Finite Group Databasebeta

← #14926097

Subgroups — #14926097

Order 2816.

2164 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073336C214yesmaximal, complemented
2#13073252C214yesmaximal, complemented
3#13072624C214yesmaximal, complemented
4#13072525C214yesmaximal, complemented
5#13071921C211yesmaximal, characteristic, complemented
6#13071897C211yesmaximal, characteristic, complemented
7#13071852C212yesmaximal, complemented
8C4×#66947C214yesmaximal, complemented
9C4×#66937C214yesmaximal, complemented
10C42×D44C212yesmaximal, complemented
11C11×#2298C211yesmaximal, characteristic, complemented
12C2×C11×#117C2211yescharacteristic
13C2×C4×C22⋊D11C2214yes—
14C2×#66947C2214yes—
15C2×#66937C2214yes—
16C2×C4×D44C2212yes—
17C2×C4×D44C2214yes—
18C2×C4×D44C2214yes—
19C2×C42×D11C2214yes—
20C11×#388C2214yes—
21C11×#387C2214yes—
22C4×C11×C4⋊C4C2212yes—
23C4×C11×C22⋊C4C2212yes—
24C11×#376C2211yescharacteristic
25C43×C11C2211yescharacteristic
26#10622607C2214yes—
27#10622604C2212yes—
28#10622603C2214yes—
29#10622602C2214yes—
30#10622596C2212yes—
31#10622594C2214yes—
32#10622574C2214yes—
33#10622573C2212yes—
34#10622570C2214yes—
35#10622569C2214yes—
36#10622566C2212yes—
37#10622564C2214yes—
38C4×(C2×D11)⋊C4C2214yes—
39C4×(C2×D11)⋊C4C2214yes—
40C4×(C2×D11)⋊C4C2214yes—
41C4×(C2×D11)⋊C4C2214yes—
42C4×C4⋊Dic11C2212yes—
43C4×C4⋊Dic11C2214yes—
44C4×Dic11⋊C4C2214yes—
45#10622290C2214yes—
46#10622284C2214yes—
47#10622282C2214yes—
48#10622282C2214yes—
49#10622280C2214yes—
50#10622278C2214yes—
51#10622278C2214yes—
52#10622277C2214yes—
53#10622273C2214yes—
54#10622270C2214yes—
55#10622268C2214yes—
56#10622260C2214yes—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11C2314yes—
59C22×D44C2312yes—
60C22×D44C2314yes—
61C22×C4×D11C2314yes—
62C22×C4×D11C2314yes—
63C22×C4×D11C2314yes—
64C11×#117—24no—
65C2×C11×C4⋊C4C2314yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4C2314yes—
68C2×C11×C22⋊C4C2312yes—
69C2×C42×C11C2312yes—
70C2×C42×C11C2312yes—
71C2×C42×C11C2314yes—
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11C2314yes—
75C4×C22⋊D11—48no—
76C2×(C2×D11)⋊C4C2314yes—
77C2×(C2×D11)⋊C4C2314yes—
78C2×(C2×D11)⋊C4C2314yes—
79C2×(C2×D11)⋊C4C2314yes—
80C2×(C2×D11)⋊C4C2314yes—
81C2×(C2×D11)⋊C4C2314yes—
82C2×(C2×D11)⋊C4C2314yes—
83C2×(C2×D11)⋊C4C2314yes—
84C2×C4⋊Dic11C2314yes—
85C2×C4⋊Dic11C2312yes—
86C2×C4⋊Dic11C2314yes—
87C2×Dic11⋊C4C2314yes—
88C2×Dic11⋊C4C2314yes—
89C2×Dic11⋊C4C2314yes—
90C2×C4×Dic11C2314yes—
91C2×C4×Dic11C2314yes—
92C2×C4×Dic11C2314yes—
93#66947—216no—
94#66937—216no—
95C4×D44—28no—
96C4×D44—216no—
97C4×D44—48no—
98C42×D11—48no—
99C11×#95C2314yes—
100C11×#95C2314yes—
101C11×#95C2314yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104C11⋊#95C2314yes—
105C11⋊#95C2312yes—
106C11⋊#95C2314yes—
107C11⋊#95C2314yes—
108C11⋊#95C2312yes—
109C11⋊#95C2314yes—
110#34967—111nomaximal, Sylow
111C24×C11C2411yescharacteristic
112C23×D11C2414yes—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11C2412yes—
116C22×C4×C11C2414yes—
117C22×C4×C11C2411yescharacteristic
118C22×C4×C11C2414yes—
119C22×C4×C11C2412yes—
120C22×C4×C11C2411yescharacteristic
121C2×C22⋊D11—28no—
122C2×C22⋊D11—28no—
123C2×C22⋊D11—44no—
124C22×Dic11C2414yes—
125C22×Dic11C2414yes—
126C22×Dic11C2414yes—
127C2×D44—28no—
128C2×D44—28no—
129C2×D44—28no—
130C2×D44—24no—
131C2×D44—44no—
132C2×C4×D11—28no—
133C2×C4×D11—28no—
134C2×C4×D11—28no—
135C2×C4×D11—28no—
136C2×C4×D11—28no—
137C2×C4×D11—28no—
138C2×C4×D11—28no—
139C2×C4×D11—44no—
140C2×C4×D11—44no—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—24no—
143C11×C22⋊C4—28no—
144C11×C22⋊C4—24no—
145C42×C11—28no—
146C42×C11—22no—
147C42×C11—24no—
148C42×C11—24no—
149C42×C11#4114yes—
150C22⋊Dic11—44no—
151(C2×D11)⋊C4—28no—
152(C2×D11)⋊C4—28no—
153(C2×D11)⋊C4—28no—
154(C2×D11)⋊C4—28no—
155(C2×D11)⋊C4—44no—
156(C2×D11)⋊C4—44no—
157(C2×D11)⋊C4—44no—
158(C2×D11)⋊C4#41116yes—
159C4⋊Dic11—28no—
160C4⋊Dic11—24no—
161C4⋊Dic11—44no—
162Dic11⋊C4—28no—
163Dic11⋊C4—28no—
164Dic11⋊C4—44no—
165C4×Dic11—28no—
166C4×Dic11—44no—
167C4×Dic11—44no—
168#2522—114no—
169#2516—114no—
170#2464—114no—
171#2457—114no—
172#2402—111no—
173#2397—111no—
174#2392—112no—
175C4×#123—114no—
176C4×#121—114no—
177#2298D1111yescharacteristic, complemented
178C42×D4—112no—
179C23×C11—21no—
180C23×C11—24no—
181C23×C11—22no—
182C23×C11C2511yescharacteristic
183C22×D11—24no—
184C22×D11—24no—
185C22×D11—24no—
186C22×D11—24no—
187C22×D11—24no—
188C22×D11—24no—
189C22×D11C2×#4118yes—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—44no—
201C2×C4×C11C2×#4114yes—
202C2×C4×C11C2×#4112yes—
203C2×C4×C11C2×#4118yes—
204C2×C4×C11H(5,𝔽2)14yes—
205C22⋊D11—416no—
206C2×Dic11—24no—
207C2×Dic11—24no—
208C2×Dic11—24no—
209C2×Dic11—24no—
210C2×Dic11—24no—
211C2×Dic11—24no—
212C2×Dic11—24no—
213C2×Dic11—24no—
214C2×Dic11C2×#4118yes—
215D44—216no—
216D44—416no—
217C4×D11—416no—
218C4×D11—416no—
219C4×D11—416no—
220C2×#123—114no—
221C2×#121—114no—
222C2×C4×D4—114no—
223C2×C4×D4—112no—
224C2×C4×D4—114no—
225C2×C4×D4—114no—
226C2×#117C2×D1111yescharacteristic
227C22×C42—114no—
228#400—114no—
229#399—114no—
230#398—112no—
231#398—114no—
232#397—112no—
233#396—114no—
234#394—112no—
235#394—114no—
236#392—112no—
237#392—114no—
238#390—114no—
239#389—114no—
240#388—114no—
241#388—114no—
242#388—114no—
243#388—114no—
244#388C2×D1114yes—
245#387—114no—
246#387—114no—
247#387C2×D1114yes—
248#386—114no—
249#386—114no—
250#386—114no—
251#385—114no—
252#381—114no—
253#380—114no—
254C4×C4⋊C4—114no—
255C4×C4⋊C4—112no—
256C4×C4⋊C4—114no—
257C4×C4⋊C4C2×D1112yes—
258C4×C22⋊C4—114no—
259C4×C22⋊C4—114no—
260C4×C22⋊C4—114no—
261C4×C22⋊C4—114no—
262C4×C22⋊C4C2×D1112yes—
263#376C2×D1111yescharacteristic
264C43C2×D1111yescharacteristic
265C22×C11—42no—
266C22×C11—41no—
267C22×C11—44no—
268C22×C11C22×#4111yescharacteristic
269C22×C11C22×#4114yes—
270C22×C11C2×H(5,𝔽2)12yes—
271C2×D11—28no—
272C2×D11—28no—
273C2×D11—28no—
274C2×D11—44no—
275C2×D11—44no—
276C2×D11—44no—
277C2×D11—44no—
278C4×C11—24no—
279C4×C11—28no—
280C4×C11—42no—
281C4×C11—41no—
282C4×C11—44no—
283C4×C11#54014yes—
284Dic11—28no—
285Dic11—44no—
286Dic11—44no—
287C22×D4—114no—
288C22×D4—112no—
289C22×D4—114no—
290C23×C4—114no—
291C23×C4—114no—
292C23×C4—114no—
293C23×C4C22×D1111yescharacteristic
294#123—2216no—
295#121—2216no—
296C4×D4—2216no—
297C4×D4—228no—
298C4×D4—448no—
299C4×D4—448no—
300#117—24no—
301C2×C4⋊C4—114no—
302C2×C4⋊C4—112no—
303C2×C4⋊C4—114no—
304C2×C4⋊C4—114no—
305C2×C4⋊C4—114no—
306C2×C4⋊C4—114no—
307C2×C4⋊C4C22×D1112yes—
308C2×C4⋊C4C22×D1114yes—
309C2×C22⋊C4—114no—
310C2×C22⋊C4—114no—
311C2×C22⋊C4—114no—
312C2×C22⋊C4—114no—
313C2×C22⋊C4—114no—
314C2×C22⋊C4—114no—
315C2×C22⋊C4—114no—
316C2×C22⋊C4—114no—
317C2×C22⋊C4—114no—
318C2×C22⋊C4C22×D1112yes—
319C2×C22⋊C4C22×D1114yes—
320C2×C42—114no—
321C2×C42—114no—
322C2×C42—114no—
323C2×C42—448no—
324C2×C42C22×D1114yes—
325C2×C42C22×D1111yescharacteristic
326C2×C42C22×D1112yes—
327C2×C42C22×D1112yes—
328C2×C42C22×D1111yescharacteristic
329#95—114no—
330#95—114no—
331#95—112no—
332#95—112no—
333#95—114no—
334#95—114no—
335#95—114no—
336#95—114no—
337#95C22×D1114yes—
338#95C22×D1114yes—
339#95C22×D1114yes—
340C2×C11—81no—
341C2×C11#344412yes—
342C2×C11C2×#54011yescharacteristic
343C2×C11#348114yes—
344D11—48no—
345C24—114no—
346C24C23×D1111yescharacteristic
347C2×D4—228no—
348C2×D4—228no—
349C2×D4—228no—
350C2×D4—228no—
351C2×D4—228no—
352C2×D4—224no—
353C2×D4—444no—
354C2×D4—444no—
355C22×C4—22no—
356C22×C4—24no—
357C22×C4—114no—
358C22×C4—114no—
359C22×C4—114no—
360C22×C4—228no—
361C22×C4—228no—
362C22×C4—228no—
363C22×C4—228no—
364C22×C4—228no—
365C22×C4—228no—
366C22×C4—228no—
367C22×C4—444no—
368C22×C4—444no—
369C22×C4C23×D1112yes—
370C22×C4C23×D1114yes—
371C22×C4C23×D1111yescharacteristic
372C22×C4C23×D1112yes—
373C22×C4C23×D1114yes—
374C22×C4C23×D1111yescharacteristic
375C4⋊C4—24no—
376C4⋊C4—28no—
377C4⋊C4—228no—
378C4⋊C4—228no—
379C4⋊C4—228no—
380C4⋊C4—224no—
381C4⋊C4—444no—
382C4⋊C4—444no—
383C22⋊C4—24no—
384C22⋊C4—28no—
385C22⋊C4—1116no—
386C22⋊C4—228no—
387C22⋊C4—228no—
388C22⋊C4—228no—
389C22⋊C4—228no—
390C22⋊C4—444no—
391C22⋊C4—444no—
392C22⋊C4—444no—
393C22⋊C4—444no—
394C42—22no—
395C42—28no—
396C42—24no—
397C42—24no—
398C42—228no—
399C42—444no—
400C42—444no—
401C42#433914yes—
402C11#3496711yescharacteristic, complemented, Sylow
403C23—21no—
404C23—24no—
405C23—22no—
406C23—118no—
407C23—224no—
408C23—224no—
409C23—224no—
410C23—224no—
411C23—224no—
412C23—224no—
413C23C24×D1111yescharacteristic
414D4—2216no—
415D4—4416no—
416D4—4416no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—22no—
427C2×C4—44no—
428C2×C4—118no—
429C2×C4—224no—
430C2×C4—224no—
431C2×C4—224no—
432C2×C4—224no—
433C2×C4—224no—
434C2×C4—224no—
435C2×C4—224no—
436C2×C4—224no—
437C2×C4—4416no—
438C2×C4—4416no—
439C2×C4—4416no—
440C2×C4C2×#433914yes—
441C2×C4C2×#433912yes—
442C2×C4#41×D1118yes—
443C2×C4#6704214yes—
444C22—42no—
445C22—44no—
446C22—41no—
447C22—228no—
448C22—228no—
449C22—228no—
450C22—444no—
451C22—444no—
452C22—444no—
453C22—444no—
454C22C22×#433911yescharacteristic
455C22C2×#41×D1114yes—
456C22C2×#6704212yes—
457C4—24no—
458C4—28no—
459C4—42no—
460C4—44no—
461C4—41no—
462C4—228no—
463C4—444no—
464C4—444no—
465C4#1062306614yes—
466C2—81no—
467C2—448no—
468C2#1308190912yes—
469C2C2×#1062306611yescharacteristic
470C2#1308222214yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2298C2
hypercenter#2298D11
hypocenterC11#34967
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2298

Complements

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

NH ≅ G/Ntype
1. #13073336C2semidirect
2. #13073252C2semidirect
3. #13072624C2semidirect
4. #13072525C2semidirect
5. #13071921C2semidirect
6. #13071897C2semidirect
7. #13071852C2semidirect
8. C4×#66947C2semidirect
9. C4×#66937C2semidirect
10. C42×D44C2semidirect
11. C11×#2298C2semidirect
177. #2298D11semidirect
402. C11#34967semidirect

Maximal subgroups

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

subgroupindex
#130733362
#130732522
#130726242
#130725252
#130719212
#130718972
#130718522
C4×#669472
C4×#669372
C42×D442
C11×#22982
#3496711