
22C2×#3667—24no—
23C2×#3667C2214yescomplemented
24C22×C9⋊C8C2212yes—
25#63369C2218yescomplemented
26#63368C2218yescomplemented
27C22×#235—31no—
28C22×C3×C4⋊C4D311yescharacteristic
29C22×#208—31no—
30C2×#810—32no—
31#4966—38no—
32C2×#809—32no—
33C24×C9D411yescharacteristic
34C23×D9—21no—
35C22×C4×C9—22no—
36C22×C4×C9—24no—
37C22×C4×C9—44no—
38C22×C4×C9C2×C414yes—
39C22×C4×C9D411yescharacteristic
40C22×C4×C9D412yes—
41C22×C4×C9D414yes—
42C22×C4×C9C2311yescharacteristic
43C22×C4×C9C2312yes—
44C2×#611—28no—
45C2×#611—24no—
46C22×Dic9—21no—
47#3697—216no—
48#3697—28no—
49#3697C2×C4116yescomplemented
50C2×D36—21no—
51C2×D36—22no—
52C2×D36C2×C414yescomplemented
53C2×D36C2312yes—
54C2×C4×D9—28no—
55C2×C4×D9—24no—
56C2×Dic18—21no—
57C2×Dic18—22no—
58C2×Dic18C2×C414yescomplemented
59C2×Dic18C2312yes—
60C9×C4⋊C4—22no—
61C9×C4⋊C4—24no—
62C9×C4⋊C4C2314yes—
63#3667—28no—
64C2×C9⋊C8—24no—
65C2×C9⋊C8C2314yes—
66C2×#417—91noSylow
67C23×C3×C4—21no—
68C23×C3×C4C2×D311yescharacteristic
69C22×#67—61no—
70C2×#235—38no—
71C2×#235—34no—
72C2×#235—64no—
73C2×#235—62no—
74C22×D12—31no—
75C22×C4×D3—61no—
76C22×Dic6—31no—
77C2×C3×C4⋊C4—21no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4C2×D312yes—
80C2×C3×C4⋊C4C2×D314yes—
81C2×#208—34no—
82C2×#208—64no—
83C22×C3⋊C8—32no—
84#810—38no—
85#809—38no—
86C23×C9—22no—
87C23×C9—22no—
88C23×C9C22⋊C414yes—
89C23×C9C2×D412yes—
90C23×C9C2×D411yescharacteristic
91C22×D9—24no—
92C22×D9—22no—
93C22×D9—42no—
94C22×D9—42no—
95C2×C4×C9—24no—
96C2×C4×C9—48no—
97C2×C4×C9—44no—
98C2×C4×C9C22⋊C414yes—
99C2×C4×C9C22⋊C418yes—
100C2×C4×C9C22×C412yes—
101C2×C4×C9C22×C414yes—
102C2×C4×C9C2×D412yes—
103C2×C4×C9C2×D414yes—
104C2×C4×C9C2×D411yescharacteristic
105C2×C4×C9C2×D412yes—
106C2×C4×C9C2411yescharacteristic
107#611—216no—
108C2×Dic9—24no—
109C2×Dic9—22no—
110D36—24no—
111D36—22no—
112D36C22×C414yescomplemented
113C4×D9—216no—
114Dic18—24no—
115Dic18—22no—
116Dic18C22×C414yescomplemented
117C9⋊C8—24no—
118C22×#41—91no—
119C22×M16—91no—
120C22×C4⋊C4D911yescharacteristic, complemented
121#417—98no—
122C2×#103—92no—
123C2×#102—92no—
124C24×C3#6711yescharacteristic
125C23×D3—61no—
126C22×C3×C4—24no—
127C22×C3×C4—22no—
128C22×C3×C4—44no—
129C22×C3×C4C4×D314yes—
130C22×C3×C4D1214yes—
131C22×C3×C4#6711yescharacteristic
132C22×C3×C4#6712yes—
133C22×C3×C4C22×D311yescharacteristic
134C22×C3×C4C22×D312yes—
135C2×#67—68no—
136C2×#67—64no—
137C22×Dic3—61no—
138#235—316no—
139#235—616no—
140#235—68no—
141C2×D12—34no—
142C2×D12—32no—
143C2×D12—62no—
144C2×D12—61no—
145C2×C4×D3—68no—
146C2×C4×D3—64no—
147C2×Dic6—34no—
148C2×Dic6—32no—
149C2×Dic6—62no—
150C2×Dic6—61no—
151C3×C4⋊C4—22no—
152C3×C4⋊C4—24no—
153C3×C4⋊C4C22×D314yes—
154#208—68no—
155C2×C3⋊C8—34no—
156C2×C3⋊C8—64no—
157C22×C9—22no—
158C22×C9—22no—
159C22×C9—28no—
160C22×C9C2×C22⋊C414yes—
161C22×C9C2×C22⋊C412yes—
162C22×C9AGL(1,ℤ/8)12yes—
163C22×C9#13712yes—
164C22×C9C22×D411yescharacteristic
165C2×D9—24no—
166C2×D9—42no—
167C2×D9—42no—
168C2×D9—48no—
169C4×C9—44no—
170C4×C9C2×C22⋊C412yes—
171C4×C9C2×C22⋊C414yes—
172C4×C9C23×C411yescharacteristic
173C4×C9C22×D411yescharacteristic
174Dic9—24no—
175C2×#41—98no—
176C2×#41—94no—
177C2×#41—184no—
178C2×#41—182no—
179C22×Q8—91no—
180C22×D4—91no—
181C22×D4—181no—
182C23×C4—21no—
183C23×C4—181no—
184C23×C4C2×D911yescharacteristic
185C2×M16—94no—
186C2×M16—184no—
187C22×C8—92no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C2×D912yes—
191C2×C4⋊C4C2×D914yescomplemented
192#103—98no—
193#102—98no—
194C23×C3—22no—
195C23×C3—22no—
196C23×C3(C2×D3)⋊C414yes—
197C23×C3C2×#6712yes—
198C23×C3C2×#6711yescharacteristic
199C22×D3—64no—
200C22×D3—62no—
201C22×D3—122no—
202C22×D3—122no—
203C2×C3×C4—24no—
204C2×C3×C4—48no—
205C2×C3×C4—44no—
206C2×C3×C4(C2×D3)⋊C414yes—
207C2×C3×C4(C2×D3)⋊C418yes—
208C2×C3×C4C2×C4×D312yes—
209C2×C3×C4C2×C4×D314yes—
210C2×C3×C4C2×D1212yes—
211C2×C3×C4C2×D1214yes—
212C2×C3×C4C2×#6711yescharacteristic
213C2×C3×C4C2×#6712yes—
214C2×C3×C4C23×D311yescharacteristic
215#67—616no—
216C2×Dic3—64no—
217C2×Dic3—62no—
218D12—34no—
219D12—64no—
220D12—62no—
221C4×D3—616no—
222Dic6—34no—
223Dic6—64no—
224Dic6—62no—
225C3⋊C8—64no—
226C2×C9—24no—
227C2×C9#41714yescomplemented
228C2×C9C22×C22⋊C411yescharacteristic
229C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
230C2×C9C2×#13711yescharacteristic
231D9—44no—
232C24—181no—
233C24#61111yescharacteristic
234#41—916no—
235#41—1816no—
236#41—188no—
237C2×Q8—94no—
238C2×Q8—92no—
239C2×Q8—182no—
240C2×Q8—181no—
241C2×D4—94no—
242C2×D4—92no—
243C2×D4—188no—
244C2×D4—184no—
245C2×D4—182no—
246C2×D4—181no—
247C22×C4—24no—
248C22×C4—22no—
249C22×C4—44no—
250C22×C4—181no—
251C22×C4—188no—
252C22×C4—184no—
253C22×C4C4×D914yes—
254C22×C4D3614yes—
255C22×C4#61112yes—
256C22×C4#61111yescharacteristic
257C22×C4C22×D912yes—
258C22×C4C22×D911yescharacteristic
259M16—188no—
260C2×C8—94no—
261C2×C8—184no—
262C4⋊C4—22no—
263C4⋊C4—24no—
264C4⋊C4C22×D914yes—
265C22×C3—28no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3C2×(C2×D3)⋊C414yes—
269C22×C3C2×(C2×D3)⋊C412yes—
270C22×C3#93212yes—
271C22×C3#94212yes—
272C22×C3C22×#6711yescharacteristic
273C2×D3—64no—
274C2×D3—128no—
275C2×D3—122no—
276C2×D3—122no—
277C3×C4—44no—
278C3×C4C2×(C2×D3)⋊C412yes—
279C3×C4C2×(C2×D3)⋊C414yes—
280C3×C4C22×C4×D311yescharacteristic
281C3×C4C22×D1211yescharacteristic
282Dic3—64no—
283C9C2×#41711yescharacteristic, complemented, Sylow
284C23—22no—
285C23—22no—
286C23—184no—
287C23—182no—
288C23—362no—
289C23—362no—
290C23(C2×D9)⋊C414yes—
291C23C2×#61112yes—
292C23C2×#61111yescharacteristic
293Q8—94no—
294Q8—184no—
295Q8—182no—
296D4—94no—
297D4—1816no—
298D4—184no—
299D4—182no—
300C2×C4—24no—
301C2×C4—48no—
302C2×C4—44no—
303C2×C4—184no—
304C2×C4—182no—
305C2×C4—1816no—
306C2×C4(C2×D9)⋊C414yes—
307C2×C4(C2×D9)⋊C418yes—
308C2×C4C2×C4×D912yes—
309C2×C4C2×C4×D914yes—
310C2×C4C2×D3612yes—
311C2×C4C2×D3614yes—
312C2×C4C2×#61112yes—
313C2×C4C2×#61111yescharacteristic
314C2×C4C23×D911yescharacteristic
315C8—184no—
316C2×C3—24no—
317C2×C3#496614yes—
318C2×C3C22×(C2×D3)⋊C411yescharacteristic
319C2×C3C2×#93211yescharacteristic
320C2×C3C2×#94211yescharacteristic
321D3—124no—
322C22—22no—
323C22—22no—
324C22—28no—
325C22—184no—
326C22—362no—
327C22—362no—
328C22—368no—
329C22C2×(C2×D9)⋊C414yes—
330C22C2×(C2×D9)⋊C412yes—
331C22#6349512yes—
332C22#6350512yes—
333C22C22×#61111yescharacteristic
334C4—44no—
335C4—184no—
336C4C2×(C2×D9)⋊C414yes—
337C4C2×(C2×D9)⋊C412yes—
338C4C22×C4×D911yescharacteristic
339C4C22×D3611yescharacteristic
340C3C2×#496611yescharacteristic
341C2—24no—
342C2—364no—
343C2#1058864914yesdirect product factor
344C2C22×(C2×D9)⋊C411yescharacteristic
345C2C2×#6349511yescharacteristic
346C2C2×#6350511yescharacteristic
subgroupG/H
centerC23C2×#611
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC22×C9×C4⋊C4C2
socleC23×C3C2×#67
prime radicalC22×#3697C2
cosocleC2×C4×C9C24
hypercenterC22×C4⋊C4D9
hypocenterC9C2×#417
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C9×C4⋊C4C2semidirect
3. C22×#3667C2semidirect
4. #10588649C2direct (N × H)
5. C2×#63369C2semidirect
6. C2×#63368C2semidirect
13. C2×#3697C4semidirect
21. C2×C9×C4⋊C4C22semidirect
23. C2×#3667C22semidirect
25. #63369C22semidirect
26. #63368C22semidirect
49. #3697C2×C4semidirect
52. C2×D36C2×C4semidirect
58. C2×Dic18C2×C4semidirect
112. D36C22×C4semidirect
116. Dic18C22×C4semidirect
120. C22×C4⋊C4D9semidirect
191. C2×C4⋊C4C2×D9semidirect
227. C2×C9#417semidirect
283. C9C2×#417semidirect
343. C2#10588649direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#36972
C22×C9×C4⋊C42
C22×#36672
#105886492
C2×#633692
C2×#633682
C2×#49663