Finite Group Databasebeta

← #14788704

Subgroups — #14788704

Order 2816.

1380 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623108C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic, complemented
3C2×#10622639C211yesmaximal, characteristic, complemented
4#13069850C212yesmaximal, complemented
5#13069703C212yesmaximal, complemented
6#13069557C211yesmaximal, characteristic, complemented
7#13069439C211yesmaximal, characteristic, complemented
8#13068953C212yesmaximal, complemented
9#13068862C212yesmaximal, complemented
10#13068623C211yesmaximal, characteristic, complemented
11C11×#2581C211yesmaximal, characteristic, complemented
12C22×#4343—21no—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C22×#4325C2211yescharacteristic
16C22×#4325C2212yes—
17#10623108—24no—
18#10623108—24no—
19C2×#66948—22no—
20C2×#66948—21no—
21C2×#66927C2212yes—
22C2×#66927C2211yescharacteristic
23C2×C4×D44C2212yes—
24C2×C4×D44C2211yescharacteristic
25C11×#400—21no—
26C11×#395—21no—
27C11×#391C2212yes—
28C11×#389C2212yes—
29C11×#387—22no—
30C11×#382C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622640—24no—
33#10622639—24no—
34C2×#66873C2211yescharacteristic
35C2×#66873C2212yes—
36C2×#66873C2212yes—
37C2×#66873C2212yes—
38C2×#66873C2212yes—
39C2×#66871C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C2×#4343—28no—
48C2×#4343—48no—
49C22×D44—22no—
50C22×D44—21no—
51C22×D44—22no—
52C22×D44—21no—
53C22×D44C2312yes—
54C22×D44C2311yescharacteristic
55C22×C4×D11—22no—
56C22×C4×D11—21no—
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4D412yes—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C42×C11—21no—
68C2×C42×C11C2312yes—
69C2×C42×C11C2311yescharacteristic
70C2×#4325—22no—
71C2×#4325—22no—
72C2×#4325—24no—
73C2×#4325—24no—
74C2×#4325—22no—
75C2×#4325—42no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2312yes—
81C22×C11⋊C8C2311yescharacteristic
82#66948—28no—
83#66948—216no—
84#66927—24no—
85#66927—24no—
86#66927—22no—
87#66927D414yes—
88C4×D44—24no—
89C4×D44—22no—
90C4×D44—24no—
91C4×D44D414yes—
92C11×#95—21no—
93C11×#95—21no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95—22no—
97#66899—22no—
98#66873—22no—
99#66873—24no—
100#66873—24no—
101#66873—42no—
102#66873—42no—
103#66871—22no—
104C4⋊(C11⋊C8)—22no—
105#66867—22no—
106#24200—111nomaximal, Sylow
107C23×D11—22no—
108C23×D11—21no—
109C2×Q8×C11—22no—
110C2×Q8×C11—24no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11#4112yescomplemented
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—21no—
126#4343—432no—
127C2×D44—28no—
128C2×D44—28no—
129C2×D44—24no—
130C2×D44—24no—
131C2×D44—22no—
132C2×D44—21no—
133C2×D44—22no—
134C2×D44—21no—
135C2×D44—22no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—22no—
139C2×D44—21no—
140C2×D44—22no—
141C2×D44—44no—
142C2×D44—44no—
143C2×D44—44no—
144C2×D44—82no—
145C2×D44—82no—
146C2×D44—82no—
147C2×D44C2×D414yes—
148C2×D44C2×D412yes—
149C2×C4×D11—28no—
150C2×C4×D11—24no—
151C2×C4×D11—44no—
152C2×C4×D11—44no—
153C2×C4×D11—44no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—44no—
162C42×C11—22no—
163C42×C11—22no—
164C42×C11—42no—
165C42×C11C2×D412yes—
166C42×C11C2×D412yes—
167#4325—28no—
168#4325—48no—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4—24no—
171C4⋊Dic11—21no—
172C4⋊Dic11C2×D412yes—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8#4112yescomplemented
182C2×#550—111no—
183C2×#460—111no—
184C2×#440—111no—
185#2581D1111yescharacteristic, complemented
186#2041—112no—
187#2014—112no—
188#1985—111no—
189#1961—111no—
190#1877—112no—
191#1862—112no—
192#1804—111no—
193C23×C11C22×D411yescharacteristic
194C22×D11—24no—
195C22×D11—22no—
196C22×D11—41no—
197C22×D11—42no—
198C22×D11—42no—
199C22×D11—41no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206Q8×C11—28no—
207Q8×C11—22no—
208Q8×C11—22no—
209Q8×C11—41no—
210Q8×C11—41no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11#12012yes—
227C2×C4×C11#12012yes—
228C2×C4×C11AGL(1,ℤ/8)14yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×C4×C112−1+411yescharacteristic
235C2×Dic11—22no—
236C2×Dic11—42no—
237D44—22no—
238D44—22no—
239D44—24no—
240D44—24no—
241D44—48no—
242D44—416no—
243D44—42no—
244D44—42no—
245D44—41no—
246D44—41no—
247D44—84no—
248D44—88no—
249C4×D11—48no—
250C4×D11—416no—
251C11⋊C8—22no—
252C11⋊C8—41no—
253C11⋊C8—42no—
254C22×#41—221no—
255C22×SD16—111no—
256C22×SD16—112no—
257#550—224no—
258#550—224no—
259C2×#127—111no—
260C2×#127—112no—
261C2×#121—222no—
262C2×#121—221no—
263C2×C4×Q8C2×D1111yescharacteristic
264C2×C4×Q8C2×D1111yescharacteristic
265C2×C4×D4—111no—
266C2×C4×D4—112no—
267#460—224no—
268#440—224no—
269C2×#107—111no—
270C2×C4⋊C8—111no—
271C2×#103—111no—
272C2×#102—112no—
273C2×#102—112no—
274C2×#102—111no—
275C2×#102—112no—
276C2×#102—112no—
277C2×#97—111no—
278#400—21no—
279#395—21no—
280#391C2×D1112yes—
281#389C2×D1112yes—
282#387—22no—
283#382C2×D1111yescharacteristic
284#340—112no—
285#336—112no—
286#336—112no—
287C22×C11C2×#12011yescharacteristic
288C22×C11#54811yescharacteristic
289C22×C11#55011yescharacteristic
290C22×C11C2×AGL(1,ℤ/8)12yes—
291C22×C11#57712yes—
292C2×D11—42no—
293C2×D11—44no—
294C2×D11—44no—
295C2×D11—42no—
296C2×D11—44no—
297C2×D11—42no—
298C2×D11—82no—
299C2×D11—82no—
300C2×D11—82no—
301C2×D11—82no—
302C2×D11—82no—
303C2×D11—82no—
304C4×C11—22no—
305C4×C11—24no—
306C4×C11—22no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—82no—
310C4×C11—81no—
311C4×C11#52511yescharacteristic
312C4×C11#53711yescharacteristic
313C4×C11#54611yescharacteristic
314C4×C11#54711yescharacteristic
315Dic11—42no—
316C2×#41—228no—
317C2×#41—448no—
318C22×Q8C22⋊D1111yescharacteristic
319C22×Q8C22×D1111yescharacteristic
320C22×D4—111no—
321C22×D4—112no—
322C22×D4—221no—
323C22×D4—222no—
324C22×D4—222no—
325C22×D4—221no—
326C23×C4—222no—
327C23×C4—221no—
328C2×SD16—222no—
329C2×SD16—222no—
330C2×SD16—222no—
331C2×SD16—224no—
332C2×SD16—224no—
333C2×SD16—442no—
334C22×C8—111no—
335C22×C8—112no—
336C22×C8—111no—
337#127—114no—
338#127—224no—
339#127—224no—
340#127—222no—
341#121—228no—
342#121—2216no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×D4—114no—
348C4×D4—224no—
349C4×D4—224no—
350C4×D4—222no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4C22⋊D1112yes—
355C2×C4⋊C4C22⋊D1111yescharacteristic
356C2×C4⋊C4C22×D1111yescharacteristic
357C2×C4⋊C4C22×D1112yes—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—221no—
360C2×C42—21no—
361C2×C42C22×D1112yes—
362C2×C42C22×D1111yescharacteristic
363#107—222no—
364C4⋊C8—222no—
365#103—222no—
366#102—224no—
367#102—222no—
368#102—224no—
369#102—442no—
370#102—442no—
371#97—222no—
372#95—21no—
373#95—21no—
374#95—22no—
375#95—22no—
376#95—22no—
377C2×C11#240711yescharacteristic
378C2×C11#300311yescharacteristic
379C2×C11#300911yescharacteristic
380C2×C11#336812yes—
381C2×C11#339712yes—
382D11—82no—
383D11—84no—
384C24—222no—
385C24—221no—
386#41—4432no—
387C2×Q8—22no—
388C2×Q8—24no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8#434312yescomplemented
395C2×D4—112no—
396C2×D4—114no—
397C2×D4—228no—
398C2×D4—228no—
399C2×D4—224no—
400C2×D4—224no—
401C2×D4—222no—
402C2×D4—221no—
403C2×D4—221no—
404C2×D4—222no—
405C2×D4—221no—
406C2×D4—222no—
407C2×D4—222no—
408C2×D4—221no—
409C2×D4—221no—
410C2×D4—222no—
411C2×D4—444no—
412C2×D4—444no—
413C2×D4—444no—
414C2×D4—882no—
415C2×D4—882no—
416C2×D4—882no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—228no—
421C22×C4—221no—
422C22×C4—224no—
423C22×C4—444no—
424C22×C4—444no—
425C22×C4—444no—
426C22×C4C2×C22⋊D1112yes—
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C2×C22⋊D1112yes—
430C22×C4C23×D1111yescharacteristic
431SD16—228no—
432SD16—448no—
433C2×C8—112no—
434C2×C8—221no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—222no—
438C2×C8—222no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—222no—
442C4⋊C4—24no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—42no—
449C4⋊C4—44no—
450C4⋊C4—112no—
451C4⋊C4—221no—
452C22⋊C4—228no—
453C22⋊C4—224no—
454C42—22no—
455C42—22no—
456C42—42no—
457C42D4×D1112yes—
458C42D4×D1112yes—
459C11#2420011yescharacteristic, complemented, Sylow
460C23—224no—
461C23—222no—
462C23—441no—
463C23—442no—
464C23—442no—
465C23—442no—
466C23—442no—
467C23—442no—
468C23—441no—
469C23—442no—
470C23—442no—
471C23—442no—
472C23C22×C22⋊D1111yescharacteristic
473Q8—28no—
474Q8—22no—
475Q8—22no—
476Q8—41no—
477Q8—41no—
478D4—222no—
479D4—222no—
480D4—224no—
481D4—224no—
482D4—448no—
483D4—4416no—
484D4—442no—
485D4—442no—
486D4—441no—
487D4—441no—
488D4—884no—
489D4—888no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—222no—
506C2×C4—448no—
507C2×C4—4416no—
508C2×C4—442no—
509C2×C4#6699012yes—
510C2×C4#6699012yes—
511C2×C4#6700214yes—
512C2×C4C2×D4×D1111yescharacteristic
513C2×C4C2×D4×D1111yescharacteristic
514C2×C4C2×#434311yescharacteristic
515C2×C4#6704011yescharacteristic
516C2×C4#41×D1111yescharacteristic
517C2×C4#6704211yescharacteristic
518C8—222no—
519C8—441no—
520C8—442no—
521C22—442no—
522C22—444no—
523C22—442no—
524C22—444no—
525C22—444no—
526C22—442no—
527C22—882no—
528C22—882no—
529C22—882no—
530C22—882no—
531C22—882no—
532C22—882no—
533C22C2×#6699011yescharacteristic
534C22#1062334811yescharacteristic
535C22C2×#6700212yes—
536C22#1062336511yescharacteristic
537C22#1062336812yes—
538C4—22no—
539C4—24no—
540C4—22no—
541C4—42no—
542C4—42no—
543C4—82no—
544C4—81no—
545C4—442no—
546C4#1062315811yescharacteristic
547C4#1062316011yescharacteristic
548C4#1062316111yescharacteristic
549C4#1062316211yescharacteristic
550C2—882no—
551C2—884no—
552C2#1307196311yescharacteristic
553C2#1307784211yescharacteristic
554C2#1307789111yescharacteristic
555C2#1308134512yes—
556C2#1308163612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2581C2
socleC23×C11C22×D4
prime radicalC2×#10623108C2
hypercenter#2581D11
hypocenterC11#24200
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2581

Complements

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

NH ≅ G/Ntype
2. C2×#10622640C2semidirect
3. C2×#10622639C2semidirect
4. #13069850C2semidirect
5. #13069703C2semidirect
6. #13069557C2semidirect
7. #13069439C2semidirect
8. #13068953C2semidirect
9. #13068862C2semidirect
10. #13068623C2semidirect
11. C11×#2581C2semidirect
116. C2×Q8×C11#41semidirect
181. C2×C11⋊C8#41semidirect
185. #2581D11semidirect
394. C2×Q8#4343semidirect
459. C11#24200semidirect

Maximal subgroups

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

subgroupindex
C2×#106231082
C2×#106226402
C2×#106226392
#130698502
#130697032
#130695572
#130694392
#130689532
#130688622
#130686232
C11×#25812
#2420011