Finite Group Databasebeta

← #13071407

Subgroups — #13071407

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×#66988C211yesmaximal, characteristic
2C11×#386C211yesmaximal, characteristic
3#10622834C211yesmaximal, characteristic
4#10622823C211yesmaximal, characteristic, complemented
5C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
6#10622558C211yesmaximal, characteristic, complemented
7#10622558C211yesmaximal, characteristic, complemented
8#10622558C211yesmaximal, characteristic, complemented
9#10622557C211yesmaximal, characteristic, complemented
10#10622555C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
12#10622268C211yesmaximal, characteristic, complemented
13#10622265C211yesmaximal, characteristic, complemented
14#10622262C211yesmaximal, characteristic, complemented
15#10622260C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C23×Dic11C2211yescharacteristic
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29#66988C418yescomplemented
30C2×C4⋊Dic11C2211yescharacteristic
31C2×Dic11⋊C4C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×C4×Dic11C2211yescharacteristic
38C2×C4×Dic11C2211yescharacteristic
39C2×C4×Dic11C2211yescharacteristic
40C2×C4×Dic11C2211yescharacteristic
41C2×C4×Dic11C2211yescharacteristic
42C11×#95C2211yescharacteristic
43C11×#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C24×C11C2311yescharacteristic
53C24×C11C2311yescharacteristic
54C2×D4×C11—41no—
55C2×D4×C11—41no—
56C2×D4×C11C2×C414yes—
57C22×C4×C11—22no—
58C22×C4×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×Dic11—41no—
66C22×Dic11—41no—
67C22×Dic11C2×C414yescomplemented
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C22×Dic11C2311yescharacteristic
76C11×C22⋊C4—22no—
77C11×C22⋊C4—41no—
78C11×C22⋊C4—41no—
79C22⋊Dic11—22no—
80C22⋊Dic11—22no—
81C22⋊Dic11—41no—
82C22⋊Dic11—41no—
83C22⋊Dic11C2×C414yes—
84C22⋊Dic11C2×C414yes—
85C22⋊Dic11C2×C414yescomplemented
86C4⋊Dic11—41no—
87Dic11⋊C4—22no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91Dic11⋊C4C2×C414yescomplemented
92Dic11⋊C4C2×C414yescomplemented
93C4×Dic11—22no—
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×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11C22×C412yes—
112C23×C11C22×C412yes—
113C23×C11C2411yescharacteristic
114D4×C11—44no—
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—44no—
129C2×C4×C11C22×C412yes—
130C2×C4×C11#4112yes—
131C2×Dic11—21no—
132C2×Dic11—21no—
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×Dic11C22×C412yes—
155C2×Dic11#4112yes—
156C2×#123—111no—
157#390—111no—
158#389—111no—
159#388—111no—
160#388—111no—
161#388—111no—
162#388—111no—
163#387—111no—
164#387—111no—
165#386D1111yescharacteristic
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—22no—
175C22×C11—22no—
176C22×C11—22no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11C23×C411yescharacteristic
186C22×C11C2×#4111yescharacteristic
187C22×C11C2×#4111yescharacteristic
188C22×C11H(5,𝔽2)11yescharacteristic
189C22×C11H(5,𝔽2)11yescharacteristic
190C22×C11H(5,𝔽2)11yescharacteristic
191C22×C112−1+411yescharacteristic
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197Dic11—22no—
198Dic11—22no—
199Dic11—22no—
200Dic11—22no—
201Dic11—22no—
202Dic11—41no—
203Dic11—41no—
204Dic11—41no—
205C22×D4C2×D1111yescharacteristic
206C23×C4—111no—
207C23×C4C2×D1111yescharacteristic
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⋊C4—111no—
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×C42—111no—
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×C11—42no—
243C2×C11C4×#4111yescharacteristic
244C2×C11#51811yescharacteristic
245C2×C11#52011yescharacteristic
246C2×C11#53811yescharacteristic
247C2×C11#53911yescharacteristic
248C2×C11#54011yescharacteristic
249C2×C11#54211yescharacteristic
250C24C22×D1111yescharacteristic
251C24C22×D1111yescharacteristic
252C2×D4—41no—
253C2×D4—41no—
254C2×D4C4×D1114yes—
255C22×C4—22no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—111no—
262C22×C4—111no—
263C22×C4—114no—
264C22×C4—111no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—441no—
268C22×C4—441no—
269C22×C4C22×D1111yescharacteristic
270C22×C4C22×D1111yescharacteristic
271C22×C4C22×D1111yescharacteristic
272C22×C4C22×D1111yescharacteristic
273C22×C4C22×D1111yescharacteristic
274C4⋊C4—114no—
275C4⋊C4—114no—
276C4⋊C4—222no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C22⋊C4—22no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—114no—
285C22⋊C4—114no—
286C22⋊C4—114no—
287C22⋊C4—222no—
288C22⋊C4—222no—
289C22⋊C4—441no—
290C22⋊C4—441no—
291C42—222no—
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—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C2×C4×D1112yes—
310C23C2×C4×D1112yes—
311C23C23×D1111yescharacteristic
312D4—44no—
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—44no—
327C2×C4—112no—
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—221no—
350C2×C4—221no—
351C2×C4—444no—
352C2×C4C2×C4×D1112yes—
353C2×C4#434112yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22C22×C4×D1111yescharacteristic
369C22C2×#434111yescharacteristic
370C22#6703711yescharacteristic
371C22#6703711yescharacteristic
372C22#6703711yescharacteristic
373C22#41×D1111yescharacteristic
374C22#6704311yescharacteristic
375C4—22no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—222no—
381C4—222no—
382C4—222no—
383C4—222no—
384C4—222no—
385C4—441no—
386C4—441no—
387C4—441no—
388C2—42no—
389C2—42no—
390C2#1062301711yescharacteristic
391C2C4×#434111yescharacteristic
392C2#1062307711yescharacteristic
393C2#1062312411yescharacteristic
394C2#1062313411yescharacteristic
395C2#1062314611yescharacteristic
396C2#1062319111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC11×#386C2
socle, cosocleC23×C11C24
prime radicalC22×D4×C11C22
hypercenter#386D11
hypocenterC11#2335
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
4. #10622823C2semidirect
5. C4×C22⋊Dic11C2semidirect
6. #10622558C2semidirect
7. #10622558C2semidirect
8. #10622558C2semidirect
9. #10622557C2semidirect
10. #10622555C2semidirect
11. C22⋊C4×Dic11C2semidirect
12. #10622268C2semidirect
13. #10622265C2semidirect
14. #10622262C2semidirect
15. #10622260C2semidirect
29. #66988C4semidirect
67. C22×Dic11C2×C4semidirect
85. C22⋊Dic11C2×C4semidirect
91. Dic11⋊C4C2×C4semidirect
92. Dic11⋊C4C2×C4semidirect
296. C11#2335semidirect

Maximal subgroups

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

subgroupindex
C2×#669882
C11×#3862
#106228342
#106228232
C4×C22⋊Dic112
#106225582
#106225572
#106225552
C22⋊C4×Dic112
#106222682
#106222652
#106222622
#106222602
#233511