Finite Group Databasebeta

← #14907017

Subgroups — #14907017

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081719C211yesmaximal, characteristic, complemented
2#13081718C211yesmaximal, characteristic, complemented
3#13077517C211yesmaximal, characteristic
4#13070455C214yesmaximal, complemented
5#13070450C214yesmaximal, complemented
6#13070381C211yesmaximal, characteristic, complemented
7C2×#10622146C211yesmaximal, characteristic, complemented
8#13070212C211yesmaximal, characteristic, complemented
9C2×C11×#350C211yesmaximal, characteristic, complemented
10C2×C11×#131C2211yescharacteristic
11#10623353C411yescharacteristic
12C2×#66954C2211yescharacteristic
13C2×C11×M32C2211yescharacteristic
14C22×C11×C16C2211yescharacteristic
15#10622849C411yescharacteristic
16#10622758C414yes—
17#10622757C2214yes—
18#10622753—22no—
19#10622753C2214yescomplemented
20#10622752C411yescharacteristic
21#10622737C411yescharacteristic
22#10622714C2211yescharacteristic
23C2×#66876—22no—
24C2×#66876C2211yescharacteristic
25C2×#66876C2211yescharacteristic
26#10622520C2214yescomplemented
27D11×M32—22no—
28#10622514—22no—
29C11×#350C2212yescomplemented
30C11×#350C2212yescomplemented
31#10622149C2214yescomplemented
32#10622146C2212yescomplemented
33#10622146C2212yescomplemented
34#10622140C2212yescomplemented
35C16×Dic11C2212yescomplemented
36C2×C11×#41C2×C411yescharacteristic
37C2×#4339C2×C411yescharacteristic
38C11×#131—21no—
39C11×#131—21no—
40C11×#131C2×C412yes—
41C11×#131C2312yes—
42C2×C11×M16—21no—
43C2×C11×M16C2×C411yescharacteristic
44C22×C8×C11—21no—
45C22×C8×C11C2311yescharacteristic
46#67004C812yes—
47#67003C2×C414yes—
48#67002C812yes—
49#66995C812yes—
50#66985C812yes—
51#66979C2×C411yescharacteristic
52C2×#4318C2×C411yescharacteristic
53C2×#4318C2×C411yescharacteristic
54#66954—21no—
55#66954—21no—
56#66954C2×C412yes—
57#66954C2312yes—
58C2×#4313—21no—
59C2×C8×D11—21no—
60C11×M32—21no—
61C11×M32C2312yes—
62C2×C11×C16—21no—
63C2×C11×C16—21no—
64C2×C11×C16—21no—
65C2×C11×C16C2311yescharacteristic
66C2×C11×C16C2311yescharacteristic
67#66901C2×C414yes—
68#66889C2×C414yes—
69#66886C2×C414yes—
70#66879C2×C412yes—
71C8×Dic11C2312yes—
72#66876—21no—
73#66876—24no—
74#66876D412yes—
75#66876D412yes—
76#66876C2312yes—
77C2×C11⋊C16—21no—
78C2×C11⋊C16—24no—
79C2×C11⋊C16C2312yes—
80#66862—24no—
81C16×D11—24no—
82#33442—111nomaximal, Sylow
83C11×#41—21no—
84C11×#41—21no—
85C11×#41C2×C812yes—
86C11×#41C22×C412yes—
87C2×Q8×C11C2×C811yescharacteristic
88C2×D4×C11—21no—
89C2×D4×C11C2×C811yescharacteristic
90C22×C4×C11—21no—
91C22×C4×C11C22×C411yescharacteristic
92C2×C22⋊D11—21no—
93#4339—21no—
94#4339—21no—
95#4339C2×C812yes—
96#4339C22×C412yes—
97C2×D44C2×C811yescharacteristic
98C2×C4×D11—21no—
99C2×Dic22C2×C811yescharacteristic
100C11×M16—22no—
101C11×M16—22no—
102C11×M16—21no—
103C11×M16C22×C412yes—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—21no—
107C2×C8×C11C22×C411yescharacteristic
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11#4111yescharacteristic
111C2×C8×C11#4111yescharacteristic
112C2×C8×C11C2411yescharacteristic
113C22⋊Dic11—21no—
114#4326C2×C814yes—
115#4325C2×C814yes—
116#4324C2×C814yes—
117#4323C2×C814yes—
118C4⋊Dic11—21no—
119C4×Dic11C22×C412yes—
120#4318—21no—
121#4318C2×C812yes—
122#4318C2×C812yes—
123#4318C22×C412yes—
124C2×C11⋊C8—21no—
125C2×C11⋊C8C22×C412yes—
126#4313—22no—
127#4313—22no—
128C8×D11—22no—
129C8×D11—22no—
130C11×C16—22no—
131C11×C16—21no—
132C11×C16—21no—
133C11⋊C16—22no—
134C11⋊C16C2×D414yes—
135#3407—111no—
136#3407—111no—
137#2955—111no—
138#2171—114no—
139#2170—114no—
140#2153—111no—
141C2×#350—111no—
142C2×#350D1111yescharacteristic, complemented
143#2108—111no—
144C23×C11—21no—
145C23×C11#13111yescharacteristic
146C22×D11—21no—
147Q8×C11—21no—
148Q8×C11C22×C812yes—
149D4×C11—22no—
150D4×C11—22no—
151D4×C11—21no—
152D4×C11C22×C812yes—
153C2×C4×C11—21no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11C22×C811yescharacteristic
159C2×C4×C11C22×C811yescharacteristic
160C2×C4×C11#13111yescharacteristic
161C2×C4×C11C23×C411yescharacteristic
162C22⋊D11—22no—
163C22⋊D11—22no—
164C2×Dic11—21no—
165C2×Dic11—22no—
166D44—21no—
167D44C22×C812yes—
168C4×D11—22no—
169C4×D11—22no—
170Dic22—21no—
171Dic22C22×C812yes—
172C8×C11—22no—
173C8×C11C4×D411yescharacteristic
174C8×C11C4×D411yescharacteristic
175C8×C11C22×D411yescharacteristic
176C8×C11C2×#4111yescharacteristic
177C11⋊C8—22no—
178C11⋊C8C22×C814yes—
179#575—111no—
180C2×#131—111no—
181C2×#131C2×D1111yescharacteristic
182#504—114no—
183#504—114no—
184#504—222no—
185#504—222no—
186C2×M32—111no—
187C2×M32—111no—
188C2×M32—222no—
189C2×M32—222no—
190C2×M32C2×D1111yescharacteristic
191C22×C16C2×D1111yescharacteristic
192#444—114no—
193#443—114no—
194#430—111no—
195#421—111no—
196#421—111no—
197#405—111no—
198#364—114no—
199#350—112no—
200#350—112no—
201#350C2×D1112yescomplemented
202#350C2×D1112yescomplemented
203#346—112no—
204C4×C16—112no—
205C22×C11—22no—
206C22×C11—41no—
207C22×C11—81no—
208C22×C11C8×D411yescharacteristic
209C22×C11C8×D411yescharacteristic
210C22×C11C2×#13111yescharacteristic
211C2×D11—22no—
212C2×D11—81no—
213C4×C11—22no—
214C4×C11C8×D411yescharacteristic
215C4×C11C8×D411yescharacteristic
216C4×C11C2×C4×D411yescharacteristic
217C4×C11C23×C811yescharacteristic
218Dic11—22no—
219Dic11—42no—
220C2×#41—111no—
221C2×#41C4×D1111yescharacteristic
222#137—112no—
223#137—112no—
224AGL(1,ℤ/8)—112no—
225AGL(1,ℤ/8)—112no—
226#135—114no—
227#131—21no—
228#131—21no—
229#131—112no—
230#131—112no—
231#131—221no—
232#131—221no—
233#131C4×D1112yes—
234#131C22×D1112yes—
235C2×M16—21no—
236C2×M16—111no—
237C2×M16—111no—
238C2×M16—221no—
239C2×M16C4×D1111yescharacteristic
240C22×C8—21no—
241C22×C8—221no—
242C22×C8C22×D1111yescharacteristic
243#117—111no—
244M32—21no—
245M32—112no—
246M32—112no—
247M32—112no—
248M32—224no—
249M32—224no—
250M32—221no—
251M32C22×D1112yes—
252C2×C16—21no—
253C2×C16—21no—
254C2×C16—21no—
255C2×C16—112no—
256C2×C16—224no—
257C2×C16—224no—
258C2×C16—221no—
259C2×C16C22×D1111yescharacteristic
260C2×C16C22×D1111yescharacteristic
261#108—114no—
262#104—114no—
263#104—114no—
264#97—112no—
265C4×C8—112no—
266C2×C11—21no—
267C2×C11—21no—
268C2×C11—21no—
269C2×C11—42no—
270C2×C11C2×C8×D411yescharacteristic
271D11—42no—
272#41—21no—
273#41—21no—
274#41—112no—
275#41—112no—
276#41—221no—
277#41—221no—
278#41C8×D1112yes—
279#41C2×C4×D1112yes—
280C2×Q8—111no—
281C2×Q8C8×D1111yescharacteristic
282C2×D4—21no—
283C2×D4—111no—
284C2×D4—221no—
285C2×D4C8×D1111yescharacteristic
286C22×C4—21no—
287C22×C4—221no—
288C22×C4C2×C4×D1111yescharacteristic
289Q16—114no—
290SD16—114no—
291SD16—114no—
292D8—114no—
293M16—21no—
294M16—22no—
295M16—22no—
296M16—112no—
297M16—112no—
298M16—112no—
299M16—221no—
300M16—222no—
301M16—222no—
302M16C2×C4×D1112yes—
303C2×C8—21no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—112no—
307C2×C8—221no—
308C2×C8—222no—
309C2×C8—222no—
310C2×C8C2×C4×D1111yescharacteristic
311C2×C8D4×D1111yescharacteristic
312C2×C8D4×D1111yescharacteristic
313C2×C8#434111yescharacteristic
314C2×C8#434111yescharacteristic
315C2×C8C23×D1111yescharacteristic
316C4⋊C4—221no—
317C22⋊C4—221no—
318C42—112no—
319C16—22no—
320C16—21no—
321C16—21no—
322C16—114no—
323C16—222no—
324C11#3344211yescharacteristic, complemented, Sylow
325C23—21no—
326C23—221no—
327C23#6696011yescharacteristic
328Q8—21no—
329Q8—112no—
330Q8—221no—
331Q8C2×C8×D1112yes—
332D4—22no—
333D4—22no—
334D4—21no—
335D4—112no—
336D4—222no—
337D4—222no—
338D4—221no—
339D4C2×C8×D1112yes—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—221no—
344C2×C4—222no—
345C2×C4—222no—
346C2×C4—222no—
347C2×C4(C22⋊D11)⋊C411yescharacteristic
348C2×C4(C22⋊D11)⋊C411yescharacteristic
349C2×C4C2×C8×D1111yescharacteristic
350C2×C4C2×C8×D1111yescharacteristic
351C2×C4#6696011yescharacteristic
352C2×C4C22×C4×D1111yescharacteristic
353C8—22no—
354C8—114no—
355C8—222no—
356C8(C22⋊D11)⋊C411yescharacteristic
357C8(C22⋊D11)⋊C411yescharacteristic
358C8C2×D4×D1111yescharacteristic
359C8C2×#434111yescharacteristic
360C22—22no—
361C22—41no—
362C22—81no—
363C22—222no—
364C22—881no—
365C22(C22⋊D11)⋊C811yescharacteristic
366C22(C22⋊D11)⋊C811yescharacteristic
367C22C2×#6696011yescharacteristic
368C4—22no—
369C4—222no—
370C4—442no—
371C4(C22⋊D11)⋊C811yescharacteristic
372C4(C22⋊D11)⋊C811yescharacteristic
373C4C2×(C22⋊D11)⋊C411yescharacteristic
374C4C22×C8×D1111yescharacteristic
375C2—21no—
376C2—21no—
377C2—21no—
378C2—42no—
379C2—442no—
380C2C2×(C22⋊D11)⋊C811yescharacteristic
subgroupG/H
centerC8C2×D4×D11
commutatorC4×C11C23×C8
FrattiniC2×C8C23×D11
FittingC2×C11×#350C2
socleC2×C11C2×C8×D4
prime radical#10623353C4
cosocleC2×C8×C11C24
hypercenterC2×#350D11
hypocenterC11#33442
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
1. #13081719C2semidirect
2. #13081718C2semidirect
4. #13070455C2semidirect
5. #13070450C2semidirect
6. #13070381C2semidirect
7. C2×#10622146C2semidirect
8. #13070212C2semidirect
9. C2×C11×#350C2semidirect
19. #10622753C22semidirect
26. #10622520C22semidirect
29. C11×#350C22semidirect
30. C11×#350C22semidirect
31. #10622149C22semidirect
32. #10622146C22semidirect
33. #10622146C22semidirect
34. #10622140C22semidirect
35. C16×Dic11C22semidirect
142. C2×#350D11semidirect
201. #350C2×D11semidirect
202. #350C2×D11semidirect
324. C11#33442semidirect

Maximal subgroups

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

subgroupindex
#130817192
#130817182
#130775172
#130704552
#130704502
#130703812
C2×#106221462
#130702122
C2×C11×#3502
#3344211