Finite Group Databasebeta

← #14650449

Subgroups — #14650449

Order 2816.

426 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 113 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#13079757C211yesmaximal, characteristic
2#13077557C211yesmaximal, characteristic
3#13069435C211yesmaximal, characteristic
4#13067287C211yesmaximal, characteristic
5#13066474C211yesmaximal, characteristic
6#13066446C211yesmaximal, characteristic
7C11×#1518C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#382C2211yescharacteristic
12#10622694C412yescomplemented
13#10622692C412yescomplemented
14#10622656—22no—
15#10622637—22no—
16#10622637—22no—
17#10622633—22no—
18#10622612—21no—
19#10622610—21no—
20C2×#66874—21no—
21C2×#66874—21no—
22#10622538C2211yescharacteristic
23#10622537C2211yescharacteristic
24C2×#66867C2211yescharacteristic
25C11×#328—22no—
26#10622124—22no—
27C22×Dic22—21no—
28C11×C4⋊Q8C2×C411yescharacteristic
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×#125—21no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8D412yes—
33C4×Q8×C11—21no—
34C4×Q8×C11D412yes—
35C11×#117—21no—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×#4318—21no—
41C22×C11⋊C8D411yescharacteristic
42C22×C11⋊C8D411yescharacteristic
43#66922—21no—
44#66922—21no—
45#66922—21no—
46#66922C2×C412yes—
47C11×C4⋊C8—21no—
48C11×C22⋊C8—21no—
49C4×C8×C11—21no—
50C11×#95—21no—
51C11×#95—21no—
52#66899—24no—
53C22⋊(C11⋊C8)—21no—
54#66874—42no—
55#66874—42no—
56#66872—24no—
57C4⋊(C11⋊C8)—24no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D412yes—
61#66867—22no—
62#66867—21no—
63#66867—21no—
64C4×C11⋊C8—22no—
65C4×C11⋊C8C2×C412yes—
66#9292—111nomaximal, Sylow
67C2×Q8×C11—21no—
68C2×Q8×C11C22⋊C412yes—
69C22×C4×C11—41no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×Dic11—41no—
74C2×Dic22—22no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C2×C8×C11—41no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4C22⋊C412yes—
89C11×C22⋊C4—22no—
90C42×C11—22no—
91C42×C11C22×C411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11#4111yescharacteristic
95C4⋊Dic11—22no—
96C4⋊Dic11—22no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99#4318—41no—
100#4318—41no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8SD1612yes—
109#3229—111no—
110#2961—111no—
111#1960—111no—
112#1546—111no—
113#1518D1111yescharacteristic
114#1286—111no—
115#1275—111no—
116C23×C11#12111yescharacteristic
117Q8×C11—42no—
118Q8×C11—81no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11—81no—
126C2×C4×C11C2×C22⋊C411yescharacteristic
127C2×C4×C11C4×D411yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12311yescharacteristic
132C2×C4×C11C2×SD1611yescharacteristic
133C2×C4×C11#13511yescharacteristic
134C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C11#13711yescharacteristic
136C2×Dic11—42no—
137C2×Dic11—81no—
138C2×Dic11—81no—
139Dic22—42no—
140Dic22—42no—
141Dic22—81no—
142Dic22—81no—
143C8×C11—81no—
144C11⋊C8—22no—
145C11⋊C8—42no—
146C11⋊C8—41no—
147C11⋊C8—42no—
148#533C2×D1111yescharacteristic
149C2×C4⋊Q8—111no—
150#498—112no—
151#487—112no—
152#483—222no—
153#475—222no—
154#446—222no—
155#446—222no—
156#431—111no—
157#431C2×D1111yescharacteristic
158#424—221no—
159#423—111no—
160C2×#103—221no—
161C2×#103—221no—
162#405—221no—
163C2×#97—111no—
164#382C2×D1111yescharacteristic
165#332—222no—
166#328—22no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11#38611yescharacteristic
170C22×C11#46011yescharacteristic
171C22×C11#46411yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—42no—
177C4×C11—42no—
178C4×C11—161no—
179C4×C11C4×SD1611yescharacteristic
180C4×C11#44011yescharacteristic
181C4×C11#44811yescharacteristic
182C4×C11#44911yescharacteristic
183Dic11—82no—
184C22×Q8—221no—
185C2×M16—221no—
186C22×C8—111no—
187C22×C8—111no—
188C4⋊Q8—112no—
189C4⋊Q8—221no—
190C4⋊Q8—221no—
191C4⋊Q8—221no—
192C4⋊Q8C4×D1111yescharacteristic
193C4⋊Q8C4×D1111yescharacteristic
194#125—21no—
195C22⋊Q8—21no—
196C22⋊Q8C22⋊D1112yes—
197C4×Q8—21no—
198C4×Q8D4412yes—
199#117—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C42C22×D1111yescharacteristic
204#106—224no—
205C4⋊C8—21no—
206C4⋊C8—112no—
207C4⋊C8—224no—
208C4⋊C8—221no—
209C4⋊C8—221no—
210#103—224no—
211#103—442no—
212#103—442no—
213C22⋊C8—21no—
214C22⋊C8—221no—
215#97—222no—
216#97—221no—
217#97—221no—
218C4×C8—21no—
219C4×C8—112no—
220C4×C8—222no—
221#95—21no—
222#95—21no—
223C2×C11—21no—
224C2×C11—21no—
225C2×C11#188011yescharacteristic
226C2×C11#190211yescharacteristic
227C2×C11#190911yescharacteristic
228C2×Q8—21no—
229C2×Q8—222no—
230C2×Q8—441no—
231C2×Q8—441no—
232C2×Q8—441no—
233C2×Q8—441no—
234C2×Q8—441no—
235C2×Q8(C2×D11)⋊C412yes—
236C22×C4—41no—
237C22×C4—441no—
238C22×C4D4×D1111yescharacteristic
239C22×C4#434111yescharacteristic
240C22×C4C2×C22⋊D1111yescharacteristic
241M16—441no—
242M16—441no—
243C2×C8—41no—
244C2×C8—112no—
245C2×C8—221no—
246C2×C8—221no—
247C2×C8—222no—
248C2×C8—221no—
249C2×C8—221no—
250C2×C8—221no—
251C2×C8—222no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—222no—
260C4⋊C4—222no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4(C2×D11)⋊C412yes—
264C22⋊C4—22no—
265C42—22no—
266C42C2×C4×D1111yescharacteristic
267C42C2×D4411yescharacteristic
268C42D4×D1111yescharacteristic
269C42#434111yescharacteristic
270C11#929211yescharacteristic, complemented, Sylow
271C23#6699211yescharacteristic
272Q8—42no—
273Q8—81no—
274Q8—442no—
275Q8—442no—
276Q8—881no—
277Q8—881no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—442no—
286C2×C4—881no—
287C2×C4—881no—
288C2×C4(C22⋊D11)⋊C411yescharacteristic
289C2×C4(C22⋊D11)⋊C411yescharacteristic
290C2×C4#6693511yescharacteristic
291C2×C4#6693911yescharacteristic
292C2×C4SD16×D1111yescharacteristic
293C2×C4#6696711yescharacteristic
294C2×C4#6697111yescharacteristic
295C2×C4#6697211yescharacteristic
296C2×C4C2×(C2×D11)⋊C411yescharacteristic
297C2×C4#6699211yescharacteristic
298C8—81no—
299C8—222no—
300C8—442no—
301C8—441no—
302C8—442no—
303C22—21no—
304C22—21no—
305C22#1062257111yescharacteristic
306C22#1062277611yescharacteristic
307C22#1062279811yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—42no—
313C4—42no—
314C4—161no—
315C4—882no—
316C4#1062240111yescharacteristic
317C4#1062241911yescharacteristic
318C4#1062242411yescharacteristic
319C4#1062243011yescharacteristic
320C2—21no—
321C2—21no—
322C2#1306896911yescharacteristic
323C2#1306908711yescharacteristic
324C2#1306913611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1518C2
socleC22×C11#386
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1518D11
hypocenterC11#9292
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
12. #10622694C4semidirect
13. #10622692C4semidirect
270. C11#9292semidirect

Maximal subgroups

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

subgroupindex
#130797572
#130775572
#130694352
#130672872
#130664742
#130664462
C11×#15182
#929211