Finite Group Databasebeta

← #14724997

Subgroups — #14724997

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078663C211yesmaximal, characteristic
2#13077772C211yesmaximal, characteristic, complemented
3#13077651C211yesmaximal, characteristic, complemented
4#13067527C211yesmaximal, characteristic, complemented
5#13067515C211yesmaximal, characteristic, complemented
6#13067462C211yesmaximal, characteristic, complemented
7#13067449C211yesmaximal, characteristic, complemented
8#13067448C211yesmaximal, characteristic, complemented
9#13067442C211yesmaximal, characteristic, complemented
10#13067437C211yesmaximal, characteristic, complemented
11#13067425C211yesmaximal, characteristic, complemented
12#13067399C211yesmaximal, characteristic, complemented
13#13067077C211yesmaximal, characteristic, complemented
14#13066908C211yesmaximal, characteristic, complemented
15C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17#10623010C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C4×C8×C11C2211yescharacteristic
20#10622831C411yescharacteristic
21#10622830C411yescharacteristic
22#10622820—21no—
23C2×C22⋊(C11⋊C8)—21no—
24#10622724—21no—
25C8×C22⋊D11—21no—
26C4×#4324C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28#10622629C411yescharacteristic
29#10622629C411yescharacteristic
30C4×#4323C2211yescharacteristic
31C4×#4323C2211yescharacteristic
32#10622625C2211yescharacteristic
33#10622625C2211yescharacteristic
34#10622624—21no—
35#10622624—21no—
36D4×C11⋊C8C2211yescharacteristic
37D4×C11⋊C8C2211yescharacteristic
38#10622622C411yescharacteristic
39#10622622C411yescharacteristic
40#10622583C411yescharacteristic
41#10622581C411yescharacteristic
42#10622539C2211yescharacteristic
43#10622538C2211yescharacteristic
44#10622538C2211yescharacteristic
45#10622453—21no—
46#10622452—21no—
47#10622451C2211yescharacteristic, complemented
48#10622447C2211yescharacteristic, complemented
49#10622444C2211yescharacteristic, complemented
50#10622443C2211yescharacteristic, complemented
51C11×D4⋊C8C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×D4⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic, complemented
56#10622118C2211yescharacteristic, complemented
57#10622117C2211yescharacteristic, complemented
58#10622117C2211yescharacteristic, complemented
59#10622097C2211yescharacteristic, complemented
60#10622097C2211yescharacteristic, complemented
61#10622094C2211yescharacteristic, complemented
62#10622094C2211yescharacteristic, complemented
63#10622092C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C22×D4×C11C2×C411yescharacteristic
68C23×C4×C11—21no—
69C22×C8×C11—21no—
70C22×C8×C11—21no—
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C4×D4×C11C2×C411yescharacteristic
74C4×D4×C11C2×C411yescharacteristic
75C4×D4×C11C2311yescharacteristic
76C4×D4×C11C2311yescharacteristic
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80C2×#4324C2×C411yescharacteristic
81C2×#4324C2×C411yescharacteristic
82C2×#4323C2×C411yescharacteristic
83C2×#4323C2×C411yescharacteristic
84#66983C2×C411yescharacteristic
85#66982—21no—
86C4×C22⋊D11—21no—
87#66977C2×C411yescharacteristic
88C2×#4318—21no—
89C2×#4318—21no—
90C22×C11⋊C8—21no—
91C22×C11⋊C8—21no—
92C2×#4313—21no—
93C2×C8×D11—21no—
94#66929—21no—
95#66928C2×C411yescharacteristic
96C4×D44C2311yescharacteristic
97#66925—21no—
98#66923C2×C411yescharacteristic
99C4×Dic22C2311yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C4×C8×C11—21no—
104C4×C8×C11C2311yescharacteristic
105C4×C8×C11C2311yescharacteristic
106#66896C2×C411yescharacteristic
107#66896C2×C411yescharacteristic
108#66896C2×C411yescharacteristic
109#66896C2×C411yescharacteristic
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)—21no—
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)C2×C411yescharacteristic
116C22⋊(C11⋊C8)C2×C411yescharacteristic
117C22⋊(C11⋊C8)D411yescharacteristic
118C22⋊(C11⋊C8)D411yescharacteristic
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121#66879—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124C8×Dic11—21no—
125#66874C2×C411yescharacteristic
126#66874C2×C411yescharacteristic
127#66873C2×C411yescharacteristic
128#66873C2×C411yescharacteristic
129#66872C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66871C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133C4⋊(C11⋊C8)C2×C411yescharacteristic
134C4⋊(C11⋊C8)C2×C411yescharacteristic
135C4⋊(C11⋊C8)D411yescharacteristic
136C4⋊(C11⋊C8)D411yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18020—111nomaximal, Sylow
145C24×C11—21no—
146C2×D4×C11—22no—
147C2×D4×C11—21no—
148C2×D4×C11—41no—
149C2×D4×C11C22×C411yescharacteristic
150C2×D4×C11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—81no—
157C22×C4×C11—81no—
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C2×C22⋊D11—21no—
162C2×D44C22×C411yescharacteristic
163C2×C4×D11—21no—
164C2×Dic22C22×C411yescharacteristic
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—42no—
170C2×C8×C11—81no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C22×C411yescharacteristic
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C42×C11C22×C411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11#4111yescharacteristic
181C42×C11C2411yescharacteristic
182C22⋊Dic11—21no—
183#4324—22no—
184#4324—41no—
185#4323—22no—
186#4323—41no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191C4⋊Dic11C22×C411yescharacteristic
192C4⋊Dic11C22×C411yescharacteristic
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197C4×Dic11—21no—
198#4318—81no—
199#4318—81no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—81no—
203C2×C11⋊C8—81no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212#4313—81no—
213C8×D11—81no—
214#3105—111no—
215#2994—111no—
216#2974—111no—
217#1594—111no—
218#1592—111no—
219#1583—111no—
220#1582—111no—
221#1581—111no—
222#1581—111no—
223#1580—111no—
224SD16⋊C8—111no—
225#1573—111no—
226#1494—111no—
227C2×D4⋊C8D1111yescharacteristic, complemented
228#1452—111no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—81no—
234C23×C11C4×D411yescharacteristic
235C22×D11—21no—
236D4×C11—21no—
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—42no—
240D4×C11#13112yes—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—81no—
253C2×C4×C11—81no—
254C2×C4×C11—81no—
255C2×C4×C11C4×D411yescharacteristic
256C2×C4×C11C4×D411yescharacteristic
257C2×C4×C11C4×D411yescharacteristic
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C22⋊D11—42no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265D44—21no—
266D44—21no—
267C4×D11—41no—
268C4×D11—41no—
269Dic22—21no—
270Dic22—21no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11—41no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285#529—111no—
286C2×C4×D4C2×D1111yescharacteristic
287#484—111no—
288#481—111no—
289#478—111no—
290#478—111no—
291#463—111no—
292#463—111no—
293#450—111no—
294#447—111no—
295#446—111no—
296C8×Q8—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299C4×D8—111no—
300C4×D8—111no—
301#436—111no—
302#436—111no—
303#436—111no—
304#435—221no—
305#435—221no—
306#435—221no—
307C8×D4—111no—
308C8×D4—111no—
309C8×D4—111no—
310C8×D4—221no—
311#433—221no—
312#432—111no—
313#431—111no—
314#431—111no—
315#424—221no—
316C2×C4⋊C8C2×D1111yescharacteristic
317#407—221no—
318C2×C22⋊C8—221no—
319C2×C4×C8C2×D1111yescharacteristic
320#335—111no—
321#335—111no—
322#334—111no—
323#334—111no—
324Q8⋊C8—111no—
325Q8⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8C2×D1111yescharacteristic
329D4⋊C8C2×D1111yescharacteristic
330D4⋊C8C2×D1111yescharacteristic
331D4⋊C8C2×D1111yescharacteristic
332#322—111no—
333#322—111no—
334#322—111no—
335#322—111no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—22no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—84no—
345C22×C11#44412yes—
346C22×C11C2×C4×D411yescharacteristic
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11C2×#13111yescharacteristic
357C4×C11#56811yescharacteristic
358C4×C11#57611yescharacteristic
359C4×C11#57711yescharacteristic
360Dic11—41no—
361Dic11—41no—
362Dic11—41no—
363C22×D4C4×D1111yescharacteristic
364C23×C4—21no—
365C2×SD16—111no—
366C2×SD16—111no—
367C2×D8—111no—
368C2×D8—111no—
369C2×M16—221no—
370C2×M16—221no—
371C2×M16—221no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—221no—
375C22×C8—221no—
376C22×C8—221no—
377#126—221no—
378#125—111no—
379#124—111no—
380#123—221no—
381C22⋊Q8—111no—
382#121—111no—
383C4×Q8—111no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—111no—
387C4×D4—221no—
388C4×D4C4×D1111yescharacteristic
389C4×D4C4×D1111yescharacteristic
390C4×D4C22×D1111yescharacteristic
391C4×D4C22×D1111yescharacteristic
392#117—221no—
393C2×C4⋊C4C4×D1111yescharacteristic
394C2×C22⋊C4—21no—
395C2×C42C22×D1111yescharacteristic
396#107—111no—
397#107—111no—
398#106—111no—
399#106—111no—
400C4⋊C8—21no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—221no—
408C4⋊C8—221no—
409C4⋊C8C22×D1111yescharacteristic
410C4⋊C8C22×D1111yescharacteristic
411#103—111no—
412#103—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416#102—111no—
417#102—111no—
418#102—111no—
419C22⋊C8—111no—
420C22⋊C8—111no—
421C22⋊C8—111no—
422C22⋊C8—111no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429C22⋊C8—221no—
430#97—221no—
431#97—221no—
432C4×C8—21no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—221no—
438C4×C8C22×D1111yescharacteristic
439C4×C8C22×D1111yescharacteristic
440C2×C11—22no—
441C2×C11—42no—
442C2×C11—81no—
443C2×C11#293311yescharacteristic
444C2×C11#294611yescharacteristic
445C2×C11C2×#44411yescharacteristic
446D11—81no—
447C24—21no—
448C2×Q8—111no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—111no—
453C2×D4—221no—
454C2×D4C2×C4×D1111yescharacteristic
455C2×D4C2×C4×D1111yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—81no—
462C22×C4—81no—
463C22×C4—221no—
464C22×C4C2×C4×D1111yescharacteristic
465C22×C4D4×D1111yescharacteristic
466C22×C4#434111yescharacteristic
467SD16—222no—
468SD16—441no—
469D8—222no—
470D8—441no—
471M16—881no—
472M16—881no—
473M16—881no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—42no—
479C2×C8—81no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—111no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—881no—
491C2×C8—881no—
492C2×C8—881no—
493C4⋊C4—21no—
494C4⋊C4—111no—
495C4⋊C4—111no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4C2×C4×D1111yescharacteristic
501C4⋊C4C2×C4×D1111yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C42—221no—
512C42C2×C4×D1111yescharacteristic
513C42D4×D1111yescharacteristic
514C42#434111yescharacteristic
515C42C23×D1111yescharacteristic
516C11#1802011yescharacteristic, complemented, Sylow
517C23—21no—
518C23—21no—
519C23—42no—
520C23—42no—
521C23—81no—
522C23—221no—
523C23(C22⋊D11)⋊C411yescharacteristic
524Q8—221no—
525Q8—221no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—42no—
530D4—221no—
531D4—221no—
532D4—442no—
533D4#6695412yes—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4(C22⋊D11)⋊C411yescharacteristic
554C2×C4(C22⋊D11)⋊C411yescharacteristic
555C2×C4(C22⋊D11)⋊C411yescharacteristic
556C2×C4C22×C4×D1111yescharacteristic
557C2×C4C2×D4×D1111yescharacteristic
558C2×C4C2×#434111yescharacteristic
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—221no—
564C8—221no—
565C8—221no—
566C8—221no—
567C8—221no—
568C8—221no—
569C8—221no—
570C8—221no—
571C8—441no—
572C8—441no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—84no—
582C22—441no—
583C22—441no—
584C22—441no—
585C22#1062243612yes—
586C22C2×(C22⋊D11)⋊C411yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—441no—
594C4—441no—
595C4—441no—
596C4C2×#6695411yescharacteristic
597C4#1062327611yescharacteristic
598C4#1062328811yescharacteristic
599C4#1062329311yescharacteristic
600C2—22no—
601C2—42no—
602C2—81no—
603C2—881no—
604C2#1307733711yescharacteristic
605C2#1307744211yescharacteristic
606C2C2×#1062243611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×D4⋊C8C2
socleC22×C11C2×C4×D4
prime radical#10622830C4
cosocleC42×C11C24
hypercenterC2×D4⋊C8D11
hypocenterC11#18020
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #13077772C2semidirect
3. #13077651C2semidirect
4. #13067527C2semidirect
5. #13067515C2semidirect
6. #13067462C2semidirect
7. #13067449C2semidirect
8. #13067448C2semidirect
9. #13067442C2semidirect
10. #13067437C2semidirect
11. #13067425C2semidirect
12. #13067399C2semidirect
13. #13067077C2semidirect
14. #13066908C2semidirect
15. C2×C11×D4⋊C8C2semidirect
47. #10622451C22semidirect
48. #10622447C22semidirect
49. #10622444C22semidirect
50. #10622443C22semidirect
55. #10622118C22semidirect
56. #10622118C22semidirect
57. #10622117C22semidirect
58. #10622117C22semidirect
59. #10622097C22semidirect
60. #10622097C22semidirect
61. #10622094C22semidirect
62. #10622094C22semidirect
63. #10622092C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. #10622092C22semidirect
227. C2×D4⋊C8D11semidirect
516. C11#18020semidirect

Maximal subgroups

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

subgroupindex
#130786632
#130777722
#130776512
#130675272
#130675152
#130674622
#130674492
#130674482
#130674422
#130674372
#130674252
#130673992
#130670772
#130669082
C2×C11×D4⋊C82
#1802011