Finite Group Databasebeta

← #14644136

Subgroups — #14644136

Order 2816.

914 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 155 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
1D11×#407C212yesmaximal
2#13070996C211yesmaximal, characteristic
3#13066525C212yesmaximal, complemented
4#13066524C211yesmaximal, characteristic, complemented
5C11×#1306C211yesmaximal, characteristic, complemented
6C23×C4×D11C2211yescharacteristic
7C2×M16×D11—22no—
8C2×#66930C412yes—
9C11×#407C2212yes—
10C11×#381C2211yescharacteristic
11#10622824C2211yescharacteristic
12#10622820C2212yes—
13#10622739—22no—
14#10622568C412yes—
15#10622339—22no—
16#10622339C414yescomplemented
17D11×C22⋊C8—22no—
18D11×C22⋊C8C414yescomplemented
19#10622280—22no—
20#10622279—22no—
21C24×D11C2×C411yescharacteristic
22C23×C4×C11C2311yescharacteristic
23C23×Dic11C2×C411yescharacteristic
24C22×C4×D11—44no—
25C22×C4×D11C2×C412yes—
26C22×C4×D11C2×C412yes—
27C22×C4×D11D412yes—
28C22×C4×D11D411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×C4×D11D412yes—
31C22×C4×D11Q811yescharacteristic
32C22×C4×D11Q811yescharacteristic
33C2×C11×M16—22no—
34C2×C11×C22⋊C4C2×C412yes—
35C2×C22⋊Dic11C2×C412yes—
36C2×(C2×D11)⋊C4—24no—
37C2×Dic11⋊C4—22no—
38C2×C4×Dic11—22no—
39C2×#4318—22no—
40M16×D11—48no—
41C2×#4313—24no—
42C2×C8×D11—24no—
43#66930—44no—
44C11×C22⋊C8—22no—
45C11×C22⋊C8C2×C414yes—
46C11×#95—22no—
47C11⋊#95—22no—
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)C2×C414yes—
50(C2×D11)⋊C8—24no—
51(C2×D11)⋊C8—24no—
52#8112—111nomaximal, Sylow
53C24×C11C22×C411yescharacteristic
54C23×D11—44no—
55C23×D11—42no—
56C23×D11C4212yes—
57C23×D11C22⋊C412yes—
58C23×D11C4⋊C411yescharacteristic
59C23×D11C4⋊C411yescharacteristic
60C22×C4×C11—22no—
61C22×C4×C11—42no—
62C22×C4×C11C22×C412yes—
63C22×C4×C11C2×D412yes—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×Q811yescharacteristic
66C22×Dic11—24no—
67C22×Dic11—22no—
68C22×Dic11C4211yescharacteristic
69C22×Dic11C4211yescharacteristic
70C22×Dic11C22⋊C411yescharacteristic
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C4⋊C411yescharacteristic
73C22×Dic11C4⋊C411yescharacteristic
74C2×C4×D11—28no—
75C2×C4×D11—44no—
76C2×C4×D11—44no—
77C2×C4×D11—44no—
78C2×C4×D11—42no—
79C2×C4×D11—42no—
80C2×C4×D11—42no—
81C2×C4×D11—42no—
82C2×C4×D11C22⋊C412yes—
83C2×C4×D11C22⋊C412yes—
84C2×C4×D11C22⋊C412yes—
85C2×C4×D11C22⋊C412yes—
86C2×C4×D11C4⋊C412yes—
87C2×C4×D11C4⋊C412yes—
88C2×C4×D11C4⋊C412yes—
89C2×C4×D11C4⋊C412yes—
90C11×M16—44no—
91C2×C8×C11—24no—
92C11×C22⋊C4—42no—
93C22⋊Dic11—42no—
94(C2×D11)⋊C4—48no—
95Dic11⋊C4—44no—
96C4×Dic11—44no—
97#4318—44no—
98C2×C11⋊C8—24no—
99#4313—48no—
100C8×D11—48no—
101C2×#407—112no—
102#2280—111no—
103#1306—112no—
104#1306—111no—
105#1306D1111yescharacteristic, complemented
106C23×C11—22no—
107C23×C11—42no—
108C23×C11C2×C4211yescharacteristic
109C23×C11C2×C22⋊C411yescharacteristic
110C23×C11C2×C4⋊C411yescharacteristic
111C22×D11—24no—
112C22×D11—24no—
113C22×D11—24no—
114C22×D11—24no—
115C22×D11—42no—
116C22×D11—41no—
117C22×D11—41no—
118C22×D11—42no—
119C22×D11—42no—
120C22×D11—42no—
121C22×D11—416no—
122C22×D11#9512yes—
123C22×D11#9512yes—
124C2×C4×C11—24no—
125C2×C4×C11—42no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—44no—
129C2×C4×C11—42no—
130C2×C4×C11C2×C22⋊C412yes—
131C2×C4×C11C2×C4⋊C412yes—
132C2×Dic11—22no—
133C2×Dic11—22no—
134C2×Dic11—22no—
135C2×Dic11—22no—
136C2×Dic11—22no—
137C2×Dic11—44no—
138C2×Dic11—42no—
139C2×Dic11#9511yescharacteristic
140C2×Dic11#9511yescharacteristic
141C2×Dic11#9511yescharacteristic
142C2×Dic11#9511yescharacteristic
143C2×Dic11#9914yes—
144C4×D11—24no—
145C4×D11—24no—
146C4×D11—24no—
147C4×D11—24no—
148C4×D11—42no—
149C4×D11—42no—
150C4×D11—42no—
151C4×D11—42no—
152C8×C11—44no—
153C11⋊C8—44no—
154C24×C4—111no—
155C22×M16—222no—
156C2×#117—112no—
157#407—112no—
158#407—114no—
159#407—222no—
160#407—222no—
161#407C2×D1112yes—
162C2×C22⋊C8—114no—
163C2×C22⋊C8—222no—
164#381—111no—
165#381C2×D1111yescharacteristic
166#380—222no—
167#379—112no—
168C4×C22⋊C4—222no—
169C22×C11—22no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—44no—
175C22×C11C2×#9511yescharacteristic
176C22×C11C2×#9912yes—
177C2×D11—22no—
178C2×D11—22no—
179C2×D11—22no—
180C2×D11—22no—
181C2×D11—22no—
182C2×D11—44no—
183C2×D11—48no—
184C2×D11—48no—
185C2×D11—44no—
186C2×D11#34414yes—
187C4×C11—22no—
188C4×C11—22no—
189C4×C11—82no—
190Dic11—21no—
191Dic11—21no—
192Dic11—82no—
193Dic11#34212yes—
194Dic11#34212yes—
195C25—111no—
196C23×C4—111no—
197C23×C4—112no—
198C23×C4—112no—
199C23×C4—112no—
200C23×C4—112no—
201C23×C4—111no—
202C23×C4—111no—
203C23×C4—111no—
204C23×C4—111no—
205C23×C4—444no—
206C23×C4C22×D1111yescharacteristic
207C2×M16—22no—
208C2×M16—224no—
209C2×M16—222no—
210C2×M16—448no—
211C22×C8—224no—
212#117—444no—
213C2×C4⋊C4—222no—
214C2×C22⋊C4—112no—
215C2×C22⋊C4—224no—
216C2×C22⋊C4C4×D1112yes—
217C2×C42—222no—
218C22⋊C8—22no—
219C22⋊C8—114no—
220C22⋊C8—224no—
221C22⋊C8—224no—
222C22⋊C8—222no—
223C22⋊C8C4×D1114yes—
224#95—22no—
225#95—222no—
226C2×C11—22no—
227C2×C11—41no—
228C2×C11—41no—
229C2×C11C2×#34211yescharacteristic
230C2×C11C2×#34412yes—
231D11—24no—
232D11—42no—
233C24—112no—
234C24—111no—
235C24—112no—
236C24—111no—
237C24—442no—
238C24—444no—
239C24C2×C4×D1111yescharacteristic
240C22×C4—22no—
241C22×C4—42no—
242C22×C4—111no—
243C22×C4—111no—
244C22×C4—111no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—112no—
249C22×C4—112no—
250C22×C4—112no—
251C22×C4—112no—
252C22×C4—112no—
253C22×C4—112no—
254C22×C4—112no—
255C22×C4—112no—
256C22×C4—228no—
257C22×C4—224no—
258C22×C4—222no—
259C22×C4—444no—
260C22×C4—444no—
261C22×C4—444no—
262C22×C4—442no—
263C22×C4—442no—
264C22×C4—442no—
265C22×C4—442no—
266C22×C4C2×C4×D1112yes—
267C22×C4D4×D1112yes—
268C22×C4D4×D1111yescharacteristic
269C22×C4Q8×D1111yescharacteristic
270M16—44no—
271M16—448no—
272M16—444no—
273C2×C8—24no—
274C2×C8—224no—
275C2×C8—448no—
276C4⋊C4—444no—
277C22⋊C4—42no—
278C22⋊C4—448no—
279C22⋊C4—442no—
280C42—444no—
281C11#811211yescharacteristic, complemented, Sylow
282C23—22no—
283C23—42no—
284C23—112no—
285C23—112no—
286C23—224no—
287C23—224no—
288C23—224no—
289C23—224no—
290C23—442no—
291C23—441no—
292C23—441no—
293C23—442no—
294C23—442no—
295C23—442no—
296C23—4416no—
297C23C42×D1111yescharacteristic
298C23C22⋊C4×D1111yescharacteristic
299C23C4⋊C4×D1111yescharacteristic
300C2×C4—24no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—44no—
305C2×C4—42no—
306C2×C4—111no—
307C2×C4—111no—
308C2×C4—114no—
309C2×C4—111no—
310C2×C4—111no—
311C2×C4—224no—
312C2×C4—224no—
313C2×C4—224no—
314C2×C4—224no—
315C2×C4—222no—
316C2×C4—222no—
317C2×C4—222no—
318C2×C4—222no—
319C2×C4—222no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4—444no—
325C2×C4—442no—
326C2×C4C22⋊C4×D1112yes—
327C2×C4C4⋊C4×D1112yes—
328C8—44no—
329C8—444no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22—44no—
336C22—114no—
337C22—222no—
338C22—222no—
339C22—222no—
340C22—222no—
341C22—222no—
342C22—448no—
343C22—444no—
344C22—448no—
345C22—444no—
346C22D11×#9511yescharacteristic
347C22D11×#9912yes—
348C4—22no—
349C4—22no—
350C4—82no—
351C4—112no—
352C4—112no—
353C4—221no—
354C4—221no—
355C4—882no—
356C2—22no—
357C2—41no—
358C2—41no—
359C2—224no—
360C2—442no—
361C2D11×#34211yescharacteristic
362C2D11×#34412yes—
subgroupG/H
centerC22D11×#95
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1306C2
socleC22×C11C2×#95
prime radicalC24×D11C2×C4
cosocleC23×C4×C11C23
hypercenter#1306D11
hypocenterC11#8112
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
3. #13066525C2semidirect
4. #13066524C2semidirect
5. C11×#1306C2semidirect
16. #10622339C4semidirect
18. D11×C22⋊C8C4semidirect
105. #1306D11semidirect
281. C11#8112semidirect

Maximal subgroups

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

subgroupindex
D11×#4072
#130709962
#130665252
#130665242
C11×#13062
#811211