Finite Group Databasebeta

← #14735035

Subgroups — #14735035

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079822C211yesmaximal, characteristic, complemented
2#13079619C211yesmaximal, characteristic, complemented
3#13079002C211yesmaximal, characteristic, complemented
4#13067939C214yesmaximal, complemented
5#13067933C214yesmaximal, complemented
6#13067240C211yesmaximal, characteristic, complemented
7#13067218C211yesmaximal, characteristic, complemented
8#13067214C211yesmaximal, characteristic, complemented
9C2×C11×#562C211yesmaximal, characteristic
10C11×#562—22no—
11C11×#562—22no—
12C11×#562—22no—
13C11×#562C2214yes—
14C2×C11×#125C2211yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×C11×#124C2211yescharacteristic
17C2×C11×#123—21no—
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×C22⋊Q8—21no—
21C2×C11×#121—21no—
22C2×C11×#121—21no—
23#10623001C2211yescharacteristic
24#10622841—21no—
25#10622838—21no—
26#10622831—21no—
27#10622828—21no—
28#10622682C2212yescomplemented
29#10622678C2212yescomplemented
30#10622676—22no—
31#10622673C2212yescomplemented
32#10622669—22no—
33#10622668C2212yescomplemented
34#10622668C2212yescomplemented
35#10622668C2212yescomplemented
36#10622667—22no—
37#10622584—21no—
38#10622583—21no—
39#10622539C2211yescharacteristic
40#10622539C2211yescharacteristic
41C4×#4318C2211yescharacteristic
42#10622181C2214yescomplemented
43#10622178C2214yescomplemented
44#10622178C2214yescomplemented
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11D411yescharacteristic
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C11×#125—21no—
54C11×#125—21no—
55C11×#125D412yes—
56C11×#125C2312yes—
57C11×#124—21no—
58C11×#124—21no—
59C11×#124—21no—
60C11×#124—21no—
61C11×#124D412yes—
62C11×#124D412yes—
63C11×#124C2312yes—
64C11×#124C2312yes—
65C11×#123—24no—
66C11×#123—24no—
67C11×#123—24no—
68C11×#123—24no—
69C11×C22⋊Q8—24no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8—24no—
73C11×#121—24no—
74C11×#121—24no—
75C11×#121—24no—
76C11×#121—24no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C42×C11C2311yescharacteristic
90C2×#4326—22no—
91C2×#4324—22no—
92#66979—21no—
93#66977—21no—
94#66977—21no—
95C2×#4318—21no—
96#66923—21no—
97#66922C2311yescharacteristic
98#66922C2311yescharacteristic
99C4×Dic22—21no—
100C4×Dic22—21no—
101#66899—22no—
102#66899—22no—
103#66899—22no—
104#66896—22no—
105#66896—22no—
106#66896—22no—
107C22⋊(C11⋊C8)—21no—
108C22⋊(C11⋊C8)—21no—
109#66874—22no—
110#66874—22no—
111#66872—22no—
112#66871—22no—
113C4⋊(C11⋊C8)—21no—
114C4⋊(C11⋊C8)—21no—
115#66867C2312yes—
116#66867C2312yes—
117#66867C2312yes—
118C4×C11⋊C8—21no—
119#18998—111nomaximal, Sylow
120C24×C11—21no—
121C24×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—42no—
125C2×Q8×C11—81no—
126C2×Q8×C11C2×D412yes—
127C2×Q8×C11C2×D412yes—
128C2×D4×C11—24no—
129C2×D4×C11—24no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—42no—
133C2×D4×C11—81no—
134C2×D4×C11—82no—
135C2×D4×C11—82no—
136C2×D4×C11C2×D412yes—
137C2×D4×C11C2×D412yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—82no—
145C22×C4×C11—82no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C2×Dic22—21no—
150C2×Dic22—21no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4C2×D412yes—
160C11×C4⋊C4C2×D412yes—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C42×C11C2×D411yescharacteristic
172C42×C11C2×D411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11C2411yescharacteristic
175C22⋊Dic11—41no—
176#4326—82no—
177#4324—82no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182Dic11⋊C4—41no—
183Dic11⋊C4—41no—
184C4×Dic11—41no—
185#4318—42no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×#562D1111yescharacteristic
190#3236—111no—
191#3215—111no—
192#3140—111no—
193#1662—114no—
194#1661—114no—
195#1533—111no—
196#1528—111no—
197#1527—111no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11#12011yescharacteristic
207Q8×C11—42no—
208Q8×C11—42no—
209Q8×C11—81no—
210Q8×C11—81no—
211D4×C11—42no—
212D4×C11—42no—
213D4×C11—81no—
214D4×C11—81no—
215D4×C11—84no—
216D4×C11—84no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—84no—
229C2×C4×C11—84no—
230C2×C4×C11#12011yescharacteristic
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×Dic11—41no—
237C2×Dic11—41no—
238Dic22—42no—
239Dic22—42no—
240C11⋊C8—42no—
241C11⋊C8—42no—
242C11⋊C8—42no—
243#562—22no—
244#562—22no—
245#562—22no—
246#562C2×D1114yes—
247#533—111no—
248C2×#125C2×D1111yescharacteristic
249C2×#124C2×D1111yescharacteristic
250C2×#124C2×D1111yescharacteristic
251C2×#123—21no—
252C2×#123—21no—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8—21no—
255C2×#121—21no—
256C2×#121—21no—
257#501—112no—
258#497—112no—
259#491—112no—
260#489—112no—
261#489—112no—
262#489—112no—
263#488—222no—
264#484—221no—
265#483—221no—
266#479—222no—
267#464—222no—
268#451—221no—
269#450—221no—
270#432—111no—
271#432—111no—
272#419—221no—
273#418—221no—
274C4×M16—111no—
275#330—114no—
276#329—114no—
277#329—114no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—84no—
287C22×C11—84no—
288C22×C11#45512yes—
289C22×C11C2×#12011yescharacteristic
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—42no—
297C4×C11—42no—
298C4×C11—42no—
299C4×C11—42no—
300Dic11—81no—
301Dic11—81no—
302C22×Q8C22⋊D1111yescharacteristic
303C22×Q8C22⋊D1111yescharacteristic
304C22×D4—21no—
305C22×D4—21no—
306C22×D4C22⋊D1111yescharacteristic
307C22×D4C22⋊D1111yescharacteristic
308C23×C4—21no—
309C23×C4—21no—
310C2×Q16—222no—
311C2×SD16—222no—
312C2×M16—221no—
313C4⋊Q8—111no—
314C4⋊Q8—111no—
315#125—21no—
316#125—21no—
317#125—221no—
318#125C22⋊D1112yes—
319#125C22×D1112yes—
320#124—21no—
321#124—21no—
322#124—21no—
323#124—21no—
324#124C22⋊D1112yes—
325#124C22⋊D1112yes—
326#124C22×D1112yes—
327#124C22×D1112yes—
328#123—24no—
329#123—24no—
330#123—24no—
331#123—24no—
332C22⋊Q8—24no—
333C22⋊Q8—24no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336C22⋊Q8—221no—
337C22⋊Q8—221no—
338#121—24no—
339#121—24no—
340#121—24no—
341#121—24no—
342C4×Q8—221no—
343C4×Q8—221no—
344#117—221no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4C22⋊D1111yescharacteristic
350C2×C4⋊C4C22⋊D1111yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C42C22×D1111yescharacteristic
358#107—222no—
359#106—222no—
360C4⋊C8—221no—
361C4⋊C8—221no—
362#103—222no—
363#103—222no—
364#103—222no—
365#103—222no—
366#103—222no—
367#102—222no—
368#102—222no—
369#102—222no—
370C22⋊C8—221no—
371C22⋊C8—221no—
372#97—112no—
373#97—112no—
374#97—112no—
375C4×C8—221no—
376C2×C11—22no—
377C2×C11—82no—
378C2×C11—82no—
379C2×C11C2×#45511yescharacteristic
380C2×C11#301911yescharacteristic
381C2×C11#302011yescharacteristic
382C24—21no—
383C24—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—42no—
387C2×Q8—81no—
388C2×Q8—221no—
389C2×Q8—221no—
390C2×Q8C2×C22⋊D1112yes—
391C2×Q8C2×C22⋊D1112yes—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—42no—
397C2×D4—81no—
398C2×D4—82no—
399C2×D4—82no—
400C2×D4C2×C22⋊D1112yes—
401C2×D4C2×C22⋊D1112yes—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—82no—
409C22×C4—82no—
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C2×C22⋊D1111yescharacteristic
412C22×C4C2×C22⋊D1111yescharacteristic
413Q16—882no—
414SD16—882no—
415M16—442no—
416C2×C8—222no—
417C2×C8—222no—
418C2×C8—222no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—221no—
430C4⋊C4—221no—
431C4⋊C4—441no—
432C4⋊C4—441no—
433C4⋊C4C2×C22⋊D1112yes—
434C4⋊C4C2×C22⋊D1112yes—
435C22⋊C4—24no—
436C22⋊C4—24no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—441no—
446C42—441no—
447C42C2×C22⋊D1111yescharacteristic
448C42C2×C22⋊D1111yescharacteristic
449C42C2×C22⋊D1111yescharacteristic
450C42C23×D1111yescharacteristic
451C11#1899811yescharacteristic, complemented, Sylow
452C23—22no—
453C23—22no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23#6700611yescharacteristic
461Q8—42no—
462Q8—42no—
463Q8—81no—
464Q8—81no—
465Q8—442no—
466Q8—442no—
467D4—42no—
468D4—42no—
469D4—81no—
470D4—81no—
471D4—84no—
472D4—84no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—84no—
485C2×C4—84no—
486C2×C4—441no—
487C2×C4—441no—
488C2×C4#6700611yescharacteristic
489C2×C4#6700611yescharacteristic
490C2×C4#6700611yescharacteristic
491C2×C4C22×C22⋊D1111yescharacteristic
492C2×C4C22×C22⋊D1111yescharacteristic
493C2×C4C22×C22⋊D1111yescharacteristic
494C8—442no—
495C8—442no—
496C8—442no—
497C22—21no—
498C22—21no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—84no—
506C22—84no—
507C22#1062285512yes—
508C22C2×#6700611yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—42no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—881no—
520C4—881no—
521C2—22no—
522C2—82no—
523C2—82no—
524C2C2×#1062285511yescharacteristic
525C2#1307797311yescharacteristic
526C2#1307798011yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC2×C11×#562C2
socleC22×C11C2×#120
hypercenterC2×#562D11
hypocenterC11#18998
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. #13079822C2semidirect
2. #13079619C2semidirect
3. #13079002C2semidirect
4. #13067939C2semidirect
5. #13067933C2semidirect
6. #13067240C2semidirect
7. #13067218C2semidirect
8. #13067214C2semidirect
28. #10622682C22semidirect
29. #10622678C22semidirect
31. #10622673C22semidirect
33. #10622668C22semidirect
34. #10622668C22semidirect
35. #10622668C22semidirect
42. #10622181C22semidirect
43. #10622178C22semidirect
44. #10622178C22semidirect
451. C11#18998semidirect

Maximal subgroups

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

subgroupindex
#130798222
#130796192
#130790022
#130679392
#130679332
#130672402
#130672182
#130672142
C2×C11×#5622
#1899811