Finite Group Databasebeta

← #14788578

Subgroups — #14788578

Order 2816.

1146 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic
3C2×C4×#4326C211yesmaximal, characteristic, complemented
4#13069857C212yesmaximal, complemented
5#13069709C212yesmaximal, complemented
6#13069553C211yesmaximal, characteristic, complemented
7#13069421C211yesmaximal, characteristic
8#13068953C212yesmaximal, complemented
9#13068862C212yesmaximal, complemented
10#13068618C211yesmaximal, characteristic, complemented
11C11×#2582C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#67000—21no—
15C22×#4326C2211yescharacteristic
16C22×#4325C2212yes—
17#10623116—24no—
18#10623116—24no—
19C2×#66947—22no—
20C2×#66946—21no—
21C2×#66928C2212yes—
22C2×#66927C2211yescharacteristic
23C2×C4×D44C2212yes—
24C2×C4×Dic22C2211yescharacteristic
25C11×#398—22no—
26C11×#391—21no—
27C11×#391C2212yes—
28C11×#389—21no—
29C11×#389C2212yes—
30C11×#384C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C4×#4326—24no—
33#10622640—24no—
34C2×#66874C2211yescharacteristic
35C2×#66874C2212yes—
36C2×#66873C2212yes—
37C2×#66873C2212yes—
38C2×#66873C2212yes—
39C2×#66871C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×D44—21no—
48C22×D44—21no—
49C22×D44C2312yes—
50C22×C4×D11—22no—
51C22×Dic22C2311yescharacteristic
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4D412yes—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C42×C11—21no—
65C2×C42×C11C2312yes—
66C2×C42×C11C2311yescharacteristic
67#67000—28no—
68C2×#4326—22no—
69C2×#4326—22no—
70C2×#4326—22no—
71C2×#4325—24no—
72C2×#4325—24no—
73C2×#4325—42no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×Dic11⋊C4—21no—
79C2×C4×Dic11—21no—
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2312yes—
82C22×C11⋊C8C2311yescharacteristic
83#66947—216no—
84#66946—28no—
85#66928—24no—
86#66928—24no—
87#66927—22no—
88#66927D414yes—
89C4×D44—24no—
90C4×D44—24no—
91C4×Dic22—22no—
92C4×Dic22D414yes—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95—22no—
96#66899—22no—
97#66874—22no—
98#66874—42no—
99#66873—24no—
100#66873—24no—
101#66873—42no—
102#66871—22no—
103C4⋊(C11⋊C8)—22no—
104C4×C11⋊C8—22no—
105#24190—111nomaximal, Sylow
106C23×D11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11#4112yes—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—21no—
125C22×Dic11—21no—
126C2×D44—24no—
127C2×D44—24no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—42no—
134C2×D44—42no—
135C2×D44—81no—
136C2×D44—81no—
137C2×D44C2×D414yes—
138C2×C4×D11—28no—
139C2×C4×D11—82no—
140C2×C4×D11—82no—
141C2×Dic22—21no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22C2×D412yes—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—81no—
156C11×C4⋊C4—82no—
157C42×C11—22no—
158C42×C11—22no—
159C42×C11—42no—
160C42×C11C2×D412yes—
161C42×C11C2×D412yes—
162#4326—28no—
163#4325—48no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—28no—
166(C2×D11)⋊C4—28no—
167C4⋊Dic11—21no—
168C4⋊Dic11C2×D412yes—
169Dic11⋊C4—24no—
170C4×Dic11—24no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8#4112yes—
180C2×#559—111no—
181C2×#460—111no—
182C2×C4×Q16—111no—
183#2582D1111yescharacteristic, complemented
184#2042—112no—
185#2015—112no—
186#1984—111no—
187#1957—111no—
188#1877—112no—
189#1862—112no—
190#1803—111no—
191C23×C11C22×D411yescharacteristic
192C22×D11—24no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—42no—
199Q8×C11—22no—
200Q8×C11—22no—
201Q8×C11—41no—
202Q8×C11—41no—
203Q8×C11—44no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11#12012yes—
222C2×C4×C11#12012yes—
223C2×C4×C11#13512yes—
224C2×C4×C11#13712yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11H(5,𝔽2)11yescharacteristic
230C2×C4×C112−1+411yescharacteristic
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237D44—24no—
238D44—24no—
239D44—42no—
240D44—42no—
241D44—48no—
242D44—84no—
243C4×D11—88no—
244Dic22—22no—
245Dic22—22no—
246Dic22—41no—
247Dic22—41no—
248C11⋊C8—22no—
249C11⋊C8—41no—
250C11⋊C8—42no—
251C22×Q16—111no—
252C22×SD16—112no—
253#559—224no—
254#559—224no—
255C2×#127—111no—
256C2×#124—112no—
257C2×#124—221no—
258C2×#123—222no—
259C2×C4×Q8—111no—
260C2×C4×Q8C2×D1111yescharacteristic
261C2×C4×Q8C2×D1111yescharacteristic
262C2×C4×D4—112no—
263C2×C4×D4—221no—
264#460—224no—
265C4×Q16—224no—
266C2×#107—111no—
267C2×C4⋊C8—111no—
268C2×#103—111no—
269C2×#103—111no—
270C2×#103—112no—
271C2×#102—112no—
272C2×#102—112no—
273C2×#102—112no—
274C2×C4×C8—111no—
275#398—22no—
276#391—21no—
277#391C2×D1112yes—
278#389—21no—
279#389C2×D1112yes—
280#384C2×D1111yescharacteristic
281#340—112no—
282#336—112no—
283#336—112no—
284C22×C11C2×#12011yescharacteristic
285C22×C11#54811yescharacteristic
286C22×C11#55011yescharacteristic
287C22×C11C2×#13511yescharacteristic
288C22×C11C2×#13711yescharacteristic
289C22×C11#57611yescharacteristic
290C22×C11#57711yescharacteristic
291C2×D11—44no—
292C2×D11—44no—
293C2×D11—44no—
294C2×D11—82no—
295C2×D11—82no—
296C2×D11—82no—
297C2×D11—82no—
298C4×C11—22no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—82no—
303C4×C11—81no—
304C4×C11#45214yes—
305C4×C11#52511yescharacteristic
306C4×C11#53711yescharacteristic
307C4×C11#54611yescharacteristic
308C4×C11#54711yescharacteristic
309Dic11—42no—
310Dic11—42no—
311C22×Q8—111no—
312C22×Q8C22⋊D1111yescharacteristic
313C22×Q8C22×D1111yescharacteristic
314C22×D4—112no—
315C22×D4—221no—
316C22×D4—221no—
317C23×C4—222no—
318C2×Q16—222no—
319C2×Q16—222no—
320C2×Q16—222no—
321C2×SD16—224no—
322C2×SD16—224no—
323C2×SD16—442no—
324C22×C8—111no—
325C22×C8—112no—
326C22×C8—111no—
327#127—114no—
328#127—222no—
329#124—224no—
330#124—224no—
331#124—228no—
332#123—2216no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×Q8—114no—
338C4×Q8—222no—
339C4×D4—224no—
340C4×D4—224no—
341C4×D4—228no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4C22⋊D1111yescharacteristic
349C2×C4⋊C4C22⋊D1112yes—
350C2×C4⋊C4C22×D1111yescharacteristic
351C2×C4⋊C4C22×D1112yes—
352C2×C22⋊C4—222no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4—222no—
355C2×C42—21no—
356C2×C42—221no—
357C2×C42C22×D1112yes—
358C2×C42C22×D1111yescharacteristic
359#107—222no—
360C4⋊C8—222no—
361#103—222no—
362#103—222no—
363#103—442no—
364#102—224no—
365#102—224no—
366#102—442no—
367C4×C8—222no—
368#95—22no—
369#95—22no—
370#95—22no—
371C2×C11#240711yescharacteristic
372C2×C11C2×#45211yescharacteristic
373C2×C11#301211yescharacteristic
374C2×C11#336511yescharacteristic
375C2×C11#337511yescharacteristic
376C2×C11#339611yescharacteristic
377C2×C11#340011yescharacteristic
378D11—84no—
379C24—222no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—112no—
389C2×Q8—221no—
390C2×Q8—221no—
391C2×Q8—221no—
392C2×Q8—221no—
393C2×Q8—221no—
394C2×Q8#434312yes—
395C2×D4—114no—
396C2×D4—224no—
397C2×D4—224no—
398C2×D4—222no—
399C2×D4—222no—
400C2×D4—222no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—442no—
404C2×D4—442no—
405C2×D4—881no—
406C2×D4—881no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—228no—
411C22×C4—221no—
412C22×C4—221no—
413C22×C4—882no—
414C22×C4—882no—
415C22×C4C2×C22⋊D1112yes—
416C22×C4C2×C22⋊D1112yes—
417C22×C4C2×C22⋊D1111yescharacteristic
418C22×C4C2×C22⋊D1111yescharacteristic
419C22×C4C23×D1111yescharacteristic
420Q16—228no—
421SD16—448no—
422C2×C8—112no—
423C2×C8—221no—
424C2×C8—221no—
425C2×C8—221no—
426C2×C8—222no—
427C2×C8—222no—
428C2×C8—221no—
429C2×C8—221no—
430C2×C8—222no—
431C4⋊C4—22no—
432C4⋊C4—24no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—42no—
438C4⋊C4—42no—
439C4⋊C4—81no—
440C4⋊C4—82no—
441C4⋊C4—112no—
442C4⋊C4—224no—
443C4⋊C4—221no—
444C22⋊C4—228no—
445C22⋊C4—228no—
446C22⋊C4—228no—
447C42—22no—
448C42—22no—
449C42—42no—
450C42—224no—
451C42D4×D1112yes—
452C42D4×D1112yes—
453C11#2419011yescharacteristic, complemented, Sylow
454C23—224no—
455C23—442no—
456C23—442no—
457C23—442no—
458C23—442no—
459C23—442no—
460C23—442no—
461C23C22×C22⋊D1111yescharacteristic
462Q8—22no—
463Q8—22no—
464Q8—41no—
465Q8—41no—
466Q8—44no—
467Q8—222no—
468Q8—222no—
469Q8—441no—
470Q8—441no—
471D4—224no—
472D4—224no—
473D4—442no—
474D4—442no—
475D4—448no—
476D4—884no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—441no—
497C2×C4—441no—
498C2×C4—441no—
499C2×C4—441no—
500C2×C4—888no—
501C2×C4#6699012yes—
502C2×C4#6699012yes—
503C2×C4#6699512yes—
504C2×C4#6700312yes—
505C2×C4C2×D4×D1111yescharacteristic
506C2×C4C2×D4×D1111yescharacteristic
507C2×C4C2×#434311yescharacteristic
508C2×C4#6704011yescharacteristic
509C2×C4#41×D1111yescharacteristic
510C2×C4#6704211yescharacteristic
511C8—222no—
512C8—441no—
513C8—442no—
514C22—444no—
515C22—444no—
516C22—444no—
517C22—882no—
518C22—882no—
519C22—882no—
520C22—882no—
521C22C2×#6699011yescharacteristic
522C22C2×#6699511yescharacteristic
523C22#1062334811yescharacteristic
524C22C2×#6700311yescharacteristic
525C22#1062336511yescharacteristic
526C22#1062336611yescharacteristic
527C22#1062336811yescharacteristic
528C4—22no—
529C4—42no—
530C4—42no—
531C4—42no—
532C4—82no—
533C4—81no—
534C4—442no—
535C4—442no—
536C4#1062266014yes—
537C4#1062315811yescharacteristic
538C4#1062316011yescharacteristic
539C4#1062316111yescharacteristic
540C4#1062316211yescharacteristic
541C2—884no—
542C2#1307196311yescharacteristic
543C2C2×#1062266011yescharacteristic
544C2#1307791711yescharacteristic
545C2#1308131211yescharacteristic
546C2#1308143011yescharacteristic
547C2#1308162411yescharacteristic
548C2#1308166511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2582C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#2582D11
hypocenterC11#24190
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2582

Complements

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

NH ≅ G/Ntype
3. C2×C4×#4326C2semidirect
4. #13069857C2semidirect
5. #13069709C2semidirect
6. #13069553C2semidirect
8. #13068953C2semidirect
9. #13068862C2semidirect
10. #13068618C2semidirect
11. C11×#2582C2semidirect
183. #2582D11semidirect
453. C11#24190semidirect

Maximal subgroups

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

subgroupindex
C2×#106231162
C2×#106226402
C2×C4×#43262
#130698572
#130697092
#130695532
#130694212
#130689532
#130688622
#130686182
C11×#25822
#2419011