Finite Group Databasebeta

← #14676181

Subgroups — #14676181

Order 2816.

1710 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622549C211yesmaximal, characteristic
2C2×C4×C4⋊Dic11C211yesmaximal, characteristic
3#13066887C212yesmaximal
4#13066884C212yesmaximal
5#13066848C214yesmaximal
6#13066846C214yesmaximal
7C22×C4×Q8×C11C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C2×C4×Q8×C11—24no—
10C2×C4×Q8×C11—24no—
11C2×C4×Q8×C11C418yescomplemented
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2212yes—
15C22×C42×C11C2211yescharacteristic
16C22×C4⋊Dic11C2212yes—
17C22×C4⋊Dic11C2212yes—
18C22×C4×Dic11C2212yes—
19C2×C11⋊#95C2218yes—
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2218yes—
24#10622549—24no—
25C4×C4⋊Dic11—24no—
26C22×Q8×C11—22no—
27C22×Q8×C11—22no—
28C22×Q8×C11—28no—
29C22×Q8×C11C2×C414yes—
30C23×C4×C11C2312yes—
31C23×C4×C11C2311yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×Dic11C2314yes—
36C23×Dic11C2314yes—
37C4×Q8×C11—232no—
38C2×C11×C4⋊C4—24no—
39C2×C11×C4⋊C4—24no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4C2×C414yes—
43C2×C11×C4⋊C4C2×C418yes—
44C2×C42×C11—24no—
45C2×C42×C11—24no—
46C2×C42×C11C2×C418yes—
47C2×C42×C11C2×C414yes—
48C2×C42×C11D414yes—
49C2×C42×C11D414yes—
50C2×C4⋊Dic11—24no—
51C2×C4⋊Dic11—24no—
52C2×C4⋊Dic11—24no—
53C2×C4⋊Dic11—28no—
54C2×C4⋊Dic11Q818yescomplemented
55C2×C4×Dic11—24no—
56C2×C4×Dic11—44no—
57C11⋊#95—24no—
58C11⋊#95—24no—
59C11⋊#95—24no—
60C11⋊#95—216no—
61C11⋊#95—48no—
62#13925—111nomaximal, Sylow
63C24×C11C2411yescharacteristic
64C2×Q8×C11—216no—
65C2×Q8×C11—216no—
66C2×Q8×C11—28no—
67C2×Q8×C11—216no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—24no—
77C22×C4×C11—24no—
78C22×C4×C11C22×C414yes—
79C22×C4×C11C22×C412yes—
80C22×C4×C11C22×C412yes—
81C22×C4×C11C22×C414yes—
82C22×C4×C11C22×C412yes—
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2×D412yes—
85C22×C4×C11C2×D412yes—
86C22×C4×C11C2×D412yes—
87C22×C4×C11C2×D412yes—
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2×Q814yes—
90C22×C4×C11#4118yes—
91C22×C4×C11#4114yes—
92C22×Dic11—24no—
93C22×Dic11—24no—
94C22×Dic11—28no—
95C22×Dic11—24no—
96C22×Dic11—28no—
97C22×Dic11—28no—
98C22×Dic11—28no—
99C22×Dic11—24no—
100C22×Dic11—24no—
101C22×Dic11C2×Q818yes—
102C11×C4⋊C4—216no—
103C11×C4⋊C4—28no—
104C42×C11—216no—
105C42×C11C22⋊C4116yes—
106C4⋊Dic11—216no—
107C4⋊Dic11—48no—
108C4×Dic11—48no—
109C22×C4×Q8D1111yescharacteristic
110C2×#382—111no—
111C2×C4×C4⋊C4—111no—
112#1446—112no—
113#1445—112no—
114#1436—114no—
115C4⋊#95—114no—
116C23×C11C23×C411yescharacteristic
117C23×C11C22×D411yescharacteristic
118C23×C11C22×D411yescharacteristic
119C23×C11C22×Q812yes—
120C23×C11C2×#4114yes—
121C23×C11C2×#4112yes—
122C23×C11H(5,𝔽2)12yes—
123C23×C112−1+412yes—
124Q8×C11—232no—
125C2×C4×C11—24no—
126C2×C4×C11—24no—
127C2×C4×C11—24no—
128C2×C4×C11—24no—
129C2×C4×C11—24no—
130C2×C4×C11—24no—
131C2×C4×C11—28no—
132C2×C4×C11—28no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—24no—
136C2×C4×C11—24no—
137C2×C4×C11—28no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—44no—
141C2×C4×C11C2×C22⋊C414yes—
142C2×C4×C11C2×C22⋊C414yes—
143C2×C4×C11C2×C22⋊C414yes—
144C2×C4×C11#11718yes—
145C2×C4×C11C4×Q818yes—
146C2×C4×C11C22⋊Q818yes—
147C2×C4×C11#12414yes—
148C2×C4×C11C4⋊Q814yes—
149C2×Dic11—28no—
150C2×Dic11—216no—
151C2×Dic11—44no—
152C2×Dic11—44no—
153C2×Dic11—48no—
154C2×Dic11—44no—
155C2×Dic11—44no—
156C2×Dic11—44no—
157C2×Dic11—48no—
158C2×Dic11—48no—
159C23×Q8C2×D1111yescharacteristic
160C2×C4×Q8—24no—
161C2×C4×Q8—24no—
162C2×C4×Q8Dic1118yescomplemented
163C22×C4⋊C4—112no—
164C22×C4⋊C4—112no—
165C22×C4⋊C4C2×D1112yes—
166C22×C4⋊C4C2×D1111yescharacteristic
167C22×C42—112no—
168C22×C42C2×D1112yes—
169C22×C42C2×D1111yescharacteristic
170#382—224no—
171C4×C4⋊C4—224no—
172C2×#95—118no—
173C2×#95—112no—
174C2×#95—112no—
175C2×#95—112no—
176C2×#95—118no—
177C22×C11C22×C22⋊C411yescharacteristic
178C22×C11C2×#11712yes—
179C22×C11C2×C4×Q812yes—
180C22×C11#52012yes—
181C22×C11C2×C22⋊Q812yes—
182C22×C11#52512yes—
183C22×C11#52512yes—
184C22×C11C2×#12411yescharacteristic
185C22×C11C2×C4⋊Q811yescharacteristic
186C22×C11#53511yescharacteristic
187C22×C11#53611yescharacteristic
188C22×C11#53712yes—
189C22×C11#55414yes—
190C22×C11#55614yes—
191C22×C11#55714yes—
192C22×C11#55914yes—
193C4×C11—24no—
194C4×C11—24no—
195C4×C11—28no—
196C4×C11—44no—
197C4×C11#39118yes—
198Dic11—48no—
199Dic11—84no—
200C22×Q8—28no—
201C22×Q8—22no—
202C22×Q8—22no—
203C22×Q8C2×Dic1114yes—
204C23×C4—114no—
205C23×C4—114no—
206C23×C4C22×D1112yes—
207C23×C4C22×D1112yes—
208C23×C4C22×D1111yescharacteristic
209C23×C4C22×D1111yescharacteristic
210C23×C4C22×D1111yescharacteristic
211C4×Q8—232no—
212C2×C4⋊C4—24no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—118no—
217C2×C4⋊C4—224no—
218C2×C4⋊C4—224no—
219C2×C4⋊C4—228no—
220C2×C4⋊C4—224no—
221C2×C4⋊C4C2×Dic1114yes—
222C2×C4⋊C4C2×Dic1118yes—
223C2×C42—24no—
224C2×C42—24no—
225C2×C42—224no—
226C2×C42—444no—
227C2×C42C2×Dic1118yes—
228C2×C42C2×Dic1114yes—
229C2×C42C22⋊D1114yes—
230C2×C42C22⋊D1114yes—
231#95—2216no—
232#95—224no—
233#95—224no—
234#95—224no—
235#95—448no—
236C2×C11#228011yescharacteristic
237C2×C11C2×#39111yescharacteristic
238C2×C11#231111yescharacteristic
239C2×C11#235514yes—
240C2×C11#258012yes—
241C2×C11#258112yes—
242C2×C11#258412yes—
243C2×C11#259212yes—
244C24C23×D1111yescharacteristic
245C2×Q8—216no—
246C2×Q8—216no—
247C2×Q8—216no—
248C2×Q8—28no—
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—118no—
260C22×C4—228no—
261C22×C4—224no—
262C22×C4—228no—
263C22×C4—224no—
264C22×C4—228no—
265C22×C4—228no—
266C22×C4—224no—
267C22×C4—224no—
268C22×C4—224no—
269C22×C4#433918yes—
270C22×C4Q8×D1114yes—
271C22×C4#434314yes—
272C22×C4C22×Dic1114yes—
273C22×C4C22×Dic1114yes—
274C22×C4C22×Dic1112yes—
275C22×C4C22×Dic1112yes—
276C22×C4C22×Dic1112yes—
277C22×C4C2×C22⋊D1112yes—
278C22×C4C2×C22⋊D1112yes—
279C22×C4C2×C22⋊D1112yes—
280C22×C4C2×C22⋊D1112yes—
281C22×C4C2×C22⋊D1112yes—
282C22×C4C2×C22⋊D1112yes—
283C4⋊C4—216no—
284C4⋊C4—28no—
285C4⋊C4—2216no—
286C4⋊C4—448no—
287C42—216no—
288C42—448no—
289C42C22⋊Dic11116yes—
290C11#1392511yescharacteristic, complemented, Sylow
291C23C2×#433914yes—
292C23C2×Q8×D1112yes—
293C23C2×#434312yes—
294C23#6704212yes—
295C23#6704312yes—
296C23C23×Dic1111yescharacteristic
297C23C22×C22⋊D1111yescharacteristic
298C23C22×C22⋊D1111yescharacteristic
299Q8—232no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—28no—
303C2×C4—28no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—28no—
312C2×C4—24no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—44no—
316C2×C4—228no—
317C2×C4—2216no—
318C2×C4—444no—
319C2×C4—444no—
320C2×C4—448no—
321C2×C4—444no—
322C2×C4—444no—
323C2×C4—444no—
324C2×C4—448no—
325C2×C4—448no—
326C2×C4#6697918yes—
327C2×C4#6699714yes—
328C2×C4Q8×Dic1118yes—
329C2×C4#6699918yes—
330C2×C4#6700014yes—
331C2×C4C2×C22⋊Dic1114yes—
332C2×C4C2×C22⋊Dic1114yes—
333C2×C4C2×C22⋊Dic1114yes—
334C22#1062309814yes—
335C22#1062311014yes—
336C22#1062311514yes—
337C22#1062311614yes—
338C22C2×#6697912yes—
339C22#1062332212yes—
340C22#1062332212yes—
341C22C2×#6699711yescharacteristic
342C22C2×Q8×Dic1112yes—
343C22C2×#6699912yes—
344C22C2×#6700011yescharacteristic
345C22#1062335611yescharacteristic
346C22#1062335812yes—
347C22#1062336111yescharacteristic
348C22#1062336412yes—
349C22C22×C22⋊Dic1111yescharacteristic
350C4—24no—
351C4—28no—
352C4—24no—
353C4—44no—
354C4—448no—
355C4—884no—
356C4#1062284318yes—
357C2#1307099911yescharacteristic
358C2C2×#1062284311yescharacteristic
359C2#1307120811yescharacteristic
360C2#1307157314yes—
361C2#1307397412yes—
362C2#1307398212yes—
363C2#1307400412yes—
364C2#1307410412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×Q8×C11C2
socle, prime radical, cosocleC24×C11C24
hypercenterC22×C4×Q8D11
hypocenterC11#13925
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
11. C2×C4×Q8×C11C4semidirect
54. C2×C4⋊Dic11Q8semidirect
162. C2×C4×Q8Dic11semidirect
290. C11#13925semidirect

Maximal subgroups

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

subgroupindex
C2×#106225492
C2×C4×C4⋊Dic112
#130668872
#130668842
#130668482
#130668462
C22×C4×Q8×C112
#1392511