Finite Group Databasebeta

← #14907233

Subgroups — #14907233

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#13077533C211yesmaximal, characteristic, complemented
2#13077500C211yesmaximal, characteristic, complemented
3#13070515C214yesmaximal, complemented
4#13070508C214yesmaximal, complemented
5C2×#10622151C211yesmaximal, characteristic, complemented
6#13070365C211yesmaximal, characteristic, complemented
7C2×#10622204C211yesmaximal, characteristic, complemented
8#13070220C211yesmaximal, characteristic, complemented
9C11×#3414C211yesmaximal, characteristic
10C2×C11×#135C2211yescharacteristic
11C2×C11×#135C2211yescharacteristic
12#10623358—21no—
13#10623350—21no—
14C11×#510C412yescomplemented
15C11×#510C2212yes—
16C11×#509C412yescomplemented
17C11×#509C2212yes—
18C11×#508C414yescomplemented
19C2×C11×M32C2211yescharacteristic
20#10622849—21no—
21#10622845—21no—
22#10622810C2214yes—
23#10622809—22no—
24#10622797C2212yescomplemented
25SD16×Dic11—22no—
26#10622765C2212yescomplemented
27C2×#66883C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29#10622714C2211yescharacteristic
30C2×#66876C2211yescharacteristic
31#10622204C2214yes—
32#10622203C2212yescomplemented
33#10622201C2212yescomplemented
34#10622151C2214yescomplemented
35#10622150C2214yescomplemented
36C2×C11×#41—21no—
37C2×C11×#41—21no—
38C11×#135—21no—
39C11×#135—21no—
40C11×#135—21no—
41C11×#135—21no—
42C11×#135C2×C412yes—
43C11×#135C2×C412yes—
44C11×#135C2×C412yescomplemented
45C11×#135C2312yes—
46C2×C11×Q16C2×C411yescharacteristic, complemented
47C2×C11×Q16C2311yescharacteristic
48C2×C11×SD16—21no—
49C2×C11×SD16—21no—
50C2×C11×D8C2×C411yescharacteristic, complemented
51C2×C11×D8C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53#67001—24no—
54#67001—42no—
55Q8×Dic11—22no—
56D4×Dic11—22no—
57D4×Dic11—42no—
58#66979—41no—
59#66979D411yescharacteristic
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—41no—
62C2×#4318—21no—
63C2×#4318—42no—
64C2×#4318D411yescharacteristic
65C11×Q32C2×C414yescomplemented
66C11×SD32C2×C414yescomplemented
67C11×SD32C2×C414yescomplemented
68C11×D16C2×C414yescomplemented
69C11×M32C2×C412yescomplemented
70C11×M32C2312yes—
71C2×C11×C16C2×C412yescomplemented
72#66901—24no—
73#66899—22no—
74#66896—22no—
75#66883—21no—
76#66883C2312yes—
77#66881—21no—
78#66881C2312yes—
79#66879C2312yes—
80C8×Dic11D412yes—
81#66876—21no—
82#66876C2312yes—
83C2×C11⋊C16—21no—
84#33469—111nomaximal, Sylow
85C11×#41—22no—
86C11×#41—22no—
87C11×#41—22no—
88C11×#41—22no—
89C11×#41—41no—
90C11×#41—41no—
91C11×#41—41no—
92C11×#41—41no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C22×Dic11—42no—
103C22×Dic11—41no—
104C11×Q16—21no—
105C11×Q16—21no—
106C11×Q16C22×C412yes—
107C11×Q16C22×C412yes—
108C11×SD16—22no—
109C11×SD16—22no—
110C11×SD16—22no—
111C11×SD16—22no—
112C11×D8—21no—
113C11×D8—21no—
114C11×D8C22×C412yes—
115C11×D8C22×C412yes—
116C2×C8×C11C22×C411yescharacteristic
117C2×C8×C11C22×C411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11#4111yescharacteristic
120C2×C8×C11#4111yescharacteristic
121C2×C8×C11C2411yescharacteristic
122C22⋊Dic11—21no—
123C22⋊Dic11—42no—
124C4⋊Dic11—21no—
125C4⋊Dic11—22no—
126C4⋊Dic11—42no—
127C4⋊Dic11—41no—
128C4×Dic11—42no—
129C4×Dic11C2×D412yes—
130#4318—21no—
131#4318—21no—
132#4318—22no—
133#4318—44no—
134#4318—41no—
135C2×C11⋊C8—44no—
136C2×C11⋊C8—41no—
137C2×C11⋊C8C2×D412yes—
138C11×C16C22×C414yes—
139C11⋊C16—22no—
140#3414D1111yescharacteristic
141#2957—111no—
142#2952—111no—
143AGL(1,ℤ/16)—114no—
144#2180—114no—
145C2×#365—111no—
146#2148—111no—
147C2×#360—111no—
148#2110—111no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11AGL(1,ℤ/8)11yescharacteristic
152Q8×C11—22no—
153Q8×C11—22no—
154Q8×C11—41no—
155Q8×C11—41no—
156D4×C11—22no—
157D4×C11—22no—
158D4×C11—42no—
159D4×C11—42no—
160D4×C11—42no—
161D4×C11—42no—
162D4×C11—41no—
163D4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11C4×D411yescharacteristic
171C2×C4×C11C4×D411yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C2×Dic11—22no—
177C2×Dic11—42no—
178C2×Dic11—162no—
179C2×Dic11—161no—
180C8×C11C4×D411yescharacteristic
181C8×C11C4×D411yescharacteristic
182C8×C11C23×C411yescharacteristic
183C8×C11C2×#4111yescharacteristic
184C11⋊C8—22no—
185C11⋊C8—42no—
186C2×#135C2×D1111yescharacteristic
187C2×#135C2×D1111yescharacteristic
188#568—221no—
189#520—221no—
190#510Dic1112yescomplemented
191#510C2×D1112yes—
192#509Dic1112yescomplemented
193#509C2×D1112yes—
194#508Dic1114yescomplemented
195C2×M32—111no—
196C2×M32C2×D1111yescharacteristic
197#444—114no—
198#443—222no—
199#442—112no—
200#441—112no—
201C4×SD16—222no—
202C2×#108—111no—
203C2×#106—111no—
204#421—221no—
205#417—221no—
206#405—111no—
207#365—114no—
208#362—112no—
209#361—112no—
210#360—114no—
211#347—114no—
212C22×C11—41no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—161no—
218C22×C11#44211yescharacteristic
219C22×C11#44211yescharacteristic
220C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
221C4×C11—42no—
222C4×C11—42no—
223C4×C11#44211yescharacteristic
224C4×C11#44211yescharacteristic
225C4×C11C2×C4×D411yescharacteristic
226C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
227Dic11—42no—
228Dic11—82no—
229C2×#41—21no—
230C2×#41—21no—
231#135—21no—
232#135—21no—
233#135—21no—
234#135—21no—
235#135C2×Dic1112yes—
236#135C2×Dic1112yes—
237#135C2×Dic1112yescomplemented
238#135C22×D1112yes—
239C2×Q16C2×Dic1111yescharacteristic, complemented
240C2×Q16C22×D1111yescharacteristic
241C2×SD16—21no—
242C2×SD16—21no—
243C2×D8C2×Dic1111yescharacteristic, complemented
244C2×D8C22×D1111yescharacteristic
245#131—224no—
246#131—442no—
247C2×M16—111no—
248C2×M16—221no—
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—
258Q32C2×Dic1114yescomplemented
259SD32C2×Dic1114yescomplemented
260SD32C2×Dic1114yescomplemented
261D16C2×Dic1114yescomplemented
262M32—112no—
263M32—221no—
264M32C2×Dic1112yescomplemented
265M32C22×D1112yes—
266C2×C16—221no—
267C2×C16C2×Dic1112yescomplemented
268#108—112no—
269#108—221no—
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×C11—82no—
282C2×C11C2×#44211yescharacteristic
283#41—22no—
284#41—22no—
285#41—22no—
286#41—22no—
287#41—41no—
288#41—41no—
289#41—41no—
290#41—41no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—41no—
296C2×D4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—442no—
300C22×C4—441no—
301C22×C4D4×D1111yescharacteristic
302Q16—21no—
303Q16—21no—
304Q16C22×Dic1112yes—
305Q16C22×Dic1112yes—
306SD16—22no—
307SD16—22no—
308SD16—22no—
309SD16—22no—
310D8—21no—
311D8—21no—
312D8C22×Dic1112yes—
313D8C22×Dic1112yes—
314M16—221no—
315M16—221no—
316M16—222no—
317M16—444no—
318M16—441no—
319C2×C8—112no—
320C2×C8—444no—
321C2×C8—441no—
322C2×C8D4×D1111yescharacteristic
323C2×C8#434111yescharacteristic
324C2×C8#434111yescharacteristic
325C2×C8C22×Dic1111yescharacteristic
326C2×C8C22×Dic1111yescharacteristic
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—222no—
337C16C22×Dic1114yes—
338C11#3346911yescharacteristic, complemented, Sylow
339C23—41no—
340C23—41no—
341C23#6696411yescharacteristic
342Q8—22no—
343Q8—22no—
344Q8—41no—
345Q8—41no—
346D4—22no—
347D4—22no—
348D4—42no—
349D4—42no—
350D4—42no—
351D4—42no—
352D4—41no—
353D4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—222no—
361C2×C4—442no—
362C2×C4—1762no—
363C2×C4—1761no—
364C2×C4#6696411yescharacteristic
365C2×C4#6696411yescharacteristic
366C2×C4#6696411yescharacteristic
367C2×C4D4×Dic1111yescharacteristic
368C2×C4D4×Dic1111yescharacteristic
369C2×C4C2×D4×D1111yescharacteristic
370C8—222no—
371C8—442no—
372C8D4×Dic1111yescharacteristic
373C8D4×Dic1111yescharacteristic
374C8C2×#434111yescharacteristic
375C8C23×Dic1111yescharacteristic
376C22—41no—
377C22—42no—
378C22—42no—
379C22—81no—
380C22—81no—
381C22—161no—
382C22#1062276511yescharacteristic
383C22#1062276511yescharacteristic
384C22C2×#6696411yescharacteristic
385C4—42no—
386C4—42no—
387C4—442no—
388C4—882no—
389C4#1062276511yescharacteristic
390C4#1062276511yescharacteristic
391C4C2×#6696411yescharacteristic
392C4C2×D4×Dic1111yescharacteristic
393C2—21no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2—82no—
398C2C2×#1062276511yescharacteristic
subgroupG/H
centerC2C2×#10622765
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3414C2
socleC2×C11C2×#442
cosocleC2×C8×C11C24
hypercenter#3414D11
hypocenterC11#33469
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ #3414

Complements

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

NH ≅ G/Ntype
1. #13077533C2semidirect
2. #13077500C2semidirect
3. #13070515C2semidirect
4. #13070508C2semidirect
5. C2×#10622151C2semidirect
6. #13070365C2semidirect
7. C2×#10622204C2semidirect
8. #13070220C2semidirect
14. C11×#510C4semidirect
16. C11×#509C4semidirect
18. C11×#508C4semidirect
24. #10622797C22semidirect
26. #10622765C22semidirect
32. #10622203C22semidirect
33. #10622201C22semidirect
34. #10622151C22semidirect
35. #10622150C22semidirect
44. C11×#135C2×C4semidirect
46. C2×C11×Q16C2×C4semidirect
50. C2×C11×D8C2×C4semidirect
65. C11×Q32C2×C4semidirect
66. C11×SD32C2×C4semidirect
67. C11×SD32C2×C4semidirect
68. C11×D16C2×C4semidirect
69. C11×M32C2×C4semidirect
71. C2×C11×C16C2×C4semidirect
190. #510Dic11semidirect
192. #509Dic11semidirect
194. #508Dic11semidirect
237. #135C2×Dic11semidirect
239. C2×Q16C2×Dic11semidirect
243. C2×D8C2×Dic11semidirect
258. Q32C2×Dic11semidirect
259. SD32C2×Dic11semidirect
260. SD32C2×Dic11semidirect
261. D16C2×Dic11semidirect
264. M32C2×Dic11semidirect
267. C2×C16C2×Dic11semidirect
338. C11#33469semidirect

Maximal subgroups

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

subgroupindex
#130775332
#130775002
#130705152
#130705082
C2×#106221512
#130703652
C2×#106222042
#130702202
C11×#34142
#3346911