Finite Group Databasebeta

← #14664855

Subgroups — #14664855

Order 2816.

412 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 83 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×#467C211yesmaximal, characteristic
2#13070225C211yesmaximal, characteristic
3#13068640C211yesmaximal, characteristic
4#13066629C211yesmaximal, characteristic, complemented
5#13066628C211yesmaximal, characteristic, complemented
6#13066627C211yesmaximal, characteristic, complemented
7C11×#1348C211yesmaximal, characteristic, complemented
8C2×Q16×D11C411yescharacteristic, complemented
9C22×C8×D11C2211yescharacteristic
10D11×C22⋊Q8—21no—
11C11×#467C2211yescharacteristic
12#10622801C411yescharacteristic, complemented
13#10622729C2211yescharacteristic
14#10622664—21no—
15#10622600—21no—
16C2×#66872—21no—
17C2×#66862—21no—
18#10622500C411yescharacteristic, complemented
19D11×#107C411yescharacteristic, complemented
20#10622426—21no—
21D11×#103—21no—
22C11×C22⋊C16C2211yescharacteristic
23C11×#340C2211yescharacteristic
24#10622189C2211yescharacteristic
25C22⋊(C11⋊C16)C2211yescharacteristic
26(C2×D11)⋊C16—21no—
27C2×Q8×D11—21no—
28C22×C4×D11D411yescharacteristic
29C2×C11×Q16C2×C411yescharacteristic
30C22×C8×C11C2311yescharacteristic
31C11×C22⋊Q8—21no—
32C2×C11×C4⋊C4—21no—
33#66999—21no—
34C2×#4326—21no—
35C2×(C2×D11)⋊C4—41no—
36C2×C4⋊Dic11—21no—
37#66977—21no—
38C22×C11⋊C8D411yescharacteristic
39Q16×D11—42no—
40C2×Dic44C2×C411yescharacteristic
41C2×C8×D11—42no—
42C2×C8×D11C2×C411yescharacteristic
43C2×C8×D11C2×C411yescharacteristic
44C2×C8×D11D411yescharacteristic
45C2×C8×D11D411yescharacteristic
46#66950—21no—
47#66949—41no—
48C4⋊C4×D11—21no—
49C4⋊C4×D11—41no—
50C22⋊C4×D11—41no—
51#66931—41no—
52C2×C11×C16—21no—
53C11×#107C2×C411yescharacteristic
54C11×#103—21no—
55#66899—21no—
56C11⋊#95—41no—
57#66882C2×C411yescharacteristic
58#66880—21no—
59C2×C11⋊C16—21no—
60#66874—21no—
61#66872—42no—
62#66871—21no—
63#66862—42no—
64#11889—111nomaximal, Sylow
65C23×D11D811yescharacteristic
66C2×Q8×C11—21no—
67C22×C4×C11—41no—
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—41no—
70C22×Dic11D811yescharacteristic
71Q8×D11—42no—
72Q8×D11—42no—
73C2×C4×D11—41no—
74C2×C4×D11—41no—
75C2×C4×D11—41no—
76C2×C4×D11—41no—
77C2×C4×D11C22⋊C411yescharacteristic
78C2×C4×D11C22⋊C411yescharacteristic
79C2×C4×D11SD1611yescharacteristic
80C2×C4×D11SD1611yescharacteristic
81C2×Dic22—21no—
82C2×Dic22—41no—
83C11×Q16—41no—
84C2×C8×C11—41no—
85C2×C8×C11C22×C411yescharacteristic
86C2×C8×C11C2×D411yescharacteristic
87C11×C4⋊C4—21no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C22⋊C4—41no—
92C22⋊Dic11—41no—
93#4326—42no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—82no—
97C4⋊Dic11—21no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101Dic11⋊C4—41no—
102Dic11⋊C4—41no—
103Dic11⋊C4—41no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8C22⋊C411yescharacteristic
106C2×C11⋊C8C22⋊C411yescharacteristic
107Dic44—41no—
108C8×D11—22no—
109C8×D11—22no—
110C8×D11—41no—
111C8×D11—41no—
112C11×C16—41no—
113C11⋊C16—41no—
114C2×#467—111no—
115#2112—111no—
116#1807—111no—
117#1348—111no—
118#1348—111no—
119#1348—111no—
120#1348D1111yescharacteristic, complemented
121C23×C11C2×D811yescharacteristic
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—22no—
125C22×D11—41no—
126C22×D11#10211yescharacteristic
127C22×D11#10211yescharacteristic
128Q8×C11—41no—
129Q8×C11—41no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—81no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11C2×C22⋊C411yescharacteristic
138C2×C4×C11C2×SD1611yescharacteristic
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—81no—
143C2×Dic11—81no—
144C2×Dic11—81no—
145C2×Dic11#10211yescharacteristic
146C2×Dic11#10211yescharacteristic
147C4×D11—21no—
148C4×D11—21no—
149C4×D11—21no—
150C4×D11—21no—
151C4×D11—41no—
152C4×D11—41no—
153C4×D11—82no—
154C4×D11—82no—
155Dic22—41no—
156Dic22—41no—
157Dic22—82no—
158C8×C11—21no—
159C8×C11—21no—
160C11⋊C8—21no—
161C11⋊C8#9912yes—
162C22×Q16—111no—
163C23×C8—111no—
164C2×C22⋊Q8—221no—
165C2×M32—221no—
166#467—111no—
167#467—111no—
168#467—111no—
169#467—221no—
170#467—221no—
171#467C2×D1111yescharacteristic
172C2×#107—111no—
173C2×#106—221no—
174C2×#103—221no—
175#380—221no—
176C22⋊C16—111no—
177C22⋊C16—221no—
178C22⋊C16C2×D1111yescharacteristic
179#340—111no—
180#340C2×D1111yescharacteristic
181C22×C11—21no—
182C22×C11—21no—
183C22×C11C2×#10211yescharacteristic
184C22×C11#51011yescharacteristic
185C22×C11#51011yescharacteristic
186C2×D11—21no—
187C2×D11—21no—
188C2×D11—21no—
189C2×D11—21no—
190C2×D11—21no—
191C2×D11—42no—
192C2×D11—42no—
193C2×D11#36012yes—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—161no—
198C4×C11C2×#9911yescharacteristic
199C4×C11#42111yescharacteristic
200Dic11—21no—
201Dic11—21no—
202Dic11—81no—
203Dic11—81no—
204Dic11—161no—
205C22×Q8—221no—
206C23×C4—111no—
207C2×Q16—111no—
208C2×Q16—221no—
209C2×Q16—442no—
210C2×Q16C4×D1111yescharacteristic
211C22×C8—111no—
212C22×C8—111no—
213C22×C8—111no—
214C22×C8—111no—
215C22×C8—111no—
216C22×C8—442no—
217C22×C8C22×D1111yescharacteristic
218C22⋊Q8—21no—
219C22⋊Q8—221no—
220C22⋊Q8—221no—
221C22⋊Q8—221no—
222C22⋊Q8—441no—
223C22⋊Q8—441no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—441no—
228C2×C22⋊C4—441no—
229C2×C22⋊C4—441no—
230M32—442no—
231C2×C16—21no—
232C2×C16—221no—
233#107—111no—
234#107—221no—
235#107C4×D1111yescharacteristic
236#106—442no—
237#103—21no—
238#103—221no—
239#103—221no—
240#103—221no—
241#95—441no—
242C2×C11—21no—
243C2×C11—21no—
244C2×C11#151911yescharacteristic
245C2×C11#214111yescharacteristic
246C2×C11C2×#36011yescharacteristic
247D11—22no—
248D11—41no—
249C24—111no—
250C2×Q8—21no—
251C2×Q8—221no—
252C2×Q8—441no—
253C2×Q8—442no—
254C2×Q8—442no—
255C22×C4—41no—
256C22×C4—111no—
257C22×C4—111no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—441no—
262C22×C4—441no—
263C22×C4—441no—
264C22×C4—441no—
265C22×C4—441no—
266C22×C4D4×D1111yescharacteristic
267Q16—41no—
268Q16—441no—
269Q16—442no—
270C2×C8—41no—
271C2×C8—111no—
272C2×C8—111no—
273C2×C8—222no—
274C2×C8—222no—
275C2×C8—222no—
276C2×C8—441no—
277C2×C8—441no—
278C2×C8C2×C4×D1111yescharacteristic
279C2×C8D4×D1111yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—221no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C22⋊C4—41no—
292C22⋊C4—441no—
293C22⋊C4—441no—
294C22⋊C4—441no—
295C22⋊C4—882no—
296C16—41no—
297C16—441no—
298C11#1188911yescharacteristic, complemented, Sylow
299C23—111no—
300C23—111no—
301C23—222no—
302C23—221no—
303C23—221no—
304C23—441no—
305C23D8×D1111yescharacteristic
306Q8—41no—
307Q8—41no—
308Q8—441no—
309Q8—441no—
310Q8—882no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—111no—
319C2×C4—111no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—882no—
330C2×C4—882no—
331C2×C4—881no—
332C2×C4—881no—
333C2×C4—881no—
334C2×C4C22⋊C4×D1111yescharacteristic
335C2×C4SD16×D1111yescharacteristic
336C8—21no—
337C8—21no—
338C8—112no—
339C8—221no—
340C22—21no—
341C22—21no—
342C22—112no—
343C22—221no—
344C22—221no—
345C22—221no—
346C22—221no—
347C22—221no—
348C22—442no—
349C22—442no—
350C22D11×#10211yescharacteristic
351C22#1062252811yescharacteristic
352C22#1062253111yescharacteristic
353C4—21no—
354C4—81no—
355C4—81no—
356C4—161no—
357C4—221no—
358C4—221no—
359C4—881no—
360C4—881no—
361C4—1761no—
362C4D11×#9911yescharacteristic
363C4#1062243411yescharacteristic
364C2—21no—
365C2—21no—
366C2—222no—
367C2—441no—
368C2#1306718211yescharacteristic
369C2#1307033411yescharacteristic
370C2D11×#36011yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1348C2
socleC22×C11C2×#102
prime radicalC23×D11D8
cosocleC22×C8×C11C23
hypercenter#1348D11
hypocenterC11#11889
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1348

Complements

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

NH ≅ G/Ntype
4. #13066629C2semidirect
5. #13066628C2semidirect
6. #13066627C2semidirect
7. C11×#1348C2semidirect
8. C2×Q16×D11C4semidirect
12. #10622801C4semidirect
18. #10622500C4semidirect
19. D11×#107C4semidirect
120. #1348D11semidirect
298. C11#11889semidirect

Maximal subgroups

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

subgroupindex
D11×#4672
#130702252
#130686402
#130666292
#130666282
#130666272
C11×#13482
#1188911