Finite Group Databasebeta

← #14725621

Subgroups — #14725621

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#13077614C211yesmaximal, characteristic, complemented
3#13077360C211yesmaximal, characteristic, complemented
4#13067527C211yesmaximal, characteristic, complemented
5#13067509C211yesmaximal, characteristic, complemented
6#13067497C211yesmaximal, characteristic, complemented
7#13067477C211yesmaximal, characteristic, complemented
8#13067449C211yesmaximal, characteristic, complemented
9#13067448C211yesmaximal, characteristic, complemented
10#13067425C211yesmaximal, characteristic, complemented
11#13067408C211yesmaximal, characteristic, complemented
12#13067369C211yesmaximal, characteristic, complemented
13#13067030C211yesmaximal, characteristic, complemented
14#13066919C211yesmaximal, characteristic, complemented
15C11×#1484C211yesmaximal, characteristic, complemented
16C11×#532C2211yescharacteristic
17C2×#67001—21no—
18#10623010C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C4×C11×M16C2211yescharacteristic
21#10622847—21no—
22#10622702C411yescharacteristic
23#10622693C411yescharacteristic
24#10622687C411yescharacteristic
25#10622684C411yescharacteristic
26#10622655C411yescharacteristic
27#10622655C411yescharacteristic
28#10622652C411yescharacteristic
29#10622652C411yescharacteristic
30C4×#4324C2211yescharacteristic
31C4×#4324C2211yescharacteristic
32C4×#4323C2211yescharacteristic
33C4×#4323C2211yescharacteristic
34#10622625C2211yescharacteristic
35#10622625C2211yescharacteristic
36#10622624—21no—
37#10622624—21no—
38D4×C11⋊C8C2211yescharacteristic
39D4×C11⋊C8C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C4×#4318C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622451C2211yescharacteristic
44#10622447C2211yescharacteristic
45#10622444C2211yescharacteristic
46#10622443C2211yescharacteristic
47#10622342—21no—
48#10622341—21no—
49#10622303—21no—
50#10622302—21no—
51C11×D4⋊C8C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×D4⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622117C2211yescharacteristic
58#10622117C2211yescharacteristic
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×M16—21no—
69C11×C4⋊Q8C2×C411yescharacteristic
70C11×#127C2×C411yescharacteristic
71C11×#124—21no—
72C11×#121—21no—
73C11×#121C2×C411yescharacteristic
74C11×#121C2×C411yescharacteristic
75C4×D4×C11—21no—
76C4×D4×C11C2311yescharacteristic
77C4×D4×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79#67001—44no—
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—
90C2×#4318C2×C411yescharacteristic
91C2×#4318C2×C411yescharacteristic
92C2×#4318D411yescharacteristic
93C2×#4318D411yescharacteristic
94C22×C11⋊C8—21no—
95C22×C11⋊C8—21no—
96C22×C11⋊C8—21no—
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⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×C22⋊C8—21no—
108C11×#97—21no—
109C4×C8×C11—21no—
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66896C2×C411yescharacteristic
113#66896C2×C411yescharacteristic
114#66896C2×C411yescharacteristic
115#66896C2×C411yescharacteristic
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122#66879—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125C8×Dic11—21no—
126#66874C2×C411yescharacteristic
127#66874C2×C411yescharacteristic
128#66873C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867C2×C411yescharacteristic
138#66867C2×C411yescharacteristic
139#66867D411yescharacteristic
140#66867D411yescharacteristic
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—42no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C4⋊C4C22×C411yescharacteristic
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C42×C11C22×C411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11#4111yescharacteristic
179C42×C11C2411yescharacteristic
180C22⋊Dic11—21no—
181#4324—22no—
182#4324—41no—
183#4323—22no—
184#4323—41no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189C4⋊Dic11C22×C411yescharacteristic
190C4⋊Dic11C22×C411yescharacteristic
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195C4×Dic11—21no—
196#4318—22no—
197#4318—22no—
198#4318—41no—
199#4318—41no—
200#4318—42no—
201#4318—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—42no—
205C2×C11⋊C8—42no—
206C2×C11⋊C8—42no—
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C22×C411yescharacteristic
210C2×C11⋊C8C22×C411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215#4313—42no—
216C8×D11—42no—
217#3171—111no—
218#2969—111no—
219#2935—111no—
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#1484D1111yescharacteristic, complemented
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—22no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11—41no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8#13112yescomplemented
285C11⋊C8AGL(1,ℤ/8)12yes—
286C2×#131—221no—
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—111no—
305#436—111no—
306#436—221no—
307#435—221no—
308#435—221no—
309#435—221no—
310C8×D4—111no—
311C8×D4—111no—
312C8×D4—111no—
313#433—221no—
314#431C2×D1111yescharacteristic
315C2×C4⋊C8—111no—
316#408—221no—
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⋊C8C2×D1111yescharacteristic
330D4⋊C8C2×D1111yescharacteristic
331D4⋊C8C2×D1111yescharacteristic
332D4⋊C8C2×D1111yescharacteristic
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—444no—
369C2×M16—21no—
370C2×M16—111no—
371C2×M16—111no—
372C2×M16—111no—
373C2×M16—111no—
374C2×M16—221no—
375C2×M16—221no—
376C2×M16—221no—
377C22×C8—221no—
378C22×C8—221no—
379C22×C8—221no—
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—111no—
406C4⋊C8—111no—
407C4⋊C8—221no—
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—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427#97—21no—
428#97—111no—
429#97—111no—
430#97—111no—
431#97—111no—
432#97—221no—
433C4×C8—21no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—111no—
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×C4D4×D1111yescharacteristic
465C22×C4#434111yescharacteristic
466SD16—222no—
467SD16—441no—
468D8—222no—
469D8—441no—
470M16—42no—
471M16—222no—
472M16—222no—
473M16—442no—
474M16—442no—
475M16—441no—
476M16—441no—
477M16—442no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—111no—
488C2×C8—111no—
489C2×C8—111no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—442no—
493C2×C8—442no—
494C2×C8—442no—
495C2×C8—442no—
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
516C42D4×D1111yescharacteristic
517C42#434111yescharacteristic
518C42C23×D1111yescharacteristic
519C11#1807611yescharacteristic, complemented, Sylow
520C23—21no—
521C23—21no—
522C23—221no—
523C23(C22⋊D11)⋊C411yescharacteristic
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×C4(C22⋊D11)⋊C411yescharacteristic
555C2×C4(C22⋊D11)⋊C411yescharacteristic
556C2×C4(C22⋊D11)⋊C411yescharacteristic
557C2×C4C22×C4×D1111yescharacteristic
558C2×C4C2×D4×D1111yescharacteristic
559C2×C4C2×#434111yescharacteristic
560C8—22no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—112no—
565C8—112no—
566C8—221no—
567C8—221no—
568C8—221no—
569C8—221no—
570C8—221no—
571C8—221no—
572C8—441no—
573C8—441no—
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×(C22⋊D11)⋊C411yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—441no—
594C4—441no—
595C4—441no—
596C4D11×#13111yescharacteristic
597C4#1062328111yescharacteristic
598C4D11×AGL(1,ℤ/8)11yescharacteristic
599C4#1062330411yescharacteristic
600C2—41no—
601C2—81no—
602C2—81no—
603C2—881no—
604C2#1307735611yescharacteristic
605C2#1307742011yescharacteristic
606C2#1307752211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1484C2
socleC22×C11C2×C4×D4
prime radical#13079205C2
cosocleC42×C11C24
hypercenter#1484D11
hypocenterC11#18076
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1484

Complements

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

NH ≅ G/Ntype
2. #13077614C2semidirect
3. #13077360C2semidirect
4. #13067527C2semidirect
5. #13067509C2semidirect
6. #13067497C2semidirect
7. #13067477C2semidirect
8. #13067449C2semidirect
9. #13067448C2semidirect
10. #13067425C2semidirect
11. #13067408C2semidirect
12. #13067369C2semidirect
13. #13067030C2semidirect
14. #13066919C2semidirect
15. C11×#1484C2semidirect
229. #1484D11semidirect
284. 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
#130776142
#130773602
#130675272
#130675092
#130674972
#130674772
#130674492
#130674482
#130674252
#130674082
#130673692
#130670302
#130669192
C11×#14842
#1807611