Finite Group Databasebeta

← #14732305

Subgroups — #14732305

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079564C211yesmaximal, characteristic, complemented
2#13078624C211yesmaximal, characteristic
3#13078421C211yesmaximal, characteristic, complemented
4#13067823C214yesmaximal, complemented
5#13067750C214yesmaximal, complemented
6#13067297C211yesmaximal, characteristic, complemented
7#13067041C211yesmaximal, characteristic
8#13067011C211yesmaximal, characteristic, complemented
9C2×C11×#554C211yesmaximal, characteristic
10C11×#554—22no—
11C11×#554—22no—
12C11×#554—22no—
13C11×#554C2214yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125—21no—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—22no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4—21no—
22#10623001C2211yescharacteristic
23#10622841—22no—
24#10622838—21no—
25#10622831—21no—
26#10622705C2212yescomplemented
27#10622703—22no—
28#10622694C2212yescomplemented
29#10622635—22no—
30#10622634C2212yescomplemented
31#10622633C2212yescomplemented
32#10622632C2212yes—
33C4×#4324—22no—
34#10622621C2212yes—
35#10622584—21no—
36#10622577—21no—
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40#10622184C2214yescomplemented
41Q8⋊(C11⋊C8)C2214yescomplemented
42D4⋊(C11⋊C8)C2214yes—
43C22×Q8×C11D411yescharacteristic
44C22×Q8×C11D412yes—
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8D412yes—
51C11×C4⋊Q8C2312yes—
52C11×#125—24no—
53C11×#125—24no—
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8—28no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—28no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11D412yes—
61C4×Q8×C11C2312yes—
62C4×D4×C11—24no—
63C4×D4×C11—24no—
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11D412yes—
67C4×D4×C11C2312yes—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×#4326—24no—
82C2×#4324—22no—
83#66979—21no—
84#66977—21no—
85#66977—21no—
86C2×#4318—21no—
87#66923—21no—
88#66922C2311yescharacteristic
89#66922C2311yescharacteristic
90C4×Dic22—21no—
91C4×Dic22—21no—
92#66899—22no—
93#66899—22no—
94#66899—24no—
95#66896—22no—
96C22⋊(C11⋊C8)—21no—
97C22⋊(C11⋊C8)—21no—
98#66874—22no—
99#66872—22no—
100#66872—22no—
101#66871—22no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)C2312yes—
105C4⋊(C11⋊C8)C2312yes—
106C4×C11⋊C8—21no—
107C4×C11⋊C8C2312yes—
108#18753—111nomaximal, Sylow
109C24×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—82no—
115C2×Q8×C11C2×D412yes—
116C2×Q8×C11C2×D414yes—
117C2×D4×C11—24no—
118C2×D4×C11—21no—
119C2×D4×C11C2×D412yes—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—28no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—84no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C2×Dic22—21no—
134C2×Dic22—21no—
135C11×C4⋊C4—28no—
136C11×C4⋊C4—28no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4C2×D412yes—
146C11×C4⋊C4C2×D412yes—
147C11×C22⋊C4—28no—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—22no—
150C42×C11—22no—
151C42×C11—22no—
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2411yescharacteristic
156C22⋊Dic11—41no—
157#4326—84no—
158#4324—44no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165C4×Dic11—41no—
166#4318—42no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×#554D1111yescharacteristic
171#3209—111no—
172#3101—111no—
173#3078—111no—
174#1643—114no—
175#1632—114no—
176#1548—111no—
177#1486—111no—
178#1479—111no—
179C23×C11—24no—
180C23×C11—22no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11#12011yescharacteristic
184Q8×C11—22no—
185Q8×C11—22no—
186Q8×C11—44no—
187Q8×C11—42no—
188Q8×C11—82no—
189D4×C11—24no—
190D4×C11—22no—
191D4×C11#13714yes—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—44no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—44no—
205C2×C4×C11—88no—
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11#12011yescharacteristic
208C2×C4×C11#12011yescharacteristic
209C2×C4×C11#13512yes—
210C2×C4×C11#13712yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×Dic11—41no—
215C2×Dic11—41no—
216Dic22—42no—
217Dic22—42no—
218C11⋊C8—42no—
219C11⋊C8—42no—
220C11⋊C8—42no—
221#554—22no—
222#554—22no—
223#554—22no—
224#554C2×D1114yes—
225#533—111no—
226C2×C4⋊Q8C2×D1111yescharacteristic
227C2×#125—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—22no—
230C2×C4×Q8C2×D1111yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4C2×D1111yescharacteristic
233C22×C4⋊C4—21no—
234#494—112no—
235#487—112no—
236#483—221no—
237#479—222no—
238#477—112no—
239#476—112no—
240#475—112no—
241#462—222no—
242#461—112no—
243#451—222no—
244#450—221no—
245C4×SD16—222no—
246#431—111no—
247#431—111no—
248#428—221no—
249#423—111no—
250#419—221no—
251#333—114no—
252Q8⋊C8—114no—
253D4⋊C8—114no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—24no—
257C22×C11—48no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11#45212yes—
261C22×C11C2×#12011yescharacteristic
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—44no—
269C4×C11#45212yes—
270C4×C11C2×#13511yescharacteristic
271C4×C11C2×#13712yes—
272C4×C11C2×#13711yescharacteristic
273Dic11—81no—
274Dic11—81no—
275C22×Q8C22⋊D1111yescharacteristic
276C22×Q8C22⋊D1112yes—
277C22×D4C22⋊D1111yescharacteristic
278C23×C4—22no—
279C23×C4—21no—
280C2×Q16—224no—
281C2×SD16—222no—
282C2×M16—221no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—111no—
286C4⋊Q8—111no—
287C4⋊Q8C22⋊D1112yes—
288C4⋊Q8C22×D1112yes—
289#125—24no—
290#125—24no—
291#125—221no—
292C22⋊Q8—24no—
293C22⋊Q8—28no—
294C22⋊Q8—24no—
295C22⋊Q8—28no—
296C22⋊Q8—221no—
297C22⋊Q8—221no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×Q8—221no—
301C4×Q8—221no—
302C4×Q8C22⋊D1112yes—
303C4×Q8C22×D1112yes—
304C4×D4—24no—
305C4×D4—24no—
306C4×D4—21no—
307C4×D4—21no—
308C4×D4C22⋊D1112yes—
309C4×D4C22×D1112yes—
310#117—221no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4C22⋊D1111yescharacteristic
319C2×C4⋊C4C22⋊D1111yescharacteristic
320C2×C22⋊C4—22no—
321C2×C22⋊C4—21no—
322C2×C42—21no—
323C2×C42C22×D1111yescharacteristic
324#107—222no—
325#106—222no—
326#106—222no—
327C4⋊C8—112no—
328C4⋊C8—112no—
329C4⋊C8—221no—
330C4⋊C8—221no—
331#103—222no—
332#103—222no—
333#103—224no—
334#103—222no—
335#102—222no—
336C22⋊C8—221no—
337C22⋊C8—221no—
338C4×C8—112no—
339C4×C8—221no—
340C2×C11—22no—
341C2×C11—44no—
342C2×C11C2×#45211yescharacteristic
343C2×C11#300411yescharacteristic
344C2×C11#301911yescharacteristic
345C24—21no—
346C2×Q8—21no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—82no—
351C2×Q8—221no—
352C2×Q8—221no—
353C2×Q8C2×C22⋊D1112yes—
354C2×Q8C2×C22⋊D1114yes—
355C2×D4—24no—
356C2×D4—21no—
357C2×D4C2×C22⋊D1112yes—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—28no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—84no—
368C22×C4C2×C22⋊D1111yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370C22×C4C2×C22⋊D1111yescharacteristic
371Q16—884no—
372SD16—444no—
373M16—442no—
374C2×C8—222no—
375C2×C8—222no—
376C2×C8—222no—
377C4⋊C4—28no—
378C4⋊C4—28no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4C2×C22⋊D1112yes—
394C4⋊C4C2×C22⋊D1112yes—
395C22⋊C4—28no—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—441no—
399C42—22no—
400C42—22no—
401C42—441no—
402C42C2×C22⋊D1111yescharacteristic
403C42C2×C22⋊D1111yescharacteristic
404C42C2×C22⋊D1111yescharacteristic
405C42C23×D1111yescharacteristic
406C11#1875311yescharacteristic, complemented, Sylow
407C23—24no—
408C23—22no—
409C23—42no—
410C23—42no—
411C23#6700611yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—44no—
415Q8—42no—
416Q8—82no—
417Q8—442no—
418Q8—442no—
419D4—24no—
420D4—22no—
421D4#6699514yes—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—88no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4#6700312yes—
439C2×C4#6700412yes—
440C2×C4#6700611yescharacteristic
441C2×C4#6700611yescharacteristic
442C2×C4#6700611yescharacteristic
443C2×C4C22×C22⋊D1111yescharacteristic
444C2×C4C22×C22⋊D1111yescharacteristic
445C2×C4C22×C22⋊D1111yescharacteristic
446C8—442no—
447C8—442no—
448C8—442no—
449C22—21no—
450C22—21no—
451C22—24no—
452C22—48no—
453C22—42no—
454C22—42no—
455C22#1062285212yes—
456C22C2×#6700611yescharacteristic
457C4—21no—
458C4—21no—
459C4—21no—
460C4—42no—
461C4—42no—
462C4—42no—
463C4—44no—
464C4—881no—
465C4—881no—
466C4#1062285212yes—
467C4C2×#6699512yes—
468C4C2×#6700311yescharacteristic
469C4C2×#6700411yescharacteristic
470C2—22no—
471C2—44no—
472C2C2×#1062285211yescharacteristic
473C2#1307785011yescharacteristic
474C2#1307797311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#554C2
socleC22×C11C2×#120
prime radicalC22×D4×C11D4
hypercenterC2×#554D11
hypocenterC11#18753
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #13079564C2semidirect
3. #13078421C2semidirect
4. #13067823C2semidirect
5. #13067750C2semidirect
6. #13067297C2semidirect
8. #13067011C2semidirect
26. #10622705C22semidirect
28. #10622694C22semidirect
30. #10622634C22semidirect
31. #10622633C22semidirect
40. #10622184C22semidirect
41. Q8⋊(C11⋊C8)C22semidirect
406. C11#18753semidirect

Maximal subgroups

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

subgroupindex
#130795642
#130786242
#130784212
#130678232
#130677502
#130672972
#130670412
#130670112
C2×C11×#5542
#1875311