Finite Group Databasebeta

← #14752185

Subgroups — #14752185

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622341C211yesmaximal, characteristic
2C2×#10622724C211yesmaximal, characteristic
3C2×#10622714C211yesmaximal, characteristic, complemented
4C2×#10622302C211yesmaximal, characteristic, complemented
5#13071079C211yesmaximal, characteristic
6#13068490C211yesmaximal, characteristic, complemented
7#13068489C211yesmaximal, characteristic, complemented
8#13068464C211yesmaximal, characteristic, complemented
9#13068400C211yesmaximal, characteristic, complemented
10#13068399C211yesmaximal, characteristic, complemented
11#13068386C211yesmaximal, characteristic, complemented
12#13068384C211yesmaximal, characteristic, complemented
13#13068381C211yesmaximal, characteristic, complemented
14C4×#66879C211yesmaximal, characteristic, complemented
15C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28#10622724C418yescomplemented
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31#10622714—24no—
32C2×#66879C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×C8×Dic11C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41C2×C8×Dic11C2211yescharacteristic
42#10622570C412yes—
43#10622557C412yes—
44C4×(C2×D11)⋊C4C2211yescharacteristic
45C4×Dic11⋊C4C2211yescharacteristic
46C42×Dic11C2211yescharacteristic
47C2×#66867C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622341C418yescomplemented
50#10622302—24no—
51#10622283C412yes—
52#10622260C412yes—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11C2×C411yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11C2×C414yes—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C22⋊C4C2×C412yes—
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11C2×C412yes—
73C2×C22⋊Dic11C2×C411yescharacteristic
74C4×C22⋊D11C2×C414yes—
75C4×C22⋊D11C2×C414yes—
76C2×(C2×D11)⋊C4C2×C412yes—
77C2×(C2×D11)⋊C4C2×C412yes—
78C2×(C2×D11)⋊C4C2×C411yescharacteristic
79#66979—22no—
80#66979—22no—
81C2×C4⋊Dic11C2×C412yes—
82C2×Dic11⋊C4C2×C412yes—
83C2×Dic11⋊C4C2×C412yes—
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×C4×Dic11C2×C412yes—
86C2×C4×Dic11C2×C412yes—
87C2×C4×Dic11C2311yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C2×#4318—22no—
91C2×#4318—22no—
92C2×#4318C2×C414yes—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×#4313—22no—
98C2×#4313—22no—
99C2×#4313C2×C414yes—
100C2×C8×D11—22no—
101C2×C8×D11—22no—
102C2×C8×D11C2×C414yes—
103#66925—22no—
104#66925—22no—
105C11×C22⋊C8C2×C414yes—
106C4×C8×C11—22no—
107C4×C8×C11—22no—
108C11×#95C2×C412yes—
109C11⋊#95C2×C412yes—
110C11⋊#95C2×C412yes—
111C22⋊(C11⋊C8)C2×C414yes—
112(C2×D11)⋊C8C2×C414yes—
113(C2×D11)⋊C8C2×C414yes—
114#66879—22no—
115#66879—22no—
116#66879C2×C414yes—
117#66879C2×C414yes—
118#66879D414yescomplemented
119Dic11⋊C8C2×C414yes—
120Dic11⋊C8C2×C414yes—
121C8×Dic11—22no—
122C8×Dic11—22no—
123C8×Dic11—22no—
124#66867—22no—
125C4×C11⋊C8—22no—
126#20492—111nomaximal, Sylow
127C24×C11C22×C411yescharacteristic
128C23×D11C22×C411yescharacteristic
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C412yes—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—42no—
140C2×C22⋊D11C4214yes—
141C22×Dic11C22×C412yes—
142C22×Dic11C22×C411yescharacteristic
143C22×Dic11C22×C411yescharacteristic
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C412yes—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11C22×C412yes—
151C2×C4×D11C22×C412yes—
152C2×C8×C11—28no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11C22×C412yes—
160C2×C8×C11C22×C412yes—
161C2×C8×C11C22×C412yes—
162C2×C8×C11C22×C412yes—
163C2×C8×C11C2×D412yes—
164C2×C8×C11#4112yes—
165C11×C22⋊C4—24no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C22⋊Dic11—24no—
171C22⋊Dic11C4214yes—
172(C2×D11)⋊C4—24no—
173(C2×D11)⋊C4—24no—
174(C2×D11)⋊C4C4214yes—
175C4⋊Dic11—24no—
176Dic11⋊C4—24no—
177Dic11⋊C4—42no—
178Dic11⋊C4C4214yes—
179C4×Dic11—24no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182C4×Dic11—42no—
183C4×Dic11C22×C412yes—
184C4×Dic11C22×C412yes—
185C4×Dic11C2×D412yes—
186C4×Dic11#4112yes—
187#4318—28no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8C22×C412yes—
195C2×C11⋊C8C22×C412yes—
196C2×C11⋊C8C22×C412yes—
197C2×C11⋊C8C22×C412yes—
198C2×C11⋊C8C2×D412yes—
199C2×C11⋊C8#4112yes—
200#4313—28no—
201C8×D11—28no—
202C2×#435—111no—
203C2×#435—111no—
204C2×#405—111no—
205C2×#405—111no—
206#2293—111no—
207#1771—111no—
208#1771—111no—
209C4×C4⋊C8—111no—
210#1753—111no—
211#1753—111no—
212C8×C22⋊C4—111no—
213C8×C22⋊C4D1111yescharacteristic, complemented
214#1750—111no—
215#1750—111no—
216C4×#97—111no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11C2×C4212yes—
222C23×C11C23×C411yescharacteristic
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—22no—
226C22×D11—22no—
227C22×D11C2×C4212yes—
228C2×C4×C11—21no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11C2×C4212yes—
240C2×C4×C11#13114yes—
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C22⋊D11—44no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11C2×C4212yes—
258C2×Dic11C2×C4212yes—
259C2×Dic11C2×C4212yes—
260C2×Dic11C4×D414yes—
261C4×D11—22no—
262C4×D11—22no—
263C4×D11—22no—
264C4×D11—22no—
265C8×C11—22no—
266C8×C11—22no—
267C8×C11—22no—
268C8×C11C4×D414yes—
269C11⋊C8—22no—
270C11⋊C8—22no—
271C11⋊C8—22no—
272C11⋊C8C4×D414yes—
273C22×M16—111no—
274C22×M16—111no—
275C23×C8—111no—
276C23×C8C2×D1111yescharacteristic
277C2×C4×D4—111no—
278C2×#117—111no—
279C2×#117—111no—
280#435—118no—
281#435—118no—
282C2×C4⋊C8—111no—
283C2×C4⋊C8—111no—
284C2×C22⋊C8—111no—
285C2×C22⋊C8—111no—
286C2×C22⋊C8—111no—
287C2×C22⋊C8C2×D1111yescharacteristic
288#405—224no—
289#405—224no—
290C2×#97—111no—
291C2×#97—111no—
292C2×#97—111no—
293C2×#97—111no—
294C2×#97—111no—
295C2×#97—111no—
296C2×C4×C8—111no—
297C2×C4×C8—111no—
298C2×C4×C8—111no—
299C2×C4×C8—111no—
300C2×C4×C8C2×D1111yescharacteristic
301C2×C4×C8C2×D1111yescharacteristic
302#390—112no—
303#389—112no—
304#388—112no—
305#388—112no—
306C4×C4⋊C4—111no—
307C4×C22⋊C4—111no—
308C4×C22⋊C4C2×D1111yescharacteristic
309C43—111no—
310#336—111no—
311#336—111no—
312#336—111no—
313#336—111no—
314#336C2×D1111yescharacteristic
315#336C2×D1111yescharacteristic
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11C22×C4211yescharacteristic
322C22×C11C2×C4×D411yescharacteristic
323C22×C11C4×#4111yescharacteristic
324C22×C11C2×#13112yes—
325C22×C11#56812yes—
326C2×D11—22no—
327C2×D11—22no—
328C2×D11—22no—
329C2×D11—42no—
330C2×D11—42no—
331C4×C11—24no—
332C4×C11—22no—
333C4×C11—42no—
334C4×C11C2×C4×D411yescharacteristic
335C4×C11C2×C4×D411yescharacteristic
336C4×C11C4×#4111yescharacteristic
337C4×C11C4×#4111yescharacteristic
338Dic11—22no—
339Dic11—22no—
340Dic11—24no—
341Dic11—22no—
342Dic11—42no—
343C22×D4—111no—
344C23×C4—111no—
345C23×C4C22×D1111yescharacteristic
346C2×M16—114no—
347C2×M16—114no—
348C2×M16—222no—
349C2×M16—222no—
350C2×M16—222no—
351C2×M16—222no—
352C22×C8—22no—
353C22×C8—22no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—114no—
359C22×C8—222no—
360C22×C8—222no—
361C22×C8C4×D1114yes—
362C22×C8C22×D1111yescharacteristic
363C22×C8C22×D1111yescharacteristic
364C22×C8C22×D1111yescharacteristic
365C22×C8C22×D1111yescharacteristic
366C4×D4—114no—
367C4×D4—114no—
368#117—222no—
369#117—222no—
370#117—222no—
371#117—222no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—112no—
375C2×C4⋊C4—112no—
376C2×C22⋊C4—111no—
377C2×C22⋊C4—111no—
378C2×C22⋊C4—112no—
379C2×C22⋊C4—112no—
380C2×C22⋊C4—112no—
381C2×C22⋊C4C4×D1112yes—
382C2×C42—111no—
383C2×C42—111no—
384C2×C42—112no—
385C2×C42—111no—
386C2×C42—112no—
387C2×C42C22×D1111yescharacteristic
388C2×C42C22×D1111yescharacteristic
389C4⋊C8—114no—
390C4⋊C8—114no—
391C22⋊C8—114no—
392C22⋊C8—114no—
393C22⋊C8—114no—
394C22⋊C8C4×D1114yes—
395#97—114no—
396#97—114no—
397#97—114no—
398#97—222no—
399#97—222no—
400#97—222no—
401C4×C8—22no—
402C4×C8—22no—
403C4×C8—222no—
404C4×C8—222no—
405C4×C8—222no—
406C4×C8—222no—
407#95—112no—
408#95—112no—
409#95C4×D1112yes—
410C2×C11—42no—
411C2×C11C42×D411yescharacteristic
412C2×C11#287311yescharacteristic
413C2×C11C4×#13111yescharacteristic
414C2×C11#293512yes—
415C2×C11#296812yes—
416D11—42no—
417C24—111no—
418C24C2×C4×D1111yescharacteristic
419C2×D4—114no—
420C2×D4—442no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—112no—
428C22×C4—111no—
429C22×C4—112no—
430C22×C4—112no—
431C22×C4—112no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4C2×C4×D1112yes—
437C22×C4C2×C4×D1111yescharacteristic
438C22×C4C2×C4×D1112yes—
439C22×C4C2×C4×D1112yes—
440C22×C4C2×C4×D1112yes—
441C22×C4C23×D1111yescharacteristic
442M16—228no—
443M16—228no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—28no—
451C2×C8—112no—
452C2×C8—112no—
453C2×C8—112no—
454C2×C8—112no—
455C2×C8—112no—
456C2×C8—112no—
457C2×C8—228no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8C2×C4×D1112yes—
465C2×C8C2×C4×D1112yes—
466C2×C8C2×C4×D1112yes—
467C2×C8C2×C4×D1112yes—
468C2×C8D4×D1112yes—
469C2×C8#434112yes—
470C4⋊C4—114no—
471C4⋊C4—224no—
472C4⋊C4—224no—
473C4⋊C4—442no—
474C22⋊C4—24no—
475C22⋊C4—114no—
476C22⋊C4—114no—
477C22⋊C4—224no—
478C22⋊C4—224no—
479C22⋊C4—224no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—112no—
485C42—112no—
486C42—112no—
487C42—112no—
488C42—224no—
489C42—221no—
490C42—221no—
491C42—442no—
492C11#2049211yescharacteristic, complemented, Sylow
493C23—22no—
494C23—22no—
495C23—21no—
496C23—21no—
497C23—112no—
498C23—222no—
499C23—222no—
500C23—221no—
501C23—221no—
502C23C42×D1112yes—
503C23C22×C4×D1111yescharacteristic
504D4—444no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—112no—
517C2×C4—112no—
518C2×C4—112no—
519C2×C4—114no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4C42×D1112yes—
534C2×C4#6695414yes—
535C2×C4C22×C4×D1111yescharacteristic
536C2×C4C22×C4×D1111yescharacteristic
537C2×C4C2×D4×D1111yescharacteristic
538C2×C4C2×#434111yescharacteristic
539C2×C4#41×D1111yescharacteristic
540C2×C4#41×D1111yescharacteristic
541C8—22no—
542C8—22no—
543C8—22no—
544C8—114no—
545C8—222no—
546C8—222no—
547C8—222no—
548C8(C22⋊D11)⋊C414yes—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—42no—
553C22—42no—
554C22—222no—
555C22—222no—
556C22—222no—
557C22—442no—
558C22—442no—
559C22C2×C42×D1111yescharacteristic
560C22C4×#434111yescharacteristic
561C22C4×D4×D1111yescharacteristic
562C22C2×#6695412yes—
563C22#1062328112yes—
564C4—24no—
565C4—22no—
566C4—42no—
567C4—222no—
568C4—222no—
569C4—224no—
570C4—222no—
571C4—442no—
572C4C2×(C22⋊D11)⋊C411yescharacteristic
573C4#1062305311yescharacteristic
574C4C4×#434111yescharacteristic
575C4C4×D4×D1111yescharacteristic
576C2—42no—
577C2—442no—
578C2C4×(C22⋊D11)⋊C411yescharacteristic
579C2#1307703211yescharacteristic
580C2C4×#6695411yescharacteristic
581C2#1307735512yes—
582C2#1307760412yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC8×C11×C22⋊C4C2
socleC23×C11C23×C4
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenterC8×C22⋊C4D11
hypocenterC11#20492
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#10622714C2semidirect
4. C2×#10622302C2semidirect
6. #13068490C2semidirect
7. #13068489C2semidirect
8. #13068464C2semidirect
9. #13068400C2semidirect
10. #13068399C2semidirect
11. #13068386C2semidirect
12. #13068384C2semidirect
13. #13068381C2semidirect
14. C4×#66879C2semidirect
15. C8×C11×C22⋊C4C2semidirect
28. #10622724C4semidirect
49. #10622341C4semidirect
118. #66879D4semidirect
213. C8×C22⋊C4D11semidirect
492. C11#20492semidirect

Maximal subgroups

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

subgroupindex
C2×#106223412
C2×#106227242
C2×#106227142
C2×#106223022
#130710792
#130684902
#130684892
#130684642
#130684002
#130683992
#130683862
#130683842
#130683812
C4×#668792
C8×C11×C22⋊C42
#2049211