Finite Group Databasebeta

← #14813684

Subgroups — #14813684

Order 2816.

846 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×#10622609C211yesmaximal, characteristic, complemented
2C2×#10622577C211yesmaximal, characteristic, complemented
3#13072045C211yesmaximal, characteristic
4#13070167C211yesmaximal, characteristic, complemented
5#13070098C211yesmaximal, characteristic, complemented
6#13070047C211yesmaximal, characteristic, complemented
7#13069812C211yesmaximal, characteristic, complemented
8#13069257C211yesmaximal, characteristic, complemented
9#13069201C211yesmaximal, characteristic, complemented
10#13069047C211yesmaximal, characteristic, complemented
11#13068923C211yesmaximal, characteristic, complemented
12#13068914C211yesmaximal, characteristic
13#13068815C211yesmaximal, characteristic, complemented
14#13068813C211yesmaximal, characteristic, complemented
15C11×#2352C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C11×#388—21no—
24C11×#387—21no—
25C11×#386—21no—
26C11×#382C2211yescharacteristic
27C11×#380C2211yescharacteristic
28C11×#380C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C22⋊C4—21no—
31#10622835—21no—
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622609—24no—
37#10622585—21no—
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42#10622577—24no—
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622565—21no—
50#10622558—21no—
51#10622542C2211yescharacteristic
52#10622541C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11D411yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C11×#117—22no—
69C11×#117—41no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—41no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90#66979—22no—
91#66979—41no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95#66977—22no—
96#66977—22no—
97#66977—22no—
98#66977—41no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C2×#4318—22no—
104C2×#4318—22no—
105C2×#4318—22no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C22⋊(C11⋊C8)—22no—
120C22⋊(C11⋊C8)—22no—
121C22⋊(C11⋊C8)—22no—
122#66874—22no—
123#66874—22no—
124#66874—22no—
125#66874—41no—
126#66872—22no—
127#66872—41no—
128#66872D414yescomplemented
129#66871—22no—
130#66871—22no—
131#66871—22no—
132#26154—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C24×C11C2×D411yescharacteristic
135C2×D4×C11—22no—
136C2×D4×C11—41no—
137C2×D4×C11—41no—
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×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—81no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4112yes—
160C22×C4×C11#4112yes—
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4C2×D412yes—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—81no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—42no—
190C42×C11—81no—
191C22⋊Dic11—42no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194C22⋊Dic11—42no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11C2×D412yes—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204C4×Dic11—42no—
205#4318—28no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8C2×D412yes—
217C2×C11⋊C8#4112yes—
218C2×#485—111no—
219C2×#428—111no—
220#2415—111no—
221#2352D1111yescharacteristic
222#2097—111no—
223#2085—111no—
224#2076—111no—
225#2035—111no—
226#1928—111no—
227#1920—111no—
228#1894—111no—
229#1872—111no—
230#1870—111no—
231#1854—111no—
232#1854—111no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11#12312yes—
247C23×C11C22×D411yescharacteristic
248D4×C11—44no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
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—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—84no—
281C2×C4×C11#12312yes—
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C112−1+411yescharacteristic
288C2×Dic11—22no—
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—41no—
299C2×Dic11—41no—
300Dic22—41no—
301Dic22—41no—
302Dic22—41no—
303Dic22—41no—
304C11⋊C8—22no—
305C11⋊C8—22no—
306C11⋊C8—41no—
307C11⋊C8—41no—
308C22×M16—111no—
309C2×C22⋊Q8—111no—
310C2×C22⋊Q8—111no—
311C2×C4×D4C2×D1111yescharacteristic
312C2×#117—111no—
313C2×#117C2×D1111yescharacteristic
314C22×C4⋊C4C2×D1111yescharacteristic
315#485—224no—
316#428—224no—
317C2×#107—111no—
318C2×#107—111no—
319C2×#107—111no—
320C2×#106—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×C22⋊C8—111no—
328C2×C22⋊C8—111no—
329C2×C22⋊C8—111no—
330#397—221no—
331#394—221no—
332#391—111no—
333#389—111no—
334#389—221no—
335#388—21no—
336#388—221no—
337#387—21no—
338#386—21no—
339#382C2×D1111yescharacteristic
340#380—111no—
341#380C2×D1111yescharacteristic
342#380C2×D1111yescharacteristic
343C4×C4⋊C4C2×D1111yescharacteristic
344C4×C22⋊C4—21no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#336—111no—
352#336—111no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11C2×#12311yescharacteristic
368C22×C11D4211yescharacteristic
369C22×C11#54711yescharacteristic
370C22×C11#57511yescharacteristic
371C22×C11#57511yescharacteristic
372C22×C11#57711yescharacteristic
373C22×C11#57811yescharacteristic
374C4×C11—22no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11—42no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11#52511yescharacteristic
383C4×C11#53911yescharacteristic
384C4×C11#54811yescharacteristic
385C4×C11#55311yescharacteristic
386Dic11—42no—
387Dic11—81no—
388Dic11—81no—
389Dic11—81no—
390C22×Q8—111no—
391C22×D4C22⋊D1111yescharacteristic
392C23×C4—21no—
393C23×C4C22×D1111yescharacteristic
394C23×C4C22×D1111yescharacteristic
395C2×M16—222no—
396C2×M16—222no—
397C2×M16—222no—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8—111no—
401C22×C8—111no—
402C22⋊Q8—222no—
403C22⋊Q8—222no—
404C22⋊Q8—222no—
405C22⋊Q8—441no—
406C4×D4—22no—
407C4×D4—22no—
408#117—22no—
409#117—41no—
410#117—222no—
411#117—441no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—41no—
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⋊C4C22⋊D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4C22⋊D1111yescharacteristic
434C2×C22⋊C4C22⋊D1111yescharacteristic
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—221no—
438C2×C42C22×D1111yescharacteristic
439#107—222no—
440#107—222no—
441#107—222no—
442#106—114no—
443#106—222no—
444#106—441no—
445#103—222no—
446#103—222no—
447#103—222no—
448#103—441no—
449C22⋊C8—222no—
450C22⋊C8—222no—
451C22⋊C8—222no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461C2×C11—42no—
462C2×C11—81no—
463C2×C11#244311yescharacteristic
464C2×C11#309311yescharacteristic
465C2×C11#309711yescharacteristic
466C2×C11#326911yescharacteristic
467C2×C11#327511yescharacteristic
468C2×C11#335011yescharacteristic
469C2×C11#335211yescharacteristic
470C24C2×C22⋊D1111yescharacteristic
471C24C2×C22⋊D1111yescharacteristic
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×D4—22no—
479C2×D4—41no—
480C2×D4—41no—
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—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—81no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4#433912yes—
503C22×C4#433912yes—
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C23×D1111yescharacteristic
509M16—228no—
510C2×C8—112no—
511C2×C8—112no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C4⋊C4—22no—
523C4⋊C4—21no—
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—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—442no—
538C4⋊C4—442no—
539C4⋊C4—442no—
540C4⋊C4D4×D1112yes—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—81no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C42—21no—
551C42—21no—
552C42—42no—
553C42—81no—
554C42—442no—
555C11#2615411yescharacteristic, complemented, Sylow
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23#6698212yes—
570C23C22×C22⋊D1111yescharacteristic
571Q8—441no—
572Q8—441no—
573Q8—441no—
574Q8—441no—
575D4—44no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—84no—
608C2×C4—222no—
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#6698212yes—
621C2×C4C2×#433911yescharacteristic
622C2×C4C2×#433911yescharacteristic
623C2×C4C2×D4×D1111yescharacteristic
624C2×C4#6703711yescharacteristic
625C2×C4#41×D1111yescharacteristic
626C2×C4#6704311yescharacteristic
627C8—222no—
628C8—222no—
629C8—441no—
630C8—441no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22C2×#6698211yescharacteristic
646C22D4×C22⋊D1111yescharacteristic
647C22#1062335311yescharacteristic
648C22#1062335311yescharacteristic
649C22#1062335511yescharacteristic
650C22#1062336711yescharacteristic
651C22#1062336911yescharacteristic
652C4—22no—
653C4—41no—
654C4—41no—
655C4—42no—
656C4—41no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—442no—
661C4—881no—
662C4—881no—
663C4—881no—
664C4#1062307111yescharacteristic
665C4#1062307811yescharacteristic
666C4#1062308311yescharacteristic
667C4#1062309511yescharacteristic
668C2—42no—
669C2—81no—
670C2#1307234511yescharacteristic
671C2#1307854711yescharacteristic
672C2#1307858511yescharacteristic
673C2#1308017211yescharacteristic
674C2#1308024311yescharacteristic
675C2#1308115511yescharacteristic
676C2#1308118511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2352C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2352D11
hypocenterC11#26154
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
1. C2×#10622609C2semidirect
2. C2×#10622577C2semidirect
4. #13070167C2semidirect
5. #13070098C2semidirect
6. #13070047C2semidirect
7. #13069812C2semidirect
8. #13069257C2semidirect
9. #13069201C2semidirect
10. #13069047C2semidirect
11. #13068923C2semidirect
13. #13068815C2semidirect
14. #13068813C2semidirect
128. #66872D4semidirect
555. C11#26154semidirect

Maximal subgroups

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

subgroupindex
C2×#106226092
C2×#106225772
#130720452
#130701672
#130700982
#130700472
#130698122
#130692572
#130692012
#130690472
#130689232
#130689142
#130688152
#130688132
C11×#23522
#2615411