Finite Group Databasebeta

← #14813711

Subgroups — #14813711

Order 2816.

854 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622427C211yesmaximal, characteristic, complemented
2C2×#10622734C211yesmaximal, characteristic, complemented
3#13072068C211yesmaximal, characteristic
4#13071560C211yesmaximal, characteristic
5#13070157C211yesmaximal, characteristic, complemented
6#13070096C211yesmaximal, characteristic, complemented
7#13070051C211yesmaximal, characteristic, complemented
8#13069811C211yesmaximal, characteristic, complemented
9#13069259C211yesmaximal, characteristic, complemented
10#13069207C211yesmaximal, characteristic, complemented
11#13068929C211yesmaximal, characteristic, complemented
12#13068913C211yesmaximal, characteristic
13#13068818C211yesmaximal, characteristic, complemented
14#13068808C211yesmaximal, characteristic, complemented
15C11×#1894C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C2×#66945C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C11×#380C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30#10622734—24no—
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37#10622607—21no—
38#10622600C2211yescharacteristic
39#10622600C2211yescharacteristic
40#10622597—21no—
41#10622589C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622586C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46#10622571—21no—
47#10622570—21no—
48#10622558—21no—
49#10622555—21no—
50#10622427—24no—
51#10622282—21no—
52#10622262—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11D411yescharacteristic
64C23×Dic11—21no—
65C22×C4×D11C2311yescharacteristic
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
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⋊Dic11D411yescharacteristic
81#66999—22no—
82#66999—41no—
83C4×C22⋊D11—22no—
84C4×C22⋊D11—22no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4D411yescharacteristic
90#66979—22no—
91#66979—41no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—41no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4D411yescharacteristic
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110#66945—22no—
111#66945—41no—
112C11×#103—22no—
113C11×#103—22no—
114C11×#95—21no—
115#66899—22no—
116#66899—41no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C22⋊(C11⋊C8)—22no—
124(C2×D11)⋊C8—22no—
125(C2×D11)⋊C8—22no—
126#66882—22no—
127#66882D414yescomplemented
128#66881—22no—
129#66881—22no—
130#66872—22no—
131#66872—41no—
132#26155—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—21no—
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×C11C2×D411yescharacteristic
150C22×C4×C11#4112yes—
151C22×C4×C11#4112yes—
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×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11—81no—
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C11×M16—28no—
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—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—81no—
194(C2×D11)⋊C4—81no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—42no—
202C4⋊Dic11C2×D412yes—
203C4⋊Dic11C2×D412yes—
204Dic11⋊C4—22no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207Dic11⋊C4—81no—
208Dic11⋊C4—81no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—42no—
212C4×Dic11—42no—
213C4×Dic11—42no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×#485—111no—
221C2×#428—111no—
222#2417—111no—
223#2354—111no—
224#2096—111no—
225#2084—111no—
226#2077—111no—
227#2035—111no—
228#1928—111no—
229#1921—111no—
230#1894D1111yescharacteristic, complemented
231#1873—111no—
232#1870—111no—
233#1854—111no—
234#1853—111no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11#12312yes—
242C23×C11C22×D411yescharacteristic
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11—41no—
253Q8×C11—41no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
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×C11#12312yes—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C112−1+411yescharacteristic
279C22⋊D11—44no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
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—41no—
299C2×Dic11—41no—
300C2×Dic11—84no—
301C2×Dic11#13712yes—
302C4×D11—41no—
303C4×D11—41no—
304C4×D11—41no—
305C4×D11—41no—
306C8×C11—22no—
307C8×C11—22no—
308C11⋊C8—41no—
309C11⋊C8—41no—
310C22×M16C2×D1111yescharacteristic
311C2×C22⋊Q8—111no—
312C2×C22⋊Q8C2×D1111yescharacteristic
313C2×C4×D4—111no—
314C2×#117—111no—
315C2×#117—111no—
316C22×C4⋊C4—111no—
317#485—224no—
318#428—224no—
319C2×#107—111no—
320C2×#107—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×#106—111no—
324C2×#106—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103C2×D1111yescharacteristic
328C2×#103C2×D1111yescharacteristic
329C2×C22⋊C8—111no—
330C2×C22⋊C8—111no—
331C2×C22⋊C8—111no—
332#398—221no—
333#396—221no—
334#391—111no—
335#390—221no—
336#389—111no—
337#388—221no—
338#388—221no—
339#386—221no—
340#384—111no—
341#380—111no—
342#380—111no—
343#380—221no—
344#380C2×D1111yescharacteristic
345C4×C4⋊C4—111no—
346C4×C4⋊C4—221no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340C2×D1111yescharacteristic
352#340C2×D1111yescharacteristic
353#336—111no—
354#336—111no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11C2×#12311yescharacteristic
363C22×C11D4211yescharacteristic
364C22×C11#54711yescharacteristic
365C22×C11C2×#13711yescharacteristic
366C22×C11#57511yescharacteristic
367C22×C11#57711yescharacteristic
368C22×C11#57711yescharacteristic
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C2×D11—41no—
374C2×D11—41no—
375C2×D11—41no—
376C4×C11—22no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11#52511yescharacteristic
382C4×C11#53911yescharacteristic
383C4×C11#54811yescharacteristic
384C4×C11#55311yescharacteristic
385Dic11—22no—
386Dic11—41no—
387Dic11—41no—
388Dic11—42no—
389Dic11—42no—
390Dic11—81no—
391Dic11—81no—
392C22×Q8C22×D1111yescharacteristic
393C22×D4—111no—
394C23×C4—111no—
395C23×C4—221no—
396C23×C4C22×D1111yescharacteristic
397C2×M16—22no—
398C2×M16—22no—
399C2×M16—22no—
400C22×C8—111no—
401C22×C8—111no—
402C22×C8C22×D1111yescharacteristic
403C22×C8C22×D1111yescharacteristic
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—222no—
407C22⋊Q8—441no—
408C4×D4—222no—
409C4×D4—222no—
410#117—222no—
411#117—222no—
412#117—441no—
413#117—441no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—222no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—441no—
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—111no—
433C2×C22⋊C4—111no—
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—
442C2×C42—221no—
443#107—114no—
444#107—222no—
445#106—222no—
446#106—222no—
447#106—222no—
448#106—441no—
449#103—22no—
450#103—22no—
451#103—222no—
452#103—441no—
453C22⋊C8—222no—
454C22⋊C8—222no—
455C22⋊C8—222no—
456#95—21no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463C2×C11—42no—
464C2×C11#244311yescharacteristic
465C2×C11#309511yescharacteristic
466C2×C11#309911yescharacteristic
467C2×C11#326711yescharacteristic
468C2×C11#327811yescharacteristic
469C2×C11#334811yescharacteristic
470C2×C11#335611yescharacteristic
471D11—81no—
472C24—111no—
473C24D4×D1111yescharacteristic
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×D4—222no—
481C2×D4—222no—
482C2×D4—441no—
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×C4—442no—
505C22×C4—442no—
506C22×C4—881no—
507C22×C4#433912yes—
508C22×C4D4×D1111yescharacteristic
509C22×C4#434112yes—
510C22×C4C23×D1111yescharacteristic
511M16—28no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
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—112no—
532C4⋊C4—112no—
533C4⋊C4—222no—
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—
543C4⋊C4—881no—
544C4⋊C4—881no—
545C22⋊C4—42no—
546C22⋊C4—81no—
547C22⋊C4—222no—
548C22⋊C4—222no—
549C22⋊C4—442no—
550C22⋊C4—442no—
551C22⋊C4—442no—
552C22⋊C4—881no—
553C22⋊C4—881no—
554C42—221no—
555C42—221no—
556C42—442no—
557C42—442no—
558C42—442no—
559C11#2615511yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23—221no—
571C23—221no—
572C23—221no—
573C23#6693612yes—
574C23C2×D4×D1111yescharacteristic
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579D4—444no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
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—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—222no—
606C2×C4—221no—
607C2×C4—222no—
608C2×C4—221no—
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×C4—884no—
624C2×C4#6693612yes—
625C2×C4C2×#433911yescharacteristic
626C2×C4C2×D4×D1111yescharacteristic
627C2×C4C2×#434111yescharacteristic
628C2×C4C2×#434111yescharacteristic
629C2×C4#6704211yescharacteristic
630C2×C4#6704311yescharacteristic
631C8—22no—
632C8—22no—
633C8—441no—
634C8—441no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—441no—
643C22—441no—
644C22—441no—
645C22—441no—
646C22—441no—
647C22—441no—
648C22—441no—
649C22C2×#6693611yescharacteristic
650C22#1062314011yescharacteristic
651C22#1062314211yescharacteristic
652C22#1062330611yescharacteristic
653C22D11×#13711yescharacteristic
654C22#1062330811yescharacteristic
655C22#1062330911yescharacteristic
656C4—22no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—222no—
662C4—441no—
663C4—442no—
664C4—442no—
665C4—441no—
666C4—881no—
667C4—881no—
668C4#1062308311yescharacteristic
669C4#1062309611yescharacteristic
670C4#1062311711yescharacteristic
671C4#1062319611yescharacteristic
672C2—42no—
673C2—881no—
674C2#1307235711yescharacteristic
675C2#1307856211yescharacteristic
676C2#1307860411yescharacteristic
677C2#1308014811yescharacteristic
678C2#1308027911yescharacteristic
679C2#1308112611yescharacteristic
680C2#1308122611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1894C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenter#1894D11
hypocenterC11#26155
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×#10622427C2semidirect
2. C2×#10622734C2semidirect
5. #13070157C2semidirect
6. #13070096C2semidirect
7. #13070051C2semidirect
8. #13069811C2semidirect
9. #13069259C2semidirect
10. #13069207C2semidirect
11. #13068929C2semidirect
13. #13068818C2semidirect
14. #13068808C2semidirect
15. C11×#1894C2semidirect
127. #66882D4semidirect
230. #1894D11semidirect
559. C11#26155semidirect

Maximal subgroups

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

subgroupindex
C2×#106224272
C2×#106227342
#130720682
#130715602
#130701572
#130700962
#130700512
#130698112
#130692592
#130692072
#130689292
#130689132
#130688182
#130688082
C11×#18942
#2615511