Finite Group Databasebeta

← #14757254

Subgroups — #14757254

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622494C211yesmaximal, characteristic
2C2×#10622474C211yesmaximal, characteristic
3C2×#10622450C211yesmaximal, characteristic
4D11×#382C211yesmaximal, characteristic
5C4×#66945C211yesmaximal, characteristic
6#13069387C211yesmaximal, characteristic, complemented
7#13069386C211yesmaximal, characteristic, complemented
8#13069385C211yesmaximal, characteristic, complemented
9#13069384C211yesmaximal, characteristic, complemented
10#13069383C211yesmaximal, characteristic, complemented
11#13069382C211yesmaximal, characteristic, complemented
12#13069381C211yesmaximal, characteristic, complemented
13#13068334C211yesmaximal, characteristic
14#13068334C211yesmaximal, characteristic
15C11×#1949C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#382C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32#10622590C2211yescharacteristic
33#10622590C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C4×(C2×D11)⋊C4—21no—
41#10622549C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43C42×Dic11—21no—
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622494—24no—
46#10622474—24no—
47#10622450C418yescomplemented
48#10622279—21no—
49D11×#95—21no—
50D11×#95—21no—
51#10622263—21no—
52#10622263—21no—
53#10622261—21no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11D411yescharacteristic
65C22×C4×D11D411yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11D411yescharacteristic
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C2×#4313—22no—
94C2×#4313—22no—
95C2×#4313—22no—
96C2×#4313—22no—
97C2×#4313C2×C414yes—
98C2×#4313C2×C414yes—
99#66945—22no—
100#66945—22no—
101#66945D414yes—
102#66945Q814yes—
103C4⋊C4×D11—22no—
104C4⋊C4×D11—22no—
105C4⋊C4×D11—22no—
106C4⋊C4×D11—22no—
107C42×D11C2×C414yes—
108C42×D11Q814yes—
109C11×#107—22no—
110C11×#106—22no—
111C11×C4⋊C8C2×C414yescomplemented
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124#66882—22no—
125#66881—22no—
126Dic11⋊C8C2×C414yescomplemented
127Dic11⋊C8C2×C414yescomplemented
128#66872—22no—
129#66872—22no—
130#66871—22no—
131#66871—22no—
132C4⋊(C11⋊C8)C2×C414yescomplemented
133#21172—111nomaximal, Sylow
134C23×D11C2×D411yescharacteristic
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C2×C4×D11—41no—
150C2×C4×D11—41no—
151C2×C4×D11—41no—
152C2×C4×D11—41no—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×C4×D11C4⋊C414yes—
160C2×C4×D11C4⋊C414yes—
161C2×C4×D11C22×C412yes—
162C2×C4×D11C2×D412yes—
163C2×C4×D11C2×Q812yes—
164C2×C4×D11C2×Q812yes—
165C2×C4×D11#4112yes—
166C2×C4×D11#4112yes—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C22×C412yes—
172C2×C8×C11C22×C412yes—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4C2×D412yes—
180C11×C4⋊C4C2×Q812yes—
181C42×C11—42no—
182C42×C11C22×C412yes—
183C42×C11C2×Q812yes—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—24no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11C2×D412yes—
193C4⋊Dic11C2×Q812yes—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196C4×Dic11—24no—
197C4×Dic11—24no—
198C4×Dic11—42no—
199C4×Dic11—42no—
200C4×Dic11—42no—
201C4×Dic11C4⋊C414yes—
202C4×Dic11C4⋊C414yes—
203C4×Dic11C22×C412yes—
204C4×Dic11C2×Q812yes—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8C22×C412yes—
210C2×C11⋊C8C22×C412yes—
211#4313—28no—
212#4313—28no—
213C2×#428—111no—
214C2×#428—111no—
215C2×#423—111no—
216C2×#382—111no—
217C4×#117—111no—
218#1949—111no—
219#1949—111no—
220#1949—111no—
221#1949—111no—
222#1949—111no—
223#1949—111no—
224#1949—111no—
225#1949D1111yescharacteristic, complemented
226#1736—111no—
227#1736—111no—
228C23×C11C22×D411yescharacteristic
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11C2×C4⋊C412yes—
234C22×D11#12112yes—
235C22×D11C22⋊Q812yes—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11C2×C4⋊C412yes—
253C2×C4×C11C2×C4⋊C412yes—
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×Q811yescharacteristic
257C2×C4×C11C22×Q811yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11C2×C4⋊C412yes—
277C2×Dic11C2×C4⋊C412yes—
278C2×Dic11C2×C4⋊C412yes—
279C2×Dic11#12112yes—
280C2×Dic11C22⋊Q812yes—
281C4×D11—44no—
282C4×D11—44no—
283C4×D11—84no—
284C4×D11—84no—
285C4×D11C4×D414yes—
286C4×D11C4×Q814yes—
287C4×D11#12514yes—
288C4×D11C4⋊Q814yes—
289C8×C11—22no—
290C8×C11—22no—
291C11⋊C8—22no—
292C11⋊C8—22no—
293C22×M16—111no—
294C22×M16—111no—
295C2×#117—111no—
296C2×#117—111no—
297C22×C4⋊C4—111no—
298C22×C4⋊C4—111no—
299C22×C42—111no—
300#428—224no—
301#428—224no—
302C2×#107—111no—
303C2×#107—111no—
304C2×#107—111no—
305C2×#107C2×D1111yescharacteristic
306C2×#106—111no—
307C2×#106—111no—
308C2×#106—111no—
309C2×#106C2×D1111yescharacteristic
310#423—118no—
311C2×C4⋊C8—111no—
312C2×C4⋊C8—111no—
313C2×C4⋊C8—111no—
314C2×C4⋊C8C2×D1111yescharacteristic
315#382—111no—
316#382—111no—
317#382—111no—
318#382—221no—
319#382—221no—
320#382C2×D1111yescharacteristic
321C4×C4⋊C4—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4C2×D1111yescharacteristic
325C4×C22⋊C4—221no—
326C4×C22⋊C4—221no—
327#376—221no—
328C2×#95—221no—
329C2×#95—221no—
330C43—221no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340C2×D1111yescharacteristic
338#340C2×D1111yescharacteristic
339C22×C11C22×C4⋊C411yescharacteristic
340C22×C11C2×#12111yescharacteristic
341C22×C11C2×C22⋊Q811yescharacteristic
342C22×C11#57511yescharacteristic
343C22×C11#57511yescharacteristic
344C22×C11#57511yescharacteristic
345C22×C11#57511yescharacteristic
346C2×D11—22no—
347C2×D11—22no—
348C2×D11—22no—
349C2×D11—22no—
350C2×D11—22no—
351C2×D11—22no—
352C2×D11#38914yes—
353C4×C11—22no—
354C4×C11—22no—
355C4×C11—42no—
356C4×C11—42no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11C2×C4×D411yescharacteristic
360C4×C11C2×C4×Q811yescharacteristic
361C4×C11C2×#12511yescharacteristic
362C4×C11C2×C4⋊Q811yescharacteristic
363Dic11—22no—
364Dic11—22no—
365Dic11—42no—
366Dic11—42no—
367Dic11—81no—
368Dic11—81no—
369Dic11#38914yes—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—111no—
373C23×C4—221no—
374C23×C4—221no—
375C2×M16—114no—
376C2×M16—114no—
377C2×M16—222no—
378C2×M16—222no—
379C2×M16—222no—
380C2×M16—222no—
381C22×C8—111no—
382C22×C8—111no—
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385#117—114no—
386#117—114no—
387#117—222no—
388#117—222no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C22⋊C4—221no—
404C2×C22⋊C4—221no—
405C2×C42—21no—
406C2×C42—111no—
407C2×C42—111no—
408C2×C42—111no—
409C2×C42—114no—
410C2×C42—114no—
411C2×C42—221no—
412C2×C42—221no—
413C2×C42—221no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417#107—22no—
418#107—222no—
419#107—222no—
420#107—222no—
421#106—22no—
422#106—222no—
423#106—222no—
424#106—222no—
425C4⋊C8—114no—
426C4⋊C8—114no—
427C4⋊C8—114no—
428C4⋊C8C4×D1114yescomplemented
429#95—21no—
430#95—21no—
431#95—21no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441C2×C11C2×#38911yescharacteristic
442C2×C11#291111yescharacteristic
443C2×C11#291111yescharacteristic
444C2×C11#304011yescharacteristic
445C2×C11#304011yescharacteristic
446C2×C11#308011yescharacteristic
447C2×C11#308011yescharacteristic
448D11—24no—
449C24—111no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—111no—
455C22×C4—112no—
456C22×C4—112no—
457C22×C4—112no—
458C22×C4—112no—
459C22×C4—112no—
460C22×C4—112no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—114no—
464C22×C4—114no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—441no—
470C22×C4—441no—
471C22×C4—441no—
472C22×C4—441no—
473C22×C4—442no—
474C22×C4—442no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4—442no—
479C22×C4D4×D1111yescharacteristic
480C22×C4D4×D1111yescharacteristic
481C22×C4C23×D1111yescharacteristic
482M16—228no—
483M16—228no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—112no—
489C2×C8—112no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8C2×C4×D1112yes—
495C2×C8C2×C4×D1112yes—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—112no—
503C4⋊C4—112no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—442no—
511C4⋊C4—442no—
512C4⋊C4D4×D1112yes—
513C4⋊C4Q8×D1112yes—
514C22⋊C4—224no—
515C22⋊C4—224no—
516C42—42no—
517C42—114no—
518C42—114no—
519C42—112no—
520C42—112no—
521C42—224no—
522C42—224no—
523C42—442no—
524C42—442no—
525C42—442no—
526C42C2×C4×D1112yes—
527C42Q8×D1112yes—
528C11#2117211yescharacteristic, complemented, Sylow
529C23—112no—
530C23—112no—
531C23—112no—
532C23—221no—
533C23—221no—
534C23—221no—
535C23—221no—
536C23C2×D4×D1111yescharacteristic
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—112no—
554C2×C4—112no—
555C2×C4—112no—
556C2×C4—114no—
557C2×C4—114no—
558C2×C4—114no—
559C2×C4—114no—
560C2×C4—112no—
561C2×C4—112no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—444no—
569C2×C4—444no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—884no—
581C2×C4—884no—
582C2×C4C4⋊C4×D1112yes—
583C2×C4C4⋊C4×D1112yes—
584C2×C4C22×C4×D1111yescharacteristic
585C2×C4C2×D4×D1111yescharacteristic
586C2×C4C2×Q8×D1111yescharacteristic
587C2×C4C2×Q8×D1111yescharacteristic
588C2×C4#41×D1111yescharacteristic
589C2×C4#41×D1111yescharacteristic
590C8—22no—
591C8—22no—
592C8—222no—
593C8—222no—
594C22—114no—
595C22—222no—
596C22—222no—
597C22—222no—
598C22—222no—
599C22—222no—
600C22—222no—
601C22C2×C4⋊C4×D1111yescharacteristic
602C22D11×#12111yescharacteristic
603C22D11×C22⋊Q811yescharacteristic
604C22#1062329911yescharacteristic
605C22#1062329911yescharacteristic
606C22#1062330411yescharacteristic
607C22#1062330811yescharacteristic
608C4—22no—
609C4—22no—
610C4—42no—
611C4—42no—
612C4—81no—
613C4—81no—
614C4—114no—
615C4—222no—
616C4—222no—
617C4—442no—
618C4—442no—
619C4—881no—
620C4—881no—
621C4C4×D4×D1111yescharacteristic
622C4C4×Q8×D1111yescharacteristic
623C4D11×#12511yescharacteristic
624C4D11×C4⋊Q811yescharacteristic
625C2—224no—
626C2D11×#38911yescharacteristic
627C2#1307720311yescharacteristic
628C2#1307720411yescharacteristic
629C2#1307810511yescharacteristic
630C2#1307810711yescharacteristic
631C2#1307843311yescharacteristic
632C2#1307843511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1949C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1949D11
hypocenterC11#21172
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
6. #13069387C2semidirect
7. #13069386C2semidirect
8. #13069385C2semidirect
9. #13069384C2semidirect
10. #13069383C2semidirect
11. #13069382C2semidirect
12. #13069381C2semidirect
15. C11×#1949C2semidirect
47. #10622450C4semidirect
111. C11×C4⋊C8C2×C4semidirect
126. Dic11⋊C8C2×C4semidirect
127. Dic11⋊C8C2×C4semidirect
132. C4⋊(C11⋊C8)C2×C4semidirect
225. #1949D11semidirect
428. C4⋊C8C4×D11semidirect
528. C11#21172semidirect

Maximal subgroups

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

subgroupindex
C2×#106224942
C2×#106224742
C2×#106224502
D11×#3822
C4×#669452
#130693872
#130693862
#130693852
#130693842
#130693832
#130693822
#130693812
#130683342
C11×#19492
#2117211