Finite Group Databasebeta

← #13079492

Subgroups — #13079492

Order 1408.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#537C211yesmaximal, characteristic
2#10623356C211yesmaximal, characteristic, complemented
3#10622852C211yesmaximal, characteristic, complemented
4#10622852C211yesmaximal, characteristic, complemented
5#10622847C211yesmaximal, characteristic, complemented
6#10622665C211yesmaximal, characteristic, complemented
7#10622664C211yesmaximal, characteristic, complemented
8#10622663C211yesmaximal, characteristic, complemented
9#10622658C211yesmaximal, characteristic, complemented
10#10622655C211yesmaximal, characteristic, complemented
11#10622654C211yesmaximal, characteristic, complemented
12#10622653C211yesmaximal, characteristic, complemented
13#10622648C211yesmaximal, characteristic, complemented
14#10622584C211yesmaximal, characteristic, complemented
15#10622583C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×C11×#41C2211yescharacteristic
18C22×Dic22C2211yescharacteristic
19C11×C22⋊Q8—21no—
20C11×C22⋊Q8C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22C11×#121—21no—
23C11×#121—21no—
24C11×#121—21no—
25C11×#121C2211yescharacteristic
26C11×#121C2211yescharacteristic
27C2×C11×C4⋊C4C2211yescharacteristic
28#66997—21no—
29C2×#4326C2211yescharacteristic
30C2×#4326C2211yescharacteristic
31#66989—21no—
32#66988—21no—
33#66988—21no—
34C2×#4324C2211yescharacteristic
35C2×#4324C2211yescharacteristic
36#66979C2211yescharacteristic
37#66977C2211yescharacteristic
38#66977C2211yescharacteristic
39#66977C2211yescharacteristic
40#66977C2211yescharacteristic
41C2×#4318C2211yescharacteristic
42C22×C11⋊C8C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47C22⋊(C11⋊C8)C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49C22⋊(C11⋊C8)C2211yescharacteristic
50C22⋊(C11⋊C8)C2211yescharacteristic
51#66874C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C11×#41—41no—
60C11×#41—41no—
61C11×#41—41no—
62C11×#41—41no—
63C2×Q8×C11D411yescharacteristic
64C2×Q8×C11C2311yescharacteristic
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11D411yescharacteristic
69C2×D4×C11D411yescharacteristic
70C2×D4×C11D411yescharacteristic
71C2×D4×C11C2311yescharacteristic
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C22×Dic11—21no—
78C2×Dic22—21no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×Dic22C2311yescharacteristic
82C2×Dic22C2311yescharacteristic
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4C2311yescharacteristic
87C11×C4⋊C4C2311yescharacteristic
88C11×C22⋊C4—21no—
89C11×C22⋊C4—21no—
90C11×C22⋊C4—21no—
91C11×C22⋊C4—21no—
92C22⋊Dic11—21no—
93C22⋊Dic11—21no—
94C22⋊Dic11—21no—
95C22⋊Dic11—21no—
96C22⋊Dic11—21no—
97#4326—41no—
98#4326—41no—
99#4324—41no—
100#4324—41no—
101C4⋊Dic11C2311yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107C4×Dic11—21no—
108#4318—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112C2×C11⋊C8C2311yescharacteristic
113C2×C11⋊C8C2311yescharacteristic
114#3201—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11C2×D411yescharacteristic
117C23×C11C2×D411yescharacteristic
118C23×C11C2×D411yescharacteristic
119Q8×C11—21no—
120Q8×C11—21no—
121Q8×C11—41no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—41no—
125D4×C11—41no—
126D4×C11—41no—
127D4×C11—42no—
128D4×C11—81no—
129D4×C11—81no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—42no—
140C2×C4×C11—81no—
141C2×C4×C11C2×D411yescharacteristic
142C2×C4×C11C2×D411yescharacteristic
143C2×C4×C11C2×D411yescharacteristic
144C2×C4×C11C2411yescharacteristic
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—42no—
150Dic22—21no—
151Dic22—21no—
152Dic22—21no—
153Dic22—21no—
154Dic22—42no—
155C11⋊C8—21no—
156C11⋊C8—21no—
157C11⋊C8—21no—
158C11⋊C8—21no—
159#537D1111yescharacteristic
160#536—111no—
161#485—111no—
162#484—111no—
163#483—111no—
164#482—111no—
165#470—111no—
166#468—111no—
167#467—111no—
168#465—111no—
169#452—111no—
170#452—111no—
171#451—111no—
172#448—111no—
173#408—111no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11C22×D411yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11H(5,𝔽2)11yescharacteristic
194C4×C11H(5,𝔽2)11yescharacteristic
195Dic11—41no—
196Dic11—41no—
197Dic11—41no—
198Dic11—41no—
199C2×#41C2×D1111yescharacteristic
200C2×#41C2×D1111yescharacteristic
201C22×Q8—111no—
202C2×Q16—111no—
203C2×Q16—111no—
204C2×SD16—111no—
205C2×SD16—111no—
206C2×M16—111no—
207C22×C8—111no—
208C4⋊Q8—221no—
209#124—221no—
210#123—221no—
211#123—221no—
212C22⋊Q8—21no—
213C22⋊Q8—111no—
214C22⋊Q8—111no—
215C22⋊Q8—111no—
216C22⋊Q8—111no—
217C22⋊Q8C2×D1111yescharacteristic
218C22⋊Q8C2×D1111yescharacteristic
219#121—21no—
220#121—21no—
221#121—21no—
222#121C2×D1111yescharacteristic
223#121C2×D1111yescharacteristic
224#117—111no—
225C2×C4⋊C4C2×D1111yescharacteristic
226#107—111no—
227#107—111no—
228#106—111no—
229#106—111no—
230#103—111no—
231#103—111no—
232#103—111no—
233#103—111no—
234#103—111no—
235#103—111no—
236#102—111no—
237#102—111no—
238C22⋊C8—111no—
239C22⋊C8—111no—
240C22⋊C8—111no—
241C22⋊C8—111no—
242C2×C11—41no—
243C2×C11—41no—
244C2×C11—41no—
245C2×C11—81no—
246C2×C11#53411yescharacteristic
247C2×C11#57711yescharacteristic
248C2×C11#57811yescharacteristic
249#41—41no—
250#41—41no—
251#41—41no—
252#41—41no—
253C2×Q8—111no—
254C2×Q8—111no—
255C2×Q8—221no—
256C2×Q8—441no—
257C2×Q8—441no—
258C2×Q8C22⋊D1111yescharacteristic
259C2×Q8C22×D1111yescharacteristic
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4C22⋊D1111yescharacteristic
264C2×D4C22⋊D1111yescharacteristic
265C2×D4C22⋊D1111yescharacteristic
266C2×D4C22×D1111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—221no—
270C22×C4C22×D1111yescharacteristic
271C22×C4C22×D1111yescharacteristic
272C22×C4C22×D1111yescharacteristic
273Q16—441no—
274Q16—441no—
275SD16—441no—
276SD16—441no—
277M16—441no—
278C2×C8—111no—
279C2×C8—111no—
280C2×C8—111no—
281C2×C8—111no—
282C2×C8—441no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—111no—
287C4⋊C4—111no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4C22×D1111yescharacteristic
293C4⋊C4C22×D1111yescharacteristic
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C42—221no—
304C11#320111yescharacteristic, complemented, Sylow
305C23—21no—
306C23C2×C22⋊D1111yescharacteristic
307C23C2×C22⋊D1111yescharacteristic
308C23C2×C22⋊D1111yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—41no—
312Q8—221no—
313Q8—221no—
314Q8—221no—
315Q8—221no—
316Q8—442no—
317D4—21no—
318D4—21no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—42no—
323D4—81no—
324D4—81no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—442no—
341C2×C4C2×C22⋊D1111yescharacteristic
342C2×C4C2×C22⋊D1111yescharacteristic
343C2×C4C2×C22⋊D1111yescharacteristic
344C2×C4C23×D1111yescharacteristic
345C8—221no—
346C8—221no—
347C8—221no—
348C8—221no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22C22×C22⋊D1111yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—441no—
369C4—441no—
370C4—441no—
371C4—441no—
372C4#6703711yescharacteristic
373C4#6703711yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—81no—
378C2#1062333511yescharacteristic
379C2#1062336711yescharacteristic
380C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#537C2
socleC22×C11C22×D4
hypercenter#537D11
hypocenterC11#3201
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
2. #10623356C2semidirect
3. #10622852C2semidirect
4. #10622852C2semidirect
5. #10622847C2semidirect
6. #10622665C2semidirect
7. #10622664C2semidirect
8. #10622663C2semidirect
9. #10622658C2semidirect
10. #10622655C2semidirect
11. #10622654C2semidirect
12. #10622653C2semidirect
13. #10622648C2semidirect
14. #10622584C2semidirect
15. #10622583C2semidirect
304. C11#3201semidirect

Maximal subgroups

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

subgroupindex
C11×#5372
#106233562
#106228522
#106228472
#106226652
#106226642
#106226632
#106226582
#106226552
#106226542
#106226532
#106226482
#106225842
#106225832
#320111