Finite Group Databasebeta

← #14666179

Subgroups — #14666179

Order 2816.

588 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 59 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#13073532C211yesmaximal, characteristic, complemented
2#13067551C212yesmaximal, complemented
3#13066618C212yesmaximal, complemented
4#13066562C211yesmaximal, characteristic, complemented
5C11×#2039C211yesmaximal, characteristic, complemented
6C11×#537C2211yescharacteristic
7C2×#66948—22no—
8C2×C4×D44—21no—
9C2×C11×#104—21no—
10C11×#417—21no—
11C11×#384C2211yescharacteristic
12#10622649—22no—
13#10622604—21no—
14#10622604C2212yes—
15#10622600—22no—
16C11×#343C2211yescharacteristic
17#10622175—22no—
18#10622166C2212yes—
19C2×C11×#41—21no—
20C22×D44—21no—
21C22×D44—21no—
22C22×D44D412yes—
23C22×C4×D11—22no—
24C2×C11×M16—21no—
25C11×C22⋊Q8—41no—
26C11×#121—22no—
27C11×#121—41no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×#4323—42no—
33C2×(C2×D11)⋊C4—22no—
34C2×(C2×D11)⋊C4—22no—
35C2×(C2×D11)⋊C4—22no—
36C2×C4⋊Dic11—21no—
37#66948—48no—
38C4×D44—42no—
39C4×D44—42no—
40C11×#104—42no—
41C11×#103—41no—
42C11×#102—41no—
43C11⋊#95—21no—
44C11⋊#95D412yes—
45C22⋊(C11⋊C8)—22no—
46#66873—42no—
47#12152—111nomaximal, Sylow
48C23×D11—22no—
49C11×#41—41no—
50C11×#41—41no—
51C11×#41—41no—
52C11×#41—41no—
53C2×Q8×C11—21no—
54C2×D4×C11—21no—
55C2×D4×C11—22no—
56C2×D4×C11—41no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—41no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D412yes—
62C22×Dic11—22no—
63C2×D44—24no—
64C2×D44—42no—
65C2×D44—42no—
66C2×D44—42no—
67C2×D44—44no—
68C2×D44—44no—
69C2×D44—81no—
70C2×C4×D11—44no—
71C2×C4×D11—44no—
72C2×C4×D11—44no—
73C11×M16—41no—
74C11×M16—41no—
75C2×C8×C11—41no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—44no—
79C11×C4⋊C4—41no—
80C11×C22⋊C4—42no—
81C42×C11—21no—
82C42×C11D812yescomplemented
83#4323—84no—
84(C2×D11)⋊C4—44no—
85(C2×D11)⋊C4—44no—
86(C2×D11)⋊C4—42no—
87(C2×D11)⋊C4—42no—
88C4⋊Dic11—42no—
89C2×C11⋊C8—42no—
90#2537—111no—
91#2039D1111yescharacteristic, complemented
92#1598—112no—
93#1345—112no—
94#1325—111no—
95C23×C11—41no—
96C23×C11#12011yescharacteristic
97C22×D11—24no—
98C22×D11—42no—
99C22×D11—42no—
100C22×D11—42no—
101C22×D11—42no—
102C22×D11—42no—
103C22×D11—42no—
104Q8×C11—41no—
105Q8×C11—41no—
106D4×C11—41no—
107D4×C11—41no—
108D4×C11—82no—
109D4×C11—81no—
110D4×C11—81no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—22no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—81no—
122C2×C4×C11—81no—
123C2×C4×C11C2×D811yescharacteristic
124C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128D44—48no—
129D44—44no—
130D44—82no—
131D44—84no—
132C4×D11—88no—
133C8×C11—81no—
134C11⋊C8—82no—
135#537C2×D1111yescharacteristic
136C2×#121—222no—
137C2×C4×D4—221no—
138#447—222no—
139C2×#104—21no—
140#417—21no—
141#394—112no—
142#394—221no—
143#384C2×D1111yescharacteristic
144#380—222no—
145#343C2×D1111yescharacteristic
146#327—222no—
147#324—112no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—81no—
151C22×C11—81no—
152C22×C11—81no—
153C22×C11#44711yescharacteristic
154C22×C11#45411yescharacteristic
155C22×C11B(4,𝔽2)11yescharacteristic
156C2×D11—44no—
157C2×D11—44no—
158C2×D11—44no—
159C2×D11—82no—
160C2×D11—82no—
161C2×D11—82no—
162C2×D11—82no—
163C4×C11—24no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—42no—
167C4×C11—81no—
168C4×C11—81no—
169Dic11—82no—
170C2×#41—21no—
171C22×D4—112no—
172C22×D4—221no—
173C22×D4—221no—
174C23×C4—222no—
175C2×D8—442no—
176C2×M16—21no—
177C22⋊Q8—41no—
178#121—22no—
179#121—41no—
180#121—448no—
181C4×D4—442no—
182C4×D4—442no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—221no—
185C2×C4⋊C4C22⋊D1111yescharacteristic
186C2×C4⋊C4C22×D1111yescharacteristic
187C2×C22⋊C4—222no—
188C2×C22⋊C4—222no—
189C2×C22⋊C4—222no—
190C2×C42C22⋊D1111yescharacteristic
191#104—42no—
192#103—41no—
193#102—41no—
194#102—442no—
195C22⋊C8—222no—
196#95—112no—
197#95—221no—
198C2×C11—21no—
199C2×C11—21no—
200C2×C11—161no—
201C2×C11#159811yescharacteristic
202C2×C11#219611yescharacteristic
203C2×C11#220411yescharacteristic
204D11—84no—
205C24—222no—
206#41—41no—
207#41—41no—
208#41—41no—
209#41—41no—
210C2×Q8—21no—
211C2×D4—21no—
212C2×D4—22no—
213C2×D4—41no—
214C2×D4—224no—
215C2×D4—442no—
216C2×D4—442no—
217C2×D4—442no—
218C2×D4—444no—
219C2×D4—444no—
220C2×D4—881no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—41no—
224C22×C4—222no—
225C22×C4—444no—
226C22×C4—444no—
227C22×C4—444no—
228C22×C4D4×D1112yes—
229C22×C4C2×C22⋊D1111yescharacteristic
230D8—884no—
231M16—41no—
232M16—41no—
233C2×C8—41no—
234C2×C8—442no—
235C4⋊C4—22no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—44no—
239C4⋊C4—442no—
240C22⋊C4—42no—
241C22⋊C4—444no—
242C22⋊C4—444no—
243C22⋊C4—442no—
244C22⋊C4—442no—
245C42—21no—
246C42#432312yescomplemented
247C11#1215211yescharacteristic, complemented, Sylow
248C23—41no—
249C23—224no—
250C23—442no—
251C23—442no—
252C23—442no—
253C23—442no—
254C23—442no—
255C23—442no—
256C23#6699011yescharacteristic
257Q8—41no—
258Q8—41no—
259D4—41no—
260D4—41no—
261D4—82no—
262D4—81no—
263D4—81no—
264D4—448no—
265D4—444no—
266D4—882no—
267D4—884no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—442no—
281C2×C4—442no—
282C2×C4—442no—
283C2×C4—888no—
284C2×C4C2×#432311yescharacteristic
285C2×C4#6700211yescharacteristic
286C8—81no—
287C8—882no—
288C22—21no—
289C22—21no—
290C22—81no—
291C22—81no—
292C22—81no—
293C22—444no—
294C22—444no—
295C22—444no—
296C22—882no—
297C22—882no—
298C22—882no—
299C22—882no—
300C22#1062264511yescharacteristic
301C22#1062264911yescharacteristic
302C22#1062267511yescharacteristic
303C4—24no—
304C4—21no—
305C4—21no—
306C4—42no—
307C4—81no—
308C4—81no—
309C4—882no—
310C2—21no—
311C2—21no—
312C2—161no—
313C2—884no—
314C2#1306755011yescharacteristic
315C2#1307059911yescharacteristic
316C2#1307064111yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2039C2
socleC22×C11B(4,𝔽2)
hypercenter#2039D11
hypocenterC11#12152
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2039

Complements

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

NH ≅ G/Ntype
1. #13073532C2semidirect
2. #13067551C2semidirect
3. #13066618C2semidirect
4. #13066562C2semidirect
5. C11×#2039C2semidirect
82. C42×C11D8semidirect
91. #2039D11semidirect
246. C42#4323semidirect
247. C11#12152semidirect

Maximal subgroups

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

subgroupindex
#130735322
#130675512
#130666182
#130665622
C11×#20392
#1215211