Finite Group Databasebeta

← #14651567

Subgroups — #14651567

Order 2816.

576 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 119 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#13072924C211yesmaximal, characteristic
2#13068703C212yesmaximal, complemented
3#13068604C211yesmaximal, characteristic
4#13066484C212yesmaximal, complemented
5C11×#2973C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66988—21no—
8C22×C4⋊Dic11C2211yescharacteristic
9C11×#435—24no—
10C11×#432—21no—
11C11×#407—21no—
12C2×C11×C22⋊C8C2212yes—
13C2×#66898—21no—
14#10622825—21no—
15#10622825C2212yes—
16#10622825C2211yescharacteristic
17#10622596C412yescomplemented
18#10622566C412yescomplemented
19#10622556—21no—
20#10622541—21no—
21#10622189—24no—
22#10622164—21no—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×Dic11—21no—
27C2×C11×M16—22no—
28C22×C8×C11D414yes—
29C4×D4×C11—22no—
30C4×D4×C11—22no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—22no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—22no—
38#66988—44no—
39C2×C4⋊Dic11—22no—
40C2×C4⋊Dic11—22no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—22no—
44C2×C4⋊Dic11C2×C412yes—
45C2×Dic11⋊C4—22no—
46C11×C4⋊C8—22no—
47C11×C22⋊C8—22no—
48C11×C22⋊C8—22no—
49C11×C22⋊C8—22no—
50C11×#97—22no—
51#66898—42no—
52C11⋊#95—22no—
53C11⋊#95—22no—
54C11⋊#95—22no—
55C11⋊#95C2×C412yes—
56#9474—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C24×C11C2×D411yescharacteristic
59C2×D4×C11—22no—
60C2×D4×C11—21no—
61C2×D4×C11—22no—
62C2×D4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D412yes—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4112yes—
74C22×Dic11—22no—
75C22×Dic11—22no—
76C22×Dic11—42no—
77C22×Dic11—42no—
78C22×Dic11—42no—
79C22×Dic11—41no—
80C22×Dic11—41no—
81C11×M16—82no—
82C2×C8×C11—24no—
83C2×C8×C11—44no—
84C11×C4⋊C4—22no—
85C11×C22⋊C4—22no—
86C11×C22⋊C4—22no—
87C42×C11—21no—
88C42×C11—21no—
89C22⋊Dic11—44no—
90C22⋊Dic11—42no—
91C22⋊Dic11—42no—
92C22⋊Dic11—42no—
93C4⋊Dic11—24no—
94C4⋊Dic11—42no—
95C4⋊Dic11—44no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98Dic11⋊C4—44no—
99#2973D1111yescharacteristic
100#2486—111no—
101#1823—112no—
102#1799—111no—
103#1289—112no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11C2×C22⋊C411yescharacteristic
112C23×C11#12112yes—
113C23×C11AGL(1,ℤ/8)11yescharacteristic
114C23×C11AGL(1,ℤ/8)12yes—
115C23×C11#13711yescharacteristic
116D4×C11—42no—
117D4×C11—42no—
118C2×C4×C11—24no—
119C2×C4×C11—22no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—41no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—81no—
131C2×C4×C11C4×D412yes—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12311yescharacteristic
134C2×Dic11—42no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—82no—
141C2×Dic11—82no—
142C2×Dic11—82no—
143C2×Dic11—82no—
144C2×Dic11—82no—
145C8×C11—44no—
146C2×#123—221no—
147C2×C4×D4C2×D1111yescharacteristic
148C22×C4⋊C4—111no—
149#435—24no—
150#432—21no—
151C2×#99—221no—
152#407—21no—
153C2×C22⋊C8C2×D1112yes—
154#398—112no—
155#397—112no—
156#389—221no—
157#381—221no—
158#380—111no—
159#380—112no—
160#380—221no—
161#342—221no—
162#340—224no—
163C22×C11—21no—
164C22×C11—22no—
165C22×C11—21no—
166C22×C11—22no—
167C22×C11—42no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—42no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—81no—
175C22×C11#38611yescharacteristic
176C22×C11#41711yescharacteristic
177C22×C11#41811yescharacteristic
178C22×C11#46812yes—
179C22×C11#46912yes—
180C4×C11—21no—
181C4×C11—22no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11#45812yes—
186Dic11—82no—
187Dic11—82no—
188Dic11—162no—
189C22×D4D4411yescharacteristic
190C23×C4—221no—
191C23×C4C22⋊D1111yescharacteristic
192C23×C4C22×D1111yescharacteristic
193C2×M16—22no—
194C22×C8C22⋊D1114yes—
195#123—444no—
196C4×D4—22no—
197C4×D4—22no—
198C2×C4⋊C4—112no—
199C2×C4⋊C4—222no—
200C2×C4⋊C4—222no—
201C2×C4⋊C4—222no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—222no—
205C2×C4⋊C4C4×D1111yescharacteristic
206C2×C22⋊C4—222no—
207C2×C22⋊C4—221no—
208C2×C22⋊C4—222no—
209C2×C22⋊C4C4×D1111yescharacteristic
210C2×C22⋊C4D4411yescharacteristic
211C2×C42C22⋊D1111yescharacteristic
212C4⋊C8—22no—
213#99—442no—
214C22⋊C8—22no—
215C22⋊C8—22no—
216C22⋊C8—22no—
217#97—22no—
218#95—112no—
219#95—222no—
220#95—222no—
221#95—222no—
222C2×C11—21no—
223C2×C11—22no—
224C2×C11—21no—
225C2×C11—22no—
226C2×C11—81no—
227C2×C11#189011yescharacteristic
228C2×C11#189511yescharacteristic
229C2×C11#190911yescharacteristic
230C24(C2×D11)⋊C411yescharacteristic
231C24C2×D4411yescharacteristic
232C2×D4—21no—
233C2×D4—22no—
234C2×D4—21no—
235C2×D4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—222no—
241C22×C4—222no—
242C22×C4—442no—
243C22×C4—441no—
244C22×C4—441no—
245C22×C4—442no—
246C22×C4—442no—
247C22×C4(C2×D11)⋊C411yescharacteristic
248C22×C4(C2×D11)⋊C411yescharacteristic
249C22×C4(C2×D11)⋊C411yescharacteristic
250C22×C4C2×C4×D1111yescharacteristic
251C22×C4#433912yes—
252C22×C4C2×C22⋊D1112yes—
253C22×C4C2×C22⋊D1111yescharacteristic
254M16—82no—
255C2×C8—24no—
256C2×C8—44no—
257C4⋊C4—22no—
258C4⋊C4—224no—
259C4⋊C4—444no—
260C4⋊C4—442no—
261C4⋊C4—444no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—444no—
267C22⋊C4—442no—
268C22⋊C4—442no—
269C22⋊C4—442no—
270C42—21no—
271C42—21no—
272C11#947411yescharacteristic, complemented, Sylow
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23#6696112yes—
281C23#6696111yescharacteristic
282C23#6696211yescharacteristic
283C23C2×(C2×D11)⋊C411yescharacteristic
284C23#6698312yes—
285D4—42no—
286D4—42no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—442no—
301C2×C4—442no—
302C2×C4—442no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4—882no—
307C2×C4—882no—
308C2×C4—882no—
309C2×C4—882no—
310C2×C4—882no—
311C2×C4C4×C22⋊D1112yes—
312C2×C4#6698211yescharacteristic
313C2×C4#6700611yescharacteristic
314C8—44no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—22no—
319C22—42no—
320C22—41no—
321C22—41no—
322C22—42no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22#1062274411yescharacteristic
328C22#1062274611yescharacteristic
329C22#1062274712yes—
330C22#1062274812yes—
331C22#1062282611yescharacteristic
332C4—21no—
333C4—22no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—882no—
338C4—882no—
339C4—1762no—
340C4#1062285612yes—
341C2—21no—
342C2—22no—
343C2—21no—
344C2—22no—
345C2—81no—
346C2#1306902911yescharacteristic
347C2#1306905411yescharacteristic
348C2#1306913811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2973C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC23×C4×C11C23
hypercenter#2973D11
hypocenterC11#9474
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #13068703C2semidirect
4. #13066484C2semidirect
17. #10622596C4semidirect
18. #10622566C4semidirect
272. C11#9474semidirect

Maximal subgroups

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

subgroupindex
#130729242
#130687032
#130686042
#130664842
C11×#29732
#947411