Finite Group Databasebeta

← #14780597

Subgroups — #14780597

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×#10623356C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic, complemented
4C2×#10622617C211yesmaximal, characteristic, complemented
5C2×#10622847C211yesmaximal, characteristic
6#13069624C218yesmaximal, complemented
7#13068332C211yesmaximal, characteristic, complemented
8C2×C11×#536C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C23×Q8×C11C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C11×#536—24no—
13C11×#536—24no—
14C2×C11×C4⋊Q8—21no—
15C2×C11×#124—21no—
16C2×C11×#123—22no—
17C2×C11×C22⋊Q8C2214yes—
18C2×C11×#117C2211yescharacteristic
19#10623356—24no—
20#10623356—24no—
21C2×#66997—21no—
22C22×#4326—24no—
23C22×#4326—24no—
24C22×#4326—24no—
25C22×#4326C2214yes—
26C2×#66989—21no—
27C2×#66988—22no—
28C2×#66979C2211yescharacteristic
29C2×#66977C2214yes—
30C22×#4318C2211yescharacteristic
31C23×C11⋊C8C2211yescharacteristic
32#10622847—24no—
33#10622838—24no—
34C2×#66899C2214yes—
35C2×C22⋊(C11⋊C8)C2214yes—
36#10622617—24no—
37C2×#66874C2214yes—
38#10622167C2214yes—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C22×Q8×C11—21no—
46C22×Q8×C11—22no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11D414yes—
52C22×Q8×C11D411yescharacteristic
53C22×Q8×C11C2312yes—
54C22×D4×C11D412yes—
55C22×D4×C11D411yescharacteristic
56C23×C4×C11—21no—
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×Dic11—21no—
60C22×Dic22—22no—
61C22×Dic22—22no—
62C22×Dic22—22no—
63C22×Dic22—22no—
64C22×Dic22—21no—
65C22×Dic22—22no—
66C22×Dic22D414yes—
67C22×Dic22C2312yes—
68C11×C4⋊Q8—28no—
69C11×#124—28no—
70C11×#123—216no—
71C11×C22⋊Q8—28no—
72C11×C22⋊Q8—28no—
73C11×#117—22no—
74C11×#117D414yes—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—24no—
79C2×C42×C11—21no—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11—21no—
82#66997—28no—
83C2×#4326—232no—
84C2×#4326—28no—
85C2×#4326—28no—
86C2×#4326—28no—
87#66989—28no—
88#66988—216no—
89#66979—22no—
90#66979D414yes—
91C2×C4⋊Dic11C2312yes—
92#66977—28no—
93#66977—28no—
94C2×Dic11⋊C4—24no—
95C2×C4×Dic11—21no—
96C2×#4318—22no—
97C2×#4318—22no—
98C2×#4318—22no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8—22no—
101C22×C11⋊C8D414yes—
102C22×C11⋊C8C2312yes—
103C22×C11⋊C8C2312yes—
104#66899—28no—
105C22⋊(C11⋊C8)—28no—
106#66874—28no—
107#23389—111nomaximal, Sylow
108C24×C11C2×D412yes—
109C24×C11C2×D411yescharacteristic
110C11×#41—44no—
111C11×#41—44no—
112C11×#41—44no—
113C11×#41—44no—
114C2×Q8×C11—22no—
115C2×Q8×C11—24no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—28no—
120C2×Q8×C11—28no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—42no—
126C2×Q8×C11—42no—
127C2×Q8×C11—44no—
128C2×Q8×C11—44no—
129C2×Q8×C11C2×D414yes—
130C2×D4×C11—24no—
131C2×D4×C11—24no—
132C2×D4×C11—24no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11#4112yes—
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—24no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C2×Dic22—28no—
162C2×Dic22—24no—
163C2×Dic22—28no—
164C2×Dic22—22no—
165C2×Dic22—22no—
166C2×Dic22—22no—
167C2×Dic22—22no—
168C2×Dic22—22no—
169C2×Dic22—42no—
170C2×Dic22—44no—
171C2×Dic22—42no—
172C2×Dic22—44no—
173C2×Dic22C2×D414yes—
174C11×C4⋊C4—216no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4C2×D414yes—
177C11×C22⋊C4—216no—
178C11×C22⋊C4—24no—
179C42×C11—24no—
180C22⋊Dic11—216no—
181C22⋊Dic11—24no—
182#4326—232no—
183C4⋊Dic11—22no—
184C4⋊Dic11C2×D414yes—
185Dic11⋊C4—216no—
186C4×Dic11—24no—
187#4318—44no—
188C2×C11⋊C8—28no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8C2×D414yes—
195C23×Q16—111no—
196C2×#536—111no—
197C2×#536D1111yescharacteristic
198C2×#419—111no—
199C2×#419—111no—
200C2×#408—111no—
201#2001—118no—
202#1735—111no—
203C23×C11—24no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—28no—
208C23×C11#12012yes—
209C23×C11#12012yes—
210C23×C11#12112yes—
211C23×C11C22×D411yescharacteristic
212Q8×C11—24no—
213Q8×C11—24no—
214Q8×C11—42no—
215Q8×C11—42no—
216Q8×C11—48no—
217Q8×C11—44no—
218D4×C11—48no—
219D4×C11—44no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—44no—
228C2×C4×C11—48no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11#12014yes—
234C2×C4×C11#12012yes—
235C2×C4×C11#12012yes—
236C2×C4×C11#12114yes—
237C2×C4×C11#12114yes—
238C2×C4×C11#12112yes—
239C2×C4×C11#12714yes—
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—44no—
251C2×Dic11—48no—
252Dic22—24no—
253Dic22—24no—
254Dic22—42no—
255Dic22—42no—
256Dic22—48no—
257C11⋊C8—24no—
258C11⋊C8—42no—
259C22×#41C2×D1111yescharacteristic
260C23×Q8—111no—
261C23×Q8C2×D1111yescharacteristic
262C22×Q16—114no—
263C22×Q16—224no—
264C22×Q16—224no—
265C22×Q16—224no—
266C22×M16—111no—
267C23×C8—111no—
268#536—24no—
269#536—24no—
270#536—224no—
271#536—224no—
272C2×C4⋊Q8—21no—
273C2×C4⋊Q8—221no—
274C2×#124—21no—
275C2×#124—221no—
276C2×#123—22no—
277C2×#123—222no—
278C2×C22⋊Q8—114no—
279C2×C22⋊Q8C2×D1114yes—
280C2×#117—111no—
281C2×#117C2×D1111yescharacteristic
282#419—224no—
283#419—224no—
284C2×#103—114no—
285C2×#103—114no—
286#408—224no—
287C2×C22⋊C8—114no—
288#340—114no—
289C22×C11—24no—
290C22×C11—24no—
291C22×C11—24no—
292C22×C11—42no—
293C22×C11—44no—
294C22×C11—44no—
295C22×C11—44no—
296C22×C11#39214yes—
297C22×C11C2×#12011yescharacteristic
298C22×C11C2×#12011yescharacteristic
299C22×C11C2×#12111yescharacteristic
300C22×C11#57814yes—
301C4×C11—42no—
302C4×C11—44no—
303C4×C11—44no—
304C4×C11#39214yes—
305C4×C11C2×#12011yescharacteristic
306C4×C11C2×#12111yescharacteristic
307C4×C11C2×#12111yescharacteristic
308C4×C11C2×#12711yescharacteristic
309Dic11—44no—
310Dic11—44no—
311C2×#41—22no—
312C2×#41—22no—
313C2×#41—22no—
314C2×#41—22no—
315C2×#41—22no—
316C2×#41—22no—
317C22×Q8—21no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—114no—
324C22×Q8—112no—
325C22×Q8—222no—
326C22×Q8—221no—
327C22×Q8—222no—
328C22×Q8—222no—
329C22×Q8—222no—
330C22×Q8—222no—
331C22×Q8C22⋊D1114yes—
332C22×Q8C22⋊D1111yescharacteristic
333C22×Q8C22×D1112yes—
334C22×D4C22⋊D1112yes—
335C22×D4C22⋊D1111yescharacteristic
336C23×C4—21no—
337C23×C4—221no—
338C23×C4C22×D1112yes—
339C23×C4C22×D1111yescharacteristic
340C2×Q16—228no—
341C2×Q16—228no—
342C2×Q16—2232no—
343C2×Q16—228no—
344C2×M16—222no—
345C2×M16—222no—
346C2×M16—222no—
347C22×C8—114no—
348C22×C8—112no—
349C22×C8—112no—
350C22×C8—222no—
351C22×C8—222no—
352C4⋊Q8—28no—
353C4⋊Q8—228no—
354#124—28no—
355#124—228no—
356#123—216no—
357#123—2216no—
358C22⋊Q8—28no—
359C22⋊Q8—28no—
360C22⋊Q8—228no—
361C22⋊Q8—228no—
362#117—22no—
363#117—114no—
364#117—222no—
365#117C22⋊D1114yes—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4C22×D1112yes—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—224no—
374C2×C42—21no—
375C2×C42—221no—
376#103—228no—
377#103—228no—
378C22⋊C8—228no—
379C2×C11—24no—
380C2×C11—82no—
381C2×C11C2×#39211yescharacteristic
382C2×C11#301112yes—
383C2×C11#301112yes—
384C2×C11#305912yes—
385C24C2×C22⋊D1112yes—
386C24C2×C22⋊D1111yescharacteristic
387#41—44no—
388#41—44no—
389#41—44no—
390#41—44no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—24no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—28no—
397C2×Q8—28no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—42no—
403C2×Q8—44no—
404C2×Q8—42no—
405C2×Q8—44no—
406C2×Q8—114no—
407C2×Q8—224no—
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—444no—
417C2×Q8—444no—
418C2×Q8—442no—
419C2×Q8C2×C22⋊D1114yes—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—224no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—442no—
441C22×C4—442no—
442C22×C4D4×D1112yes—
443C22×C4D4×D1112yes—
444C22×C4D4×D1112yes—
445C22×C4#434112yes—
446C22×C4C2×C22⋊D1112yes—
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C2×C22⋊D1112yes—
449C22×C4C2×C22⋊D1112yes—
450C22×C4C23×D1111yescharacteristic
451Q16—2232no—
452M16—444no—
453C2×C8—114no—
454C2×C8—228no—
455C2×C8—222no—
456C2×C8—222no—
457C2×C8—222no—
458C2×C8—222no—
459C2×C8—222no—
460C4⋊C4—216no—
461C4⋊C4—22no—
462C4⋊C4—114no—
463C4⋊C4—2216no—
464C4⋊C4—222no—
465C4⋊C4C2×C22⋊D1114yes—
466C22⋊C4—216no—
467C22⋊C4—24no—
468C22⋊C4—2216no—
469C22⋊C4—224no—
470C42—24no—
471C42—224no—
472C11#2338911yescharacteristic, complemented, Sylow
473C23—24no—
474C23—22no—
475C23—22no—
476C23—28no—
477C23—22no—
478C23#6699012yes—
479C23#6699212yes—
480C23#6700612yes—
481C23C22×C22⋊D1111yescharacteristic
482Q8—24no—
483Q8—24no—
484Q8—42no—
485Q8—42no—
486Q8—48no—
487Q8—44no—
488Q8—224no—
489Q8—224no—
490Q8—442no—
491Q8—442no—
492Q8—448no—
493D4—48no—
494D4—44no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—48no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—442no—
511C2×C4—448no—
512C2×C4—444no—
513C2×C4—442no—
514C2×C4#6699014yes—
515C2×C4#6699012yes—
516C2×C4#6699114yes—
517C2×C4#6699214yes—
518C2×C4#6699212yes—
519C2×C4#6699314yes—
520C2×C4#6700612yes—
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×#434111yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C2×C4C22×C22⋊D1111yescharacteristic
527C8—224no—
528C8—442no—
529C22—24no—
530C22—24no—
531C22—24no—
532C22—44no—
533C22—44no—
534C22—42no—
535C22—44no—
536C22#1062283614yes—
537C22C2×#6699011yescharacteristic
538C22C2×#6699211yescharacteristic
539C22#1062336914yes—
540C22C2×#6700611yescharacteristic
541C4—44no—
542C4—42no—
543C4—44no—
544C4—444no—
545C4—444no—
546C4#1062283614yes—
547C4C2×#6699011yescharacteristic
548C4C2×#6699111yescharacteristic
549C4C2×#6699211yescharacteristic
550C4C2×#6699311yescharacteristic
551C2—24no—
552C2—82no—
553C2C2×#1062283611yescharacteristic
554C2#1307790912yes—
555C2#1307791112yes—
556C2#1307826812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#536C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC2×#536D11
hypocenterC11#23389
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C23×#4326C2semidirect
3. C2×#10622838C2semidirect
4. C2×#10622617C2semidirect
6. #13069624C2semidirect
7. #13068332C2semidirect
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×#106233562
C2×#106228382
C2×#106226172
C2×#106228472
#130696242
#130683322
C2×C11×#5362
#2338911