Finite Group Databasebeta

← #13079973

Subgroups — #13079973

Order 1408.

392 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623155C211yesmaximal, characteristic, complemented
2#10623127C211yesmaximal, characteristic, complemented
3C11×#468C211yesmaximal, characteristic, complemented
4#10622778C211yesmaximal, characteristic, complemented
5#10622776C211yesmaximal, characteristic, complemented
6#10622748C211yesmaximal, characteristic, complemented
7#10622731C211yesmaximal, characteristic, complemented
8#10622662C211yesmaximal, characteristic, complemented
9#10622652C211yesmaximal, characteristic, complemented
10#10622504C211yesmaximal, characteristic, complemented
11#10622503C211yesmaximal, characteristic, complemented
12#10622432C211yesmaximal, characteristic, complemented
13#10622404C211yesmaximal, characteristic, complemented
14#10622399C211yesmaximal, characteristic, complemented
15#10622376C211yesmaximal, characteristic, complemented
16C2×#4341—21no—
17C2×C11×SD16C2211yescharacteristic
18C2×C11×M16C2211yescharacteristic
19C11×C22⋊Q8C2211yescharacteristic
20C11×#121C2211yescharacteristic
21#67000C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23C2×#4325C2211yescharacteristic
24#66993C2211yescharacteristic
25#66992—21no—
26D4×Dic11C2211yescharacteristic
27C2×#4323C2211yescharacteristic
28#66983C2211yescharacteristic
29#66983C2211yescharacteristic
30C2×C4×Dic11C2211yescharacteristic
31C2×#4318C2211yescharacteristic
32C2×D88C2211yescharacteristic
33#66951—21no—
34#66946C2211yescharacteristic
35#66946C2211yescharacteristic
36#66945—21no—
37#66943C2211yescharacteristic
38#66941C2211yescharacteristic
39#66939—21no—
40#66938—21no—
41(C22⋊D11)⋊C4—21no—
42(C22⋊D11)⋊C4—21no—
43C11×#107C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66881C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C22×Dic11—21no—
68C22×Dic11D411yescharacteristic
69C22×Dic11D411yescharacteristic
70#4341—44no—
71C2×D44C2311yescharacteristic
72C2×D44C2311yescharacteristic
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×Dic22—21no—
76C11×SD16—41no—
77C11×M16—41no—
78C2×C8×C11C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C11×C4⋊C4—21no—
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C22⋊Dic11—21no—
86#4325—41no—
87#4323—41no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100C4×Dic11—21no—
101C4×Dic11D411yescharacteristic
102C4×Dic11D411yescharacteristic
103C4×Dic11C2311yescharacteristic
104C4×Dic11C2311yescharacteristic
105#4318—41no—
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108D88—41no—
109#3251—111nomaximal, Sylow
110C23×C11—21no—
111C23×C11C2×D411yescharacteristic
112C22×D11—21no—
113C22×D11—21no—
114Q8×C11—21no—
115Q8×C11—21no—
116D4×C11—21no—
117D4×C11—21no—
118D4×C11—42no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2411yescharacteristic
126C22⋊D11—42no—
127C22⋊D11—42no—
128C22⋊D11—42no—
129C22⋊D11—42no—
130C2×Dic11—22no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—41no—
134C2×Dic11—42no—
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139D44—21no—
140D44—21no—
141D44—21no—
142D44—21no—
143C4×D11—42no—
144C4×D11—42no—
145Dic22—42no—
146C8×C11—21no—
147C8×C11—21no—
148C11⋊C8—21no—
149C11⋊C8—21no—
150#532—111no—
151#529—111no—
152#478—111no—
153#478—111no—
154#475—111no—
155#474—111no—
156#469—111no—
157#469—111no—
158#468—111no—
159#468D1111yescharacteristic, complemented
160#463—111no—
161#463—111no—
162#460—111no—
163#459—111no—
164#423—111no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11C22×D411yescharacteristic
172C2×D11—41no—
173C2×D11—41no—
174C2×D11—41no—
175C2×D11—41no—
176C2×D11—41no—
177C2×D11—41no—
178C4×C11—21no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11H(5,𝔽2)11yescharacteristic
183C4×C112−1+411yescharacteristic
184Dic11—21no—
185Dic11—21no—
186Dic11—21no—
187Dic11—41no—
188Dic11—41no—
189Dic11AGL(1,ℤ/8)12yes—
190C2×#41—221no—
191C2×SD16—111no—
192C2×SD16C2×D1111yescharacteristic
193C2×D8—111no—
194C2×D8—111no—
195C2×M16—111no—
196C2×M16C2×D1111yescharacteristic
197C4⋊Q8—111no—
198#127—111no—
199#126—221no—
200#125—111no—
201#124—111no—
202#124—221no—
203#123—221no—
204C22⋊Q8C2×D1111yescharacteristic
205#121—111no—
206#121—111no—
207#121—221no—
208#121C2×D1111yescharacteristic
209C4×Q8—111no—
210C4×D4—111no—
211C4×D4—111no—
212C4×D4—111no—
213C4×D4—221no—
214C4×D4—221no—
215#117—221no—
216C2×C42—111no—
217#107—111no—
218#107C2×D1111yescharacteristic
219#106—111no—
220#106—111no—
221C4⋊C8—111no—
222C4⋊C8—111no—
223C4⋊C8—111no—
224C4⋊C8—111no—
225#103—111no—
226#103C2×D1111yescharacteristic
227#102—111no—
228#102—111no—
229#102—111no—
230#102—111no—
231#102—111no—
232#102C2×D1111yescharacteristic
233C2×C11—41no—
234C2×C11—81no—
235C2×C11#53711yescharacteristic
236C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
237C2×C11#57511yescharacteristic
238D11—81no—
239D11—81no—
240#41—444no—
241C2×Q8—221no—
242C2×Q8C22×D1111yescharacteristic
243C2×D4—21no—
244C2×D4—111no—
245C2×D4—111no—
246C2×D4—221no—
247C2×D4—221no—
248C2×D4—221no—
249C2×D4—221no—
250C2×D4C22×D1111yescharacteristic
251C22×C4—111no—
252C22×C4—111no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4C22×D1111yescharacteristic
257SD16—41no—
258SD16—441no—
259D8—441no—
260D8—441no—
261M16—41no—
262M16—441no—
263C2×C8—111no—
264C2×C8—111no—
265C2×C8C22×D1111yescharacteristic
266C2×C8C22×D1111yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—111no—
269C4⋊C4—111no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4C22×D1111yescharacteristic
275C4⋊C4C22×D1111yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C42—111no—
286C42—111no—
287C42—111no—
288C42—111no—
289C42—221no—
290C11#325111yescharacteristic, complemented, Sylow
291C23—21no—
292C23—221no—
293C23—221no—
294C23D4×D1111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—442no—
298D4—21no—
299D4—21no—
300D4—42no—
301D4—221no—
302D4—221no—
303D4—221no—
304D4—221no—
305D4—442no—
306D4—442no—
307D4—442no—
308D4—442no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—111no—
315C2×C4—111no—
316C2×C4—111no—
317C2×C4—111no—
318C2×C4—222no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4—441no—
324C2×C4—442no—
325C2×C4D4×D1111yescharacteristic
326C2×C4C23×D1111yescharacteristic
327C8—21no—
328C8—21no—
329C8—221no—
330C8—221no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—441no—
338C22—441no—
339C22—441no—
340C22—441no—
341C22—441no—
342C22—441no—
343C22C2×D4×D1111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—112no—
349C4—221no—
350C4—221no—
351C4—221no—
352C4—441no—
353C4—441no—
354C4#6703711yescharacteristic
355C4#6704311yescharacteristic
356C2—41no—
357C2—81no—
358C2—881no—
359C2—881no—
360C2#1062312811yescharacteristic
361C2D11×AGL(1,ℤ/8)11yescharacteristic
362C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#468C2
socleC22×C11C22×D4
hypercenter#468D11
hypocenterC11#3251
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #10623155C2semidirect
2. #10623127C2semidirect
3. C11×#468C2semidirect
4. #10622778C2semidirect
5. #10622776C2semidirect
6. #10622748C2semidirect
7. #10622731C2semidirect
8. #10622662C2semidirect
9. #10622652C2semidirect
10. #10622504C2semidirect
11. #10622503C2semidirect
12. #10622432C2semidirect
13. #10622404C2semidirect
14. #10622399C2semidirect
15. #10622376C2semidirect
159. #468D11semidirect
290. C11#3251semidirect

Maximal subgroups

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

subgroupindex
#106231552
#106231272
C11×#4682
#106227782
#106227762
#106227482
#106227312
#106226622
#106226522
#106225042
#106225032
#106224322
#106224042
#106223992
#106223762
#325111