Finite Group Databasebeta

← #14909033

Subgroups — #14909033

Order 2816.

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

normal subgroups only

This group has 524 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#13079234C211yesmaximal, characteristic, complemented
2#13077519C211yesmaximal, characteristic, complemented
3#13070833C211yesmaximal, characteristic, complemented
4#13070831C211yesmaximal, characteristic, complemented
5#13070785C212yesmaximal, complemented
6#13070687C212yesmaximal, complemented
7#13070562C211yesmaximal, characteristic
8#13070511C212yesmaximal, complemented
9#13070508C212yesmaximal, complemented
10#13070429C211yesmaximal, characteristic, complemented
11C11×#2191C211yesmaximal, characteristic, complemented
12C11×#575C2211yescharacteristic
13C2×#67001—21no—
14#10623174—21no—
15C11×#510C2212yes—
16C11×#470C2211yescharacteristic
17#10622849—21no—
18#10622810—21no—
19#10622810C2212yes—
20#10622809—21no—
21#10622809C2212yes—
22#10622806C2212yes—
23#10622804C2211yescharacteristic, complemented
24#10622797C2211yescharacteristic, complemented
25#10622748C2211yescharacteristic
26#10622738C2211yescharacteristic
27#10622735C2211yescharacteristic
28#10622661—21no—
29#10622482C2211yescharacteristic, complemented
30#10622468C2211yescharacteristic, complemented
31#10622408—21no—
32#10622401—21no—
33C11×#360C2212yes—
34C11×#349C2211yescharacteristic
35#10622204C2212yes—
36#10622203C2212yescomplemented
37#10622191C2211yescharacteristic
38#10622154C2212yescomplemented
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—
55#67000—21no—
56Q8×Dic11—21no—
57C2×#4325—21no—
58#66983—21no—
59#66979D411yescharacteristic
60C2×#4318—21no—
61C2×#4318—41no—
62C22×C11⋊C8—41no—
63C22×C11⋊C8D411yescharacteristic
64C2×D88C2311yescharacteristic
65#66951—41no—
66#66950—41no—
67#66946—21no—
68#66941—21no—
69#66938—41no—
70#66936—41no—
71C11×Q32—22no—
72C11×SD32—22no—
73C11×M32C2312yes—
74C11×#106C2311yescharacteristic
75C11×#103—21no—
76#66901—22no—
77#66901—22no—
78#66899—21no—
79#66892—22no—
80#66890—22no—
81#66885—21no—
82#66883—21no—
83#66883C2312yes—
84#66881C2311yescharacteristic
85#66879D411yescharacteristic
86#66879C2311yescharacteristic
87C8×Dic11D411yescharacteristic
88C8×Dic11C2311yescharacteristic
89#66876C2312yes—
90#66873—21no—
91#66872—21no—
92#33691—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×C22⋊D11—41no—
104C2×D44—21no—
105C2×C4×D11—41no—
106C2×Dic22—41no—
107C11×Q16—21no—
108C11×Q16—22no—
109C11×Q16#4112yes—
110C11×SD16—22no—
111C11×SD16—22no—
112C11×D8—21no—
113C11×D8#4112yes—
114C11×M16—22no—
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2411yescharacteristic
117C11×C4⋊C4—21no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—41no—
120C22⋊Dic11—21no—
121#4325—41no—
122#4325—41no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129C4⋊Dic11—41no—
130Dic11⋊C4—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
145D88—22no—
146C11×C16—22no—
147C11⋊C16—22no—
148#3173—111no—
149#2955—111no—
150#2239—111no—
151#2238—111no—
152#2230—112no—
153#2212—112no—
154#2191D1111yescharacteristic, complemented
155#2190—111no—
156AGL(1,ℤ/16)—112no—
157#2180—112no—
158#2166—111no—
159C23×C11—41no—
160C23×C11AGL(1,ℤ/8)11yescharacteristic
161C22×D11—41no—
162Q8×C11—22no—
163Q8×C11—41no—
164Q8×C11—41no—
165Q8×C11—41no—
166D4×C11—22no—
167D4×C11—41no—
168D4×C11—42no—
169D4×C11—42no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C22⋊D11—161no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—41no—
183D44—41no—
184D44—41no—
185C4×D11—161no—
186Dic22—161no—
187C8×C11—21no—
188C8×C11C2×#4112yes—
189C11⋊C8—21no—
190C11⋊C8—42no—
191C11⋊C8AGL(1,ℤ/8)11yescharacteristic
192C11⋊C8AGL(1,ℤ/8)11yescharacteristic
193#575C2×D1111yescharacteristic
194C2×#131—221no—
195#542—221no—
196#510C2×D1112yes—
197#509—112no—
198#498—111no—
199#495—111no—
200#489—221no—
201#470C2×D1111yescharacteristic
202#469—111no—
203#465—221no—
204#444—112no—
205#444—221no—
206#443—112no—
207#443—221no—
208#442—111no—
209#441—111no—
210C4×SD16—221no—
211#430—111no—
212#421—221no—
213#405—111no—
214#365—112no—
215#365—112no—
216#364—112no—
217#362—112no—
218#361—112no—
219#360—112no—
220#360C2×D1112yes—
221#349—111no—
222#349C2×D1111yescharacteristic
223#347—112no—
224C22×C11—21no—
225C22×C11—41no—
226C22×C11—42no—
227C22×C11—82no—
228C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
229C2×D11—81no—
230C2×D11—81no—
231C2×D11—81no—
232C4×C11—21no—
233C4×C11—42no—
234C4×C11—81no—
235C4×C11—81no—
236C4×C11#52511yescharacteristic
237C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
238Dic11—41no—
239Dic11—41no—
240Dic11—81no—
241C2×#41—21no—
242#137—22no—
243AGL(1,ℤ/8)—22no—
244#135—21no—
245#135C22×D1112yes—
246C2×Q16C22×D1111yescharacteristic
247C2×SD16—221no—
248C2×D8—111no—
249#131—222no—
250#131—222no—
251#131—441no—
252#131—441no—
253C2×M16—221no—
254C2×M16—441no—
255C2×M16C22×D1111yescharacteristic
256C22×C8—111no—
257C22×C8—441no—
258C4⋊Q8—221no—
259#126—441no—
260#124—221no—
261#124—441no—
262#123—441no—
263C22⋊Q8—21no—
264C22⋊Q8—441no—
265#121—221no—
266C4×Q8—221no—
267C4×D4—221no—
268#117—111no—
269Q32—22no—
270SD32—22no—
271SD32—222no—
272D16—222no—
273M32—112no—
274M32C22×D1112yes—
275#108—112no—
276#108—221no—
277#106—111no—
278#106—221no—
279#106C22×D1111yescharacteristic
280#104—222no—
281#104—222no—
282#103—21no—
283#103—221no—
284#102—221no—
285#102—221no—
286#97—111no—
287#97—111no—
288C4×C8—111no—
289C4×C8—111no—
290C2×C11—21no—
291C2×C11—41no—
292C2×C11—82no—
293C2×C11#310911yescharacteristic
294D11—161no—
295#41—22no—
296#41—22no—
297#41—41no—
298#41—41no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8—441no—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4—221no—
305C2×D4—441no—
306C22×C4—41no—
307C22×C4—441no—
308C22×C4D4×D1111yescharacteristic
309Q16—21no—
310Q16—22no—
311Q16#434112yes—
312SD16—22no—
313SD16—22no—
314SD16—441no—
315SD16—441no—
316D8—21no—
317D8—222no—
318D8#434112yes—
319M16—22no—
320M16—222no—
321M16—442no—
322M16—442no—
323M16—441no—
324C2×C8—111no—
325C2×C8—111no—
326C2×C8—221no—
327C2×C8—221no—
328C2×C8—442no—
329C2×C8—442no—
330C2×C8—441no—
331C2×C8D4×D1111yescharacteristic
332C2×C8C23×D1111yescharacteristic
333C4⋊C4—21no—
334C4⋊C4—41no—
335C4⋊C4—221no—
336C4⋊C4—221no—
337C4⋊C4—441no—
338C4⋊C4—441no—
339C22⋊C4—41no—
340C22⋊C4—221no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C42—111no—
346C42—111no—
347C42—441no—
348C16—22no—
349C16—222no—
350C11#3369111yescharacteristic, complemented, Sylow
351C23—41no—
352C23—441no—
353C23#6696411yescharacteristic
354Q8—22no—
355Q8—41no—
356Q8—41no—
357Q8—41no—
358Q8—1761no—
359D4—22no—
360D4—41no—
361D4—42no—
362D4—42no—
363D4—441no—
364D4—441no—
365D4—1761no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—441no—
376C2×C4—1761no—
377C2×C4#6696411yescharacteristic
378C2×C4C2×D4×D1111yescharacteristic
379C8—21no—
380C8—111no—
381C8—111no—
382C8—221no—
383C8—442no—
384C8C2×#434112yes—
385C22—21no—
386C22—41no—
387C22—42no—
388C22—82no—
389C22—881no—
390C22—881no—
391C22—881no—
392C22C2×#6696411yescharacteristic
393C4—21no—
394C4—42no—
395C4—81no—
396C4—81no—
397C4—441no—
398C4—441no—
399C4—881no—
400C4#1062311711yescharacteristic
401C4D11×AGL(1,ℤ/8)11yescharacteristic
402C2—21no—
403C2—41no—
404C2—82no—
405C2—1761no—
406C2#1307870211yescharacteristic
subgroupG/H
centerC2#13078702
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2191C2
socleC2×C11#3109
prime radical#13070562C2
hypercenter#2191D11
hypocenterC11#33691
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. #13079234C2semidirect
2. #13077519C2semidirect
3. #13070833C2semidirect
4. #13070831C2semidirect
5. #13070785C2semidirect
6. #13070687C2semidirect
8. #13070511C2semidirect
9. #13070508C2semidirect
10. #13070429C2semidirect
11. C11×#2191C2semidirect
23. #10622804C22semidirect
24. #10622797C22semidirect
29. #10622482C22semidirect
30. #10622468C22semidirect
36. #10622203C22semidirect
38. #10622154C22semidirect
39. #10622151C22semidirect
40. #10622150C22semidirect
41. #10622149C22semidirect
42. #10622125C22semidirect
154. #2191D11semidirect
350. C11#33691semidirect

Maximal subgroups

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

subgroupindex
#130792342
#130775192
#130708332
#130708312
#130707852
#130706872
#130705622
#130705112
#130705082
#130704292
C11×#21912
#3369111