Finite Group Databasebeta

← #14789998

Subgroups — #14789998

Order 2816.

1170 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082419C211yesmaximal, characteristic, complemented
2#13078413C212yesmaximal, complemented
3#13069961C212yesmaximal, complemented
4#13069772C212yesmaximal, complemented
5#13069593C212yesmaximal, complemented
6#13069015C212yesmaximal
7#13068825C212yesmaximal, complemented
8#13068608C211yesmaximal, characteristic, complemented
9C4×C11×#127C211yesmaximal, characteristic
10C2×C11×#127C2211yescharacteristic
11C2×C4×D4×C11—22no—
12C2×C4×D4×C11C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14#10623329C2212yes—
15C2×#66977—22no—
16#10623074—22no—
17#10623070—24no—
18D4×Dic22—22no—
19#10623031C2212yes—
20#10623014—22no—
21#10623001C2212yes—
22C11×#390—22no—
23C11×#390C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C11×#384C2211yescharacteristic
26C43×C11C2211yescharacteristic
27C2×#66897C2212yes—
28#10622828C2214yes—
29#10622622—24no—
30#10622621—22no—
31#10622620—22no—
32#10622577C2214yes—
33#10622537C2212yes—
34#10622168C2212yes—
35#10622161C2214yes—
36#10622161C2214yes—
37C22×D4×C11—22no—
38C22×D4×C11C2311yescharacteristic
39C22×D4×C11C2311yescharacteristic
40C23×C4×C11—21no—
41C23×C4×C11D412yes—
42C22×Dic22—22no—
43C11×#127—22no—
44C11×#127Q814yescomplemented
45C4×D4×C11—22no—
46C4×D4×C11—22no—
47C4×D4×C11—22no—
48C4×D4×C11—22no—
49C4×D4×C11—48no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4D412yes—
57C2×C42×C11—21no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—24no—
63D4×Dic11—24no—
64D4×Dic11—24no—
65#66979C2314yes—
66C2×C4⋊Dic11—22no—
67#66977—24no—
68#66977—24no—
69#66977—22no—
70#66977—22no—
71#66977—24no—
72C2×Dic11⋊C4—24no—
73C2×#4318C2314yes—
74#66943—24no—
75#66941—24no—
76#66931—28no—
77#66931—28no—
78#66923D414yescomplemented
79#66922D412yescomplemented
80#66922D412yescomplemented
81C4×Dic22—22no—
82C4×Dic22—22no—
83#66897—24no—
84#66896—24no—
85#66896—24no—
86#66872—24no—
87#66871—24no—
88C4⋊(C11⋊C8)—22no—
89C4⋊(C11⋊C8)—22no—
90#24312—111nomaximal, Sylow
91C24×C11—21no—
92C24×C11C2×D412yes—
93C2×D4×C11—28no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—21no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—44no—
100C2×D4×C11—44no—
101C2×D4×C11C2×Q812yes—
102C2×D4×C11C2×Q812yescomplemented
103C2×D4×C11#4112yes—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—44no—
110C22×C4×C11—44no—
111C22×C4×C11—41no—
112C22×C4×C11—41no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—24no—
118C22×Dic11—24no—
119C2×Dic22—24no—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22—84no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—44no—
126C11×C22⋊C4—24no—
127C11×C22⋊C4—44no—
128C11×C22⋊C4—44no—
129C11×C22⋊C4—42no—
130C42×C11—24no—
131C42×C11—21no—
132C42×C11—22no—
133C42×C11—42no—
134C42×C11C2×D412yes—
135C42×C11C2×D412yes—
136C42×C11C2×Q812yescomplemented
137C22⋊Dic11—28no—
138C22⋊Dic11—24no—
139C4⋊Dic11—24no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11C2×D414yes—
143C4⋊Dic11C2×D414yes—
144Dic11⋊C4—28no—
145Dic11⋊C4—24no—
146Dic11⋊C4—24no—
147C4×Dic11—24no—
148#4318—24no—
149#4318—24no—
150C2×C11⋊C8—24no—
151#3501—111no—
152#3077—112no—
153C4×#127D1111yescharacteristic
154#2060—112no—
155#2027—112no—
156#1994—112no—
157#1887—112no—
158#1856—112no—
159#1800—111no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11C22⋊Q814yes—
170C23×C11C22×D411yescharacteristic
171D4×C11—24no—
172D4×C11—24no—
173D4×C11—24no—
174D4×C11—416no—
175D4×C11—42no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—44no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—82no—
190C2×C4×C11—82no—
191C2×C4×C11—82no—
192C2×C4×C11#12011yescharacteristic
193C2×C4×C11#12012yes—
194C2×C4×C11#12011yescharacteristic
195C2×C4×C11C22×D412yes—
196C2×C4×C11C22×Q811yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C112−1+412yes—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—84no—
202C2×Dic11—84no—
203Dic22—44no—
204Dic22—82no—
205Dic22—84no—
206C11⋊C8—44no—
207#554—224no—
208#554—222no—
209D4×Q8—222no—
210#544—112no—
211#543—222no—
212#533—112no—
213C2×#127C2×D1111yescharacteristic
214C2×C22⋊Q8—222no—
215#518—112no—
216C2×C4×D4—22no—
217C2×C4×D4C2×D1111yescharacteristic
218C2×C4×D4C2×D1111yescharacteristic
219#478—224no—
220#476—222no—
221#474—222no—
222#428—114no—
223#423—112no—
224#418—114no—
225C2×#100—112no—
226#390—22no—
227#390C2×D1111yescharacteristic
228#390C2×D1111yescharacteristic
229#384C2×D1111yescharacteristic
230C43C2×D1111yescharacteristic
231#343—112no—
232#339—114no—
233#339—114no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—24no—
237C22×C11—44no—
238C22×C11—44no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—82no—
243C22×C11—82no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11C2×#12011yescharacteristic
247C22×C11C2×C22⋊Q811yescharacteristic
248C22×C11#53611yescharacteristic
249C4×C11—24no—
250C4×C11—21no—
251C4×C11—22no—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—81no—
255C4×C11#45312yes—
256C4×C11#54812yes—
257C4×C11D4×Q812yes—
258Dic11—44no—
259Dic11—44no—
260C22×Q8—222no—
261C22×D4—22no—
262C22×D4C22×D1111yescharacteristic
263C22×D4C22×D1111yescharacteristic
264C23×C4—21no—
265C23×C4C22⋊D1112yes—
266C2×M16—114no—
267C4⋊Q8—112no—
268C4⋊Q8—112no—
269C4⋊Q8—224no—
270#127—22no—
271#127Dic2214yescomplemented
272#125—114no—
273#125—224no—
274C22⋊Q8—228no—
275C22⋊Q8—228no—
276C22⋊Q8—224no—
277C22⋊Q8—224no—
278C22⋊Q8—222no—
279C22⋊Q8—224no—
280C22⋊Q8—222no—
281C4×Q8—222no—
282C4×Q8—222no—
283C4×D4—22no—
284C4×D4—22no—
285C4×D4—22no—
286C4×D4—22no—
287C4×D4—48no—
288C4×D4—224no—
289C4×D4—224no—
290#117—114no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—224no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4C22×D1111yescharacteristic
295C2×C4⋊C4C22×D1111yescharacteristic
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—224no—
300C2×C22⋊C4C22⋊D1112yes—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42C22×D1111yescharacteristic
304C2×C42C22×D1111yescharacteristic
305C2×C42C22×D1111yescharacteristic
306#107—224no—
307#106—224no—
308C4⋊C8—222no—
309C4⋊C8—222no—
310#102—224no—
311#102—224no—
312#100—224no—
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—44no—
316C2×C11—82no—
317C2×C11#240911yescharacteristic
318C2×C11C2×#45311yescharacteristic
319C2×C11#301811yescharacteristic
320C24—21no—
321C24C2×C22⋊D1112yes—
322C2×Q8—224no—
323C2×Q8—222no—
324C2×Q8—222no—
325C2×Q8—884no—
326C2×D4—28no—
327C2×D4—21no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—44no—
333C2×D4—44no—
334C2×D4C2×Dic2212yes—
335C2×D4C2×Dic2212yescomplemented
336C2×D4#433912yes—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—44no—
343C22×C4—44no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—224no—
347C22×C4—224no—
348C22×C4C2×C22⋊D1111yescharacteristic
349C22×C4C2×C22⋊D1112yes—
350C22×C4C2×C22⋊D1111yescharacteristic
351C22×C4C23×D1111yescharacteristic
352M16—224no—
353M16—224no—
354C2×C8—224no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—44no—
358C4⋊C4—114no—
359C4⋊C4—114no—
360C4⋊C4—224no—
361C4⋊C4—228no—
362C4⋊C4—224no—
363C4⋊C4—222no—
364C4⋊C4—224no—
365C4⋊C4—222no—
366C22⋊C4—24no—
367C22⋊C4—44no—
368C22⋊C4—44no—
369C22⋊C4—42no—
370C22⋊C4—228no—
371C22⋊C4—224no—
372C42—24no—
373C42—21no—
374C42—22no—
375C42—42no—
376C42—224no—
377C42C2×Dic2212yescomplemented
378C42D4×D1112yes—
379C42D4×D1112yes—
380C11#2431211yescharacteristic, complemented, Sylow
381C23—22no—
382C23—22no—
383C23—22no—
384C23—42no—
385C23—42no—
386C23—42no—
387C23—42no—
388C23—41no—
389C23—41no—
390C23#6697714yes—
391C23C22×C22⋊D1111yescharacteristic
392Q8—444no—
393Q8—882no—
394Q8—884no—
395D4—24no—
396D4—24no—
397D4—24no—
398D4—416no—
399D4—42no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—224no—
417C2×C4—224no—
418C2×C4—884no—
419C2×C4—884no—
420C2×C4#6699012yes—
421C2×C4#6699011yescharacteristic
422C2×C4#6699011yescharacteristic
423C2×C4C22×Dic2211yescharacteristic
424C2×C4C2×#433911yescharacteristic
425C2×C4C2×D4×D1112yes—
426C2×C4#6704312yes—
427C8—444no—
428C22—21no—
429C22—21no—
430C22—24no—
431C22—44no—
432C22—44no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—82no—
437C22—82no—
438C22—81no—
439C22—81no—
440C22C2×#6697711yescharacteristic
441C22C2×#6699011yescharacteristic
442C22#1062335611yescharacteristic
443C4—24no—
444C4—21no—
445C4—22no—
446C4—42no—
447C4—42no—
448C4—81no—
449C4—444no—
450C4—444no—
451C4#1062269012yes—
452C4D4×Dic2212yes—
453C4#1062308312yes—
454C2—21no—
455C2—21no—
456C2—44no—
457C2—82no—
458C2#1307198111yescharacteristic
459C2C2×#1062269011yescharacteristic
460C2#1307796411yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#127C2
socleC22×C11C2×#120
prime radicalC2×C11×#127C22
hypercenterC4×#127D11
hypocenterC11#24312
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
1. #13082419C2semidirect
2. #13078413C2semidirect
3. #13069961C2semidirect
4. #13069772C2semidirect
5. #13069593C2semidirect
7. #13068825C2semidirect
8. #13068608C2semidirect
44. C11×#127Q8semidirect
78. #66923D4semidirect
79. #66922D4semidirect
80. #66922D4semidirect
102. C2×D4×C11C2×Q8semidirect
136. C42×C11C2×Q8semidirect
271. #127Dic22semidirect
335. C2×D4C2×Dic22semidirect
377. C42C2×Dic22semidirect
380. C11#24312semidirect

Maximal subgroups

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

subgroupindex
#130824192
#130784132
#130699612
#130697722
#130695932
#130690152
#130688252
#130686082
C4×C11×#1272
#2431211