Finite Group Databasebeta

← #14909046

Subgroups — #14909046

Order 2816.

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

normal subgroups only

This group has 512 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#13079270C211yesmaximal, characteristic, complemented
2#13077519C211yesmaximal, characteristic
3#13070836C211yesmaximal, characteristic, complemented
4#13070833C211yesmaximal, characteristic, complemented
5#13070790C212yesmaximal, complemented
6#13070695C212yesmaximal, complemented
7#13070567C211yesmaximal, characteristic
8#13070508C212yesmaximal, complemented
9#13070504C212yesmaximal, complemented
10#13070429C211yesmaximal, characteristic, complemented
11C11×#2191C211yesmaximal, characteristic
12C11×#575C2211yescharacteristic
13C2×#67001—21no—
14#10623156—21no—
15C11×#510C2212yes—
16C11×#470C2211yescharacteristic
17#10622849—21no—
18#10622810—21no—
19#10622810C2212yes—
20#10622809—21no—
21#10622809C2212yes—
22#10622808C2212yes—
23#10622797C2211yescharacteristic, complemented
24#10622794C2211yescharacteristic, complemented
25#10622750C2211yescharacteristic
26#10622738C2211yescharacteristic
27#10622735C2211yescharacteristic
28#10622664—21no—
29#10622471C2211yescharacteristic, complemented
30#10622466C2211yescharacteristic, complemented
31#10622410—21no—
32#10622403—21no—
33C11×#360C2212yes—
34C11×#349C2211yescharacteristic
35#10622204C2212yes—
36#10622203C2212yescomplemented
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×Q16C2311yescharacteristic
49C2×C11×M16C2311yescharacteristic
50C11×C22⋊Q8—21no—
51#67001—22no—
52#67001—22no—
53#67001—41no—
54#67001—41no—
55Q8×Dic11—21no—
56#66997—21no—
57C2×#4326—21no—
58#66979D411yescharacteristic
59#66977—21no—
60C2×#4318—21no—
61C2×#4318—41no—
62C22×C11⋊C8—41no—
63C22×C11⋊C8D411yescharacteristic
64C2×Dic44C2311yescharacteristic
65#66943—21no—
66#66943—41no—
67#66942—41no—
68#66940—21no—
69#66932—41no—
70#66932—41no—
71C11×Q32—22no—
72C11×SD32—22no—
73C11×M32C2312yes—
74C11×#106C2311yescharacteristic
75C11×#103—21no—
76#66901—22no—
77#66901—22no—
78#66899—21no—
79#66893—22no—
80#66891—22no—
81#66883—21no—
82#66883C2312yes—
83#66881C2311yescharacteristic
84#66880—21no—
85#66879D411yescharacteristic
86#66879C2311yescharacteristic
87C8×Dic11D411yescharacteristic
88C8×Dic11C2311yescharacteristic
89#66876C2312yes—
90#66874—21no—
91#66871—21no—
92#33693—111nomaximal, Sylow
93C11×#41—22no—
94C11×#41—22no—
95C11×#41—41no—
96C11×#41—41no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11C2×D411yescharacteristic
103C2×Dic22—21no—
104C11×Q16—21no—
105C11×Q16—22no—
106C11×Q16#4112yes—
107C11×SD16—22no—
108C11×SD16—22no—
109C11×D8—21no—
110C11×D8#4112yes—
111C11×M16—22no—
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2411yescharacteristic
114C11×C4⋊C4—21no—
115C11×C4⋊C4—41no—
116C11×C22⋊C4—41no—
117C22⋊Dic11—21no—
118C22⋊Dic11—41no—
119#4326—41no—
120#4326—41no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128Dic11⋊C4—41no—
129Dic11⋊C4—41no—
130C4×Dic11—41no—
131C4×Dic11—41no—
132C4×Dic11C2×D411yescharacteristic
133C4×Dic11C2×D411yescharacteristic
134#4318—22no—
135#4318—41no—
136#4318—42no—
137#4318—42no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—41no—
141C2×C11⋊C8—42no—
142C2×C11⋊C8—42no—
143C2×C11⋊C8C2×D411yescharacteristic
144C2×C11⋊C8C2×D411yescharacteristic
145Dic44—22no—
146C11×C16—22no—
147C11⋊C16—22no—
148#3177—111no—
149#2955—111no—
150#2239—111no—
151#2239—111no—
152#2231—112no—
153#2214—112no—
154#2191—111no—
155#2191D1111yescharacteristic
156#2180—112no—
157#2180—112no—
158#2166—111no—
159C23×C11—41no—
160C23×C11AGL(1,ℤ/8)11yescharacteristic
161Q8×C11—22no—
162Q8×C11—41no—
163Q8×C11—41no—
164Q8×C11—41no—
165D4×C11—22no—
166D4×C11—41no—
167D4×C11—42no—
168D4×C11—42no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182Dic22—41no—
183Dic22—41no—
184C8×C11—21no—
185C8×C11C2×#4112yes—
186C11⋊C8—21no—
187C11⋊C8—42no—
188C11⋊C8AGL(1,ℤ/8)11yescharacteristic
189C11⋊C8AGL(1,ℤ/8)11yescharacteristic
190#575C2×D1111yescharacteristic
191C2×#131—221no—
192#541—221no—
193#510—112no—
194#510C2×D1112yes—
195#499—111no—
196#494—111no—
197#491—221no—
198#470—111no—
199#470C2×D1111yescharacteristic
200#467—221no—
201#444—112no—
202#444—221no—
203#443—112no—
204#443—221no—
205#441—111no—
206#441—111no—
207C4×Q16—221no—
208#430—111no—
209#421—221no—
210#405—111no—
211#365—112no—
212#365—112no—
213#364—112no—
214#362—112no—
215#362—112no—
216#360—112no—
217#360C2×D1112yes—
218#349—111no—
219#349C2×D1111yescharacteristic
220#347—112no—
221C22×C11—21no—
222C22×C11—41no—
223C22×C11—42no—
224C22×C11—82no—
225C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
226C4×C11—21no—
227C4×C11—42no—
228C4×C11—81no—
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×Q16—221no—
243C2×Q16C22×D1111yescharacteristic
244#131—222no—
245#131—222no—
246#131—441no—
247#131—441no—
248C2×M16—221no—
249C2×M16—441no—
250C2×M16C22×D1111yescharacteristic
251C22×C8—111no—
252C22×C8—441no—
253C4⋊Q8—221no—
254#126—441no—
255#126—441no—
256#125—221no—
257#125—441no—
258#125—441no—
259C22⋊Q8—21no—
260C22⋊Q8—221no—
261C4×Q8—221no—
262C4×Q8—221no—
263#117—111no—
264Q32—22no—
265Q32—222no—
266SD32—22no—
267SD32—222no—
268M32—112no—
269M32C22×D1112yes—
270#108—112no—
271#108—221no—
272#107—221no—
273#106—111no—
274#106C22×D1111yescharacteristic
275#104—222no—
276#104—222no—
277#103—21no—
278#103—221no—
279#103—221no—
280#103—221no—
281#97—111no—
282#97—111no—
283C4×C8—111no—
284C4×C8—111no—
285C2×C11—21no—
286C2×C11—41no—
287C2×C11—82no—
288C2×C11#310911yescharacteristic
289#41—22no—
290#41—22no—
291#41—41no—
292#41—41no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—221no—
296C2×D4—21no—
297C2×D4—41no—
298C22×C4—41no—
299C22×C4D4×D1111yescharacteristic
300Q16—21no—
301Q16—22no—
302Q16—222no—
303Q16—441no—
304Q16—441no—
305Q16#434112yes—
306SD16—22no—
307SD16—22no—
308D8—21no—
309D8#434112yes—
310M16—22no—
311M16—222no—
312M16—442no—
313M16—442no—
314M16—441no—
315C2×C8—111no—
316C2×C8—111no—
317C2×C8—221no—
318C2×C8—221no—
319C2×C8—442no—
320C2×C8—442no—
321C2×C8—441no—
322C2×C8D4×D1111yescharacteristic
323C2×C8C23×D1111yescharacteristic
324C4⋊C4—21no—
325C4⋊C4—41no—
326C4⋊C4—221no—
327C4⋊C4—221no—
328C4⋊C4—441no—
329C4⋊C4—441no—
330C4⋊C4—441no—
331C4⋊C4—441no—
332C4⋊C4—441no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C22⋊C4—41no—
336C22⋊C4—221no—
337C22⋊C4—441no—
338C42—111no—
339C42—111no—
340C42—441no—
341C42—441no—
342C16—22no—
343C16—222no—
344C11#3369311yescharacteristic, complemented, Sylow
345C23—41no—
346C23#6696411yescharacteristic
347Q8—22no—
348Q8—41no—
349Q8—41no—
350Q8—41no—
351Q8—441no—
352Q8—441no—
353D4—22no—
354D4—41no—
355D4—42no—
356D4—42no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4#6696411yescharacteristic
369C2×C4C2×D4×D1111yescharacteristic
370C8—21no—
371C8—111no—
372C8—111no—
373C8—221no—
374C8—442no—
375C8C2×#434112yes—
376C22—21no—
377C22—41no—
378C22—42no—
379C22—82no—
380C22C2×#6696411yescharacteristic
381C4—21no—
382C4—42no—
383C4—81no—
384C4—81no—
385C4—441no—
386C4—441no—
387C4—881no—
388C4—881no—
389C4#1062311711yescharacteristic
390C4D11×AGL(1,ℤ/8)11yescharacteristic
391C2—21no—
392C2—41no—
393C2—82no—
394C2#1307870211yescharacteristic
subgroupG/H
centerC2#13078702
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2191C2
socleC2×C11#3109
prime radicalC11×#575C22
hypercenter#2191D11
hypocenterC11#33693
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2191

Complements

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

NH ≅ G/Ntype
1. #13079270C2semidirect
3. #13070836C2semidirect
4. #13070833C2semidirect
5. #13070790C2semidirect
6. #13070695C2semidirect
8. #13070508C2semidirect
9. #13070504C2semidirect
10. #13070429C2semidirect
23. #10622797C22semidirect
24. #10622794C22semidirect
29. #10622471C22semidirect
30. #10622466C22semidirect
36. #10622203C22semidirect
38. #10622155C22semidirect
39. #10622151C22semidirect
40. #10622150C22semidirect
41. #10622149C22semidirect
42. #10622125C22semidirect
344. C11#33693semidirect

Maximal subgroups

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

subgroupindex
#130792702
#130775192
#130708362
#130708332
#130707902
#130706952
#130705672
#130705082
#130705042
#130704292
C11×#21912
#3369311