Finite Group Databasebeta

← #13073552

Subgroups — #13073552

Order 1408.

760 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×C11×#121C211yesmaximal, characteristic, complemented
2C2×#66991C211yesmaximal, characteristic, complemented
3C2×#66989C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊D11C211yesmaximal, characteristic, complemented
5C2×#66977C211yesmaximal, characteristic, complemented
6C2×#66950C211yesmaximal, characteristic, complemented
7#10622836C212yesmaximal, complemented
8#10622834C212yesmaximal, complemented
9C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
10#10622570C212yesmaximal, complemented
11#10622562C212yesmaximal, complemented
12C22×D4×C11C2211yescharacteristic
13C22×D4×C11C2212yes—
14C23×C4×C11C2211yescharacteristic
15C22×C22⋊D11C2211yescharacteristic
16C22×C22⋊D11C2212yes—
17C22×C4×D11C2211yescharacteristic
18C22×Dic22C2211yescharacteristic
19C11×#121—24no—
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2212yes—
22C2×C22⋊Dic11C2212yes—
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2212yes—
25C2×C22⋊Dic11C2212yes—
26C2×C22⋊Dic11C2212yes—
27#66991—24no—
28#66989—24no—
29C4×C22⋊D11—24no—
30C2×(C2×D11)⋊C4C2212yes—
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×C4⋊Dic11C2212yes—
33C2×C4⋊Dic11C2211yescharacteristic
34#66977—24no—
35C2×Dic11⋊C4C2212yes—
36C2×Dic11⋊C4C2211yescharacteristic
37C2×C4×Dic11C2212yes—
38C2×C4×Dic11C2211yescharacteristic
39#66950—24no—
40C11⋊#95C2212yes—
41C24×C11C2312yes—
42C24×C11C2311yescharacteristic
43C23×D11C2311yescharacteristic
44C2×D4×C11—24no—
45C2×D4×C11—22no—
46C2×D4×C11—22no—
47C2×D4×C11—24no—
48C2×D4×C11—22no—
49C2×D4×C11—42no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2312yes—
55C22×C4×C11C2311yescharacteristic
56C2×C22⋊D11—22no—
57C2×C22⋊D11—24no—
58C2×C22⋊D11—22no—
59C2×C22⋊D11—22no—
60C2×C22⋊D11—24no—
61C2×C22⋊D11—42no—
62C22×Dic11C2311yescharacteristic
63C22×Dic11C2312yes—
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2312yes—
66C22×Dic11C2311yescharacteristic
67C2×C4×D11—22no—
68C2×C4×D11—22no—
69C2×C4×D11—22no—
70C2×Dic22—22no—
71C2×Dic22—22no—
72C2×Dic22—22no—
73C11×C4⋊C4D414yescomplemented
74C11×C22⋊C4—24no—
75C22⋊Dic11—24no—
76C22⋊Dic11—22no—
77C22⋊Dic11—24no—
78C22⋊Dic11—24no—
79C22⋊Dic11—24no—
80(C2×D11)⋊C4—22no—
81(C2×D11)⋊C4—24no—
82C4⋊Dic11—24no—
83C4⋊Dic11D414yescomplemented
84Dic11⋊C4—24no—
85Dic11⋊C4—22no—
86C4×Dic11—42no—
87C4×Dic11D414yescomplemented
88#2540—111nomaximal, Sylow
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—22no—
96C23×C11—22no—
97C23×C11—22no—
98C23×C11—22no—
99C23×C11—22no—
100C23×C11—22no—
101C23×C11—22no—
102C23×C11#4112yes—
103C23×C11C2411yescharacteristic
104C22×D11—21no—
105C22×D11—21no—
106C22×D11—21no—
107C22×D11—21no—
108C22×D11—21no—
109C22×D11—21no—
110C22×D11#4112yes—
111D4×C11—48no—
112D4×C11—44no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—44no—
119C2×C4×C11C2×D412yes—
120C2×C4×C11C2×D412yes—
121C2×C4×C11C2×D414yes—
122C2×C4×C11C2×D412yes—
123C22⋊D11—28no—
124C22⋊D11—48no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—22no—
128C2×Dic11—21no—
129C2×Dic11—22no—
130C2×Dic11—21no—
131C2×Dic11—22no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—22no—
135C2×Dic11—22no—
136C2×Dic11—21no—
137C2×Dic11C2×D412yes—
138C2×Dic11C2×D412yes—
139C2×Dic11C2×D414yes—
140C4×D11—44no—
141Dic22—44no—
142C2×#124—111no—
143C2×C22⋊Q8—111no—
144C2×C22⋊Q8—111no—
145C2×#121—111no—
146C2×#121D1111yescharacteristic, complemented
147C2×C4×D4—111no—
148#399—112no—
149#392—112no—
150#390—112no—
151#390—112no—
152C4×C4⋊C4—111no—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11—22no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—42no—
161C22×C11—42no—
162C22×C11—42no—
163C22×C11—42no—
164C22×C11—42no—
165C22×C11—42no—
166C22×C11—42no—
167C22×C11C22×D411yescharacteristic
168C22×C11C22×D411yescharacteristic
169C22×C11C22×D411yescharacteristic
170C22×C11C2×#4111yescharacteristic
171C22×C11C2×#4111yescharacteristic
172C22×C11H(5,𝔽2)11yescharacteristic
173C22×C112−1+411yescharacteristic
174C2×D11—22no—
175C2×D11—22no—
176C2×D11—22no—
177C2×D11—41no—
178C2×D11—41no—
179C2×D11—41no—
180C2×D11—41no—
181C4×C11—24no—
182C4×C11—41no—
183C4×C11#12714yes—
184Dic11—22no—
185Dic11—22no—
186Dic11—24no—
187Dic11—42no—
188Dic11—41no—
189C22×Q8—111no—
190C22×D4—111no—
191C22×D4—112no—
192C22×D4C2×D1111yescharacteristic
193C22×D4C2×D1112yes—
194C23×C4—111no—
195C23×C4C2×D1111yescharacteristic
196#124—224no—
197C22⋊Q8—224no—
198C22⋊Q8—224no—
199#121—24no—
200#121—224no—
201C4×D4—224no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—112no—
205C2×C4⋊C4—112no—
206C2×C4⋊C4C2×D1111yescharacteristic
207C2×C22⋊C4—111no—
208C2×C22⋊C4—112no—
209C2×C22⋊C4—112no—
210C2×C22⋊C4—112no—
211C2×C22⋊C4—112no—
212C2×C22⋊C4—111no—
213C2×C22⋊C4—112no—
214C2×C22⋊C4C2×D1112yes—
215C2×C42—111no—
216C2×C42—112no—
217#95—112no—
218C2×C11—42no—
219C2×C11—82no—
220C2×C11#52511yescharacteristic
221C2×C11C2×#12711yescharacteristic
222C2×C11#53711yescharacteristic
223C2×C11#54611yescharacteristic
224C2×C11#54611yescharacteristic
225C2×C11#54811yescharacteristic
226C2×C11#54811yescharacteristic
227D11—42no—
228C24—111no—
229C24C22×D1112yes—
230C24C22×D1111yescharacteristic
231C2×Q8—222no—
232C2×Q8—222no—
233C2×Q8—222no—
234C2×D4—24no—
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—24no—
238C2×D4—22no—
239C2×D4—42no—
240C2×D4—222no—
241C2×D4—224no—
242C2×D4—222no—
243C2×D4—222no—
244C2×D4—224no—
245C2×D4—442no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—111no—
250C22×C4—112no—
251C22×C4—111no—
252C22×C4—112no—
253C22×C4—111no—
254C22×C4—222no—
255C22×C4—222no—
256C22×C4—222no—
257C22×C4C22×D1111yescharacteristic
258C22×C4C22×D1112yes—
259C22×C4C22×D1111yescharacteristic
260C4⋊C4—114no—
261C4⋊C4—222no—
262C4⋊C4—224no—
263C4⋊C4—224no—
264C4⋊C4C22⋊D1114yescomplemented
265C22⋊C4—24no—
266C22⋊C4—222no—
267C22⋊C4—222no—
268C22⋊C4—224no—
269C22⋊C4—224no—
270C22⋊C4—224no—
271C22⋊C4—224no—
272C22⋊C4—224no—
273C42—114no—
274C42—442no—
275C11#254011yescharacteristic, complemented, Sylow
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—22no—
283C23—22no—
284C23—22no—
285C23—22no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—112no—
290C23—221no—
291C23—221no—
292C23—221no—
293C23—221no—
294C23—221no—
295C23—221no—
296C23#434112yes—
297C23C23×D1111yescharacteristic
298Q8—444no—
299D4—48no—
300D4—44no—
301D4—228no—
302D4—448no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—44no—
309C2×C4—112no—
310C2×C4—112no—
311C2×C4—114no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—222no—
315C2×C4—221no—
316C2×C4—222no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—222no—
320C2×C4—221no—
321C2×C4—222no—
322C2×C4—222no—
323C2×C4—221no—
324C2×C4—444no—
325C2×C4D4×D1112yes—
326C2×C4D4×D1112yes—
327C2×C4C2×C22⋊D1114yes—
328C2×C4C2×C22⋊D1112yes—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22—222no—
344C22—222no—
345C22—222no—
346C22—441no—
347C22—441no—
348C22—441no—
349C22—441no—
350C22C2×D4×D1111yescharacteristic
351C22C2×D4×D1111yescharacteristic
352C22C2×#434111yescharacteristic
353C22#6703711yescharacteristic
354C22#41×D1111yescharacteristic
355C22#6704311yescharacteristic
356C22C22×C22⋊D1111yescharacteristic
357C4—24no—
358C4—41no—
359C4—222no—
360C4—222no—
361C4—224no—
362C4—441no—
363C4—442no—
364C4#6699314yes—
365C2—42no—
366C2—82no—
367C2—442no—
368C2#1062312911yescharacteristic
369C2#1062313711yescharacteristic
370C2#1062313911yescharacteristic
371C2#1062314311yescharacteristic
372C2C2×#6699311yescharacteristic
373C2#1062333711yescharacteristic
374C2#1062336211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2540
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C11×#121C2semidirect
2. C2×#66991C2semidirect
3. C2×#66989C2semidirect
4. C2×C4×C22⋊D11C2semidirect
5. C2×#66977C2semidirect
6. C2×#66950C2semidirect
7. #10622836C2semidirect
8. #10622834C2semidirect
9. C4⋊C4×Dic11C2semidirect
10. #10622570C2semidirect
11. #10622562C2semidirect
73. C11×C4⋊C4D4semidirect
83. C4⋊Dic11D4semidirect
87. C4×Dic11D4semidirect
146. C2×#121D11semidirect
264. C4⋊C4C22⋊D11semidirect
275. C11#2540semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669912
C2×#669892
C2×C4×C22⋊D112
C2×#669772
C2×#669502
#106228362
#106228342
C4⋊C4×Dic112
#106225702
#106225622
#254011