Finite Group Databasebeta

← #13080075

Subgroups — #13080075

Order 1408.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623213C211yesmaximal, characteristic, complemented
2#10623113C211yesmaximal, characteristic, complemented
3C11×#464C211yesmaximal, characteristic, complemented
4#10622801C211yesmaximal, characteristic, complemented
5#10622798C211yesmaximal, characteristic, complemented
6#10622787C211yesmaximal, characteristic, complemented
7#10622778C211yesmaximal, characteristic, complemented
8#10622670C211yesmaximal, characteristic, complemented
9#10622634C211yesmaximal, characteristic, complemented
10#10622459C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic, complemented
12#10622425C211yesmaximal, characteristic, complemented
13#10622407C211yesmaximal, characteristic, complemented
14#10622388C211yesmaximal, characteristic
15#10622372C211yesmaximal, characteristic, complemented
16C2×C11×Q16C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C11×#124C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20#67000C2211yescharacteristic
21#66999C2211yescharacteristic
22#66999C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24C2×#4325C2211yescharacteristic
25#66991C2211yescharacteristic
26D4×Dic11C2211yescharacteristic
27C2×#4323C2211yescharacteristic
28C2×#4313C2211yescharacteristic
29C2×C8×D11C2211yescharacteristic
30#66949—21no—
31#66948C2211yescharacteristic
32#66947—21no—
33#66941C2211yescharacteristic
34#66939—21no—
35#66938—21no—
36#66932—21no—
37#66931—21no—
38#66929—21no—
39#66928—21no—
40C4×D44C2211yescharacteristic
41#66925C2211yescharacteristic
42#66922C2211yescharacteristic
43C11×C4⋊C8C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66899C2211yescharacteristic
49#66896C2211yescharacteristic
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic
52#66882C2211yescharacteristic
53#66882C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C22×Dic11—21no—
64C2×D44—21no—
65C2×D44C2311yescharacteristic
66C2×C4×D11—21no—
67C2×C4×D11C2311yescharacteristic
68C2×Dic22—21no—
69C2×Dic22—21no—
70C11×Q16—41no—
71C11×SD16—41no—
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4C2311yescharacteristic
76C11×C22⋊C4—21no—
77C11×C22⋊C4—21no—
78C42×C11—21no—
79C42×C11C2311yescharacteristic
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82#4325—41no—
83#4323—41no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4D411yescharacteristic
91(C2×D11)⋊C4D411yescharacteristic
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4D411yescharacteristic
101Dic11⋊C4D411yescharacteristic
102C4×Dic11—21no—
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#4313—41no—
107C8×D11—41no—
108#3262—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11—21no—
111C22×D11C2×D411yescharacteristic
112Q8×C11—21no—
113Q8×C11—21no—
114Q8×C11—21no—
115Q8×C11—21no—
116D4×C11—21no—
117D4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2411yescharacteristic
124C22⋊D11—81no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—81no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132D44—21no—
133D44—21no—
134D44—81no—
135C4×D11—21no—
136C4×D11—21no—
137C4×D11—81no—
138Dic22—81no—
139Dic22—81no—
140C8×C11—21no—
141C8×C11—21no—
142C11⋊C8—21no—
143C11⋊C8—21no—
144#542—111no—
145#542—111no—
146#477—111no—
147#477—111no—
148#474—111no—
149#474—111no—
150#468—111no—
151#468—111no—
152#467—111no—
153#466—111no—
154#464—111no—
155#464D1111yescharacteristic, complemented
156#463—111no—
157#463—111no—
158#424—111no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11C22×D411yescharacteristic
163C2×D11—21no—
164C2×D11—21no—
165C2×D11—21no—
166C2×D11—41no—
167C2×D11—41no—
168C2×D11—41no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11H(5,𝔽2)11yescharacteristic
175C4×C112−1+411yescharacteristic
176Dic11—21no—
177Dic11—21no—
178Dic11—21no—
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182C2×Q16C2×D1111yescharacteristic
183C2×SD16—111no—
184C2×SD16C2×D1111yescharacteristic
185C2×D8—111no—
186C2×M16—111no—
187C22×C8—111no—
188C4⋊Q8—111no—
189C4⋊Q8—111no—
190#126—221no—
191#126—221no—
192#124—111no—
193#124—221no—
194#124—221no—
195#124C2×D1111yescharacteristic
196#123—221no—
197#123—221no—
198C22⋊Q8—111no—
199C22⋊Q8—111no—
200C22⋊Q8—221no—
201C22⋊Q8—221no—
202#121—111no—
203#121—111no—
204C4×Q8—111no—
205C4×Q8C2×D1111yescharacteristic
206C4×D4—111no—
207C4×D4—111no—
208#117—111no—
209#107—111no—
210#107—111no—
211#107—111no—
212#107—111no—
213C4⋊C8—111no—
214C4⋊C8—111no—
215C4⋊C8—111no—
216C4⋊C8C2×D1111yescharacteristic
217#103—111no—
218#103—111no—
219#103—111no—
220#103C2×D1111yescharacteristic
221#102—111no—
222#102—111no—
223#102—111no—
224#102C2×D1111yescharacteristic
225C2×C11—81no—
226C2×C11#53711yescharacteristic
227C2×C11#57611yescharacteristic
228C2×C11#57811yescharacteristic
229D11—41no—
230D11—81no—
231C2×Q8—221no—
232C2×Q8—221no—
233C2×Q8C22×D1111yescharacteristic
234C2×Q8C22×D1111yescharacteristic
235C2×D4—111no—
236C2×D4—221no—
237C2×D4—221no—
238C2×D4C22×D1111yescharacteristic
239C22×C4—111no—
240C22×C4—221no—
241C22×C4—221no—
242Q16—41no—
243SD16—41no—
244SD16—441no—
245D8—441no—
246M16—441no—
247C2×C8—111no—
248C2×C8—111no—
249C2×C8—441no—
250C2×C8C22×D1111yescharacteristic
251C2×C8C22×D1111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—111no—
256C4⋊C4—111no—
257C4⋊C4—111no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4C22×D1111yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—111no—
267C22⋊C4—111no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C42—21no—
277C42—111no—
278C42—221no—
279C42C22×D1111yescharacteristic
280C11#326211yescharacteristic, complemented, Sylow
281C23—21no—
282C23—111no—
283C23—221no—
284Q8—21no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288Q8—881no—
289Q8—881no—
290D4—21no—
291D4—21no—
292D4—221no—
293D4—221no—
294D4—881no—
295D4—881no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—111no—
300C2×C4—111no—
301C2×C4—111no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—881no—
308C2×C4—881no—
309C2×C4D4×D1111yescharacteristic
310C2×C4D4×D1111yescharacteristic
311C2×C4C23×D1111yescharacteristic
312C8—21no—
313C8—21no—
314C8—221no—
315C8—221no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—221no—
320C22—221no—
321C22—221no—
322C22—441no—
323C22—441no—
324C22—441no—
325C22C2×D4×D1111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—221no—
332C4—221no—
333C4—221no—
334C4—441no—
335C4—441no—
336C4—441no—
337C4#6703711yescharacteristic
338C4#6704311yescharacteristic
339C2—81no—
340C2—441no—
341C2—881no—
342C2#1062313911yescharacteristic
343C2#1062330011yescharacteristic
344C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#464C2
socleC22×C11C22×D4
prime radical#10622388C2
hypercenter#464D11
hypocenterC11#3262
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #10623213C2semidirect
2. #10623113C2semidirect
3. C11×#464C2semidirect
4. #10622801C2semidirect
5. #10622798C2semidirect
6. #10622787C2semidirect
7. #10622778C2semidirect
8. #10622670C2semidirect
9. #10622634C2semidirect
10. #10622459C2semidirect
11. #10622452C2semidirect
12. #10622425C2semidirect
13. #10622407C2semidirect
15. #10622372C2semidirect
155. #464D11semidirect
280. C11#3262semidirect

Maximal subgroups

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

subgroupindex
#106232132
#106231132
C11×#4642
#106228012
#106227982
#106227872
#106227782
#106226702
#106226342
#106224592
#106224522
#106224252
#106224072
#106223882
#106223722
#326211