Finite Group Databasebeta

← #14762942

Subgroups — #14762942

Order 2816.

1270 conjugacy classes of subgroups; only the 231 normal subgroups are shown.

normal subgroups only

This group has 1270 conjugacy classes of subgroups — too many to draw. Only its 231 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#13082261C211yesmaximal, characteristic
2#13077092C212yesmaximal, complemented
3#13069167C214yesmaximal, complemented
4#13069033C214yesmaximal, complemented
5#13068727C211yesmaximal, characteristic, complemented
6#13068541C212yesmaximal, complemented
7C11×#1829C211yesmaximal, characteristic, complemented
8C2×#67037C2211yescharacteristic
9C22×#4341C2211yescharacteristic
10C11×#518C2211yescharacteristic
11#10623276C2214yes—
12#10623086—24no—
13#10623085—24no—
14#10623057C2212yes—
15#10623055C2212yes—
16#10623024C414yes—
17C2×#66939C414yes—
18C2×C11×#100C2212yes—
19C2×#66897C2212yes—
20C2×#66888C2214yescomplemented
21#10622745C2214yes—
22#10622739C2214yescomplemented
23#10622358—24no—
24D11×#100—24no—
25C11×#344C2214yescomplemented
26#10622171C2214yescomplemented
27C22×D4×C11C2311yescharacteristic
28C22×C22⋊D11C2×C414yes—
29C22×C22⋊D11C2×C412yes—
30C23×Dic11C2×C412yes—
31#67037—44no—
32C2×#4341—24no—
33C2×#4341—44no—
34C2×#4341D414yes—
35C2×D4×D11D414yes—
36C2×#4339C2312yes—
37C22×C4×D11C2311yescharacteristic
38C22×Dic22C2311yescharacteristic
39C2×C11×M16C2314yes—
40C4×D4×C11—24no—
41C11×#117C2312yes—
42C2×C11×C22⋊C4C2×C414yes—
43#66983—28no—
44C2×(C2×D11)⋊C4—24no—
45C2×C4⋊Dic11—24no—
46C2×#4318C2314yes—
47#66960—44no—
48M16×D11—28no—
49#66954—44no—
50#66950—24no—
51#66950—22no—
52#66948—22no—
53#66939—28no—
54#66939—24no—
55#66939C2×C414yes—
56#66939C2×C418yes—
57#66935—24no—
58#66935C2×C414yes—
59#66928—22no—
60C4×D44—24no—
61#66922—22no—
62C11×#100—24no—
63#66897—24no—
64#66888—24no—
65#66888—44no—
66#66887—24no—
67(C2×D11)⋊C8—44no—
68#21779—111nomaximal, Sylow
69C24×C11C22×C412yes—
70C23×D11C22⋊C414yes—
71C23×D11C22×C411yescharacteristic
72C2×D4×C11—24no—
73C2×D4×C11C2×D414yes—
74C22×C4×C11—24no—
75C22×C4×C11C2411yescharacteristic
76C2×C22⋊D11—24no—
77C2×C22⋊D11—44no—
78C2×C22⋊D11—48no—
79C2×C22⋊D11C22⋊C418yes—
80C2×C22⋊D11C22×C414yes—
81C22×Dic11—24no—
82C22×Dic11—44no—
83C22×Dic11C22⋊C414yes—
84C22×Dic11C22×C412yes—
85C22×Dic11C22×C411yescharacteristic
86#4341—48no—
87#4341—416no—
88D4×D11—48no—
89#4339—24no—
90#4339—24no—
91C2×D44—24no—
92C2×D44C2×D412yes—
93C2×C4×D11—22no—
94C2×C4×D11—24no—
95C2×C4×D11C2×D414yes—
96C2×Dic22—22no—
97C2×Dic22—24no—
98C2×Dic22C2×D412yes—
99C11×M16—24no—
100C11×M16—24no—
101C2×C8×C11—24no—
102C11×C4⋊C4—22no—
103C11×C22⋊C4—24no—
104C11×C22⋊C4C22×C414yes—
105C42×C11—22no—
106(C2×D11)⋊C4—24no—
107(C2×D11)⋊C4—24no—
108(C2×D11)⋊C4—28no—
109C4⋊Dic11—28no—
110C4⋊Dic11—24no—
111#4318—24no—
112#4318—24no—
113C2×C11⋊C8—24no—
114#4313—48no—
115C8×D11—48no—
116#3485—111no—
117#2888—112no—
118#1915—114no—
119#1891—114no—
120#1829—111no—
121#1829D1111yescharacteristic, complemented
122#1785—112no—
123C23×C11—24no—
124C23×C11—82no—
125C23×C11C2×C22⋊C414yes—
126C23×C11C23×C411yescharacteristic
127C22×D11—21no—
128C22×D11—22no—
129C22×D11—44no—
130C22×D11—81no—
131C22×D11—84no—
132C22×D11C2×C22⋊C414yes—
133D4×C11—28no—
134C2×C4×C11—24no—
135C2×C4×C11—84no—
136C2×C4×C11C22×D412yes—
137C2×C4×C11H(5,𝔽2)14yes—
138C22⋊D11—24no—
139C22⋊D11—24no—
140C22⋊D11—48no—
141C22⋊D11—48no—
142C2×Dic11—22no—
143C2×Dic11—21no—
144C2×Dic11—24no—
145C2×Dic11—22no—
146C2×Dic11—44no—
147C2×Dic11—48no—
148C2×Dic11C2×C22⋊C414yes—
149D44—24no—
150D44—84no—
151C4×D11—28no—
152C4×D11—44no—
153Dic22—24no—
154Dic22—44no—
155C8×C11—44no—
156C11⋊C8—44no—
157C2×H(5,𝔽2)—111no—
158C22×#41—111no—
159#568—114no—
160#547—224no—
161#546—224no—
162#536—112no—
163#534—114no—
164#525—112no—
165C2×#123—114no—
166#518C2×D1111yescharacteristic
167#413—114no—
168#413—224no—
169C2×#101—114no—
170C2×#100—112no—
171C2×#100—224no—
172C2×#100C2×D1112yes—
173#407—114no—
174#344—114no—
175#344C2×D1114yescomplemented
176C22×C11—24no—
177C22×C11—41no—
178C22×C11—44no—
179C22×C11—84no—
180C22×C11C22×C22⋊C411yescharacteristic
181C22×C11#51812yes—
182C2×D11—24no—
183C2×D11—44no—
184C2×D11—44no—
185C2×D11—42no—
186C2×D11—41no—
187C2×D11—164no—
188C4×C11—44no—
189C4×C11#53414yes—
190Dic11—24no—
191Dic11—42no—
192Dic11—41no—
193H(5,𝔽2)—444no—
194C2×#41—114no—
195C2×#41—112no—
196C2×#41—224no—
197C2×#41—444no—
198C22×Q8—111no—
199C22×D4—114no—
200C22×D4—114no—
201C22×D4—112no—
202C22×D4C22×D1111yescharacteristic
203C23×C4—112no—
204C23×C4—111no—
205#131—444no—
206#131—444no—
207C2×M16—114no—
208C2×M16—228no—
209C2×M16C22×D1114yes—
210C4⋊Q8—222no—
211#124—222no—
212#123—114no—
213#123—118no—
214#123—224no—
215#123—228no—
216C22⋊Q8—224no—
217C22⋊Q8—222no—
218#121—222no—
219#121—228no—
220#120—114no—
221#120—224no—
222C4×D4—24no—
223C4×D4—224no—
224#117C22×D1112yes—
225C2×C4⋊C4—224no—
226C2×C22⋊C4—224no—
227C2×C22⋊C4C4×D1114yes—
228#101—224no—
229#101—444no—
230#100—24no—
231#100—224no—
232#100—224no—
233C22⋊C8—444no—
234C2×C11—21no—
235C2×C11—22no—
236C2×C11—44no—
237C2×C11#230811yescharacteristic
238D11—44no—
239D11—81no—
240C24—114no—
241C24—111no—
242C24C2×C4×D1112yes—
243#41—224no—
244#41—224no—
245#41—448no—
246#41—4416no—
247C2×Q8—112no—
248C2×Q8—222no—
249C2×Q8—224no—
250C2×D4—24no—
251C2×D4—114no—
252C2×D4—118no—
253C2×D4—112no—
254C2×D4—224no—
255C2×D4—224no—
256C2×D4—448no—
257C2×D4—444no—
258C2×D4—448no—
259C2×D4D4×D1114yes—
260C22×C4—24no—
261C22×C4—114no—
262C22×C4—114no—
263C22×C4—111no—
264C22×C4—112no—
265C22×C4—224no—
266C22×C4—222no—
267C22×C4—224no—
268C22×C4—444no—
269C22×C4C23×D1111yescharacteristic
270M16—24no—
271M16—24no—
272M16—224no—
273M16—224no—
274M16—448no—
275C2×C8—24no—
276C2×C8—224no—
277C2×C8—448no—
278C4⋊C4—22no—
279C4⋊C4—224no—
280C4⋊C4—228no—
281C22⋊C4—24no—
282C22⋊C4—224no—
283C22⋊C4—224no—
284C22⋊C4—228no—
285C22⋊C4C2×C4×D1114yes—
286C42—22no—
287C11#2177911yescharacteristic, complemented, Sylow
288C23—24no—
289C23—82no—
290C23—114no—
291C23—221no—
292C23—222no—
293C23—444no—
294C23—881no—
295C23—884no—
296C23C22⋊C4×D1114yes—
297C23C22×C4×D1111yescharacteristic
298Q8—224no—
299Q8—444no—
300D4—28no—
301D4—224no—
302D4—224no—
303D4—224no—
304D4—448no—
305D4—448no—
306D4—884no—
307C2×C4—24no—
308C2×C4—84no—
309C2×C4—114no—
310C2×C4—228no—
311C2×C4—221no—
312C2×C4—222no—
313C2×C4—222no—
314C2×C4—224no—
315C2×C4—444no—
316C2×C4—448no—
317C2×C4—444no—
318C2×C4C2×D4×D1112yes—
319C2×C4#6704214yes—
320C8—44no—
321C8—444no—
322C22—24no—
323C22—41no—
324C22—44no—
325C22—84no—
326C22—224no—
327C22—444no—
328C22—442no—
329C22—444no—
330C22—441no—
331C22—1764no—
332C22C2×C22⋊C4×D1111yescharacteristic
333C22#1062305212yes—
334C4—44no—
335C4—224no—
336C4—441no—
337C4—442no—
338C4#1062318414yes—
339C2—21no—
340C2—22no—
341C2—44no—
342C2—444no—
343C2—881no—
344C2#1307119311yescharacteristic
subgroupG/H
centerC2#13071193
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1829C2
socleC2×C11#2308
prime radical#13082261C2
cosocleC22×C4×C11C24
hypercenter#1829D11
hypocenterC11#21779
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1829

Complements

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

NH ≅ G/Ntype
2. #13077092C2semidirect
3. #13069167C2semidirect
4. #13069033C2semidirect
5. #13068727C2semidirect
6. #13068541C2semidirect
7. C11×#1829C2semidirect
20. C2×#66888C22semidirect
22. #10622739C22semidirect
25. C11×#344C22semidirect
26. #10622171C22semidirect
121. #1829D11semidirect
175. #344C2×D11semidirect
287. C11#21779semidirect

Maximal subgroups

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

subgroupindex
#130822612
#130770922
#130691672
#130690332
#130687272
#130685412
C11×#18292
#2177911