Finite Group Databasebeta

← #14770475

Subgroups — #14770475

Order 2816.

1004 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#4339C211yesmaximal, characteristic
2#13071094C211yesmaximal, characteristic, complemented
3#13069596C212yesmaximal, complemented
4#13069592C211yesmaximal, characteristic, complemented
5#13069560C211yesmaximal, characteristic, complemented
6#13069560C212yesmaximal, complemented
7#13068633C211yesmaximal, characteristic
8#13068633C212yesmaximal
9#13068429C212yesmaximal
10C4×#66889C211yesmaximal, characteristic
11Q8×C11×M16C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13Q8×C22⋊D11—21no—
14#10623110C411yescharacteristic, complemented
15#10623110C412yescomplemented
16#10623109—21no—
17#10623109—22no—
18Q8×D44C411yescharacteristic, complemented
19C4×Q8×D11—21no—
20#10623098C411yescharacteristic, complemented
21#10623098C412yescomplemented
22Q8×Dic22C411yescharacteristic, complemented
23#10623042—22no—
24#10623042—21no—
25C4×#4339C2211yescharacteristic
26C4×#4339C2212yes—
27#10623001C2211yescharacteristic
28#10623001C2212yes—
29C11×#446—21no—
30C11×#446—22no—
31C8×Q8×C11—21no—
32C11×#423C2211yescharacteristic
33C11×#423C2212yes—
34C4×C11×M16C2211yescharacteristic
35C4×C11×M16C2212yes—
36#10622843—21no—
37C2×#66889C2211yescharacteristic
38C2×#66889C2212yes—
39C2×#66889C2211yescharacteristic
40#10622598—21no—
41#10622594—22no—
42C4×C4⋊Dic11C2212yes—
43C4×C4⋊Dic11C2211yescharacteristic
44#10622545C2212yes—
45C42×Dic11C2211yescharacteristic
46#10622193C2212yes—
47#10622193C2212yes—
48#10622193C2211yescharacteristic
49#10622193C2212yes—
50#10622193C2212yes—
51#10622193C2211yescharacteristic
52#10622193C2212yes—
53C22×Q8×C11D411yescharacteristic
54C2×Q8×D11—21no—
55C2×#4339C2311yescharacteristic
56C2×C11×M16C2311yescharacteristic
57C2×C11×M16C2312yes—
58C2×C11×M16C2311yescharacteristic
59C4×Q8×C11C2×C411yescharacteristic
60C4×Q8×C11C2×C411yescharacteristic
61C4×Q8×C11C2×C412yes—
62C4×Q8×C11D411yescharacteristic
63C4×Q8×C11D411yescharacteristic
64C4×Q8×C11D412yes—
65C2×C11×C4⋊C4D412yes—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2312yes—
69#66999—21no—
70#66999—22no—
71Q8×Dic11—21no—
72#66997—21no—
73#66997—22no—
74C4×C22⋊D11—21no—
75C4×C22⋊D11—22no—
76C4×C22⋊D11—21no—
77C4×C22⋊D11—22no—
78#66979C2312yes—
79#66979C2311yescharacteristic
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—22no—
82#66977—21no—
83#66977—22no—
84#66977—21no—
85#66977—22no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2312yes—
90C2×C4×Dic11C2311yescharacteristic
91#66950—22no—
92#66950—21no—
93#66949—22no—
94#66949—22no—
95#66949—22no—
96C4⋊C4×D11—22no—
97C4⋊C4×D11—21no—
98#66942—22no—
99#66942—22no—
100#66942—22no—
101#66941—22no—
102#66941—21no—
103#66940—22no—
104#66940—21no—
105C4×D44C2×C411yescharacteristic
106C4×D44C2×C412yes—
107C4×D44C2×C411yescharacteristic
108C4×D44C2×C412yes—
109#66925—22no—
110#66925—21no—
111C42×D11—21no—
112C42×D11—22no—
113#66923C2×C412yes—
114#66923C2×C412yes—
115#66923C2×C412yes—
116#66922C2×C411yescharacteristic
117#66922C2×C412yes—
118#66922C2×C411yescharacteristic
119#66922C2×C412yes—
120C4×Dic22—21no—
121C4×Dic22—22no—
122C4×Dic22—22no—
123C4×Dic22—21no—
124C4×Dic22C2×C411yescharacteristic
125C4×Dic22C2×C412yes—
126C4×Dic22C2×C411yescharacteristic
127C4×Dic22C2×C412yes—
128C11×C4⋊C8—21no—
129C11×C4⋊C8—22no—
130C11×C4⋊C8—22no—
131C11×C4⋊C8—21no—
132C11×#97—22no—
133C11×#97—21no—
134C4×C8×C11—21no—
135C4×C8×C11—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—21no—
140#66889—22no—
141#66889—24no—
142#66889Q814yescomplemented
143#22529—111nomaximal, Sylow
144C2×Q8×C11—42no—
145C2×Q8×C11C22⋊C411yescharacteristic
146C2×Q8×C11C22⋊C411yescharacteristic
147C2×Q8×C11C22⋊C412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157Q8×D11—44no—
158#4339—21no—
159#4339—21no—
160#4339C2×Q812yes—
161#4339#4112yes—
162C2×D44C22×C411yescharacteristic
163C2×C4×D11—22no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—22no—
167C2×C4×D11—21no—
168C2×Dic22—22no—
169C2×Dic22—21no—
170C2×Dic22—22no—
171C2×Dic22—21no—
172C2×Dic22C22×C411yescharacteristic
173C11×M16—21no—
174C11×M16—22no—
175C11×M16—21no—
176C11×M16—21no—
177C11×M16—22no—
178C11×M16C2×Q812yescomplemented
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—22no—
182C11×C4⋊C4C22⋊C412yes—
183C11×C4⋊C4C22⋊C411yescharacteristic
184C11×C4⋊C4C22⋊C412yes—
185C11×C4⋊C4C22⋊C411yescharacteristic
186C11×C4⋊C4C22⋊C412yes—
187C11×C4⋊C4C22⋊C412yes—
188C11×C4⋊C4C22⋊C412yes—
189C42×C11C22×C412yes—
190C42×C11C22×C411yescharacteristic
191C42×C11C22×C411yescharacteristic
192C42×C11C22×C412yes—
193C42×C11C2×D411yescharacteristic
194C42×C11C2×D412yes—
195C42×C11C2×D412yes—
196C42×C11C2×D411yescharacteristic
197C22⋊Dic11—22no—
198C22⋊Dic11—21no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—21no—
201(C2×D11)⋊C4—21no—
202(C2×D11)⋊C4—22no—
203C4⋊Dic11—22no—
204C4⋊Dic11—21no—
205C4⋊Dic11—22no—
206C4⋊Dic11—21no—
207C4⋊Dic11—42no—
208C4⋊Dic11—44no—
209C4⋊Dic11C22×C411yescharacteristic
210C4⋊Dic11C22×C412yes—
211C4⋊Dic11C22×C411yescharacteristic
212C4⋊Dic11C22×C412yes—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216Dic11⋊C4—22no—
217Dic11⋊C4—22no—
218Dic11⋊C4—22no—
219Dic11⋊C4—22no—
220Dic11⋊C4—21no—
221Dic11⋊C4—21no—
222Dic11⋊C4—22no—
223C4×Dic11—21no—
224C4×Dic11—22no—
225C4×Dic11—22no—
226C4×Dic11—21no—
227C4×Dic11—22no—
228C4×Dic11—21no—
229C4×Dic11—21no—
230C4×Dic11—22no—
231C4×Dic11—21no—
232C4×Dic11—21no—
233C4×Dic11—22no—
234C4×Dic11—42no—
235C4×Dic11—42no—
236C4×Dic11C2×Q812yescomplemented
237Q8×#41—111no—
238Q8×M16D1111yescharacteristic, complemented
239#2295—111no—
240#1995—112no—
241#1994—111no—
242#1986—111no—
243#1986—112no—
244#1806—111no—
245#1806—112no—
246#1759—112no—
247C4×#104—111no—
248C23×C11C22×D411yescharacteristic
249C22×D11—21no—
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—42no—
253C2×C4×C11—22no—
254C2×C4×C11—41no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C2×C22⋊C412yes—
259C2×C4×C11C2×C22⋊C412yes—
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C2×C22⋊C412yes—
262C2×C4×C11C2×C22⋊C412yes—
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C2×C22⋊C411yescharacteristic
265C2×C4×C11C23×C411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×Q811yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C112−1+411yescharacteristic
270C2×C4×C112−1+411yescharacteristic
271C22⋊D11—22no—
272C22⋊D11—22no—
273C2×Dic11—21no—
274C2×Dic11—22no—
275C2×Dic11—21no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—21no—
279C2×Dic11—22no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287D44—21no—
288D44C4×Q812yes—
289C4×D11—22no—
290C4×D11—22no—
291C4×D11—44no—
292C4×D11—42no—
293C4×D11—81no—
294C4×D11—82no—
295Dic22—21no—
296Dic22—44no—
297Dic22—42no—
298Dic22—81no—
299Dic22—82no—
300Dic22C4×Q812yes—
301C8×C11—22no—
302C8×C11—41no—
303C8×C11—42no—
304Q82—111no—
305#557—112no—
306#557—111no—
307#554—111no—
308#554—112no—
309#554—222no—
310#554—221no—
311D4×Q8—111no—
312D4×Q8—221no—
313#533—111no—
314#533—112no—
315#533—221no—
316#533—222no—
317C4×#41—111no—
318C4×#41—112no—
319C2×C4×Q8—221no—
320C2×C4×Q8C2×D1111yescharacteristic
321#446—21no—
322#446—22no—
323C8×Q8—21no—
324#423C2×D1111yescharacteristic
325#423C2×D1112yes—
326C2×#104—111no—
327C2×#104—111no—
328C2×#104—112no—
329C4×M16C2×D1111yescharacteristic
330C4×M16C2×D1112yes—
331#391—221no—
332#389—221no—
333#387—222no—
334C4×C4⋊C4—111no—
335C4×C4⋊C4—112no—
336#376—112no—
337C43—111no—
338#339—112no—
339#339—112no—
340#339—112no—
341#339—111no—
342#339—112no—
343#339—112no—
344#339—111no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11C22×C22⋊C411yescharacteristic
348C22×C11#54811yescharacteristic
349C22×C11D4×Q811yescharacteristic
350C2×D11—22no—
351C2×D11—41no—
352C2×D11—41no—
353C4×C11—21no—
354C4×C11—22no—
355C4×C11—22no—
356C4×C11—21no—
357C4×C11—22no—
358C4×C11—21no—
359C4×C11—22no—
360C4×C11#42112yes—
361C4×C11C2×C4×Q811yescharacteristic
362C4×C11#51911yescharacteristic
363C4×C11#54811yescharacteristic
364C4×C11D4×Q811yescharacteristic
365Dic11—22no—
366Dic11—42no—
367Dic11—42no—
368Dic11—41no—
369Dic11—42no—
370Dic11—42no—
371Dic11—41no—
372Dic11—82no—
373C2×#41—111no—
374C22×Q8—221no—
375C22×Q8D4411yescharacteristic
376C2×M16C22×D1112yes—
377C2×M16C22×D1111yescharacteristic
378C2×M16C22×D1111yescharacteristic
379C4⋊Q8—111no—
380C4⋊Q8—112no—
381C4⋊Q8—111no—
382C4⋊Q8—112no—
383C4⋊Q8—221no—
384C4⋊Q8—222no—
385C4⋊Q8—222no—
386C4⋊Q8—221no—
387#125—112no—
388#125—112no—
389#125—112no—
390#125—222no—
391#125—222no—
392#125—222no—
393C22⋊Q8—221no—
394C22⋊Q8—222no—
395C22⋊Q8—221no—
396C22⋊Q8—222no—
397C22⋊Q8—221no—
398C22⋊Q8—222no—
399C22⋊Q8—222no—
400C22⋊Q8—221no—
401C22⋊Q8—222no—
402C22⋊Q8—222no—
403C22⋊Q8—222no—
404C4×Q8—111no—
405C4×Q8—112no—
406C4×Q8—111no—
407C4×Q8—112no—
408C4×Q8—221no—
409C4×Q8—222no—
410C4×Q8—221no—
411C4×Q8—221no—
412C4×Q8—222no—
413C4×Q8—222no—
414C4×Q8—221no—
415C4×Q8C4×D1111yescharacteristic
416C4×Q8C4×D1111yescharacteristic
417C4×Q8C4×D1112yes—
418C4×Q8C22⋊D1111yescharacteristic
419C4×Q8C22⋊D1111yescharacteristic
420C4×Q8C22⋊D1112yes—
421C4×D4—111no—
422C4×D4—112no—
423C4×D4—111no—
424C4×D4—112no—
425C4×D4—221no—
426C4×D4—222no—
427C4×D4—221no—
428C4×D4—222no—
429#117—111no—
430#117—112no—
431#117—222no—
432#117—221no—
433C2×C4⋊C4—222no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—222no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4D4412yes—
438C2×C4⋊C4D4411yescharacteristic
439C2×C42—111no—
440C2×C42—111no—
441C2×C42—112no—
442C2×C42—221no—
443C2×C42—222no—
444C2×C42—221no—
445C2×C42—221no—
446C2×C42C22×D1111yescharacteristic
447C2×C42C22×D1112yes—
448C4⋊C8—21no—
449C4⋊C8—22no—
450C4⋊C8—22no—
451C4⋊C8—21no—
452#104—114no—
453#104—222no—
454#104—224no—
455#97—22no—
456#97—21no—
457C4×C8—21no—
458C4×C8—22no—
459#95—222no—
460#95—222no—
461#95—221no—
462#95—222no—
463C2×C11—21no—
464C2×C11—21no—
465C2×C11Q8×C22⋊C411yescharacteristic
466C2×C11C2×#42111yescharacteristic
467C2×C11#290111yescharacteristic
468D11—42no—
469#41—112no—
470#41—112no—
471#41—221no—
472#41—221no—
473C2×Q8—42no—
474C2×Q8—111no—
475C2×Q8—222no—
476C2×Q8—221no—
477C2×Q8—222no—
478C2×Q8—221no—
479C2×Q8—444no—
480C2×Q8(C2×D11)⋊C411yescharacteristic
481C2×Q8(C2×D11)⋊C411yescharacteristic
482C2×Q8(C2×D11)⋊C412yes—
483C2×D4—111no—
484C2×D4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—222no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4C2×D4411yescharacteristic
494C22×C4C2×D4412yes—
495C22×C4C2×D4411yescharacteristic
496C22×C4C2×D4412yes—
497C22×C4C23×D1111yescharacteristic
498M16—21no—
499M16—21no—
500M16—22no—
501M16—22no—
502M16—21no—
503M16Q8×D1112yescomplemented
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—22no—
507C4⋊C4—111no—
508C4⋊C4—112no—
509C4⋊C4—111no—
510C4⋊C4—112no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—222no—
514C4⋊C4—222no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—222no—
518C4⋊C4—222no—
519C4⋊C4—221no—
520C4⋊C4—222no—
521C4⋊C4—222no—
522C4⋊C4—222no—
523C4⋊C4—222no—
524C4⋊C4—221no—
525C4⋊C4—442no—
526C4⋊C4—444no—
527C4⋊C4(C2×D11)⋊C412yes—
528C4⋊C4(C2×D11)⋊C411yescharacteristic
529C4⋊C4(C2×D11)⋊C412yes—
530C4⋊C4(C2×D11)⋊C412yes—
531C4⋊C4(C2×D11)⋊C412yes—
532C4⋊C4(C2×D11)⋊C412yes—
533C4⋊C4(C2×D11)⋊C411yescharacteristic
534C22⋊C4—221no—
535C22⋊C4—222no—
536C22⋊C4—221no—
537C22⋊C4—222no—
538C22⋊C4—222no—
539C22⋊C4—221no—
540C42—112no—
541C42—221no—
542C42—222no—
543C42—222no—
544C42—221no—
545C42—221no—
546C42—221no—
547C42—222no—
548C42—221no—
549C42—222no—
550C42—221no—
551C42—222no—
552C42—442no—
553C42—442no—
554C42C2×C4×D1111yescharacteristic
555C42C2×C4×D1112yes—
556C42C2×C4×D1112yes—
557C42C2×C4×D1111yescharacteristic
558C42C2×C22⋊D1111yescharacteristic
559C42C2×C22⋊D1112yes—
560C42C2×C22⋊D1112yes—
561C42C2×C22⋊D1111yescharacteristic
562C11#2252911yescharacteristic, complemented, Sylow
563C23—221no—
564C23C22×D4411yescharacteristic
565Q8—22no—
566Q8—22no—
567Q8—42no—
568Q8—112no—
569Q8—221no—
570Q8—444no—
571Q8—442no—
572Q8—881no—
573Q8—882no—
574D4—112no—
575D4—222no—
576D4—222no—
577D4—221no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—221no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—221no—
588C2×C4—222no—
589C2×C4—221no—
590C2×C4—222no—
591C2×C4—444no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—881no—
601C2×C4—882no—
602C2×C4C2×(C2×D11)⋊C411yescharacteristic
603C2×C4C2×(C2×D11)⋊C412yes—
604C2×C4C2×(C2×D11)⋊C412yes—
605C2×C4C2×(C2×D11)⋊C411yescharacteristic
606C2×C4C2×(C2×D11)⋊C412yes—
607C2×C4C2×(C2×D11)⋊C412yes—
608C2×C4C2×(C2×D11)⋊C411yescharacteristic
609C2×C4C2×(C2×D11)⋊C411yescharacteristic
610C2×C4C22×C4×D1111yescharacteristic
611C2×C4C2×Q8×D1111yescharacteristic
612C2×C4#6704011yescharacteristic
613C2×C4#41×D1111yescharacteristic
614C2×C4#6704311yescharacteristic
615C2×C4C22×C22⋊D1111yescharacteristic
616C8—22no—
617C8—41no—
618C8—42no—
619C22—21no—
620C22—21no—
621C22—222no—
622C22—441no—
623C22—441no—
624C22Q8×D4411yescharacteristic
625C22#1062310711yescharacteristic
626C22C22×(C2×D11)⋊C411yescharacteristic
627C4—21no—
628C4—22no—
629C4—22no—
630C4—21no—
631C4—22no—
632C4—21no—
633C4—22no—
634C4—222no—
635C4—442no—
636C4—442no—
637C4—442no—
638C4—441no—
639C4—442no—
640C4—441no—
641C4—882no—
642C4#1062275212yes—
643C4C4×Q8×D1111yescharacteristic
644C4#1062310311yescharacteristic
645C4Q8×C22⋊D1111yescharacteristic
646C4#1062336211yescharacteristic
647C2—21no—
648C2—21no—
649C2—442no—
650C2Q8×(C2×D11)⋊C411yescharacteristic
651C2C2×#1062275211yescharacteristic
652C2#1307716111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingQ8×C11×M16C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#4339C23
cosocleC22×C4×C11C24
hypercenterQ8×M16D11
hypocenterC11#22529
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
2. #13071094C2semidirect
3. #13069596C2semidirect
4. #13069592C2semidirect
5. #13069560C2semidirect
6. #13069560C2semidirect
11. Q8×C11×M16C2semidirect
14. #10623110C4semidirect
15. #10623110C4semidirect
18. Q8×D44C4semidirect
20. #10623098C4semidirect
21. #10623098C4semidirect
22. Q8×Dic22C4semidirect
142. #66889Q8semidirect
178. C11×M16C2×Q8semidirect
236. C4×Dic11C2×Q8semidirect
238. Q8×M16D11semidirect
503. M16Q8×D11semidirect
562. C11#22529semidirect

Maximal subgroups

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

subgroupindex
Q8×#43392
#130710942
#130695962
#130695922
#130695602
#130686332
#130684292
C4×#668892
Q8×C11×M162
#2252911