Finite Group Databasebeta

← #14816823

Subgroups — #14816823

Order 2816.

820 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×#10622412C211yesmaximal, characteristic, complemented
2#13072482C211yesmaximal, characteristic
3#13071534C211yesmaximal, characteristic, complemented
4#13070139C211yesmaximal, characteristic
5#13070101C211yesmaximal, characteristic, complemented
6#13069988C211yesmaximal, characteristic
7#13069956C211yesmaximal, characteristic, complemented
8#13069344C211yesmaximal, characteristic, complemented
9#13069173C211yesmaximal, characteristic, complemented
10#13068973C211yesmaximal, characteristic
11#13068973C211yesmaximal, characteristic
12#13068886C211yesmaximal, characteristic, complemented
13#13068870C211yesmaximal, characteristic, complemented
14#13068863C211yesmaximal, characteristic
15C2×C4×C11×SD16C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C4×C11×SD16—24no—
23C2×C11×#106C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622834C2211yescharacteristic
30#10622834C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622825—21no—
34#10622823—21no—
35C2×#66881C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622590—21no—
40#10622590C2211yescharacteristic
41#10622586—21no—
42#10622586C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622562—21no—
46#10622561—21no—
47C4×Dic11⋊C4—21no—
48C4×Dic11⋊C4C2211yescharacteristic
49#10622541—21no—
50#10622541C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622412—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C2×C11×SD16—22no—
65C2×C11×SD16—22no—
66C2×C11×SD16Q814yes—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11—41no—
71C4×D4×C11—22no—
72C4×D4×C11—41no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83Q8×Dic11—22no—
84Q8×Dic11—22no—
85Q8×Dic11—22no—
86Q8×Dic11—41no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4D411yescharacteristic
100C2×Dic11⋊C4D411yescharacteristic
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66943—22no—
108#66943—41no—
109C11×#106—22no—
110C11×#103D414yes—
111C11×#102—22no—
112C4×C8×C11—22no—
113#66899—22no—
114#66899—22no—
115#66896—22no—
116#66896—41no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66881—22no—
126#66881—22no—
127Dic11⋊C8—22no—
128#66871—22no—
129#66871—41no—
130#26375—111nomaximal, Sylow
131C24×C11—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—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11C2×Q812yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—81no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C11×SD16—28no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11C2×D412yes—
167C2×C8×C11C2×Q812yes—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4C2×D412yes—
173C11×C22⋊C4—42no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—42no—
177C22⋊Dic11—42no—
178C22⋊Dic11—81no—
179C22⋊Dic11—81no—
180C22⋊Dic11—81no—
181C4⋊Dic11—24no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—42no—
190C4⋊Dic11—42no—
191C4⋊Dic11—81no—
192C4⋊Dic11#4112yes—
193Dic11⋊C4—22no—
194Dic11⋊C4—41no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—81no—
199C4×Dic11—24no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—21no—
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⋊C8—21no—
211C2×#479—111no—
212C2×C4×SD16D1111yescharacteristic
213#2454—111no—
214#2351—111no—
215#2092—111no—
216#2085—111no—
217#2065—111no—
218#2059—111no—
219#1941—111no—
220#1916—111no—
221#1880—111no—
222#1880—111no—
223#1865—111no—
224#1863—111no—
225#1862—111no—
226C23×C11—22no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11C22×D411yescharacteristic
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11—22no—
237Q8×C11C22⋊Q814yes—
238D4×C11—22no—
239D4×C11—22no—
240D4×C11—41no—
241D4×C11—41no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—84no—
257C2×C4×C11#13512yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×Q811yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C112−1+411yescharacteristic
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—21no—
276C2×Dic11—21no—
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—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C8×C11—22no—
289C8×C11—22no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C22×SD16C2×D1111yescharacteristic
293C2×#125—111no—
294C2×C4×Q8—111no—
295C2×C4×Q8—111no—
296C2×C4×Q8C2×D1111yescharacteristic
297C2×C4×D4C2×D1111yescharacteristic
298#479—224no—
299C4×SD16—24no—
300C2×#107—111no—
301C2×#107—111no—
302C2×#106—111no—
303C2×#106—111no—
304C2×#106C2×D1111yescharacteristic
305C2×C4⋊C8—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103C2×D1111yescharacteristic
309C2×#102—111no—
310C2×#102—111no—
311C2×#102C2×D1111yescharacteristic
312C2×C4×C8C2×D1111yescharacteristic
313#399—221no—
314#396—221no—
315#390—111no—
316#390—111no—
317#389—111no—
318#389—111no—
319#389—111no—
320#389—111no—
321#389—221no—
322#389—221no—
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#340—111no—
333#336—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11#52511yescharacteristic
345C22×C11D4211yescharacteristic
346C22×C11D4×Q811yescharacteristic
347C22×C11C2×#13511yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57711yescharacteristic
350C22×C11#57711yescharacteristic
351C4×C11—24no—
352C4×C11—22no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—81no—
356C4×C11C2×C22⋊Q811yescharacteristic
357C4×C11#53911yescharacteristic
358C4×C11#54711yescharacteristic
359C4×C11#55411yescharacteristic
360Dic11—41no—
361Dic11—42no—
362Dic11—41no—
363Dic11—41no—
364Dic11—41no—
365Dic11—81no—
366Dic11—81no—
367Dic11—81no—
368C22×Q8C22×D1111yescharacteristic
369C22×D4C22×D1111yescharacteristic
370C23×C4—21no—
371C2×SD16—22no—
372C2×SD16—22no—
373C2×SD16Dic2214yes—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378#125—222no—
379#125—441no—
380C4×Q8—22no—
381C4×Q8—41no—
382C4×Q8—222no—
383C4×Q8—222no—
384C4×Q8—222no—
385C4×Q8—441no—
386C4×D4—22no—
387C4×D4—41no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—111no—
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⋊C4—221no—
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—21no—
411C2×C42—111no—
412C2×C42—111no—
413C2×C42—221no—
414C2×C42—221no—
415C2×C42C22×D1111yescharacteristic
416#107—222no—
417#107—441no—
418#106—22no—
419#106—222no—
420#106—222no—
421C4⋊C8—222no—
422#103—222no—
423#103—222no—
424#103C22⋊D1114yes—
425#102—22no—
426#102—222no—
427#102—441no—
428C4×C8—22no—
429#95—111no—
430#95—111no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437C2×C11—82no—
438C2×C11#244911yescharacteristic
439C2×C11#310211yescharacteristic
440C2×C11#312611yescharacteristic
441C2×C11#327111yescharacteristic
442C2×C11#328211yescharacteristic
443C2×C11#338111yescharacteristic
444C2×C11#338811yescharacteristic
445C24—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8C2×Dic2212yes—
450C2×Q8#433912yes—
451C2×Q8C2×C22⋊D1112yes—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4C2×Dic2212yes—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—81no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4D4×D1111yescharacteristic
473C22×C4D4×D1111yescharacteristic
474C22×C4C23×D1111yescharacteristic
475SD16—28no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8C2×Dic2212yes—
487C2×C8C2×C22⋊D1112yes—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—42no—
492C4⋊C4—112no—
493C4⋊C4—224no—
494C4⋊C4—222no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—441no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4—442no—
507C4⋊C4—442no—
508C4⋊C4—881no—
509C4⋊C4—881no—
510C4⋊C4C2×C22⋊D1112yes—
511C22⋊C4—42no—
512C22⋊C4—442no—
513C22⋊C4—881no—
514C22⋊C4—881no—
515C22⋊C4—881no—
516C42—21no—
517C42—21no—
518C42—42no—
519C42—224no—
520C42—221no—
521C42—221no—
522C42—221no—
523C42—221no—
524C42—442no—
525C11#2637511yescharacteristic, complemented, Sylow
526C23—22no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23C2×D4×D1111yescharacteristic
534Q8—22no—
535Q8—22no—
536Q8—22no—
537Q8#6697714yes—
538D4—22no—
539D4—22no—
540D4—41no—
541D4—41no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—84no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
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—222no—
569C2×C4—221no—
570C2×C4—441no—
571C2×C4—441no—
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#6696912yes—
582C2×C4C22×Dic2211yescharacteristic
583C2×C4C2×#433911yescharacteristic
584C2×C4#6703711yescharacteristic
585C2×C4#41×D1111yescharacteristic
586C2×C4#6704311yescharacteristic
587C2×C4C22×C22⋊D1111yescharacteristic
588C8—22no—
589C8—22no—
590C8—441no—
591C8—441no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22D4×Dic2211yescharacteristic
600C22#1062307811yescharacteristic
601C22C2×#6696911yescharacteristic
602C22#1062329311yescharacteristic
603C22#1062329911yescharacteristic
604C22#1062330111yescharacteristic
605C22D4×C22⋊D1111yescharacteristic
606C4—22no—
607C4—24no—
608C4—42no—
609C4—41no—
610C4—81no—
611C4—441no—
612C4—441no—
613C4—442no—
614C4—441no—
615C4—441no—
616C4—881no—
617C4—881no—
618C4—881no—
619C4#1062307011yescharacteristic
620C4#1062309511yescharacteristic
621C4C2×#6697711yescharacteristic
622C4#1062335511yescharacteristic
623C2—82no—
624C2#1307241911yescharacteristic
625C2#1307863211yescharacteristic
626C2#1307890411yescharacteristic
627C2#1308020111yescharacteristic
628C2#1308032311yescharacteristic
629C2#1308148911yescharacteristic
630C2#1308155711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×C4×SD16D11
hypocenterC11#26375
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10622412C2semidirect
3. #13071534C2semidirect
5. #13070101C2semidirect
7. #13069956C2semidirect
8. #13069344C2semidirect
9. #13069173C2semidirect
12. #13068886C2semidirect
13. #13068870C2semidirect
525. C11#26375semidirect

Maximal subgroups

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

subgroupindex
C2×#106224122
#130724822
#130715342
#130701392
#130701012
#130699882
#130699562
#130693442
#130691732
#130689732
#130688862
#130688702
#130688632
C2×C4×C11×SD162
#2637511