Finite Group Databasebeta

← #14817187

Subgroups — #14817187

Order 2816.

814 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622409C211yesmaximal, characteristic, complemented
2C2×#10622430C211yesmaximal, characteristic
3#13072486C211yesmaximal, characteristic
4#13071537C211yesmaximal, characteristic, complemented
5#13070136C211yesmaximal, characteristic
6#13070097C211yesmaximal, characteristic, complemented
7#13069985C211yesmaximal, characteristic
8#13069953C211yesmaximal, characteristic, complemented
9#13069360C211yesmaximal, characteristic, complemented
10#13069181C211yesmaximal, characteristic, complemented
11#13068971C211yesmaximal, characteristic
12#13068969C211yesmaximal, characteristic
13#13068886C211yesmaximal, characteristic, complemented
14#13068878C211yesmaximal, characteristic
15C11×#1865C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33#10622607—21no—
34#10622601C2211yescharacteristic
35#10622600—21no—
36#10622598—21no—
37#10622598—21no—
38#10622598C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622598C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622552C2211yescharacteristic
45#10622549—21no—
46#10622549C2211yescharacteristic
47C4×C4⋊Dic11—21no—
48C4×C4⋊Dic11C2211yescharacteristic
49#10622430—24no—
50#10622409—24no—
51#10622290—21no—
52#10622281—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75Q8×Dic11—22no—
76Q8×Dic11—22no—
77Q8×Dic11—41no—
78Q8×Dic11—41no—
79C2×#4325—22no—
80C2×#4325—22no—
81C2×#4325Q814yes—
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⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11D411yescharacteristic
94C2×C4⋊Dic11D411yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66946—22no—
106#66946—41no—
107#66943—22no—
108#66943—41no—
109C11×#106—22no—
110C11×#103—22no—
111C11×#103D414yes—
112C11×#95—21no—
113#66899—22no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121#66885—22no—
122#66885—41no—
123#66882—22no—
124#66881—41no—
125#66879—22no—
126Dic11⋊C8—22no—
127#66873—22no—
128#66872—22no—
129#66871—22no—
130#26399—111nomaximal, Sylow
131C23×D11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11C2×D412yes—
136C2×Q8×C11C2×Q812yes—
137C2×Q8×C11#4112yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44C2×Q812yes—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—81no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11C2×D412yes—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—81no—
173C11×C4⋊C4C2×D412yes—
174C11×C4⋊C4#4112yes—
175C42×C11—24no—
176C42×C11—21no—
177C42×C11—21no—
178#4325—28no—
179(C2×D11)⋊C4—42no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—81no—
182(C2×D11)⋊C4—81no—
183(C2×D11)⋊C4—81no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—41no—
191C4⋊Dic11—41no—
192C4⋊Dic11—42no—
193C4⋊Dic11—42no—
194C4⋊Dic11—42no—
195C4⋊Dic11—42no—
196C4⋊Dic11—42no—
197C4⋊Dic11—81no—
198Dic11⋊C4—42no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8C2×Q812yes—
211C2×#479—111no—
212C2×#440—111no—
213#2454—111no—
214#2351—111no—
215#2092—111no—
216#2085—111no—
217#2065—111no—
218#2059—111no—
219#1944—111no—
220#1917—111no—
221#1880—111no—
222#1880—111no—
223#1865—111no—
224#1865D1111yescharacteristic, complemented
225#1864—111no—
226C23×C11C22×D411yescharacteristic
227C22×D11—22no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11—22no—
237Q8×C11C22⋊Q814yes—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×Q811yescharacteristic
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—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
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—
283D44—22no—
284D44—22no—
285D44—41no—
286D44—41no—
287C4×D11—84no—
288C8×C11—22no—
289C8×C11—41no—
290C11⋊C8—22no—
291C11⋊C8—41no—
292C22×SD16—111no—
293C2×#125—111no—
294C2×C4×Q8—111no—
295C2×C4×Q8—111no—
296C2×C4×Q8C2×D1111yescharacteristic
297C2×C4×D4—111no—
298#479—224no—
299#440—224no—
300C2×#107—111no—
301C2×#107—111no—
302C2×#106—111no—
303C2×#106—111no—
304C2×#106C2×D1111yescharacteristic
305C2×C4⋊C8—111no—
306C2×#103—111no—
307C2×#103C2×D1111yescharacteristic
308C2×#103C2×D1111yescharacteristic
309C2×#102—111no—
310C2×#102—111no—
311C2×#102—111no—
312C2×#97—111no—
313#399—221no—
314#396—221no—
315#390—111no—
316#390—111no—
317#389—111no—
318#389—111no—
319#389—111no—
320#389—221no—
321#389—221no—
322#389C2×D1111yescharacteristic
323#385—221no—
324#382—111no—
325#382—221no—
326#380—221no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4—221no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340C2×D1111yescharacteristic
333#336—111no—
334#336—111no—
335#336—111no—
336#336C2×D1111yescharacteristic
337C22×C11#52511yescharacteristic
338C22×C11D4211yescharacteristic
339C22×C11D4×Q811yescharacteristic
340C22×C11#57511yescharacteristic
341C22×C11#57511yescharacteristic
342C22×C11#57711yescharacteristic
343C22×C11#57711yescharacteristic
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—81no—
350C2×D11—81no—
351C4×C11—24no—
352C4×C11—41no—
353C4×C11—42no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—81no—
357C4×C11C2×C22⋊Q811yescharacteristic
358C4×C11#53911yescharacteristic
359C4×C11#54711yescharacteristic
360C4×C11#55411yescharacteristic
361Dic11—41no—
362Dic11—41no—
363Dic11—41no—
364Dic11—41no—
365Dic11—81no—
366Dic11—81no—
367Dic11—81no—
368C22×Q8C22×D1111yescharacteristic
369C22×D4—111no—
370C23×C4—221no—
371C2×SD16—114no—
372C2×SD16—222no—
373C2×SD16—222no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378#125—222no—
379#125—441no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—222no—
383C4×Q8—222no—
384C4×Q8—441no—
385C4×Q8—441no—
386C4×D4—222no—
387C4×D4—441no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
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—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C42—21no—
411C2×C42—111no—
412C2×C42—111no—
413C2×C42—221no—
414C2×C42—221no—
415C2×C42C22×D1111yescharacteristic
416#107—222no—
417#107—222no—
418#106—22no—
419#106—222no—
420#106—441no—
421C4⋊C8—222no—
422#103—22no—
423#103—222no—
424#103D4414yes—
425#102—222no—
426#102—222no—
427#102—441no—
428#97—222no—
429#95—21no—
430#95—111no—
431#95—111no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437C2×C11#244911yescharacteristic
438C2×C11#311111yescharacteristic
439C2×C11#312611yescharacteristic
440C2×C11#327111yescharacteristic
441C2×C11#327511yescharacteristic
442C2×C11#338811yescharacteristic
443C2×C11#338811yescharacteristic
444D11—82no—
445C24—221no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8C2×D4412yes—
450C2×Q8#434112yes—
451C2×Q8Q8×D1112yes—
452C2×D4—112no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—442no—
470C22×C4—442no—
471C22×C4—881no—
472C22×C4D4×D1111yescharacteristic
473C22×C4D4×D1111yescharacteristic
474C22×C4C23×D1111yescharacteristic
475SD16—228no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—112no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8C2×D4412yes—
488C4⋊C4—24no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—81no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—441no—
501C4⋊C4—441no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4—442no—
507C4⋊C4—442no—
508C4⋊C4—881no—
509C4⋊C4C2×D4412yes—
510C4⋊C4#434112yes—
511C22⋊C4—442no—
512C22⋊C4—442no—
513C22⋊C4—881no—
514C22⋊C4—881no—
515C22⋊C4—881no—
516C42—24no—
517C42—21no—
518C42—21no—
519C42—221no—
520C42—221no—
521C42—221no—
522C42—221no—
523C42—442no—
524C42—442no—
525C11#2639911yescharacteristic, complemented, Sylow
526C23—222no—
527C23—441no—
528C23—441no—
529C23—441no—
530C23—441no—
531C23—441no—
532C23—441no—
533C23C2×D4×D1111yescharacteristic
534Q8—22no—
535Q8—22no—
536Q8—22no—
537Q8#6695014yes—
538D4—222no—
539D4—222no—
540D4—441no—
541D4—441no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—441no—
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—884no—
582C2×C4C22×D4411yescharacteristic
583C2×C4C2×#434111yescharacteristic
584C2×C4C2×#434111yescharacteristic
585C2×C4C2×Q8×D1111yescharacteristic
586C2×C4#6704211yescharacteristic
587C2×C4#6704311yescharacteristic
588C8—22no—
589C8—41no—
590C8—222no—
591C8—441no—
592C22—442no—
593C22—442no—
594C22—442no—
595C22—881no—
596C22—881no—
597C22—881no—
598C22—881no—
599C22D4×D4411yescharacteristic
600C22#1062311711yescharacteristic
601C22#1062316311yescharacteristic
602C22#1062329311yescharacteristic
603C22#1062329911yescharacteristic
604C22#1062330811yescharacteristic
605C22#1062330911yescharacteristic
606C4—24no—
607C4—41no—
608C4—42no—
609C4—41no—
610C4—42no—
611C4—81no—
612C4—441no—
613C4—441no—
614C4—441no—
615C4—441no—
616C4—881no—
617C4—881no—
618C4—881no—
619C4C2×#6695011yescharacteristic
620C4#1062308611yescharacteristic
621C4#1062316611yescharacteristic
622C4#1062319611yescharacteristic
623C2—882no—
624C2#1307242311yescharacteristic
625C2#1307872611yescharacteristic
626C2#1307890111yescharacteristic
627C2#1308020311yescharacteristic
628C2#1308024911yescharacteristic
629C2#1308155911yescharacteristic
630C2#1308156811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1865C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1865D11
hypocenterC11#26399
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
1. C2×#10622409C2semidirect
4. #13071537C2semidirect
6. #13070097C2semidirect
8. #13069953C2semidirect
9. #13069360C2semidirect
10. #13069181C2semidirect
13. #13068886C2semidirect
15. C11×#1865C2semidirect
224. #1865D11semidirect
525. C11#26399semidirect

Maximal subgroups

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

subgroupindex
C2×#106224092
C2×#106224302
#130724862
#130715372
#130701362
#130700972
#130699852
#130699532
#130693602
#130691812
#130689712
#130689692
#130688862
#130688782
C11×#18652
#2639911