Finite Group Databasebeta

← #14803223

Subgroups — #14803223

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
2C2×#10622679C211yesmaximal, characteristic
3#13073611C211yesmaximal, characteristic
4#13070008C211yesmaximal, characteristic, complemented
5#13069994C211yesmaximal, characteristic, complemented
6#13069857C211yesmaximal, characteristic
7#13069857C211yesmaximal, characteristic
8#13069548C211yesmaximal, characteristic
9#13069548C211yesmaximal, characteristic
10#13069539C211yesmaximal, characteristic, complemented
11#13069340C211yesmaximal, characteristic, complemented
12#13069257C211yesmaximal, characteristic, complemented
13#13069250C211yesmaximal, characteristic, complemented
14#13068444C211yesmaximal, characteristic
15C11×#2370C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×#66928C2211yescharacteristic
18C2×#66928C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C11×#389—21no—
22C11×#389C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#387—21no—
25C11×#387—21no—
26C4×C11×C4⋊C4—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31#10622682—24no—
32#10622679—24no—
33#10622600—21no—
34#10622600—21no—
35C2×#66874C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622542C2211yescharacteristic
50#10622542C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×#66867C2211yescharacteristic
55#10622287—21no—
56#10622287—21no—
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×Dic22C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C11×#125—22no—
66C11×#125D414yes—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95#66928—22no—
96#66928—22no—
97#66928—41no—
98#66928—41no—
99C4×D44—22no—
100C4×D44—22no—
101#66922—22no—
102#66922—22no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114#66874—22no—
115#66874—22no—
116#66874—22no—
117#66874—22no—
118#66874—22no—
119#66874—22no—
120#66874—41no—
121#66874—41no—
122#66873—22no—
123#66873—22no—
124#66873—22no—
125#66873—22no—
126#66872—22no—
127#66871—22no—
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—41no—
130C4⋊(C11⋊C8)—41no—
131#66867—22no—
132#25289—111nomaximal, Sylow
133C23×D11—21no—
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×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44#4112yes—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
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—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—81no—
180C11×C4⋊C4C2×D412yes—
181C11×C4⋊C4C2×D412yes—
182C11×C4⋊C4#4112yes—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—42no—
188C42×C11—81no—
189C42×C11—81no—
190C42×C11C2×D412yes—
191C42×C11#4112yes—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—42no—
200C4⋊Dic11—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—21no—
213C2×#491—111no—
214C2×#478—111no—
215#2547—111no—
216#2370D1111yescharacteristic, complemented
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×C11C22×D411yescharacteristic
229C22×D11—22no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
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—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11#12112yes—
265C2×C4×C11#12112yes—
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×C4×C112−1+411yescharacteristic
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—
281D44—22no—
282D44—22no—
283D44—41no—
284D44—41no—
285C4×D11—84no—
286Dic22—41no—
287Dic22—41no—
288Dic22—41no—
289Dic22—41no—
290Dic22—41no—
291Dic22—41no—
292Dic22—41no—
293Dic22—41no—
294C11⋊C8—41no—
295C11⋊C8—41no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C2×C4⋊Q8—111no—
299C2×#125C2×D1111yescharacteristic
300C2×#124—111no—
301C2×#124—111no—
302C2×C4×D4—111no—
303#491—224no—
304#478—224no—
305C2×#107—111no—
306C2×#106—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8—111no—
309C2×C4⋊C8—111no—
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×#102—111no—
321C2×#102—111no—
322C2×#97—111no—
323#397—221no—
324#397—221no—
325#391—111no—
326#391—111no—
327#389—21no—
328#389C2×D1111yescharacteristic
329#389C2×D1111yescharacteristic
330#387—21no—
331#387—21no—
332#380—221no—
333#380—221no—
334C4×C4⋊C4—21no—
335C4×C4⋊C4C2×D1111yescharacteristic
336C4×C4⋊C4C2×D1111yescharacteristic
337C4×C4⋊C4C2×D1111yescharacteristic
338C4×C4⋊C4C2×D1111yescharacteristic
339#340—111no—
340#340—111no—
341#336—111no—
342#336—111no—
343C22×C11C2×#12111yescharacteristic
344C22×C11#54611yescharacteristic
345C22×C11#54811yescharacteristic
346C22×C11#57511yescharacteristic
347C22×C11#57511yescharacteristic
348C22×C11#57711yescharacteristic
349C22×C11#57811yescharacteristic
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—42no—
360C4×C11—42no—
361C4×C11—42no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—81no—
367C4×C11#52911yescharacteristic
368C4×C11#54211yescharacteristic
369C4×C11#54811yescharacteristic
370C4×C11#55011yescharacteristic
371Dic11—81no—
372Dic11—81no—
373Dic11—81no—
374C22×Q8—111no—
375C22×Q8—111no—
376C22×D4—111no—
377C23×C4—221no—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8—111no—
381C22×C8—111no—
382C4⋊Q8—222no—
383C4⋊Q8—222no—
384#125—22no—
385#125D4414yes—
386#124—222no—
387#124—222no—
388#124—441no—
389#124—441no—
390C4×D4—222no—
391C4×D4—222no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4C22⋊D1111yescharacteristic
400C2×C4⋊C4C22⋊D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42C22×D1111yescharacteristic
414C2×C42C22×D1111yescharacteristic
415C2×C42C22×D1111yescharacteristic
416#107—222no—
417#106—222no—
418C4⋊C8—222no—
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—222no—
430#102—222no—
431#102—222no—
432#102—222no—
433#97—222no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95C22⋊D1111yescharacteristic
444#95C22⋊D1111yescharacteristic
445C2×C11#242611yescharacteristic
446C2×C11#304011yescharacteristic
447C2×C11#304611yescharacteristic
448C2×C11#330711yescharacteristic
449C2×C11#331511yescharacteristic
450C2×C11#337611yescharacteristic
451C2×C11#337711yescharacteristic
452D11—82no—
453C24—221no—
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—112no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—442no—
480C22×C4—442no—
481C22×C4—442no—
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
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—21no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—42no—
511C4⋊C4—81no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4C2×D4412yes—
517C4⋊C4C2×D4412yes—
518C4⋊C4#434312yes—
519C22⋊C4—442no—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C22⋊C4—442no—
523C22⋊C4—442no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—42no—
529C42—81no—
530C42—81no—
531C42C2×D4412yes—
532C42#433912yes—
533C11#2528911yescharacteristic, complemented, Sylow
534C23—222no—
535C23—441no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23—441no—
541C23C22×C22⋊D1111yescharacteristic
542Q8—441no—
543Q8—441no—
544Q8—441no—
545Q8—441no—
546Q8—441no—
547Q8—441no—
548Q8—441no—
549Q8—441no—
550D4—222no—
551D4—222no—
552D4—441no—
553D4—441no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
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—21no—
572C2×C4—21no—
573C2×C4—41no—
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—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—884no—
592C2×C4#6698312yes—
593C2×C4#6698312yes—
594C2×C4C22×D4411yescharacteristic
595C2×C4C2×#433911yescharacteristic
596C2×C4C2×#434311yescharacteristic
597C2×C4#6704011yescharacteristic
598C2×C4#41×D1111yescharacteristic
599C2×C4#6704211yescharacteristic
600C8—441no—
601C8—441no—
602C8—441no—
603C8—441no—
604C22—442no—
605C22—442no—
606C22—442no—
607C22—881no—
608C22—881no—
609C22—881no—
610C22—881no—
611C22C2×#6698311yescharacteristic
612C22#1062334811yescharacteristic
613C22#1062335311yescharacteristic
614C22#1062335311yescharacteristic
615C22#1062336011yescharacteristic
616C22#1062336711yescharacteristic
617C22#1062336911yescharacteristic
618C4—22no—
619C4—22no—
620C4—41no—
621C4—41no—
622C4—42no—
623C4—42no—
624C4—41no—
625C4—41no—
626C4—42no—
627C4—81no—
628C4—881no—
629C4—881no—
630C4—881no—
631C4#1062310711yescharacteristic
632C4#1062310811yescharacteristic
633C4#1062311111yescharacteristic
634C4#1062311311yescharacteristic
635C2—882no—
636C2#1307217611yescharacteristic
637C2#1307811011yescharacteristic
638C2#1307816611yescharacteristic
639C2#1308058611yescharacteristic
640C2#1308070611yescharacteristic
641C2#1308144311yescharacteristic
642C2#1308145811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2370C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2370D11
hypocenterC11#25289
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
1. C2×#10622682C2semidirect
4. #13070008C2semidirect
5. #13069994C2semidirect
10. #13069539C2semidirect
11. #13069340C2semidirect
12. #13069257C2semidirect
13. #13069250C2semidirect
15. C11×#2370C2semidirect
216. #2370D11semidirect
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
C2×#106226792
#130736112
#130700082
#130699942
#130698572
#130695482
#130695392
#130693402
#130692572
#130692502
#130684442
C11×#23702
#2528911