Finite Group Databasebeta

← #14764007

Subgroups — #14764007

Order 2816.

1114 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622339C211yesmaximal, characteristic
2C2×D11×C22⋊C8C211yesmaximal, characteristic
3#13070995C211yesmaximal, characteristic
4#13068800C212yesmaximal, complemented
5#13068797C212yesmaximal, complemented
6#13068795C212yesmaximal, complemented
7#13068792C212yesmaximal, complemented
8#13068600C211yesmaximal, characteristic, complemented
9#13068598C211yesmaximal, characteristic, complemented
10#13068598C211yesmaximal, characteristic, complemented
11C11×#1798C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×#4313C2212yes—
16C22×C8×D11C2212yes—
17C2×C11×C4⋊C8C2212yescomplemented
18C2×C11×C22⋊C8C2211yescharacteristic
19C2×C11×C22⋊C8C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22C2×(C2×D11)⋊C8C2212yes—
23C2×(C2×D11)⋊C8C2212yes—
24C2×Dic11⋊C8C2212yescomplemented
25C2×Dic11⋊C8C2212yescomplemented
26#10622600C412yes—
27#10622600C412yes—
28#10622568C412yes—
29#10622556C412yes—
30C4×(C2×D11)⋊C4C2211yescharacteristic
31C4×(C2×D11)⋊C4C2211yescharacteristic
32C4×(C2×D11)⋊C4C2211yescharacteristic
33C4×(C2×D11)⋊C4C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2212yescomplemented
35#10622339—24no—
36D11×C22⋊C8—24no—
37C11×#336C2212yescomplemented
38#10622188C2212yescomplemented
39#10622188C2212yescomplemented
40#10622162C2212yescomplemented
41C24×D11C2×C411yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2×C411yescharacteristic
44C22×C4×D11—42no—
45C22×C4×D11—42no—
46C22×C4×D11C2×C411yescharacteristic
47C22×C4×D11C2×C411yescharacteristic
48C22×C4×D11D414yes—
49C22×C4×D11Q814yes—
50C22×C4×D11C2311yescharacteristic
51C22×C4×D11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C22×C8×C11C2312yes—
54C11×#117—42no—
55C2×C11×C4⋊C4C2×C412yes—
56C2×C11×C22⋊C4C2×C412yes—
57C2×C42×C11C2311yescharacteristic
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11C2×C412yes—
60C2×(C2×D11)⋊C4C2×C412yes—
61C2×(C2×D11)⋊C4C2×C412yes—
62C2×(C2×D11)⋊C4C2×C412yes—
63C2×(C2×D11)⋊C4C2×C412yes—
64#66979—42no—
65C2×C4⋊Dic11C2×C412yes—
66C2×C4×Dic11C2311yescharacteristic
67C2×C4×Dic11C2311yescharacteristic
68C22×C11⋊C8C2312yes—
69C22×C11⋊C8C2312yes—
70C2×#4313—24no—
71C2×#4313—42no—
72C2×#4313—42no—
73C2×C8×D11—24no—
74C2×C8×D11—42no—
75C2×C8×D11—42no—
76C11×C4⋊C8—42no—
77C11×C22⋊C8—22no—
78C11×C22⋊C8—22no—
79C11⋊#95C2×C412yes—
80C11⋊#95C2×C412yes—
81C11⋊#95C2×C412yes—
82C11⋊#95C2×C412yes—
83C22⋊(C11⋊C8)—22no—
84C22⋊(C11⋊C8)—22no—
85(C2×D11)⋊C8—24no—
86(C2×D11)⋊C8—24no—
87Dic11⋊C8—42no—
88Dic11⋊C8—42no—
89C4⋊(C11⋊C8)—42no—
90#21933—111nomaximal, Sylow
91C24×C11C22×C411yescharacteristic
92C23×D11—24no—
93C23×D11—41no—
94C23×D11—41no—
95C23×D11—42no—
96C23×D11C4⋊C414yes—
97C23×D11C22×C411yescharacteristic
98C23×D11C22×C411yescharacteristic
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×Q812yes—
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—41no—
108C22×Dic11—41no—
109C22×Dic11C4⋊C414yes—
110C22×Dic11C22×C412yes—
111C22×Dic11C22×C412yes—
112C22×Dic11C22×C411yescharacteristic
113C22×Dic11C22×C411yescharacteristic
114C2×C4×D11—22no—
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11—41no—
119C2×C4×D11—41no—
120C2×C4×D11—41no—
121C2×C4×D11—41no—
122C2×C4×D11—48no—
123C2×C4×D11—48no—
124C2×C4×D11C4⋊C414yes—
125C2×C4×D11C4⋊C414yes—
126C2×C4×D11C2×D412yes—
127C2×C4×D11C2×D412yes—
128C2×C4×D11C2×Q812yes—
129C2×C4×D11C2×Q812yes—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C11×C4⋊C4—42no—
137C11×C22⋊C4—42no—
138C42×C11—22no—
139C42×C11—22no—
140C22⋊Dic11—42no—
141(C2×D11)⋊C4—24no—
142(C2×D11)⋊C4—24no—
143(C2×D11)⋊C4—42no—
144(C2×D11)⋊C4—42no—
145C4⋊Dic11—42no—
146C4×Dic11—22no—
147C4×Dic11—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154#4313—48no—
155C8×D11—48no—
156C2×#407—111no—
157C22×C22⋊C8—111no—
158#2280—111no—
159#1851—112no—
160#1851—112no—
161#1850—112no—
162#1850—112no—
163#1798—111no—
164#1798—111no—
165#1798—111no—
166#1798D1111yescharacteristic, complemented
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11C2×C4⋊C412yes—
172C23×C11C23×C411yescharacteristic
173C22×D11—21no—
174C22×D11—21no—
175C22×D11—22no—
176C22×D11—21no—
177C22×D11—21no—
178C22×D11—22no—
179C22×D11—22no—
180C22×D11—28no—
181C22×D11—44no—
182C22×D11—44no—
183C22×D11—48no—
184C22×D11—48no—
185C22×D11C2×C4⋊C412yes—
186C22×D11C2×C4⋊C412yes—
187C22×D11#13114yes—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11C2×C4⋊C412yes—
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C22×Q811yescharacteristic
201C2×C4×C11H(5,𝔽2)12yes—
202C2×C4×C11H(5,𝔽2)12yes—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—44no—
214C2×Dic11C2×C4⋊C412yes—
215C2×Dic11C2×C4⋊C412yes—
216C4×D11—24no—
217C4×D11—24no—
218C4×D11—24no—
219C4×D11—24no—
220C4×D11—44no—
221C4×D11—44no—
222C8×C11—42no—
223C8×C11—42no—
224C11⋊C8—42no—
225C11⋊C8—42no—
226C24×C4—111no—
227C22×M16—112no—
228C23×C8—112no—
229C2×#117—111no—
230C2×#117C2×D1111yescharacteristic
231C2×C4⋊C8—112no—
232C2×C4⋊C8—112no—
233C2×C4⋊C8—112no—
234C2×C4⋊C8C2×D1112yescomplemented
235#407—224no—
236C2×C22⋊C8—111no—
237C2×C22⋊C8—111no—
238C2×C22⋊C8—112no—
239C2×C22⋊C8—112no—
240C2×C22⋊C8—224no—
241C2×C22⋊C8C2×D1111yescharacteristic
242C2×C22⋊C8C2×D1111yescharacteristic
243#381—112no—
244#380—112no—
245#380—112no—
246#379—112no—
247C4×C22⋊C4—111no—
248C4×C22⋊C4—111no—
249C4×C22⋊C4—111no—
250C4×C22⋊C4—111no—
251#336—112no—
252#336—112no—
253#336—112no—
254#336C2×D1112yescomplemented
255C22×C11—22no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11C22×C4⋊C411yescharacteristic
261C22×C11#51811yescharacteristic
262C22×C11#51811yescharacteristic
263C22×C11C2×#13112yes—
264C22×C11#56812yes—
265C2×D11—22no—
266C2×D11—22no—
267C2×D11—24no—
268C2×D11—24no—
269C2×D11—22no—
270C2×D11—22no—
271C2×D11—22no—
272C2×D11—416no—
273C2×D11—42no—
274C2×D11—42no—
275C2×D11#42414yes—
276C4×C11—22no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11#53412yes—
280C4×C11#54312yes—
281Dic11—22no—
282Dic11—22no—
283Dic11—42no—
284Dic11—42no—
285C25—111no—
286C23×C4—111no—
287C23×C4—111no—
288C23×C4—111no—
289C23×C4—111no—
290C23×C4—111no—
291C23×C4—114no—
292C23×C4—114no—
293C23×C4—442no—
294C23×C4—442no—
295C23×C4C22×D1111yescharacteristic
296C2×M16—224no—
297C2×M16—442no—
298C2×M16—442no—
299C22×C8—112no—
300C22×C8—112no—
301C22×C8—224no—
302C22×C8—442no—
303C22×C8—442no—
304C22×C8C22×D1112yes—
305C22×C8C22×D1112yes—
306#117—42no—
307#117—442no—
308C2×C4⋊C4—112no—
309C2×C4⋊C4C4×D1112yes—
310C2×C22⋊C4—112no—
311C2×C22⋊C4—112no—
312C2×C22⋊C4—112no—
313C2×C22⋊C4—112no—
314C2×C22⋊C4—112no—
315C2×C22⋊C4C4×D1112yes—
316C2×C42—111no—
317C2×C42—111no—
318C2×C42C22×D1111yescharacteristic
319C2×C42C22×D1111yescharacteristic
320C4⋊C8—42no—
321C4⋊C8—442no—
322C4⋊C8—442no—
323C4⋊C8—442no—
324C22⋊C8—22no—
325C22⋊C8—22no—
326C22⋊C8—224no—
327C22⋊C8—224no—
328C22⋊C8—222no—
329C22⋊C8—222no—
330#95—112no—
331#95—112no—
332#95—112no—
333#95—112no—
334C2×C11—42no—
335C2×C11#231511yescharacteristic
336C2×C11C2×#42411yescharacteristic
337C2×C11#290511yescharacteristic
338C2×C11#297612yes—
339C2×C11#297612yes—
340D11—24no—
341D11—42no—
342C24—111no—
343C24—111no—
344C24—114no—
345C24—224no—
346C24—441no—
347C24—441no—
348C24—442no—
349C24C2×C4×D1111yescharacteristic
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—111no—
353C22×C4—111no—
354C22×C4—114no—
355C22×C4—112no—
356C22×C4—112no—
357C22×C4—112no—
358C22×C4—112no—
359C22×C4—114no—
360C22×C4—114no—
361C22×C4—112no—
362C22×C4—112no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—448no—
368C22×C4—448no—
369C22×C4—441no—
370C22×C4—441no—
371C22×C4—441no—
372C22×C4—441no—
373C22×C4—441no—
374C22×C4—441no—
375C22×C4C2×C4×D1112yes—
376C22×C4C2×C4×D1112yes—
377C22×C4C2×C4×D1111yescharacteristic
378C22×C4D4×D1112yes—
379C22×C4Q8×D1112yes—
380C22×C4C23×D1111yescharacteristic
381M16—448no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—222no—
389C2×C8—222no—
390C2×C8—222no—
391C2×C8—222no—
392C2×C8—222no—
393C2×C8—222no—
394C2×C8—448no—
395C4⋊C4—42no—
396C4⋊C4—442no—
397C22⋊C4—42no—
398C22⋊C4—224no—
399C22⋊C4—224no—
400C22⋊C4—442no—
401C22⋊C4—442no—
402C22⋊C4—442no—
403C42—22no—
404C42—22no—
405C42—222no—
406C42—222no—
407C11#2193311yescharacteristic, complemented, Sylow
408C23—21no—
409C23—22no—
410C23—22no—
411C23—21no—
412C23—114no—
413C23—112no—
414C23—112no—
415C23—228no—
416C23—221no—
417C23—222no—
418C23—221no—
419C23—221no—
420C23—222no—
421C23—222no—
422C23—221no—
423C23—444no—
424C23—444no—
425C23—448no—
426C23—448no—
427C23C4⋊C4×D1112yes—
428C23C22×C4×D1111yescharacteristic
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—112no—
440C2×C4—112no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—224no—
446C2×C4—224no—
447C2×C4—224no—
448C2×C4—224no—
449C2×C4—222no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—444no—
456C2×C4—444no—
457C2×C4—444no—
458C2×C4C4⋊C4×D1112yes—
459C2×C4C2×D4×D1111yescharacteristic
460C2×C4#6703712yes—
461C2×C4C2×Q8×D1111yescharacteristic
462C2×C4#6704212yes—
463C8—42no—
464C8—42no—
465C8—442no—
466C8—442no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—42no—
471C22—42no—
472C22—114no—
473C22—222no—
474C22—224no—
475C22—224no—
476C22—222no—
477C22—222no—
478C22—222no—
479C22—222no—
480C22—4416no—
481C22—442no—
482C22—442no—
483C22#1062301711yescharacteristic
484C22C2×C4⋊C4×D1111yescharacteristic
485C22#1062305211yescharacteristic
486C22D11×#13112yes—
487C22#1062328112yes—
488C4—22no—
489C4—42no—
490C4—42no—
491C4—222no—
492C4—222no—
493C4—442no—
494C4—442no—
495C4#1062313612yes—
496C4#1062316512yes—
497C2—42no—
498C2—224no—
499C2—442no—
500C2#1307122911yescharacteristic
501C2D11×#42411yescharacteristic
502C2#1307717711yescharacteristic
503C2#1307765912yes—
504C2#1307766212yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1798C2
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1798D11
hypocenterC11#21933
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
4. #13068800C2semidirect
5. #13068797C2semidirect
6. #13068795C2semidirect
7. #13068792C2semidirect
8. #13068600C2semidirect
9. #13068598C2semidirect
10. #13068598C2semidirect
11. C11×#1798C2semidirect
17. C2×C11×C4⋊C8C22semidirect
24. C2×Dic11⋊C8C22semidirect
25. C2×Dic11⋊C8C22semidirect
34. C2×C4⋊(C11⋊C8)C22semidirect
37. C11×#336C22semidirect
38. #10622188C22semidirect
39. #10622188C22semidirect
40. #10622162C22semidirect
166. #1798D11semidirect
234. C2×C4⋊C8C2×D11semidirect
254. #336C2×D11semidirect
407. C11#21933semidirect

Maximal subgroups

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

subgroupindex
C2×#106223392
C2×D11×C22⋊C82
#130709952
#130688002
#130687972
#130687952
#130687922
#130686002
#130685982
C11×#17982
#2193311