Finite Group Databasebeta

← #14910439

Subgroups — #14910439

Order 2816.

718 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622517C211yesmaximal, characteristic, complemented
2C2×D11×D16C211yesmaximal, characteristic, complemented
3#13080304C212yesmaximal, complemented
4#13070874C211yesmaximal, characteristic, complemented
5#13070708C211yesmaximal, characteristic, complemented
6#13070670C212yesmaximal, complemented
7#13070546C212yesmaximal, complemented
8#13070537C212yesmaximal, complemented
9#13070462C211yesmaximal, characteristic, complemented
10C16×C22⋊D11C211yesmaximal, characteristic, complemented
11C11×#2215C211yesmaximal, characteristic, complemented
12C2×D8×D11C2212yes—
13C2×#66957C2212yescomplemented
14#10623143—22no—
15C2×C11×D16C2211yescharacteristic
16C22×C11×C16C2211yescharacteristic, complemented
17C11×#466C2212yescomplemented
18#10622768C2212yescomplemented
19C2×#66891C2212yescomplemented
20C2×#66890C2212yes—
21C8×C22⋊D11C2211yescharacteristic
22#10622650—22no—
23D11×D16—24no—
24C2×Dic88C2211yescharacteristic, complemented
25#10622517—24no—
26C2×#66864C2212yescomplemented
27C2×D176C2211yescharacteristic
28C2×C16×D11C2211yescharacteristic
29#10622500C2212yes—
30#10622485C2212yescomplemented
31#10622400—22no—
32#10622389—22no—
33C11×#366C2211yescharacteristic, complemented
34C11×#357C2212yescomplemented
35C22⋊(C11⋊C16)C2211yescharacteristic, complemented
36(C2×D11)⋊C16C2211yescharacteristic
37Dic11⋊C16C2211yescharacteristic, complemented
38C16×Dic11C2211yescharacteristic, complemented
39#10622130C2212yescomplemented
40#10622129C2212yescomplemented
41C2×D4×D11—22no—
42C2×#4339—22no—
43C2×C11×D8C2312yes—
44C22×C8×C11C2311yescharacteristic
45C11×#121—22no—
46#66991—42no—
47#66990—42no—
48#66989—22no—
49C2×#4324—22no—
50C2×#4323—22no—
51C4×C22⋊D11D411yescharacteristic
52D8×D11—24no—
53D8×D11—42no—
54C2×Dic44C2312yes—
55#66957—24no—
56#66957—42no—
57C2×D88C2312yes—
58C2×#4314—22no—
59C2×C8×D11C2311yescharacteristic
60#66950—22no—
61#66946—22no—
62#66936—42no—
63C22⋊C4×D11—42no—
64C11×D16—22no—
65C2×C11×C16—22no—
66C2×C11×C16C2311yescharacteristic
67C2×C11×C16C2311yescharacteristic
68C11×#107C2312yes—
69C11×#102—22no—
70C22⋊(C11⋊C8)D411yescharacteristic
71#66891—42no—
72#66890—24no—
73(C2×D11)⋊C8D411yescharacteristic
74Dic11⋊C8D411yescharacteristic
75C8×Dic11C2311yescharacteristic
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2311yescharacteristic
78#66874—22no—
79#66873—22no—
80Dic88—22no—
81#66864—24no—
82D176D414yescomplemented
83C16×D11—22no—
84#33846—111nomaximal, Sylow
85C23×D11—42no—
86C2×D4×C11—22no—
87C2×D4×C11—42no—
88C22×C4×C11C2×D411yescharacteristic
89C2×C22⋊D11—42no—
90C2×C22⋊D11—42no—
91C2×C22⋊D11D811yescharacteristic
92D4×D11—44no—
93D4×D11—82no—
94#4339—44no—
95#4339—82no—
96C2×D44—22no—
97C2×C4×D11—42no—
98C2×C4×D11—42no—
99C2×C4×D11C2×D411yescharacteristic
100C2×Dic22—22no—
101C11×D8—22no—
102C11×D8—22no—
103C2×C8×C11—21no—
104C2×C8×C11—21no—
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2411yescharacteristic
107C11×C4⋊C4—22no—
108C11×C22⋊C4—42no—
109C22⋊Dic11—42no—
110C22⋊Dic11—42no—
111C22⋊Dic11D811yescharacteristic
112#4324—82no—
113#4323—44no—
114(C2×D11)⋊C4—42no—
115(C2×D11)⋊C4—42no—
116(C2×D11)⋊C4D811yescharacteristic
117C4⋊Dic11—42no—
118Dic11⋊C4D811yescharacteristic
119C4×Dic11C2×D411yescharacteristic
120C2×C11⋊C8C2×D411yescharacteristic
121C2×C11⋊C8C2×D411yescharacteristic
122Dic44—22no—
123Dic44—22no—
124D88—22no—
125D88C2×D414yes—
126#4314—44no—
127C8×D11—21no—
128C8×D11—21no—
129C11×C16—21no—
130C11×C16C2×D412yes—
131C11⋊C16—21no—
132C11⋊C16—21no—
133C2×#508—111no—
134C22×D16—111no—
135#3280—112no—
136#2249—111no—
137#2216—111no—
138#2215D1111yescharacteristic, complemented
139#2210—112no—
140#2187—112no—
141#2186—112no—
142C4×D16—111no—
143D4×C16—111no—
144C23×C11—42no—
145C23×C11C2×D811yescharacteristic
146C22×D11—42no—
147C22×D11—84no—
148C22×D11—84no—
149C22×D11—162no—
150C22×D11C2×D811yescharacteristic
151D4×C11—42no—
152D4×C11—42no—
153D4×C11—162no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—42no—
157C2×C4×C11C2×D811yescharacteristic
158C2×C4×C11C22×D411yescharacteristic
159C22⋊D11—22no—
160C22⋊D11—84no—
161C22⋊D11—84no—
162C2×Dic11—42no—
163C2×Dic11C2×D811yescharacteristic
164C2×Dic11C2×D811yescharacteristic
165C2×Dic11C2×D811yescharacteristic
166D44—24no—
167D44—42no—
168C4×D11—21no—
169C4×D11—21no—
170C4×D11—84no—
171C4×D11—162no—
172Dic22—42no—
173Dic22—42no—
174C8×C11—21no—
175C8×C11C22×D411yescharacteristic
176C8×C11H(5,𝔽2)11yescharacteristic
177C11⋊C8—21no—
178C11⋊C8—21no—
179C2×#135—112no—
180C22×D8—112no—
181#546—222no—
182#508—224no—
183C2×Q32—111no—
184C2×SD32—112no—
185C2×SD32—112no—
186C2×D16—112no—
187C2×D16—111no—
188C2×D16—224no—
189C2×D16C2×D1111yescharacteristic
190C22×C16—111no—
191C22×C16C2×D1111yescharacteristic, complemented
192#495—112no—
193#467—112no—
194#466C2×D1112yescomplemented
195#463—222no—
196#450—222no—
197#449—222no—
198C4×D8—112no—
199C8×D4—111no—
200#366C2×D1111yescharacteristic, complemented
201C4⋊C16—111no—
202#358—112no—
203#357—112no—
204#357C2×D1112yescomplemented
205C22⋊C16—111no—
206C22⋊C16—111no—
207C4×C16—111no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—82no—
212C22×C11—82no—
213C22×C11—82no—
214C22×C11C22×D811yescharacteristic
215C2×D11—21no—
216C2×D11—21no—
217C2×D11—44no—
218C2×D11—82no—
219C2×D11—82no—
220C2×D11—168no—
221C2×D11#50812yescomplemented
222C4×C11—21no—
223C4×C11—82no—
224C4×C11D4211yescharacteristic
225C4×C11#57611yescharacteristic
226Dic11—21no—
227Dic11—21no—
228Dic11—21no—
229Dic11—82no—
230C2×#41—222no—
231C22×D4—222no—
232#135—224no—
233#135—442no—
234C2×Q16—112no—
235C2×SD16—222no—
236C2×SD16—222no—
237C2×D8—112no—
238C2×D8—222no—
239C2×D8—224no—
240C2×D8—442no—
241C2×D8C22×D1112yes—
242C22×C8—111no—
243C22×C8C22×D1111yescharacteristic
244#124—222no—
245#123—442no—
246C22⋊Q8—222no—
247#121—22no—
248#121—442no—
249#120—442no—
250C4×D4—111no—
251C4×D4—222no—
252C2×C22⋊C4—442no—
253Q32—222no—
254SD32—224no—
255SD32—442no—
256D16—22no—
257D16—114no—
258D16—224no—
259C2×C16—22no—
260C2×C16—111no—
261C2×C16—111no—
262C2×C16—222no—
263C2×C16C22×D1111yescharacteristic
264C2×C16C22×D1111yescharacteristic
265#107C22×D1112yes—
266C4⋊C8—111no—
267#103—222no—
268#102—22no—
269#102—222no—
270C22⋊C8—111no—
271C22⋊C8—111no—
272C4×C8—111no—
273C2×C11—41no—
274C2×C11—162no—
275C2×C11D4×D811yescharacteristic
276C2×C11C2×#50811yescharacteristic
277C2×C11#341511yescharacteristic
278D11—22no—
279D11—84no—
280C24—442no—
281#41—444no—
282#41—882no—
283C2×Q8—222no—
284C2×D4—22no—
285C2×D4—42no—
286C2×D4—111no—
287C2×D4—222no—
288C2×D4—442no—
289C2×D4—444no—
290C2×D4—442no—
291C2×D4—882no—
292C22×C4—111no—
293C22×C4—442no—
294C22×C4—442no—
295C22×C4D4×D1111yescharacteristic
296Q16—222no—
297Q16—222no—
298SD16—444no—
299SD16—882no—
300D8—22no—
301D8—22no—
302D8—114no—
303D8—222no—
304D8—444no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—111no—
308C2×C8—111no—
309C2×C8—221no—
310C2×C8—221no—
311C2×C8D4×D1111yescharacteristic
312C2×C8C23×D1111yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—111no—
315C4⋊C4—442no—
316C22⋊C4—42no—
317C22⋊C4—111no—
318C22⋊C4—111no—
319C22⋊C4—442no—
320C22⋊C4—442no—
321C22⋊C4—442no—
322C22⋊C4—442no—
323C42—111no—
324C16—21no—
325C16—221no—
326C16—221no—
327C16D4×D1112yes—
328C11#3384611yescharacteristic, complemented, Sylow
329C23—42no—
330C23—111no—
331C23—442no—
332C23—884no—
333C23—884no—
334C23—1762no—
335C23D8×D1111yescharacteristic
336Q8—442no—
337Q8—442no—
338D4—42no—
339D4—42no—
340D4—162no—
341D4—222no—
342D4—224no—
343D4—442no—
344D4—884no—
345D4—884no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—111no—
350C2×C4—111no—
351C2×C4—111no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—442no—
355C2×C4—884no—
356C2×C4—1762no—
357C2×C4D8×D1111yescharacteristic
358C2×C4C2×D4×D1111yescharacteristic
359C8—21no—
360C8—221no—
361C8—221no—
362C8C2×D4×D1111yescharacteristic
363C8#6704211yescharacteristic
364C22—21no—
365C22—21no—
366C22—21no—
367C22—82no—
368C22—82no—
369C22—82no—
370C22—112no—
371C22—221no—
372C22—221no—
373C22—444no—
374C22—882no—
375C22—882no—
376C22—1768no—
377C22C2×D8×D1111yescharacteristic
378C4—21no—
379C4—82no—
380C4—221no—
381C4—221no—
382C4—221no—
383C4—882no—
384C4#1062314011yescharacteristic
385C4#1062330011yescharacteristic
386C2—41no—
387C2—162no—
388C2—222no—
389C2—884no—
390C2#1308029011yescharacteristic
391C2D11×#50811yescharacteristic
392C2#1308175311yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2215C2
socleC22×C11C22×D8
hypercenter#2215D11
hypocenterC11#33846
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2215

Complements

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

NH ≅ G/Ntype
1. C2×#10622517C2semidirect
2. C2×D11×D16C2semidirect
3. #13080304C2semidirect
4. #13070874C2semidirect
5. #13070708C2semidirect
6. #13070670C2semidirect
7. #13070546C2semidirect
8. #13070537C2semidirect
9. #13070462C2semidirect
10. C16×C22⋊D11C2semidirect
11. C11×#2215C2semidirect
13. C2×#66957C22semidirect
16. C22×C11×C16C22semidirect
17. C11×#466C22semidirect
18. #10622768C22semidirect
19. C2×#66891C22semidirect
24. C2×Dic88C22semidirect
26. C2×#66864C22semidirect
30. #10622485C22semidirect
33. C11×#366C22semidirect
34. C11×#357C22semidirect
35. C22⋊(C11⋊C16)C22semidirect
37. Dic11⋊C16C22semidirect
38. C16×Dic11C22semidirect
39. #10622130C22semidirect
40. #10622129C22semidirect
82. D176D4semidirect
138. #2215D11semidirect
191. C22×C16C2×D11semidirect
194. #466C2×D11semidirect
200. #366C2×D11semidirect
204. #357C2×D11semidirect
221. C2×D11#508semidirect
328. C11#33846semidirect

Maximal subgroups

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

subgroupindex
C2×#106225172
C2×D11×D162
#130803042
#130708742
#130707082
#130706702
#130705462
#130705372
#130704622
C16×C22⋊D112
C11×#22152
#3384611