Finite Group Databasebeta

← #14908678

Subgroups — #14908678

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#13078265C211yesmaximal, characteristic
2#13077224C211yesmaximal, characteristic, complemented
3#13070832C218yesmaximal, complemented
4#13070388C211yesmaximal, characteristic, complemented
5C2×#10622154C211yesmaximal, characteristic, complemented
6C2×#10622133C211yesmaximal, characteristic, complemented
7#13070236C211yesmaximal, characteristic, complemented
8C11×#2155C211yesmaximal, characteristic, complemented
9#10623276—21no—
10C22×D88C2211yescharacteristic
11C2×#66954C2211yescharacteristic
12#10623056—21no—
13C2×C11×M32C2211yescharacteristic
14C2×C11×#108C2211yescharacteristic
15C11×#427C2211yescharacteristic
16#10622737—21no—
17C2×#66883C2211yescharacteristic
18C2×#66876C2211yescharacteristic
19#10622614—21no—
20#10622506C2214yescomplemented
21D11×#108—22no—
22#10622496—22no—
23#10622478C2214yes—
24C11×#365C2214yescomplemented
25#10622154C2214yes—
26#10622152C2214yescomplemented
27#10622133C2214yes—
28#10622125C2214yescomplemented
29C2×#4339D411yescharacteristic
30C22×D44—21no—
31C2×C11×M16—21no—
32C22×C8×C11C2311yescharacteristic
33C11×#117—21no—
34C2×#4318—21no—
35C2×#4318D411yescharacteristic
36#66960—42no—
37M16×D11—24no—
38C2×D88—21no—
39C2×D88—21no—
40C2×D88—21no—
41C2×D88—21no—
42C2×D88—21no—
43C2×D88C2312yes—
44#66954—21no—
45#66954—21no—
46#66954—21no—
47#66954—21no—
48#66954—42no—
49C2×#4313C2312yes—
50C2×C8×D11D412yes—
51#66948—24no—
52#66935—42no—
53#66928—41no—
54#66927—41no—
55C11×M32—21no—
56C11×M32C2312yes—
57C2×C11×C16—21no—
58C11×#108—21no—
59C11×#108C2312yes—
60C11×#107—21no—
61C11×#106C2312yes—
62#66886—24no—
63#66883—21no—
64#66883C2312yes—
65#66876—21no—
66#66876C2312yes—
67C2×C11⋊C16—21no—
68#66873—24no—
69#33657—111nomaximal, Sylow
70C23×D11—41no—
71C22×C4×C11C2×D411yescharacteristic
72C2×C22⋊D11SD1612yes—
73#4339—21no—
74#4339—21no—
75#4339—21no—
76#4339—21no—
77C2×D44—22no—
78C2×D44—44no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44SD1611yescharacteristic
85C2×C4×D11C2×D412yes—
86C2×Dic22SD1611yescharacteristic
87C11×M16—22no—
88C11×M16—41no—
89C2×C8×C11—41no—
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11#4111yescharacteristic
92C2×C8×C11#4111yescharacteristic
93C2×C8×C11#4111yescharacteristic
94C2×C8×C11#4111yescharacteristic
95C2×C8×C11C2411yescharacteristic
96C11×C4⋊C4—22no—
97C11×C22⋊C4—41no—
98C42×C11—41no—
99(C2×D11)⋊C4—44no—
100#4318—21no—
101#4318—21no—
102#4318—22no—
103#4318—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8C2×D412yes—
106D88—22no—
107D88—22no—
108D88—41no—
109D88—41no—
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#2155D1111yescharacteristic, complemented
123C2×#361—111no—
124C2×#361—111no—
125#2115—111no—
126C23×C11C2×SD1611yescharacteristic
127C22×D11—42no—
128C22×D11—81no—
129C22×D11—81no—
130C22×D11—162no—
131C22×D11C2×SD1612yes—
132C2×C4×C11—42no—
133C2×C4×C11#12311yescharacteristic
134C2×C4×C11#12311yescharacteristic
135C2×C4×C11C2×SD1611yescharacteristic
136C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C11C22×D411yescharacteristic
139C22⋊D11—22no—
140C22⋊D11—22no—
141C2×Dic11C2×SD1612yes—
142D44—21no—
143D44—21no—
144D44—42no—
145D44—42no—
146D44—81no—
147D44—81no—
148D44—164no—
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×D8—111no—
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#427C2×D1111yescharacteristic
174#418—221no—
175#365—114no—
176#365C2×D1114yescomplemented
177#361—114no—
178#361—114no—
179#349—114no—
180C22×C11—41no—
181C22×C11#48111yescharacteristic
182C22×C11#48111yescharacteristic
183C22×C11C22×SD1611yescharacteristic
184C2×D11—22no—
185C2×D11—42no—
186C2×D11—84no—
187C2×D11—82no—
188C2×D11—162no—
189C2×D11—162no—
190C4×C11—82no—
191C4×C11#48111yescharacteristic
192C4×C11#48111yescharacteristic
193C4×C11C2×#12311yescharacteristic
194C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
195Dic11—22no—
196C2×#41—111no—
197C22×D4—221no—
198C2×D8—112no—
199C2×D8—221no—
200C2×D8—221no—
201C2×D8—221no—
202C2×D8—221no—
203C2×D8—221no—
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—21no—
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—21no—
234#106C22×D1112yes—
235#102—224no—
236C2×C11—21no—
237C2×C11—21no—
238C2×C11—21no—
239C2×C11C2×#48111yescharacteristic
240D11—42no—
241D11—162no—
242C24—441no—
243#41—221no—
244#41—221no—
245#41—221no—
246#41—221no—
247C2×Q8—111no—
248C2×D4—112no—
249C2×D4—111no—
250C2×D4—222no—
251C2×D4—444no—
252C2×D4—441no—
253C2×D4—441no—
254C2×D4—441no—
255C2×D4—441no—
256C2×D4—441no—
257C22×C4—112no—
258C22×C4D4×D1111yescharacteristic
259D8—222no—
260D8—222no—
261D8—441no—
262D8—441no—
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#434311yescharacteristic
282C2×C8#434311yescharacteristic
283C2×C8C23×D1111yescharacteristic
284C4⋊C4—22no—
285C22⋊C4—41no—
286C22⋊C4—444no—
287C42—41no—
288C16—22no—
289C16—222no—
290C11#3365711yescharacteristic, complemented, Sylow
291C23—112no—
292C23—442no—
293C23—881no—
294C23—881no—
295C23—1762no—
296C23SD16×D1111yescharacteristic
297Q8—221no—
298Q8—221no—
299D4—222no—
300D4—222no—
301D4—221no—
302D4—221no—
303D4—442no—
304D4—442no—
305D4—881no—
306D4—881no—
307D4—1764no—
308C2×C4—42no—
309C2×C4—112no—
310C2×C4—222no—
311C2×C4—222no—
312C2×C4#6694711yescharacteristic
313C2×C4#6694711yescharacteristic
314C2×C4SD16×D1111yescharacteristic
315C2×C4#6696711yescharacteristic
316C2×C4#6696711yescharacteristic
317C2×C4C2×D4×D1111yescharacteristic
318C8—42no—
319C8—222no—
320C8—442no—
321C8#6694711yescharacteristic
322C8#6694711yescharacteristic
323C8C2×#433911yescharacteristic
324C8C2×#434311yescharacteristic
325C22—41no—
326C22—222no—
327C22—442no—
328C22—884no—
329C22—882no—
330C22—1762no—
331C22—1762no—
332C22#1062247611yescharacteristic
333C22#1062247611yescharacteristic
334C22C2×SD16×D1111yescharacteristic
335C4—82no—
336C4—222no—
337C4#1062247611yescharacteristic
338C4#1062247611yescharacteristic
339C4C2×#6694711yescharacteristic
340C4C2×#6696711yescharacteristic
341C2—21no—
342C2—21no—
343C2—21no—
344C2—442no—
345C2—1762no—
346C2C2×#1062247611yescharacteristic
subgroupG/H
centerC2C2×#10622476
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2155C2
socleC2×C11C2×#481
prime radical#13078265C2
hypercenter#2155D11
hypocenterC11#33657
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ #2155

Complements

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

NH ≅ G/Ntype
2. #13077224C2semidirect
3. #13070832C2semidirect
4. #13070388C2semidirect
5. C2×#10622154C2semidirect
6. C2×#10622133C2semidirect
7. #13070236C2semidirect
8. C11×#2155C2semidirect
20. #10622506C22semidirect
24. C11×#365C22semidirect
26. #10622152C22semidirect
28. #10622125C22semidirect
122. #2155D11semidirect
176. #365C2×D11semidirect
290. C11#33657semidirect

Maximal subgroups

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

subgroupindex
#130782652
#130772242
#130708322
#130703882
C2×#106221542
C2×#106221332
#130702362
C11×#21552
#3365711