Finite Group Databasebeta

← #14680550

Subgroups — #14680550

Order 2816.

1634 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic22C211yesmaximal, characteristic
2C2×#10622592C211yesmaximal, characteristic
3C2×#10622591C212yesmaximal
4#13066886C211yesmaximal, characteristic
5#13066874C212yesmaximal
6#13066872C211yesmaximal, characteristic
7#13066869C211yesmaximal, characteristic
8#13066867C212yesmaximal
9#13066843C211yesmaximal, characteristic
10#13066840C212yesmaximal
11C2×C11×#387C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×Dic11⋊C4C2212yes—
18C22×Dic11⋊C4C2212yes—
19C22×C4×Dic11C2212yes—
20C2×C4×Dic22—24no—
21C2×C4×Dic22—28no—
22C11×#387—24no—
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38#10622592C418yescomplemented
39#10622591—28no—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C23×Dic11C2312yes—
51C22×Dic22—22no—
52C22×Dic22—22no—
53C22×Dic22—24no—
54C22×Dic22—24no—
55C22×Dic22C2×C414yes—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—24no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4C2×C414yes—
61C2×C42×C11—24no—
62C2×C42×C11D414yes—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—24no—
65C2×Dic11⋊C4—24no—
66C2×Dic11⋊C4—24no—
67C2×Dic11⋊C4—24no—
68C2×Dic11⋊C4—24no—
69C2×Dic11⋊C4—24no—
70C2×Dic11⋊C4C2×C418yes—
71C2×C4×Dic11—24no—
72C2×C4×Dic11—24no—
73C2×C4×Dic11D418yes—
74C4×Dic22—232no—
75C11×#95—22no—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—22no—
79C11⋊#95—24no—
80C11⋊#95—22no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95—42no—
88C11⋊#95C2×C414yes—
89C11⋊#95C2×C418yes—
90#14302—111nomaximal, Sylow
91C24×C11C2411yescharacteristic
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D414yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11#4112yes—
129C22×Dic11—22no—
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×Dic11C2×D414yes—
155C22×Dic11C2×D414yes—
156C22×Dic11#4114yes—
157C2×Dic22—28no—
158C2×Dic22—28no—
159C2×Dic22—216no—
160C2×Dic22—216no—
161C2×Dic22—28no—
162C11×C4⋊C4—28no—
163C11×C4⋊C4—44no—
164C42×C11—28no—
165C4⋊Dic11—28no—
166Dic11⋊C4—216no—
167Dic11⋊C4—216no—
168C4×Dic11—216no—
169C22×C4×Q8—111no—
170C2×#395—111no—
171C2×#387—112no—
172C2×#387D1111yescharacteristic
173#1446—111no—
174#1442—111no—
175#1442—112no—
176#1441—112no—
177#1441—111no—
178#1434—111no—
179#1434—112no—
180C23×C11C23×C411yescharacteristic
181C23×C11C22×D412yes—
182C23×C11C22×D411yescharacteristic
183C23×C11C2×#4111yescharacteristic
184C23×C11C2×#4112yes—
185C23×C11H(5,𝔽2)11yescharacteristic
186C23×C112−1+412yes—
187C23×C112−1+412yes—
188C23×C112−1+411yescharacteristic
189C23×C112−1+411yescharacteristic
190C23×C112−1+411yescharacteristic
191C2×C4×C11—24no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—24no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—22no—
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—41no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11C4×D414yes—
227C2×C4×C11#12014yes—
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—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
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—
256Dic22—232no—
257C23×Q8—111no—
258C2×C4×Q8—228no—
259C2×C4×Q8—224no—
260C22×C4⋊C4—112no—
261C22×C4⋊C4—112no—
262C22×C4⋊C4—111no—
263C22×C4⋊C4C2×D1111yescharacteristic
264C22×C4⋊C4C2×D1111yescharacteristic
265C22×C42—112no—
266C22×C42C2×D1111yescharacteristic
267#395—118no—
268#387—24no—
269#387—228no—
270C2×#95—112no—
271C2×#95—111no—
272C2×#95—112no—
273C2×#95—112no—
274C2×#95—111no—
275C2×#95—112no—
276C2×#95—112no—
277C2×#95—112no—
278C2×#95—112no—
279C2×#95—112no—
280C2×#95—112no—
281C2×#95C2×D1111yescharacteristic
282C2×#95C2×D1111yescharacteristic
283C2×#95C2×D1111yescharacteristic
284C2×#95C2×D1111yescharacteristic
285C22×C11C2×C4×D411yescharacteristic
286C22×C11C2×C4×D412yes—
287C22×C11#51911yescharacteristic
288C22×C11#51912yes—
289C22×C11#52011yescharacteristic
290C22×C11C2×#12011yescharacteristic
291C22×C11#52512yes—
292C22×C11#52511yescharacteristic
293C22×C11#53611yescharacteristic
294C22×C11#53611yescharacteristic
295C22×C11#53611yescharacteristic
296C22×C11#53612yes—
297C22×C11#53612yes—
298C22×C11#53612yes—
299C22×C11#53711yescharacteristic
300C22×C11#53712yes—
301C22×C11#54112yes—
302C22×C11#54111yescharacteristic
303C22×C11#54112yes—
304C22×C11#54112yes—
305C22×C11#54112yes—
306C22×C11#54212yes—
307C22×C11#54211yescharacteristic
308C4×C11—24no—
309C4×C11—24no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—81no—
314C4×C11—81no—
315Dic11—28no—
316Dic11—44no—
317Dic11—44no—
318Dic11—82no—
319C22×Q8—114no—
320C22×Q8—224no—
321C22×Q8—224no—
322C22×Q8—222no—
323C22×Q8—222no—
324C23×C4—112no—
325C23×C4—112no—
326C23×C4—112no—
327C23×C4—112no—
328C23×C4C22×D1111yescharacteristic
329C23×C4C22×D1111yescharacteristic
330C23×C4C22×D1111yescharacteristic
331C23×C4C22×D1111yescharacteristic
332C23×C4C22×D1111yescharacteristic
333C23×C4C22×D1111yescharacteristic
334C23×C4C22×D1111yescharacteristic
335C4×Q8—2232no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—118no—
341C2×C4⋊C4—224no—
342C2×C4⋊C4—224no—
343C2×C4⋊C4—224no—
344C2×C4⋊C4—224no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4—224no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4C4×D1114yes—
349C2×C42—24no—
350C2×C42—118no—
351C2×C42—224no—
352C2×C42—224no—
353C2×C42C22⋊D1114yes—
354#95—22no—
355#95—22no—
356#95—22no—
357#95—22no—
358#95—118no—
359#95—114no—
360#95—224no—
361#95—224no—
362#95—224no—
363#95—224no—
364#95—222no—
365#95—224no—
366#95—442no—
367#95—442no—
368#95—442no—
369C2×C11C4×#12011yescharacteristic
370C2×C11#232312yes—
371C2×C11#232311yescharacteristic
372C2×C11#232712yes—
373C2×C11#232711yescharacteristic
374C2×C11#261411yescharacteristic
375C2×C11#261611yescharacteristic
376C2×C11#263411yescharacteristic
377C2×C11#263412yes—
378C2×C11#263711yescharacteristic
379C2×C11#263712yes—
380C24C23×D1111yescharacteristic
381C2×Q8—2216no—
382C2×Q8—228no—
383C2×Q8—2216no—
384C2×Q8—228no—
385C2×Q8—228no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—114no—
416C22×C4—114no—
417C22×C4—114no—
418C22×C4—114no—
419C22×C4—114no—
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×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4C2×C4×D1112yes—
444C22×C4C2×C4×D1112yes—
445C22×C4C2×C4×D1112yes—
446C22×C4#433912yes—
447C22×C4D4×D1114yes—
448C22×C4C2×C22⋊D1112yes—
449C22×C4C2×C22⋊D1112yes—
450C22×C4C2×C22⋊D1112yes—
451C4⋊C4—28no—
452C4⋊C4—44no—
453C4⋊C4—2216no—
454C4⋊C4—2216no—
455C4⋊C4—228no—
456C42—28no—
457C42—2216no—
458C11#1430211yescharacteristic, complemented, Sylow
459C23C22×C4×D1111yescharacteristic
460C23C2×#433911yescharacteristic
461C23C2×D4×D1112yes—
462C23#6704012yes—
463C23#41×D1112yes—
464C23#6704211yescharacteristic
465C23#6704311yescharacteristic
466C23#6704312yes—
467C23#6704311yescharacteristic
468C23#6704311yescharacteristic
469C23C22×C22⋊D1111yescharacteristic
470Q8—2232no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—118no—
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—224no—
517C2×C4—224no—
518C2×C4—224no—
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×C4—442no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4C4×C22⋊D1114yes—
535C2×C4#6699014yes—
536C22#1062304711yescharacteristic
537C22#1062304911yescharacteristic
538C22#1062305411yescharacteristic
539C22#1062306511yescharacteristic
540C22C4×D4×D1112yes—
541C22#1062307812yes—
542C22#1062310312yes—
543C22#1062311412yes—
544C22#1062315912yes—
545C22#1062316012yes—
546C22#1062317912yes—
547C22#1062317912yes—
548C22#1062322712yes—
549C22#1062322712yes—
550C22#1062323212yes—
551C22#1062324112yes—
552C22C2×C4×C22⋊D1111yescharacteristic
553C22C2×#6699011yescharacteristic
554C22#1062334711yescharacteristic
555C22#1062335611yescharacteristic
556C22#1062335611yescharacteristic
557C22#1062335911yescharacteristic
558C22#1062336411yescharacteristic
559C4—24no—
560C4—24no—
561C4—42no—
562C4—42no—
563C4—42no—
564C4—81no—
565C4—81no—
566C4—228no—
567C4—444no—
568C4—444no—
569C4—882no—
570C2C4×#6699011yescharacteristic
571C2#1307129712yes—
572C2#1307129811yescharacteristic
573C2#1307133112yes—
574C2#1307133211yescharacteristic
575C2#1307433711yescharacteristic
576C2#1307434611yescharacteristic
577C2#1307449311yescharacteristic
578C2#1307449612yes—
579C2#1307452411yescharacteristic
580C2#1307453012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#387C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#387D11
hypocenterC11#14302
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
38. #10622592C4semidirect
458. C11#14302semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic222
C2×#106225922
C2×#106225912
#130668862
#130668742
#130668722
#130668692
#130668672
#130668432
#130668402
C2×C11×#3872
#1430211