Finite Group Databasebeta

← #13072059

Subgroups — #13072059

Order 1408.

788 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66991C211yesmaximal, characteristic, complemented
2C2×#66991C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4C2×#66937C212yesmaximal, complemented
5C2×C4×D44C211yesmaximal, characteristic, complemented
6C11×#390C211yesmaximal, characteristic, complemented
7#10622600C211yesmaximal, characteristic, complemented
8#10622572C212yesmaximal, complemented
9#10622569C212yesmaximal, complemented
10#10622561C212yesmaximal, complemented
11#10622541C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C22×C22⋊D11C2212yes—
14C22×C22⋊D11C2212yes—
15C22×D44C2211yescharacteristic
16C22×C4×D11C2211yescharacteristic
17C22×C4×D11C2212yes—
18C22×C4×D11C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2212yes—
21C2×C11×C22⋊C4C2212yes—
22C2×C42×C11C2211yescharacteristic
23C2×C22⋊Dic11C2212yes—
24C2×C22⋊Dic11C2212yes—
25#66991—24no—
26#66991—24no—
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2212yes—
30C2×C4⋊Dic11C2211yescharacteristic
31C2×C4⋊Dic11C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
33C2×Dic11⋊C4C2212yes—
34C2×Dic11⋊C4C2212yes—
35C4⋊C4×D11—24no—
36#66937—28no—
37C4×D44—24no—
38C11⋊#95C2212yes—
39C11⋊#95C2212yes—
40C24×C11C2312yes—
41C23×D11C2311yescharacteristic
42C23×D11C2311yescharacteristic
43C2×D4×C11—22no—
44C2×D4×C11—22no—
45C2×D4×C11—22no—
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2312yes—
48C22×C4×C11C2311yescharacteristic
49C22×C4×C11C2311yescharacteristic
50C2×C22⋊D11—24no—
51C2×C22⋊D11—24no—
52C2×C22⋊D11—24no—
53C2×C22⋊D11—24no—
54C2×C22⋊D11—24no—
55C2×C22⋊D11—42no—
56C22×Dic11C2312yes—
57C22×Dic11C2311yescharacteristic
58C22×Dic11C2312yes—
59C22×Dic11C2311yescharacteristic
60C2×D44—22no—
61C2×D44—22no—
62C2×D44D414yescomplemented
63C2×C4×D11—24no—
64C2×C4×D11—24no—
65C2×C4×D11—22no—
66C2×C4×D11—22no—
67C2×C4×D11—22no—
68C2×C4×D11—22no—
69C2×C4×D11—22no—
70C2×C4×D11—42no—
71C2×C4×D11D414yescomplemented
72C11×C4⋊C4—22no—
73C11×C22⋊C4—24no—
74C11×C22⋊C4—42no—
75C42×C11—22no—
76C22⋊Dic11—24no—
77C22⋊Dic11—24no—
78(C2×D11)⋊C4—22no—
79(C2×D11)⋊C4—22no—
80(C2×D11)⋊C4—24no—
81C4⋊Dic11—22no—
82C4⋊Dic11—22no—
83C4⋊Dic11D414yescomplemented
84Dic11⋊C4—24no—
85Dic11⋊C4—24no—
86#2416—111nomaximal, Sylow
87C23×C11—22no—
88C23×C11—22no—
89C23×C11—22no—
90C23×C11—22no—
91C23×C11—22no—
92C23×C11—22no—
93C23×C11—22no—
94C23×C11C2411yescharacteristic
95C22×D11—21no—
96C22×D11—21no—
97C22×D11—21no—
98C22×D11—21no—
99C22×D11—21no—
100C22×D11—21no—
101C22×D11—21no—
102C22×D11—21no—
103C22×D11—21no—
104C22×D11—21no—
105C22×D11C2×D412yes—
106C22×D11C2×D412yes—
107C22×D11C2×D412yes—
108C22×D11#4112yes—
109D4×C11—44no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—22no—
115C2×C4×C11—21no—
116C2×C4×C11—22no—
117C2×C4×C11—21no—
118C2×C4×C11C2×D412yes—
119C2×C4×C11C2×D412yes—
120C2×C4×C11C2×D412yes—
121C2×C4×C11#4112yes—
122C22⋊D11—48no—
123C22⋊D11—48no—
124C2×Dic11—21no—
125C2×Dic11—22no—
126C2×Dic11—21no—
127C2×Dic11—22no—
128C2×Dic11—22no—
129C2×Dic11—21no—
130C2×Dic11—22no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—22no—
134C2×Dic11C2×D414yes—
135C2×Dic11C2×D412yes—
136D44—28no—
137C4×D11—28no—
138C4×D11—48no—
139C4×D11—44no—
140C2×#121—111no—
141C2×#121—111no—
142C2×#121—112no—
143C2×C4×D4—111no—
144C22×C4⋊C4—111no—
145#396—112no—
146#394—112no—
147#390D1111yescharacteristic, complemented
148#389—111no—
149#386—112no—
150#380—111no—
151C22×C11—42no—
152C22×C11—42no—
153C22×C11—42no—
154C22×C11—42no—
155C22×C11—42no—
156C22×C11—42no—
157C22×C11—42no—
158C22×C11C22×D411yescharacteristic
159C22×C11C22×D411yescharacteristic
160C22×C11C22×D411yescharacteristic
161C22×C11C2×#4111yescharacteristic
162C22×C11C2×#4111yescharacteristic
163C22×C11H(5,𝔽2)11yescharacteristic
164C22×C112−1+411yescharacteristic
165C2×D11—22no—
166C2×D11—22no—
167C2×D11—22no—
168C2×D11—22no—
169C2×D11—22no—
170C2×D11—22no—
171C2×D11—22no—
172C2×D11—22no—
173C2×D11—22no—
174C2×D11—41no—
175C2×D11—41no—
176C2×D11—41no—
177C2×D11—41no—
178C2×D11#12114yescomplemented
179C4×C11—22no—
180C4×C11—41no—
181C4×C11—42no—
182C4×C11#12114yescomplemented
183Dic11—22no—
184Dic11—24no—
185Dic11—41no—
186Dic11—42no—
187C22×D4—112no—
188C22×D4—112no—
189C22×D4—111no—
190C22×D4C2×D1111yescharacteristic
191C23×C4—111no—
192C23×C4—111no—
193C23×C4—112no—
194#121—228no—
195#121—224no—
196#121—224no—
197C4×D4—224no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—112no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—112no—
203C2×C4⋊C4—224no—
204C2×C4⋊C4C2×D1111yescharacteristic
205C2×C22⋊C4—112no—
206C2×C22⋊C4—112no—
207C2×C22⋊C4—111no—
208C2×C22⋊C4—111no—
209C2×C22⋊C4—112no—
210C2×C22⋊C4C2×D1112yes—
211C2×C22⋊C4C2×D1112yes—
212C2×C42C2×D1111yescharacteristic
213#95—112no—
214#95—112no—
215C2×C11—82no—
216C2×C11C2×#12111yescharacteristic
217C2×C11C2×#12111yescharacteristic
218C2×C11#53711yescharacteristic
219C2×C11D4211yescharacteristic
220C2×C11#54711yescharacteristic
221C2×C11#54811yescharacteristic
222C2×C11#55311yescharacteristic
223D11—24no—
224D11—42no—
225C24—111no—
226C24—111no—
227C24C22×D1112yes—
228C2×D4—22no—
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—114no—
232C2×D4—222no—
233C2×D4—222no—
234C2×D4—224no—
235C2×D4—224no—
236C2×D4—224no—
237C2×D4—224no—
238C2×D4—224no—
239C2×D4—442no—
240C22×C4—112no—
241C22×C4—111no—
242C22×C4—114no—
243C22×C4—111no—
244C22×C4—112no—
245C22×C4—224no—
246C22×C4—224no—
247C22×C4—222no—
248C22×C4—222no—
249C22×C4—222no—
250C22×C4—222no—
251C22×C4—222no—
252C22×C4—442no—
253C22×C4C22×D1111yescharacteristic
254C22×C4C22×D1112yes—
255C22×C4C22×D1111yescharacteristic
256C22×C4C22×D1111yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—114no—
259C4⋊C4—224no—
260C4⋊C4—222no—
261C4⋊C4—224no—
262C4⋊C4—222no—
263C22⋊C4—24no—
264C22⋊C4—42no—
265C22⋊C4—222no—
266C22⋊C4—222no—
267C22⋊C4—224no—
268C22⋊C4—224no—
269C22⋊C4—224no—
270C42—22no—
271C11#241611yescharacteristic, complemented, Sylow
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—22no—
278C23—22no—
279C23—112no—
280C23—112no—
281C23—112no—
282C23—112no—
283C23—221no—
284C23—221no—
285C23—221no—
286C23—221no—
287C23—221no—
288C23—221no—
289C23—221no—
290C23—221no—
291C23—221no—
292C23—221no—
293C23C23×D1111yescharacteristic
294D4—44no—
295D4—228no—
296D4—448no—
297D4—448no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—112no—
307C2×C4—114no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—222no—
311C2×C4—222no—
312C2×C4—228no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—222no—
317C2×C4—222no—
318C2×C4—222no—
319C2×C4—448no—
320C2×C4—444no—
321C2×C4#433912yes—
322C2×C4D4×D1112yes—
323C2×C4D4×D1112yes—
324C2×C4D4×D1112yes—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—42no—
329C22—42no—
330C22—42no—
331C22—42no—
332C22—114no—
333C22—222no—
334C22—222no—
335C22—222no—
336C22—222no—
337C22—222no—
338C22—222no—
339C22—222no—
340C22—222no—
341C22—222no—
342C22—441no—
343C22—441no—
344C22—441no—
345C22—441no—
346C22C2×#433911yescharacteristic
347C22C2×D4×D1111yescharacteristic
348C22C2×D4×D1111yescharacteristic
349C22C2×D4×D1111yescharacteristic
350C22#6703711yescharacteristic
351C22#41×D1111yescharacteristic
352C22#6704311yescharacteristic
353C4—22no—
354C4—42no—
355C4—41no—
356C4—224no—
357C4—222no—
358C4—441no—
359C4—442no—
360C4#6693714yescomplemented
361C2—82no—
362C2—224no—
363C2—442no—
364C2C2×#6693711yescharacteristic
365C2#1062308211yescharacteristic
366C2#1062308911yescharacteristic
367C2D11×#12111yescharacteristic
368C2#1062313911yescharacteristic
369C2#1062320811yescharacteristic
370C2#1062324811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
hypercenter#390D11
hypocenterC11#2416
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#66991C2semidirect
2. C2×#66991C2semidirect
3. C2×C4⋊C4×D11C2semidirect
4. C2×#66937C2semidirect
5. C2×C4×D44C2semidirect
6. C11×#390C2semidirect
7. #10622600C2semidirect
8. #10622572C2semidirect
9. #10622569C2semidirect
10. #10622561C2semidirect
11. #10622541C2semidirect
62. C2×D44D4semidirect
71. C2×C4×D11D4semidirect
83. C4⋊Dic11D4semidirect
147. #390D11semidirect
178. C2×D11#121semidirect
182. C4×C11#121semidirect
271. C11#2416semidirect
360. C4#66937semidirect

Maximal subgroups

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

subgroupindex
C2×#669912
C2×C4⋊C4×D112
C2×#669372
C2×C4×D442
C11×#3902
#106226002
#106225722
#106225692
#106225612
#106225412
#241611