Finite Group Databasebeta

← #14667608

Subgroups — #14667608

Order 2816.

366 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 65 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#13080226C211yesmaximal, characteristic
2#13070855C211yesmaximal, characteristic, complemented
3#13068136C211yesmaximal, characteristic, complemented
4#13066660C211yesmaximal, characteristic, complemented
5#13066583C211yesmaximal, characteristic, complemented
6#13066573C211yesmaximal, characteristic, complemented
7C11×#2224C211yesmaximal, characteristic, complemented
8C2×#66964—21no—
9#10623085—21no—
10C11×#500C2211yescharacteristic, complemented
11C4×C11×D8C2211yescharacteristic
12#10622697—21no—
13#10622629—21no—
14#10622499—21no—
15#10622396—21no—
16#10622386—21no—
17#10622309C2211yescharacteristic
18#10622301C2211yescharacteristic
19C11×#366—21no—
20C11×C4⋊C16C2211yescharacteristic, complemented
21C11×#357—21no—
22#10622184—21no—
23#10622130—21no—
24#10622129—21no—
25#10622099C2211yescharacteristic, complemented
26#10622095C2211yescharacteristic, complemented
27C2×#4341—21no—
28C2×D4×D11—21no—
29C2×C11×D8D411yescharacteristic
30C11×C4⋊Q8—21no—
31C4×D4×C11—21no—
32C2×#4324—21no—
33C2×#4323—21no—
34#66983—41no—
35C2×(C2×D11)⋊C4—41no—
36#66964—42no—
37#66964—42no—
38C2×Dic44D411yescharacteristic
39C2×D88D411yescharacteristic
40C2×#4314—21no—
41C2×#4313—21no—
42#66950—21no—
43#66948—21no—
44#66939—41no—
45#66935—41no—
46#66928—21no—
47C4×D44D411yescharacteristic
48C2×C11×C16—21no—
49C11×#107—21no—
50C11×#107—21no—
51C11×#107D411yescharacteristic
52C11×#102—21no—
53C4×C8×C11C2311yescharacteristic
54(C2×D11)⋊C8—21no—
55C2×C11⋊C16—21no—
56#66874—21no—
57#66873—21no—
58#66873—41no—
59#66872—41no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)D411yescharacteristic
62#12376—111nomaximal, Sylow
63C23×D11—41no—
64C2×Q8×C11—41no—
65C2×D4×C11—21no—
66C22×C4×C11—41no—
67C2×C22⋊D11—41no—
68C2×C22⋊D11—41no—
69C22×Dic11—41no—
70#4341—42no—
71#4341—81no—
72D4×D11—42no—
73D4×D11—81no—
74C2×D44—21no—
75C2×D44—41no—
76C2×D44D811yescharacteristic
77C2×C4×D11—21no—
78C2×Dic22—21no—
79C11×D8—21no—
80C11×D8SD1612yes—
81C2×C8×C11C2×D411yescharacteristic
82C2×C8×C11C2×D411yescharacteristic
83C11×C4⋊C4—21no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C22⋊C4—41no—
87C42×C11C2×D411yescharacteristic
88#4324—42no—
89#4323—42no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—41no—
92(C2×D11)⋊C4—41no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11D811yescharacteristic
97C2×C11⋊C8—21no—
98C2×C11⋊C8—41no—
99Dic44—41no—
100D88—41no—
101#4314—41no—
102#4314—41no—
103#4313—41no—
104#4313—41no—
105C11×C16—41no—
106C11⋊C16—41no—
107#3273—111no—
108#2243—111no—
109#2224D1111yescharacteristic, complemented
110#1695—111no—
111#1360—111no—
112#1333—111no—
113#1330—111no—
114C23×C11—41no—
115C22×D11—21no—
116C22×D11—41no—
117C22×D11—82no—
118C22×D11—82no—
119C22×D11—161no—
120Q8×C11—161no—
121D4×C11—22no—
122D4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—81no—
125C2×C4×C11—161no—
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11C2×D811yescharacteristic
128C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
129C22⋊D11—82no—
130C22⋊D11—82no—
131C2×Dic11—21no—
132C2×Dic11—41no—
133C2×Dic11—82no—
134D44—41no—
135D44—41no—
136D44—41no—
137D44—161no—
138C4×D11—41no—
139C4×D11—41no—
140Dic22—41no—
141Dic22—41no—
142C8×C11—21no—
143C8×C11C2×SD1611yescharacteristic
144C8×C11AGL(1,ℤ/8)11yescharacteristic
145C11⋊C8—41no—
146C11⋊C8—81no—
147C2×AGL(1,ℤ/8)—221no—
148#546—221no—
149#500C2×D1111yescharacteristic, complemented
150#495—111no—
151#476—221no—
152#468—221no—
153#463—221no—
154#452—221no—
155#447—221no—
156C4×D8C2×D1111yescharacteristic
157#436—111no—
158#366—21no—
159C4⋊C16C2×D1111yescharacteristic, complemented
160#358—221no—
161#357—21no—
162#357—221no—
163#346—111no—
164#334—111no—
165#333—221no—
166C22×C11—42no—
167C22×C11—81no—
168C22×C11—81no—
169C22×C11#44711yescharacteristic
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—41no—
173C2×D11—81no—
174C2×D11—81no—
175C2×D11—81no—
176C2×D11—164no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—81no—
180C4×C11—161no—
181C4×C11#45011yescharacteristic
182C4×C11#45511yescharacteristic
183Dic11—41no—
184Dic11—81no—
185C2×#41—221no—
186C22×D4—221no—
187AGL(1,ℤ/8)—442no—
188AGL(1,ℤ/8)—442no—
189C2×Q16—111no—
190C2×SD16—221no—
191C2×SD16—221no—
192C2×D8—111no—
193C2×D8—221no—
194C2×D8C22⋊D1111yescharacteristic
195C2×M16—221no—
196C4⋊Q8—21no—
197#124—221no—
198#123—441no—
199C22⋊Q8—221no—
200#121—221no—
201#121—441no—
202#120—441no—
203C4×D4—21no—
204C4×D4—111no—
205C2×C22⋊C4—441no—
206C2×C16—21no—
207C2×C16—221no—
208#107—21no—
209#107—21no—
210#107C22⋊D1111yescharacteristic
211#106—441no—
212C4⋊C8—111no—
213C4⋊C8—221no—
214#103—221no—
215#102—21no—
216#102—221no—
217#102—441no—
218C22⋊C8—221no—
219C4×C8C22×D1111yescharacteristic
220C2×C11—82no—
221C2×C11#163911yescharacteristic
222C2×C11#219111yescharacteristic
223C2×C11#219211yescharacteristic
224D11—81no—
225D11—161no—
226C24—441no—
227#41—442no—
228#41—881no—
229C2×Q8—41no—
230C2×Q8—221no—
231C2×D4—21no—
232C2×D4—111no—
233C2×D4—221no—
234C2×D4—441no—
235C2×D4—441no—
236C2×D4—442no—
237C2×D4—441no—
238C2×D4—881no—
239C22×C4—41no—
240C22×C4—221no—
241C22×C4—441no—
242Q16—441no—
243SD16—442no—
244SD16—441no—
245SD16—441no—
246D8—21no—
247D8—441no—
248D8—442no—
249D8#432512yes—
250M16—441no—
251M16—441no—
252C2×C8—221no—
253C2×C8—441no—
254C2×C8D4×D1111yescharacteristic
255C2×C8C2×C22⋊D1111yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—111no—
260C4⋊C4—441no—
261C22⋊C4—41no—
262C22⋊C4—221no—
263C22⋊C4—441no—
264C22⋊C4—441no—
265C22⋊C4—441no—
266C22⋊C4—441no—
267C42D4×D1111yescharacteristic
268C16—41no—
269C16—441no—
270C11#1237611yescharacteristic, complemented, Sylow
271C23—41no—
272C23—221no—
273C23—441no—
274C23—882no—
275C23—882no—
276C23—1761no—
277Q8—161no—
278Q8—441no—
279Q8—441no—
280D4—22no—
281D4—41no—
282D4—441no—
283D4—441no—
284D4—441no—
285D4—882no—
286D4—882no—
287D4—1761no—
288C2×C4—41no—
289C2×C4—81no—
290C2×C4—161no—
291C2×C4—221no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—882no—
296C2×C4D8×D1111yescharacteristic
297C2×C4#6696411yescharacteristic
298C2×C4#6699011yescharacteristic
299C8—21no—
300C8—441no—
301C8—881no—
302C8C2×#432511yescharacteristic
303C8#6700211yescharacteristic
304C22—42no—
305C22—81no—
306C22—81no—
307C22—441no—
308C22—441no—
309C22—441no—
310C22—881no—
311C22—881no—
312C22—881no—
313C22—1764no—
314C22#1062276911yescharacteristic
315C4—21no—
316C4—21no—
317C4—81no—
318C4—161no—
319C4—441no—
320C4—881no—
321C4#1062265911yescharacteristic
322C4#1062281511yescharacteristic
323C2—82no—
324C2—881no—
325C2—1761no—
326C2#1306779411yescharacteristic
327C2#1307056511yescharacteristic
328C2#1307057211yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2224C2
socleC22×C11#447
prime radical#13080226C2
hypercenter#2224D11
hypocenterC11#12376
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2224

Complements

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

NH ≅ G/Ntype
2. #13070855C2semidirect
3. #13068136C2semidirect
4. #13066660C2semidirect
5. #13066583C2semidirect
6. #13066573C2semidirect
7. C11×#2224C2semidirect
10. C11×#500C22semidirect
20. C11×C4⋊C16C22semidirect
25. #10622099C22semidirect
26. #10622095C22semidirect
109. #2224D11semidirect
149. #500C2×D11semidirect
159. C4⋊C16C2×D11semidirect
270. C11#12376semidirect

Maximal subgroups

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

subgroupindex
#130802262
#130708552
#130681362
#130666602
#130665832
#130665732
C11×#22242
#1237611