Finite Group Databasebeta

← #14802044

Subgroups — #14802044

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×#10622334C211yesmaximal, characteristic
2C2×#10622729C211yesmaximal, characteristic
3#13073101C211yesmaximal, characteristic
4#13071619C211yesmaximal, characteristic
5#13070099C211yesmaximal, characteristic, complemented
6#13070036C211yesmaximal, characteristic, complemented
7#13069996C211yesmaximal, characteristic, complemented
8#13069939C211yesmaximal, characteristic, complemented
9#13069386C211yesmaximal, characteristic, complemented
10#13069251C211yesmaximal, characteristic, complemented
11#13068956C211yesmaximal, characteristic, complemented
12#13068921C211yesmaximal, characteristic
13#13068632C211yesmaximal, characteristic, complemented
14C2×#10622189C211yesmaximal, characteristic
15C11×#1850C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C22×Dic44C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27#10622729—24no—
28C2×#66882C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37#10622559—21no—
38#10622556—21no—
39#10622556—21no—
40C22⋊C4×Dic11—21no—
41#10622549C2211yescharacteristic
42#10622549C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622334—24no—
49#10622272—21no—
50#10622272—21no—
51#10622268—21no—
52#10622260—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C23×Dic11—21no—
64C22×Dic22C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C22×C8×C11—22no—
67C22×C8×C11—22no—
68C22×C8×C11—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C11×C22⋊C4D411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—41no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91#66977—22no—
92#66977—22no—
93#66977—22no—
94#66977D414yes—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×Dic44—22no—
102C2×Dic44—22no—
103C2×Dic44—41no—
104C4×Dic22—22no—
105C4×Dic22—41no—
106C11×C4⋊C8—22no—
107C11×C4⋊C8—41no—
108C11×C22⋊C8—22no—
109C11×#95D411yescharacteristic
110C11×#95D411yescharacteristic
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123#66882—22no—
124#66881—22no—
125#66881—22no—
126#66880—22no—
127#66880—22no—
128#66880—22no—
129#66880—22no—
130#66880—22no—
131#66880—41no—
132#25208—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D412yes—
144C22×C4×C11#4112yes—
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157C22×Dic11—42no—
158C22×Dic11—42no—
159C22×Dic11—81no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22C2×D412yes—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—44no—
184C2×C8×C11#4112yes—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C22⋊Dic11—24no—
192C22⋊Dic11—42no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—42no—
204C4⋊Dic11—42no—
205C4⋊Dic11C2×D412yes—
206C4⋊Dic11#4112yes—
207Dic11⋊C4—24no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—81no—
211C4×Dic11—42no—
212C4×Dic11—81no—
213Dic44—44no—
214C2×#483—111no—
215C2×#467—111no—
216#2503—111no—
217#2360—111no—
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#1850D1111yescharacteristic
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
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11#12112yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C112−1+411yescharacteristic
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—84no—
287C2×Dic11—84no—
288Dic22—22no—
289Dic22—22no—
290Dic22—41no—
291Dic22—41no—
292Dic22—41no—
293Dic22—41no—
294Dic22—41no—
295Dic22—41no—
296C8×C11—22no—
297C8×C11—41no—
298C8×C11—41no—
299C8×C11—41no—
300C22×Q16—111no—
301C23×C8C2×D1111yescharacteristic
302C2×C22⋊Q8—111no—
303C2×C22⋊Q8—111no—
304C2×C4×Q8—111no—
305C22×C4⋊C4—111no—
306C22×C4⋊C4—111no—
307#483—224no—
308#467—224no—
309C2×#107—111no—
310C2×#106—111no—
311C2×#106—111no—
312C2×C4⋊C8C2×D1111yescharacteristic
313C2×C4⋊C8C2×D1111yescharacteristic
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×C22⋊C8C2×D1111yescharacteristic
321#400—221no—
322#400—221no—
323#391—111no—
324#391—111no—
325#391—111no—
326#389—111no—
327#389—221no—
328#387—221no—
329#385—221no—
330#382—111no—
331#382—111no—
332#381—221no—
333#381—221no—
334C4×C4⋊C4—111no—
335C4×C22⋊C4—221no—
336C4×C22⋊C4C2×D1111yescharacteristic
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#336C2×D1111yescharacteristic
344#336C2×D1111yescharacteristic
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—41no—
363C4×C11—41no—
364C4×C11#52911yescharacteristic
365C4×C11#53911yescharacteristic
366C4×C11#54611yescharacteristic
367C4×C11#54711yescharacteristic
368Dic11—42no—
369Dic11—42no—
370Dic11—42no—
371Dic11—81no—
372Dic11—81no—
373Dic11—81no—
374Dic11—81no—
375Dic11—81no—
376C22×Q8—111no—
377C22×Q8—111no—
378C23×C4—221no—
379C23×C4—221no—
380C23×C4C22×D1111yescharacteristic
381C2×Q16—222no—
382C2×Q16—222no—
383C2×Q16—441no—
384C22×C8—22no—
385C22×C8—22no—
386C22×C8—41no—
387C22×C8C22×D1111yescharacteristic
388C22×C8C22×D1111yescharacteristic
389C22×C8C22×D1111yescharacteristic
390C22×C8C22×D1111yescharacteristic
391C22⋊Q8—114no—
392C22⋊Q8—222no—
393C22⋊Q8—222no—
394C22⋊Q8—222no—
395C4×Q8—222no—
396C4×Q8—441no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—222no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—441no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4D4411yescharacteristic
416C2×C22⋊C4D4411yescharacteristic
417C2×C42—221no—
418C2×C42—221no—
419C2×C42C22×D1111yescharacteristic
420C2×C42C22×D1111yescharacteristic
421#107—222no—
422#106—222no—
423#106—222no—
424C4⋊C8—22no—
425C4⋊C8—41no—
426#103—222no—
427#103—222no—
428#103—222no—
429#103—222no—
430#103—222no—
431#103—441no—
432C22⋊C8—22no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
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#95D4411yescharacteristic
446#95D4411yescharacteristic
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×D4411yescharacteristic
456C2×Q8—112no—
457C2×Q8—221no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—442no—
481C22×C4—442no—
482C22×C4—442no—
483C22×C4—442no—
484C22×C4—442no—
485C22×C4—881no—
486C22×C4C2×D4411yescharacteristic
487C22×C4C2×D4411yescharacteristic
488C22×C4C2×D4411yescharacteristic
489C22×C4C2×D4411yescharacteristic
490C22×C4C2×D4411yescharacteristic
491C22×C4D4×D1112yes—
492C22×C4#434312yes—
493C22×C4C23×D1111yescharacteristic
494Q16—444no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—44no—
507C2×C8#434112yes—
508C4⋊C4—112no—
509C4⋊C4—112no—
510C4⋊C4—224no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—442no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—881no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—224no—
529C22⋊C4—442no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—442no—
535C42—881no—
536C11#2520811yescharacteristic, complemented, Sylow
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23#6694812yes—
542C23#6695712yes—
543C23#6696212yes—
544C23C22×D4411yescharacteristic
545Q8—222no—
546Q8—222no—
547Q8—441no—
548Q8—441no—
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—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
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—884no—
596C2×C4—884no—
597C2×C4#6694812yes—
598C2×C4C2×D4×D1111yescharacteristic
599C2×C4C2×#434111yescharacteristic
600C2×C4#6703711yescharacteristic
601C2×C4C2×#434311yescharacteristic
602C2×C4#41×D1111yescharacteristic
603C2×C4#6704311yescharacteristic
604C8—22no—
605C8—41no—
606C8—41no—
607C8—41no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22#1062245814yes—
615C22C2×#6694811yescharacteristic
616C22#1062308511yescharacteristic
617C22#1062308611yescharacteristic
618C22C2×#6695711yescharacteristic
619C22C2×#6696211yescharacteristic
620C22#1062328211yescharacteristic
621C22#1062328411yescharacteristic
622C4—22no—
623C4—41no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—442no—
628C4—442no—
629C4—442no—
630C4—881no—
631C4—881no—
632C4—881no—
633C4—881no—
634C4—881no—
635C4#1062312211yescharacteristic
636C4#1062315511yescharacteristic
637C4#1062317611yescharacteristic
638C4#1062318611yescharacteristic
639C2—24no—
640C2#1307216511yescharacteristic
641C2C2×#1062245811yescharacteristic
642C2#1307816811yescharacteristic
643C2#1308045311yescharacteristic
644C2#1308066911yescharacteristic
645C2#1308098511yescharacteristic
646C2#1308107311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1850C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1850D11
hypocenterC11#25208
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
5. #13070099C2semidirect
6. #13070036C2semidirect
7. #13069996C2semidirect
8. #13069939C2semidirect
9. #13069386C2semidirect
10. #13069251C2semidirect
11. #13068956C2semidirect
13. #13068632C2semidirect
536. C11#25208semidirect

Maximal subgroups

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

subgroupindex
C2×#106223342
C2×#106227292
#130731012
#130716192
#130700992
#130700362
#130699962
#130699392
#130693862
#130692512
#130689562
#130689212
#130686322
C2×#106221892
C11×#18502
#2520811