Finite Group Databasebeta

← #14789921

Subgroups — #14789921

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622676C212yesmaximal, complemented
2C4×#66977C211yesmaximal, characteristic
3#13069951C212yesmaximal, complemented
4#13069764C212yesmaximal, complemented
5#13069574C212yesmaximal, complemented
6#13068923C211yesmaximal, characteristic
7#13068923C211yesmaximal, characteristic
8#13068809C211yesmaximal, characteristic
9#13068804C211yesmaximal, characteristic
10#13068596C211yesmaximal, characteristic
11C22×C11×#125C211yesmaximal, characteristic
12C2×C11×#125—28no—
13C2×C11×#125—21no—
14C2×C11×#125—21no—
15C2×C11×#125C2212yes—
16C2×C11×#125C2212yes—
17C22×C11×C4⋊C4—21no—
18C22×C11×C4⋊C4—21no—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24#10622825C2211yescharacteristic
25#10622823—21no—
26C4×C22⋊Dic11—21no—
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29#10622676—28no—
30C2×#66874C2212yes—
31C2×#66874C2212yes—
32C2×#66872C2212yes—
33C2×#66871C2212yes—
34C4×C4⋊Dic11C2211yescharacteristic
35#10622546—21no—
36C4×Dic11⋊C4—21no—
37#10622542C2211yescharacteristic
38#10622541C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622162C2212yes—
45C23×C4×C11—21no—
46C23×C4×C11—21no—
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C22×Dic22C2311yescharacteristic
51C11×#125—28no—
52C11×#125—28no—
53C11×#125—24no—
54C11×#125—24no—
55C11×#125—24no—
56C11×#125D418yes—
57C2×C11×C4⋊C4—28no—
58C2×C11×C4⋊C4—28no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C42×C11—24no—
70C2×C42×C11D411yescharacteristic
71C2×C42×C11D411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79#66977—22no—
80#66977Q814yes—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C22×C11⋊C8C2312yes—
87C22×C11⋊C8C2312yes—
88C4×Dic22—24no—
89C11⋊#95—21no—
90C11⋊#95—21no—
91C11⋊#95—21no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C22⋊(C11⋊C8)—22no—
95C22⋊(C11⋊C8)—22no—
96#66874—24no—
97#66874—24no—
98#66872—24no—
99#66871—24no—
100C4⋊(C11⋊C8)—24no—
101#24307—111nomaximal, Sylow
102C24×C11C2×D411yescharacteristic
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—24no—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—41no—
114C22×C4×C11—41no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×Q812yes—
125C22×C4×C11#4112yes—
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C2×Dic22—22no—
132C2×Dic22—21no—
133C2×Dic22—22no—
134C2×Dic22C2×Q812yes—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—28no—
138C11×C4⋊C4—28no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—28no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4C2×D414yes—
144C11×C4⋊C4C2×D414yes—
145C42×C11—22no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11C2×D414yes—
149C22⋊Dic11—24no—
150C22⋊Dic11—42no—
151C4⋊Dic11—22no—
152C4⋊Dic11—21no—
153C4⋊Dic11—22no—
154C4⋊Dic11C2×Q812yes—
155Dic11⋊C4—24no—
156Dic11⋊C4—42no—
157Dic11⋊C4—42no—
158C4×Dic11—42no—
159C4×Dic11—42no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C22×#125D1111yescharacteristic
167C2×#479—112no—
168C4×C22⋊Q8—111no—
169#2059—112no—
170#2026—112no—
171#1989—112no—
172#1872—111no—
173#1872—111no—
174#1853—111no—
175#1852—111no—
176#1797—111no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11C22⋊Q812yes—
182C23×C11#13512yes—
183C23×C11#13712yes—
184C23×C11C22×D411yescharacteristic
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—44no—
202C2×C4×C11—44no—
203C2×C4×C11—48no—
204C2×C4×C11—48no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11#12012yes—
210C2×C4×C11#12012yes—
211C2×C4×C11C22⋊Q812yes—
212C2×C4×C11C22×D412yes—
213C2×C4×C11C22×Q811yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C112−1+412yes—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228Dic22—24no—
229Dic22—42no—
230C11⋊C8—42no—
231C11⋊C8—42no—
232C2×#125—28no—
233C2×#125—21no—
234C2×#125—21no—
235C2×#125C2×D1112yes—
236C2×#125C2×D1112yes—
237C2×C22⋊Q8—111no—
238C2×C4×Q8—111no—
239C22×C4⋊C4—21no—
240C22×C4⋊C4—21no—
241C22×C4⋊C4C2×D1111yescharacteristic
242C22×C4⋊C4C2×D1111yescharacteristic
243C22×C42C2×D1111yescharacteristic
244#479—228no—
245C2×#107—112no—
246C2×#106—112no—
247C2×C4⋊C8—112no—
248C2×#103—112no—
249C2×#103—112no—
250C2×C22⋊C8—111no—
251C2×C22⋊C8—111no—
252#391—111no—
253#389—111no—
254#387—221no—
255#385—221no—
256#380—111no—
257C4×C4⋊C4—111no—
258C4×C4⋊C4—221no—
259C4×C22⋊C4—221no—
260#340—112no—
261#340—112no—
262#340—112no—
263#340—112no—
264#336—112no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—22no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11#47914yescomplemented
272C22×C11C2×#12011yescharacteristic
273C22×C11C2×C22⋊Q811yescharacteristic
274C22×C11#53611yescharacteristic
275C22×C11C2×#13511yescharacteristic
276C22×C11C2×#13711yescharacteristic
277C22×C11#57511yescharacteristic
278C22×C11#57511yescharacteristic
279C4×C11—22no—
280C4×C11—22no—
281C4×C11—22no—
282C4×C11—41no—
283C4×C11—44no—
284C4×C11—41no—
285C4×C11—44no—
286C4×C11#54812yes—
287C4×C11D4×Q812yes—
288Dic11—42no—
289Dic11—42no—
290Dic11—81no—
291Dic11—81no—
292C22×Q8—111no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4C22⋊D1111yescharacteristic
296C23×C4C22⋊D1111yescharacteristic
297C23×C4C22×D1111yescharacteristic
298C22×C8—112no—
299C22×C8—112no—
300#125—28no—
301#125—28no—
302#125—24no—
303#125—24no—
304#125—24no—
305#125C22⋊D1118yes—
306C22⋊Q8—114no—
307C22⋊Q8—222no—
308C4×Q8—224no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4C22×D1112yes—
326C2×C4⋊C4C22×D1112yes—
327C2×C22⋊C4—221no—
328C2×C22⋊C4—221no—
329C2×C42—24no—
330C2×C42—221no—
331C2×C42—221no—
332C2×C42C22⋊D1111yescharacteristic
333C2×C42C22⋊D1111yescharacteristic
334C2×C42C22×D1111yescharacteristic
335C2×C42C22×D1111yescharacteristic
336#107—224no—
337#106—224no—
338C4⋊C8—224no—
339#103—224no—
340#103—224no—
341C22⋊C8—222no—
342C22⋊C8—222no—
343#95—221no—
344#95—221no—
345#95—221no—
346#95—221no—
347#95—221no—
348C2×C11—24no—
349C2×C11#240911yescharacteristic
350C2×C11#300211yescharacteristic
351C2×C11#300711yescharacteristic
352C2×C11C2×#47911yescharacteristic
353C2×C11#308011yescharacteristic
354C2×C11#323211yescharacteristic
355C2×C11#323611yescharacteristic
356C24C2×C22⋊D1111yescharacteristic
357C2×Q8—112no—
358C2×Q8—221no—
359C2×Q8—222no—
360C2×Q8—222no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4Q8×D1112yes—
382C22×C4#434312yes—
383C22×C4C2×C22⋊D1111yescharacteristic
384C22×C4C2×C22⋊D1111yescharacteristic
385C22×C4C2×C22⋊D1111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387C22×C4C2×C22⋊D1111yescharacteristic
388C22×C4C23×D1111yescharacteristic
389C2×C8—222no—
390C2×C8—222no—
391C2×C8—222no—
392C2×C8—222no—
393C2×C8—222no—
394C2×C8—222no—
395C4⋊C4—24no—
396C4⋊C4—24no—
397C4⋊C4—28no—
398C4⋊C4—28no—
399C4⋊C4—28no—
400C4⋊C4—28no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—112no—
404C4⋊C4—224no—
405C4⋊C4—221no—
406C4⋊C4—222no—
407C4⋊C4—222no—
408C4⋊C4—442no—
409C4⋊C4—442no—
410C4⋊C4C2×C22⋊D1114yes—
411C4⋊C4C2×C22⋊D1114yes—
412C22⋊C4—224no—
413C22⋊C4—442no—
414C42—22no—
415C42—22no—
416C42—22no—
417C42—442no—
418C42—442no—
419C42C2×C22⋊D1114yes—
420C11#2430711yescharacteristic, complemented, Sylow
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23#6699912yes—
426C23#6700312yes—
427C23#6700412yes—
428C23C22×C22⋊D1111yescharacteristic
429Q8—224no—
430Q8—442no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—44no—
448C2×C4—44no—
449C2×C4—48no—
450C2×C4—48no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4#6699912yes—
468C2×C4#6700612yes—
469C2×C4#6700612yes—
470C2×C4C2×Q8×D1111yescharacteristic
471C2×C4C2×#434311yescharacteristic
472C2×C4#6704012yes—
473C2×C4C22×C22⋊D1112yes—
474C8—442no—
475C8—442no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22#1062267614yescomplemented
483C22C2×#6699911yescharacteristic
484C22#1062334711yescharacteristic
485C22C2×#6700311yescharacteristic
486C22#1062335311yescharacteristic
487C22#1062335311yescharacteristic
488C22C2×#6700411yescharacteristic
489C22C2×#6700611yescharacteristic
490C4—22no—
491C4—22no—
492C4—22no—
493C4—41no—
494C4—44no—
495C4—41no—
496C4—44no—
497C4—442no—
498C4—442no—
499C4—881no—
500C4—881no—
501C4Q8×C22⋊D1112yes—
502C4#1062334812yes—
503C2—24no—
504C2#1307197511yescharacteristic
505C2#1307783411yescharacteristic
506C2#1307787611yescharacteristic
507C2C2×#1062267611yescharacteristic
508C2#1307843411yescharacteristic
509C2#1307978411yescharacteristic
510C2#1307982211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#125C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC22×#125D11
hypocenterC11#24307
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. C2×#10622676C2semidirect
3. #13069951C2semidirect
4. #13069764C2semidirect
5. #13069574C2semidirect
271. C22×C11#479semidirect
420. C11#24307semidirect
482. C22#10622676semidirect

Maximal subgroups

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

subgroupindex
C2×#106226762
C4×#669772
#130699512
#130697642
#130695742
#130689232
#130688092
#130688042
#130685962
C22×C11×#1252
#2430711