Finite Group Databasebeta

← #14675290

Subgroups — #14675290

Order 2816.

1602 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622594C212yesmaximal
2C2×C4×C4⋊Dic11C211yesmaximal, characteristic
3C2×#10622545C211yesmaximal, characteristic
4#13066850C212yesmaximal
5#13066848C212yesmaximal
6#13066843C211yesmaximal, characteristic
7#13066843C211yesmaximal, characteristic
8#13066843C211yesmaximal, characteristic
9C4×C11⋊#95C211yesmaximal, characteristic
10#95×Dic11C212yesmaximal
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C4⋊Dic11C2212yes—
18C22×C4×Dic11C2212yes—
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2212yes—
21C4×C11×C4⋊C4C418yescomplemented
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36#10622594C4116yescomplemented
37C4×C4⋊Dic11—24no—
38#10622545—24no—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4C2×C418yes—
53C2×C11×C4⋊C4C2×C414yes—
54C2×C11×C4⋊C4C2×C414yes—
55C2×C42×C11—22no—
56C2×C42×C11—22no—
57C2×C42×C11—24no—
58C2×C42×C11—22no—
59C2×C42×C11—22no—
60C2×C42×C11C2×C414yes—
61C2×C42×C11C2×C414yes—
62C2×C42×C11C2×C414yes—
63C2×C4⋊Dic11—24no—
64C2×C4⋊Dic11—24no—
65C2×C4⋊Dic11C2×C418yes—
66C2×C4×Dic11—24no—
67C2×C4×Dic11—24no—
68C2×C4×Dic11—24no—
69C2×C4×Dic11—24no—
70C2×C4×Dic11—24no—
71C2×C4×Dic11—24no—
72C2×C4×Dic11—42no—
73C2×C4×Dic11—42no—
74C2×C4×Dic11C2×C418yes—
75C11×#95C2×C414yes—
76C11×#95C2×C414yes—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95—24no—
80C11⋊#95—24no—
81C11⋊#95—22no—
82C11⋊#95—24no—
83C11⋊#95—42no—
84C11⋊#95C2×C418yes—
85C11⋊#95C2×C418yes—
86C11⋊#95C2×C418yes—
87C11⋊#95C2×C418yes—
88C11⋊#95D414yes—
89#13815—111nomaximal, Sylow
90C24×C11C2411yescharacteristic
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C22×C414yes—
117C22×C4×C11C22×C414yes—
118C22×C4×C11C22×C414yes—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11#4112yes—
127C22×C4×C11#4114yes—
128C22×C4×C11#4112yes—
129C22×C4×C11#4112yes—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11C22×C414yes—
153C22×Dic11C22×C414yes—
154C22×Dic11C22×C414yes—
155C22×Dic11C22×C414yes—
156C22×Dic11C2×D414yes—
157C22×Dic11#4114yes—
158C11×C4⋊C4—28no—
159C11×C4⋊C4C42116yescomplemented
160C42×C11—28no—
161C42×C11—28no—
162C42×C11—28no—
163C4⋊Dic11—216no—
164C4×Dic11—216no—
165C4×Dic11—48no—
166C4×Dic11—48no—
167C2×#387—112no—
168C2×C4×C4⋊C4—111no—
169C2×C4×C4⋊C4D1111yescharacteristic
170C2×#376—111no—
171#1436—112no—
172#1436—112no—
173#1434—111no—
174#1434—111no—
175#1434—111no—
176C4×#95—111no—
177C4×#95—112no—
178C23×C11C23×C412yes—
179C23×C11C23×C411yescharacteristic
180C23×C11C22×D411yescharacteristic
181C23×C11C2×#4111yescharacteristic
182C23×C11C2×#4112yes—
183C23×C11C2×#4111yescharacteristic
184C23×C11C2×#4111yescharacteristic
185C23×C11C2×#4112yes—
186C23×C11H(5,𝔽2)11yescharacteristic
187C23×C112−1+412yes—
188C23×C112−1+411yescharacteristic
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11C2×C4214yes—
223C2×C4×C11C2×C4214yes—
224C2×C4×C11C2×C4214yes—
225C2×C4×C11#11714yes—
226C2×C4×C11#11714yes—
227C2×C4×C11C4×D414yes—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11C4×D418yes—
256C22×C4⋊C4—112no—
257C22×C4⋊C4C2×D1111yescharacteristic
258C22×C4⋊C4C2×D1111yescharacteristic
259C22×C42—112no—
260C22×C42—112no—
261C22×C42—112no—
262C22×C42C2×D1111yescharacteristic
263C22×C42C2×D1111yescharacteristic
264C22×C42C2×D1111yescharacteristic
265#387—1116no—
266C4×C4⋊C4—224no—
267C4×C4⋊C4Dic1118yescomplemented
268#376—224no—
269C2×#95—112no—
270C2×#95—112no—
271C2×#95—111no—
272C2×#95—112no—
273C2×#95—112no—
274C2×#95—111no—
275C2×#95—112no—
276C2×#95—112no—
277C2×#95—111no—
278C2×#95—111no—
279C2×#95—112no—
280C2×#95—112no—
281C2×#95C2×D1111yescharacteristic
282C2×#95C2×D1111yescharacteristic
283C22×C11C22×C4211yescharacteristic
284C22×C11C2×#11711yescharacteristic
285C22×C11C2×#11711yescharacteristic
286C22×C11C2×C4×D411yescharacteristic
287C22×C11C2×C4×D412yes—
288C22×C11C4×#4112yes—
289C22×C11C4×#4112yes—
290C22×C11C4×#4112yes—
291C22×C11C4×#4111yescharacteristic
292C22×C11#51911yescharacteristic
293C22×C11#51912yes—
294C22×C11#52011yescharacteristic
295C22×C11#52012yes—
296C22×C11#54611yescharacteristic
297C22×C11#54712yes—
298C22×C11#54811yescharacteristic
299C22×C11#55112yes—
300C22×C11#55212yes—
301C22×C11#55212yes—
302C22×C11#55211yescharacteristic
303C22×C11#55212yes—
304C22×C11#55311yescharacteristic
305C22×C11#55612yes—
306C4×C11—24no—
307C4×C11—24no—
308C4×C11—24no—
309C4×C11—24no—
310C4×C11—24no—
311C4×C11—24no—
312C4×C11—42no—
313Dic11—28no—
314Dic11—44no—
315Dic11—44no—
316Dic11—44no—
317C23×C4—112no—
318C23×C4—112no—
319C23×C4—112no—
320C23×C4—112no—
321C23×C4C22×D1111yescharacteristic
322C23×C4C22×D1111yescharacteristic
323C23×C4C22×D1111yescharacteristic
324C23×C4C22×D1111yescharacteristic
325C23×C4C22×D1111yescharacteristic
326C23×C4C22×D1111yescharacteristic
327C23×C4C22×D1111yescharacteristic
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—118no—
331C2×C4⋊C4—224no—
332C2×C4⋊C4—224no—
333C2×C4⋊C4C4×D1118yes—
334C2×C4⋊C4C2×Dic1114yes—
335C2×C4⋊C4C2×Dic1114yes—
336C2×C42—24no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—118no—
342C2×C42—224no—
343C2×C42—224no—
344C2×C42—224no—
345C2×C42—224no—
346C2×C42—224no—
347C2×C42—224no—
348C2×C42—442no—
349C2×C42—442no—
350C2×C42C2×Dic1114yes—
351C2×C42C2×Dic1114yes—
352C2×C42C2×Dic1114yes—
353#95—118no—
354#95—118no—
355#95—118no—
356#95—118no—
357#95—114no—
358#95—224no—
359#95—224no—
360#95—224no—
361#95—222no—
362#95—222no—
363#95—222no—
364#95—442no—
365#95C2×Dic1114yes—
366#95C2×Dic1114yes—
367C2×C11C4×#11711yescharacteristic
368C2×C11C42×D411yescharacteristic
369C2×C11#227611yescharacteristic
370C2×C11#234311yescharacteristic
371C2×C11#234411yescharacteristic
372C2×C11#235211yescharacteristic
373C2×C11#235611yescharacteristic
374C2×C11#235912yes—
375C2×C11#236212yes—
376C2×C11#237112yes—
377C2×C11#237312yes—
378C24C23×D1111yescharacteristic
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—114no—
404C22×C4—114no—
405C22×C4—114no—
406C22×C4—114no—
407C22×C4—114no—
408C22×C4—114no—
409C22×C4—222no—
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—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4C2×C4×D1114yes—
432C22×C4C2×C4×D1114yes—
433C22×C4C2×C4×D1114yes—
434C22×C4#433912yes—
435C22×C4#433914yes—
436C22×C4#433912yes—
437C22×C4D4×D1112yes—
438C22×C4#434112yes—
439C22×C4C22×Dic1112yes—
440C22×C4C22×Dic1112yes—
441C22×C4C22×Dic1112yes—
442C22×C4C22×Dic1112yes—
443C22×C4C22×Dic1112yes—
444C22×C4C22×Dic1112yes—
445C22×C4C22×Dic1112yes—
446C4⋊C4—28no—
447C4⋊C4—2216no—
448C4⋊C4C4×Dic11116yescomplemented
449C42—28no—
450C42—28no—
451C42—28no—
452C42—2216no—
453C42—448no—
454C42—448no—
455C11#1381511yescharacteristic, complemented, Sylow
456C23C22×C4×D1112yes—
457C23C2×#433912yes—
458C23C2×#433911yescharacteristic
459C23C2×#433911yescharacteristic
460C23C2×D4×D1111yescharacteristic
461C23C2×#434111yescharacteristic
462C23#6704012yes—
463C23#41×D1112yes—
464C23#6704211yescharacteristic
465C23#6704311yescharacteristic
466C23C23×Dic1111yescharacteristic
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—118no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4C2×C4×Dic1114yes—
529C2×C4C2×C4×Dic1114yes—
530C2×C4C2×C4×Dic1114yes—
531C2×C4#6697914yes—
532C2×C4#6697914yes—
533C2×C4D4×Dic1114yes—
534C22C4×#433912yes—
535C22C4×#433912yes—
536C22#1062303812yes—
537C22#1062304412yes—
538C22#1062305812yes—
539C22#1062306212yes—
540C22C4×#434112yes—
541C22#1062307211yescharacteristic
542C22C4×D4×D1112yes—
543C22#1062308111yescharacteristic
544C22#1062308311yescharacteristic
545C22#1062309611yescharacteristic
546C22#1062309912yes—
547C22#1062310312yes—
548C22#1062310512yes—
549C22#1062311212yes—
550C22C22×C4×Dic1111yescharacteristic
551C22C2×#6697911yescharacteristic
552C22C2×#6697911yescharacteristic
553C22C2×D4×Dic1111yescharacteristic
554C22#1062334311yescharacteristic
555C22#41×Dic1111yescharacteristic
556C22#1062335811yescharacteristic
557C4—24no—
558C4—24no—
559C4—24no—
560C4—24no—
561C4—24no—
562C4—24no—
563C4—42no—
564C4—228no—
565C4—444no—
566C4—444no—
567C4—444no—
568C2C4×#6697911yescharacteristic
569C2C4×D4×Dic1111yescharacteristic
570C2#1307098111yescharacteristic
571C2#1307147611yescharacteristic
572C2#1307148511yescharacteristic
573C2#1307154511yescharacteristic
574C2#1307158111yescharacteristic
575C2#1307161312yes—
576C2#1307164412yes—
577C2#1307171912yes—
578C2#1307174112yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C4×C11×C4⋊C4C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#13815
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
21. C4×C11×C4⋊C4C4semidirect
36. #10622594C4semidirect
159. C11×C4⋊C4C42semidirect
267. C4×C4⋊C4Dic11semidirect
448. C4⋊C4C4×Dic11semidirect
455. C11#13815semidirect

Maximal subgroups

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

subgroupindex
C2×#106225942
C2×C4×C4⋊Dic112
C2×#106225452
#130668502
#130668482
#130668432
C4×C11⋊#952
#95×Dic112
C2×C4×C11×C4⋊C42
#1381511