Finite Group Databasebeta

← #14788735

Subgroups — #14788735

Order 2816.

1036 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×#10623098C211yesmaximal, characteristic
2C2×#10622644C211yesmaximal, characteristic
3#13073978C211yesmaximal, characteristic
4#13069860C212yesmaximal
5#13069714C212yesmaximal
6#13069556C211yesmaximal, characteristic
7#13069436C211yesmaximal, characteristic
8#13068954C212yesmaximal
9#13068881C212yesmaximal
10#13068631C211yesmaximal, characteristic
11C2×C11×#441C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#66997C2212yes—
16C22×#4326C2212yes—
17#10623098—24no—
18#10623098—24no—
19C2×#66942—22no—
20C2×#66940C2212yes—
21C2×#66923—21no—
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22—21no—
24C2×C4×Dic22C2211yescharacteristic
25C11×#441—24no—
26C2×C11×#106C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30#10622843C2212yes—
31C2×#66899C2212yes—
32C2×#66880C2212yes—
33C2×#66880C2212yes—
34#10622644—24no—
35#10622599—21no—
36#10622592—21no—
37#10622586C2212yes—
38C2×#66874C2212yes—
39#10622549C2211yescharacteristic
40#10622546—22no—
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42#10622188C2212yes—
43#10622188C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×Dic22D411yescharacteristic
48C22×Dic22C2312yes—
49C2×C11×Q16—22no—
50C2×C11×Q16—22no—
51C2×C11×Q16—22no—
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11D414yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65#66997—24no—
66#66997—24no—
67C2×#4326—24no—
68C2×#4326—24no—
69C2×#4326—42no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11D411yescharacteristic
73C2×C4⋊Dic11C2312yes—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4D412yes—
79C2×C4×Dic11—22no—
80C2×C4×Dic11C2312yes—
81C22×C11⋊C8C2312yes—
82#66942—216no—
83#66940—24no—
84#66940—24no—
85#66923—28no—
86#66922—22no—
87#66922D414yes—
88C4×Dic22—28no—
89C4×Dic22—22no—
90C4×Dic22—22no—
91C11×#106—22no—
92C11×#103—22no—
93C11×#103—22no—
94C11×#97—22no—
95#66899—42no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101#66880—24no—
102#66880—42no—
103#66874—24no—
104C4⋊(C11⋊C8)—22no—
105#24203—111nomaximal, Sylow
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11C2×D412yes—
117C2×Q8×C11#4112yes—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11C2×D412yes—
128C22×Dic11C2×D412yes—
129C2×Dic22—24no—
130C2×Dic22—22no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22C2×D414yes—
137C11×Q16—28no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11#4112yes—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4C2×D412yes—
150C42×C11—24no—
151C42×C11—42no—
152C42×C11C2×D412yes—
153C42×C11C2×D412yes—
154#4326—48no—
155C4⋊Dic11—24no—
156C4⋊Dic11—22no—
157C4⋊Dic11—24no—
158C4⋊Dic11—22no—
159C4⋊Dic11—22no—
160Dic11⋊C4—28no—
161Dic11⋊C4—28no—
162Dic11⋊C4—28no—
163Dic11⋊C4—24no—
164Dic11⋊C4—44no—
165C4×Dic11—28no—
166C4×Dic11—22no—
167C4×Dic11—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×#557—111no—
172C2×#462—111no—
173C2×#441D1111yescharacteristic
174#2581—111no—
175#2043—112no—
176#2016—112no—
177#1985—111no—
178#1960—111no—
179#1878—112no—
180#1865—112no—
181#1805—111no—
182C23×C11C22×D411yescharacteristic
183Q8×C11—22no—
184Q8×C11—22no—
185Q8×C11—22no—
186Q8×C11—22no—
187Q8×C11—41no—
188Q8×C11—41no—
189Q8×C11—41no—
190Q8×C11—41no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11#12012yes—
204C2×C4×C11#12012yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11H(5,𝔽2)11yescharacteristic
210C2×C4×C112−1+411yescharacteristic
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—24no—
215C2×Dic11—24no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11#13714yes—
222Dic22—28no—
223Dic22—24no—
224Dic22—24no—
225Dic22—42no—
226Dic22—42no—
227C8×C11—22no—
228C8×C11—41no—
229C11⋊C8—42no—
230C22×Q16—112no—
231C22×Q16C2×D1111yescharacteristic
232#557—224no—
233#557—224no—
234C2×C4⋊Q8—112no—
235C2×C4⋊Q8—111no—
236C2×#125—221no—
237C2×#125—222no—
238C2×C4×Q8—111no—
239C2×C4×Q8—112no—
240C2×C4×Q8—221no—
241C2×C4×Q8C2×D1111yescharacteristic
242C2×C4×Q8C2×D1111yescharacteristic
243#462—224no—
244#441—24no—
245C2×#106C2×D1111yescharacteristic
246C2×C4⋊C8—111no—
247C2×#103—112no—
248C2×#103—112no—
249C2×#103—112no—
250C2×#103—112no—
251C2×#103C2×D1111yescharacteristic
252C2×#103C2×D1111yescharacteristic
253C2×#97C2×D1111yescharacteristic
254#400—221no—
255#395—221no—
256#391—112no—
257#389—112no—
258#387—222no—
259#382—111no—
260#340—112no—
261#336—112no—
262#336—112no—
263C22×C11C2×#12011yescharacteristic
264C22×C11#54811yescharacteristic
265C22×C11#55011yescharacteristic
266C22×C11C2×#13712yes—
267C22×C11#57812yes—
268C4×C11—22no—
269C4×C11—22no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—81no—
274C4×C11#52511yescharacteristic
275C4×C11#53711yescharacteristic
276C4×C11#54611yescharacteristic
277C4×C11#54711yescharacteristic
278Dic11—24no—
279Dic11—44no—
280Dic11—42no—
281Dic11—82no—
282C22×Q8—111no—
283C22×Q8—112no—
284C22×Q8C22×D1111yescharacteristic
285C22×Q8C22×D1111yescharacteristic
286C2×Q16—22no—
287C2×Q16—22no—
288C2×Q16—22no—
289C2×Q16—224no—
290C2×Q16—224no—
291C2×Q16—442no—
292C22×C8—112no—
293C22×C8C22×D1111yescharacteristic
294C22×C8C22×D1111yescharacteristic
295C4⋊Q8—114no—
296C4⋊Q8—224no—
297C4⋊Q8—224no—
298C4⋊Q8—222no—
299#125—228no—
300#125—2216no—
301C4×Q8—22no—
302C4×Q8—22no—
303C4×Q8—22no—
304C4×Q8—228no—
305C4×Q8—224no—
306C4×Q8—224no—
307C4×Q8—222no—
308C4×Q8—222no—
309C4×Q8C22⋊D1114yes—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—112no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4—112no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4C22×D1111yescharacteristic
322C2×C4⋊C4C22×D1111yescharacteristic
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—112no—
326C2×C42—222no—
327C2×C42C22×D1111yescharacteristic
328#106—22no—
329C4⋊C8—222no—
330#103—22no—
331#103—22no—
332#103—224no—
333#103—224no—
334#103—442no—
335#103—442no—
336#97—22no—
337#95—222no—
338#95—222no—
339#95—222no—
340#95—221no—
341#95—221no—
342C2×C11#240711yescharacteristic
343C2×C11#300411yescharacteristic
344C2×C11#301111yescharacteristic
345C2×C11#337412yes—
346C2×C11#339812yes—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—114no—
358C2×Q8—224no—
359C2×Q8—222no—
360C2×Q8—222no—
361C2×Q8—222no—
362C2×Q8—222no—
363C2×Q8—222no—
364C2×Q8—222no—
365C2×Q8#433912yes—
366C2×Q8C2×C22⋊D1112yes—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—112no—
372C22×C4—112no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4D4×D1111yescharacteristic
376C22×C4D4×D1111yescharacteristic
377C22×C4C23×D1111yescharacteristic
378Q16—28no—
379Q16—448no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—222no—
386C2×C8—222no—
387C2×C8—222no—
388C2×C8#433912yes—
389C4⋊C4—24no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—42no—
394C4⋊C4—228no—
395C4⋊C4—228no—
396C4⋊C4—228no—
397C4⋊C4—224no—
398C4⋊C4—222no—
399C4⋊C4—224no—
400C4⋊C4—224no—
401C4⋊C4—222no—
402C4⋊C4—222no—
403C4⋊C4—444no—
404C4⋊C4C2×C22⋊D1112yes—
405C42—24no—
406C42—42no—
407C42—228no—
408C42—222no—
409C42—222no—
410C42D4×D1112yes—
411C42C2×C22⋊D1112yes—
412C11#2420311yescharacteristic, complemented, Sylow
413C23C2×D4×D1111yescharacteristic
414Q8—22no—
415Q8—22no—
416Q8—22no—
417Q8—22no—
418Q8—41no—
419Q8—41no—
420Q8—41no—
421Q8—41no—
422Q8—228no—
423Q8—224no—
424Q8—224no—
425Q8—442no—
426Q8—442no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—114no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—224no—
443C2×C4—222no—
444C2×C4—224no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4#6699012yes—
451C2×C4#6699012yes—
452C2×C4C2×#433911yescharacteristic
453C2×C4C2×#433911yescharacteristic
454C2×C4C2×D4×D1111yescharacteristic
455C2×C4#6704211yescharacteristic
456C2×C4#6704311yescharacteristic
457C2×C4C22×C22⋊D1111yescharacteristic
458C8—22no—
459C8—41no—
460C8—442no—
461C22#1062308311yescharacteristic
462C22#1062308411yescharacteristic
463C22D11×#13712yes—
464C22#1062331012yes—
465C22C2×#6699011yescharacteristic
466C4—22no—
467C4—22no—
468C4—42no—
469C4—42no—
470C4—42no—
471C4—81no—
472C4—224no—
473C4—444no—
474C4—442no—
475C4—882no—
476C4#1062308111yescharacteristic
477C4#1062308211yescharacteristic
478C4#1062332211yescharacteristic
479C4#1062336411yescharacteristic
480C2#1307196111yescharacteristic
481C2#1307784811yescharacteristic
482C2#1307791011yescharacteristic
483C2#1308142012yes—
484C2#1308164812yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#441C2
socle, prime radicalC23×C11C22×D4
hypercenterC2×#441D11
hypocenterC11#24203
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
412. C11#24203semidirect

Maximal subgroups

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

subgroupindex
C2×#106230982
C2×#106226442
#130739782
#130698602
#130697142
#130695562
#130694362
#130689542
#130688812
#130686312
C2×C11×#4412
#2420311