Finite Group Databasebeta

← #14648710

Subgroups — #14648710

Order 2816.

578 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 111 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×#10622673C211yesmaximal, characteristic
2#13071790C211yesmaximal, characteristic
3#13069589C212yesmaximal, complemented
4#13066498C212yesmaximal, complemented
5C2×C11×#329C211yesmaximal, characteristic
6C2×C11×#124C2211yescharacteristic
7C22×#4326—21no—
8C22×#4324—21no—
9C2×#66922C2211yescharacteristic
10C2×C11×#97C2212yes—
11#10622843—21no—
12#10622833—21no—
13#10622673—22no—
14#10622673C414yescomplemented
15#10622564—22no—
16#10622563—22no—
17#10622549C2212yes—
18C2×#66867C2211yescharacteristic
19C11×#329—22no—
20#10622189—22no—
21#10622189—22no—
22C22×Q8×C11D411yescharacteristic
23C22×D4×C11D411yescharacteristic
24C23×Dic11—21no—
25C22×Dic22—21no—
26C22×C8×C11—22no—
27C11×#124—22no—
28C11×#124C2×C412yes—
29C11×#124D412yes—
30C2×C11×C22⋊C4—22no—
31C2×C42×C11C2311yescharacteristic
32C2×C22⋊Dic11—22no—
33C2×C22⋊Dic11—21no—
34C2×#4326—24no—
35C2×#4326—42no—
36C2×#4326—42no—
37C2×#4324—24no—
38C2×#4324—42no—
39C2×#4324—42no—
40C2×C4⋊Dic11—22no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D412yes—
43C2×C4⋊Dic11D412yes—
44C2×C4×Dic11—21no—
45C22×C11⋊C8—21no—
46#66922—22no—
47#66922—21no—
48#66922C2×C412yescomplemented
49C11×#97—22no—
50C11×#97—22no—
51C11⋊#95—22no—
52C11⋊#95—22no—
53C11⋊#95—22no—
54#66867—21no—
55#66867C2×C412yescomplemented
56#9003—111nomaximal, Sylow
57C24×C11—21no—
58C2×Q8×C11—21no—
59C2×Q8×C11—41no—
60C2×Q8×C11—41no—
61C2×Q8×C11C22⋊C412yes—
62C2×D4×C11—21no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11C22⋊C412yes—
66C22×C4×C11—21no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D412yes—
69C22×Dic11—22no—
70C22×Dic11—22no—
71C22×Dic11—41no—
72C22×Dic11—81no—
73C22×Dic11—82no—
74C2×Dic22—22no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C2×C8×C11—24no—
81C2×C8×C11—42no—
82C2×C8×C11—42no—
83C11×C22⋊C4—24no—
84C11×C22⋊C4—24no—
85C42×C11C22×C411yescharacteristic
86C42×C11C2×D411yescharacteristic
87C42×C11#4112yes—
88C22⋊Dic11—81no—
89C22⋊Dic11—82no—
90#4326—48no—
91#4324—48no—
92C4⋊Dic11—24no—
93C4⋊Dic11—42no—
94C4⋊Dic11—42no—
95C4⋊Dic11—42no—
96C4⋊Dic11—81no—
97C4×Dic11—81no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—22no—
101C2×#497—111no—
102#2379—111no—
103#1993—112no—
104C2×#329D1111yescharacteristic
105#1295—112no—
106C23×C11—22no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11—42no—
110C23×C11—42no—
111C23×C11#12011yescharacteristic
112Q8×C11—42no—
113Q8×C11—81no—
114D4×C11—42no—
115D4×C11—81no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11C2×C22⋊C411yescharacteristic
124C2×C4×C11C4×D412yes—
125C2×C4×C11#12112yes—
126C2×C4×C11#12311yescharacteristic
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—84no—
135C2×Dic11—81no—
136C2×Dic11—81no—
137Dic22—42no—
138Dic22—42no—
139Dic22—81no—
140Dic22—81no—
141C8×C11—44no—
142C11⋊C8—24no—
143C22×Q16—221no—
144C22×SD16—221no—
145C2×C4⋊Q8—111no—
146C2×#124C2×D1111yescharacteristic
147#497—114no—
148#497—222no—
149C2×#97—111no—
150C2×#97C2×D1112yes—
151#391—221no—
152#388—222no—
153#386—221no—
154#385—222no—
155#382—112no—
156#340—222no—
157#340—222no—
158#329—22no—
159C22×C11—44no—
160C22×C11—42no—
161C22×C11—81no—
162C22×C11—81no—
163C22×C11—82no—
164C22×C11#38611yescharacteristic
165C22×C11#45311yescharacteristic
166C22×C11#45311yescharacteristic
167C22×C11#45512yes—
168C22×C11#45612yes—
169C4×C11—22no—
170C4×C11—22no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—42no—
174Dic11—82no—
175Dic11—82no—
176Dic11—82no—
177C22×Q8—221no—
178C22×Q8D4411yescharacteristic
179C22×D4D4411yescharacteristic
180C23×C4—221no—
181C2×Q16—224no—
182C2×Q16—442no—
183C2×Q16—442no—
184C2×SD16—224no—
185C2×SD16—442no—
186C2×SD16—442no—
187C22×C8—22no—
188C22×C8—221no—
189C4⋊Q8—112no—
190C4⋊Q8—222no—
191C4⋊Q8—221no—
192#124—22no—
193#124C4×D1112yes—
194#124C22⋊D1112yes—
195C2×C4⋊C4—112no—
196C2×C4⋊C4—112no—
197C2×C4⋊C4—222no—
198C2×C4⋊C4—221no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—222no—
201C2×C22⋊C4—221no—
202C2×C42—221no—
203C2×C42C22×D1111yescharacteristic
204#97—22no—
205#97—22no—
206#97—112no—
207#97—221no—
208#95—222no—
209#95—222no—
210#95—222no—
211C2×C11—82no—
212C2×C11#165911yescharacteristic
213C2×C11#166011yescharacteristic
214C2×C11#166112yes—
215C2×C11#188212yes—
216C2×C11#188711yescharacteristic
217C24—21no—
218C2×Q8—21no—
219C2×Q8—41no—
220C2×Q8—41no—
221C2×Q8—222no—
222C2×Q8—441no—
223C2×Q8—441no—
224C2×Q8—441no—
225C2×Q8—441no—
226C2×Q8—441no—
227C2×Q8(C2×D11)⋊C412yes—
228C2×D4—21no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4(C2×D11)⋊C412yes—
232C22×C4—21no—
233C22×C4—222no—
234C22×C4—222no—
235C22×C4—441no—
236C22×C4—881no—
237C22×C4—882no—
238C22×C4C2×D4411yescharacteristic
239C22×C4D4×D1112yes—
240Q16—448no—
241SD16—448no—
242C2×C8—24no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—222no—
246C2×C8—222no—
247C2×C8—222no—
248C4⋊C4—224no—
249C4⋊C4—442no—
250C4⋊C4—442no—
251C4⋊C4—442no—
252C4⋊C4—881no—
253C22⋊C4—24no—
254C22⋊C4—24no—
255C22⋊C4—881no—
256C22⋊C4—882no—
257C42—881no—
258C42C2×C4×D1111yescharacteristic
259C42#434112yes—
260C42C2×C22⋊D1111yescharacteristic
261C11#900311yescharacteristic, complemented, Sylow
262C23—22no—
263C23—41no—
264C23—41no—
265C23—42no—
266C23—42no—
267C23#6693511yescharacteristic
268Q8—42no—
269Q8—81no—
270Q8—442no—
271Q8—442no—
272Q8—881no—
273Q8—881no—
274D4—42no—
275D4—81no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—442no—
284C2×C4—442no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—442no—
290C2×C4—884no—
291C2×C4—881no—
292C2×C4—881no—
293C2×C4(C22⋊D11)⋊C412yes—
294C2×C4#6693911yescharacteristic
295C2×C4C2×(C2×D11)⋊C411yescharacteristic
296C2×C4#6699212yes—
297C8—44no—
298C8—224no—
299C22—44no—
300C22—42no—
301C22—81no—
302C22—81no—
303C22—82no—
304C22#1062236011yescharacteristic
305C22#1062236011yescharacteristic
306C22#1062243812yes—
307C22#1062243912yes—
308C22#1062257111yescharacteristic
309C4—22no—
310C4—22no—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—882no—
315C4—882no—
316C4—882no—
317C2—82no—
318C2#1306792311yescharacteristic
319C2#1306792811yescharacteristic
320C2#1306793412yes—
321C2#1306898312yes—
322C2#1306901211yescharacteristic
subgroupG/H
centerC23#66935
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#329C2
socleC23×C11#120
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenterC2×#329D11
hypocenterC11#9003
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
3. #13069589C2semidirect
4. #13066498C2semidirect
14. #10622673C4semidirect
48. #66922C2×C4semidirect
55. #66867C2×C4semidirect
261. C11#9003semidirect

Maximal subgroups

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

subgroupindex
C2×#106226732
#130717902
#130695892
#130664982
C2×C11×#3292
#900311