Finite Group Databasebeta

← #14735106

Subgroups — #14735106

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079822C211yesmaximal, characteristic, complemented
2#13079619C211yesmaximal, characteristic
3#13079165C211yesmaximal, characteristic, complemented
4#13067950C214yesmaximal, complemented
5#13067927C214yesmaximal, complemented
6#13067243C211yesmaximal, characteristic, complemented
7#13067218C211yesmaximal, characteristic, complemented
8#13067214C211yesmaximal, characteristic
9C2×C11×#563C211yesmaximal, characteristic
10C11×#563—22no—
11C11×#563—22no—
12C11×#563—22no—
13C11×#563C2214yes—
14C2×C11×C4⋊Q8—21no—
15C2×C11×#126—21no—
16C2×C11×#126—21no—
17C2×C11×#125C2211yescharacteristic
18C2×C11×#125C2211yescharacteristic
19C2×C11×#124C2211yescharacteristic
20C2×C11×#123—21no—
21C2×C11×C22⋊Q8—21no—
22C2×C11×C22⋊Q8—21no—
23#10623001C2211yescharacteristic
24#10622841—21no—
25#10622831—21no—
26#10622682C2212yescomplemented
27#10622678C2212yescomplemented
28#10622678C2212yescomplemented
29#10622678C2212yescomplemented
30#10622677—22no—
31#10622676—22no—
32#10622673C2212yes—
33#10622668C2212yes—
34#10622667—22no—
35#10622584—21no—
36#10622583—21no—
37#10622577—21no—
38#10622577—21no—
39#10622539C2211yescharacteristic
40#10622539C2211yescharacteristic
41C4×#4318C2211yescharacteristic
42#10622181C2214yescomplemented
43#10622181C2214yescomplemented
44#10622178C2214yes—
45C22×Q8×C11—21no—
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11D411yescharacteristic
48C23×C4×C11—21no—
49C11×C4⋊Q8—24no—
50C11×C4⋊Q8—24no—
51C11×#126—24no—
52C11×#126—24no—
53C11×#126—24no—
54C11×#126—24no—
55C11×#125—21no—
56C11×#125—21no—
57C11×#125—21no—
58C11×#125—21no—
59C11×#125D412yes—
60C11×#125D412yes—
61C11×#125C2312yes—
62C11×#125C2312yes—
63C11×#124—21no—
64C11×#124—21no—
65C11×#124D412yes—
66C11×#124C2312yes—
67C11×#123—24no—
68C11×#123—24no—
69C11×C22⋊Q8—24no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8—24no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D411yescharacteristic
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×C42×C11—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#66896—22no—
103C22⋊(C11⋊C8)—21no—
104C22⋊(C11⋊C8)—21no—
105#66874—22no—
106#66874—22no—
107#66872—22no—
108#66872—22no—
109#66872—22no—
110#66871—22no—
111#66871—22no—
112#66871—22no—
113C4⋊(C11⋊C8)—21no—
114C4⋊(C11⋊C8)—21no—
115#66867C2312yes—
116#66867C2312yes—
117#66867C2312yes—
118C4×C11⋊C8—21no—
119#19007—111nomaximal, Sylow
120C24×C11—21no—
121C2×Q8×C11—24no—
122C2×Q8×C11—21no—
123C2×Q8×C11—81no—
124C2×Q8×C11—82no—
125C2×Q8×C11C2×D412yes—
126C2×D4×C11—21no—
127C2×D4×C11—81no—
128C2×D4×C11C2×D412yes—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—24no—
135C22×C4×C11—82no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C2×Dic22—21no—
140C2×Dic22—21no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4C2×D412yes—
156C11×C4⋊C4C2×D412yes—
157C11×C4⋊C4C2×D412yes—
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C42×C11—24no—
167C42×C11C2×D411yescharacteristic
168C42×C11C2×D411yescharacteristic
169C42×C11C2×D411yescharacteristic
170C42×C11C2411yescharacteristic
171C22⋊Dic11—41no—
172#4326—82no—
173#4324—82no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178Dic11⋊C4—41no—
179Dic11⋊C4—41no—
180C4×Dic11—41no—
181#4318—24no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×#563D1111yescharacteristic
186#3236—111no—
187#3215—111no—
188#3166—111no—
189#1664—114no—
190#1660—114no—
191#1534—111no—
192#1528—111no—
193#1527—111no—
194C23×C11—22no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11#12011yescharacteristic
199Q8×C11—42no—
200Q8×C11—81no—
201Q8×C11—84no—
202D4×C11—42no—
203D4×C11—81no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—84no—
218C2×C4×C11#12011yescharacteristic
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11#12011yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×Dic11—41no—
225C2×Dic11—41no—
226Dic22—42no—
227Dic22—42no—
228C11⋊C8—24no—
229C11⋊C8—42no—
230C11⋊C8—42no—
231#563—22no—
232#563—22no—
233#563—22no—
234#563C2×D1114yes—
235#533—111no—
236C2×C4⋊Q8—21no—
237C2×#126—21no—
238C2×#126—21no—
239C2×#125C2×D1111yescharacteristic
240C2×#125C2×D1111yescharacteristic
241C2×#124C2×D1111yescharacteristic
242C2×#123—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245#501—112no—
246#501—112no—
247#501—112no—
248#499—222no—
249#497—112no—
250#491—112no—
251#489—112no—
252#484—221no—
253#483—221no—
254#479—222no—
255#464—222no—
256#451—221no—
257#450—221no—
258#432—111no—
259#432—111no—
260#428—221no—
261#428—221no—
262C4×M16—111no—
263#330—114no—
264#330—114no—
265#329—114no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—84no—
272C22×C11#45612yes—
273C22×C11C2×#12011yescharacteristic
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—42no—
285Dic11—81no—
286Dic11—81no—
287C22×Q8—21no—
288C22×Q8C22⋊D1111yescharacteristic
289C22×D4C22⋊D1111yescharacteristic
290C23×C4—21no—
291C2×Q16—222no—
292C2×SD16—222no—
293C2×M16—221no—
294C4⋊Q8—24no—
295C4⋊Q8—24no—
296C4⋊Q8—111no—
297C4⋊Q8—111no—
298#126—24no—
299#126—24no—
300#126—24no—
301#126—24no—
302#125—21no—
303#125—21no—
304#125—21no—
305#125—21no—
306#125—221no—
307#125C22⋊D1112yes—
308#125C22⋊D1112yes—
309#125C22×D1112yes—
310#125C22×D1112yes—
311#124—21no—
312#124—21no—
313#124C22⋊D1112yes—
314#124C22×D1112yes—
315#123—24no—
316#123—24no—
317C22⋊Q8—24no—
318C22⋊Q8—24no—
319C22⋊Q8—24no—
320C22⋊Q8—24no—
321C22⋊Q8—221no—
322C22⋊Q8—221no—
323C4×Q8—221no—
324C4×Q8—221no—
325#117—221no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4C22⋊D1111yescharacteristic
333C2×C4⋊C4C22⋊D1111yescharacteristic
334C2×C4⋊C4C22⋊D1111yescharacteristic
335C2×C4⋊C4C22⋊D1111yescharacteristic
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C42—21no—
342C2×C42C22×D1111yescharacteristic
343#107—222no—
344#107—222no—
345#107—222no—
346#106—222no—
347#106—222no—
348#106—222no—
349C4⋊C8—221no—
350C4⋊C8—221no—
351#103—222no—
352#103—222no—
353#103—222no—
354#102—222no—
355C22⋊C8—221no—
356C22⋊C8—221no—
357#97—112no—
358#97—112no—
359#97—112no—
360C4×C8—221no—
361C2×C11—22no—
362C2×C11—82no—
363C2×C11C2×#45611yescharacteristic
364C2×C11#301911yescharacteristic
365C2×C11#302011yescharacteristic
366C24—21no—
367C2×Q8—24no—
368C2×Q8—21no—
369C2×Q8—81no—
370C2×Q8—82no—
371C2×Q8—221no—
372C2×Q8—221no—
373C2×Q8C2×C22⋊D1112yes—
374C2×D4—21no—
375C2×D4—81no—
376C2×D4C2×C22⋊D1112yes—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—24no—
383C22×C4—82no—
384C22×C4C2×C22⋊D1111yescharacteristic
385C22×C4C2×C22⋊D1111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387Q16—882no—
388SD16—882no—
389M16—224no—
390C2×C8—222no—
391C2×C8—222no—
392C2×C8—222no—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—221no—
408C4⋊C4—221no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4—441no—
412C4⋊C4—441no—
413C4⋊C4C2×C22⋊D1112yes—
414C4⋊C4C2×C22⋊D1112yes—
415C4⋊C4C2×C22⋊D1112yes—
416C4⋊C4C2×C22⋊D1112yes—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—441no—
425C42—24no—
426C42—441no—
427C42C2×C22⋊D1111yescharacteristic
428C42C2×C22⋊D1111yescharacteristic
429C42C2×C22⋊D1111yescharacteristic
430C42C23×D1111yescharacteristic
431C11#1900711yescharacteristic, complemented, Sylow
432C23—22no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23#6700611yescharacteristic
437Q8—42no—
438Q8—81no—
439Q8—84no—
440Q8—442no—
441Q8—442no—
442D4—42no—
443D4—81no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—84no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4#6700611yescharacteristic
461C2×C4#6700611yescharacteristic
462C2×C4#6700611yescharacteristic
463C2×C4C22×C22⋊D1111yescharacteristic
464C2×C4C22×C22⋊D1111yescharacteristic
465C2×C4C22×C22⋊D1111yescharacteristic
466C8—224no—
467C8—442no—
468C8—442no—
469C22—21no—
470C22—21no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—84no—
475C22#1062285912yes—
476C22C2×#6700611yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—42no—
484C4—42no—
485C4—42no—
486C4—42no—
487C4—42no—
488C4—881no—
489C4—881no—
490C2—22no—
491C2—82no—
492C2C2×#1062285911yescharacteristic
493C2#1307797311yescharacteristic
494C2#1307798011yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#563C2
socleC22×C11C2×#120
prime radicalC22×D4×C11D4
hypercenterC2×#563D11
hypocenterC11#19007
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#563

Complements

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

NH ≅ G/Ntype
1. #13079822C2semidirect
3. #13079165C2semidirect
4. #13067950C2semidirect
5. #13067927C2semidirect
6. #13067243C2semidirect
7. #13067218C2semidirect
26. #10622682C22semidirect
27. #10622678C22semidirect
28. #10622678C22semidirect
29. #10622678C22semidirect
42. #10622181C22semidirect
43. #10622181C22semidirect
431. C11#19007semidirect

Maximal subgroups

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

subgroupindex
#130798222
#130796192
#130791652
#130679502
#130679272
#130672432
#130672182
#130672142
C2×C11×#5632
#1900711