Finite Group Databasebeta

← #14764954

Subgroups — #14764954

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622352C211yesmaximal, characteristic
2C4×#66977C211yesmaximal, characteristic
3C2×#10622542C211yesmaximal, characteristic
4#13069477C212yesmaximal, complemented
5#13069292C212yesmaximal, complemented
6#13069258C212yesmaximal, complemented
7#13068956C212yesmaximal, complemented
8#13068921C211yesmaximal, characteristic
9#13068806C211yesmaximal, characteristic
10#13068552C211yesmaximal, characteristic
11C4×C11×C22⋊C8C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C2×#66977C2211yescharacteristic
16C22×Dic44C2212yes—
17C2×C4×Dic22C2211yescharacteristic
18C2×C11×C22⋊C8C2211yescharacteristic
19C2×C11×C22⋊C8C2211yescharacteristic
20C2×C4×C8×C11C2212yes—
21#10622825C2211yescharacteristic
22#10622823—21no—
23C4×C22⋊Dic11—21no—
24C2×C11⋊#95—21no—
25C2×C11⋊#95—21no—
26C2×#66882C2212yes—
27C2×#66880C2212yes—
28C2×#66880C2212yes—
29C2×#66880C2212yes—
30C2×#66880C2212yes—
31C4×C4⋊Dic11C2211yescharacteristic
32#10622546—21no—
33C4×Dic11⋊C4—21no—
34#10622542—21no—
35#10622542—21no—
36#10622542C2211yescharacteristic
37#10622542C2212yes—
38#10622542C2212yes—
39#10622541C2211yescharacteristic
40#10622352C418yescomplemented
41C11×#336C2212yes—
42#10622189C2212yes—
43#10622189C2212yes—
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11—21no—
48C23×Dic11—21no—
49C22×Dic22—21no—
50C22×Dic22—22no—
51C22×Dic22—42no—
52C22×Dic22—42no—
53C22×Dic22C2×C414yes—
54C22×Dic22C2311yescharacteristic
55C22×Dic22C2312yes—
56C22×C8×C11C2312yes—
57C22×C8×C11C2312yes—
58C2×C42×C11—42no—
59C2×C42×C11D411yescharacteristic
60C2×C42×C11D411yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—42no—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71#66977—22no—
72#66977C2×C414yes—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C2×Dic44—42no—
79C2×Dic44—42no—
80C2×Dic44C2×C418yescomplemented
81C4×Dic22—42no—
82C11×C22⋊C8—22no—
83C11×C22⋊C8C2×C414yes—
84C4×C8×C11—42no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95—21no—
91C11⋊#95—21no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94#66882—42no—
95#66880—42no—
96#66880—42no—
97#66880—42no—
98#66880C2×C418yescomplemented
99#22044—111nomaximal, Sylow
100C24×C11C2×D411yescharacteristic
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11Q1614yescomplemented
109C22×C4×C11C22×C412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11#4112yes—
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—24no—
118C22×Dic11—22no—
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—22no—
123C22×Dic11—21no—
124C22×Dic11—42no—
125C22×Dic11—42no—
126C22×Dic11—42no—
127C22×Dic11—42no—
128C22×Dic11—42no—
129C2×Dic22—24no—
130C2×Dic22—21no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22—22no—
137C2×Dic22—22no—
138C2×Dic22—48no—
139C2×Dic22—42no—
140C2×Dic22—42no—
141C2×Dic22—48no—
142C2×Dic22C22×C414yes—
143C2×Dic22C22×C412yes—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11C22×C414yes—
150C42×C11—22no—
151C42×C11—22no—
152C42×C11—41no—
153C42×C11—41no—
154C22⋊Dic11—24no—
155C22⋊Dic11—42no—
156C4⋊Dic11—21no—
157C4⋊Dic11—22no—
158C4⋊Dic11—22no—
159C4⋊Dic11—22no—
160C4⋊Dic11—22no—
161C4⋊Dic11—42no—
162C4⋊Dic11C22×C412yes—
163Dic11⋊C4—24no—
164Dic11⋊C4—42no—
165Dic11⋊C4—42no—
166C4×Dic11—42no—
167C4×Dic11—42no—
168Dic44—48no—
169C2×#451—111no—
170C4×C22⋊Q8—111no—
171C2×#391—111no—
172#1969—112no—
173#1933—112no—
174#1928—112no—
175#1878—112no—
176#1872—111no—
177#1852—111no—
178#1787—111no—
179C4×C22⋊C8D1111yescharacteristic
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11C4×D412yes—
185C23×C11C2×Q1612yes—
186C23×C11#13512yes—
187C23×C11C22×D411yescharacteristic
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—44no—
202C2×C4×C11—44no—
203C2×C4×C11C4×D412yes—
204C2×C4×C11C2×Q1612yes—
205C2×C4×C11C2×Q1612yes—
206C2×C4×C11#13712yes—
207C2×C4×C11C23×C411yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11H(5,𝔽2)12yes—
210C2×C4×C11H(5,𝔽2)12yes—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—24no—
214C2×Dic11—48no—
215C2×Dic11—41no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—42no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—42no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—42no—
230C2×Dic11—84no—
231Dic22—24no—
232Dic22—24no—
233Dic22—24no—
234Dic22—48no—
235Dic22—42no—
236Dic22—42no—
237Dic22—42no—
238C8×C11—24no—
239C8×C11—42no—
240C23×Q8—111no—
241C22×Q16—112no—
242C2×C22⋊Q8—111no—
243C2×C4×Q8—111no—
244C22×C4⋊C4—111no—
245C22×C42C2×D1111yescharacteristic
246#451—118no—
247C2×#107—112no—
248C2×#103—112no—
249C2×#103—112no—
250C2×#103—112no—
251C2×#103—112no—
252C2×C22⋊C8C2×D1111yescharacteristic
253C2×C22⋊C8C2×D1111yescharacteristic
254C2×C4×C8C2×D1112yes—
255#391—112no—
256#391—112no—
257#391—111no—
258#391—221no—
259#391—221no—
260#389—111no—
261#387—221no—
262#385—221no—
263#380—111no—
264C4×C4⋊C4—111no—
265C4×C4⋊C4—221no—
266C4×C22⋊C4—221no—
267C2×#95—221no—
268C2×#95—221no—
269#340—112no—
270#340—112no—
271#336C2×D1112yes—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11C4×Q1614yes—
279C22×C11C2×C4×D411yescharacteristic
280C22×C11#53411yescharacteristic
281C22×C11#53511yescharacteristic
282C22×C11C22×Q1611yescharacteristic
283C22×C11C2×#13511yescharacteristic
284C22×C11C2×#13711yescharacteristic
285C22×C11#57511yescharacteristic
286C4×C11—22no—
287C4×C11—22no—
288C4×C11—22no—
289C4×C11—22no—
290C4×C11—41no—
291C4×C11#51812yes—
292C4×C11#53812yes—
293Dic11—44no—
294Dic11—42no—
295Dic11—42no—
296Dic11—81no—
297Dic11—81no—
298Dic11—82no—
299C22×Q8—114no—
300C22×Q8—111no—
301C22×Q8—112no—
302C22×Q8—221no—
303C22×Q8—222no—
304C22×Q8—442no—
305C22×Q8—442no—
306C23×C4—221no—
307C23×C4—221no—
308C23×C4D4411yescharacteristic
309C23×C4D4411yescharacteristic
310C23×C4C22×D1111yescharacteristic
311C2×Q16—118no—
312C2×Q16—442no—
313C2×Q16—442no—
314C22×C8C22×D1112yes—
315C22×C8C22×D1112yes—
316C22⋊Q8—114no—
317C22⋊Q8—222no—
318C4×Q8—442no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—442no—
328C2×C22⋊C4—221no—
329C2×C22⋊C4—221no—
330C2×C42—42no—
331C2×C42—221no—
332C2×C42—221no—
333C2×C42D4411yescharacteristic
334C2×C42D4411yescharacteristic
335C2×C42C22×D1111yescharacteristic
336C2×C42C22×D1111yescharacteristic
337#107—442no—
338#103—118no—
339#103—442no—
340#103—442no—
341#103—442no—
342C22⋊C8—22no—
343C22⋊C8C4×D1114yes—
344C4×C8—42no—
345#95—222no—
346#95—222no—
347#95—222no—
348#95—222no—
349#95—221no—
350#95—221no—
351#95—221no—
352#95—221no—
353#95—221no—
354C2×C11—24no—
355C2×C11#232111yescharacteristic
356C2×C11C2×C4×Q1611yescharacteristic
357C2×C11C4×#13711yescharacteristic
358C2×C11#318911yescharacteristic
359C2×C11#319011yescharacteristic
360C2×C11#320911yescharacteristic
361C2×C11#321111yescharacteristic
362C24C2×D4411yescharacteristic
363C2×Q8—114no—
364C2×Q8—112no—
365C2×Q8—224no—
366C2×Q8—221no—
367C2×Q8—222no—
368C2×Q8—222no—
369C2×Q8—222no—
370C2×Q8—222no—
371C2×Q8—222no—
372C2×Q8—222no—
373C2×Q8—222no—
374C2×Q8—448no—
375C2×Q8—442no—
376C2×Q8—442no—
377C2×Q8—448no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—224no—
386C22×C4—222no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4—221no—
390C22×C4—222no—
391C22×C4—221no—
392C22×C4—442no—
393C22×C4—442no—
394C22×C4—442no—
395C22×C4—442no—
396C22×C4—442no—
397C22×C4Dic4414yescomplemented
398C22×C4C2×C4×D1112yes—
399C22×C4C2×D4411yescharacteristic
400C22×C4C2×D4411yescharacteristic
401C22×C4C2×D4411yescharacteristic
402C22×C4C2×D4411yescharacteristic
403C22×C4C2×D4411yescharacteristic
404C22×C4#433912yes—
405C22×C4C23×D1111yescharacteristic
406Q16—448no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8C2×C4×D1114yes—
413C4⋊C4—112no—
414C4⋊C4—224no—
415C4⋊C4—221no—
416C4⋊C4—222no—
417C4⋊C4—222no—
418C4⋊C4—222no—
419C4⋊C4—222no—
420C4⋊C4—442no—
421C4⋊C4—442no—
422C4⋊C4—442no—
423C22⋊C4—224no—
424C22⋊C4—442no—
425C42—22no—
426C42—22no—
427C42—41no—
428C42—41no—
429C42—442no—
430C42—442no—
431C11#2204411yescharacteristic, complemented, Sylow
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23C4×D4412yes—
437C23#6695712yes—
438C23C2×Dic4412yes—
439C23C22×D4411yescharacteristic
440Q8—224no—
441Q8—224no—
442Q8—224no—
443Q8—448no—
444Q8—442no—
445Q8—442no—
446Q8—442no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—224no—
465C2×C4—448no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—442no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—442no—
478C2×C4—441no—
479C2×C4—442no—
480C2×C4—441no—
481C2×C4—884no—
482C2×C4C4×D4412yes—
483C2×C4C2×Dic4412yes—
484C2×C4C2×Dic4412yes—
485C2×C4#6696212yes—
486C2×C4C22×C4×D1111yescharacteristic
487C2×C4C2×#433911yescharacteristic
488C2×C4#6703712yes—
489C2×C4#6704212yes—
490C8—24no—
491C8—42no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22C4×Dic4414yes—
499C22C2×C4×D4411yescharacteristic
500C22#1062302411yescharacteristic
501C22#1062305611yescharacteristic
502C22C2×#6695711yescharacteristic
503C22C22×Dic4411yescharacteristic
504C22C2×#6696211yescharacteristic
505C22#1062327911yescharacteristic
506C4—22no—
507C4—22no—
508C4—22no—
509C4—22no—
510C4—41no—
511C4—444no—
512C4—442no—
513C4—442no—
514C4—882no—
515C4—881no—
516C4—881no—
517C4#1062307612yes—
518C4#1062309112yes—
519C2—24no—
520C2#1307127611yescharacteristic
521C2C2×C4×Dic4411yescharacteristic
522C2C4×#6696211yescharacteristic
523C2#1307939111yescharacteristic
524C2#1307939911yescharacteristic
525C2#1307956611yescharacteristic
526C2#1307958311yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×C22⋊C8C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC4×C22⋊C8D11
hypocenterC11#22044
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. #13069477C2semidirect
5. #13069292C2semidirect
6. #13069258C2semidirect
7. #13068956C2semidirect
40. #10622352C4semidirect
80. C2×Dic44C2×C4semidirect
98. #66880C2×C4semidirect
108. C22×C4×C11Q16semidirect
397. C22×C4Dic44semidirect
431. C11#22044semidirect

Maximal subgroups

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

subgroupindex
C2×#106223522
C4×#669772
C2×#106225422
#130694772
#130692922
#130692582
#130689562
#130689212
#130688062
#130685522
C4×C11×C22⋊C82
#2204411