Finite Group Databasebeta

← #14912435

Subgroups — #14912435

Order 2816.

2358 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4339C211yesmaximal, characteristic
2#13071262C214yesmaximal, complemented
3#13071254C214yesmaximal, complemented
4#13071243C218yesmaximal, complemented
5#13071113C214yesmaximal, complemented
6#13071104C212yesmaximal
7#13071098C212yesmaximal, complemented
8#13071008C214yesmaximal, complemented
9C2×#10622545C211yesmaximal, characteristic, complemented
10C4×C11×#117C211yesmaximal, characteristic, complemented
11C22×#4339C2211yescharacteristic
12C2×C11×#117C2212yes—
13C22×C42×C11C2211yescharacteristic
14C2×C4×C22⋊D11C2214yes—
15C2×#66979C2211yescharacteristic
16C22×C4×Dic11C2212yes—
17C4×#4339C4116yescomplemented
18C2×C4×D44C2212yes—
19C2×#66925C2212yes—
20C2×C42×D11C2212yes—
21C2×C4×Dic22C2212yes—
22C4×C11×C4⋊C4C2214yes—
23C4×C11×C22⋊C4C2214yes—
24C11×#376C2212yes—
25C43×C11C2212yes—
26C2×C11⋊#95C2214yes—
27#10622601C2214yes—
28#10622587C2214yes—
29#10622586C2218yes—
30#10622571C2218yes—
31#10622559C2218yes—
32#10622553C22116yes—
33C4×(C2×D11)⋊C4C2218yes—
34#10622546C22116yes—
35#10622545C2212yes—
36#10622545C2214yes—
37#10622545C2212yes—
38C4×Dic11⋊C4C2218yes—
39#10622280C2218yes—
40#10622277C2218yes—
41#10622264C2218yes—
42#10622263C2218yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C22×C22⋊D11C2312yes—
46C23×Dic11C2314yes—
47C2×#4339—28no—
48C2×#4339C2×C418yes—
49C22×D44C2311yescharacteristic
50C22×C4×D11C2312yes—
51C22×C4×D11C2314yes—
52C22×Dic22C2311yescharacteristic
53C11×#117—28no—
54C2×C11×C4⋊C4C2314yes—
55C2×C11×C22⋊C4C2314yes—
56C2×C42×C11C2×C418yes—
57C2×C42×C11C2314yes—
58C2×C42×C11C2318yes—
59C2×C42×C11C2312yes—
60C2×C42×C11C2311yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11C2312yes—
63C4×C22⋊D11C2×C4132yes—
64C2×(C2×D11)⋊C4C23116yes—
65C2×(C2×D11)⋊C4C2314yes—
66#66979C2×C418yes—
67C2×C4⋊Dic11C2312yes—
68C2×Dic11⋊C4C23116yes—
69C2×Dic11⋊C4C2314yes—
70C2×C4×Dic11—28no—
71C2×C4×Dic11C2314yes—
72C2×C4×Dic11C2314yes—
73C2×C4×Dic11C2314yes—
74C2×C4×Dic11C2312yes—
75C4×D44C2×C4116yescomplemented
76#66925C2×C4116yescomplemented
77C42×D11C2×C4116yescomplemented
78C4×Dic22C2×C4116yescomplemented
79C11×#95C2318yes—
80C11⋊#95C2314yes—
81C11⋊#95C23116yes—
82C11⋊#95C2314yes—
83C11⋊#95C23116yes—
84C11⋊#95C2318yes—
85#34056—111nomaximal, Sylow
86C24×C11C2411yescharacteristic
87C23×D11C2412yes—
88C22×C4×C11—44no—
89C22×C4×C11C22×C418yes—
90C22×C4×C11C22×C414yes—
91C22×C4×C11#4118yes—
92C22×C4×C11C2418yes—
93C22×C4×C11C2412yes—
94C22×C4×C11C2412yes—
95C22×C4×C11C2411yescharacteristic
96C22×C4×C11C2411yescharacteristic
97C2×C22⋊D11—28no—
98C2×C22⋊D11C22×C418yes—
99C22×Dic11—28no—
100C22×Dic11—48no—
101C22×Dic11C2418yes—
102C22×Dic11C2412yes—
103C22×Dic11C2414yes—
104#4339—232no—
105C2×D44—24no—
106C2×D44C22×C414yes—
107C2×C4×D11—28no—
108C2×C4×D11—48no—
109C2×C4×D11C22×C418yes—
110C2×C4×D11C22×C4116yes—
111C2×Dic22—24no—
112C2×Dic22C22×C414yes—
113C11×C4⋊C4—28no—
114C11×C22⋊C4—28no—
115C42×C11—28no—
116C42×C11—48no—
117C42×C11C22×C418yes—
118C42×C11C22×C414yes—
119C42×C11C22×C414yes—
120C22⋊Dic11C22×C418yes—
121(C2×D11)⋊C4—416no—
122(C2×D11)⋊C4C22×C4116yes—
123C4⋊Dic11C22×C418yes—
124Dic11⋊C4—416no—
125Dic11⋊C4C22×C4116yes—
126C4×Dic11—28no—
127C4×Dic11—28no—
128C4×Dic11C22×C4116yes—
129C4×Dic11C22×C418yes—
130C2×C4×#41—111no—
131#2320—114no—
132#2319—114no—
133#2318—118no—
134#2298—114no—
135#2297—112no—
136#2296—112no—
137#2283—114no—
138C4×#117D1111yescharacteristic, complemented
139C2×#376—111no—
140C23×C11—24no—
141C23×C11C23×C412yes—
142C23×C11C2×#4114yes—
143C23×C11C2511yescharacteristic
144C22×D11—24no—
145C22×D11—28no—
146C22×D11C23×C414yes—
147C2×C4×C11—24no—
148C2×C4×C11—24no—
149C2×C4×C11—28no—
150C2×C4×C11—216no—
151C2×C4×C11—48no—
152C2×C4×C11#117116yes—
153C2×C4×C11C23×C414yes—
154C2×C4×C11C23×C414yes—
155C2×C4×C11C23×C412yes—
156C2×C4×C11C23×C412yes—
157C2×C4×C11C2×#4114yes—
158C2×C4×C11C2×#4114yes—
159C22⋊D11—216no—
160C2×Dic11—24no—
161C2×Dic11—28no—
162C2×Dic11—28no—
163C2×Dic11—28no—
164C2×Dic11—28no—
165C2×Dic11—416no—
166C2×Dic11C23×C414yes—
167C2×Dic11C23×C418yes—
168D44—28no—
169C4×D11—216no—
170C4×D11—416no—
171Dic22—28no—
172C22×#41—111no—
173C4×#41—1116no—
174C2×C4×Q8—112no—
175C2×C4×D4—114no—
176C2×C4×D4—112no—
177C2×#117—111no—
178C2×#117—112no—
179C2×#117C2×D1112yes—
180C22×C42—112no—
181C22×C42—112no—
182C22×C42C2×D1111yescharacteristic
183#391—114no—
184#390—114no—
185#389—118no—
186#388—1116no—
187#387—1116no—
188#386—118no—
189#385—118no—
190#383—118no—
191#382—118no—
192#381—118no—
193#380—118no—
194C4×C4⋊C4—118no—
195C4×C4⋊C4C2×D1114yes—
196C4×C22⋊C4—118no—
197C4×C22⋊C4C2×D1114yes—
198#376—114no—
199#376—112no—
200#376—112no—
201#376C2×D1112yes—
202C2×#95—114no—
203C43C2×D1112yes—
204C22×C11—24no—
205C22×C11—28no—
206C22×C11C2×#11714yes—
207C22×C11C24×C411yescharacteristic
208C22×C11C22×#4112yes—
209C22×C11#58514yes—
210C2×D11—24no—
211C2×D11—28no—
212C2×D11—48no—
213C4×C11—24no—
214C4×C11—24no—
215C4×C11—48no—
216C4×C11C2×#11714yes—
217C4×C11C2×#11714yes—
218Dic11—24no—
219Dic11—28no—
220Dic11—48no—
221C2×#41—118no—
222C2×#41—228no—
223C22×Q8—111no—
224C22×D4—112no—
225C22×D4—111no—
226C23×C4—112no—
227C23×C4—114no—
228C23×C4—114no—
229C23×C4C22×D1112yes—
230C23×C4C22×D1111yescharacteristic
231C4×Q8—1116no—
232C4×D4—1132no—
233C4×D4—1116no—
234#117—28no—
235#117—118no—
236#117—1116no—
237C2×C4⋊C4—114no—
238C2×C4⋊C4—112no—
239C2×C4⋊C4—1116no—
240C2×C4⋊C4C22×D1114yes—
241C2×C22⋊C4—112no—
242C2×C22⋊C4—114no—
243C2×C22⋊C4—1116no—
244C2×C22⋊C4C22×D1114yes—
245C2×C42—114no—
246C2×C42—112no—
247C2×C42—1116no—
248C2×C42—114no—
249C2×C42—114no—
250C2×C42—228no—
251C2×C42C4×D1118yes—
252C2×C42C22×D1114yes—
253C2×C42C22×D1118yes—
254C2×C42C22×D1112yes—
255C2×C42C22×D1111yescharacteristic
256C2×C42C22×D1111yescharacteristic
257#95—114no—
258#95—114no—
259#95—118no—
260#95—1116no—
261#95—1116no—
262#95C22×D1118yes—
263C2×C11—24no—
264C2×C11C22×#11711yescharacteristic
265C2×C11#342812yes—
266C2×C11#345514yes—
267D11—44no—
268C24—112no—
269C24C23×D1111yescharacteristic
270#41—2232no—
271C2×Q8—114no—
272C2×Q8—224no—
273C2×D4—118no—
274C2×D4—114no—
275C2×D4—228no—
276C2×D4—224no—
277C22×C4—44no—
278C22×C4—112no—
279C22×C4—114no—
280C22×C4—118no—
281C22×C4—1116no—
282C22×C4—118no—
283C22×C4—228no—
284C22×C4—228no—
285C22×C4—448no—
286C22×C4—448no—
287C22×C4C2×C4×D1118yes—
288C22×C4C2×C4×D1114yes—
289C22×C4#433918yes—
290C22×C4C23×D1118yes—
291C22×C4C23×D1112yes—
292C22×C4C23×D1112yes—
293C22×C4C23×D1111yescharacteristic
294C22×C4C23×D1111yescharacteristic
295C4⋊C4—28no—
296C4⋊C4—1116no—
297C4⋊C4—118no—
298C4⋊C4—4416no—
299C22⋊C4—28no—
300C22⋊C4—118no—
301C22⋊C4—1116no—
302C22⋊C4—4416no—
303C42—28no—
304C42—48no—
305C42—118no—
306C42—1116no—
307C42—228no—
308C42—228no—
309C42C2×C4×D1114yes—
310C42C2×C4×D1114yes—
311C42C2×C4×D1118yes—
312C11#3405611yescharacteristic, complemented, Sylow
313C23—24no—
314C23—114no—
315C23—224no—
316C23—228no—
317C23C22×C4×D1112yes—
318C23C2×#433914yes—
319C23C24×D1111yescharacteristic
320Q8—228no—
321D4—2216no—
322D4—228no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—28no—
326C2×C4—216no—
327C2×C4—48no—
328C2×C4—118no—
329C2×C4—114no—
330C2×C4—224no—
331C2×C4—228no—
332C2×C4—2216no—
333C2×C4—228no—
334C2×C4—228no—
335C2×C4—228no—
336C2×C4—4416no—
337C2×C4—4416no—
338C2×C4#66925116yes—
339C2×C4C22×C4×D1114yes—
340C2×C4C22×C4×D1114yes—
341C2×C4C22×C4×D1112yes—
342C2×C4C22×C4×D1112yes—
343C2×C4C2×#433914yes—
344C2×C4C2×#433914yes—
345C22—28no—
346C22—24no—
347C22—224no—
348C22—228no—
349C22—448no—
350C22C2×#6692514yes—
351C22C23×C4×D1111yescharacteristic
352C22C22×#433912yes—
353C22#1062345314yes—
354C4—24no—
355C4—24no—
356C4—48no—
357C4—224no—
358C4—228no—
359C4—448no—
360C4C2×#6692514yes—
361C4C2×#6692514yes—
362C2—24no—
363C2—444no—
364C2C22×#6692511yescharacteristic
365C2#1308181712yes—
366C2#1308200114yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC4×C11×#117C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenterC4×#117D11
hypocenterC11#34056
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
2. #13071262C2semidirect
3. #13071254C2semidirect
4. #13071243C2semidirect
5. #13071113C2semidirect
7. #13071098C2semidirect
8. #13071008C2semidirect
9. C2×#10622545C2semidirect
10. C4×C11×#117C2semidirect
17. C4×#4339C4semidirect
75. C4×D44C2×C4semidirect
76. #66925C2×C4semidirect
77. C42×D11C2×C4semidirect
78. C4×Dic22C2×C4semidirect
138. C4×#117D11semidirect
312. C11#34056semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43392
#130712622
#130712542
#130712432
#130711132
#130711042
#130710982
#130710082
C2×#106225452
C4×C11×#1172
#3405611