Finite Group Databasebeta

← #14907235

Subgroups — #14907235

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081750C211yesmaximal, characteristic
2#13077532C211yesmaximal, characteristic, complemented
3#13077500C211yesmaximal, characteristic, complemented
4#13070517C214yesmaximal, complemented
5#13070510C214yesmaximal, complemented
6C2×#10622132C211yesmaximal, characteristic, complemented
7C2×#10622156C211yesmaximal, characteristic, complemented
8#13070220C211yesmaximal, characteristic, complemented
9C11×#2148C211yesmaximal, characteristic, complemented
10C2×C11×#135C2211yescharacteristic
11#10623358—21no—
12#10623276—21no—
13C2×#66957C2211yescharacteristic
14C2×C11×M32C2211yescharacteristic
15C2×C11×#108C2211yescharacteristic
16#10622845—21no—
17#10622808C412yescomplemented
18#10622807C414yescomplemented
19#10622806C412yescomplemented
20#10622797C2212yescomplemented
21#10622792C2212yes—
22SD16×Dic11—22no—
23#10622765C2212yescomplemented
24#10622760C2212yes—
25#10622752—21no—
26C2×#66881C2211yescharacteristic
27#10622714C2211yescharacteristic
28C2×#66876C2211yescharacteristic
29#10622508—22no—
30#10622507C2214yes—
31C11×#362C2212yescomplemented
32C11×#361C2212yescomplemented
33#10622156C2214yes—
34#10622150C2214yescomplemented
35#10622132C2214yescomplemented
36C2×C11×#41—21no—
37C2×#4339—21no—
38C11×#135—21no—
39C11×#135—21no—
40C11×#135C2×C412yes—
41C11×#135C2×C412yes—
42C2×C11×Q16C2311yescharacteristic
43C2×C11×SD16—21no—
44C2×C11×D8C2311yescharacteristic
45C2×C11×M16—21no—
46C22×C8×C11C2311yescharacteristic
47Q8×Dic11—22no—
48D4×Dic11—22no—
49D4×Dic11—42no—
50#66979—41no—
51#66979D411yescharacteristic
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—41no—
54C2×#4318D411yescharacteristic
55#66960—24no—
56M16×D11—42no—
57C2×Dic44C2×C411yescharacteristic, complemented
58#66957—21no—
59#66957—21no—
60#66957C2×C412yescomplemented
61#66957C2312yes—
62C2×D88C2×C411yescharacteristic, complemented
63C2×#4314—21no—
64#66954—42no—
65C11×M32—21no—
66C11×M32C2312yes—
67C2×C11×C16—21no—
68C11×#108—21no—
69C11×#108C2312yes—
70#66899—22no—
71#66896—22no—
72#66893C2×C414yescomplemented
73#66892C2×C414yescomplemented
74#66891C2×C414yescomplemented
75#66890C2×C414yescomplemented
76#66889—24no—
77#66881—21no—
78#66881C2312yes—
79#66879C2312yes—
80C8×Dic11D412yes—
81#66876C2×C412yescomplemented
82#66876C2312yes—
83C2×C11⋊C16C2×C412yescomplemented
84#33469—111nomaximal, Sylow
85C11×#41—22no—
86C11×#41—22no—
87C11×#41—41no—
88C11×#41—41no—
89C2×Q8×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—41no—
95C22×Dic11—42no—
96C22×Dic11—41no—
97#4339—22no—
98#4339—22no—
99#4339—41no—
100#4339—41no—
101C2×D44—21no—
102C2×C4×D11—41no—
103C2×Dic22—21no—
104C11×Q16—21no—
105C11×Q16C22×C412yes—
106C11×SD16—22no—
107C11×SD16—22no—
108C11×D8—21no—
109C11×D8C22×C412yes—
110C11×M16—22no—
111C11×M16—41no—
112C2×C8×C11—41no—
113C2×C8×C11C22×C411yescharacteristic
114C2×C8×C11C22×C411yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11#4111yescharacteristic
117C2×C8×C11#4111yescharacteristic
118C2×C8×C11C2411yescharacteristic
119C22⋊Dic11—21no—
120C22⋊Dic11—42no—
121C4⋊Dic11—21no—
122C4⋊Dic11—22no—
123C4⋊Dic11—42no—
124C4⋊Dic11—41no—
125C4×Dic11—42no—
126C4×Dic11C2×D412yes—
127#4318—21no—
128#4318—21no—
129C2×C11⋊C8C2×D412yes—
130Dic44—21no—
131Dic44C22×C412yes—
132D88—21no—
133D88C22×C412yes—
134#4314—22no—
135#4314—22no—
136#4313—44no—
137C8×D11—44no—
138C11×C16—22no—
139C11⋊C16C22×C414yes—
140#3414—111no—
141#2957—111no—
142#2952—111no—
143AGL(1,ℤ/16)—114no—
144#2180—114no—
145C2×#365—111no—
146#2148D1111yescharacteristic, complemented
147C2×#360—111no—
148#2110—111no—
149C23×C11—41no—
150C23×C11AGL(1,ℤ/8)11yescharacteristic
151C22×D11—41no—
152Q8×C11—22no—
153Q8×C11—41no—
154D4×C11—22no—
155D4×C11—42no—
156D4×C11—42no—
157D4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11C4×D411yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C22⋊D11—42no—
168C22⋊D11—42no—
169C2×Dic11—22no—
170C2×Dic11—41no—
171C2×Dic11—42no—
172C2×Dic11—162no—
173C2×Dic11—161no—
174D44—22no—
175D44—41no—
176C4×D11—42no—
177C4×D11—42no—
178Dic22—22no—
179Dic22—41no—
180C8×C11—42no—
181C8×C11C4×D411yescharacteristic
182C8×C11C4×D411yescharacteristic
183C8×C11C23×C411yescharacteristic
184C8×C11C2×#4111yescharacteristic
185C11⋊C8—22no—
186C2×#135—111no—
187C2×#135C2×D1111yescharacteristic
188#568—221no—
189#520—221no—
190#510—112no—
191#510—112no—
192#509—112no—
193#509—112no—
194#508—114no—
195C2×M32—111no—
196C2×M32C2×D1111yescharacteristic
197#444—114no—
198#443—222no—
199#442—112no—
200#441—112no—
201C4×SD16—222no—
202C2×#108C2×D1111yescharacteristic
203C2×#106—111no—
204#421—221no—
205#417—221no—
206#405—111no—
207#365—114no—
208#362C2×D1112yescomplemented
209#361C2×D1112yescomplemented
210#360—114no—
211#347—114no—
212C22×C11—41no—
213C22×C11—42no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11#44211yescharacteristic
217C22×C11#44211yescharacteristic
218C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
219C2×D11—42no—
220C2×D11—161no—
221C4×C11—42no—
222C4×C11#44211yescharacteristic
223C4×C11#44211yescharacteristic
224C4×C11C2×C4×D411yescharacteristic
225C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
226Dic11—42no—
227Dic11—42no—
228Dic11—82no—
229C2×#41—21no—
230C2×#41—221no—
231#135—21no—
232#135—21no—
233#135—112no—
234#135—112no—
235#135—221no—
236#135—221no—
237#135C4×D1112yes—
238#135C4×D1112yes—
239C2×Q16—111no—
240C2×Q16C22×D1111yescharacteristic
241C2×SD16—21no—
242C2×SD16—221no—
243C2×D8—111no—
244C2×D8C22×D1111yescharacteristic
245#131—224no—
246#131—442no—
247C2×M16—21no—
248C2×M16—111no—
249C2×M16—442no—
250C22×C8C22×D1111yescharacteristic
251C4×Q8—222no—
252C4×D4—222no—
253C4×D4—442no—
254#117—111no—
255#117—441no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—441no—
258Q32—114no—
259SD32—114no—
260SD32—114no—
261D16—114no—
262M32—21no—
263M32—112no—
264M32—112no—
265M32C22×D1112yes—
266C2×C16—21no—
267C2×C16—112no—
268#108—21no—
269#108C22×D1112yes—
270#106—112no—
271#106—221no—
272#104—224no—
273#103—222no—
274#102—222no—
275#97—112no—
276C4×C8—112no—
277C2×C11—21no—
278C2×C11—21no—
279C2×C11—21no—
280C2×C11—82no—
281C2×C11C2×#44211yescharacteristic
282D11—82no—
283#41—22no—
284#41—22no—
285#41—41no—
286#41—41no—
287#41—222no—
288#41—222no—
289#41—441no—
290#41—441no—
291C2×Q8—21no—
292C2×Q8—221no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4—221no—
296C2×D4—441no—
297C22×C4—41no—
298C22×C4—442no—
299C22×C4—441no—
300C22×C4—441no—
301C22×C4D4×D1111yescharacteristic
302Q16—21no—
303Q16—112no—
304Q16—221no—
305Q16C2×C4×D1112yes—
306SD16—22no—
307SD16—22no—
308SD16—222no—
309SD16—222no—
310D8—21no—
311D8—112no—
312D8—221no—
313D8C2×C4×D1112yes—
314M16—22no—
315M16—41no—
316M16—221no—
317M16—221no—
318M16—444no—
319C2×C8—41no—
320C2×C8—112no—
321C2×C8—444no—
322C2×C8C2×C4×D1111yescharacteristic
323C2×C8C2×C4×D1111yescharacteristic
324C2×C8D4×D1111yescharacteristic
325C2×C8#434111yescharacteristic
326C2×C8#434111yescharacteristic
327C2×C8C23×D1111yescharacteristic
328C4⋊C4—221no—
329C4⋊C4—222no—
330C4⋊C4—442no—
331C4⋊C4—441no—
332C22⋊C4—221no—
333C22⋊C4—442no—
334C42—112no—
335C42—442no—
336C16—22no—
337C16—114no—
338C11#3346911yescharacteristic, complemented, Sylow
339C23—41no—
340C23—441no—
341C23#6696711yescharacteristic
342Q8—22no—
343Q8—41no—
344Q8—222no—
345Q8—441no—
346D4—22no—
347D4—42no—
348D4—42no—
349D4—41no—
350D4—222no—
351D4—442no—
352D4—442no—
353D4—441no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—222no—
358C2×C4—441no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—1762no—
363C2×C4—1761no—
364C2×C4(C22⋊D11)⋊C411yescharacteristic
365C2×C4(C22⋊D11)⋊C411yescharacteristic
366C2×C4#6696411yescharacteristic
367C2×C4#6696411yescharacteristic
368C2×C4#6696711yescharacteristic
369C2×C4C2×D4×D1111yescharacteristic
370C8—42no—
371C8—222no—
372C8(C22⋊D11)⋊C411yescharacteristic
373C8(C22⋊D11)⋊C411yescharacteristic
374C8C22×C4×D1111yescharacteristic
375C8C2×#434111yescharacteristic
376C22—41no—
377C22—42no—
378C22—81no—
379C22—81no—
380C22—442no—
381C22—1761no—
382C22#1062239811yescharacteristic
383C22#1062239811yescharacteristic
384C22C2×#6696711yescharacteristic
385C4—42no—
386C4—442no—
387C4—442no—
388C4—882no—
389C4#1062239811yescharacteristic
390C4#1062239811yescharacteristic
391C4C2×(C22⋊D11)⋊C411yescharacteristic
392C4C2×#6696411yescharacteristic
393C2—21no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2—882no—
398C2C2×#1062239811yescharacteristic
subgroupG/H
centerC2C2×#10622398
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2148C2
socleC2×C11C2×#442
prime radical#13081750C2
cosocleC2×C8×C11C24
hypercenter#2148D11
hypocenterC11#33469
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ #2148

Complements

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

NH ≅ G/Ntype
2. #13077532C2semidirect
3. #13077500C2semidirect
4. #13070517C2semidirect
5. #13070510C2semidirect
6. C2×#10622132C2semidirect
7. C2×#10622156C2semidirect
8. #13070220C2semidirect
9. C11×#2148C2semidirect
17. #10622808C4semidirect
18. #10622807C4semidirect
19. #10622806C4semidirect
20. #10622797C22semidirect
23. #10622765C22semidirect
31. C11×#362C22semidirect
32. C11×#361C22semidirect
34. #10622150C22semidirect
35. #10622132C22semidirect
57. C2×Dic44C2×C4semidirect
60. #66957C2×C4semidirect
62. C2×D88C2×C4semidirect
72. #66893C2×C4semidirect
73. #66892C2×C4semidirect
74. #66891C2×C4semidirect
75. #66890C2×C4semidirect
81. #66876C2×C4semidirect
83. C2×C11⋊C16C2×C4semidirect
146. #2148D11semidirect
208. #362C2×D11semidirect
209. #361C2×D11semidirect
338. C11#33469semidirect

Maximal subgroups

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

subgroupindex
#130817502
#130775322
#130775002
#130705172
#130705102
C2×#106221322
C2×#106221562
#130702202
C11×#21482
#3346911