Finite Group Databasebeta

← #14780598

Subgroups — #14780598

Order 2816.

1950 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
1C23×#4326C211yesmaximal, characteristic, complemented
2C2×#10623057C211yesmaximal, characteristic
3C2×#10623347C211yesmaximal, characteristic
4C2×#10622733C211yesmaximal, characteristic, complemented
5C2×#10622742C211yesmaximal, characteristic
6#13069625C218yesmaximal, complemented
7#13068332C211yesmaximal, characteristic, complemented
8C2×C11×#419C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C22×#4339C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14#10623347—24no—
15#10623347—24no—
16C2×#67000—21no—
17C2×#66999C2214yes—
18C2×#66997—21no—
19C22×#4326—24no—
20C22×#4326—24no—
21C22×#4326—24no—
22C22×#4326C2214yes—
23C2×#66982—22no—
24C2×#66979C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26#10623057—24no—
27#10623057—24no—
28C2×#66950C2214yes—
29C2×#66939—22no—
30C2×#66928—21no—
31C2×#66922—21no—
32C11×#419—24no—
33C2×C11×#103C2214yes—
34#10622742—24no—
35#10622733—24no—
36C2×(C2×D11)⋊C8C2214yes—
37C2×#66880C2214yes—
38#10622167C2214yes—
39C22×Q8×C11—21no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11—22no—
45C22×Q8×C11D414yes—
46C22×Q8×C11C2312yes—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11D412yes—
50C23×Dic11—21no—
51C2×#4339—22no—
52C2×#4339—22no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339—22no—
57C22×D44D411yescharacteristic
58C22×C4×D11C2312yes—
59C22×Dic22—22no—
60C22×Dic22—22no—
61C22×Dic22—22no—
62C22×Dic22—22no—
63C22×Dic22—21no—
64C22×Dic22—22no—
65C22×Dic22D411yescharacteristic
66C22×Dic22D414yes—
67C22×Dic22C2312yes—
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C22×C8×C11C2312yes—
72C11×#117—22no—
73C11×#117D414yes—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C22⋊Dic11—21no—
78#67000—28no—
79#66999—28no—
80#66999—28no—
81#66997—28no—
82C2×#4326—232no—
83C2×#4326—28no—
84C2×#4326—28no—
85C2×#4326—28no—
86#66982—216no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89#66979—22no—
90#66979D414yes—
91C2×C4⋊Dic11—24no—
92C2×C4⋊Dic11C2312yes—
93C2×Dic11⋊C4—24no—
94C2×C4×Dic11—21no—
95C22×C11⋊C8—22no—
96C22×C11⋊C8—22no—
97C22×C11⋊C8D414yes—
98C22×C11⋊C8C2312yes—
99#66950—28no—
100#66950—28no—
101#66939—216no—
102#66928—28no—
103#66922—28no—
104C11×#103—28no—
105(C2×D11)⋊C8—28no—
106#66880—28no—
107#23389—111nomaximal, Sylow
108C24×C11C2×D411yescharacteristic
109C23×D11C2×D412yes—
110C2×Q8×C11—24no—
111C2×Q8×C11—22no—
112C2×Q8×C11—28no—
113C2×Q8×C11—28no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—42no—
119C2×Q8×C11—42no—
120C2×Q8×C11—44no—
121C2×Q8×C11—44no—
122C2×Q8×C11C2×D414yes—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—24no—
137C2×C22⋊D11—24no—
138C2×C22⋊D11—24no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—42no—
143C22×Dic11—42no—
144C22×Dic11C2×D412yes—
145#4339—44no—
146#4339—44no—
147#4339—44no—
148#4339—44no—
149C2×D44—22no—
150C2×D44—22no—
151C2×D44—22no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×Dic22—28no—
159C2×Dic22—22no—
160C2×Dic22—24no—
161C2×Dic22—22no—
162C2×Dic22—28no—
163C2×Dic22—22no—
164C2×Dic22—22no—
165C2×Dic22—22no—
166C2×Dic22—22no—
167C2×Dic22—22no—
168C2×Dic22—22no—
169C2×Dic22—42no—
170C2×Dic22—42no—
171C2×Dic22—44no—
172C2×Dic22—44no—
173C2×Dic22C2×D414yes—
174C11×M16—44no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4C2×D414yes—
180C11×C22⋊C4—24no—
181C42×C11—24no—
182C22⋊Dic11—24no—
183#4326—232no—
184(C2×D11)⋊C4—216no—
185(C2×D11)⋊C4—216no—
186C4⋊Dic11—216no—
187C4⋊Dic11—22no—
188C4⋊Dic11C2×D414yes—
189Dic11⋊C4—216no—
190C4×Dic11—24no—
191C2×C11⋊C8—28no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8C2×D414yes—
195C23×Q16—111no—
196C2×#536—111no—
197C2×#536—111no—
198C2×#419—111no—
199C2×#419D1111yescharacteristic, complemented
200C2×#408—111no—
201#2001—118no—
202#1735—111no—
203C23×C11—24no—
204C23×C11#12012yes—
205C23×C11#12012yes—
206C23×C11#12112yes—
207C23×C11C22×D411yescharacteristic
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—28no—
212Q8×C11—24no—
213Q8×C11—24no—
214Q8×C11—42no—
215Q8×C11—42no—
216Q8×C11—48no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—44no—
222C2×C4×C11—48no—
223C2×C4×C11#12014yes—
224C2×C4×C11#12012yes—
225C2×C4×C11#12012yes—
226C2×C4×C11#12114yes—
227C2×C4×C11#12112yes—
228C2×C4×C11#12114yes—
229C2×C4×C11#12714yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C22⋊D11—48no—
237C2×Dic11—24no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—22no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—44no—
245C2×Dic11—48no—
246D44—44no—
247C4×D11—42no—
248C4×D11—42no—
249C4×D11—42no—
250C4×D11—42no—
251Dic22—24no—
252Dic22—24no—
253Dic22—42no—
254Dic22—42no—
255Dic22—48no—
256Dic22—44no—
257C8×C11—42no—
258C11⋊C8—24no—
259C22×#41—111no—
260C23×Q8—111no—
261C23×Q8C2×D1111yescharacteristic
262C22×Q16—114no—
263C22×Q16—224no—
264C22×Q16—224no—
265C22×Q16—224no—
266C22×M16C2×D1111yescharacteristic
267C23×C8—111no—
268#536—224no—
269#536—224no—
270#536—224no—
271#536—224no—
272C2×C4⋊Q8—221no—
273C2×C4⋊Q8—221no—
274C2×#124—221no—
275C2×#124—221no—
276C2×#123—222no—
277C2×#123—222no—
278C2×C22⋊Q8—114no—
279C2×C22⋊Q8—114no—
280C2×#117—111no—
281C2×#117C2×D1111yescharacteristic
282#419—24no—
283#419—224no—
284C2×#103—114no—
285C2×#103C2×D1114yes—
286#408—224no—
287C2×C22⋊C8—114no—
288#340—114no—
289C22×C11—24no—
290C22×C11—24no—
291C22×C11—24no—
292C22×C11#39214yes—
293C22×C11C2×#12011yescharacteristic
294C22×C11C2×#12011yescharacteristic
295C22×C11C2×#12111yescharacteristic
296C22×C11#57814yes—
297C2×D11—42no—
298C2×D11—44no—
299C2×D11—44no—
300C2×D11—44no—
301C4×C11—44no—
302C4×C11—44no—
303C4×C11#39214yes—
304C4×C11C2×#12011yescharacteristic
305C4×C11C2×#12111yescharacteristic
306C4×C11C2×#12111yescharacteristic
307C4×C11C2×#12711yescharacteristic
308Dic11—44no—
309Dic11—42no—
310Dic11—44no—
311C2×#41—222no—
312C2×#41—222no—
313C2×#41—222no—
314C2×#41—222no—
315C2×#41—222no—
316C2×#41—222no—
317C22×Q8—21no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—111no—
324C22×Q8—114no—
325C22×Q8—112no—
326C22×Q8—221no—
327C22×Q8—222no—
328C22×Q8—222no—
329C22×Q8—222no—
330C22×Q8—222no—
331C22×Q8—222no—
332C22×Q8D4414yes—
333C22×Q8C22×D1112yes—
334C22×D4—112no—
335C22×D4—111no—
336C23×C4—21no—
337C23×C4—112no—
338C23×C4—221no—
339C23×C4C22×D1111yescharacteristic
340C2×Q16—228no—
341C2×Q16—228no—
342C2×Q16—2232no—
343C2×Q16—228no—
344C2×M16—22no—
345C2×M16—22no—
346C2×M16—22no—
347C22×C8—114no—
348C22×C8—112no—
349C22×C8—222no—
350C22×C8—222no—
351C22×C8C22×D1112yes—
352C4⋊Q8—228no—
353C4⋊Q8—228no—
354#124—228no—
355#124—228no—
356#123—2216no—
357#123—2216no—
358C22⋊Q8—228no—
359C22⋊Q8—228no—
360C22⋊Q8—228no—
361C22⋊Q8—228no—
362#117—22no—
363#117—114no—
364#117—222no—
365#117C22⋊D1114yes—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—224no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4C22×D1112yes—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—224no—
372C2×C22⋊C4—224no—
373C2×C22⋊C4—221no—
374C2×C42—21no—
375C2×C42—221no—
376#103—28no—
377#103—228no—
378C22⋊C8—228no—
379C2×C11—24no—
380C2×C11C2×#39211yescharacteristic
381C2×C11#301112yes—
382C2×C11#301112yes—
383C2×C11#305912yes—
384D11—82no—
385C24—112no—
386C24D4×D1111yescharacteristic
387#41—444no—
388#41—444no—
389#41—444no—
390#41—444no—
391C2×Q8—24no—
392C2×Q8—22no—
393C2×Q8—28no—
394C2×Q8—28no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—42no—
400C2×Q8—44no—
401C2×Q8—42no—
402C2×Q8—44no—
403C2×Q8—114no—
404C2×Q8—222no—
405C2×Q8—222no—
406C2×Q8—224no—
407C2×Q8—222no—
408C2×Q8—222no—
409C2×Q8—228no—
410C2×Q8—228no—
411C2×Q8—222no—
412C2×Q8—222no—
413C2×Q8—222no—
414C2×Q8—222no—
415C2×Q8—442no—
416C2×Q8—442no—
417C2×Q8—444no—
418C2×Q8—444no—
419C2×Q8C2×D4414yes—
420C2×D4—224no—
421C2×D4—224no—
422C2×D4—224no—
423C2×D4—222no—
424C2×D4—222no—
425C2×D4—222no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—112no—
432C22×C4—224no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—442no—
442C22×C4—442no—
443C22×C4C2×D4412yes—
444C22×C4#433912yes—
445C22×C4D4×D1111yescharacteristic
446C22×C4D4×D1112yes—
447C22×C4D4×D1112yes—
448C22×C4D4×D1112yes—
449C22×C4C2×C22⋊D1112yes—
450C22×C4C23×D1111yescharacteristic
451Q16—2232no—
452M16—44no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—114no—
457C2×C8—228no—
458C2×C8—222no—
459C2×C8—222no—
460C4⋊C4—22no—
461C4⋊C4—114no—
462C4⋊C4—2216no—
463C4⋊C4—2216no—
464C4⋊C4—222no—
465C4⋊C4C2×C22⋊D1114yes—
466C22⋊C4—24no—
467C22⋊C4—2216no—
468C22⋊C4—2216no—
469C22⋊C4—224no—
470C42—24no—
471C42—224no—
472C11#2338911yescharacteristic, complemented, Sylow
473C23—24no—
474C23—222no—
475C23—222no—
476C23—228no—
477C23—222no—
478C23#6693512yes—
479C23#6693712yes—
480C23#6699012yes—
481C23C2×D4×D1111yescharacteristic
482Q8—24no—
483Q8—24no—
484Q8—42no—
485Q8—42no—
486Q8—48no—
487Q8—224no—
488Q8—224no—
489Q8—442no—
490Q8—442no—
491Q8—448no—
492Q8—444no—
493D4—448no—
494D4—444no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—42no—
498C2×C4—44no—
499C2×C4—42no—
500C2×C4—48no—
501C2×C4—224no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—224no—
505C2×C4—222no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—444no—
509C2×C4—448no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4#6693514yes—
515C2×C4#6693512yes—
516C2×C4#6693714yes—
517C2×C4#6693712yes—
518C2×C4#6698314yes—
519C2×C4#6699012yes—
520C2×C4#6699314yes—
521C2×C4C22×D4411yescharacteristic
522C2×C4C2×#433911yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×D4×D1111yescharacteristic
525C2×C4C2×D4×D1111yescharacteristic
526C2×C4C22×C22⋊D1111yescharacteristic
527C8—42no—
528C8—224no—
529C22—24no—
530C22—24no—
531C22—24no—
532C22—444no—
533C22—444no—
534C22—442no—
535C22—444no—
536C22#1062257314yes—
537C22C2×#6693511yescharacteristic
538C22C2×#6693711yescharacteristic
539C22#1062331014yes—
540C22C2×#6699011yescharacteristic
541C4—44no—
542C4—44no—
543C4—444no—
544C4—442no—
545C4—444no—
546C4#1062257314yes—
547C4C2×#6693511yescharacteristic
548C4C2×#6693711yescharacteristic
549C4C2×#6698311yescharacteristic
550C4C2×#6699311yescharacteristic
551C2—24no—
552C2—882no—
553C2C2×#1062257311yescharacteristic
554C2#1307791012yes—
555C2#1307791212yes—
556C2#1307827012yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#419C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#419D11
hypocenterC11#23389
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
1. C23×#4326C2semidirect
4. C2×#10622733C2semidirect
6. #13069625C2semidirect
7. #13068332C2semidirect
8. C2×C11×#419C2semidirect
199. C2×#419D11semidirect
472. C11#23389semidirect

Maximal subgroups

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

subgroupindex
C23×#43262
C2×#106230572
C2×#106233472
C2×#106227332
C2×#106227422
#130696252
#130683322
C2×C11×#4192
#2338911