Finite Group Databasebeta

← #14826908

Subgroups — #14826908

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073202C211yesmaximal, characteristic, complemented
2#13071680C211yesmaximal, characteristic, complemented
3#13070143C211yesmaximal, characteristic, complemented
4#13069927C211yesmaximal, characteristic, complemented
5#13069851C211yesmaximal, characteristic, complemented
6#13069689C211yesmaximal, characteristic
7#13069482C211yesmaximal, characteristic, complemented
8#13069237C211yesmaximal, characteristic, complemented
9#13069237C211yesmaximal, characteristic, complemented
10#13069188C211yesmaximal, characteristic, complemented
11#13068963C211yesmaximal, characteristic, complemented
12#13068963C211yesmaximal, characteristic, complemented
13#13068617C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic, complemented
15C11×#1916C211yesmaximal, characteristic, complemented
16C22×D88C2211yescharacteristic
17C22×D88C2211yescharacteristic
18C2×#66951—21no—
19C2×#66946—21no—
20C2×#66927C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66882C2211yescharacteristic
36#10622607—21no—
37#10622601—21no—
38#10622552C2211yescharacteristic
39#10622552C2211yescharacteristic
40#10622552C2211yescharacteristic
41#10622552C2211yescharacteristic
42#10622552C2211yescharacteristic
43#10622548C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622287—21no—
48#10622283—21no—
49#10622278—21no—
50#10622278—21no—
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D44—21no—
60C22×D44—21no—
61C22×D44C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×D88—22no—
98C2×D88—22no—
99C2×D88—22no—
100C2×D88—41no—
101C2×D88—41no—
102C2×D88—41no—
103#66951—44no—
104#66946—44no—
105#66927—22no—
106#66927—22no—
107C4×D44—22no—
108C4×D44—22no—
109C4×D44—41no—
110C4×D44—41no—
111C11×C4⋊C8—41no—
112C4×C8×C11—41no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118#66885—22no—
119#66885—22no—
120#66885—22no—
121#66885—22no—
122#66885—41no—
123#66885—41no—
124#66885—41no—
125#66885—41no—
126#66882—22no—
127#66882—41no—
128#27062—111nomaximal, Sylow
129C23×D11—21no—
130C23×D11—21no—
131C23×D11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C2×D44—24no—
145C2×D44—24no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—42no—
163C2×D44—42no—
164C2×D44—81no—
165C2×D44—81no—
166C2×D44#4112yes—
167C2×D44#4112yes—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—81no—
173C2×C4×D11—81no—
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—21no—
184C2×C8×C11—21no—
185C2×C8×C11#4112yes—
186C11×C4⋊C4—41no—
187C11×C4⋊C4D814yescomplemented
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—81no—
203(C2×D11)⋊C4—81no—
204(C2×D11)⋊C4—81no—
205(C2×D11)⋊C4—81no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—42no—
216C4⋊Dic11—81no—
217C4⋊Dic11#4112yes—
218Dic11⋊C4—42no—
219C4×Dic11—42no—
220C4×Dic11—42no—
221D88—44no—
222D88—44no—
223#2512—111no—
224#2366—111no—
225#2093—111no—
226#2054—111no—
227#2041—111no—
228#2011—111no—
229#1970—111no—
230#1925—111no—
231#1925—111no—
232#1918—111no—
233#1916D1111yescharacteristic, complemented
234#1879—111no—
235#1879—111no—
236#1802—111no—
237C4×#102—111no—
238C23×C11C22×D411yescharacteristic
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—41no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11C2×D812yes—
276C2×C4×C11C2×D812yes—
277C2×C4×C11C2×D812yes—
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×Dic11—22no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299D44—22no—
300D44—22no—
301D44—22no—
302D44—22no—
303D44—48no—
304D44—41no—
305D44—41no—
306D44—41no—
307D44—41no—
308D44—41no—
309D44—41no—
310D44—41no—
311D44—41no—
312D44—84no—
313C4×D11—84no—
314C4×D11—84no—
315C8×C11—22no—
316C8×C11—41no—
317C8×C11—41no—
318C8×C11—41no—
319C22×D8—111no—
320C22×D8—111no—
321C2×#127—111no—
322C2×#126—221no—
323C2×C4×D4—111no—
324C2×C4×D4—111no—
325C2×C4×D4—221no—
326C2×#107—111no—
327C2×#107—111no—
328C2×C4⋊C8C2×D1111yescharacteristic
329C2×#102—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×#102—111no—
334C2×#102—111no—
335C2×#102—111no—
336C2×#102—111no—
337C2×C4×C8C2×D1111yescharacteristic
338#397—221no—
339#396—221no—
340#390—111no—
341#390—111no—
342#390—111no—
343#390—111no—
344#390—111no—
345#390—221no—
346#389—111no—
347#388—221no—
348#386—221no—
349#386—221no—
350#384—111no—
351C4×C4⋊C4—111no—
352C4×C4⋊C4—111no—
353C4×C4⋊C4C2×D1111yescharacteristic
354#340—111no—
355#340—111no—
356#340—111no—
357#340—111no—
358#336C2×D1111yescharacteristic
359#336C2×D1111yescharacteristic
360#336C2×D1111yescharacteristic
361#336C2×D1111yescharacteristic
362C22×C11#52511yescharacteristic
363C22×C11#54611yescharacteristic
364C22×C11#55011yescharacteristic
365C22×C11C22×D811yescharacteristic
366C22×C11#57511yescharacteristic
367C22×C11#57611yescharacteristic
368C22×C11#57711yescharacteristic
369C2×D11—42no—
370C2×D11—42no—
371C2×D11—42no—
372C2×D11—42no—
373C2×D11—42no—
374C2×D11—42no—
375C2×D11—81no—
376C2×D11—81no—
377C2×D11—81no—
378C2×D11—81no—
379C2×D11—81no—
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C2×D11—81no—
384C2×D11—81no—
385C2×D11—81no—
386C2×D11—81no—
387C2×D11—81no—
388C2×D11—81no—
389C2×D11—81no—
390C4×C11—22no—
391C4×C11—22no—
392C4×C11—22no—
393C4×C11—41no—
394C4×C11—41no—
395C4×C11—41no—
396C4×C11#52911yescharacteristic
397C4×C11#53811yescharacteristic
398C4×C11#55111yescharacteristic
399C4×C11#55311yescharacteristic
400Dic11—42no—
401Dic11—81no—
402Dic11—81no—
403Dic11—81no—
404Dic11—81no—
405C22×D4—111no—
406C22×D4—111no—
407C22×D4—111no—
408C22×D4—221no—
409C22×D4—221no—
410C23×C4—221no—
411C23×C4—221no—
412C2×D8—222no—
413C2×D8—222no—
414C2×D8—222no—
415C2×D8—441no—
416C2×D8—441no—
417C2×D8—441no—
418C22×C8C22×D1111yescharacteristic
419C22×C8C22×D1111yescharacteristic
420C22×C8C22×D1111yescharacteristic
421C22×C8C22×D1111yescharacteristic
422#127—222no—
423#127—222no—
424#126—444no—
425C4×D4—222no—
426C4×D4—222no—
427C4×D4—441no—
428C4×D4—441no—
429C4×D4—444no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4D4411yescharacteristic
439C2×C4⋊C4D4411yescharacteristic
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C42—221no—
453C2×C42—221no—
454C2×C42C22×D1111yescharacteristic
455C2×C42C22×D1111yescharacteristic
456C2×C42C22×D1111yescharacteristic
457#107—222no—
458#107—441no—
459C4⋊C8—41no—
460#102—222no—
461#102—222no—
462#102—222no—
463#102—222no—
464#102—441no—
465#102—441no—
466#102—441no—
467#102—441no—
468C4×C8—41no—
469#95—221no—
470#95—221no—
471#95—221no—
472#95D4411yescharacteristic
473#95D4411yescharacteristic
474C2×C11#246711yescharacteristic
475C2×C11#310011yescharacteristic
476C2×C11#311811yescharacteristic
477C2×C11#329411yescharacteristic
478C2×C11#330911yescharacteristic
479C2×C11#339111yescharacteristic
480C2×C11#340111yescharacteristic
481D11—82no—
482D11—82no—
483D11—161no—
484C24—221no—
485C24—221no—
486C24—221no—
487C2×D4—112no—
488C2×D4—112no—
489C2×D4—224no—
490C2×D4—224no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—221no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—221no—
499C2×D4—221no—
500C2×D4—221no—
501C2×D4—221no—
502C2×D4—221no—
503C2×D4—221no—
504C2×D4—221no—
505C2×D4—221no—
506C2×D4—221no—
507C2×D4—442no—
508C2×D4—442no—
509C2×D4—881no—
510C2×D4—881no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4—442no—
520C22×C4—881no—
521C22×C4—881no—
522C22×C4C2×D4411yescharacteristic
523C22×C4C2×D4411yescharacteristic
524C22×C4C2×D4411yescharacteristic
525C22×C4C2×D4411yescharacteristic
526C22×C4C2×D4411yescharacteristic
527C22×C4C2×D4411yescharacteristic
528C22×C4C23×D1111yescharacteristic
529D8—444no—
530D8—444no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8#434312yes—
543C4⋊C4—41no—
544C4⋊C4—112no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—442no—
555C4⋊C4—442no—
556C4⋊C4—881no—
557C4⋊C4D8814yescomplemented
558C22⋊C4—442no—
559C22⋊C4—442no—
560C22⋊C4—442no—
561C22⋊C4—442no—
562C22⋊C4—442no—
563C22⋊C4—442no—
564C22⋊C4—442no—
565C22⋊C4—442no—
566C22⋊C4—881no—
567C22⋊C4—881no—
568C22⋊C4—881no—
569C22⋊C4—881no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—442no—
577C42—442no—
578C11#2706211yescharacteristic, complemented, Sylow
579C23—222no—
580C23—222no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23—441no—
585C23—441no—
586C23—441no—
587C23—441no—
588C23—441no—
589C23—441no—
590C23—441no—
591C23—441no—
592C23—441no—
593C23—441no—
594C23—441no—
595C23—441no—
596C23—441no—
597C23—441no—
598C23—441no—
599C23—441no—
600C23C22×D4411yescharacteristic
601D4—222no—
602D4—222no—
603D4—222no—
604D4—222no—
605D4—448no—
606D4—441no—
607D4—441no—
608D4—441no—
609D4—441no—
610D4—441no—
611D4—441no—
612D4—441no—
613D4—441no—
614D4—884no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—222no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—884no—
646C2×C4—884no—
647C2×C4C2×D8812yes—
648C2×C4C2×D8812yes—
649C2×C4C2×D8812yes—
650C2×C4#6703711yescharacteristic
651C2×C4C2×#434311yescharacteristic
652C2×C4#41×D1111yescharacteristic
653C2×C4#41×D1111yescharacteristic
654C2×C4#41×D1111yescharacteristic
655C2×C4#6704211yescharacteristic
656C8—22no—
657C8—41no—
658C8—41no—
659C8—41no—
660C22—442no—
661C22—442no—
662C22—442no—
663C22—442no—
664C22—442no—
665C22—442no—
666C22—881no—
667C22—881no—
668C22—881no—
669C22—881no—
670C22—881no—
671C22—881no—
672C22—881no—
673C22—881no—
674C22—881no—
675C22—881no—
676C22—881no—
677C22—881no—
678C22—881no—
679C22—881no—
680C22—881no—
681C22#1062305511yescharacteristic
682C22#1062308511yescharacteristic
683C22#1062310811yescharacteristic
684C22C22×D8811yescharacteristic
685C22#1062327911yescharacteristic
686C22#1062328211yescharacteristic
687C22#1062328311yescharacteristic
688C4—22no—
689C4—22no—
690C4—22no—
691C4—41no—
692C4—41no—
693C4—41no—
694C4—442no—
695C4—881no—
696C4—881no—
697C4—881no—
698C4—881no—
699C4#1062316811yescharacteristic
700C4#1062318811yescharacteristic
701C4#1062322211yescharacteristic
702C4#1062324011yescharacteristic
703C2—882no—
704C2—882no—
705C2—1761no—
706C2#1307266511yescharacteristic
707C2#1307861711yescharacteristic
708C2#1307880211yescharacteristic
709C2#1308043011yescharacteristic
710C2#1308062411yescharacteristic
711C2#1308159111yescharacteristic
712C2#1308168411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1916C2
socleC23×C11C22×D4
prime radical#13069689C2
hypercenter#1916D11
hypocenterC11#27062
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
1. #13073202C2semidirect
2. #13071680C2semidirect
3. #13070143C2semidirect
4. #13069927C2semidirect
5. #13069851C2semidirect
7. #13069482C2semidirect
8. #13069237C2semidirect
9. #13069237C2semidirect
10. #13069188C2semidirect
11. #13068963C2semidirect
12. #13068963C2semidirect
13. #13068617C2semidirect
14. C4×#66885C2semidirect
15. C11×#1916C2semidirect
187. C11×C4⋊C4D8semidirect
233. #1916D11semidirect
557. C4⋊C4D88semidirect
578. C11#27062semidirect

Maximal subgroups

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

subgroupindex
#130732022
#130716802
#130701432
#130699272
#130698512
#130696892
#130694822
#130692372
#130691882
#130689632
#130686172
C4×#668852
C11×#19162
#2706211