Finite Group Databasebeta

← #14651165

Subgroups — #14651165

Order 2816.

514 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 109 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#13077656C211yesmaximal, characteristic
2#13073790C211yesmaximal, characteristic
3#13068605C211yesmaximal, characteristic
4#13067297C211yesmaximal, characteristic, complemented
5#13066518C211yesmaximal, characteristic, complemented
6#13066517C211yesmaximal, characteristic, complemented
7C11×#1548C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622844C414yes—
13C2×#66887—21no—
14#10622601—21no—
15#10622600—22no—
16#10622590—21no—
17C4×C4⋊Dic11C2211yescharacteristic
18#10622538C2211yescharacteristic
19#10622537C2211yescharacteristic
20#10622451—22no—
21#10622339—22no—
22#10622301—22no—
23C11×#333—22no—
24#10622192—21no—
25#10622184—22no—
26C22×Q8×C11C2×C412yes—
27C22×D44D411yescharacteristic
28C22×C4×D11D412yes—
29C2×C11×M16—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37C2×(C2×D11)⋊C4—24no—
38C2×(C2×D11)⋊C4C2×C412yes—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11D411yescharacteristic
41C2×C4×Dic11—21no—
42C2×#4318—21no—
43C2×#4313—24no—
44C4×D44—21no—
45C4×D44—21no—
46C4×D44—21no—
47C4×D44—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8D412yes—
51C11×C22⋊C8—21no—
52C4×C8×C11—21no—
53C11⋊#95—24no—
54C11⋊#95C2×C412yes—
55C22⋊(C11⋊C8)—21no—
56#66887—42no—
57(C2×D11)⋊C8—24no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D412yes—
61C4×C11⋊C8—21no—
62#9399—111nomaximal, Sylow
63C23×D11C22⋊C412yes—
64C2×Q8×C11—22no—
65C2×Q8×C11—22no—
66C2×Q8×C11—82no—
67C22×C4×C11—22no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—22no—
72C22×Dic11C22⋊C412yes—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—21no—
79C2×C4×D11—22no—
80C2×C4×D11—22no—
81C2×C4×D11—44no—
82C11×M16—41no—
83C11×M16—41no—
84C2×C8×C11—22no—
85C2×C8×C11—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11#4111yescharacteristic
93C42×C11#4111yescharacteristic
94(C2×D11)⋊C4—22no—
95(C2×D11)⋊C4—22no—
96(C2×D11)⋊C4—84no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—42no—
100C4×Dic11—41no—
101C4×Dic11—41no—
102#4318—41no—
103#4318—41no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—41no—
106#4313—84no—
107#2975—111no—
108#2563—111no—
109#1800—111no—
110#1548—111no—
111#1548D1111yescharacteristic, complemented
112#1303—111no—
113#1303—111no—
114C23×C11C2×C22⋊C411yescharacteristic
115C22×D11—22no—
116C22×D11—22no—
117C22×D11—22no—
118C22×D11—42no—
119C22×D11—42no—
120Q8×C11—82no—
121Q8×C11—82no—
122C2×C4×C11—22no—
123C2×C4×C11—41no—
124C2×C4×C11—44no—
125C2×C4×C11—42no—
126C2×C4×C11C4×D411yescharacteristic
127C2×C4×C11C4×D411yescharacteristic
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12311yescharacteristic
132C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C11#13711yescharacteristic
134C2×C4×C11#13711yescharacteristic
135C2×C4×C11#13711yescharacteristic
136C2×Dic11—22no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141D44—41no—
142D44—41no—
143D44—41no—
144D44—41no—
145C4×D11—44no—
146C4×D11—82no—
147C8×C11—42no—
148C8×C11—81no—
149C11⋊C8—42no—
150C11⋊C8—81no—
151C2×C4⋊Q8C2×D1111yescharacteristic
152C2×C4×D4—111no—
153#436—222no—
154#436—222no—
155#431—111no—
156#431C2×D1111yescharacteristic
157#423—111no—
158#423C2×D1111yescharacteristic
159C2×#100—221no—
160#407—222no—
161#393—114no—
162#390—221no—
163#382—221no—
164#380—222no—
165C4×C4⋊C4—111no—
166#343—221no—
167#333—22no—
168#333—222no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11#38611yescharacteristic
172C22×C11#41711yescharacteristic
173C22×C11#41911yescharacteristic
174C2×D11—44no—
175C2×D11—42no—
176C2×D11—42no—
177C2×D11—42no—
178C2×D11—82no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—82no—
183C4×C11#45512yes—
184C4×C11#46811yescharacteristic
185C4×C11#46811yescharacteristic
186C4×C11#47011yescharacteristic
187C4×C11#47011yescharacteristic
188Dic11—42no—
189Dic11—82no—
190C22×Q8C4×D1112yes—
191C22×D4—111no—
192C23×C4—112no—
193C2×M16—21no—
194C2×M16—224no—
195C2×M16—221no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4×D4—221no—
201C4×D4—221no—
202C4×D4—221no—
203C4×D4—221no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—221no—
208C2×C22⋊C4—112no—
209C2×C22⋊C4—224no—
210C2×C42—221no—
211C2×C42C22×D1111yescharacteristic
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—112no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217C4⋊C8C22⋊D1112yes—
218#100—442no—
219C22⋊C8—21no—
220C22⋊C8—224no—
221C22⋊C8—221no—
222C4×C8—21no—
223C4×C8—221no—
224#95—112no—
225#95—224no—
226C2×C11—21no—
227C2×C11—21no—
228C2×C11#188511yescharacteristic
229C2×C11#189411yescharacteristic
230C2×C11#191411yescharacteristic
231D11—82no—
232C24—112no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—82no—
236C2×D4—221no—
237C2×D4—221no—
238C2×D4—221no—
239C2×D4—221no—
240C2×D4—221no—
241C2×D4—221no—
242C22×C4—22no—
243C22×C4—112no—
244C22×C4—222no—
245C22×C4—222no—
246C22×C4—222no—
247C22×C4—444no—
248C22×C4C2×C4×D1111yescharacteristic
249C22×C4D4×D1111yescharacteristic
250C22×C4D4×D1111yescharacteristic
251M16—41no—
252M16—41no—
253M16—441no—
254M16—441no—
255M16—884no—
256C2×C8—22no—
257C2×C8—41no—
258C2×C8—222no—
259C2×C8—441no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—442no—
267C22⋊C4—222no—
268C22⋊C4—222no—
269C22⋊C4—884no—
270C42—441no—
271C42—441no—
272C42#433911yescharacteristic
273C42D4×D1111yescharacteristic
274C42#434111yescharacteristic
275C42C2×C22⋊D1111yescharacteristic
276C11#939911yescharacteristic, complemented, Sylow
277C23—222no—
278C23—222no—
279C23—222no—
280C23—442no—
281C23—442no—
282C23C22⋊C4×D1111yescharacteristic
283Q8—82no—
284Q8—82no—
285D4—441no—
286D4—441no—
287D4—441no—
288D4—441no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—44no—
292C2×C4—42no—
293C2×C4—222no—
294C2×C4—444no—
295C2×C4—442no—
296C2×C4—442no—
297C2×C4—442no—
298C2×C4—442no—
299C2×C4—882no—
300C2×C4(C22⋊D11)⋊C411yescharacteristic
301C2×C4#6693611yescharacteristic
302C2×C4#6693711yescharacteristic
303C2×C4#6696711yescharacteristic
304C2×C4#6696811yescharacteristic
305C2×C4#6697111yescharacteristic
306C2×C4#6697111yescharacteristic
307C2×C4C4×C22⋊D1111yescharacteristic
308C2×C4#6699011yescharacteristic
309C2×C4#6699111yescharacteristic
310C8—42no—
311C8—81no—
312C8—442no—
313C8—881no—
314C22—21no—
315C22—21no—
316C22—444no—
317C22—442no—
318C22—442no—
319C22—442no—
320C22—882no—
321C22#1062241511yescharacteristic
322C22#1062241611yescharacteristic
323C22#1062256911yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—82no—
328C4—442no—
329C4—882no—
330C4#1062242511yescharacteristic
331C4#1062242911yescharacteristic
332C4#1062278711yescharacteristic
333C4#1062280211yescharacteristic
334C4#1062281512yes—
335C2—21no—
336C2—21no—
337C2—882no—
338C2#1306900111yescharacteristic
339C2#1306904611yescharacteristic
340C2#1306916011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1548C2
socleC22×C11#386
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1548D11
hypocenterC11#9399
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
4. #13067297C2semidirect
5. #13066518C2semidirect
6. #13066517C2semidirect
7. C11×#1548C2semidirect
111. #1548D11semidirect
276. C11#9399semidirect

Maximal subgroups

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

subgroupindex
#130776562
#130737902
#130686052
#130672972
#130665182
#130665172
C11×#15482
#939911