Finite Group Databasebeta

← #13072202

Subgroups — #13072202

Order 1408.

832 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66948C211yesmaximal, characteristic, complemented
2C2×#66948C211yesmaximal, characteristic, complemented
3C2×#66948C212yesmaximal, complemented
4C2×#66946C211yesmaximal, characteristic, complemented
5C2×#66927C211yesmaximal, characteristic, complemented
6C11×#389C211yesmaximal, characteristic, complemented
7#10622604C212yesmaximal, complemented
8#10622601C211yesmaximal, characteristic, complemented
9C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
10#10622284C212yesmaximal, complemented
11#10622278C212yesmaximal, complemented
12C22×D44C2211yescharacteristic
13C22×D44C2212yes—
14C22×D44C2212yes—
15C22×D44C2212yes—
16C22×D44C2212yes—
17C22×D44C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C22×C4×D11C2212yes—
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2212yes—
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C42×C11C2211yescharacteristic
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2212yes—
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×C4×Dic11C2211yescharacteristic
32#66948—24no—
33#66948—24no—
34#66948—28no—
35#66946—24no—
36#66927—24no—
37C11×#95C2212yes—
38C11⋊#95C2211yescharacteristic
39C11⋊#95C2211yescharacteristic
40C23×D11C2312yes—
41C23×D11C2312yes—
42C23×D11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2312yes—
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2311yescharacteristic
50C22×Dic11C2311yescharacteristic
51C2×D44—24no—
52C2×D44—24no—
53C2×D44—24no—
54C2×D44—24no—
55C2×D44—24no—
56C2×D44—22no—
57C2×D44—22no—
58C2×D44—24no—
59C2×D44—22no—
60C2×D44—24no—
61C2×D44—22no—
62C2×D44—24no—
63C2×D44—22no—
64C2×D44—42no—
65C2×D44—42no—
66C2×D44—42no—
67C2×D44—42no—
68C2×D44D414yescomplemented
69C2×C4×D11—24no—
70C2×C4×D11—24no—
71C2×C4×D11—22no—
72C2×C4×D11—22no—
73C2×C4×D11—22no—
74C2×C4×D11—42no—
75C11×C4⋊C4—24no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4D414yescomplemented
78C42×C11—22no—
79(C2×D11)⋊C4—24no—
80(C2×D11)⋊C4—24no—
81(C2×D11)⋊C4—24no—
82(C2×D11)⋊C4—24no—
83(C2×D11)⋊C4—22no—
84(C2×D11)⋊C4—42no—
85(C2×D11)⋊C4D414yescomplemented
86C4×Dic11—22no—
87#2428—111nomaximal, Sylow
88C23×C11C2411yescharacteristic
89C22×D11—22no—
90C22×D11—21no—
91C22×D11—21no—
92C22×D11—22no—
93C22×D11—21no—
94C22×D11—21no—
95C22×D11—22no—
96C22×D11—22no—
97C22×D11—22no—
98C22×D11—21no—
99C22×D11—22no—
100C22×D11—21no—
101C22×D11—22no—
102C22×D11—22no—
103C22×D11—22no—
104C22×D11—22no—
105C22×D11—22no—
106C22×D11—22no—
107C22×D11—22no—
108C22×D11C2×D414yes—
109C22×D11C2×D412yes—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11C2×D414yes—
120C2×C4×C11C2×D412yes—
121C2×C4×C11C2×D412yes—
122C2×C4×C11C2×D412yes—
123C2×C4×C11#4112yes—
124C2×C4×C11#4112yes—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11C2×D412yes—
134D44—28no—
135D44—48no—
136D44—48no—
137D44—48no—
138D44—48no—
139D44—44no—
140C4×D11—48no—
141C4×D11—44no—
142C2×#127—111no—
143C2×#121—112no—
144C2×#121—111no—
145C2×#121—111no—
146C2×C4×D4—111no—
147#394—112no—
148#392—112no—
149#390—111no—
150#389D1111yescharacteristic, complemented
151#386—112no—
152C4×C22⋊C4—111no—
153C22×C11C22×D411yescharacteristic
154C22×C11C22×D411yescharacteristic
155C22×C11C22×D411yescharacteristic
156C22×C11C2×#4111yescharacteristic
157C22×C11C2×#4111yescharacteristic
158C22×C11H(5,𝔽2)11yescharacteristic
159C22×C11H(5,𝔽2)11yescharacteristic
160C2×D11—24no—
161C2×D11—22no—
162C2×D11—22no—
163C2×D11—24no—
164C2×D11—22no—
165C2×D11—24no—
166C2×D11—41no—
167C2×D11—42no—
168C2×D11—41no—
169C2×D11—42no—
170C2×D11—42no—
171C2×D11—41no—
172C2×D11—42no—
173C2×D11—41no—
174C2×D11—42no—
175C2×D11—42no—
176C2×D11—42no—
177C2×D11—42no—
178C2×D11—42no—
179C2×D11—42no—
180C2×D11—42no—
181C4×C11—24no—
182C4×C11—22no—
183C4×C11—22no—
184C4×C11—42no—
185C4×C11#12114yescomplemented
186Dic11—22no—
187Dic11—41no—
188Dic11—41no—
189C22×D4—111no—
190C22×D4—111no—
191C22×D4—112no—
192C22×D4—112no—
193C22×D4—112no—
194C22×D4—112no—
195C23×C4—111no—
196C23×C4—112no—
197#127—224no—
198#121—228no—
199#121—224no—
200#121—224no—
201C4×D4—224no—
202C2×C4⋊C4C2×D1111yescharacteristic
203C2×C4⋊C4C2×D1112yes—
204C2×C4⋊C4C2×D1111yescharacteristic
205C2×C22⋊C4—111no—
206C2×C22⋊C4—112no—
207C2×C22⋊C4—112no—
208C2×C22⋊C4—112no—
209C2×C22⋊C4—112no—
210C2×C22⋊C4—111no—
211C2×C22⋊C4—112no—
212C2×C42—111no—
213C2×C42C2×D1111yescharacteristic
214#95—111no—
215#95—111no—
216#95C2×D1112yes—
217C2×C11C2×#12111yescharacteristic
218C2×C11#53211yescharacteristic
219C2×C11#54011yescharacteristic
220C2×C11D4211yescharacteristic
221C2×C11D4211yescharacteristic
222C2×C11#54611yescharacteristic
223C2×C11#55011yescharacteristic
224D11—44no—
225D11—42no—
226D11—82no—
227C24—111no—
228C24—112no—
229C24—112no—
230C2×D4—114no—
231C2×D4—224no—
232C2×D4—224no—
233C2×D4—224no—
234C2×D4—224no—
235C2×D4—224no—
236C2×D4—222no—
237C2×D4—224no—
238C2×D4—222no—
239C2×D4—224no—
240C2×D4—222no—
241C2×D4—222no—
242C2×D4—224no—
243C2×D4—222no—
244C2×D4—442no—
245C2×D4—442no—
246C2×D4—442no—
247C2×D4—442no—
248C22×C4—111no—
249C22×C4—111no—
250C22×C4—111no—
251C22×C4—224no—
252C22×C4—224no—
253C22×C4—222no—
254C22×C4—222no—
255C22×C4—222no—
256C22×C4—442no—
257C22×C4C22×D1112yes—
258C22×C4C22×D1112yes—
259C22×C4C22×D1111yescharacteristic
260C22×C4C22×D1111yescharacteristic
261C22×C4C22×D1111yescharacteristic
262C4⋊C4—24no—
263C4⋊C4—22no—
264C4⋊C4D4414yescomplemented
265C22⋊C4—114no—
266C22⋊C4—224no—
267C22⋊C4—224no—
268C22⋊C4—224no—
269C22⋊C4—224no—
270C22⋊C4—222no—
271C22⋊C4—442no—
272C42—22no—
273C42—222no—
274C11#242811yescharacteristic, complemented, Sylow
275C23—112no—
276C23—114no—
277C23—222no—
278C23—221no—
279C23—222no—
280C23—221no—
281C23—221no—
282C23—221no—
283C23—222no—
284C23—222no—
285C23—222no—
286C23—221no—
287C23—222no—
288C23—221no—
289C23—222no—
290C23—222no—
291C23—222no—
292C23—222no—
293C23—222no—
294C23—222no—
295C23—222no—
296C23C23×D1111yescharacteristic
297D4—228no—
298D4—448no—
299D4—448no—
300D4—448no—
301D4—448no—
302D4—444no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—112no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—448no—
322C2×C4—444no—
323C2×C4C2×D4414yes—
324C2×C4C2×D4412yes—
325C2×C4D4×D1112yes—
326C2×C4D4×D1112yes—
327C2×C4#434312yes—
328C2×C4#434312yes—
329C22—222no—
330C22—224no—
331C22—222no—
332C22—224no—
333C22—222no—
334C22—224no—
335C22—442no—
336C22—441no—
337C22—442no—
338C22—442no—
339C22—441no—
340C22—441no—
341C22—441no—
342C22—442no—
343C22—442no—
344C22—442no—
345C22—442no—
346C22—442no—
347C22—442no—
348C22—442no—
349C22—442no—
350C22C22×D4411yescharacteristic
351C22C2×D4×D1111yescharacteristic
352C22C2×D4×D1111yescharacteristic
353C22C2×#434311yescharacteristic
354C22C2×#434311yescharacteristic
355C22#6704211yescharacteristic
356C22#6704211yescharacteristic
357C4—24no—
358C4—22no—
359C4—22no—
360C4—42no—
361C4—222no—
362C4—441no—
363C4—441no—
364C4#6694814yescomplemented
365C2—442no—
366C2—444no—
367C2—882no—
368C2C2×#6694811yescharacteristic
369C2D4×D4411yescharacteristic
370C2#1062310811yescharacteristic
371C2#1062314011yescharacteristic
372C2#1062316111yescharacteristic
373C2#1062322911yescharacteristic
374C2#1062325611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#389C2
hypercenter#389D11
hypocenterC11#2428
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#66948C2semidirect
2. C2×#66948C2semidirect
3. C2×#66948C2semidirect
4. C2×#66946C2semidirect
5. C2×#66927C2semidirect
6. C11×#389C2semidirect
7. #10622604C2semidirect
8. #10622601C2semidirect
9. C4×(C2×D11)⋊C4C2semidirect
10. #10622284C2semidirect
11. #10622278C2semidirect
68. C2×D44D4semidirect
77. C11×C4⋊C4D4semidirect
85. (C2×D11)⋊C4D4semidirect
150. #389D11semidirect
185. C4×C11#121semidirect
264. C4⋊C4D44semidirect
274. C11#2428semidirect
364. C4#66948semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×#669462
C2×#669272
C11×#3892
#106226042
#106226012
C4×(C2×D11)⋊C42
#106222842
#106222782
#242811