Finite Group Databasebeta

← #14781179

Subgroups — #14781179

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082021C211yesmaximal, characteristic, complemented
2#13070995C211yesmaximal, characteristic
3#13070995C212yesmaximal
4#13069784C214yesmaximal, complemented
5#13069781C214yesmaximal
6#13068348C212yesmaximal, complemented
7C11×#1740C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C2×C11×#117C2212yes—
10C2×C11×#117C2211yescharacteristic
11C2×#66979C2211yescharacteristic
12C2×#66979C2212yes—
13#10623050—24no—
14#10623048—24no—
15#10623031—22no—
16#10623014C2214yes—
17#10623001—22no—
18#10622600—22no—
19#10622600—24no—
20#10622568C2212yes—
21#10622568C2214yes—
22#10622556C2212yes—
23#10622556C2214yes—
24C4×(C2×D11)⋊C4—22no—
25C4×(C2×D11)⋊C4—24no—
26C11×#342C2214yes—
27#10622165C2218yes—
28C24×D11C2311yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C23×Dic11C2311yescharacteristic
31C22×C4×D11—21no—
32C22×C4×D11—22no—
33C22×C4×D11—21no—
34C22×C4×D11—22no—
35C22×C4×D11—24no—
36C22×C4×D11—22no—
37C22×C4×D11Q814yescomplemented
38C11×#117—22no—
39C11×#117—22no—
40C11×#117—24no—
41C11×#117—24no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4D412yes—
44C2×C11×C22⋊C4C2314yes—
45C2×C11×C22⋊C4C2312yes—
46C2×C42×C11—22no—
47C2×C42×C11D412yes—
48C2×C22⋊Dic11C2312yes—
49C2×C22⋊Dic11C2314yes—
50C2×(C2×D11)⋊C4—24no—
51C2×(C2×D11)⋊C4—28no—
52#66979—22no—
53#66979—22no—
54#66979—22no—
55#66979—22no—
56#66979—24no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11D414yes—
59#66977—28no—
60C2×C4×Dic11—21no—
61C2×C4×Dic11D414yes—
62#66943—28no—
63#66941—28no—
64#66931—216no—
65#66923—24no—
66#66922—24no—
67C4×Dic22—28no—
68C11⋊#95—24no—
69C11⋊#95—28no—
70#23467—111nomaximal, Sylow
71C24×C11C2411yescharacteristic
72C23×D11—21no—
73C23×D11—22no—
74C23×D11—22no—
75C23×D11—21no—
76C23×D11—44no—
77C23×D11C2×Q812yes—
78C22×C4×C11—24no—
79C22×C4×C11C2×D414yes—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2×Q812yes—
85C22×C4×C11#4114yes—
86C22×C4×C11#4112yes—
87C22×Dic11—21no—
88C22×Dic11—22no—
89C22×Dic11—22no—
90C22×Dic11—22no—
91C22×Dic11—21no—
92C22×Dic11C2×D418yes—
93C22×Dic11C2×Q812yes—
94C2×C4×D11—28no—
95C2×C4×D11—28no—
96C2×C4×D11—24no—
97C2×C4×D11—24no—
98C2×C4×D11—42no—
99C2×C4×D11—41no—
100C2×C4×D11—41no—
101C2×C4×D11—42no—
102C2×C4×D11—42no—
103C2×C4×D11—44no—
104C2×C4×D11—44no—
105C2×Dic22—28no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—44no—
108C11×C22⋊C4—24no—
109C11×C22⋊C4—24no—
110C11×C22⋊C4—24no—
111C42×C11—22no—
112C42×C11—22no—
113C42×C11—44no—
114C22⋊Dic11—24no—
115C22⋊Dic11—24no—
116C22⋊Dic11—24no—
117(C2×D11)⋊C4—48no—
118(C2×D11)⋊C4—416no—
119C4⋊Dic11—28no—
120C4⋊Dic11—24no—
121C4⋊Dic11—24no—
122C4⋊Dic11—42no—
123Dic11⋊C4—216no—
124C4×Dic11—24no—
125C4×Dic11—24no—
126C4×Dic11—42no—
127#3458—111no—
128#2280—112no—
129#2280—111no—
130#2030—114no—
131#2029—114no—
132#1740—112no—
133#1740D1111yescharacteristic, complemented
134C23×C11—42no—
135C23×C11C22×D411yescharacteristic
136C23×C11C22×D412yes—
137C23×C11C22×Q811yescharacteristic
138C23×C11C2×#4112yes—
139C23×C11C2×#4111yescharacteristic
140C22×D11—24no—
141C22×D11—28no—
142C22×D11—24no—
143C22×D11—22no—
144C22×D11—44no—
145C22×D11—48no—
146C22×D11—44no—
147C22×D11—42no—
148C22×D11—44no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11—42no—
152C2×C4×C11—24no—
153C2×C4×C11—44no—
154C2×C4×C11—48no—
155C2×C4×C11—44no—
156C2×C4×C11#12012yes—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11C22⋊Q814yes—
160C2×C4×C11C22⋊Q814yes—
161C2×C4×C11C22⋊Q812yes—
162C2×C4×C11C22⋊Q812yes—
163C2×C4×C11#12412yes—
164C2×C4×C11#12412yes—
165C2×C4×C11#12414yes—
166C2×C4×C11#12414yes—
167C2×Dic11—28no—
168C2×Dic11—24no—
169C2×Dic11—22no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—42no—
173C2×Dic11—48no—
174C2×Dic11—44no—
175C2×Dic11—42no—
176C4×D11—48no—
177C4×D11—44no—
178C4×D11—44no—
179Dic22—88no—
180C24×C4—111no—
181#544—224no—
182#544—222no—
183#543—114no—
184#533—224no—
185#533—222no—
186C2×#117—112no—
187C2×#117—111no—
188C2×#117C2×D1112yes—
189C2×#117C2×D1111yescharacteristic
190#381—114no—
191#381—112no—
192#380—224no—
193#380—222no—
194#379—114no—
195#379—112no—
196C4×C22⋊C4—224no—
197C4×C22⋊C4—222no—
198#342—118no—
199#342C2×D1114yes—
200C22×C11—22no—
201C22×C11—24no—
202C22×C11—41no—
203C22×C11—42no—
204C22×C11—41no—
205C22×C11C2×#12011yescharacteristic
206C22×C11C2×C22⋊Q812yes—
207C22×C11C2×C22⋊Q811yescharacteristic
208C22×C11C2×#12411yescharacteristic
209C22×C11C2×#12412yes—
210C2×D11—28no—
211C2×D11—24no—
212C2×D11—44no—
213C2×D11—48no—
214C2×D11—44no—
215C2×D11—42no—
216C2×D11—42no—
217C2×D11—44no—
218C4×C11—44no—
219C4×C11—84no—
220C4×C11#39314yes—
221C4×C11#39312yes—
222C4×C11#39312yes—
223Dic11—42no—
224Dic11—48no—
225Dic11—82no—
226C25—111no—
227C23×C4—111no—
228C23×C4—114no—
229C23×C4—221no—
230C23×C4—221no—
231C23×C4—224no—
232C23×C4—222no—
233C23×C4—222no—
234C23×C4—222no—
235C23×C4C22×D1111yescharacteristic
236C4⋊Q8—224no—
237C4⋊Q8—228no—
238#125—224no—
239#125—228no—
240C22⋊Q8—2216no—
241C22⋊Q8—228no—
242C4×Q8—228no—
243#117—22no—
244#117—22no—
245#117—24no—
246#117—24no—
247#117—222no—
248#117—222no—
249#117—222no—
250#117—222no—
251#117—224no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—114no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4D4412yes—
256C2×C22⋊C4—114no—
257C2×C22⋊C4—112no—
258C2×C22⋊C4—228no—
259C2×C22⋊C4—224no—
260C2×C22⋊C4C22×D1114yes—
261C2×C22⋊C4C22×D1112yes—
262C2×C42—22no—
263C2×C42—114no—
264C2×C42—221no—
265C2×C42D4412yes—
266#95—228no—
267#95—224no—
268C2×C11—21no—
269C2×C11—22no—
270C2×C11—22no—
271C2×C11—21no—
272C2×C11C2×#39311yescharacteristic
273C2×C11#302512yes—
274D11—44no—
275C24—112no—
276C24—221no—
277C24—222no—
278C24—222no—
279C24—221no—
280C24—444no—
281C24C23×D1111yescharacteristic
282C2×Q8—228no—
283C22×C4—24no—
284C22×C4—112no—
285C22×C4—118no—
286C22×C4—221no—
287C22×C4—222no—
288C22×C4—222no—
289C22×C4—221no—
290C22×C4—228no—
291C22×C4—228no—
292C22×C4—224no—
293C22×C4—224no—
294C22×C4—222no—
295C22×C4—442no—
296C22×C4—442no—
297C22×C4—441no—
298C22×C4—442no—
299C22×C4—441no—
300C22×C4—444no—
301C22×C4—444no—
302C22×C4C2×D4414yes—
303C22×C4C2×D4411yescharacteristic
304C22×C4C2×D4411yescharacteristic
305C22×C4#433914yes—
306C22×C4D4×D1112yes—
307C22×C4D4×D1112yes—
308C22×C4#434112yes—
309C22×C4Q8×D1112yes—
310C4⋊C4—24no—
311C4⋊C4—44no—
312C4⋊C4—2216no—
313C4⋊C4—228no—
314C4⋊C4—224no—
315C4⋊C4—224no—
316C4⋊C4—442no—
317C22⋊C4—24no—
318C22⋊C4—24no—
319C22⋊C4—24no—
320C22⋊C4—224no—
321C22⋊C4—224no—
322C22⋊C4—224no—
323C22⋊C4—448no—
324C22⋊C4—4416no—
325C42—22no—
326C42—22no—
327C42—44no—
328C42—224no—
329C42—224no—
330C42—442no—
331C11#2346711yescharacteristic, complemented, Sylow
332C23—42no—
333C23—224no—
334C23—228no—
335C23—224no—
336C23—222no—
337C23—442no—
338C23—444no—
339C23—444no—
340C23—448no—
341C23—444no—
342C23—441no—
343C23—441no—
344C23—442no—
345C23C22×D4411yescharacteristic
346C23C2×#433912yes—
347C23C2×D4×D1112yes—
348C23C2×#434111yescharacteristic
349C23C2×Q8×D1111yescharacteristic
350Q8—888no—
351C2×C4—24no—
352C2×C4—44no—
353C2×C4—48no—
354C2×C4—44no—
355C2×C4—228no—
356C2×C4—224no—
357C2×C4—222no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—442no—
361C2×C4—444no—
362C2×C4—448no—
363C2×C4—444no—
364C2×C4—448no—
365C2×C4—444no—
366C2×C4—442no—
367C2×C4#6692812yes—
368C2×C4#6692812yes—
369C2×C4#6693511yescharacteristic
370C2×C4#6693512yes—
371C2×C4#6693511yescharacteristic
372C2×C4#6693814yes—
373C2×C4#6693814yes—
374C2×C4#6694914yes—
375C2×C4#6694914yes—
376C2×C4#6695012yes—
377C2×C4#6695012yes—
378C22—22no—
379C22—24no—
380C22—42no—
381C22—41no—
382C22—41no—
383C22—228no—
384C22—224no—
385C22—448no—
386C22—444no—
387C22—444no—
388C22—442no—
389C22—442no—
390C22—444no—
391C22C2×#6692811yescharacteristic
392C22C2×#6693511yescharacteristic
393C22C2×#6693812yes—
394C22C2×#6694912yes—
395C22C2×#6695011yescharacteristic
396C4—44no—
397C4—84no—
398C4—442no—
399C4—448no—
400C4—882no—
401C4#1062228612yes—
402C4#1062228614yes—
403C4#1062228612yes—
404C2—22no—
405C2—21no—
406C2—22no—
407C2—21no—
408C2—444no—
409C2C2×#1062228611yescharacteristic
410C2#1307801012yes—
subgroupG/H
centerC2×C4#66935
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#1740C2
socleC22×C11C2×#120
prime radicalC24×D11C23
hypercenter#1740D11
hypocenterC11#23467
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1740

Complements

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

NH ≅ G/Ntype
1. #13082021C2semidirect
4. #13069784C2semidirect
6. #13068348C2semidirect
7. C11×#1740C2semidirect
37. C22×C4×D11Q8semidirect
133. #1740D11semidirect
331. C11#23467semidirect

Maximal subgroups

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

subgroupindex
#130820212
#130709952
#130697842
#130697812
#130683482
C11×#17402
#2346711