Finite Group Databasebeta

← #13080014

Subgroups — #13080014

Order 1408.

354 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#10623211C211yesmaximal, characteristic, complemented
2#10623088C211yesmaximal, characteristic, complemented
3C11×#463C211yesmaximal, characteristic, complemented
4#10622787C211yesmaximal, characteristic, complemented
5#10622779C211yesmaximal, characteristic, complemented
6#10622772C211yesmaximal, characteristic
7#10622766C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622622C211yesmaximal, characteristic, complemented
10#10622450C211yesmaximal, characteristic, complemented
11#10622442C211yesmaximal, characteristic, complemented
12#10622429C211yesmaximal, characteristic, complemented
13#10622412C211yesmaximal, characteristic, complemented
14#10622393C211yesmaximal, characteristic, complemented
15#10622379C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C2×C11×D8C2211yescharacteristic
18C11×#124C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20#66999C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23#66991C2211yescharacteristic
24#66991C2211yescharacteristic
25#66989C2211yescharacteristic
26D4×Dic11C2211yescharacteristic
27C2×#4324C2211yescharacteristic
28C4×C22⋊D11—21no—
29#66979—21no—
30C2×#4313C2211yescharacteristic
31C2×#4313C2211yescharacteristic
32#66950C2211yescharacteristic
33#66943C2211yescharacteristic
34#66936—21no—
35#66936—21no—
36(C22⋊D11)⋊C4—21no—
37#66932—21no—
38#66932—21no—
39#66930—21no—
40C42×D11C2211yescharacteristic
41#66923C2211yescharacteristic
42C4×Dic22C2211yescharacteristic
43C11×C4⋊C8C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C22×Dic11—21no—
66C2×C4×D11D411yescharacteristic
67C2×C4×D11D411yescharacteristic
68C2×C4×D11C2311yescharacteristic
69C2×Dic22C2311yescharacteristic
70C11×SD16—41no—
71C11×D8—41no—
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C22⋊C4—21no—
76C11×C22⋊C4—21no—
77C11×C22⋊C4—21no—
78C42×C11C2311yescharacteristic
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84#4326—41no—
85#4324—41no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11D411yescharacteristic
102C4×Dic11D411yescharacteristic
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#4313—41no—
107#4313—41no—
108#3256—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11—21no—
111C22×D11C2×D411yescharacteristic
112Q8×C11—21no—
113Q8×C11—21no—
114D4×C11—21no—
115D4×C11—21no—
116D4×C11—21no—
117D4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—42no—
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2411yescharacteristic
124C22⋊D11—42no—
125C22⋊D11—42no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—42no—
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134C4×D11—21no—
135C4×D11—21no—
136C4×D11—41no—
137C4×D11—41no—
138Dic22—21no—
139Dic22—21no—
140C8×C11—21no—
141C8×C11—21no—
142C11⋊C8—21no—
143C11⋊C8—21no—
144#529—111no—
145#529—111no—
146#479—111no—
147#479—111no—
148#478—111no—
149#478—111no—
150#470—111no—
151#469—111no—
152#468—111no—
153#468—111no—
154#464—111no—
155#464—111no—
156#463—111no—
157#463D1111yescharacteristic, complemented
158#423—111no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11C22×D411yescharacteristic
166C2×D11—21no—
167C2×D11—21no—
168C2×D11—21no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11H(5,𝔽2)11yescharacteristic
174C4×C112−1+411yescharacteristic
175Dic11—21no—
176Dic11—21no—
177Dic11—21no—
178Dic11—41no—
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182C2×Q16—111no—
183C2×SD16—111no—
184C2×SD16C2×D1111yescharacteristic
185C2×D8C2×D1111yescharacteristic
186C2×M16—111no—
187C2×M16—111no—
188#126—221no—
189#126—221no—
190#125—111no—
191#125—111no—
192#124—111no—
193#124C2×D1111yescharacteristic
194#123—221no—
195#123—221no—
196C22⋊Q8—111no—
197C22⋊Q8—111no—
198#121—111no—
199#121—111no—
200C4×Q8—111no—
201C4×Q8—111no—
202C4×D4—111no—
203C4×D4—221no—
204C4×D4—221no—
205C4×D4C2×D1111yescharacteristic
206#117—221no—
207#117—221no—
208C2×C42—111no—
209#107—111no—
210#107—111no—
211#106—111no—
212#106—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—81no—
227C2×C11#53711yescharacteristic
228C2×C11#57511yescharacteristic
229C2×C11#57511yescharacteristic
230D11—41no—
231C2×Q8—111no—
232C2×Q8C22×D1111yescharacteristic
233C2×D4—221no—
234C2×D4—221no—
235C2×D4C22×D1111yescharacteristic
236C2×D4C22×D1111yescharacteristic
237C22×C4—21no—
238C22×C4—111no—
239C22×C4—111no—
240C22×C4—111no—
241C22×C4—221no—
242Q16—441no—
243SD16—41no—
244SD16—441no—
245D8—41no—
246M16—441no—
247M16—441no—
248C2×C8—111no—
249C2×C8—111no—
250C2×C8C22×D1111yescharacteristic
251C2×C8C22×D1111yescharacteristic
252C4⋊C4—111no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
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—21no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C42—111no—
275C42—111no—
276C42—111no—
277C42—221no—
278C42—221no—
279C42C22×D1111yescharacteristic
280C11#325611yescharacteristic, complemented, Sylow
281C23—21no—
282C23—21no—
283C23—111no—
284Q8—21no—
285Q8—21no—
286Q8—221no—
287Q8—221no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—442no—
293D4—442no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—111no—
298C2×C4—111no—
299C2×C4—111no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—442no—
309C2×C4D4×D1111yescharacteristic
310C2×C4D4×D1111yescharacteristic
311C2×C4C23×D1111yescharacteristic
312C8—21no—
313C8—21no—
314C8—221no—
315C8—221no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—221no—
323C22—221no—
324C22—221no—
325C22C2×D4×D1111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—221no—
331C4—221no—
332C4—221no—
333C4—441no—
334C4—441no—
335C4—441no—
336C4—441no—
337C4#6703711yescharacteristic
338C4#6704311yescharacteristic
339C2—81no—
340C2—81no—
341C2—441no—
342C2#1062313911yescharacteristic
343C2#1062329911yescharacteristic
344C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#463C2
socleC22×C11C22×D4
prime radical#10622772C2
hypercenter#463D11
hypocenterC11#3256
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #10623211C2semidirect
2. #10623088C2semidirect
3. C11×#463C2semidirect
4. #10622787C2semidirect
5. #10622779C2semidirect
7. #10622766C2semidirect
8. #10622667C2semidirect
9. #10622622C2semidirect
10. #10622450C2semidirect
11. #10622442C2semidirect
12. #10622429C2semidirect
13. #10622412C2semidirect
14. #10622393C2semidirect
15. #10622379C2semidirect
157. #463D11semidirect
280. C11#3256semidirect

Maximal subgroups

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

subgroupindex
#106232112
#106230882
C11×#4632
#106227872
#106227792
#106227722
#106227662
#106226672
#106226222
#106224502
#106224422
#106224292
#106224122
#106223932
#106223792
#325611