Finite Group Databasebeta

← #13081633

Subgroups — #13081633

Order 1408.

406 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623249C211yesmaximal, characteristic, complemented
2#10623202C211yesmaximal, characteristic, complemented
3C11×#496C211yesmaximal, characteristic, complemented
4#10622788C211yesmaximal, characteristic, complemented
5#10622777C211yesmaximal, characteristic, complemented
6#10622776C211yesmaximal, characteristic, complemented
7#10622775C211yesmaximal, characteristic, complemented
8#10622767C211yesmaximal, characteristic, complemented
9#10622766C211yesmaximal, characteristic, complemented
10#10622763C211yesmaximal, characteristic, complemented
11D8×Dic11C211yesmaximal, characteristic, complemented
12#10622688C211yesmaximal, characteristic, complemented
13#10622670C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C2×#4341—21no—
17C2×C11×SD16C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C2×C11×D8C2211yescharacteristic
20C2×C11×D8C2211yescharacteristic
21C11×#127C2211yescharacteristic
22C11×#124C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24#66997C2211yescharacteristic
25C2×#4325C2211yescharacteristic
26#66993C2211yescharacteristic
27#66993C2211yescharacteristic
28#66992—21no—
29#66992—21no—
30#66991—21no—
31#66989C2211yescharacteristic
32D4×Dic11C2211yescharacteristic
33D4×Dic11C2211yescharacteristic
34D4×Dic11C2211yescharacteristic
35C2×#4324C2211yescharacteristic
36C2×#4324C2211yescharacteristic
37C2×#4323C2211yescharacteristic
38C2×#4314C2211yescharacteristic
39#66932—21no—
40#66932—21no—
41#66931—21no—
42#66930—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—
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72#4341—44no—
73C2×D44C2311yescharacteristic
74C2×C4×D11—21no—
75C2×Dic22D411yescharacteristic
76C2×Dic22C2311yescharacteristic
77C11×SD16—22no—
78C11×SD16—41no—
79C11×D8—22no—
80C11×D8—41no—
81C2×C8×C11C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C42×C11C2311yescharacteristic
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91#4325—41no—
92#4324—41no—
93#4324—41no—
94#4323—41no—
95(C2×D11)⋊C4—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11D411yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4D411yescharacteristic
104Dic11⋊C4D411yescharacteristic
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11C2311yescharacteristic
108C4×Dic11C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111#4314—22no—
112#3397—111nomaximal, Sylow
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C22×D11—21no—
117Q8×C11—21no—
118Q8×C11—21no—
119D4×C11—21no—
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—21no—
125D4×C11—42no—
126D4×C11—81no—
127C2×C4×C11—21no—
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C22⋊D11—42no—
132C22⋊D11—42no—
133C22⋊D11—81no—
134C22⋊D11—81no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143C2×Dic11C2×D411yescharacteristic
144C2×Dic11C2×D411yescharacteristic
145D44—21no—
146D44—21no—
147C4×D11—42no—
148Dic22—22no—
149Dic22—21no—
150Dic22—21no—
151C8×C11—21no—
152C8×C11#4112yescomplemented
153C11⋊C8—21no—
154C11⋊C8—21no—
155#556—111no—
156#550—111no—
157#496—111no—
158#496D1111yescharacteristic, complemented
159#492—111no—
160#463—111no—
161#463—111no—
162#461—111no—
163#460—111no—
164#460—111no—
165#459—111no—
166#446—111no—
167#440—111no—
168#440—111no—
169C4×D8—111no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11C22×D411yescharacteristic
180C2×D11—41no—
181C2×D11—41no—
182C2×D11—41no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—41no—
186C4×C11C2×#4111yescharacteristic
187C4×C11H(5,𝔽2)11yescharacteristic
188Dic11—21no—
189Dic11—21no—
190Dic11—21no—
191Dic11—41no—
192Dic11—41no—
193Dic11—41no—
194Dic11AGL(1,ℤ/8)12yes—
195C2×#41—221no—
196C2×SD16—111no—
197C2×SD16—111no—
198C2×SD16—111no—
199C2×SD16—111no—
200C2×SD16C2×D1111yescharacteristic
201C2×SD16C2×D1111yescharacteristic
202C2×D8—111no—
203C2×D8C2×D1111yescharacteristic
204C2×D8C2×D1111yescharacteristic
205C4⋊Q8—111no—
206#127—111no—
207#127—111no—
208#127C2×D1111yescharacteristic
209#126—221no—
210#126—221no—
211#124—111no—
212#124C2×D1111yescharacteristic
213C22⋊Q8—221no—
214#121—221no—
215#121—221no—
216#121—221no—
217C4×Q8—111no—
218C4×Q8—111no—
219C4×Q8—111no—
220C4×D4—111no—
221C4×D4—111no—
222C4×D4—111no—
223C4×D4—111no—
224#117—221no—
225#107—111no—
226C4⋊C8—111no—
227C4⋊C8—111no—
228C4⋊C8—111no—
229#103—111no—
230#103—111no—
231#102—111no—
232#102—111no—
233#102—111no—
234#102—111no—
235#97—111no—
236#97C2×D1111yescharacteristic
237C4×C8—111no—
238C2×C11—81no—
239C2×C11—81no—
240C2×C11—81no—
241C2×C11#55011yescharacteristic
242C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
243C2×C11#57711yescharacteristic
244D11—81no—
245#41—444no—
246C2×Q8—111no—
247C2×Q8—111no—
248C2×Q8C22×D1111yescharacteristic
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—111no—
252C2×D4—221no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4C22×D1111yescharacteristic
257C2×D4C22×D1111yescharacteristic
258C2×D4C22×D1111yescharacteristic
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263SD16—22no—
264SD16—41no—
265SD16—222no—
266SD16—441no—
267SD16—441no—
268SD16—441no—
269D8—22no—
270D8—41no—
271D8—441no—
272C2×C8—111no—
273C2×C8—111no—
274C2×C8C22×D1111yescharacteristic
275C2×C8C22×D1111yescharacteristic
276C4⋊C4—111no—
277C4⋊C4—111no—
278C4⋊C4—111no—
279C4⋊C4—111no—
280C4⋊C4—111no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C42—111no—
294C42—111no—
295C42—221no—
296C42—221no—
297C42C22×D1111yescharacteristic
298C11#339711yescharacteristic, complemented, Sylow
299C23—21no—
300C23—21no—
301C23—21no—
302C23—221no—
303Q8—21no—
304Q8—21no—
305Q8—222no—
306Q8—221no—
307Q8—221no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—81no—
316D4—221no—
317D4—221no—
318D4—442no—
319D4—442no—
320D4—881no—
321D4—881no—
322C2×C4—21no—
323C2×C4—111no—
324C2×C4—111no—
325C2×C4—111no—
326C2×C4—111no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—442no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—442no—
334C2×C4D4×D1111yescharacteristic
335C2×C4D4×D1111yescharacteristic
336C2×C4C23×D1111yescharacteristic
337C8—21no—
338C8—221no—
339C8—221no—
340C8#434112yescomplemented
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—441no—
351C22—441no—
352C22—441no—
353C22C2×D4×D1111yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—112no—
358C4—221no—
359C4—221no—
360C4—221no—
361C4—441no—
362C4—441no—
363C4—441no—
364C4C2×#434111yescharacteristic
365C4#6703711yescharacteristic
366C2—81no—
367C2—81no—
368C2—81no—
369C2—881no—
370C2#1062324911yescharacteristic
371C2D11×AGL(1,ℤ/8)11yescharacteristic
372C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#496C2
socleC22×C11C22×D4
hypercenter#496D11
hypocenterC11#3397
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. #10623249C2semidirect
2. #10623202C2semidirect
3. C11×#496C2semidirect
4. #10622788C2semidirect
5. #10622777C2semidirect
6. #10622776C2semidirect
7. #10622775C2semidirect
8. #10622767C2semidirect
9. #10622766C2semidirect
10. #10622763C2semidirect
11. D8×Dic11C2semidirect
12. #10622688C2semidirect
13. #10622670C2semidirect
14. #10622323C2semidirect
15. #10622314C2semidirect
152. C8×C11#41semidirect
158. #496D11semidirect
298. C11#3397semidirect
340. C8#4341semidirect

Maximal subgroups

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

subgroupindex
#106232492
#106232022
C11×#4962
#106227882
#106227772
#106227762
#106227752
#106227672
#106227662
#106227632
D8×Dic112
#106226882
#106226702
#106223232
#106223142
#339711