Finite Group Databasebeta

← #14664918

Subgroups — #14664918

Order 2816.

440 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 107 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#13068608C211yesmaximal, characteristic
2#13066934C211yesmaximal, characteristic
3#13066643C214yesmaximal, complemented
4C11×#2487C211yesmaximal, characteristic
5C2×C4×D4×C11C2211yescharacteristic
6C22×C11×C4⋊C4C411yescharacteristic
7C11×#400C2212yes—
8C11×#399C412yes—
9C11×#389—21no—
10C11×#386—21no—
11C11×#385—21no—
12C11×#380—21no—
13C11×#380C411yescharacteristic
14C2×#66897—21no—
15C2×C22⋊(C11⋊C8)—21no—
16#10622537—21no—
17#10622168C2212yes—
18#10622166C2212yes—
19#10622163—21no—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11—21no—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C4×D4×C11—41no—
25C4×D4×C11—41no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—41no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4C2×C412yes—
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×#4318—22no—
39C22×C11⋊C8—41no—
40C11×#95—22no—
41C11×#95—22no—
42C11×#95C2×C412yes—
43#66897—42no—
44C22⋊(C11⋊C8)—22no—
45C22⋊(C11⋊C8)—41no—
46C4⋊(C11⋊C8)—41no—
47C4⋊(C11⋊C8)—41no—
48#11903—111nomaximal, Sylow
49C24×C11C22⋊C411yescharacteristic
50C24×C11C22⋊C411yescharacteristic
51C2×D4×C11—41no—
52C2×D4×C11—41no—
53C2×D4×C11SD1612yes—
54C2×D4×C11Q1612yes—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11—82no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C11×C4⋊C4—41no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—82no—
76C11×C22⋊C4—41no—
77C11×C22⋊C4—41no—
78C11×C22⋊C4—42no—
79C11×C22⋊C4—82no—
80C42×C11—21no—
81C42×C11—21no—
82#4318—42no—
83#4318—42no—
84C2×C11⋊C8—42no—
85C2×C11⋊C8—42no—
86C2×C11⋊C8—82no—
87#2487D1111yescharacteristic
88#1800—111no—
89#1459—111no—
90#1353—114no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11—41no—
99C23×C11#10312yes—
100C23×C11#10312yes—
101C23×C11C2×C22⋊C411yescharacteristic
102D4×C11—42no—
103D4×C11—42no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—81no—
123C2×C4×C11—84no—
124C2×C4×C11#9911yescharacteristic
125C2×C4×C11#9911yescharacteristic
126C2×C4×C11C2×SD1611yescharacteristic
127C2×C4×C11C2×Q1611yescharacteristic
128C11⋊C8—82no—
129C11⋊C8—82no—
130C2×C4×D4C2×D1111yescharacteristic
131C22×C4⋊C4Dic1111yescharacteristic
132#423—221no—
133C2×#100—221no—
134C2×C22⋊C8—221no—
135#400C2×D1112yes—
136#399Dic1112yes—
137#389—21no—
138#386—21no—
139#385—21no—
140#380—21no—
141#380Dic1111yescharacteristic
142#343—112no—
143#324—112no—
144#323—221no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—22no—
148C22×C11—22no—
149C22×C11—42no—
150C22×C11—42no—
151C22×C11—42no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—81no—
157C22×C11C2×#9911yescharacteristic
158C22×C11C2×#10311yescharacteristic
159C22×C11#42111yescharacteristic
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11—82no—
167C4×C11—82no—
168C4×C11#35212yes—
169C22×D4C22⋊D1111yescharacteristic
170C23×C4—21no—
171C23×C4C2×Dic1111yescharacteristic
172C23×C4C22⋊D1111yescharacteristic
173C2×M16—222no—
174C22×C8—441no—
175C4×D4—41no—
176C4×D4—41no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4C2×Dic1112yes—
183C2×C4⋊C4C22×D1111yescharacteristic
184C2×C22⋊C4—21no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4C2×Dic1111yescharacteristic
187C2×C22⋊C4C22⋊D1111yescharacteristic
188C2×C42C22⋊D1111yescharacteristic
189C4⋊C8—441no—
190C4⋊C8—441no—
191#100—442no—
192C22⋊C8—222no—
193C22⋊C8—441no—
194#95—22no—
195#95—22no—
196#95C2×Dic1112yes—
197C2×C11—21no—
198C2×C11—21no—
199C2×C11—42no—
200C2×C11—42no—
201C2×C11#152011yescharacteristic
202C2×C11C2×#35211yescharacteristic
203C2×C11#213411yescharacteristic
204C24C22⋊Dic1111yescharacteristic
205C24C22⋊Dic1111yescharacteristic
206C2×D4—41no—
207C2×D4—41no—
208C2×D4#432512yes—
209C2×D4#432612yes—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—82no—
220C22×C4C22⋊Dic1111yescharacteristic
221C22×C4C22⋊Dic1111yescharacteristic
222C22×C4C22×Dic1111yescharacteristic
223C22×C4C2×C22⋊D1111yescharacteristic
224C22×C4C2×C22⋊D1111yescharacteristic
225M16—442no—
226M16—442no—
227C2×C8—442no—
228C2×C8—442no—
229C2×C8—882no—
230C4⋊C4—41no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—82no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—42no—
239C22⋊C4—82no—
240C42—21no—
241C42—21no—
242C11#1190311yescharacteristic, complemented, Sylow
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23#6689912yes—
252C23#6689912yes—
253C23C2×C22⋊Dic1111yescharacteristic
254D4—42no—
255D4—42no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—81no—
275C2×C4—84no—
276C2×C4#6689811yescharacteristic
277C2×C4#6689811yescharacteristic
278C2×C4C2×#432511yescharacteristic
279C2×C4C2×#432611yescharacteristic
280C8—882no—
281C8—882no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—22no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—81no—
294C22C2×#6689811yescharacteristic
295C22C2×#6689911yescharacteristic
296C22#1062284911yescharacteristic
297C4—21no—
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—82no—
304C4—82no—
305C4#1062217712yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—42no—
310C2#1306718811yescharacteristic
311C2C2×#1062217711yescharacteristic
312C2#1307030811yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2487C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C4⋊C4C23
hypercenter#2487D11
hypocenterC11#11903
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2487

Complements

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

NH ≅ G/Ntype
3. #13066643C2semidirect
242. C11#11903semidirect

Maximal subgroups

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

subgroupindex
#130686082
#130669342
#130666432
C11×#24872
#1190311