Finite Group Databasebeta

← #13082495

Subgroups — #13082495

Order 1408.

992 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#533C211yesmaximal, characteristic, complemented
2#10623259C211yesmaximal, characteristic, complemented
3#10623259C211yesmaximal, characteristic, complemented
4#10623259C211yesmaximal, characteristic, complemented
5D11×C4⋊Q8C211yesmaximal, characteristic, complemented
6#10623225C212yesmaximal, complemented
7#10623216C212yesmaximal, complemented
8#10623172C212yesmaximal, complemented
9#10623170C212yesmaximal, complemented
10#10623159C212yesmaximal
11#10623156C212yesmaximal, complemented
12#10623114C212yesmaximal, complemented
13#10623112C212yesmaximal, complemented
14#10623103C212yesmaximal, complemented
15#10623100C212yesmaximal, complemented
16#10623064C212yesmaximal, complemented
17#10623060C212yesmaximal, complemented
18C4×#4339C211yesmaximal, characteristic
19#10623001C211yesmaximal, characteristic, complemented
20C2×Q8×D11C2212yes—
21C2×#4339C2211yescharacteristic
22C11×C4⋊Q8C2211yescharacteristic
23C11×C4⋊Q8C2211yescharacteristic
24C11×#125C2212yes—
25C11×C22⋊Q8C2212yes—
26C11×C22⋊Q8C2212yes—
27C4×Q8×C11C2212yes—
28C4×Q8×C11C2212yes—
29C11×#117C2212yes—
30C2×C42×C11C2211yescharacteristic
31#66999C2212yes—
32#66999C2212yes—
33#66999C2212yes—
34Q8×Dic11C2212yes—
35Q8×Dic11C2212yes—
36Q8×Dic11C2212yes—
37#66997C2212yes—
38C4×C22⋊D11C2211yescharacteristic
39C4×C22⋊D11C2211yescharacteristic
40C4×C22⋊D11C2211yescharacteristic
41C4×C22⋊D11C2211yescharacteristic
42#66979C2212yes—
43#66979C2211yescharacteristic
44#66977C2212yes—
45#66977C2212yes—
46#66951C2214yes—
47#66950C2212yes—
48#66950C2212yes—
49#66950C2212yes—
50#66947C2214yes—
51#66945C2212yes—
52#66945C2212yes—
53#66945C2212yes—
54#66945C2214yes—
55C4⋊C4×D11C2212yes—
56C4⋊C4×D11C2212yes—
57#66943C2212yes—
58#66943C2212yes—
59#66943C2212yes—
60#66943C2214yes—
61#66942C2214yes—
62#66942C2214yes—
63#66941C2212yes—
64#66941C2212yes—
65#66941C2214yes—
66#66940C2212yes—
67#66940C2212yes—
68#66940C2212yes—
69#66940C2214yes—
70#66938C2214yes—
71#66936C2214yes—
72#66932C2214yes—
73#66932C2214yes—
74#66929C2214yes—
75C4×D44C2211yescharacteristic
76C4×D44C2211yescharacteristic
77#66925C2211yescharacteristic
78#66925C2211yescharacteristic
79#66925C2214yes—
80C42×D11C2211yescharacteristic
81C42×D11C2211yescharacteristic
82#66923C2212yes—
83#66923C2214yes—
84#66922C2211yescharacteristic
85#66922C2211yescharacteristic
86C4×Dic22C2212yes—
87C4×Dic22C2212yes—
88C4×Dic22C2211yescharacteristic
89C4×Dic22C2211yescharacteristic
90C4×Dic22C2214yes—
91C2×Q8×C11C2312yes—
92C2×Q8×C11C2312yes—
93C22×C4×C11C2311yescharacteristic
94C22×C4×C11C2311yescharacteristic
95C22×C4×C11C2311yescharacteristic
96C2×C22⋊D11C2311yescharacteristic
97C2×C22⋊D11C2311yescharacteristic
98Q8×D11—28no—
99#4339—24no—
100C2×D44C2311yescharacteristic
101C2×C4×D11C2311yescharacteristic
102C2×C4×D11C2311yescharacteristic
103C2×C4×D11C2311yescharacteristic
104C2×C4×D11C2311yescharacteristic
105C2×C4×D11C2311yescharacteristic
106C2×C4×D11C2314yes—
107C2×C4×D11C2311yescharacteristic
108C2×Dic22C2311yescharacteristic
109C2×Dic22C2312yes—
110C2×Dic22C2312yes—
111C2×Dic22C2314yes—
112C11×C4⋊C4C2312yes—
113C11×C4⋊C4C2314yes—
114C11×C4⋊C4C2312yes—
115C11×C4⋊C4C2312yes—
116C11×C4⋊C4C2314yes—
117C11×C4⋊C4C2312yes—
118C11×C22⋊C4C2314yes—
119C42×C11C2311yescharacteristic
120C42×C11C2311yescharacteristic
121C42×C11C2311yescharacteristic
122C42×C11C2314yes—
123C42×C11C2311yescharacteristic
124C22⋊Dic11C2311yescharacteristic
125C22⋊Dic11C2311yescharacteristic
126C22⋊Dic11C2314yes—
127(C2×D11)⋊C4C2311yescharacteristic
128(C2×D11)⋊C4C2311yescharacteristic
129(C2×D11)⋊C4C2311yescharacteristic
130(C2×D11)⋊C4C2311yescharacteristic
131(C2×D11)⋊C4C2314yes—
132(C2×D11)⋊C4C2314yes—
133(C2×D11)⋊C4C2314yes—
134C4⋊Dic11C2312yes—
135C4⋊Dic11C2312yes—
136C4⋊Dic11C2311yescharacteristic
137C4⋊Dic11C2311yescharacteristic
138C4⋊Dic11C2314yes—
139C4⋊Dic11C2312yes—
140C4⋊Dic11C2312yes—
141C4⋊Dic11C2314yes—
142C4⋊Dic11C2314yes—
143Dic11⋊C4C2311yescharacteristic
144Dic11⋊C4C2314yes—
145Dic11⋊C4C2311yescharacteristic
146Dic11⋊C4C2314yes—
147Dic11⋊C4C2311yescharacteristic
148Dic11⋊C4C2311yescharacteristic
149Dic11⋊C4C2314yes—
150Dic11⋊C4C2314yes—
151Dic11⋊C4C2314yes—
152Dic11⋊C4C2314yes—
153Dic11⋊C4C2314yes—
154C4×Dic11C2314yes—
155C4×Dic11C2311yescharacteristic
156C4×Dic11C2311yescharacteristic
157C4×Dic11C2311yescharacteristic
158C4×Dic11C2311yescharacteristic
159C4×Dic11C2314yes—
160C4×Dic11C2314yes—
161C4×Dic11C2311yescharacteristic
162C4×Dic11C2311yescharacteristic
163C4×Dic11C2314yes—
164#3509—111nomaximal, Sylow
165C23×C11C2411yescharacteristic
166C22×D11C2411yescharacteristic
167C22×D11C2411yescharacteristic
168Q8×C11—24no—
169Q8×C11—24no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11C2411yescharacteristic
174C2×C4×C11C2414yes—
175C2×C4×C11C2414yes—
176C2×C4×C11C2411yescharacteristic
177C2×C4×C11C2411yescharacteristic
178C2×C4×C11C2411yescharacteristic
179C2×C4×C11C2411yescharacteristic
180C2×C4×C11C2411yescharacteristic
181C22⋊D11—22no—
182C22⋊D11—22no—
183C2×Dic11C2411yescharacteristic
184C2×Dic11C2411yescharacteristic
185C2×Dic11C2414yes—
186C2×Dic11C2411yescharacteristic
187C2×Dic11C2411yescharacteristic
188C2×Dic11C2411yescharacteristic
189C2×Dic11C2414yes—
190C2×Dic11C2411yescharacteristic
191D44—22no—
192C4×D11—28no—
193C4×D11—22no—
194C4×D11—22no—
195C4×D11—22no—
196C4×D11—22no—
197C4×D11—22no—
198C4×D11#4114yes—
199Dic22—24no—
200Dic22—24no—
201Dic22—22no—
202Dic22—28no—
203#557—112no—
204#557—112no—
205#556—112no—
206#556—112no—
207#552—112no—
208#552—112no—
209#552—112no—
210#552—112no—
211#541—112no—
212#541—112no—
213#536—112no—
214#533—111no—
215#533—111no—
216#533—111no—
217#533—111no—
218#533D1111yescharacteristic, complemented
219C2×C4⋊Q8—111no—
220#519—112no—
221C4×#41—111no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11C2511yescharacteristic
226C2×D11—21no—
227C2×D11—21no—
228C2×D11—21no—
229C2×D11—21no—
230C2×D11—21no—
231C2×D11C2×#4112yes—
232C4×C11—21no—
233C4×C11—24no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—24no—
237C4×C11C2×#4112yes—
238C4×C112−1+412yes—
239C4×C112−1+412yes—
240Dic11—24no—
241Dic11—21no—
242Dic11—24no—
243Dic11—21no—
244Dic11—21no—
245Dic11—21no—
246Dic11—21no—
247Dic11C2×#4112yes—
248C2×#41—111no—
249C22×Q8—112no—
250C4⋊Q8—112no—
251C4⋊Q8—112no—
252C4⋊Q8—112no—
253C4⋊Q8—114no—
254C4⋊Q8—111no—
255C4⋊Q8—111no—
256C4⋊Q8C2×D1111yescharacteristic
257C4⋊Q8C2×D1111yescharacteristic
258#126—114no—
259#126—114no—
260#126—114no—
261#126—114no—
262#125—112no—
263#125—112no—
264#125—112no—
265#125—114no—
266#125—114no—
267#125—114no—
268#125—112no—
269#125—114no—
270#125C2×D1112yes—
271#124—114no—
272#123—114no—
273#123—114no—
274C22⋊Q8—112no—
275C22⋊Q8—112no—
276C22⋊Q8—112no—
277C22⋊Q8—112no—
278C22⋊Q8—112no—
279C22⋊Q8—112no—
280C22⋊Q8—112no—
281C22⋊Q8—112no—
282C22⋊Q8C2×D1112yes—
283C22⋊Q8C2×D1112yes—
284C4×Q8—112no—
285C4×Q8—112no—
286C4×Q8—112no—
287C4×Q8—112no—
288C4×Q8—114no—
289C4×Q8—112no—
290C4×Q8—112no—
291C4×Q8—111no—
292C4×Q8—111no—
293C4×Q8—112no—
294C4×Q8—114no—
295C4×Q8—112no—
296C4×Q8C2×D1112yes—
297C4×Q8C2×D1112yes—
298C4×D4—111no—
299C4×D4—111no—
300C4×D4—111no—
301C4×D4—111no—
302C4×D4—111no—
303C4×D4—111no—
304#117—111no—
305#117—112no—
306#117—112no—
307#117—114no—
308#117—112no—
309#117—112no—
310#117—111no—
311#117—111no—
312#117—114no—
313#117C2×D1112yes—
314C2×C4⋊C4—112no—
315C2×C4⋊C4—112no—
316C2×C42—111no—
317C2×C42—111no—
318C2×C42C2×D1111yescharacteristic
319C2×C11—41no—
320C2×C11C22×#4111yescharacteristic
321C2×C11C2×2−1+411yescharacteristic
322C2×C11C2×2−1+411yescharacteristic
323D11—22no—
324D11—41no—
325#41—224no—
326C2×Q8—112no—
327C2×Q8—112no—
328C2×Q8—114no—
329C2×Q8—111no—
330C2×Q8—228no—
331C2×Q8C22×D1112yes—
332C2×Q8C22×D1112yes—
333C2×D4—111no—
334C2×D4—111no—
335C2×D4—111no—
336C22×C4—111no—
337C22×C4—111no—
338C22×C4—111no—
339C22×C4—111no—
340C22×C4—111no—
341C22×C4—111no—
342C22×C4—114no—
343C22×C4C22×D1111yescharacteristic
344C22×C4C22×D1111yescharacteristic
345C22×C4C22×D1111yescharacteristic
346C4⋊C4—112no—
347C4⋊C4—112no—
348C4⋊C4—114no—
349C4⋊C4—114no—
350C4⋊C4—112no—
351C4⋊C4—111no—
352C4⋊C4—111no—
353C4⋊C4—111no—
354C4⋊C4—111no—
355C4⋊C4—111no—
356C4⋊C4—111no—
357C4⋊C4—112no—
358C4⋊C4—114no—
359C4⋊C4—114no—
360C4⋊C4—114no—
361C4⋊C4—114no—
362C4⋊C4—114no—
363C4⋊C4—114no—
364C4⋊C4—114no—
365C4⋊C4—114no—
366C4⋊C4C22×D1112yes—
367C4⋊C4C22×D1112yes—
368C4⋊C4C22×D1112yes—
369C4⋊C4C22×D1112yes—
370C4⋊C4C22×D1114yes—
371C4⋊C4C22×D1114yes—
372C22⋊C4—111no—
373C22⋊C4—111no—
374C22⋊C4—114no—
375C22⋊C4—111no—
376C22⋊C4—111no—
377C22⋊C4—114no—
378C22⋊C4—111no—
379C22⋊C4—111no—
380C22⋊C4—114no—
381C22⋊C4—114no—
382C22⋊C4C22×D1114yes—
383C42—111no—
384C42—111no—
385C42—111no—
386C42—111no—
387C42—111no—
388C42—111no—
389C42—114no—
390C42—114no—
391C42—114no—
392C42—114no—
393C42C22×D1111yescharacteristic
394C42C22×D1111yescharacteristic
395C42C22×D1111yescharacteristic
396C42C22×D1111yescharacteristic
397C42C22×D1114yes—
398C11#350911yescharacteristic, complemented, Sylow
399C23—111no—
400C23—111no—
401C23C23×D1111yescharacteristic
402Q8—24no—
403Q8—24no—
404Q8—228no—
405Q8—222no—
406Q8—224no—
407Q8—224no—
408D4—222no—
409D4—222no—
410D4—222no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—111no—
415C2×C4—114no—
416C2×C4—111no—
417C2×C4—111no—
418C2×C4—114no—
419C2×C4—111no—
420C2×C4—111no—
421C2×C4—114no—
422C2×C4—111no—
423C2×C4—228no—
424C2×C4—222no—
425C2×C4—222no—
426C2×C4—222no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4C23×D1111yescharacteristic
430C2×C4C23×D1114yes—
431C2×C4C23×D1114yes—
432C2×C4C23×D1111yescharacteristic
433C2×C4C23×D1111yescharacteristic
434C2×C4C23×D1111yescharacteristic
435C2×C4C23×D1111yescharacteristic
436C2×C4C23×D1111yescharacteristic
437C22—21no—
438C22—21no—
439C22—21no—
440C22—112no—
441C22—221no—
442C22—221no—
443C22—221no—
444C22—221no—
445C22—221no—
446C22C24×D1111yescharacteristic
447C4—21no—
448C4—21no—
449C4—24no—
450C4—21no—
451C4—24no—
452C4—112no—
453C4—221no—
454C4—221no—
455C4—224no—
456C4—221no—
457C4—224no—
458C4—221no—
459C4—221no—
460C4#6704012yes—
461C4#41×D1112yes—
462C4#6704312yes—
463C2—41no—
464C2—222no—
465C2—441no—
466C2C2×#6704011yescharacteristic
467C2C2×#41×D1111yescharacteristic
468C2C2×#6704311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#533C2
prime radicalC2×#4339C22
hypercenter#533D11
hypocenterC11#3509
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C11×#533C2semidirect
2. #10623259C2semidirect
3. #10623259C2semidirect
4. #10623259C2semidirect
5. D11×C4⋊Q8C2semidirect
6. #10623225C2semidirect
7. #10623216C2semidirect
8. #10623172C2semidirect
9. #10623170C2semidirect
11. #10623156C2semidirect
12. #10623114C2semidirect
13. #10623112C2semidirect
14. #10623103C2semidirect
15. #10623100C2semidirect
16. #10623064C2semidirect
17. #10623060C2semidirect
19. #10623001C2semidirect
218. #533D11semidirect
398. C11#3509semidirect

Maximal subgroups

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

subgroupindex
C11×#5332
#106232592
D11×C4⋊Q82
#106232252
#106232162
#106231722
#106231702
#106231592
#106231562
#106231142
#106231122
#106231032
#106231002
#106230642
#106230602
C4×#43392
#106230012
#350911