Finite Group Databasebeta

← #14960492

Subgroups — #14960492

Order 2816.

1356 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076854C214yesmaximal, complemented
2#13076809C214yesmaximal
3#13076790C214yesmaximal, complemented
4#13076766C214yesmaximal
5#13071923C214yesmaximal, complemented
6#13071921C211yesmaximal, characteristic, complemented
7#13071916C214yesmaximal
8#13071909C211yesmaximal, characteristic, complemented
9#13071884C212yesmaximal
10#13071093C212yesmaximal, complemented
11C11×#2298C211yesmaximal, characteristic
12C2×C11×#117C2211yescharacteristic
13C2×C4×Dic22C2212yes—
14C11×#388C2214yes—
15C11×#387C2214yes—
16C4×C11×C4⋊C4C2212yes—
17C4×C11×C22⋊C4C2212yes—
18C11×#376C2211yescharacteristic
19C43×C11C2211yescharacteristic
20C4×C22⋊Dic11C2214yes—
21#10622599C2212yes—
22#10622597C2214yes—
23#10622597C2214yes—
24#10622596C2214yes—
25#10622595C2214yes—
26#10622593C2214yes—
27#10622592C2212yes—
28#10622566C2214yes—
29#10622565C2214yes—
30#10622565C2214yes—
31#10622562C2212yes—
32#10622561C2214yes—
33#10622561C2214yes—
34#10622560C2212yes—
35C4×C4⋊Dic11C2212yes—
36C4×C4⋊Dic11C2214yes—
37#10622546C2214yes—
38#10622546C2214yes—
39#10622545C2214yes—
40C4×Dic11⋊C4C2214yes—
41C4×Dic11⋊C4C2214yes—
42C4×Dic11⋊C4C2214yes—
43#10622542C2214yes—
44#10622541C2214yes—
45C11⋊#401C2214yes—
46#10622274C2214yes—
47#10622273C2214yes—
48#10622273C2214yes—
49#10622272C2214yes—
50#10622272C2214yes—
51#10622271C2214yes—
52#10622271C2214yes—
53#10622271C2214yes—
54#10622270C2214yes—
55#10622270C2214yes—
56#10622269C2214yes—
57C23×C4×C11C2311yescharacteristic
58C22×Dic22C2312yes—
59C11×#117—24no—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2314yes—
62C2×C11×C22⋊C4C2312yes—
63C2×C11×C22⋊C4C2314yes—
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2312yes—
66C2×C42×C11C2312yes—
67C2×C42×C11C2314yes—
68C2×C42×C11C2311yescharacteristic
69C2×C22⋊Dic11C2314yes—
70C2×C22⋊Dic11C2314yes—
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2314yes—
73C2×C4⋊Dic11C2314yes—
74C2×C4⋊Dic11C2314yes—
75C2×Dic11⋊C4C2314yes—
76C2×Dic11⋊C4C2314yes—
77C2×Dic11⋊C4C2314yes—
78C2×Dic11⋊C4C2314yes—
79C2×Dic11⋊C4C2314yes—
80C2×Dic11⋊C4C2314yes—
81C2×Dic11⋊C4C2314yes—
82C2×C4×Dic11C2314yes—
83C2×C4×Dic11C2314yes—
84C4×Dic22—28no—
85C11×#95C2314yes—
86C11×#95C2314yes—
87C11×#95C2314yes—
88C11⋊#95C2314yes—
89C11⋊#95C2312yes—
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⋊#95C2312yes—
104#36700—111nomaximal, Sylow
105C24×C11C2411yescharacteristic
106C22×C4×C11—22no—
107C22×C4×C11—24no—
108C22×C4×C11C2411yescharacteristic
109C22×C4×C11C2414yes—
110C22×C4×C11C2414yes—
111C22×C4×C11C2412yes—
112C22×C4×C11C2412yes—
113C22×C4×C11C2411yescharacteristic
114C22×Dic11C2414yes—
115C22×Dic11C2414yes—
116C22×Dic11C2414yes—
117C22×Dic11C2414yes—
118C2×Dic22—24no—
119C2×Dic22—44no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—44no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—44no—
124C42×C11—22no—
125C42×C11—24no—
126C42×C11—24no—
127C42×C11—44no—
128C42×C11#4114yes—
129C22⋊Dic11—44no—
130C22⋊Dic11—44no—
131C4⋊Dic11—24no—
132C4⋊Dic11—44no—
133C4⋊Dic11—44no—
134C4⋊Dic11—44no—
135Dic11⋊C4—28no—
136Dic11⋊C4—44no—
137Dic11⋊C4—44no—
138Dic11⋊C4—44no—
139Dic11⋊C4—44no—
140Dic11⋊C4—44no—
141Dic11⋊C4—44no—
142C4×Dic11—28no—
143C4×Dic11—28no—
144#2839—114no—
145#2836—114no—
146#2833—114no—
147#2831—114no—
148#2402—114no—
149#2402—111no—
150#2401—114no—
151#2399—111no—
152#2396—112no—
153#2298D1111yescharacteristic
154#2295—112no—
155C23×C11—21no—
156C23×C11—22no—
157C23×C11—24no—
158C23×C11C2511yescharacteristic
159C2×C4×C11—24no—
160C2×C4×C11—22no—
161C2×C4×C11—21no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—22no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—44no—
171C2×C4×C11C2×#4114yes—
172C2×C4×C11C2×#4112yes—
173C2×C4×C112−1+414yes—
174C2×Dic11—24no—
175C2×Dic11—24no—
176C2×Dic11—24no—
177C2×Dic11—24no—
178C2×Dic11—24no—
179C2×Dic11—24no—
180C2×Dic11—24no—
181C2×Dic11—24no—
182C2×Dic11—24no—
183C2×Dic11—24no—
184C2×Dic11—24no—
185C2×Dic11—24no—
186Dic22—48no—
187C2×C4×Q8—112no—
188C2×#117C2×D1111yescharacteristic
189#401—114no—
190#400—114no—
191#400—112no—
192#400—114no—
193#400—114no—
194#400—114no—
195#400—114no—
196#400—114no—
197#400—114no—
198#400—114no—
199#399—112no—
200#398—114no—
201#398—114no—
202#398—114no—
203#398—114no—
204#398—114no—
205#398—114no—
206#398—114no—
207#397—114no—
208#397—114no—
209#397—114no—
210#396—114no—
211#396—114no—
212#395—112no—
213#395—114no—
214#393—112no—
215#391—114no—
216#389—114no—
217#388C2×D1114yes—
218#387—114no—
219#387—114no—
220#387C2×D1114yes—
221C4×C4⋊C4—114no—
222C4×C4⋊C4—114no—
223C4×C4⋊C4—114no—
224C4×C4⋊C4—112no—
225C4×C4⋊C4—114no—
226C4×C4⋊C4C2×D1112yes—
227C4×C22⋊C4—114no—
228C4×C22⋊C4C2×D1112yes—
229#376—114no—
230#376C2×D1111yescharacteristic
231C43C2×D1111yescharacteristic
232C22×C11—41no—
233C22×C11—42no—
234C22×C11—44no—
235C22×C11C22×#4111yescharacteristic
236C22×C11C2×2−1+412yes—
237C22×C11#58514yes—
238C4×C11—24no—
239C4×C11—41no—
240C4×C11—42no—
241C4×C11—44no—
242C4×C11—44no—
243C4×C11#54114yes—
244Dic11—44no—
245Dic11—44no—
246Dic11—44no—
247Dic11—44no—
248C22×Q8—112no—
249C23×C4C22×D1111yescharacteristic
250C4×Q8—228no—
251#117—24no—
252C2×C4⋊C4—114no—
253C2×C4⋊C4—112no—
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⋊C4—114no—
261C2×C4⋊C4—114no—
262C2×C4⋊C4—114no—
263C2×C4⋊C4C22×D1112yes—
264C2×C4⋊C4C22×D1114yes—
265C2×C22⋊C4—114no—
266C2×C22⋊C4—114no—
267C2×C22⋊C4C22×D1112yes—
268C2×C22⋊C4C22×D1114yes—
269C2×C42—114no—
270C2×C42—114no—
271C2×C42C22×D1111yescharacteristic
272C2×C42C22×D1112yes—
273C2×C42C22×D1112yes—
274C2×C42C22×D1114yes—
275C2×C42C22×D1111yescharacteristic
276#95—114no—
277#95—114no—
278#95—114no—
279#95—114no—
280#95—114no—
281#95—114no—
282#95—112no—
283#95—112no—
284#95—114no—
285#95—114no—
286#95—114no—
287#95—114no—
288#95—114no—
289#95—114no—
290#95—114no—
291#95—114no—
292#95C22×D1114yes—
293#95C22×D1114yes—
294#95C22×D1114yes—
295C2×C11—81no—
296C2×C11C2×#54111yescharacteristic
297C2×C11#345512yes—
298C2×C11#353114yes—
299C24C23×D1111yescharacteristic
300C2×Q8—224no—
301C2×Q8—444no—
302C22×C4—22no—
303C22×C4—24no—
304C22×C4—114no—
305C22×C4—114no—
306C22×C4—114no—
307C22×C4—114no—
308C22×C4C23×D1111yescharacteristic
309C22×C4C23×D1114yes—
310C22×C4C23×D1114yes—
311C22×C4C23×D1112yes—
312C22×C4C23×D1112yes—
313C22×C4C23×D1111yescharacteristic
314C4⋊C4—24no—
315C4⋊C4—44no—
316C4⋊C4—228no—
317C4⋊C4—224no—
318C4⋊C4—444no—
319C4⋊C4—444no—
320C4⋊C4—444no—
321C4⋊C4—444no—
322C4⋊C4—444no—
323C4⋊C4—444no—
324C4⋊C4—444no—
325C4⋊C4—444no—
326C4⋊C4—444no—
327C22⋊C4—24no—
328C22⋊C4—44no—
329C22⋊C4—444no—
330C22⋊C4—444no—
331C42—22no—
332C42—24no—
333C42—24no—
334C42—44no—
335C42—228no—
336C42—228no—
337C42#433914yes—
338C11#3670011yescharacteristic, complemented, Sylow
339C23—21no—
340C23—22no—
341C23—24no—
342C23C24×D1111yescharacteristic
343Q8—448no—
344C2×C4—24no—
345C2×C4—22no—
346C2×C4—21no—
347C2×C4—24no—
348C2×C4—24no—
349C2×C4—22no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—44no—
356C2×C4—224no—
357C2×C4—224no—
358C2×C4—224no—
359C2×C4—224no—
360C2×C4—224no—
361C2×C4—224no—
362C2×C4—224no—
363C2×C4—224no—
364C2×C4—224no—
365C2×C4—224no—
366C2×C4—224no—
367C2×C4—224no—
368C2×C4C2×#433914yes—
369C2×C4C2×#433912yes—
370C2×C4#6704314yes—
371C22—41no—
372C22—44no—
373C22—42no—
374C22C22×#433911yescharacteristic
375C22C2×#6704312yes—
376C22#1062345314yes—
377C4—24no—
378C4—41no—
379C4—44no—
380C4—44no—
381C4—42no—
382C4—444no—
383C4—444no—
384C4—444no—
385C4—444no—
386C4#1062304914yes—
387C2—81no—
388C2C2×#1062304911yescharacteristic
389C2#1308200112yes—
390C2#1308276114yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2298C2
prime radicalC24×C11C24
hypercenter#2298D11
hypocenterC11#36700
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2298

Complements

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

NH ≅ G/Ntype
1. #13076854C2semidirect
3. #13076790C2semidirect
5. #13071923C2semidirect
6. #13071921C2semidirect
8. #13071909C2semidirect
10. #13071093C2semidirect
338. C11#36700semidirect

Maximal subgroups

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

subgroupindex
#130768542
#130768092
#130767902
#130767662
#130719232
#130719212
#130719162
#130719092
#130718842
#130710932
C11×#22982
#3670011