Finite Group Databasebeta

← #13081206

Subgroups — #13081206

Order 1408.

386 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#10623147C211yesmaximal, characteristic, complemented
2#10623142C211yesmaximal, characteristic, complemented
3C11×#469C211yesmaximal, characteristic, complemented
4#10622772C211yesmaximal, characteristic, complemented
5D8×Dic11C211yesmaximal, characteristic, complemented
6#10622741C211yesmaximal, characteristic, complemented
7#10622734C211yesmaximal, characteristic, complemented
8#10622648C211yesmaximal, characteristic, complemented
9#10622647C211yesmaximal, characteristic, complemented
10#10622474C211yesmaximal, characteristic, complemented
11#10622468C211yesmaximal, characteristic, complemented
12#10622397C211yesmaximal, characteristic, complemented
13#10622390C211yesmaximal, characteristic, complemented
14#10622374C211yesmaximal, characteristic, complemented
15#10622372C211yesmaximal, characteristic, complemented
16C2×#4341—21no—
17C2×C11×D8C2211yescharacteristic
18C2×C11×M16C2211yescharacteristic
19C11×#121C2211yescharacteristic
20C11×#121C2211yescharacteristic
21#66992—21no—
22#66991C2211yescharacteristic
23#66991C2211yescharacteristic
24#66989—21no—
25#66988—21no—
26D4×Dic11C2211yescharacteristic
27D4×Dic11C2211yescharacteristic
28C4×C22⋊D11C2211yescharacteristic
29#66979C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31C2×#4313C2211yescharacteristic
32#66945C2211yescharacteristic
33C4⋊C4×D11C2211yescharacteristic
34#66941C2211yescharacteristic
35#66941C2211yescharacteristic
36#66938—21no—
37#66936—21no—
38#66931—21no—
39#66930—21no—
40C11×#106C2211yescharacteristic
41C11×#102C2211yescharacteristic
42C11×#102C2211yescharacteristic
43#66896C2211yescharacteristic
44#66896C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47C22⋊(C11⋊C8)C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66882C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66881C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54C8×Dic11C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66872C2211yescharacteristic
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—
70#4341—44no—
71C2×C4×D11—21no—
72C2×C4×D11C2311yescharacteristic
73C2×Dic22—21no—
74C2×Dic22—21no—
75C11×D8—22no—
76C11×M16—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⋊Dic11—21no—
88C22⋊Dic11D411yescharacteristic
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4D411yescharacteristic
91C4⋊Dic11—21no—
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4D411yescharacteristic
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#4313—22no—
106#3354—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—81no—
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—42no—
133C2×Dic11C2×D411yescharacteristic
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136C4×D11—21no—
137C4×D11—21no—
138C4×D11—42no—
139Dic22—42no—
140Dic22—81no—
141C8×C11—21no—
142C8×C11#4112yescomplemented
143C11⋊C8—21no—
144C11⋊C8—21no—
145#555—111no—
146#547—111no—
147#498—111no—
148#482—111no—
149#482—111no—
150#481—111no—
151#481—111no—
152#476—111no—
153#474—111no—
154#469—111no—
155#469D1111yescharacteristic, complemented
156C4×D8—111no—
157#436—111no—
158#428—111no—
159#428—111no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
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—41no—
181Dic11—41no—
182Dic11—41no—
183Dic11—41no—
184Dic11AGL(1,ℤ/8)12yes—
185C2×#41—221no—
186C2×D8C2×D1111yescharacteristic
187C2×M16—111no—
188C2×M16C2×D1111yescharacteristic
189C4⋊Q8—111no—
190C4⋊Q8—111no—
191#124—221no—
192#124—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—
204#117—111no—
205#117—111no—
206#117—221no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—111no—
209#107—111no—
210#107—111no—
211#107—111no—
212#106—111no—
213#106—111no—
214#106—111no—
215#106—111no—
216#106—111no—
217#106C2×D1111yescharacteristic
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—
227C4×C8—111no—
228C2×C11—41no—
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×Q8—221no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—111no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4C22×D1111yescharacteristic
244C2×D4C22×D1111yescharacteristic
245C22×C4—111no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4C22×D1111yescharacteristic
251D8—22no—
252M16—22no—
253M16—222no—
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⋊C4C22×D1111yescharacteristic
268C4⋊C4C22×D1111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—111no—
272C22⋊C4—111no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C42—111no—
280C42—221no—
281C42—221no—
282C11#335411yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23—111no—
286C23D4×D1111yescharacteristic
287Q8—442no—
288Q8—881no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—21no—
293D4—42no—
294D4—81no—
295D4—222no—
296D4—442no—
297D4—881no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—111no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—442no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4—442no—
315C2×C4D4×D1111yescharacteristic
316C2×C4C23×D1111yescharacteristic
317C8—21no—
318C8—221no—
319C8—221no—
320C8#434112yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—221no—
331C22—221no—
332C22—221no—
333C22C2×D4×D1111yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—112no—
338C4—221no—
339C4—221no—
340C4—441no—
341C4—441no—
342C4—441no—
343C4—441no—
344C4C2×#434111yescharacteristic
345C4#6704311yescharacteristic
346C2—41no—
347C2—81no—
348C2—81no—
349C2—441no—
350C2#1062314211yescharacteristic
351C2D11×AGL(1,ℤ/8)11yescharacteristic
352C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#469C2
socleC22×C11C22×D4
hypercenter#469D11
hypocenterC11#3354
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #10623147C2semidirect
2. #10623142C2semidirect
3. C11×#469C2semidirect
4. #10622772C2semidirect
5. D8×Dic11C2semidirect
6. #10622741C2semidirect
7. #10622734C2semidirect
8. #10622648C2semidirect
9. #10622647C2semidirect
10. #10622474C2semidirect
11. #10622468C2semidirect
12. #10622397C2semidirect
13. #10622390C2semidirect
14. #10622374C2semidirect
15. #10622372C2semidirect
142. C8×C11#41semidirect
155. #469D11semidirect
282. C11#3354semidirect
320. C8#4341semidirect

Maximal subgroups

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

subgroupindex
#106231472
#106231422
C11×#4692
#106227722
D8×Dic112
#106227412
#106227342
#106226482
#106226472
#106224742
#106224682
#106223972
#106223902
#106223742
#106223722
#335411