Finite Group Databasebeta

← #14908305

Subgroups — #14908305

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×#10622520C211yesmaximal, characteristic, complemented
2#13078282C211yesmaximal, characteristic, complemented
3#13078260C211yesmaximal, characteristic, complemented
4#13070726C212yesmaximal, complemented
5#13070716C212yesmaximal, complemented
6#13070709C212yesmaximal, complemented
7#13070699C212yesmaximal, complemented
8#13070404C211yesmaximal, characteristic, complemented
9#13070323C211yesmaximal, characteristic, complemented
10C2×#10622200C211yesmaximal, characteristic, complemented
11C2×C11×#509C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C22×C11×D8C2211yescharacteristic
14#10623364—21no—
15#10623336—21no—
16C2×#66954C2211yescharacteristic
17C11×#509—24no—
18C2×C11×SD32C2212yes—
19C2×C11×D16C2212yes—
20C2×C11×M32C2211yescharacteristic
21#10622845—21no—
22#10622828—21no—
23#10622801C2212yescomplemented
24#10622787—22no—
25#10622772—22no—
26#10622770C2212yes—
27#10622770C2212yes—
28#10622770C2212yescomplemented
29#10622719C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C22×C11⋊C16C2211yescharacteristic
32#10622520—24no—
33C2×#66862C2212yescomplemented
34C2×C16×D11C2212yescomplemented
35#10622202C2211yescharacteristic, complemented
36#10622202C2211yescharacteristic, complemented
37#10622200C2212yes—
38#10622200C2212yes—
39#10622200C2211yescharacteristic, complemented
40#10622200C2211yescharacteristic, complemented
41#10622143C2212yescomplemented
42#10622142C2212yescomplemented
43C2×C11×#41—21no—
44C22×D4×C11—21no—
45C2×#4339D411yescharacteristic
46C11×#135—22no—
47C11×#135—22no—
48C2×C11×Q16C2311yescharacteristic
49C2×C11×SD16—21no—
50C2×C11×D8—22no—
51C2×C11×D8—21no—
52C2×C11×D8—22no—
53C2×C11×D8C2311yescharacteristic
54C2×C11×D8C2312yes—
55C22×C8×C11C2311yescharacteristic
56#67006—42no—
57#66999—22no—
58#66993—41no—
59#66992—42no—
60#66991—22no—
61#66991—22no—
62#66991—22no—
63#66989—41no—
64#66983—41no—
65#66979—21no—
66C2×C4⋊Dic11—21no—
67#66977—41no—
68C2×#4318D411yescharacteristic
69#66954—22no—
70#66954—22no—
71C2×#4313D412yes—
72C2×C8×D11C2312yes—
73C11×SD32—24no—
74C11×D16—24no—
75C11×M32D414yescomplemented
76C2×C11×C16C2312yes—
77#66899—22no—
78#66896—22no—
79#66896—22no—
80#66896—22no—
81#66882—21no—
82#66882C2311yescharacteristic
83#66882C2311yescharacteristic
84#66882C2312yes—
85#66881—21no—
86C2×C11⋊C16—22no—
87C2×C11⋊C16C2311yescharacteristic
88C2×C11⋊C16C2311yescharacteristic
89#66862—24no—
90C16×D11—24no—
91#33612—111nomaximal, Sylow
92C24×C11—41no—
93C11×#41—42no—
94C11×#41—42no—
95C2×Q8×C11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—21no—
98C2×D4×C11—41no—
99C2×D4×C11—42no—
100C2×D4×C11—41no—
101C2×D4×C11—42no—
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C2×C22⋊D11—42no—
105C2×C22⋊D11—42no—
106C2×C22⋊D11—42no—
107C2×C22⋊D11D812yes—
108C22×Dic11—41no—
109#4339—22no—
110#4339—22no—
111C2×D44D811yescharacteristic
112C2×C4×D11C2×D412yes—
113C2×Dic22D811yescharacteristic
114C11×Q16—21no—
115C11×Q16—21no—
116C11×SD16—42no—
117C11×D8—21no—
118C11×D8—22no—
119C11×D8—22no—
120C11×D8—21no—
121C11×D8—42no—
122C2×C8×C11C2×D412yes—
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11#4112yes—
125C2×C8×C11C2411yescharacteristic
126C22⋊Dic11—42no—
127C22⋊Dic11—42no—
128C22⋊Dic11—42no—
129C22⋊Dic11—41no—
130(C2×D11)⋊C4—42no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133C4⋊Dic11—22no—
134C4⋊Dic11—41no—
135Dic11⋊C4—42no—
136C4×Dic11—41no—
137#4318—22no—
138C2×C11⋊C8C2×D412yes—
139#4313—24no—
140C8×D11—22no—
141C8×D11—22no—
142C11×C16C2×D414yes—
143C11⋊C16—21no—
144C11⋊C16—21no—
145C2×#509D1111yescharacteristic, complemented
146C2×#504—111no—
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×C11—41no—
157C23×C11—42no—
158C23×C11—82no—
159C23×C11—161no—
160C23×C11—161no—
161C23×C11C2×D811yescharacteristic
162C22×D11C2×D812yes—
163Q8×C11—41no—
164Q8×C11—41no—
165D4×C11—42no—
166D4×C11—41no—
167D4×C11—42no—
168D4×C11—41no—
169D4×C11—82no—
170D4×C11—82no—
171C2×C4×C11—41no—
172C2×C4×C11—82no—
173C2×C4×C11#12112yes—
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11#13512yes—
176C2×C4×C11C22×D411yescharacteristic
177C22⋊D11—24no—
178C22⋊D11—162no—
179C22⋊D11—162no—
180C22⋊D11—162no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—42no—
184C2×Dic11—161no—
185C2×Dic11C2×D812yes—
186D44—22no—
187C4×D11—22no—
188C4×D11—22no—
189Dic22—22no—
190C8×C11#12112yes—
191C8×C11C22×D411yescharacteristic
192C8×C11C2×#4111yescharacteristic
193C11⋊C8—22no—
194C2×#135C2×D1111yescharacteristic
195C22×D8C2×D1111yescharacteristic
196C2×#131—111no—
197#537—221no—
198#535—221no—
199#509—24no—
200C2×SD32C2×D1112yes—
201C2×D16C2×D1112yes—
202#504—224no—
203C2×M32—112no—
204C2×M32C2×D1111yescharacteristic
205C22×C16—111no—
206C22×C16—112no—
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—82no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11—82no—
231C22×C11—81no—
232C22×C11—82no—
233C22×C11—164no—
234C22×C11#46612yes—
235C22×C11C22×D811yescharacteristic
236C2×D11—22no—
237C2×D11—22no—
238C2×D11—22no—
239C4×C11—81no—
240C4×C11#46612yes—
241C4×C11C2×#12111yescharacteristic
242C4×C11C2×#13511yescharacteristic
243Dic11—22no—
244Dic11—82no—
245Dic11—81no—
246Dic11—81no—
247C2×#41—21no—
248C2×#41—111no—
249C22×D4—21no—
250#135—22no—
251#135—22no—
252C2×Q16C22×D1111yescharacteristic
253C2×SD16—21no—
254C2×D8—21no—
255C2×D8—22no—
256C2×D8—22no—
257C2×D8C22×D1112yes—
258C2×D8C22×D1111yescharacteristic
259#131—222no—
260#131—222no—
261C2×M16—111no—
262C2×M16—112no—
263C22×C8—112no—
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—24no—
278D16—24no—
279M32—224no—
280M32C22⋊D1114yescomplemented
281C2×C16—111no—
282C2×C16—111no—
283C2×C16—222no—
284C2×C16—224no—
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—161no—
297C2×C11—162no—
298C2×C11C2×#46611yescharacteristic
299C2×C11#341511yescharacteristic
300C2×C11#341611yescharacteristic
301D11—42no—
302C24—41no—
303#41—42no—
304#41—42no—
305#41—222no—
306#41—222no—
307C2×Q8—21no—
308C2×Q8—111no—
309C2×D4—22no—
310C2×D4—21no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—42no—
314C2×D4—42no—
315C2×D4—112no—
316C2×D4—111no—
317C2×D4—442no—
318C2×D4—442no—
319C2×D4—442no—
320C22×C4—41no—
321C22×C4—112no—
322C22×C4—441no—
323C22×C4D4×D1111yescharacteristic
324Q16—21no—
325Q16—21no—
326SD16—42no—
327D8—22no—
328D8—21no—
329D8—21no—
330D8—22no—
331D8—42no—
332M16—222no—
333M16—224no—
334C2×C8—112no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8D4×D1111yescharacteristic
338C2×C8#434112yes—
339C2×C8C2×C22⋊D1112yes—
340C2×C8C23×D1111yescharacteristic
341C4⋊C4—221no—
342C4⋊C4—221no—
343C4⋊C4—222no—
344C4⋊C4—442no—
345C4⋊C4—441no—
346C22⋊C4—442no—
347C22⋊C4—442no—
348C22⋊C4—442no—
349C22⋊C4—442no—
350C22⋊C4—441no—
351C42—441no—
352C16—221no—
353C16—221no—
354C16C2×C22⋊D1114yes—
355C11#3361211yescharacteristic, complemented, Sylow
356C23—41no—
357C23—42no—
358C23—82no—
359C23—112no—
360C23—161no—
361C23—161no—
362C23D8×D1111yescharacteristic
363Q8—41no—
364Q8—41no—
365Q8—222no—
366D4—42no—
367D4—41no—
368D4—42no—
369D4—41no—
370D4—82no—
371D4—82no—
372D4—224no—
373D4—222no—
374D4—1762no—
375D4—1762no—
376D4—1762no—
377C2×C4—41no—
378C2×C4—82no—
379C2×C4—112no—
380C2×C4—222no—
381C2×C4—222no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—442no—
385C2×C4—1761no—
386C2×C4D8×D1111yescharacteristic
387C2×C4#6696512yes—
388C2×C4#6699112yes—
389C2×C4C2×D4×D1111yescharacteristic
390C8—222no—
391C8#6699112yes—
392C8C2×#434111yescharacteristic
393C8C22×C22⋊D1111yescharacteristic
394C22—21no—
395C22—21no—
396C22—81no—
397C22—82no—
398C22—82no—
399C22—81no—
400C22—81no—
401C22—82no—
402C22—164no—
403C22—222no—
404C22—222no—
405C22—222no—
406C22#1062277012yes—
407C22C2×D8×D1111yescharacteristic
408C4—81no—
409C4—222no—
410C4—882no—
411C4—881no—
412C4—881no—
413C4#1062277012yes—
414C4C2×#6696511yescharacteristic
415C4C2×#6699111yescharacteristic
416C2—22no—
417C2—162no—
418C2—161no—
419C2—442no—
420C2C2×#1062277011yescharacteristic
421C2#1308175611yescharacteristic
422C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#509C2
socleC22×C11C22×D8
hypercenterC2×#509D11
hypocenterC11#33612
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. C2×#10622520C2semidirect
2. #13078282C2semidirect
3. #13078260C2semidirect
4. #13070726C2semidirect
5. #13070716C2semidirect
6. #13070709C2semidirect
7. #13070699C2semidirect
8. #13070404C2semidirect
9. #13070323C2semidirect
10. C2×#10622200C2semidirect
11. C2×C11×#509C2semidirect
23. #10622801C22semidirect
28. #10622770C22semidirect
33. C2×#66862C22semidirect
34. C2×C16×D11C22semidirect
35. #10622202C22semidirect
36. #10622202C22semidirect
39. #10622200C22semidirect
40. #10622200C22semidirect
41. #10622143C22semidirect
42. #10622142C22semidirect
75. C11×M32D4semidirect
145. C2×#509D11semidirect
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×#106225202
#130782822
#130782602
#130707262
#130707162
#130707092
#130706992
#130704042
#130703232
C2×#106222002
C2×C11×#5092
#3361211