Finite Group Databasebeta

← #13072032

Subgroups — #13072032

Order 1408.

704 conjugacy classes of subgroups.

The subgroup lattice has 364 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×#66945C211yesmaximal, characteristic, complemented
4C2×C4×D44C211yesmaximal, characteristic, complemented
5C11×#389C211yesmaximal, characteristic, complemented
6#10622604C212yesmaximal, complemented
7#10622601C212yesmaximal, complemented
8#10622600C211yesmaximal, characteristic, complemented
9#10622552C211yesmaximal, characteristic, complemented
10#10622284C212yesmaximal, complemented
11#10622283C212yesmaximal, complemented
12C22×D44C2211yescharacteristic
13C22×D44C2211yescharacteristic
14C22×D44C2212yes—
15C22×D44C2212yes—
16C22×C4×D11C2211yescharacteristic
17C22×C4×D11C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C4⋊C4C2212yes—
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C42×C11C2211yescharacteristic
22C2×(C2×D11)⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×(C2×D11)⋊C4C2212yes—
29C2×(C2×D11)⋊C4C2212yes—
30C2×C4⋊Dic11C2211yescharacteristic
31C2×C4⋊Dic11C2211yescharacteristic
32C2×C4×Dic11C2212yes—
33#66948—24no—
34#66948—24no—
35#66945—24no—
36C4×D44—24no—
37C11×#95C2212yes—
38C11⋊#95C2212yes—
39C23×D11C2312yes—
40C23×D11C2311yescharacteristic
41C23×D11C2311yescharacteristic
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2312yes—
45C22×C4×C11C2311yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C22×Dic11C2312yes—
49C22×Dic11C2311yescharacteristic
50C2×D44—22no—
51C2×D44—24no—
52C2×D44—22no—
53C2×D44—24no—
54C2×D44—24no—
55C2×D44—22no—
56C2×D44—22no—
57C2×D44—22no—
58C2×D44—22no—
59C2×D44—42no—
60C2×D44—42no—
61C2×D44—42no—
62C2×C4×D11—22no—
63C2×C4×D11—22no—
64C2×C4×D11—22no—
65C2×C4×D11—22no—
66C2×C4×D11—22no—
67C2×C4×D11D414yescomplemented
68C11×C4⋊C4—22no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4D414yescomplemented
71C42×C11—22no—
72(C2×D11)⋊C4—22no—
73(C2×D11)⋊C4—24no—
74(C2×D11)⋊C4—22no—
75(C2×D11)⋊C4—24no—
76(C2×D11)⋊C4—24no—
77(C2×D11)⋊C4—24no—
78(C2×D11)⋊C4—42no—
79(C2×D11)⋊C4—42no—
80C4⋊Dic11—22no—
81C4⋊Dic11—22no—
82C4×Dic11—24no—
83#2414—111nomaximal, Sylow
84C23×C11C2411yescharacteristic
85C22×D11—21no—
86C22×D11—21no—
87C22×D11—21no—
88C22×D11—21no—
89C22×D11—21no—
90C22×D11—21no—
91C22×D11—21no—
92C22×D11—21no—
93C22×D11—21no—
94C22×D11—21no—
95C22×D11—21no—
96C22×D11—21no—
97C22×D11—22no—
98C22×D11—22no—
99C22×D11—22no—
100C22×D11—22no—
101C22×D11—22no—
102C22×D11—22no—
103C22×D11—22no—
104C22×D11C2×D412yes—
105C22×D11#4112yes—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—21no—
111C2×C4×C11—22no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11C2×D414yes—
117C2×C4×C11C2×D412yes—
118C2×C4×C11C2×D412yes—
119C2×C4×C11#4112yes—
120C2×C4×C11#4112yes—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—22no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—22no—
127C2×Dic11—21no—
128C2×Dic11—22no—
129C2×Dic11C2×D412yes—
130D44—28no—
131D44—48no—
132D44—48no—
133D44—44no—
134C4×D11—28no—
135C4×D11—44no—
136C2×#121—111no—
137C2×#121—111no—
138C2×C4×D4—111no—
139C2×#117—111no—
140#394—112no—
141#392—112no—
142#390—112no—
143#390—111no—
144#389D1111yescharacteristic, complemented
145#388—112no—
146#380—111no—
147C22×C11C22×D411yescharacteristic
148C22×C11C22×D411yescharacteristic
149C22×C11C2×#4111yescharacteristic
150C22×C11C2×#4111yescharacteristic
151C22×C11C2×#4111yescharacteristic
152C22×C11H(5,𝔽2)11yescharacteristic
153C22×C11H(5,𝔽2)11yescharacteristic
154C2×D11—22no—
155C2×D11—22no—
156C2×D11—22no—
157C2×D11—22no—
158C2×D11—22no—
159C2×D11—22no—
160C2×D11—41no—
161C2×D11—41no—
162C2×D11—41no—
163C2×D11—41no—
164C2×D11—41no—
165C2×D11—41no—
166C2×D11—41no—
167C2×D11—41no—
168C2×D11—42no—
169C2×D11—42no—
170C2×D11—42no—
171C2×D11—42no—
172C2×D11—42no—
173C2×D11—42no—
174C2×D11—42no—
175C4×C11—22no—
176C4×C11—24no—
177C4×C11—41no—
178C4×C11—42no—
179C4×C11#12114yes—
180Dic11—22no—
181Dic11—41no—
182Dic11—42no—
183C22×D4—111no—
184C22×D4—111no—
185C22×D4—112no—
186C22×D4—112no—
187C23×C4—111no—
188C23×C4—111no—
189#121—224no—
190#121—224no—
191C4×D4—224no—
192#117—224no—
193C2×C4⋊C4—111no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4C2×D1111yescharacteristic
196C2×C4⋊C4C2×D1112yes—
197C2×C4⋊C4C2×D1111yescharacteristic
198C2×C22⋊C4—112no—
199C2×C22⋊C4—111no—
200C2×C22⋊C4—111no—
201C2×C22⋊C4—112no—
202C2×C22⋊C4—112no—
203C2×C22⋊C4—112no—
204C2×C22⋊C4—112no—
205C2×C22⋊C4—112no—
206C2×C42—112no—
207C2×C42C2×D1111yescharacteristic
208#95—112no—
209#95C2×D1112yes—
210C2×C11C2×#12111yescharacteristic
211C2×C11#52511yescharacteristic
212C2×C11#53511yescharacteristic
213C2×C11#54611yescharacteristic
214C2×C11#55011yescharacteristic
215C2×C11#55311yescharacteristic
216C2×C11#55511yescharacteristic
217D11—42no—
218D11—42no—
219D11—82no—
220C24—111no—
221C24—111no—
222C24—112no—
223C2×D4—222no—
224C2×D4—222no—
225C2×D4—224no—
226C2×D4—224no—
227C2×D4—224no—
228C2×D4—222no—
229C2×D4—222no—
230C2×D4—222no—
231C2×D4—222no—
232C2×D4—442no—
233C2×D4—442no—
234C2×D4—442no—
235C22×C4—111no—
236C22×C4—114no—
237C22×C4—111no—
238C22×C4—112no—
239C22×C4—222no—
240C22×C4—222no—
241C22×C4—222no—
242C22×C4—222no—
243C22×C4—222no—
244C22×C4C22×D1112yes—
245C22×C4C22×D1111yescharacteristic
246C22×C4C22×D1112yes—
247C22×C4C22×D1111yescharacteristic
248C22×C4C22×D1111yescharacteristic
249C4⋊C4—22no—
250C4⋊C4—42no—
251C4⋊C4—222no—
252C4⋊C4—222no—
253C4⋊C4D4414yescomplemented
254C22⋊C4—222no—
255C22⋊C4—224no—
256C22⋊C4—222no—
257C22⋊C4—224no—
258C22⋊C4—224no—
259C22⋊C4—224no—
260C22⋊C4—442no—
261C22⋊C4—442no—
262C42—22no—
263C42—224no—
264C11#241411yescharacteristic, complemented, Sylow
265C23—112no—
266C23—112no—
267C23—221no—
268C23—221no—
269C23—221no—
270C23—221no—
271C23—221no—
272C23—221no—
273C23—221no—
274C23—221no—
275C23—221no—
276C23—221no—
277C23—221no—
278C23—221no—
279C23—222no—
280C23—222no—
281C23—222no—
282C23—222no—
283C23—222no—
284C23—222no—
285C23—222no—
286C23C23×D1111yescharacteristic
287D4—228no—
288D4—448no—
289D4—448no—
290D4—444no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—112no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—228no—
305C2×C4—222no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—222no—
309C2×C4—221no—
310C2×C4—222no—
311C2×C4—444no—
312C2×C4C2×D4414yes—
313C2×C4C2×D4412yes—
314C2×C4D4×D1112yes—
315C2×C4#434312yes—
316C2×C4#434312yes—
317C22—222no—
318C22—222no—
319C22—222no—
320C22—222no—
321C22—222no—
322C22—222no—
323C22—441no—
324C22—441no—
325C22—441no—
326C22—441no—
327C22—441no—
328C22—441no—
329C22—441no—
330C22—441no—
331C22—442no—
332C22—442no—
333C22—442no—
334C22—442no—
335C22—442no—
336C22—442no—
337C22—442no—
338C22C22×D4411yescharacteristic
339C22C2×D4×D1111yescharacteristic
340C22#6703711yescharacteristic
341C22C2×#434311yescharacteristic
342C22C2×#434311yescharacteristic
343C22#41×D1111yescharacteristic
344C22#6704211yescharacteristic
345C4—24no—
346C4—22no—
347C4—42no—
348C4—41no—
349C4—222no—
350C4—441no—
351C4—442no—
352C4#6694814yes—
353C2—442no—
354C2—442no—
355C2—882no—
356C2C2×#6694811yescharacteristic
357C2#1062308511yescharacteristic
358C2#1062310811yescharacteristic
359C2#1062313811yescharacteristic
360C2#1062315811yescharacteristic
361C2#1062322611yescharacteristic
362C2#1062326511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#389C2
hypercenter#389D11
hypocenterC11#2414
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×#66945C2semidirect
4. C2×C4×D44C2semidirect
5. C11×#389C2semidirect
6. #10622604C2semidirect
7. #10622601C2semidirect
8. #10622600C2semidirect
9. #10622552C2semidirect
10. #10622284C2semidirect
11. #10622283C2semidirect
67. C2×C4×D11D4semidirect
70. C11×C4⋊C4D4semidirect
144. #389D11semidirect
253. C4⋊C4D44semidirect
264. C11#2414semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×#669452
C2×C4×D442
C11×#3892
#106226042
#106226012
#106226002
#106225522
#106222842
#106222832
#241411