Finite Group Databasebeta

← #14670366

Subgroups — #14670366

Order 2816.

490 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622485C211yesmaximal, characteristic
2C2×#10622127C211yesmaximal, characteristic, complemented
3C2×#10622147C211yesmaximal, characteristic
4C2×#10622129C211yesmaximal, characteristic
5#13069350C211yesmaximal, characteristic, complemented
6#13066693C211yesmaximal, characteristic, complemented
7C11×#1380C211yesmaximal, characteristic, complemented
8C22×D88C2211yescharacteristic
9C2×#66946—21no—
10C22×C11×C16C2211yescharacteristic
11C2×C11×#107C2211yescharacteristic
12C2×C11×#107C2211yescharacteristic
13C2×#66882C2211yescharacteristic
14C2×C8×Dic11C2211yescharacteristic
15C22×C11⋊C16C2211yescharacteristic
16#10622598—21no—
17C2×#66873—21no—
18#10622485—22no—
19#10622485—22no—
20#10622167—21no—
21#10622147—22no—
22#10622129C414yescomplemented
23#10622127—22no—
24C22×D44—21no—
25C22×C4×D11—41no—
26C22×C8×C11C2311yescharacteristic
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×(C2×D11)⋊C4—41no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—41no—
32C2×C4×Dic11D411yescharacteristic
33C22×C11⋊C8D411yescharacteristic
34C2×D88—21no—
35C2×D88—21no—
36C2×D88—21no—
37C2×D88C2×C412yes—
38C2×D88D412yes—
39C2×D88Q812yes—
40#66946—24no—
41#66946—42no—
42C2×C11×C16—21no—
43C2×C11×C16—21no—
44C2×C11×C16—21no—
45C11×#107—21no—
46C11×#107—21no—
47C11×#107C2×C412yescomplemented
48C11×#107D412yes—
49C11⋊#95—41no—
50#66882—21no—
51#66882—21no—
52C8×Dic11—21no—
53C8×Dic11—21no—
54C2×C11⋊C16—21no—
55C2×C11⋊C16—21no—
56C2×C11⋊C16C2×C412yescomplemented
57#66873—24no—
58#12935—111nomaximal, Sylow
59C23×D11—41no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—41no—
64C22×Dic11D811yescharacteristic
65C22×Dic11D811yescharacteristic
66C2×D44—22no—
67C2×D44—22no—
68C2×D44—22no—
69C2×D44—41no—
70C2×D44—41no—
71C2×D44—41no—
72C2×C4×D11—44no—
73C2×C4×D11—82no—
74C2×C4×D11—82no—
75C2×C8×C11C22×C411yescharacteristic
76C2×C8×C11C2×D411yescharacteristic
77C2×C8×C11C2×D411yescharacteristic
78C2×C8×C11C2×Q811yescharacteristic
79C2×C8×C11#4111yescharacteristic
80C2×C8×C11#4111yescharacteristic
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85(C2×D11)⋊C4—44no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88C4⋊Dic11—82no—
89C4×Dic11—21no—
90C4×Dic11—21no—
91C2×C11⋊C8—21no—
92C2×C11⋊C8—21no—
93C2×C11⋊C8—21no—
94D88—22no—
95D88—22no—
96D88—22no—
97D88C4⋊C414yescomplemented
98C11×C16—41no—
99C11⋊C16—22no—
100C2×C4×D8—111no—
101C2×#366—111no—
102C2×#357—111no—
103C2×#357—111no—
104#1942—111no—
105#1380D1111yescharacteristic, complemented
106#1374—111no—
107C23×C11C2×D811yescharacteristic
108C22×D11—42no—
109C22×D11—42no—
110C22×D11—42no—
111C22×D11—81no—
112C22×D11—81no—
113C22×D11—81no—
114C22×D11—81no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—81no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11C4×D411yescharacteristic
122C2×C4×C11#12011yescharacteristic
123C2×C4×C11C22⋊Q811yescharacteristic
124C2×C4×C11#13511yescharacteristic
125C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C11#13711yescharacteristic
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—81no—
133C2×Dic11—81no—
134C2×Dic11—81no—
135C2×Dic11D1612yes—
136D44—24no—
137D44—42no—
138D44—42no—
139D44—42no—
140C4×D11—88no—
141C8×C11C2×C4⋊C411yescharacteristic
142C8×C11C4×D411yescharacteristic
143C8×C11C22⋊Q811yescharacteristic
144C8×C11#12311yescharacteristic
145C11⋊C8—41no—
146C22×D8—111no—
147C2×C4×D4—221no—
148C22×C16—111no—
149C22×C16C2×D1111yescharacteristic
150C4×D8—222no—
151C4×D8—222no—
152C2×#107—111no—
153C2×#107C2×D1111yescharacteristic
154C2×#107C2×D1111yescharacteristic
155C2×#102—221no—
156C2×C4×C8—111no—
157#389—221no—
158#366—222no—
159#357—114no—
160#357—222no—
161#340—221no—
162C22×C11C4×D811yescharacteristic
163C22×C11#44711yescharacteristic
164C22×C11#47411yescharacteristic
165C22×C11C2×D1611yescharacteristic
166C22×C11#50811yescharacteristic
167C22×C11#50911yescharacteristic
168C22×C11#51011yescharacteristic
169C2×D11—44no—
170C2×D11—82no—
171C2×D11—82no—
172C2×D11—82no—
173C2×D11—82no—
174C2×D11—82no—
175C2×D11—82no—
176C4×C11—82no—
177C4×C11—82no—
178C4×C11#38511yescharacteristic
179C4×C11#44011yescharacteristic
180C4×C11#45211yescharacteristic
181C4×C11#47811yescharacteristic
182Dic11—22no—
183Dic11—41no—
184Dic11—161no—
185C22×D4—221no—
186C23×C4—441no—
187C2×D8—112no—
188C2×D8—112no—
189C2×D8—112no—
190C2×D8—221no—
191C2×D8—221no—
192C2×D8—221no—
193C22×C8—111no—
194C22×C8C22×D1111yescharacteristic
195C4×D4—224no—
196C4×D4—442no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—441no—
201C2×C22⋊C4—441no—
202C2×C42—111no—
203C2×C16—21no—
204C2×C16—21no—
205C2×C16—21no—
206C2×C16—112no—
207C2×C16—221no—
208C2×C16—221no—
209#107—21no—
210#107—21no—
211#107—221no—
212#107—221no—
213#107C4×D1112yescomplemented
214#107D4412yes—
215#102—224no—
216C4×C8—221no—
217C4×C8—221no—
218#95—441no—
219C2×C11#186211yescharacteristic
220C2×C11C4×D1611yescharacteristic
221C2×C11#217511yescharacteristic
222C2×C11#218411yescharacteristic
223C2×C11#218911yescharacteristic
224C2×C11#222411yescharacteristic
225C2×C11#222811yescharacteristic
226D11—84no—
227C24—441no—
228C2×D4—222no—
229C2×D4—222no—
230C2×D4—222no—
231C2×D4—441no—
232C2×D4—441no—
233C2×D4—441no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—111no—
237C22×C4—111no—
238C22×C4—444no—
239C22×C4—441no—
240C22×C4—882no—
241C22×C4—882no—
242C22×C4D4×D1111yescharacteristic
243D8—114no—
244D8—222no—
245D8—222no—
246D8—222no—
247C2×C8—221no—
248C2×C8—221no—
249C2×C8—221no—
250C2×C8C2×C4×D1111yescharacteristic
251C2×C8C2×D4411yescharacteristic
252C2×C8#433911yescharacteristic
253C2×C8D4×D1111yescharacteristic
254C2×C8#434111yescharacteristic
255C2×C8Q8×D1111yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C4⋊C4—882no—
263C22⋊C4—444no—
264C42—221no—
265C42—221no—
266C16—41no—
267C16—222no—
268C11#1293511yescharacteristic, complemented, Sylow
269C23—442no—
270C23—442no—
271C23—442no—
272C23—881no—
273C23—881no—
274C23—881no—
275C23—881no—
276C23D8×D1111yescharacteristic
277D4—224no—
278D4—442no—
279D4—442no—
280D4—442no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—112no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—888no—
294C2×C4—881no—
295C2×C4—881no—
296C2×C4—881no—
297C2×C4(C22⋊D11)⋊C411yescharacteristic
298C2×C4#6693511yescharacteristic
299C2×C4#6694911yescharacteristic
300C2×C4#6696711yescharacteristic
301C2×C4#6696911yescharacteristic
302C2×C4#6697111yescharacteristic
303C8—441no—
304C8C4×D4411yescharacteristic
305C8#6693611yescharacteristic
306C8C4⋊C4×D1111yescharacteristic
307C8#6695011yescharacteristic
308C22—444no—
309C22—882no—
310C22—882no—
311C22—882no—
312C22—882no—
313C22—882no—
314C22—882no—
315C22#1062236911yescharacteristic
316C22#1062238611yescharacteristic
317C22#1062250311yescharacteristic
318C22D11×D1611yescharacteristic
319C22#1062252711yescharacteristic
320C22#1062252911yescharacteristic
321C22#1062253111yescharacteristic
322C4—82no—
323C4—82no—
324C4—222no—
325C4—441no—
326C4—1761no—
327C4#1062228111yescharacteristic
328C4#1062242311yescharacteristic
329C4#1062243011yescharacteristic
330C4#1062248411yescharacteristic
331C2—884no—
332C2#1306886411yescharacteristic
333C2#1307046011yescharacteristic
334C2#1307048311yescharacteristic
335C2#1307052911yescharacteristic
336C2#1307055911yescharacteristic
337C2#1307075211yescharacteristic
338C2#1307077211yescharacteristic
subgroupG/H
centerC23D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1380C2
socleC23×C11C2×D8
prime radicalC22×D88C22
cosocleC22×C8×C11C23
hypercenter#1380D11
hypocenterC11#12935
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
2. C2×#10622127C2semidirect
5. #13069350C2semidirect
6. #13066693C2semidirect
7. C11×#1380C2semidirect
22. #10622129C4semidirect
47. C11×#107C2×C4semidirect
56. C2×C11⋊C16C2×C4semidirect
97. D88C4⋊C4semidirect
105. #1380D11semidirect
213. #107C4×D11semidirect
268. C11#12935semidirect

Maximal subgroups

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

subgroupindex
C2×#106224852
C2×#106221272
C2×#106221472
C2×#106221292
#130693502
#130666932
C11×#13802
#1293511