Finite Group Databasebeta

← #14909008

Subgroups — #14909008

Order 2816.

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

normal subgroups only

This group has 520 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#13079356C211yesmaximal, characteristic, complemented
2#13077526C211yesmaximal, characteristic
3#13070836C211yesmaximal, characteristic, complemented
4#13070833C211yesmaximal, characteristic, complemented
5#13070785C212yesmaximal, complemented
6#13070695C212yesmaximal, complemented
7#13070567C211yesmaximal, characteristic
8#13070508C212yesmaximal, complemented
9#13070504C212yesmaximal, complemented
10#13070425C211yesmaximal, characteristic, complemented
11C11×#2191C211yesmaximal, characteristic
12C11×#575C2211yescharacteristic
13#10623350—21no—
14#10623153—21no—
15C11×#510C2212yes—
16C11×#470C2211yescharacteristic
17C2×#66901—21no—
18#10622810—21no—
19#10622810C2212yes—
20#10622809—21no—
21#10622809C2212yes—
22#10622808C2212yes—
23#10622797C2211yescharacteristic, complemented
24#10622794C2211yescharacteristic, complemented
25#10622750C2211yescharacteristic
26#10622738C2211yescharacteristic
27M16×Dic11C2211yescharacteristic
28#10622665—21no—
29#10622468C2211yescharacteristic, complemented
30#10622466C2211yescharacteristic, complemented
31#10622405—21no—
32#10622402—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—42no—
54Q8×Dic11—21no—
55#66997—21no—
56C2×#4326—21no—
57#66977—21no—
58C2×C4×Dic11D411yescharacteristic
59C2×#4318—21no—
60C2×#4318—42no—
61C2×#4318D411yescharacteristic
62C2×Dic44C2311yescharacteristic
63#66942—41no—
64#66941—21no—
65#66940—21no—
66#66940—41no—
67#66931—41no—
68#66930—41no—
69C11×Q32—22no—
70C11×SD32—22no—
71C11×M32C2312yes—
72C11×#106C2311yescharacteristic
73C11×#103—21no—
74#66901—22no—
75#66901—22no—
76#66899—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#66872—21no—
90#33689—111nomaximal, Sylow
91C11×#41—22no—
92C11×#41—22no—
93C11×#41—41no—
94C11×#41—41no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C22×Dic11—21no—
102C2×Dic22—21no—
103C2×Dic22—41no—
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—41no—
118#4326—42no—
119C4⋊Dic11—21no—
120C4⋊Dic11—41no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126C4×Dic11—21no—
127C4×Dic11—41no—
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#3185—111no—
145#2956—111no—
146#2239—111no—
147#2239—111no—
148#2230—112no—
149#2214—112no—
150#2191—111no—
151#2191D1111yescharacteristic
152#2180—112no—
153#2180—112no—
154#2165—111no—
155C23×C11—41no—
156C23×C11AGL(1,ℤ/8)11yescharacteristic
157Q8×C11—22no—
158Q8×C11—41no—
159Q8×C11—41no—
160Q8×C11—41no—
161D4×C11—22no—
162D4×C11—41no—
163D4×C11—42no—
164D4×C11—42no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11C22×D411yescharacteristic
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—42no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179Dic22—41no—
180Dic22—41no—
181Dic22—82no—
182C8×C11—21no—
183C8×C11C2×#4112yes—
184C11⋊C8—21no—
185C11⋊C8—42no—
186C11⋊C8AGL(1,ℤ/8)12yes—
187#575C2×D1111yescharacteristic
188#568—221no—
189#533—221no—
190#510—112no—
191#510C2×D1112yes—
192#498—111no—
193#494—111no—
194#487—221no—
195#470—111no—
196#470—221no—
197#470C2×D1111yescharacteristic
198#444—112no—
199#444—221no—
200#443—112no—
201#443—221no—
202#441—111no—
203#441—111no—
204#441—221no—
205#430—111no—
206C2×#104—221no—
207C4×M16—111no—
208#365—112no—
209#365—112no—
210#364—112no—
211#362—112no—
212#362—112no—
213#360—112no—
214#360C2×D1112yes—
215#349—111no—
216#349C2×D1111yescharacteristic
217#347—112no—
218C22×C11—21no—
219C22×C11—41no—
220C22×C11—42no—
221C22×C11—161no—
222C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
223C4×C11—21no—
224C4×C11—42no—
225C4×C11—81no—
226C4×C11—81no—
227C4×C11#52511yescharacteristic
228C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
229Dic11—22no—
230Dic11—41no—
231Dic11—81no—
232Dic11—81no—
233C2×#41—21no—
234#137—22no—
235AGL(1,ℤ/8)—22no—
236#135—21no—
237#135C22×D1112yes—
238C2×Q16—111no—
239C2×Q16—221no—
240C2×Q16C22×D1111yescharacteristic
241#131—222no—
242#131—222no—
243#131—442no—
244C2×M16—111no—
245C2×M16—221no—
246C2×M16—442no—
247C2×M16C22×D1111yescharacteristic
248C4⋊Q8—221no—
249C4⋊Q8—221no—
250#125—441no—
251C22⋊Q8—21no—
252C22⋊Q8—221no—
253C22⋊Q8—441no—
254C4×Q8—221no—
255C4×Q8—221no—
256C4×Q8—441no—
257#117—441no—
258C2×C42—111no—
259Q32—22no—
260Q32—222no—
261SD32—22no—
262SD32—222no—
263M32—112no—
264M32C22×D1112yes—
265#108—112no—
266#108—221no—
267#106—111no—
268#106—221no—
269#106C22×D1111yescharacteristic
270#104—222no—
271#104—222no—
272#103—21no—
273#103—221no—
274#103—221no—
275#103—221no—
276#97—111no—
277#97—111no—
278C4×C8—111no—
279C4×C8—111no—
280C2×C11—21no—
281C2×C11—41no—
282C2×C11—82no—
283C2×C11#310911yescharacteristic
284#41—22no—
285#41—22no—
286#41—41no—
287#41—41no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—221no—
291C2×Q8—441no—
292C2×D4—21no—
293C2×D4—41no—
294C22×C4—41no—
295C22×C4—221no—
296C22×C4D4×D1111yescharacteristic
297Q16—21no—
298Q16—22no—
299Q16—222no—
300Q16—442no—
301Q16#434112yes—
302SD16—22no—
303SD16—22no—
304D8—21no—
305D8#434112yes—
306M16—22no—
307M16—222no—
308M16—222no—
309M16—442no—
310M16—442no—
311M16—441no—
312C2×C8—111no—
313C2×C8—111no—
314C2×C8—442no—
315C2×C8—442no—
316C2×C8—441no—
317C2×C8D4×D1111yescharacteristic
318C2×C8C23×D1111yescharacteristic
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—221no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C4⋊C4—441no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C22⋊C4—41no—
329C22⋊C4—441no—
330C42—111no—
331C42—111no—
332C42—221no—
333C42—441no—
334C42—441no—
335C16—22no—
336C16—222no—
337C11#3368911yescharacteristic, complemented, Sylow
338C23—41no—
339C23#6696411yescharacteristic
340Q8—22no—
341Q8—41no—
342Q8—41no—
343Q8—41no—
344Q8—441no—
345Q8—441no—
346Q8—882no—
347D4—22no—
348D4—41no—
349D4—42no—
350D4—42no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—442no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4#6696411yescharacteristic
364C2×C4C2×D4×D1111yescharacteristic
365C8—21no—
366C8—112no—
367C8—221no—
368C8—442no—
369C8C2×#434112yes—
370C22—21no—
371C22—41no—
372C22—42no—
373C22—161no—
374C22C2×#6696411yescharacteristic
375C4—21no—
376C4—42no—
377C4—81no—
378C4—81no—
379C4—222no—
380C4—441no—
381C4—881no—
382C4—881no—
383C4#1062311711yescharacteristic
384C4D11×AGL(1,ℤ/8)11yescharacteristic
385C2—21no—
386C2—41no—
387C2—82no—
388C2#1307870211yescharacteristic
subgroupG/H
centerC2#13078702
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2191C2
socleC2×C11#3109
prime radicalC11×#575C22
hypercenter#2191D11
hypocenterC11#33689
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. #13079356C2semidirect
3. #13070836C2semidirect
4. #13070833C2semidirect
5. #13070785C2semidirect
6. #13070695C2semidirect
8. #13070508C2semidirect
9. #13070504C2semidirect
10. #13070425C2semidirect
23. #10622797C22semidirect
24. #10622794C22semidirect
29. #10622468C22semidirect
30. #10622466C22semidirect
36. #10622203C22semidirect
38. #10622155C22semidirect
39. #10622151C22semidirect
40. #10622150C22semidirect
41. #10622149C22semidirect
42. #10622125C22semidirect
337. C11#33689semidirect

Maximal subgroups

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

subgroupindex
#130793562
#130775262
#130708362
#130708332
#130707852
#130706952
#130705672
#130705082
#130705042
#130704252
C11×#21912
#3368911