Finite Group Databasebeta

← #13071413

Subgroups — #13071413

Order 1408.

532 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66936C211yesmaximal, characteristic
2C11×#388C211yesmaximal, characteristic, complemented
3#10622600C211yesmaximal, characteristic, complemented
4#10622585C211yesmaximal, characteristic, complemented
5#10622571C211yesmaximal, characteristic
6#10622570C211yesmaximal, characteristic
7#10622563C211yesmaximal, characteristic, complemented
8#10622557C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
10#10622553C211yesmaximal, characteristic, complemented
11C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
12#10622283C211yesmaximal, characteristic, complemented
13#10622279C211yesmaximal, characteristic, complemented
14#10622268C211yesmaximal, characteristic, complemented
15#10622267C211yesmaximal, characteristic, complemented
16C22×C22⋊D11C2211yescharacteristic
17C23×Dic11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C42×C11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×C4⋊Dic11C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
33C2×C4⋊Dic11C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×C4×Dic11C2211yescharacteristic
38C2×C4×Dic11C2211yescharacteristic
39C2×C4×Dic11C2211yescharacteristic
40C2×C4×Dic11C2211yescharacteristic
41#66936C418yescomplemented
42C11×#95C2211yescharacteristic
43C11×#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C24×C11C2311yescharacteristic
53C23×D11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C2×C22⋊D11—41no—
61C2×C22⋊D11—41no—
62C2×C22⋊D11C2×C414yes—
63C22×Dic11—22no—
64C22×Dic11—41no—
65C22×Dic11—41no—
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C2×C4×D11—41no—
74C2×C4×D11—41no—
75C2×C4×D11C2×C414yescomplemented
76C11×C4⋊C4—41no—
77C11×C22⋊C4—22no—
78C11×C22⋊C4—41no—
79C11×C22⋊C4C2×C414yes—
80C42×C11—22no—
81C22⋊Dic11—41no—
82C22⋊Dic11C2×C414yes—
83(C2×D11)⋊C4—22no—
84(C2×D11)⋊C4—22no—
85(C2×D11)⋊C4—41no—
86(C2×D11)⋊C4—41no—
87(C2×D11)⋊C4C2×C414yescomplemented
88C4⋊Dic11—22no—
89C4⋊Dic11—41no—
90C4⋊Dic11C2×C414yescomplemented
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93Dic11⋊C4C2×C414yescomplemented
94C4×Dic11—41no—
95C4×Dic11—41no—
96C4×Dic11—41no—
97C4×Dic11—41no—
98#2335—111nomaximal, Sylow
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11C22×C412yes—
106C23×C11C2411yescharacteristic
107C22×D11—21no—
108C22×D11—21no—
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11—21no—
113C22×D11C22×C412yes—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11C22×C412yes—
130C2×C4×C11C22×C412yes—
131C2×C4×C11#4112yes—
132C22⋊D11—44no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—44no—
151C2×Dic11C22×C412yes—
152C2×Dic11C22×C412yes—
153C2×Dic11C22×C412yes—
154C2×Dic11#4112yes—
155C4×D11—44no—
156C2×#123—111no—
157#390—111no—
158#389—111no—
159#388—111no—
160#388—111no—
161#388—111no—
162#388D1111yescharacteristic, complemented
163#387—111no—
164#387—111no—
165#386—111no—
166#385—111no—
167#380—111no—
168C4×C4⋊C4—111no—
169C4×C22⋊C4—111no—
170C4×C22⋊C4—111no—
171C22×C11—22no—
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11C23×C411yescharacteristic
179C22×C11C2×#4111yescharacteristic
180C22×C11C2×#4111yescharacteristic
181C22×C11H(5,𝔽2)11yescharacteristic
182C22×C11H(5,𝔽2)11yescharacteristic
183C22×C11H(5,𝔽2)11yescharacteristic
184C22×C112−1+411yescharacteristic
185C2×D11—22no—
186C2×D11—22no—
187C2×D11—22no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—22no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—41no—
198Dic11—22no—
199Dic11—22no—
200Dic11—22no—
201Dic11—22no—
202Dic11—41no—
203Dic11—41no—
204Dic11—41no—
205C22×D4—111no—
206C23×C4—111no—
207C23×C4—111no—
208#123—118no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4C2×D1111yescharacteristic
216C2×C22⋊C4—111no—
217C2×C22⋊C4—111no—
218C2×C22⋊C4—111no—
219C2×C22⋊C4—111no—
220C2×C22⋊C4—111no—
221C2×C22⋊C4—111no—
222C2×C22⋊C4—111no—
223C2×C22⋊C4C2×D1111yescharacteristic
224C2×C22⋊C4C2×D1111yescharacteristic
225C2×C22⋊C4C2×D1111yescharacteristic
226C2×C42—111no—
227C2×C42—111no—
228C2×C42—111no—
229C2×C42—111no—
230C2×C42C2×D1111yescharacteristic
231#95—111no—
232#95—111no—
233#95—111no—
234#95—111no—
235#95—111no—
236#95—111no—
237#95—111no—
238#95—111no—
239#95C2×D1111yescharacteristic
240#95C2×D1111yescharacteristic
241C2×C11—42no—
242C2×C11C4×#4111yescharacteristic
243C2×C11#51811yescharacteristic
244C2×C11#52011yescharacteristic
245C2×C11#53811yescharacteristic
246C2×C11#53911yescharacteristic
247C2×C11#54011yescharacteristic
248C2×C11#54211yescharacteristic
249D11—42no—
250C24—111no—
251C24C22×D1111yescharacteristic
252C2×D4—114no—
253C2×D4—441no—
254C2×D4—441no—
255C22×C4—111no—
256C22×C4—111no—
257C22×C4—111no—
258C22×C4—111no—
259C22×C4—114no—
260C22×C4—111no—
261C22×C4—111no—
262C22×C4—111no—
263C22×C4—222no—
264C22×C4—441no—
265C22×C4—441no—
266C22×C4—441no—
267C22×C4—441no—
268C22×C4C22×D1111yescharacteristic
269C22×C4C22×D1111yescharacteristic
270C22×C4C22×D1111yescharacteristic
271C22×C4C22×D1111yescharacteristic
272C22×C4C22×D1111yescharacteristic
273C22×C4C22×D1111yescharacteristic
274C4⋊C4—41no—
275C4⋊C4—114no—
276C4⋊C4—114no—
277C4⋊C4—222no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C22⋊C4—22no—
282C22⋊C4—41no—
283C22⋊C4—114no—
284C22⋊C4—114no—
285C22⋊C4—222no—
286C22⋊C4—222no—
287C22⋊C4—441no—
288C22⋊C4—441no—
289C22⋊C4—441no—
290C22⋊C4C4×D1114yes—
291C42—22no—
292C42—441no—
293C42—441no—
294C42—441no—
295C42—441no—
296C11#233511yescharacteristic, complemented, Sylow
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—112no—
304C23—221no—
305C23—221no—
306C23—221no—
307C23—221no—
308C23—221no—
309C23—221no—
310C23C2×C4×D1112yes—
311C23C23×D1111yescharacteristic
312D4—444no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—112no—
329C2×C4—112no—
330C2×C4—112no—
331C2×C4—112no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—444no—
350C2×C4—444no—
351C2×C4C2×C4×D1112yes—
352C2×C4C2×C4×D1112yes—
353C2×C4#434112yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—222no—
362C22—222no—
363C22—222no—
364C22—441no—
365C22—441no—
366C22—441no—
367C22—441no—
368C22C22×C4×D1111yescharacteristic
369C22C2×#434111yescharacteristic
370C22#6703711yescharacteristic
371C22#41×D1111yescharacteristic
372C22#6704211yescharacteristic
373C22#6704211yescharacteristic
374C22#6704311yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—222no—
382C4—222no—
383C4—222no—
384C4—222no—
385C4—441no—
386C4—441no—
387C4—441no—
388C2—42no—
389C2—442no—
390C2#1062305411yescharacteristic
391C2C4×#434111yescharacteristic
392C2#1062307611yescharacteristic
393C2#1062315011yescharacteristic
394C2#1062319611yescharacteristic
395C2#1062320011yescharacteristic
396C2#1062323511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC11×#388C2
socle, cosocleC23×C11C24
prime radicalC22×C22⋊D11C22
hypercenter#388D11
hypocenterC11#2335
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C11×#388C2semidirect
3. #10622600C2semidirect
4. #10622585C2semidirect
7. #10622563C2semidirect
8. #10622557C2semidirect
9. C22⋊C4×Dic11C2semidirect
10. #10622553C2semidirect
11. C4×C4⋊Dic11C2semidirect
12. #10622283C2semidirect
13. #10622279C2semidirect
14. #10622268C2semidirect
15. #10622267C2semidirect
41. #66936C4semidirect
75. C2×C4×D11C2×C4semidirect
87. (C2×D11)⋊C4C2×C4semidirect
90. C4⋊Dic11C2×C4semidirect
93. Dic11⋊C4C2×C4semidirect
162. #388D11semidirect
296. C11#2335semidirect

Maximal subgroups

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

subgroupindex
C2×#669362
C11×#3882
#106226002
#106225852
#106225712
#106225702
#106225632
#106225572
C22⋊C4×Dic112
#106225532
C4×C4⋊Dic112
#106222832
#106222792
#106222682
#106222672
#233511