Finite Group Databasebeta

← #14802040

Subgroups — #14802040

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622656C211yesmaximal, characteristic
2C2×#10622664C211yesmaximal, characteristic
3#13073101C211yesmaximal, characteristic
4#13070097C211yesmaximal, characteristic, complemented
5#13070034C211yesmaximal, characteristic, complemented
6#13069994C211yesmaximal, characteristic, complemented
7#13069938C211yesmaximal, characteristic, complemented
8#13069384C211yesmaximal, characteristic, complemented
9#13069250C211yesmaximal, characteristic, complemented
10#13068957C211yesmaximal, characteristic, complemented
11#13068923C211yesmaximal, characteristic
12#13068796C211yesmaximal, characteristic
13#13068631C211yesmaximal, characteristic, complemented
14C2×#10622167C211yesmaximal, characteristic
15C11×#2360C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C11×#391C2211yescharacteristic
24C11×#389—21no—
25C11×#389C2211yescharacteristic
26C11×#387—21no—
27C11×#385—21no—
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4—21no—
30C4×C11×C22⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622664—24no—
36#10622656—24no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622556—21no—
44#10622556—21no—
45#10622549C2211yescharacteristic
46#10622549C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622542C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622272—21no—
52#10622272—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C22×Dic22C2311yescharacteristic
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8D414yes—
68C4×Q8×C11—22no—
69C4×Q8×C11—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—41no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×#4326—22no—
88C2×#4326—22no—
89C2×#4326—41no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96#66977—22no—
97#66977—22no—
98C2×Dic11⋊C4—21no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8—22no—
101C22×C11⋊C8—41no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95D411yescharacteristic
111C11×#95D411yescharacteristic
112#66899—22no—
113#66899—22no—
114#66899—22no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C22⋊(C11⋊C8)—22no—
124#66874—22no—
125#66874—22no—
126#66874—41no—
127#66872—22no—
128#66872—22no—
129#66871—22no—
130C4⋊(C11⋊C8)—22no—
131C4⋊(C11⋊C8)—41no—
132#25208—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C2×D412yes—
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—42no—
149C22×C4×C11—42no—
150C22×C4×C11—81no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11#4112yes—
158C22×C4×C11C2411yescharacteristic
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—42no—
164C22×Dic11—42no—
165C22×Dic11—42no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—81no—
180C11×C4⋊C4C2×D412yes—
181C11×C4⋊C4#4112yes—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—42no—
190C42×C11—81no—
191C22⋊Dic11—42no—
192#4326—44no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—42no—
200Dic11⋊C4—42no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
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—44no—
213C2×C11⋊C8#4112yes—
214C2×#483—111no—
215C2×#467—111no—
216#2503—111no—
217#2360D1111yescharacteristic
218#2085—111no—
219#2074—111no—
220#2066—111no—
221#2056—111no—
222#1949—111no—
223#1927—111no—
224#1878—111no—
225#1872—111no—
226#1850—111no—
227#1805—111no—
228C2×#340—111no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11#12112yes—
234C23×C11#13512yes—
235C23×C11#13712yes—
236C23×C11C22×D411yescharacteristic
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—41no—
240Q8×C11—41no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
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—84no—
272C2×C4×C11#12112yes—
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
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
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—84no—
292Dic22—41no—
293Dic22—41no—
294Dic22—41no—
295Dic22—41no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C22×Q16—111no—
301C23×C8—111no—
302C2×C22⋊Q8—111no—
303C2×C22⋊Q8C2×D1111yescharacteristic
304C2×C4×Q8C2×D1111yescharacteristic
305C22×C4⋊C4—111no—
306C22×C4⋊C4C2×D1111yescharacteristic
307#483—224no—
308#467—224no—
309C2×#107—111no—
310C2×#106—111no—
311C2×#106—111no—
312C2×C4⋊C8—111no—
313C2×C4⋊C8—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×C22⋊C8—111no—
321#400—221no—
322#400—221no—
323#391—111no—
324#391—111no—
325#391C2×D1111yescharacteristic
326#389—21no—
327#389C2×D1111yescharacteristic
328#387—21no—
329#385—21no—
330#382—111no—
331#382—111no—
332#381—221no—
333#381—221no—
334C4×C4⋊C4C2×D1111yescharacteristic
335C4×C22⋊C4—21no—
336C4×C22⋊C4C2×D1111yescharacteristic
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#336—111no—
344#336—111no—
345C22×C11—22no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11#46414yes—
352C22×C11C2×#12111yescharacteristic
353C22×C11#54611yescharacteristic
354C22×C11#54711yescharacteristic
355C22×C11C2×#13511yescharacteristic
356C22×C11C2×#13711yescharacteristic
357C22×C11#57711yescharacteristic
358C22×C11#57811yescharacteristic
359C4×C11—22no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—42no—
363C4×C11—41no—
364C4×C11—42no—
365C4×C11—42no—
366C4×C11—41no—
367C4×C11—81no—
368C4×C11#52911yescharacteristic
369C4×C11#53911yescharacteristic
370C4×C11#54611yescharacteristic
371C4×C11#54711yescharacteristic
372Dic11—81no—
373Dic11—81no—
374Dic11—81no—
375Dic11—81no—
376C22×Q8—111no—
377C22×Q8C22×D1111yescharacteristic
378C23×C4—21no—
379C23×C4—221no—
380C23×C4C22×D1111yescharacteristic
381C2×Q16—222no—
382C2×Q16—222no—
383C2×Q16—441no—
384C22×C8—111no—
385C22×C8—111no—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8—222no—
389C22×C8—222no—
390C22×C8—441no—
391C22⋊Q8—22no—
392C22⋊Q8—222no—
393C22⋊Q8—222no—
394C22⋊Q8D4414yes—
395C4×Q8—22no—
396C4×Q8—41no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—41no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4C22⋊D1111yescharacteristic
416C2×C22⋊C4C22⋊D1111yescharacteristic
417C2×C42—21no—
418C2×C42—21no—
419C2×C42C22×D1111yescharacteristic
420C2×C42C22×D1111yescharacteristic
421#107—222no—
422#106—222no—
423#106—222no—
424C4⋊C8—222no—
425C4⋊C8—441no—
426#103—222no—
427#103—222no—
428#103—222no—
429#103—222no—
430#103—222no—
431#103—441no—
432C22⋊C8—222no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95C22⋊D1111yescharacteristic
446#95C22⋊D1111yescharacteristic
447C2×C11—24no—
448C2×C11#242511yescharacteristic
449C2×C11C2×#46411yescharacteristic
450C2×C11#304611yescharacteristic
451C2×C11#329611yescharacteristic
452C2×C11#331211yescharacteristic
453C2×C11#333611yescharacteristic
454C2×C11#334411yescharacteristic
455C24C2×C22⋊D1111yescharacteristic
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8C2×D4412yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—81no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—442no—
484C22×C4—442no—
485C22×C4—442no—
486C22×C4C2×D4412yes—
487C22×C4#433912yes—
488C22×C4C2×C22⋊D1111yescharacteristic
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C23×D1111yescharacteristic
494Q16—444no—
495C2×C8—112no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—444no—
508C4⋊C4—24no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—42no—
514C4⋊C4—42no—
515C4⋊C4—81no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4C2×D4412yes—
525C4⋊C4#434112yes—
526C22⋊C4—24no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—442no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—42no—
535C42—81no—
536C11#2520811yescharacteristic, complemented, Sylow
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23#6698312yes—
542C23#6699512yes—
543C23#6700312yes—
544C23C22×C22⋊D1111yescharacteristic
545Q8—22no—
546Q8—22no—
547Q8—41no—
548Q8—41no—
549Q8—441no—
550Q8—441no—
551Q8—441no—
552Q8—441no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—84no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—884no—
597C2×C4#6698312yes—
598C2×C4C22×D4411yescharacteristic
599C2×C4C2×#433911yescharacteristic
600C2×C4C2×#434111yescharacteristic
601C2×C4#6703711yescharacteristic
602C2×C4#41×D1111yescharacteristic
603C2×C4#6704311yescharacteristic
604C8—222no—
605C8—441no—
606C8—441no—
607C8—441no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22#1062264114yes—
615C22C2×#6698311yescharacteristic
616C22#1062333711yescharacteristic
617C22C2×#6699511yescharacteristic
618C22C2×#6700311yescharacteristic
619C22#1062335511yescharacteristic
620C22#1062336711yescharacteristic
621C22#1062336911yescharacteristic
622C4—22no—
623C4—42no—
624C4—41no—
625C4—41no—
626C4—42no—
627C4—41no—
628C4—42no—
629C4—41no—
630C4—81no—
631C4—881no—
632C4—881no—
633C4—881no—
634C4—881no—
635C4#1062306911yescharacteristic
636C4#1062308511yescharacteristic
637C4#1062308611yescharacteristic
638C4#1062309511yescharacteristic
639C2—24no—
640C2#1307216111yescharacteristic
641C2C2×#1062264111yescharacteristic
642C2#1307816611yescharacteristic
643C2#1308045111yescharacteristic
644C2#1308066711yescharacteristic
645C2#1308097811yescharacteristic
646C2#1308106511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2360C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2360D11
hypocenterC11#25208
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
4. #13070097C2semidirect
5. #13070034C2semidirect
6. #13069994C2semidirect
7. #13069938C2semidirect
8. #13069384C2semidirect
9. #13069250C2semidirect
10. #13068957C2semidirect
13. #13068631C2semidirect
536. C11#25208semidirect

Maximal subgroups

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

subgroupindex
C2×#106226562
C2×#106226642
#130731012
#130700972
#130700342
#130699942
#130699382
#130693842
#130692502
#130689572
#130689232
#130687962
#130686312
C2×#106221672
C11×#23602
#2520811