Finite Group Databasebeta

← #14645129

Subgroups — #14645129

Order 2816.

1518 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 1518 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66983C211yesmaximal, characteristic
2#13068526C211yesmaximal, characteristic, complemented
3C2×#10622106C214yesmaximal, complemented
4C11×#1779C211yesmaximal, characteristic, complemented
5C24×C4×C11C2211yescharacteristic
6C23×C22⋊D11C412yes—
7C23×D44C411yescharacteristic
8C2×#66983—22no—
9C2×#66983—22no—
10C2×#66983—28no—
11C22×(C2×D11)⋊C4C2212yes—
12C22×C4⋊Dic11C411yescharacteristic
13C2×C11×C22⋊C8—22no—
14C2×C11×C22⋊C8C2212yes—
15C2×C22⋊(C11⋊C8)—22no—
16C2×C22⋊(C11⋊C8)C2212yes—
17#10622106—28no—
18C25×C11C2×C411yescharacteristic
19C24×D11C2×C412yes—
20C23×C4×C11—24no—
21C23×C4×C11—44no—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D412yes—
24C23×C4×C11D412yes—
25C23×C4×C11C2311yescharacteristic
26C22×C22⋊D11—24no—
27C22×C22⋊D11—24no—
28C22×C22⋊D11—24no—
29C22×C22⋊D11—48no—
30C23×Dic11C2×C412yes—
31C22×D44—24no—
32C22×D44—22no—
33C22×D44—44no—
34C22×C8×C11—22no—
35#66983—216no—
36#66983—216no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4—24no—
39C2×(C2×D11)⋊C4—22no—
40C2×(C2×D11)⋊C4D418yes—
41C2×C4⋊Dic11—22no—
42C2×C4⋊Dic11—24no—
43C22×C11⋊C8—22no—
44C11×C22⋊C8—24no—
45C11×C22⋊C8—44no—
46C22⋊(C11⋊C8)—24no—
47C22⋊(C11⋊C8)—44no—
48#8307—111nomaximal, Sylow
49C24×C11—24no—
50C24×C11—22no—
51C24×C11—22no—
52C24×C11—22no—
53C24×C11—42no—
54C24×C11C22⋊C412yes—
55C24×C11C22×C411yescharacteristic
56C23×D11—22no—
57C23×D11—22no—
58C23×D11—24no—
59C23×D11—24no—
60C23×D11—44no—
61C23×D11—44no—
62C23×D11C22⋊C414yes—
63C22×C4×C11—22no—
64C22×C4×C11—24no—
65C22×C4×C11—24no—
66C22×C4×C11—24no—
67C22×C4×C11—24no—
68C22×C4×C11—24no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11—42no—
72C22×C4×C11—416no—
73C22×C4×C11C22⋊C412yes—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D414yes—
77C2×C22⋊D11—216no—
78C2×C22⋊D11—416no—
79C2×C22⋊D11—48no—
80C2×C22⋊D11—416no—
81C2×C22⋊D11—48no—
82C22×Dic11—22no—
83C22×Dic11—22no—
84C22×Dic11—44no—
85C22×Dic11C22⋊C414yes—
86C2×D44—28no—
87C2×D44—416no—
88C2×D44—44no—
89C2×D44—44no—
90C2×C8×C11—44no—
91C2×C8×C11—42no—
92(C2×D11)⋊C4—28no—
93(C2×D11)⋊C4—28no—
94C4⋊Dic11—28no—
95C2×C11⋊C8—44no—
96C2×C11⋊C8—42no—
97C22×#121—111no—
98#1779—111no—
99#1779D1111yescharacteristic, complemented
100C2×#323—114no—
101C23×C11—22no—
102C23×C11—22no—
103C23×C11—28no—
104C23×C11—22no—
105C23×C11—22no—
106C23×C11—22no—
107C23×C11—22no—
108C23×C11—22no—
109C23×C11—22no—
110C23×C11—48no—
111C23×C11—48no—
112C23×C11—44no—
113C23×C11—44no—
114C23×C11#10014yes—
115C23×C11C2×C22⋊C412yes—
116C23×C11C2×C22⋊C411yescharacteristic
117C23×C11#13112yes—
118C23×C11#13112yes—
119C22×D11—24no—
120C22×D11—28no—
121C22×D11—44no—
122C22×D11—44no—
123C22×D11—42no—
124C22×D11—42no—
125C22×D11—44no—
126C22×D11—44no—
127C22×D11—44no—
128C22×D11—44no—
129C22×D11—44no—
130C22×D11—88no—
131C22×D11—88no—
132C2×C4×C11—28no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—44no—
138C2×C4×C11—48no—
139C2×C4×C11—48no—
140C2×C4×C11#9914yes—
141C2×C4×C11#12012yes—
142C2×C4×C11#12012yes—
143C22⋊D11—432no—
144C2×Dic11—24no—
145C2×Dic11—44no—
146C2×Dic11—44no—
147C2×Dic11—44no—
148D44—416no—
149C8×C11—82no—
150C11⋊C8—82no—
151C23×D4—112no—
152C23×D4—111no—
153C24×C4C2×D1111yescharacteristic
154C2×#121—228no—
155C2×#121—222no—
156C2×#121—222no—
157C22×C4⋊C4—111no—
158C22×C22⋊C4—112no—
159C2×C22⋊C8—22no—
160C2×C22⋊C8—112no—
161C2×C22⋊C8—222no—
162C2×C22⋊C8C2×D1112yes—
163#323—228no—
164C22×C11—24no—
165C22×C11—24no—
166C22×C11—22no—
167C22×C11—22no—
168C22×C11—24no—
169C22×C11—24no—
170C22×C11—24no—
171C22×C11—416no—
172C22×C11—42no—
173C22×C11—42no—
174C22×C11—42no—
175C22×C11—42no—
176C22×C11#37911yescharacteristic
177C22×C11#40811yescharacteristic
178C22×C11#40811yescharacteristic
179C22×C11#40814yes—
180C22×C11C2×#9912yes—
181C22×C11C2×#10012yes—
182C2×D11—44no—
183C2×D11—44no—
184C2×D11—44no—
185C2×D11—88no—
186C2×D11—84no—
187C2×D11—84no—
188C2×D11—88no—
189C4×C11—24no—
190C4×C11—22no—
191C4×C11—22no—
192Dic11—44no—
193C25—112no—
194C25C4×D1111yescharacteristic
195C22×D4—224no—
196C22×D4—224no—
197C22×D4—224no—
198C22×D4—224no—
199C22×D4—222no—
200C22×D4—444no—
201C22×D4—448no—
202C23×C4—24no—
203C23×C4—44no—
204C23×C4—112no—
205C23×C4C4×D1111yescharacteristic
206C23×C4D4412yes—
207C23×C4C22⋊D1112yes—
208C23×C4C22×D1111yescharacteristic
209C22×C8—22no—
210C22×C8—222no—
211#121—2216no—
212#121—2216no—
213C2×C4⋊C4—224no—
214C2×C4⋊C4—222no—
215C2×C22⋊C4—118no—
216C2×C22⋊C4—222no—
217C2×C22⋊C4—224no—
218C2×C22⋊C4—222no—
219C22⋊C8—24no—
220C22⋊C8—44no—
221C22⋊C8—224no—
222C22⋊C8—444no—
223C2×C11—24no—
224C2×C11—44no—
225C2×C11#147112yes—
226C2×C11#147112yes—
227C2×C11#178011yescharacteristic
228C2×C11#178111yescharacteristic
229C2×C11#178311yescharacteristic
230D11—84no—
231C24—24no—
232C24—22no—
233C24—22no—
234C24—22no—
235C24—42no—
236C24—114no—
237C24—222no—
238C24—222no—
239C24—224no—
240C24—224no—
241C24—444no—
242C24—444no—
243C24(C2×D11)⋊C412yes—
244C24C2×C4×D1111yescharacteristic
245C2×D4—228no—
246C2×D4—2216no—
247C2×D4—4416no—
248C2×D4—444no—
249C2×D4—4416no—
250C2×D4—448no—
251C2×D4—4416no—
252C2×D4—448no—
253C2×D4—444no—
254C22×C4—22no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—416no—
264C22×C4—114no—
265C22×C4—222no—
266C22×C4—222no—
267C22×C4—444no—
268C22×C4(C2×D11)⋊C412yes—
269C22×C4C2×D4411yescharacteristic
270C22×C4D4×D1114yes—
271C22×C4C2×C22⋊D1111yescharacteristic
272C2×C8—44no—
273C2×C8—42no—
274C2×C8—444no—
275C2×C8—442no—
276C4⋊C4—228no—
277C22⋊C4—228no—
278C22⋊C4—228no—
279C11#830711yescharacteristic, complemented, Sylow
280C23—22no—
281C23—22no—
282C23—28no—
283C23—22no—
284C23—22no—
285C23—22no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—48no—
290C23—48no—
291C23—44no—
292C23—44no—
293C23—224no—
294C23—228no—
295C23—444no—
296C23—444no—
297C23—444no—
298C23—444no—
299C23—442no—
300C23—442no—
301C23—444no—
302C23—444no—
303C23—444no—
304C23—888no—
305C23—888no—
306C23#6688714yes—
307C23C22⋊C4×D1112yes—
308C23#6695412yes—
309C23#6696012yes—
310C23C2×(C2×D11)⋊C411yescharacteristic
311D4—4416no—
312D4—4432no—
313C2×C4—28no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—44no—
319C2×C4—48no—
320C2×C4—48no—
321C2×C4—224no—
322C2×C4—444no—
323C2×C4—444no—
324C2×C4—444no—
325C2×C4#6687014yes—
326C2×C4#6693512yes—
327C2×C4#6699012yes—
328C8—82no—
329C8—882no—
330C22—24no—
331C22—24no—
332C22—22no—
333C22—22no—
334C22—24no—
335C22—24no—
336C22—24no—
337C22—416no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22—42no—
342C22—444no—
343C22—444no—
344C22—444no—
345C22—888no—
346C22—888no—
347C22—884no—
348C22—884no—
349C22#1062234014yes—
350C22C2×#6687012yes—
351C22#1062256811yescharacteristic
352C22#1062272311yescharacteristic
353C22#1062274211yescharacteristic
354C22C2×#6688712yes—
355C4—22no—
356C4—22no—
357C4—24no—
358C4—444no—
359C2—24no—
360C2—44no—
361C2—884no—
362C2#1306697512yes—
363C2#1306697712yes—
364C2#1306852711yescharacteristic
365C2#1306853011yescharacteristic
366C2#1306853611yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1779C2
socleC23×C11C2×C22⋊C4
prime radicalC22×#66983C2
cosocleC23×C4×C11C23
hypercenter#1779D11
hypocenterC11#8307
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. #13068526C2semidirect
3. C2×#10622106C2semidirect
4. C11×#1779C2semidirect
99. #1779D11semidirect
279. C11#8307semidirect

Maximal subgroups

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

subgroupindex
C22×#669832
#130685262
C2×#106221062
C11×#17792
#830711