Finite Group Databasebeta

← #14960494

Subgroups — #14960494

Order 2816.

1304 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076891C211yesmaximal, characteristic
2#13076864C214yesmaximal
3#13076862C214yesmaximal
4#13076860C214yesmaximal
5#13076683C212yesmaximal
6#13071922C214yesmaximal
7#13071920C214yesmaximal
8#13071920C214yesmaximal
9#125×Dic11C212yesmaximal
10#13071171C211yesmaximal, characteristic
11C11×#2822C211yesmaximal, characteristic
12C2×C11×#125C2212yes—
13C2×#66923C2211yescharacteristic
14C11×#400C2214yes—
15C11×#398C2214yes—
16C11×#398C2214yes—
17C11×#382C2211yescharacteristic
18#10622599C2214yes—
19#10622599C2214yes—
20#10622598C2212yes—
21#10622598C2212yes—
22#10622597C2214yes—
23#10622597C2214yes—
24#10622597C2214yes—
25#10622596C2214yes—
26#10622596C2214yes—
27#10622595C2214yes—
28#10622595C2214yes—
29#10622594C2214yes—
30#10622594C2214yes—
31#10622593C2214yes—
32C4⋊C4×Dic11C2214yes—
33C4⋊C4×Dic11C2212yes—
34C4⋊C4×Dic11C2212yes—
35C4⋊C4×Dic11C2214yes—
36C4⋊C4×Dic11C2214yes—
37C4⋊C4×Dic11C2212yes—
38#10622586C2212yes—
39#10622549C2212yes—
40C42×Dic11C2211yescharacteristic
41#10622274C2214yes—
42#10622274C2214yes—
43#10622273C2214yes—
44#10622273C2214yes—
45#10622273C2214yes—
46#10622272C2214yes—
47#10622272C2214yes—
48#10622271C2214yes—
49#10622271C2214yes—
50#10622270C2214yes—
51#10622270C2214yes—
52#10622265C2214yes—
53#10622262C2214yes—
54#10622262C2214yes—
55#10622262C2214yes—
56#10622261C2214yes—
57C11×#125—28no—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2314yes—
60C2×C11×C4⋊C4C2314yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2314yes—
64C2×C42×C11C2311yescharacteristic
65C2×C4⋊Dic11C2312yes—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2314yes—
68C2×C4⋊Dic11C2314yes—
69C2×C4⋊Dic11C2314yes—
70C2×C4⋊Dic11C2312yes—
71C2×Dic11⋊C4C2314yes—
72C2×Dic11⋊C4C2314yes—
73C2×Dic11⋊C4C2314yes—
74C2×Dic11⋊C4C2314yes—
75C2×Dic11⋊C4C2314yes—
76C2×Dic11⋊C4C2314yes—
77C2×C4×Dic11C2314yes—
78C2×C4×Dic11C2314yes—
79C2×C4×Dic11C2314yes—
80C2×C4×Dic11C2312yes—
81C2×C4×Dic11C2311yescharacteristic
82C2×C4×Dic11C2312yes—
83C2×C4×Dic11C2311yescharacteristic
84#66923—24no—
85C11×#95C2314yes—
86C11×#95C2314yes—
87C11×#95C2314yes—
88C11×#95C2314yes—
89C11⋊#95C2314yes—
90C11⋊#95C2314yes—
91C11⋊#95C2314yes—
92C11⋊#95C2314yes—
93C11⋊#95C2314yes—
94C11⋊#95C2314yes—
95C11⋊#95C2314yes—
96C11⋊#95C2314yes—
97C11⋊#95C2314yes—
98C11⋊#95C2314yes—
99C11⋊#95C2314yes—
100C11⋊#95C2314yes—
101C11⋊#95C2314yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104#36701—111nomaximal, Sylow
105C22×C4×C11C2414yes—
106C22×C4×C11C2414yes—
107C22×C4×C11C2414yes—
108C22×C4×C11C2411yescharacteristic
109C22×C4×C11C2412yes—
110C22×Dic11C2412yes—
111C22×Dic11C2411yescharacteristic
112C22×Dic11C2414yes—
113C22×Dic11C2414yes—
114C22×Dic11C2414yes—
115C22×Dic11C2411yescharacteristic
116C11×C4⋊C4—24no—
117C11×C4⋊C4—28no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—28no—
120C11×C4⋊C4—42no—
121C11×C4⋊C4—44no—
122C42×C11#4114yes—
123C4⋊Dic11—24no—
124C4⋊Dic11—42no—
125C4⋊Dic11—42no—
126C4⋊Dic11—44no—
127C4⋊Dic11—44no—
128C4⋊Dic11—44no—
129Dic11⋊C4—28no—
130Dic11⋊C4—44no—
131Dic11⋊C4—44no—
132Dic11⋊C4—44no—
133Dic11⋊C4—44no—
134Dic11⋊C4—44no—
135C4×Dic11—24no—
136C4×Dic11—22no—
137C4×Dic11—28no—
138C4×Dic11—28no—
139C4×Dic11—28no—
140C4×Dic11—42no—
141C4×Dic11—41no—
142#2845—111no—
143#2839—114no—
144#2839—114no—
145#2839—114no—
146#2822—112no—
147#2822D1111yescharacteristic
148#2402—114no—
149#2402—114no—
150#2402—114no—
151C4×#125—111no—
152C4×#125—112no—
153C23×C11C2511yescharacteristic
154C2×C4×C11—21no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—21no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11C2×#4114yes—
168C2×C4×C11C2×#4112yes—
169C2×Dic11—24no—
170C2×Dic11—24no—
171C2×Dic11—22no—
172C2×Dic11—21no—
173C2×Dic11—24no—
174C2×Dic11—24no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—24no—
179C2×Dic11—24no—
180C2×Dic11—24no—
181C2×Dic11—24no—
182C2×Dic11—24no—
183C2×Dic112−1+414yes—
184C2×Dic112−1+412yes—
185C2×#125—111no—
186C2×#125C2×D1112yes—
187#400—114no—
188#400—114no—
189#400—114no—
190#400—114no—
191#400—114no—
192#400—114no—
193#400—114no—
194#400—114no—
195#400—114no—
196#400—114no—
197#400—114no—
198#400C2×D1114yes—
199#398—114no—
200#398—114no—
201#398—114no—
202#398—114no—
203#398—114no—
204#398—114no—
205#398—114no—
206#398—114no—
207#398—114no—
208#398—114no—
209#398C2×D1114yes—
210#398C2×D1114yes—
211#389—112no—
212#389—112no—
213#389—112no—
214#387—114no—
215#387—114no—
216#387—114no—
217#382—112no—
218#382C2×D1111yescharacteristic
219C4×C4⋊C4—114no—
220C4×C4⋊C4—114no—
221C4×C4⋊C4—112no—
222C4×C4⋊C4—112no—
223C4×C4⋊C4—112no—
224C4×C4⋊C4—114no—
225C4×C4⋊C4—114no—
226C4×C4⋊C4—114no—
227C4×C4⋊C4—114no—
228#376—114no—
229C43—111no—
230C22×C11C22×#4111yescharacteristic
231C22×C11C2×2−1+412yes—
232C22×C11C2×2−1+411yescharacteristic
233C22×C11#58511yescharacteristic
234C22×C11#58512yes—
235C4×C11—24no—
236C4×C11—22no—
237C4×C11—44no—
238C4×C11—44no—
239C4×C11—44no—
240Dic11—44no—
241Dic11—42no—
242Dic11—44no—
243Dic11—41no—
244Dic11—44no—
245Dic11#56414yes—
246#125—28no—
247#125—224no—
248C2×C4⋊C4—114no—
249C2×C4⋊C4—112no—
250C2×C4⋊C4—112no—
251C2×C4⋊C4—112no—
252C2×C4⋊C4—114no—
253C2×C4⋊C4—114no—
254C2×C4⋊C4—114no—
255C2×C4⋊C4—114no—
256C2×C4⋊C4—114no—
257C2×C4⋊C4—114no—
258C2×C4⋊C4—114no—
259C2×C4⋊C4—114no—
260C2×C4⋊C4C22×D1114yes—
261C2×C4⋊C4C22×D1114yes—
262C2×C4⋊C4C22×D1112yes—
263C2×C4⋊C4C22×D1112yes—
264C2×C4⋊C4C22×D1112yes—
265C2×C4⋊C4C22×D1114yes—
266C2×C42—111no—
267C2×C42—112no—
268C2×C42—114no—
269C2×C42—114no—
270C2×C42—114no—
271C2×C42—111no—
272C2×C42—112no—
273C2×C42C22×D1111yescharacteristic
274#95—114no—
275#95—114no—
276#95—114no—
277#95—114no—
278#95—114no—
279#95—114no—
280#95—114no—
281#95—114no—
282#95—114no—
283#95—114no—
284#95—114no—
285#95—114no—
286#95—114no—
287#95—114no—
288#95—114no—
289#95C22×D1114yes—
290#95C22×D1114yes—
291#95C22×D1114yes—
292#95C22×D1114yes—
293C2×C11#346112yes—
294C2×C11#346111yescharacteristic
295C2×C11C2×#56411yescharacteristic
296C2×C11#353112yes—
297C2×C11#353111yescharacteristic
298C22×C4—111no—
299C22×C4—112no—
300C22×C4—111no—
301C22×C4—114no—
302C22×C4—114no—
303C22×C4—114no—
304C22×C4C23×D1114yes—
305C22×C4C23×D1114yes—
306C22×C4C23×D1114yes—
307C22×C4C23×D1111yescharacteristic
308C22×C4C23×D1112yes—
309C4⋊C4—28no—
310C4⋊C4—28no—
311C4⋊C4—24no—
312C4⋊C4—24no—
313C4⋊C4—42no—
314C4⋊C4—44no—
315C4⋊C4—228no—
316C4⋊C4—224no—
317C4⋊C4—444no—
318C4⋊C4—444no—
319C4⋊C4—444no—
320C4⋊C4—444no—
321C4⋊C4—444no—
322C4⋊C4—442no—
323C4⋊C4—442no—
324C4⋊C4—444no—
325C4⋊C4—444no—
326C4⋊C4—444no—
327C42—224no—
328C42—222no—
329C42—228no—
330C42—228no—
331C42—228no—
332C42—441no—
333C42—442no—
334C42#434114yes—
335C11#3670111yescharacteristic, complemented, Sylow
336C23C24×D1111yescharacteristic
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—114no—
351C2×C4—112no—
352C2×C4—224no—
353C2×C4—222no—
354C2×C4—224no—
355C2×C4—222no—
356C2×C4—224no—
357C2×C4—221no—
358C2×C4—224no—
359C2×C4—224no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—224no—
363C2×C4—224no—
364C2×C4—224no—
365C2×C4—224no—
366C2×C4C2×#434114yes—
367C2×C4C2×#434112yes—
368C22C22×#434111yescharacteristic
369C22#1062345511yescharacteristic
370C22D11×2−1+412yes—
371C22D11×2−1+411yescharacteristic
372C22#1062345712yes—
373C4—24no—
374C4—22no—
375C4—44no—
376C4—44no—
377C4—44no—
378C4—114no—
379C4—442no—
380C4—444no—
381C4—441no—
382C4—444no—
383C4—444no—
384C2#1308204012yes—
385C2#1308204411yescharacteristic
386C2D11×#56411yescharacteristic
387C2#1308276212yes—
388C2#1308276411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, prime radical, cosocleC23×C11C25
FittingC11×#2822C2
hypercenter#2822D11
hypocenterC11#36701
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2822

Complements

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

NH ≅ G/Ntype
335. C11#36701semidirect

Maximal subgroups

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

subgroupindex
#130768912
#130768642
#130768622
#130768602
#130766832
#130719222
#130719202
#125×Dic112
#130711712
C11×#28222
#3670111