Finite Group Databasebeta

← #14720101

Subgroups — #14720101

Order 2816.

1016 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic
2#13077650C212yesmaximal, complemented
3#13066967C212yesmaximal, complemented
4#13066963C214yesmaximal, complemented
5#13066960C211yesmaximal, characteristic, complemented
6#13066953C212yesmaximal, complemented
7#13066933C212yesmaximal, complemented
8C11×#1461C211yesmaximal, characteristic, complemented
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#67000C412yes—
11#10623116—22no—
12#10623116—22no—
13#10623116—24no—
14C2×#66947C412yes—
15C2×#66947C2212yes—
16C2×#66946C2212yes—
17C2×#66928C411yescharacteristic
18C2×#66928C2211yescharacteristic
19C2×#66927C411yescharacteristic
20C2×C4×D44C411yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C4×Dic22C411yescharacteristic
23C11×#431C2212yes—
24#10622539C2212yes—
25#10622449—24no—
26#10622339C2214yes—
27D11×C22⋊C8C2214yes—
28#10622301—22no—
29C8×D44—22no—
30C11×#324C2211yescharacteristic
31C11×#324C2211yescharacteristic
32C11×#324C2212yes—
33#10622166C2212yes—
34#10622166C2212yes—
35#10622106C2214yes—
36#10622106C2214yes—
37C22×Q8×C11C2×C411yescharacteristic
38C22×D44C2×C412yes—
39C22×D44C2×C411yescharacteristic
40C22×D44C2×C412yes—
41C22×D44C2×C411yescharacteristic
42C22×C4×D11C2×C412yes—
43C22×C4×D11C2312yes—
44C22×Dic22C2×C411yescharacteristic
45C4×Q8×C11—22no—
46C4×Q8×C11—22no—
47C2×C11×C4⋊C4C2×C411yescharacteristic
48C2×C11×C4⋊C4C2311yescharacteristic
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C42×C11C2×C411yescharacteristic
51C2×C42×C11C2×C411yescharacteristic
52C2×C42×C11C2311yescharacteristic
53#67000—24no—
54#67000—24no—
55C2×(C2×D11)⋊C4C2×C412yes—
56C2×(C2×D11)⋊C4C2×C412yes—
57C2×(C2×D11)⋊C4C2×C412yes—
58C2×(C2×D11)⋊C4C2×C412yes—
59C2×(C2×D11)⋊C4C2×C412yes—
60C2×(C2×D11)⋊C4C2312yes—
61C2×C4⋊Dic11C2×C411yescharacteristic
62C2×Dic11⋊C4C2×C412yes—
63C2×C4×Dic11C2×C412yes—
64C2×#4313—24no—
65C2×C8×D11—24no—
66#66947—24no—
67#66947—24no—
68#66947—24no—
69#66947—24no—
70#66946—24no—
71#66946—24no—
72#66928—22no—
73#66928—22no—
74#66928—22no—
75#66928—22no—
76#66927—22no—
77#66927—22no—
78C4×D44—22no—
79C4×D44—21no—
80C4×D44—21no—
81C4×D44D412yes—
82C4×D44D412yes—
83C4×D44D414yes—
84C4×Dic22—22no—
85C4×Dic22—21no—
86C4×Dic22—21no—
87C11×C4⋊C8—22no—
88C11×C22⋊C8C2312yes—
89C11×C22⋊C8C2312yes—
90C4×C8×C11—22no—
91C22⋊(C11⋊C8)C2314yes—
92(C2×D11)⋊C8—24no—
93(C2×D11)⋊C8—24no—
94C4⋊(C11⋊C8)—22no—
95#66867—22no—
96#17429—111nomaximal, Sylow
97C23×D11C22×C412yes—
98C23×D11C22×C412yes—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11—41no—
102C22×C4×C11C22×C411yescharacteristic
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C22×C411yescharacteristic
105C22×C4×C11C22×C411yescharacteristic
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C22×C411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11C22×C412yes—
110C22×Dic11C22×C412yes—
111C2×D44—24no—
112C2×D44—24no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—24no—
116C2×D44—42no—
117C2×D44—42no—
118C2×D44—42no—
119C2×D44—82no—
120C2×D44C22⋊C412yes—
121C2×D44C22⋊C412yes—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—82no—
125C2×C4×D11—82no—
126C2×C4×D11C2×D414yes—
127C2×C4×D11C2×D414yes—
128C2×Dic22—21no—
129C2×Dic22—21no—
130C2×Dic22—42no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C42×C11—21no—
137C42×C11—21no—
138C42×C11—21no—
139C42×C11—21no—
140C42×C11C2×D412yes—
141C42×C11C2×D412yes—
142(C2×D11)⋊C4—22no—
143(C2×D11)⋊C4—22no—
144(C2×D11)⋊C4—24no—
145(C2×D11)⋊C4—24no—
146(C2×D11)⋊C4—24no—
147(C2×D11)⋊C4—24no—
148(C2×D11)⋊C4C22⋊C414yes—
149(C2×D11)⋊C4C22⋊C414yes—
150C4⋊Dic11C22⋊C412yes—
151C4⋊Dic11C22⋊C411yescharacteristic
152C4⋊Dic11C22⋊C411yescharacteristic
153Dic11⋊C4—22no—
154Dic11⋊C4—22no—
155C4×Dic11—22no—
156C4×Dic11—22no—
157C2×C11⋊C8—24no—
158#4313—84no—
159C8×D11—84no—
160C2×#559—111no—
161#2974—112no—
162#1469—112no—
163#1468—114no—
164#1467—111no—
165#1465—112no—
166#1461D1111yescharacteristic, complemented
167#1459—112no—
168C23×C11C23×C411yescharacteristic
169C22×D11—22no—
170C22×D11—22no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—22no—
174C22×D11—42no—
175C22×D11—42no—
176C22×D11—42no—
177C22×D11—42no—
178C22×D11C2×C22⋊C414yes—
179Q8×C11—44no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11C2×C22⋊C411yescharacteristic
194C2×C4×C11C2×C22⋊C412yes—
195C2×C4×C11C2×C22⋊C411yescharacteristic
196C2×C4×C11#13112yes—
197C2×C4×C11C22×D412yes—
198C2×Dic11—22no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11C2×C22⋊C412yes—
202C2×Dic11C2×C22⋊C412yes—
203D44—24no—
204D44—42no—
205D44—48no—
206D44—42no—
207D44—42no—
208D44—84no—
209C4×D11—44no—
210C4×D11—44no—
211C4×D11—82no—
212C4×D11—82no—
213Dic22—42no—
214Dic22—42no—
215C8×C11—42no—
216C8×C11—42no—
217C11⋊C8—44no—
218#559—222no—
219#559—224no—
220#559—222no—
221C2×#127—111no—
222C2×#124—112no—
223C2×#124—111no—
224C2×#124—111no—
225C2×#123—112no—
226C2×#123—112no—
227C2×C4×Q8—111no—
228C2×C4×Q8C2×D1111yescharacteristic
229C2×C4×D4—112no—
230C2×C4×D4—111no—
231C2×C4×D4—111no—
232#436—222no—
233#435—224no—
234C8×D4—222no—
235#432—112no—
236#431C2×D1112yes—
237#407—114no—
238C2×C22⋊C8—114no—
239#324—112no—
240#324—112no—
241#324C2×D1111yescharacteristic
242#324C2×D1111yescharacteristic
243#324C2×D1112yes—
244#323—114no—
245#323—114no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11C22×C22⋊C411yescharacteristic
249C22×C11C2×#13111yescharacteristic
250C22×C11#56811yescharacteristic
251C2×D11—24no—
252C2×D11—24no—
253C2×D11—24no—
254C2×D11—42no—
255C2×D11—42no—
256C2×D11—42no—
257C2×D11—82no—
258C2×D11—82no—
259C2×D11—82no—
260C2×D11—82no—
261C4×C11—22no—
262C4×C11—22no—
263C4×C11—22no—
264C4×C11—21no—
265C4×C11—41no—
266C4×C11—41no—
267C4×C11—41no—
268C4×C11#41312yes—
269Dic11—22no—
270Dic11—22no—
271Dic11—42no—
272C22×Q8—111no—
273C22×Q8C4×D1111yescharacteristic
274C22×D4—111no—
275C22×D4—112no—
276C22×D4—111no—
277C22×D4—112no—
278C23×C4—112no—
279C23×C4—112no—
280C2×M16—224no—
281C22×C8—224no—
282#127—222no—
283#127—222no—
284#124—222no—
285#124—222no—
286#124—224no—
287#124—224no—
288#124—222no—
289#124—222no—
290#123—224no—
291#123—224no—
292#123—224no—
293#123—224no—
294C4×Q8—22no—
295C4×Q8—22no—
296C4×Q8—222no—
297C4×Q8—221no—
298C4×Q8—221no—
299C4×D4—112no—
300C4×D4—114no—
301C4×D4—112no—
302C4×D4—222no—
303C4×D4—221no—
304C4×D4—221no—
305C4×D4—224no—
306C4×D4—224no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—112no—
309C2×C4⋊C4C4×D1111yescharacteristic
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C4⋊C4C22×D1111yescharacteristic
312C2×C22⋊C4—112no—
313C2×C22⋊C4—112no—
314C2×C22⋊C4—112no—
315C2×C22⋊C4—112no—
316C2×C22⋊C4—112no—
317C2×C22⋊C4—112no—
318C2×C42—112no—
319C2×C42C4×D1111yescharacteristic
320C2×C42C4×D1111yescharacteristic
321C2×C42C22×D1111yescharacteristic
322C4⋊C8—22no—
323C4⋊C8—222no—
324C22⋊C8—114no—
325C22⋊C8—224no—
326C22⋊C8—224no—
327C22⋊C8C22×D1112yes—
328C22⋊C8C22×D1112yes—
329#97—222no—
330C4×C8—22no—
331C2×C11—21no—
332C2×C11—21no—
333C2×C11#288011yescharacteristic
334C2×C11#288311yescharacteristic
335C2×C11C2×#41311yescharacteristic
336D11—44no—
337D11—82no—
338C24—112no—
339C24—112no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—41no—
343C2×Q8—221no—
344C2×Q8—221no—
345C2×Q8—442no—
346C2×D4—112no—
347C2×D4—112no—
348C2×D4—224no—
349C2×D4—224no—
350C2×D4—221no—
351C2×D4—221no—
352C2×D4—224no—
353C2×D4—442no—
354C2×D4—442no—
355C2×D4—442no—
356C2×D4—882no—
357C22×C4—112no—
358C22×C4—114no—
359C22×C4—114no—
360C22×C4—112no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—882no—
364C22×C4—882no—
365C22×C4C2×C4×D1111yescharacteristic
366C22×C4C2×C4×D1111yescharacteristic
367C22×C4C2×C4×D1111yescharacteristic
368C22×C4C2×C4×D1111yescharacteristic
369C22×C4C2×C4×D1111yescharacteristic
370C22×C4C2×C4×D1111yescharacteristic
371C22×C4C23×D1111yescharacteristic
372M16—884no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—224no—
376C2×C8—884no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—112no—
381C4⋊C4—111no—
382C4⋊C4—111no—
383C4⋊C4—222no—
384C4⋊C4—222no—
385C22⋊C4—114no—
386C22⋊C4—114no—
387C22⋊C4—222no—
388C22⋊C4—222no—
389C22⋊C4—224no—
390C22⋊C4—224no—
391C22⋊C4—224no—
392C22⋊C4—224no—
393C42—21no—
394C42—21no—
395C42—21no—
396C42—21no—
397C42—222no—
398C42—222no—
399C42D4×D1112yes—
400C42D4×D1112yes—
401C11#1742911yescharacteristic, complemented, Sylow
402C23—114no—
403C23—222no—
404C23—222no—
405C23—222no—
406C23—222no—
407C23—222no—
408C23—442no—
409C23—442no—
410C23—442no—
411C23—442no—
412C23C22×C4×D1111yescharacteristic
413Q8—44no—
414Q8—442no—
415Q8—442no—
416D4—224no—
417D4—442no—
418D4—448no—
419D4—442no—
420D4—442no—
421D4—884no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—112no—
436C2×C4—112no—
437C2×C4—222no—
438C2×C4—444no—
439C2×C4—444no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—882no—
443C2×C4—882no—
444C2×C4C22⋊C4×D1111yescharacteristic
445C2×C4C22⋊C4×D1112yes—
446C2×C4C22⋊C4×D1111yescharacteristic
447C2×C4#6695412yes—
448C2×C4C2×D4×D1112yes—
449C8—42no—
450C8—42no—
451C8—444no—
452C22—21no—
453C22—21no—
454C22—224no—
455C22—224no—
456C22—224no—
457C22—442no—
458C22—442no—
459C22—442no—
460C22—882no—
461C22—882no—
462C22—882no—
463C22—882no—
464C22C2×C22⋊C4×D1111yescharacteristic
465C22C2×#6695411yescharacteristic
466C22#1062327611yescharacteristic
467C4—22no—
468C4—22no—
469C4—22no—
470C4—21no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—222no—
475C4—222no—
476C4—442no—
477C4#1062236412yes—
478C2—21no—
479C2—21no—
480C2—444no—
481C2—882no—
482C2#1307706211yescharacteristic
483C2#1307707511yescharacteristic
484C2C2×#1062236411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1461C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66927C4
cosocleC22×C4×C11C24
hypercenter#1461D11
hypocenterC11#17429
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. #13077650C2semidirect
3. #13066967C2semidirect
4. #13066963C2semidirect
5. #13066960C2semidirect
6. #13066953C2semidirect
7. #13066933C2semidirect
8. C11×#1461C2semidirect
166. #1461D11semidirect
401. C11#17429semidirect

Maximal subgroups

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

subgroupindex
C2×#106231162
#130776502
#130669672
#130669632
#130669602
#130669532
#130669332
C11×#14612
#1742911