Finite Group Databasebeta

← #13080353

Subgroups — #13080353

Order 1408.

482 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#548C211yesmaximal, characteristic, complemented
2C2×#67003C211yesmaximal, characteristic, complemented
3C22×#4326C211yesmaximal, characteristic, complemented
4#10623083C211yesmaximal, characteristic, complemented
5#10622852C211yesmaximal, characteristic, complemented
6#10622840C211yesmaximal, characteristic, complemented
7#10622672C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622664C211yesmaximal, characteristic, complemented
10#10622660C211yesmaximal, characteristic, complemented
11#10622653C211yesmaximal, characteristic, complemented
12#10622651C211yesmaximal, characteristic, complemented
13C4×#4326C211yesmaximal, characteristic, complemented
14#10622641C211yesmaximal, characteristic, complemented
15D4×C11⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic
18C2×#4339C2211yescharacteristic
19C22×Dic22C2211yescharacteristic
20C11×#124—21no—
21C11×#124C2211yescharacteristic
22C11×C22⋊Q8—21no—
23C11×C22⋊Q8C2211yescharacteristic
24C11×#121—21no—
25C11×#121C2211yescharacteristic
26C4×Q8×C11C2211yescharacteristic
27C4×D4×C11—21no—
28C4×D4×C11C2211yescharacteristic
29#67003—24no—
30C2×#4326—24no—
31C2×#4326C2211yescharacteristic
32C2×#4326C2211yescharacteristic
33C2×#4326C2211yescharacteristic
34C2×#4326C2211yescharacteristic
35C2×#4325C2211yescharacteristic
36C2×#4325C2211yescharacteristic
37#66992—21no—
38C2×#4324C2211yescharacteristic
39C2×#4324C2211yescharacteristic
40C2×#4323C2211yescharacteristic
41#66983C2211yescharacteristic
42#66977C2211yescharacteristic
43C22×C11⋊C8C2211yescharacteristic
44C22×C11⋊C8C2211yescharacteristic
45#66949—21no—
46#66938—21no—
47(C22⋊D11)⋊C4—21no—
48#66928C2211yescharacteristic
49C4×Dic22C2211yescharacteristic
50#66899C2211yescharacteristic
51#66899C2211yescharacteristic
52#66896C2211yescharacteristic
53C22⋊(C11⋊C8)C2211yescharacteristic
54C22⋊(C11⋊C8)C2211yescharacteristic
55#66874C2211yescharacteristic
56#66874C2211yescharacteristic
57#66873C2211yescharacteristic
58#66871C2211yescharacteristic
59C4⋊(C11⋊C8)C2211yescharacteristic
60C4×C11⋊C8C2211yescharacteristic
61C11×#41—22no—
62C11×#41—41no—
63C2×Q8×C11—21no—
64C2×Q8×C11—22no—
65C2×Q8×C11—41no—
66C2×Q8×C11C2311yescharacteristic
67C2×Q8×C11C2311yescharacteristic
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11D411yescharacteristic
71C2×D4×C11C2311yescharacteristic
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C2×C22⋊D11—21no—
77C2×C22⋊D11—21no—
78C22×Dic11—21no—
79#4339—22no—
80#4339—41no—
81C2×D44C2311yescharacteristic
82C2×C4×D11—21no—
83C2×Dic22—22no—
84C2×Dic22—21no—
85C2×Dic22—41no—
86C2×Dic22C2311yescharacteristic
87C2×Dic22C2311yescharacteristic
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4D411yescharacteristic
91C11×C4⋊C4C2311yescharacteristic
92C11×C22⋊C4—21no—
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C11×C22⋊C4—21no—
96C11×C22⋊C4D411yescharacteristic
97C11×C22⋊C4D411yescharacteristic
98C42×C11—21no—
99C42×C11C2311yescharacteristic
100C22⋊Dic11—21no—
101#4326—22no—
102#4326—22no—
103#4326—22no—
104#4326D414yescomplemented
105#4325—22no—
106#4325—41no—
107#4324—22no—
108#4324—41no—
109#4323—22no—
110(C2×D11)⋊C4—21no—
111(C2×D11)⋊C4—21no—
112(C2×D11)⋊C4—21no—
113C4⋊Dic11C2311yescharacteristic
114Dic11⋊C4—21no—
115Dic11⋊C4—21no—
116C4×Dic11—21no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8C2311yescharacteristic
120C2×C11⋊C8C2311yescharacteristic
121C2×C11⋊C8C2311yescharacteristic
122C2×C11⋊C8C2311yescharacteristic
123#3285—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11C2×D411yescharacteristic
126C23×C11C2×D411yescharacteristic
127C22×D11—21no—
128Q8×C11—21no—
129Q8×C11—21no—
130Q8×C11—21no—
131Q8×C11—42no—
132Q8×C11C2×D412yes—
133D4×C11—22no—
134D4×C11—21no—
135D4×C11—21no—
136D4×C11—42no—
137D4×C11—42no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11C2×D411yescharacteristic
148C2×C4×C11C2×D411yescharacteristic
149C2×C4×C11C2×D411yescharacteristic
150C2×C4×C11C2×D411yescharacteristic
151C2×C4×C11C2411yescharacteristic
152C22⋊D11—42no—
153C22⋊D11—42no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—42no—
158D44—21no—
159D44—21no—
160C4×D11—42no—
161Dic22—21no—
162Dic22—21no—
163Dic22—21no—
164Dic22—42no—
165Dic22C2×D412yes—
166C11⋊C8—21no—
167C11⋊C8—21no—
168C11⋊C8—21no—
169C11⋊C8C2×D412yes—
170C2×#135—111no—
171C22×Q16—111no—
172#548—111no—
173#548D1111yescharacteristic, complemented
174#495—111no—
175#467—111no—
176#466—111no—
177#464—111no—
178#464—111no—
179#452—111no—
180#452—111no—
181#448—111no—
182#448—111no—
183C4×Q16—111no—
184C8×D4—111no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11#13512yescomplemented
194C22×C11C22×D411yescharacteristic
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—41no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—22no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11C22×D411yescharacteristic
206C4×C11H(5,𝔽2)11yescharacteristic
207Dic11—22no—
208Dic11—41no—
209Dic11—41no—
210C2×#41—111no—
211C2×#41C2×D1111yescharacteristic
212C22×Q8—111no—
213C22×Q8C2×D1111yescharacteristic
214#135—224no—
215C2×Q16—111no—
216C2×Q16—111no—
217C2×Q16—111no—
218C2×Q16—111no—
219C2×Q16—224no—
220C2×SD16—111no—
221C2×SD16—111no—
222C2×SD16—111no—
223C2×SD16—111no—
224C2×D8—111no—
225C22×C8—111no—
226C22×C8—111no—
227#124—21no—
228#124—111no—
229#124—221no—
230#124C2×D1111yescharacteristic
231C22⋊Q8—21no—
232C22⋊Q8—111no—
233C22⋊Q8—221no—
234C22⋊Q8C2×D1111yescharacteristic
235#121—21no—
236#121—111no—
237#121—221no—
238#121C2×D1111yescharacteristic
239C4×Q8—111no—
240C4×Q8C2×D1111yescharacteristic
241C4×D4—21no—
242C4×D4—221no—
243C4×D4C2×D1111yescharacteristic
244#107—111no—
245C4⋊C8—111no—
246#103—111no—
247#103—111no—
248#103—111no—
249#103—111no—
250#102—111no—
251#102—111no—
252C22⋊C8—111no—
253C22⋊C8—111no—
254C4×C8—111no—
255C2×C11—22no—
256C2×C11—41no—
257C2×C11—81no—
258C2×C11D4211yescharacteristic
259C2×C11C2×#13511yescharacteristic
260C2×C11#57811yescharacteristic
261D11—81no—
262#41—22no—
263#41—41no—
264#41—222no—
265#41—441no—
266C2×Q8—21no—
267C2×Q8—22no—
268C2×Q8—41no—
269C2×Q8—111no—
270C2×Q8—111no—
271C2×Q8—222no—
272C2×Q8—221no—
273C2×Q8—441no—
274C2×Q8C22×D1111yescharacteristic
275C2×Q8C22×D1111yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—111no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4C22⋊D1111yescharacteristic
282C2×D4C22×D1111yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4C22×D1111yescharacteristic
288C22×C4C22×D1111yescharacteristic
289Q16—114no—
290Q16—222no—
291Q16—222no—
292Q16—222no—
293SD16—222no—
294SD16—222no—
295SD16—441no—
296SD16—441no—
297D8—222no—
298C2×C8—111no—
299C2×C8—111no—
300C2×C8—111no—
301C2×C8—111no—
302C2×C8—222no—
303C2×C8—222no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—111no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4C22⋊D1111yescharacteristic
310C4⋊C4C22×D1111yescharacteristic
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—221no—
316C22⋊C4—221no—
317C22⋊C4—221no—
318C22⋊C4—221no—
319C22⋊C4C22⋊D1111yescharacteristic
320C22⋊C4C22⋊D1111yescharacteristic
321C42—21no—
322C42—221no—
323C42C22×D1111yescharacteristic
324C11#328511yescharacteristic, complemented, Sylow
325C23—21no—
326C23—221no—
327C23C2×C22⋊D1111yescharacteristic
328C23C2×C22⋊D1111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—42no—
333Q8—112no—
334Q8—221no—
335Q8—221no—
336Q8—221no—
337Q8—442no—
338Q8D4×D1112yes—
339D4—22no—
340D4—21no—
341D4—21no—
342D4—42no—
343D4—42no—
344D4—221no—
345D4—221no—
346D4—442no—
347D4—442no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4C2×C22⋊D1111yescharacteristic
363C2×C4C2×C22⋊D1111yescharacteristic
364C2×C4C2×C22⋊D1111yescharacteristic
365C2×C4C2×C22⋊D1111yescharacteristic
366C2×C4C23×D1111yescharacteristic
367C8—112no—
368C8—221no—
369C8—221no—
370C8—221no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—441no—
380C22—441no—
381C22—441no—
382C22#6700312yescomplemented
383C22C22×C22⋊D1111yescharacteristic
384C4—21no—
385C4—21no—
386C4—22no—
387C4—21no—
388C4—21no—
389C4—41no—
390C4—41no—
391C4—222no—
392C4—441no—
393C4—441no—
394C4C2×D4×D1111yescharacteristic
395C4#6703711yescharacteristic
396C2—22no—
397C2—41no—
398C2—81no—
399C2—881no—
400C2D4×C22⋊D1111yescharacteristic
401C2C2×#6700311yescharacteristic
402C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#548C2
socleC22×C11C22×D4
hypercenter#548D11
hypocenterC11#3285
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C11×#548C2semidirect
2. C2×#67003C2semidirect
3. C22×#4326C2semidirect
4. #10623083C2semidirect
5. #10622852C2semidirect
6. #10622840C2semidirect
7. #10622672C2semidirect
8. #10622667C2semidirect
9. #10622664C2semidirect
10. #10622660C2semidirect
11. #10622653C2semidirect
12. #10622651C2semidirect
13. C4×#4326C2semidirect
14. #10622641C2semidirect
15. D4×C11⋊C8C2semidirect
104. #4326D4semidirect
173. #548D11semidirect
193. C22×C11#135semidirect
324. C11#3285semidirect
382. C22#67003semidirect

Maximal subgroups

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

subgroupindex
C11×#5482
C2×#670032
C22×#43262
#106230832
#106228522
#106228402
#106226722
#106226672
#106226642
#106226602
#106226532
#106226512
C4×#43262
#106226412
D4×C11⋊C82
#328511