Finite Group Databasebeta

← #13080939

Subgroups — #13080939

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#10623038C211yesmaximal, characteristic, complemented
3C11×#417C211yesmaximal, characteristic, complemented
4#10622851C211yesmaximal, characteristic, complemented
5#10622748C211yesmaximal, characteristic, complemented
6#10622741C211yesmaximal, characteristic, complemented
7#10622581C211yesmaximal, characteristic, complemented
8#10622424C211yesmaximal, characteristic, complemented
9#10622416C211yesmaximal, characteristic, complemented
10#10622404C211yesmaximal, characteristic, complemented
11#10622401C211yesmaximal, characteristic, complemented
12#10622399C211yesmaximal, characteristic, complemented
13#10622395C211yesmaximal, characteristic, complemented
14#10622390C211yesmaximal, characteristic, complemented
15#10622373C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×#4339—21no—
19C2×C11×M16C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22C2×#4325C2211yescharacteristic
23#66993—21no—
24#66993C2211yescharacteristic
25#66991—21no—
26#66991C2211yescharacteristic
27C2×#4323C2211yescharacteristic
28#66983—21no—
29#66983C2211yescharacteristic
30#66983C2211yescharacteristic
31#66982—21no—
32C4×C22⋊D11—21no—
33C4×C22⋊D11C2211yescharacteristic
34C2×D88C2211yescharacteristic
35C2×#4313C2211yescharacteristic
36#66949—21no—
37#66948C2211yescharacteristic
38#66947—21no—
39#66946C2211yescharacteristic
40C4⋊C4×D11C2211yescharacteristic
41#66941C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52#66881C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54C8×Dic11C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58#66872C2211yescharacteristic
59C11×#41—22no—
60C11×#41—41no—
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11—21no—
63C2×D4×C11C2311yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C2×C22⋊D11—21no—
72C2×C22⋊D11D411yescharacteristic
73#4343—22no—
74#4343—41no—
75#4339—44no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44C2311yescharacteristic
79C2×D44C2311yescharacteristic
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11C2311yescharacteristic
84C2×Dic22—21no—
85C11×M16—41no—
86C2×C8×C11C2311yescharacteristic
87C2×C8×C11C2311yescharacteristic
88C11×C4⋊C4—21no—
89C11×C4⋊C4C2311yescharacteristic
90C11×C4⋊C4C2311yescharacteristic
91C22⋊Dic11—21no—
92C22⋊Dic11D411yescharacteristic
93#4325—22no—
94#4323—41no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4D411yescharacteristic
100C4⋊Dic11—21no—
101C4⋊Dic11C2311yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4D411yescharacteristic
106C4×Dic11—21no—
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110D88—41no—
111#4313—41no—
112#3332—111nomaximal, Sylow
113C23×C11—21no—
114C23×C11C2×D411yescharacteristic
115C22×D11—21no—
116C22×D11—21no—
117C22×D11C2×D411yescharacteristic
118Q8×C11—21no—
119Q8×C11#4112yescomplemented
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—42no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2411yescharacteristic
132C22⋊D11—22no—
133C22⋊D11—42no—
134C22⋊D11—42no—
135C22⋊D11—81no—
136C22⋊D11—81no—
137C22⋊D11—81no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11C2×D411yescharacteristic
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143D44—21no—
144D44—21no—
145D44—21no—
146D44—21no—
147D44—42no—
148D44—42no—
149C4×D11—21no—
150C4×D11—21no—
151C4×D11—42no—
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#449—111no—
170C4×SD16—111no—
171#436—111no—
172#417—111no—
173#417D1111yescharacteristic, complemented
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11C22×D411yescharacteristic
181C2×D11—21no—
182C2×D11—21no—
183C2×D11—21no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—41no—
190C4×C11—21no—
191C4×C11—22no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11C2×#4111yescharacteristic
195C4×C11H(5,𝔽2)11yescharacteristic
196Dic11—21no—
197Dic11—21no—
198Dic11—41no—
199Dic11—41no—
200Dic11AGL(1,ℤ/8)12yes—
201C2×#41—111no—
202C2×#41—221no—
203C2×#41C2×D1111yescharacteristic
204C2×SD16—111no—
205C2×D8—111no—
206C2×D8—111no—
207C2×M16—111no—
208C2×M16C2×D1111yescharacteristic
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—111no—
219#121—221no—
220#121—221no—
221C4×Q8—111no—
222C4×D4—111no—
223C4×D4—111no—
224C4×D4—221no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4C2×D1111yescharacteristic
227#106—111no—
228#106—111no—
229#106—111no—
230C4⋊C8—111no—
231#103—111no—
232#103C2×D1111yescharacteristic
233#103C2×D1111yescharacteristic
234#102—111no—
235#102—111no—
236#102—111no—
237#102—111no—
238#102—111no—
239#102C2×D1111yescharacteristic
240#102C2×D1111yescharacteristic
241C22⋊C8—111no—
242C22⋊C8—111no—
243C4×C8—111no—
244C2×C11—41no—
245C2×C11—81no—
246C2×C11#54611yescharacteristic
247C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
248C2×C11#57711yescharacteristic
249D11—41no—
250D11—81no—
251D11—81no—
252#41—22no—
253#41—41no—
254#41—222no—
255#41—444no—
256#41—441no—
257C2×Q8—221no—
258C2×Q8C22×D1111yescharacteristic
259C2×D4—21no—
260C2×D4—111no—
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×D4—221no—
270C2×D4C22×D1111yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—111no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4C22×D1111yescharacteristic
278SD16—222no—
279D8—441no—
280D8—441no—
281M16—41no—
282M16—441no—
283C2×C8—111no—
284C2×C8—111no—
285C2×C8C22×D1111yescharacteristic
286C2×C8C22×D1111yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—111no—
289C4⋊C4—111no—
290C4⋊C4—111no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4C22×D1111yescharacteristic
295C4⋊C4C22×D1111yescharacteristic
296C22⋊C4—111no—
297C22⋊C4—111no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C42—111no—
304C42—221no—
305C11#333211yescharacteristic, complemented, Sylow
306C23—21no—
307C23—111no—
308C23—221no—
309C23—221no—
310C23D4×D1111yescharacteristic
311Q8—21no—
312Q8—442no—
313Q8#433912yescomplemented
314D4—21no—
315D4—21no—
316D4—42no—
317D4—222no—
318D4—221no—
319D4—221no—
320D4—221no—
321D4—221no—
322D4—442no—
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—21no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—111no—
337C2×C4—111no—
338C2×C4—111no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
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—221no—
359C22—221no—
360C22—221no—
361C22—441no—
362C22—441no—
363C22—441no—
364C22—441no—
365C22—441no—
366C22—441no—
367C22C2×D4×D1111yescharacteristic
368C4—21no—
369C4—22no—
370C4—41no—
371C4—41no—
372C4—112no—
373C4—221no—
374C4—221no—
375C4—441no—
376C4—441no—
377C4C2×#433911yescharacteristic
378C4#6703711yescharacteristic
379C2—41no—
380C2—81no—
381C2—441no—
382C2—881no—
383C2—881no—
384C2#1062302111yescharacteristic
385C2D11×AGL(1,ℤ/8)11yescharacteristic
386C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#417C2
socleC22×C11C22×D4
hypercenter#417D11
hypocenterC11#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #10623365C2semidirect
2. #10623038C2semidirect
3. C11×#417C2semidirect
4. #10622851C2semidirect
5. #10622748C2semidirect
6. #10622741C2semidirect
7. #10622581C2semidirect
8. #10622424C2semidirect
9. #10622416C2semidirect
10. #10622404C2semidirect
11. #10622401C2semidirect
12. #10622399C2semidirect
13. #10622395C2semidirect
14. #10622390C2semidirect
15. #10622373C2semidirect
119. Q8×C11#41semidirect
173. #417D11semidirect
305. C11#3332semidirect
313. Q8#4339semidirect

Maximal subgroups

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

subgroupindex
#106233652
#106230382
C11×#4172
#106228512
#106227482
#106227412
#106225812
#106224242
#106224162
#106224042
#106224012
#106223992
#106223952
#106223902
#106223732
#333211