Finite Group Databasebeta

← #13080604

Subgroups — #13080604

Order 1408.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623257C211yesmaximal, characteristic, complemented
2#10623107C211yesmaximal, characteristic, complemented
3C11×#477C211yesmaximal, characteristic, complemented
4#10622702C211yesmaximal, characteristic, complemented
5#10622639C211yesmaximal, characteristic, complemented
6#10622499C211yesmaximal, characteristic, complemented
7#10622497C211yesmaximal, characteristic, complemented
8#10622496C211yesmaximal, characteristic, complemented
9#10622495C211yesmaximal, characteristic, complemented
10#10622457C211yesmaximal, characteristic, complemented
11#10622449C211yesmaximal, characteristic, complemented
12#10622424C211yesmaximal, characteristic, complemented
13#10622419C211yesmaximal, characteristic, complemented
14#10622416C211yesmaximal, characteristic, complemented
15D11×#103C211yesmaximal, characteristic, complemented
16C2×#4343—21no—
17C2×#4343C2211yescharacteristic
18C2×Q8×D11C2211yescharacteristic
19C11×C4⋊Q8C2211yescharacteristic
20C4×Q8×C11C2211yescharacteristic
21#66999—21no—
22C2×#4325C2211yescharacteristic
23C2×D88C2211yescharacteristic
24C2×#4314C2211yescharacteristic
25C2×#4313C2211yescharacteristic
26C2×C8×D11C2211yescharacteristic
27#66950—21no—
28#66950C2211yescharacteristic
29#66948—21no—
30#66948C2211yescharacteristic
31#66948C2211yescharacteristic
32#66948C2211yescharacteristic
33#66947—21no—
34#66947—21no—
35C4⋊C4×D11C2211yescharacteristic
36C4⋊C4×D11C2211yescharacteristic
37#66928—21no—
38#66928C2211yescharacteristic
39C4×D44—21no—
40C4×D44C2211yescharacteristic
41C4×D44C2211yescharacteristic
42C11×#107C2211yescharacteristic
43C11×#107C2211yescharacteristic
44C11×C4⋊C8C2211yescharacteristic
45C11×#103C2211yescharacteristic
46C11×#103C2211yescharacteristic
47#66899C2211yescharacteristic
48#66885C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66880C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61#4343—22no—
62#4343—41no—
63#4343—44no—
64Q8×D11—22no—
65Q8×D11—41no—
66C2×D44—21no—
67C2×D44—21no—
68C2×D44—21no—
69C2×D44—21no—
70C2×D44D411yescharacteristic
71C2×D44C2311yescharacteristic
72C2×D44C2311yescharacteristic
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×C4×D11C2311yescharacteristic
80C2×Dic22—21no—
81C2×Dic22C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4C2311yescharacteristic
87C11×C4⋊C4C2311yescharacteristic
88C11×C4⋊C4C2311yescharacteristic
89C42×C11—21no—
90C42×C11C2311yescharacteristic
91#4325—22no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4D411yescharacteristic
100(C2×D11)⋊C4D411yescharacteristic
101C4⋊Dic11—21no—
102C4⋊Dic11D411yescharacteristic
103C4⋊Dic11C2311yescharacteristic
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108D88—41no—
109#4314—41no—
110#4313—41no—
111C8×D11—41no—
112#3308—111nomaximal, Sylow
113C22×D11—21no—
114C22×D11—21no—
115C22×D11C2×D411yescharacteristic
116C22×D11C2×D411yescharacteristic
117Q8×C11—21no—
118Q8×C11—42no—
119Q8×C11#4112yescomplemented
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2411yescharacteristic
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131D44—22no—
132D44—21no—
133D44—21no—
134D44—21no—
135D44—21no—
136D44—42no—
137D44—42no—
138D44—42no—
139D44—42no—
140C4×D11—21no—
141C4×D11—21no—
142C4×D11—21no—
143C4×D11—21no—
144C4×D11—42no—
145C4×D11—42no—
146C4×D11—42no—
147C4×D11—42no—
148C4×D11—42no—
149Dic22—21no—
150Dic22—21no—
151Dic22—42no—
152C8×C11—21no—
153C8×C11—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156#548—111no—
157#547—111no—
158#489—111no—
159#484—111no—
160#480—111no—
161#477D1111yescharacteristic, complemented
162#468—111no—
163#466—111no—
164#463—111no—
165#449—111no—
166#448—111no—
167#440—111no—
168#435—111no—
169#417—111no—
170C2×#103—111no—
171C22×C11C22×D411yescharacteristic
172C2×D11—21no—
173C2×D11—21no—
174C2×D11—21no—
175C2×D11—21no—
176C2×D11—21no—
177C2×D11—41no—
178C2×D11—41no—
179C2×D11—41no—
180C2×D11—41no—
181C2×D11—41no—
182C2×D11—41no—
183C2×D11AGL(1,ℤ/8)12yes—
184C4×C11—22no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11C2×#4111yescharacteristic
191C4×C11H(5,𝔽2)11yescharacteristic
192Dic11—21no—
193Dic11—21no—
194Dic11—41no—
195Dic11—41no—
196C2×#41—111no—
197C2×#41—221no—
198C22×Q8—111no—
199C2×SD16—111no—
200C2×SD16—111no—
201C2×D8—111no—
202C2×M16—111no—
203C22×C8—111no—
204C4⋊Q8C2×D1111yescharacteristic
205#124—111no—
206#124—221no—
207#123—221no—
208#123—221no—
209C22⋊Q8—111no—
210C22⋊Q8—221no—
211C22⋊Q8—221no—
212#121—111no—
213#121—111no—
214#121—111no—
215#121—221no—
216C4×Q8C2×D1111yescharacteristic
217C4×D4—111no—
218C4×D4—111no—
219C4×D4—221no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222#107—111no—
223#107C2×D1111yescharacteristic
224#107C2×D1111yescharacteristic
225C4⋊C8C2×D1111yescharacteristic
226#103—111no—
227#103—111no—
228#103—111no—
229#103—111no—
230#103C2×D1111yescharacteristic
231#103C2×D1111yescharacteristic
232#102—111no—
233#102—111no—
234#102—111no—
235#102—111no—
236C22⋊C8—111no—
237C22⋊C8—111no—
238#97—111no—
239C2×C11#54611yescharacteristic
240C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
241C2×C11#57811yescharacteristic
242D11—22no—
243D11—41no—
244D11—81no—
245D11—81no—
246#41—222no—
247#41—441no—
248#41—444no—
249C2×Q8—21no—
250C2×Q8—111no—
251C2×Q8—221no—
252C2×Q8—222no—
253C2×Q8—441no—
254C2×Q8C22×D1111yescharacteristic
255C2×D4—111no—
256C2×D4—111no—
257C2×D4—111no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—221no—
262C22×C4—111no—
263C22×C4—111no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—221no—
269SD16—222no—
270SD16—441no—
271D8—441no—
272M16—441no—
273C2×C8—111no—
274C2×C8—111no—
275C2×C8—441no—
276C2×C8C22×D1111yescharacteristic
277C2×C8C22×D1111yescharacteristic
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—111no—
281C4⋊C4—111no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4C22×D1111yescharacteristic
286C4⋊C4C22×D1111yescharacteristic
287C4⋊C4C22×D1111yescharacteristic
288C22⋊C4—111no—
289C22⋊C4—111no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C42—21no—
298C42C22×D1111yescharacteristic
299C11#330811yescharacteristic, complemented, Sylow
300C23—111no—
301C23—111no—
302C23—221no—
303C23—221no—
304Q8—21no—
305Q8—42no—
306Q8—221no—
307Q8—221no—
308Q8—442no—
309Q8#434312yescomplemented
310D4—222no—
311D4—221no—
312D4—221no—
313D4—221no—
314D4—221no—
315D4—442no—
316D4—442no—
317D4—442no—
318D4—442no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—111no—
324C2×C4—111no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—442no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4D4×D1111yescharacteristic
337C2×C4D4×D1111yescharacteristic
338C2×C4C23×D1111yescharacteristic
339C8—21no—
340C8—21no—
341C8—221no—
342C8—221no—
343C22—112no—
344C22—221no—
345C22—221no—
346C22—221no—
347C22—221no—
348C22—221no—
349C22—441no—
350C22—441no—
351C22—441no—
352C22—441no—
353C22—441no—
354C22—441no—
355C22C2×D4×D1111yescharacteristic
356C4—21no—
357C4—21no—
358C4—22no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—221no—
363C4—221no—
364C4—441no—
365C4—441no—
366C4C2×#434311yescharacteristic
367C4#6704211yescharacteristic
368C2—222no—
369C2—441no—
370C2—881no—
371C2—881no—
372C2#1062316111yescharacteristic
373C2#1062329711yescharacteristic
374C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#477C2
socleC22×C11C22×D4
hypercenter#477D11
hypocenterC11#3308
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #10623257C2semidirect
2. #10623107C2semidirect
3. C11×#477C2semidirect
4. #10622702C2semidirect
5. #10622639C2semidirect
6. #10622499C2semidirect
7. #10622497C2semidirect
8. #10622496C2semidirect
9. #10622495C2semidirect
10. #10622457C2semidirect
11. #10622449C2semidirect
12. #10622424C2semidirect
13. #10622419C2semidirect
14. #10622416C2semidirect
15. D11×#103C2semidirect
119. Q8×C11#41semidirect
161. #477D11semidirect
299. C11#3308semidirect
309. Q8#4343semidirect

Maximal subgroups

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

subgroupindex
#106232572
#106231072
C11×#4772
#106227022
#106226392
#106224992
#106224972
#106224962
#106224952
#106224572
#106224492
#106224242
#106224192
#106224162
D11×#1032
#330811