Finite Group Databasebeta

← #14737745

Subgroups — #14737745

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622307C211yesmaximal, characteristic, complemented
2#13078103C211yesmaximal, characteristic, complemented
3#13078096C211yesmaximal, characteristic
4#13068060C214yesmaximal, complemented
5#13068053C214yesmaximal, complemented
6#13067375C211yesmaximal, characteristic, complemented
7#13067287C211yesmaximal, characteristic, complemented
8#13067283C211yesmaximal, characteristic, complemented
9C8×C11×#41C211yesmaximal, characteristic, complemented
10C4×C11×#41C2211yescharacteristic
11C2×#67004—21no—
12C2×#67002—21no—
13C2×#66927C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C8×Q8×C11C2212yescomplemented
16C8×D4×C11—22no—
17C8×D4×C11C2212yescomplemented
18C11×#431—21no—
19C11×#431C2211yescharacteristic
20C2×C4×C8×C11—21no—
21C2×C4×C8×C11C2211yescharacteristic
22C2×#66885—22no—
23#10622644—21no—
24#10622644C2212yescomplemented
25#10622640—21no—
26#10622640C2212yes—
27#10622632—21no—
28#10622632C2212yescomplemented
29#10622628—21no—
30#10622628C2212yes—
31#10622617—21no—
32#10622614—21no—
33#10622537C2211yescharacteristic
34#10622537C2211yescharacteristic
35#10622307—21no—
36#10622307—21no—
37#10622307C2214yes—
38#10622124C2214yescomplemented
39#10622123C2214yes—
40#10622096C2214yescomplemented
41C2×C11×#41D411yescharacteristic
42C22×D44—21no—
43C22×D44—21no—
44C22×D44—21no—
45C22×Dic22—21no—
46C22×C8×C11—22no—
47C22×C8×C11D412yes—
48C4×Q8×C11D411yescharacteristic
49C4×Q8×C11C2311yescharacteristic
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11D411yescharacteristic
53C4×D4×C11C2311yescharacteristic
54C11×#117—21no—
55C11×#117D411yescharacteristic
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58#67004—44no—
59#67002—44no—
60C2×#4326—22no—
61C2×#4325—22no—
62C2×#4324—22no—
63C2×#4323—22no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×#4318—21no—
67C2×#4318—21no—
68#66927—21no—
69#66927—21no—
70#66927—21no—
71#66927C2312yes—
72#66922—21no—
73#66922—21no—
74#66922—21no—
75#66922C2312yes—
76C11×C4⋊C8—22no—
77C11×C4⋊C8C2312yes—
78C11×C22⋊C8—21no—
79C11×C22⋊C8—22no—
80C4×C8×C11—22no—
81C4×C8×C11—21no—
82C4×C8×C11D411yescharacteristic
83C4×C8×C11D411yescharacteristic
84C4×C8×C11C2312yes—
85#66885—24no—
86#66885—24no—
87#66874—22no—
88#66874—22no—
89#66873—22no—
90#66873—22no—
91C4⋊(C11⋊C8)—21no—
92C4⋊(C11⋊C8)—21no—
93C4⋊(C11⋊C8)C2312yes—
94C4⋊(C11⋊C8)C2312yes—
95#19276—111nomaximal, Sylow
96C23×D11—41no—
97C11×#41—22no—
98C11×#41D814yes—
99C2×Q8×C11C2×D411yescharacteristic
100C2×D4×C11—21no—
101C2×D4×C11C2×D411yescharacteristic
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C22×Dic11—41no—
109C2×D44—22no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—44no—
113C2×D44—41no—
114C2×D44—41no—
115C2×D44—41no—
116C2×D44—42no—
117C2×D44—42no—
118C2×D44—82no—
119C2×Dic22—22no—
120C2×Dic22—41no—
121C2×Dic22—42no—
122C2×Dic22—42no—
123C2×C8×C11—22no—
124C2×C8×C11—42no—
125C2×C8×C11—44no—
126C2×C8×C11C2×D412yes—
127C2×C8×C11C2×D412yes—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4C2×D411yescharacteristic
131C11×C4⋊C4C2×D411yescharacteristic
132C11×C22⋊C4—21no—
133C11×C22⋊C4—21no—
134C11×C22⋊C4—21no—
135C42×C11—21no—
136C42×C11—21no—
137C42×C11—21no—
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C42×C11#4111yescharacteristic
141C42×C11C2411yescharacteristic
142#4326—44no—
143#4325—44no—
144#4324—44no—
145#4323—44no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—41no—
149C4⋊Dic11—41no—
150#4318—42no—
151#4318—42no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×#486—111no—
155#3039—111no—
156#3038—111no—
157C8×#41D1111yescharacteristic, complemented
158#1682—114no—
159#1681—114no—
160#1567—111no—
161#1546—111no—
162#1545—111no—
163C23×C11—21no—
164C23×C11#12111yescharacteristic
165C22×D11—42no—
166C22×D11—82no—
167C22×D11—82no—
168C22×D11—82no—
169Q8×C11—21no—
170Q8×C11C2×D812yes—
171D4×C11—24no—
172D4×C11—21no—
173D4×C11C2×D812yes—
174C2×C4×C11—21no—
175C2×C4×C11—22no—
176C2×C4×C11—24no—
177C2×C4×C11—22no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11C2×D812yes—
186C2×C4×C11#13512yes—
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C2×Dic11—42no—
191C2×Dic11—82no—
192D44—42no—
193D44—42no—
194D44—44no—
195D44—82no—
196D44—82no—
197D44—82no—
198D44—82no—
199Dic22—42no—
200Dic22—42no—
201Dic22—82no—
202C8×C11—22no—
203C8×C11—22no—
204C8×C11—42no—
205C11⋊C8—42no—
206C11⋊C8—42no—
207C2×#137—221no—
208C2×AGL(1,ℤ/8)—221no—
209C2×C4⋊Q8—111no—
210C2×#127—111no—
211C4×#41C2×D1111yescharacteristic
212#486—114no—
213#486—221no—
214#486—221no—
215#462—112no—
216#462—221no—
217#461—112no—
218#461—221no—
219#460—112no—
220#460—221no—
221#459—112no—
222#459—221no—
223C8×Q8C2×D1112yescomplemented
224C8×D4—22no—
225C8×D4C2×D1112yescomplemented
226#431—21no—
227#431C2×D1111yescharacteristic
228#423—111no—
229#423—111no—
230#419—221no—
231#418—221no—
232C2×#102—222no—
233C2×C4×C8—21no—
234C2×C4×C8C2×D1111yescharacteristic
235#335—114no—
236#332—114no—
237#331—114no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—22no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11#46612yes—
244C22×C11C2×#12111yescharacteristic
245C2×D11—82no—
246C2×D11—82no—
247C2×D11—82no—
248C2×D11—164no—
249C4×C11—21no—
250C4×C11—22no—
251C4×C11—21no—
252C4×C11—41no—
253C4×C11—41no—
254C4×C11#46612yes—
255C4×C11#47112yes—
256C4×C11C22×D811yescharacteristic
257C4×C11C2×#13511yescharacteristic
258C4×C11#57512yes—
259Dic11—82no—
260C2×#41D4411yescharacteristic
261C22×Q8—221no—
262C22×D4—221no—
263C22×D4—221no—
264C22×D4—221no—
265#137—444no—
266AGL(1,ℤ/8)—444no—
267C2×Q16—222no—
268C2×SD16—222no—
269C2×SD16—222no—
270C2×D8—222no—
271C2×M16—221no—
272C2×M16—221no—
273C22×C8—22no—
274C22×C8C22⋊D1112yes—
275C4⋊Q8—112no—
276C4⋊Q8—221no—
277C4⋊Q8—221no—
278C4⋊Q8—221no—
279#127—112no—
280#127—221no—
281#127—221no—
282#127—221no—
283C4×Q8D4411yescharacteristic
284C4×Q8C22×D1111yescharacteristic
285C4×D4—21no—
286C4×D4—21no—
287C4×D4D4411yescharacteristic
288C4×D4C22×D1111yescharacteristic
289#117—21no—
290#117D4411yescharacteristic
291C2×C4⋊C4—221no—
292C2×C4⋊C4—221no—
293C2×C42—21no—
294C2×C42C22×D1111yescharacteristic
295C4⋊C8—22no—
296C4⋊C8—112no—
297C4⋊C8—112no—
298C4⋊C8—221no—
299C4⋊C8—221no—
300C4⋊C8C22×D1112yes—
301#103—222no—
302#103—222no—
303#102—224no—
304#102—224no—
305#102—222no—
306#102—222no—
307C22⋊C8—21no—
308C22⋊C8—22no—
309C4×C8—22no—
310C4×C8—21no—
311C4×C8C22⋊D1111yescharacteristic
312C4×C8C22⋊D1111yescharacteristic
313C4×C8C22×D1112yes—
314C2×C11—22no—
315C2×C11—42no—
316C2×C11#304011yescharacteristic
317C2×C11C2×#46611yescharacteristic
318C2×C11C2×#47111yescharacteristic
319D11—162no—
320C24—441no—
321#41—22no—
322#41D8814yes—
323C2×Q8—222no—
324C2×Q8—441no—
325C2×Q8—442no—
326C2×Q8—442no—
327C2×Q8C2×D4411yescharacteristic
328C2×D4—21no—
329C2×D4—222no—
330C2×D4—222no—
331C2×D4—222no—
332C2×D4—444no—
333C2×D4—442no—
334C2×D4—442no—
335C2×D4—441no—
336C2×D4—441no—
337C2×D4—441no—
338C2×D4—882no—
339C2×D4C2×D4411yescharacteristic
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—441no—
344C22×C4C2×D4411yescharacteristic
345C22×C4#433911yescharacteristic
346C22×C4C2×C22⋊D1111yescharacteristic
347Q16—444no—
348SD16—444no—
349SD16—444no—
350D8—444no—
351M16—442no—
352M16—442no—
353C2×C8—22no—
354C2×C8—42no—
355C2×C8—44no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8C2×C22⋊D1112yes—
359C2×C8C2×C22⋊D1112yes—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—222no—
363C4⋊C4—222no—
364C4⋊C4—441no—
365C4⋊C4—441no—
366C4⋊C4C2×D4411yescharacteristic
367C4⋊C4C2×D4411yescharacteristic
368C22⋊C4—21no—
369C22⋊C4—21no—
370C22⋊C4—21no—
371C42—21no—
372C42—21no—
373C42—21no—
374C42C2×D4411yescharacteristic
375C42#433911yescharacteristic
376C42C2×C22⋊D1111yescharacteristic
377C42C23×D1111yescharacteristic
378C11#1927611yescharacteristic, complemented, Sylow
379C23—21no—
380C23—442no—
381C23—882no—
382C23—882no—
383C23—882no—
384C23#6698311yescharacteristic
385Q8—21no—
386Q8—442no—
387Q8—442no—
388Q8—882no—
389Q8C2×D8812yes—
390D4—24no—
391D4—21no—
392D4—442no—
393D4—442no—
394D4—444no—
395D4—882no—
396D4—882no—
397D4—882no—
398D4—882no—
399D4C2×D8812yes—
400C2×C4—21no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—442no—
409C2×C4—882no—
410C2×C4C2×D8812yes—
411C2×C4#6695712yes—
412C2×C4#6698311yescharacteristic
413C2×C4#6698311yescharacteristic
414C2×C4#6698311yescharacteristic
415C2×C4C22×D4411yescharacteristic
416C2×C4C2×#433911yescharacteristic
417C2×C4C22×C22⋊D1111yescharacteristic
418C8—22no—
419C8—22no—
420C8—42no—
421C8—442no—
422C8—442no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—41no—
427C22—41no—
428C22—882no—
429C22—882no—
430C22—882no—
431C22—1764no—
432C22#1062272812yes—
433C22C2×#6698311yescharacteristic
434C4—21no—
435C4—21no—
436C4—22no—
437C4—41no—
438C4—41no—
439C4—882no—
440C4#1062272812yes—
441C4#1062275412yes—
442C4C22×D8811yescharacteristic
443C4C2×#6695711yescharacteristic
444C4#1062335312yes—
445C2—22no—
446C2—42no—
447C2—1762no—
448C2#1307811011yescharacteristic
449C2C2×#1062272811yescharacteristic
450C2C2×#1062275411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC8×C11×#41C2
socleC22×C11C2×#121
prime radical#13078096C2
hypercenterC8×#41D11
hypocenterC11#19276
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
1. C2×#10622307C2semidirect
2. #13078103C2semidirect
4. #13068060C2semidirect
5. #13068053C2semidirect
6. #13067375C2semidirect
7. #13067287C2semidirect
8. #13067283C2semidirect
9. C8×C11×#41C2semidirect
15. C8×Q8×C11C22semidirect
17. C8×D4×C11C22semidirect
24. #10622644C22semidirect
28. #10622632C22semidirect
38. #10622124C22semidirect
40. #10622096C22semidirect
157. C8×#41D11semidirect
223. C8×Q8C2×D11semidirect
225. C8×D4C2×D11semidirect
378. C11#19276semidirect

Maximal subgroups

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

subgroupindex
C2×#106223072
#130781032
#130780962
#130680602
#130680532
#130673752
#130672872
#130672832
C8×C11×#412
#1927611