Finite Group Databasebeta

← #13080600

Subgroups — #13080600

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#10623362C211yesmaximal, characteristic, complemented
2#10623142C211yesmaximal, characteristic, complemented
3C11×#449C211yesmaximal, characteristic, complemented
4#10622845C211yesmaximal, characteristic, complemented
5#10622783C211yesmaximal, characteristic, complemented
6#10622777C211yesmaximal, characteristic, complemented
7#10622770C211yesmaximal, characteristic, complemented
8#10622766C211yesmaximal, characteristic, complemented
9#10622655C211yesmaximal, characteristic, complemented
10D11×#103C211yesmaximal, characteristic, complemented
11#10622407C211yesmaximal, characteristic, complemented
12#10622387C211yesmaximal, characteristic, complemented
13#10622378C211yesmaximal, characteristic, complemented
14#10622341C211yesmaximal, characteristic, complemented
15#10622335C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×#4341—21no—
19C2×C11×SD16C2211yescharacteristic
20C2×C11×D8C2211yescharacteristic
21C11×#121C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23#66991—21no—
24#66991C2211yescharacteristic
25#66991C2211yescharacteristic
26#66989—21no—
27#66989C2211yescharacteristic
28#66988—21no—
29D4×Dic11C2211yescharacteristic
30C2×#4324C2211yescharacteristic
31C4×C22⋊D11—21no—
32C4×C22⋊D11C2211yescharacteristic
33C2×C4⋊Dic11C2211yescharacteristic
34#66977—21no—
35#66977C2211yescharacteristic
36C2×#4318C2211yescharacteristic
37C2×C8×D11C2211yescharacteristic
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(C2×D11)⋊C8C2211yescharacteristic
51#66882C2211yescharacteristic
52#66882C2211yescharacteristic
53#66880C2211yescharacteristic
54#66880C2211yescharacteristic
55#66879C2211yescharacteristic
56Dic11⋊C8C2211yescharacteristic
57#66874C2211yescharacteristic
58#66871C2211yescharacteristic
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⋊D11D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73Q8×D11—22no—
74Q8×D11—41no—
75#4341—44no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×Dic22—21no—
80C2×Dic22—21no—
81C2×Dic22C2311yescharacteristic
82C11×SD16—22no—
83C11×D8—41no—
84C2×C8×C11C2311yescharacteristic
85C2×C8×C11C2311yescharacteristic
86C11×C4⋊C4C2311yescharacteristic
87C11×C22⋊C4—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92C22⋊Dic11—21no—
93C22⋊Dic11—21no—
94C22⋊Dic11D411yescharacteristic
95#4324—41no—
96(C2×D11)⋊C4D411yescharacteristic
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4D411yescharacteristic
106C4×Dic11—21no—
107C4×Dic11C2311yescharacteristic
108#4318—41no—
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C8×D11—41no—
112#3308—111nomaximal, Sylow
113C23×C11—21no—
114C23×C11—21no—
115C23×C11C2×D411yescharacteristic
116C22×D11C2×D411yescharacteristic
117Q8×C11—21no—
118Q8×C11#4112yescomplemented
119D4×C11—21no—
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—42no—
124D4×C11—42no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—42no—
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2411yescharacteristic
132C22⋊D11—22no—
133C22⋊D11—42no—
134C22⋊D11—42no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143C2×Dic11C2×D411yescharacteristic
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—42no—
147C4×D11—42no—
148Dic22—21no—
149Dic22—21no—
150Dic22—42no—
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#477—111no—
162#468—111no—
163#466—111no—
164#463—111no—
165#449D1111yescharacteristic, complemented
166#448—111no—
167#440—111no—
168#435—111no—
169#417—111no—
170C2×#103—111no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11C22×D411yescharacteristic
181C2×D11—21no—
182C2×D11—21no—
183C2×D11AGL(1,ℤ/8)12yes—
184C4×C11—21no—
185C4×C11—22no—
186C4×C11—41no—
187C4×C11C2×#4111yescharacteristic
188C4×C11H(5,𝔽2)11yescharacteristic
189Dic11—21no—
190Dic11—21no—
191Dic11—21no—
192Dic11—41no—
193Dic11—41no—
194Dic11—41no—
195Dic11—41no—
196C2×#41—221no—
197C2×#41C2×D1111yescharacteristic
198C22×Q8—111no—
199C2×SD16—111no—
200C2×SD16C2×D1111yescharacteristic
201C2×D8C2×D1111yescharacteristic
202C2×M16—111no—
203C22×C8—111no—
204C4⋊Q8—111no—
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—221no—
215#121C2×D1111yescharacteristic
216C4×Q8—111no—
217C4×D4—111no—
218C4×D4—111no—
219C4×D4—221no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222#107—111no—
223#107—111no—
224#107—111no—
225C4⋊C8—111no—
226#103—111no—
227#103—111no—
228#103—111no—
229#103—111no—
230#103—111no—
231#103C2×D1111yescharacteristic
232#102—111no—
233#102—111no—
234#102—111no—
235#102C2×D1111yescharacteristic
236C22⋊C8—111no—
237C22⋊C8C2×D1111yescharacteristic
238#97—111no—
239C2×C11—41no—
240C2×C11—81no—
241C2×C11—81no—
242C2×C11#54611yescharacteristic
243C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
244C2×C11#57811yescharacteristic
245D11—22no—
246#41—22no—
247#41—41no—
248#41—444no—
249C2×Q8—111no—
250C2×Q8—221no—
251C2×Q8—221no—
252C2×Q8—222no—
253C2×Q8—441no—
254C2×Q8C22×D1111yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—111no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4C22×D1111yescharacteristic
261C2×D4C22×D1111yescharacteristic
262C22×C4—21no—
263C22×C4—111no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4C22×D1111yescharacteristic
269SD16—22no—
270SD16—441no—
271D8—41no—
272M16—441no—
273C2×C8—111no—
274C2×C8—111no—
275C2×C8—441no—
276C2×C8C22×D1111yescharacteristic
277C2×C8C22×D1111yescharacteristic
278C4⋊C4—111no—
279C4⋊C4—111no—
280C4⋊C4—111no—
281C4⋊C4—111no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4C22×D1111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—111no—
290C22⋊C4—111no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C42—111no—
298C42—221no—
299C11#330811yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—111no—
303C23D4×D1111yescharacteristic
304Q8—21no—
305Q8—221no—
306Q8—221no—
307Q8—442no—
308Q8—442no—
309Q8#434112yescomplemented
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—42no—
316D4—222no—
317D4—442no—
318D4—442no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—111no—
325C2×C4—111no—
326C2×C4—111no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—442no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4D4×D1111yescharacteristic
338C2×C4C23×D1111yescharacteristic
339C8—21no—
340C8—21no—
341C8—221no—
342C8—221no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—112no—
353C22—221no—
354C22—221no—
355C22C2×D4×D1111yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—221no—
360C4—221no—
361C4—221no—
362C4—441no—
363C4—441no—
364C4—441no—
365C4—441no—
366C4C2×#434111yescharacteristic
367C4#6703711yescharacteristic
368C2—41no—
369C2—81no—
370C2—81no—
371C2—222no—
372C2#1062312211yescharacteristic
373C2#1062330211yescharacteristic
374C2D11×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#3308
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. #10623362C2semidirect
2. #10623142C2semidirect
3. C11×#449C2semidirect
4. #10622845C2semidirect
5. #10622783C2semidirect
6. #10622777C2semidirect
7. #10622770C2semidirect
8. #10622766C2semidirect
9. #10622655C2semidirect
10. D11×#103C2semidirect
11. #10622407C2semidirect
12. #10622387C2semidirect
13. #10622378C2semidirect
14. #10622341C2semidirect
15. #10622335C2semidirect
118. Q8×C11#41semidirect
165. #449D11semidirect
299. C11#3308semidirect
309. Q8#4341semidirect

Maximal subgroups

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

subgroupindex
#106233622
#106231422
C11×#4492
#106228452
#106227832
#106227772
#106227702
#106227662
#106226552
D11×#1032
#106224072
#106223872
#106223782
#106223412
#106223352
#330811