Finite Group Databasebeta

← #14782868

Subgroups — #14782868

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622608C211yesmaximal, characteristic
2C2×#10622731C211yesmaximal, characteristic
3#13071098C211yesmaximal, characteristic
4C2×#10622598C211yesmaximal, characteristic
5#13070120C212yesmaximal, complemented
6#13070119C212yesmaximal, complemented
7#13070113C212yesmaximal, complemented
8#13070108C212yesmaximal, complemented
9#13068336C211yesmaximal, characteristic
10#13068335C211yesmaximal, characteristic
11C11×#1736C211yesmaximal, characteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×C4⋊Dic11—21no—
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C2×C11⋊#95—21no—
21#10622731—24no—
22C2×Dic11⋊C8C2212yes—
23C2×Dic11⋊C8C2212yes—
24#10622608—24no—
25#10622598—21no—
26#10622598—21no—
27#10622598C2212yes—
28#10622598C2212yes—
29#10622586C2211yescharacteristic
30#10622586C2211yescharacteristic
31#10622586C2211yescharacteristic
32#10622586C2211yescharacteristic
33C2×#66872C2212yes—
34C2×#66871C2212yes—
35#10622559—21no—
36#10622559—21no—
37C4×Dic11⋊C4—21no—
38C4×Dic11⋊C4—21no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622189C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C23×C4×C11—21no—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11—21no—
48C23×Dic11D411yescharacteristic
49C23×Dic11D411yescharacteristic
50C2×C11×M16—22no—
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C22×C8×C11C2312yes—
54C11×#117—22no—
55C11×#117—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4Q814yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—21no—
63C2×C42×C11—21no—
64C2×C22⋊Dic11—21no—
65#66979—22no—
66#66979Q814yes—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—44no—
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C2×#4318—22no—
88C2×#4318—22no—
89C2×#4318D414yes—
90C22×C11⋊C8C2312yes—
91C11⋊#95—21no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C11⋊#95—21no—
95C11⋊#95—22no—
96C11⋊#95—22no—
97Dic11⋊C8—24no—
98Dic11⋊C8—24no—
99#66872—24no—
100#66871—24no—
101#23670—111nomaximal, Sylow
102C24×C11C2×D411yescharacteristic
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×Q812yes—
112C22×C4×C11C2×Q812yes—
113C22×C4×C11#4112yes—
114C22×C4×C11#4112yes—
115C22×C4×C11#4112yes—
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—22no—
124C22×Dic11—41no—
125C22×Dic11—41no—
126C22×Dic11—42no—
127C22×Dic11—42no—
128C22×Dic11—42no—
129C22×Dic11C2×D411yescharacteristic
130C22×Dic11C2×D411yescharacteristic
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C11×M16—44no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4C2×Q814yes—
144C11×C22⋊C4—42no—
145C42×C11—42no—
146C22⋊Dic11—24no—
147C4⋊Dic11—22no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—22no—
151C4⋊Dic11—44no—
152C4⋊Dic11—44no—
153C4⋊Dic11—42no—
154C4⋊Dic11C2×Q812yes—
155C4⋊Dic11C2×Q812yes—
156Dic11⋊C4—42no—
157Dic11⋊C4—42no—
158Dic11⋊C4—42no—
159Dic11⋊C4—42no—
160C4×Dic11—22no—
161C4×Dic11—22no—
162C4×Dic11—24no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C4×Dic11—21no—
166C4×Dic11—21no—
167#4318—28no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8C2×D414yes—
171C2×#428—111no—
172C2×#423—111no—
173#2296—111no—
174C2×#389—111no—
175#2088—112no—
176#2088—112no—
177#2087—112no—
178#2086—112no—
179#1736—111no—
180#1736—111no—
181#1736D1111yescharacteristic
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11#12112yes—
187C23×C11C22⋊Q812yes—
188C23×C11C22⋊Q812yes—
189C23×C11C22×D411yescharacteristic
190C2×C4×C11—24no—
191C2×C4×C11—48no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11#12112yes—
201C2×C4×C11C22⋊Q812yes—
202C2×C4×C11C22⋊Q812yes—
203C2×C4×C11#12314yes—
204C2×C4×C11#12514yes—
205C2×C4×C11#12514yes—
206C2×C4×C11C4⋊Q814yes—
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×Q811yescharacteristic
209C2×C4×C11C22×Q811yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224C2×Dic11—21no—
225C2×Dic11—44no—
226C2×Dic11—44no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—84no—
235C2×Dic11AGL(1,ℤ/8)12yes—
236C2×Dic11#13712yes—
237C8×C11—42no—
238C11⋊C8—24no—
239C22×M16—111no—
240C22×M16C2×D1111yescharacteristic
241C2×#117—111no—
242C2×#117C2×D1111yescharacteristic
243C22×C4⋊C4—111no—
244C22×C4⋊C4—221no—
245C22×C4⋊C4C2×D1111yescharacteristic
246C22×C42—111no—
247#428—224no—
248C2×#107—112no—
249C2×#106—112no—
250#423—224no—
251C2×C4⋊C8—112no—
252C2×C4⋊C8—112no—
253#389—111no—
254#389—112no—
255#389—111no—
256#389—112no—
257#389—111no—
258#389—111no—
259#389—221no—
260#389—221no—
261#385—221no—
262#385—221no—
263C4×C4⋊C4—221no—
264C4×C4⋊C4—221no—
265C2×#95—221no—
266#340—112no—
267#340—112no—
268#340—112no—
269#340—112no—
270#340C2×D1112yes—
271#340C2×D1112yes—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11#39814yes—
279C22×C11C2×#12111yescharacteristic
280C22×C11C2×C22⋊Q811yescharacteristic
281C22×C11C2×C22⋊Q811yescharacteristic
282C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C11C2×#13711yescharacteristic
284C22×C11#57511yescharacteristic
285C22×C11#57511yescharacteristic
286C4×C11—44no—
287C4×C11—81no—
288C4×C11—81no—
289C4×C11#39814yes—
290C4×C11C2×#12311yescharacteristic
291C4×C11C2×#12511yescharacteristic
292C4×C11C2×#12511yescharacteristic
293C4×C11C2×C4⋊Q811yescharacteristic
294Dic11—22no—
295Dic11—22no—
296Dic11—42no—
297Dic11—42no—
298Dic11—41no—
299Dic11—41no—
300Dic11—82no—
301C23×C4—21no—
302C23×C4—111no—
303C23×C4—111no—
304C23×C4—221no—
305C23×C4C22×D1111yescharacteristic
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—114no—
310C2×M16—222no—
311C2×M16—222no—
312C22×C8—112no—
313C22×C8C22×D1112yes—
314#117—22no—
315#117—22no—
316#117—114no—
317#117—222no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—112no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4—222no—
326C2×C4⋊C4—222no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—444no—
333C2×C4⋊C4Dic2214yes—
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C4⋊C4C22×D1112yes—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—221no—
339C2×C42—21no—
340C2×C42—111no—
341C2×C42—111no—
342C2×C42—111no—
343C2×C42—111no—
344C2×C42—222no—
345C2×C42—221no—
346C2×C42—222no—
347#107—224no—
348#106—224no—
349C4⋊C8—224no—
350C4⋊C8—224no—
351#95—222no—
352#95—222no—
353#95—221no—
354#95—221no—
355#95—221no—
356#95—221no—
357C2×C11—24no—
358C2×C11C2×#39811yescharacteristic
359C2×C11#305511yescharacteristic
360C2×C11#305611yescharacteristic
361C2×C11#307711yescharacteristic
362C2×C11#307811yescharacteristic
363C2×C11#307911yescharacteristic
364C2×C11#308011yescharacteristic
365C24D4×D1111yescharacteristic
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—111no—
373C22×C4—111no—
374C22×C4—111no—
375C22×C4—111no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4—222no—
383C22×C4—441no—
384C22×C4—441no—
385C22×C4—442no—
386C22×C4—442no—
387C22×C4—442no—
388C22×C4C2×Dic2212yes—
389C22×C4#433912yes—
390C22×C4#433912yes—
391C22×C4D4×D1111yescharacteristic
392C22×C4D4×D1112yes—
393C22×C4#434112yes—
394C22×C4Q8×D1112yes—
395C22×C4C23×D1111yescharacteristic
396M16—44no—
397M16—228no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—114no—
402C2×C8—222no—
403C2×C8—222no—
404C4⋊C4—24no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—112no—
411C4⋊C4—112no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—222no—
415C4⋊C4—222no—
416C4⋊C4—444no—
417C4⋊C4—442no—
418C4⋊C4—442no—
419C4⋊C4—444no—
420C4⋊C4—442no—
421C4⋊C4—442no—
422C4⋊C4—442no—
423C4⋊C4C2×Dic2214yes—
424C22⋊C4—42no—
425C22⋊C4—224no—
426C42—42no—
427C42—222no—
428C42—222no—
429C42—224no—
430C42—221no—
431C42—221no—
432C42—221no—
433C42—221no—
434C11#2367011yescharacteristic, complemented, Sylow
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23#6693112yes—
440C23#6693712yes—
441C23#6694912yes—
442C23C2×D4×D1111yescharacteristic
443C2×C4—24no—
444C2×C4—48no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—112no—
454C2×C4—112no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—221no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—221no—
464C2×C4—221no—
465C2×C4—221no—
466C2×C4—221no—
467C2×C4—444no—
468C2×C4—444no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—884no—
477C2×C4#6692314yes—
478C2×C4#6693112yes—
479C2×C4#6693614yes—
480C2×C4#6693712yes—
481C2×C4#6694114yes—
482C2×C4#6694214yes—
483C2×C4#6694912yes—
484C2×C4C22×Dic2211yescharacteristic
485C2×C4C2×#433911yescharacteristic
486C2×C4C2×#433911yescharacteristic
487C2×C4C2×D4×D1111yescharacteristic
488C2×C4C2×#434111yescharacteristic
489C2×C4C2×Q8×D1111yescharacteristic
490C8—42no—
491C8—224no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22#1062227014yes—
499C22C2×#6693111yescharacteristic
500C22C2×#6693711yescharacteristic
501C22C2×#6694911yescharacteristic
502C22D11×AGL(1,ℤ/8)11yescharacteristic
503C22#1062330411yescharacteristic
504C22D11×#13711yescharacteristic
505C22#1062330811yescharacteristic
506C4—44no—
507C4—81no—
508C4—81no—
509C4—222no—
510C4—222no—
511C4—442no—
512C4—442no—
513C4—441no—
514C4—441no—
515C4—882no—
516C4#1062227014yes—
517C4C2×#6692311yescharacteristic
518C4C2×#6693611yescharacteristic
519C4C2×#6694111yescharacteristic
520C4C2×#6694211yescharacteristic
521C2—24no—
522C2C2×#1062227011yescharacteristic
523C2#1307823811yescharacteristic
524C2#1307824911yescharacteristic
525C2#1307841011yescharacteristic
526C2#1307841811yescharacteristic
527C2#1307842911yescharacteristic
528C2#1307843711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1736D11
hypocenterC11#23670
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
5. #13070120C2semidirect
6. #13070119C2semidirect
7. #13070113C2semidirect
8. #13070108C2semidirect
434. C11#23670semidirect

Maximal subgroups

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

subgroupindex
C2×#106226082
C2×#106227312
#130710982
C2×#106225982
#130701202
#130701192
#130701132
#130701082
#130683362
#130683352
C11×#17362
#2367011