Finite Group Databasebeta

← #14908675

Subgroups — #14908675

Order 2816.

566 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078260C211yesmaximal, characteristic
2#13077224C211yesmaximal, characteristic, complemented
3#13070829C218yesmaximal, complemented
4#13070390C211yesmaximal, characteristic, complemented
5#13070389C211yesmaximal, characteristic, complemented
6C2×#10622201C211yesmaximal, characteristic, complemented
7#13070236C211yesmaximal, characteristic, complemented
8C2×C11×#361C211yesmaximal, characteristic, complemented
9C22×C11×D8C2211yescharacteristic
10#10623336—21no—
11#10623276—21no—
12C2×#66954C2211yescharacteristic
13C2×C11×M32C2211yescharacteristic
14C2×C11×#108C2211yescharacteristic
15#10622828—21no—
16#10622772C2214yes—
17#10622770—22no—
18#10622737—21no—
19C2×#66883C2211yescharacteristic
20#10622719C2211yescharacteristic
21C2×#66876C2211yescharacteristic
22#10622506C2214yescomplemented
23D11×#108—22no—
24C11×#361C2214yes—
25#10622201C2214yes—
26#10622152C2214yescomplemented
27#10622151C2214yescomplemented
28#10622132C2214yescomplemented
29C22×D4×C11—21no—
30C2×#4339D411yescharacteristic
31C2×C11×D8—21no—
32C2×C11×D8—21no—
33C2×C11×D8—21no—
34C2×C11×D8—21no—
35C2×C11×D8—21no—
36C2×C11×D8C2312yes—
37C2×C11×M16—21no—
38C22×C8×C11C2311yescharacteristic
39#67006—42no—
40#66993—41no—
41#66991—24no—
42#66989—41no—
43#66979—21no—
44C2×#4318—21no—
45C2×#4318D411yescharacteristic
46#66960—42no—
47M16×D11—24no—
48#66954—21no—
49#66954—21no—
50#66954—21no—
51#66954—21no—
52#66954—42no—
53C2×#4313C2312yes—
54C2×C8×D11D412yes—
55C11×M32—21no—
56C11×M32C2312yes—
57C2×C11×C16—21no—
58C11×#108—21no—
59C11×#108C2312yes—
60#66896—24no—
61#66886—24no—
62#66883—21no—
63#66883C2312yes—
64#66882—21no—
65#66881C2312yes—
66#66876—21no—
67#66876C2312yes—
68C2×C11⋊C16—21no—
69#33657—111nomaximal, Sylow
70C24×C11—41no—
71C2×D4×C11—22no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C2×C22⋊D11—44no—
79C2×C22⋊D11SD1612yes—
80#4339—21no—
81#4339—21no—
82#4339—21no—
83#4339—21no—
84C2×D44SD1611yescharacteristic
85C2×C4×D11C2×D412yes—
86C2×Dic22SD1611yescharacteristic
87C11×D8—22no—
88C11×D8—22no—
89C11×D8—41no—
90C11×D8—41no—
91C11×M16—22no—
92C11×M16—41no—
93C2×C8×C11—41no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11#4111yescharacteristic
96C2×C8×C11#4111yescharacteristic
97C2×C8×C11#4111yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C2×C8×C11C2411yescharacteristic
100C22⋊Dic11—44no—
101C22⋊Dic11—41no—
102C4⋊Dic11—22no—
103C4×Dic11—41no—
104#4318—21no—
105#4318—21no—
106#4318—22no—
107#4318—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8C2×D412yes—
110#4313—22no—
111#4313—22no—
112#4313—44no—
113C8×D11—22no—
114C8×D11—22no—
115C8×D11—44no—
116C11×C16—22no—
117C11⋊C16—22no—
118#3058—111no—
119#2916—111no—
120#2238—118no—
121#2155—111no—
122#2155—111no—
123C2×#361—111no—
124C2×#361D1111yescharacteristic, complemented
125#2115—111no—
126C23×C11—42no—
127C23×C11—81no—
128C23×C11—81no—
129C23×C11—162no—
130C23×C11C2×SD1611yescharacteristic
131C22×D11C2×SD1612yes—
132D4×C11—42no—
133D4×C11—42no—
134D4×C11—81no—
135D4×C11—81no—
136C2×C4×C11#12311yescharacteristic
137C2×C4×C11#12311yescharacteristic
138C2×C4×C11C2×SD1611yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11C22×D411yescharacteristic
142C22⋊D11—22no—
143C22⋊D11—22no—
144C22⋊D11—164no—
145C2×Dic11—42no—
146C2×Dic11C2×SD1612yes—
147D44—21no—
148D44—21no—
149C4×D11—22no—
150C4×D11—22no—
151Dic22—21no—
152Dic22—21no—
153C8×C11—42no—
154C8×C11#12311yescharacteristic
155C8×C11#12311yescharacteristic
156C8×C11C2×#4111yescharacteristic
157C8×C11C2×#4111yescharacteristic
158C11⋊C8—22no—
159C11⋊C8—42no—
160C22×D8C2×D1111yescharacteristic
161#568—221no—
162C2×#131—111no—
163#535—221no—
164C2×M32—111no—
165C2×M32C2×D1111yescharacteristic
166#469—114no—
167#466—222no—
168#430—114no—
169#430—221no—
170C2×#108—111no—
171C2×#108—222no—
172C2×#108C2×D1111yescharacteristic
173#427—111no—
174#418—221no—
175#365—114no—
176#365—114no—
177#361—114no—
178#361C2×D1114yes—
179#349—114no—
180C22×C11—41no—
181C22×C11—84no—
182C22×C11—82no—
183C22×C11—162no—
184C22×C11—162no—
185C22×C11#48111yescharacteristic
186C22×C11#48111yescharacteristic
187C22×C11C22×SD1611yescharacteristic
188C2×D11—22no—
189C2×D11—42no—
190C4×C11#48111yescharacteristic
191C4×C11#48111yescharacteristic
192C4×C11C2×#12311yescharacteristic
193C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
194Dic11—22no—
195Dic11—82no—
196C2×#41—111no—
197C22×D4—21no—
198C2×D8—21no—
199C2×D8—21no—
200C2×D8—21no—
201C2×D8—21no—
202C2×D8—21no—
203C2×D8C22×D1112yes—
204#131—221no—
205#131—221no—
206#131—221no—
207#131—221no—
208#131—442no—
209#131—442no—
210C2×M16—21no—
211C2×M16—111no—
212C2×M16—112no—
213C2×M16—224no—
214C2×M16—221no—
215C22×C8—112no—
216C22×C8C22×D1111yescharacteristic
217#127—441no—
218#124—441no—
219#121—224no—
220#120—442no—
221#117—221no—
222M32—21no—
223M32—112no—
224M32—221no—
225M32C22×D1112yes—
226C2×C16—21no—
227C2×C16—221no—
228#108—21no—
229#108—112no—
230#108—224no—
231#108—221no—
232#108C22×D1112yes—
233#107—221no—
234#106—112no—
235#102—224no—
236C2×C11—21no—
237C2×C11—21no—
238C2×C11—21no—
239C2×C11—162no—
240C2×C11C2×#48111yescharacteristic
241D11—42no—
242C24—41no—
243#41—221no—
244#41—221no—
245#41—221no—
246#41—221no—
247C2×Q8—111no—
248C2×D4—22no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—112no—
255C2×D4—111no—
256C2×D4—444no—
257C22×C4—112no—
258C22×C4D4×D1111yescharacteristic
259D8—22no—
260D8—22no—
261D8—41no—
262D8—41no—
263M16—22no—
264M16—41no—
265M16—221no—
266M16—221no—
267M16—222no—
268M16—222no—
269M16—222no—
270M16—444no—
271M16—441no—
272C2×C8—41no—
273C2×C8—112no—
274C2×C8—222no—
275C2×C8—222no—
276C2×C8—444no—
277C2×C8—441no—
278C2×C8#433911yescharacteristic
279C2×C8#433911yescharacteristic
280C2×C8D4×D1111yescharacteristic
281C2×C8#434111yescharacteristic
282C2×C8#434111yescharacteristic
283C2×C8C23×D1111yescharacteristic
284C4⋊C4—222no—
285C22⋊C4—444no—
286C22⋊C4—441no—
287C42—441no—
288C16—22no—
289C16—222no—
290C11#3365711yescharacteristic, complemented, Sylow
291C23—42no—
292C23—81no—
293C23—81no—
294C23—112no—
295C23—162no—
296C23SD16×D1111yescharacteristic
297Q8—221no—
298Q8—221no—
299D4—42no—
300D4—42no—
301D4—81no—
302D4—81no—
303D4—222no—
304D4—222no—
305D4—221no—
306D4—221no—
307D4—1764no—
308C2×C4—112no—
309C2×C4—222no—
310C2×C4—222no—
311C2×C4—442no—
312C2×C4#6693611yescharacteristic
313C2×C4#6693611yescharacteristic
314C2×C4#6696411yescharacteristic
315C2×C4#6696411yescharacteristic
316C2×C4SD16×D1111yescharacteristic
317C2×C4C2×D4×D1111yescharacteristic
318C8—42no—
319C8—222no—
320C8—442no—
321C8#6693611yescharacteristic
322C8#6693611yescharacteristic
323C8C2×#433911yescharacteristic
324C8C2×#434111yescharacteristic
325C22—41no—
326C22—84no—
327C22—82no—
328C22—162no—
329C22—162no—
330C22—222no—
331C22—442no—
332C22#1062239011yescharacteristic
333C22#1062239011yescharacteristic
334C22C2×SD16×D1111yescharacteristic
335C4—222no—
336C4—882no—
337C4#1062239011yescharacteristic
338C4#1062239011yescharacteristic
339C4C2×#6693611yescharacteristic
340C4C2×#6696411yescharacteristic
341C2—21no—
342C2—21no—
343C2—21no—
344C2—162no—
345C2—442no—
346C2C2×#1062239011yescharacteristic
subgroupG/H
centerC2C2×#10622390
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#361C2
socleC2×C11C2×#481
prime radical#13078260C2
hypercenterC2×#361D11
hypocenterC11#33657
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
2. #13077224C2semidirect
3. #13070829C2semidirect
4. #13070390C2semidirect
5. #13070389C2semidirect
6. C2×#10622201C2semidirect
7. #13070236C2semidirect
8. C2×C11×#361C2semidirect
22. #10622506C22semidirect
26. #10622152C22semidirect
27. #10622151C22semidirect
28. #10622132C22semidirect
124. C2×#361D11semidirect
290. C11#33657semidirect

Maximal subgroups

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

subgroupindex
#130782602
#130772242
#130708292
#130703902
#130703892
C2×#106222012
#130702362
C2×C11×#3612
#3365711