Finite Group Databasebeta

← #14732353

Subgroups — #14732353

Order 2816.

1170 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079760C211yesmaximal, characteristic, complemented
2#13078624C211yesmaximal, characteristic, complemented
3#13078413C211yesmaximal, characteristic, complemented
4#13067900C214yesmaximal, complemented
5#13067767C214yesmaximal, complemented
6#13067288C211yesmaximal, characteristic, complemented
7#13067041C211yesmaximal, characteristic, complemented
8#13067007C211yesmaximal, characteristic, complemented
9C2×C11×#547C211yesmaximal, characteristic
10C22×C11×#41—21no—
11C11×#547—22no—
12C11×#547—22no—
13C11×#547—22no—
14C11×#547C2214yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#123—22no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×#121—21no—
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4—21no—
22#10623001C2211yescharacteristic
23#10622831—21no—
24#10622828—21no—
25#10622707—22no—
26#10622706C2212yescomplemented
27#10622692C2212yescomplemented
28#10622632C2212yescomplemented
29C4×#4324—22no—
30#10622622—22no—
31#10622621C2212yescomplemented
32#10622621C2212yescomplemented
33#10622620C2212yescomplemented
34#10622584—21no—
35#10622584—22no—
36#10622577—21no—
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40#10622185C2214yescomplemented
41D4⋊(C11⋊C8)C2214yescomplemented
42D4⋊(C11⋊C8)C2214yescomplemented
43C2×C11×#41—24no—
44C2×C11×#41—24no—
45C2×C11×#41—44no—
46C2×C11×#41—44no—
47C22×Q8×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11D411yescharacteristic
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—22no—
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8D412yes—
57C11×C4⋊Q8C2312yes—
58C11×#123—28no—
59C11×#123—28no—
60C11×C22⋊Q8—24no—
61C11×C22⋊Q8—24no—
62C11×#121—24no—
63C11×#121—24no—
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C4×D4×C11—21no—
68C4×D4×C11D412yes—
69C4×D4×C11D412yes—
70C4×D4×C11C2312yes—
71C4×D4×C11C2312yes—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D412yes—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4324—22no—
84#66979—21no—
85#66977—21no—
86#66977—21no—
87C2×#4318—21no—
88#66923—21no—
89#66922C2311yescharacteristic
90#66922C2311yescharacteristic
91C4×Dic22—21no—
92C4×Dic22—21no—
93#66896—22no—
94#66896—22no—
95#66896—22no—
96C22⋊(C11⋊C8)—21no—
97C22⋊(C11⋊C8)—21no—
98#66874—22no—
99#66874—24no—
100#66872—22no—
101#66872—22no—
102#66872—24no—
103#66871—22no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2312yes—
108C4×C11⋊C8—21no—
109C4×C11⋊C8C2312yes—
110#18757—111nomaximal, Sylow
111C24×C11—21no—
112C24×C11—21no—
113C11×#41—48no—
114C11×#41—416no—
115C11×#41—48no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—42no—
119C2×Q8×C11—42no—
120C2×D4×C11—28no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—22no—
124C2×D4×C11—42no—
125C2×D4×C11—48no—
126C2×D4×C11SD1614yescomplemented
127C2×D4×C11C2×D412yes—
128C2×D4×C11C2×D412yes—
129C22×C4×C11—28no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—44no—
138C22×C4×C11—48no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C2×Dic22—21no—
145C2×Dic22—21no—
146C11×C4⋊C4—28no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4C2×D412yes—
153C11×C4⋊C4C2×D412yes—
154C11×C4⋊C4C2×D414yes—
155C11×C22⋊C4—28no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160C42×C11C2×D411yescharacteristic
161C42×C11C2×D411yescharacteristic
162C42×C11C2×D411yescharacteristic
163C42×C11C2411yescharacteristic
164C22⋊Dic11—41no—
165#4324—44no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170Dic11⋊C4—41no—
171Dic11⋊C4—41no—
172C4×Dic11—41no—
173#4318—42no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×#547D1111yescharacteristic
178#3229—111no—
179#3101—111no—
180#3077—111no—
181#1654—114no—
182#1635—114no—
183#1546—111no—
184#1486—111no—
185#1478—111no—
186C23×C11—22no—
187C23×C11—24no—
188C23×C11—22no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11#12011yescharacteristic
195Q8×C11—42no—
196Q8×C11—42no—
197Q8×C11—44no—
198D4×C11—22no—
199D4×C11—22no—
200D4×C11—22no—
201D4×C11—24no—
202D4×C11—42no—
203D4×C11—416no—
204D4×C11C2×SD1614yes—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—41no—
210C2×C4×C11—44no—
211C2×C4×C11—42no—
212C2×C4×C11—416no—
213C2×C4×C11—42no—
214C2×C4×C11—44no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—44no—
218C2×C4×C11—44no—
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11#12011yescharacteristic
221C2×C4×C11#12011yescharacteristic
222C2×C4×C11C2×SD1612yes—
223C2×C4×C11AGL(1,ℤ/8)12yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×Dic11—41no—
228C2×Dic11—41no—
229Dic22—42no—
230Dic22—42no—
231C11⋊C8—42no—
232C11⋊C8—42no—
233C11⋊C8—42no—
234C22×#41—21no—
235#547—22no—
236#547—22no—
237#547—22no—
238#547C2×D1114yes—
239#533—111no—
240C2×C4⋊Q8C2×D1111yescharacteristic
241C2×#123—22no—
242C2×C22⋊Q8—21no—
243C2×#121—21no—
244C2×C4×D4C2×D1111yescharacteristic
245C2×C4×D4C2×D1111yescharacteristic
246C22×C4⋊C4—21no—
247#498—112no—
248#487—112no—
249#483—221no—
250#483—222no—
251#478—222no—
252#476—112no—
253#476—112no—
254#475—222no—
255#474—112no—
256#461—112no—
257#450—221no—
258C4×SD16—222no—
259#431—111no—
260#431—111no—
261#428—221no—
262#423—111no—
263#418—221no—
264#332—114no—
265D4⋊C8—114no—
266D4⋊C8—114no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—24no—
270C22×C11—48no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—84no—
277C22×C11#45012yes—
278C22×C11C2×#12011yescharacteristic
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—42no—
283C4×C11—44no—
284C4×C11—42no—
285C4×C11#45012yes—
286C4×C11C22×SD1611yescharacteristic
287C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
288C4×C11#57512yes—
289Dic11—81no—
290Dic11—81no—
291C2×#41—24no—
292C2×#41—24no—
293C2×#41—44no—
294C2×#41—44no—
295C22×Q8—21no—
296C22×D4—22no—
297C22×D4C22⋊D1111yescharacteristic
298C22×D4C22⋊D1111yescharacteristic
299C23×C4—22no—
300C23×C4—21no—
301C23×C4—21no—
302C2×SD16—222no—
303C2×M16—221no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—111no—
307C4⋊Q8—111no—
308C4⋊Q8C22⋊D1112yes—
309C4⋊Q8C22×D1112yes—
310#125—221no—
311#123—28no—
312#123—28no—
313C22⋊Q8—24no—
314C22⋊Q8—24no—
315C22⋊Q8—221no—
316C22⋊Q8—221no—
317#121—24no—
318#121—24no—
319C4×Q8—221no—
320C4×Q8—221no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4C22⋊D1112yes—
326C4×D4C22⋊D1112yes—
327C4×D4C22×D1112yes—
328C4×D4C22×D1112yes—
329#117—221no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4C22⋊D1111yescharacteristic
335C2×C4⋊C4C22⋊D1111yescharacteristic
336C2×C4⋊C4C22⋊D1112yes—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C42C22×D1111yescharacteristic
341#107—222no—
342#106—222no—
343#106—222no—
344#106—224no—
345C4⋊C8—112no—
346C4⋊C8—112no—
347C4⋊C8—221no—
348C4⋊C8—221no—
349#103—222no—
350#103—224no—
351#102—222no—
352#102—222no—
353#102—222no—
354C22⋊C8—221no—
355C22⋊C8—221no—
356C4×C8—112no—
357C4×C8—221no—
358C2×C11—22no—
359C2×C11—44no—
360C2×C11—82no—
361C2×C11C2×#45011yescharacteristic
362C2×C11#300511yescharacteristic
363C2×C11#302011yescharacteristic
364C24—21no—
365C24—21no—
366#41—48no—
367#41—416no—
368#41—48no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—42no—
372C2×Q8—42no—
373C2×Q8—221no—
374C2×Q8—221no—
375C2×D4—28no—
376C2×D4—22no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—42no—
380C2×D4—48no—
381C2×D4#432414yescomplemented
382C2×D4C2×C22⋊D1112yes—
383C2×D4C2×C22⋊D1112yes—
384C22×C4—28no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—44no—
393C22×C4—48no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4C2×C22⋊D1111yescharacteristic
397C22×C4C2×C22⋊D1111yescharacteristic
398C22×C4C2×C22⋊D1111yescharacteristic
399SD16—444no—
400M16—442no—
401C2×C8—222no—
402C2×C8—222no—
403C2×C8—222no—
404C4⋊C4—28no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—441no—
415C4⋊C4—441no—
416C4⋊C4C2×C22⋊D1112yes—
417C4⋊C4C2×C22⋊D1114yes—
418C4⋊C4C2×C22⋊D1112yes—
419C22⋊C4—28no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—441no—
425C42—441no—
426C42C2×C22⋊D1111yescharacteristic
427C42C2×C22⋊D1111yescharacteristic
428C42C2×C22⋊D1111yescharacteristic
429C42C23×D1111yescharacteristic
430C11#1875711yescharacteristic, complemented, Sylow
431C23—24no—
432C23—22no—
433C23—22no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23#6700611yescharacteristic
440Q8—42no—
441Q8—42no—
442Q8—44no—
443Q8—442no—
444Q8—442no—
445D4—22no—
446D4—24no—
447D4—22no—
448D4—22no—
449D4—42no—
450D4—416no—
451D4C2×#432414yes—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—41no—
457C2×C4—44no—
458C2×C4—42no—
459C2×C4—416no—
460C2×C4—42no—
461C2×C4—44no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4#6698512yes—
469C2×C4C2×#432412yes—
470C2×C4#6700611yescharacteristic
471C2×C4#6700611yescharacteristic
472C2×C4#6700611yescharacteristic
473C2×C4C22×C22⋊D1111yescharacteristic
474C2×C4C22×C22⋊D1111yescharacteristic
475C2×C4C22×C22⋊D1111yescharacteristic
476C8—442no—
477C8—442no—
478C8—442no—
479C22—21no—
480C22—21no—
481C22—24no—
482C22—48no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—84no—
489C22#1062283112yes—
490C22C2×#6700611yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—42no—
495C4—44no—
496C4—42no—
497C4—881no—
498C4—881no—
499C4#1062283112yes—
500C4C2×#6698511yescharacteristic
501C4C22×#432411yescharacteristic
502C4#1062335312yes—
503C2—22no—
504C2—44no—
505C2—82no—
506C2C2×#1062283111yescharacteristic
507C2#1307785811yescharacteristic
508C2#1307798011yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC2×C11×#547C2
socleC22×C11C2×#120
hypercenterC2×#547D11
hypocenterC11#18757
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13079760C2semidirect
2. #13078624C2semidirect
3. #13078413C2semidirect
4. #13067900C2semidirect
5. #13067767C2semidirect
6. #13067288C2semidirect
7. #13067041C2semidirect
8. #13067007C2semidirect
26. #10622706C22semidirect
27. #10622692C22semidirect
28. #10622632C22semidirect
31. #10622621C22semidirect
32. #10622621C22semidirect
33. #10622620C22semidirect
40. #10622185C22semidirect
41. D4⋊(C11⋊C8)C22semidirect
42. D4⋊(C11⋊C8)C22semidirect
126. C2×D4×C11SD16semidirect
381. C2×D4#4324semidirect
430. C11#18757semidirect

Maximal subgroups

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

subgroupindex
#130797602
#130786242
#130784132
#130679002
#130677672
#130672882
#130670412
#130670072
C2×C11×#5472
#1875711