Finite Group Databasebeta

← #14804140

Subgroups — #14804140

Order 2816.

832 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622490C211yesmaximal, characteristic, complemented
2C2×#10622343C211yesmaximal, characteristic
3#13073781C211yesmaximal, characteristic
4#13073540C211yesmaximal, characteristic
5#13070054C211yesmaximal, characteristic, complemented
6#13069815C211yesmaximal, characteristic, complemented
7#13069813C211yesmaximal, characteristic, complemented
8#13069583C211yesmaximal, characteristic, complemented
9#13069378C211yesmaximal, characteristic, complemented
10#13069048C211yesmaximal, characteristic, complemented
11#13069037C211yesmaximal, characteristic, complemented
12#13068650C211yesmaximal, characteristic, complemented
13#13068639C211yesmaximal, characteristic, complemented
14#13068445C211yesmaximal, characteristic, complemented
15C11×#2076C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊D11C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C2×#66950C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C11×#380C2211yescharacteristic
26C11×#380C2211yescharacteristic
27#10622825C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622600C2211yescharacteristic
37#10622589C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43#10622574—21no—
44#10622570—21no—
45#10622561—21no—
46#10622557—21no—
47#10622490—24no—
48#10622343—24no—
49#10622289—21no—
50#10622282—21no—
51#10622273—21no—
52#10622260—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11D411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11D411yescharacteristic
76C4×C22⋊D11—22no—
77C4×C22⋊D11—22no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4D411yescharacteristic
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88#66977—22no—
89#66977—41no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4D411yescharacteristic
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8—22no—
100C22×C11⋊C8—22no—
101C22×C11⋊C8—41no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C2×#4313—22no—
105C2×#4313—22no—
106C2×#4313—41no—
107#66950—22no—
108#66950—41no—
109#66943—22no—
110#66943—22no—
111#66940—22no—
112#66940—22no—
113C11×#107—22no—
114C11×C22⋊C8—22no—
115C11×#95—21no—
116C11×#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122(C2×D11)⋊C8—22no—
123#66881—41no—
124#66880—22no—
125#66880—22no—
126#66879—22no—
127Dic11⋊C8D414yes—
128#66874—22no—
129#66874—22no—
130#66872—22no—
131#66872—41no—
132#25357—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C23×D11C2×D411yescharacteristic
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—22no—
148C2×C22⋊D11—22no—
149C2×C22⋊D11—41no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22#4112yes—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11C2×D412yes—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C22⋊C4—81no—
184C11×C22⋊C4—81no—
185C22⋊Dic11—22no—
186C22⋊Dic11—42no—
187C22⋊Dic11—42no—
188(C2×D11)⋊C4—22no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—81no—
192(C2×D11)⋊C4—81no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—42no—
200C4⋊Dic11—42no—
201Dic11⋊C4—22no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—81no—
207C4×Dic11—42no—
208C4×Dic11—81no—
209C4×Dic11C2×D412yes—
210C4×Dic11#4112yes—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—44no—
216C2×C11⋊C8C2×D412yes—
217C2×C11⋊C8#4112yes—
218#4313—44no—
219C2×#479—111no—
220C2×#435—111no—
221#2562—111no—
222#2538—111no—
223#2077—111no—
224#2076D1111yescharacteristic, complemented
225#2035—111no—
226#2035—111no—
227#1992—111no—
228#1948—111no—
229#1894—111no—
230#1892—111no—
231#1809—111no—
232#1807—111no—
233#1763—111no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11#13712yes—
241C23×C11C22×D411yescharacteristic
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
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×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C22⋊D11—44no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—22no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11#12112yes—
295C2×Dic11#12112yes—
296C4×D11—41no—
297C4×D11—41no—
298C4×D11—41no—
299C4×D11—41no—
300Dic22—22no—
301Dic22—22no—
302Dic22—41no—
303Dic22—41no—
304C8×C11—22no—
305C8×C11—41no—
306C11⋊C8—22no—
307C11⋊C8—22no—
308C22×M16—111no—
309C23×C8—111no—
310C2×#125—111no—
311C2×C22⋊Q8—111no—
312C2×C22⋊Q8—111no—
313C2×C4×Q8—111no—
314C2×C4×D4—111no—
315#479—224no—
316#435—224no—
317C2×#107C2×D1111yescharacteristic
318C2×#106—111no—
319C2×#106—111no—
320C2×#106—111no—
321C2×C4⋊C8—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×C22⋊C8—111no—
327C2×C22⋊C8C2×D1111yescharacteristic
328C2×#97—111no—
329#400—221no—
330#396—221no—
331#396—221no—
332#394—221no—
333#390—221no—
334#389—221no—
335#388—221no—
336#388—221no—
337#384—111no—
338#380—111no—
339#380—111no—
340#380—111no—
341#380—111no—
342#380C2×D1111yescharacteristic
343#380C2×D1111yescharacteristic
344C4×C4⋊C4—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340C2×D1111yescharacteristic
351#340C2×D1111yescharacteristic
352#340C2×D1111yescharacteristic
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11C2×#12111yescharacteristic
361C22×C11#54611yescharacteristic
362C22×C11#54711yescharacteristic
363C22×C11C2×#13711yescharacteristic
364C22×C11#57511yescharacteristic
365C22×C11#57711yescharacteristic
366C22×C11#57711yescharacteristic
367C2×D11—41no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C2×D11—41no—
374C4×C11—41no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11#52911yescharacteristic
380C4×C11#54211yescharacteristic
381C4×C11#54611yescharacteristic
382C4×C11#54811yescharacteristic
383Dic11—22no—
384Dic11—22no—
385Dic11—42no—
386Dic11—41no—
387Dic11—81no—
388Dic11—81no—
389Dic11—81no—
390C22×Q8—111no—
391C22×D4—111no—
392C23×C4—111no—
393C23×C4C22×D1111yescharacteristic
394C2×M16—222no—
395C2×M16—222no—
396C2×M16—441no—
397C22×C8—111no—
398C22×C8—111no—
399C22×C8—222no—
400C22×C8—222no—
401C22×C8—441no—
402C22×C8C22×D1111yescharacteristic
403C22×C8C22×D1111yescharacteristic
404#125—222no—
405#125—222no—
406C22⋊Q8—222no—
407C22⋊Q8—222no—
408C22⋊Q8—441no—
409C22⋊Q8—441no—
410C4×Q8—222no—
411C4×Q8—222no—
412C4×D4—222no—
413C4×D4—222no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—111no—
432C2×C22⋊C4—111no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C42—111no—
440C2×C42—221no—
441C2×C42—221no—
442#107—22no—
443#106—222no—
444#106—441no—
445#106—441no—
446C4⋊C8—114no—
447#103—222no—
448#103—222no—
449#103—222no—
450#103—222no—
451C22⋊C8—22no—
452C22⋊C8—222no—
453#97—222no—
454#95—21no—
455#95—21no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461C2×C11—42no—
462C2×C11#242711yescharacteristic
463C2×C11#305611yescharacteristic
464C2×C11#306011yescharacteristic
465C2×C11#331711yescharacteristic
466C2×C11#332011yescharacteristic
467C2×C11#334411yescharacteristic
468C2×C11#335011yescharacteristic
469D11—81no—
470C24—111no—
471C24D4×D1111yescharacteristic
472C2×Q8—112no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×D4—222no—
479C2×D4—222no—
480C2×D4—441no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4D4×D1111yescharacteristic
505C22×C4C23×D1111yescharacteristic
506M16—444no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—112no—
513C2×C8—112no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—444no—
519C2×C8D4×D1112yes—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—222no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—442no—
536C4⋊C4—442no—
537C4⋊C4—442no—
538C4⋊C4—442no—
539C4⋊C4—442no—
540C4⋊C4—442no—
541C4⋊C4—881no—
542C22⋊C4—81no—
543C22⋊C4—81no—
544C22⋊C4—222no—
545C22⋊C4—222no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C22⋊C4—881no—
551C22⋊C4—881no—
552C42—112no—
553C42—112no—
554C42—442no—
555C42—881no—
556C11#2535711yescharacteristic, complemented, Sylow
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23#6697112yes—
571C23C2×D4×D1111yescharacteristic
572Q8—222no—
573Q8—222no—
574Q8—441no—
575Q8—441no—
576D4—444no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—112no—
597C2×C4—112no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—222no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4C2×D4×D1111yescharacteristic
622C2×C4#41×D1111yescharacteristic
623C2×C4#41×D1111yescharacteristic
624C2×C4#41×D1111yescharacteristic
625C2×C4#6704211yescharacteristic
626C2×C4#6704311yescharacteristic
627C8—22no—
628C8—41no—
629C8—222no—
630C8—222no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22—441no—
642C22—441no—
643C22—441no—
644C22—441no—
645C22D11×#12111yescharacteristic
646C22#1062318511yescharacteristic
647C22#1062318611yescharacteristic
648C22C2×#6697111yescharacteristic
649C22#1062329911yescharacteristic
650C22#1062330611yescharacteristic
651C22#1062330611yescharacteristic
652C4—41no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—222no—
658C4—222no—
659C4—441no—
660C4—442no—
661C4—881no—
662C4—881no—
663C4—881no—
664C4#1062318511yescharacteristic
665C4#1062320811yescharacteristic
666C4#1062323711yescharacteristic
667C4#1062324111yescharacteristic
668C2—42no—
669C2—881no—
670C2#1307218811yescharacteristic
671C2#1307824311yescharacteristic
672C2#1307827611yescharacteristic
673C2#1308074011yescharacteristic
674C2#1308078511yescharacteristic
675C2#1308106911yescharacteristic
676C2#1308116511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2076C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenter#2076D11
hypocenterC11#25357
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2076

Complements

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

NH ≅ G/Ntype
1. C2×#10622490C2semidirect
5. #13070054C2semidirect
6. #13069815C2semidirect
7. #13069813C2semidirect
8. #13069583C2semidirect
9. #13069378C2semidirect
10. #13069048C2semidirect
11. #13069037C2semidirect
12. #13068650C2semidirect
13. #13068639C2semidirect
14. #13068445C2semidirect
15. C11×#2076C2semidirect
224. #2076D11semidirect
556. C11#25357semidirect

Maximal subgroups

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

subgroupindex
C2×#106224902
C2×#106223432
#130737812
#130735402
#130700542
#130698152
#130698132
#130695832
#130693782
#130690482
#130690372
#130686502
#130686392
#130684452
C11×#20762
#2535711