Finite Group Databasebeta

← #14675321

Subgroups — #14675321

Order 2816.

1690 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622260C212yesmaximal
2C2×C4×Dic11⋊C4C212yesmaximal
3C2×C4×Dic11⋊C4C211yesmaximal, characteristic
4#13066850C212yesmaximal
5#13066849C212yesmaximal
6#13066846C211yesmaximal, characteristic
7Dic11⋊#95C211yesmaximal, characteristic
8Dic11⋊#95C211yesmaximal, characteristic
9#95×Dic11C211yesmaximal, characteristic
10#95×Dic11C211yesmaximal, characteristic
11C4×C11×#95C211yesmaximal, characteristic
12C22×C42×C11C2212yes—
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2212yes—
15C22×Dic11⋊C4C2212yes—
16C22×Dic11⋊C4C2212yes—
17C22×Dic11⋊C4C2211yescharacteristic
18C22×Dic11⋊C4C2211yescharacteristic
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2212yes—
25C2×C11×#95C2211yescharacteristic
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C4×Dic11⋊C4—28no—
36C4×Dic11⋊C4C418yescomplemented
37#10622260C4116yescomplemented
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C2×C42×C11—24no—
50C2×C42×C11—24no—
51C2×C42×C11—42no—
52C2×C42×C11—42no—
53C2×C42×C11C2×C414yes—
54C2×C4⋊Dic11—42no—
55C2×C4⋊Dic11—42no—
56C2×C4⋊Dic11C2×C418yes—
57C2×Dic11⋊C4—24no—
58C2×Dic11⋊C4—24no—
59C2×Dic11⋊C4—42no—
60C2×Dic11⋊C4—42no—
61C2×Dic11⋊C4C2×C418yes—
62C2×Dic11⋊C4C2×C418yes—
63C2×Dic11⋊C4C2×C418yes—
64C2×Dic11⋊C4C2×C414yes—
65C2×Dic11⋊C4C2×C414yes—
66C2×Dic11⋊C4D414yes—
67C2×Dic11⋊C4Q814yes—
68C2×C4×Dic11—24no—
69C2×C4×Dic11—24no—
70C2×C4×Dic11—24no—
71C2×C4×Dic11—24no—
72C2×C4×Dic11—24no—
73C2×C4×Dic11—42no—
74C2×C4×Dic11—42no—
75C2×C4×Dic11C2×C418yes—
76C2×C4×Dic11C2×C414yes—
77C2×C4×Dic11C2×C414yes—
78C11×#95—22no—
79C11×#95C2×C418yes—
80C11×#95Q814yes—
81C11⋊#95—24no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—42no—
87C11⋊#95C2×C418yes—
88C11⋊#95C2×C414yes—
89C11⋊#95C2×C414yes—
90#13818—111nomaximal, Sylow
91C24×C11C2411yescharacteristic
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11C22×C414yes—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C22×C414yes—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C22×C414yes—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×Q812yes—
117C22×C4×C11C2×Q814yes—
118C22×C4×C11C2×Q812yes—
119C22×C4×C11#4112yes—
120C22×C4×C11#4114yes—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11C22×C412yes—
143C22×Dic11C22×C414yes—
144C22×Dic11C22×C414yes—
145C22×Dic11C22×C412yes—
146C22×Dic11C22×C414yes—
147C22×Dic11C22×C412yes—
148C22×Dic11C22×C412yes—
149C22×Dic11C22×C414yes—
150C22×Dic11C2×D412yes—
151C22×Dic11C2×D412yes—
152C22×Dic11C2×Q812yes—
153C22×Dic11C2×Q812yes—
154C22×Dic11#4114yes—
155C42×C11—44no—
156C42×C11—48no—
157C4⋊Dic11—48no—
158Dic11⋊C4—216no—
159Dic11⋊C4—48no—
160Dic11⋊C4C42116yescomplemented
161Dic11⋊C4C4⋊C4116yescomplemented
162C4×Dic11—28no—
163C4×Dic11—216no—
164C4×Dic11—44no—
165C4×Dic11—48no—
166C2×#389—112no—
167C2×C4×C4⋊C4—111no—
168C2×C4×C4⋊C4—112no—
169#1436—112no—
170#1436—112no—
171C4⋊#95—111no—
172C4⋊#95—111no—
173C4⋊#95—111no—
174C4×#95—111no—
175C4×#95—111no—
176C4×#95D1111yescharacteristic
177C23×C11C23×C411yescharacteristic
178C23×C11C23×C412yes—
179C23×C11C22×D411yescharacteristic
180C23×C11C22×Q811yescharacteristic
181C23×C11C22×Q811yescharacteristic
182C23×C11C2×#4112yes—
183C23×C11C2×#4111yescharacteristic
184C23×C11C2×#4112yes—
185C23×C11H(5,𝔽2)12yes—
186C23×C11H(5,𝔽2)11yescharacteristic
187C23×C112−1+411yescharacteristic
188C2×C4×C11—22no—
189C2×C4×C11—24no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11C2×C4214yes—
214C2×C4×C11C2×C4⋊C414yes—
215C2×C4×C11C4×Q814yes—
216C2×C4×C11C4×Q818yes—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—24no—
221C2×Dic11—22no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—22no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—22no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11C2×C4214yes—
245C2×Dic11C2×C4214yes—
246C2×Dic11C2×C4⋊C414yes—
247C2×Dic11C2×C4⋊C414yes—
248C2×Dic11#11714yes—
249C2×Dic11C4×D418yes—
250C2×Dic11C4×Q818yes—
251C22×C4⋊C4—111no—
252C22×C4⋊C4—111no—
253C22×C4⋊C4—112no—
254C22×C4⋊C4—112no—
255C22×C4⋊C4—112no—
256C22×C42—111no—
257C22×C42—112no—
258C22×C42—111no—
259C22×C42—112no—
260C22×C42C2×D1112yes—
261C22×C42C2×D1111yescharacteristic
262#389—1116no—
263C4×C4⋊C4—118no—
264C4×C4⋊C4—228no—
265C2×#95—112no—
266C2×#95—111no—
267C2×#95—111no—
268C2×#95—111no—
269C2×#95—111no—
270C2×#95—112no—
271C2×#95—112no—
272C2×#95—112no—
273C2×#95—112no—
274C2×#95C2×D1111yescharacteristic
275C2×#95C2×D1111yescharacteristic
276C2×#95C2×D1112yes—
277C22×C11C22×C4211yescharacteristic
278C22×C11C22×C4⋊C411yescharacteristic
279C22×C11C2×#11711yescharacteristic
280C22×C11C2×C4×D412yes—
281C22×C11C2×C4×Q811yescharacteristic
282C22×C11C2×C4×Q812yes—
283C22×C11C2×C4×Q812yes—
284C22×C11C4×#4111yescharacteristic
285C22×C11C4×#4112yes—
286C22×C11#51811yescharacteristic
287C22×C11#51812yes—
288C22×C11#52011yescharacteristic
289C22×C11#52012yes—
290C22×C11#54612yes—
291C22×C11D4×Q811yescharacteristic
292C22×C11#55011yescharacteristic
293C22×C11#55212yes—
294C22×C11#55312yes—
295C22×C11#55412yes—
296C22×C11#55412yes—
297C22×C11#55512yes—
298C22×C11#55711yescharacteristic
299C22×C11Q8211yescharacteristic
300C4×C11—24no—
301C4×C11—24no—
302C4×C11—28no—
303C4×C11—24no—
304C4×C11—44no—
305Dic11—24no—
306Dic11—24no—
307Dic11—42no—
308Dic11—44no—
309Dic11—44no—
310Dic11C4×C4⋊C418yes—
311C23×C4—111no—
312C23×C4—111no—
313C23×C4—111no—
314C23×C4—112no—
315C23×C4—112no—
316C23×C4—111no—
317C23×C4C22×D1112yes—
318C23×C4C22×D1112yes—
319C23×C4C22×D1111yescharacteristic
320C23×C4C22×D1111yescharacteristic
321C23×C4C22×D1111yescharacteristic
322C2×C4⋊C4—114no—
323C2×C4⋊C4—114no—
324C2×C4⋊C4—118no—
325C2×C4⋊C4—114no—
326C2×C4⋊C4—114no—
327C2×C4⋊C4—118no—
328C2×C4⋊C4—118no—
329C2×C4⋊C4—118no—
330C2×C4⋊C4—224no—
331C2×C4⋊C4—224no—
332C2×C4⋊C4—442no—
333C2×C4⋊C4—442no—
334C2×C4⋊C4—442no—
335C2×C4⋊C4—442no—
336C2×C42—24no—
337C2×C42—24no—
338C2×C42—42no—
339C2×C42—42no—
340C2×C42—114no—
341C2×C42—118no—
342C2×C42—114no—
343C2×C42—224no—
344C2×C42—224no—
345C2×C42—224no—
346C2×C42—224no—
347C2×C42—224no—
348C2×C42—442no—
349C2×C42—442no—
350C2×C42C4×D1114yes—
351#95—22no—
352#95—114no—
353#95—114no—
354#95—118no—
355#95—224no—
356#95—222no—
357#95—222no—
358#95—224no—
359#95—224no—
360#95—442no—
361#95Dic2214yes—
362#95C4×D1118yes—
363C2×C11C2×C4×C4⋊C411yescharacteristic
364C2×C11C42×Q811yescharacteristic
365C2×C11#227511yescharacteristic
366C2×C11#234511yescharacteristic
367C2×C11#234611yescharacteristic
368C2×C11#234911yescharacteristic
369C2×C11Q8×C4⋊C411yescharacteristic
370C2×C11#236012yes—
371C2×C11#236312yes—
372C2×C11#236912yes—
373C2×C11#237012yes—
374C24C23×D1111yescharacteristic
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—112no—
393C22×C4—114no—
394C22×C4—112no—
395C22×C4—112no—
396C22×C4—114no—
397C22×C4—112no—
398C22×C4—112no—
399C22×C4—114no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—112no—
403C22×C4—114no—
404C22×C4—114no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—221no—
409C22×C4—221no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—221no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—221no—
426C22×C4C2×Dic2214yes—
427C22×C4C2×Dic2212yes—
428C22×C4C2×C4×D1114yes—
429C22×C4C2×C4×D1114yes—
430C22×C4C2×C4×D1112yes—
431C22×C4C2×C4×D1112yes—
432C22×C4C2×C4×D1114yes—
433C22×C4C2×C4×D1112yes—
434C22×C4#433912yes—
435C22×C4#433914yes—
436C22×C4D4×D1112yes—
437C22×C4Q8×D1112yes—
438C4⋊C4—1116no—
439C4⋊C4—1116no—
440C4⋊C4—2216no—
441C4⋊C4—448no—
442C4⋊C4—448no—
443C42—44no—
444C42—48no—
445C42—228no—
446C42—2216no—
447C42—444no—
448C42—448no—
449C11#1381811yescharacteristic, complemented, Sylow
450C23C22×Dic2211yescharacteristic
451C23C22×C4×D1111yescharacteristic
452C23C22×C4×D1112yes—
453C23C2×#433912yes—
454C23C2×#433911yescharacteristic
455C23C2×D4×D1111yescharacteristic
456C23#6703712yes—
457C23C2×Q8×D1111yescharacteristic
458C23#41×D1112yes—
459C23#6704211yescharacteristic
460C23#6704311yescharacteristic
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—114no—
487C2×C4—114no—
488C2×C4—114no—
489C2×C4—118no—
490C2×C4—118no—
491C2×C4—114no—
492C2×C4—114no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—222no—
499C2×C4—224no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4C4×Dic2218yes—
521C2×C4C4×Dic2214yes—
522C2×C4C42×D1114yes—
523C2×C4C4⋊C4×D1114yes—
524C22C2×C4×Dic2212yes—
525C22C2×C4×Dic2211yescharacteristic
526C22C2×C42×D1111yescharacteristic
527C22C4×#433912yes—
528C22C4×#433911yescharacteristic
529C22#1062301711yescharacteristic
530C22#1062302112yes—
531C22C2×C4⋊C4×D1111yescharacteristic
532C22#1062304212yes—
533C22D11×#11711yescharacteristic
534C22#1062305411yescharacteristic
535C22#1062306212yes—
536C22#1062306312yes—
537C22D4×Dic2211yescharacteristic
538C22#1062307012yes—
539C22#1062307112yes—
540C22C4×D4×D1112yes—
541C22#1062307612yes—
542C22#1062307712yes—
543C22#1062308411yescharacteristic
544C22Q8×Dic2211yescharacteristic
545C22#1062309811yescharacteristic
546C22C4×Q8×D1112yes—
547C4—28no—
548C4—24no—
549C4—24no—
550C4—24no—
551C4—44no—
552C4—118no—
553C4—224no—
554C4—224no—
555C4—444no—
556C4—444no—
557C4—442no—
558C2C4×C4⋊C4×D1111yescharacteristic
559C2C42×Dic2211yescharacteristic
560C2#1307097511yescharacteristic
561C2#1307149411yescharacteristic
562C2#1307150211yescharacteristic
563C2#1307152311yescharacteristic
564C2C4⋊C4×Dic2211yescharacteristic
565C2#1307162212yes—
566C2#1307165512yes—
567C2#1307170312yes—
568C2#1307171312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC4×C11×#95C2
socle, prime radical, cosocleC24×C11C24
hypercenterC4×#95D11
hypocenterC11#13818
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
36. C4×Dic11⋊C4C4semidirect
37. #10622260C4semidirect
160. Dic11⋊C4C42semidirect
161. Dic11⋊C4C4⋊C4semidirect
449. C11#13818semidirect

Maximal subgroups

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

subgroupindex
C2×#106222602
C2×C4×Dic11⋊C42
#130668502
#130668492
#130668462
Dic11⋊#952
#95×Dic112
C4×C11×#952
#1381811