Finite Group Databasebeta

← #14762321

Subgroups — #14762321

Order 2816.

1094 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622803C211yesmaximal, characteristic
2C2×Q16×Dic11C211yesmaximal, characteristic, complemented
3C2×#10622403C211yesmaximal, characteristic, complemented
4C2×#10622465C211yesmaximal, characteristic
5C2×#10622401C211yesmaximal, characteristic
6#13071185C211yesmaximal, characteristic, complemented
7#13071159C211yesmaximal, characteristic
8#13069500C211yesmaximal, characteristic
9#13069497C211yesmaximal, characteristic
10#13069486C211yesmaximal, characteristic, complemented
11#13069434C211yesmaximal, characteristic, complemented
12#13069429C211yesmaximal, characteristic
13#13068781C211yesmaximal, characteristic, complemented
14#97×Dic11C211yesmaximal, characteristic, complemented
15C11×#1971C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C2×#67000C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×#66997C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C22×#4314C2211yescharacteristic
24C2×#66946C2211yescharacteristic
25C2×#66940C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30C11×#391C2211yescharacteristic
31C11×#391C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622803C418yescomplemented
35Q16×Dic11—24no—
36C2×#66885C2211yescharacteristic
37C2×#66882C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66879C2211yescharacteristic
40C2×#66879C2211yescharacteristic
41C2×C8×Dic11C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43#10622590C2211yescharacteristic
44#10622589C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622552C2211yescharacteristic
50C42×Dic11C2211yescharacteristic
51#10622542C2211yescharacteristic
52C2×#66867C2211yescharacteristic
53#10622465—24no—
54#10622403—24no—
55#10622401—24no—
56#10622283—22no—
57#10622279—22no—
58#10622262—22no—
59#10622260—22no—
60C22×Q8×C11C2311yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×Dic22C2311yescharacteristic
65C2×C11×Q16—22no—
66C2×C11×Q16—22no—
67C2×C11×Q16C2×C414yescomplemented
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73#67000—22no—
74#67000C2×C414yes—
75Q8×Dic11—22no—
76Q8×Dic11—22no—
77Q8×Dic11—22no—
78Q8×Dic11—22no—
79#66997—22no—
80#66997C2×C414yescomplemented
81C2×#4326—22no—
82C2×#4326—22no—
83C2×#4326C2×C414yescomplemented
84C2×#4325—22no—
85C2×#4325—22no—
86C2×#4325C2×C414yes—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—22no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11D412yes—
101C2×C4×Dic11D412yes—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C2×#4314—22no—
107C2×#4314—22no—
108C2×#4314C2×C414yes—
109#66946—22no—
110#66946—22no—
111#66940—22no—
112#66940—22no—
113C11×#106—22no—
114C11×#103—22no—
115C11×#103—22no—
116C11×#97—22no—
117C11×#95—22no—
118C11×#95—22no—
119#66899—22no—
120#66899—22no—
121C11⋊#95—22no—
122C11⋊#95—22no—
123#66885—22no—
124#66882—22no—
125#66880—22no—
126#66879—22no—
127#66879C2×C414yescomplemented
128C8×Dic11D414yes—
129C8×Dic11D414yes—
130#66874—22no—
131#66873—22no—
132#66872—22no—
133#66871—22no—
134#66867—22no—
135C4×#497—111nomaximal, Sylow
136C23×D11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C22×C412yes—
148C2×Q8×C11C22×C412yes—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11C2×D412yes—
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44C22×C412yes—
167C2×C4×D11—42no—
168C2×C4×D11—44no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22C22×C412yes—
175C11×Q16—28no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C22×C412yes—
179C2×C8×C11C2×D412yes—
180C2×C8×C11C2×D412yes—
181C2×C8×C11#4112yes—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C42×C11—21no—
187C42×C11—21no—
188#4326—28no—
189#4325—28no—
190(C2×D11)⋊C4—28no—
191(C2×D11)⋊C4—44no—
192(C2×D11)⋊C4—42no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—42no—
198C4⋊Dic11—42no—
199Dic11⋊C4—28no—
200Dic11⋊C4—44no—
201Dic11⋊C4—42no—
202C4×Dic11—24no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205C4×Dic11—42no—
206C4×Dic11—42no—
207C4×Dic11C22×C412yes—
208C4×Dic11C2×D412yes—
209C4×Dic11C2×D412yes—
210C4×Dic11#4112yes—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8C22×C412yes—
214C2×C11⋊C8C2×D412yes—
215C2×C11⋊C8C2×D412yes—
216C2×C11⋊C8#4112yes—
217#4314—28no—
218C2×#497—111no—
219C2×C4×Q16—111no—
220C2×C4×Q16—111no—
221C2×C4×SD16—111no—
222C2×C4×SD16—111no—
223C4×C4⋊Q8—111no—
224C4×#124—111no—
225#1973—111no—
226#1973—111no—
227#1971—111no—
228#1971D1111yescharacteristic, complemented
229#1960—111no—
230#1959—111no—
231#1847—111no—
232C4×#97—111no—
233C23×C11C22×D411yescharacteristic
234C22×D11—22no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—42no—
238C22×D11—42no—
239Q8×C11—22no—
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
246Q8×C11—41no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
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—42no—
259C2×C4×C11—42no—
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11C4×D414yes—
277C2×Dic11#12712yes—
278C2×Dic11#12712yes—
279C2×Dic11#13714yes—
280D44—22no—
281D44—22no—
282D44—41no—
283D44—41no—
284C4×D11—84no—
285Dic22—22no—
286Dic22—22no—
287Dic22—41no—
288Dic22—41no—
289C8×C11—22no—
290C8×C11C4×D414yes—
291C11⋊C8—22no—
292C11⋊C8C4×D414yes—
293C22×Q16—111no—
294C22×Q16C2×D1111yescharacteristic
295C22×SD16—111no—
296C22×SD16—111no—
297C2×C4⋊Q8—111no—
298C2×#124—111no—
299C2×C4×Q8—111no—
300C2×C4×Q8—111no—
301C2×C4×Q8—111no—
302C2×C4×D4—111no—
303#497—118no—
304C4×Q16—224no—
305C4×Q16—224no—
306C4×SD16—224no—
307C4×SD16—224no—
308C2×#107—111no—
309C2×#107—111no—
310C2×#106—111no—
311C2×#106C2×D1111yescharacteristic
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103C2×D1111yescharacteristic
317C2×#103C2×D1111yescharacteristic
318C2×#102—111no—
319C2×#102—111no—
320C2×#97—111no—
321C2×#97—111no—
322C2×#97—111no—
323C2×#97C2×D1111yescharacteristic
324C2×C4×C8—111no—
325C2×C4×C8—111no—
326#391—111no—
327#391C2×D1111yescharacteristic
328#391C2×D1111yescharacteristic
329#390—111no—
330#389—222no—
331#388—222no—
332#384—111no—
333#382—111no—
334C4×C4⋊C4—222no—
335C4×C22⋊C4—222no—
336C43—111no—
337C22×C11C2×C4×D411yescharacteristic
338C22×C11C2×#12711yescharacteristic
339C22×C11#53211yescharacteristic
340C22×C11C2×#13712yes—
341C22×C11#57512yes—
342C2×D11—42no—
343C2×D11—44no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—82no—
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11C2×C4×D411yescharacteristic
353C4×C11C2×C4×D411yescharacteristic
354C4×C11#53211yescharacteristic
355C4×C11#53211yescharacteristic
356Dic11—22no—
357Dic11—24no—
358Dic11—42no—
359Dic11—81no—
360Dic11—81no—
361Dic11#49714yescomplemented
362C22×Q8—111no—
363C22×Q8C22×D1111yescharacteristic
364C22×Q8C22×D1111yescharacteristic
365C22×D4—111no—
366C23×C4—221no—
367C2×Q16—22no—
368C2×Q16—22no—
369C2×Q16—114no—
370C2×Q16—222no—
371C2×Q16—222no—
372C2×Q16C4×D1114yescomplemented
373C2×SD16—114no—
374C2×SD16—114no—
375C2×SD16—222no—
376C2×SD16—222no—
377C2×SD16—222no—
378C2×SD16—222no—
379C22×C8—111no—
380C22×C8—111no—
381C22×C8C22×D1111yescharacteristic
382C22×C8C22×D1111yescharacteristic
383C4⋊Q8—114no—
384C4⋊Q8—222no—
385#124—114no—
386#124—222no—
387C4×Q8—222no—
388C4×Q8—222no—
389C4×Q8—222no—
390C4×Q8—222no—
391C4×Q8—222no—
392C4×Q8—222no—
393C4×D4—222no—
394C4×D4—222no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C22⋊C4—222no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—222no—
407C2×C42—111no—
408C2×C42—111no—
409C2×C42—112no—
410C2×C42—112no—
411C2×C42—221no—
412C2×C42—221no—
413C2×C42—221no—
414C2×C42C22×D1111yescharacteristic
415#107—222no—
416#107—222no—
417#106—22no—
418#106—222no—
419#103—22no—
420#103—22no—
421#103—222no—
422#103—222no—
423#103—222no—
424#103—222no—
425#102—222no—
426#102—222no—
427#97—22no—
428#97—114no—
429#97—222no—
430#97—222no—
431C4×C8—114no—
432C4×C8—114no—
433#95—22no—
434#95—22no—
435#95—222no—
436#95—222no—
437C2×C11C4×#12711yescharacteristic
438C2×C11C4×#13712yes—
439C2×C11C2×#49711yescharacteristic
440C2×C11#315011yescharacteristic
441C2×C11#317212yes—
442D11—82no—
443C24—221no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—112no—
455C2×Q8—221no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8C2×C4×D1112yes—
461C2×Q8C2×C4×D1112yes—
462C2×D4—112no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—111no—
473C22×C4—112no—
474C22×C4—111no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—442no—
479C22×C4—444no—
480C22×C4D4×D1112yes—
481C22×C4C23×D1111yescharacteristic
482Q16—28no—
483Q16—228no—
484SD16—228no—
485SD16—228no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—112no—
489C2×C8—112no—
490C2×C8—112no—
491C2×C8—112no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8C2×C4×D1112yes—
495C2×C8D4×D1112yes—
496C2×C8D4×D1112yes—
497C2×C8#434112yes—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—228no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—442no—
508C4⋊C4—442no—
509C4⋊C4—442no—
510C4⋊C4—444no—
511C22⋊C4—228no—
512C22⋊C4—444no—
513C22⋊C4—442no—
514C42—21no—
515C42—21no—
516C42—112no—
517C42—112no—
518C42—112no—
519C42—112no—
520C42—224no—
521C42—442no—
522C42—442no—
523C42—442no—
524C42—442no—
525C11C4×#49711yescharacteristic, complemented, Sylow
526C23—222no—
527C23—441no—
528C23—442no—
529C23—442no—
530C23—441no—
531C23C2×D4×D1111yescharacteristic
532Q8—22no—
533Q8—22no—
534Q8—22no—
535Q8—22no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540Q8—222no—
541Q8—222no—
542Q8—441no—
543Q8—441no—
544D4—222no—
545D4—222no—
546D4—441no—
547D4—441no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—112no—
562C2×C4—114no—
563C2×C4—112no—
564C2×C4—114no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—884no—
576C2×C4C22×C4×D1111yescharacteristic
577C2×C4C2×D4×D1111yescharacteristic
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4C2×#434111yescharacteristic
580C2×C4#41×D1111yescharacteristic
581C2×C4#41×D1111yescharacteristic
582C8—22no—
583C8—114no—
584C8—222no—
585C8(C22⋊D11)⋊C414yes—
586C22—442no—
587C22—444no—
588C22—881no—
589C22—881no—
590C22—882no—
591C22C4×D4×D1111yescharacteristic
592C22#1062312711yescharacteristic
593C22D11×#12711yescharacteristic
594C22D11×#13712yes—
595C22#1062330812yes—
596C4—42no—
597C4—42no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—114no—
602C4—222no—
603C4—224no—
604C4—442no—
605C4—881no—
606C4—881no—
607C4C2×(C22⋊D11)⋊C411yescharacteristic
608C4C4×D4×D1111yescharacteristic
609C4#1062312711yescharacteristic
610C4#1062319911yescharacteristic
611C2—882no—
612C2#1307118011yescharacteristic
613C2#1307743212yes—
614C2D11×#49711yescharacteristic
615C2#1307906011yescharacteristic
616C2#1307921712yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1971C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1971D11
hypocenterC11C4×#497
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1971

Complements

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

NH ≅ G/Ntype
2. C2×Q16×Dic11C2semidirect
3. C2×#10622403C2semidirect
6. #13071185C2semidirect
10. #13069486C2semidirect
11. #13069434C2semidirect
13. #13068781C2semidirect
14. #97×Dic11C2semidirect
15. C11×#1971C2semidirect
34. #10622803C4semidirect
67. C2×C11×Q16C2×C4semidirect
80. #66997C2×C4semidirect
83. C2×#4326C2×C4semidirect
127. #66879C2×C4semidirect
228. #1971D11semidirect
361. Dic11#497semidirect
372. C2×Q16C4×D11semidirect
525. C11C4×#497semidirect

Maximal subgroups

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

subgroupindex
C2×#106228032
C2×Q16×Dic112
C2×#106224032
C2×#106224652
C2×#106224012
#130711852
#130711592
#130695002
#130694972
#130694862
#130694342
#130694292
#130687812
#97×Dic112
C11×#19712
C4×#49711