Finite Group Databasebeta

← #14720765

Subgroups — #14720765

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082231C211yesmaximal, characteristic
2#13077741C211yesmaximal, characteristic, complemented
3#13067077C212yesmaximal, complemented
4#13067072C211yesmaximal, characteristic, complemented
5#13067064C212yesmaximal, complemented
6#13067056C211yesmaximal, characteristic, complemented
7#13067038C211yesmaximal, characteristic, complemented
8#13067030C212yesmaximal, complemented
9#13066999C211yesmaximal, characteristic, complemented
10C2×#10622094C212yesmaximal, complemented
11C4×C11×#131C211yesmaximal, characteristic, complemented
12C2×C11×#131—21no—
13C4×C11×#41C2211yescharacteristic
14#10623355—21no—
15#10623115C411yescharacteristic
16#10623109—21no—
17#10623098C411yescharacteristic
18#10623086C411yescharacteristic
19#10623083C412yes—
20#10623072C412yes—
21#10623069—22no—
22D4×Dic22C411yescharacteristic
23C4×#4341—21no—
24#10623064—21no—
25#10623062—22no—
26#10623010C2212yes—
27C4×#4339C2211yescharacteristic
28#10623001C2211yescharacteristic
29C2×C4×Dic22C2212yes—
30C11×#405—22no—
31C11×#405—21no—
32C4×C11×M16C2212yes—
33C4×C11×M16C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35C2×C4×C8×C11C2212yes—
36#10622637—21no—
37#10622624—22no—
38D4×C11⋊C8—21no—
39#10622539C2212yes—
40#10622538C2211yescharacteristic
41#10622537C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2212yes—
43#10622097C2211yescharacteristic
44#10622097C2212yes—
45#10622097C2211yescharacteristic
46#10622094C2212yes—
47#10622094C2212yes—
48#10622094C2212yes—
49#10622094C2212yes—
50#10622094C2211yescharacteristic
51#10622094C2212yes—
52#10622094C2211yescharacteristic
53C2×C11×#41D411yescharacteristic
54C2×#4341—21no—
55C2×#4339C2×C411yescharacteristic
56C22×Dic22C2×C412yes—
57C11×#131—28no—
58C2×C11×M16—22no—
59C2×C11×M16—21no—
60C22×C8×C11—22no—
61C22×C8×C11—21no—
62C4×Q8×C11C2×C411yescharacteristic
63C4×Q8×C11D411yescharacteristic
64C4×D4×C11C2×C411yescharacteristic
65C4×D4×C11C2×C412yes—
66C4×D4×C11D411yescharacteristic
67C4×D4×C11D412yes—
68C11×#117D412yes—
69C11×#117D411yescharacteristic
70C2×C42×C11C2312yes—
71C2×C42×C11C2311yescharacteristic
72#66999—21no—
73#66997—21no—
74#66992—22no—
75#66988—22no—
76D4×Dic11—21no—
77#66983C2×C412yes—
78#66982—22no—
79C4×C22⋊D11—21no—
80C4×C22⋊D11—21no—
81C4×C22⋊D11—22no—
82#66979—21no—
83#66979C2×C411yescharacteristic
84C2×C4⋊Dic11C2×C412yes—
85#66977—21no—
86#66977C2×C412yes—
87#66977C2×C412yes—
88C2×Dic11⋊C4—22no—
89C2×C4×Dic11—22no—
90C2×#4318—21no—
91C22×C11⋊C8—22no—
92#66951—22no—
93#66950—21no—
94#66949—22no—
95#66945—21no—
96#66942—22no—
97#66942—22no—
98#66941—21no—
99#66940—21no—
100#66939—22no—
101#66938—22no—
102(C22⋊D11)⋊C4—22no—
103#66932—22no—
104#66931—22no—
105#66930—22no—
106#66929—22no—
107#66928C2×C412yes—
108C4×D44C2×C411yescharacteristic
109C4×D44C2311yescharacteristic
110#66925—21no—
111#66925—22no—
112C42×D11—21no—
113#66923—21no—
114#66923C2×C412yes—
115#66922C2×C411yescharacteristic
116#66922C2×C411yescharacteristic
117C4×Dic22—22no—
118C4×Dic22—22no—
119C4×Dic22—21no—
120C4×Dic22C2×C412yes—
121C4×Dic22C2×C412yes—
122C4×Dic22C2×C411yescharacteristic
123C4×Dic22C2311yescharacteristic
124C4×Dic22C2312yes—
125C11×#97—22no—
126C11×#97—21no—
127C4×C8×C11—22no—
128C4×C8×C11—21no—
129C4×C8×C11C2311yescharacteristic
130C4×C8×C11C2312yes—
131C4×C8×C11C2311yescharacteristic
132C22⋊(C11⋊C8)—21no—
133C22⋊(C11⋊C8)—22no—
134C4⋊(C11⋊C8)—22no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2312yes—
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—22no—
140C4×C11⋊C8—21no—
141#17519—111nomaximal, Sylow
142C11×#41—24no—
143C2×Q8×C11C22⋊C411yescharacteristic
144C2×D4×C11C22⋊C412yes—
145C2×D4×C11C22⋊C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C22×C412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C2×C22⋊D11—22no—
153C2×C22⋊D11—21no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156#4341—44no—
157#4339—22no—
158#4339—41no—
159C2×D44C22×C411yescharacteristic
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×Dic22—24no—
164C2×Dic22—22no—
165C2×Dic22—21no—
166C2×Dic22—42no—
167C2×Dic22C22×C412yes—
168C2×Dic22C22×C411yescharacteristic
169C11×M16—28no—
170C11×M16—24no—
171C2×C8×C11—28no—
172C2×C8×C11—24no—
173C2×C8×C11—21no—
174C2×C8×C11—22no—
175C2×C8×C11—21no—
176C11×C4⋊C4C22⋊C411yescharacteristic
177C11×C4⋊C4C22⋊C411yescharacteristic
178C11×C4⋊C4C22⋊C412yes—
179C11×C4⋊C4C22⋊C412yes—
180C11×C22⋊C4C22⋊C412yes—
181C11×C22⋊C4C22⋊C412yes—
182C11×C22⋊C4C22⋊C412yes—
183C42×C11C22×C412yes—
184C42×C11C22×C411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D412yes—
187C42×C11C2×D412yes—
188C42×C11C2×D411yescharacteristic
189C42×C11C2411yescharacteristic
190C22⋊Dic11—22no—
191C22⋊Dic11—21no—
192C22⋊Dic11—22no—
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—21no—
198C4⋊Dic11—22no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11C22×C411yescharacteristic
203C4⋊Dic11C22×C412yes—
204C4⋊Dic11C22×C411yescharacteristic
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—21no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—21no—
213Dic11⋊C4—22no—
214C4×Dic11—22no—
215C4×Dic11—22no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—22no—
220#4318—81no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—22no—
224C2×C11⋊C8—82no—
225#3482—111no—
226#2990—111no—
227C4×#131D1111yescharacteristic, complemented
228#1494—112no—
229#1493—111no—
230#1491—112no—
231#1489—111no—
232#1485—111no—
233#1483—112no—
234#1476—111no—
235C2×Q8⋊C8—112no—
236C23×C11C2×C22⋊C411yescharacteristic
237C23×C11C2×C22⋊C412yes—
238C22×D11—21no—
239Q8×C11—22no—
240D4×C11—24no—
241D4×C11#10414yes—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11C2×C22⋊C412yes—
253C2×C4×C11C2×C22⋊C411yescharacteristic
254C2×C4×C11C2×C22⋊C412yes—
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C2×C22⋊C412yes—
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C22⋊D11—42no—
262C22⋊D11—44no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—44no—
269C2×Dic11—44no—
270D44—21no—
271D44—21no—
272C4×D11—42no—
273C4×D11—41no—
274C4×D11—41no—
275C4×D11—42no—
276Dic22—21no—
277Dic22—22no—
278Dic22—22no—
279Dic22—44no—
280Dic22—42no—
281Dic22#13112yescomplemented
282C8×C11—22no—
283C8×C11—24no—
284C8×C11—22no—
285C11⋊C8—41no—
286C11⋊C8—42no—
287C11⋊C8—41no—
288C2×#131—21no—
289#557—111no—
290#556—111no—
291#556—221no—
292#552—112no—
293#552—222no—
294D4×Q8—111no—
295#548—112no—
296#547—111no—
297#547—221no—
298#533—111no—
299#533—221no—
300#529—112no—
301#529—222no—
302C4×#41—111no—
303C4×#41—221no—
304C4×#41C2×D1111yescharacteristic
305C2×C4×Q8—112no—
306#446—221no—
307#435—222no—
308C8×D4—221no—
309#432—112no—
310#431—111no—
311#423—111no—
312C2×C4⋊C8—112no—
313#405—22no—
314#405—21no—
315C4×M16C2×D1112yes—
316C4×M16C2×D1111yescharacteristic
317C2×C4×C8C2×D1112yes—
318C2×C4×C8C2×D1111yescharacteristic
319Q8⋊C8—111no—
320Q8⋊C8—112no—
321Q8⋊C8—112no—
322Q8⋊C8—112no—
323Q8⋊C8—111no—
324Q8⋊C8—112no—
325Q8⋊C8—112no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—112no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11C2×#10414yes—
335C22×C11C22×C22⋊C411yescharacteristic
336C2×D11—41no—
337C2×D11—41no—
338C2×D11—41no—
339C4×C11—22no—
340C4×C11—21no—
341C4×C11—22no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—22no—
345C4×C11C2×#10412yes—
346C4×C11C2×#13111yescharacteristic
347C4×C11#56811yescharacteristic
348C4×C11#57711yescharacteristic
349C4×C11#57811yescharacteristic
350Dic11—22no—
351Dic11—42no—
352Dic11—41no—
353Dic11—42no—
354Dic11—41no—
355C2×#41—111no—
356C2×#41—221no—
357C2×#41C22⋊D1111yescharacteristic
358C22×Q8—112no—
359#131—28no—
360C2×M16—22no—
361C2×M16—21no—
362C2×M16—221no—
363C22×C8—22no—
364C22×C8—21no—
365C22×C8—222no—
366C4⋊Q8—111no—
367C4⋊Q8—111no—
368C4⋊Q8—221no—
369C4⋊Q8—221no—
370#126—222no—
371#126—222no—
372#126—222no—
373#125—112no—
374#125—222no—
375#125—222no—
376#125—221no—
377#124—112no—
378#124—222no—
379#123—222no—
380#123—222no—
381#123—222no—
382C22⋊Q8—112no—
383C22⋊Q8—112no—
384C22⋊Q8—221no—
385C22⋊Q8—221no—
386C22⋊Q8—221no—
387C22⋊Q8—222no—
388C22⋊Q8—222no—
389#121—112no—
390#121—222no—
391C4×Q8—112no—
392C4×Q8—112no—
393C4×Q8—111no—
394C4×Q8—111no—
395C4×Q8—112no—
396C4×Q8—221no—
397C4×Q8—222no—
398C4×Q8—221no—
399C4×Q8—222no—
400C4×Q8C4×D1111yescharacteristic
401C4×Q8D4411yescharacteristic
402C4×D4—111no—
403C4×D4—111no—
404C4×D4—221no—
405C4×D4—221no—
406C4×D4—222no—
407C4×D4—221no—
408C4×D4—222no—
409C4×D4C4×D1111yescharacteristic
410C4×D4C4×D1112yes—
411C4×D4D4411yescharacteristic
412C4×D4D4412yes—
413#117—111no—
414#117—221no—
415#117—221no—
416#117—222no—
417#117—222no—
418#117—221no—
419#117C22⋊D1112yes—
420#117C22⋊D1111yescharacteristic
421C2×C4⋊C4—112no—
422C2×C4⋊C4—222no—
423C2×C42—222no—
424C2×C42—221no—
425C2×C42C22×D1112yes—
426C2×C42C22×D1111yescharacteristic
427C4⋊C8—111no—
428C4⋊C8—112no—
429C4⋊C8—111no—
430C4⋊C8—222no—
431C4⋊C8—221no—
432C22⋊C8—221no—
433C22⋊C8—222no—
434#97—21no—
435#97—22no—
436#97—222no—
437C4×C8—21no—
438C4×C8—22no—
439C4×C8—221no—
440C4×C8C22×D1111yescharacteristic
441C4×C8C22×D1111yescharacteristic
442C4×C8C22×D1112yes—
443C2×C11—24no—
444C2×C11—41no—
445C2×C11#288011yescharacteristic
446C2×C11#289811yescharacteristic
447C2×C11C22×#10411yescharacteristic
448D11—81no—
449#41—24no—
450#41—222no—
451#41—441no—
452#41—444no—
453C2×Q8—111no—
454C2×Q8—112no—
455C2×Q8—224no—
456C2×Q8—222no—
457C2×Q8—221no—
458C2×Q8—442no—
459C2×Q8(C2×D11)⋊C411yescharacteristic
460C2×D4—111no—
461C2×D4—222no—
462C2×D4—221no—
463C2×D4(C2×D11)⋊C412yes—
464C2×D4(C2×D11)⋊C411yescharacteristic
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4C2×C4×D1112yes—
471C22×C4C2×C4×D1111yescharacteristic
472C22×C4C2×D4412yes—
473C22×C4C2×D4411yescharacteristic
474C22×C4C2×C22⋊D1112yes—
475C22×C4C2×C22⋊D1111yescharacteristic
476M16—28no—
477M16—24no—
478M16—881no—
479C2×C8—28no—
480C2×C8—24no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—22no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—222no—
487C2×C8—882no—
488C4⋊C4—111no—
489C4⋊C4—112no—
490C4⋊C4—111no—
491C4⋊C4—222no—
492C4⋊C4—222no—
493C4⋊C4—222no—
494C4⋊C4—221no—
495C4⋊C4—222no—
496C4⋊C4—221no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—221no—
500C4⋊C4—222no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—222no—
504C4⋊C4(C2×D11)⋊C411yescharacteristic
505C4⋊C4(C2×D11)⋊C412yes—
506C4⋊C4(C2×D11)⋊C411yescharacteristic
507C4⋊C4(C2×D11)⋊C412yes—
508C22⋊C4—221no—
509C22⋊C4—222no—
510C22⋊C4—222no—
511C22⋊C4—221no—
512C22⋊C4—222no—
513C22⋊C4—222no—
514C22⋊C4—222no—
515C22⋊C4—221no—
516C22⋊C4(C2×D11)⋊C412yes—
517C22⋊C4(C2×D11)⋊C412yes—
518C22⋊C4(C2×D11)⋊C412yes—
519C42—221no—
520C42—222no—
521C42—221no—
522C42—222no—
523C42—221no—
524C42—222no—
525C42C2×C4×D1111yescharacteristic
526C42C2×C4×D1112yes—
527C42C2×D4411yescharacteristic
528C42C2×D4412yes—
529C42C2×C22⋊D1111yescharacteristic
530C42C2×C22⋊D1112yes—
531C42C23×D1111yescharacteristic
532C11#1751911yescharacteristic, complemented, Sylow
533C23—221no—
534C23C2×(C2×D11)⋊C411yescharacteristic
535C23C2×(C2×D11)⋊C412yes—
536Q8—22no—
537Q8—112no—
538Q8—221no—
539Q8—222no—
540Q8—222no—
541Q8—444no—
542Q8—442no—
543D4—24no—
544D4—221no—
545D4—221no—
546D4—442no—
547D4—444no—
548D4#6686914yes—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—442no—
565C2×C4—444no—
566C2×C4—444no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—442no—
570C2×C4C2×(C2×D11)⋊C412yes—
571C2×C4C2×(C2×D11)⋊C411yescharacteristic
572C2×C4C2×(C2×D11)⋊C412yes—
573C2×C4C2×(C2×D11)⋊C411yescharacteristic
574C2×C4C2×(C2×D11)⋊C412yes—
575C2×C4C2×(C2×D11)⋊C411yescharacteristic
576C2×C4C22×C4×D1111yescharacteristic
577C2×C4C22×D4411yescharacteristic
578C2×C4C22×C22⋊D1111yescharacteristic
579C8—22no—
580C8—24no—
581C8—22no—
582C8—441no—
583C8—442no—
584C8—441no—
585C22—22no—
586C22—22no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—441no—
591C22—441no—
592C22—441no—
593C22C2×#6686914yes—
594C22C22×(C2×D11)⋊C411yescharacteristic
595C4—21no—
596C4—22no—
597C4—22no—
598C4—21no—
599C4—21no—
600C4—22no—
601C4—222no—
602C4—442no—
603C4—441no—
604C4—441no—
605C4—442no—
606C4C2×#6686912yes—
607C4D11×#13111yescharacteristic
608C4#1062328111yescharacteristic
609C4#1062328211yescharacteristic
610C4#1062328411yescharacteristic
611C2—24no—
612C2—41no—
613C2—881no—
614C2#1307706311yescharacteristic
615C2#1307715011yescharacteristic
616C2C22×#6686911yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC4×C11×#131C2
socleC22×C11C22×C22⋊C4
prime radical#13082231C2
cosocleC42×C11C24
hypercenterC4×#131D11
hypocenterC11#17519
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×#131

Complements

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

NH ≅ G/Ntype
2. #13077741C2semidirect
3. #13067077C2semidirect
4. #13067072C2semidirect
5. #13067064C2semidirect
6. #13067056C2semidirect
7. #13067038C2semidirect
8. #13067030C2semidirect
9. #13066999C2semidirect
10. C2×#10622094C2semidirect
11. C4×C11×#131C2semidirect
227. C4×#131D11semidirect
281. Dic22#131semidirect
532. C11#17519semidirect

Maximal subgroups

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

subgroupindex
#130822312
#130777412
#130670772
#130670722
#130670642
#130670562
#130670382
#130670302
#130669992
C2×#106220942
C4×C11×#1312
#1751911