Finite Group Databasebeta

← #14651443

Subgroups — #14651443

Order 2816.

490 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 107 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#13077645C211yesmaximal, characteristic
2#13067243C212yesmaximal, complemented
3#13066957C211yesmaximal, characteristic
4#13066472C212yesmaximal, complemented
5C11×#2566C211yesmaximal, characteristic
6C2×C11×#125C2211yescharacteristic
7C2×C4×D4×C11C2211yescharacteristic
8C11×#396—21no—
9C11×#396—21no—
10C11×#390C411yescharacteristic
11C11×#390C411yescharacteristic
12C11×#385—21no—
13C11×#385—21no—
14C11×#384C411yescharacteristic
15C11×#382C411yescharacteristic
16C4×C11×C4⋊C4C2211yescharacteristic
17#10622820—21no—
18C2×C22⋊(C11⋊C8)—21no—
19#10622624—24no—
20#10622539C2212yes—
21#10622539C2212yes—
22#10622181—24no—
23#10622163—21no—
24#10622163—21no—
25C22×D4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C11×#125—22no—
29C11×#125—22no—
30C4×D4×C11—22no—
31C4×D4×C11—22no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4D411yescharacteristic
45C2×C11×C22⋊C4D411yescharacteristic
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11C2×C411yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×#4318—22no—
50C22×C11⋊C8—22no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C22⋊(C11⋊C8)—22no—
55C22⋊(C11⋊C8)—22no—
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—22no—
58C4⋊(C11⋊C8)—22no—
59C4⋊(C11⋊C8)—22no—
60#66867—22no—
61#66867D414yes—
62#9449—111nomaximal, Sylow
63C24×C11C22⋊C411yescharacteristic
64C24×C11C22⋊C411yescharacteristic
65C2×D4×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—41no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—81no—
77C22×C4×C11—81no—
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—42no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—81no—
91C11×C4⋊C4—81no—
92C11×C22⋊C4—22no—
93C11×C22⋊C4—22no—
94C11×C22⋊C4—42no—
95C11×C22⋊C4—42no—
96C11×C22⋊C4—81no—
97C11×C22⋊C4—81no—
98C42×C11—41no—
99C42×C11—41no—
100C42×C11C2×D412yes—
101C42×C11#4112yes—
102#4318—82no—
103C2×C11⋊C8—24no—
104C2×C11⋊C8—42no—
105C2×C11⋊C8—82no—
106#2973—111no—
107#2566D1111yescharacteristic
108#1534—112no—
109#1466—111no—
110#1285—112no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11#10112yes—
121C23×C11C2×C22⋊C411yescharacteristic
122D4×C11—44no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—22no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11C4×D412yes—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12112yes—
150C2×C4×C11#12311yescharacteristic
151C11⋊C8—44no—
152C11⋊C8—82no—
153C2×#125C2×D1111yescharacteristic
154C2×C4×D4C2×D1111yescharacteristic
155#435—224no—
156#432—112no—
157#432—112no—
158#407—221no—
159C2×C22⋊C8—221no—
160#396—21no—
161#396—21no—
162#390Dic1111yescharacteristic
163#390Dic1111yescharacteristic
164#385—21no—
165#385—21no—
166#384Dic1111yescharacteristic
167#382Dic1111yescharacteristic
168C4×C4⋊C4C2×D1111yescharacteristic
169#330—224no—
170#323—221no—
171#323—221no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—22no—
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×C11—81no—
184C22×C11#38611yescharacteristic
185C22×C11C2×#10111yescharacteristic
186C22×C11#41311yescharacteristic
187C4×C11—22no—
188C4×C11—22no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—42no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—81no—
197C22×D4C2×Dic1111yescharacteristic
198C23×C4C22⋊D1111yescharacteristic
199C23×C4C22⋊D1111yescharacteristic
200C2×M16—222no—
201C22×C8—222no—
202#125—22no—
203#125—22no—
204C4×D4—22no—
205C4×D4—22no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4C2×Dic1111yescharacteristic
212C2×C4⋊C4C2×Dic1111yescharacteristic
213C2×C4⋊C4C2×Dic1111yescharacteristic
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4C22⋊D1111yescharacteristic
219C2×C22⋊C4C22⋊D1111yescharacteristic
220C2×C42C2×Dic1111yescharacteristic
221C2×C42C2×Dic1111yescharacteristic
222C2×C42C22×D1111yescharacteristic
223C4⋊C8—222no—
224C4⋊C8—222no—
225C22⋊C8—222no—
226C22⋊C8—222no—
227C22⋊C8—222no—
228C22⋊C8—222no—
229#97—114no—
230#97—222no—
231#95—21no—
232#95—21no—
233#95—21no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11—42no—
237C2×C11—81no—
238C2×C11#188411yescharacteristic
239C2×C11#190111yescharacteristic
240C2×C11#191111yescharacteristic
241C24C22⋊Dic1111yescharacteristic
242C24C22⋊Dic1111yescharacteristic
243C2×D4—22no—
244C2×D4—22no—
245C2×D4—41no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—81no—
255C22×C4—81no—
256C22×C4C22⋊Dic1111yescharacteristic
257C22×C4C22⋊Dic1111yescharacteristic
258C22×C4C22×Dic1111yescharacteristic
259C22×C4C2×C22⋊D1111yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261M16—882no—
262C2×C8—224no—
263C2×C8—442no—
264C2×C8—882no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—81no—
273C4⋊C4—81no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C22⋊C4—81no—
279C22⋊C4—81no—
280C42—41no—
281C42—41no—
282C42D4×D1112yes—
283C42#434112yes—
284C11#944911yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23#6690012yes—
295C23C2×C22⋊Dic1111yescharacteristic
296D4—44no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4D4×Dic1112yes—
322C2×C4#6698811yescharacteristic
323C2×C4#6699011yescharacteristic
324C2×C4#6699212yes—
325C8—444no—
326C8—882no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22#1062283311yescharacteristic
340C22C2×#6690011yescharacteristic
341C22#1062285011yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—22no—
346C4—42no—
347C4—41no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—81no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—81no—
356C2#1306900011yescharacteristic
357C2#1306908511yescharacteristic
358C2#1306914911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2566C2
socleC22×C11#386
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#2566D11
hypocenterC11#9449
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2566

Complements

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

NH ≅ G/Ntype
2. #13067243C2semidirect
4. #13066472C2semidirect
284. C11#9449semidirect

Maximal subgroups

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

subgroupindex
#130776452
#130672432
#130669572
#130664722
C11×#25662
#944911