Finite Group Databasebeta

← #14753534

Subgroups — #14753534

Order 2816.

1430 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
1C22×#66945C211yesmaximal, characteristic
2D11×#407C212yesmaximal
3#13068698C214yesmaximal, complemented
4#13068696C211yesmaximal, characteristic, complemented
5#13068694C212yesmaximal, complemented
6#13068353C214yesmaximal, complemented
7C11×#1821C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×(C2×D11)⋊C4C412yes—
11C22×C4⋊Dic11C2211yescharacteristic
12C22×C4×Dic11C412yes—
13C2×M16×D11C2214yes—
14C2×#66945—22no—
15C2×#66945—22no—
16C2×#66945—22no—
17C2×#66945—22no—
18C2×#66945C412yes—
19C2×#66945C412yes—
20C2×#66945C2212yes—
21C2×#66945C2212yes—
22C11×#407C2212yes—
23#10622820C2212yes—
24#10622739C2214yes—
25#10622339—22no—
26#10622339—22no—
27D11×C22⋊C8—22no—
28D11×C22⋊C8—22no—
29C11×#343C2214yescomplemented
30#10622192C2218yescomplemented
31#10622168C2214yescomplemented
32C24×D11C2×C411yescharacteristic
33C23×C4×C11C2×C412yes—
34C23×C4×C11C2311yescharacteristic
35C23×Dic11C2×C411yescharacteristic
36C23×Dic11C2×C412yes—
37C22×C4×D11—28no—
38C22×C4×D11C2×C411yescharacteristic
39C22×C4×D11C2×C411yescharacteristic
40C22×C4×D11D412yes—
41C22×C4×D11D412yes—
42C22×C4×D11D412yes—
43C22×C4×D11D412yes—
44C22×C4×D11C2311yescharacteristic
45C22×C4×D11C2311yescharacteristic
46C2×C11×M16C2314yes—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4C2×C412yes—
50C2×C11×C4⋊C4C2312yes—
51C2×(C2×D11)⋊C4—24no—
52C2×(C2×D11)⋊C4—24no—
53C2×(C2×D11)⋊C4C2×C414yes—
54C2×(C2×D11)⋊C4C2×C414yes—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11C2×C412yes—
58C2×C4⋊Dic11C2312yes—
59C2×C4×Dic11—22no—
60C2×C4×Dic11—22no—
61C2×C4×Dic11—22no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11C2×C414yes—
64C2×C4×Dic11C2×C414yes—
65C2×#4318C2314yes—
66M16×D11—216no—
67C2×#4313—24no—
68C2×C8×D11—24no—
69#66945—24no—
70#66945—24no—
71#66945—24no—
72#66945—24no—
73#66945—24no—
74#66945—24no—
75#66945—24no—
76#66945—24no—
77C11×C22⋊C8—22no—
78C11×C22⋊C8—22no—
79C22⋊(C11⋊C8)—22no—
80C22⋊(C11⋊C8)—22no—
81(C2×D11)⋊C8—24no—
82(C2×D11)⋊C8—24no—
83#20694—111nomaximal, Sylow
84C24×C11C22×C411yescharacteristic
85C23×D11—24no—
86C23×D11—42no—
87C23×D11—42no—
88C23×D11C22⋊C412yes—
89C23×D11C22⋊C412yes—
90C23×D11C22×C411yescharacteristic
91C23×D11C22×C411yescharacteristic
92C22×C4×C11—24no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—44no—
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C22×C414yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—24no—
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11—44no—
105C22×Dic11C22⋊C411yescharacteristic
106C22×Dic11C22⋊C411yescharacteristic
107C22×Dic11C22⋊C411yescharacteristic
108C22×Dic11C22⋊C411yescharacteristic
109C22×Dic11C22×C411yescharacteristic
110C22×Dic11C22×C414yes—
111C22×Dic11C22×C411yescharacteristic
112C2×C4×D11—24no—
113C2×C4×D11—28no—
114C2×C4×D11—28no—
115C2×C4×D11—28no—
116C2×C4×D11—28no—
117C2×C4×D11—24no—
118C2×C4×D11—24no—
119C2×C4×D11C22⋊C412yes—
120C2×C4×D11C22⋊C412yes—
121C2×C4×D11C22⋊C412yes—
122C2×C4×D11C22⋊C412yes—
123C2×C4×D11C2×D412yes—
124C2×C4×D11C2×D412yes—
125C2×C4×D11C2×D412yes—
126C2×C4×D11C2×D412yes—
127C2×C4×D11#4118yes—
128C11×M16—28no—
129C2×C8×C11—24no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—24no—
132(C2×D11)⋊C4—28no—
133(C2×D11)⋊C4—28no—
134C4⋊Dic11—24no—
135C4⋊Dic11—24no—
136C4×Dic11—24no—
137C4×Dic11—24no—
138C4×Dic11—24no—
139C4×Dic11—24no—
140#4318—28no—
141C2×C11⋊C8—24no—
142#4313—48no—
143C8×D11—48no—
144C22×#117—111no—
145C2×#407—112no—
146#1822—114no—
147#1821—112no—
148#1821—111no—
149#1821D1111yescharacteristic, complemented
150#1742—114no—
151C23×C11—22no—
152C23×C11—22no—
153C23×C11—22no—
154C23×C11C2×C22⋊C411yescharacteristic
155C23×C11C2×C22⋊C411yescharacteristic
156C23×C11C23×C411yescharacteristic
157C22×D11—22no—
158C22×D11—24no—
159C22×D11—24no—
160C22×D11—24no—
161C22×D11—24no—
162C22×D11—42no—
163C22×D11—42no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—416no—
169C22×D11C2×C22⋊C412yes—
170C22×D11C2×C22⋊C412yes—
171C22×D11#11714yes—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—44no—
177C2×C4×C11—44no—
178C2×C4×C11—44no—
179C2×C4×C11C2×C22⋊C412yes—
180C2×C4×C11C22×D412yes—
181C2×C4×C11C2×#4114yes—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—24no—
188C2×Dic11—44no—
189C2×Dic11—44no—
190C2×Dic11—44no—
191C2×Dic11C2×C22⋊C411yescharacteristic
192C2×Dic11C2×C22⋊C411yescharacteristic
193C2×Dic11C2×C22⋊C411yescharacteristic
194C2×Dic11C2×C22⋊C411yescharacteristic
195C2×Dic11#11714yes—
196C4×D11—24no—
197C4×D11—24no—
198C4×D11—24no—
199C4×D11—24no—
200C4×D11—24no—
201C4×D11—24no—
202C4×D11#12318yes—
203C4×D11#12318yes—
204C8×C11—44no—
205C11⋊C8—44no—
206C24×C4—111no—
207C22×M16—114no—
208C2×#117—112no—
209C2×#117—112no—
210C2×#117—112no—
211C2×#117—112no—
212C2×#117—222no—
213C2×#117—222no—
214C2×#117—222no—
215C2×#117—222no—
216C22×C4⋊C4—111no—
217C22×C4⋊C4C2×D1111yescharacteristic
218C22×C22⋊C4—112no—
219C22×C42—112no—
220#407—112no—
221#407—114no—
222#407—222no—
223#407—222no—
224#407C2×D1112yes—
225C2×C22⋊C8—222no—
226C2×C22⋊C8—222no—
227#343—118no—
228#343—114no—
229#343C2×D1114yescomplemented
230C22×C11—28no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11#41312yes—
238C22×C11#41312yes—
239C22×C11C22×C22⋊C411yescharacteristic
240C22×C11C2×#11712yes—
241C2×D11—22no—
242C2×D11—22no—
243C2×D11—22no—
244C2×D11—22no—
245C2×D11—22no—
246C2×D11—44no—
247C2×D11—48no—
248C2×D11—48no—
249C2×D11—44no—
250C2×D11#38114yes—
251C4×C11—22no—
252C4×C11—44no—
253C4×C11C2×#12314yes—
254Dic11—21no—
255Dic11—21no—
256Dic11—44no—
257Dic11#38112yes—
258Dic11#38112yes—
259C25—111no—
260C23×C4—111no—
261C23×C4—111no—
262C23×C4—111no—
263C23×C4—111no—
264C23×C4—112no—
265C23×C4—112no—
266C23×C4—112no—
267C23×C4—112no—
268C23×C4—111no—
269C23×C4—112no—
270C23×C4—228no—
271C23×C4C4×D1112yes—
272C23×C4C22×D1111yescharacteristic
273C2×M16—114no—
274C2×M16—224no—
275C2×M16—2216no—
276C2×M16C22×D1114yes—
277C22×C8—224no—
278#117—224no—
279#117—224no—
280#117—224no—
281#117—224no—
282#117—224no—
283#117—224no—
284#117—224no—
285#117—224no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—112no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4C4×D1112yes—
293C2×C4⋊C4C22×D1112yes—
294C2×C22⋊C4—114no—
295C2×C22⋊C4—114no—
296C2×C22⋊C4—224no—
297C2×C22⋊C4—224no—
298C2×C42—114no—
299C2×C42—114no—
300C2×C42—222no—
301C2×C42—222no—
302C2×C42—222no—
303C2×C42—222no—
304C22⋊C8—22no—
305C22⋊C8—22no—
306C22⋊C8—224no—
307C22⋊C8—224no—
308C22⋊C8—222no—
309C22⋊C8—222no—
310C2×C11—22no—
311C2×C11—22no—
312C2×C11—22no—
313C2×C11C2×#38111yescharacteristic
314C2×C11C2×#41311yescharacteristic
315C2×C11C2×#41311yescharacteristic
316D11—24no—
317D11—42no—
318C24—111no—
319C24—112no—
320C24—112no—
321C24—111no—
322C24—224no—
323C24—442no—
324C24—442no—
325C24C2×C4×D1111yescharacteristic
326C22×C4—24no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—44no—
330C22×C4—111no—
331C22×C4—112no—
332C22×C4—112no—
333C22×C4—118no—
334C22×C4—111no—
335C22×C4—111no—
336C22×C4—111no—
337C22×C4—111no—
338C22×C4—111no—
339C22×C4—112no—
340C22×C4—112no—
341C22×C4—112no—
342C22×C4—112no—
343C22×C4—112no—
344C22×C4—112no—
345C22×C4—114no—
346C22×C4—224no—
347C22×C4—228no—
348C22×C4—228no—
349C22×C4—228no—
350C22×C4—228no—
351C22×C4—224no—
352C22×C4—224no—
353C22×C4—224no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—444no—
357C22×C4C2×C4×D1111yescharacteristic
358C22×C4C2×C4×D1114yes—
359C22×C4D4×D1112yes—
360C22×C4D4×D1112yes—
361C22×C4C23×D1111yescharacteristic
362M16—28no—
363M16—228no—
364M16—448no—
365C2×C8—24no—
366C2×C8—224no—
367C2×C8—448no—
368C4⋊C4—24no—
369C4⋊C4—24no—
370C4⋊C4—224no—
371C4⋊C4—224no—
372C22⋊C4—228no—
373C22⋊C4—228no—
374C42—224no—
375C42—224no—
376C42—224no—
377C42—224no—
378C11#2069411yescharacteristic, complemented, Sylow
379C23—22no—
380C23—22no—
381C23—22no—
382C23—112no—
383C23—114no—
384C23—112no—
385C23—224no—
386C23—224no—
387C23—222no—
388C23—224no—
389C23—224no—
390C23—442no—
391C23—441no—
392C23—441no—
393C23—442no—
394C23—441no—
395C23—441no—
396C23—4416no—
397C23C22⋊C4×D1111yescharacteristic
398C23C22⋊C4×D1111yescharacteristic
399C23C22×C4×D1111yescharacteristic
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—44no—
405C2×C4—44no—
406C2×C4—44no—
407C2×C4—111no—
408C2×C4—111no—
409C2×C4—114no—
410C2×C4—118no—
411C2×C4—118no—
412C2×C4—111no—
413C2×C4—111no—
414C2×C4—224no—
415C2×C4—224no—
416C2×C4—224no—
417C2×C4—224no—
418C2×C4—222no—
419C2×C4—222no—
420C2×C4—222no—
421C2×C4—222no—
422C2×C4—222no—
423C2×C4—224no—
424C2×C4—224no—
425C2×C4—224no—
426C2×C4—444no—
427C2×C4—444no—
428C2×C4—444no—
429C2×C4C22⋊C4×D1112yes—
430C2×C4C2×D4×D1112yes—
431C2×C4#41×D1114yes—
432C8—44no—
433C8—444no—
434C22—28no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—114no—
442C22—222no—
443C22—222no—
444C22—222no—
445C22—222no—
446C22—222no—
447C22—444no—
448C22—448no—
449C22—448no—
450C22—444no—
451C22#1062235812yes—
452C22#1062236412yes—
453C22C2×C22⋊C4×D1111yescharacteristic
454C22D11×#11712yes—
455C4—22no—
456C4—44no—
457C4—112no—
458C4—112no—
459C4—221no—
460C4—221no—
461C4—444no—
462C4D11×#12314yes—
463C2—22no—
464C2—22no—
465C2—22no—
466C2—224no—
467C2—442no—
468C2D11×#38111yescharacteristic
469C2C2×#1062235811yescharacteristic
470C2C2×#1062236411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1821C2
socleC22×C11C22×C22⋊C4
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1821D11
hypocenterC11#20694
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
3. #13068698C2semidirect
4. #13068696C2semidirect
5. #13068694C2semidirect
6. #13068353C2semidirect
7. C11×#1821C2semidirect
29. C11×#343C22semidirect
30. #10622192C22semidirect
31. #10622168C22semidirect
149. #1821D11semidirect
229. #343C2×D11semidirect
378. C11#20694semidirect

Maximal subgroups

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

subgroupindex
C22×#669452
D11×#4072
#130686982
#130686962
#130686942
#130683532
C11×#18212
#2069411