Finite Group Databasebeta

← #14680972

Subgroups — #14680972

Order 2816.

2150 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×#10622824C211yesmaximal, characteristic, complemented
2C2×#10622825C211yesmaximal, characteristic, complemented
3#13066869C212yesmaximal, complemented
4#13066865C212yesmaximal, complemented
5#13066861C212yesmaximal, complemented
6#13066857C212yesmaximal
7#13066843C212yesmaximal, complemented
8#13066839C212yesmaximal, complemented
9C22×C4×D4×C11C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C2×C4×D4×C11—24no—
14C2×C4×D4×C11—24no—
15C2×C4×D4×C11C418yescomplemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C22⋊Dic11C2214yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C4⋊Dic11C2212yes—
24#10622825—24no—
25#10622824—24no—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2214yes—
32C25×C11C2311yescharacteristic
33C25×C11C2311yescharacteristic
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11—24no—
37C22×D4×C11—24no—
38C22×D4×C11C2×C414yes—
39C23×C4×C11—22no—
40C23×C4×C11—22no—
41C23×C4×C11—44no—
42C23×C4×C11—44no—
43C23×C4×C11C2×C414yes—
44C23×C4×C11C2×C414yes—
45C23×C4×C11D414yes—
46C23×C4×C11D414yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×Dic11C2314yes—
53C23×Dic11C2314yes—
54C4×D4×C11—232no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4C2×C414yes—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4C2×C414yes—
63C2×C11×C22⋊C4C2×C414yes—
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11C2×C414yes—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—28no—
70C2×C22⋊Dic11—44no—
71C2×C22⋊Dic11—44no—
72C2×C22⋊Dic11—44no—
73C2×C22⋊Dic11—44no—
74C2×C4⋊Dic11—24no—
75C2×C4⋊Dic11—44no—
76C11⋊#95—24no—
77C11⋊#95—24no—
78C11⋊#95—24no—
79C11⋊#95—28no—
80C11⋊#95—44no—
81C11⋊#95—44no—
82#14344—111nomaximal, Sylow
83C24×C11—21no—
84C24×C11—21no—
85C24×C11—22no—
86C24×C11—22no—
87C24×C11—22no—
88C24×C11—22no—
89C24×C11—22no—
90C24×C11—24no—
91C24×C11—24no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11C22×C412yes—
95C24×C11C22×C412yes—
96C24×C11C2×D412yes—
97C24×C11C2×D412yes—
98C24×C11#4114yes—
99C24×C11C2411yescharacteristic
100C2×D4×C11—216no—
101C2×D4×C11—216no—
102C2×D4×C11—28no—
103C2×D4×C11—28no—
104C2×D4×C11—28no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—24no—
109C22×C4×C11—24no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—28no—
118C22×C4×C11—48no—
119C22×C4×C11—48no—
120C22×C4×C11—48no—
121C22×C4×C11—48no—
122C22×C4×C11—48no—
123C22×C4×C11—48no—
124C22×C4×C11C22⋊C4116yescomplemented
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11#4114yes—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C11×C4⋊C4—28no—
150C11×C22⋊C4—28no—
151C11×C22⋊C4—28no—
152C42×C11—28no—
153C22⋊Dic11—48no—
154C22⋊Dic11—48no—
155C22⋊Dic11—416no—
156C4⋊Dic11—48no—
157C22×C4×D4D1111yescharacteristic
158C2×#381—111no—
159C2×#380—111no—
160#1441—112no—
161#1440—112no—
162#1439—112no—
163#1438—112no—
164#1434—112no—
165C22⋊#95—112no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—24no—
171C23×C11—24no—
172C23×C11—24no—
173C23×C11—24no—
174C23×C11—24no—
175C23×C11—24no—
176C23×C11—24no—
177C23×C11—24no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—24no—
183C23×C11—28no—
184C23×C11—28no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—42no—
190C23×C11—44no—
191C23×C11—44no—
192C23×C11—44no—
193C23×C11—44no—
194C23×C11—44no—
195C23×C11—44no—
196C23×C11C2×C22⋊C414yes—
197C23×C11#11714yes—
198C23×C11C23×C411yescharacteristic
199C23×C11C22×D411yescharacteristic
200C23×C11C22×D411yescharacteristic
201C23×C11C2×#4112yes—
202C23×C11C2×#4112yes—
203C23×C11H(5,𝔽2)14yes—
204C23×C11H(5,𝔽2)12yes—
205C23×C112−1+412yes—
206D4×C11—232no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—416no—
222C2×C4×C11—416no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11C2×C22⋊C414yes—
229C2×C4×C11C2×C22⋊C414yes—
230C2×C4×C11#11714yes—
231C2×Dic11—44no—
232C2×Dic11—44no—
233C2×Dic11—44no—
234C2×Dic11—44no—
235C2×Dic11—44no—
236C2×Dic11—44no—
237C2×Dic11—44no—
238C2×Dic11—44no—
239C2×Dic11—44no—
240C2×Dic11—44no—
241C2×Dic11—44no—
242C2×Dic11—44no—
243C2×Dic11—44no—
244C2×Dic11—44no—
245C23×D4C2×D1111yescharacteristic
246C24×C4C2×D1111yescharacteristic
247C24×C4C2×D1111yescharacteristic
248C2×C4×D4—24no—
249C2×C4×D4—24no—
250C2×C4×D4Dic1118yescomplemented
251C22×C4⋊C4—112no—
252C22×C4⋊C4C2×D1111yescharacteristic
253C22×C22⋊C4—114no—
254C22×C22⋊C4—112no—
255C22×C22⋊C4—112no—
256C22×C22⋊C4C2×D1111yescharacteristic
257C22×C22⋊C4C2×D1111yescharacteristic
258C22×C42C2×D1111yescharacteristic
259#381—224no—
260#380—224no—
261C2×#95—112no—
262C2×#95—112no—
263C2×#95—114no—
264C2×#95—112no—
265C2×#95—114no—
266C2×#95—114no—
267C22×C11—24no—
268C22×C11—24no—
269C22×C11—28no—
270C22×C11—24no—
271C22×C11—24no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—44no—
275C22×C11—44no—
276C22×C11—44no—
277C22×C11—48no—
278C22×C11—48no—
279C22×C11—44no—
280C22×C11—44no—
281C22×C11—44no—
282C22×C11—44no—
283C22×C11C22×C22⋊C411yescharacteristic
284C22×C11C2×#11711yescharacteristic
285C22×C11C2×#11711yescharacteristic
286C22×C11#51812yes—
287C22×C11#52012yes—
288C22×C11#52512yes—
289C22×C11#52512yes—
290C22×C11#53412yes—
291C22×C11#53412yes—
292C22×C11#53511yescharacteristic
293C22×C11#53611yescharacteristic
294C22×C11#53712yes—
295C22×C11#53814yes—
296C22×C11#53914yes—
297C22×C11#54014yes—
298C22×C11#54214yes—
299C4×C11—24no—
300C4×C11—24no—
301C4×C11—24no—
302C4×C11—42no—
303C4×C11—42no—
304Dic11—84no—
305Dic11—84no—
306C25C22×D1111yescharacteristic
307C25C22×D1111yescharacteristic
308C22×D4—24no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—24no—
312C22×D4C2×Dic1114yes—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—44no—
316C23×C4—44no—
317C23×C4—114no—
318C23×C4—114no—
319C23×C4C2×Dic1114yes—
320C23×C4C2×Dic1114yes—
321C23×C4C22⋊D1114yes—
322C23×C4C22⋊D1114yes—
323C23×C4C22×D1111yescharacteristic
324C23×C4C22×D1111yescharacteristic
325C23×C4C22×D1111yescharacteristic
326C23×C4C22×D1111yescharacteristic
327C23×C4C22×D1111yescharacteristic
328C4×D4—232no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—224no—
332C2×C4⋊C4—444no—
333C2×C4⋊C4C2×Dic1114yes—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—228no—
339C2×C22⋊C4—224no—
340C2×C22⋊C4—224no—
341C2×C22⋊C4—444no—
342C2×C22⋊C4—444no—
343C2×C22⋊C4—444no—
344C2×C22⋊C4—444no—
345C2×C22⋊C4C2×Dic1114yes—
346C2×C22⋊C4C2×Dic1114yes—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42C2×Dic1114yes—
350#95—228no—
351#95—224no—
352#95—224no—
353#95—224no—
354#95—444no—
355#95—444no—
356C2×C11—44no—
357C2×C11—44no—
358C2×C11#228011yescharacteristic
359C2×C11#230811yescharacteristic
360C2×C11#231111yescharacteristic
361C2×C11#231812yes—
362C2×C11#231912yes—
363C2×C11#263014yes—
364C2×C11#263512yes—
365C2×C11#263812yes—
366C24—22no—
367C24—22no—
368C24—22no—
369C24—24no—
370C24—24no—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—22no—
375C24—21no—
376C24—21no—
377C24#433914yes—
378C24C22×Dic1112yes—
379C24C22×Dic1112yes—
380C24C2×C22⋊D1112yes—
381C24C2×C22⋊D1112yes—
382C24C23×D1111yescharacteristic
383C2×D4—216no—
384C2×D4—216no—
385C2×D4—28no—
386C2×D4—28no—
387C2×D4—28no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—24no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—28no—
401C22×C4—48no—
402C22×C4—48no—
403C22×C4—48no—
404C22×C4—48no—
405C22×C4—48no—
406C22×C4—48no—
407C22×C4—224no—
408C22×C4—224no—
409C22×C4—224no—
410C22×C4—224no—
411C22×C4—224no—
412C22×C4—224no—
413C22×C4—224no—
414C22×C4—224no—
415C22×C4—224no—
416C22×C4—224no—
417C22×C4—224no—
418C22×C4—224no—
419C22×C4—224no—
420C22×C4—224no—
421C22×C4C22⋊Dic11116yescomplemented
422C22×C4#433914yes—
423C22×C4C22×Dic1112yes—
424C22×C4C22×Dic1112yes—
425C22×C4C22×Dic1112yes—
426C22×C4C22×Dic1112yes—
427C22×C4C22×Dic1112yes—
428C22×C4C2×C22⋊D1112yes—
429C22×C4C2×C22⋊D1112yes—
430C22×C4C2×C22⋊D1112yes—
431C22×C4C2×C22⋊D1112yes—
432C4⋊C4—28no—
433C4⋊C4—448no—
434C22⋊C4—28no—
435C22⋊C4—28no—
436C22⋊C4—448no—
437C22⋊C4—4416no—
438C22⋊C4—448no—
439C42—28no—
440C11#1434411yescharacteristic, complemented, Sylow
441C23—22no—
442C23—22no—
443C23—22no—
444C23—24no—
445C23—24no—
446C23—24no—
447C23—24no—
448C23—24no—
449C23—24no—
450C23—24no—
451C23—24no—
452C23—28no—
453C23—28no—
454C23—22no—
455C23—24no—
456C23—24no—
457C23—22no—
458C23—24no—
459C23—22no—
460C23—42no—
461C23—42no—
462C23—44no—
463C23—44no—
464C23—44no—
465C23—44no—
466C23—44no—
467C23—44no—
468C23—41no—
469C23—41no—
470C23—42no—
471C23#6697914yes—
472C23C2×C22⋊Dic1114yes—
473C23C2×#433912yes—
474C23C2×#433912yes—
475C23#6703714yes—
476C23#6704212yes—
477C23#6704312yes—
478C23C23×Dic1111yescharacteristic
479C23C22×C22⋊D1111yescharacteristic
480C23C22×C22⋊D1111yescharacteristic
481D4—232no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—416no—
497C2×C4—416no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—444no—
504C2×C4—444no—
505C2×C4—444no—
506C2×C4—444no—
507C2×C4—444no—
508C2×C4—444no—
509C2×C4—444no—
510C2×C4—444no—
511C2×C4—444no—
512C2×C4—444no—
513C2×C4—444no—
514C2×C4—444no—
515C2×C4—444no—
516C2×C4—444no—
517C2×C4#6697914yes—
518C2×C4C2×C22⋊Dic1114yes—
519C2×C4C2×C22⋊Dic1114yes—
520C22—24no—
521C22—24no—
522C22—28no—
523C22—24no—
524C22—24no—
525C22—48no—
526C22—48no—
527C22—44no—
528C22—44no—
529C22—42no—
530C22—44no—
531C22—44no—
532C22—42no—
533C22—44no—
534C22—44no—
535C22—44no—
536C22#1062309114yes—
537C22#1062309214yes—
538C22#1062309314yes—
539C22#1062309514yes—
540C22C2×#6697911yescharacteristic
541C22C2×#6697911yescharacteristic
542C22#1062332212yes—
543C22#1062332212yes—
544C22#1062332912yes—
545C22#1062333512yes—
546C22#1062333512yes—
547C22#1062335611yescharacteristic
548C22#1062335812yes—
549C22#1062336111yescharacteristic
550C22#1062336412yes—
551C22C22×C22⋊Dic1111yescharacteristic
552C4—24no—
553C4—24no—
554C4—24no—
555C4—42no—
556C4—42no—
557C4—884no—
558C4—884no—
559C2—44no—
560C2—44no—
561C2#1307099911yescharacteristic
562C2#1307119411yescharacteristic
563C2#1307120811yescharacteristic
564C2#1307124912yes—
565C2#1307125912yes—
566C2#1307445314yes—
567C2#1307450012yes—
568C2#1307453312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×D4×C11C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11#14344
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10622824C2semidirect
2. C2×#10622825C2semidirect
3. #13066869C2semidirect
4. #13066865C2semidirect
5. #13066861C2semidirect
7. #13066843C2semidirect
8. #13066839C2semidirect
15. C2×C4×D4×C11C4semidirect
124. C22×C4×C11C22⋊C4semidirect
250. C2×C4×D4Dic11semidirect
421. C22×C4C22⋊Dic11semidirect
440. C11#14344semidirect

Maximal subgroups

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

subgroupindex
C2×#106228242
C2×#106228252
#130668692
#130668652
#130668612
#130668572
#130668432
#130668392
C22×C4×D4×C112
#1434411