Finite Group Databasebeta

← #14916627

Subgroups — #14916627

Order 2816.

2610 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071790C214yesmaximal, complemented
2#13071706C212yesmaximal, complemented
3#13071681C212yesmaximal, complemented
4#13071565C214yesmaximal, complemented
5D4×C4⋊Dic11C214yesmaximal, complemented
6#13071311C218yesmaximal, complemented
7#13071208C214yesmaximal, complemented
8#13071023C212yesmaximal, complemented
9C2×C11×#532C211yesmaximal, characteristic
10C22×C11×#41C2212yes—
11C11×#532C4116yescomplemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C2×C11×#124C2212yes—
15C2×C11×#121C2214yes—
16C2×C4×D4×C11C2214yes—
17C22×C42×C11C2211yescharacteristic
18C2×D4×Dic11C2218yes—
19C2×#66979C2214yes—
20C2×#66979C2214yes—
21C22×C4⋊Dic11C2214yes—
22#10622843C2218yes—
23#10622834C2218yes—
24#10622834C2218yes—
25#10622833C2218yes—
26#10622833C2218yes—
27#10622825C2214yes—
28#10622825C2218yes—
29#10622825C2214yes—
30#10622598C2218yes—
31C4⋊C4×Dic11C2218yes—
32#10622564C22116yes—
33#10622563C22116yes—
34#10622549C2214yes—
35#10622548C2212yes—
36#10622548C2212yes—
37C4×C4⋊Dic11C2214yes—
38C4×C4⋊Dic11C2214yes—
39C2×C11×#41—44no—
40C2×C11×#41—44no—
41C2×C11×#41C2×C4116yescomplemented
42C22×Q8×C11C2312yes—
43C22×D4×C11C2314yes—
44C22×D4×C11C2312yes—
45C22×D4×C11C2314yes—
46C23×C4×C11C2314yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×Dic11C2318yes—
50C11×C4⋊Q8C2×C418yescomplemented
51C11×#127C2×C418yes—
52C11×#124C2×C4116yescomplemented
53C11×#121C2×C4132yescomplemented
54C4×D4×C11C2×C4132yescomplemented
55C2×C11×C4⋊C4C2314yes—
56C2×C11×C22⋊C4C2318yes—
57C2×C42×C11C2×C418yescomplemented
58C2×C42×C11C2311yescharacteristic
59C2×C42×C11C2312yes—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11C2318yes—
62C2×C22⋊Dic11C2318yes—
63C2×C22⋊Dic11C23116yes—
64D4×Dic11—416no—
65#66979—48no—
66#66979—48no—
67C2×C4⋊Dic11—48no—
68C2×C4⋊Dic11C2314yes—
69C2×C4⋊Dic11C2314yes—
70C2×C4⋊Dic11C2314yes—
71C2×C4⋊Dic11C2314yes—
72C2×C4⋊Dic11C2314yes—
73C2×C4⋊Dic11C2314yes—
74C2×C4⋊Dic11C2318yes—
75C2×C4×Dic11C2318yes—
76C2×C4×Dic11C2318yes—
77C11⋊#95C2318yes—
78C11⋊#95C2318yes—
79C11⋊#95C23116yes—
80#34368—111nomaximal, Sylow
81C24×C11C2411yescharacteristic
82C24×C11C2414yes—
83C11×#41—432no—
84C2×Q8×C11—42no—
85C2×Q8×C11—42no—
86C2×Q8×C11C22×C418yes—
87C2×D4×C11—28no—
88C2×D4×C11—28no—
89C2×D4×C11—44no—
90C2×D4×C11—44no—
91C2×D4×C11—42no—
92C2×D4×C11—42no—
93C2×D4×C11C22×C4116yes—
94C2×D4×C11C22×C4116yes—
95C2×D4×C11C22×C418yes—
96C22×C4×C11—28no—
97C22×C4×C11—24no—
98C22×C4×C11—28no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—24no—
102C22×C4×C11C22×C418yes—
103C22×C4×C11C22×C414yes—
104C22×C4×C11C22×C4116yes—
105C22×C4×C11C2411yescharacteristic
106C22×C4×C11C2414yes—
107C22×C4×C11C2412yes—
108C22×C4×C11C2411yescharacteristic
109C22×C4×C11C2412yes—
110C22×Dic11—48no—
111C22×Dic11—416no—
112C22×Dic11C2418yes—
113C22×Dic11C2418yes—
114C11×C4⋊C4C22×C4116yes—
115C11×C22⋊C4C22×C4132yes—
116C42×C11C22×C418yes—
117C42×C11C22×C414yes—
118C42×C11C22×C414yes—
119C22⋊Dic11—48no—
120C22⋊Dic11—48no—
121C22⋊Dic11—416no—
122C4⋊Dic11—28no—
123C4⋊Dic11—28no—
124C4⋊Dic11—28no—
125C4⋊Dic11—28no—
126C4⋊Dic11—48no—
127C4⋊Dic11—44no—
128C4⋊Dic11—44no—
129C4×Dic11—216no—
130C4×Dic11—48no—
131C2×#532D1111yescharacteristic
132#2379—114no—
133#2369—112no—
134#2366—112no—
135#2354—114no—
136D4×C4⋊C4—114no—
137#2324—118no—
138#2311—114no—
139#2285—112no—
140C23×C11—22no—
141C23×C11—28no—
142C23×C11—24no—
143C23×C11—24no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—22no—
147C23×C11—28no—
148C23×C11C23×C418yes—
149C23×C11C23×C412yes—
150C23×C11C2511yescharacteristic
151Q8×C11—48no—
152D4×C11—232no—
153D4×C11—48no—
154D4×C11—416no—
155C2×C4×C11—24no—
156C2×C4×C11—22no—
157C2×C4×C11—24no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—22no—
161C2×C4×C11—232no—
162C2×C4×C11—28no—
163C2×C4×C11—216no—
164C2×C4×C11C23×C414yes—
165C2×C4×C11C23×C412yes—
166C2×C4×C11C23×C418yes—
167C2×C4×C11C23×C412yes—
168C2×C4×C11C23×C414yes—
169C2×C4×C11H(5,𝔽2)12yes—
170C2×C4×C11H(5,𝔽2)12yes—
171C2×C4×C11H(5,𝔽2)14yes—
172C2×C4×C112−1+414yes—
173C2×Dic11—28no—
174C2×Dic11—28no—
175C2×Dic11—28no—
176C2×Dic11—28no—
177C2×Dic11—28no—
178C2×Dic11—28no—
179C2×Dic11—816no—
180C22×#41C2×D1112yes—
181#532Dic11116yescomplemented
182C2×C4⋊Q8C2×D1111yescharacteristic
183C2×#127C2×D1111yescharacteristic
184C2×#124C2×D1112yes—
185C2×#121C2×D1114yes—
186C2×C4×D4—118no—
187C2×C4×D4C2×D1114yes—
188C2×#117—114no—
189C2×#117—114no—
190C22×C4⋊C4—114no—
191C22×C42C2×D1111yescharacteristic
192#391—118no—
193#390—118no—
194#390—118no—
195#389—118no—
196#388—1116no—
197#386—118no—
198#386—118no—
199#385—1116no—
200#384—112no—
201#384—112no—
202#382—114no—
203#380—114no—
204#380—118no—
205#380—114no—
206C4×C4⋊C4—118no—
207C4×C4⋊C4—114no—
208C4×C4⋊C4—114no—
209C22×C11—22no—
210C22×C11—28no—
211C22×C11—24no—
212C22×C11—216no—
213C22×C11—42no—
214C22×C11—48no—
215C22×C11—41no—
216C22×C11—44no—
217C22×C11—44no—
218C22×C11—41no—
219C22×C11C24×C411yescharacteristic
220C22×C11C2×H(5,𝔽2)11yescharacteristic
221C22×C11C2×H(5,𝔽2)11yescharacteristic
222C22×C11C2×H(5,𝔽2)12yes—
223C22×C11C2×2−1+412yes—
224C4×C11—22no—
225C4×C11—28no—
226C4×C11—24no—
227C4×C11#51814yes—
228C4×C11#52018yes—
229Dic11—48no—
230Dic11—48no—
231C2×#41—44no—
232C2×#41—44no—
233C2×#41C2×Dic11116yescomplemented
234C22×Q8C22×D1112yes—
235C22×D4C22×D1114yes—
236C22×D4C22×D1114yes—
237C22×D4C22×D1112yes—
238C23×C4—118no—
239C23×C4C22×D1114yes—
240C23×C4C22×D1112yes—
241C23×C4C22×D1111yescharacteristic
242C4⋊Q8C2×Dic1118yescomplemented
243#127C2×Dic1118yes—
244#124C2×Dic11116yescomplemented
245#121C2×Dic11132yescomplemented
246C4×D4—4416no—
247C4×D4C2×Dic11132yescomplemented
248#117—448no—
249#117—448no—
250C2×C4⋊C4—114no—
251C2×C4⋊C4—114no—
252C2×C4⋊C4—114no—
253C2×C4⋊C4—114no—
254C2×C4⋊C4—118no—
255C2×C4⋊C4—114no—
256C2×C4⋊C4—114no—
257C2×C4⋊C4—448no—
258C2×C4⋊C4C22×D1114yes—
259C2×C22⋊C4—118no—
260C2×C22⋊C4—118no—
261C2×C22⋊C4—1116no—
262C2×C22⋊C4C22×D1118yes—
263C2×C42—118no—
264C2×C42—118no—
265C2×C42C2×Dic1118yescomplemented
266C2×C42C22×D1112yes—
267C2×C42C22×D1111yescharacteristic
268C2×C42C22×D1111yescharacteristic
269#95—118no—
270#95—118no—
271#95—1116no—
272C2×C11—42no—
273C2×C11—48no—
274C2×C11C2×#51811yescharacteristic
275C2×C11C2×#52012yes—
276C2×C11#354812yes—
277C2×C11#354911yescharacteristic
278C2×C11#355011yescharacteristic
279C24C23×D1111yescharacteristic
280C24C23×D1114yes—
281#41—432no—
282C2×Q8—42no—
283C2×Q8—42no—
284C2×Q8C22×Dic1118yes—
285C2×D4—28no—
286C2×D4—28no—
287C2×D4—44no—
288C2×D4—44no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4C22×Dic11116yes—
292C2×D4C22×Dic11116yes—
293C2×D4C22×Dic1118yes—
294C22×C4—28no—
295C22×C4—28no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—118no—
301C22×C4—118no—
302C22×C4—448no—
303C22×C4—4416no—
304C22×C4C22×Dic1118yes—
305C22×C4C22×Dic1114yes—
306C22×C4C22×Dic11116yes—
307C22×C4C23×D1111yescharacteristic
308C22×C4C23×D1114yes—
309C22×C4C23×D1112yes—
310C22×C4C23×D1111yescharacteristic
311C22×C4C23×D1112yes—
312C4⋊C4—228no—
313C4⋊C4—228no—
314C4⋊C4—228no—
315C4⋊C4—228no—
316C4⋊C4—448no—
317C4⋊C4—444no—
318C4⋊C4—444no—
319C4⋊C4C22×Dic11116yes—
320C22⋊C4—448no—
321C22⋊C4—448no—
322C22⋊C4—4416no—
323C22⋊C4C22×Dic11132yes—
324C42—2216no—
325C42—448no—
326C42C22×Dic1118yes—
327C42C22×Dic1114yes—
328C42C22×Dic1114yes—
329C11#3436811yescharacteristic, complemented, Sylow
330C23—24no—
331C23—24no—
332C23—21no—
333C23—21no—
334C23—22no—
335C23—28no—
336C23—22no—
337C23—28no—
338C23C23×Dic1118yes—
339C23C23×Dic1112yes—
340C23C24×D1111yescharacteristic
341Q8—48no—
342D4—232no—
343D4—48no—
344D4—416no—
345C2×C4—24no—
346C2×C4—24no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—232no—
352C2×C4—28no—
353C2×C4—216no—
354C2×C4—228no—
355C2×C4—228no—
356C2×C4—228no—
357C2×C4—228no—
358C2×C4—228no—
359C2×C4—228no—
360C2×C4—8816no—
361C2×C4#6703712yes—
362C2×C4#6703712yes—
363C2×C4#6704214yes—
364C2×C4#6704314yes—
365C2×C4C23×Dic1114yes—
366C2×C4C23×Dic1112yes—
367C2×C4C23×Dic1118yes—
368C2×C4C23×Dic1112yes—
369C2×C4C23×Dic1114yes—
370C22—22no—
371C22—28no—
372C22—24no—
373C22—216no—
374C22—48no—
375C22—42no—
376C22—44no—
377C22—41no—
378C22—44no—
379C22—41no—
380C22C2×#6703711yescharacteristic
381C22C2×#6703711yescharacteristic
382C22C2×#6704212yes—
383C22C2×#6704312yes—
384C22C24×Dic1111yescharacteristic
385C4—22no—
386C4—28no—
387C4—24no—
388C4—448no—
389C4—448no—
390C4#1062332914yes—
391C4#1062335818yes—
392C2—42no—
393C2—48no—
394C2C2×#1062332911yescharacteristic
395C2C2×#1062335812yes—
396C2#1308301412yes—
397C2#1308302111yescharacteristic
398C2#1308303011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
Fitting, prime radicalC2×C11×#532C2
socle, cosocleC23×C11C25
hypercenterC2×#532D11
hypocenterC11#34368
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #13071790C2semidirect
2. #13071706C2semidirect
3. #13071681C2semidirect
4. #13071565C2semidirect
5. D4×C4⋊Dic11C2semidirect
6. #13071311C2semidirect
7. #13071208C2semidirect
8. #13071023C2semidirect
11. C11×#532C4semidirect
41. C2×C11×#41C2×C4semidirect
50. C11×C4⋊Q8C2×C4semidirect
52. C11×#124C2×C4semidirect
53. C11×#121C2×C4semidirect
54. C4×D4×C11C2×C4semidirect
57. C2×C42×C11C2×C4semidirect
181. #532Dic11semidirect
233. C2×#41C2×Dic11semidirect
242. C4⋊Q8C2×Dic11semidirect
244. #124C2×Dic11semidirect
245. #121C2×Dic11semidirect
247. C4×D4C2×Dic11semidirect
265. C2×C42C2×Dic11semidirect
329. C11#34368semidirect

Maximal subgroups

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

subgroupindex
#130717902
#130717062
#130716812
#130715652
D4×C4⋊Dic112
#130713112
#130712082
#130710232
C2×C11×#5322
#3436811