Finite Group Databasebeta

← #14739067

Subgroups — #14739067

Order 2816.

740 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079536C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic, complemented
3C2×#10622640C211yesmaximal, characteristic, complemented
4#13068060C214yesmaximal, complemented
5#13067976C214yesmaximal, complemented
6#13067391C211yesmaximal, characteristic, complemented
7#13067283C211yesmaximal, characteristic, complemented
8#13067263C211yesmaximal, characteristic, complemented
9C11×#2982C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66995—21no—
12C22×#4325—21no—
13#10623008C2211yescharacteristic
14C2×#66927C2211yescharacteristic
15C8×Q8×C11—22no—
16C8×Q8×C11C2214yescomplemented
17C11×#431—22no—
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20#10622644C2212yescomplemented
21#10622641—22no—
22#10622640—22no—
23#10622640C2214yes—
24#10622640C2212yescomplemented
25#10622579—21no—
26C2×#66873—21no—
27#10622537C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29#10622456—22no—
30#10622345—22no—
31#10622308C2212yes—
32#10622307C2212yes—
33#10622124C2212yescomplemented
34#10622123C2214yes—
35#10622123C2212yescomplemented
36#10622096C2214yescomplemented
37C22×Q8×C11D411yescharacteristic
38C2×#4339—21no—
39C22×D44—21no—
40C22×D44—21no—
41C22×D44—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11D412yes—
45C4×Q8×C11C2312yes—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C42×C11—21no—
49C2×C42×C11C2311yescharacteristic
50C2×#4326—22no—
51#66995—44no—
52C2×#4325—24no—
53C2×#4325—22no—
54C2×#4325—44no—
55#66983—21no—
56#66983—21no—
57C2×#4318—21no—
58C22×C11⋊C8—21no—
59C2×D88—24no—
60#66928—21no—
61#66927—21no—
62#66927—21no—
63#66927—21no—
64#66927C2312yes—
65#66927C2311yescharacteristic
66C4×D44—21no—
67C4×D44—21no—
68#66922C2311yescharacteristic
69C11×C4⋊C8—24no—
70C11×C4⋊C8D412yes—
71C11×C4⋊C8C2312yes—
72C11×C22⋊C8—21no—
73C11×C22⋊C8D412yes—
74C4×C8×C11—24no—
75C4×C8×C11—21no—
76C4×C8×C11C2312yes—
77#66885—24no—
78#66874—22no—
79#66873—24no—
80#66873—22no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)—21no—
83C4⋊(C11⋊C8)C2312yes—
84C4⋊(C11⋊C8)C2312yes—
85#19398—111nomaximal, Sylow
86C23×D11—41no—
87C2×Q8×C11—21no—
88C2×Q8×C11—22no—
89C2×Q8×C11D814yescomplemented
90C2×Q8×C11C2×D412yes—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C2×C22⋊D11—41no—
97#4339—42no—
98#4339—42no—
99C2×D44—22no—
100C2×D44—21no—
101C2×D44—22no—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44—22no—
105C2×D44—41no—
106C2×D44—41no—
107C2×D44—41no—
108C2×D44—42no—
109C2×D44—42no—
110C2×D44—82no—
111C2×D44—82no—
112C2×C4×D11—41no—
113C2×Dic22—21no—
114C2×C8×C11—22no—
115C2×C8×C11C2×D414yes—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4C2×D412yes—
120C42×C11—22no—
121C42×C11—22no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4111yescharacteristic
125C42×C11C2411yescharacteristic
126#4326—44no—
127#4325—48no—
128#4325—44no—
129(C2×D11)⋊C4—41no—
130(C2×D11)⋊C4—41no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133#4318—42no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—42no—
137D88—84no—
138#3205—111no—
139#3037—111no—
140C2×#460—111no—
141#2982D1111yescharacteristic, complemented
142#1682—114no—
143#1668—114no—
144#1571—111no—
145#1545—111no—
146#1540—111no—
147C23×C11#12111yescharacteristic
148C22×D11—41no—
149C22×D11—42no—
150C22×D11—82no—
151C22×D11—82no—
152C22×D11—82no—
153Q8×C11—22no—
154Q8×C11—24no—
155Q8×C11C2×D814yes—
156C2×C4×C11—22no—
157C2×C4×C11—24no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—41no—
161C2×C4×C11—81no—
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11C2×D812yes—
166C2×C4×C11#13512yes—
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C2×#4111yescharacteristic
170C22⋊D11—82no—
171C2×Dic11—41no—
172D44—42no—
173D44—41no—
174D44—42no—
175D44—41no—
176D44—42no—
177D44—44no—
178D44—81no—
179D44—82no—
180D44—82no—
181D44—82no—
182D44—82no—
183C4×D11—82no—
184Dic22—41no—
185Dic22—41no—
186C8×C11—24no—
187C8×C11—42no—
188C11⋊C8—42no—
189C11⋊C8—42no—
190C2×#137—221no—
191C22×SD16—221no—
192#532—111no—
193C2×#127—111no—
194C2×C4×Q8C2×D1111yescharacteristic
195#493—112no—
196#486—112no—
197#464—222no—
198#462—112no—
199#460—112no—
200#460—114no—
201#460—222no—
202#459—222no—
203#447—222no—
204C8×Q8—22no—
205C8×Q8C2×D1114yescomplemented
206#431—22no—
207#431C2×D1111yescharacteristic
208#431C2×D1111yescharacteristic
209#423—111no—
210C2×C4⋊C8—111no—
211#417—221no—
212C2×#102—221no—
213#335—114no—
214#332—112no—
215#331—112no—
216#331—114no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11#46612yes—
220C22×C11C2×#12111yescharacteristic
221C2×D11—82no—
222C2×D11—81no—
223C2×D11—82no—
224C2×D11—81no—
225C2×D11—82no—
226C2×D11—81no—
227C2×D11—164no—
228C4×C11—21no—
229C4×C11—24no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—42no—
233C4×C11#46612yes—
234C4×C11C22×D811yescharacteristic
235C4×C11C2×#13511yescharacteristic
236C4×C11#57712yes—
237Dic11—81no—
238C2×#41—221no—
239C22×Q8D4411yescharacteristic
240C22×D4—221no—
241C22×D4—221no—
242C22×D4—221no—
243#137—444no—
244C2×Q16—222no—
245C2×SD16—224no—
246C2×SD16—222no—
247C2×SD16—444no—
248C2×D8—224no—
249C2×M16—221no—
250C22×C8—221no—
251C4⋊Q8—111no—
252#127—112no—
253#127—111no—
254#127—221no—
255#127—221no—
256#127—221no—
257#124—221no—
258#121—221no—
259#121—221no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8D4412yes—
263C4×Q8C22×D1112yes—
264C4×D4—221no—
265C4×D4—221no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4D4411yescharacteristic
268C2×C42—21no—
269C2×C42C22×D1111yescharacteristic
270C4⋊C8—24no—
271C4⋊C8—112no—
272C4⋊C8—112no—
273C4⋊C8—221no—
274C4⋊C8—221no—
275C4⋊C8C22⋊D1112yes—
276C4⋊C8C22×D1112yes—
277#103—222no—
278#102—224no—
279#102—224no—
280#102—222no—
281C22⋊C8—21no—
282C22⋊C8C22⋊D1112yes—
283C4×C8—24no—
284C4×C8—21no—
285C4×C8C22×D1112yes—
286C2×C11—22no—
287C2×C11#304311yescharacteristic
288C2×C11C2×#46611yescharacteristic
289C2×C11#306811yescharacteristic
290D11—161no—
291D11—162no—
292C24—441no—
293#41—442no—
294#41—442no—
295C2×Q8—22no—
296C2×Q8—21no—
297C2×Q8—221no—
298C2×Q8D8814yescomplemented
299C2×Q8C2×D4412yes—
300C2×D4—221no—
301C2×D4—222no—
302C2×D4—221no—
303C2×D4—222no—
304C2×D4—222no—
305C2×D4—221no—
306C2×D4—441no—
307C2×D4—442no—
308C2×D4—442no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4—882no—
313C2×D4—882no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—441no—
317C22×C4C2×D4411yescharacteristic
318C22×C4#433911yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320Q16—444no—
321SD16—448no—
322SD16—444no—
323D8—884no—
324M16—442no—
325C2×C8—22no—
326C2×C8—222no—
327C2×C8—222no—
328C2×C8—442no—
329C2×C8C2×C22⋊D1114yes—
330C4⋊C4—22no—
331C4⋊C4—21no—
332C4⋊C4—22no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C4⋊C4C2×D4412yes—
336C22⋊C4—441no—
337C22⋊C4—441no—
338C42—22no—
339C42—22no—
340C42C2×D4411yescharacteristic
341C42#433911yescharacteristic
342C42C2×C22⋊D1111yescharacteristic
343C42C23×D1111yescharacteristic
344C11#1939811yescharacteristic, complemented, Sylow
345C23—441no—
346C23—442no—
347C23—882no—
348C23—882no—
349C23—882no—
350C23#6698311yescharacteristic
351Q8—24no—
352Q8—22no—
353Q8—441no—
354Q8—441no—
355Q8C2×D8814yes—
356D4—442no—
357D4—441no—
358D4—442no—
359D4—441no—
360D4—442no—
361D4—444no—
362D4—882no—
363D4—881no—
364D4—882no—
365D4—882no—
366D4—882no—
367D4—882no—
368C2×C4—24no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—441no—
375C2×C4—882no—
376C2×C4C2×D8812yes—
377C2×C4#6695712yes—
378C2×C4#6698311yescharacteristic
379C2×C4#6698311yescharacteristic
380C2×C4#6698311yescharacteristic
381C2×C4C22×D4411yescharacteristic
382C2×C4C2×#433911yescharacteristic
383C2×C4C22×C22⋊D1111yescharacteristic
384C8—24no—
385C8—42no—
386C8—442no—
387C8—442no—
388C22—21no—
389C22—21no—
390C22—882no—
391C22—881no—
392C22—882no—
393C22—881no—
394C22—881no—
395C22—882no—
396C22—1764no—
397C22#1062272812yes—
398C22C2×#6698311yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—24no—
403C4—42no—
404C4—881no—
405C4#1062272812yes—
406C4C22×D8811yescharacteristic
407C4C2×#6695711yescharacteristic
408C4#1062336812yes—
409C2—22no—
410C2—1762no—
411C2—1761no—
412C2#1307813711yescharacteristic
413C2C2×#1062272811yescharacteristic
414C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2982C2
socleC22×C11C2×#121
prime radical#13079536C2
hypercenter#2982D11
hypocenterC11#19398
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. #13078088C2semidirect
3. C2×#10622640C2semidirect
4. #13068060C2semidirect
5. #13067976C2semidirect
6. #13067391C2semidirect
7. #13067283C2semidirect
8. #13067263C2semidirect
9. C11×#2982C2semidirect
16. C8×Q8×C11C22semidirect
20. #10622644C22semidirect
24. #10622640C22semidirect
33. #10622124C22semidirect
35. #10622123C22semidirect
36. #10622096C22semidirect
89. C2×Q8×C11D8semidirect
141. #2982D11semidirect
205. C8×Q8C2×D11semidirect
298. C2×Q8D88semidirect
344. C11#19398semidirect

Maximal subgroups

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

subgroupindex
#130795362
#130780882
C2×#106226402
#130680602
#130679762
#130673912
#130672832
#130672632
C11×#29822
#1939811