Finite Group Databasebeta

← #14909016

Subgroups — #14909016

Order 2816.

526 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079340C211yesmaximal, characteristic, complemented
2#13077526C211yesmaximal, characteristic, complemented
3#13070836C211yesmaximal, characteristic, complemented
4#13070828C211yesmaximal, characteristic, complemented
5#13070790C212yesmaximal, complemented
6#13070683C212yesmaximal, complemented
7#13070567C211yesmaximal, characteristic, complemented
8#13070515C212yesmaximal, complemented
9#13070504C212yesmaximal, complemented
10#13070425C211yesmaximal, characteristic, complemented
11C11×#2190C211yesmaximal, characteristic
12C11×#575C2211yescharacteristic
13#10623350—21no—
14#10623131—21no—
15C11×#509C2212yes—
16C11×#469C2211yescharacteristic
17C2×#66901—21no—
18#10622810—21no—
19#10622810C2212yes—
20#10622809—21no—
21#10622809C2212yes—
22#10622808C2212yes—
23#10622768C2211yescharacteristic, complemented
24#10622765C2211yescharacteristic, complemented
25#10622750C2211yescharacteristic
26#10622738C2211yescharacteristic
27M16×Dic11C2211yescharacteristic
28#10622655—21no—
29#10622471C2211yescharacteristic, complemented
30#10622466C2211yescharacteristic, complemented
31#10622381—21no—
32#10622370—21no—
33C11×#360C2212yes—
34C11×#349C2211yescharacteristic
35#10622204C2212yes—
36#10622201C2212yescomplemented
37#10622191C2211yescharacteristic
38#10622155C2212yescomplemented
39#10622151C2212yescomplemented
40#10622150C2212yescomplemented
41#10622149C2212yescomplemented
42#10622125C2212yescomplemented
43C2×C11×#41—21no—
44C11×#137—22no—
45C11×AGL(1,ℤ/8)—22no—
46C11×#135—21no—
47C11×#135C2312yes—
48C2×C11×D8C2311yescharacteristic
49C2×C11×M16C2311yescharacteristic
50C11×#121—21no—
51#67001—22no—
52#67001—22no—
53#67001—42no—
54#66989—21no—
55#66988—41no—
56D4×Dic11—21no—
57D4×Dic11—41no—
58C2×#4324—21no—
59#66977—21no—
60C2×C4×Dic11D411yescharacteristic
61C2×#4318—21no—
62C2×#4318—42no—
63C2×#4318D411yescharacteristic
64C2×Dic44C2311yescharacteristic
65#66943—21no—
66#66940—21no—
67#66932—41no—
68#66930—41no—
69C11×SD32—22no—
70C11×D16—22no—
71C11×M32C2312yes—
72C11×#106C2311yescharacteristic
73C11×#102—21no—
74#66901—22no—
75#66901—22no—
76#66896—21no—
77#66893—22no—
78#66891—22no—
79#66883—21no—
80#66883C2312yes—
81#66881C2311yescharacteristic
82#66880—21no—
83#66879D411yescharacteristic
84#66879C2311yescharacteristic
85C8×Dic11D411yescharacteristic
86C8×Dic11C2311yescharacteristic
87#66876C2312yes—
88#66874—21no—
89#66871—21no—
90#33690—111nomaximal, Sylow
91C11×#41—22no—
92C11×#41—22no—
93C11×#41—41no—
94C11×#41—41no—
95C2×Q8×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C22×Dic11—21no—
103C22×Dic11—41no—
104C2×Dic22—21no—
105C11×Q16—21no—
106C11×Q16#4112yes—
107C11×SD16—22no—
108C11×SD16—22no—
109C11×D8—21no—
110C11×D8—22no—
111C11×D8#4112yes—
112C11×M16—22no—
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2411yescharacteristic
115C11×C4⋊C4—21no—
116C11×C22⋊C4—41no—
117C22⋊Dic11—41no—
118C22⋊Dic11—41no—
119C22⋊Dic11—41no—
120C22⋊Dic11—41no—
121#4324—42no—
122C4⋊Dic11—21no—
123C4⋊Dic11—41no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127C4×Dic11—21no—
128C4×Dic11—41no—
129C4×Dic11C2×D411yescharacteristic
130C4×Dic11C2×D411yescharacteristic
131#4318—22no—
132#4318—22no—
133#4318—41no—
134#4318—42no—
135#4318—42no—
136C2×C11⋊C8—41no—
137C2×C11⋊C8—42no—
138C2×C11⋊C8—42no—
139C2×C11⋊C8C2×D411yescharacteristic
140C2×C11⋊C8C2×D411yescharacteristic
141Dic44—22no—
142C11×C16—22no—
143C11⋊C16—22no—
144#3183—111no—
145#2956—111no—
146#2239—111no—
147#2238—111no—
148#2231—112no—
149#2212—112no—
150#2191—111no—
151#2190D1111yescharacteristic
152AGL(1,ℤ/16)—112no—
153#2180—112no—
154#2165—111no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11AGL(1,ℤ/8)11yescharacteristic
158Q8×C11—22no—
159Q8×C11—41no—
160D4×C11—22no—
161D4×C11—41no—
162D4×C11—42no—
163D4×C11—42no—
164D4×C11—41no—
165D4×C11—41no—
166D4×C11—82no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—81no—
180C2×Dic11—82no—
181Dic22—41no—
182Dic22—41no—
183C8×C11—21no—
184C8×C11C2×#4112yes—
185C11⋊C8—21no—
186C11⋊C8—42no—
187C11⋊C8AGL(1,ℤ/8)12yes—
188#575C2×D1111yescharacteristic
189#568—221no—
190#529—221no—
191#510—112no—
192#509C2×D1112yes—
193#499—111no—
194#495—111no—
195#488—221no—
196#470—111no—
197#469C2×D1111yescharacteristic
198#468—221no—
199#444—112no—
200#444—221no—
201#443—112no—
202#443—221no—
203#442—111no—
204#441—111no—
205#440—221no—
206#430—111no—
207C2×#104—221no—
208C4×M16—111no—
209#365—112no—
210#365—112no—
211#364—112no—
212#362—112no—
213#361—112no—
214#360—112no—
215#360C2×D1112yes—
216#349—111no—
217#349C2×D1111yescharacteristic
218#347—112no—
219C22×C11—21no—
220C22×C11—41no—
221C22×C11—42no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—161no—
226C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
227C4×C11—21no—
228C4×C11—42no—
229C4×C11—81no—
230C4×C11#52511yescharacteristic
231C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
232Dic11—41no—
233Dic11—41no—
234Dic11—81no—
235Dic11—81no—
236C2×#41—21no—
237#137—22no—
238AGL(1,ℤ/8)—22no—
239#135—21no—
240#135C22×D1112yes—
241C2×Q16—111no—
242C2×SD16—221no—
243C2×D8C22×D1111yescharacteristic
244#131—222no—
245#131—222no—
246#131—442no—
247C2×M16—111no—
248C2×M16—221no—
249C2×M16—442no—
250C2×M16C22×D1111yescharacteristic
251#126—441no—
252#125—221no—
253#124—221no—
254#123—441no—
255C22⋊Q8—221no—
256#121—21no—
257C4×Q8—221no—
258C4×D4—221no—
259C4×D4—441no—
260#117—441no—
261C2×C42—111no—
262Q32—222no—
263SD32—22no—
264SD32—222no—
265D16—22no—
266M32—112no—
267M32C22×D1112yes—
268#108—112no—
269#108—221no—
270#107—221no—
271#106—111no—
272#106C22×D1111yescharacteristic
273#104—222no—
274#104—222no—
275#103—221no—
276#103—221no—
277#102—21no—
278#102—221no—
279#97—111no—
280#97—111no—
281C4×C8—111no—
282C4×C8—111no—
283C2×C11—21no—
284C2×C11—41no—
285C2×C11—82no—
286C2×C11—161no—
287C2×C11#310911yescharacteristic
288#41—22no—
289#41—22no—
290#41—41no—
291#41—41no—
292C2×Q8—21no—
293C2×Q8—221no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—41no—
298C22×C4—41no—
299C22×C4—221no—
300C22×C4—441no—
301C22×C4D4×D1111yescharacteristic
302Q16—21no—
303Q16—222no—
304Q16#434112yes—
305SD16—22no—
306SD16—22no—
307SD16—442no—
308D8—21no—
309D8—22no—
310D8#434112yes—
311M16—22no—
312M16—222no—
313M16—222no—
314M16—442no—
315M16—442no—
316M16—441no—
317C2×C8—111no—
318C2×C8—111no—
319C2×C8—442no—
320C2×C8—442no—
321C2×C8—441no—
322C2×C8D4×D1111yescharacteristic
323C2×C8C23×D1111yescharacteristic
324C4⋊C4—21no—
325C4⋊C4—221no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C4⋊C4—441no—
329C4⋊C4—441no—
330C22⋊C4—41no—
331C22⋊C4—441no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C22⋊C4—441no—
335C42—111no—
336C42—111no—
337C42—221no—
338C42—441no—
339C16—22no—
340C16—222no—
341C11#3369011yescharacteristic, complemented, Sylow
342C23—41no—
343C23—41no—
344C23#6696411yescharacteristic
345Q8—22no—
346Q8—41no—
347Q8—441no—
348Q8—441no—
349D4—22no—
350D4—41no—
351D4—42no—
352D4—42no—
353D4—41no—
354D4—41no—
355D4—82no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—881no—
367C2×C4—882no—
368C2×C4#6696411yescharacteristic
369C2×C4C2×D4×D1111yescharacteristic
370C8—21no—
371C8—112no—
372C8—221no—
373C8—442no—
374C8C2×#434112yes—
375C22—21no—
376C22—41no—
377C22—42no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—161no—
382C22C2×#6696411yescharacteristic
383C4—21no—
384C4—42no—
385C4—81no—
386C4—441no—
387C4—441no—
388C4—881no—
389C4—881no—
390C4#1062311711yescharacteristic
391C4D11×AGL(1,ℤ/8)11yescharacteristic
392C2—21no—
393C2—41no—
394C2—82no—
395C2—161no—
396C2#1307870211yescharacteristic
subgroupG/H
centerC2#13078702
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#2190C2
socleC2×C11#3109
hypercenter#2190D11
hypocenterC11#33690
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2190

Complements

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

NH ≅ G/Ntype
1. #13079340C2semidirect
2. #13077526C2semidirect
3. #13070836C2semidirect
4. #13070828C2semidirect
5. #13070790C2semidirect
6. #13070683C2semidirect
7. #13070567C2semidirect
8. #13070515C2semidirect
9. #13070504C2semidirect
10. #13070425C2semidirect
23. #10622768C22semidirect
24. #10622765C22semidirect
29. #10622471C22semidirect
30. #10622466C22semidirect
36. #10622201C22semidirect
38. #10622155C22semidirect
39. #10622151C22semidirect
40. #10622150C22semidirect
41. #10622149C22semidirect
42. #10622125C22semidirect
341. C11#33690semidirect

Maximal subgroups

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

subgroupindex
#130793402
#130775262
#130708362
#130708282
#130707902
#130706832
#130705672
#130705152
#130705042
#130704252
C11×#21902
#3369011