Finite Group Databasebeta

← #14908309

Subgroups — #14908309

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×#10622760C211yesmaximal, characteristic, complemented
2C2×#10622514C211yesmaximal, characteristic, complemented
3#13078288C211yesmaximal, characteristic, complemented
4#13078260C211yesmaximal, characteristic, complemented
5#13070728C212yesmaximal, complemented
6#13070718C212yesmaximal, complemented
7#13070711C212yesmaximal, complemented
8#13070701C212yesmaximal, complemented
9#13070402C211yesmaximal, characteristic, complemented
10#13070324C211yesmaximal, characteristic, complemented
11C2×C11×#357C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13#10623336—21no—
14C2×#66957C2211yescharacteristic
15C2×#66954C2211yescharacteristic
16#10623041—21no—
17C22×C11×C16C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19#10622828—21no—
20#10622772—22no—
21#10622770C2212yes—
22#10622770C2212yes—
23C2×#66891C2212yes—
24#10622760—24no—
25C2×#66890C2212yes—
26#10622719C2211yescharacteristic
27C2×#66876C2211yescharacteristic
28#10622579—21no—
29#10622514—24no—
30C2×#66862C2212yescomplemented
31C2×C16×D11C2212yescomplemented
32#10622500C2212yescomplemented
33#10622499—22no—
34#10622496C2212yescomplemented
35C11×#357C2212yes—
36C11×#357C2212yes—
37#10622147C2211yescharacteristic, complemented
38#10622147C2211yescharacteristic, complemented
39#10622141C2211yescharacteristic, complemented
40#10622141C2211yescharacteristic, complemented
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43C22×D4×C11—21no—
44C2×#4339—21no—
45C2×#4339D411yescharacteristic
46C2×C11×D8—22no—
47C2×C11×D8—21no—
48C2×C11×D8—22no—
49C2×C11×D8C2312yes—
50C22×C8×C11C2311yescharacteristic
51C2×C11×C4⋊C4—21no—
52#67006—42no—
53#66993—41no—
54#66991—22no—
55#66991—22no—
56#66989—41no—
57#66983—42no—
58#66979—21no—
59C2×#4318D411yescharacteristic
60C2×Dic44C2311yescharacteristic
61#66957—22no—
62#66957—22no—
63C2×D88C2311yescharacteristic
64C2×#4314—21no—
65#66954—22no—
66#66954—22no—
67C2×#4313D412yes—
68C2×C8×D11C2312yes—
69#66950—22no—
70#66950—41no—
71#66948—22no—
72#66948—41no—
73C2×C11×C16—22no—
74C2×C11×C16C2311yescharacteristic
75C2×C11×C16C2311yescharacteristic
76C11×#107—21no—
77C11×#107C2312yes—
78#66896—22no—
79#66896—22no—
80#66891—24no—
81#66890—24no—
82#66882C2311yescharacteristic
83#66882C2311yescharacteristic
84#66881—21no—
85#66876D414yescomplemented
86C2×C11⋊C16C2312yes—
87#66874—22no—
88#66873—22no—
89#66862—24no—
90C16×D11—24no—
91#33612—111nomaximal, Sylow
92C24×C11—41no—
93C2×D4×C11—22no—
94C2×D4×C11—42no—
95C2×D4×C11—41no—
96C2×D4×C11—42no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C2×C22⋊D11—41no—
100C2×C22⋊D11—42no—
101C2×C22⋊D11—42no—
102C2×C22⋊D11D812yes—
103#4339—22no—
104#4339—22no—
105#4339—42no—
106#4339—42no—
107C2×D44—21no—
108C2×D44—42no—
109C2×D44D811yescharacteristic
110C2×C4×D11—41no—
111C2×C4×D11C2×D412yes—
112C2×Dic22—21no—
113C2×Dic22D811yescharacteristic
114C11×D8—22no—
115C11×D8—22no—
116C11×D8—42no—
117C2×C8×C11C2×D412yes—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11#4112yes—
120C2×C8×C11C2411yescharacteristic
121C11×C4⋊C4—22no—
122C11×C4⋊C4—41no—
123C22⋊Dic11—42no—
124C22⋊Dic11—42no—
125C22⋊Dic11—41no—
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—42no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130C4⋊Dic11—42no—
131C4×Dic11—41no—
132#4318—22no—
133C2×C11⋊C8C2×D412yes—
134Dic44—21no—
135Dic44—21no—
136D88—21no—
137D88—21no—
138#4314—42no—
139#4313—24no—
140C8×D11—22no—
141C8×D11—22no—
142C11×C16—21no—
143C11×C16—21no—
144C11⋊C16C2×D414yes—
145C2×#509—111no—
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×#357D1111yescharacteristic, complemented
156C23×C11—42no—
157C23×C11—82no—
158C23×C11—161no—
159C23×C11—161no—
160C23×C11C2×D811yescharacteristic
161C22×D11—41no—
162C22×D11C2×D812yes—
163D4×C11—42no—
164D4×C11—42no—
165D4×C11—82no—
166C2×C4×C11—42no—
167C2×C4×C11—161no—
168C2×C4×C11#12112yes—
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11#13512yes—
171C2×C4×C11C22×D411yescharacteristic
172C22⋊D11—24no—
173C22⋊D11—82no—
174C22⋊D11—162no—
175C22⋊D11—162no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11C2×D812yes—
180D44—22no—
181D44—41no—
182D44—41no—
183D44—162no—
184C4×D11—22no—
185C4×D11—22no—
186C4×D11—82no—
187Dic22—22no—
188Dic22—41no—
189Dic22—41no—
190C8×C11#12112yes—
191C8×C11C22×D411yescharacteristic
192C8×C11C2×#4111yescharacteristic
193C11⋊C8—22no—
194C2×#135—111no—
195C22×D8C2×D1111yescharacteristic
196C2×#131—111no—
197#537—221no—
198#535—221no—
199#509—224no—
200C2×SD32—112no—
201C2×D16—112no—
202#504—224no—
203C2×M32—111no—
204C2×M32—112no—
205C22×C16—112no—
206C22×C16C2×D1111yescharacteristic
207#469—222no—
208#468—222no—
209#467—112no—
210#466—112no—
211#466—112no—
212#466—112no—
213#427—111no—
214C2×#107C2×D1111yescharacteristic
215#418—221no—
216#417—221no—
217#367—112no—
218#366—112no—
219#358—111no—
220#358—111no—
221#357—111no—
222#357—111no—
223#357C2×D1112yes—
224#357C2×D1112yes—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—82no—
228C22×C11—82no—
229C22×C11—82no—
230C22×C11—164no—
231C22×C11#46612yes—
232C22×C11C22×D811yescharacteristic
233C2×D11—22no—
234C2×D11—22no—
235C2×D11—22no—
236C2×D11—81no—
237C2×D11—81no—
238C2×D11—81no—
239C4×C11—82no—
240C4×C11#46612yes—
241C4×C11C2×#12111yescharacteristic
242C4×C11C2×#13511yescharacteristic
243Dic11—22no—
244Dic11—81no—
245Dic11—81no—
246Dic11—81no—
247C2×#41—111no—
248C2×#41—221no—
249C22×D4—21no—
250#135—222no—
251#135—222no—
252C2×Q16—111no—
253C2×SD16—221no—
254C2×D8—22no—
255C2×D8—22no—
256C2×D8—21no—
257C2×D8—111no—
258C2×D8C22×D1112yes—
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—21no—
277SD32—224no—
278D16—224no—
279M32—114no—
280M32—224no—
281C2×C16—22no—
282C2×C16—112no—
283C2×C16—224no—
284C2×C16C22×D1111yescharacteristic
285C2×C16C22×D1111yescharacteristic
286#107—21no—
287#107—111no—
288#107—111no—
289#107C22×D1112yes—
290#106—221no—
291#103—222no—
292#102—222no—
293#102—222no—
294#102—222no—
295C2×C11—22no—
296C2×C11—162no—
297C2×C11C2×#46611yescharacteristic
298C2×C11#341511yescharacteristic
299C2×C11#341611yescharacteristic
300D11—42no—
301D11—161no—
302C24—41no—
303#41—222no—
304#41—222no—
305#41—442no—
306#41—442no—
307C2×Q8—111no—
308C2×Q8—221no—
309C2×D4—22no—
310C2×D4—42no—
311C2×D4—41no—
312C2×D4—42no—
313C2×D4—112no—
314C2×D4—111no—
315C2×D4—221no—
316C2×D4—442no—
317C2×D4—441no—
318C2×D4—442no—
319C2×D4—442no—
320C22×C4—41no—
321C22×C4—112no—
322C22×C4—441no—
323C22×C4D4×D1111yescharacteristic
324Q16—221no—
325Q16—221no—
326SD16—442no—
327D8—22no—
328D8—22no—
329D8—42no—
330D8—221no—
331D8—221no—
332M16—222no—
333M16—224no—
334C2×C8—112no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8#433912yes—
338C2×C8D4×D1111yescharacteristic
339C2×C8D4×D1112yes—
340C2×C8C23×D1111yescharacteristic
341C4⋊C4—22no—
342C4⋊C4—41no—
343C4⋊C4—221no—
344C4⋊C4—221no—
345C4⋊C4—442no—
346C22⋊C4—442no—
347C22⋊C4—442no—
348C22⋊C4—442no—
349C22⋊C4—442no—
350C22⋊C4—441no—
351C42—441no—
352C16—21no—
353C16—21no—
354C16—114no—
355C11#3361211yescharacteristic, complemented, Sylow
356C23—42no—
357C23—82no—
358C23—112no—
359C23—161no—
360C23—161no—
361C23—441no—
362C23D8×D1111yescharacteristic
363Q8—222no—
364Q8—441no—
365Q8—441no—
366D4—42no—
367D4—42no—
368D4—82no—
369D4—224no—
370D4—222no—
371D4—441no—
372D4—441no—
373D4—882no—
374D4—1762no—
375D4—1762no—
376D4—1762no—
377C2×C4—42no—
378C2×C4—112no—
379C2×C4—161no—
380C2×C4—222no—
381C2×C4—222no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—882no—
386C2×C4#6693712yes—
387C2×C4D8×D1111yescharacteristic
388C2×C4#6696912yes—
389C2×C4C2×D4×D1111yescharacteristic
390C8—222no—
391C8#6693712yes—
392C8C2×#433911yescharacteristic
393C8C2×D4×D1111yescharacteristic
394C22—21no—
395C22—21no—
396C22—82no—
397C22—82no—
398C22—82no—
399C22—164no—
400C22—222no—
401C22—222no—
402C22—222no—
403C22—881no—
404C22—881no—
405C22—881no—
406C22#1062238812yes—
407C22C2×D8×D1111yescharacteristic
408C4—82no—
409C4—222no—
410C4—881no—
411C4—881no—
412C4—881no—
413C4#1062238812yes—
414C4C2×#6693711yescharacteristic
415C4C2×#6696911yescharacteristic
416C2—22no—
417C2—162no—
418C2—442no—
419C2—1761no—
420C2C2×#1062238811yescharacteristic
421C2#1308175311yescharacteristic
422C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#357C2
socleC22×C11C22×D8
hypercenterC2×#357D11
hypocenterC11#33612
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
1. C2×#10622760C2semidirect
2. C2×#10622514C2semidirect
3. #13078288C2semidirect
4. #13078260C2semidirect
5. #13070728C2semidirect
6. #13070718C2semidirect
7. #13070711C2semidirect
8. #13070701C2semidirect
9. #13070402C2semidirect
10. #13070324C2semidirect
11. C2×C11×#357C2semidirect
30. C2×#66862C22semidirect
31. C2×C16×D11C22semidirect
32. #10622500C22semidirect
34. #10622496C22semidirect
37. #10622147C22semidirect
38. #10622147C22semidirect
39. #10622141C22semidirect
40. #10622141C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
85. #66876D4semidirect
155. C2×#357D11semidirect
355. C11#33612semidirect

Maximal subgroups

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

subgroupindex
C2×#106227602
C2×#106225142
#130782882
#130782602
#130707282
#130707182
#130707112
#130707012
#130704022
#130703242
C2×C11×#3572
#3361211