Finite Group Databasebeta

← #14724321

Subgroups — #14724321

Order 2816.

666 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079176C211yesmaximal, characteristic
2#13077329C211yesmaximal, characteristic
3#13067516C214yesmaximal, complemented
4#13067426C214yesmaximal, complemented
5#13067374C211yesmaximal, characteristic, complemented
6#13067071C211yesmaximal, characteristic, complemented
7#13067066C211yesmaximal, characteristic
8C2×#10622092C211yesmaximal, characteristic, complemented
9C11×#2960C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×#66954—21no—
12#10623008C2211yescharacteristic
13C11×#446—21no—
14C11×#446C2212yes—
15C8×Q8×C11—21no—
16C8×Q8×C11C2212yes—
17C11×#424—21no—
18C11×#423C2211yescharacteristic
19C11×#405—21no—
20C2×C4×C8×C11C2211yescharacteristic
21#10622723—21no—
22#10622701C411yescharacteristic
23#10622698C411yescharacteristic
24#10622694C411yescharacteristic
25#10622692C411yescharacteristic
26#10622661C414yes—
27C4×#4325C2214yes—
28#10622537C2211yescharacteristic
29C2×C4×C11⋊C8C2211yescharacteristic
30C2×C4×C11⋊C8C2211yescharacteristic
31#10622301—21no—
32#10622301C2212yes—
33C8×D44—21no—
34C8×D44C2212yes—
35Q8⋊(C11⋊C8)C2214yes—
36#10622121C2214yes—
37#10622117C2214yes—
38#10622092C2212yes—
39#10622092C2212yes—
40C2×#4339—21no—
41C2×C11×M16—21no—
42C22×C8×C11D411yescharacteristic
43C22×C8×C11D411yescharacteristic
44C11×C4⋊Q8C2×C411yescharacteristic
45C11×C4⋊Q8C2×C411yescharacteristic
46C11×#125—21no—
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8C2×C412yes—
49C4×Q8×C11—21no—
50C4×Q8×C11C2312yes—
51C11×#117—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4325C2×C414yes—
54#66983—21no—
55#66983C2×C412yes—
56C2×#4318—21no—
57C22×C11⋊C8—21no—
58C22×C11⋊C8C2×C412yes—
59#66954—44no—
60C2×#4313—22no—
61C2×C8×D11—22no—
62#66928—21no—
63#66927C2×C411yescharacteristic
64C4×D44—21no—
65C4×D44C2312yes—
66#66922C2×C411yescharacteristic
67C11×C4⋊C8—22no—
68C11×C4⋊C8—22no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8C2312yes—
71C11×#97—22no—
72C4×C8×C11—22no—
73C4×C8×C11D411yescharacteristic
74C4×C8×C11D411yescharacteristic
75C4×C8×C11C2311yescharacteristic
76C4×C8×C11C2311yescharacteristic
77#66899C2×C414yes—
78(C2×D11)⋊C8—22no—
79(C2×D11)⋊C8—22no—
80#66873C2×C414yes—
81#66872C2×C414yes—
82C4⋊(C11⋊C8)—21no—
83C4⋊(C11⋊C8)C2312yes—
84C4×C11⋊C8—21no—
85C4×C11⋊C8C2×C411yescharacteristic
86C4×C11⋊C8C2×C411yescharacteristic
87C4×C11⋊C8C2312yes—
88C4×C11⋊C8C2312yes—
89#17960—111nomaximal, Sylow
90C2×Q8×C11—21no—
91C2×Q8×C11C22×C412yes—
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C2×C22⋊D11—22no—
96#4339—42no—
97#4339—42no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44C22×C412yes—
101C2×C4×D11—22no—
102C2×Dic22—21no—
103C11×M16—42no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2×D411yescharacteristic
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4C22×C412yes—
117C11×C22⋊C4—22no—
118C42×C11—22no—
119C42×C11C22×C411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122C42×C11C2411yescharacteristic
123#4325—28no—
124(C2×D11)⋊C4—22no—
125(C2×D11)⋊C4—22no—
126C4⋊Dic11—21no—
127C4⋊Dic11C22×C412yes—
128#4318—42no—
129C2×C11⋊C8—24no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—42no—
133C2×C11⋊C8C22×C412yes—
134C2×C11⋊C8C22×C412yes—
135#4313—44no—
136C8×D11—44no—
137#3167—111no—
138#2960D1111yescharacteristic, complemented
139#2931—111no—
140#1592—114no—
141SD16⋊C8—114no—
142#1567—111no—
143#1493—111no—
144#1492—111no—
145C2×#322—111no—
146C23×C11C4×D411yescharacteristic
147C22×D11—22no—
148Q8×C11—24no—
149Q8×C11—42no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)12yes—
158C2×C4×C11#13712yes—
159C2×C4×C11C23×C411yescharacteristic
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C2×#4111yescharacteristic
162C22⋊D11—44no—
163C2×Dic11—22no—
164D44—24no—
165D44—42no—
166D44—42no—
167C4×D11—42no—
168C4×D11—42no—
169Dic22—42no—
170C8×C11—21no—
171C8×C11—21no—
172C8×C11—21no—
173C8×C11—21no—
174C8×C11—42no—
175C11⋊C8—22no—
176C11⋊C8—42no—
177C11⋊C8—42no—
178C11⋊C8#13114yescomplemented
179C2×#131—221no—
180#533C2×D1111yescharacteristic
181#532—111no—
182#498—111no—
183#492—111no—
184#487—111no—
185#486—111no—
186#465—114no—
187#446—21no—
188#446C2×D1112yes—
189C8×Q8—21no—
190C8×Q8C2×D1112yes—
191C4×SD16—114no—
192#436—112no—
193#436—221no—
194C8×D4—112no—
195C8×D4—221no—
196#424—21no—
197#423—111no—
198#423C2×D1111yescharacteristic
199#408—221no—
200#405—21no—
201C2×C4×C8—111no—
202C2×C4×C8—111no—
203C2×C4×C8C2×D1111yescharacteristic
204#335—114no—
205Q8⋊C8—114no—
206D4⋊C8—114no—
207#322—112no—
208#322—112no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11#44012yes—
212C22×C11C2×C4×D411yescharacteristic
213C2×D11—42no—
214C2×D11—42no—
215C2×D11—42no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—42no—
219C4×C11—42no—
220C4×C11#44012yes—
221C4×C11#44412yes—
222C4×C11C2×#13112yes—
223C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
224C4×C11C2×#13711yescharacteristic
225Dic11—42no—
226C2×#41—221no—
227C2×SD16—114no—
228#131—444no—
229C2×M16—21no—
230C2×M16—221no—
231C2×M16—222no—
232C22×C8—112no—
233C22×C8—221no—
234C22×C8—222no—
235C22×C8C22⋊D1111yescharacteristic
236C22×C8C22⋊D1111yescharacteristic
237C4⋊Q8—111no—
238C4⋊Q8C4×D1111yescharacteristic
239C4⋊Q8C4×D1111yescharacteristic
240#127—111no—
241#125—21no—
242#124—221no—
243C22⋊Q8—21no—
244C22⋊Q8C4×D1112yes—
245#121—112no—
246#121—221no—
247C4×Q8—21no—
248C4×Q8C22×D1112yes—
249C4×D4—112no—
250C4×D4—221no—
251#117—21no—
252C2×C42C22×D1111yescharacteristic
253#106—114no—
254C4⋊C8—22no—
255C4⋊C8—22no—
256C4⋊C8—21no—
257C4⋊C8—112no—
258C4⋊C8—221no—
259C4⋊C8C22×D1112yes—
260#103—114no—
261#102—114no—
262C22⋊C8—222no—
263C22⋊C8—222no—
264#97—22no—
265C4×C8—22no—
266C4×C8—111no—
267C4×C8—111no—
268C4×C8—112no—
269C4×C8—112no—
270C4×C8—221no—
271C4×C8C22⋊D1111yescharacteristic
272C4×C8C22⋊D1111yescharacteristic
273C4×C8C22×D1111yescharacteristic
274C4×C8C22×D1111yescharacteristic
275C2×C11—22no—
276C2×C11#293111yescharacteristic
277C2×C11C2×#44011yescharacteristic
278C2×C11C2×#44411yescharacteristic
279D11—82no—
280#41—442no—
281#41—442no—
282C2×Q8—21no—
283C2×Q8—221no—
284C2×Q8C2×C4×D1112yes—
285C2×D4—112no—
286C2×D4—222no—
287C2×D4—221no—
288C2×D4—221no—
289C22×C4—222no—
290C22×C4C2×C4×D1111yescharacteristic
291C22×C4#433911yescharacteristic
292C22×C4C2×C22⋊D1111yescharacteristic
293SD16—228no—
294M16—42no—
295M16—444no—
296M16—442no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—112no—
301C2×C8—112no—
302C2×C8—224no—
303C2×C8—222no—
304C2×C8—222no—
305C2×C8—444no—
306C2×C8—442no—
307C2×C8C2×C22⋊D1111yescharacteristic
308C2×C8C2×C22⋊D1111yescharacteristic
309C2×C8C2×C22⋊D1111yescharacteristic
310C2×C8C2×C22⋊D1111yescharacteristic
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—112no—
317C4⋊C4—221no—
318C4⋊C4C2×C4×D1112yes—
319C22⋊C4—22no—
320C22⋊C4—222no—
321C22⋊C4—222no—
322C42—22no—
323C42C2×C4×D1111yescharacteristic
324C42#433911yescharacteristic
325C42C2×C22⋊D1111yescharacteristic
326C42C23×D1111yescharacteristic
327C11#1796011yescharacteristic, complemented, Sylow
328C23—222no—
329C23C4×C22⋊D1111yescharacteristic
330Q8—24no—
331Q8—42no—
332Q8—442no—
333D4—224no—
334D4—444no—
335D4—442no—
336D4—442no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—222no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4C4×C22⋊D1111yescharacteristic
345C2×C4C4×C22⋊D1111yescharacteristic
346C2×C4C4×C22⋊D1111yescharacteristic
347C2×C4#6699512yes—
348C2×C4#6700212yes—
349C2×C4C22×C4×D1111yescharacteristic
350C2×C4C2×#433911yescharacteristic
351C2×C4C22×C22⋊D1111yescharacteristic
352C8—21no—
353C8—21no—
354C8—21no—
355C8—21no—
356C8—42no—
357C8—114no—
358C8—222no—
359C8—442no—
360C8—442no—
361C22—21no—
362C22—21no—
363C22—442no—
364C22—442no—
365C22—442no—
366C22#1062263912yes—
367C22C2×C4×C22⋊D1111yescharacteristic
368C4—21no—
369C4—21no—
370C4—42no—
371C4—42no—
372C4—442no—
373C4#1062263912yes—
374C4#1062275812yes—
375C4D11×#13112yes—
376C4C2×#6699511yescharacteristic
377C4C2×#6700211yescharacteristic
378C2—22no—
379C2—882no—
380C2#1307732611yescharacteristic
381C2C2×#1062263911yescharacteristic
382C2C2×#1062275811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2960C2
socleC22×C11C2×C4×D4
prime radical#10623008C22
cosocleC42×C11C24
hypercenter#2960D11
hypocenterC11#17960
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #2960

Complements

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

NH ≅ G/Ntype
3. #13067516C2semidirect
4. #13067426C2semidirect
5. #13067374C2semidirect
6. #13067071C2semidirect
8. C2×#10622092C2semidirect
9. C11×#2960C2semidirect
138. #2960D11semidirect
178. C11⋊C8#131semidirect
327. C11#17960semidirect

Maximal subgroups

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

subgroupindex
#130791762
#130773292
#130675162
#130674262
#130673742
#130670712
#130670662
C2×#106220922
C11×#29602
#1796011