Finite Group Databasebeta

← #14662862

Subgroups — #14662862

Order 2816.

734 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 93 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
1#13071193C211yesmaximal, characteristic
2D11×#323C212yesmaximal, complemented
3#13066546C211yesmaximal, characteristic, complemented
4#13066543C212yesmaximal, complemented
5C11×#1317C211yesmaximal, characteristic, complemented
6C23×D44C411yescharacteristic
7C2×C22⋊C4×D11C411yescharacteristic
8C2×C22⋊C4×D11C2211yescharacteristic
9C11×#381C2211yescharacteristic
10#10622824C411yescharacteristic
11#10622568C411yescharacteristic
12#10622568C2211yescharacteristic
13D11×C22⋊C8—22no—
14#10622278—22no—
15#10622278—22no—
16C11×#323C2212yes—
17#10622163C2212yes—
18#10622106—22no—
19C24×D11C2×C411yescharacteristic
20C24×D11C2×C411yescharacteristic
21C23×C4×C11C2×C411yescharacteristic
22C22×D44—21no—
23C22×D44—21no—
24C22×D44—22no—
25C22×D44—42no—
26C22×D44—42no—
27C22×D44C814yescomplemented
28C22×C4×D11—21no—
29C22×C4×D11D412yes—
30C2×C11×C22⋊C4C2×C411yescharacteristic
31C2×C11×C22⋊C4C2311yescharacteristic
32C2×C22⋊Dic11C2×C411yescharacteristic
33C2×C22⋊Dic11C2×C411yescharacteristic
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4—22no—
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4D412yes—
38C2×C8×D11—42no—
39C22⋊C4×D11—42no—
40C22⋊C4×D11—42no—
41C11×C22⋊C8—22no—
42C11×#95—22no—
43C11⋊#95—22no—
44C22⋊(C11⋊C8)—22no—
45(C2×D11)⋊C8—42no—
46#11426—111nomaximal, Sylow
47C24×C11C22×C411yescharacteristic
48C23×D11—22no—
49C23×D11—22no—
50C23×D11—21no—
51C23×D11—21no—
52C23×D11—41no—
53C23×D11—41no—
54C23×D11—82no—
55C23×D11—82no—
56C23×D11C22⋊C411yescharacteristic
57C23×D11C22⋊C411yescharacteristic
58C23×D11C2×C812yes—
59C23×D11C2×C812yescomplemented
60C23×D11M1612yes—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11C2×C812yescomplemented
67C22×C4×C11C2×D412yes—
68C22×Dic11—21no—
69C22×Dic11C22⋊C412yes—
70C2×D44—24no—
71C2×D44—24no—
72C2×D44—48no—
73C2×D44—48no—
74C2×D44—42no—
75C2×D44—42no—
76C2×D44—42no—
77C2×D44—42no—
78C2×C4×D11—22no—
79C2×C4×D11—22no—
80C2×C4×D11—42no—
81C2×C4×D11—82no—
82C2×C4×D11—82no—
83C2×C8×C11—42no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C22⋊Dic11—41no—
87C22⋊Dic11—41no—
88(C2×D11)⋊C4—42no—
89(C2×D11)⋊C4—42no—
90(C2×D11)⋊C4—82no—
91(C2×D11)⋊C4—82no—
92C2×C11⋊C8—42no—
93C8×D11—84no—
94#2308—111no—
95C2×#323—112no—
96#1317—111no—
97#1317D1111yescharacteristic, complemented
98#1316—112no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—42no—
102C23×C11C2×C22⋊C411yescharacteristic
103C23×C11C22×C811yescharacteristic
104C23×C11C2×M1611yescharacteristic
105C22×D11—21no—
106C22×D11—21no—
107C22×D11—24no—
108C22×D11—24no—
109C22×D11—22no—
110C22×D11—42no—
111C22×D11—42no—
112C22×D11—42no—
113C22×D11—42no—
114C22×D11—42no—
115C22×D11—41no—
116C22×D11—41no—
117C22×D11—42no—
118C22×D11—82no—
119C22×D11—82no—
120C22×D11—84no—
121C22×D11—82no—
122C22×D11—82no—
123C22×D11—82no—
124C22×D11—82no—
125C22×D11—84no—
126C22×D11—84no—
127C22×D11C22⋊C812yes—
128C22×D11C22⋊C812yes—
129C22×D11#9912yes—
130C22×D11#10012yes—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—42no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×Dic11—22no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143C2×Dic11—41no—
144D44—48no—
145D44—48no—
146C4×D11—44no—
147C4×D11—82no—
148C4×D11—84no—
149C8×C11—82no—
150C11⋊C8—82no—
151C23×D4—111no—
152C22×C22⋊C4—111no—
153C22×C22⋊C4—111no—
154C2×C22⋊C8—222no—
155#386—222no—
156#386—222no—
157#381—111no—
158#381C2×D1111yescharacteristic
159#379—111no—
160#379—111no—
161#323—112no—
162#323—222no—
163#323C2×D1112yes—
164C22×C11—22no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—42no—
170C22×C11—42no—
171C22×C11C2×C22⋊C811yescharacteristic
172C22×C11C2×#9911yescharacteristic
173C22×C11C2×#10011yescharacteristic
174C2×D11—22no—
175C2×D11—22no—
176C2×D11—22no—
177C2×D11—42no—
178C2×D11—42no—
179C2×D11—42no—
180C2×D11—42no—
181C2×D11—42no—
182C2×D11—42no—
183C2×D11—42no—
184C2×D11—42no—
185C2×D11—84no—
186C2×D11—84no—
187C2×D11—82no—
188C2×D11—84no—
189C2×D11—82no—
190C2×D11—84no—
191C2×D11#32314yes—
192C4×C11—42no—
193C4×C11—42no—
194C4×C11—81no—
195Dic11—42no—
196Dic11—81no—
197C25—111no—
198C25—111no—
199C22×D4—114no—
200C22×D4—221no—
201C22×D4—221no—
202C22×D4—222no—
203C22×D4—442no—
204C22×D4—442no—
205C23×C4—112no—
206C23×C4—221no—
207C23×C4C4×D1111yescharacteristic
208C22×C8—442no—
209C2×C22⋊C4—111no—
210C2×C22⋊C4—112no—
211C2×C22⋊C4—111no—
212C2×C22⋊C4—221no—
213C2×C22⋊C4—222no—
214C2×C22⋊C4—222no—
215C2×C22⋊C4—442no—
216C2×C22⋊C4—442no—
217C2×C22⋊C4C4×D1111yescharacteristic
218C2×C22⋊C4C22×D1111yescharacteristic
219C22⋊C8—22no—
220C22⋊C8—222no—
221C22⋊C8—442no—
222#95—22no—
223#95—222no—
224C2×C11—21no—
225C2×C11—21no—
226C2×C11—41no—
227C2×C11—41no—
228C2×C11C2×#32311yescharacteristic
229C2×C11#212112yes—
230D11—24no—
231D11—42no—
232D11—82no—
233C24—111no—
234C24—111no—
235C24—112no—
236C24—112no—
237C24—112no—
238C24—222no—
239C24—222no—
240C24—221no—
241C24—221no—
242C24—441no—
243C24—441no—
244C24—882no—
245C24—882no—
246C24C2×C4×D1111yescharacteristic
247C2×D4—224no—
248C2×D4—224no—
249C2×D4—442no—
250C2×D4—442no—
251C2×D4—448no—
252C2×D4—442no—
253C2×D4—442no—
254C2×D4—448no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—112no—
261C22×C4—222no—
262C22×C4—222no—
263C22×C4—221no—
264C22×C4—442no—
265C22×C4—882no—
266C22×C4—882no—
267C22×C4C8×D1112yescomplemented
268C22×C4D4×D1112yes—
269C2×C8—42no—
270C2×C8—442no—
271C2×C8—884no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—442no—
275C22⋊C4—442no—
276C22⋊C4—441no—
277C22⋊C4—441no—
278C22⋊C4—882no—
279C22⋊C4—882no—
280C11#1142611yescharacteristic, complemented, Sylow
281C23—21no—
282C23—21no—
283C23—42no—
284C23—112no—
285C23—112no—
286C23—112no—
287C23—112no—
288C23—224no—
289C23—224no—
290C23—221no—
291C23—221no—
292C23—222no—
293C23—442no—
294C23—442no—
295C23—442no—
296C23—442no—
297C23—442no—
298C23—442no—
299C23—441no—
300C23—441no—
301C23—882no—
302C23—882no—
303C23—882no—
304C23—882no—
305C23—882no—
306C23—882no—
307C23—884no—
308C23—884no—
309C23—884no—
310C23C22⋊C4×D1111yescharacteristic
311C23C2×C8×D1111yescharacteristic
312C23M16×D1111yescharacteristic
313D4—448no—
314D4—448no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—222no—
325C2×C4—444no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—441no—
329C2×C4—882no—
330C2×C4—884no—
331C8—82no—
332C8—882no—
333C22—22no—
334C22—21no—
335C22—21no—
336C22—41no—
337C22—41no—
338C22—42no—
339C22—42no—
340C22—114no—
341C22—222no—
342C22—222no—
343C22—222no—
344C22—442no—
345C22—442no—
346C22—442no—
347C22—442no—
348C22—442no—
349C22—442no—
350C22—442no—
351C22—442no—
352C22—882no—
353C22—884no—
354C22—884no—
355C22—884no—
356C22—884no—
357C22—882no—
358C22D11×C22⋊C811yescharacteristic
359C22D11×#9911yescharacteristic
360C22D11×#10011yescharacteristic
361C4—42no—
362C4—42no—
363C4—81no—
364C4—442no—
365C4—881no—
366C2—21no—
367C2—21no—
368C2—41no—
369C2—41no—
370C2—224no—
371C2—442no—
372C2—882no—
373C2D11×#32311yescharacteristic
374C2#1307026112yes—
subgroupG/H
centerC22D11×#99
commutatorC23×C11C22×C8
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1317C2
socleC22×C11C2×#99
prime radicalC23×D44C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1317D11
hypocenterC11#11426
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
2. D11×#323C2semidirect
3. #13066546C2semidirect
4. #13066543C2semidirect
5. C11×#1317C2semidirect
27. C22×D44C8semidirect
59. C23×D11C2×C8semidirect
66. C22×C4×C11C2×C8semidirect
97. #1317D11semidirect
267. C22×C4C8×D11semidirect
280. C11#11426semidirect

Maximal subgroups

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

subgroupindex
#130711932
D11×#3232
#130665462
#130665432
C11×#13172
#1142611