Finite Group Databasebeta

← #13081083

Subgroups — #13081083

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#10623226C211yesmaximal, characteristic, complemented
2#10623082C211yesmaximal, characteristic, complemented
3C11×#478C211yesmaximal, characteristic, complemented
4#10622678C211yesmaximal, characteristic, complemented
5#10622627C211yesmaximal, characteristic, complemented
6#10622495C211yesmaximal, characteristic, complemented
7#10622494C211yesmaximal, characteristic, complemented
8#10622476C211yesmaximal, characteristic, complemented
9D11×#106C211yesmaximal, characteristic, complemented
10#10622455C211yesmaximal, characteristic, complemented
11#10622449C211yesmaximal, characteristic, complemented
12#10622395C211yesmaximal, characteristic, complemented
13#10622392C211yesmaximal, characteristic, complemented
14#10622390C211yesmaximal, characteristic, complemented
15#10622388C211yesmaximal, characteristic, complemented
16C2×#4339—21no—
17C11×#125C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#66991C2211yescharacteristic
20#66991C2211yescharacteristic
21C2×#4323C2211yescharacteristic
22#66977—21no—
23C2×#4313C2211yescharacteristic
24C2×C8×D11C2211yescharacteristic
25#66951—21no—
26#66948—21no—
27#66948C2211yescharacteristic
28#66948C2211yescharacteristic
29#66947—21no—
30#66946—21no—
31#66945C2211yescharacteristic
32C4⋊C4×D11C2211yescharacteristic
33C4⋊C4×D11C2211yescharacteristic
34C4⋊C4×D11C2211yescharacteristic
35#66936—21no—
36#66936—21no—
37C4×D44C2211yescharacteristic
38C4×D44C2211yescharacteristic
39#66922C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×C4⋊C8C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#102C2211yescharacteristic
45#66896C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66881C2211yescharacteristic
51#66881C2211yescharacteristic
52#66873C2211yescharacteristic
53#66872C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×D4×C11C2311yescharacteristic
60C22×C4×C11—21no—
61C2×C22⋊D11—21no—
62C2×C22⋊D11—21no—
63#4339—44no—
64C2×D44—21no—
65C2×D44—21no—
66C2×D44D411yescharacteristic
67C2×D44C2311yescharacteristic
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11C2311yescharacteristic
73C2×C4×D11C2311yescharacteristic
74C2×Dic22—21no—
75C2×C8×C11C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C22⋊C4—21no—
83C42×C11C2311yescharacteristic
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86#4323—22no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4D411yescharacteristic
92(C2×D11)⋊C4D411yescharacteristic
93C4⋊Dic11—21no—
94C4⋊Dic11D411yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C4×Dic11—21no—
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104#4313—22no—
105C8×D11—22no—
106#3345—111nomaximal, Sylow
107C23×C11—21no—
108C22×D11—21no—
109C22×D11C2×D411yescharacteristic
110C22×D11C2×D411yescharacteristic
111D4×C11—21no—
112D4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—42no—
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C22⋊D11—42no—
121C22⋊D11—42no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127D44—22no—
128D44—21no—
129D44—21no—
130D44—42no—
131D44—81no—
132C4×D11—21no—
133C4×D11—21no—
134C4×D11—21no—
135C4×D11—21no—
136C4×D11—42no—
137C4×D11—42no—
138C4×D11—81no—
139C4×D11—81no—
140Dic22—42no—
141C8×C11—21no—
142C8×C11—21no—
143C11⋊C8—21no—
144C11⋊C8#4112yescomplemented
145#553—111no—
146#547—111no—
147#501—111no—
148#482—111no—
149#481—111no—
150#481—111no—
151#480—111no—
152#478D1111yescharacteristic, complemented
153#476—111no—
154#469—111no—
155#466—111no—
156#442—111no—
157#435—111no—
158#428—111no—
159C2×#106—111no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11C22×D411yescharacteristic
164C2×D11—21no—
165C2×D11—21no—
166C2×D11—21no—
167C2×D11—21no—
168C2×D11—21no—
169C2×D11—41no—
170C2×D11—41no—
171C2×D11—41no—
172C2×D11AGL(1,ℤ/8)12yes—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11C2×#4111yescharacteristic
179C4×C112−1+411yescharacteristic
180Dic11—21no—
181Dic11—21no—
182Dic11—41no—
183Dic11—41no—
184Dic11—41no—
185C2×#41—221no—
186C2×D8—111no—
187C2×M16—111no—
188C22×C8—111no—
189C4⋊Q8—111no—
190#126—221no—
191#125C2×D1111yescharacteristic
192#123—221no—
193#123—221no—
194#123—221no—
195C22⋊Q8—221no—
196#121—111no—
197#121—111no—
198#121—111no—
199#121—111no—
200#121—221no—
201C4×D4—111no—
202C4×D4—111no—
203C4×D4—221no—
204C4×D4C2×D1111yescharacteristic
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#106C2×D1111yescharacteristic
218C4⋊C8C2×D1111yescharacteristic
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—81no—
229C2×C11#54711yescharacteristic
230C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
231C2×C11#57711yescharacteristic
232D11—22no—
233D11—41no—
234D11—81no—
235#41—444no—
236C2×Q8—221no—
237C2×D4—111no—
238C2×D4—111no—
239C2×D4—221no—
240C2×D4—221no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4C22×D1111yescharacteristic
244C22×C4—21no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4—221no—
251D8—222no—
252M16—222no—
253C2×C8—111no—
254C2×C8—111no—
255C2×C8—222no—
256C2×C8C22×D1111yescharacteristic
257C2×C8C22×D1111yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—111no—
261C4⋊C4—111no—
262C4⋊C4—111no—
263C4⋊C4—111no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4C22×D1111yescharacteristic
269C4⋊C4C22×D1111yescharacteristic
270C4⋊C4C22×D1111yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—111no—
273C22⋊C4—111no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C42—221no—
281C42C22×D1111yescharacteristic
282C11#334511yescharacteristic, complemented, Sylow
283C23—21no—
284C23—111no—
285C23—111no—
286C23—221no—
287Q8—442no—
288D4—21no—
289D4—21no—
290D4—222no—
291D4—221no—
292D4—221no—
293D4—442no—
294D4—442no—
295D4—442no—
296D4—881no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—42no—
301C2×C4—111no—
302C2×C4—111no—
303C2×C4—221no—
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—881no—
313C2×C4—881no—
314C2×C4D4×D1111yescharacteristic
315C2×C4D4×D1111yescharacteristic
316C2×C4C23×D1111yescharacteristic
317C8—21no—
318C8—21no—
319C8—112no—
320C8—221no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—112no—
325C22—221no—
326C22—221no—
327C22—221no—
328C22—221no—
329C22—221no—
330C22—441no—
331C22—441no—
332C22—441no—
333C22C2×D4×D1111yescharacteristic
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—221no—
340C4—221no—
341C4—441no—
342C4—441no—
343C4—441no—
344C4#6704011yescharacteristic
345C4#41×D1111yescharacteristic
346C2—81no—
347C2—222no—
348C2—441no—
349C2—881no—
350C2#1062316211yescharacteristic
351C2#1062330111yescharacteristic
352C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#478C2
socleC22×C11C22×D4
hypercenter#478D11
hypocenterC11#3345
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #10623226C2semidirect
2. #10623082C2semidirect
3. C11×#478C2semidirect
4. #10622678C2semidirect
5. #10622627C2semidirect
6. #10622495C2semidirect
7. #10622494C2semidirect
8. #10622476C2semidirect
9. D11×#106C2semidirect
10. #10622455C2semidirect
11. #10622449C2semidirect
12. #10622395C2semidirect
13. #10622392C2semidirect
14. #10622390C2semidirect
15. #10622388C2semidirect
144. C11⋊C8#41semidirect
152. #478D11semidirect
282. C11#3345semidirect

Maximal subgroups

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

subgroupindex
#106232262
#106230822
C11×#4782
#106226782
#106226272
#106224952
#106224942
#106224762
D11×#1062
#106224552
#106224492
#106223952
#106223922
#106223902
#106223882
#334511