Finite Group Databasebeta

← #14907115

Subgroups — #14907115

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622760C211yesmaximal, characteristic
2#13077493C211yesmaximal, characteristic, complemented
3#13070490C212yesmaximal, complemented
4#13070480C212yesmaximal, complemented
5C4×#66891C212yesmaximal, complemented
6C4×#66890C212yesmaximal, complemented
7#13070405C211yesmaximal, characteristic, complemented
8#13070321C211yesmaximal, characteristic, complemented
9C2×#10622200C211yesmaximal, characteristic, complemented
10#13070213C211yesmaximal, characteristic, complemented
11C11×#2948C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C11×#518—21no—
14C2×#66957C2211yescharacteristic
15#10623054—21no—
16C11×#442—22no—
17C4×C11×D8C2212yes—
18C4×C11×D8C2212yes—
19C11×#427C2211yescharacteristic
20C11×#418—21no—
21C11×#405C2211yescharacteristic
22C2×#66891C2212yes—
23#10622760C418yescomplemented
24C2×#66890C2212yes—
25#10622746—21no—
26C2×#66882C2211yescharacteristic
27C2×#66876C2211yescharacteristic
28C22×C11⋊C16C2211yescharacteristic
29#10622323—22no—
30C4×Dic44C2212yescomplemented
31C4×D88C2212yescomplemented
32#10622200C2212yes—
33#10622200C2212yes—
34#10622130C2211yescharacteristic, complemented
35#10622130C2211yescharacteristic, complemented
36#10622129C2211yescharacteristic, complemented
37#10622129C2211yescharacteristic, complemented
38#10622128C2212yescomplemented
39#10622127C2212yescomplemented
40#10622099C2212yescomplemented
41C4×C11⋊C16C2212yescomplemented
42C22×D4×C11—21no—
43C2×#4339—21no—
44C2×C11×D8—21no—
45C2×C11×D8—22no—
46C2×C11×D8C2×C414yescomplemented
47C2×C11×D8C2312yes—
48C2×C11×M16D411yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C4×D4×C11—22no—
51C4×D4×C11—22no—
52C4×D4×C11—41no—
53C4×D4×C11—41no—
54C11×#117—21no—
55C11×#117D411yescharacteristic
56C2×C11×C22⋊C4—42no—
57C2×C4⋊Dic11—21no—
58C2×Dic44C2311yescharacteristic
59#66957—22no—
60#66957C2×C414yescomplemented
61C2×D88C2311yescharacteristic
62C2×#4314—21no—
63#66945—41no—
64C4⋊C4×D11—41no—
65(C22⋊D11)⋊C4—42no—
66C4×D44—22no—
67C4×Dic22—22no—
68C11×#107C2311yescharacteristic
69C11×#107C2311yescharacteristic
70C11×#106—21no—
71C11×#102—22no—
72C11×#102—22no—
73C11×#97D412yes—
74C4×C8×C11C2312yes—
75#66891C2×C418yescomplemented
76#66890C2×C418yescomplemented
77#66885—22no—
78#66882—21no—
79#66882C2312yes—
80#66880—22no—
81#66876C2×C414yescomplemented
82C2×C11⋊C16—22no—
83C2×C11⋊C16C2311yescharacteristic
84C2×C11⋊C16C2311yescharacteristic
85C2×C11⋊C16C2312yes—
86#33454—111nomaximal, Sylow
87C24×C11—41no—
88C2×D4×C11—24no—
89C2×D4×C11—22no—
90C2×D4×C11—41no—
91C2×D4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11C2×D411yescharacteristic
95C2×C22⋊D11—41no—
96C22×Dic11—41no—
97#4339—24no—
98#4339—42no—
99C2×D44—21no—
100C2×C4×D11—41no—
101C2×C4×D11—42no—
102C2×Dic22—21no—
103C11×D8—24no—
104C11×D8—22no—
105C11×D8C22×C414yes—
106C11×M16—22no—
107C2×C8×C11C22×C412yes—
108C2×C8×C11C2×D412yes—
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11#4112yes—
111C2×C8×C11C2411yescharacteristic
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4D811yescharacteristic
115C11×C4⋊C4D811yescharacteristic
116C11×C22⋊C4—41no—
117C11×C22⋊C4—42no—
118C11×C22⋊C4—42no—
119C11×C22⋊C4D812yes—
120C42×C11—41no—
121C42×C11C2×D412yes—
122(C2×D11)⋊C4—42no—
123C4⋊Dic11—22no—
124C4⋊Dic11—41no—
125Dic11⋊C4—42no—
126C4×Dic11—42no—
127Dic44—21no—
128Dic44C22×C412yes—
129D88—21no—
130D88C22×C412yes—
131#4314—24no—
132C11⋊C16—21no—
133C11⋊C16—21no—
134C11⋊C16C22×C414yes—
135C2×#509—111no—
136#2951—111no—
137#2948D1111yescharacteristic, complemented
138#2177—112no—
139#2175—112no—
140C4×SD32—112no—
141C4×D16—112no—
142#2159—111no—
143#2138—111no—
144C2×#357—111no—
145#2108—111no—
146C23×C11—42no—
147C23×C11—44no—
148C23×C11—161no—
149C23×C11—161no—
150C23×C11C2×D811yescharacteristic
151C22×D11—41no—
152D4×C11—24no—
153D4×C11—42no—
154D4×C11—44no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—162no—
158C2×C4×C11—162no—
159C2×C4×C11C4×D412yes—
160C2×C4×C11C2×D812yes—
161C2×C4×C11C2×D812yes—
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11#13512yes—
164C2×C4×C11C22×D411yescharacteristic
165C22⋊D11—44no—
166C2×Dic11—41no—
167C2×Dic11—42no—
168C2×Dic11—161no—
169D44—22no—
170D44—41no—
171C4×D11—44no—
172C4×D11—162no—
173Dic22—22no—
174Dic22—41no—
175C8×C11—22no—
176C8×C11C4×D412yes—
177C8×C11C23×C411yescharacteristic
178C8×C11C2×#4111yescharacteristic
179C2×#135—111no—
180C22×D8C2×D1111yescharacteristic
181#520—221no—
182#518—21no—
183#509—118no—
184C2×SD32—112no—
185C2×D16—112no—
186C2×M32—111no—
187C22×C16—111no—
188#442—22no—
189#440—222no—
190C4×Q16—112no—
191C4×D8—112no—
192C4×D8C2×D1112yes—
193C4×D8C2×D1112yes—
194#427C2×D1111yescharacteristic
195C2×#107—111no—
196#418—21no—
197#417—221no—
198#405C2×D1111yescharacteristic
199#367—112no—
200#366—112no—
201#358—111no—
202#358—111no—
203#357—112no—
204#357—112no—
205#357—111no—
206#357—111no—
207#346—112no—
208C4×C16—112no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—44no—
212C22×C11—82no—
213C22×C11—82no—
214C22×C11—164no—
215C22×C11C4×D812yes—
216C22×C11C22×D811yescharacteristic
217C2×D11—42no—
218C2×D11—81no—
219C2×D11—81no—
220C4×C11—22no—
221C4×C11—22no—
222C4×C11—81no—
223C4×C11—81no—
224C4×C11C4×D812yes—
225C4×C11C2×C4×D411yescharacteristic
226C4×C11C2×#13511yescharacteristic
227Dic11—42no—
228Dic11—82no—
229C2×#41—221no—
230C22×D4—21no—
231#135—114no—
232#135—222no—
233C2×Q16—111no—
234C2×SD16—221no—
235C2×D8—22no—
236C2×D8—21no—
237C2×D8—111no—
238C2×D8C4×D1114yescomplemented
239C2×D8C22×D1112yes—
240C2×M16C22⋊D1111yescharacteristic
241C22×C8C22×D1111yescharacteristic
242C4×Q8—222no—
243C4×D4—22no—
244C4×D4—22no—
245C4×D4—41no—
246C4×D4—41no—
247C4×D4—222no—
248C4×D4—442no—
249#117—21no—
250#117—441no—
251#117C22⋊D1111yescharacteristic
252C2×C4⋊C4—221no—
253C2×C4⋊C4—441no—
254C2×C22⋊C4—42no—
255SD32—118no—
256D16—118no—
257M32—114no—
258C2×C16—112no—
259C2×C16—111no—
260C2×C16—111no—
261C2×C16—222no—
262#107—112no—
263#107—221no—
264#107C22×D1111yescharacteristic
265#107C22×D1111yescharacteristic
266#106—21no—
267#103—222no—
268#102—22no—
269#102—22no—
270#102—222no—
271#97C22⋊D1112yes—
272C4×C8C22×D1112yes—
273C2×C11—22no—
274C2×C11—84no—
275C2×C11C2×C4×D811yescharacteristic
276C2×C11#341511yescharacteristic
277C2×C11#341611yescharacteristic
278D11—82no—
279C24—41no—
280#41—224no—
281#41—442no—
282C2×Q8—221no—
283C2×D4—24no—
284C2×D4—22no—
285C2×D4—41no—
286C2×D4—42no—
287C2×D4—221no—
288C2×D4—441no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—441no—
292C22×C4—441no—
293C22×C4—442no—
294C22×C4C2×C22⋊D1111yescharacteristic
295Q16—112no—
296Q16—221no—
297SD16—224no—
298D8—24no—
299D8—22no—
300D8—112no—
301D8—221no—
302D8C2×C4×D1114yes—
303M16—22no—
304C2×C8C2×C4×D1112yes—
305C2×C8#433912yes—
306C2×C8C2×C22⋊D1112yes—
307C2×C8C2×C22⋊D1111yescharacteristic
308C2×C8C23×D1111yescharacteristic
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—222no—
312C4⋊C4—441no—
313C4⋊C4—442no—
314C4⋊C4#432311yescharacteristic
315C4⋊C4#432311yescharacteristic
316C22⋊C4—41no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—442no—
320C22⋊C4#432312yes—
321C42—41no—
322C42—442no—
323C42C2×C22⋊D1112yes—
324C16—114no—
325C16—221no—
326C16—221no—
327C11#3345411yescharacteristic, complemented, Sylow
328C23—42no—
329C23—44no—
330C23—161no—
331C23—161no—
332C23—441no—
333C23C2×#432311yescharacteristic
334Q8—222no—
335Q8—441no—
336D4—24no—
337D4—42no—
338D4—44no—
339D4—222no—
340D4—444no—
341D4—441no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—162no—
345C2×C4—162no—
346C2×C4—441no—
347C2×C4—444no—
348C2×C4—442no—
349C2×C4—1762no—
350C2×C4—1761no—
351C2×C4C4×C22⋊D1112yes—
352C2×C4C2×#432312yes—
353C2×C4C2×#432312yes—
354C2×C4C2×#432311yescharacteristic
355C2×C4#6700312yes—
356C2×C4C22×C22⋊D1111yescharacteristic
357C8—22no—
358C8C4×C22⋊D1112yes—
359C8C22×C4×D1111yescharacteristic
360C8C2×#433911yescharacteristic
361C22—21no—
362C22—21no—
363C22—44no—
364C22—82no—
365C22—82no—
366C22—164no—
367C22—442no—
368C22—881no—
369C22—881no—
370C22C4×#432312yes—
371C22C22×#432311yescharacteristic
372C4—22no—
373C4—22no—
374C4—81no—
375C4—81no—
376C4—442no—
377C4—882no—
378C4C4×#432312yes—
379C4C2×C4×C22⋊D1111yescharacteristic
380C4C2×#6700311yescharacteristic
381C2—22no—
382C2—84no—
383C2—882no—
384C2C2×C4×#432311yescharacteristic
385C2#1308175511yescharacteristic
386C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2948C2
socleC22×C11C22×D8
prime radicalC2×#10622760C2
cosocleC2×C8×C11C24
hypercenter#2948D11
hypocenterC11#33454
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2948

Complements

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

NH ≅ G/Ntype
2. #13077493C2semidirect
3. #13070490C2semidirect
4. #13070480C2semidirect
5. C4×#66891C2semidirect
6. C4×#66890C2semidirect
7. #13070405C2semidirect
8. #13070321C2semidirect
9. C2×#10622200C2semidirect
10. #13070213C2semidirect
11. C11×#2948C2semidirect
23. #10622760C4semidirect
30. C4×Dic44C22semidirect
31. C4×D88C22semidirect
34. #10622130C22semidirect
35. #10622130C22semidirect
36. #10622129C22semidirect
37. #10622129C22semidirect
38. #10622128C22semidirect
39. #10622127C22semidirect
40. #10622099C22semidirect
41. C4×C11⋊C16C22semidirect
46. C2×C11×D8C2×C4semidirect
60. #66957C2×C4semidirect
75. #66891C2×C4semidirect
76. #66890C2×C4semidirect
81. #66876C2×C4semidirect
137. #2948D11semidirect
238. C2×D8C4×D11semidirect
327. C11#33454semidirect

Maximal subgroups

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

subgroupindex
C2×#106227602
#130774932
#130704902
#130704802
C4×#668912
C4×#668902
#130704052
#130703212
C2×#106222002
#130702132
C11×#29482
#3345411