Finite Group Databasebeta

← #14664326

Subgroups — #14664326

Order 2816.

786 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 87 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#13071972C211yesmaximal, characteristic
2C4×#66898C211yesmaximal, characteristic, complemented
3#13066614C214yesmaximal, complemented
4C11×#1466C211yesmaximal, characteristic, complemented
5C23×D44C411yescharacteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66990—21no—
8C2×#66983—21no—
9C11×#432—21no—
10C2×#66898—21no—
11#10622825C411yescharacteristic, complemented
12C4×C22⋊Dic11—21no—
13#10622604C412yescomplemented
14#10622573C2212yes—
15#10622568—21no—
16#10622552—21no—
17C11×#323—21no—
18C11×#323C2212yescomplemented
19#10622164C2212yescomplemented
20C24×D11—21no—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C22×C22⋊D11—22no—
25C22×D44—21no—
26C22×D44—44no—
27C22×D44—41no—
28C22×D44—41no—
29C22×D44C2×C412yes—
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C11×C22⋊C4C2311yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C22⋊Dic11—22no—
37C2×C22⋊Dic11—21no—
38#66990—44no—
39#66983—44no—
40C2×(C2×D11)⋊C4—22no—
41C2×(C2×D11)⋊C4—22no—
42C2×(C2×D11)⋊C4—22no—
43C2×C4⋊Dic11—21no—
44C2×C4×Dic11—41no—
45C11×C4⋊C8—41no—
46C11×C22⋊C8—22no—
47C11×#97—41no—
48#66898—24no—
49C11⋊#95—41no—
50C11⋊#95C2×C412yes—
51#11772—111nomaximal, Sylow
52C24×C11C22⋊C411yescharacteristic
53C24×C11C2×D411yescharacteristic
54C23×D11—22no—
55C23×D11—44no—
56C23×D11—42no—
57C23×D11—42no—
58C23×D11—42no—
59C23×D11—82no—
60C2×D4×C11—22no—
61C2×D4×C11—22no—
62C2×D4×C11—41no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—42no—
68C22×C4×C11—42no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C2×C22⋊D11—44no—
75C2×C22⋊D11—44no—
76C2×C22⋊D11—82no—
77C22×Dic11—22no—
78C22×Dic11—42no—
79C2×D44—24no—
80C2×D44—42no—
81C2×D44—42no—
82C2×D44—44no—
83C2×D44—44no—
84C2×D44—48no—
85C2×D44—44no—
86C2×D44—41no—
87C2×D44—41no—
88C2×C8×C11—42no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C42×C11—21no—
93C42×C11—21no—
94C22⋊Dic11—24no—
95C22⋊Dic11—42no—
96C22⋊Dic11—42no—
97(C2×D11)⋊C4—44no—
98(C2×D11)⋊C4—44no—
99(C2×D11)⋊C4—82no—
100C4⋊Dic11—42no—
101C4×Dic11—82no—
102#2408—111no—
103C4×#99—111no—
104#1466D1111yescharacteristic, complemented
105#1343—114no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11#10412yes—
115C23×C11C2×C22⋊C411yescharacteristic
116C23×C11AGL(1,ℤ/8)12yes—
117C22×D11—24no—
118C22×D11—42no—
119C22×D11—42no—
120C22×D11—42no—
121C22×D11—48no—
122C22×D11—42no—
123C22×D11—42no—
124C22×D11—42no—
125C22×D11—88no—
126C22×D11—88no—
127C22×D11—84no—
128C22×D11—84no—
129D4×C11—44no—
130C2×C4×C11—22no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—81no—
144C2×C4×C11#9911yescharacteristic
145C2×C4×C11#9911yescharacteristic
146C22⋊D11—88no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—44no—
150C2×Dic11—42no—
151C2×Dic11—82no—
152C2×Dic11—82no—
153D44—44no—
154D44—44no—
155D44—44no—
156D44—44no—
157C8×C11—82no—
158C23×D4—111no—
159C2×#121—221no—
160C2×#120—221no—
161C2×C4×D4C2×D1111yescharacteristic
162#432—21no—
163C2×#99—221no—
164#394—112no—
165#392—112no—
166#390—221no—
167#380—111no—
168#379—221no—
169C4×C22⋊C4—221no—
170#342—112no—
171#323—21no—
172#323C2×D1112yescomplemented
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—22no—
176C22×C11—22no—
177C22×C11—42no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—81no—
185C22×C11C2×#9911yescharacteristic
186C22×C11#41811yescharacteristic
187C22×C11C2×#10411yescharacteristic
188C2×D11—44no—
189C2×D11—44no—
190C2×D11—44no—
191C2×D11—82no—
192C2×D11—82no—
193C2×D11—816no—
194C2×D11—82no—
195C2×D11—82no—
196C4×C11—21no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—41no—
200C4×C11—41no—
201C4×C11AΣL(1,𝔽16)12yes—
202Dic11—82no—
203Dic11—84no—
204C25—221no—
205C22×D4—112no—
206C22×D4—222no—
207C22×D4—221no—
208C22×D4—441no—
209C22×D4—441no—
210C22×D4—444no—
211C22×D4D4411yescharacteristic
212C23×C4C4×D1111yescharacteristic
213C23×C4D4411yescharacteristic
214#121—444no—
215#120—444no—
216C4×D4—41no—
217C4×D4—41no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4C4×D1111yescharacteristic
220C2×C22⋊C4—222no—
221C2×C22⋊C4—221no—
222C2×C22⋊C4—222no—
223C2×C22⋊C4—222no—
224C2×C22⋊C4—222no—
225C2×C22⋊C4C22⋊D1111yescharacteristic
226C2×C22⋊C4C22×D1111yescharacteristic
227C2×C42—441no—
228C2×C42C22⋊D1111yescharacteristic
229C4⋊C8—41no—
230#99—224no—
231C22⋊C8—22no—
232#97—41no—
233#95—112no—
234#95—441no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—42no—
238C2×C11—42no—
239C2×C11#150711yescharacteristic
240C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
241C2×C11#212811yescharacteristic
242D11—84no—
243C24—222no—
244C24—442no—
245C24—442no—
246C24—444no—
247C24—442no—
248C24—882no—
249C24(C2×D11)⋊C411yescharacteristic
250C24C2×D4411yescharacteristic
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—41no—
254C2×D4—224no—
255C2×D4—442no—
256C2×D4—442no—
257C2×D4—448no—
258C2×D4—444no—
259C2×D4—444no—
260C2×D4—444no—
261C2×D4—444no—
262C2×D4—444no—
263C2×D4—441no—
264C2×D4—441no—
265C2×D4—882no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—222no—
273C22×C4—442no—
274C22×C4(C2×D11)⋊C411yescharacteristic
275C22×C4(C2×D11)⋊C411yescharacteristic
276C22×C4(C2×D11)⋊C411yescharacteristic
277C22×C4C2×C4×D1111yescharacteristic
278C22×C4C2×C22⋊D1111yescharacteristic
279C2×C8—42no—
280C4⋊C4—41no—
281C4⋊C4—442no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—224no—
285C22⋊C4—444no—
286C22⋊C4—444no—
287C22⋊C4—442no—
288C22⋊C4—442no—
289C22⋊C4—882no—
290C42—21no—
291C42—21no—
292C42—882no—
293C11#1177211yescharacteristic, complemented, Sylow
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—224no—
303C23—442no—
304C23—442no—
305C23—442no—
306C23—448no—
307C23—442no—
308C23—442no—
309C23—442no—
310C23—884no—
311C23—888no—
312C23—888no—
313C23—884no—
314C23#6688912yes—
315C23#6696112yes—
316C23C2×(C2×D11)⋊C411yescharacteristic
317D4—44no—
318D4—444no—
319D4—444no—
320D4—444no—
321D4—444no—
322D4—888no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—444no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—882no—
342C2×C4—882no—
343C2×C4#6687011yescharacteristic
344C2×C4#6687011yescharacteristic
345C8—82no—
346C22—21no—
347C22—21no—
348C22—22no—
349C22—22no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—81no—
358C22—444no—
359C22—444no—
360C22—444no—
361C22—882no—
362C22—882no—
363C22—8816no—
364C22—882no—
365C22—882no—
366C22C2×#6687011yescharacteristic
367C22#1062274411yescharacteristic
368C22C2×#6688911yescharacteristic
369C4—21no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—882no—
375C4—884no—
376C4#1062211312yes—
377C2—21no—
378C2—21no—
379C2—42no—
380C2—42no—
381C2—884no—
382C2#1306713311yescharacteristic
383C2C2×#1062211311yescharacteristic
384C2#1307028711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1466C2
socleC22×C11C2×#99
prime radical#13071972C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1466D11
hypocenterC11#11772
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
2. C4×#66898C2semidirect
3. #13066614C2semidirect
4. C11×#1466C2semidirect
5. C23×D44C4semidirect
11. #10622825C4semidirect
13. #10622604C4semidirect
18. C11×#323C22semidirect
19. #10622164C22semidirect
104. #1466D11semidirect
172. #323C2×D11semidirect
293. C11#11772semidirect

Maximal subgroups

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

subgroupindex
#130719722
C4×#668982
#130666142
C11×#14662
#1177211