Finite Group Databasebeta

← #14757160

Subgroups — #14757160

Order 2816.

1058 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622494C211yesmaximal, characteristic
2C2×#10622474C211yesmaximal, characteristic
3C2×#10622320C211yesmaximal, characteristic
4#13071097C211yesmaximal, characteristic
5D11×#389C211yesmaximal, characteristic
6#13069359C211yesmaximal, characteristic, complemented
7#13069356C211yesmaximal, characteristic, complemented
8#13069351C211yesmaximal, characteristic, complemented
9#13069350C211yesmaximal, characteristic, complemented
10#13069348C211yesmaximal, characteristic, complemented
11#13069343C211yesmaximal, characteristic, complemented
12#13069342C211yesmaximal, characteristic, complemented
13#13068334C211yesmaximal, characteristic
14#13068334C211yesmaximal, characteristic
15C11×#1943C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11—21no—
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C42×D11C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622602—21no—
34#10622598C2211yescharacteristic
35#10622598C2211yescharacteristic
36C4⋊C4×Dic11—21no—
37#10622586C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622585—21no—
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47#10622494C418yescomplemented
48#10622474—24no—
49#10622320—24no—
50#10622281—21no—
51D11×#95—21no—
52#10622262—21no—
53#10622260—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⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11D411yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×#4313—22no—
98C2×#4313—22no—
99C2×#4313C2×C414yes—
100C2×#4313D414yes—
101C2×#4313Q814yes—
102C2×#4313Q814yes—
103#66945—22no—
104#66945—22no—
105#66945—22no—
106#66945C2×C414yes—
107C4⋊C4×D11—22no—
108C4⋊C4×D11—22no—
109C4⋊C4×D11—22no—
110C4⋊C4×D11—44no—
111C4⋊C4×D11C2×C414yes—
112C42×D11—22no—
113C42×D11—22no—
114C11×#107C2×C414yescomplemented
115C11×#106—22no—
116C11×#97—22no—
117C11×#95—21no—
118C11×#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125#66882—22no—
126#66881C2×C414yescomplemented
127C8×Dic11—22no—
128C8×Dic11—22no—
129#66872—22no—
130#66872C2×C414yescomplemented
131#66871—22no—
132#66871C2×C414yescomplemented
133#66867—22no—
134#21159—111nomaximal, Sylow
135C23×D11C2×D411yescharacteristic
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—24no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—41no—
156C2×C4×D11—41no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11C22×C412yes—
163C2×C4×D11C2×D412yes—
164C2×C4×D11C2×Q812yes—
165C2×C4×D11C2×Q812yes—
166C2×C4×D11#4112yes—
167C2×C4×D11#4112yes—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C22×C412yes—
171C2×C8×C11C2×D412yes—
172C2×C8×C11C2×Q812yes—
173C2×C8×C11C2×Q812yes—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4C22×C412yes—
183C11×C4⋊C4C22×C412yes—
184C42×C11—21no—
185C42×C11—21no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—42no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—42no—
195C4⋊Dic11—42no—
196C4⋊Dic11C22×C412yes—
197C4⋊Dic11C22×C412yes—
198Dic11⋊C4—24no—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204C4×Dic11—24no—
205C4×Dic11—22no—
206C4×Dic11—22no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—42no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C22×C412yes—
213C2×C11⋊C8C2×D412yes—
214C2×C11⋊C8C2×Q812yes—
215C2×C11⋊C8C2×Q812yes—
216#4313—28no—
217#4313C4⋊C4116yescomplemented
218C2×#428—111no—
219C2×#428—111no—
220C2×C4×M16—111no—
221#2296—111no—
222C2×#389—111no—
223#1944—111no—
224#1944—111no—
225#1943—111no—
226#1943D1111yescharacteristic, complemented
227#1942—111no—
228#1942—111no—
229#1941—111no—
230#1941—111no—
231#1736—111no—
232#1736—111no—
233C23×C11C22×D411yescharacteristic
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11C4×D412yes—
239C22×D11#12112yes—
240C22×D11C4⋊Q812yes—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11C23×C411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×Q811yescharacteristic
262C2×C4×C11C22×Q811yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11C4×D412yes—
282C2×Dic11#12112yes—
283C2×Dic11C4⋊Q812yes—
284C2×Dic11AGL(1,ℤ/8)12yes—
285C2×Dic11#13712yes—
286C4×D11—44no—
287C4×D11—44no—
288C4×D11—48no—
289C4×D11—84no—
290C4×D11C2×C4⋊C414yes—
291C4×D11C4×Q814yes—
292C4×D11C22⋊Q814yes—
293C4×D11#12514yes—
294C8×C11—22no—
295C8×C11C2×C4⋊C414yescomplemented
296C11⋊C8—22no—
297C11⋊C8C2×C4⋊C414yescomplemented
298C22×M16—111no—
299C22×M16—111no—
300C2×#117—111no—
301C2×#117—111no—
302C22×C4⋊C4—111no—
303C22×C4⋊C4—111no—
304C22×C4⋊C4—221no—
305C22×C42—111no—
306#428—118no—
307#428—224no—
308C2×#107—111no—
309C2×#107—111no—
310C2×#107—111no—
311C2×#107C2×D1111yescharacteristic
312C2×#106—111no—
313C2×#106—111no—
314C2×#106—111no—
315C2×#106C2×D1111yescharacteristic
316C4×M16—224no—
317C2×#97—111no—
318C2×#97C2×D1111yescharacteristic
319C2×C4×C8—111no—
320C2×C4×C8—111no—
321#389—111no—
322#389—111no—
323#389—111no—
324#389—111no—
325#389—111no—
326#389—111no—
327#389—221no—
328#389—221no—
329#389C2×D1111yescharacteristic
330#389C2×D1111yescharacteristic
331#385—221no—
332#385—221no—
333C4×C4⋊C4—221no—
334C4×C4⋊C4—221no—
335C2×#95—221no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340C2×D1111yescharacteristic
343#340C2×D1111yescharacteristic
344C22×C11C2×C4×D411yescharacteristic
345C22×C11C2×#12111yescharacteristic
346C22×C11C2×C4⋊Q811yescharacteristic
347C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
348C22×C11C2×#13711yescharacteristic
349C22×C11#57511yescharacteristic
350C22×C11#57511yescharacteristic
351C2×D11—22no—
352C2×D11—22no—
353C2×D11—22no—
354C2×D11—22no—
355C2×D11—22no—
356C2×D11—22no—
357C2×D11#38914yes—
358C4×C11—42no—
359C4×C11—42no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—81no—
363C4×C11—81no—
364C4×C11C22×C4⋊C411yescharacteristic
365C4×C11C2×C4×Q811yescharacteristic
366C4×C11C2×C22⋊Q811yescharacteristic
367C4×C11C2×#12511yescharacteristic
368Dic11—22no—
369Dic11—22no—
370Dic11—42no—
371Dic11—42no—
372Dic11—81no—
373Dic11—81no—
374Dic11#38914yes—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—221no—
379C23×C4—221no—
380C2×M16—114no—
381C2×M16—114no—
382C2×M16—114no—
383C2×M16—114no—
384C2×M16—222no—
385C2×M16—222no—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8C22×D1111yescharacteristic
389C22×C8C22×D1111yescharacteristic
390#117—114no—
391#117—222no—
392#117—222no—
393#117—222no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—222no—
403C2×C4⋊C4—222no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—444no—
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—111no—
422C2×C42—222no—
423C2×C42—222no—
424C2×C42—221no—
425C2×C42—221no—
426C2×C42C22×D1111yescharacteristic
427#107—114no—
428#107—222no—
429#107—222no—
430#107C4×D1114yescomplemented
431#106—22no—
432#106—114no—
433#106—114no—
434#106—222no—
435#97—22no—
436#97—222no—
437C4×C8—222no—
438C4×C8—222no—
439#95—21no—
440#95—21no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447C2×C11C2×#38911yescharacteristic
448C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
449C2×C11C4×#13711yescharacteristic
450C2×C11#305511yescharacteristic
451C2×C11#305611yescharacteristic
452C2×C11#316511yescharacteristic
453C2×C11#316611yescharacteristic
454D11—24no—
455C24—111no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—111no—
461C22×C4—112no—
462C22×C4—112no—
463C22×C4—112no—
464C22×C4—112no—
465C22×C4—112no—
466C22×C4—112no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—224no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—441no—
479C22×C4—441no—
480C22×C4—442no—
481C22×C4—442no—
482C22×C4—442no—
483C22×C4—442no—
484C22×C4—442no—
485C22×C4D4×D1111yescharacteristic
486C22×C4D4×D1111yescharacteristic
487C22×C4C23×D1111yescharacteristic
488M16—1116no—
489M16—228no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—112no—
493C2×C8—112no—
494C2×C8—112no—
495C2×C8—112no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8C2×C4×D1112yes—
499C2×C8D4×D1112yes—
500C2×C8Q8×D1112yes—
501C2×C8Q8×D1112yes—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—112no—
511C4⋊C4—112no—
512C4⋊C4—224no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—442no—
520C4⋊C4—442no—
521C4⋊C4—442no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4C2×C4×D1112yes—
527C4⋊C4C2×C4×D1112yes—
528C22⋊C4—224no—
529C22⋊C4—442no—
530C42—21no—
531C42—21no—
532C42—222no—
533C42—222no—
534C42—224no—
535C42—221no—
536C42—221no—
537C42—442no—
538C11#2115911yescharacteristic, complemented, Sylow
539C23—112no—
540C23—112no—
541C23—112no—
542C23—221no—
543C23—221no—
544C23—221no—
545C23—221no—
546C23C2×D4×D1111yescharacteristic
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—112no—
566C2×C4—112no—
567C2×C4—112no—
568C2×C4—114no—
569C2×C4—114no—
570C2×C4—114no—
571C2×C4—114no—
572C2×C4—112no—
573C2×C4—112no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—444no—
581C2×C4—444no—
582C2×C4—448no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—884no—
594C2×C4C22×C4×D1111yescharacteristic
595C2×C4C2×D4×D1111yescharacteristic
596C2×C4C2×Q8×D1111yescharacteristic
597C2×C4C2×Q8×D1111yescharacteristic
598C2×C4#41×D1111yescharacteristic
599C2×C4#41×D1111yescharacteristic
600C8—22no—
601C8—114no—
602C8—222no—
603C8C4⋊C4×D1114yescomplemented
604C22—114no—
605C22—222no—
606C22—222no—
607C22—222no—
608C22—222no—
609C22—222no—
610C22—222no—
611C22C4×D4×D1111yescharacteristic
612C22D11×#12111yescharacteristic
613C22D11×C4⋊Q811yescharacteristic
614C22D11×AGL(1,ℤ/8)11yescharacteristic
615C22#1062330411yescharacteristic
616C22D11×#13711yescharacteristic
617C22#1062330811yescharacteristic
618C4—42no—
619C4—42no—
620C4—41no—
621C4—41no—
622C4—81no—
623C4—81no—
624C4—114no—
625C4—222no—
626C4—222no—
627C4—442no—
628C4—442no—
629C4—881no—
630C4—881no—
631C4C2×C4⋊C4×D1111yescharacteristic
632C4C4×Q8×D1111yescharacteristic
633C4D11×C22⋊Q811yescharacteristic
634C4D11×#12511yescharacteristic
635C2—224no—
636C2D11×#38911yescharacteristic
637C2#1307742711yescharacteristic
638C2#1307743211yescharacteristic
639C2#1307823011yescharacteristic
640C2#1307824111yescharacteristic
641C2#1307916111yescharacteristic
642C2#1307916711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1943C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1943D11
hypocenterC11#21159
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1943

Complements

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

NH ≅ G/Ntype
6. #13069359C2semidirect
7. #13069356C2semidirect
8. #13069351C2semidirect
9. #13069350C2semidirect
10. #13069348C2semidirect
11. #13069343C2semidirect
12. #13069342C2semidirect
15. C11×#1943C2semidirect
47. #10622494C4semidirect
114. C11×#107C2×C4semidirect
126. #66881C2×C4semidirect
130. #66872C2×C4semidirect
132. #66871C2×C4semidirect
217. #4313C4⋊C4semidirect
226. #1943D11semidirect
295. C8×C11C2×C4⋊C4semidirect
297. C11⋊C8C2×C4⋊C4semidirect
430. #107C4×D11semidirect
538. C11#21159semidirect
603. C8C4⋊C4×D11semidirect

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×#106223202
#130710972
D11×#3892
#130693592
#130693562
#130693512
#130693502
#130693482
#130693432
#130693422
#130683342
C11×#19432
#2115911