Finite Group Databasebeta

← #14907154

Subgroups — #14907154

Order 2816.

674 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×#10622807C211yesmaximal, characteristic
2#13077492C211yesmaximal, characteristic, complemented
3#13077490C211yesmaximal, characteristic, complemented
4#13070483C212yesmaximal, complemented
5#13070477C212yesmaximal, complemented
6#13070472C212yesmaximal, complemented
7#13070460C212yesmaximal, complemented
8C2×#10622127C211yesmaximal, characteristic, complemented
9#13070329C211yesmaximal, characteristic, complemented
10#13070215C211yesmaximal, characteristic, complemented
11C11×#2139C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13#10623358—21no—
14C2×#66957C2211yescharacteristic
15#10623035—21no—
16C2×C11×M32C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18#10622845—21no—
19#10622807C418yescomplemented
20Q16×Dic11C2212yes—
21C2×#66893C2211yescharacteristic
22C2×#66892C2211yescharacteristic
23#10622777—22no—
24D8×Dic11C2212yes—
25C2×#66891C2211yescharacteristic
26C2×#66890C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28#10622714C2211yescharacteristic
29C22×C11⋊C16C2211yescharacteristic
30#10622579—21no—
31#10622502—22no—
32#10622486C2212yes—
33#10622485C2212yes—
34C11×#358C2212yes—
35C11×#357C2212yes—
36#10622147C2212yes—
37#10622141C2212yes—
38#10622140C2212yes—
39C16×Dic11C2212yes—
40#10622127C2212yes—
41#10622127C2212yes—
42C2×C11×#41—21no—
43C2×#4339—21no—
44C11×#135—22no—
45C11×#135C2×C414yescomplemented
46C2×C11×Q16C2311yescharacteristic
47C2×C11×SD16—21no—
48C2×C11×D8C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C2×C11×C4⋊C4—21no—
51Q8×Dic11—22no—
52D4×Dic11—22no—
53D4×Dic11—42no—
54C4×C22⋊D11—42no—
55#66979—41no—
56#66979D411yescharacteristic
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—41no—
59C2×#4318D411yescharacteristic
60C2×Dic44C2311yescharacteristic
61#66957—22no—
62#66957C2×C414yescomplemented
63C2×D88C2311yescharacteristic
64C2×#4314—21no—
65#66946—22no—
66#66945—41no—
67C4⋊C4×D11—41no—
68#66940—22no—
69C11×M32—22no—
70C2×C11×C16C2312yes—
71C11×#107—21no—
72C11×#107C2312yes—
73#66899—22no—
74#66896—22no—
75#66893C2×C414yescomplemented
76#66892C2×C414yescomplemented
77#66891C2×C414yescomplemented
78#66890C2×C414yescomplemented
79#66882—21no—
80#66882C2312yes—
81#66879D412yes—
82C8×Dic11C2312yes—
83C2×C11⋊C16C2×C414yescomplemented
84C2×C11⋊C16C2311yescharacteristic
85C2×C11⋊C16C2311yescharacteristic
86#66874—22no—
87#66873—22no—
88#33459—111nomaximal, Sylow
89C11×#41—24no—
90C11×#41—42no—
91C2×Q8×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C2×C22⋊D11—41no—
98C22×Dic11—42no—
99C22×Dic11—41no—
100#4339—24no—
101#4339—42no—
102C2×D44—21no—
103C2×C4×D11—42no—
104C2×C4×D11—41no—
105C2×Dic22—21no—
106C11×Q16—21no—
107C11×Q16C22×C412yes—
108C11×SD16—24no—
109C11×D8—21no—
110C11×D8C22×C412yes—
111C2×C8×C11C22×C412yes—
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11#4112yes—
114C2×C8×C11C2411yescharacteristic
115C11×C4⋊C4—22no—
116C11×C4⋊C4—41no—
117C22⋊Dic11—42no—
118C22⋊Dic11D812yes—
119(C2×D11)⋊C4—42no—
120C4⋊Dic11—22no—
121C4⋊Dic11—42no—
122C4⋊Dic11—41no—
123C4⋊Dic11D811yescharacteristic
124C4⋊Dic11D811yescharacteristic
125Dic11⋊C4—42no—
126C4×Dic11—42no—
127C4×Dic11—42no—
128C4×Dic11C2×D412yes—
129#4318—22no—
130C2×C11⋊C8C2×D412yes—
131Dic44—21no—
132Dic44C22×C412yes—
133D88—21no—
134D88C22×C412yes—
135#4314—24no—
136C11×C16—22no—
137C11⋊C16C22×C412yes—
138C11⋊C16C22×C412yes—
139C2×#508—111no—
140#2951—111no—
141#2951—111no—
142#2175—112no—
143#2175—112no—
144C4×Q32—112no—
145C4×D16—112no—
146C2×#366—111no—
147#2139—111no—
148#2139D1111yescharacteristic, complemented
149#2108—111no—
150C23×C11—41no—
151C23×C11C2×D811yescharacteristic
152C22×D11—41no—
153Q8×C11—22no—
154Q8×C11—41no—
155D4×C11—22no—
156D4×C11—44no—
157D4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—44no—
160C2×C4×C11—42no—
161C2×C4×C11—161no—
162C2×C4×C11C4×D412yes—
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11#13512yes—
165C2×C4×C11C22×D411yescharacteristic
166C22⋊D11—44no—
167C2×Dic11—41no—
168C2×Dic11—42no—
169C2×Dic11—162no—
170C2×Dic11—161no—
171C2×Dic11C2×D812yes—
172C2×Dic11C2×D812yes—
173D44—22no—
174D44—41no—
175C4×D11—44no—
176C4×D11—162no—
177Dic22—22no—
178Dic22—41no—
179C8×C11C4×D412yes—
180C8×C11C23×C411yescharacteristic
181C8×C11C2×#4111yescharacteristic
182C11⋊C8—22no—
183C2×#135—111no—
184C2×#135C2×D1111yescharacteristic
185#520—221no—
186#520—221no—
187#508—118no—
188C2×Q32—111no—
189C2×SD32—111no—
190C2×SD32—111no—
191C2×D16—111no—
192C2×M32C2×D1111yescharacteristic
193C22×C16—111no—
194#440—222no—
195#440—222no—
196C4×Q16—112no—
197C4×Q16—112no—
198C4×D8—112no—
199C4×D8—112no—
200C2×#107—111no—
201C2×#107C2×D1111yescharacteristic
202#417—221no—
203#417—221no—
204#405—111no—
205#366—112no—
206#366—112no—
207#358—112no—
208#358C2×D1112yes—
209#357—112no—
210#357C2×D1112yes—
211#346—112no—
212C4×C16—112no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—42no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11C4×D812yes—
219C22×C11C22×D811yescharacteristic
220C2×D11—42no—
221C2×D11—81no—
222C2×D11—81no—
223C4×C11—42no—
224C4×C11—82no—
225C4×C11C4×D812yes—
226C4×C11C2×C4×D411yescharacteristic
227C4×C11C2×#13511yescharacteristic
228Dic11—22no—
229Dic11—22no—
230Dic11—42no—
231Dic11—82no—
232C2×#41—21no—
233C2×#41—221no—
234#135—22no—
235#135—114no—
236#135—222no—
237#135C4×D1114yescomplemented
238C2×Q16—111no—
239C2×Q16C22×D1111yescharacteristic
240C2×SD16—21no—
241C2×SD16—221no—
242C2×D8—111no—
243C2×D8C22×D1111yescharacteristic
244C2×M16—111no—
245C22×C8C22×D1111yescharacteristic
246C4×Q8—222no—
247C4×Q8—222no—
248C4×D4—222no—
249C4×D4—222no—
250C4×D4—442no—
251C4×D4—442no—
252#117—111no—
253#117—441no—
254#117—441no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—441no—
258C2×C4⋊C4—441no—
259Q32—114no—
260SD32—114no—
261SD32—114no—
262D16—114no—
263M32—22no—
264C2×C16—114no—
265C2×C16—111no—
266C2×C16—111no—
267C2×C16C22×D1112yes—
268#107—21no—
269#107—112no—
270#107—221no—
271#107C22×D1112yes—
272#103—222no—
273#103—222no—
274#102—222no—
275#102—222no—
276#97—112no—
277C4×C8—112no—
278C2×C11—22no—
279C2×C11—82no—
280C2×C11C2×C4×D811yescharacteristic
281C2×C11#341511yescharacteristic
282C2×C11#341711yescharacteristic
283D11—82no—
284#41—24no—
285#41—42no—
286#41—224no—
287#41—442no—
288C2×Q8—21no—
289C2×Q8—221no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—221no—
293C2×D4—441no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—442no—
297C22×C4—442no—
298C22×C4—441no—
299C22×C4—441no—
300C22×C4D4×D1111yescharacteristic
301Q16—21no—
302Q16—112no—
303Q16—221no—
304Q16C2×C4×D1112yes—
305SD16—24no—
306SD16—224no—
307D8—21no—
308D8—112no—
309D8—221no—
310D8C2×C4×D1112yes—
311M16—222no—
312C2×C8—112no—
313C2×C8C2×C4×D1112yes—
314C2×C8D4×D1111yescharacteristic
315C2×C8#434112yes—
316C2×C8C23×D1111yescharacteristic
317C4⋊C4—22no—
318C4⋊C4—41no—
319C4⋊C4—111no—
320C4⋊C4—111no—
321C4⋊C4—222no—
322C4⋊C4—442no—
323C4⋊C4—442no—
324C4⋊C4—441no—
325C22⋊C4—112no—
326C22⋊C4—442no—
327C22⋊C4—442no—
328C42—112no—
329C42—442no—
330C42—442no—
331C16—22no—
332C16—112no—
333C16—112no—
334C11#3345911yescharacteristic, complemented, Sylow
335C23—41no—
336C23—441no—
337C23D8×D1111yescharacteristic
338Q8—22no—
339Q8—41no—
340Q8—222no—
341Q8—441no—
342D4—22no—
343D4—44no—
344D4—41no—
345D4—222no—
346D4—444no—
347D4—441no—
348C2×C4—41no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—112no—
352C2×C4—112no—
353C2×C4—161no—
354C2×C4—441no—
355C2×C4—444no—
356C2×C4—442no—
357C2×C4—1762no—
358C2×C4—1762no—
359C2×C4—1761no—
360C2×C4(C22⋊D11)⋊C412yes—
361C2×C4D8×D1111yescharacteristic
362C2×C4#6696912yes—
363C2×C4C2×D4×D1111yescharacteristic
364C8—222no—
365C8(C22⋊D11)⋊C412yes—
366C8C22×C4×D1111yescharacteristic
367C8C2×#434111yescharacteristic
368C22—21no—
369C22—21no—
370C22—42no—
371C22—81no—
372C22—81no—
373C22—442no—
374C22—881no—
375C22—881no—
376C22#1062236912yes—
377C22C2×D8×D1111yescharacteristic
378C4—42no—
379C4—82no—
380C4—222no—
381C4—222no—
382C4—442no—
383C4—882no—
384C4#1062236912yes—
385C4C2×(C22⋊D11)⋊C411yescharacteristic
386C4C2×#6696911yescharacteristic
387C2—22no—
388C2—82no—
389C2—882no—
390C2C2×#1062236911yescharacteristic
391C2#1308175611yescharacteristic
392C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2139C2
socleC22×C11C22×D8
prime radicalC2×#10622807C2
cosocleC2×C8×C11C24
hypercenter#2139D11
hypocenterC11#33459
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2139

Complements

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

NH ≅ G/Ntype
2. #13077492C2semidirect
3. #13077490C2semidirect
4. #13070483C2semidirect
5. #13070477C2semidirect
6. #13070472C2semidirect
7. #13070460C2semidirect
8. C2×#10622127C2semidirect
9. #13070329C2semidirect
10. #13070215C2semidirect
11. C11×#2139C2semidirect
19. #10622807C4semidirect
45. C11×#135C2×C4semidirect
62. #66957C2×C4semidirect
75. #66893C2×C4semidirect
76. #66892C2×C4semidirect
77. #66891C2×C4semidirect
78. #66890C2×C4semidirect
83. C2×C11⋊C16C2×C4semidirect
148. #2139D11semidirect
237. #135C4×D11semidirect
334. C11#33459semidirect

Maximal subgroups

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

subgroupindex
C2×#106228072
#130774922
#130774902
#130704832
#130704772
#130704722
#130704602
C2×#106221272
#130703292
#130702152
C11×#21392
#3345911