Finite Group Databasebeta

← #15617558

Subgroups — #15617558

Order 2816.

2122 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623053C211yesmaximal, characteristic
2#13077280C2116yesmaximal, complemented
3#13077252C214yesmaximal, complemented
4#13077247C214yesmaximal, complemented
5C2×#10622731C212yesmaximal, complemented
6#13077060C212yesmaximal
7#13077035C211yesmaximal, characteristic, complemented
8C11×#2873C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C22×C11×M16C2212yes—
11C2×C11×#117C2211yescharacteristic
12C22×C4×Dic11C2211yescharacteristic
13C22×#4318C2212yes—
14#10623053C414yes—
15#10623053C414yes—
16#10623053C2218yes—
17C2×#66946C412yes—
18C2×#66940C412yes—
19C2×(C22⋊D11)⋊C4C414yes—
20C2×#66925C2212yes—
21C2×C42×D11C2212yes—
22C11×#405C2218yescomplemented
23C4×C11×M16C2214yes—
24#10622742C2218yes—
25#10622739C2218yes—
26#10622731C2214yes—
27#10622731C2214yes—
28#10622731C2218yescomplemented
29#10622723C2218yes—
30C2×Dic11⋊C8C2218yescomplemented
31#10622610C2218yescomplemented
32C4×#4318C2214yes—
33#10622322C22116yescomplemented
34#10622318C22116yescomplemented
35#10622303C22116yescomplemented
36#10622298C22116yescomplemented
37C23×C4×C11C2311yescharacteristic
38C22×C22⋊D11C2×C412yes—
39C23×Dic11C2×C412yes—
40C2×#4339—28no—
41C2×#4339C2×C414yes—
42C2×#4339C2314yes—
43C22×D44C2×C411yescharacteristic
44C22×C4×D11C2×C414yes—
45C22×C4×D11C2312yes—
46C22×Dic22C2×C411yescharacteristic
47C2×C11×M16—28no—
48C2×C11×M16C2314yes—
49C2×C11×M16C2314yes—
50C22×C8×C11C2314yes—
51C11×#117C2×C414yes—
52C11×#117C2314yes—
53C2×C11×C4⋊C4C2×C412yes—
54C2×C11×C22⋊C4C2×C412yes—
55C2×C42×C11C2312yes—
56C2×(C2×D11)⋊C4C2×C414yes—
57C2×Dic11⋊C4C2×C414yes—
58C2×C4×Dic11C2×C414yes—
59C2×C4×Dic11C2×C412yes—
60C2×C4×Dic11C2×C412yes—
61C2×C4×Dic11C2×C412yes—
62C2×C4×Dic11C2311yescharacteristic
63C2×C4×Dic11C2311yescharacteristic
64C2×C4×Dic11C2314yes—
65C2×#4318—28no—
66C2×#4318C2314yes—
67C2×#4318C2314yes—
68C22×C11⋊C8C2314yes—
69#66946C2×C418yes—
70#66946C2×C418yes—
71#66940C2×C418yes—
72#66940C2×C418yes—
73(C22⋊D11)⋊C4C2×C4116yes—
74(C22⋊D11)⋊C4C2×C4116yes—
75#66925C2×C418yes—
76#66925C2318yes—
77C42×D11C2×C414yes—
78C42×D11C2×C414yes—
79C42×D11C2318yes—
80C11×#97C2318yes—
81C4×C8×C11C2318yes—
82(C2×D11)⋊C8C23132yes—
83Dic11⋊C8C23116yes—
84Dic11⋊C8C23116yes—
85#66867C2318yes—
86C4×C11⋊C8C2318yes—
87#60125—111nomaximal, Sylow
88C24×C11C22×C411yescharacteristic
89C23×D11C22×C412yes—
90C22×C4×C11C22×C414yes—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C22×C412yes—
93C22×C4×C11#4118yes—
94C22×C4×C11C2412yes—
95C22×C4×C11C2411yescharacteristic
96C2×C22⋊D11—28no—
97C2×C22⋊D11C22×C418yes—
98C22×Dic11—44no—
99C22×Dic11C22×C414yes—
100C22×Dic11C22×C412yes—
101C22×Dic11C22×C412yes—
102C22×Dic11C22×C414yes—
103C22×Dic11C22×C412yes—
104#4339—216no—
105#4339—28no—
106#4339—28no—
107C2×D44—24no—
108C2×D44C22×C414yes—
109C2×C4×D11—28no—
110C2×C4×D11—48no—
111C2×C4×D11C22×C414yes—
112C2×C4×D11C22×C418yes—
113C2×C4×D11C22×C418yes—
114C2×C4×D11C2414yes—
115C2×Dic22—24no—
116C2×Dic22C22×C414yes—
117C11×M16—28no—
118C11×M16—28no—
119C2×C8×C11—28no—
120C2×C8×C11C2418yes—
121C11×C4⋊C4C22×C418yes—
122C11×C22⋊C4C22×C418yes—
123C42×C11C22×C414yes—
124C42×C11C2414yes—
125(C2×D11)⋊C4C22×C4116yes—
126Dic11⋊C4C22×C4116yes—
127C4×Dic11C22×C411yescharacteristic
128C4×Dic11C22×C411yescharacteristic
129C4×Dic11C22×C418yes—
130C4×Dic11C22×C418yes—
131C4×Dic11C22×C412yes—
132C4×Dic11C22×C414yes—
133C4×Dic11C22×C414yes—
134C4×Dic11C2412yes—
135C4×Dic11C2412yes—
136#4318—28no—
137#4318—28no—
138C2×C11⋊C8—28no—
139C2×C11⋊C8C2418yes—
140C2×C4×#41—111no—
141#2925—1116no—
142#2921—114no—
143#2920—114no—
144C2×#423—112no—
145#2879—112no—
146#2873—111no—
147#2873D1111yescharacteristic, complemented
148C23×C11—42no—
149C23×C11#11714yes—
150C23×C11C23×C412yes—
151C23×C11C23×C411yescharacteristic
152C22×D11—24no—
153C22×D11—44no—
154C22×D11C23×C414yes—
155C2×C4×C11—44no—
156C2×C4×C11#11714yes—
157C2×C4×C11#11718yes—
158C2×C4×C11C23×C418yes—
159C2×C4×C11C23×C411yescharacteristic
160C2×C4×C11C23×C412yes—
161C2×C4×C11C2×#4114yes—
162C2×C4×C11C2×#4114yes—
163C2×C4×C11C2×#4114yes—
164C2×C4×C11C2511yescharacteristic
165C22⋊D11—216no—
166C2×Dic11—24no—
167C2×Dic11—24no—
168C2×Dic11—28no—
169C2×Dic11—44no—
170C2×Dic11—42no—
171C2×Dic11C23×C412yes—
172C2×Dic11C23×C414yes—
173C2×Dic11C23×C414yes—
174C2×Dic11C23×C412yes—
175D44—28no—
176C4×D11—28no—
177C4×D11—28no—
178C4×D11—216no—
179C4×D11—48no—
180Dic22—28no—
181C8×C11—28no—
182C11⋊C8—28no—
183C22×#41—111no—
184C22×M16—112no—
185C22×M16C2×D1112yes—
186C4×#41—118no—
187C4×#41—114no—
188C4×#41—114no—
189C2×C4×Q8—112no—
190C2×C4×D4—112no—
191C2×C4×D4—114no—
192C2×#117—112no—
193C2×#117C2×D1111yescharacteristic
194C22×C42—111no—
195C22×C42—112no—
196#433—1116no—
197#433—1116no—
198#432—1116no—
199#431—1116no—
200#423—114no—
201#423—114no—
202#423—118no—
203C2×C4⋊C8—118no—
204#408—118no—
205#408—118no—
206#407—118no—
207#405—118no—
208#405C2×D1118yescomplemented
209C4×M16—114no—
210C4×M16C2×D1114yes—
211C22×C11—22no—
212C22×C11—24no—
213C22×C11—44no—
214C22×C11C2×#11712yes—
215C22×C11C2×#11714yes—
216C22×C11C24×C411yescharacteristic
217C2×D11—24no—
218C2×D11—28no—
219C2×D11—48no—
220C4×C11—28no—
221C4×C11C2×#11714yes—
222C4×C11C2×#11712yes—
223C4×C11C22×#4112yes—
224Dic11—24no—
225Dic11—22no—
226Dic11—24no—
227Dic11#56814yes—
228C2×#41—114no—
229C2×#41—114no—
230C2×#41—228no—
231C22×Q8—111no—
232C22×D4—112no—
233C22×D4—111no—
234C23×C4—112no—
235C23×C4—112no—
236C23×C4—114no—
237C23×C4C22×D1111yescharacteristic
238C2×M16—28no—
239C2×M16—114no—
240C2×M16—114no—
241C2×M16—228no—
242C2×M16C22×D1114yes—
243C2×M16C22×D1114yes—
244C22×C8—114no—
245C22×C8C22×D1114yes—
246C4×Q8—118no—
247C4×Q8—118no—
248C4×D4—118no—
249C4×D4—118no—
250C4×D4—1116no—
251C4×D4—1116no—
252#117—118no—
253#117—118no—
254#117C4×D1114yes—
255#117C22×D1114yes—
256C2×C4⋊C4—114no—
257C2×C4⋊C4C4×D1112yes—
258C2×C22⋊C4—114no—
259C2×C22⋊C4C4×D1112yes—
260C2×C42—114no—
261C2×C42—112no—
262C2×C42—112no—
263C2×C42—112no—
264C2×C42—111no—
265C2×C42—114no—
266C2×C42—111no—
267C2×C42—114no—
268C2×C42—114no—
269C2×C42—118no—
270C2×C42C22×D1112yes—
271C4⋊C8—1116no—
272C4⋊C8—1116no—
273C22⋊C8—1132no—
274#97—118no—
275#97C22×D1118yes—
276C4×C8—118no—
277C4×C8C22×D1118yes—
278C2×C11—22no—
279C2×C11—24no—
280C2×C11C22×#11711yescharacteristic
281C2×C11C2×#56812yes—
282D11—44no—
283C24—112no—
284C24C2×C4×D1111yescharacteristic
285#41—2216no—
286#41—228no—
287#41—228no—
288C2×Q8—114no—
289C2×Q8—224no—
290C2×D4—118no—
291C2×D4—114no—
292C2×D4—228no—
293C2×D4—224no—
294C22×C4—112no—
295C22×C4—112no—
296C22×C4—114no—
297C22×C4—112no—
298C22×C4—114no—
299C22×C4—114no—
300C22×C4—118no—
301C22×C4—114no—
302C22×C4—118no—
303C22×C4—228no—
304C22×C4—448no—
305C22×C4—444no—
306C22×C4C2×C4×D1114yes—
307C22×C4C2×C4×D1111yescharacteristic
308C22×C4C2×C4×D1112yes—
309C22×C4#433918yes—
310C22×C4C23×D1111yescharacteristic
311C22×C4C23×D1112yes—
312M16—28no—
313M16—28no—
314M16—228no—
315M16—228no—
316C2×C8—28no—
317C2×C8—118no—
318C2×C8—228no—
319C2×C8C23×D1118yes—
320C4⋊C4—1116no—
321C4⋊C4C2×C4×D1118yes—
322C22⋊C4—1116no—
323C22⋊C4C2×C4×D1118yes—
324C42—111no—
325C42—111no—
326C42—112no—
327C42—114no—
328C42—118no—
329C42—114no—
330C42—118no—
331C42—112no—
332C42—112no—
333C42C2×C4×D1114yes—
334C42C23×D1114yes—
335C11#6012511yescharacteristic, complemented, Sylow
336C23—42no—
337C23—114no—
338C23—224no—
339C23—444no—
340C23#6692514yes—
341C23C22×C4×D1112yes—
342C23C22×C4×D1111yescharacteristic
343Q8—228no—
344D4—2216no—
345D4—228no—
346C2×C4—44no—
347C2×C4—112no—
348C2×C4—112no—
349C2×C4—114no—
350C2×C4—114no—
351C2×C4—2216no—
352C2×C4—224no—
353C2×C4—228no—
354C2×C4—224no—
355C2×C4—228no—
356C2×C4—228no—
357C2×C4—448no—
358C2×C4—444no—
359C2×C4—442no—
360C2×C4#6692514yes—
361C2×C4#6692518yes—
362C2×C4C22×C4×D1118yes—
363C2×C4C22×C4×D1111yescharacteristic
364C2×C4C22×C4×D1112yes—
365C2×C4C2×#433914yes—
366C2×C4C2×#433914yes—
367C2×C4C2×#433914yes—
368C2×C4C24×D1111yescharacteristic
369C8—28no—
370C8—228no—
371C22—22no—
372C22—24no—
373C22—44no—
374C22—224no—
375C22—228no—
376C22—448no—
377C22C2×#6692512yes—
378C22C2×#6692514yes—
379C22C23×C4×D1111yescharacteristic
380C4—28no—
381C4—114no—
382C4—224no—
383C4—222no—
384C4—224no—
385C4C2×#6692512yes—
386C4C2×#6692514yes—
387C4C22×#433912yes—
388C2—22no—
389C2—24no—
390C2—444no—
391C2C22×#6692511yescharacteristic
392C2D11×#56812yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2873C2
prime radicalC22×#4339C22
cosocleC2×C4×C11C25
hypercenter#2873D11
hypocenterC11#60125
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2873

Complements

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

NH ≅ G/Ntype
2. #13077280C2semidirect
3. #13077252C2semidirect
4. #13077247C2semidirect
5. C2×#10622731C2semidirect
7. #13077035C2semidirect
8. C11×#2873C2semidirect
22. C11×#405C22semidirect
28. #10622731C22semidirect
30. C2×Dic11⋊C8C22semidirect
31. #10622610C22semidirect
33. #10622322C22semidirect
34. #10622318C22semidirect
35. #10622303C22semidirect
36. #10622298C22semidirect
147. #2873D11semidirect
208. #405C2×D11semidirect
335. C11#60125semidirect

Maximal subgroups

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

subgroupindex
C2×#106230532
#130772802
#130772522
#130772472
C2×#106227312
#130770602
#130770352
C11×#28732
#6012511