Finite Group Databasebeta

← #14926839

Subgroups — #14926839

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
1#13076955C212yesmaximal
2#13076926C212yesmaximal
3#13074730C211yesmaximal, characteristic
4#13074730C211yesmaximal, characteristic
5#13074429C212yesmaximal
6#13074022C214yesmaximal, complemented
7#13074007C214yesmaximal, complemented
8#13073304C214yesmaximal, complemented
9#13072598C214yesmaximal, complemented
10#13071349C212yesmaximal
11#13071219C212yesmaximal
12C4×#66977C212yesmaximal
13C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C2×#66977C2212yes—
20C2×#66977C2212yes—
21C2×#66923C2212yes—
22C2×C4×Dic22C2212yes—
23C4×C11×C4⋊C4C2214yes—
24C4×C11×C4⋊C4C2214yes—
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27#10622825C2212yes—
28#10622825C2212yes—
29#10622825C2212yes—
30#10622825C2212yes—
31#10622824C2214yes—
32#10622823C2214yes—
33#10622823C2214yes—
34C4×C22⋊Dic11C2214yes—
35#10622599C2214yes—
36#10622597C2214yes—
37#10622597C2214yes—
38#10622594C2214yes—
39#10622594C2214yes—
40#10622594C2214yes—
41#10622594C2214yes—
42#10622592C2214yes—
43#10622549C2212yes—
44C4×C4⋊Dic11C2212yes—
45#10622546C2214yes—
46#10622546C2214yes—
47#10622546C2214yes—
48#10622546C2214yes—
49#10622546C2214yes—
50C4×Dic11⋊C4C2214yes—
51#10622542C2212yes—
52#10622542C2212yes—
53#10622542C2212yes—
54#10622541C2212yes—
55#10622541C2212yes—
56#10622541C2212yes—
57#10622541C2212yes—
58#10622541C2212yes—
59#10622274C2214yes—
60#10622274C2214yes—
61#10622269C2214yes—
62#10622269C2214yes—
63#10622268C2214yes—
64#10622267C2214yes—
65#10622260C2214yes—
66#10622259C2214yes—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C22×Dic22C2312yes—
75C22×Dic22C2312yes—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4Q818yescomplemented
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C42×C11—24no—
81C2×C42×C11—42no—
82C2×C42×C11—42no—
83C2×C42×C11C2312yes—
84C2×C42×C11C2312yes—
85C2×C42×C11C2312yes—
86C2×C42×C11C2312yes—
87C2×C42×C11C2312yes—
88C2×C42×C11C2312yes—
89C2×C22⋊Dic11C2314yes—
90C2×C22⋊Dic11C2314yes—
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2312yes—
94C2×C4⋊Dic11C2312yes—
95C2×C4⋊Dic11C2312yes—
96C2×C4⋊Dic11C2312yes—
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2312yes—
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2312yes—
101#66977—28no—
102#66977—28no—
103C2×Dic11⋊C4C2314yes—
104C2×Dic11⋊C4C2314yes—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2314yes—
108C2×Dic11⋊C4C2314yes—
109C2×C4×Dic11C2314yes—
110C2×C4×Dic11C2314yes—
111#66923—44no—
112C4×Dic22—44no—
113C11×#95C2314yes—
114C11×#95C2314yes—
115C11⋊#95C2314yes—
116C11⋊#95C2314yes—
117C11⋊#95C2314yes—
118C11⋊#95C2314yes—
119C11⋊#95C2314yes—
120C11⋊#95C2314yes—
121C11⋊#95C2314yes—
122C11⋊#95C2314yes—
123C11⋊#95C2314yes—
124C11⋊#95C2314yes—
125C11⋊#95C2314yes—
126C11⋊#95C2314yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129#35013—111nomaximal, Sylow
130C24×C11C2411yescharacteristic
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—41no—
138C22×C4×C11—41no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11C2×Q814yes—
148C22×C4×C11C2×Q814yes—
149C22×C4×C11C2×Q814yes—
150C22×C4×C11#4114yes—
151C22×C4×C11#4114yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C22×Dic11C2414yes—
161C22×Dic11C2414yes—
162C22×Dic11C2414yes—
163C22×Dic11C2414yes—
164C2×Dic22—24no—
165C2×Dic22—24no—
166C2×Dic22—42no—
167C2×Dic22—42no—
168C2×Dic22—42no—
169C2×Dic22—42no—
170C11×C4⋊C4—28no—
171C11×C4⋊C4C2×Q8116yes—
172C42×C11—24no—
173C42×C11—24no—
174C42×C11—24no—
175C42×C11—24no—
176C42×C11—42no—
177C42×C11—42no—
178C22⋊Dic11—28no—
179C22⋊Dic11—28no—
180C4⋊Dic11—24no—
181C4⋊Dic11—24no—
182C4⋊Dic11—42no—
183C4⋊Dic11—42no—
184C4⋊Dic11—42no—
185C4⋊Dic11—42no—
186C4⋊Dic11—42no—
187C4⋊Dic11—42no—
188C4⋊Dic11—42no—
189C4⋊Dic11—42no—
190Dic11⋊C4—28no—
191Dic11⋊C4—28no—
192Dic11⋊C4—28no—
193Dic11⋊C4—28no—
194Dic11⋊C4—44no—
195Dic11⋊C4—44no—
196C4×Dic11—44no—
197C4×Dic11—44no—
198#2855—112no—
199#2851—112no—
200#2659—111no—
201#2659—111no—
202#2627—112no—
203#2586—114no—
204#2585—114no—
205#2520—114no—
206#2462—114no—
207#2329—112no—
208#2313—112no—
209C4×C22⋊Q8—112no—
210C2×C4×C4⋊C4D1111yescharacteristic
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11C22×Q812yes—
216C23×C11C2×#4112yes—
217C23×C11C2×#4112yes—
218C23×C11C2511yescharacteristic
219C2×C4×C11—28no—
220C2×C4×C11—28no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—44no—
239C2×C4×C11—44no—
240C2×C4×C11—44no—
241C2×C4×C11—44no—
242C2×C4×C11—44no—
243C2×C4×C11C22×Q814yes—
244C2×C4×C11C22×Q814yes—
245C2×C4×C11C22×Q814yes—
246C2×C4×C11C2×#4114yes—
247C2×C4×C11C2×#4114yes—
248C2×C4×C11H(5,𝔽2)12yes—
249C2×C4×C112−1+412yes—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262Dic22—48no—
263Dic22—84no—
264C2×#125—112no—
265C2×C22⋊Q8—112no—
266C2×C22⋊Q8—112no—
267C2×C4×Q8—112no—
268C22×C4⋊C4C2×D1111yescharacteristic
269C22×C4⋊C4C2×D1111yescharacteristic
270C22×C42C2×D1111yescharacteristic
271C22×C42C2×D1111yescharacteristic
272C22×C42C2×D1111yescharacteristic
273#400—114no—
274#398—114no—
275#398—114no—
276#398—114no—
277#398—114no—
278#395—114no—
279#395—114no—
280#395—114no—
281#391—112no—
282#391—112no—
283#391—112no—
284#391—114no—
285#389—112no—
286#389—112no—
287#389—112no—
288#389—112no—
289#389—112no—
290#389—114no—
291#387—114no—
292#387—114no—
293#387—114no—
294#387—114no—
295#387—114no—
296#387—114no—
297#387—114no—
298#387—114no—
299#387—114no—
300#387—114no—
301#387—114no—
302#385—114no—
303#385—114no—
304#382—112no—
305#381—114no—
306#380—112no—
307#380—112no—
308#380—112no—
309#380—112no—
310C4×C4⋊C4—114no—
311C4×C4⋊C4—112no—
312C4×C4⋊C4C2×D1114yes—
313C4×C4⋊C4C2×D1114yes—
314C4×C22⋊C4—114no—
315C2×#95C2×D1111yescharacteristic
316C2×#95C2×D1111yescharacteristic
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11#53314yes—
324C22×C11C23×Q811yescharacteristic
325C22×C11C22×#4111yescharacteristic
326C22×C11C22×#4111yescharacteristic
327C22×C11C2×H(5,𝔽2)11yescharacteristic
328C22×C11C2×2−1+411yescharacteristic
329C22×C11#58511yescharacteristic
330C22×C11#58511yescharacteristic
331C4×C11—24no—
332C4×C11—24no—
333C4×C11—24no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—24no—
337C4×C11—24no—
338C4×C11—42no—
339Dic11—44no—
340Dic11—44no—
341Dic11—44no—
342Dic11—44no—
343C22×Q8—112no—
344C22×Q8—112no—
345C23×C4C22×D1111yescharacteristic
346C23×C4C22×D1111yescharacteristic
347C23×C4C22×D1111yescharacteristic
348C23×C4C22×D1111yescharacteristic
349C23×C4C22×D1111yescharacteristic
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1111yescharacteristic
352#125—444no—
353C22⋊Q8—228no—
354C22⋊Q8—228no—
355C4×Q8—444no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—114no—
358C2×C4⋊C4—114no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—114no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—112no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—112no—
372C2×C4⋊C4—114no—
373C2×C4⋊C4Dic2218yescomplemented
374C2×C4⋊C4C22×D1114yes—
375C2×C4⋊C4C22×D1114yes—
376C2×C22⋊C4—114no—
377C2×C22⋊C4—114no—
378C2×C42—24no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—114no—
382C2×C42—114no—
383C2×C42C22×D1112yes—
384C2×C42C22×D1112yes—
385C2×C42C22×D1112yes—
386C2×C42C22×D1112yes—
387C2×C42C22×D1112yes—
388C2×C42C22×D1112yes—
389#95—114no—
390#95—114no—
391#95—114no—
392#95—114no—
393#95—114no—
394#95—114no—
395#95—114no—
396#95—114no—
397#95—114no—
398#95—114no—
399#95—114no—
400#95—114no—
401#95—114no—
402#95—114no—
403#95C22×D1114yes—
404#95C22×D1114yes—
405C2×C11—24no—
406C2×C11C2×#53311yescharacteristic
407C2×C11#345911yescharacteristic
408C2×C11#346111yescharacteristic
409C2×C11#349111yescharacteristic
410C2×C11#349211yescharacteristic
411C2×C11#350111yescharacteristic
412C2×C11#350211yescharacteristic
413C24C23×D1111yescharacteristic
414C2×Q8—224no—
415C2×Q8—224no—
416C2×Q8—442no—
417C2×Q8—442no—
418C2×Q8—442no—
419C2×Q8—442no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—114no—
437C22×C4—114no—
438C22×C4—114no—
439C22×C4—114no—
440C22×C4C2×Dic2214yes—
441C22×C4C2×Dic2214yes—
442C22×C4C2×Dic2214yes—
443C22×C4#433914yes—
444C22×C4#433914yes—
445C22×C4C23×D1112yes—
446C22×C4C23×D1112yes—
447C22×C4C23×D1112yes—
448C22×C4C23×D1112yes—
449C22×C4C23×D1112yes—
450C22×C4C23×D1112yes—
451C22×C4C23×D1111yescharacteristic
452C22×C4C23×D1111yescharacteristic
453C4⋊C4—28no—
454C4⋊C4—228no—
455C4⋊C4—228no—
456C4⋊C4—224no—
457C4⋊C4—224no—
458C4⋊C4—228no—
459C4⋊C4—228no—
460C4⋊C4—442no—
461C4⋊C4—444no—
462C4⋊C4—442no—
463C4⋊C4—442no—
464C4⋊C4—444no—
465C4⋊C4—442no—
466C4⋊C4—442no—
467C4⋊C4—442no—
468C4⋊C4—442no—
469C4⋊C4—442no—
470C4⋊C4C2×Dic22116yes—
471C22⋊C4—228no—
472C22⋊C4—228no—
473C42—24no—
474C42—24no—
475C42—24no—
476C42—24no—
477C42—42no—
478C42—42no—
479C42—444no—
480C42—444no—
481C11#3501311yescharacteristic, complemented, Sylow
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23C22×Dic2212yes—
487C23C2×#433912yes—
488C23C2×#433912yes—
489C23C24×D1111yescharacteristic
490Q8—448no—
491Q8—884no—
492C2×C4—28no—
493C2×C4—28no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—44no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—44no—
515C2×C4—44no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—224no—
528C2×C4C22×Dic2214yes—
529C2×C4C22×Dic2214yes—
530C2×C4C22×Dic2214yes—
531C2×C4C2×#433914yes—
532C2×C4C2×#433914yes—
533C2×C4#6703712yes—
534C2×C4#6704012yes—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22#1062300114yes—
542C22C23×Dic2211yescharacteristic
543C22C22×#433911yescharacteristic
544C22C22×#433911yescharacteristic
545C22C2×#6703711yescharacteristic
546C22C2×#6704011yescharacteristic
547C22#1062345311yescharacteristic
548C22#1062345311yescharacteristic
549C4—24no—
550C4—24no—
551C4—24no—
552C4—24no—
553C4—24no—
554C4—22no—
555C4—22no—
556C4—42no—
557C4—444no—
558C4—444no—
559C4—444no—
560C4—444no—
561C2—24no—
562C2C2×#1062300111yescharacteristic
563C2#1308202511yescharacteristic
564C2#1308204911yescharacteristic
565C2#1308231411yescharacteristic
566C2#1308232511yescharacteristic
567C2#1308241911yescharacteristic
568C2#1308242611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C4×C11×C4⋊C4C2
prime radicalC24×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#35013
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #13074022C2semidirect
7. #13074007C2semidirect
8. #13073304C2semidirect
9. #13072598C2semidirect
77. C2×C11×C4⋊C4Q8semidirect
373. C2×C4⋊C4Dic22semidirect
481. C11#35013semidirect

Maximal subgroups

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

subgroupindex
#130769552
#130769262
#130747302
#130744292
#130740222
#130740072
#130733042
#130725982
#130713492
#130712192
C4×#669772
C2×C4×C11×C4⋊C42
#3501311