Finite Group Databasebeta

← #14803233

Subgroups — #14803233

Order 2816.

792 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622682C211yesmaximal, characteristic, complemented
2#13073608C211yesmaximal, characteristic
3#13071716C211yesmaximal, characteristic, complemented
4#13070006C211yesmaximal, characteristic, complemented
5#13069992C211yesmaximal, characteristic, complemented
6#13069856C211yesmaximal, characteristic
7#13069856C211yesmaximal, characteristic
8#13069547C211yesmaximal, characteristic
9#13069547C211yesmaximal, characteristic
10#13069538C211yesmaximal, characteristic, complemented
11#13069337C211yesmaximal, characteristic, complemented
12#13069256C211yesmaximal, characteristic, complemented
13#13069249C211yesmaximal, characteristic, complemented
14#13068441C211yesmaximal, characteristic
15C2×C11×#478C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66989C2211yescharacteristic
19C2×#66989C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C11×#478—24no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29#10622825—21no—
30#10622825—21no—
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37#10622682—24no—
38#10622598—21no—
39#10622598C2211yescharacteristic
40#10622598C2211yescharacteristic
41#10622594—21no—
42#10622594—21no—
43C4⋊C4×Dic11—21no—
44C4⋊C4×Dic11C2211yescharacteristic
45C4⋊C4×Dic11C2211yescharacteristic
46#10622587C2211yescharacteristic
47#10622587C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52#10622566—21no—
53#10622566—21no—
54C4×C4⋊Dic11C2211yescharacteristic
55C4×C4⋊Dic11C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C22×Dic22C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#125—22no—
68C11×#125D414yes—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82#66989—22no—
83#66989—22no—
84#66989—41no—
85#66989—41no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11D411yescharacteristic
91C2×C4⋊Dic11D411yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66922—22no—
102#66922—22no—
103C11×#107—22no—
104C11×#106—22no—
105C11×C4⋊C8—22no—
106C11×#102—22no—
107C11×#102—22no—
108#66896—22no—
109#66896—22no—
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—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121#66880—22no—
122#66880—22no—
123#66880—41no—
124#66880—41no—
125Dic11⋊C8—41no—
126Dic11⋊C8—41no—
127#66874—22no—
128#66874—22no—
129#66874—22no—
130#66874—22no—
131#66867—22no—
132#25289—111nomaximal, Sylow
133C24×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11#4112yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
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×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4C2×D412yes—
182C11×C4⋊C4C2×D412yes—
183C11×C22⋊C4—42no—
184C42×C11C2×D412yes—
185C42×C11#4112yes—
186C22⋊Dic11—42no—
187C22⋊Dic11—42no—
188C22⋊Dic11—42no—
189C22⋊Dic11—42no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—41no—
194C4⋊Dic11—41no—
195C4⋊Dic11—42no—
196C4⋊Dic11—42no—
197C4⋊Dic11—42no—
198C4⋊Dic11—81no—
199C4⋊Dic11#4112yes—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—42no—
205C4×Dic11—81no—
206C4×Dic11—81no—
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×#491—111no—
214C2×#478D1111yescharacteristic
215#2547—111no—
216#2370—111no—
217#2068—111no—
218#2066—111no—
219#2042—111no—
220#2042—111no—
221#1983—111no—
222#1983—111no—
223#1981—111no—
224#1940—111no—
225#1928—111no—
226#1927—111no—
227#1762—111no—
228C23×C11—22no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11C22×D411yescharacteristic
236D4×C11—22no—
237D4×C11—22no—
238D4×C11—41no—
239D4×C11—41no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—84no—
254C2×C4×C11#12112yes—
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—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—22no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
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—
286Dic22—41no—
287Dic22—41no—
288Dic22—41no—
289Dic22—41no—
290Dic22—41no—
291Dic22—41no—
292Dic22—41no—
293Dic22—41no—
294C8×C11—41no—
295C8×C11—41no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C2×C4⋊Q8—111no—
299C2×#125C2×D1111yescharacteristic
300C2×#124—111no—
301C2×#124—111no—
302C2×C4×D4C2×D1111yescharacteristic
303#491—224no—
304#478—24no—
305C2×#107C2×D1111yescharacteristic
306C2×#106C2×D1111yescharacteristic
307C2×C4⋊C8—111no—
308C2×C4⋊C8—111no—
309C2×C4⋊C8C2×D1111yescharacteristic
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#102—111no—
319C2×#102—111no—
320C2×#102C2×D1111yescharacteristic
321C2×#102C2×D1111yescharacteristic
322C2×#97—111no—
323#397—221no—
324#397—221no—
325#391—111no—
326#391—111no—
327#389—111no—
328#389—111no—
329#389—221no—
330#387—221no—
331#387—221no—
332#380—221no—
333#380—221no—
334C4×C4⋊C4—111no—
335C4×C4⋊C4—111no—
336C4×C4⋊C4—111no—
337C4×C4⋊C4—111no—
338C4×C4⋊C4—221no—
339#340—111no—
340#340—111no—
341#336—111no—
342#336—111no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11C2×#12111yescharacteristic
351C22×C11#54611yescharacteristic
352C22×C11#54811yescharacteristic
353C22×C11#57511yescharacteristic
354C22×C11#57511yescharacteristic
355C22×C11#57711yescharacteristic
356C22×C11#57811yescharacteristic
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—42no—
360C4×C11—42no—
361C4×C11—81no—
362C4×C11#52911yescharacteristic
363C4×C11#54211yescharacteristic
364C4×C11#54811yescharacteristic
365C4×C11#55011yescharacteristic
366Dic11—42no—
367Dic11—41no—
368Dic11—41no—
369Dic11—41no—
370Dic11—41no—
371Dic11—81no—
372Dic11—81no—
373Dic11—81no—
374C22×Q8—111no—
375C22×Q8—111no—
376C22×D4C22×D1111yescharacteristic
377C23×C4—21no—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8C22×D1111yescharacteristic
381C22×C8C22×D1111yescharacteristic
382C4⋊Q8—222no—
383C4⋊Q8—222no—
384#125—22no—
385#125C22⋊D1114yes—
386#124—222no—
387#124—222no—
388#124—441no—
389#124—441no—
390C4×D4—22no—
391C4×D4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C42—111no—
411C2×C42—111no—
412C2×C42—221no—
413C2×C42—221no—
414C2×C42—221no—
415C2×C42C22×D1111yescharacteristic
416#107—22no—
417#106—22no—
418C4⋊C8—22no—
419C4⋊C8—441no—
420C4⋊C8—441no—
421#103—222no—
422#103—222no—
423#103—222no—
424#103—222no—
425#103—222no—
426#103—222no—
427#103—441no—
428#103—441no—
429#102—22no—
430#102—22no—
431#102—222no—
432#102—222no—
433#97—222no—
434#95—111no—
435#95—111no—
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—
445C2×C11—82no—
446C2×C11#242611yescharacteristic
447C2×C11#304011yescharacteristic
448C2×C11#304611yescharacteristic
449C2×C11#330711yescharacteristic
450C2×C11#331511yescharacteristic
451C2×C11#337611yescharacteristic
452C2×C11#337711yescharacteristic
453C24—21no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8—221no—
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×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4#434312yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C4⋊C4—24no—
502C4⋊C4—24no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—112no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—441no—
512C4⋊C4—441no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—881no—
517C4⋊C4C2×C22⋊D1112yes—
518C4⋊C4C2×C22⋊D1112yes—
519C22⋊C4—42no—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C22⋊C4—442no—
523C22⋊C4—442no—
524C42—221no—
525C42—221no—
526C42—221no—
527C42—221no—
528C42—442no—
529C42—881no—
530C42—881no—
531C42#434112yes—
532C42C2×C22⋊D1112yes—
533C11#2528911yescharacteristic, complemented, Sylow
534C23—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23C2×D4×D1111yescharacteristic
542Q8—441no—
543Q8—441no—
544Q8—441no—
545Q8—441no—
546Q8—441no—
547Q8—441no—
548Q8—441no—
549Q8—441no—
550D4—22no—
551D4—22no—
552D4—41no—
553D4—41no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—84no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—222no—
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#6699212yes—
593C2×C4#6699212yes—
594C2×C4C2×#434111yescharacteristic
595C2×C4C2×#434311yescharacteristic
596C2×C4#6704011yescharacteristic
597C2×C4#41×D1111yescharacteristic
598C2×C4#6704211yescharacteristic
599C2×C4C22×C22⋊D1111yescharacteristic
600C8—41no—
601C8—41no—
602C8—441no—
603C8—441no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22#1062316111yescharacteristic
612C22#1062316411yescharacteristic
613C22#1062330111yescharacteristic
614C22#1062330211yescharacteristic
615C22#1062330411yescharacteristic
616C22#1062330411yescharacteristic
617C22C2×#6699211yescharacteristic
618C4—22no—
619C4—22no—
620C4—42no—
621C4—42no—
622C4—81no—
623C4—441no—
624C4—441no—
625C4—442no—
626C4—441no—
627C4—441no—
628C4—881no—
629C4—881no—
630C4—881no—
631C4#1062315511yescharacteristic
632C4#1062317411yescharacteristic
633C4#1062334811yescharacteristic
634C4#1062336511yescharacteristic
635C2—82no—
636C2#1307218411yescharacteristic
637C2#1307810811yescharacteristic
638C2#1307816411yescharacteristic
639C2#1308058911yescharacteristic
640C2#1308070911yescharacteristic
641C2#1308144611yescharacteristic
642C2#1308146111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#478C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#478D11
hypocenterC11#25289
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#10622682C2semidirect
3. #13071716C2semidirect
4. #13070006C2semidirect
5. #13069992C2semidirect
10. #13069538C2semidirect
11. #13069337C2semidirect
12. #13069256C2semidirect
13. #13069249C2semidirect
533. C11#25289semidirect

Maximal subgroups

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

subgroupindex
C2×#106226822
#130736082
#130717162
#130700062
#130699922
#130698562
#130695472
#130695382
#130693372
#130692562
#130692492
#130684412
C2×C11×#4782
#2528911