Finite Group Databasebeta

← #14811766

Subgroups — #14811766

Order 2816.

732 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072323C211yesmaximal, characteristic
2#13071485C211yesmaximal, characteristic
3#13070182C211yesmaximal, characteristic, complemented
4#13070119C211yesmaximal, characteristic, complemented
5#13070106C211yesmaximal, characteristic, complemented
6#13069953C211yesmaximal, characteristic, complemented
7#13069570C211yesmaximal, characteristic, complemented
8#13069378C211yesmaximal, characteristic, complemented
9#13069207C211yesmaximal, characteristic, complemented
10#13069190C211yesmaximal, characteristic, complemented
11#13068815C211yesmaximal, characteristic
12#13068799C211yesmaximal, characteristic
13#13068706C211yesmaximal, characteristic
14#13068649C211yesmaximal, characteristic
15C11×#1736C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66979—21no—
20C2×#66943C2211yescharacteristic
21#10622825C2211yescharacteristic
22#10622825C2211yescharacteristic
23#10622824—21no—
24C4×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30#10622598C2211yescharacteristic
31#10622598C2211yescharacteristic
32#10622598C2211yescharacteristic
33#10622594—21no—
34#10622594—21no—
35#10622589C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622562—21no—
42#10622561—21no—
43#10622546—21no—
44#10622541—21no—
45C11×#340C2211yescharacteristic
46C11×#340C2211yescharacteristic
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C2×C11×M16—22no—
62C2×C11×M16—22no—
63C2×C11×M16—41no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#117—22no—
67C11×#117—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4Q814yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11D411yescharacteristic
80C2×C22⋊Dic11D411yescharacteristic
81#66979—44no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100#66943—22no—
101#66943—41no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95D411yescharacteristic
111C11⋊#95D411yescharacteristic
112C22⋊(C11⋊C8)—22no—
113#66882—22no—
114#66881—41no—
115Dic11⋊C8—22no—
116Dic11⋊C8—41no—
117#66872—41no—
118#66871—22no—
119#26014—111nomaximal, Sylow
120C24×C11C2×D411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—24no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×Q812yes—
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C11×M16—44no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11#4112yes—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4C2×Q812yes—
158C11×C4⋊C4C2×Q812yes—
159C11×C4⋊C4#4112yes—
160C11×C22⋊C4—42no—
161C42×C11—42no—
162C22⋊Dic11—22no—
163C22⋊Dic11—41no—
164C22⋊Dic11—42no—
165C22⋊Dic11—81no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—42no—
175C4⋊Dic11—42no—
176C4⋊Dic11—42no—
177C4⋊Dic11—42no—
178Dic11⋊C4—42no—
179Dic11⋊C4—42no—
180Dic11⋊C4—81no—
181Dic11⋊C4—81no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—42no—
187C4×Dic11—42no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194#2441—111no—
195#2344—111no—
196#2100—111no—
197#2088—111no—
198#2086—111no—
199#2059—111no—
200#1989—111no—
201#1948—111no—
202#1921—111no—
203#1918—111no—
204#1854—111no—
205#1851—111no—
206#1824—111no—
207#1809—111no—
208#1736D1111yescharacteristic
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11C22⋊Q812yes—
216C23×C11C22×D411yescharacteristic
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—48no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11C22⋊Q812yes—
237C2×C4×C11C22×Q811yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C2×C4×C112−1+411yescharacteristic
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11AGL(1,ℤ/8)12yes—
267C8×C11—22no—
268C8×C11—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C22×M16C2×D1111yescharacteristic
272C2×#125—111no—
273C2×#117—221no—
274C2×#117C2×D1111yescharacteristic
275C22×C4⋊C4C2×D1111yescharacteristic
276C2×#107—111no—
277C2×#107—111no—
278C2×#106—111no—
279C2×#106—111no—
280C2×C4⋊C8—111no—
281C2×C4⋊C8—111no—
282C2×C22⋊C8—111no—
283#399—221no—
284#396—221no—
285#389—111no—
286#389—111no—
287#389—111no—
288#389—111no—
289#389—221no—
290#387—221no—
291#387—221no—
292#387—221no—
293#384—111no—
294#381—221no—
295#380—111no—
296#380—111no—
297C4×C4⋊C4—111no—
298C4×C4⋊C4—111no—
299C4×C22⋊C4—111no—
300#340—111no—
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340C2×D1111yescharacteristic
309#340C2×D1111yescharacteristic
310#340C2×D1111yescharacteristic
311#340C2×D1111yescharacteristic
312#336—111no—
313#336—111no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11C2×C22⋊Q811yescharacteristic
322C22×C11#54611yescharacteristic
323C22×C11#54711yescharacteristic
324C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C11#57511yescharacteristic
326C22×C11#57711yescharacteristic
327C22×C11#57811yescharacteristic
328C4×C11—22no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11—42no—
332C4×C11—81no—
333C4×C11#53311yescharacteristic
334C4×C11#54411yescharacteristic
335C4×C11#55111yescharacteristic
336C4×C11#55211yescharacteristic
337Dic11—22no—
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341Dic11—81no—
342Dic11—81no—
343Dic11—81no—
344Dic11—81no—
345C23×C4—21no—
346C23×C4C22×D1111yescharacteristic
347C2×M16—22no—
348C2×M16—22no—
349C2×M16—41no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8C22×D1111yescharacteristic
353C22×C8C22×D1111yescharacteristic
354#125—222no—
355#125—441no—
356#117—22no—
357#117—41no—
358#117—444no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4Dic2214yes—
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—111no—
380C2×C22⋊C4—111no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C42—21no—
384C2×C42—111no—
385C2×C42—111no—
386C2×C42—221no—
387C2×C42—221no—
388#107—222no—
389#107—222no—
390#106—441no—
391#106—441no—
392C4⋊C8—222no—
393C4⋊C8—441no—
394C22⋊C8—222no—
395#95—111no—
396#95—111no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405C2×C11—42no—
406C2×C11#243811yescharacteristic
407C2×C11#307711yescharacteristic
408C2×C11#308211yescharacteristic
409C2×C11#331711yescharacteristic
410C2×C11#333011yescharacteristic
411C2×C11#334511yescharacteristic
412C2×C11#335211yescharacteristic
413C24D4×D1111yescharacteristic
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—24no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4C2×Dic2212yes—
434C22×C4D4×D1111yescharacteristic
435C22×C4#434112yes—
436C22×C4C23×D1111yescharacteristic
437M16—44no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8#433912yes—
450C4⋊C4—24no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—442no—
465C4⋊C4—442no—
466C4⋊C4—442no—
467C4⋊C4—442no—
468C4⋊C4—442no—
469C4⋊C4—442no—
470C4⋊C4—881no—
471C4⋊C4—881no—
472C4⋊C4C2×Dic2212yes—
473C4⋊C4C2×Dic2212yes—
474C4⋊C4#433912yes—
475C22⋊C4—42no—
476C22⋊C4—222no—
477C22⋊C4—441no—
478C22⋊C4—442no—
479C22⋊C4—881no—
480C42—42no—
481C42—221no—
482C42—221no—
483C42—221no—
484C42—221no—
485C42—442no—
486C42—442no—
487C11#2601411yescharacteristic, complemented, Sylow
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23#6693112yes—
495C23C2×D4×D1111yescharacteristic
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—48no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—112no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4#6693112yes—
540C2×C4C22×Dic2211yescharacteristic
541C2×C4C2×#433911yescharacteristic
542C2×C4C2×#433911yescharacteristic
543C2×C4C2×#434111yescharacteristic
544C2×C4#6703711yescharacteristic
545C2×C4#6704011yescharacteristic
546C8—22no—
547C8—41no—
548C8—441no—
549C8—441no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C2×#6693111yescharacteristic
558C22#1062302111yescharacteristic
559C22#1062303811yescharacteristic
560C22D11×AGL(1,ℤ/8)11yescharacteristic
561C22#1062330411yescharacteristic
562C22#1062330911yescharacteristic
563C22#1062331011yescharacteristic
564C4—22no—
565C4—42no—
566C4—42no—
567C4—42no—
568C4—81no—
569C4—222no—
570C4—441no—
571C4—441no—
572C4—441no—
573C4—881no—
574C4—881no—
575C4—881no—
576C4—881no—
577C4#1062300111yescharacteristic
578C4#1062302611yescharacteristic
579C4#1062303111yescharacteristic
580C4#1062304411yescharacteristic
581C2—42no—
582C2#1307229211yescharacteristic
583C2#1307841011yescharacteristic
584C2#1307846011yescharacteristic
585C2#1308074311yescharacteristic
586C2#1308091711yescharacteristic
587C2#1308108711yescharacteristic
588C2#1308118711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1736D11
hypocenterC11#26014
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
3. #13070182C2semidirect
4. #13070119C2semidirect
5. #13070106C2semidirect
6. #13069953C2semidirect
7. #13069570C2semidirect
8. #13069378C2semidirect
9. #13069207C2semidirect
10. #13069190C2semidirect
487. C11#26014semidirect

Maximal subgroups

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

subgroupindex
#130723232
#130714852
#130701822
#130701192
#130701062
#130699532
#130695702
#130693782
#130692072
#130691902
#130688152
#130687992
#130687062
#130686492
C11×#17362
#2601411