Finite Group Databasebeta

← #14763217

Subgroups — #14763217

Order 2816.

1474 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic
2#13070994C212yesmaximal
3#13069599C218yesmaximal, complemented
4#13068690C211yesmaximal, characteristic
5#13068688C212yesmaximal
6C11×#1819C211yesmaximal, characteristic
7C24×Dic11C2211yescharacteristic
8C23×Dic22C411yescharacteristic, complemented
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic11C2211yescharacteristic
11C22×C4⋊Dic11C411yescharacteristic, complemented
12C22×Dic11⋊C4C411yescharacteristic, complemented
13C22×Dic11⋊C4C411yescharacteristic, complemented
14C2×#66931—22no—
15C2×#66931—22no—
16C2×#66931—22no—
17C2×#66931—22no—
18C2×#66931C414yescomplemented
19C2×#66931C2214yes—
20C2×#66930—22no—
21C11×#379C2212yes—
22#10622860C2212yes—
23#10622556—22no—
24#10622555—22no—
25#10622555C2214yes—
26C22⋊C4×Dic11—22no—
27C22⋊C4×Dic11C2214yes—
28C11×#342C2214yes—
29#10622165C2218yes—
30#10622164C2214yes—
31C25×C11C2311yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C411yescharacteristic
34C23×Dic11—44no—
35C23×Dic11C2×C411yescharacteristic
36C23×Dic11C2×C411yescharacteristic
37C23×Dic11C2×C411yescharacteristic
38C23×Dic11C2×C412yes—
39C23×Dic11C2×C411yescharacteristic
40C23×Dic11D412yes—
41C23×Dic11D412yes—
42C23×Dic11D412yes—
43C23×Dic11D412yes—
44C23×Dic11C2312yes—
45C22×Dic22—21no—
46C22×Dic22—22no—
47C22×Dic22—21no—
48C22×Dic22—44no—
49C22×Dic22C2×C414yes—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4C2×C412yes—
55C2×C11×C22⋊C4C2314yes—
56C2×C11×C22⋊C4C2312yes—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11C2×C412yes—
62C2×C22⋊Dic11C2314yes—
63C2×C22⋊Dic11C2312yes—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11C2×C414yes—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—21no—
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—24no—
75C2×Dic11⋊C4C2×C414yes—
76C2×Dic11⋊C4C2×C414yes—
77C2×C4×Dic11—24no—
78#66931—24no—
79#66931—24no—
80#66931—24no—
81#66931—24no—
82#66931—24no—
83#66931—24no—
84#66931—24no—
85#66931—24no—
86#66930—48no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89#21825—111nomaximal, Sylow
90C24×C11—24no—
91C24×C11—42no—
92C24×C11—42no—
93C24×C11C22×C411yescharacteristic
94C24×C11C22×C411yescharacteristic
95C24×C11C2×D412yes—
96C24×C11C2×D412yes—
97C24×C11C2411yescharacteristic
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—24no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C22×C412yes—
107C22×Dic11—28no—
108C22×Dic11—24no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—24no—
114C22×Dic11—42no—
115C22×Dic11—44no—
116C22×Dic11—42no—
117C22×Dic11—42no—
118C22×Dic11—44no—
119C22×Dic11—44no—
120C22×Dic11—44no—
121C22×Dic11—44no—
122C22×Dic11C22⋊C412yes—
123C22×Dic11C22⋊C412yes—
124C22×Dic11C22⋊C412yes—
125C22×Dic11C22⋊C411yescharacteristic
126C22×Dic11C22⋊C412yes—
127C22×Dic11C22⋊C412yes—
128C22×Dic11C22⋊C412yes—
129C22×Dic11C22⋊C411yescharacteristic
130C22×Dic11C22⋊C411yescharacteristic
131C22×Dic11C22⋊C411yescharacteristic
132C22×Dic11C22×C412yes—
133C22×Dic11C22×C412yes—
134C22×Dic11C22×C412yes—
135C22×Dic11C22×C412yes—
136C22×Dic11C2×D412yes—
137C22×Dic11C2×D412yes—
138C22×Dic11C2×D412yes—
139C22×Dic11C2×D412yes—
140C2×Dic22—24no—
141C2×Dic22—24no—
142C2×Dic22—48no—
143C2×Dic22—44no—
144C2×Dic22—44no—
145C2×Dic22—48no—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—28no—
149C11×C22⋊C4—44no—
150C11×C22⋊C4—44no—
151C22⋊Dic11—24no—
152C22⋊Dic11—24no—
153C22⋊Dic11—28no—
154C22⋊Dic11—44no—
155C22⋊Dic11—44no—
156C4⋊Dic11—24no—
157C4⋊Dic11—24no—
158Dic11⋊C4—24no—
159Dic11⋊C4—24no—
160Dic11⋊C4—24no—
161Dic11⋊C4—24no—
162Dic11⋊C4—48no—
163C4×Dic11—48no—
164C22×C22⋊Q8—111no—
165#2280—112no—
166#1996—118no—
167#1819—112no—
168#1819—111no—
169#1819D1111yescharacteristic
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—24no—
175C23×C11—24no—
176C23×C11—24no—
177C23×C11—24no—
178C23×C11—41no—
179C23×C11—42no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—42no—
183C23×C11—41no—
184C23×C11—416no—
185C23×C11C2×C22⋊C412yes—
186C23×C11C2×C22⋊C411yescharacteristic
187C23×C11C2×C22⋊C411yescharacteristic
188C23×C11C23×C411yescharacteristic
189C23×C11C22×D412yes—
190C23×C112−1+414yes—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—44no—
200C2×C4×C11—44no—
201C2×C4×C11—44no—
202C2×Dic11—22no—
203C2×Dic11—24no—
204C2×Dic11—24no—
205C2×Dic11—24no—
206C2×Dic11—24no—
207C2×Dic11—24no—
208C2×Dic11—24no—
209C2×Dic11—24no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—44no—
226C2×Dic11—44no—
227C2×Dic11—44no—
228C2×Dic11#9914yes—
229C2×Dic11C2×C22⋊C412yes—
230C2×Dic11C2×C22⋊C412yes—
231C2×Dic11C2×C22⋊C412yes—
232C2×Dic11C2×C22⋊C412yes—
233Dic22—48no—
234Dic22—48no—
235C23×Q8—111no—
236C24×C4—111no—
237C2×C22⋊Q8—114no—
238C2×C22⋊Q8—114no—
239C2×C22⋊Q8—222no—
240C2×C22⋊Q8—222no—
241C2×C22⋊Q8—222no—
242C2×C22⋊Q8—222no—
243C2×#117—222no—
244C22×C4⋊C4—111no—
245C22×C4⋊C4—111no—
246C22×C4⋊C4—111no—
247C22×C22⋊C4—111no—
248C22×C22⋊C4C2×D1111yescharacteristic
249#381—222no—
250#380—114no—
251#380—222no—
252#379—112no—
253#379C2×D1112yes—
254C4×C22⋊C4—114no—
255C4×C22⋊C4—222no—
256#342—114no—
257#342—118no—
258#342C2×D1114yes—
259C22×C11—28no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—22no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—22no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—44no—
272C22×C11—48no—
273C22×C11—48no—
274C22×C11—44no—
275C22×C11C2×#9912yes—
276C22×C11#41012yes—
277C22×C11C22×C22⋊C411yescharacteristic
278C22×C11#51912yes—
279C22×C11#53614yes—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—84no—
283Dic11—22no—
284Dic11—22no—
285Dic11—22no—
286Dic11—42no—
287Dic11—42no—
288Dic11—84no—
289Dic11C2×#9914yes—
290C25C22×D1111yescharacteristic
291C22×Q8—114no—
292C22×Q8—221no—
293C22×Q8—222no—
294C22×Q8—221no—
295C22×Q8—444no—
296C23×C4—111no—
297C23×C4—112no—
298C23×C4—111no—
299C23×C4—112no—
300C23×C4—112no—
301C23×C4—112no—
302C23×C4—112no—
303C23×C4—112no—
304C23×C4—111no—
305C23×C4—111no—
306C23×C4—444no—
307C23×C4C4×D1111yescharacteristic
308C23×C4C4×D1111yescharacteristic
309C22⋊Q8—224no—
310C22⋊Q8—224no—
311C22⋊Q8—224no—
312C22⋊Q8—224no—
313C22⋊Q8—224no—
314C22⋊Q8—224no—
315C22⋊Q8—224no—
316C22⋊Q8—224no—
317#117—448no—
318C2×C4⋊C4—114no—
319C2×C4⋊C4—114no—
320C2×C4⋊C4—114no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4—222no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—224no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—112no—
336C2×C22⋊C4—112no—
337C2×C22⋊C4—114no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4C4×D1112yes—
343C2×C22⋊C4C22×D1114yes—
344C2×C22⋊C4C22×D1112yes—
345C2×C42—224no—
346#95—224no—
347#95—224no—
348C2×C11—24no—
349C2×C11—22no—
350C2×C11—22no—
351C2×C11—22no—
352C2×C11—42no—
353C2×C11#231011yescharacteristic
354C2×C11C22×#9911yescharacteristic
355C2×C11C2×#41011yescharacteristic
356C24—24no—
357C24—42no—
358C24—42no—
359C24C2×C4×D1111yescharacteristic
360C24C2×C4×D1111yescharacteristic
361C24D4×D1112yes—
362C24D4×D1112yes—
363C24C23×D1111yescharacteristic
364C2×Q8—224no—
365C2×Q8—224no—
366C2×Q8—444no—
367C2×Q8—448no—
368C2×Q8—448no—
369C2×Q8—444no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—24no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—111no—
378C22×C4—112no—
379C22×C4—112no—
380C22×C4—111no—
381C22×C4—112no—
382C22×C4—112no—
383C22×C4—112no—
384C22×C4—112no—
385C22×C4—112no—
386C22×C4—111no—
387C22×C4—111no—
388C22×C4—112no—
389C22×C4—112no—
390C22×C4—112no—
391C22×C4—112no—
392C22×C4—112no—
393C22×C4—112no—
394C22×C4—112no—
395C22×C4—228no—
396C22×C4—224no—
397C22×C4—221no—
398C22×C4—221no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4—224no—
402C22×C4—444no—
403C22×C4—444no—
404C22×C4—444no—
405C22×C4—444no—
406C22×C4—444no—
407C22×C4—442no—
408C22×C4—442no—
409C22×C4—442no—
410C22×C4C2×C4×D1112yes—
411C22×C4C2×C4×D1112yes—
412C4⋊C4—224no—
413C4⋊C4—224no—
414C4⋊C4—224no—
415C4⋊C4—224no—
416C4⋊C4—224no—
417C4⋊C4—224no—
418C4⋊C4—448no—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C22⋊C4—28no—
422C22⋊C4—44no—
423C22⋊C4—44no—
424C22⋊C4—224no—
425C22⋊C4—224no—
426C22⋊C4—228no—
427C22⋊C4—444no—
428C22⋊C4—444no—
429C42—448no—
430C11#2182511yescharacteristic, complemented, Sylow
431C23—22no—
432C23—22no—
433C23—22no—
434C23—22no—
435C23—24no—
436C23—24no—
437C23—24no—
438C23—24no—
439C23—41no—
440C23—42no—
441C23—41no—
442C23—41no—
443C23—42no—
444C23—41no—
445C23—416no—
446C23C22⋊C4×D1112yes—
447C23C22⋊C4×D1111yescharacteristic
448C23C22⋊C4×D1111yescharacteristic
449C23C22×C4×D1111yescharacteristic
450C23C2×D4×D1112yes—
451C23#6704314yes—
452Q8—448no—
453Q8—448no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—44no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—112no—
466C2×C4—114no—
467C2×C4—112no—
468C2×C4—112no—
469C2×C4—112no—
470C2×C4—224no—
471C2×C4—224no—
472C2×C4—224no—
473C2×C4—224no—
474C2×C4—224no—
475C2×C4—224no—
476C2×C4—222no—
477C2×C4—224no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4—442no—
483C2×C4—442no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—444no—
494C2×C4—444no—
495C2×C4—444no—
496C22—28no—
497C22—21no—
498C22—21no—
499C22—22no—
500C22—21no—
501C22—21no—
502C22—22no—
503C22—21no—
504C22—21no—
505C22—22no—
506C22—22no—
507C22—22no—
508C22—44no—
509C22—48no—
510C22—48no—
511C22—44no—
512C22#1062235312yes—
513C22D11×#9912yes—
514C22C2×C22⋊C4×D1111yescharacteristic
515C22#1062304712yes—
516C22#1062317914yes—
517C4—42no—
518C4—42no—
519C4—84no—
520C4—114no—
521C4—222no—
522C4—222no—
523C4—222no—
524C4—442no—
525C4—442no—
526C4—884no—
527C2—24no—
528C2—22no—
529C2—22no—
530C2—22no—
531C2—42no—
532C2#1307120111yescharacteristic
533C2C2×D11×#9911yescharacteristic
534C2C2×#1062235311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#1819C2
socleC22×C11C22×C22⋊C4
prime radicalC25×C11C23
cosocleC24×C11C24
hypercenter#1819D11
hypocenterC11#21825
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
3. #13069599C2semidirect
8. C23×Dic22C4semidirect
11. C22×C4⋊Dic11C4semidirect
12. C22×Dic11⋊C4C4semidirect
13. C22×Dic11⋊C4C4semidirect
18. C2×#66931C4semidirect
430. C11#21825semidirect

Maximal subgroups

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

subgroupindex
C22×#669312
#130709942
#130695992
#130686902
#130686882
C11×#18192
#2182511