Finite Group Databasebeta

← #14909237

Subgroups — #14909237

Order 2816.

826 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622792C211yesmaximal, characteristic, complemented
2C2×#10622760C211yesmaximal, characteristic, complemented
3C2×#10622517C211yesmaximal, characteristic, complemented
4#13079105C211yesmaximal, characteristic, complemented
5#13079097C211yesmaximal, characteristic, complemented
6#13070886C212yesmaximal, complemented
7#13070881C212yesmaximal, complemented
8#13070876C212yesmaximal, complemented
9#13070870C212yesmaximal, complemented
10#13070212C211yesmaximal, characteristic, complemented
11C22×C11×SD32C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C22×C11×D8C2211yescharacteristic
14#10623347—21no—
15C2×#66995—21no—
16#10623336—21no—
17C2×#66985—21no—
18C2×#66957C2211yescharacteristic
19C2×#66957C2211yescharacteristic
20C2×C11×SD32—24no—
21C2×C11×SD32C2212yes—
22C2×C11×SD32C2212yes—
23C22×C11×C16C2211yescharacteristic
24#10622804C2212yescomplemented
25#10622803—22no—
26#10622794C2212yescomplemented
27C2×#66893C2212yescomplemented
28#10622792—24no—
29C2×#66892C2212yescomplemented
30#10622768C2212yes—
31#10622767—22no—
32#10622764C2212yes—
33C2×#66891C2212yes—
34#10622760—24no—
35C2×#66890C2212yes—
36#10622714C2211yescharacteristic
37C2×#66876C2211yescharacteristic
38C2×Dic88C2211yescharacteristic, complemented
39#10622517—24no—
40C2×#66864C2211yescharacteristic, complemented
41C2×#66864C2211yescharacteristic, complemented
42C2×D176C2211yescharacteristic, complemented
43#10622140C2212yescomplemented
44C16×Dic11C2212yescomplemented
45C22×Q8×C11—21no—
46C22×D4×C11—21no—
47C2×#4339—21no—
48C2×#4339—21no—
49C2×C11×Q16—22no—
50C2×C11×Q16—22no—
51C2×C11×Q16—21no—
52C2×C11×Q16C2312yes—
53C2×C11×D8—22no—
54C2×C11×D8—22no—
55C2×C11×D8—21no—
56C2×C11×D8C2312yes—
57C22×C8×C11C2311yescharacteristic
58#67006—42no—
59#67000—22no—
60#66999—42no—
61#66997—22no—
62C2×#4326—22no—
63#66995—44no—
64C2×#4325—22no—
65#66993—22no—
66#66991—42no—
67#66989—22no—
68C2×#4324—22no—
69#66985—44no—
70C2×#4323—22no—
71#66982—42no—
72#66979D411yescharacteristic
73C2×#4318D411yescharacteristic
74C2×Dic44C2311yescharacteristic
75C2×Dic44C2311yescharacteristic
76#66957—22no—
77#66957—22no—
78#66957—22no—
79#66957—22no—
80C2×D88C2311yescharacteristic
81C2×D88C2311yescharacteristic
82C2×#4314—21no—
83C2×#4314—21no—
84C11×SD32—24no—
85C11×SD32—24no—
86C2×C11×C16D414yescomplemented
87C2×C11×C16C2311yescharacteristic
88C2×C11×C16C2311yescharacteristic
89#66893—24no—
90#66892—24no—
91#66891—24no—
92#66890—24no—
93#66879D412yes—
94C8×Dic11C2312yes—
95#66876D414yescomplemented
96C2×C11⋊C16C2312yes—
97Dic88—22no—
98#66864—22no—
99#66864—22no—
100D176—22no—
101#33722—111nomaximal, Sylow
102C24×C11—41no—
103C2×Q8×C11—22no—
104C2×Q8×C11—41no—
105C2×Q8×C11—42no—
106C2×Q8×C11—42no—
107C2×D4×C11—22no—
108C2×D4×C11—42no—
109C2×D4×C11—42no—
110C2×D4×C11—41no—
111C22×C4×C11—41no—
112C22×C4×C11C2×D411yescharacteristic
113C2×C22⋊D11—44no—
114C2×C22⋊D11—41no—
115C2×C22⋊D11—41no—
116#4339—42no—
117#4339—42no—
118#4339—42no—
119#4339—42no—
120C2×D44—21no—
121C2×D44—21no—
122C2×C4×D11—41no—
123C2×C4×D11—41no—
124C2×Dic22—21no—
125C2×Dic22—21no—
126C11×Q16—22no—
127C11×Q16—22no—
128C11×Q16—42no—
129C11×D8—22no—
130C11×D8—22no—
131C11×D8—42no—
132C2×C8×C11C2×D412yes—
133C2×C8×C11C2×D412yes—
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2411yescharacteristic
136C22⋊Dic11—44no—
137C22⋊Dic11D812yes—
138#4326—44no—
139#4325—44no—
140#4324—44no—
141#4323—44no—
142(C2×D11)⋊C4—44no—
143C4⋊Dic11D812yes—
144Dic11⋊C4—44no—
145C4×Dic11C2×D412yes—
146#4318D814yes—
147C2×C11⋊C8C2×D412yes—
148Dic44—21no—
149Dic44—21no—
150Dic44—21no—
151Dic44—21no—
152D88—21no—
153D88—21no—
154D88—21no—
155D88—21no—
156#4314—42no—
157#4314—42no—
158C11×C16C2×D412yes—
159C11×C16C2×D412yes—
160C11⋊C16C2×D414yes—
161C2×#510—111no—
162C2×#509—111no—
163C2×#508—111no—
164C22×SD32D1111yescharacteristic, complemented
165#3156—111no—
166#3155—111no—
167#2251—112no—
168#2250—112no—
169#2249—112no—
170#2248—112no—
171#2108—111no—
172C23×C11—42no—
173C23×C11—82no—
174C23×C11—162no—
175C23×C11C2×D811yescharacteristic
176C22×D11—41no—
177C22×D11—41no—
178Q8×C11—42no—
179Q8×C11—42no—
180Q8×C11—82no—
181D4×C11—42no—
182D4×C11—42no—
183D4×C11—82no—
184C2×C4×C11—42no—
185C2×C4×C11—82no—
186C2×C4×C11#12712yes—
187C2×C4×C11C2×D812yes—
188C2×C4×C11C2×D811yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C22⋊D11—82no—
191C22⋊D11—82no—
192C22⋊D11—164no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11C2×D814yes—
196D44—41no—
197D44—41no—
198D44—41no—
199D44—41no—
200C4×D11—82no—
201C4×D11—82no—
202Dic22—41no—
203Dic22—41no—
204Dic22—41no—
205Dic22—41no—
206C8×C11#12712yes—
207C8×C11C22×D411yescharacteristic
208C8×C11C22×D411yescharacteristic
209C11⋊C8C2×D814yes—
210C2×#137—221no—
211C2×AGL(1,ℤ/8)—221no—
212C2×#135—111no—
213C2×#135—111no—
214C22×Q16C2×D1111yescharacteristic
215C22×D8C2×D1111yescharacteristic
216#536—221no—
217#535—221no—
218#510—224no—
219#509—224no—
220#508—224no—
221C2×Q32—112no—
222C2×Q32—111no—
223C2×SD32—24no—
224C2×SD32—112no—
225C2×SD32—112no—
226C2×SD32—111no—
227C2×SD32—111no—
228C2×SD32C2×D1112yes—
229C2×SD32C2×D1112yes—
230C2×D16—112no—
231C2×D16—111no—
232C2×M32—111no—
233C22×C16C2×D1111yescharacteristic
234#497—222no—
235#496—222no—
236#495—112no—
237#495—112no—
238#494—112no—
239#493—112no—
240#405—111no—
241#346—112no—
242C4×C16—112no—
243C22×C11—22no—
244C22×C11—82no—
245C22×C11—84no—
246C22×C11—164no—
247C22×C11#49312yes—
248C22×C11C22×D811yescharacteristic
249C2×D11—81no—
250C2×D11—81no—
251C2×D11—82no—
252C2×D11—82no—
253C4×C11—82no—
254C4×C11#49312yes—
255C4×C11C2×#12711yescharacteristic
256C4×C11C22×D811yescharacteristic
257Dic11—24no—
258Dic11—81no—
259Dic11—81no—
260C2×#41—221no—
261C2×#41—221no—
262C22×Q8—21no—
263C22×D4—21no—
264#137—444no—
265AGL(1,ℤ/8)—444no—
266#135—222no—
267#135—222no—
268#135—222no—
269#135—222no—
270C2×Q16—22no—
271C2×Q16—21no—
272C2×Q16—22no—
273C2×Q16—111no—
274C2×Q16—111no—
275C2×Q16—222no—
276C2×Q16C22×D1112yes—
277C2×SD16—222no—
278C2×SD16—222no—
279C2×SD16—221no—
280C2×SD16—221no—
281C2×D8—22no—
282C2×D8—21no—
283C2×D8—22no—
284C2×D8—111no—
285C2×D8—111no—
286C2×D8—222no—
287C2×D8C22×D1112yes—
288C2×M16—111no—
289C22×C8C22×D1111yescharacteristic
290C4⋊Q8—222no—
291#127—222no—
292#124—222no—
293#124—222no—
294#123—442no—
295C22⋊Q8—442no—
296#121—442no—
297#120—442no—
298#117—111no—
299Q32—224no—
300Q32—222no—
301SD32—24no—
302SD32—24no—
303SD32—224no—
304SD32—224no—
305SD32—222no—
306SD32—222no—
307D16—224no—
308D16—222no—
309M32—114no—
310C2×C16—112no—
311C2×C16C22⋊D1114yescomplemented
312C2×C16C22×D1111yescharacteristic
313C2×C16C22×D1111yescharacteristic
314#97—112no—
315C4×C8—112no—
316C2×C11—22no—
317C2×C11—162no—
318C2×C11C2×#49311yescharacteristic
319C2×C11#341612yes—
320D11—161no—
321D11—161no—
322C24—41no—
323#41—442no—
324#41—442no—
325#41—442no—
326#41—442no—
327C2×Q8—22no—
328C2×Q8—41no—
329C2×Q8—42no—
330C2×Q8—42no—
331C2×Q8—221no—
332C2×Q8—221no—
333C2×D4—22no—
334C2×D4—42no—
335C2×D4—41no—
336C2×D4—42no—
337C2×D4—221no—
338C2×D4—221no—
339C2×D4—444no—
340C2×D4—441no—
341C2×D4—441no—
342C22×C4—41no—
343C22×C4—441no—
344C22×C4—441no—
345C22×C4D4×D1111yescharacteristic
346Q16—22no—
347Q16—22no—
348Q16—42no—
349Q16—221no—
350Q16—221no—
351Q16—221no—
352Q16—221no—
353Q16—444no—
354SD16—444no—
355SD16—444no—
356SD16—442no—
357SD16—442no—
358D8—22no—
359D8—22no—
360D8—42no—
361D8—221no—
362D8—221no—
363D8—221no—
364D8—221no—
365D8—444no—
366M16—114no—
367C2×C8—112no—
368C2×C8D4×D1111yescharacteristic
369C2×C8D4×D1112yes—
370C2×C8C2×C22⋊D1112yes—
371C2×C8C23×D1111yescharacteristic
372C4⋊C4—112no—
373C4⋊C4—444no—
374C22⋊C4—112no—
375C22⋊C4—444no—
376C22⋊C4—444no—
377C42—112no—
378C16—114no—
379C16C2×C22⋊D1112yes—
380C16C2×C22⋊D1112yes—
381C11#3372211yescharacteristic, complemented, Sylow
382C23—42no—
383C23—82no—
384C23—162no—
385C23—441no—
386C23—441no—
387C23D8×D1111yescharacteristic
388Q8—42no—
389Q8—42no—
390Q8—82no—
391Q8—441no—
392Q8—441no—
393Q8—441no—
394Q8—441no—
395D4—42no—
396D4—42no—
397D4—82no—
398D4—441no—
399D4—441no—
400D4—441no—
401D4—441no—
402D4—882no—
403D4—882no—
404D4—1764no—
405C2×C4—42no—
406C2×C4—82no—
407C2×C4—114no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—882no—
411C2×C4—882no—
412C2×C4D8×D1111yescharacteristic
413C2×C4D8×D1112yes—
414C2×C4#6699312yes—
415C2×C4C2×D4×D1111yescharacteristic
416C8—114no—
417C8#6699312yes—
418C8C2×D4×D1111yescharacteristic
419C8C22×C22⋊D1111yescharacteristic
420C22—22no—
421C22—84no—
422C22—82no—
423C22—164no—
424C22—882no—
425C22—882no—
426C22—881no—
427C22—881no—
428C22#1062276412yes—
429C22C2×D8×D1111yescharacteristic
430C4—82no—
431C4—224no—
432C4—881no—
433C4—881no—
434C4#1062276412yes—
435C4C2×D8×D1111yescharacteristic
436C4C2×#6699311yescharacteristic
437C2—22no—
438C2—162no—
439C2—1761no—
440C2—1761no—
441C2C2×#1062276411yescharacteristic
442C2#1308175812yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC22×C11×SD32C2
socleC22×C11C22×D8
hypercenterC22×SD32D11
hypocenterC11#33722
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#10622792C2semidirect
2. C2×#10622760C2semidirect
3. C2×#10622517C2semidirect
4. #13079105C2semidirect
5. #13079097C2semidirect
6. #13070886C2semidirect
7. #13070881C2semidirect
8. #13070876C2semidirect
9. #13070870C2semidirect
10. #13070212C2semidirect
11. C22×C11×SD32C2semidirect
24. #10622804C22semidirect
26. #10622794C22semidirect
27. C2×#66893C22semidirect
29. C2×#66892C22semidirect
38. C2×Dic88C22semidirect
40. C2×#66864C22semidirect
41. C2×#66864C22semidirect
42. C2×D176C22semidirect
43. #10622140C22semidirect
44. C16×Dic11C22semidirect
86. C2×C11×C16D4semidirect
95. #66876D4semidirect
164. C22×SD32D11semidirect
311. C2×C16C22⋊D11semidirect
381. C11#33722semidirect

Maximal subgroups

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

subgroupindex
C2×#106227922
C2×#106227602
C2×#106225172
#130791052
#130790972
#130708862
#130708812
#130708762
#130708702
#130702122
C22×C11×SD322
#3372211