Finite Group Databasebeta

← #13081092

Subgroups — #13081092

Order 1408.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623149C211yesmaximal, characteristic, complemented
2#10623142C211yesmaximal, characteristic, complemented
3C11×#466C211yesmaximal, characteristic, complemented
4#10622772C211yesmaximal, characteristic, complemented
5#10622765C211yesmaximal, characteristic, complemented
6#10622724C211yesmaximal, characteristic, complemented
7C2×#66881C211yesmaximal, characteristic, complemented
8#10622647C211yesmaximal, characteristic, complemented
9#10622646C211yesmaximal, characteristic, complemented
10#10622494C211yesmaximal, characteristic, complemented
11#10622489C211yesmaximal, characteristic, complemented
12#10622392C211yesmaximal, characteristic, complemented
13#10622390C211yesmaximal, characteristic, complemented
14#10622376C211yesmaximal, characteristic, complemented
15#10622374C211yesmaximal, characteristic, complemented
16C2×#4341—21no—
17C2×C11×D8C2211yescharacteristic
18C22×C8×C11C2211yescharacteristic
19C11×#121C2211yescharacteristic
20C11×#121C2211yescharacteristic
21#66992—21no—
22#66991C2211yescharacteristic
23#66991C2211yescharacteristic
24#66988—21no—
25D4×Dic11—21no—
26D4×Dic11C2211yescharacteristic
27D4×Dic11C2211yescharacteristic
28C4×C22⋊D11C2211yescharacteristic
29C2×C4⋊Dic11C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31C2×#4313C2211yescharacteristic
32#66945C2211yescharacteristic
33C4⋊C4×D11C2211yescharacteristic
34#66943C2211yescharacteristic
35#66941C2211yescharacteristic
36#66939—21no—
37#66936—21no—
38#66932—21no—
39#66931—21no—
40C11×#107C2211yescharacteristic
41C11×#102C2211yescharacteristic
42C11×#102C2211yescharacteristic
43#66896C2211yescharacteristic
44#66896C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47C22⋊(C11⋊C8)C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66881C2211yescharacteristic
50#66881C2211yescharacteristic
51#66881C2211yescharacteristic
52#66881C2211yescharacteristic
53#66879C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11D411yescharacteristic
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71#4341—44no—
72C2×C4×D11—21no—
73C2×C4×D11C2311yescharacteristic
74C2×Dic22—21no—
75C11×D8—22no—
76C2×C8×C11—22no—
77C2×C8×C11C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C22⋊C4—21no—
82C11×C22⋊C4—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11D411yescharacteristic
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4D411yescharacteristic
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4D411yescharacteristic
101C4×Dic11—21no—
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#4313—22no—
106#3345—111nomaximal, Sylow
107C23×C11—21no—
108C23×C11—21no—
109C23×C11C2×D411yescharacteristic
110C22×D11C2×D411yescharacteristic
111D4×C11—21no—
112D4×C11—21no—
113D4×C11—21no—
114D4×C11—21no—
115D4×C11—42no—
116D4×C11—42no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2411yescharacteristic
123C22⋊D11—22no—
124C22⋊D11—42no—
125C22⋊D11—81no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—81no—
133C2×Dic11—81no—
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137C4×D11—21no—
138C4×D11—21no—
139C4×D11—42no—
140Dic22—42no—
141C8×C11—21no—
142C8×C11#4112yescomplemented
143C11⋊C8—21no—
144C11⋊C8—21no—
145#553—111no—
146#547—111no—
147#501—111no—
148#482—111no—
149#481—111no—
150#481—111no—
151#480—111no—
152#478—111no—
153#476—111no—
154#469—111no—
155#466D1111yescharacteristic, complemented
156#442—111no—
157#435—111no—
158#428—111no—
159C2×#106—111no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11AGL(1,ℤ/8)12yes—
169C22×C11C22×D411yescharacteristic
170C2×D11—21no—
171C2×D11—21no—
172C2×D11—21no—
173C4×C11—21no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11C2×#4111yescharacteristic
177C4×C112−1+411yescharacteristic
178Dic11—21no—
179Dic11—21no—
180Dic11—21no—
181Dic11—41no—
182Dic11—41no—
183Dic11—41no—
184Dic11—41no—
185C2×#41—221no—
186C2×D8C2×D1111yescharacteristic
187C2×M16—111no—
188C22×C8C2×D1111yescharacteristic
189C4⋊Q8—111no—
190#126—221no—
191#125—111no—
192#123—221no—
193#123—221no—
194#123—221no—
195C22⋊Q8—221no—
196#121—111no—
197#121—111no—
198#121—221no—
199#121C2×D1111yescharacteristic
200#121C2×D1111yescharacteristic
201C4×D4—111no—
202C4×D4—111no—
203C4×D4—111no—
204C4×D4—221no—
205#117—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—111no—
209#107—111no—
210#107—111no—
211#107C2×D1111yescharacteristic
212#106—111no—
213#106—111no—
214#106—111no—
215#106—111no—
216#106—111no—
217#106—111no—
218C4⋊C8—111no—
219#102—111no—
220#102—111no—
221#102—111no—
222#102—111no—
223#102C2×D1111yescharacteristic
224#102C2×D1111yescharacteristic
225C22⋊C8—111no—
226C22⋊C8—111no—
227#97—111no—
228C2×C11—22no—
229C2×C11—81no—
230C2×C11—81no—
231C2×C11#54711yescharacteristic
232C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
233C2×C11#57711yescharacteristic
234D11—41no—
235#41—444no—
236C2×Q8—221no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—111no—
240C2×D4—221no—
241C2×D4—221no—
242C2×D4C22×D1111yescharacteristic
243C2×D4C22×D1111yescharacteristic
244C22×C4—111no—
245C22×C4—221no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4C22×D1111yescharacteristic
251D8—22no—
252M16—222no—
253C2×C8—22no—
254C2×C8—111no—
255C2×C8—111no—
256C2×C8C22×D1111yescharacteristic
257C2×C8C22×D1111yescharacteristic
258C4⋊C4—111no—
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—111no—
262C4⋊C4—111no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4C22×D1111yescharacteristic
270C4⋊C4C22×D1111yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—111no—
274C22⋊C4—111no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C42—111no—
281C42—221no—
282C11#334511yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23—111no—
286C23D4×D1111yescharacteristic
287Q8—442no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—42no—
294D4—222no—
295D4—442no—
296D4—881no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—111no—
302C2×C4—111no—
303C2×C4—111no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—442no—
311C2×C4—442no—
312C2×C4—442no—
313C2×C4—881no—
314C2×C4—881no—
315C2×C4D4×D1111yescharacteristic
316C2×C4C23×D1111yescharacteristic
317C8—21no—
318C8—221no—
319C8—221no—
320C8#434112yescomplemented
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—221no—
330C22—221no—
331C22—221no—
332C22#6696412yes—
333C22C2×D4×D1111yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—221no—
338C4—221no—
339C4—221no—
340C4—441no—
341C4—441no—
342C4—441no—
343C4—441no—
344C4C2×#434111yescharacteristic
345C4#6704311yescharacteristic
346C2—22no—
347C2—81no—
348C2—81no—
349C2—441no—
350C2#1062314211yescharacteristic
351C2C2×#6696411yescharacteristic
352C2#1062330111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#466C2
socleC22×C11C22×D4
hypercenter#466D11
hypocenterC11#3345
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #10623149C2semidirect
2. #10623142C2semidirect
3. C11×#466C2semidirect
4. #10622772C2semidirect
5. #10622765C2semidirect
6. #10622724C2semidirect
7. C2×#66881C2semidirect
8. #10622647C2semidirect
9. #10622646C2semidirect
10. #10622494C2semidirect
11. #10622489C2semidirect
12. #10622392C2semidirect
13. #10622390C2semidirect
14. #10622376C2semidirect
15. #10622374C2semidirect
142. C8×C11#41semidirect
155. #466D11semidirect
282. C11#3345semidirect
320. C8#4341semidirect

Maximal subgroups

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

subgroupindex
#106231492
#106231422
C11×#4662
#106227722
#106227652
#106227242
C2×#668812
#106226472
#106226462
#106224942
#106224892
#106223922
#106223902
#106223762
#106223742
#334511