Finite Group Databasebeta

← #14908311

Subgroups — #14908311

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622521C211yesmaximal, characteristic, complemented
2#13078286C211yesmaximal, characteristic, complemented
3#13078264C211yesmaximal, characteristic, complemented
4#13070729C212yesmaximal, complemented
5#13070719C212yesmaximal, complemented
6#13070712C212yesmaximal, complemented
7#13070702C212yesmaximal, complemented
8#13070404C211yesmaximal, characteristic, complemented
9#13070324C211yesmaximal, characteristic, complemented
10C2×#10622147C211yesmaximal, characteristic, complemented
11C2×C11×#504C211yesmaximal, characteristic, complemented
12C2×C11×#131C2211yescharacteristic
13#10623364—21no—
14#10623361—21no—
15C2×#66957C2211yescharacteristic
16C22×D88C2211yescharacteristic
17C11×#504—24no—
18C2×C11×M32C2211yescharacteristic
19C2×C11×M32C2212yescomplemented
20C22×C11×C16C2211yescharacteristic
21C22×C11×C16C2212yescomplemented
22#10622748—22no—
23#10622747—22no—
24#10622746—21no—
25#10622744—21no—
26#10622729C2212yescomplemented
27#10622728C2212yes—
28#10622728C2212yes—
29#10622728C2212yescomplemented
30#10622719C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32#10622521—24no—
33C2×#66864C2212yes—
34C2×D176C2212yes—
35#10622147C2212yes—
36#10622147C2212yes—
37#10622147C2211yescharacteristic, complemented
38#10622147C2211yescharacteristic, complemented
39#10622143C2212yescomplemented
40#10622142C2212yescomplemented
41#10622141C2211yescharacteristic, complemented
42#10622141C2211yescharacteristic, complemented
43C2×C11×#41D411yescharacteristic
44C2×#4339—21no—
45C22×D44—21no—
46C11×#131—22no—
47C11×#131—22no—
48C2×C11×M16D411yescharacteristic
49C2×C11×M16D412yes—
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52#67000—41no—
53#66999—41no—
54#66993—41no—
55#66992—42no—
56#66991—41no—
57#66990—42no—
58#66983—22no—
59#66983—22no—
60#66983—22no—
61#66979—21no—
62C2×C4⋊Dic11—21no—
63#66977—22no—
64C2×Dic44C2311yescharacteristic
65#66957—22no—
66#66957—22no—
67C2×D88—22no—
68C2×D88—22no—
69C2×D88—21no—
70C2×D88C2312yes—
71C2×D88C2311yescharacteristic
72C2×#4314—21no—
73C11×M32—24no—
74C11×M32D414yescomplemented
75C2×C11×C16—22no—
76C2×C11×C16—24no—
77C2×C11×C16C2311yescharacteristic
78C2×C11×C16C2311yescharacteristic
79C2×C11×C16C2312yes—
80#66885—22no—
81#66885—22no—
82#66885—22no—
83#66882—21no—
84#66882C2311yescharacteristic
85#66882C2311yescharacteristic
86#66882C2312yes—
87#66881—21no—
88#66880—22no—
89#66864—24no—
90D176—24no—
91#33612—111nomaximal, Sylow
92C23×D11—41no—
93C11×#41—22no—
94C11×#41—22no—
95C2×Q8×C11D811yescharacteristic
96C2×D4×C11D812yes—
97C2×D4×C11D811yescharacteristic
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C2×C22⋊D11—41no—
101C2×C22⋊D11—42no—
102C2×C22⋊D11—42no—
103C2×C22⋊D11—42no—
104C22×Dic11—41no—
105#4339—42no—
106#4339—42no—
107C2×D44—21no—
108C2×D44—22no—
109C2×D44—42no—
110C2×D44—41no—
111C2×D44—42no—
112C2×C4×D11—41no—
113C2×Dic22—21no—
114C11×M16—24no—
115C11×M16—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11C2×D412yes—
119C2×C8×C11C2×D412yes—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11#4112yes—
122C2×C8×C11C2411yescharacteristic
123C22⋊Dic11—42no—
124C22⋊Dic11—41no—
125(C2×D11)⋊C4—42no—
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—42no—
128C4⋊Dic11—22no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C4⋊Dic11—41no—
132Dic11⋊C4—42no—
133C4×Dic11—41no—
134Dic44—21no—
135Dic44—21no—
136D88—21no—
137D88—22no—
138D88—22no—
139D88—21no—
140D88—42no—
141#4314—42no—
142C11×C16—21no—
143C11×C16—21no—
144C11×C16C2×D414yes—
145C2×#509—111no—
146C2×#504D1111yescharacteristic, complemented
147#3061—111no—
148#3058—111no—
149#2220—112no—
150#2218—112no—
151#2217—112no—
152#2215—112no—
153#2159—111no—
154#2138—111no—
155C2×#357—111no—
156C23×C11C2×D812yes—
157C23×C11C2×D811yescharacteristic
158C22×D11—41no—
159C22×D11—42no—
160C22×D11—82no—
161C22×D11—161no—
162C22×D11—161no—
163Q8×C11—22no—
164D4×C11—24no—
165D4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11#12112yes—
169C2×C4×C11C2×D812yes—
170C2×C4×C11C2×D811yescharacteristic
171C2×C4×C11#13512yes—
172C2×C4×C11C22×D411yescharacteristic
173C22⋊D11—82no—
174C22⋊D11—162no—
175C22⋊D11—162no—
176C22⋊D11—162no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—42no—
181C2×Dic11—161no—
182D44—41no—
183D44—42no—
184D44—42no—
185D44—41no—
186D44—82no—
187C4×D11—82no—
188Dic22—41no—
189Dic22—41no—
190C8×C11—22no—
191C8×C11#12112yes—
192C8×C11C22×D411yescharacteristic
193C8×C11C2×#4111yescharacteristic
194C2×#135—111no—
195C22×D8—111no—
196C2×#131C2×D1111yescharacteristic
197#537—221no—
198#535—221no—
199#509—224no—
200C2×SD32—112no—
201C2×D16—112no—
202#504—24no—
203C2×M32C2×D1111yescharacteristic
204C2×M32C2×D1112yescomplemented
205C22×C16C2×D1111yescharacteristic
206C22×C16C2×D1112yescomplemented
207#469—222no—
208#468—222no—
209#467—112no—
210#466—112no—
211#466—112no—
212#466—112no—
213#427—111no—
214C2×#107—111no—
215#418—221no—
216#417—221no—
217#367—112no—
218#366—112no—
219#358—111no—
220#358—111no—
221#357—112no—
222#357—112no—
223#357—111no—
224#357—111no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—22no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11#46612yes—
231C22×C11C22×D811yescharacteristic
232C2×D11—82no—
233C2×D11—81no—
234C2×D11—81no—
235C2×D11—82no—
236C2×D11—82no—
237C2×D11—81no—
238C2×D11—164no—
239C4×C11—22no—
240C4×C11#46612yes—
241C4×C11C2×#12111yescharacteristic
242C4×C11C2×#13511yescharacteristic
243Dic11—82no—
244Dic11—81no—
245Dic11—81no—
246Dic11—81no—
247C2×#41—221no—
248C2×#41D4411yescharacteristic
249C22×D4—221no—
250#135—222no—
251#135—222no—
252C2×Q16—111no—
253C2×SD16—221no—
254C2×D8—112no—
255C2×D8—111no—
256C2×D8—221no—
257C2×D8—222no—
258C2×D8—222no—
259#131—22no—
260#131—22no—
261C2×M16D4411yescharacteristic
262C2×M16D4412yes—
263C22×C8C22×D1112yes—
264C22×C8C22×D1111yescharacteristic
265#127—441no—
266#124—441no—
267C22⋊Q8—222no—
268C22⋊Q8—441no—
269#121—222no—
270#121—222no—
271#121—222no—
272#121—441no—
273#121—442no—
274#120—442no—
275#117—221no—
276C2×C4⋊C4—221no—
277SD32—224no—
278D16—224no—
279M32—24no—
280M32C22⋊D1114yescomplemented
281C2×C16—22no—
282C2×C16—24no—
283C2×C16C22×D1111yescharacteristic
284C2×C16C22×D1111yescharacteristic
285C2×C16C22×D1112yes—
286#107—112no—
287#107—111no—
288#107—111no—
289#107—221no—
290#106—221no—
291#103—222no—
292#102—222no—
293#102—222no—
294#102—222no—
295C2×C11—22no—
296C2×C11—42no—
297C2×C11C2×#46611yescharacteristic
298C2×C11#341511yescharacteristic
299C2×C11#341611yescharacteristic
300D11—161no—
301D11—162no—
302C24—441no—
303#41—22no—
304#41—22no—
305#41—442no—
306#41—442no—
307C2×Q8—221no—
308C2×Q8D8811yescharacteristic
309C2×D4—222no—
310C2×D4—221no—
311C2×D4—441no—
312C2×D4—442no—
313C2×D4—442no—
314C2×D4—442no—
315C2×D4—441no—
316C2×D4—442no—
317C2×D4—442no—
318C2×D4D8812yes—
319C2×D4D8811yescharacteristic
320C22×C4—441no—
321C22×C4—441no—
322C22×C4C2×D4412yes—
323C22×C4C2×D4411yescharacteristic
324Q16—221no—
325Q16—221no—
326SD16—442no—
327D8—222no—
328D8—221no—
329D8—221no—
330D8—222no—
331D8—442no—
332M16—22no—
333M16—24no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8C2×D4412yes—
337C2×C8C2×D4411yescharacteristic
338C2×C8#433912yes—
339C2×C8C2×C22⋊D1112yes—
340C2×C8C23×D1111yescharacteristic
341C4⋊C4—221no—
342C4⋊C4—221no—
343C4⋊C4—222no—
344C4⋊C4—441no—
345C4⋊C4—442no—
346C22⋊C4—441no—
347C22⋊C4—442no—
348C22⋊C4—442no—
349C22⋊C4—442no—
350C22⋊C4—442no—
351C42—441no—
352C16—21no—
353C16—21no—
354C16C2×C22⋊D1114yes—
355C11#3361211yescharacteristic, complemented, Sylow
356C23—441no—
357C23—442no—
358C23—882no—
359C23—1761no—
360C23—1761no—
361C23C2×D8812yes—
362C23C2×D8811yescharacteristic
363Q8—22no—
364Q8—441no—
365Q8—441no—
366D4—24no—
367D4—22no—
368D4—442no—
369D4—441no—
370D4—442no—
371D4—441no—
372D4—882no—
373D4—882no—
374D4—1762no—
375D4—1762no—
376D4—1762no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—442no—
382C2×C4—441no—
383C2×C4—882no—
384C2×C4—1761no—
385C2×C4C2×D8812yes—
386C2×C4C2×D8811yescharacteristic
387C2×C4#6695712yes—
388C2×C4#6698312yes—
389C2×C4C22×D4411yescharacteristic
390C8—22no—
391C8#6698312yes—
392C8C2×#433911yescharacteristic
393C8C22×C22⋊D1111yescharacteristic
394C22—21no—
395C22—21no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—881no—
400C22—882no—
401C22—882no—
402C22—881no—
403C22—881no—
404C22—882no—
405C22—1764no—
406C22#1062272812yes—
407C22C22×D8811yescharacteristic
408C4—22no—
409C4—882no—
410C4—881no—
411C4—881no—
412C4—881no—
413C4#1062272812yes—
414C4C2×#6695711yescharacteristic
415C4C2×#6698311yescharacteristic
416C2—22no—
417C2—42no—
418C2—1762no—
419C2—1761no—
420C2C2×#1062272811yescharacteristic
421C2#1308175711yescharacteristic
422C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#504C2
socleC22×C11C22×D8
hypercenterC2×#504D11
hypocenterC11#33612
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
1. C2×#10622521C2semidirect
2. #13078286C2semidirect
3. #13078264C2semidirect
4. #13070729C2semidirect
5. #13070719C2semidirect
6. #13070712C2semidirect
7. #13070702C2semidirect
8. #13070404C2semidirect
9. #13070324C2semidirect
10. C2×#10622147C2semidirect
11. C2×C11×#504C2semidirect
19. C2×C11×M32C22semidirect
21. C22×C11×C16C22semidirect
26. #10622729C22semidirect
29. #10622728C22semidirect
37. #10622147C22semidirect
38. #10622147C22semidirect
39. #10622143C22semidirect
40. #10622142C22semidirect
41. #10622141C22semidirect
42. #10622141C22semidirect
74. C11×M32D4semidirect
146. C2×#504D11semidirect
204. C2×M32C2×D11semidirect
206. C22×C16C2×D11semidirect
280. M32C22⋊D11semidirect
355. C11#33612semidirect

Maximal subgroups

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

subgroupindex
C2×#106225212
#130782862
#130782642
#130707292
#130707192
#130707122
#130707022
#130704042
#130703242
C2×#106221472
C2×C11×#5042
#3361211