Finite Group Databasebeta

← #14917235

Subgroups — #14917235

Order 2816.

2286 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623356C211yesmaximal, characteristic
2#13071786C212yesmaximal, complemented
3#13071766C212yesmaximal, complemented
4#13071751C212yesmaximal, complemented
5#13071725C212yesmaximal, complemented
6#13071643C212yesmaximal, complemented
7#13071621C212yesmaximal, complemented
8#13071503C212yesmaximal, complemented
9#13071448C212yesmaximal, complemented
10#13071407C214yesmaximal, complemented
11#13071359C214yesmaximal, complemented
12#13071294C212yesmaximal, complemented
13#13071144C212yesmaximal, complemented
14#13071107C211yesmaximal, characteristic
15C11×#2311C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20#10623356C4116yescomplemented
21C2×#66997C2212yes—
22C2×#66989C2212yes—
23C2×#66988C2212yes—
24C2×#66988C2212yes—
25C2×#66979C2211yescharacteristic
26C2×#66979C2211yescharacteristic
27C2×#66977C2212yes—
28C2×#66977C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C2×#66940C2212yes—
31C2×#66940C2212yes—
32C11×#391C2212yes—
33C11×#390C2212yes—
34C11×#386C2212yes—
35C11×#386C2212yes—
36C11×#380C2212yes—
37C11×#380C2212yes—
38#10622843C2212yes—
39#10622834C2212yes—
40#10622833C2211yescharacteristic
41#10622833C2211yescharacteristic
42#10622833C2211yescharacteristic
43#10622833C2211yescharacteristic
44#10622823C2214yes—
45C4×C22⋊Dic11C2212yes—
46C4×C22⋊Dic11C2212yes—
47C4×C22⋊Dic11C2214yes—
48#10622591C2214yes—
49C4⋊C4×Dic11C2212yes—
50C4⋊C4×Dic11C2212yes—
51#10622587C2212yes—
52#10622587C2212yes—
53#10622586C2212yes—
54#10622586C2212yes—
55#10622585C2214yes—
56#10622559C2214yes—
57#10622558C2214yes—
58#10622558C2214yes—
59#10622558C2214yes—
60#10622558C2214yes—
61#10622557C2214yes—
62#10622557C2214yes—
63#10622555C2214yes—
64C22⋊C4×Dic11C2214yes—
65C22⋊C4×Dic11C2214yes—
66#10622546C2214yes—
67C4×Dic11⋊C4C2214yes—
68#10622268C2214yes—
69#10622265C2214yes—
70#10622263C2214yes—
71#10622262C2214yes—
72#10622261C2214yes—
73#10622260C2214yes—
74#10622259C2214yes—
75#10622259C2214yes—
76C2×C11×#41—42no—
77C2×C11×#41—42no—
78C2×C11×#41C2×C418yes—
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2312yes—
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2312yes—
90C22×Dic22—42no—
91C22×Dic22—42no—
92C22×Dic22C2×C418yescomplemented
93C22×Dic22C2312yes—
94C22×Dic22C2312yes—
95C11×#117—42no—
96C2×C11×C4⋊C4—42no—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C22⋊C4C2314yes—
101C2×C11×C22⋊C4C2314yes—
102C2×C11×C22⋊C4C2312yes—
103C2×C42×C11C2312yes—
104C2×C22⋊Dic11C2312yes—
105C2×C22⋊Dic11C2312yes—
106C2×C22⋊Dic11C2311yescharacteristic
107C2×C22⋊Dic11C2311yescharacteristic
108C2×C22⋊Dic11C2312yes—
109C2×C22⋊Dic11C2312yes—
110C2×C22⋊Dic11C2314yes—
111C2×C22⋊Dic11C2314yes—
112C2×C22⋊Dic11C2312yes—
113#66997C2×C4116yescomplemented
114#66989C2×C4116yes—
115#66988C2×C4116yescomplemented
116#66988C2×C4116yescomplemented
117#66979—42no—
118#66979C2×C418yescomplemented
119C2×C4⋊Dic11C2312yes—
120C2×C4⋊Dic11C2312yes—
121#66977C2×C4116yescomplemented
122#66977C2×C4116yescomplemented
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2314yes—
126C2×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C2314yes—
128C2×Dic11⋊C4C2314yes—
129C2×C4×Dic11—42no—
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2314yes—
133C2×C4×Dic11C2314yes—
134C2×C4×Dic11C2314yes—
135C2×C4×Dic11C2314yes—
136C2×C4×Dic11C2312yes—
137C2×C4×Dic11C2312yes—
138#66940—44no—
139#66940—44no—
140C11×#95C2314yes—
141C11×#95C2314yes—
142C11⋊#95C2312yes—
143C11⋊#95C2312yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2312yes—
153C11⋊#95C2312yes—
154#34412—111nomaximal, Sylow
155C24×C11C2411yescharacteristic
156C24×C11C2411yescharacteristic
157C24×C11C2411yescharacteristic
158C11×#41—416no—
159C2×Q8×C11—41no—
160C2×Q8×C11—41no—
161C2×Q8×C11C22×C414yes—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11—41no—
166C2×D4×C11—41no—
167C2×D4×C11—41no—
168C2×D4×C11C22×C414yes—
169C2×D4×C11C22×C414yes—
170C2×D4×C11C22×C414yes—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—42no—
178C22×C4×C11—44no—
179C22×C4×C11C22×C414yes—
180C22×C4×C11C22×C414yes—
181C22×C4×C11C22×C414yes—
182C22×C4×C11C2414yes—
183C22×C4×C11C2414yes—
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C22×C4×C11C2411yescharacteristic
188C22×Dic11—24no—
189C22×Dic11—41no—
190C22×Dic11—41no—
191C22×Dic11—42no—
192C22×Dic11—42no—
193C22×Dic11—42no—
194C22×Dic11C22×C418yes—
195C22×Dic11C2412yes—
196C22×Dic11C2412yes—
197C22×Dic11C2412yes—
198C22×Dic11C2414yes—
199C22×Dic11C2414yes—
200C22×Dic11C2412yes—
201C2×Dic22—24no—
202C2×Dic22—24no—
203C2×Dic22—416no—
204C2×Dic22—42no—
205C2×Dic22—42no—
206C2×Dic22C22×C418yes—
207C2×Dic22C22×C418yes—
208C11×C4⋊C4—24no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—42no—
211C11×C22⋊C4—44no—
212C11×C22⋊C4—44no—
213C11×C22⋊C4—42no—
214C42×C11—42no—
215C22⋊Dic11—24no—
216C22⋊Dic11—24no—
217C22⋊Dic11—41no—
218C22⋊Dic11—41no—
219C22⋊Dic11—42no—
220C22⋊Dic11—42no—
221C22⋊Dic11C22×C4116yes—
222C22⋊Dic11C22×C4116yes—
223C22⋊Dic11C22×C418yes—
224C4⋊Dic11—42no—
225C4⋊Dic11C22×C418yes—
226Dic11⋊C4—44no—
227Dic11⋊C4—44no—
228Dic11⋊C4—44no—
229Dic11⋊C4—44no—
230Dic11⋊C4C22×C4116yes—
231Dic11⋊C4C22×C4116yes—
232C4×Dic11—28no—
233C4×Dic11—24no—
234C4×Dic11—24no—
235C4×Dic11—44no—
236C4×Dic11—44no—
237C4×Dic11—42no—
238C4×Dic11—44no—
239C4×Dic11C22×C418yes—
240C2×#536—111no—
241#2379—112no—
242#2376—112no—
243#2374—112no—
244#2372—112no—
245#2362—112no—
246#2360—112no—
247#2346—112no—
248Q8×C22⋊C4—112no—
249#2335—114no—
250#2331—114no—
251#2323—112no—
252#2311D1111yescharacteristic
253C4×C22⋊Q8—112no—
254#2297—111no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11C23×C412yes—
268C23×C11C23×C412yes—
269C23×C11C23×C412yes—
270C23×C11C2511yescharacteristic
271Q8×C11—44no—
272D4×C11—44no—
273D4×C11—44no—
274D4×C11—44no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—28no—
282C2×C4×C11—28no—
283C2×C4×C11—28no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—84no—
291C2×C4×C11C23×C412yes—
292C2×C4×C11C23×C412yes—
293C2×C4×C11C23×C412yes—
294C2×C4×C11C23×C412yes—
295C2×C4×C11H(5,𝔽2)12yes—
296C2×C4×C11H(5,𝔽2)12yes—
297C2×Dic11—22no—
298C2×Dic11—24no—
299C2×Dic11—24no—
300C2×Dic11—24no—
301C2×Dic11—22no—
302C2×Dic11—24no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—48no—
313C2×Dic11—44no—
314C2×Dic11—44no—
315C2×Dic11C23×C418yes—
316C2×Dic11C23×C418yes—
317C2×Dic112−1+414yes—
318Dic22—216no—
319Dic22—48no—
320C22×#41C2×D1111yescharacteristic
321C23×Q8—111no—
322#536—1116no—
323C2×C4⋊Q8—112no—
324C2×#124—112no—
325C2×#123—112no—
326C2×#123—112no—
327C2×C22⋊Q8—112no—
328C2×C22⋊Q8—112no—
329C2×C4×Q8—112no—
330C2×C4×Q8—112no—
331C2×#117—111no—
332C2×#117—111no—
333C2×#117C2×D1111yescharacteristic
334C22×C4⋊C4C2×D1111yescharacteristic
335C22×C42—111no—
336#391—112no—
337#391—112no—
338#391—112no—
339#391—114no—
340#391—114no—
341#391C2×D1112yes—
342#390—112no—
343#390C2×D1112yes—
344#389—112no—
345#389—114no—
346#389—112no—
347#389—114no—
348#388—114no—
349#388—114no—
350#388—114no—
351#388—114no—
352#388—114no—
353#388—114no—
354#387—114no—
355#387—114no—
356#387—114no—
357#387—114no—
358#386—111no—
359#386—111no—
360#386—111no—
361#386—111no—
362#386C2×D1112yes—
363#386C2×D1112yes—
364#385—114no—
365#385—114no—
366#382—114no—
367#380—114no—
368#380C2×D1112yes—
369#380C2×D1112yes—
370C4×C4⋊C4—112no—
371C4×C4⋊C4—112no—
372C4×C4⋊C4—114no—
373C4×C4⋊C4—114no—
374C4×C22⋊C4—114no—
375C4×C22⋊C4—112no—
376C4×C22⋊C4—112no—
377C4×C22⋊C4—114no—
378C4×C22⋊C4—114no—
379#376—114no—
380C22×C11—22no—
381C22×C11—22no—
382C22×C11—22no—
383C22×C11—24no—
384C22×C11—24no—
385C22×C11—24no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—42no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11C24×C411yescharacteristic
396C22×C11C2×H(5,𝔽2)11yescharacteristic
397C22×C11C2×H(5,𝔽2)11yescharacteristic
398C22×C11C2×2−1+412yes—
399C22×C11#58512yes—
400C4×C11—22no—
401C4×C11—22no—
402C4×C11—22no—
403C4×C11—44no—
404C4×C11—44no—
405C4×C11#51814yes—
406Dic11—28no—
407Dic11—28no—
408Dic11—24no—
409Dic11—42no—
410Dic11—42no—
411Dic11—42no—
412C2×#41—42no—
413C2×#41—42no—
414C2×#41C4×D1118yes—
415C22×Q8—118no—
416C22×Q8—112no—
417C22×Q8—112no—
418C22×Q8—442no—
419C22×Q8—442no—
420C22×Q8C22×D1111yescharacteristic
421C22×D4C22×D1111yescharacteristic
422C22×D4C22×D1111yescharacteristic
423C22×D4C22×D1111yescharacteristic
424C23×C4—112no—
425C23×C4—111no—
426C23×C4—111no—
427C23×C4C22×D1111yescharacteristic
428C23×C4C22×D1111yescharacteristic
429C23×C4C22×D1111yescharacteristic
430C23×C4C22×D1112yes—
431C4⋊Q8—1116no—
432#124—1116no—
433#123—1116no—
434#123—1116no—
435C22⋊Q8—1116no—
436C22⋊Q8—1116no—
437C4×Q8—444no—
438C4×Q8—444no—
439#117—42no—
440#117—118no—
441#117—442no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—112no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—114no—
446C2×C4⋊C4—112no—
447C2×C4⋊C4—114no—
448C2×C4⋊C4—114no—
449C2×C4⋊C4—114no—
450C2×C4⋊C4—114no—
451C2×C4⋊C4C22×D1112yes—
452C2×C4⋊C4C22×D1112yes—
453C2×C4⋊C4C22×D1112yes—
454C2×C22⋊C4—112no—
455C2×C22⋊C4—114no—
456C2×C22⋊C4—114no—
457C2×C22⋊C4—112no—
458C2×C22⋊C4—112no—
459C2×C22⋊C4—111no—
460C2×C22⋊C4—111no—
461C2×C22⋊C4—112no—
462C2×C22⋊C4—112no—
463C2×C22⋊C4C22×D1112yes—
464C2×C22⋊C4C22×D1114yes—
465C2×C22⋊C4C22×D1114yes—
466C2×C42—112no—
467C2×C42—112no—
468C2×C42—112no—
469C2×C42—114no—
470C2×C42—114no—
471C2×C42—114no—
472C2×C42—114no—
473C2×C42—112no—
474C2×C42—442no—
475C2×C42C22×D1112yes—
476#95—112no—
477#95—114no—
478#95—114no—
479#95—114no—
480#95—112no—
481#95—114no—
482#95—112no—
483#95—114no—
484#95—112no—
485#95—114no—
486#95—114no—
487#95—114no—
488#95C22×D1114yes—
489#95C22×D1114yes—
490C2×C11—42no—
491C2×C11—42no—
492C2×C11—42no—
493C2×C11C2×#51811yescharacteristic
494C2×C11C4×2−1+412yes—
495C2×C11#353811yescharacteristic
496C2×C11#354011yescharacteristic
497C2×C11#354712yes—
498C24C23×D1111yescharacteristic
499C24C23×D1111yescharacteristic
500C24C23×D1111yescharacteristic
501#41—416no—
502C2×Q8—41no—
503C2×Q8—41no—
504C2×Q8—118no—
505C2×Q8—118no—
506C2×Q8—224no—
507C2×Q8—224no—
508C2×Q8—442no—
509C2×Q8—442no—
510C2×Q8—4416no—
511C2×Q8C2×C4×D1114yes—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4C2×C4×D1114yes—
519C2×D4C2×C4×D1114yes—
520C2×D4C2×C4×D1114yes—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—42no—
528C22×C4—44no—
529C22×C4—112no—
530C22×C4—114no—
531C22×C4—114no—
532C22×C4—118no—
533C22×C4—112no—
534C22×C4—112no—
535C22×C4—112no—
536C22×C4—224no—
537C22×C4—441no—
538C22×C4—441no—
539C22×C4—442no—
540C22×C4—442no—
541C22×C4—442no—
542C22×C4C2×C4×D1114yes—
543C22×C4C2×C4×D1114yes—
544C22×C4C2×C4×D1114yes—
545C22×C4C23×D1114yes—
546C22×C4C23×D1114yes—
547C22×C4C23×D1111yescharacteristic
548C22×C4C23×D1111yescharacteristic
549C22×C4C23×D1111yescharacteristic
550C22×C4C23×D1111yescharacteristic
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—42no—
554C4⋊C4—118no—
555C4⋊C4—1116no—
556C4⋊C4—1116no—
557C4⋊C4—442no—
558C4⋊C4—444no—
559C4⋊C4—444no—
560C4⋊C4—444no—
561C4⋊C4—444no—
562C22⋊C4—42no—
563C22⋊C4—44no—
564C22⋊C4—44no—
565C22⋊C4—118no—
566C22⋊C4—1116no—
567C22⋊C4—1116no—
568C22⋊C4—224no—
569C22⋊C4—224no—
570C22⋊C4—441no—
571C22⋊C4—441no—
572C22⋊C4—442no—
573C22⋊C4—442no—
574C42—42no—
575C42—118no—
576C42—228no—
577C42—224no—
578C42—224no—
579C42—442no—
580C42—444no—
581C42—444no—
582C42—444no—
583C11#3441211yescharacteristic, complemented, Sylow
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23C22×C4×D1112yes—
597C23C22×C4×D1112yes—
598C23C22×C4×D1112yes—
599C23C24×D1111yescharacteristic
600Q8—44no—
601Q8—2216no—
602Q8—448no—
603D4—44no—
604D4—44no—
605D4—44no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—28no—
613C2×C4—28no—
614C2×C4—28no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—84no—
622C2×C4—118no—
623C2×C4—118no—
624C2×C4—114no—
625C2×C4—222no—
626C2×C4—224no—
627C2×C4—224no—
628C2×C4—224no—
629C2×C4—224no—
630C2×C4—222no—
631C2×C4—222no—
632C2×C4—222no—
633C2×C4—222no—
634C2×C4—222no—
635C2×C4—222no—
636C2×C4—222no—
637C2×C4—222no—
638C2×C4—222no—
639C2×C4—222no—
640C2×C4—448no—
641C2×C4—444no—
642C2×C4—444no—
643C2×C4C22×C4×D1112yes—
644C2×C4C22×C4×D1112yes—
645C2×C4C22×C4×D1112yes—
646C2×C4C22×C4×D1112yes—
647C2×C4#6703712yes—
648C2×C4#6703712yes—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—24no—
653C22—24no—
654C22—24no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22C23×C4×D1111yescharacteristic
665C22C2×#6703711yescharacteristic
666C22C2×#6703711yescharacteristic
667C22#1062345512yes—
668C22D11×2−1+412yes—
669C4—22no—
670C4—22no—
671C4—22no—
672C4—44no—
673C4—44no—
674C4—228no—
675C4—228no—
676C4—224no—
677C4—442no—
678C4—442no—
679C4—442no—
680C4#1062301714yes—
681C2—42no—
682C2—42no—
683C2—42no—
684C2C2×#1062301711yescharacteristic
685C2#1308182712yes—
686C2#1308285911yescharacteristic
687C2#1308288211yescharacteristic
688C2#1308299512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2311C2
socle, cosocleC23×C11C25
prime radicalC22×C11×#41C22
hypercenter#2311D11
hypocenterC11#34412
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. #13071786C2semidirect
3. #13071766C2semidirect
4. #13071751C2semidirect
5. #13071725C2semidirect
6. #13071643C2semidirect
7. #13071621C2semidirect
8. #13071503C2semidirect
9. #13071448C2semidirect
10. #13071407C2semidirect
11. #13071359C2semidirect
12. #13071294C2semidirect
13. #13071144C2semidirect
20. #10623356C4semidirect
92. C22×Dic22C2×C4semidirect
113. #66997C2×C4semidirect
115. #66988C2×C4semidirect
116. #66988C2×C4semidirect
118. #66979C2×C4semidirect
121. #66977C2×C4semidirect
122. #66977C2×C4semidirect
583. C11#34412semidirect

Maximal subgroups

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

subgroupindex
C2×#106233562
#130717862
#130717662
#130717512
#130717252
#130716432
#130716212
#130715032
#130714482
#130714072
#130713592
#130712942
#130711442
#130711072
C11×#23112
#3441211