Finite Group Databasebeta

← #14908312

Subgroups — #14908312

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
2C2×#10622520C211yesmaximal, characteristic, complemented
3#13078288C211yesmaximal, characteristic, complemented
4#13078265C211yesmaximal, characteristic, complemented
5#13070730C212yesmaximal, complemented
6#13070720C212yesmaximal, complemented
7#13070713C212yesmaximal, complemented
8#13070703C212yesmaximal, complemented
9#13070321C211yesmaximal, characteristic, complemented
10C2×#10622129C211yesmaximal, characteristic, complemented
11C11×#2159C211yesmaximal, characteristic, complemented
12C2×#66957C2211yescharacteristic
13C22×D88C2211yescharacteristic
14C2×#66954C2211yescharacteristic
15#10623056—21no—
16#10623041—21no—
17C2×C11×M32C2211yescharacteristic
18C11×#427C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C22×C11⋊C16C2211yescharacteristic
21#10622614—21no—
22#10622579—21no—
23#10622521—24no—
24#10622520—24no—
25C2×#66864C2212yes—
26C2×D176C2212yes—
27C2×#66862C2212yescomplemented
28C2×C16×D11C2212yescomplemented
29#10622500C2212yescomplemented
30#10622499—22no—
31#10622496C2212yes—
32#10622496C2212yes—
33#10622496C2212yescomplemented
34#10622478—22no—
35C11×#367C2212yescomplemented
36C11×#366C2212yescomplemented
37#10622130C2211yescharacteristic, complemented
38#10622130C2211yescharacteristic, complemented
39#10622129C2212yes—
40#10622129C2212yes—
41#10622129C2211yescharacteristic, complemented
42#10622129C2211yescharacteristic, complemented
43C2×#4339—21no—
44C2×#4339D411yescharacteristic
45C22×D44—21no—
46C22×C8×C11C2311yescharacteristic
47C11×#117—21no—
48C2×C11×C4⋊C4—21no—
49#66983—42no—
50C2×#4318D411yescharacteristic
51C2×Dic44C2311yescharacteristic
52#66957—22no—
53#66957—22no—
54C2×D88—22no—
55C2×D88—22no—
56C2×D88—21no—
57C2×D88C2312yes—
58C2×D88C2311yescharacteristic
59C2×#4314—21no—
60#66954—22no—
61#66954—22no—
62C2×#4313D412yes—
63C2×C8×D11C2312yes—
64#66950—22no—
65#66950—41no—
66#66948—22no—
67#66948—22no—
68#66948—22no—
69#66948—41no—
70#66935—42no—
71#66928—41no—
72#66927—41no—
73C11×M32D414yescomplemented
74C2×C11×C16C2312yes—
75C11×#107—21no—
76C11×#107C2311yescharacteristic
77C11×#107C2311yescharacteristic
78C11×#107C2312yes—
79C11×#106—21no—
80C2×C11⋊C16—22no—
81C2×C11⋊C16C2311yescharacteristic
82C2×C11⋊C16C2311yescharacteristic
83#66874—22no—
84#66873—22no—
85#66873—22no—
86#66873—22no—
87#66864—24no—
88D176—24no—
89#66862—24no—
90C16×D11—24no—
91#33612—111nomaximal, Sylow
92C23×D11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C2×C22⋊D11—41no—
96C2×C22⋊D11D812yes—
97#4339—22no—
98#4339—22no—
99#4339—42no—
100#4339—42no—
101C2×D44—21no—
102C2×D44—22no—
103C2×D44—42no—
104C2×D44—42no—
105C2×D44—42no—
106C2×D44—42no—
107C2×D44—41no—
108C2×D44—42no—
109C2×D44D811yescharacteristic
110C2×C4×D11—41no—
111C2×C4×D11C2×D412yes—
112C2×Dic22—21no—
113C2×Dic22D811yescharacteristic
114C2×C8×C11C2×D412yes—
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11#4112yes—
117C2×C8×C11C2411yescharacteristic
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—41no—
122C11×C22⋊C4—41no—
123C42×C11—41no—
124(C2×D11)⋊C4—42no—
125(C2×D11)⋊C4—42no—
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—42no—
128C4⋊Dic11—42no—
129#4318—22no—
130C2×C11⋊C8C2×D412yes—
131Dic44—21no—
132Dic44—21no—
133D88—21no—
134D88—22no—
135D88—22no—
136D88—21no—
137D88—42no—
138#4314—42no—
139#4313—24no—
140C8×D11—22no—
141C8×D11—22no—
142C11×C16C2×D414yes—
143C11⋊C16—21no—
144C11⋊C16—21no—
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#2159D1111yescharacteristic, complemented
154#2138—111no—
155C2×#357—111no—
156C23×C11C2×D811yescharacteristic
157C22×D11—41no—
158C22×D11—42no—
159C22×D11—82no—
160C22×D11—161no—
161C22×D11—161no—
162C22×D11C2×D812yes—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—161no—
167C2×C4×C11#12112yes—
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11#13512yes—
170C2×C4×C11C22×D411yescharacteristic
171C22⋊D11—24no—
172C22⋊D11—82no—
173C2×Dic11—41no—
174C2×Dic11C2×D812yes—
175D44—22no—
176D44—41no—
177D44—42no—
178D44—42no—
179D44—41no—
180D44—82no—
181D44—162no—
182D44—162no—
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×D8—111no—
196C2×#131—111no—
197#537—221no—
198#535—221no—
199#509—224no—
200C2×SD32—112no—
201C2×D16—112no—
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#427C2×D1111yescharacteristic
214C2×#107C2×D1111yescharacteristic
215#418—221no—
216#417—221no—
217#367C2×D1112yescomplemented
218#366C2×D1112yescomplemented
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#46612yes—
228C22×C11C22×D811yescharacteristic
229C2×D11—22no—
230C2×D11—22no—
231C2×D11—22no—
232C2×D11—82no—
233C2×D11—81no—
234C2×D11—81no—
235C2×D11—82no—
236C2×D11—82no—
237C2×D11—81no—
238C2×D11—164no—
239C4×C11—82no—
240C4×C11—81no—
241C4×C11—81no—
242C4×C11#46612yes—
243C4×C11C2×#12111yescharacteristic
244C4×C11C2×#13511yescharacteristic
245Dic11—22no—
246Dic11—81no—
247C2×#41—111no—
248C2×#41—221no—
249C22×D4—221no—
250#135—222no—
251#135—222no—
252C2×Q16—111no—
253C2×SD16—221no—
254C2×D8—112no—
255C2×D8—111no—
256C2×D8—222no—
257C2×D8—221no—
258C2×D8—222no—
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—21no—
276C2×C4⋊C4—21no—
277SD32—224no—
278D16—224no—
279M32—224no—
280M32D4414yescomplemented
281C2×C16—111no—
282C2×C16—111no—
283C2×C16—222no—
284C2×C16—224no—
285C2×C16C22×D1112yes—
286#107—21no—
287#107C22×D1112yes—
288#107C22×D1111yescharacteristic
289#107C22×D1111yescharacteristic
290#106—21no—
291#103—222no—
292#102—222no—
293#102—222no—
294#102—222no—
295C2×C11—22no—
296C2×C11C2×#46611yescharacteristic
297C2×C11#341511yescharacteristic
298C2×C11#341611yescharacteristic
299D11—42no—
300D11—161no—
301D11—162no—
302C24—441no—
303#41—222no—
304#41—222no—
305#41—442no—
306#41—442no—
307C2×Q8—111no—
308C2×Q8—221no—
309C2×D4—112no—
310C2×D4—111no—
311C2×D4—222no—
312C2×D4—221no—
313C2×D4—442no—
314C2×D4—442no—
315C2×D4—442no—
316C2×D4—441no—
317C2×D4—442no—
318C2×D4—441no—
319C2×D4—442no—
320C22×C4—41no—
321C22×C4—112no—
322C22×C4—441no—
323C22×C4D4×D1111yescharacteristic
324Q16—221no—
325Q16—221no—
326SD16—442no—
327D8—221no—
328D8—222no—
329D8—222no—
330D8—221no—
331D8—442no—
332M16—222no—
333M16—224no—
334C2×C8—112no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8C2×D4412yes—
338C2×C8D4×D1111yescharacteristic
339C2×C8#434312yes—
340C2×C8C23×D1111yescharacteristic
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—22no—
344C4⋊C4—41no—
345C4⋊C4—442no—
346C22⋊C4—41no—
347C22⋊C4—442no—
348C22⋊C4—442no—
349C22⋊C4—442no—
350C22⋊C4—442no—
351C42—41no—
352C16—221no—
353C16—221no—
354C16C2×D4414yes—
355C11#3361211yescharacteristic, complemented, Sylow
356C23—112no—
357C23—441no—
358C23—442no—
359C23—882no—
360C23—1761no—
361C23—1761no—
362C23D8×D1111yescharacteristic
363Q8—222no—
364Q8—441no—
365Q8—441no—
366D4—224no—
367D4—222no—
368D4—442no—
369D4—441no—
370D4—442no—
371D4—441no—
372D4—882no—
373D4—882no—
374D4—1762no—
375D4—1762no—
376D4—1762no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—112no—
381C2×C4—161no—
382C2×C4—222no—
383C2×C4—222no—
384C2×C4—441no—
385C2×C4—882no—
386C2×C4#6694812yes—
387C2×C4D8×D1111yescharacteristic
388C2×C4#6697212yes—
389C2×C4C2×D4×D1111yescharacteristic
390C8—222no—
391C8#6694812yes—
392C8C22×D4411yescharacteristic
393C8C2×#434311yescharacteristic
394C22—21no—
395C22—21no—
396C22—222no—
397C22—222no—
398C22—222no—
399C22—881no—
400C22—882no—
401C22—882no—
402C22—881no—
403C22—881no—
404C22—882no—
405C22—1764no—
406C22#1062249612yes—
407C22C2×D8×D1111yescharacteristic
408C4—82no—
409C4—81no—
410C4—81no—
411C4—222no—
412C4—881no—
413C4#1062249612yes—
414C4C2×#6694811yescharacteristic
415C4C2×#6697211yescharacteristic
416C2—22no—
417C2—442no—
418C2—1762no—
419C2—1761no—
420C2C2×#1062249611yescharacteristic
421C2#1308175611yescharacteristic
422C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
hypercenter#2159D11
hypocenterC11#33612
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
1. C2×#10622521C2semidirect
2. C2×#10622520C2semidirect
3. #13078288C2semidirect
4. #13078265C2semidirect
5. #13070730C2semidirect
6. #13070720C2semidirect
7. #13070713C2semidirect
8. #13070703C2semidirect
9. #13070321C2semidirect
10. C2×#10622129C2semidirect
11. C11×#2159C2semidirect
27. C2×#66862C22semidirect
28. C2×C16×D11C22semidirect
29. #10622500C22semidirect
33. #10622496C22semidirect
35. C11×#367C22semidirect
36. C11×#366C22semidirect
37. #10622130C22semidirect
38. #10622130C22semidirect
41. #10622129C22semidirect
42. #10622129C22semidirect
73. C11×M32D4semidirect
153. #2159D11semidirect
217. #367C2×D11semidirect
218. #366C2×D11semidirect
280. M32D44semidirect
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
C2×#106225202
#130782882
#130782652
#130707302
#130707202
#130707132
#130707032
#130703212
C2×#106221292
C11×#21592
#3361211