Finite Group Databasebeta

← #14804127

Subgroups — #14804127

Order 2816.

840 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622404C211yesmaximal, characteristic, complemented
2C2×#10622740C211yesmaximal, characteristic
3#13073786C211yesmaximal, characteristic
4#13073523C211yesmaximal, characteristic
5#13070052C211yesmaximal, characteristic, complemented
6#13070051C211yesmaximal, characteristic, complemented
7#13069818C211yesmaximal, characteristic, complemented
8#13069809C211yesmaximal, characteristic, complemented
9#13069587C211yesmaximal, characteristic, complemented
10#13069387C211yesmaximal, characteristic, complemented
11#13069036C211yesmaximal, characteristic, complemented
12#13068649C211yesmaximal, characteristic, complemented
13#13068640C211yesmaximal, characteristic, complemented
14#13068448C211yesmaximal, characteristic, complemented
15C11×#1894C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C2×#66941C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C11×#380C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28#10622825C2211yescharacteristic
29#10622825C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31#10622740—24no—
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37#10622603—21no—
38#10622600C2211yescharacteristic
39#10622600C2211yescharacteristic
40#10622600C2211yescharacteristic
41#10622597—21no—
42#10622590C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46#10622574—21no—
47#10622570—21no—
48#10622560—21no—
49#10622558—21no—
50#10622404—24no—
51#10622286—21no—
52#10622263—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11D411yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×Dic22—21no—
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—41no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11D411yescharacteristic
82#66999—22no—
83#66999—41no—
84Q8×Dic11—22no—
85Q8×Dic11—22no—
86C4×C22⋊D11—22no—
87C4×C22⋊D11—22no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4D411yescharacteristic
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4D411yescharacteristic
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C2×C8×D11—22no—
107C2×C8×D11—22no—
108C2×C8×D11—41no—
109#66941—22no—
110#66941—22no—
111C11×#103—22no—
112C11×#103—22no—
113C11×#95—21no—
114#66899—22no—
115#66899—22no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C22⋊(C11⋊C8)—22no—
125(C2×D11)⋊C8—22no—
126#66882—41no—
127#66881—22no—
128#66879—22no—
129Dic11⋊C8D414yes—
130#66872—22no—
131#66872—41no—
132#25356—111nomaximal, Sylow
133C24×C11C2×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×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—22no—
154C2×C22⋊D11—22no—
155C2×C22⋊D11—41no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
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×Dic22—42no—
170C2×Dic22—81no—
171C2×Dic22—81no—
172C11×M16—44no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11C2×D412yes—
178C2×C8×C11#4112yes—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—42no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—81no—
188C22⋊Dic11—22no—
189C22⋊Dic11—42no—
190C22⋊Dic11—81no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—81no—
195(C2×D11)⋊C4—81no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—42no—
205Dic11⋊C4—22no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C4×Dic11C2×D412yes—
211C4×Dic11#4112yes—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8C2×D412yes—
218C8×D11—44no—
219C2×#475—111no—
220C2×#435—111no—
221#2563—111no—
222#2536—111no—
223#2077—111no—
224#2077—111no—
225#2036—111no—
226#2035—111no—
227#1993—111no—
228#1949—111no—
229#1894D1111yescharacteristic, complemented
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—21no—
241C23×C11C22×D411yescharacteristic
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—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
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×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C2×C4×C112−1+411yescharacteristic
278C22⋊D11—44no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
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—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11#12112yes—
299C2×Dic11#12112yes—
300C4×D11—41no—
301C4×D11—41no—
302C4×D11—41no—
303C4×D11—41no—
304Dic22—84no—
305C8×C11—22no—
306C8×C11—22no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309C22×M16C2×D1111yescharacteristic
310C23×C8—111no—
311C2×C4⋊Q8—111no—
312C2×C22⋊Q8—111no—
313C2×C22⋊Q8C2×D1111yescharacteristic
314C2×C4×Q8—111no—
315C2×C4×D4—111no—
316#475—224no—
317#435—224no—
318C2×#107—111no—
319C2×#106—111no—
320C2×#106—111no—
321C2×#106—111no—
322C2×C4⋊C8—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#103C2×D1111yescharacteristic
326C2×#103C2×D1111yescharacteristic
327C2×C22⋊C8—111no—
328C2×C22⋊C8—111no—
329C2×#97—111no—
330#398—221no—
331#394—221no—
332#393—221no—
333#393—221no—
334#390—221no—
335#388—221no—
336#388—221no—
337#382—111no—
338#382—221no—
339#380—111no—
340#380—111no—
341#380—111no—
342#380—111no—
343#380—111no—
344#380C2×D1111yescharacteristic
345C4×C4⋊C4—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340C2×D1111yescharacteristic
353#340C2×D1111yescharacteristic
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11C2×#12111yescharacteristic
362C22×C11#54611yescharacteristic
363C22×C11#54711yescharacteristic
364C22×C11C2×#13711yescharacteristic
365C22×C11#57511yescharacteristic
366C22×C11#57711yescharacteristic
367C22×C11#57711yescharacteristic
368C2×D11—22no—
369C2×D11—22no—
370C2×D11—22no—
371C2×D11—41no—
372C2×D11—41no—
373C2×D11—41no—
374C2×D11—41no—
375C4×C11—41no—
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—22no—
385Dic11—22no—
386Dic11—41no—
387Dic11—81no—
388Dic11—81no—
389Dic11—81no—
390Dic11—81no—
391C22×Q8—221no—
392C22×Q8C22×D1111yescharacteristic
393C22×D4—111no—
394C23×C4—111no—
395C23×C4C22×D1111yescharacteristic
396C2×M16—22no—
397C2×M16—22no—
398C2×M16—41no—
399C22×C8—111no—
400C22×C8—111no—
401C22×C8—222no—
402C22×C8—222no—
403C22×C8—441no—
404C22×C8C22×D1111yescharacteristic
405C22×C8C22×D1111yescharacteristic
406C4⋊Q8—222no—
407C4⋊Q8—222no—
408C22⋊Q8—22no—
409C22⋊Q8—41no—
410C22⋊Q8—222no—
411C22⋊Q8—441no—
412C4×Q8—222no—
413C4×Q8—222no—
414C4×D4—222no—
415C4×D4—222no—
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⋊C4C22×D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—111no—
431C2×C22⋊C4—111no—
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×C42—111no—
439C2×C42—221no—
440C2×C42—221no—
441#107—441no—
442#106—222no—
443#106—222no—
444#106—441no—
445C4⋊C8—114no—
446#103—22no—
447#103—22no—
448#103—222no—
449#103—222no—
450C22⋊C8—222no—
451C22⋊C8—222no—
452#97—222no—
453#95—21no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462C2×C11—81no—
463C2×C11#242711yescharacteristic
464C2×C11#305611yescharacteristic
465C2×C11#305711yescharacteristic
466C2×C11#331611yescharacteristic
467C2×C11#332111yescharacteristic
468C2×C11#334411yescharacteristic
469C2×C11#334811yescharacteristic
470D11—42no—
471C24—111no—
472C24D4×D1111yescharacteristic
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—442no—
479C2×Q8—881no—
480C2×Q8—881no—
481C2×Q8#433912yes—
482C2×D4—222no—
483C2×D4—222no—
484C2×D4—441no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4D4×D1111yescharacteristic
509C22×C4C23×D1111yescharacteristic
510M16—44no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—112no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—444no—
522C2×C8D4×D1112yes—
523C2×C8#434112yes—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—222no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—442no—
541C4⋊C4—442no—
542C4⋊C4—442no—
543C22⋊C4—42no—
544C22⋊C4—81no—
545C22⋊C4—222no—
546C22⋊C4—222no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C22⋊C4—881no—
551C22⋊C4—881no—
552C22⋊C4—881no—
553C42—112no—
554C42—112no—
555C42—442no—
556C42—442no—
557C11#2535611yescharacteristic, complemented, Sylow
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—112no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23—221no—
571C23—221no—
572C23C2×D4×D1111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577Q8—884no—
578D4—444no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
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—41no—
597C2×C4—41no—
598C2×C4—112no—
599C2×C4—112no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
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×C4—441no—
622C2×C4—441no—
623C2×C4C2×#433911yescharacteristic
624C2×C4C2×D4×D1111yescharacteristic
625C2×C4C2×#434111yescharacteristic
626C2×C4#6703711yescharacteristic
627C2×C4#41×D1111yescharacteristic
628C2×C4#6704311yescharacteristic
629C8—22no—
630C8—22no—
631C8—222no—
632C8—441no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—222no—
641C22—222no—
642C22—222no—
643C22—441no—
644C22—441no—
645C22—441no—
646C22—441no—
647C22#1062302111yescharacteristic
648C22D11×#12111yescharacteristic
649C22#1062314211yescharacteristic
650C22#1062330611yescharacteristic
651C22D11×#13711yescharacteristic
652C22#1062330811yescharacteristic
653C22#1062330911yescharacteristic
654C4—41no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4—222no—
660C4—222no—
661C4—441no—
662C4—881no—
663C4—881no—
664C4—881no—
665C4—881no—
666C4#1062306911yescharacteristic
667C4#1062308311yescharacteristic
668C4#1062312211yescharacteristic
669C4#1062319311yescharacteristic
670C2—81no—
671C2—442no—
672C2#1307219011yescharacteristic
673C2#1307824511yescharacteristic
674C2#1307825311yescharacteristic
675C2#1308072811yescharacteristic
676C2#1308080311yescharacteristic
677C2#1308106611yescharacteristic
678C2#1308112611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1894C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenter#1894D11
hypocenterC11#25356
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
1. C2×#10622404C2semidirect
5. #13070052C2semidirect
6. #13070051C2semidirect
7. #13069818C2semidirect
8. #13069809C2semidirect
9. #13069587C2semidirect
10. #13069387C2semidirect
11. #13069036C2semidirect
12. #13068649C2semidirect
13. #13068640C2semidirect
14. #13068448C2semidirect
15. C11×#1894C2semidirect
229. #1894D11semidirect
557. C11#25356semidirect

Maximal subgroups

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

subgroupindex
C2×#106224042
C2×#106227402
#130737862
#130735232
#130700522
#130700512
#130698182
#130698092
#130695872
#130693872
#130690362
#130686492
#130686402
#130684482
C11×#18942
#2535611