Finite Group Databasebeta

← #14651202

Subgroups — #14651202

Order 2816.

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

normal subgroups only

This group has 554 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#13077699C211yesmaximal, characteristic, complemented
2#13073618C211yesmaximal, characteristic
3#13068609C211yesmaximal, characteristic, complemented
4#13067285C211yesmaximal, characteristic
5#13067283C211yesmaximal, characteristic
6#13066519C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C2×#66928—21no—
9C2×#66927C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14C2×#66888—21no—
15#10622601—22no—
16#10622552—21no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622444—22no—
20#10622332—22no—
21#10622292—22no—
22#10622285C414yes—
23#10622192—21no—
24#10622123—22no—
25#10622123—22no—
26C22×D44—21no—
27C22×D44—21no—
28C22×D44C2×C412yes—
29C22×Dic22D411yescharacteristic
30C2×C11×M16—21no—
31C2×C11×C4⋊C4—21no—
32C2×C42×C11—21no—
33C2×C42×C11C2311yescharacteristic
34C2×(C2×D11)⋊C4—24no—
35C2×(C2×D11)⋊C4—24no—
36C2×C4⋊Dic11D411yescharacteristic
37C2×Dic11⋊C4C2×C412yes—
38C2×C4×Dic11D412yes—
39C2×#4318—21no—
40#66928—42no—
41#66928—42no—
42#66927—21no—
43#66927—21no—
44#66927—21no—
45#66927—21no—
46C4×Dic22—21no—
47C4×Dic22—21no—
48C4×Dic22—21no—
49C4×Dic22—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8D412yes—
53C11×C22⋊C8—21no—
54C4×C8×C11—21no—
55C11×#95C2×C412yes—
56C22⋊(C11⋊C8)—21no—
57#66888—42no—
58#66879—24no—
59Dic11⋊C8—24no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)D412yes—
63C4×C11⋊C8—21no—
64#9406—111nomaximal, Sylow
65C23×D11—22no—
66C22×C4×C11—22no—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11C22⋊C412yes—
71C22×Dic11C22⋊C412yes—
72C2×D44—22no—
73C2×D44—22no—
74C2×D44—44no—
75C2×D44—41no—
76C2×D44—41no—
77C2×D44—41no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—82no—
84C2×Dic22—21no—
85C2×Dic22—21no—
86C2×Dic22—21no—
87C2×Dic22—21no—
88C2×Dic22—21no—
89C2×Dic22—21no—
90C11×M16—41no—
91C11×M16—41no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C11×C4⋊C4—42no—
95C42×C11—41no—
96C42×C11—41no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101(C2×D11)⋊C4—48no—
102(C2×D11)⋊C4—84no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105Dic11⋊C4—22no—
106Dic11⋊C4—22no—
107C4×Dic11—22no—
108C4×Dic11—22no—
109#4318—41no—
110#4318—41no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—41no—
113#2983—111no—
114#2548—111no—
115#1801—111no—
116#1545—111no—
117#1545—111no—
118#1303—111no—
119#1303D1111yescharacteristic, complemented
120C23×C11C2×C22⋊C411yescharacteristic
121C22×D11—44no—
122C22×D11—44no—
123C22×D11—42no—
124C22×D11—42no—
125C22×D11—42no—
126C2×C4×C11—22no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12311yescharacteristic
137C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11#13711yescharacteristic
141C2×Dic11—22no—
142C2×Dic11—22no—
143C2×Dic11—22no—
144C2×Dic11—22no—
145C2×Dic11—42no—
146D44—82no—
147D44—82no—
148D44—82no—
149D44—82no—
150D44—81no—
151D44—81no—
152D44—81no—
153D44—81no—
154Dic22—41no—
155Dic22—41no—
156Dic22—41no—
157Dic22—41no—
158C8×C11—42no—
159C8×C11—81no—
160C11⋊C8—42no—
161C11⋊C8—81no—
162C2×#127—111no—
163C2×#124—221no—
164C2×C4×Q8—111no—
165#446—222no—
166#446—222no—
167#432—222no—
168#431—111no—
169#431C2×D1111yescharacteristic
170#423—111no—
171#423C2×D1111yescharacteristic
172C2×#101—221no—
173#394—114no—
174#390—221no—
175#390—222no—
176C4×C4⋊C4C2×D1111yescharacteristic
177#343—221no—
178#331—222no—
179#331—222no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11#38611yescharacteristic
183C22×C11#41711yescharacteristic
184C22×C11#41811yescharacteristic
185C2×D11—84no—
186C2×D11—84no—
187C2×D11—82no—
188C2×D11—82no—
189C2×D11—82no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—82no—
194C4×C11#45412yes—
195C4×C11#46811yescharacteristic
196C4×C11#46811yescharacteristic
197C4×C11#46911yescharacteristic
198C4×C11#46911yescharacteristic
199Dic11—42no—
200Dic11—42no—
201C22×Q8—111no—
202C22×D4—112no—
203C22×D4—221no—
204C22×D4—221no—
205C2×M16—21no—
206C2×M16—221no—
207#127—221no—
208#127—221no—
209#127—221no—
210#127—221no—
211#124—442no—
212#124—442no—
213C4×Q8—221no—
214C4×Q8—221no—
215C4×Q8—221no—
216C4×Q8—221no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—112no—
219C2×C4⋊C4—111no—
220C2×C22⋊C4—224no—
221C2×C22⋊C4—224no—
222C2×C42—21no—
223C2×C42—112no—
224C2×C42C22×D1111yescharacteristic
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—112no—
228C4⋊C8—224no—
229C4⋊C8—221no—
230C4⋊C8—221no—
231C4⋊C8D4412yes—
232#101—442no—
233C22⋊C8—21no—
234C22⋊C8—221no—
235#97—224no—
236C4×C8—21no—
237C4×C8—221no—
238#95C4×D1112yes—
239C2×C11—21no—
240C2×C11—21no—
241C2×C11#188811yescharacteristic
242C2×C11#189511yescharacteristic
243C2×C11#191411yescharacteristic
244D11—162no—
245C24—222no—
246C2×Q8—221no—
247C2×Q8—221no—
248C2×Q8—221no—
249C2×Q8—221no—
250C2×Q8—221no—
251C2×Q8—221no—
252C2×D4—222no—
253C2×D4—222no—
254C2×D4—444no—
255C2×D4—441no—
256C2×D4—441no—
257C2×D4—441no—
258C2×D4—441no—
259C2×D4—441no—
260C2×D4—441no—
261C2×D4—441no—
262C2×D4—441no—
263C2×D4—882no—
264C22×C4—22no—
265C22×C4—112no—
266C22×C4—112no—
267C22×C4C2×C4×D1111yescharacteristic
268C22×C4D4×D1111yescharacteristic
269C22×C4D4×D1111yescharacteristic
270M16—41no—
271M16—41no—
272M16—441no—
273M16—441no—
274C2×C8—22no—
275C2×C8—41no—
276C2×C8—222no—
277C2×C8—441no—
278C4⋊C4—42no—
279C4⋊C4—222no—
280C4⋊C4—221no—
281C4⋊C4—222no—
282C4⋊C4—221no—
283C22⋊C4—448no—
284C22⋊C4—884no—
285C42—41no—
286C42—41no—
287C42—222no—
288C42—222no—
289C42C2×D4411yescharacteristic
290C42#433911yescharacteristic
291C42D4×D1111yescharacteristic
292C42#434311yescharacteristic
293C11#940611yescharacteristic, complemented, Sylow
294C23—444no—
295C23—444no—
296C23—442no—
297C23—442no—
298C23—442no—
299C23C22⋊C4×D1111yescharacteristic
300Q8—441no—
301Q8—441no—
302Q8—441no—
303Q8—441no—
304D4—882no—
305D4—882no—
306D4—882no—
307D4—881no—
308D4—881no—
309D4—881no—
310D4—881no—
311D4—882no—
312C2×C4—22no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—222no—
318C2×C4—222no—
319C2×C4—222no—
320C2×C4—222no—
321C2×C4—442no—
322C2×C4C4×D4411yescharacteristic
323C2×C4#6693511yescharacteristic
324C2×C4#6693711yescharacteristic
325C2×C4#6694611yescharacteristic
326C2×C4#6694711yescharacteristic
327C2×C4#6694811yescharacteristic
328C2×C4#6696411yescharacteristic
329C2×C4#6696711yescharacteristic
330C2×C4#6696711yescharacteristic
331C2×C4#6697111yescharacteristic
332C8—42no—
333C8—81no—
334C8—442no—
335C8—881no—
336C22—21no—
337C22—21no—
338C22—884no—
339C22—884no—
340C22—882no—
341C22—882no—
342C22—882no—
343C22#1062227811yescharacteristic
344C22#1062238311yescharacteristic
345C22#1062241611yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—82no—
350C4—442no—
351C4—442no—
352C4#1062239511yescharacteristic
353C4#1062242511yescharacteristic
354C4#1062244012yes—
355C4#1062247811yescharacteristic
356C4#1062249911yescharacteristic
357C2—21no—
358C2—21no—
359C2—1762no—
360C2#1306901811yescharacteristic
361C2#1306905311yescharacteristic
362C2#1306916211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1303C2
socleC22×C11#386
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1303D11
hypocenterC11#9406
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
1. #13077699C2semidirect
3. #13068609C2semidirect
6. #13066519C2semidirect
7. C11×#1303C2semidirect
119. #1303D11semidirect
293. C11#9406semidirect

Maximal subgroups

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

subgroupindex
#130776992
#130736182
#130686092
#130672852
#130672832
#130665192
C11×#13032
#940611