Finite Group Databasebeta

← #13077832

Subgroups — #13077832

Order 1408.

764 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4339C211yesmaximal, characteristic, complemented
2C11×#525C211yesmaximal, characteristic, complemented
3C2×#67003C212yesmaximal, complemented
4C2×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
5#10622663C211yesmaximal, characteristic, complemented
6#10622660C212yesmaximal, complemented
7#10622659C211yesmaximal, characteristic, complemented
8#10622653C211yesmaximal, characteristic, complemented
9#10622650C212yesmaximal, complemented
10#10622649C211yesmaximal, characteristic, complemented
11#10622615C212yesmaximal, complemented
12C2×C11×#41C2211yescharacteristic, complemented
13C23×C4×C11C2211yescharacteristic
14C22×C22⋊D11—21no—
15C2×#4339—21no—
16C2×#4339—21no—
17C2×#4339—28no—
18C2×#4339C2212yes—
19C2×#4339C2212yes—
20C22×D44C2211yescharacteristic
21C22×C4×D11—21no—
22C22×Dic22C2211yescharacteristic
23C11×#123—21no—
24C11×C22⋊Q8C2211yescharacteristic
25C11×C22⋊Q8C2211yescharacteristic, complemented
26C11×#121C2211yescharacteristic
27C11×#121C2211yescharacteristic, complemented
28C11×#120—21no—
29C4×D4×C11—21no—
30C4×D4×C11—21no—
31C11×#117C2211yescharacteristic, complemented
32#67003—28no—
33C2×#4326C2212yescomplemented
34C2×#4325C2212yescomplemented
35C2×#4324C2212yescomplemented
36C2×#4323C2212yescomplemented
37C22×C11⋊C8C2212yescomplemented
38C22⋊(C11⋊C8)C2211yescharacteristic
39C22⋊(C11⋊C8)C2211yescharacteristic
40C22⋊(C11⋊C8)C2212yescomplemented
41#66874C2212yescomplemented
42#66874C2212yescomplemented
43#66873C2212yescomplemented
44#66873C2212yescomplemented
45C24×C11D411yescharacteristic
46C23×D11—21no—
47C11×#41—24no—
48C2×Q8×C11C2311yescharacteristic
49C2×D4×C11—21no—
50C2×D4×C11—21no—
51C2×D4×C11—21no—
52C2×D4×C11C2311yescharacteristic
53C22×C4×C11—24no—
54C22×C4×C11—21no—
55C22×C4×C11D411yescharacteristic
56C22×C4×C11D411yescharacteristic
57C22×C4×C11D411yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C2×C22⋊D11—28no—
62C2×C22⋊D11—22no—
63C2×C22⋊D11—22no—
64C22×Dic11—21no—
65#4339—28no—
66#4339—28no—
67#4339—24no—
68#4339—24no—
69#4339—24no—
70#4339D418yescomplemented
71C2×D44—24no—
72C2×D44—21no—
73C2×D44C2312yes—
74C2×C4×D11—28no—
75C2×C4×D11—22no—
76C2×C4×D11—22no—
77C2×Dic22—24no—
78C2×Dic22—21no—
79C2×Dic22C2312yes—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C22⋊C4—21no—
85C11×C22⋊C4—21no—
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C11×C22⋊C4—21no—
89C42×C11—21no—
90#4326—24no—
91#4325—24no—
92#4324—24no—
93#4323—24no—
94C2×C11⋊C8—24no—
95C2×C11⋊C8C2312yes—
96C2×C11⋊C8C2312yes—
97#3002—111nomaximal, Sylow
98C23×C11—22no—
99C23×C11—22no—
100C23×C11—21no—
101C23×C11—41no—
102C23×C11C2×D411yescharacteristic
103C23×C11C2×D411yescharacteristic
104C23×C11C2×D411yescharacteristic
105C22×D11—24no—
106C22×D11—22no—
107C22×D11—42no—
108C22×D11—42no—
109Q8×C11—22no—
110D4×C11—22no—
111D4×C11—42no—
112D4×C11—42no—
113D4×C11—42no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—42no—
123C2×C4×C11C2×D414yes—
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C22⋊D11—28no—
129C22⋊D11—28no—
130C2×Dic11—24no—
131C2×Dic11—22no—
132D44—24no—
133D44—22no—
134D44C2×D414yes—
135C4×D11—28no—
136C4×D11—28no—
137Dic22—24no—
138Dic22—22no—
139Dic22C2×D414yes—
140C11⋊C8—22no—
141C11⋊C8—22no—
142C22×#41—111no—
143C2×#135—112no—
144#525D1111yescharacteristic, complemented
145#452—112no—
146#451—111no—
147#450—111no—
148#449—112no—
149#448—111no—
150#447—111no—
151#416—112no—
152C2×C22⋊C8—111no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—44no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11#12012yes—
165C22×C11#13512yescomplemented
166C22×C11C22×D411yescharacteristic
167C2×D11—24no—
168C2×D11—48no—
169C2×D11—42no—
170C2×D11—42no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11#12012yes—
177C4×C11C22×D412yes—
178Dic11—24no—
179C2×#41—112no—
180C2×#41—112no—
181C2×#41—228no—
182C2×#41—221no—
183C2×#41—221no—
184C2×#41C2×D1111yescharacteristic, complemented
185C22×Q8—111no—
186C22×D4—111no—
187C22×D4—221no—
188C23×C4—221no—
189C23×C4C2×D1111yescharacteristic
190#135—228no—
191C2×Q16—112no—
192C2×SD16—112no—
193C2×SD16—112no—
194C2×D8—112no—
195C22×C8—112no—
196#123—21no—
197C22⋊Q8C2×D1111yescharacteristic
198C22⋊Q8C2×D1111yescharacteristic, complemented
199#121C2×D1111yescharacteristic
200#121C2×D1111yescharacteristic, complemented
201#120—21no—
202C4×D4—21no—
203C4×D4—21no—
204#117C2×D1111yescharacteristic, complemented
205#103—112no—
206#103—112no—
207#102—112no—
208#102—112no—
209C22⋊C8—111no—
210C22⋊C8—111no—
211C22⋊C8—112no—
212C2×C11—22no—
213C2×C11—22no—
214C2×C11—41no—
215C2×C11—81no—
216C2×C11C2×#12011yescharacteristic
217C2×C11C2×#13511yescharacteristic
218C2×C11#57511yescharacteristic
219D11—44no—
220C24—221no—
221C24C22⋊D1111yescharacteristic
222#41—24no—
223#41—118no—
224#41—224no—
225#41—224no—
226#41—228no—
227#41—228no—
228#41—224no—
229C2×Q8—112no—
230C2×Q8—224no—
231C2×Q8—221no—
232C2×Q8C22×D1111yescharacteristic
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—112no—
237C2×D4—224no—
238C2×D4—228no—
239C2×D4—222no—
240C2×D4—222no—
241C2×D4—221no—
242C2×D4C22×D1111yescharacteristic
243C22×C4—24no—
244C22×C4—21no—
245C22×C4—228no—
246C22×C4—221no—
247C22×C4—222no—
248C22×C4—222no—
249C22×C4C22⋊D1111yescharacteristic
250C22×C4C22⋊D1111yescharacteristic
251C22×C4C22⋊D1111yescharacteristic
252C22×C4C22×D1111yescharacteristic
253C22×C4C22×D1111yescharacteristic
254C22×C4C22×D1111yescharacteristic
255Q16—224no—
256SD16—224no—
257SD16—224no—
258D8—224no—
259C2×C8—112no—
260C2×C8—112no—
261C2×C8—224no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4C22×D1111yescharacteristic
265C4⋊C4C22×D1111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C42—21no—
272C11#300211yescharacteristic, complemented, Sylow
273C23—22no—
274C23—22no—
275C23—21no—
276C23—41no—
277C23—224no—
278C23—222no—
279C23—442no—
280C23—442no—
281C23C2×C22⋊D1111yescharacteristic
282C23C2×C22⋊D1111yescharacteristic
283C23C2×C22⋊D1111yescharacteristic
284Q8—22no—
285Q8—114no—
286Q8—224no—
287Q8—222no—
288D4—22no—
289D4—42no—
290D4—42no—
291D4—42no—
292D4—114no—
293D4—224no—
294D4—228no—
295D4—228no—
296D4—222no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—228no—
307C2×C4—224no—
308C2×C4—222no—
309C2×C4—228no—
310C2×C4D4×D1114yes—
311C2×C4C2×C22⋊D1111yescharacteristic
312C2×C4C2×C22⋊D1111yescharacteristic
313C2×C4C2×C22⋊D1111yescharacteristic
314C2×C4C23×D1111yescharacteristic
315C8—222no—
316C8—222no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—44no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—224no—
329C22—448no—
330C22—442no—
331C22—442no—
332C22#6699012yes—
333C22#6700312yescomplemented
334C22C22×C22⋊D1111yescharacteristic
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—224no—
341C4#6699012yes—
342C4C2×D4×D1112yes—
343C2—22no—
344C2—22no—
345C2—41no—
346C2—81no—
347C2—444no—
348C2C2×#6699011yescharacteristic
349C2C2×#6700311yescharacteristic
350C2#1062335311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#525C2
socleC22×C11C22×D4
hypercenter#525D11
hypocenterC11#3002
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×#4339C2semidirect
2. C11×#525C2semidirect
3. C2×#67003C2semidirect
4. C2×C22⋊(C11⋊C8)C2semidirect
5. #10622663C2semidirect
6. #10622660C2semidirect
7. #10622659C2semidirect
8. #10622653C2semidirect
9. #10622650C2semidirect
10. #10622649C2semidirect
11. #10622615C2semidirect
12. C2×C11×#41C22semidirect
25. C11×C22⋊Q8C22semidirect
27. C11×#121C22semidirect
31. C11×#117C22semidirect
33. C2×#4326C22semidirect
34. C2×#4325C22semidirect
35. C2×#4324C22semidirect
36. C2×#4323C22semidirect
37. C22×C11⋊C8C22semidirect
40. C22⋊(C11⋊C8)C22semidirect
41. #66874C22semidirect
42. #66874C22semidirect
43. #66873C22semidirect
44. #66873C22semidirect
70. #4339D4semidirect
144. #525D11semidirect
165. C22×C11#135semidirect
184. C2×#41C2×D11semidirect
198. C22⋊Q8C2×D11semidirect
200. #121C2×D11semidirect
204. #117C2×D11semidirect
272. C11#3002semidirect
333. C22#67003semidirect

Maximal subgroups

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

subgroupindex
C22×#43392
C11×#5252
C2×#670032
C2×C22⋊(C11⋊C8)2
#106226632
#106226602
#106226592
#106226532
#106226502
#106226492
#106226152
#300211