Finite Group Databasebeta

← #14664118

Subgroups — #14664118

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#13074500C211yesmaximal, characteristic
2C4×#66898C211yesmaximal, characteristic, complemented
3#13066641C212yesmaximal, complemented
4#13066614C212yesmaximal, complemented
5C11×#1460C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66983C411yescharacteristic, complemented
8C11×#431—21no—
9#10622836—21no—
10C2×#66898—21no—
11#10622826—21no—
12#10622824C411yescharacteristic, complemented
13C4×C22⋊Dic11—21no—
14#10622604C411yescharacteristic, complemented
15#10622599C411yescharacteristic, complemented
16#10622573C2211yescharacteristic
17#10622572—21no—
18#10622562C2211yescharacteristic
19#10622553—21no—
20C11×#323—21no—
21C11×#323C2212yes—
22#10622164C2212yes—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C22×D44C2×C411yescharacteristic
29C4×D4×C11—41no—
30C4×D4×C11—41no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C11×C22⋊C4C2311yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—22no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38#66983—41no—
39#66983—41no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×C4⋊Dic11C2×C411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11—41no—
47C11×C4⋊C8—41no—
48C11×C22⋊C8—22no—
49C4×C8×C11—41no—
50#66898—24no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—41no—
55C11⋊#95C2×C411yescharacteristic
56C11⋊#95C2×C411yescharacteristic
57#11729—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C2×D411yescharacteristic
60C23×D11—21no—
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—41no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—81no—
69C22×C4×C11—81no—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C2×C22⋊D11—42no—
76C2×C22⋊D11—42no—
77C2×C22⋊D11—81no—
78C2×C22⋊D11—81no—
79C2×C22⋊D11—81no—
80C2×C22⋊D11—81no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—42no—
85C2×D44—41no—
86C2×D44—81no—
87C2×C8×C11—42no—
88C11×C4⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C42×C11—21no—
92C42×C11—21no—
93C22⋊Dic11—24no—
94C22⋊Dic11—42no—
95C22⋊Dic11—81no—
96C22⋊Dic11—81no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—81no—
101(C2×D11)⋊C4—81no—
102C4⋊Dic11—41no—
103Dic11⋊C4—81no—
104C4×Dic11—82no—
105#2635—111no—
106C4×#99—111no—
107#1460D1111yescharacteristic, complemented
108#1352—112no—
109#1343—112no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11C2×C22⋊C411yescharacteristic
120C23×C11#13512yes—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128D4×C11—44no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11#9911yescharacteristic
143C2×C4×C11#9911yescharacteristic
144C2×C4×C11#10412yes—
145C22⋊D11—84no—
146C22⋊D11—84no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—44no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—82no—
158C2×Dic11—82no—
159D44—82no—
160C8×C11—82no—
161C2×#121—111no—
162C2×C4×D4C2×D1111yescharacteristic
163#431—21no—
164C2×#99—221no—
165#400—111no—
166#399—111no—
167#394—111no—
168#394—221no—
169#392—111no—
170#392—221no—
171#388—221no—
172#386—221no—
173#381—111no—
174C4×C22⋊C4—221no—
175#342—112no—
176#323—21no—
177#323C2×D1112yes—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—22no—
181C22×C11—42no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11C2×#9911yescharacteristic
191C22×C11#41611yescharacteristic
192C22×C11C2×#10411yescharacteristic
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—22no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—41no—
206Dic11—81no—
207Dic11—81no—
208Dic11—84no—
209Dic11—81no—
210C22×D4—111no—
211C22×D4—221no—
212C22×D4—221no—
213C22×D4D4411yescharacteristic
214C23×C4C4×D1111yescharacteristic
215C23×C4D4411yescharacteristic
216#121—441no—
217#121—441no—
218C4×D4—41no—
219C4×D4—41no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4C4×D1111yescharacteristic
223C2×C22⋊C4—222no—
224C2×C22⋊C4—221no—
225C2×C22⋊C4—221no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4C22⋊D1111yescharacteristic
231C2×C22⋊C4C22×D1111yescharacteristic
232C2×C42—441no—
233C2×C42C22⋊D1111yescharacteristic
234C4⋊C8—41no—
235#99—224no—
236C22⋊C8—22no—
237C4×C8—41no—
238#95—111no—
239#95—111no—
240#95—221no—
241#95—221no—
242#95—221no—
243#95—441no—
244C2×C11—21no—
245C2×C11—21no—
246C2×C11—42no—
247C2×C11—81no—
248C2×C11#150111yescharacteristic
249C2×C11#212111yescharacteristic
250C2×C11#212811yescharacteristic
251D11—161no—
252C24—221no—
253C24(C2×D11)⋊C411yescharacteristic
254C24C2×D4411yescharacteristic
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—41no—
258C2×D4—441no—
259C2×D4—442no—
260C2×D4—442no—
261C2×D4—881no—
262C2×D4—881no—
263C2×D4—881no—
264C2×D4—881no—
265C2×D4—881no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—81no—
271C22×C4—81no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—442no—
276C22×C4(C2×D11)⋊C411yescharacteristic
277C22×C4(C2×D11)⋊C411yescharacteristic
278C22×C4(C2×D11)⋊C411yescharacteristic
279C22×C4C2×C4×D1111yescharacteristic
280C22×C4C2×C22⋊D1111yescharacteristic
281C2×C8—42no—
282C4⋊C4—41no—
283C4⋊C4—441no—
284C4⋊C4—881no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—224no—
288C22⋊C4—442no—
289C22⋊C4—441no—
290C22⋊C4—441no—
291C22⋊C4—442no—
292C22⋊C4—881no—
293C22⋊C4—881no—
294C22⋊C4—881no—
295C22⋊C4—881no—
296C42—21no—
297C42—21no—
298C42—882no—
299C11#1172911yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—441no—
310C23—441no—
311C23—441no—
312C23—441no—
313C23—441no—
314C23—441no—
315C23—441no—
316C23#6695712yes—
317C23C2×(C2×D11)⋊C411yescharacteristic
318D4—44no—
319D4—882no—
320D4—884no—
321D4—884no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—444no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—882no—
346C2×C4—882no—
347C2×C4#6687011yescharacteristic
348C2×C4#6687011yescharacteristic
349C2×C4#6688912yes—
350C8—82no—
351C22—21no—
352C22—21no—
353C22—22no—
354C22—42no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—881no—
364C22—881no—
365C22—881no—
366C22—881no—
367C22—881no—
368C22—881no—
369C22—881no—
370C22C2×#6687011yescharacteristic
371C22#1062272611yescharacteristic
372C22C2×#6688911yescharacteristic
373C4—22no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—881no—
380C4—881no—
381C4—884no—
382C4—881no—
383C2—21no—
384C2—21no—
385C2—42no—
386C2—81no—
387C2—1761no—
388C2#1306710811yescharacteristic
389C2#1307026311yescharacteristic
390C2#1307028711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1460C2
socleC22×C11C2×#99
prime radical#13074500C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1460D11
hypocenterC11#11729
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. C4×#66898C2semidirect
3. #13066641C2semidirect
4. #13066614C2semidirect
5. C11×#1460C2semidirect
7. C2×#66983C4semidirect
12. #10622824C4semidirect
14. #10622604C4semidirect
15. #10622599C4semidirect
107. #1460D11semidirect
299. C11#11729semidirect

Maximal subgroups

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

subgroupindex
#130745002
C4×#668982
#130666412
#130666142
C11×#14602
#1172911