Finite Group Databasebeta

← #13081701

Subgroups — #13081701

Order 1408.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623244C211yesmaximal, characteristic, complemented
2#10623212C211yesmaximal, characteristic, complemented
3C11×#496C211yesmaximal, characteristic, complemented
4#10622781C211yesmaximal, characteristic, complemented
5#10622779C211yesmaximal, characteristic, complemented
6#10622778C211yesmaximal, characteristic, complemented
7#10622777C211yesmaximal, characteristic, complemented
8#10622767C211yesmaximal, characteristic, complemented
9#10622766C211yesmaximal, characteristic, complemented
10#10622763C211yesmaximal, characteristic, complemented
11D8×Dic11C211yesmaximal, characteristic, complemented
12#10622685C211yesmaximal, characteristic, complemented
13#10622667C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C2×C11×D8C2211yescharacteristic
19C2×C11×D8C2211yescharacteristic
20C11×#127C2211yescharacteristic
21C11×#124C2211yescharacteristic
22#67000C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24C2×#4326C2211yescharacteristic
25#66993C2211yescharacteristic
26#66989—21no—
27#66989C2211yescharacteristic
28#66989C2211yescharacteristic
29#66988—21no—
30#66988—21no—
31D4×Dic11—21no—
32D4×Dic11C2211yescharacteristic
33D4×Dic11C2211yescharacteristic
34D4×Dic11C2211yescharacteristic
35C2×#4324C2211yescharacteristic
36C2×#4323C2211yescharacteristic
37C2×#4323C2211yescharacteristic
38C2×#4314C2211yescharacteristic
39#66939—21no—
40#66938—21no—
41#66936—21no—
42(C22⋊D11)⋊C4—21no—
43C4×D44C2211yescharacteristic
44C4×Dic22C2211yescharacteristic
45C4×Dic22C2211yescharacteristic
46C11×#97C2211yescharacteristic
47#66899C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50#66896C2211yescharacteristic
51#66885C2211yescharacteristic
52#66882C2211yescharacteristic
53#66880C2211yescharacteristic
54#66879C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56Dic11⋊C8C2211yescharacteristic
57C8×Dic11C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C2×D44C2311yescharacteristic
71C2×C4×D11—21no—
72C2×Dic22D411yescharacteristic
73C2×Dic22C2311yescharacteristic
74C11×SD16—22no—
75C11×SD16—41no—
76C11×D8—22no—
77C11×D8—41no—
78C2×C8×C11C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C11×C22⋊C4—21no—
81C11×C22⋊C4—21no—
82C42×C11C2311yescharacteristic
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90#4326—41no—
91#4324—41no—
92#4323—41no—
93#4323—41no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11D411yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101Dic11⋊C4—21no—
102Dic11⋊C4D411yescharacteristic
103Dic11⋊C4D411yescharacteristic
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4314—22no—
111#3403—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C22×D11—21no—
116Q8×C11—21no—
117Q8×C11—21no—
118D4×C11—21no—
119D4×C11—21no—
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—42no—
125D4×C11—81no—
126C2×C4×C11—21no—
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2411yescharacteristic
130C22⋊D11—42no—
131C22⋊D11—81no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—81no—
136C2×Dic11—81no—
137C2×Dic11—81no—
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140C2×Dic11C2×D411yescharacteristic
141C2×Dic11C2×D411yescharacteristic
142D44—21no—
143D44—21no—
144C4×D11—81no—
145Dic22—21no—
146Dic22—21no—
147Dic22—41no—
148C8×C11—21no—
149C8×C11#4112yes—
150C11⋊C8—21no—
151C11⋊C8—21no—
152#559—111no—
153#559—111no—
154#496—111no—
155#496D1111yescharacteristic, complemented
156#495—111no—
157#464—111no—
158#464—111no—
159#463—111no—
160#463—111no—
161#459—111no—
162#459—111no—
163#446—111no—
164#440—111no—
165#440—111no—
166C4×D8—111no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11C22×D411yescharacteristic
177C2×D11—41no—
178C2×D11—41no—
179C2×D11—41no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—41no—
183C4×C11C2×#4111yescharacteristic
184C4×C11H(5,𝔽2)11yescharacteristic
185Dic11—21no—
186Dic11—21no—
187Dic11—21no—
188Dic11—21no—
189Dic11—41no—
190Dic11—41no—
191Dic11—41no—
192C2×Q16—111no—
193C2×SD16—111no—
194C2×SD16—111no—
195C2×SD16C2×D1111yescharacteristic
196C2×SD16C2×D1111yescharacteristic
197C2×D8—111no—
198C2×D8—111no—
199C2×D8C2×D1111yescharacteristic
200C2×D8C2×D1111yescharacteristic
201#127—111no—
202#127C2×D1111yescharacteristic
203#124—111no—
204#124—111no—
205#124—111no—
206#124—221no—
207#124—221no—
208#124C2×D1111yescharacteristic
209#123—221no—
210#123—221no—
211#123—221no—
212#123—221no—
213C4×Q8—111no—
214C4×Q8—111no—
215C4×Q8—111no—
216C4×D4—111no—
217C4×D4—111no—
218C4×D4—111no—
219C4×D4—111no—
220C4×D4—221no—
221C4×D4—221no—
222#107—111no—
223C4⋊C8—111no—
224C4⋊C8—111no—
225C4⋊C8—111no—
226#103—111no—
227#103—111no—
228#102—111no—
229#102—111no—
230#102—111no—
231#102—111no—
232#97—111no—
233#97C2×D1111yescharacteristic
234C4×C8—111no—
235C2×C11—81no—
236C2×C11—81no—
237C2×C11—81no—
238C2×C11#55011yescharacteristic
239C2×C11#57511yescharacteristic
240C2×C11#57611yescharacteristic
241D11—81no—
242C2×Q8—111no—
243C2×Q8—111no—
244C2×Q8C22×D1111yescharacteristic
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—111no—
248C2×D4—221no—
249C2×D4—221no—
250C2×D4C22×D1111yescharacteristic
251C2×D4C22×D1111yescharacteristic
252C2×D4C22×D1111yescharacteristic
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257Q16—441no—
258SD16—22no—
259SD16—41no—
260SD16—222no—
261SD16—441no—
262D8—22no—
263D8—41no—
264D8—441no—
265D8—441no—
266C2×C8—111no—
267C2×C8—111no—
268C2×C8C22×D1111yescharacteristic
269C2×C8C22×D1111yescharacteristic
270C4⋊C4—111no—
271C4⋊C4—111no—
272C4⋊C4—111no—
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C42—111no—
290C42—111no—
291C42—221no—
292C42—221no—
293C42C22×D1111yescharacteristic
294C11#340311yescharacteristic, complemented, Sylow
295C23—21no—
296C23—21no—
297C23—21no—
298C23—221no—
299Q8—21no—
300Q8—21no—
301Q8—221no—
302Q8—221no—
303Q8—441no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—21no—
310D4—42no—
311D4—81no—
312D4—221no—
313D4—221no—
314D4—442no—
315D4—881no—
316C2×C4—21no—
317C2×C4—111no—
318C2×C4—111no—
319C2×C4—111no—
320C2×C4—111no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—881no—
325C2×C4—881no—
326C2×C4—881no—
327C2×C4—881no—
328C2×C4D4×D1111yescharacteristic
329C2×C4D4×D1111yescharacteristic
330C2×C4C23×D1111yescharacteristic
331C8—21no—
332C8—221no—
333C8—221no—
334C8#434112yes—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—441no—
345C22—441no—
346C22—441no—
347C22C2×D4×D1111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—221no—
352C4—221no—
353C4—221no—
354C4—221no—
355C4—441no—
356C4—441no—
357C4—441no—
358C4C2×#434111yescharacteristic
359C4#6703711yescharacteristic
360C2—81no—
361C2—81no—
362C2—81no—
363C2—881no—
364C2#1062324911yescharacteristic
365C2#1062330411yescharacteristic
366C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#496C2
socleC22×C11C22×D4
hypercenter#496D11
hypocenterC11#3403
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #10623244C2semidirect
2. #10623212C2semidirect
3. C11×#496C2semidirect
4. #10622781C2semidirect
5. #10622779C2semidirect
6. #10622778C2semidirect
7. #10622777C2semidirect
8. #10622767C2semidirect
9. #10622766C2semidirect
10. #10622763C2semidirect
11. D8×Dic11C2semidirect
12. #10622685C2semidirect
13. #10622667C2semidirect
14. #10622323C2semidirect
15. #10622314C2semidirect
155. #496D11semidirect
294. C11#3403semidirect

Maximal subgroups

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

subgroupindex
#106232442
#106232122
C11×#4962
#106227812
#106227792
#106227782
#106227772
#106227672
#106227662
#106227632
D8×Dic112
#106226852
#106226672
#106223232
#106223142
#340311