Finite Group Databasebeta

← #14664355

Subgroups — #14664355

Order 2816.

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

normal subgroups only

This group has 768 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
2#13066954C211yesmaximal, characteristic, complemented
3#13066618C214yesmaximal, complemented
4C4×C11×#100C211yesmaximal, characteristic, complemented
5C23×D44C411yescharacteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66990—21no—
8C2×#66983—21no—
9C2×C11×#100—21no—
10C4×C11×M16—21no—
11#10622825C411yescharacteristic
12#10622820—21no—
13#10622604C2212yes—
14#10622573C412yes—
15#10622568—21no—
16#10622552—21no—
17C11×#343C2212yescomplemented
18#10622166C2212yescomplemented
19#10622163—21no—
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—
30C2×C11×M16—22no—
31C4×D4×C11—41no—
32C4×D4×C11—41no—
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4D411yescharacteristic
36C2×C42×C11D411yescharacteristic
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×#4318—41no—
45C11×#100—24no—
46C11×#97—41no—
47C4×C8×C11—41no—
48C11⋊#95C2×C412yes—
49C22⋊(C11⋊C8)—22no—
50C22⋊(C11⋊C8)—41no—
51#11779—111nomaximal, Sylow
52C24×C11C22⋊C411yescharacteristic
53C24×C11C22⋊C411yescharacteristic
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×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C2×C22⋊D11—44no—
75C2×C22⋊D11—44no—
76C2×C22⋊D11—82no—
77C22×Dic11—22no—
78C2×D44—24no—
79C2×D44—42no—
80C2×D44—42no—
81C2×D44—44no—
82C2×D44—44no—
83C2×D44—48no—
84C2×D44—44no—
85C2×D44—41no—
86C2×D44—41no—
87C11×M16—24no—
88C11×M16—42no—
89C2×C8×C11—42no—
90C11×C4⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C42×C11—21no—
94C42×C11—21no—
95C22⋊Dic11—42no—
96(C2×D11)⋊C4—44no—
97(C2×D11)⋊C4—44no—
98(C2×D11)⋊C4—82no—
99C4⋊Dic11—42no—
100#4318—82no—
101C2×C11⋊C8—42no—
102#2408—111no—
103C4×#100D1111yescharacteristic, complemented
104#1465—111no—
105#1345—114no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11#10412yes—
116C23×C11C2×C22⋊C411yescharacteristic
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—21no—
131C2×C4×C11—21no—
132C2×C4×C11—22no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—81no—
143C2×C4×C11#9911yescharacteristic
144C2×C4×C11#9911yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)12yes—
146C22⋊D11—88no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150D44—44no—
151D44—44no—
152D44—44no—
153D44—44no—
154C8×C11—44no—
155C11⋊C8—82no—
156C23×D4—111no—
157C2×#121—221no—
158C2×#120—221no—
159C2×C4×D4C2×D1111yescharacteristic
160C2×#100—21no—
161#407—221no—
162C4×M16—21no—
163#394—112no—
164#392—112no—
165#390—221no—
166#380—111no—
167#379—221no—
168#343C2×D1112yescomplemented
169#324—112no—
170#323—221no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—22no—
174C22×C11—42no—
175C22×C11—42no—
176C22×C11—42no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—81no—
183C22×C11C2×#9911yescharacteristic
184C22×C11#41811yescharacteristic
185C22×C11C2×#10411yescharacteristic
186C2×D11—44no—
187C2×D11—44no—
188C2×D11—44no—
189C2×D11—82no—
190C2×D11—82no—
191C2×D11—816no—
192C2×D11—82no—
193C2×D11—82no—
194C4×C11—21no—
195C4×C11—22no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11AΣL(1,𝔽16)12yes—
200Dic11—82no—
201C25—221no—
202C22×D4—112no—
203C22×D4—222no—
204C22×D4—221no—
205C22×D4—441no—
206C22×D4—441no—
207C22×D4—444no—
208C22×D4C22⋊D1111yescharacteristic
209C23×C4C4×D1111yescharacteristic
210C23×C4D4411yescharacteristic
211C2×M16—22no—
212C2×M16—441no—
213#121—444no—
214#120—444no—
215C4×D4—41no—
216C4×D4—41no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4C22×D1111yescharacteristic
219C2×C22⋊C4—221no—
220C2×C22⋊C4—222no—
221C2×C22⋊C4—222no—
222C2×C22⋊C4—222no—
223C2×C22⋊C4C4×D1111yescharacteristic
224C2×C22⋊C4D4411yescharacteristic
225C2×C42C22⋊D1111yescharacteristic
226#100—24no—
227C22⋊C8—222no—
228C22⋊C8—441no—
229#97—41no—
230C4×C8—41no—
231#95—112no—
232C2×C11—21no—
233C2×C11—21no—
234C2×C11—42no—
235C2×C11—81no—
236C2×C11#150711yescharacteristic
237C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
238C2×C11#213411yescharacteristic
239D11—84no—
240C24—222no—
241C24—442no—
242C24—442no—
243C24—444no—
244C24—442no—
245C24—882no—
246C24(C2×D11)⋊C411yescharacteristic
247C24(C2×D11)⋊C411yescharacteristic
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—41no—
251C2×D4—224no—
252C2×D4—442no—
253C2×D4—442no—
254C2×D4—448no—
255C2×D4—444no—
256C2×D4—444no—
257C2×D4—444no—
258C2×D4—444no—
259C2×D4—444no—
260C2×D4—441no—
261C2×D4—441no—
262C2×D4—882no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—222no—
270C22×C4(C2×D11)⋊C411yescharacteristic
271C22×C4(C2×D11)⋊C411yescharacteristic
272C22×C4C2×C4×D1111yescharacteristic
273C22×C4C2×D4411yescharacteristic
274C22×C4C2×C22⋊D1111yescharacteristic
275M16—24no—
276M16—42no—
277M16—882no—
278C2×C8—42no—
279C2×C8—442no—
280C4⋊C4—41no—
281C4⋊C4—442no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—444no—
285C22⋊C4—442no—
286C22⋊C4—444no—
287C22⋊C4—882no—
288C42—21no—
289C42—21no—
290C11#1177911yescharacteristic, complemented, Sylow
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—224no—
301C23—442no—
302C23—442no—
303C23—442no—
304C23—448no—
305C23—442no—
306C23—442no—
307C23—442no—
308C23—884no—
309C23—888no—
310C23—888no—
311C23—884no—
312C23#6686912yes—
313C23C2×(C2×D11)⋊C411yescharacteristic
314D4—44no—
315D4—444no—
316D4—444no—
317D4—444no—
318D4—444no—
319D4—888no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—442no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4#6687011yescharacteristic
337C2×C4#6687011yescharacteristic
338C2×C4#6700212yes—
339C8—44no—
340C8—882no—
341C22—21no—
342C22—21no—
343C22—22no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—81no—
353C22—444no—
354C22—444no—
355C22—444no—
356C22—882no—
357C22—882no—
358C22—8816no—
359C22—882no—
360C22—882no—
361C22C2×#6686911yescharacteristic
362C22C2×#6687011yescharacteristic
363C22#1062261411yescharacteristic
364C4—22no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—882no—
370C4#1062211312yes—
371C2—21no—
372C2—21no—
373C2—42no—
374C2—81no—
375C2—884no—
376C2#1306713111yescharacteristic
377C2C2×#1062211311yescharacteristic
378C2#1307030711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC4×C11×#100C2
socleC22×C11C2×#99
prime radical#13071972C2
cosocleC2×C11×C4⋊C4C23
hypercenterC4×#100D11
hypocenterC11#11779
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
2. #13066954C2semidirect
3. #13066618C2semidirect
4. C4×C11×#100C2semidirect
17. C11×#343C22semidirect
18. #10622166C22semidirect
103. C4×#100D11semidirect
168. #343C2×D11semidirect
290. C11#11779semidirect

Maximal subgroups

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

subgroupindex
#130719722
#130669542
#130666182
C4×C11×#1002
#1177911