Finite Group Databasebeta

← #14670664

Subgroups — #14670664

Order 2816.

508 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C16×D11C211yesmaximal, characteristic, complemented
2#13077308C211yesmaximal, characteristic
3C2×#10622199C211yesmaximal, characteristic, complemented
4#13070226C211yesmaximal, characteristic, complemented
5#13066706C211yesmaximal, characteristic, complemented
6#13066704C211yesmaximal, characteristic, complemented
7C2×C11×#350C211yesmaximal, characteristic, complemented
8C2×C11×#131C2211yescharacteristic
9#10623359C411yescharacteristic
10C22×C8×D11C2211yescharacteristic
11C2×C11×M32C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13#10622847C411yescharacteristic
14#10622740—22no—
15#10622739C411yescharacteristic
16#10622732C411yescharacteristic
17C8×C22⋊D11—22no—
18#10622714C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20C22×C11⋊C16C2211yescharacteristic
21C2×C16×D11—22no—
22C2×C16×D11—22no—
23C2×C16×D11—22no—
24C11×#350—22no—
25#10622199—22no—
26(C2×D11)⋊C16—22no—
27C2×C11×#41C2×C411yescharacteristic
28C22×C4×D11C2×C411yescharacteristic
29C11×#131—21no—
30C11×#131—21no—
31C11×#131—21no—
32C11×#131—21no—
33C2×C11×M16—21no—
34C2×C11×M16C2×C411yescharacteristic
35C22×C8×C11—21no—
36C22×C8×C11C2311yescharacteristic
37#66999C812yes—
38#66991C812yes—
39#66990—21no—
40#66988—21no—
41C4×C22⋊D11—22no—
42#66979C2×C411yescharacteristic
43C2×#4318C2×C411yescharacteristic
44C22×C11⋊C8C2×C411yescharacteristic
45C2×C8×D11—21no—
46C2×C8×D11—21no—
47C2×C8×D11—21no—
48C2×C8×D11—21no—
49C2×C8×D11D412yes—
50C2×C8×D11D412yes—
51C11×M32—21no—
52C11×M32—21no—
53C2×C11×C16—21no—
54C2×C11×C16—21no—
55C2×C11×C16—21no—
56C2×C11×C16D412yescomplemented
57C22⋊(C11⋊C8)—22no—
58(C2×D11)⋊C8—22no—
59#66879—21no—
60Dic11⋊C8—22no—
61C8×Dic11—21no—
62#66876—21no—
63#66876—21no—
64C2×C11⋊C16—21no—
65C2×C11⋊C16—21no—
66C2×C11⋊C16—21no—
67C2×C11⋊C16D412yescomplemented
68C16×D11—28no—
69#12983—111nomaximal, Sylow
70C23×D11M1611yescharacteristic
71C11×#41—21no—
72C11×#41—21no—
73C11×#41—21no—
74C11×#41—21no—
75C2×Q8×C11C2×C811yescharacteristic
76C2×D4×C11—21no—
77C2×D4×C11C2×C811yescharacteristic
78C22×C4×C11—21no—
79C22×C4×C11C22×C411yescharacteristic
80C2×C22⋊D11—22no—
81C22×Dic11M1611yescharacteristic
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11C22⋊C412yes—
87C2×C4×D11C2×C812yes—
88C11×M16—21no—
89C11×M16—21no—
90C11×M16—41no—
91C11×M16—41no—
92C2×C8×C11—21no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11#4111yescharacteristic
100C2×C8×C11#4111yescharacteristic
101C22⋊Dic11—22no—
102C22⋊Dic11—21no—
103(C2×D11)⋊C4—22no—
104C4⋊Dic11C2×C812yes—
105Dic11⋊C4—22no—
106C4×Dic11—21no—
107#4318—21no—
108#4318—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8C22⋊C412yes—
113C8×D11—22no—
114C8×D11—22no—
115C8×D11—22no—
116C8×D11—22no—
117C11×C16—22no—
118C11×C16—41no—
119C11⋊C16—22no—
120C11⋊C16—41no—
121C23×C16—111no—
122#2929—111no—
123C2×#350—111no—
124C2×#350D1111yescharacteristic, complemented
125#2112—111no—
126#1379—111no—
127#1379—111no—
128C23×C11—21no—
129C23×C11C2×M1611yescharacteristic
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—24no—
133C22×D11C22⋊C812yes—
134Q8×C11—21no—
135Q8×C11—21no—
136D4×C11—21no—
137D4×C11—21no—
138D4×C11—41no—
139D4×C11—41no—
140C2×C4×C11—21no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11C2×C22⋊C411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11C22×C811yescharacteristic
147C2×C4×C11#13111yescharacteristic
148C2×C4×C11#13111yescharacteristic
149C22⋊D11—44no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—22no—
153C2×Dic11C22⋊C812yes—
154C4×D11—22no—
155C4×D11—22no—
156C4×D11—22no—
157C4×D11—22no—
158C8×C11—41no—
159C8×C11#12011yescharacteristic
160C8×C11#12111yescharacteristic
161C8×C11#12111yescharacteristic
162C8×C11#12311yescharacteristic
163C11⋊C8—22no—
164C11⋊C8—41no—
165C2×#131C2×D1111yescharacteristic
166C23×C8—111no—
167#525—111no—
168C2×M32—111no—
169C2×M32C2×D1111yescharacteristic
170C22×C16—111no—
171C22×C16—222no—
172C22×C16—222no—
173C22×C16—222no—
174C22×C16C2×D1111yescharacteristic
175#435—222no—
176C8×D4—222no—
177#424—111no—
178#408—111no—
179#407—111no—
180#405—111no—
181#350—22no—
182#350—222no—
183C22⋊C16—222no—
184C22×C11—22no—
185C22×C11—42no—
186C22×C11—41no—
187C22×C11C2×C22⋊C811yescharacteristic
188C22×C11#43511yescharacteristic
189C22×C11#43511yescharacteristic
190C2×D11—24no—
191C2×D11—24no—
192C2×D11—22no—
193C2×D11—22no—
194C2×D11#35014yescomplemented
195C4×C11—41no—
196C4×C11#38611yescharacteristic
197C4×C11#40811yescharacteristic
198C4×C11C8×D411yescharacteristic
199C4×C11C8×D411yescharacteristic
200Dic11—22no—
201Dic11—42no—
202C2×#41C4×D1111yescharacteristic
203C23×C4—111no—
204#131—21no—
205#131—21no—
206#131—21no—
207#131—21no—
208C2×M16—21no—
209C2×M16—111no—
210C2×M16C4×D1111yescharacteristic
211C22×C8—21no—
212C22×C8—111no—
213C22×C8—112no—
214C22×C8—112no—
215C22×C8—221no—
216C22×C8—221no—
217C22×C8—221no—
218C22×C8—221no—
219C22×C8C22×D1111yescharacteristic
220#123—221no—
221C22⋊Q8—112no—
222#121—112no—
223#120—221no—
224C4×D4—222no—
225#117—111no—
226M32—21no—
227M32—21no—
228M32—221no—
229M32—221no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—112no—
234C2×C16—228no—
235C2×C16—221no—
236C2×C16—221no—
237C2×C16—221no—
238C2×C16C22⋊D1112yescomplemented
239C4⋊C8—222no—
240C22⋊C8—222no—
241C22⋊C8—222no—
242#97—221no—
243C4×C8—221no—
244C2×C11—21no—
245C2×C11—21no—
246C2×C11—81no—
247C2×C11#186911yescharacteristic
248C2×C11C2×#35012yes—
249D11—24no—
250C24—111no—
251#41—21no—
252#41—21no—
253#41—21no—
254#41—21no—
255C2×Q8C8×D1111yescharacteristic
256C2×D4—21no—
257C2×D4—222no—
258C2×D4C8×D1111yescharacteristic
259C22×C4—21no—
260C22×C4—111no—
261C22×C4—112no—
262C22×C4—112no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4C2×C4×D1111yescharacteristic
268M16—21no—
269M16—21no—
270M16—41no—
271M16—41no—
272M16—221no—
273M16—221no—
274C2×C8—21no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—112no—
278C2×C8—221no—
279C2×C8—221no—
280C2×C8—222no—
281C2×C8—222no—
282C2×C8—222no—
283C2×C8—222no—
284C2×C8—221no—
285C2×C8#433911yescharacteristic
286C2×C8D4×D1111yescharacteristic
287C2×C8D4×D1111yescharacteristic
288C2×C8D4×D1111yescharacteristic
289C2×C8#434111yescharacteristic
290C2×C8C2×C22⋊D1111yescharacteristic
291C4⋊C4—112no—
292C4⋊C4—222no—
293C22⋊C4—222no—
294C22⋊C4—222no—
295C22⋊C4—221no—
296C42—221no—
297C16—22no—
298C16—41no—
299C16—222no—
300C16—441no—
301C11#1298311yescharacteristic, complemented, Sylow
302C23—21no—
303C23—112no—
304C23—224no—
305C23—221no—
306C23—221no—
307C23M16×D1111yescharacteristic
308Q8—21no—
309Q8—21no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—41no—
314D4—444no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—112no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—222no—
322C2×C4—222no—
323C2×C4—222no—
324C2×C4—222no—
325C2×C4—222no—
326C2×C4C22⋊C4×D1111yescharacteristic
327C2×C4(C22⋊D11)⋊C411yescharacteristic
328C2×C4C2×C8×D1111yescharacteristic
329C2×C4#6695411yescharacteristic
330C2×C4#6696011yescharacteristic
331C2×C4C4×C22⋊D1111yescharacteristic
332C8—41no—
333C8—222no—
334C8—441no—
335C8#6693611yescharacteristic
336C8#6693711yescharacteristic
337C8#6699011yescharacteristic
338C8#6699111yescharacteristic
339C22—22no—
340C22—41no—
341C22—42no—
342C22—114no—
343C22—224no—
344C22—224no—
345C22—222no—
346C22—222no—
347C22D11×C22⋊C811yescharacteristic
348C22#1062234111yescharacteristic
349C22#1062274011yescharacteristic
350C4—41no—
351C4—222no—
352C4—442no—
353C4(C22⋊D11)⋊C811yescharacteristic
354C4#1062234011yescharacteristic
355C4#1062256911yescharacteristic
356C4C8×C22⋊D1111yescharacteristic
357C2—21no—
358C2—21no—
359C2—81no—
360C2—224no—
361C2#1306890511yescharacteristic
362C2D11×#35012yes—
subgroupG/H
centerC2×C8D4×D11
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC2×C11×#350C2
socleC22×C11C2×C22⋊C8
prime radical#10623359C4
cosocleC22×C8×C11C23
hypercenterC2×#350D11
hypocenterC11#12983
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
1. C22×C16×D11C2semidirect
3. C2×#10622199C2semidirect
4. #13070226C2semidirect
5. #13066706C2semidirect
6. #13066704C2semidirect
7. C2×C11×#350C2semidirect
56. C2×C11×C16D4semidirect
67. C2×C11⋊C16D4semidirect
124. C2×#350D11semidirect
194. C2×D11#350semidirect
238. C2×C16C22⋊D11semidirect
301. C11#12983semidirect

Maximal subgroups

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

subgroupindex
C22×C16×D112
#130773082
C2×#106221992
#130702262
#130667062
#130667042
C2×C11×#3502
#1298311