Finite Group Databasebeta

← #14804264

Subgroups — #14804264

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622689C211yesmaximal, characteristic
2C2×#10622688C211yesmaximal, characteristic
3C2×#10622632C212yesmaximal, complemented
4#13073604C211yesmaximal, characteristic, complemented
5#13069933C212yesmaximal, complemented
6#13069698C212yesmaximal, complemented
7#13069539C211yesmaximal, characteristic, complemented
8#13069335C211yesmaximal, characteristic, complemented
9#13068950C212yesmaximal, complemented
10C4×#66874C211yesmaximal, characteristic, complemented
11C11×#2366C211yesmaximal, characteristic
12C2×C11×#127C2211yescharacteristic
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11C2212yes—
15C22×#4324C2212yes—
16C22×#4324C2212yes—
17C22×#4324C2212yes—
18C2×#66922C2211yescharacteristic
19C2×#66922C2212yes—
20C2×C4×Dic22C2211yescharacteristic
21C11×#390—21no—
22C11×#390C2212yes—
23C11×#386—22no—
24C4×C11×C4⋊C4C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66896C2212yes—
27#10622689—24no—
28#10622688—24no—
29#10622632—28no—
30#10622598—21no—
31#10622598—21no—
32C2×#66874C2212yes—
33C2×#66874C2211yescharacteristic
34C2×#66874C2212yes—
35C2×#66874C2211yescharacteristic
36#10622542C2212yes—
37C2×C4⋊(C11⋊C8)C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622274—22no—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43#10622162C2212yes—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2312yes—
47C23×C4×C11—22no—
48C22×Dic22C2312yes—
49C22×Dic22C2311yescharacteristic
50C11×#127—22no—
51C11×#127D414yes—
52C4×D4×C11—24no—
53C4×D4×C11—42no—
54C4×D4×C11—44no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11—21no—
63C2×C42×C11C2312yes—
64C2×C42×C11C2311yescharacteristic
65C2×#4324—24no—
66C2×#4324—24no—
67C2×#4324—24no—
68C2×#4324—24no—
69C2×#4324—24no—
70C2×#4324—24no—
71C2×#4324—42no—
72C2×#4324—42no—
73C2×#4324—42no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×C4×Dic11—21no—
81C22×C11⋊C8C2312yes—
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84#66922—24no—
85#66922—22no—
86#66922—22no—
87#66922—42no—
88C4×Dic22—22no—
89C4×Dic22—22no—
90C11×#95—21no—
91C11×#95D412yes—
92#66896—24no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95#66874—24no—
96#66874—22no—
97#66874—42no—
98#66874D414yescomplemented
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)—24no—
101C4×C11⋊C8—22no—
102#25368—111nomaximal, Sylow
103C24×C11—22no—
104C2×D4×C11—24no—
105C2×D4×C11—24no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—42no—
112C2×D4×C11—42no—
113C2×D4×C11—81no—
114C2×D4×C11—81no—
115C2×D4×C11C2×D414yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—44no—
119C22×C4×C11—44no—
120C22×C4×C11—82no—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C2×Dic22—21no—
130C2×Dic22—22no—
131C2×Dic22—22no—
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22—21no—
137C2×Dic22—21no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22C2×D412yes—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4SD1614yescomplemented
146C11×C4⋊C4C2×D412yes—
147C11×C22⋊C4—44no—
148C11×C22⋊C4—44no—
149C11×C22⋊C4—82no—
150C42×C11—22no—
151C42×C11—22no—
152C42×C11—42no—
153C42×C11C2×D412yes—
154C42×C11#4112yes—
155#4324—48no—
156#4324—48no—
157#4324—48no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—44no—
161C4⋊Dic11—44no—
162C4⋊Dic11—42no—
163C4⋊Dic11—42no—
164Dic11⋊C4—42no—
165C4×Dic11—42no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8C2×D412yes—
174C2×C11⋊C8#4112yes—
175C2×#492—111no—
176C2×#460—111no—
177C2×#461—112no—
178#2546—111no—
179#2366D1111yescharacteristic
180#2055—112no—
181#2013—112no—
182#1981—111no—
183#1939—111no—
184#1877—112no—
185C4×#103—111no—
186C23×C11—24no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11C22×D411yescharacteristic
194D4×C11—24no—
195D4×C11—24no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—48no—
199D4×C11—84no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—88no—
214C2×C4×C11#12112yes—
215C2×C4×C11#12112yes—
216C2×C4×C11C2×SD1614yes—
217C2×C4×C11C2×SD1612yes—
218C2×C4×C11#13712yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11H(5,𝔽2)11yescharacteristic
224C2×C4×C11H(5,𝔽2)11yescharacteristic
225C2×Dic11—22no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234Dic22—22no—
235Dic22—22no—
236Dic22—41no—
237Dic22—41no—
238Dic22—42no—
239Dic22—42no—
240Dic22—42no—
241Dic22—42no—
242C11⋊C8—22no—
243C11⋊C8—22no—
244C11⋊C8—42no—
245C22×SD16—112no—
246C22×SD16—112no—
247C22×SD16—112no—
248C2×C4⋊Q8—111no—
249C2×C4⋊Q8—112no—
250C2×#127C2×D1111yescharacteristic
251C2×C4×Q8—111no—
252C2×C4×D4—21no—
253C2×C4×D4C2×D1112yes—
254#492—224no—
255#461—228no—
256#460—224no—
257C2×C4⋊C8—112no—
258C2×C4⋊C8—111no—
259C2×#103—111no—
260C2×#103—112no—
261C2×#103—111no—
262C2×#103—112no—
263C2×#102—112no—
264C2×C4×C8—111no—
265#398—222no—
266#391—112no—
267#390—21no—
268#390C2×D1112yes—
269#389—221no—
270#389—221no—
271#386—22no—
272C4×C4⋊C4C2×D1111yescharacteristic
273C4×C4⋊C4C2×D1111yescharacteristic
274#340—111no—
275#340—111no—
276#336—112no—
277C22×C11—44no—
278C22×C11—44no—
279C22×C11—44no—
280C22×C11—82no—
281C22×C11—82no—
282C22×C11—82no—
283C22×C11—82no—
284C22×C11C2×#12111yescharacteristic
285C22×C11D4211yescharacteristic
286C22×C11#55011yescharacteristic
287C22×C11C22×SD1611yescharacteristic
288C22×C11C2×#13711yescharacteristic
289C22×C11#57711yescharacteristic
290C22×C11#57711yescharacteristic
291C4×C11—24no—
292C4×C11—22no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11—81no—
296C4×C11#46114yescomplemented
297C4×C11#53211yescharacteristic
298C4×C11#54011yescharacteristic
299C4×C11D4211yescharacteristic
300C4×C11#54611yescharacteristic
301Dic11—42no—
302Dic11—82no—
303Dic11—81no—
304C22×Q8—111no—
305C22×Q8—112no—
306C22×D4—21no—
307C22×D4—21no—
308C22×D4C22×D1112yes—
309C23×C4—22no—
310C2×SD16—224no—
311C2×SD16—224no—
312C2×SD16—224no—
313C2×SD16—224no—
314C2×SD16—224no—
315C2×SD16—224no—
316C2×SD16—442no—
317C2×SD16—442no—
318C2×SD16—442no—
319C22×C8—111no—
320C22×C8—111no—
321C22×C8—112no—
322C4⋊Q8—224no—
323C4⋊Q8—222no—
324C4⋊Q8—222no—
325C4⋊Q8—442no—
326#127—22no—
327#127D4414yes—
328C4×Q8—222no—
329C4×Q8—222no—
330C4×D4—24no—
331C4×D4—42no—
332C4×D4—44no—
333C2×C4⋊C4—111no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—222no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4C22⋊D1111yescharacteristic
340C2×C4⋊C4C22⋊D1111yescharacteristic
341C2×C4⋊C4C22×D1111yescharacteristic
342C2×C4⋊C4C22×D1111yescharacteristic
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C42—21no—
347C2×C42—221no—
348C2×C42C22×D1112yes—
349C2×C42C22×D1111yescharacteristic
350C4⋊C8—224no—
351C4⋊C8—222no—
352#103—114no—
353#103—222no—
354#103—224no—
355#103—442no—
356#102—224no—
357C4×C8—222no—
358#95—21no—
359#95—222no—
360#95—222no—
361#95C22⋊D1112yes—
362C2×C11—84no—
363C2×C11#242811yescharacteristic
364C2×C11C2×#46111yescharacteristic
365C2×C11#304211yescharacteristic
366C2×C11#327811yescharacteristic
367C2×C11D4×SD1611yescharacteristic
368C2×C11#339211yescharacteristic
369C2×C11#340011yescharacteristic
370C24—22no—
371C2×Q8—112no—
372C2×Q8—221no—
373C2×Q8—221no—
374C2×Q8—222no—
375C2×Q8—221no—
376C2×Q8—222no—
377C2×Q8—222no—
378C2×Q8—222no—
379C2×Q8—221no—
380C2×Q8—222no—
381C2×Q8—221no—
382C2×Q8—222no—
383C2×D4—24no—
384C2×D4—24no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4—81no—
393C2×D4—81no—
394C2×D4C2×D4414yes—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—44no—
398C22×C4—44no—
399C22×C4—82no—
400C22×C4—221no—
401C22×C4—221no—
402C22×C4—222no—
403C22×C4C2×C22⋊D1112yes—
404C22×C4C2×C22⋊D1111yescharacteristic
405C22×C4C2×C22⋊D1112yes—
406C22×C4C2×C22⋊D1111yescharacteristic
407C22×C4C23×D1111yescharacteristic
408SD16—448no—
409SD16—448no—
410SD16—448no—
411C2×C8—112no—
412C2×C8—112no—
413C2×C8—221no—
414C2×C8—221no—
415C2×C8—221no—
416C2×C8—221no—
417C2×C8—222no—
418C2×C8—222no—
419C2×C8—222no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—221no—
425C4⋊C4—221no—
426C4⋊C4—444no—
427C4⋊C4—444no—
428C4⋊C4—442no—
429C4⋊C4—442no—
430C4⋊C4—442no—
431C4⋊C4#432414yescomplemented
432C4⋊C4D4×D1112yes—
433C22⋊C4—44no—
434C22⋊C4—44no—
435C22⋊C4—82no—
436C42—22no—
437C42—22no—
438C42—42no—
439C42—442no—
440C42C2×D4412yes—
441C42#433912yes—
442C11#2536811yescharacteristic, complemented, Sylow
443C23—24no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23C22×C22⋊D1111yescharacteristic
451Q8—222no—
452Q8—222no—
453Q8—441no—
454Q8—441no—
455Q8—442no—
456Q8—442no—
457Q8—442no—
458Q8—442no—
459D4—24no—
460D4—24no—
461D4—42no—
462D4—42no—
463D4—48no—
464D4—84no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—88no—
479C2×C4—222no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—441no—
487C2×C4—441no—
488C2×C4#6698312yes—
489C2×C4#6698312yes—
490C2×C4C2×#432414yes—
491C2×C4C2×#432412yes—
492C2×C4#6700412yes—
493C2×C4C22×D4411yescharacteristic
494C2×C4C2×#433911yescharacteristic
495C2×C4C2×D4×D1111yescharacteristic
496C2×C4#6703711yescharacteristic
497C2×C4#41×D1111yescharacteristic
498C2×C4#6704211yescharacteristic
499C8—222no—
500C8—222no—
501C8—442no—
502C22—44no—
503C22—44no—
504C22—44no—
505C22—82no—
506C22—82no—
507C22—82no—
508C22—82no—
509C22C2×#6698311yescharacteristic
510C22C22×#432411yescharacteristic
511C22D4×C22⋊D1111yescharacteristic
512C22C2×#6700411yescharacteristic
513C22#1062336511yescharacteristic
514C22#1062336711yescharacteristic
515C22#1062336711yescharacteristic
516C4—22no—
517C4—24no—
518C4—42no—
519C4—42no—
520C4—81no—
521C4—442no—
522C4—882no—
523C4—881no—
524C4#1062263214yescomplemented
525C4#1062307911yescharacteristic
526C4D4×D4411yescharacteristic
527C4#1062308511yescharacteristic
528C4#1062309311yescharacteristic
529C2—84no—
530C2#1307219811yescharacteristic
531C2C2×#1062263211yescharacteristic
532C2#1307812811yescharacteristic
533C2#1308028211yescharacteristic
534C2D4×#432411yescharacteristic
535C2#1308159711yescharacteristic
536C2#1308166911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2366C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenter#2366D11
hypocenterC11#25368
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
3. C2×#10622632C2semidirect
4. #13073604C2semidirect
5. #13069933C2semidirect
6. #13069698C2semidirect
7. #13069539C2semidirect
8. #13069335C2semidirect
9. #13068950C2semidirect
10. C4×#66874C2semidirect
98. #66874D4semidirect
145. C11×C4⋊C4SD16semidirect
296. C4×C11#461semidirect
431. C4⋊C4#4324semidirect
442. C11#25368semidirect
524. C4#10622632semidirect

Maximal subgroups

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

subgroupindex
C2×#106226892
C2×#106226882
C2×#106226322
#130736042
#130699332
#130696982
#130695392
#130693352
#130689502
C4×#668742
C11×#23662
#2536811