Finite Group Databasebeta

← #14910406

Subgroups — #14910406

Order 2816.

668 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 139 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×#10622528C212yesmaximal, complemented
2#13080356C212yesmaximal, complemented
3#13070726C212yesmaximal, complemented
4#13070675C212yesmaximal, complemented
5#13070548C212yesmaximal, complemented
6#13070536C212yesmaximal, complemented
7C4×Dic88C211yesmaximal, characteristic, complemented
8#13070449C211yesmaximal, characteristic, complemented
9C11×#2249C211yesmaximal, characteristic, complemented
10C2×Q16×D11C2212yes—
11C2×#66965C2212yes—
12#10623208—22no—
13C2×C11×Q32C2211yescharacteristic
14C2×C11×SD32C2212yes—
15C2×C11×D16C2211yescharacteristic
16C11×#495C2212yes—
17#10622801C2212yes—
18C2×#66893C2212yes—
19#10622786—22no—
20#10622783—22no—
21#10622770C2212yes—
22C2×#66891C2212yes—
23#10622667—22no—
24#10622528—28no—
25C2×Dic88C2211yescharacteristic
26C2×#66862C2212yes—
27C4×Dic44C2212yes—
28C8×D44C2211yescharacteristic
29C4×C11×C16C2211yescharacteristic
30#10622202C2212yes—
31#10622200C2212yes—
32(C2×D11)⋊C16C2212yes—
33#10622142C2211yescharacteristic
34#10622141C2212yes—
35C4⋊(C11⋊C16)C2211yescharacteristic
36C2×Q8×D11—22no—
37C2×#4341—22no—
38C2×C11×Q16C2312yes—
39C2×C11×SD16—22no—
40C2×C11×D8C2312yes—
41C11×#124—22no—
42#66999—22no—
43C2×#4326—22no—
44#66991—22no—
45C2×#4324—22no—
46Q16×D11—24no—
47Q16×D11—42no—
48#66965—24no—
49#66965—42no—
50C2×Dic44C2312yes—
51C2×C8×D11C2312yes—
52#66938—42no—
53#66937—42no—
54(C22⋊D11)⋊C4—42no—
55#66931—42no—
56C4×D44D411yescharacteristic
57C4×Dic22—22no—
58C11×Q32—41no—
59C11×SD32—24no—
60C11×D16—41no—
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C4×C8×C11C2311yescharacteristic
64#66899—22no—
65#66896—22no—
66#66893—24no—
67#66891—24no—
68(C2×D11)⋊C8D412yes—
69#66882C2312yes—
70#66880—22no—
71C2×C11⋊C16C2312yes—
72C4⋊(C11⋊C8)D411yescharacteristic
73Dic88D414yescomplemented
74#66862—24no—
75#33843—111nomaximal, Sylow
76C2×Q8×C11—22no—
77C2×D4×C11—22no—
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C22×Dic11—42no—
81Q8×D11—44no—
82Q8×D11—82no—
83#4341—44no—
84#4341—82no—
85C2×D44D811yescharacteristic
86C2×C4×D11—42no—
87C2×C4×D11C2×D412yes—
88C2×Dic22—22no—
89C2×Dic22—42no—
90C11×Q16—22no—
91C11×Q16—22no—
92C11×SD16—82no—
93C11×D8—22no—
94C11×D8—22no—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2411yescharacteristic
97C11×C22⋊C4—42no—
98C11×C22⋊C4—42no—
99C42×C11C2×D411yescharacteristic
100C22⋊Dic11—42no—
101#4326—44no—
102#4324—44no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4D812yes—
105C4⋊Dic11—22no—
106C4⋊Dic11D811yescharacteristic
107Dic11⋊C4—42no—
108Dic11⋊C4—42no—
109C4×Dic11—42no—
110C2×C11⋊C8C2×D412yes—
111Dic44—22no—
112Dic44C2×D414yes—
113C8×D11—22no—
114C8×D11—22no—
115C11×C16—21no—
116C11×C16C2×D412yes—
117C11⋊C16—22no—
118C2×#510—112no—
119#3285—112no—
120#2249D1111yescharacteristic, complemented
121#2220—112no—
122#2211—112no—
123#2188—112no—
124#2186—112no—
125C4×Q32—111no—
126#2169—111no—
127C23×C11—42no—
128C22×D11C2×D812yes—
129Q8×C11—42no—
130Q8×C11—42no—
131D4×C11—42no—
132D4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11C2×D811yescharacteristic
135C2×C4×C11C2×D811yescharacteristic
136C2×C4×C11C22×D411yescharacteristic
137C22⋊D11—84no—
138C22⋊D11—84no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—84no—
142C2×Dic11C2×D812yes—
143D44—41no—
144C4×D11—22no—
145C4×D11—22no—
146C4×D11—84no—
147Dic22—24no—
148Dic22—42no—
149Dic22—84no—
150C8×C11—21no—
151C8×C11C22×D411yescharacteristic
152C8×C11H(5,𝔽2)11yescharacteristic
153C11⋊C8—22no—
154C2×#135—112no—
155C22×Q16—112no—
156#548—222no—
157#510—228no—
158C2×Q32—112no—
159C2×Q32—111no—
160C2×Q32C2×D1111yescharacteristic
161C2×SD32—112no—
162C2×SD32C2×D1112yes—
163C2×D16C2×D1111yescharacteristic
164C2×M32—112no—
165#495C2×D1112yes—
166#467—112no—
167#466—112no—
168#464—222no—
169#452—222no—
170#448—222no—
171C4×Q16—112no—
172C8×D4—111no—
173#366—111no—
174C4⋊C16—111no—
175#358—112no—
176#358—112no—
177#357—112no—
178C22⋊C16—112no—
179C4×C16C2×D1111yescharacteristic
180C22×C11—82no—
181C22×C11—82no—
182C22×C11—82no—
183C22×C11C22×D811yescharacteristic
184C2×D11—22no—
185C2×D11—22no—
186C2×D11—22no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—82no—
190C4×C11D4211yescharacteristic
191C4×C11#57611yescharacteristic
192Dic11—22no—
193Dic11—44no—
194Dic11—82no—
195C2×#41—222no—
196C22×Q8—222no—
197#135—224no—
198#135—442no—
199C2×Q16—112no—
200C2×Q16—222no—
201C2×Q16—224no—
202C2×Q16—442no—
203C2×Q16C22×D1112yes—
204C2×SD16—22no—
205C2×SD16—222no—
206C2×D8C22×D1112yes—
207C22×C8—112no—
208#124—22no—
209#124—442no—
210C22⋊Q8—222no—
211C22⋊Q8—442no—
212#121—222no—
213#121—442no—
214C4×Q8—222no—
215C4×D4—111no—
216C4×D4—442no—
217Q32—41no—
218Q32—114no—
219Q32—224no—
220SD32—24no—
221SD32—224no—
222D16—41no—
223M32—224no—
224C2×C16—112no—
225C2×C16C22×D1111yescharacteristic
226C2×C16C22×D1111yescharacteristic
227#107—112no—
228C4⋊C8—111no—
229#103—222no—
230#103—222no—
231#102—222no—
232C22⋊C8—112no—
233C4×C8C22×D1111yescharacteristic
234C2×C11—162no—
235C2×C11D4×D811yescharacteristic
236C2×C11#341411yescharacteristic
237C2×C11#341711yescharacteristic
238D11—42no—
239#41—444no—
240#41—882no—
241C2×Q8—22no—
242C2×Q8—222no—
243C2×Q8—442no—
244C2×Q8—444no—
245C2×Q8—882no—
246C2×D4—22no—
247C2×D4—111no—
248C2×D4—442no—
249C2×D4—442no—
250C22×C4—112no—
251C22×C4—442no—
252C22×C4—442no—
253Q16—22no—
254Q16—22no—
255Q16—114no—
256Q16—222no—
257Q16—444no—
258SD16—82no—
259SD16—444no—
260D8—22no—
261D8—22no—
262C2×C8—112no—
263C2×C8—222no—
264C2×C8—222no—
265C2×C8D4×D1111yescharacteristic
266C2×C8C23×D1111yescharacteristic
267C4⋊C4—111no—
268C4⋊C4—222no—
269C4⋊C4—442no—
270C4⋊C4—442no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—112no—
274C22⋊C4—442no—
275C22⋊C4—442no—
276C42—442no—
277C42D4×D1111yescharacteristic
278C16—21no—
279C16—222no—
280C16D4×D1112yes—
281C11#3384311yescharacteristic, complemented, Sylow
282C23—42no—
283C23—112no—
284Q8—42no—
285Q8—42no—
286Q8—224no—
287Q8—442no—
288Q8—884no—
289D4—42no—
290D4—42no—
291D4—441no—
292D4—884no—
293D4—884no—
294C2×C4—42no—
295C2×C4—112no—
296C2×C4—222no—
297C2×C4—222no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—884no—
301C2×C4—884no—
302C2×C4D8×D1111yescharacteristic
303C2×C4D8×D1111yescharacteristic
304C2×C4C2×D4×D1111yescharacteristic
305C8—21no—
306C8—222no—
307C8C2×D4×D1111yescharacteristic
308C8#6703711yescharacteristic
309C22—82no—
310C22—82no—
311C22—82no—
312C22—222no—
313C22—222no—
314C22—222no—
315C22C2×D8×D1111yescharacteristic
316C4—21no—
317C4—21no—
318C4—82no—
319C4—222no—
320C4—444no—
321C4—882no—
322C4#1062324811yescharacteristic
323C4#1062328811yescharacteristic
324C2—162no—
325C2—442no—
326C2#1308029111yescharacteristic
327C2#1308174911yescharacteristic
328C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2249C2
socleC22×C11C22×D8
hypercenter#2249D11
hypocenterC11#33843
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2249

Complements

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

NH ≅ G/Ntype
1. C2×#10622528C2semidirect
2. #13080356C2semidirect
3. #13070726C2semidirect
4. #13070675C2semidirect
5. #13070548C2semidirect
6. #13070536C2semidirect
7. C4×Dic88C2semidirect
8. #13070449C2semidirect
9. C11×#2249C2semidirect
73. Dic88D4semidirect
120. #2249D11semidirect
281. C11#33843semidirect

Maximal subgroups

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

subgroupindex
C2×#106225282
#130803562
#130707262
#130706752
#130705482
#130705362
C4×Dic882
#130704492
C11×#22492
#3384311