Finite Group Databasebeta

← #14649559

Subgroups — #14649559

Order 2816.

648 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C2×#10622550C211yesmaximal, characteristic, complemented
2#13068684C211yesmaximal, characteristic, complemented
3C2×#10622175C212yesmaximal
4#13066494C212yesmaximal, complemented
5C11×#2854C211yesmaximal, characteristic
6C2×C11×#123—21no—
7C2×C11×#121C2211yescharacteristic
8C22×C42×C11C2211yescharacteristic
9C11×#390C412yescomplemented
10C11×#389C412yescomplemented
11C11×#388—22no—
12C11×#386—21no—
13C11×#380C2211yescharacteristic
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2212yes—
17C2×C22⋊(C11⋊C8)C2212yes—
18#10622550—24no—
19#10622175—24no—
20#10622162—22no—
21C22×D4×C11—21no—
22C22×D4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×Dic11—22no—
27C11×#123—44no—
28C11×#121—22no—
29C11×#121—22no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2×C412yes—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—21no—
37C2×C42×C11—22no—
38C2×C42×C11—22no—
39C2×C42×C11C2×C412yes—
40C2×C42×C11D412yes—
41C22×C11⋊C8—22no—
42C11×#95—22no—
43C11×#95—21no—
44C11⋊#95—24no—
45C11⋊#95—24no—
46C11⋊#95—22no—
47C11⋊#95D414yes—
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)—22no—
50#9157—111nomaximal, Sylow
51C24×C11—21no—
52C24×C11C2×D411yescharacteristic
53C2×D4×C11—22no—
54C2×D4×C11—42no—
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11—42no—
58C2×D4×C11—42no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—21no—
67C22×C4×C11—42no—
68C22×C4×C11—42no—
69C22×C4×C11C22⋊C412yes—
70C22×C4×C11C22⋊C412yes—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D412yes—
74C22×C4×C11#4112yes—
75C22×Dic11—24no—
76C22×Dic11—44no—
77C22×Dic11—44no—
78C22×Dic11—42no—
79C22×Dic11—42no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—44no—
82C11×C4⋊C4—42no—
83C11×C22⋊C4—44no—
84C11×C22⋊C4—44no—
85C11×C22⋊C4—42no—
86C11×C22⋊C4—42no—
87C42×C11—24no—
88C42×C11—24no—
89C2×C11⋊C8—44no—
90C2×C11⋊C8—42no—
91#2854D1111yescharacteristic
92C2×#383—111no—
93#1817—111no—
94C2×#327—112no—
95#1294—112no—
96C23×C11—22no—
97C23×C11—22no—
98C23×C11—41no—
99C23×C11—42no—
100C23×C11—41no—
101C23×C11—41no—
102C23×C11—42no—
103C23×C11C2×C22⋊C411yescharacteristic
104C23×C11#12011yescharacteristic
105C23×C11#12311yescharacteristic
106C23×C11#13512yes—
107C23×C11AGL(1,ℤ/8)12yes—
108D4×C11—82no—
109D4×C11—82no—
110D4×C11—82no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—41no—
126C2×C4×C11—42no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11C4×D412yes—
132C2×C4×C11#12112yes—
133C2×Dic11—44no—
134C2×Dic11—44no—
135C2×Dic11—44no—
136C2×Dic11—84no—
137C2×Dic11—84no—
138C11⋊C8—82no—
139C2×#123—21no—
140C2×#121C2×D1111yescharacteristic
141C22×C42C2×D1111yescharacteristic
142C2×C22⋊C8—112no—
143#390Dic1112yescomplemented
144#389Dic1112yescomplemented
145#388—22no—
146#386—21no—
147#383—224no—
148#380C2×D1111yescharacteristic
149C2×#95—112no—
150C2×#95—221no—
151C2×#95—221no—
152#336—222no—
153#327—224no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—24no—
159C22×C11—24no—
160C22×C11—81no—
161C22×C11—81no—
162C22×C11—81no—
163C22×C11—82no—
164C22×C11—82no—
165C22×C11#38611yescharacteristic
166C22×C11#41012yes—
167C22×C11#41611yescharacteristic
168C22×C11#41811yescharacteristic
169C22×C11#42112yes—
170C22×C11#44912yes—
171C22×C11#48212yes—
172C4×C11—22no—
173C4×C11—22no—
174C4×C11—42no—
175C4×C11—42no—
176C4×C11—81no—
177C4×C11—82no—
178Dic11—84no—
179C22×D4—21no—
180C22×D4C2×Dic1111yescharacteristic
181C23×C4—222no—
182C23×C4C22⋊D1111yescharacteristic
183C23×C4C22⋊D1111yescharacteristic
184C23×C4C22×D1111yescharacteristic
185C22×C8—222no—
186#123—44no—
187#121—22no—
188#121—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4C2×Dic1111yescharacteristic
191C2×C4⋊C4C2×Dic1112yes—
192C2×C22⋊C4—21no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—21no—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42C2×Dic1112yes—
199C2×C42C22⋊D1112yes—
200C22⋊C8—222no—
201C22⋊C8—222no—
202#95—22no—
203#95—21no—
204#95—114no—
205#95—224no—
206#95—224no—
207#95—222no—
208C2×C11—22no—
209C2×C11—22no—
210C2×C11—161no—
211C2×C11#151412yes—
212C2×C11#152112yes—
213C2×C11#187511yescharacteristic
214C2×C11#189711yescharacteristic
215C2×C11#189911yescharacteristic
216C24—21no—
217C24C2×C22⋊D1111yescharacteristic
218C2×D4—22no—
219C2×D4—42no—
220C2×D4—42no—
221C2×D4—41no—
222C2×D4—41no—
223C2×D4—42no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—224no—
235C22×C4—444no—
236C22×C4—444no—
237C22×C4—442no—
238C22×C4—442no—
239C22×C4C22⋊Dic1112yes—
240C22×C4C22⋊Dic1112yes—
241C22×C4D4×D1112yes—
242C22×C4#434112yes—
243C22×C4C22×Dic1111yescharacteristic
244C22×C4C2×C22⋊D1111yescharacteristic
245C2×C8—444no—
246C2×C8—442no—
247C4⋊C4—22no—
248C4⋊C4—42no—
249C4⋊C4—44no—
250C22⋊C4—44no—
251C22⋊C4—44no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C42—24no—
255C42—24no—
256C11#915711yescharacteristic, complemented, Sylow
257C23—22no—
258C23—22no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23—42no—
263C23—42no—
264C23#6698512yes—
265C23#6698811yescharacteristic
266C23#6699011yescharacteristic
267C23#6700312yes—
268C23C2×C22⋊Dic1111yescharacteristic
269D4—82no—
270D4—82no—
271D4—82no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—444no—
293C2×C4—444no—
294C2×C4—444no—
295C2×C4—884no—
296C2×C4—884no—
297C2×C4D4×Dic1112yes—
298C2×C4#6699212yes—
299C8—882no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—24no—
305C22—24no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22—82no—
310C22—82no—
311C22#1062264812yes—
312C22#1062265012yes—
313C22#1062282811yescharacteristic
314C22#1062283311yescharacteristic
315C22#1062284611yescharacteristic
316C22#1062284912yes—
317C22#1062285312yes—
318C4—22no—
319C4—22no—
320C4—42no—
321C4—42no—
322C4—81no—
323C4—82no—
324C4—884no—
325C2—22no—
326C2—22no—
327C2—161no—
328C2#1306716312yes—
329C2#1306719312yes—
330C2#1306893911yescharacteristic
331C2#1306906511yescharacteristic
332C2#1306907511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2854C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#2854D11
hypocenterC11#9157
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2854

Complements

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

NH ≅ G/Ntype
1. C2×#10622550C2semidirect
2. #13068684C2semidirect
4. #13066494C2semidirect
9. C11×#390C4semidirect
10. C11×#389C4semidirect
143. #390Dic11semidirect
144. #389Dic11semidirect
256. C11#9157semidirect

Maximal subgroups

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

subgroupindex
C2×#106225502
#130686842
C2×#106221752
#130664942
C11×#28542
#915711