Finite Group Databasebeta

← #14647337

Subgroups — #14647337

Order 2816.

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

normal subgroups only

This group has 498 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#13071524C211yesmaximal, characteristic
2#13068605C211yesmaximal, characteristic
3#13066936C211yesmaximal, characteristic
4#13066518C211yesmaximal, characteristic, complemented
5#13066517C211yesmaximal, characteristic, complemented
6#13066474C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8C2×#66946—21no—
9C2×C4×D44C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#382C2211yescharacteristic
13C2×#66887—21no—
14#10622586—21no—
15C4×C4⋊Dic11C2211yescharacteristic
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18#10622281—22no—
19#10622280C412yes—
20D11×#95C412yes—
21#10622192—21no—
22#10622106—22no—
23C22×D44D411yescharacteristic
24C22×C4×D11—22no—
25C22×C4×D11C2×C412yes—
26C2×C11×M16—21no—
27C2×C11×C4⋊C4—21no—
28C2×C42×C11C2311yescharacteristic
29C2×(C2×D11)⋊C4—22no—
30C2×(C2×D11)⋊C4D412yes—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11D411yescharacteristic
33C2×Dic11⋊C4—22no—
34C2×C4×Dic11—21no—
35C2×#4318—21no—
36#66946—42no—
37#66946—42no—
38C4×D44—21no—
39C4×D44—21no—
40C4×D44—21no—
41C4×D44—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×C22⋊C8—21no—
46C4×C8×C11—21no—
47C11×#95—21no—
48C11×#95C2×C412yes—
49C11⋊#95—22no—
50C11⋊#95C2×C411yescharacteristic
51C11⋊#95C2×C411yescharacteristic
52C22⋊(C11⋊C8)—21no—
53#66887—42no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4×C11⋊C8—21no—
58#8764—111nomaximal, Sylow
59C23×D11C22⋊C412yes—
60C22×C4×C11—22no—
61C22×C4×C11C22×C411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—21no—
65C22×Dic11—21no—
66C22×Dic11C22⋊C412yes—
67C2×D44—21no—
68C2×D44—21no—
69C2×D44—21no—
70C2×D44—21no—
71C2×D44D812yes—
72C2×D44SD1612yes—
73C2×C4×D11—22no—
74C2×C4×D11—22no—
75C2×C4×D11—44no—
76C2×C4×D11—44no—
77C2×C4×D11—82no—
78C2×C4×D11—82no—
79C11×M16—41no—
80C11×M16—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C42×C11#4111yescharacteristic
86C42×C11#4111yescharacteristic
87C42×C11#4111yescharacteristic
88C42×C11#4111yescharacteristic
89(C2×D11)⋊C4—22no—
90(C2×D11)⋊C4—22no—
91(C2×D11)⋊C4—44no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—42no—
95Dic11⋊C4—82no—
96C4×Dic11—41no—
97C4×Dic11—41no—
98#4318—41no—
99#4318—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102#2349—111no—
103#1800—111no—
104#1460—111no—
105#1303—111no—
106#1303—111no—
107#1286—111no—
108#1286D1111yescharacteristic, complemented
109C23×C11C2×C22⋊C411yescharacteristic
110C22×D11—22no—
111C22×D11—22no—
112C22×D11—42no—
113C22×D11—42no—
114C22×D11#10214yes—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11#11711yescharacteristic
121C2×C4×C11#11711yescharacteristic
122C2×C4×C11#12311yescharacteristic
123C2×C4×C11#12311yescharacteristic
124C2×C4×C11#12311yescharacteristic
125C2×C4×C11#12311yescharacteristic
126C2×C4×C11C2×D811yescharacteristic
127C2×C4×C11C2×SD1611yescharacteristic
128C2×C4×C11#13711yescharacteristic
129C2×C4×C11#13711yescharacteristic
130C2×Dic11—22no—
131C2×Dic11—22no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—42no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138D44—22no—
139D44—22no—
140D44—22no—
141D44—22no—
142C4×D11—82no—
143C4×D11—82no—
144C4×D11—88no—
145C8×C11—81no—
146C8×C11—81no—
147C11⋊C8—81no—
148C11⋊C8—81no—
149C2×C4×D4—111no—
150C2×C4×D4—221no—
151#431—111no—
152#431C2×D1111yescharacteristic
153#423—111no—
154#423C2×D1111yescharacteristic
155C2×#100—221no—
156#389—221no—
157#385—222no—
158#382C2×D1111yescharacteristic
159#380—112no—
160C4×C4⋊C4—111no—
161C2×#95—112no—
162#343—221no—
163#323—222no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11#38111yescharacteristic
167C22×C11C2×#10211yescharacteristic
168C22×C11#41911yescharacteristic
169C2×D11—24no—
170C2×D11—44no—
171C2×D11—42no—
172C2×D11—42no—
173C2×D11—44no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—82no—
179C4×C11#48011yescharacteristic
180C4×C11#48011yescharacteristic
181C4×C11#48311yescharacteristic
182C4×C11#48311yescharacteristic
183Dic11—42no—
184Dic11—42no—
185Dic11—81no—
186C22×D4—111no—
187C23×C4—112no—
188C23×C4—222no—
189C2×M16—21no—
190C2×M16—221no—
191C4×D4—221no—
192C4×D4—221no—
193C4×D4—221no—
194C4×D4—221no—
195C4×D4—442no—
196C4×D4—442no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—222no—
201C2×C22⋊C4—112no—
202C2×C22⋊C4—222no—
203C2×C42—221no—
204C2×C42C22×D1111yescharacteristic
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—221no—
209C4⋊C8—221no—
210C4⋊C8—221no—
211#100—442no—
212C22⋊C8—21no—
213C22⋊C8—221no—
214C4×C8—21no—
215C4×C8—221no—
216#95—21no—
217#95—111no—
218#95—111no—
219#95—222no—
220#95C4×D1112yes—
221C2×C11—21no—
222C2×C11—21no—
223C2×C11#182311yescharacteristic
224C2×C11#182711yescharacteristic
225C2×C11#182911yescharacteristic
226D11—44no—
227C24—112no—
228C2×D4—112no—
229C2×D4—112no—
230C2×D4—221no—
231C2×D4—221no—
232C2×D4—221no—
233C2×D4—221no—
234C22×C4—22no—
235C22×C4—112no—
236C22×C4—221no—
237C22×C4—222no—
238C22×C4—222no—
239C22×C4—221no—
240C22×C4—444no—
241C22×C4—444no—
242C22×C4—882no—
243C22×C4—882no—
244C22×C4C2×C4×D1111yescharacteristic
245C22×C4D4×D1111yescharacteristic
246C22×C4D4×D1111yescharacteristic
247M16—41no—
248M16—41no—
249M16—441no—
250M16—441no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—441no—
254C2×C8—441no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—442no—
260C4⋊C4—882no—
261C22⋊C4—222no—
262C22⋊C4—222no—
263C22⋊C4—444no—
264C42—441no—
265C42—441no—
266C42#433911yescharacteristic
267C42#433911yescharacteristic
268C42#434111yescharacteristic
269C42#434311yescharacteristic
270C11#876411yescharacteristic, complemented, Sylow
271C23—114no—
272C23—222no—
273C23—222no—
274C23—442no—
275C23—442no—
276C23C22⋊C4×D1111yescharacteristic
277D4—222no—
278D4—222no—
279D4—222no—
280D4—222no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—222no—
287C2×C4—222no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—442no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—882no—
295C2×C4—882no—
296C2×C4—888no—
297C2×C4#6692511yescharacteristic
298C2×C4#6693611yescharacteristic
299C2×C4#6693611yescharacteristic
300C2×C4#6694511yescharacteristic
301C2×C4#6694711yescharacteristic
302C2×C4#6694711yescharacteristic
303C2×C4D8×D1111yescharacteristic
304C2×C4SD16×D1111yescharacteristic
305C2×C4#6696811yescharacteristic
306C2×C4#6697111yescharacteristic
307C8—81no—
308C8—81no—
309C8—881no—
310C8—881no—
311C22—21no—
312C22—21no—
313C22—224no—
314C22—444no—
315C22—444no—
316C22—442no—
317C22—442no—
318C22#1062227711yescharacteristic
319C22D11×#10211yescharacteristic
320C22#1062241511yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—82no—
326C4—442no—
327C4—442no—
328C4—881no—
329C4#1062238711yescharacteristic
330C4#1062241811yescharacteristic
331C4#1062247511yescharacteristic
332C4#1062249511yescharacteristic
333C2—21no—
334C2—21no—
335C2—444no—
336C2#1306870111yescharacteristic
337C2#1306871811yescharacteristic
338C2#1306872611yescharacteristic
subgroupG/H
centerC22#10622277
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#381
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1286D11
hypocenterC11#8764
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
4. #13066518C2semidirect
5. #13066517C2semidirect
6. #13066474C2semidirect
7. C11×#1286C2semidirect
108. #1286D11semidirect
270. C11#8764semidirect

Maximal subgroups

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

subgroupindex
#130715242
#130686052
#130669362
#130665182
#130665172
#130664742
C11×#12862
#876411