Finite Group Databasebeta

← #14772016

Subgroups — #14772016

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622451C211yesmaximal, characteristic
2C2×#10622494C211yesmaximal, characteristic, complemented
3C2×#10622474C211yesmaximal, characteristic, complemented
4#13071548C211yesmaximal, characteristic
5#13071542C211yesmaximal, characteristic
6#13069386C211yesmaximal, characteristic, complemented
7#13068818C211yesmaximal, characteristic, complemented
8#13068812C211yesmaximal, characteristic, complemented
9#13068810C211yesmaximal, characteristic, complemented
10#13068807C211yesmaximal, characteristic, complemented
11#13068778C211yesmaximal, characteristic, complemented
12#13068648C211yesmaximal, characteristic, complemented
13#13068648C211yesmaximal, characteristic, complemented
14C4×#66872C211yesmaximal, characteristic, complemented
15C11×#1949C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#382C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32#10622600C2211yescharacteristic
33#10622600C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622553—21no—
43C4×(C2×D11)⋊C4—21no—
44#10622549C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622494—24no—
48#10622474—24no—
49#10622451C418yescomplemented
50#10622282—21no—
51#10622279—21no—
52#10622278—21no—
53#10622278—21no—
54#10622267—21no—
55#10622266—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D44D411yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11C2311yescharacteristic
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×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4D411yescharacteristic
82C2×(C2×D11)⋊C4D411yescharacteristic
83C2×C4⋊Dic11D411yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C2×#4313—22no—
96C2×#4313—22no—
97C2×#4313—22no—
98C2×#4313—22no—
99C2×#4313C2×C414yescomplemented
100C2×#4313C2×C414yescomplemented
101#66945—22no—
102#66945—22no—
103#66945—41no—
104#66945—41no—
105C4⋊C4×D11—22no—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—41no—
108C4⋊C4×D11—41no—
109C4×D44C2×C414yes—
110C4×D44Q814yes—
111C11×#107—22no—
112C11×#106—22no—
113C11×C4⋊C8C2×C414yescomplemented
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(C2×D11)⋊C8C2×C414yescomplemented
125(C2×D11)⋊C8C2×C414yescomplemented
126#66882—22no—
127#66881—22no—
128#66872—22no—
129#66872—41no—
130#66872—41no—
131#66872D414yescomplemented
132#66871—22no—
133#66871—22no—
134C4×C11⋊C8C2×C414yescomplemented
135#22666—111nomaximal, Sylow
136C23×D11C2×D411yescharacteristic
137C23×D11C2×D411yescharacteristic
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C2×D44—41no—
152C2×D44—41no—
153C2×D44C4⋊C414yes—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—81no—
167C2×C4×D11—81no—
168C2×C4×D11C22×C412yes—
169C2×C4×D11C22×C412yes—
170C2×C4×D11C2×Q812yes—
171C2×C4×D11C2×Q812yes—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11C22×C412yes—
177C2×C8×C11C22×C412yes—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4C2×D412yes—
186C42×C11—81no—
187C42×C11C22×C412yes—
188C42×C11C2×Q812yes—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—81no—
194(C2×D11)⋊C4—81no—
195(C2×D11)⋊C4C4⋊C414yes—
196(C2×D11)⋊C4C4⋊C414yes—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11C4⋊C414yes—
205C4⋊Dic11C2×D412yes—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C4×Dic11—81no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8C22×C412yes—
214C2×C11⋊C8C22×C412yes—
215C2×C11⋊C8C2×D412yes—
216C2×C11⋊C8#4112yes—
217#4313—28no—
218#4313—28no—
219C2×#436—111no—
220C2×#428—111no—
221C2×#428—111no—
222#2352—111no—
223#2352—111no—
224#1949—111no—
225#1949D1111yescharacteristic, complemented
226#1854—111no—
227#1854—111no—
228#1853—111no—
229#1853—111no—
230#1846—111no—
231#1809—111no—
232#1809—111no—
233C4×#106—111no—
234C23×C11C22×D411yescharacteristic
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11C2×C4⋊C412yes—
248C22×D11C2×C4⋊C412yes—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11C2×C4⋊C412yes—
266C2×C4×C11C2×C4⋊C412yes—
267C2×C4×C11C23×C411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×Q811yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×C4×C112−1+411yescharacteristic
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—22no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11C2×C4⋊C412yes—
290C2×Dic11C2×C4⋊C412yes—
291D44—44no—
292C4×D11—22no—
293C4×D11—22no—
294C4×D11—22no—
295C4×D11—22no—
296C4×D11—22no—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—22no—
300C4×D11—84no—
301C4×D11—84no—
302C8×C11—22no—
303C8×C11—22no—
304C11⋊C8—22no—
305C11⋊C8C4×D414yes—
306C22×M16—111no—
307C22×M16—111no—
308C2×C4×D4—111no—
309C2×#117—111no—
310C2×#117—111no—
311C22×C4⋊C4—111no—
312C22×C4⋊C4—111no—
313#436—118no—
314#428—224no—
315#428—224no—
316C2×#107—111no—
317C2×#107—111no—
318C2×#107—111no—
319C2×#107C2×D1111yescharacteristic
320C2×#106—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×#106—111no—
324C2×#106—111no—
325C2×#106C2×D1111yescharacteristic
326C2×C4⋊C8C2×D1111yescharacteristic
327C2×C22⋊C8—111no—
328C2×C22⋊C8—111no—
329C2×C4×C8—111no—
330#388—221no—
331#388—221no—
332#387—221no—
333#387—221no—
334#386—221no—
335#386—221no—
336#382—111no—
337#382C2×D1111yescharacteristic
338#380—111no—
339#380—111no—
340#380—111no—
341#380—111no—
342C4×C4⋊C4—111no—
343C4×C4⋊C4C2×D1111yescharacteristic
344C4×C22⋊C4—221no—
345C4×C22⋊C4—221no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340C2×D1111yescharacteristic
351#340C2×D1111yescharacteristic
352C22×C11C22×C4⋊C411yescharacteristic
353C22×C11D4211yescharacteristic
354C22×C11#54711yescharacteristic
355C22×C11#57511yescharacteristic
356C22×C11#57511yescharacteristic
357C22×C11#57711yescharacteristic
358C22×C11#57711yescharacteristic
359C2×D11—22no—
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—22no—
364C2×D11—22no—
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—41no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C4×C11—22no—
374C4×C11—22no—
375C4×C11—42no—
376C4×C11—81no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11C2×C4×D411yescharacteristic
380C4×C11#52011yescharacteristic
381C4×C11D4×Q811yescharacteristic
382C4×C11#55411yescharacteristic
383Dic11—22no—
384Dic11—22no—
385Dic11—42no—
386Dic11—81no—
387Dic11—81no—
388Dic11—81no—
389C22×D4—111no—
390C23×C4—111no—
391C23×C4—111no—
392C23×C4—221no—
393C23×C4—221no—
394C2×M16—114no—
395C2×M16—114no—
396C2×M16—222no—
397C2×M16—222no—
398C2×M16—222no—
399C2×M16—222no—
400C22×C8—111no—
401C22×C8—111no—
402C22×C8C22×D1111yescharacteristic
403C22×C8C22×D1111yescharacteristic
404C4×D4—114no—
405C4×D4—114no—
406#117—222no—
407#117—222no—
408#117—441no—
409#117—441no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—222no—
416C2×C4⋊C4—222no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—441no—
420C2×C4⋊C4—441no—
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C22⋊C4—111no—
426C2×C22⋊C4—111no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C42—21no—
434C2×C42—221no—
435C2×C42—221no—
436C2×C42—221no—
437C2×C42C22×D1111yescharacteristic
438#107—22no—
439#107—222no—
440#107—222no—
441#107—222no—
442#106—22no—
443#106—114no—
444#106—222no—
445#106—222no—
446#106—441no—
447#106—441no—
448C4⋊C8C4×D1114yescomplemented
449C22⋊C8—114no—
450C22⋊C8—114no—
451C4×C8—114no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462C2×C11D4×C4⋊C411yescharacteristic
463C2×C11#291111yescharacteristic
464C2×C11#291211yescharacteristic
465C2×C11#327511yescharacteristic
466C2×C11#327511yescharacteristic
467C2×C11#335111yescharacteristic
468C2×C11#335111yescharacteristic
469D11—42no—
470D11—42no—
471C24—111no—
472C24—111no—
473C2×D4—114no—
474C2×D4—441no—
475C2×D4—441no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—112no—
483C22×C4—112no—
484C22×C4—112no—
485C22×C4—112no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—442no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—881no—
503C22×C4—881no—
504C22×C4D4×D1111yescharacteristic
505C22×C4D4×D1111yescharacteristic
506C22×C4C23×D1111yescharacteristic
507M16—228no—
508M16—228no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—112no—
514C2×C8—112no—
515C2×C8—112no—
516C2×C8—112no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8C2×C4×D1112yes—
520C2×C8C2×C4×D1112yes—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—114no—
529C4⋊C4—112no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—442no—
538C4⋊C4—442no—
539C4⋊C4D4×D1112yes—
540C22⋊C4—114no—
541C22⋊C4—114no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—442no—
545C22⋊C4—442no—
546C22⋊C4—881no—
547C22⋊C4—881no—
548C42—81no—
549C42—442no—
550C42—442no—
551C42—881no—
552C42C2×C4×D1112yes—
553C42Q8×D1112yes—
554C11#2266611yescharacteristic, complemented, Sylow
555C23—112no—
556C23—112no—
557C23—221no—
558C23—221no—
559C23—221no—
560C23—221no—
561C23—221no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23C2×D4×D1111yescharacteristic
570D4—444no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—112no—
588C2×C4—112no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—884no—
614C2×C4—884no—
615C2×C4C4⋊C4×D1112yes—
616C2×C4C4⋊C4×D1112yes—
617C2×C4C22×C4×D1111yescharacteristic
618C2×C4C2×D4×D1111yescharacteristic
619C2×C4C2×Q8×D1111yescharacteristic
620C2×C4#6704011yescharacteristic
621C2×C4#41×D1111yescharacteristic
622C2×C4#6704211yescharacteristic
623C8—22no—
624C8—22no—
625C8—114no—
626C8—222no—
627C22—222no—
628C22—222no—
629C22—222no—
630C22—222no—
631C22—222no—
632C22—222no—
633C22—441no—
634C22—441no—
635C22—441no—
636C22—441no—
637C22—441no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22C2×C4⋊C4×D1111yescharacteristic
642C22#1062314011yescharacteristic
643C22#1062316211yescharacteristic
644C22#1062329911yescharacteristic
645C22#1062329911yescharacteristic
646C22#1062330611yescharacteristic
647C22#1062330911yescharacteristic
648C4—22no—
649C4—22no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4—222no—
655C4—222no—
656C4—442no—
657C4—881no—
658C4—881no—
659C4—881no—
660C4C4×D4×D1111yescharacteristic
661C4#1062310511yescharacteristic
662C4#1062322111yescharacteristic
663C4#1062325811yescharacteristic
664C2—442no—
665C2—442no—
666C2#1307151711yescharacteristic
667C2#1307720411yescharacteristic
668C2#1307721011yescharacteristic
669C2#1308024211yescharacteristic
670C2#1308025311yescharacteristic
671C2#1308117311yescharacteristic
672C2#1308118311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1949C2
socleC23×C11C22×D4
prime radicalC22×D44D4
cosocleC22×C4×C11C24
hypercenter#1949D11
hypocenterC11#22666
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
2. C2×#10622494C2semidirect
3. C2×#10622474C2semidirect
6. #13069386C2semidirect
7. #13068818C2semidirect
8. #13068812C2semidirect
9. #13068810C2semidirect
10. #13068807C2semidirect
11. #13068778C2semidirect
12. #13068648C2semidirect
13. #13068648C2semidirect
14. C4×#66872C2semidirect
15. C11×#1949C2semidirect
49. #10622451C4semidirect
99. C2×#4313C2×C4semidirect
100. C2×#4313C2×C4semidirect
113. C11×C4⋊C8C2×C4semidirect
124. (C2×D11)⋊C8C2×C4semidirect
125. (C2×D11)⋊C8C2×C4semidirect
131. #66872D4semidirect
134. C4×C11⋊C8C2×C4semidirect
225. #1949D11semidirect
448. C4⋊C8C4×D11semidirect
554. C11#22666semidirect

Maximal subgroups

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

subgroupindex
C2×#106224512
C2×#106224942
C2×#106224742
#130715482
#130715422
#130693862
#130688182
#130688122
#130688102
#130688072
#130687782
#130686482
C4×#668722
C11×#19492
#2266611