Finite Group Databasebeta

← #14664255

Subgroups — #14664255

Order 2816.

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

normal subgroups only

This group has 486 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
1#13074303C211yesmaximal, characteristic
2#13068349C211yesmaximal, characteristic, complemented
3#13066638C212yesmaximal, complemented
4#13066614C212yesmaximal
5C11×#1464C211yesmaximal, characteristic, complemented
6C2×C11×#117C2211yescharacteristic
7C2×#66979—21no—
8C2×#66928C411yescharacteristic, complemented
9C11×#432—21no—
10#10622826—21no—
11#10622604C411yescharacteristic, complemented
12#10622603—21no—
13#10622592C411yescharacteristic, complemented
14#10622573C2211yescharacteristic
15#10622570—21no—
16#10622560C2211yescharacteristic
17#10622553—21no—
18#10622545C411yescharacteristic, complemented
19C11×#324—21no—
20C11×#323C2212yes—
21#10622164—21no—
22#10622164C2212yes—
23C23×C4×C11D411yescharacteristic
24C22×C22⋊D11—21no—
25C22×D44C2×C411yescharacteristic
26C22×Dic22C2×C411yescharacteristic
27C11×#117—41no—
28C11×#117—41no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4D411yescharacteristic
32C2×C11×C22⋊C4C2311yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—22no—
36C2×C22⋊Dic11—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42#66979—24no—
43#66979—42no—
44C2×C4⋊Dic11—41no—
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11—21no—
47C2×C4×Dic11—41no—
48#66928—41no—
49#66928—41no—
50C11×C4⋊C8—41no—
51C11×C22⋊C8—22no—
52C11×#97—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C11⋊#95C2×C411yescharacteristic
58#11758—111nomaximal, Sylow
59C24×C11C2×D411yescharacteristic
60C23×D11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—22no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C2×C22⋊D11—42no—
73C2×C22⋊D11—41no—
74C2×C22⋊D11—41no—
75C2×C22⋊D11—81no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—42no—
80C2×D44—41no—
81C2×D44—81no—
82C2×Dic22—41no—
83C2×Dic22—81no—
84C2×C8×C11—42no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—21no—
92C42×C11—21no—
93C22⋊Dic11—24no—
94C22⋊Dic11—42no—
95C22⋊Dic11—81no—
96(C2×D11)⋊C4—42no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—81no—
102C4⋊Dic11—44no—
103Dic11⋊C4—81no—
104C4×Dic11—44no—
105C4×Dic11—42no—
106#2610—111no—
107#1740—111no—
108#1464D1111yescharacteristic, complemented
109#1351—112no—
110#1343—112no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11C2×C22⋊C411yescharacteristic
116C23×C11AGL(1,ℤ/8)11yescharacteristic
117C23×C11#13711yescharacteristic
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
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—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11#9911yescharacteristic
142C2×C4×C11#9911yescharacteristic
143C2×C4×C11#10412yes—
144C22⋊D11—82no—
145C22⋊D11—82no—
146C2×Dic11—22no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—44no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—82no—
157C2×Dic11—82no—
158D44—82no—
159Dic22—82no—
160C8×C11—82no—
161C2×#124—111no—
162C2×#117—221no—
163C2×#117C2×D1111yescharacteristic
164#432—21no—
165#395—111no—
166#394—111no—
167#393—111no—
168#392—111no—
169#390—221no—
170#388—221no—
171#388—221no—
172#386—221no—
173#376—111no—
174#342—112no—
175#342—221no—
176#324—21no—
177#323C2×D1112yes—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—81no—
187C22×C11C2×#9911yescharacteristic
188C22×C11#41711yescharacteristic
189C22×C11C2×#10411yescharacteristic
190C2×D11—81no—
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—22no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—41no—
204Dic11—42no—
205Dic11—81no—
206Dic11—84no—
207Dic11—81no—
208C22×Q8—111no—
209C22×D4—111no—
210C22×D4—221no—
211C23×C4D4411yescharacteristic
212#124—441no—
213#124—441no—
214#117—41no—
215#117—41no—
216#117—224no—
217#117—442no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—441no—
220C2×C4⋊C4C4×D1111yescharacteristic
221C2×C4⋊C4C22⋊D1111yescharacteristic
222C2×C22⋊C4—222no—
223C2×C22⋊C4—221no—
224C2×C22⋊C4—221no—
225C2×C22⋊C4—221no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4D4411yescharacteristic
230C2×C22⋊C4C22×D1111yescharacteristic
231C2×C42—221no—
232C2×C42—441no—
233C2×C42C4×D1111yescharacteristic
234C2×C42C22⋊D1111yescharacteristic
235C4⋊C8—41no—
236C22⋊C8—22no—
237#97—41no—
238#95—111no—
239#95—111no—
240#95—221no—
241#95—221no—
242#95—221no—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11—41no—
246C2×C11—41no—
247C2×C11#150411yescharacteristic
248C2×C11#212211yescharacteristic
249C2×C11#212611yescharacteristic
250D11—161no—
251C24—221no—
252C24C2×D4411yescharacteristic
253C2×Q8—441no—
254C2×Q8—881no—
255C2×D4—441no—
256C2×D4—442no—
257C2×D4—441no—
258C2×D4—441no—
259C2×D4—881no—
260C2×D4—881no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—442no—
270C22×C4(C2×D11)⋊C411yescharacteristic
271C22×C4(C2×D11)⋊C411yescharacteristic
272C22×C4(C2×D11)⋊C411yescharacteristic
273C22×C4(C2×D11)⋊C411yescharacteristic
274C22×C4C2×C4×D1111yescharacteristic
275C22×C4C2×C22⋊D1111yescharacteristic
276C2×C8—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—444no—
280C4⋊C4—881no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—224no—
284C22⋊C4—442no—
285C22⋊C4—442no—
286C22⋊C4—442no—
287C22⋊C4—441no—
288C22⋊C4—441no—
289C22⋊C4—442no—
290C22⋊C4—881no—
291C22⋊C4—881no—
292C42—21no—
293C42—21no—
294C42—21no—
295C42—21no—
296C42—444no—
297C42—442no—
298C11#1175811yescharacteristic, complemented, Sylow
299C23—21no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23—441no—
304C23—441no—
305C23—441no—
306C23—441no—
307C23—441no—
308C23—441no—
309C23—441no—
310C23#6696111yescharacteristic
311C23#6696211yescharacteristic
312C23C2×(C2×D11)⋊C411yescharacteristic
313Q8—882no—
314D4—882no—
315D4—882no—
316D4—882no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—222no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—444no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—882no—
344C2×C4—882no—
345C2×C4#6687011yescharacteristic
346C2×C4#6687011yescharacteristic
347C2×C4#6688912yes—
348C8—82no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—81no—
358C22—881no—
359C22—881no—
360C22—881no—
361C22—881no—
362C22—881no—
363C22—881no—
364C22—881no—
365C22C2×#6687011yescharacteristic
366C22#1062274611yescharacteristic
367C22C2×#6688911yescharacteristic
368C4—21no—
369C4—21no—
370C4—22no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—442no—
376C4—881no—
377C4—884no—
378C4—881no—
379C2—21no—
380C2—21no—
381C2—41no—
382C2—41no—
383C2—1761no—
384C2#1306712111yescharacteristic
385C2#1307026711yescharacteristic
386C2#1307027911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1464C2
socleC22×C11C2×#99
prime radical#10622573C22
cosocleC2×C11×C22⋊C4C23
hypercenter#1464D11
hypocenterC11#11758
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #13068349C2semidirect
3. #13066638C2semidirect
5. C11×#1464C2semidirect
8. C2×#66928C4semidirect
11. #10622604C4semidirect
13. #10622592C4semidirect
18. #10622545C4semidirect
108. #1464D11semidirect
298. C11#11758semidirect

Maximal subgroups

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

subgroupindex
#130743032
#130683492
#130666382
#130666142
C11×#14642
#1175811