Finite Group Databasebeta

← #14725627

Subgroups — #14725627

Order 2816.

656 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#13079205C211yesmaximal, characteristic
2#13077620C211yesmaximal, characteristic, complemented
3#13067528C211yesmaximal, characteristic, complemented
4#13067504C211yesmaximal, characteristic, complemented
5#13067492C211yesmaximal, characteristic, complemented
6#13067480C211yesmaximal, characteristic, complemented
7#13067452C211yesmaximal, characteristic, complemented
8#13067443C211yesmaximal, characteristic, complemented
9#13067428C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11#13067366C211yesmaximal, characteristic, complemented
12#13067033C211yesmaximal, characteristic, complemented
13#13067027C211yesmaximal, characteristic, complemented
14#13066919C211yesmaximal, characteristic, complemented
15C11×#2935C211yesmaximal, characteristic, complemented
16C2×C11×#131—21no—
17C11×#532C2211yescharacteristic
18#10623010C2211yescharacteristic
19C11×#436C2211yescharacteristic
20C11×#436C2211yescharacteristic
21C11×#435—21no—
22C11×#435—21no—
23C8×D4×C11C2211yescharacteristic
24C8×D4×C11C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#408—21no—
27C4×C11×M16C2211yescharacteristic
28#10622741—21no—
29#10622740—21no—
30#10622702C411yescharacteristic
31#10622693C411yescharacteristic
32#10622687C411yescharacteristic
33#10622684C411yescharacteristic
34#10622655C411yescharacteristic
35#10622655C411yescharacteristic
36#10622652C411yescharacteristic
37#10622652C411yescharacteristic
38C4×#4324C2211yescharacteristic
39C4×#4324C2211yescharacteristic
40C4×#4323C2211yescharacteristic
41C4×#4323C2211yescharacteristic
42#10622538C2211yescharacteristic
43C4×#4318C2211yescharacteristic
44C4×#4318C2211yescharacteristic
45#10622322—21no—
46#10622321—21no—
47#10622301C2211yescharacteristic
48C8×D44C2211yescharacteristic
49#10622292C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51D4⋊(C11⋊C8)C2211yescharacteristic
52D4⋊(C11⋊C8)C2211yescharacteristic
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41—21no—
68C11×#131—44no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C2×C11×M16D411yescharacteristic
72C2×C11×M16D411yescharacteristic
73C22×C8×C11—21no—
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C11×C4⋊Q8C2×C411yescharacteristic
77C11×#127C2×C411yescharacteristic
78C11×#124—21no—
79C11×#121—21no—
80C11×#121C2×C411yescharacteristic
81C11×#121C2×C411yescharacteristic
82C4×D4×C11—21no—
83C4×D4×C11C2311yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×#4324C2×C411yescharacteristic
87C2×#4324C2×C411yescharacteristic
88C2×#4323C2×C411yescharacteristic
89C2×#4323C2×C411yescharacteristic
90#66983C2×C411yescharacteristic
91#66982—21no—
92C4×C22⋊D11—21no—
93#66977C2×C411yescharacteristic
94C2×#4318—21no—
95C2×#4318C2×C411yescharacteristic
96C2×#4318C2×C411yescharacteristic
97C2×#4313—21no—
98C2×C8×D11—21no—
99#66929—21no—
100#66928C2×C411yescharacteristic
101C4×D44C2311yescharacteristic
102#66925—21no—
103#66923C2×C411yescharacteristic
104C4×Dic22C2311yescharacteristic
105C11×C4⋊C8—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×C22⋊C8—21no—
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C11×C22⋊C8—21no—
112C11×#97D411yescharacteristic
113C11×#97D411yescharacteristic
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116#66896C2×C411yescharacteristic
117#66896C2×C411yescharacteristic
118#66896C2×C411yescharacteristic
119#66896C2×C411yescharacteristic
120C22⋊(C11⋊C8)—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123#66879—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126C8×Dic11—21no—
127#66874C2×C411yescharacteristic
128#66874C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66873C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66872C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867—21no—
138#66867C2×C411yescharacteristic
139#66867C2×C411yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18076—111nomaximal, Sylow
146C11×#41—42no—
147C11×#41—42no—
148C2×Q8×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11C22×C411yescharacteristic
154C2×D4×C11C22×C411yescharacteristic
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C2×C22⋊D11—21no—
161C2×D44C22×C411yescharacteristic
162C2×C4×D11—21no—
163C2×Dic22C22×C411yescharacteristic
164C11×M16—22no—
165C11×M16—41no—
166C11×M16—42no—
167C11×M16—42no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—42no—
171C2×C8×C11—42no—
172C2×C8×C11—42no—
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C11×C4⋊C4—21no—
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C42×C11C22×C411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11#4111yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—21no—
189#4324—22no—
190#4324—41no—
191#4323—22no—
192#4323—41no—
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—21no—
195(C2×D11)⋊C4—21no—
196(C2×D11)⋊C4—21no—
197C4⋊Dic11C22×C411yescharacteristic
198C4⋊Dic11C22×C411yescharacteristic
199Dic11⋊C4—21no—
200Dic11⋊C4—21no—
201Dic11⋊C4—21no—
202Dic11⋊C4—21no—
203C4×Dic11—21no—
204#4318—22no—
205#4318—41no—
206#4318—42no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8C22×C411yescharacteristic
212C2×C11⋊C8C22×C411yescharacteristic
213C2×C11⋊C8C22×C411yescharacteristic
214C2×C11⋊C8C22×C411yescharacteristic
215#4313—42no—
216C8×D11—42no—
217#3171—111no—
218#2969—111no—
219#2935D1111yescharacteristic, complemented
220#1594—111no—
221#1590—111no—
222#1588—111no—
223#1586—111no—
224#1582—111no—
225#1581—111no—
226SD16⋊C8—111no—
227C8×D8—111no—
228#1565—111no—
229#1484—111no—
230#1483—111no—
231#1455—111no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11C4×D411yescharacteristic
235C22×D11—21no—
236Q8×C11—42no—
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—42no—
242D4×C11—42no—
243D4×C11—42no—
244D4×C11—81no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11C4×D411yescharacteristic
257C2×C4×C11C4×D411yescharacteristic
258C2×C4×C11C4×D411yescharacteristic
259C2×C4×C11C23×C411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C22⋊D11—81no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266D44—21no—
267D44—21no—
268C4×D11—41no—
269C4×D11—41no—
270Dic22—21no—
271Dic22—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11AGL(1,ℤ/8)12yes—
278C11⋊C8—22no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C11⋊C8#13112yescomplemented
286C2×#131—21no—
287#532C2×D1111yescharacteristic
288#529—111no—
289#501—111no—
290#496—111no—
291#490—111no—
292#489—111no—
293#469—111no—
294#469—111no—
295#468—111no—
296#468—111no—
297#446—111no—
298C8×Q8—111no—
299C4×SD16—111no—
300C4×SD16—111no—
301C4×D8—111no—
302C4×D8—111no—
303#436—111no—
304#436—221no—
305#436C2×D1111yescharacteristic
306#436C2×D1111yescharacteristic
307#435—21no—
308#435—21no—
309#435—221no—
310C8×D4—111no—
311C8×D4C2×D1111yescharacteristic
312C8×D4C2×D1111yescharacteristic
313#433—221no—
314#431—111no—
315C2×C4⋊C8C2×D1111yescharacteristic
316#408—21no—
317#405—221no—
318C4×M16—111no—
319C4×M16—111no—
320C4×M16C2×D1111yescharacteristic
321#335—111no—
322#335—111no—
323#334—111no—
324#334—111no—
325Q8⋊C8—111no—
326Q8⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8—111no—
333#322—111no—
334#322—111no—
335#322—111no—
336C82—111no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
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×C11C2×AGL(1,ℤ/8)11yescharacteristic
359C4×C11#57511yescharacteristic
360Dic11—41no—
361Dic11—41no—
362Dic11—41no—
363C2×#41—21no—
364C2×SD16—111no—
365C2×SD16—111no—
366C2×D8—111no—
367C2×D8—111no—
368#131—44no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—111no—
372C2×M16—111no—
373C2×M16—221no—
374C2×M16—221no—
375C2×M16C22⋊D1111yescharacteristic
376C2×M16C22⋊D1111yescharacteristic
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—221no—
381C4⋊Q8C4×D1111yescharacteristic
382#127C4×D1111yescharacteristic
383#126—221no—
384#125—111no—
385#124—21no—
386#124—111no—
387#123—221no—
388C22⋊Q8—111no—
389#121—21no—
390#121—111no—
391#121C4×D1111yescharacteristic
392#121C4×D1111yescharacteristic
393C4×Q8—111no—
394C4×D4—21no—
395C4×D4—111no—
396C4×D4—221no—
397C4×D4C22×D1111yescharacteristic
398C4×D4C22×D1111yescharacteristic
399#117—221no—
400C2×C42C22×D1111yescharacteristic
401#107—111no—
402#107—111no—
403#106—111no—
404#106—111no—
405C4⋊C8—21no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—221no—
409C4⋊C8—221no—
410C4⋊C8C22×D1111yescharacteristic
411C4⋊C8C22×D1111yescharacteristic
412#103—111no—
413#103—111no—
414#102—111no—
415#102—111no—
416#102—111no—
417#102—111no—
418#102—111no—
419#102—111no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427#97—111no—
428#97—111no—
429#97—221no—
430#97—221no—
431#97C22⋊D1111yescharacteristic
432#97C22⋊D1111yescharacteristic
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—221no—
438C4×C8—221no—
439C4×C8C22×D1111yescharacteristic
440C4×C8C22×D1111yescharacteristic
441C2×C11—41no—
442C2×C11—81no—
443C2×C11—81no—
444C2×C11#293511yescharacteristic
445C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
446C2×C11#295611yescharacteristic
447D11—81no—
448#41—42no—
449#41—42no—
450C2×Q8—21no—
451C2×Q8—111no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—111no—
457C2×D4—221no—
458C2×D4C2×C4×D1111yescharacteristic
459C2×D4C2×C4×D1111yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—221no—
463C22×C4C2×C4×D1111yescharacteristic
464C22×C4#433911yescharacteristic
465C22×C4C2×C22⋊D1111yescharacteristic
466SD16—222no—
467SD16—441no—
468D8—222no—
469D8—441no—
470M16—22no—
471M16—41no—
472M16—42no—
473M16—42no—
474M16—222no—
475M16—442no—
476M16—441no—
477M16—442no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—42no—
481C2×C8—42no—
482C2×C8—42no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—442no—
492C2×C8C2×C22⋊D1111yescharacteristic
493C2×C8C2×C22⋊D1111yescharacteristic
494C2×C8C2×C22⋊D1111yescharacteristic
495C2×C8C2×C22⋊D1111yescharacteristic
496C4⋊C4—21no—
497C4⋊C4—111no—
498C4⋊C4—111no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4C2×C4×D1111yescharacteristic
504C4⋊C4C2×C4×D1111yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C22⋊C4—221no—
512C22⋊C4—221no—
513C22⋊C4—221no—
514C42—221no—
515C42C2×C4×D1111yescharacteristic
516C42#433911yescharacteristic
517C42C2×C22⋊D1111yescharacteristic
518C42C23×D1111yescharacteristic
519C11#1807611yescharacteristic, complemented, Sylow
520C23—21no—
521C23—21no—
522C23—221no—
523C23C4×C22⋊D1111yescharacteristic
524Q8—42no—
525Q8—221no—
526Q8—221no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—42no—
533D4—42no—
534D4—81no—
535D4—221no—
536D4—221no—
537D4—881no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4C4×C22⋊D1111yescharacteristic
555C2×C4C4×C22⋊D1111yescharacteristic
556C2×C4C4×C22⋊D1111yescharacteristic
557C2×C4C22×C4×D1111yescharacteristic
558C2×C4C2×#433911yescharacteristic
559C2×C4C22×C22⋊D1111yescharacteristic
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—112no—
566C8—222no—
567C8—221no—
568C8—221no—
569C8—221no—
570C8—441no—
571C8—441no—
572C8—441no—
573C8#6698512yes—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—441no—
584C22—441no—
585C22—441no—
586C22C2×C4×C22⋊D1111yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—441no—
594C4—441no—
595C4—441no—
596C4D11×#13111yescharacteristic
597C4#1062328111yescharacteristic
598C4C2×#6698511yescharacteristic
599C4#1062335311yescharacteristic
600C2—41no—
601C2—81no—
602C2—81no—
603C2—881no—
604C2#1307735811yescharacteristic
605C2C4×#6698511yescharacteristic
606C2#1307752311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2935C2
socleC22×C11C2×C4×D4
prime radical#13079205C2
cosocleC42×C11C24
hypercenter#2935D11
hypocenterC11#18076
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2935

Complements

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

NH ≅ G/Ntype
2. #13077620C2semidirect
3. #13067528C2semidirect
4. #13067504C2semidirect
5. #13067492C2semidirect
6. #13067480C2semidirect
7. #13067452C2semidirect
8. #13067443C2semidirect
9. #13067428C2semidirect
10. C8×#4323C2semidirect
11. #13067366C2semidirect
12. #13067033C2semidirect
13. #13067027C2semidirect
14. #13066919C2semidirect
15. C11×#2935C2semidirect
219. #2935D11semidirect
285. C11⋊C8#131semidirect
519. C11#18076semidirect

Maximal subgroups

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

subgroupindex
#130792052
#130776202
#130675282
#130675042
#130674922
#130674802
#130674522
#130674432
#130674282
C8×#43232
#130673662
#130670332
#130670272
#130669192
C11×#29352
#1807611