Finite Group Databasebeta

← #14812579

Subgroups — #14812579

Order 2816.

774 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622491C211yesmaximal, characteristic, complemented
2#13072334C211yesmaximal, characteristic
3#13072323C211yesmaximal, characteristic
4#13070100C211yesmaximal, characteristic, complemented
5#13070095C211yesmaximal, characteristic, complemented
6#13069956C211yesmaximal, characteristic, complemented
7#13069952C211yesmaximal, characteristic, complemented
8#13069355C211yesmaximal, characteristic, complemented
9#13069342C211yesmaximal, characteristic, complemented
10#13068815C211yesmaximal, characteristic
11#13068809C211yesmaximal, characteristic
12#13068781C211yesmaximal, characteristic, complemented
13#13068649C211yesmaximal, characteristic
14#13068397C211yesmaximal, characteristic
15C2×C11×#428C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66943C2211yescharacteristic
20C2×#66943C2211yescharacteristic
21C11×#428—24no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26#10622825—21no—
27#10622825C2211yescharacteristic
28#10622825C2211yescharacteristic
29#10622823—21no—
30C4×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622599—21no—
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622597—21no—
40#10622590C2211yescharacteristic
41#10622589C2211yescharacteristic
42#10622586C2211yescharacteristic
43#10622586C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48#10622562—21no—
49#10622561—21no—
50#10622546—21no—
51#10622541—21no—
52#10622491—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16Q814yes—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×#117—22no—
69C11×#117—41no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—41no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11D411yescharacteristic
82C2×C22⋊Dic11D411yescharacteristic
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66943—22no—
102#66943—22no—
103#66943—41no—
104#66943—41no—
105C11×#107—22no—
106C11×#107D414yes—
107C11×#106—22no—
108C11×#106—22no—
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⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119C22⋊(C11⋊C8)Q814yes—
120#66882—22no—
121#66881—22no—
122#66879—22no—
123C8×Dic11—22no—
124#66872—22no—
125#66872—22no—
126#66872—41no—
127#66871—41no—
128#26075—111nomaximal, Sylow
129C24×C11C2×D411yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—81no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×Q812yes—
143C22×C4×C11C2×Q812yes—
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C11×M16—28no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11C2×D412yes—
157C2×C8×C11C2×Q812yes—
158C2×C8×C11C2×Q812yes—
159C2×C8×C11#4112yes—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4C2×D412yes—
168C11×C4⋊C4C2×D412yes—
169C11×C22⋊C4—42no—
170C42×C11—42no—
171C22⋊Dic11—41no—
172C22⋊Dic11—41no—
173C22⋊Dic11—42no—
174C22⋊Dic11—81no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—42no—
184C4⋊Dic11—42no—
185C4⋊Dic11—42no—
186C4⋊Dic11—81no—
187Dic11⋊C4—42no—
188Dic11⋊C4—42no—
189Dic11⋊C4—42no—
190Dic11⋊C4—81no—
191Dic11⋊C4—81no—
192Dic11⋊C4—81no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8C2×Q812yes—
202C2×C11⋊C8C2×Q812yes—
203C2×#499—111no—
204C2×#428D1111yescharacteristic
205#2442—111no—
206#2441—111no—
207#2085—111no—
208#2084—111no—
209#2059—111no—
210#2059—111no—
211#1943—111no—
212#1941—111no—
213#1854—111no—
214#1853—111no—
215#1847—111no—
216#1809—111no—
217#1753—111no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11C4⋊Q812yes—
225C23×C11C22×D411yescharacteristic
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—84no—
245C2×C4×C11C4⋊Q812yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×Q811yescharacteristic
248C2×C4×C11C22×Q811yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
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—
276C8×C11—22no—
277C8×C11C22⋊Q814yes—
278C11⋊C8—22no—
279C11⋊C8—22no—
280C22×M16C2×D1111yescharacteristic
281C2×#125—111no—
282C2×#125—111no—
283C2×#117C2×D1111yescharacteristic
284C22×C4⋊C4C2×D1111yescharacteristic
285#499—224no—
286#428—24no—
287C2×#107—111no—
288C2×#107—111no—
289C2×#107C2×D1111yescharacteristic
290C2×#107C2×D1111yescharacteristic
291C2×#106—111no—
292C2×#106—111no—
293C2×#106—111no—
294C2×#106—111no—
295C2×#106C2×D1111yescharacteristic
296C2×#106C2×D1111yescharacteristic
297C2×C22⋊C8—111no—
298C2×#97—111no—
299C2×C4×C8—111no—
300#400—221no—
301#399—221no—
302#398—221no—
303#396—221no—
304#389—111no—
305#389—111no—
306#389—111no—
307#389—111no—
308#389—221no—
309#387—221no—
310#385—221no—
311#384—111no—
312#382—111no—
313#380—111no—
314#380—111no—
315#380—221no—
316C4×C22⋊C4—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#336—111no—
324#336—111no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11C2×C4⋊Q811yescharacteristic
333C22×C11D4211yescharacteristic
334C22×C11#54711yescharacteristic
335C22×C11#57511yescharacteristic
336C22×C11#57511yescharacteristic
337C22×C11#57711yescharacteristic
338C22×C11#57711yescharacteristic
339C4×C11—22no—
340C4×C11—42no—
341C4×C11—42no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11C2×C22⋊Q811yescharacteristic
345C4×C11#54411yescharacteristic
346C4×C11D4×Q811yescharacteristic
347C4×C11#55411yescharacteristic
348Dic11—41no—
349Dic11—41no—
350Dic11—41no—
351Dic11—41no—
352Dic11—81no—
353Dic11—81no—
354Dic11—81no—
355Dic11—81no—
356C23×C4—21no—
357C23×C4C22×D1111yescharacteristic
358C2×M16—22no—
359C2×M16—22no—
360C2×M16Dic2214yes—
361C22×C8—111no—
362C22×C8—111no—
363C22×C8C22×D1111yescharacteristic
364C22×C8C22×D1111yescharacteristic
365#125—222no—
366#125—222no—
367#125—441no—
368#125—441no—
369#117—22no—
370#117—41no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—41no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—111no—
394C2×C22⋊C4—111no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C42—21no—
398C2×C42—111no—
399C2×C42—111no—
400#107—22no—
401#107—222no—
402#107—441no—
403#107C22⋊D1114yes—
404#106—22no—
405#106—22no—
406#106—222no—
407#106—222no—
408#106—222no—
409#106—441no—
410C22⋊C8—114no—
411#97—222no—
412C4×C8—222no—
413#95—111no—
414#95—111no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423C2×C11—42no—
424C2×C11#244011yescharacteristic
425C2×C11#316311yescharacteristic
426C2×C11#316611yescharacteristic
427C2×C11#326711yescharacteristic
428C2×C11#327111yescharacteristic
429C2×C11#335111yescharacteristic
430C2×C11#335111yescharacteristic
431C24D4×D1111yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—81no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4C2×Dic2212yes—
452C22×C4D4×D1111yescharacteristic
453C22×C4Q8×D1112yes—
454C22×C4C23×D1111yescharacteristic
455M16—28no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—112no—
459C2×C8—112no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8C2×Dic2212yes—
465C2×C8C2×Dic2212yes—
466C2×C8#433912yes—
467C2×C8C2×C22⋊D1112yes—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—42no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—442no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C4⋊C4—442no—
487C4⋊C4—442no—
488C4⋊C4—442no—
489C4⋊C4—881no—
490C4⋊C4—881no—
491C4⋊C4—881no—
492C4⋊C4—881no—
493C4⋊C4C2×C22⋊D1112yes—
494C4⋊C4C2×C22⋊D1112yes—
495C22⋊C4—42no—
496C22⋊C4—441no—
497C22⋊C4—441no—
498C22⋊C4—442no—
499C22⋊C4—881no—
500C42—42no—
501C42—221no—
502C42—221no—
503C42—221no—
504C42—221no—
505C11#2607511yescharacteristic, complemented, Sylow
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23#6694112yes—
513C23C2×D4×D1111yescharacteristic
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—84no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4#6694112yes—
558C2×C4C22×Dic2211yescharacteristic
559C2×C4C2×#433911yescharacteristic
560C2×C4#6703711yescharacteristic
561C2×C4C2×Q8×D1111yescharacteristic
562C2×C4#6704011yescharacteristic
563C2×C4C22×C22⋊D1111yescharacteristic
564C8—22no—
565C8—222no—
566C8—222no—
567C8#6697714yes—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22C2×#6694111yescharacteristic
576C22#1062303811yescharacteristic
577C22#1062330411yescharacteristic
578C22#1062330611yescharacteristic
579C22#1062330811yescharacteristic
580C22#1062330911yescharacteristic
581C22D4×C22⋊D1111yescharacteristic
582C4—22no—
583C4—42no—
584C4—42no—
585C4—81no—
586C4—81no—
587C4—441no—
588C4—441no—
589C4—441no—
590C4—441no—
591C4—881no—
592C4—881no—
593C4—881no—
594C4—881no—
595C4#1062303111yescharacteristic
596C4#1062304211yescharacteristic
597C4C2×#6697711yescharacteristic
598C4Q8×C22⋊D1111yescharacteristic
599C2—42no—
600C2#1307231211yescharacteristic
601C2#1307914611yescharacteristic
602C2#1307916611yescharacteristic
603C2#1308013511yescharacteristic
604C2#1308019511yescharacteristic
605C2#1308117211yescharacteristic
606C2#1308117711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#428D11
hypocenterC11#26075
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#10622491C2semidirect
4. #13070100C2semidirect
5. #13070095C2semidirect
6. #13069956C2semidirect
7. #13069952C2semidirect
8. #13069355C2semidirect
9. #13069342C2semidirect
12. #13068781C2semidirect
505. C11#26075semidirect

Maximal subgroups

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

subgroupindex
C2×#106224912
#130723342
#130723232
#130701002
#130700952
#130699562
#130699522
#130693552
#130693422
#130688152
#130688092
#130687812
#130686492
#130683972
C2×C11×#4282
#2607511