Finite Group Databasebeta

← #14767641

Subgroups — #14767641

Order 2816.

986 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622325C211yesmaximal, characteristic
2#13071341C211yesmaximal, characteristic, complemented
3#13071327C211yesmaximal, characteristic, complemented
4#13069427C211yesmaximal, characteristic, complemented
5#13069422C211yesmaximal, characteristic, complemented
6#13068970C212yesmaximal, complemented
7#13068963C212yesmaximal, complemented
8#13068963C212yesmaximal, complemented
9#13068949C212yesmaximal, complemented
10#13068750C211yesmaximal, characteristic, complemented
11C11×#1746C211yesmaximal, characteristic, complemented
12C22×D88C2212yes—
13C22×#4314C2212yes—
14C2×#66928C2211yescharacteristic
15C2×#66927C2211yescharacteristic
16C2×C4×D44C2212yes—
17C2×C4×D44C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C2×C11×#97C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C11×#376C2211yescharacteristic
22C2×#66885C2212yes—
23C2×#66885C2212yes—
24C2×#66885C2212yes—
25C2×#66880C2212yes—
26#10622552C2211yescharacteristic
27#10622552C2212yes—
28#10622549C2211yescharacteristic
29#10622548C2211yescharacteristic
30#10622542C2211yescharacteristic
31#10622325C418yescomplemented
32#10622283—22no—
33#10622281—22no—
34#10622278—22no—
35#10622278—22no—
36C11×#336C2212yes—
37C11×#336C2212yes—
38#10622189C2212yes—
39#10622189C2212yes—
40C22×D44—22no—
41C22×D44C2312yes—
42C22×D44C2311yescharacteristic
43C22×C4×D11—22no—
44C22×C4×D11—21no—
45C22×Dic22C2311yescharacteristic
46C22×C8×C11C2312yes—
47C22×C8×C11C2312yes—
48C2×C42×C11C2311yescharacteristic
49C2×C42×C11C2311yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C2×(C2×D11)⋊C4—22no—
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11C2311yescharacteristic
59C2×C4⋊Dic11C2311yescharacteristic
60C2×C4⋊Dic11C2312yes—
61C2×Dic11⋊C4—21no—
62C2×C4×Dic11—21no—
63C2×D88—42no—
64C2×D88—42no—
65C2×D88C2×C418yescomplemented
66C2×#4314—42no—
67C2×#4314—42no—
68C2×#4314C2×C418yescomplemented
69#66928—22no—
70#66928C2×C414yescomplemented
71#66927—22no—
72#66927C2×C414yescomplemented
73C4×D44—42no—
74C4×D44—42no—
75C4×D44—42no—
76C4×Dic22—42no—
77C11×#97C2×C414yescomplemented
78C4×C8×C11—22no—
79C11×#95D412yes—
80C11×#95D412yes—
81C11⋊#95—22no—
82C11⋊#95—22no—
83#66885—42no—
84#66885—42no—
85#66885—42no—
86#66880—42no—
87#22279—111nomaximal, Sylow
88C23×D11—21no—
89C23×D11—22no—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2411yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—22no—
98C22×Dic11—21no—
99C2×D44—28no—
100C2×D44—22no—
101C2×D44—21no—
102C2×D44—22no—
103C2×D44—22no—
104C2×D44—22no—
105C2×D44—22no—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44—82no—
109C2×D44—82no—
110C2×D44C22×C414yes—
111C2×D44C22×C412yes—
112C2×C4×D11—42no—
113C2×C4×D11—44no—
114C2×C4×D11—82no—
115C2×C4×D11—82no—
116C2×C4×D11—82no—
117C2×Dic22—21no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22C22×C412yes—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11C22×C414yes—
127C42×C11—22no—
128C42×C11—22no—
129C42×C11C22×C412yes—
130C42×C11#4112yes—
131(C2×D11)⋊C4—28no—
132(C2×D11)⋊C4—42no—
133(C2×D11)⋊C4—44no—
134(C2×D11)⋊C4—82no—
135(C2×D11)⋊C4—82no—
136(C2×D11)⋊C4—82no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—82no—
142Dic11⋊C4—42no—
143C4×Dic11—42no—
144D88—48no—
145#4314—48no—
146C2×#496—111no—
147#2328—111no—
148#2326—111no—
149#1958—111no—
150#1957—111no—
151#1880—112no—
152#1879—112no—
153#1879—112no—
154#1877—112no—
155#1836—111no—
156#1746D1111yescharacteristic, complemented
157C23×C11C22×D411yescharacteristic
158C22×D11—22no—
159C22×D11—24no—
160C22×D11—41no—
161C22×D11—42no—
162C22×D11—42no—
163C22×D11—41no—
164C22×D11—42no—
165C22×D11—42no—
166C22×D11—42no—
167C22×D11—42no—
168C22×D11—42no—
169C22×D11—42no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11C4×D414yes—
180C2×C4×C11C23×C411yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11H(5,𝔽2)12yes—
183C2×C4×C11H(5,𝔽2)12yes—
184C2×Dic11—22no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194D44—24no—
195D44—24no—
196D44—24no—
197D44—42no—
198D44—42no—
199D44—42no—
200D44—88no—
201C4×D11—84no—
202C4×D11—88no—
203Dic22—24no—
204Dic22—42no—
205C8×C11—24no—
206C8×C11—42no—
207C22×SD16—112no—
208C22×D8—112no—
209C2×#127—111no—
210C2×#124—111no—
211C2×C4×Q8—111no—
212C2×C4×D4—111no—
213C2×C4×D4—112no—
214#496—118no—
215C2×#103—112no—
216C2×#102—112no—
217C2×#102—112no—
218C2×#102—112no—
219C2×#97C2×D1111yescharacteristic
220C2×C4×C8C2×D1111yescharacteristic
221#391—111no—
222#390—111no—
223#390—112no—
224#388—222no—
225#386—222no—
226#386—222no—
227#385—222no—
228#384—111no—
229#382—111no—
230#376C2×D1111yescharacteristic
231#340—112no—
232#340—112no—
233#336C2×D1112yes—
234#336C2×D1112yes—
235C22×C11C2×C4×D411yescharacteristic
236C22×C11#53511yescharacteristic
237C22×C11#53511yescharacteristic
238C22×C11#57612yes—
239C22×C11#57712yes—
240C2×D11—42no—
241C2×D11—44no—
242C2×D11—44no—
243C2×D11—44no—
244C2×D11—44no—
245C2×D11—82no—
246C2×D11—81no—
247C2×D11—81no—
248C2×D11—82no—
249C2×D11—82no—
250C2×D11—82no—
251C2×D11—82no—
252C4×C11—24no—
253C4×C11—41no—
254C4×C11—41no—
255C4×C11—42no—
256C4×C11#51812yes—
257C4×C11#54012yes—
258Dic11—42no—
259Dic11—81no—
260Dic11—81no—
261Dic11—82no—
262C22×Q8—111no—
263C22×D4—111no—
264C22×D4—112no—
265C22×D4—222no—
266C23×C4—221no—
267C23×C4—222no—
268C2×SD16—118no—
269C2×SD16—442no—
270C2×SD16—442no—
271C2×D8—118no—
272C2×D8—442no—
273C2×D8—442no—
274C22×C8C22×D1112yes—
275C22×C8C22×D1112yes—
276#127—114no—
277#127—222no—
278#124—114no—
279#124—222no—
280C4×Q8—442no—
281C4×D4—442no—
282C4×D4—442no—
283C4×D4—442no—
284C2×C4⋊C4—112no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—222no—
289C2×C22⋊C4—222no—
290C2×C22⋊C4—222no—
291C2×C22⋊C4—221no—
292C2×C22⋊C4—222no—
293C2×C22⋊C4—222no—
294C2×C22⋊C4—222no—
295C2×C42—221no—
296C2×C42C22×D1111yescharacteristic
297C2×C42C22×D1111yescharacteristic
298C2×C42C22×D1111yescharacteristic
299#103—442no—
300#102—442no—
301#102—442no—
302#102—442no—
303#97C4×D1114yescomplemented
304C4×C8—22no—
305#95—222no—
306#95—222no—
307#95D4412yes—
308#95D4412yes—
309C2×C11#232811yescharacteristic
310C2×C11#294612yes—
311C2×C11#322011yescharacteristic
312C2×C11#322111yescharacteristic
313C2×C11#322412yes—
314D11—82no—
315D11—84no—
316C24—221no—
317C24—222no—
318C2×Q8—112no—
319C2×Q8—221no—
320C2×Q8—222no—
321C2×Q8—222no—
322C2×D4—112no—
323C2×D4—114no—
324C2×D4—228no—
325C2×D4—221no—
326C2×D4—222no—
327C2×D4—222no—
328C2×D4—222no—
329C2×D4—222no—
330C2×D4—222no—
331C2×D4—222no—
332C2×D4—222no—
333C2×D4—882no—
334C2×D4—882no—
335C22×C4—221no—
336C22×C4—222no—
337C22×C4—221no—
338C22×C4—221no—
339C22×C4—444no—
340C22×C4—442no—
341C22×C4—882no—
342C22×C4—882no—
343C22×C4—882no—
344C22×C4C2×D4412yes—
345C22×C4C2×D4411yescharacteristic
346C22×C4C2×D4411yescharacteristic
347C22×C4C2×D4412yes—
348C22×C4C23×D1111yescharacteristic
349SD16—448no—
350D8—448no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8C2×C4×D1114yes—
357C4⋊C4—222no—
358C4⋊C4—222no—
359C4⋊C4—222no—
360C4⋊C4—222no—
361C4⋊C4—442no—
362C4⋊C4—882no—
363C22⋊C4—228no—
364C22⋊C4—442no—
365C22⋊C4—444no—
366C22⋊C4—882no—
367C22⋊C4—882no—
368C22⋊C4—882no—
369C42—22no—
370C42—22no—
371C42—442no—
372C42C2×C4×D1112yes—
373C42#433912yes—
374C11#2227911yescharacteristic, complemented, Sylow
375C23—222no—
376C23—224no—
377C23—442no—
378C23—442no—
379C23—442no—
380C23—442no—
381C23—442no—
382C23—442no—
383C23—441no—
384C23—442no—
385C23—442no—
386C23—441no—
387C23C22×D4411yescharacteristic
388Q8—224no—
389Q8—442no—
390D4—224no—
391D4—224no—
392D4—224no—
393D4—442no—
394D4—442no—
395D4—442no—
396D4—888no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—21no—
406C2×C4—222no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—442no—
416C2×C4—884no—
417C2×C4—888no—
418C2×C4C4×D4414yes—
419C2×C4C22×C4×D1111yescharacteristic
420C2×C4C2×#433911yescharacteristic
421C2×C4#6704212yes—
422C2×C4#6704212yes—
423C8—24no—
424C8—42no—
425C22—444no—
426C22—444no—
427C22—444no—
428C22—442no—
429C22—444no—
430C22—881no—
431C22—882no—
432C22—882no—
433C22—881no—
434C22—882no—
435C22—882no—
436C22—882no—
437C22C2×C4×D4411yescharacteristic
438C22#1062305611yescharacteristic
439C22#1062305611yescharacteristic
440C22#1062328212yes—
441C22#1062328312yes—
442C4—24no—
443C4—41no—
444C4—41no—
445C4—42no—
446C4—442no—
447C4—881no—
448C4—881no—
449C4—882no—
450C4#1062305212yes—
451C4#1062306612yes—
452C2—884no—
453C2—882no—
454C2#1307134111yescharacteristic
455C2#1307745012yes—
456C2#1307966811yescharacteristic
457C2#1307967911yescharacteristic
458C2#1307971212yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1746C2
socleC23×C11C22×D4
prime radicalC2×#10622325C2
cosocleC22×C4×C11C24
hypercenter#1746D11
hypocenterC11#22279
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #1746

Complements

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

NH ≅ G/Ntype
2. #13071341C2semidirect
3. #13071327C2semidirect
4. #13069427C2semidirect
5. #13069422C2semidirect
6. #13068970C2semidirect
7. #13068963C2semidirect
8. #13068963C2semidirect
9. #13068949C2semidirect
10. #13068750C2semidirect
11. C11×#1746C2semidirect
31. #10622325C4semidirect
65. C2×D88C2×C4semidirect
68. C2×#4314C2×C4semidirect
70. #66928C2×C4semidirect
72. #66927C2×C4semidirect
77. C11×#97C2×C4semidirect
156. #1746D11semidirect
303. #97C4×D11semidirect
374. C11#22279semidirect

Maximal subgroups

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

subgroupindex
C2×#106223252
#130713412
#130713272
#130694272
#130694222
#130689702
#130689632
#130689492
#130687502
C11×#17462
#2227911