Finite Group Databasebeta

← #14908085

Subgroups — #14908085

Order 2816.

748 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 748 conjugacy classes of subgroups — too many to draw. Only its 171 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
1C2×#10622760C211yesmaximal, characteristic, complemented
2#13079097C211yesmaximal, characteristic, complemented
3#13077468C211yesmaximal, characteristic, complemented
4#13070669C214yesmaximal, complemented
5#13070649C214yesmaximal, complemented
6#13070374C211yesmaximal, characteristic, complemented
7#13070332C211yesmaximal, characteristic, complemented
8#13070324C211yesmaximal, characteristic, complemented
9C22×C11×D16C211yesmaximal, characteristic, complemented
10C22×C11×D8C2211yescharacteristic
11C22×C11×D8C2211yescharacteristic
12#10623336—21no—
13#10623329—21no—
14C2×#66985—21no—
15C2×#66957C2211yescharacteristic
16C2×C11×D16—24no—
17C2×C11×D16C2214yes—
18C22×C11×C16C2211yescharacteristic
19#10622828—21no—
20#10622768C2212yescomplemented
21#10622767—22no—
22#10622765—22no—
23#10622764C2212yescomplemented
24D8×Dic11C2214yescomplemented
25C2×#66891C2212yescomplemented
26#10622760—24no—
27C2×#66890C2212yescomplemented
28#10622719C2211yescharacteristic
29#10622714C2211yescharacteristic
30C2×#66876C2211yescharacteristic
31#10622200C2214yescomplemented
32#10622147C2212yescomplemented
33#10622141C2212yescomplemented
34Dic11⋊C16C2214yescomplemented
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C2×#4339—21no—
38C2×C11×D8—21no—
39C2×C11×D8—22no—
40C2×C11×D8—21no—
41C2×C11×D8—22no—
42C2×C11×D8—22no—
43C2×C11×D8D414yescomplemented
44C2×C11×D8C2312yes—
45C2×C11×D8C2312yes—
46C22×C8×C11C2311yescharacteristic
47#67006—42no—
48C2×C22⋊Dic11—42no—
49#66993—22no—
50#66991—42no—
51#66989—22no—
52D4×Dic11—24no—
53D4×Dic11—42no—
54C2×#4324—22no—
55#66985—44no—
56C2×#4323—22no—
57#66979—21no—
58#66979D411yescharacteristic
59C2×#4318D411yescharacteristic
60C2×Dic44C2311yescharacteristic
61#66957—22no—
62#66957—22no—
63C2×D88C2311yescharacteristic
64C2×#4314—21no—
65C11×D16—28no—
66C2×C11×C16—22no—
67C2×C11×C16C2312yes—
68#66896—24no—
69#66891—24no—
70#66890—24no—
71#66882C2312yes—
72#66881—21no—
73#66879D412yes—
74C8×Dic11C2312yes—
75#66876—22no—
76C2×C11⋊C16C2312yes—
77#33585—111nomaximal, Sylow
78C24×C11—41no—
79C24×C11—41no—
80C2×D4×C11—24no—
81C2×D4×C11—22no—
82C2×D4×C11—22no—
83C2×D4×C11—42no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—42no—
87C2×D4×C11—42no—
88C22×C4×C11C2×D411yescharacteristic
89C2×C22⋊D11—44no—
90C2×C22⋊D11—41no—
91C22×Dic11—44no—
92#4339—42no—
93#4339—42no—
94C2×D44—21no—
95C2×C4×D11—41no—
96C2×Dic22—21no—
97C11×D8—24no—
98C11×D8—22no—
99C11×D8—22no—
100C11×D8—22no—
101C11×D8—42no—
102C11×D8C2×D414yes—
103C2×C8×C11C2×D412yes—
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11#4112yes—
106C2×C8×C11C2411yescharacteristic
107C22⋊Dic11—44no—
108C22⋊Dic11—44no—
109C22⋊Dic11—41no—
110C22⋊Dic11D812yes—
111#4324—44no—
112#4323—44no—
113C4⋊Dic11—22no—
114C4⋊Dic11D812yes—
115C4×Dic11—41no—
116C4×Dic11C2×D412yes—
117#4318—22no—
118C2×C11⋊C8C2×D412yes—
119Dic44—21no—
120Dic44—21no—
121D88—21no—
122D88—21no—
123#4314—42no—
124C11×C16—22no—
125C11⋊C16—22no—
126C2×#509—111no—
127C22×D16D1111yescharacteristic, complemented
128#3155—111no—
129#2948—111no—
130#2210—114no—
131#2206—114no—
132#2151—111no—
133#2140—111no—
134#2138—111no—
135C23×C11—42no—
136C23×C11—44no—
137C23×C11—42no—
138C23×C11—82no—
139C23×C11—162no—
140C23×C11—162no—
141C23×C11C2×D811yescharacteristic
142C22×D11—41no—
143D4×C11—24no—
144D4×C11—42no—
145D4×C11—42no—
146D4×C11—42no—
147D4×C11—44no—
148D4×C11—82no—
149C2×C4×C11#12112yes—
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)12yes—
152C2×C4×C11C22×D411yescharacteristic
153C22⋊D11—82no—
154C22⋊D11—164no—
155C2×Dic11—42no—
156C2×Dic11—41no—
157C2×Dic11—164no—
158C2×Dic11C2×D814yes—
159D44—41no—
160D44—41no—
161C4×D11—82no—
162Dic22—41no—
163Dic22—41no—
164C8×C11#12112yes—
165C8×C11C22×D411yescharacteristic
166C8×C11C2×#4111yescharacteristic
167C11⋊C8—22no—
168C2×AGL(1,ℤ/8)—221no—
169C2×#135—111no—
170C22×D8C2×D1111yescharacteristic
171C22×D8C2×D1111yescharacteristic
172#535—221no—
173#518—221no—
174#509—224no—
175C2×SD32—112no—
176C2×D16—24no—
177C2×D16—112no—
178C2×D16C2×D1114yes—
179C2×M32—111no—
180C22×C16C2×D1111yescharacteristic
181#496—222no—
182#495—112no—
183#493—112no—
184#442—222no—
185C4×D8—114no—
186#427—111no—
187#418—221no—
188#405—111no—
189C4⋊C16—114no—
190#358—112no—
191#357—114no—
192#357—112no—
193C22×C11—22no—
194C22×C11—44no—
195C22×C11—84no—
196C22×C11—84no—
197C22×C11—82no—
198C22×C11—164no—
199C22×C11—164no—
200C22×C11#45912yes—
201C22×C11C22×D811yescharacteristic
202C2×D11—82no—
203C2×D11—81no—
204C4×C11#45912yes—
205C4×C11C2×#12111yescharacteristic
206C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
207Dic11—24no—
208Dic11—82no—
209Dic11—81no—
210C2×#41—221no—
211C22×D4—21no—
212C22×D4—21no—
213AGL(1,ℤ/8)—444no—
214#135—222no—
215#135—222no—
216C2×Q16—111no—
217C2×SD16—222no—
218C2×SD16—221no—
219C2×D8—21no—
220C2×D8—21no—
221C2×D8—22no—
222C2×D8—22no—
223C2×D8—22no—
224C2×D8—111no—
225C2×D8—222no—
226C2×D8C22⋊D1114yescomplemented
227C2×D8C22×D1112yes—
228C2×D8C22×D1112yes—
229C2×M16—111no—
230C22×C8C22×D1111yescharacteristic
231#127—222no—
232#124—222no—
233#121—442no—
234#120—442no—
235C4×D4—224no—
236C4×D4—442no—
237#117—111no—
238#117—221no—
239C2×C22⋊C4—442no—
240SD32—224no—
241D16—28no—
242D16—224no—
243M32—222no—
244C2×C16—22no—
245C2×C16—112no—
246C2×C16C22×D1112yes—
247#107—112no—
248#106—221no—
249#102—224no—
250#97—112no—
251C4×C8—112no—
252C2×C11—22no—
253C2×C11—84no—
254C2×C11—162no—
255C2×C11C2×#45911yescharacteristic
256C2×C11#341512yes—
257D11—161no—
258C24—41no—
259C24—41no—
260#41—442no—
261#41—442no—
262C2×Q8—221no—
263C2×D4—24no—
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—42no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—221no—
272C2×D4—444no—
273C2×D4—441no—
274C22×C4—444no—
275C22×C4—441no—
276C22×C4D4×D1111yescharacteristic
277Q16—221no—
278Q16—221no—
279SD16—444no—
280SD16—442no—
281D8—24no—
282D8—22no—
283D8—22no—
284D8—22no—
285D8—42no—
286D8—221no—
287D8—221no—
288D8—444no—
289D8C2×C22⋊D1114yes—
290M16—222no—
291C2×C8—112no—
292C2×C8D4×D1111yescharacteristic
293C2×C8#434112yes—
294C2×C8C2×C22⋊D1112yes—
295C2×C8C23×D1111yescharacteristic
296C4⋊C4—112no—
297C4⋊C4—222no—
298C22⋊C4—112no—
299C22⋊C4—444no—
300C22⋊C4—444no—
301C22⋊C4—441no—
302C42—112no—
303C42—441no—
304C16—22no—
305C16—222no—
306C11#3358511yescharacteristic, complemented, Sylow
307C23—42no—
308C23—44no—
309C23—42no—
310C23—82no—
311C23—162no—
312C23—162no—
313C23—441no—
314C23D8×D1111yescharacteristic
315Q8—441no—
316Q8—441no—
317D4—24no—
318D4—44no—
319D4—42no—
320D4—42no—
321D4—42no—
322D4—82no—
323D4—441no—
324D4—441no—
325D4—882no—
326D4—1764no—
327C2×C4—114no—
328C2×C4—442no—
329C2×C4—441no—
330C2×C4—882no—
331C2×C4—1764no—
332C2×C4D8×D1111yescharacteristic
333C2×C4#6696412yes—
334C2×C4#6699212yes—
335C2×C4C2×D4×D1111yescharacteristic
336C8—222no—
337C8#6699212yes—
338C8C2×#434111yescharacteristic
339C8C22×C22⋊D1111yescharacteristic
340C22—22no—
341C22—44no—
342C22—84no—
343C22—82no—
344C22—84no—
345C22—164no—
346C22—164no—
347C22—881no—
348C22—882no—
349C22#1062276312yes—
350C22C2×D8×D1111yescharacteristic
351C4—224no—
352C4—881no—
353C4—882no—
354C4#1062276312yes—
355C4C2×#6696411yescharacteristic
356C4C2×#6699211yescharacteristic
357C2—22no—
358C2—84no—
359C2—162no—
360C2—1761no—
361C2C2×#1062276311yescharacteristic
362C2#1308175312yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC22×C11×D16C2
socleC22×C11C22×D8
hypercenterC22×D16D11
hypocenterC11#33585
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×D16

Complements

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

NH ≅ G/Ntype
1. C2×#10622760C2semidirect
2. #13079097C2semidirect
3. #13077468C2semidirect
4. #13070669C2semidirect
5. #13070649C2semidirect
6. #13070374C2semidirect
7. #13070332C2semidirect
8. #13070324C2semidirect
9. C22×C11×D16C2semidirect
20. #10622768C22semidirect
23. #10622764C22semidirect
24. D8×Dic11C22semidirect
25. C2×#66891C22semidirect
27. C2×#66890C22semidirect
31. #10622200C22semidirect
32. #10622147C22semidirect
33. #10622141C22semidirect
34. Dic11⋊C16C22semidirect
43. C2×C11×D8D4semidirect
127. C22×D16D11semidirect
226. C2×D8C22⋊D11semidirect
306. C11#33585semidirect

Maximal subgroups

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

subgroupindex
C2×#106227602
#130790972
#130774682
#130706692
#130706492
#130703742
#130703322
#130703242
C22×C11×D162
#3358511