Finite Group Databasebeta

← #14804133

Subgroups — #14804133

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×#10622449C211yesmaximal, characteristic
2#13073783C211yesmaximal, characteristic
3#13073534C211yesmaximal, characteristic
4#13070050C211yesmaximal, characteristic, complemented
5#13070045C211yesmaximal, characteristic, complemented
6#13069811C211yesmaximal, characteristic, complemented
7#13069811C211yesmaximal, characteristic, complemented
8#13069586C211yesmaximal, characteristic, complemented
9#13069380C211yesmaximal, characteristic, complemented
10#13069046C211yesmaximal, characteristic, complemented
11#13069036C211yesmaximal, characteristic, complemented
12#13068650C211yesmaximal, characteristic, complemented
13#13068638C211yesmaximal, characteristic, complemented
14#13068446C211yesmaximal, characteristic, complemented
15C2×C11×#479C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×#66999C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#479—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35#10622607—21no—
36#10622607—21no—
37#10622604—21no—
38#10622603—21no—
39#10622603—21no—
40#10622600C2211yescharacteristic
41#10622600C2211yescharacteristic
42#10622600C2211yescharacteristic
43#10622600C2211yescharacteristic
44#10622600C2211yescharacteristic
45#10622600C2211yescharacteristic
46#10622599—21no—
47#10622552—21no—
48#10622548C2211yescharacteristic
49C4×C4⋊Dic11C2211yescharacteristic
50#10622541—21no—
51C2×#66867C2211yescharacteristic
52#10622449—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44D411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#125—22no—
68C11×#125—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79#66999—22no—
80#66999—22no—
81#66999—41no—
82#66999—41no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4D411yescharacteristic
92C2×(C2×D11)⋊C4D411yescharacteristic
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C2×#4313—22no—
106C2×#4313—22no—
107C2×#4313—41no—
108C2×C8×D11—22no—
109C2×C8×D11—22no—
110C2×C8×D11—41no—
111C4×D44—22no—
112C4×D44—22no—
113C11×#107—22no—
114C11×#106—22no—
115C11×C4⋊C8D414yes—
116C11×#103—22no—
117C11×#103—22no—
118#66899—22no—
119#66899—22no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127(C2×D11)⋊C8—22no—
128(C2×D11)⋊C8—22no—
129#66881—41no—
130#66881—41no—
131#66867—22no—
132#25357—111nomaximal, Sylow
133C23×D11C2×D411yescharacteristic
134C23×D11C2×D411yescharacteristic
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11#4112yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—41no—
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×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11C2×D412yes—
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—42no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—42no—
184C42×C11—42no—
185C42×C11C2×D412yes—
186C42×C11#4112yes—
187(C2×D11)⋊C4—22no—
188(C2×D11)⋊C4—22no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—81no—
194(C2×D11)⋊C4—81no—
195(C2×D11)⋊C4—81no—
196(C2×D11)⋊C4—81no—
197C4⋊Dic11—22no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—42no—
207C4⋊Dic11—81no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210C4×Dic11—81no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8#4112yes—
217#4313—44no—
218C8×D11—44no—
219C2×#479D1111yescharacteristic, complemented
220C2×#435—111no—
221#2562—111no—
222#2538—111no—
223#2077—111no—
224#2076—111no—
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×C11C22×D411yescharacteristic
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11#13712yes—
249Q8×C11—22no—
250Q8×C11—22no—
251Q8×C11—41no—
252Q8×C11—41no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
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×C11—41no—
269C2×C4×C11#12112yes—
270C2×C4×C11#12112yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
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—41no—
295D44—44no—
296C4×D11—41no—
297C4×D11—41no—
298C4×D11—41no—
299C4×D11—41no—
300C4×D11—41no—
301C4×D11—41no—
302C4×D11—41no—
303C4×D11—41no—
304C8×C11—22no—
305C8×C11—22no—
306C11⋊C8—22no—
307C11⋊C8—41no—
308C22×M16—111no—
309C23×C8—111no—
310C2×#125C2×D1111yescharacteristic
311C2×C22⋊Q8—111no—
312C2×C22⋊Q8—111no—
313C2×C4×Q8C2×D1111yescharacteristic
314C2×C4×D4—111no—
315#479—24no—
316#435—224no—
317C2×#107C2×D1111yescharacteristic
318C2×#106—111no—
319C2×#106—111no—
320C2×#106C2×D1111yescharacteristic
321C2×C4⋊C8C2×D1111yescharacteristic
322C2×#103—111no—
323C2×#103—111no—
324C2×#103C2×D1111yescharacteristic
325C2×#103C2×D1111yescharacteristic
326C2×C22⋊C8—111no—
327C2×C22⋊C8—111no—
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#380—111no—
343#380—111no—
344C4×C4⋊C4—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353C22×C11C2×#12111yescharacteristic
354C22×C11#54611yescharacteristic
355C22×C11#54711yescharacteristic
356C22×C11C2×#13711yescharacteristic
357C22×C11#57511yescharacteristic
358C22×C11#57711yescharacteristic
359C22×C11#57711yescharacteristic
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—41no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C2×D11—41no—
374C4×C11—22no—
375C4×C11—22no—
376C4×C11—42no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11#52911yescharacteristic
381C4×C11#54211yescharacteristic
382C4×C11#54611yescharacteristic
383C4×C11#54811yescharacteristic
384Dic11—41no—
385Dic11—41no—
386Dic11—81no—
387Dic11—81no—
388Dic11—81no—
389Dic11—81no—
390C22×Q8C22×D1111yescharacteristic
391C22×D4—111no—
392C23×C4—111no—
393C23×C4—111no—
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—22no—
405#125—22no—
406C22⋊Q8—222no—
407C22⋊Q8—222no—
408C22⋊Q8—441no—
409C22⋊Q8—441no—
410C4×Q8—22no—
411C4×Q8—22no—
412C4×D4—222no—
413C4×D4—222no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C22⋊C4—111no—
430C2×C22⋊C4—111no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
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—21no—
440C2×C42—221no—
441C2×C42C22×D1111yescharacteristic
442#107—22no—
443#106—22no—
444#106—441no—
445#106—441no—
446C4⋊C8C22⋊D1114yes—
447#103—22no—
448#103—22no—
449#103—222no—
450#103—222no—
451C22⋊C8—222no—
452C22⋊C8—222no—
453#97—222no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461C2×C11#242711yescharacteristic
462C2×C11#305611yescharacteristic
463C2×C11#306011yescharacteristic
464C2×C11#331711yescharacteristic
465C2×C11#332011yescharacteristic
466C2×C11#334411yescharacteristic
467C2×C11#335011yescharacteristic
468D11—42no—
469D11—81no—
470C24—111no—
471C24—111no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8#434312yes—
478C2×D4—222no—
479C2×D4—222no—
480C2×D4—441no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
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×C4D4×D1111yescharacteristic
504C22×C4D4×D1111yescharacteristic
505C22×C4C23×D1111yescharacteristic
506M16—444no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—112no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—444no—
518C2×C8C2×C22⋊D1112yes—
519C2×C8C2×C22⋊D1112yes—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—222no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—442no—
539C4⋊C4—442no—
540C4⋊C4—442no—
541C4⋊C4—881no—
542C22⋊C4—222no—
543C22⋊C4—222no—
544C22⋊C4—442no—
545C22⋊C4—442no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—881no—
549C22⋊C4—881no—
550C22⋊C4—881no—
551C22⋊C4—881no—
552C42—42no—
553C42—881no—
554C42#434112yes—
555C42C2×C22⋊D1112yes—
556C11#2535711yescharacteristic, complemented, Sylow
557C23—112no—
558C23—221no—
559C23—221no—
560C23—221no—
561C23—221no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23—221no—
571C23C2×D4×D1111yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—41no—
575Q8—41no—
576D4—444no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
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—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
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#6699112yes—
620C2×C4#6699112yes—
621C2×C4C2×#434111yescharacteristic
622C2×C4C2×#434311yescharacteristic
623C2×C4#6704011yescharacteristic
624C2×C4#41×D1111yescharacteristic
625C2×C4#6704211yescharacteristic
626C2×C4C22×C22⋊D1111yescharacteristic
627C8—22no—
628C8—22no—
629C8—222no—
630C8—441no—
631C22—222no—
632C22—222no—
633C22—222no—
634C22—441no—
635C22—441no—
636C22—441no—
637C22—441no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22—441no—
642C22—441no—
643C22—441no—
644C22—441no—
645C22#1062316111yescharacteristic
646C22#1062316211yescharacteristic
647C22#1062330111yescharacteristic
648C22#1062330111yescharacteristic
649C22D11×#13711yescharacteristic
650C22#1062330811yescharacteristic
651C22C2×#6699111yescharacteristic
652C4—22no—
653C4—22no—
654C4—42no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4—441no—
659C4—441no—
660C4—881no—
661C4—881no—
662C4—881no—
663C4—881no—
664C4#1062315511yescharacteristic
665C4#1062317411yescharacteristic
666C4#1062334811yescharacteristic
667C4#1062336011yescharacteristic
668C2—442no—
669C2—881no—
670C2#1307218911yescharacteristic
671C2#1307824011yescharacteristic
672C2#1307827411yescharacteristic
673C2#1308073911yescharacteristic
674C2#1308078411yescharacteristic
675C2#1308107811yescharacteristic
676C2#1308115811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#479C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×#479D11
hypocenterC11#25357
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
4. #13070050C2semidirect
5. #13070045C2semidirect
6. #13069811C2semidirect
7. #13069811C2semidirect
8. #13069586C2semidirect
9. #13069380C2semidirect
10. #13069046C2semidirect
11. #13069036C2semidirect
12. #13068650C2semidirect
13. #13068638C2semidirect
14. #13068446C2semidirect
15. C2×C11×#479C2semidirect
219. C2×#479D11semidirect
556. C11#25357semidirect

Maximal subgroups

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

subgroupindex
C2×#106224492
#130737832
#130735342
#130700502
#130700452
#130698112
#130695862
#130693802
#130690462
#130690362
#130686502
#130686382
#130684462
C2×C11×#4792
#2535711