Finite Group Databasebeta

← #14645841

Subgroups — #14645841

Order 2816.

1516 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1516 conjugacy classes of subgroups — too many to draw. Only its 171 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
1C2×#10623248C211yesmaximal, characteristic
2#13068613C212yesmaximal, complemented
3C2×#10622182C211yesmaximal, characteristic, complemented
4C2×#10622097C212yesmaximal, complemented
5C11×#1957C211yesmaximal, characteristic, complemented
6C22×D4×D11—22no—
7C2×C11×#127C2211yescharacteristic
8C2×#66991—22no—
9C2×#66990—22no—
10#10623248—22no—
11#10623248—24no—
12#10623248C414yescomplemented
13C2×C4×D44C2212yes—
14C2×C11×#102—22no—
15C2×C4×C8×C11C2211yescharacteristic, complemented
16C11×#384C2211yescharacteristic, complemented
17C2×#66873—22no—
18C2×C4⋊(C11⋊C8)C2212yescomplemented
19#10622182—22no—
20#10622167—22no—
21#10622097—24no—
22C24×D11—22no—
23C22×D4×C11—22no—
24C22×D4×C11D412yes—
25C22×C22⋊D11—24no—
26C2×D4×D11—28no—
27C2×D4×D11—28no—
28C2×D4×D11—44no—
29C2×D4×D11—44no—
30C2×D4×D11—44no—
31C2×D4×D11—44no—
32C22×D44D412yes—
33C22×C4×D11—22no—
34C22×C8×C11—21no—
35C11×#127—22no—
36C11×#127C2×C412yes—
37C11×#127D412yes—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41C2×C22⋊Dic11—22no—
42#66991—28no—
43#66991—28no—
44#66990—28no—
45#66990—28no—
46C2×(C2×D11)⋊C4—22no—
47C2×C4⋊Dic11D412yes—
48C22×C11⋊C8—22no—
49C4×D44—22no—
50C4×D44—22no—
51C4×D44C2×C414yes—
52C4×D44D414yes—
53C11×#102—44no—
54C4×C8×C11—22no—
55#66873—44no—
56C4⋊(C11⋊C8)—22no—
57C4⋊(C11⋊C8)—22no—
58#8443—111nomaximal, Sylow
59C24×C11—22no—
60C23×D11—22no—
61C23×D11—28no—
62C23×D11—48no—
63C23×D11—48no—
64C23×D11—82no—
65C23×D11—82no—
66C2×D4×C11—24no—
67C2×D4×C11—24no—
68C2×D4×C11—22no—
69C2×D4×C11—42no—
70C2×D4×C11—42no—
71C2×D4×C11—42no—
72C2×D4×C11—42no—
73C2×D4×C11—42no—
74C2×D4×C11—42no—
75C2×D4×C11C22⋊C414yes—
76C22×C4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D412yes—
79C2×C22⋊D11—216no—
80C2×C22⋊D11—48no—
81C2×C22⋊D11—48no—
82C22×Dic11—22no—
83D4×D11—416no—
84D4×D11—416no—
85D4×D11—416no—
86D4×D11—416no—
87C2×D44—22no—
88C2×D44—22no—
89C2×D44—22no—
90C2×D44C22⋊C414yes—
91C2×D44D814yes—
92C2×D44SD1614yes—
93C2×C4×D11—24no—
94C2×C4×D11—24no—
95C2×C4×D11—42no—
96C2×C4×D11—42no—
97C2×C4×D11—42no—
98C2×C4×D11—42no—
99C2×C8×C11—22no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—42no—
104C11×C4⋊C4—42no—
105C42×C11C22×C411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D412yes—
108C22⋊Dic11—28no—
109(C2×D11)⋊C4—24no—
110(C2×D11)⋊C4—24no—
111C4⋊Dic11—22no—
112C4⋊Dic11C22⋊C414yes—
113C2×C11⋊C8—42no—
114C2×C11⋊C8—42no—
115C2×C11⋊C8—42no—
116C2×D42—111no—
117#1957D1111yescharacteristic, complemented
118#1802—112no—
119C2×#331—111no—
120C2×D4⋊C8—112no—
121C23×C11—24no—
122C23×C11—44no—
123C23×C11—44no—
124C23×C11—42no—
125C23×C11—42no—
126C23×C11#12011yescharacteristic
127C22×D11—24no—
128C22×D11—24no—
129C22×D11—24no—
130C22×D11—432no—
131C22×D11—42no—
132C22×D11—42no—
133C22×D11—42no—
134C22×D11—42no—
135C22×D11—88no—
136C22×D11—88no—
137C22×D11—88no—
138C22×D11—816no—
139D4×C11—44no—
140D4×C11—44no—
141D4×C11—44no—
142D4×C11—44no—
143D4×C11—44no—
144D4×C11—82no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—82no—
148C2×C4×C11—81no—
149C2×C4×C11C2×C22⋊C412yes—
150C2×C4×C11C2×C22⋊C411yescharacteristic
151C2×C4×C11#12012yes—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11C2×D812yes—
154C2×C4×C11C2×SD1612yes—
155C2×C4×C11AGL(1,ℤ/8)12yes—
156C2×C4×C11AGL(1,ℤ/8)12yes—
157C22⋊D11—432no—
158C2×Dic11—24no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161D44—24no—
162D44—24no—
163D44—24no—
164D44#10218yescomplemented
165C4×D11—44no—
166C4×D11—44no—
167C4×D11—44no—
168C4×D11—44no—
169C8×C11—42no—
170C11⋊C8—82no—
171C23×D4—222no—
172D42—114no—
173D42—224no—
174D42—222no—
175C2×#127C2×D1111yescharacteristic
176C2×#121—222no—
177C2×#120—222no—
178C2×C4×D4—112no—
179C2×C4⋊C8—112no—
180C2×#102—22no—
181C2×#102—222no—
182C2×C4×C8C2×D1111yescharacteristic, complemented
183#384C2×D1111yescharacteristic, complemented
184#340—222no—
185#331—222no—
186D4⋊C8—224no—
187C22×C11—44no—
188C22×C11—48no—
189C22×C11—82no—
190C22×C11—82no—
191C22×C11—84no—
192C22×C11#37911yescharacteristic
193C22×C11#44712yes—
194C22×C11#45012yes—
195C22×C11#45311yescharacteristic
196C22×C11#45511yescharacteristic
197C2×D11—28no—
198C2×D11—44no—
199C2×D11—44no—
200C2×D11—44no—
201C2×D11—44no—
202C2×D11—44no—
203C2×D11—44no—
204C2×D11—832no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—161no—
208C4×C11C2×#10212yes—
209C4×C11#41812yes—
210C4×C11#44712yes—
211C4×C11#45012yes—
212Dic11—44no—
213C25—222no—
214C22×D4—22no—
215C22×D4—112no—
216C22×D4—228no—
217C22×D4—228no—
218C22×D4—224no—
219C22×D4—444no—
220C22×D4—444no—
221C22×D4—444no—
222C22×D4—444no—
223C22×D4C22⋊D1112yes—
224C23×C4—222no—
225C22×C8—21no—
226C22×C8—222no—
227#127—22no—
228#127C4×D1112yes—
229#127D4412yes—
230#121—228no—
231#121—228no—
232#120—228no—
233#120—228no—
234C4×D4—114no—
235C4×D4—114no—
236C4×D4—222no—
237C4×D4—222no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—112no—
241C2×C22⋊C4—222no—
242C2×C22⋊C4—222no—
243C2×C42C22×D1111yescharacteristic
244C4⋊C8—222no—
245C4⋊C8—222no—
246#102—44no—
247#102—444no—
248C4×C8—22no—
249C2×C11—84no—
250C2×C11#161911yescharacteristic
251C2×C11#162911yescharacteristic
252C2×C11#163912yes—
253C2×C11#178612yes—
254C2×C11#179211yescharacteristic
255D11—48no—
256C24—22no—
257C24—228no—
258C24—222no—
259C24—448no—
260C24—448no—
261C24—882no—
262C24—882no—
263C2×D4—24no—
264C2×D4—24no—
265C2×D4—22no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—42no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—114no—
273C2×D4—114no—
274C2×D4—114no—
275C2×D4—2216no—
276C2×D4—222no—
277C2×D4—222no—
278C2×D4—222no—
279C2×D4—4416no—
280C2×D4—4416no—
281C2×D4—4416no—
282C2×D4—4416no—
283C2×D4—448no—
284C2×D4—448no—
285C2×D4(C2×D11)⋊C414yes—
286C22×C4—41no—
287C22×C4—222no—
288C22×C4—224no—
289C22×C4—224no—
290C22×C4—442no—
291C22×C4—442no—
292C22×C4—442no—
293C22×C4—442no—
294C22×C4D4×D1112yes—
295C22×C4C2×C22⋊D1111yescharacteristic
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—442no—
300C2×C8—442no—
301C2×C8—442no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—114no—
306C4⋊C4—222no—
307C22⋊C4—228no—
308C22⋊C4—224no—
309C22⋊C4—224no—
310C42C2×C4×D1111yescharacteristic
311C42C2×D4411yescharacteristic
312C42D4×D1112yes—
313C11#844311yescharacteristic, complemented, Sylow
314C23—24no—
315C23—44no—
316C23—44no—
317C23—42no—
318C23—42no—
319C23—224no—
320C23—224no—
321C23—224no—
322C23—4432no—
323C23—442no—
324C23—442no—
325C23—442no—
326C23—442no—
327C23—888no—
328C23—8816no—
329C23—888no—
330C23—888no—
331C23#6699011yescharacteristic
332D4—44no—
333D4—44no—
334D4—44no—
335D4—44no—
336D4—44no—
337D4—82no—
338D4—118no—
339D4—224no—
340D4—224no—
341D4—224no—
342D4—4432no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—82no—
346C2×C4—81no—
347C2×C4—224no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—444no—
351C2×C4—444no—
352C2×C4—444no—
353C2×C4—444no—
354C2×C4C22⋊C4×D1112yes—
355C2×C4#6693512yes—
356C2×C4D8×D1112yes—
357C2×C4#6696412yes—
358C2×C4SD16×D1112yes—
359C2×C4#6696712yes—
360C2×C4C2×(C2×D11)⋊C411yescharacteristic
361C2×C4#6699011yescharacteristic
362C8—42no—
363C8—882no—
364C22—48no—
365C22—44no—
366C22—84no—
367C22—82no—
368C22—82no—
369C22—228no—
370C22—444no—
371C22—444no—
372C22—444no—
373C22—444no—
374C22—444no—
375C22—444no—
376C22—8832no—
377C22#1062256811yescharacteristic
378C22#1062267411yescharacteristic
379C22#1062269011yescharacteristic
380C22#1062276912yes—
381C22#1062278212yes—
382C4—21no—
383C4—21no—
384C4—161no—
385C4—444no—
386C4D11×#10212yes—
387C4#1062238312yes—
388C4#1062238612yes—
389C4#1062238912yes—
390C2—84no—
391C2—448no—
392C2#1306766811yescharacteristic
393C2#1306773011yescharacteristic
394C2#1306779212yes—
395C2#1306854512yes—
396C2#1306856911yescharacteristic
subgroupG/H
centerC23#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1957C2
socleC23×C11#120
prime radicalC2×#10623248C2
cosocleC2×C42×C11C23
hypercenter#1957D11
hypocenterC11#8443
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #13068613C2semidirect
3. C2×#10622182C2semidirect
4. C2×#10622097C2semidirect
5. C11×#1957C2semidirect
12. #10623248C4semidirect
15. C2×C4×C8×C11C22semidirect
16. C11×#384C22semidirect
18. C2×C4⋊(C11⋊C8)C22semidirect
117. #1957D11semidirect
164. D44#102semidirect
182. C2×C4×C8C2×D11semidirect
183. #384C2×D11semidirect
313. C11#8443semidirect

Maximal subgroups

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

subgroupindex
C2×#106232482
#130686132
C2×#106221822
C2×#106220972
C11×#19572
#844311