Finite Group Databasebeta

← #14763593

Subgroups — #14763593

Order 2816.

1254 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071230C211yesmaximal, characteristic, complemented
2#13071214C211yesmaximal, characteristic, complemented
3#13069602C212yesmaximal, complemented
4#13069453C212yesmaximal, complemented
5#13069070C214yesmaximal, complemented
6#13068604C214yesmaximal, complemented
7C2×C11×#538C211yesmaximal, characteristic
8C11×#538—24no—
9C11×#538—24no—
10C2×C11×#126C412yescomplemented
11C2×C11×#124C412yescomplemented
12C2×C11×#123C412yescomplemented
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×C11×#121C412yescomplemented
15C2×C11×#121C2211yescharacteristic
16C2×C11×#120C2212yes—
17C2×C4×D4×C11C2212yes—
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20#10622860C2212yes—
21C2×#66898C2218yes—
22#10622825C2212yes—
23#10622825C2212yes—
24#10622825C2212yes—
25C4×C22⋊Dic11C2212yes—
26#10622564—24no—
27#10622563—24no—
28#10622164C2218yes—
29C25×C11C2311yescharacteristic
30C22×Q8×C11C2×C411yescharacteristic, complemented
31C22×D4×C11C2×C412yes—
32C22×D4×C11C2×C412yes—
33C22×D4×C11C2×C411yescharacteristic, complemented
34C22×D4×C11C2312yes—
35C23×C4×C11C2×C412yescomplemented
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×Dic11—22no—
39C11×#126—28no—
40C11×#124—28no—
41C11×#123—28no—
42C11×C22⋊Q8—22no—
43C11×C22⋊Q8—22no—
44C11×#121—22no—
45C11×#121—22no—
46C11×#121—28no—
47C11×#120—24no—
48C11×#120—24no—
49C4×D4×C11—24no—
50C4×D4×C11—24no—
51C2×C11×C4⋊C4C2×C412yescomplemented
52C2×C11×C4⋊C4C2×C412yescomplemented
53C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
54C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
55C2×C11×C22⋊C4C2×C412yes—
56C2×C11×C22⋊C4C2×C412yes—
57C2×C11×C22⋊C4C2×C412yes—
58C2×C11×C22⋊C4C2×C412yes—
59C2×C11×C22⋊C4C2×C412yescomplemented
60C2×C11×C22⋊C4C2×C412yescomplemented
61C2×C11×C22⋊C4D414yes—
62C2×C11×C22⋊C4D414yes—
63C2×C11×C22⋊C4C2312yes—
64C2×C42×C11C2×C412yescomplemented
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—44no—
69C2×C22⋊Dic11C2314yes—
70C2×C22⋊Dic11C2314yes—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4×Dic11—22no—
75#66898—48no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80#21876—111nomaximal, Sylow
81C24×C11—22no—
82C24×C11—22no—
83C24×C11—81no—
84C24×C11—81no—
85C24×C11C22×C412yes—
86C24×C11C22×C412yes—
87C24×C11C2×D412yes—
88C24×C11C2×D412yes—
89C24×C11C2411yescharacteristic
90C2×Q8×C11—22no—
91C2×Q8×C11—81no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—24no—
95C2×D4×C11—24no—
96C2×D4×C11—24no—
97C2×D4×C11—24no—
98C2×D4×C11—22no—
99C2×D4×C11—82no—
100C2×D4×C11—82no—
101C2×D4×C11—81no—
102C22×C4×C11—24no—
103C22×C4×C11—81no—
104C22×C4×C11—81no—
105C22×C4×C11—82no—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C22×C412yes—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C22×C412yes—
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×Dic11—24no—
117C22×Dic11—24no—
118C22×Dic11—44no—
119C22×Dic11—82no—
120C22×Dic11—82no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—24no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C22⋊C4—24no—
126C11×C22⋊C4—24no—
127C11×C22⋊C4—22no—
128C11×C22⋊C4—22no—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—24no—
131C11×C22⋊C4C22⋊C418yes—
132C11×C22⋊C4C22⋊C418yes—
133C42×C11—24no—
134C22⋊Dic11—24no—
135C22⋊Dic11—28no—
136C22⋊Dic11—24no—
137C22⋊Dic11—44no—
138C22⋊Dic11—82no—
139C22⋊Dic11—82no—
140C4⋊Dic11—82no—
141C4⋊Dic11—82no—
142C4⋊Dic11—82no—
143C4×Dic11—82no—
144C2×#538D1111yescharacteristic
145#2315—111no—
146#2312—111no—
147#1996—112no—
148#1964—112no—
149#1898—114no—
150#1799—114no—
151C23×C11—22no—
152C23×C11—22no—
153C23×C11—24no—
154C23×C11—24no—
155C23×C11—22no—
156C23×C11—24no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11—84no—
168C23×C11—84no—
169C23×C11C2×C22⋊C414yes—
170C23×C11C23×C411yescharacteristic
171C23×C11C22×D411yescharacteristic
172C23×C11C22×D411yescharacteristic
173C23×C11H(5,𝔽2)12yes—
174C23×C112−1+412yes—
175Q8×C11—82no—
176D4×C11—42no—
177D4×C11—42no—
178D4×C11—44no—
179D4×C11—82no—
180D4×C11—84no—
181D4×C11—84no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—24no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—84no—
196C2×C4×C11C2×C22⋊C414yes—
197C2×C4×C11C2×C22⋊C412yes—
198C2×C4×C11C2×C22⋊C412yes—
199C2×Dic11—44no—
200C2×Dic11—44no—
201C2×Dic11—44no—
202C2×Dic11—44no—
203C2×Dic11—44no—
204C2×Dic11—44no—
205C2×Dic11—88no—
206#538—24no—
207#538—24no—
208C2×#126Dic1112yescomplemented
209C2×#124Dic1112yescomplemented
210C2×#123Dic1112yescomplemented
211C2×C22⋊Q8C2×D1111yescharacteristic
212C2×#121Dic1112yescomplemented
213C2×#121C2×D1111yescharacteristic
214C2×#120C2×D1112yes—
215C2×C4×D4C2×D1112yes—
216C22×C22⋊C4—112no—
217C22×C22⋊C4C2×D1111yescharacteristic
218C2×#99—118no—
219#388—224no—
220#385—224no—
221#380—112no—
222#380—112no—
223#380—112no—
224#379—112no—
225C4×C22⋊C4—112no—
226#342—118no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—24no—
234C22×C11—24no—
235C22×C11—24no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—44no—
239C22×C11—44no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—42no—
243C22×C11—84no—
244C22×C11—84no—
245C22×C11—84no—
246C22×C11C22×C22⋊C411yescharacteristic
247C22×C11#52012yes—
248C22×C11#53511yescharacteristic
249C22×C11#53611yescharacteristic
250C22×C11#53712yes—
251C4×C11—24no—
252C4×C11—22no—
253C4×C11—22no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—42no—
257Dic11—84no—
258Dic11—84no—
259C25C22×D1111yescharacteristic
260C22×Q8C2×Dic1111yescharacteristic, complemented
261C22×D4C2×Dic1112yes—
262C22×D4C2×Dic1112yes—
263C22×D4C2×Dic1111yescharacteristic, complemented
264C22×D4C22×D1112yes—
265C23×C4—222no—
266C23×C4C2×Dic1112yescomplemented
267C23×C4C22×D1111yescharacteristic
268C23×C4C22×D1111yescharacteristic
269#126—28no—
270#124—28no—
271#123—28no—
272C22⋊Q8—22no—
273C22⋊Q8—22no—
274#121—22no—
275#121—22no—
276#121—28no—
277#120—24no—
278#120—24no—
279C4×D4—24no—
280C4×D4—24no—
281C2×C4⋊C4—222no—
282C2×C4⋊C4—222no—
283C2×C4⋊C4—222no—
284C2×C4⋊C4C2×Dic1112yescomplemented
285C2×C4⋊C4C2×Dic1112yescomplemented
286C2×C4⋊C4C2×Dic1111yescharacteristic, complemented
287C2×C4⋊C4C2×Dic1111yescharacteristic, complemented
288C2×C22⋊C4—114no—
289C2×C22⋊C4—114no—
290C2×C22⋊C4—222no—
291C2×C22⋊C4—222no—
292C2×C22⋊C4—222no—
293C2×C22⋊C4—444no—
294C2×C22⋊C4C2×Dic1112yes—
295C2×C22⋊C4C2×Dic1112yes—
296C2×C22⋊C4C2×Dic1112yes—
297C2×C22⋊C4C2×Dic1112yes—
298C2×C22⋊C4C2×Dic1112yescomplemented
299C2×C22⋊C4C2×Dic1112yescomplemented
300C2×C22⋊C4C22⋊D1114yes—
301C2×C22⋊C4C22⋊D1114yes—
302C2×C22⋊C4C22×D1112yes—
303C2×C42—222no—
304C2×C42C2×Dic1112yescomplemented
305#99—448no—
306#95—222no—
307#95—222no—
308#95—222no—
309#95—222no—
310C2×C11—21no—
311C2×C11—22no—
312C2×C11—21no—
313C2×C11—22no—
314C2×C11—44no—
315C2×C11—82no—
316C2×C11#231111yescharacteristic
317C2×C11#288311yescharacteristic
318C2×C11#288311yescharacteristic
319C24—22no—
320C24—22no—
321C24—81no—
322C24—81no—
323C24C22×Dic1112yes—
324C24C22×Dic1112yes—
325C24C2×C22⋊D1112yes—
326C24C2×C22⋊D1112yes—
327C24C23×D1111yescharacteristic
328C2×Q8—22no—
329C2×Q8—81no—
330C2×D4—24no—
331C2×D4—24no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—22no—
337C2×D4—82no—
338C2×D4—82no—
339C2×D4—81no—
340C22×C4—24no—
341C22×C4—81no—
342C22×C4—81no—
343C22×C4—82no—
344C22×C4—224no—
345C22×C4—224no—
346C22×C4—444no—
347C22×C4—882no—
348C22×C4—882no—
349C22×C4C22×Dic1112yes—
350C22×C4C22×Dic1112yes—
351C22×C4C22×Dic1112yes—
352C22×C4C22×Dic1112yes—
353C22×C4C22×Dic1111yescharacteristic
354C22×C4C22×Dic1111yescharacteristic
355C22×C4C2×C22⋊D1112yes—
356C22×C4C2×C22⋊D1112yes—
357C22×C4C2×C22⋊D1112yes—
358C22×C4C2×C22⋊D1112yes—
359C4⋊C4—24no—
360C4⋊C4—24no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—882no—
364C4⋊C4—882no—
365C4⋊C4—882no—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—22no—
369C22⋊C4—22no—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—224no—
373C22⋊C4—228no—
374C22⋊C4—224no—
375C22⋊C4—444no—
376C22⋊C4—882no—
377C22⋊C4—882no—
378C22⋊C4C22⋊Dic1118yes—
379C22⋊C4C22⋊Dic1118yes—
380C42—24no—
381C42—882no—
382C11#2187611yescharacteristic, complemented, Sylow
383C23—22no—
384C23—22no—
385C23—24no—
386C23—24no—
387C23—22no—
388C23—24no—
389C23—41no—
390C23—41no—
391C23—42no—
392C23—42no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—42no—
399C23—84no—
400C23—84no—
401C23C2×C22⋊Dic1114yes—
402C23#6704212yes—
403C23#6704312yes—
404C23C23×Dic1111yescharacteristic
405C23C22×C22⋊D1111yescharacteristic
406C23C22×C22⋊D1111yescharacteristic
407Q8—82no—
408D4—42no—
409D4—42no—
410D4—44no—
411D4—82no—
412D4—84no—
413D4—84no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—84no—
428C2×C4—444no—
429C2×C4—444no—
430C2×C4—444no—
431C2×C4—444no—
432C2×C4—444no—
433C2×C4—444no—
434C2×C4—888no—
435C2×C4C2×C22⋊Dic1114yes—
436C2×C4C2×C22⋊Dic1112yes—
437C2×C4C2×C22⋊Dic1112yes—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—24no—
445C22—24no—
446C22—24no—
447C22—42no—
448C22—42no—
449C22—44no—
450C22—44no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—84no—
455C22—84no—
456C22—84no—
457C22#1062335611yescharacteristic
458C22#1062335812yes—
459C22#1062336111yescharacteristic
460C22#1062336412yes—
461C22C22×C22⋊Dic1111yescharacteristic
462C4—24no—
463C4—22no—
464C4—22no—
465C4—42no—
466C4—42no—
467C4—42no—
468C4—884no—
469C4—884no—
470C2—21no—
471C2—22no—
472C2—21no—
473C2—22no—
474C2—44no—
475C2—82no—
476C2#1307120811yescharacteristic
477C2#1307707711yescharacteristic
478C2#1307707711yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
Fitting, prime radicalC2×C11×#538C2
socleC22×C11C22×C22⋊C4
cosocleC24×C11C24
hypercenterC2×#538D11
hypocenterC11#21876
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. #13071230C2semidirect
2. #13071214C2semidirect
3. #13069602C2semidirect
4. #13069453C2semidirect
5. #13069070C2semidirect
6. #13068604C2semidirect
10. C2×C11×#126C4semidirect
11. C2×C11×#124C4semidirect
12. C2×C11×#123C4semidirect
14. C2×C11×#121C4semidirect
30. C22×Q8×C11C2×C4semidirect
33. C22×D4×C11C2×C4semidirect
35. C23×C4×C11C2×C4semidirect
51. C2×C11×C4⋊C4C2×C4semidirect
52. C2×C11×C4⋊C4C2×C4semidirect
53. C2×C11×C4⋊C4C2×C4semidirect
54. C2×C11×C4⋊C4C2×C4semidirect
59. C2×C11×C22⋊C4C2×C4semidirect
60. C2×C11×C22⋊C4C2×C4semidirect
64. C2×C42×C11C2×C4semidirect
208. C2×#126Dic11semidirect
209. C2×#124Dic11semidirect
210. C2×#123Dic11semidirect
212. C2×#121Dic11semidirect
260. C22×Q8C2×Dic11semidirect
263. C22×D4C2×Dic11semidirect
266. C23×C4C2×Dic11semidirect
284. C2×C4⋊C4C2×Dic11semidirect
285. C2×C4⋊C4C2×Dic11semidirect
286. C2×C4⋊C4C2×Dic11semidirect
287. C2×C4⋊C4C2×Dic11semidirect
298. C2×C22⋊C4C2×Dic11semidirect
299. C2×C22⋊C4C2×Dic11semidirect
304. C2×C42C2×Dic11semidirect
382. C11#21876semidirect

Maximal subgroups

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

subgroupindex
#130712302
#130712142
#130696022
#130694532
#130690702
#130686042
C2×C11×#5382
#2187611