Finite Group Databasebeta

← #14763286

Subgroups — #14763286

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66943C211yesmaximal, characteristic
2C2×#10622332C211yesmaximal, characteristic
3#13071018C211yesmaximal, characteristic
4#13069583C214yesmaximal, complemented
5#13069570C214yesmaximal, complemented
6#13068707C211yesmaximal, characteristic
7#13068704C211yesmaximal, characteristic
8#13068702C211yesmaximal, characteristic
9C11×#1823C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic11—21no—
12C22×C4⋊Dic11C2211yescharacteristic
13C22×Dic11⋊C4—21no—
14C22×C4×Dic11C2211yescharacteristic
15C2×#66943—21no—
16C2×#66943—21no—
17C2×#66943—24no—
18C2×#66943C418yescomplemented
19C2×#66943C2212yes—
20C2×#66943C2212yes—
21C2×#66930—21no—
22C2×C11×C22⋊C8C2211yescharacteristic
23C11×#380C2211yescharacteristic
24#10622825C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×#66879C2212yes—
27C2×Dic11⋊C8C2212yes—
28#10622589C2212yes—
29C4⋊C4×Dic11C2212yes—
30#10622555—21no—
31#10622332—24no—
32#10622263—21no—
33#10622262—21no—
34C11×#340C2214yes—
35#10622189C2214yes—
36#10622167C2214yes—
37#10622167C2214yes—
38C23×C4×C11—21no—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11—21no—
41C23×Dic11D411yescharacteristic
42C23×Dic11D411yescharacteristic
43C22×C8×C11C2312yes—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4C2×C414yes—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C22⋊C4—21no—
50C2×C22⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11—28no—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11C2×C414yes—
57C2×C4⋊Dic11C2312yes—
58C2×C4⋊Dic11C2312yes—
59C2×Dic11⋊C4—28no—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11C2×C414yes—
66C2×C4×Dic11D411yescharacteristic
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11D414yes—
69C2×C4×Dic11C2311yescharacteristic
70C2×C4×Dic11C2311yescharacteristic
71C22×C11⋊C8C2312yes—
72#66943—28no—
73#66943—28no—
74#66943—24no—
75#66943—24no—
76#66943C2×C418yes—
77#66943C2×C418yes—
78#66930—44no—
79C11×C22⋊C8—22no—
80C11×#95—21no—
81C11⋊#95—21no—
82C11⋊#95—22no—
83C22⋊(C11⋊C8)—22no—
84#66879—24no—
85Dic11⋊C8—24no—
86#21838—111nomaximal, Sylow
87C24×C11C2×D411yescharacteristic
88C22×C4×C11—24no—
89C22×C4×C11—24no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11C22×C412yes—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—24no—
99C22×Dic11—22no—
100C22×Dic11—22no—
101C22×Dic11—22no—
102C22×Dic11—22no—
103C22×Dic11—42no—
104C22×Dic11—44no—
105C22×Dic11C22⋊C414yes—
106C22×Dic11C22⋊C414yes—
107C22×Dic11C2×D411yescharacteristic
108C22×Dic11C2×D411yescharacteristic
109C22×Dic11C2×D411yescharacteristic
110C22×Dic11C2×D411yescharacteristic
111C2×C8×C11—22no—
112C2×C8×C11—24no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4C22×C414yes—
117C11×C22⋊C4—42no—
118C22⋊Dic11—42no—
119C4⋊Dic11—28no—
120C4⋊Dic11—28no—
121C4⋊Dic11—24no—
122C4⋊Dic11—22no—
123C4⋊Dic11—24no—
124C4⋊Dic11C22×C414yes—
125Dic11⋊C4—28no—
126Dic11⋊C4—28no—
127Dic11⋊C4—44no—
128Dic11⋊C4—44no—
129C4×Dic11—44no—
130C4×Dic11C22⋊C414yes—
131C4×Dic11C22⋊C414yes—
132C4×Dic11C22×C412yes—
133C4×Dic11C22×C412yes—
134C4×Dic11C2×D412yes—
135C4×Dic11C2×D412yes—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—24no—
138C22×#125—111no—
139C2×#432—111no—
140#2285—111no—
141#1992—114no—
142#1989—114no—
143#1824—111no—
144#1824—111no—
145#1823—111no—
146#1823D1111yescharacteristic
147C23×C11—22no—
148C23×C11—22no—
149C23×C11C2×C22⋊C412yes—
150C23×C11AGL(1,ℤ/8)12yes—
151C23×C11#13712yes—
152C23×C11C22×D411yescharacteristic
153C2×C4×C11—22no—
154C2×C4×C11—24no—
155C2×C4×C11—24no—
156C2×C4×C11—24no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—48no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11C2×C22⋊C412yes—
164C2×C4×C11C23×C411yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C112−1+414yes—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—28no—
174C2×Dic11—24no—
175C2×Dic11—44no—
176C2×Dic11—48no—
177C2×Dic11—44no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11C2×C22⋊C412yes—
182C2×Dic11C2×C22⋊C412yes—
183C2×Dic11C2×C22⋊C412yes—
184C2×Dic11C2×C22⋊C412yes—
185C8×C11—42no—
186C11⋊C8—42no—
187C2×#125—112no—
188C2×#125—112no—
189C2×#125—118no—
190C2×#125—221no—
191C2×#125—221no—
192C2×#125—224no—
193C2×#117—221no—
194C22×C4⋊C4—111no—
195C22×C4⋊C4—221no—
196C22×C4⋊C4—221no—
197C22×C4⋊C4C2×D1111yescharacteristic
198C22×C42—111no—
199#432—224no—
200C2×C4⋊C8—112no—
201C2×C22⋊C8—111no—
202C2×C22⋊C8C2×D1111yescharacteristic
203C2×#97—112no—
204#384—112no—
205#382—221no—
206#380—111no—
207#380—221no—
208#380C2×D1111yescharacteristic
209C4×C4⋊C4—112no—
210C4×C4⋊C4—221no—
211#340—114no—
212#340—114no—
213#340—114no—
214#340C2×D1114yes—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11—24no—
218C22×C11—24no—
219C22×C11#41714yes—
220C22×C11C22×C22⋊C411yescharacteristic
221C22×C11#53612yes—
222C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
223C22×C11C2×#13711yescharacteristic
224C22×C11#57512yes—
225C4×C11—22no—
226C4×C11—44no—
227C4×C11—82no—
228C4×C11#51912yes—
229C4×C11#53612yes—
230Dic11—22no—
231Dic11—22no—
232Dic11—22no—
233Dic11—22no—
234Dic11—44no—
235Dic11—82no—
236C23×C4—21no—
237C23×C4—111no—
238C23×C4—111no—
239C23×C4—221no—
240C23×C4C22×D1111yescharacteristic
241C22×C8—112no—
242C22×C8C22×D1112yes—
243#125—118no—
244#125—118no—
245#125—228no—
246#125—228no—
247#125—224no—
248#125—224no—
249#117—444no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—114no—
253C2×C4⋊C4—112no—
254C2×C4⋊C4—112no—
255C2×C4⋊C4—228no—
256C2×C4⋊C4—222no—
257C2×C4⋊C4—222no—
258C2×C4⋊C4—228no—
259C2×C4⋊C4—222no—
260C2×C4⋊C4—222no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—222no—
263C2×C4⋊C4—222no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4C4×D1114yes—
266C2×C4⋊C4C22×D1112yes—
267C2×C4⋊C4C22×D1112yes—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—221no—
270C2×C42—114no—
271C2×C42—111no—
272C2×C42—111no—
273C2×C42—114no—
274C2×C42—111no—
275C2×C42—111no—
276C2×C42—222no—
277C4⋊C8—224no—
278C22⋊C8—22no—
279C22⋊C8—222no—
280#97—224no—
281#95—21no—
282#95—222no—
283#95—221no—
284C2×C11—24no—
285C2×C11#231011yescharacteristic
286C2×C11C2×#41711yescharacteristic
287C2×C11#289611yescharacteristic
288C2×C11#323412yes—
289C2×C11#323612yes—
290C24D4×D1111yescharacteristic
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—114no—
298C22×C4—111no—
299C22×C4—111no—
300C22×C4—111no—
301C22×C4—111no—
302C22×C4—114no—
303C22×C4—222no—
304C22×C4—222no—
305C22×C4—224no—
306C22×C4—222no—
307C22×C4—222no—
308C22×C4—442no—
309C22×C4—444no—
310C22×C4C2×C4×D1112yes—
311C22×C4D4×D1111yescharacteristic
312C22×C4D4×D1112yes—
313C22×C4C23×D1111yescharacteristic
314C2×C8—22no—
315C2×C8—24no—
316C2×C8—222no—
317C2×C8—224no—
318C4⋊C4—24no—
319C4⋊C4—22no—
320C4⋊C4—24no—
321C4⋊C4—114no—
322C4⋊C4—228no—
323C4⋊C4—228no—
324C4⋊C4—228no—
325C4⋊C4—228no—
326C4⋊C4—224no—
327C4⋊C4—222no—
328C4⋊C4—224no—
329C4⋊C4—444no—
330C4⋊C4—444no—
331C4⋊C4C2×C4×D1114yes—
332C22⋊C4—42no—
333C22⋊C4—442no—
334C42—114no—
335C42—114no—
336C42—112no—
337C42—112no—
338C42—112no—
339C42—112no—
340C42—444no—
341C11#2183811yescharacteristic, complemented, Sylow
342C23—22no—
343C23—22no—
344C23C22⋊C4×D1112yes—
345C23#6696412yes—
346C23#6696812yes—
347C23C2×D4×D1111yescharacteristic
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—48no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—112no—
359C2×C4—112no—
360C2×C4—112no—
361C2×C4—112no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—222no—
367C2×C4—222no—
368C2×C4—228no—
369C2×C4—224no—
370C2×C4—444no—
371C2×C4—448no—
372C2×C4—444no—
373C2×C4—442no—
374C2×C4—442no—
375C2×C4—442no—
376C2×C4C22⋊C4×D1112yes—
377C2×C4C22×C4×D1111yescharacteristic
378C2×C4C2×D4×D1111yescharacteristic
379C2×C4#6704314yes—
380C8—42no—
381C8—442no—
382C22—24no—
383C22—22no—
384C22—22no—
385C22—24no—
386C22#1062238414yes—
387C22C2×C22⋊C4×D1111yescharacteristic
388C22#1062317912yes—
389C22C2×#6696411yescharacteristic
390C22C2×#6696811yescharacteristic
391C22#1062330812yes—
392C4—22no—
393C4—44no—
394C4—82no—
395C4—222no—
396C4—222no—
397C4—222no—
398C4—222no—
399C4—444no—
400C4—882no—
401C4#1062304712yes—
402C4#1062317912yes—
403C2—24no—
404C2#1307120111yescharacteristic
405C2C2×#1062238411yescharacteristic
406C2#1307713411yescharacteristic
407C2#1307980312yes—
408C2#1307981912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1823C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1823D11
hypocenterC11#21838
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
4. #13069583C2semidirect
5. #13069570C2semidirect
18. C2×#66943C4semidirect
341. C11#21838semidirect

Maximal subgroups

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

subgroupindex
C22×#669432
C2×#106223322
#130710182
#130695832
#130695702
#130687072
#130687042
#130687022
C11×#18232
#2183811