Finite Group Databasebeta

← #14803227

Subgroups — #14803227

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×#10622316C211yesmaximal, characteristic, complemented
2C2×#10622460C211yesmaximal, characteristic
3#13073611C211yesmaximal, characteristic
4#13071710C211yesmaximal, characteristic, complemented
5#13070010C211yesmaximal, characteristic, complemented
6#13069996C211yesmaximal, characteristic, complemented
7#13069858C211yesmaximal, characteristic
8#13069858C211yesmaximal, characteristic
9#13069546C211yesmaximal, characteristic
10#13069546C211yesmaximal, characteristic
11#13069538C211yesmaximal, characteristic, complemented
12#13069258C211yesmaximal, characteristic, complemented
13#13069251C211yesmaximal, characteristic, complemented
14#13068442C211yesmaximal, characteristic
15C11×#1940C211yesmaximal, characteristic, complemented
16C2×#66928C2211yescharacteristic
17C2×#66928C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×#66923C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40#10622600—21no—
41#10622600—21no—
42#10622591—21no—
43#10622585—21no—
44C4×C4⋊Dic11C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622542C2211yescharacteristic
49#10622541C2211yescharacteristic
50#10622541C2211yescharacteristic
51#10622460—24no—
52#10622316—24no—
53#10622287—21no—
54#10622287—21no—
55#10622265—21no—
56#10622262—21no—
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×Dic22C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93#66928—22no—
94#66928—22no—
95#66928—41no—
96#66928—41no—
97C4×D44—22no—
98C4×D44—22no—
99#66923—22no—
100#66923D414yes—
101#66922—22no—
102#66922—22no—
103C11×C4⋊C8—22no—
104C11×C4⋊C8—41no—
105C11×C4⋊C8—41no—
106C11×#97—22no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118#66885—22no—
119#66885—22no—
120#66885—22no—
121#66885—22no—
122#66882—22no—
123#66881—22no—
124#66880—22no—
125#66880—22no—
126#66880—22no—
127#66880—22no—
128#66880—22no—
129#66880—22no—
130#66880—41no—
131#66880—41no—
132#25289—111nomaximal, Sylow
133C23×D11—21no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
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—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
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—
181C11×C4⋊C4—41no—
182C11×C4⋊C4—41no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11C2×D412yes—
188C42×C11#4112yes—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—42no—
202C4⋊Dic11—42no—
203C4⋊Dic11C2×D412yes—
204C4⋊Dic11C2×D412yes—
205C4⋊Dic11#4112yes—
206Dic11⋊C4—24no—
207Dic11⋊C4—24no—
208Dic11⋊C4—42no—
209Dic11⋊C4—81no—
210C4×Dic11—42no—
211C4×Dic11—81no—
212C4×Dic11—81no—
213C2×#491—111no—
214C2×#478—111no—
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#1940D1111yescharacteristic, complemented
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—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
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#12112yes—
253C2×C4×C11#12112yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—41no—
264C2×Dic11—41no—
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—
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—
294C8×C11—41no—
295C8×C11—41no—
296C8×C11—41no—
297C8×C11—41no—
298C2×C4⋊Q8—111no—
299C2×#125—111no—
300C2×#124—111no—
301C2×#124—111no—
302C2×C4×D4—111no—
303#491—224no—
304#478—224no—
305C2×#107—111no—
306C2×#106—111no—
307C2×C4⋊C8C2×D1111yescharacteristic
308C2×C4⋊C8C2×D1111yescharacteristic
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×#102—111no—
321C2×#102—111no—
322C2×#97C2×D1111yescharacteristic
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—221no—
338C4×C4⋊C4C2×D1111yescharacteristic
339#340—111no—
340#340—111no—
341#336C2×D1111yescharacteristic
342#336C2×D1111yescharacteristic
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—41no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11#52911yescharacteristic
364C4×C11#54211yescharacteristic
365C4×C11#54811yescharacteristic
366C4×C11#55011yescharacteristic
367Dic11—42no—
368Dic11—42no—
369Dic11—42no—
370Dic11—81no—
371Dic11—81no—
372Dic11—81no—
373Dic11—81no—
374C22×Q8—111no—
375C22×Q8—111no—
376C22×D4—111no—
377C23×C4—221no—
378C22×C8C22×D1111yescharacteristic
379C22×C8C22×D1111yescharacteristic
380C22×C8C22×D1111yescharacteristic
381C22×C8C22×D1111yescharacteristic
382C4⋊Q8—222no—
383C4⋊Q8—222no—
384#125—114no—
385#125—222no—
386#124—222no—
387#124—222no—
388#124—441no—
389#124—441no—
390C4×D4—222no—
391C4×D4—222no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4D4411yescharacteristic
404C2×C4⋊C4D4411yescharacteristic
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C42—221no—
411C2×C42—221no—
412C2×C42—221no—
413C2×C42C22×D1111yescharacteristic
414C2×C42C22×D1111yescharacteristic
415C2×C42C22×D1111yescharacteristic
416#107—222no—
417#106—222no—
418C4⋊C8—22no—
419C4⋊C8—41no—
420C4⋊C8—41no—
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—22no—
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#95D4411yescharacteristic
444#95D4411yescharacteristic
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—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—442no—
480C22×C4—442no—
481C22×C4—442no—
482C22×C4C2×D4411yescharacteristic
483C22×C4C2×D4411yescharacteristic
484C22×C4C2×D4411yescharacteristic
485C22×C4C2×D4411yescharacteristic
486C22×C4C2×D4411yescharacteristic
487C22×C4C2×D4411yescharacteristic
488C22×C4C23×D1111yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—112no—
504C4⋊C4—112no—
505C4⋊C4—112no—
506C4⋊C4—224no—
507C4⋊C4—224no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—881no—
519C22⋊C4—442no—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C22⋊C4—442no—
523C22⋊C4—442no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—442no—
529C42—881no—
530C42—881no—
531C42D4×D1112yes—
532C42#434312yes—
533C11#2528911yescharacteristic, complemented, Sylow
534C23—222no—
535C23—441no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23—441no—
541C23C22×D4411yescharacteristic
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—21no—
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—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—441no—
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—884no—
592C2×C4#6694812yes—
593C2×C4#6694812yes—
594C2×C4C2×D4×D1111yescharacteristic
595C2×C4#6703711yescharacteristic
596C2×C4C2×#434311yescharacteristic
597C2×C4#6704011yescharacteristic
598C2×C4#41×D1111yescharacteristic
599C2×C4#41×D1111yescharacteristic
600C8—41no—
601C8—41no—
602C8—41no—
603C8—41no—
604C22—442no—
605C22—442no—
606C22—442no—
607C22—881no—
608C22—881no—
609C22—881no—
610C22—881no—
611C22C2×#6694811yescharacteristic
612C22#1062308511yescharacteristic
613C22#1062310711yescharacteristic
614C22#1062327911yescharacteristic
615C22#1062327911yescharacteristic
616C22#1062328211yescharacteristic
617C22#1062328411yescharacteristic
618C4—22no—
619C4—22no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—442no—
625C4—442no—
626C4—442no—
627C4—881no—
628C4—881no—
629C4—881no—
630C4—881no—
631C4#1062313011yescharacteristic
632C4#1062316411yescharacteristic
633C4#1062322211yescharacteristic
634C4#1062326411yescharacteristic
635C2—882no—
636C2#1307218011yescharacteristic
637C2#1307811111yescharacteristic
638C2#1307816811yescharacteristic
639C2#1308059411yescharacteristic
640C2#1308071411yescharacteristic
641C2#1308144511yescharacteristic
642C2#1308146011yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1940C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1940D11
hypocenterC11#25289
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
1. C2×#10622316C2semidirect
4. #13071710C2semidirect
5. #13070010C2semidirect
6. #13069996C2semidirect
11. #13069538C2semidirect
12. #13069258C2semidirect
13. #13069251C2semidirect
15. C11×#1940C2semidirect
224. #1940D11semidirect
533. C11#25289semidirect

Maximal subgroups

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

subgroupindex
C2×#106223162
C2×#106224602
#130736112
#130717102
#130700102
#130699962
#130698582
#130695462
#130695382
#130692582
#130692512
#130684422
C11×#19402
#2528911