Finite Group Databasebeta

← #13079608

Subgroups — #13079608

Order 1408.

434 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623363C211yesmaximal, characteristic, complemented
2#10623127C211yesmaximal, characteristic, complemented
3C11×#449C211yesmaximal, characteristic, complemented
4#10622851C211yesmaximal, characteristic, complemented
5#10622789C211yesmaximal, characteristic, complemented
6#10622775C211yesmaximal, characteristic, complemented
7#10622767C211yesmaximal, characteristic, complemented
8#10622763C211yesmaximal, characteristic, complemented
9#10622650C211yesmaximal, characteristic, complemented
10#10622431C211yesmaximal, characteristic, complemented
11#10622408C211yesmaximal, characteristic, complemented
12#10622399C211yesmaximal, characteristic, complemented
13#10622378C211yesmaximal, characteristic, complemented
14#10622347C211yesmaximal, characteristic, complemented
15#10622332C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4341—21no—
18C2×#4339C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C2×C11×D8C2211yescharacteristic
21C11×#121C2211yescharacteristic
22#67000C2211yescharacteristic
23#66997C2211yescharacteristic
24C2×#4325C2211yescharacteristic
25#66993C2211yescharacteristic
26#66993C2211yescharacteristic
27#66992—21no—
28#66992—21no—
29#66992—21no—
30#66989C2211yescharacteristic
31D4×Dic11C2211yescharacteristic
32C2×#4324C2211yescharacteristic
33C2×#4323C2211yescharacteristic
34C2×#4323C2211yescharacteristic
35#66983C2211yescharacteristic
36C4×C22⋊D11—21no—
37C4×C22⋊D11—21no—
38C2×C4×Dic11C2211yescharacteristic
39C2×D88C2211yescharacteristic
40C2×#4314C2211yescharacteristic
41#66946C2211yescharacteristic
42#66941C2211yescharacteristic
43#66938—21no—
44(C22⋊D11)⋊C4—21no—
45C11×#103C2211yescharacteristic
46C11×#102C2211yescharacteristic
47C11×C22⋊C8C2211yescharacteristic
48#66899C2211yescharacteristic
49#66896C2211yescharacteristic
50C22⋊(C11⋊C8)C2211yescharacteristic
51#66885C2211yescharacteristic
52#66880C2211yescharacteristic
53#66879C2211yescharacteristic
54#66879C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56Dic11⋊C8C2211yescharacteristic
57#66874C2211yescharacteristic
58#66873C2211yescharacteristic
59C11×#41—41no—
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⋊D11—21no—
74C22×Dic11—21no—
75C22×Dic11D411yescharacteristic
76C22×Dic11D411yescharacteristic
77#4341—44no—
78#4339—41no—
79#4339—41no—
80C2×D44C2311yescharacteristic
81C2×D44C2311yescharacteristic
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×Dic22—21no—
85C2×Dic22C2311yescharacteristic
86C11×SD16—41no—
87C11×D8—41no—
88C2×C8×C11C2311yescharacteristic
89C2×C8×C11C2311yescharacteristic
90C11×C4⋊C4C2311yescharacteristic
91C11×C22⋊C4—21no—
92C22⋊Dic11—21no—
93C22⋊Dic11—21no—
94C22⋊Dic11—21no—
95#4325—41no—
96#4324—41no—
97#4323—41no—
98#4323—41no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103C4⋊Dic11C2311yescharacteristic
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107C4×Dic11D411yescharacteristic
108C4×Dic11D411yescharacteristic
109C4×Dic11C2311yescharacteristic
110C4×Dic11C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112C2×C11⋊C8C2311yescharacteristic
113D88—41no—
114#4314—41no—
115#3214—111nomaximal, Sylow
116C23×C11—21no—
117C23×C11—21no—
118C23×C11C2×D411yescharacteristic
119C22×D11—21no—
120C22×D11—21no—
121Q8×C11—21no—
122Q8×C11—21no—
123D4×C11—21no—
124D4×C11—21no—
125D4×C11—21no—
126D4×C11—21no—
127D4×C11—42no—
128D4×C11—42no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—42no—
134C2×C4×C11C2×D411yescharacteristic
135C2×C4×C11C2411yescharacteristic
136C22⋊D11—42no—
137C22⋊D11—42no—
138C22⋊D11—42no—
139C22⋊D11—42no—
140C22⋊D11—42no—
141C22⋊D11—42no—
142C2×Dic11—22no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—41no—
146C2×Dic11—42no—
147C2×Dic11C2×D411yescharacteristic
148C2×Dic11C2×D411yescharacteristic
149C2×Dic11C2×D411yescharacteristic
150C2×Dic11C2×D411yescharacteristic
151D44—21no—
152D44—21no—
153D44—21no—
154D44—21no—
155C4×D11—42no—
156C4×D11—42no—
157Dic22—21no—
158Dic22—21no—
159Dic22—42no—
160C8×C11—21no—
161C8×C11—21no—
162C11⋊C8—21no—
163C11⋊C8—21no—
164#532—111no—
165#532—111no—
166#496—111no—
167#496—111no—
168#489—111no—
169#489—111no—
170#461—111no—
171#461—111no—
172#459—111no—
173#459—111no—
174#449—111no—
175#449—111no—
176#449—111no—
177#449D1111yescharacteristic, complemented
178#432—111no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11C22×D411yescharacteristic
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C2×D11—41no—
195C4×C11—21no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11H(5,𝔽2)11yescharacteristic
199C4×C11H(5,𝔽2)11yescharacteristic
200Dic11—21no—
201Dic11—21no—
202Dic11—21no—
203Dic11—41no—
204Dic11—41no—
205Dic11AGL(1,ℤ/8)12yes—
206C2×#41—111no—
207C2×#41—221no—
208C2×#41C2×D1111yescharacteristic
209C2×SD16—111no—
210C2×SD16—111no—
211C2×SD16—111no—
212C2×SD16C2×D1111yescharacteristic
213C2×D8—111no—
214C2×D8—111no—
215C2×D8—111no—
216C2×D8C2×D1111yescharacteristic
217C4⋊Q8—111no—
218C4⋊Q8—111no—
219#127—111no—
220#127—111no—
221#124—111no—
222#124—111no—
223#124—221no—
224#121—111no—
225#121—221no—
226#121—221no—
227#121—221no—
228#121C2×D1111yescharacteristic
229C4×D4—111no—
230C4×D4—111no—
231C4×D4—221no—
232C4×D4—221no—
233C4×D4—221no—
234C2×C42—111no—
235C4⋊C8—111no—
236C4⋊C8—111no—
237#103—111no—
238#103—111no—
239#103—111no—
240#103C2×D1111yescharacteristic
241#102—111no—
242#102—111no—
243#102—111no—
244#102C2×D1111yescharacteristic
245C22⋊C8—111no—
246C22⋊C8C2×D1111yescharacteristic
247#97—111no—
248#97—111no—
249C2×C11—41no—
250C2×C11—81no—
251C2×C11—81no—
252C2×C11#53511yescharacteristic
253C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
254C2×C11#57511yescharacteristic
255D11—81no—
256D11—81no—
257#41—41no—
258#41—41no—
259#41—441no—
260#41—441no—
261#41—444no—
262C2×Q8—111no—
263C2×Q8—221no—
264C2×Q8C22×D1111yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—111no—
268C2×D4—111no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4C22×D1111yescharacteristic
276C2×D4C22×D1111yescharacteristic
277C22×C4—21no—
278C22×C4—111no—
279C22×C4—111no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4C22×D1111yescharacteristic
284SD16—41no—
285SD16—441no—
286SD16—441no—
287SD16—441no—
288D8—41no—
289D8—441no—
290D8—441no—
291D8—441no—
292C2×C8—111no—
293C2×C8—111no—
294C2×C8C22×D1111yescharacteristic
295C2×C8C22×D1111yescharacteristic
296C4⋊C4—111no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4C22×D1111yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C42—111no—
310C42—111no—
311C42—111no—
312C42—111no—
313C11#321411yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—221no—
317C23—221no—
318C23D4×D1111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—221no—
322Q8—221no—
323Q8—442no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—42no—
330D4—221no—
331D4—221no—
332D4—221no—
333D4—221no—
334D4—442no—
335D4—442no—
336D4—442no—
337D4—442no—
338D4—442no—
339D4—442no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—111no—
346C2×C4—111no—
347C2×C4—111no—
348C2×C4—111no—
349C2×C4—222no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4—442no—
355C2×C4—441no—
356C2×C4D4×D1111yescharacteristic
357C2×C4C23×D1111yescharacteristic
358C8—21no—
359C8—21no—
360C8—221no—
361C8—221no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—441no—
372C22—441no—
373C22—441no—
374C22—441no—
375C22—441no—
376C22—441no—
377C22C2×D4×D1111yescharacteristic
378C4—21no—
379C4—41no—
380C4—41no—
381C4—112no—
382C4—221no—
383C4—221no—
384C4—221no—
385C4—441no—
386C4—441no—
387C4#6703711yescharacteristic
388C4#6703711yescharacteristic
389C2—41no—
390C2—81no—
391C2—81no—
392C2—881no—
393C2—881no—
394C2#1062312311yescharacteristic
395C2#1062329911yescharacteristic
396C2D11×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#3214
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. #10623363C2semidirect
2. #10623127C2semidirect
3. C11×#449C2semidirect
4. #10622851C2semidirect
5. #10622789C2semidirect
6. #10622775C2semidirect
7. #10622767C2semidirect
8. #10622763C2semidirect
9. #10622650C2semidirect
10. #10622431C2semidirect
11. #10622408C2semidirect
12. #10622399C2semidirect
13. #10622378C2semidirect
14. #10622347C2semidirect
15. #10622332C2semidirect
177. #449D11semidirect
313. C11#3214semidirect

Maximal subgroups

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

subgroupindex
#106233632
#106231272
C11×#4492
#106228512
#106227892
#106227752
#106227672
#106227632
#106226502
#106224312
#106224082
#106223992
#106223782
#106223472
#106223322
#321411