Finite Group Databasebeta

← #14909032

Subgroups — #14909032

Order 2816.

524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079233C211yesmaximal, characteristic, complemented
2#13070835C211yesmaximal, characteristic, complemented
3#13070830C211yesmaximal, characteristic, complemented
4#13070787C212yesmaximal, complemented
5#13070685C212yesmaximal, complemented
6#13070567C211yesmaximal, characteristic, complemented
7#13070562C211yesmaximal, characteristic
8#13070514C212yesmaximal, complemented
9#13070507C212yesmaximal, complemented
10#13070432C211yesmaximal, characteristic, complemented
11C11×#2955C211yesmaximal, characteristic, complemented
12C11×#575C2211yescharacteristic
13C2×C11×#131—21no—
14#10623065—21no—
15C11×#444—21no—
16C11×#444C2212yes—
17C11×#443—21no—
18C11×#443C2212yes—
19C11×#430C2211yescharacteristic
20C11×#421—21no—
21C11×#405C2211yescharacteristic
22#10622808C2212yes—
23#10622806C2212yes—
24#10622750C2211yescharacteristic
25#10622748C2211yescharacteristic
26#10622727—21no—
27#10622329C2211yescharacteristic, complemented
28#10622327—21no—
29#10622324C2211yescharacteristic, complemented
30#10622309C2211yescharacteristic, complemented
31C4×#4314—21no—
32#10622293C2211yescharacteristic, complemented
33#10622204C2212yes—
34#10622204C2212yes—
35#10622191C2211yescharacteristic
36#10622191C2211yescharacteristic
37#10622134C2212yescomplemented
38#10622133C2212yescomplemented
39#10622132C2212yescomplemented
40#10622132C2212yescomplemented
41#10622104C2212yescomplemented
42#10622101C2212yescomplemented
43C2×C11×#41—21no—
44C11×#137—22no—
45C11×AGL(1,ℤ/8)—22no—
46C11×#135—21no—
47C11×#135C2312yes—
48C11×#131—22no—
49C11×#131—22no—
50C11×#131—41no—
51C11×#131—41no—
52C2×C11×M16—21no—
53C2×C11×M16—41no—
54C2×C11×M16C2311yescharacteristic
55C22×C8×C11—41no—
56C22×C8×C11D411yescharacteristic
57C11×#117D411yescharacteristic
58#66983—21no—
59#66977—21no—
60C2×Dic44C2311yescharacteristic
61C2×D88C2311yescharacteristic
62C2×#4314—21no—
63#66951—41no—
64#66949—41no—
65#66938—41no—
66#66936—41no—
67#66928—21no—
68C4×D44—21no—
69#66922—21no—
70C4×Dic22—21no—
71C11×#108—21no—
72C11×#108C2312yes—
73C11×#104—22no—
74C11×#104—22no—
75C11×#97D411yescharacteristic
76C11×#97C2311yescharacteristic
77C4×C8×C11D411yescharacteristic
78C4×C8×C11C2311yescharacteristic
79#66893—22no—
80#66892—22no—
81#66891—22no—
82#66890—22no—
83#66885—21no—
84#66885—21no—
85#66881—21no—
86#66881C2311yescharacteristic
87#66881C2311yescharacteristic
88#66880—21no—
89#66880—21no—
90#66876C2312yes—
91#66876C2312yes—
92#33691—111nomaximal, Sylow
93C11×#41—22no—
94C11×#41—22no—
95C11×#41—41no—
96C11×#41—41no—
97C2×Q8×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—41no—
103C2×D44—21no—
104C2×C4×D11—41no—
105C2×Dic22—21no—
106C2×Dic22—41no—
107C11×Q16—21no—
108C11×Q16#4112yes—
109C11×SD16—22no—
110C11×SD16—22no—
111C11×D8—21no—
112C11×D8#4112yes—
113C11×M16—22no—
114C11×M16—22no—
115C11×M16—41no—
116C11×M16—42no—
117C11×M16—42no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—41no—
121C2×C8×C11—42no—
122C2×C8×C11—42no—
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2411yescharacteristic
127C11×C4⋊C4—21no—
128C11×C22⋊C4—21no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C22⋊Dic11—41no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—41no—
139Dic11⋊C4—41no—
140Dic11⋊C4—41no—
141C4×Dic11—41no—
142Dic44—22no—
143D88—22no—
144#4314—41no—
145#4314—41no—
146C11⋊C16—22no—
147C11⋊C16—22no—
148#3173—111no—
149#2955D1111yescharacteristic, complemented
150#2239—111no—
151#2238—111no—
152#2230—112no—
153#2212—112no—
154#2191—111no—
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—
164D4×C11—22no—
165D4×C11—41no—
166D4×C11—42no—
167D4×C11—42no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C22⋊D11—161no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181D44—41no—
182D44—41no—
183C4×D11—161no—
184Dic22—41no—
185Dic22—41no—
186Dic22—161no—
187C8×C11—21no—
188C8×C11—21no—
189C8×C11—42no—
190C8×C11AGL(1,ℤ/8)11yescharacteristic
191C8×C11AGL(1,ℤ/8)11yescharacteristic
192C8×C11C2×#4112yes—
193#575C2×D1111yescharacteristic
194C2×#131—21no—
195#542—221no—
196#510—112no—
197#509—112no—
198#498—111no—
199#495—111no—
200#489—221no—
201#470—111no—
202#469—111no—
203#465—221no—
204#444—21no—
205#444C2×D1112yes—
206#443—21no—
207#443C2×D1112yes—
208#442—111no—
209#441—111no—
210C4×SD16—221no—
211#430C2×D1111yescharacteristic
212#421—21no—
213#405C2×D1111yescharacteristic
214#365—112no—
215#365—112no—
216#364—112no—
217#362—112no—
218#361—112no—
219#360—112no—
220#360—112no—
221#349—111no—
222#349—111no—
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—41no—
234C4×C11—41no—
235C4×C11—42no—
236C4×C11#52511yescharacteristic
237C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
238Dic11—81no—
239Dic11—81no—
240Dic11—81no—
241C2×#41—21no—
242#137—22no—
243AGL(1,ℤ/8)—22no—
244#135—21no—
245#135C22×D1112yes—
246C2×Q16—111no—
247C2×SD16—221no—
248C2×D8—111no—
249#131—22no—
250#131—22no—
251#131—41no—
252#131—41no—
253C2×M16—21no—
254C2×M16—41no—
255C2×M16C22×D1111yescharacteristic
256C22×C8—41no—
257C22×C8C22⋊D1111yescharacteristic
258C4⋊Q8—221no—
259#126—441no—
260#124—221no—
261#124—441no—
262#123—441no—
263C22⋊Q8—221no—
264C22⋊Q8—441no—
265#121—221no—
266C4×Q8—221no—
267C4×D4—221no—
268#117C22⋊D1111yescharacteristic
269Q32—222no—
270SD32—222no—
271SD32—222no—
272D16—222no—
273M32—112no—
274M32—112no—
275#108—21no—
276#108C22×D1112yes—
277#106—111no—
278#106—111no—
279#106—221no—
280#104—22no—
281#104—22no—
282#103—221no—
283#103—221no—
284#102—221no—
285#102—221no—
286#97C22⋊D1111yescharacteristic
287#97C22×D1111yescharacteristic
288C4×C8C22⋊D1111yescharacteristic
289C4×C8C22×D1111yescharacteristic
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—221no—
301C2×Q8—441no—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4—221no—
305C2×D4—441no—
306C22×C4—41no—
307C22×C4—441no—
308C22×C4C2×C22⋊D1111yescharacteristic
309Q16—21no—
310Q16—222no—
311Q16#433912yes—
312SD16—22no—
313SD16—22no—
314SD16—441no—
315SD16—441no—
316D8—21no—
317D8—222no—
318D8#433912yes—
319M16—22no—
320M16—22no—
321M16—42no—
322M16—41no—
323M16—42no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—42no—
327C2×C8—41no—
328C2×C8—42no—
329C2×C8C2×C22⋊D1111yescharacteristic
330C2×C8C2×C22⋊D1111yescharacteristic
331C2×C8C2×C22⋊D1111yescharacteristic
332C2×C8C23×D1111yescharacteristic
333C4⋊C4—21no—
334C4⋊C4—221no—
335C4⋊C4—221no—
336C4⋊C4—441no—
337C4⋊C4—441no—
338C4⋊C4—441no—
339C22⋊C4—21no—
340C22⋊C4—441no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C42—441no—
346C42C2×C22⋊D1111yescharacteristic
347C42C2×C22⋊D1111yescharacteristic
348C16—222no—
349C16—222no—
350C11#3369111yescharacteristic, complemented, Sylow
351C23—41no—
352C23—441no—
353C23#6700211yescharacteristic
354Q8—22no—
355Q8—41no—
356Q8—441no—
357Q8—441no—
358Q8—1761no—
359D4—22no—
360D4—41no—
361D4—42no—
362D4—42no—
363D4—441no—
364D4—441no—
365D4—1761no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—1761no—
377C2×C4#6700211yescharacteristic
378C2×C4C22×C22⋊D1111yescharacteristic
379C8—21no—
380C8—21no—
381C8—42no—
382C8#6698511yescharacteristic
383C8#6698511yescharacteristic
384C8C2×#433912yes—
385C22—21no—
386C22—41no—
387C22—42no—
388C22—82no—
389C22—881no—
390C22—881no—
391C22—881no—
392C22C2×#6700211yescharacteristic
393C4—21no—
394C4—41no—
395C4—41no—
396C4—42no—
397C4—881no—
398C4—881no—
399C4—881no—
400C4#1062332211yescharacteristic
401C4C2×#6698511yescharacteristic
402C2—21no—
403C2—41no—
404C2—82no—
405C2—1761no—
406C2#1307870711yescharacteristic
subgroupG/H
centerC2#13078707
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2955C2
socleC2×C11#3109
prime radical#13070562C2
hypercenter#2955D11
hypocenterC11#33691
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2955

Complements

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

NH ≅ G/Ntype
1. #13079233C2semidirect
2. #13070835C2semidirect
3. #13070830C2semidirect
4. #13070787C2semidirect
5. #13070685C2semidirect
6. #13070567C2semidirect
8. #13070514C2semidirect
9. #13070507C2semidirect
10. #13070432C2semidirect
11. C11×#2955C2semidirect
27. #10622329C22semidirect
29. #10622324C22semidirect
30. #10622309C22semidirect
32. #10622293C22semidirect
37. #10622134C22semidirect
38. #10622133C22semidirect
39. #10622132C22semidirect
40. #10622132C22semidirect
41. #10622104C22semidirect
42. #10622101C22semidirect
149. #2955D11semidirect
350. C11#33691semidirect

Maximal subgroups

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

subgroupindex
#130792332
#130708352
#130708302
#130707872
#130706852
#130705672
#130705622
#130705142
#130705072
#130704322
C11×#29552
#3369111