Finite Group Databasebeta

← #13080936

Subgroups — #13080936

Order 1408.

430 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623365C211yesmaximal, characteristic, complemented
2#10623142C211yesmaximal, characteristic, complemented
3C11×#449C211yesmaximal, characteristic, complemented
4#10622845C211yesmaximal, characteristic, complemented
5#10622785C211yesmaximal, characteristic, complemented
6SD16×Dic11C211yesmaximal, characteristic, complemented
7#10622772C211yesmaximal, characteristic, complemented
8#10622763C211yesmaximal, characteristic, complemented
9#10622652C211yesmaximal, characteristic, complemented
10#10622416C211yesmaximal, characteristic, complemented
11#10622404C211yesmaximal, characteristic, complemented
12#10622390C211yesmaximal, characteristic, complemented
13#10622373C211yesmaximal, characteristic, complemented
14#10622348C211yesmaximal, characteristic, complemented
15#10622342C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×#4341—21no—
19C2×C11×SD16C2211yescharacteristic
20C2×C11×D8C2211yescharacteristic
21C11×#121C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23#66993—21no—
24#66993C2211yescharacteristic
25#66991—21no—
26#66991C2211yescharacteristic
27#66991C2211yescharacteristic
28#66988—21no—
29D4×Dic11C2211yescharacteristic
30C2×#4323C2211yescharacteristic
31#66983—21no—
32#66983C2211yescharacteristic
33C4×C22⋊D11—21no—
34C4×C22⋊D11C2211yescharacteristic
35C2×C4⋊Dic11C2211yescharacteristic
36C2×#4318C2211yescharacteristic
37C2×#4313C2211yescharacteristic
38C4⋊C4×D11C2211yescharacteristic
39#66941C2211yescharacteristic
40#66936—21no—
41#66931—21no—
42C11×#103C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53#66881C2211yescharacteristic
54#66881C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56C8×Dic11C2211yescharacteristic
57#66873C2211yescharacteristic
58#66872C2211yescharacteristic
59C11×#41—22no—
60C11×#41—41no—
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11C2311yescharacteristic
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C2×C22⋊D11—21no—
72C2×C22⋊D11—21no—
73C2×C22⋊D11D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11—21no—
76#4343—22no—
77#4343—41no—
78#4341—44no—
79C2×D44—21no—
80C2×D44C2311yescharacteristic
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11C2311yescharacteristic
84C2×Dic22—21no—
85C11×SD16—22no—
86C11×D8—41no—
87C2×C8×C11C2311yescharacteristic
88C2×C8×C11C2311yescharacteristic
89C11×C4⋊C4C2311yescharacteristic
90C11×C22⋊C4—21no—
91C22⋊Dic11—21no—
92C22⋊Dic11—21no—
93C22⋊Dic11—21no—
94C22⋊Dic11D411yescharacteristic
95#4323—41no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4D411yescharacteristic
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4D411yescharacteristic
106C4×Dic11—21no—
107C4×Dic11C2311yescharacteristic
108#4318—41no—
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111#4313—41no—
112#3332—111nomaximal, Sylow
113C23×C11—21no—
114C23×C11—21no—
115C23×C11C2×D411yescharacteristic
116C22×D11—21no—
117C22×D11C2×D411yescharacteristic
118Q8×C11—21no—
119Q8×C11#4112yescomplemented
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—42no—
125D4×C11—42no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—42no—
131C2×C4×C11C2×D411yescharacteristic
132C2×C4×C11C2411yescharacteristic
133C22⋊D11—22no—
134C22⋊D11—42no—
135C22⋊D11—42no—
136C22⋊D11—81no—
137C22⋊D11—81no—
138C22⋊D11—81no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11C2×D411yescharacteristic
145C2×Dic11C2×D411yescharacteristic
146C2×Dic11C2×D411yescharacteristic
147D44—21no—
148D44—21no—
149D44—42no—
150C4×D11—21no—
151C4×D11—21no—
152C4×D11—42no—
153C4×D11—42no—
154Dic22—42no—
155C8×C11—21no—
156C8×C11—21no—
157C11⋊C8—21no—
158C11⋊C8—21no—
159#550—111no—
160#547—111no—
161#486—111no—
162#481—111no—
163#481—111no—
164#475—111no—
165#469—111no—
166#469—111no—
167#459—111no—
168#449—111no—
169#449D1111yescharacteristic, complemented
170C4×SD16—111no—
171#436—111no—
172#417—111no—
173#417—111no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11C22×D411yescharacteristic
184C2×D11—21no—
185C2×D11—21no—
186C2×D11—21no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—41no—
190C4×C11—21no—
191C4×C11—22no—
192C4×C11—41no—
193C4×C11C2×#4111yescharacteristic
194C4×C11H(5,𝔽2)11yescharacteristic
195Dic11—21no—
196Dic11—21no—
197Dic11—41no—
198Dic11—41no—
199Dic11—41no—
200Dic11AGL(1,ℤ/8)12yes—
201C2×#41—111no—
202C2×#41—221no—
203C2×#41C2×D1111yescharacteristic
204C2×SD16C2×D1111yescharacteristic
205C2×D8—111no—
206C2×D8C2×D1111yescharacteristic
207C2×M16—111no—
208C2×M16—111no—
209C4⋊Q8—111no—
210#127—111no—
211#127—221no—
212#123—221no—
213#123—221no—
214C22⋊Q8—221no—
215#121—111no—
216#121—111no—
217#121—111no—
218#121—221no—
219#121—221no—
220#121C2×D1111yescharacteristic
221C4×Q8—111no—
222C4×D4—111no—
223C4×D4—111no—
224C4×D4—221no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227#106—111no—
228#106—111no—
229#106—111no—
230C4⋊C8—111no—
231#103—111no—
232#103—111no—
233#103C2×D1111yescharacteristic
234#102—111no—
235#102—111no—
236#102—111no—
237#102—111no—
238#102—111no—
239#102—111no—
240#102C2×D1111yescharacteristic
241C22⋊C8—111no—
242C22⋊C8C2×D1111yescharacteristic
243C4×C8—111no—
244C2×C11—41no—
245C2×C11—81no—
246C2×C11—81no—
247C2×C11#54611yescharacteristic
248C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
249C2×C11#57711yescharacteristic
250D11—41no—
251D11—81no—
252#41—22no—
253#41—41no—
254#41—222no—
255#41—441no—
256#41—444no—
257C2×Q8—221no—
258C2×Q8C22×D1111yescharacteristic
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—111no—
262C2×D4—111no—
263C2×D4—221no—
264C2×D4—221no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4C22×D1111yescharacteristic
270C2×D4C22×D1111yescharacteristic
271C22×C4—21no—
272C22×C4—111no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4C22×D1111yescharacteristic
278SD16—22no—
279D8—41no—
280D8—441no—
281M16—441no—
282M16—441no—
283C2×C8—111no—
284C2×C8—111no—
285C2×C8C22×D1111yescharacteristic
286C2×C8C22×D1111yescharacteristic
287C4⋊C4—111no—
288C4⋊C4—111no—
289C4⋊C4—111no—
290C4⋊C4—111no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4C22×D1111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—111no—
298C22⋊C4—111no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C42—111no—
304C42—221no—
305C11#333211yescharacteristic, complemented, Sylow
306C23—21no—
307C23—21no—
308C23—111no—
309C23—221no—
310C23D4×D1111yescharacteristic
311Q8—21no—
312Q8—442no—
313Q8#434112yescomplemented
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—42no—
320D4—222no—
321D4—221no—
322D4—221no—
323D4—442no—
324D4—442no—
325D4—442no—
326D4—881no—
327D4—881no—
328D4—881no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—111no—
335C2×C4—111no—
336C2×C4—111no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4D4×D1111yescharacteristic
347C2×C4C23×D1111yescharacteristic
348C8—21no—
349C8—21no—
350C8—221no—
351C8—221no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—221no—
362C22—221no—
363C22—221no—
364C22—441no—
365C22—441no—
366C22—441no—
367C22C2×D4×D1111yescharacteristic
368C4—21no—
369C4—22no—
370C4—41no—
371C4—112no—
372C4—221no—
373C4—221no—
374C4—441no—
375C4—441no—
376C4—441no—
377C4C2×#434111yescharacteristic
378C4#6703711yescharacteristic
379C2—41no—
380C2—81no—
381C2—81no—
382C2—441no—
383C2—881no—
384C2#1062312211yescharacteristic
385C2#1062330111yescharacteristic
386C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#449C2
socleC22×C11C22×D4
hypercenter#449D11
hypocenterC11#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #10623365C2semidirect
2. #10623142C2semidirect
3. C11×#449C2semidirect
4. #10622845C2semidirect
5. #10622785C2semidirect
6. SD16×Dic11C2semidirect
7. #10622772C2semidirect
8. #10622763C2semidirect
9. #10622652C2semidirect
10. #10622416C2semidirect
11. #10622404C2semidirect
12. #10622390C2semidirect
13. #10622373C2semidirect
14. #10622348C2semidirect
15. #10622342C2semidirect
119. Q8×C11#41semidirect
169. #449D11semidirect
305. C11#3332semidirect
313. Q8#4341semidirect

Maximal subgroups

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

subgroupindex
#106233652
#106231422
C11×#4492
#106228452
#106227852
SD16×Dic112
#106227722
#106227632
#106226522
#106224162
#106224042
#106223902
#106223732
#106223482
#106223422
#333211