Finite Group Databasebeta

← #14812644

Subgroups — #14812644

Order 2816.

782 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622469C211yesmaximal, characteristic, complemented
2C2×#10622608C211yesmaximal, characteristic
3#13072341C211yesmaximal, characteristic
4#13072301C211yesmaximal, characteristic
5#13070103C211yesmaximal, characteristic, complemented
6#13070101C211yesmaximal, characteristic, complemented
7#13069952C211yesmaximal, characteristic, complemented
8#13069943C211yesmaximal, characteristic, complemented
9#13069353C211yesmaximal, characteristic, complemented
10#13069348C211yesmaximal, characteristic, complemented
11#13068806C211yesmaximal, characteristic
12#13068779C211yesmaximal, characteristic, complemented
13#13068647C211yesmaximal, characteristic
14#13068402C211yesmaximal, characteristic
15C11×#1854C211yesmaximal, characteristic
16C2×C11×#117C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C2×#66943C2211yescharacteristic
20C2×#66941C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C11×#380C2211yescharacteristic
25#10622825C2211yescharacteristic
26C4×C22⋊Dic11C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31#10622608—24no—
32#10622598C2211yescharacteristic
33#10622598C2211yescharacteristic
34#10622590C2211yescharacteristic
35#10622590C2211yescharacteristic
36#10622586C2211yescharacteristic
37#10622586C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622563—21no—
45#10622561—21no—
46#10622560—21no—
47#10622555—21no—
48#10622546—21no—
49#10622542—21no—
50#10622469—24no—
51#10622274—21no—
52#10622273—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×Dic22—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#117—22no—
67C11×#117—41no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11D411yescharacteristic
77C2×C22⋊Dic11D411yescharacteristic
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—41no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C2×#4318—22no—
95C2×#4318—22no—
96C2×#4318Q814yescomplemented
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99#66943—22no—
100#66943—41no—
101#66941—22no—
102#66941—41no—
103C11×#107—41no—
104C11×#106—22no—
105C11×C22⋊C8Q814yescomplemented
106C11×#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118#66882—22no—
119#66882—41no—
120#66879—22no—
121C8×Dic11—22no—
122#66872—22no—
123#66872—22no—
124#66872—22no—
125#66871—22no—
126#66871—22no—
127#66871D414yes—
128#26079—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×C11C2×D411yescharacteristic
139C22×C4×C11C2×Q812yes—
140C22×C4×C11C2×Q812yes—
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—42no—
147C22×Dic11—42no—
148C22×Dic11—81no—
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C2×Dic22—42no—
154C2×Dic22—42no—
155C2×Dic22—81no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11C2×Q812yes—
161C2×C8×C11C2×Q812yes—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C2×D412yes—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—42no—
172C42×C11—42no—
173C22⋊Dic11—41no—
174C22⋊Dic11—41no—
175C22⋊Dic11—81no—
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—81no—
186C4⋊Dic11—81no—
187C4⋊Dic11C2×D412yes—
188Dic11⋊C4—42no—
189Dic11⋊C4—42no—
190Dic11⋊C4—42no—
191Dic11⋊C4—81no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196#4318—28no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C2×D412yes—
200C2×C11⋊C8C2×Q812yes—
201C2×C11⋊C8C2×Q812yes—
202C2×C11⋊C8#4112yes—
203C2×#501—111no—
204C2×#428—111no—
205#2442—111no—
206#2439—111no—
207#2085—111no—
208#2085—111no—
209#2059—111no—
210#2057—111no—
211#1943—111no—
212#1942—111no—
213#1854D1111yescharacteristic
214#1852—111no—
215#1846—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—41no—
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×C11C4⋊Q812yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×Q811yescharacteristic
247C2×C4×C11C22×Q811yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11H(5,𝔽2)11yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—22no—
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—84no—
276Dic22—84no—
277C8×C11—22no—
278C8×C11—22no—
279C11⋊C8—22no—
280C11⋊C8C22⋊Q814yes—
281C22×M16—111no—
282C2×C4⋊Q8—111no—
283C2×#125—111no—
284C2×#117C2×D1111yescharacteristic
285C22×C4⋊C4—111no—
286#501—224no—
287#428—224no—
288C2×#107—111no—
289C2×#107—111no—
290C2×#107—111no—
291C2×#107—111no—
292C2×#107—111no—
293C2×#107C2×D1111yescharacteristic
294C2×#106—111no—
295C2×#106—111no—
296C2×#106—111no—
297C2×#106C2×D1111yescharacteristic
298C2×C22⋊C8C2×D1111yescharacteristic
299C2×#97—111no—
300C2×C4×C8—111no—
301#400—221no—
302#398—221no—
303#396—221no—
304#393—221no—
305#391—221no—
306#389—111no—
307#389—111no—
308#389—111no—
309#389—111no—
310#387—221no—
311#385—221no—
312#382—111no—
313#382—111no—
314#380—111no—
315#380—221no—
316#380C2×D1111yescharacteristic
317C4×C22⋊C4—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340C2×D1111yescharacteristic
323#340C2×D1111yescharacteristic
324#336—111no—
325#336—111no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11C2×C4⋊Q811yescharacteristic
334C22×C11D4211yescharacteristic
335C22×C11#54711yescharacteristic
336C22×C11#57511yescharacteristic
337C22×C11#57511yescharacteristic
338C22×C11#57611yescharacteristic
339C22×C11#57811yescharacteristic
340C4×C11—22no—
341C4×C11—42no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11C2×C22⋊Q811yescharacteristic
346C4×C11#54411yescharacteristic
347C4×C11D4×Q811yescharacteristic
348C4×C11#55411yescharacteristic
349Dic11—41no—
350Dic11—41no—
351Dic11—41no—
352Dic11—42no—
353Dic11—41no—
354Dic11—81no—
355Dic11—81no—
356Dic11—81no—
357C22×Q8—221no—
358C23×C4—221no—
359C23×C4C22×D1111yescharacteristic
360C2×M16—114no—
361C2×M16—222no—
362C2×M16—222no—
363C22×C8—111no—
364C22×C8—111no—
365C22×C8C22×D1111yescharacteristic
366C22×C8C22×D1111yescharacteristic
367C4⋊Q8—222no—
368C4⋊Q8—441no—
369#125—222no—
370#125—441no—
371#117—22no—
372#117—41no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—222no—
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—441no—
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—111no—
394C2×C22⋊C4—111no—
395C2×C22⋊C4—221no—
396C2×C42—21no—
397C2×C42—111no—
398C2×C42—111no—
399#107—41no—
400#107—114no—
401#107—222no—
402#107—222no—
403#107—222no—
404#107—441no—
405#106—22no—
406#106—222no—
407#106—222no—
408#106—222no—
409C22⋊C8Dic2214yescomplemented
410#97—222no—
411C4×C8—222no—
412#95—21no—
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—
423#95—221no—
424C2×C11—42no—
425C2×C11#244011yescharacteristic
426C2×C11#316411yescharacteristic
427C2×C11#316611yescharacteristic
428C2×C11#327311yescharacteristic
429C2×C11#327711yescharacteristic
430C2×C11#334711yescharacteristic
431C2×C11#334911yescharacteristic
432C24D4×D1111yescharacteristic
433C2×Q8—442no—
434C2×Q8—442no—
435C2×Q8—881no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—442no—
453C22×C4—442no—
454C22×C4—881no—
455C22×C4C2×Dic2212yes—
456C22×C4D4×D1111yescharacteristic
457C22×C4Q8×D1112yes—
458C22×C4C23×D1111yescharacteristic
459M16—228no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—112no—
465C2×C8—112no—
466C2×C8—112no—
467C2×C8—112no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8C2×Dic2212yes—
471C2×C8C2×Dic2212yes—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—112no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—442no—
488C4⋊C4—442no—
489C4⋊C4—442no—
490C4⋊C4—442no—
491C4⋊C4—442no—
492C4⋊C4—881no—
493C4⋊C4—881no—
494C4⋊C4—881no—
495C4⋊C4D4×D1112yes—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22⋊C4—441no—
499C22⋊C4—441no—
500C22⋊C4—881no—
501C42—42no—
502C42—221no—
503C42—221no—
504C42—221no—
505C42—221no—
506C11#2607911yescharacteristic, complemented, Sylow
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23#6694112yes—
514C23C2×D4×D1111yescharacteristic
515Q8—884no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
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—41no—
533C2×C4—41no—
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—222no—
545C2×C4—221no—
546C2×C4—221no—
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—441no—
558C2×C4—884no—
559C2×C4#6694112yes—
560C2×C4C22×Dic2211yescharacteristic
561C2×C4C2×D4×D1111yescharacteristic
562C2×C4#6703711yescharacteristic
563C2×C4C2×Q8×D1111yescharacteristic
564C2×C4#41×D1111yescharacteristic
565C2×C4#6704311yescharacteristic
566C8—22no—
567C8—22no—
568C8—114no—
569C8—222no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22C2×#6694111yescharacteristic
578C22#1062312111yescharacteristic
579C22#1062318611yescharacteristic
580C22#1062330011yescharacteristic
581C22#1062330211yescharacteristic
582C22#1062330411yescharacteristic
583C22#1062330811yescharacteristic
584C4—22no—
585C4—42no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—441no—
590C4—441no—
591C4—441no—
592C4—442no—
593C4—441no—
594C4—881no—
595C4—881no—
596C4—881no—
597C4D4×Dic2211yescharacteristic
598C4#1062307011yescharacteristic
599C4#1062315411yescharacteristic
600C4D11×C22⋊Q811yescharacteristic
601C2—42no—
602C2#1307231711yescharacteristic
603C2#1307915611yescharacteristic
604C2#1307916611yescharacteristic
605C2#1308022011yescharacteristic
606C2#1308026611yescharacteristic
607C2#1308110911yescharacteristic
608C2#1308114911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1854C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1854D11
hypocenterC11#26079
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
1. C2×#10622469C2semidirect
5. #13070103C2semidirect
6. #13070101C2semidirect
7. #13069952C2semidirect
8. #13069943C2semidirect
9. #13069353C2semidirect
10. #13069348C2semidirect
12. #13068779C2semidirect
96. C2×#4318Q8semidirect
105. C11×C22⋊C8Q8semidirect
409. C22⋊C8Dic22semidirect
506. C11#26079semidirect

Maximal subgroups

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

subgroupindex
C2×#106224692
C2×#106226082
#130723412
#130723012
#130701032
#130701012
#130699522
#130699432
#130693532
#130693482
#130688062
#130687792
#130686472
#130684022
C11×#18542
#2607911