Finite Group Databasebeta

← #14920936

Subgroups — #14920936

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074643C214yesmaximal, complemented
2#13074598C214yesmaximal, complemented
3#13074591C211yesmaximal, characteristic, complemented
4#13074576C212yesmaximal, complemented
5#13074559C211yesmaximal, characteristic, complemented
6#13074446C211yesmaximal, characteristic, complemented
7#13074405C212yesmaximal, complemented
8#13074366C211yesmaximal, characteristic
9#13071879C214yesmaximal, complemented
10#13071860C214yesmaximal, complemented
11C4×#66927C211yesmaximal, characteristic, complemented
12C4×#66923C211yesmaximal, characteristic, complemented
13C4×#66983C212yesmaximal, complemented
14#13071080C212yesmaximal, complemented
15C4×C11×#117C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C2×#66983C2212yes—
20C2×C4×C22⋊D11C2214yes—
21C2×#66927C2211yescharacteristic
22C2×C4×D44C2212yes—
23C2×C4×D44C2214yes—
24C2×#66925C2214yes—
25C2×#66923C2211yescharacteristic
26C4×C11×C4⋊C4C2212yes—
27C4×C11×C4⋊C4C2212yes—
28C4×C11×C22⋊C4C2212yes—
29C4×C11×C22⋊C4C2212yes—
30C11×#376C2211yescharacteristic
31C11×#376C2211yescharacteristic
32C43×C11C2211yescharacteristic
33C43×C11C2211yescharacteristic
34#10622826C2214yes—
35#10622825C2212yes—
36#10622606C2214yes—
37#10622605C2214yes—
38#10622604C2214yes—
39#10622597C2214yes—
40#10622573C2214yes—
41#10622572C2214yes—
42#10622572C2214yes—
43#10622561C2214yes—
44#10622553C2214yes—
45#10622553C2214yes—
46#10622553C2214yes—
47#10622552C2212yes—
48#10622552C2212yes—
49#10622552C2214yes—
50#10622552C2212yes—
51#10622552C2212yes—
52C4×(C2×D11)⋊C4C2214yes—
53C4×(C2×D11)⋊C4C2214yes—
54#10622549C2211yescharacteristic
55#10622548C2211yescharacteristic
56C4×C4⋊Dic11C2212yes—
57#10622546C2214yes—
58C4×Dic11⋊C4C2214yes—
59#10622541C2212yes—
60#10622541C2212yes—
61#10622541C2212yes—
62#10622541C2212yes—
63#10622289C2214yes—
64#10622288C2214yes—
65#10622288C2214yes—
66#10622288C2214yes—
67#10622285C2214yes—
68#10622285C2214yes—
69#10622273C2214yes—
70#10622270C2214yes—
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C22×C22⋊D11C2314yes—
75C22×D44C2312yes—
76C22×D44C2314yes—
77C22×C4×D11C2314yes—
78C11×#117—24no—
79C11×#117—24no—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C22⋊C4C2312yes—
83C2×C11×C22⋊C4C2312yes—
84C2×C42×C11—24no—
85C2×C42×C11C2312yes—
86C2×C42×C11C2312yes—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2312yes—
94C2×C42×C11C2312yes—
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C22⋊Dic11C2314yes—
98#66983—28no—
99C4×C22⋊D11—48no—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2314yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2314yes—
105C2×(C2×D11)⋊C4C2314yes—
106C2×(C2×D11)⋊C4C2314yes—
107C2×(C2×D11)⋊C4C2314yes—
108C2×(C2×D11)⋊C4C2314yes—
109C2×(C2×D11)⋊C4C2314yes—
110C2×C4⋊Dic11C2312yes—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2312yes—
113C2×C4⋊Dic11C2314yes—
114C2×Dic11⋊C4C2314yes—
115C2×Dic11⋊C4C2314yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2314yes—
119C2×C4×Dic11C2314yes—
120#66927—24no—
121C4×D44—28no—
122C4×D44—48no—
123#66925—48no—
124#66923—24no—
125C11×#95C2312yes—
126C11×#95C2312yes—
127C11×#95C2312yes—
128C11×#95C2312yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136#34621—111nomaximal, Sylow
137C24×C11C2411yescharacteristic
138C23×D11C2414yes—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—42no—
145C22×C4×C11#4114yes—
146C22×C4×C11C2411yescharacteristic
147C22×C4×C11C2412yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×C4×C11C2412yes—
154C22×C4×C11C2411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—28no—
157C2×C22⋊D11—44no—
158C2×C22⋊D11—44no—
159C22×Dic11C2414yes—
160C22×Dic11C2414yes—
161C22×Dic11C2414yes—
162C2×D44—24no—
163C2×D44—28no—
164C2×D44—24no—
165C2×D44—24no—
166C2×D44—44no—
167C2×D44—44no—
168C2×C4×D11—28no—
169C2×C4×D11—28no—
170C2×C4×D11—28no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11—22no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11—24no—
182C42×C11—24no—
183C42×C11—42no—
184C42×C11—42no—
185C42×C11#4114yes—
186C42×C11#4114yes—
187C22⋊Dic11—44no—
188(C2×D11)⋊C4—28no—
189(C2×D11)⋊C4—28no—
190(C2×D11)⋊C4—44no—
191(C2×D11)⋊C4—44no—
192(C2×D11)⋊C4—44no—
193(C2×D11)⋊C4—44no—
194(C2×D11)⋊C4—44no—
195(C2×D11)⋊C4—44no—
196(C2×D11)⋊C4—44no—
197(C2×D11)⋊C4—44no—
198C4⋊Dic11—24no—
199C4⋊Dic11—24no—
200C4⋊Dic11—24no—
201C4⋊Dic11—44no—
202Dic11⋊C4—28no—
203Dic11⋊C4—44no—
204Dic11⋊C4—44no—
205Dic11⋊C4—44no—
206Dic11⋊C4—44no—
207C4×Dic11—28no—
208#2651—114no—
209#2648—114no—
210#2647—111no—
211#2644—112no—
212#2641—111no—
213#2629—111no—
214#2624—112no—
215#2619—111no—
216#2395—114no—
217#2392—114no—
218C4×#127—111no—
219C4×#125—111no—
220C4×#121—112no—
221#2293—112no—
222C4×#117D1111yescharacteristic, complemented
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11C2×#4112yes—
228C23×C11C2511yescharacteristic
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—24no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—28no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—44no—
256C2×C4×C11—44no—
257C2×C4×C11C2×#4114yes—
258C2×C4×C11C2×#4112yes—
259C2×C4×C11C2×#4112yes—
260C2×C4×C11C2×#4112yes—
261C2×C4×C11C2×#4112yes—
262C2×C4×C11C2×#4112yes—
263C2×C4×C11C2×#4112yes—
264C2×C4×C11H(5,𝔽2)14yes—
265C22⋊D11—416no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275D44—416no—
276D44—48no—
277C4×D11—416no—
278C2×#127—111no—
279C2×#125—111no—
280C2×#121—112no—
281C2×C4×D4—114no—
282C2×C4×D4—112no—
283C2×C4×D4—114no—
284C2×#117—114no—
285C2×#117C2×D1111yescharacteristic
286C2×#117C2×D1111yescharacteristic
287C22×C42C2×D1111yescharacteristic
288#400—114no—
289#399—114no—
290#398—114no—
291#398—114no—
292#397—114no—
293#397—114no—
294#397—114no—
295#397—114no—
296#396—114no—
297#396—114no—
298#394—114no—
299#394—114no—
300#394—114no—
301#394—114no—
302#394—114no—
303#392—114no—
304#390—112no—
305#390—114no—
306#390—112no—
307#390—112no—
308#390—112no—
309#389—112no—
310#389—112no—
311#389—112no—
312#389—112no—
313#388—114no—
314#388—114no—
315#388—114no—
316#387—114no—
317#386—114no—
318#384—111no—
319#382—111no—
320#380—112no—
321C4×C4⋊C4—114no—
322C4×C4⋊C4—112no—
323C4×C4⋊C4C2×D1112yes—
324C4×C4⋊C4C2×D1112yes—
325C4×C22⋊C4—114no—
326C4×C22⋊C4—114no—
327C4×C22⋊C4C2×D1112yes—
328C4×C22⋊C4C2×D1112yes—
329#376C2×D1111yescharacteristic
330#376C2×D1111yescharacteristic
331C43C2×D1111yescharacteristic
332C43C2×D1111yescharacteristic
333C22×C11—22no—
334C22×C11—24no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—42no—
338C22×C11C22×#4111yescharacteristic
339C22×C11C22×#4111yescharacteristic
340C22×C11C22×#4111yescharacteristic
341C22×C11C2×H(5,𝔽2)12yes—
342C22×C11#58512yes—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—44no—
347C2×D11—44no—
348C2×D11—44no—
349C2×D11—44no—
350C4×C11—22no—
351C4×C11—22no—
352C4×C11—24no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—42no—
357C4×C11—42no—
358C4×C11#52914yes—
359C4×C11#54014yes—
360Dic11—44no—
361Dic11—44no—
362Dic11—44no—
363C22×D4—114no—
364C22×D4—112no—
365C22×D4—114no—
366C23×C4—114no—
367C23×C4C22×D1111yescharacteristic
368C23×C4C22×D1111yescharacteristic
369C23×C4C22×D1111yescharacteristic
370#127—224no—
371#125—224no—
372#121—228no—
373C4×D4—228no—
374C4×D4—448no—
375C4×D4—448no—
376#117—24no—
377#117—24no—
378#117—448no—
379C2×C4⋊C4—112no—
380C2×C4⋊C4—112no—
381C2×C4⋊C4—112no—
382C2×C4⋊C4—114no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—114no—
385C2×C4⋊C4—114no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4C22×D1112yes—
389C2×C4⋊C4C22×D1112yes—
390C2×C22⋊C4—114no—
391C2×C22⋊C4—114no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—114no—
397C2×C22⋊C4—114no—
398C2×C22⋊C4—114no—
399C2×C22⋊C4—114no—
400C2×C22⋊C4—114no—
401C2×C22⋊C4C22×D1112yes—
402C2×C22⋊C4C22×D1112yes—
403C2×C42—24no—
404C2×C42—114no—
405C2×C42C22×D1111yescharacteristic
406C2×C42C22×D1111yescharacteristic
407C2×C42C22×D1111yescharacteristic
408C2×C42C22×D1111yescharacteristic
409C2×C42C22×D1111yescharacteristic
410C2×C42C22×D1112yes—
411C2×C42C22×D1112yes—
412C2×C42C22×D1111yescharacteristic
413C2×C42C22×D1112yes—
414C2×C42C22×D1112yes—
415C2×C42C22×D1111yescharacteristic
416C2×C42C22×D1111yescharacteristic
417#95—114no—
418#95—114no—
419#95—114no—
420#95—114no—
421#95—114no—
422#95—114no—
423#95—114no—
424#95C22×D1112yes—
425#95C22×D1112yes—
426#95C22×D1112yes—
427#95C22×D1112yes—
428C2×C11—42no—
429C2×C11C2×#52911yescharacteristic
430C2×C11C2×#54011yescharacteristic
431C2×C11#345511yescharacteristic
432C2×C11#346012yes—
433C2×C11#346012yes—
434D11—84no—
435C24—114no—
436C24C23×D1111yescharacteristic
437C2×D4—228no—
438C2×D4—224no—
439C2×D4—224no—
440C2×D4—228no—
441C2×D4—224no—
442C2×D4—444no—
443C2×D4—444no—
444C2×D4—444no—
445C2×D4—444no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—42no—
452C22×C4—114no—
453C22×C4—114no—
454C22×C4—114no—
455C22×C4—228no—
456C22×C4—228no—
457C22×C4—228no—
458C22×C4#433914yes—
459C22×C4C23×D1111yescharacteristic
460C22×C4C23×D1112yes—
461C22×C4C23×D1112yes—
462C22×C4C23×D1112yes—
463C22×C4C23×D1111yescharacteristic
464C22×C4C23×D1111yescharacteristic
465C22×C4C23×D1111yescharacteristic
466C22×C4C23×D1112yes—
467C22×C4C23×D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469C4⋊C4—24no—
470C4⋊C4—24no—
471C4⋊C4—224no—
472C4⋊C4—224no—
473C4⋊C4—228no—
474C4⋊C4—224no—
475C4⋊C4—444no—
476C4⋊C4—444no—
477C4⋊C4—444no—
478C4⋊C4—444no—
479C4⋊C4—444no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—228no—
483C22⋊C4—228no—
484C22⋊C4—444no—
485C22⋊C4—444no—
486C22⋊C4—444no—
487C22⋊C4—444no—
488C22⋊C4—444no—
489C22⋊C4—444no—
490C22⋊C4—444no—
491C22⋊C4—444no—
492C22⋊C4—444no—
493C42—22no—
494C42—22no—
495C42—22no—
496C42—22no—
497C42—22no—
498C42—22no—
499C42—24no—
500C42—24no—
501C42—42no—
502C42—42no—
503C42—228no—
504C42#433914yes—
505C42#433914yes—
506C11#3462111yescharacteristic, complemented, Sylow
507C23—21no—
508C23—21no—
509C23—22no—
510C23—22no—
511C23—224no—
512C23—224no—
513C23—224no—
514C23—224no—
515C23—224no—
516C23—224no—
517C23—224no—
518C23C2×#433912yes—
519C23C24×D1111yescharacteristic
520D4—4416no—
521D4—4416no—
522D4—448no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—28no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—224no—
545C2×C4—224no—
546C2×C4—224no—
547C2×C4—224no—
548C2×C4—224no—
549C2×C4—224no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—4416no—
554C2×C4C2×#433912yes—
555C2×C4C2×#433914yes—
556C2×C4C2×#433912yes—
557C2×C4C2×#433912yes—
558C2×C4C2×#433912yes—
559C2×C4C2×#433912yes—
560C2×C4C2×#433912yes—
561C2×C4#6704214yes—
562C22—22no—
563C22—24no—
564C22—41no—
565C22—41no—
566C22—42no—
567C22—444no—
568C22—444no—
569C22—444no—
570C22—444no—
571C22—444no—
572C22—444no—
573C22—444no—
574C22C22×#433911yescharacteristic
575C22C22×#433911yescharacteristic
576C22C22×#433911yescharacteristic
577C22C2×#6704212yes—
578C22#1062345312yes—
579C4—22no—
580C4—22no—
581C4—24no—
582C4—41no—
583C4—41no—
584C4—42no—
585C4—42no—
586C4—42no—
587C4—444no—
588C4—444no—
589C4—444no—
590C4#1062301014yes—
591C4#1062306614yes—
592C2—42no—
593C2—884no—
594C2C2×#1062301011yescharacteristic
595C2C2×#1062306611yescharacteristic
596C2#1308200611yescharacteristic
597C2#1308203212yes—
598C2#1308203212yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#117C2
prime radical#13074366C2
hypercenterC4×#117D11
hypocenterC11#34621
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
1. #13074643C2semidirect
2. #13074598C2semidirect
3. #13074591C2semidirect
4. #13074576C2semidirect
5. #13074559C2semidirect
6. #13074446C2semidirect
7. #13074405C2semidirect
9. #13071879C2semidirect
10. #13071860C2semidirect
11. C4×#66927C2semidirect
12. C4×#66923C2semidirect
13. C4×#66983C2semidirect
14. #13071080C2semidirect
15. C4×C11×#117C2semidirect
222. C4×#117D11semidirect
506. C11#34621semidirect

Maximal subgroups

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

subgroupindex
#130746432
#130745982
#130745912
#130745762
#130745592
#130744462
#130744052
#130743662
#130718792
#130718602
C4×#669272
C4×#669232
C4×#669832
#130710802
C4×C11×#1172
#3462111