Finite Group Databasebeta

← #14649468

Subgroups — #14649468

Order 2816.

612 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#13076968C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3C2×#10622120C212yesmaximal, complemented
4#13066500C212yesmaximal, complemented
5C2×C11×#423C211yesmaximal, characteristic
6C22×C11×M16—21no—
7C22×C42×C11C2211yescharacteristic
8C2×#66977—21no—
9C2×#66922C2211yescharacteristic
10C11×#423—24no—
11C2×C11×C4⋊C8—21no—
12C2×C11×C4⋊C8C2212yes—
13#10622825—21no—
14#10622825C412yes—
15C2×C22⋊(C11⋊C8)—21no—
16#10622548C2211yescharacteristic
17#10622542—21no—
18#10622541—21no—
19#10622541C412yes—
20C2×C4⋊(C11⋊C8)C2212yes—
21#10622162—21no—
22#10622120—24no—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×Dic22—21no—
27C2×C11×M16—24no—
28C2×C11×M16—42no—
29C2×C11×M16—42no—
30C22×C8×C11—22no—
31C2×C42×C11—22no—
32C2×C42×C11—22no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C2×C22⋊Dic11—22no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11C2×C412yes—
42C2×C4⋊Dic11C2×C412yes—
43#66977—42no—
44#66977—42no—
45C2×Dic11⋊C4—22no—
46C22×C11⋊C8—22no—
47#66922—22no—
48#66922—22no—
49C11×C4⋊C8—24no—
50C11×C4⋊C8—22no—
51C11×C4⋊C8D414yes—
52C11⋊#95—22no—
53C11⋊#95—22no—
54C22⋊(C11⋊C8)—42no—
55C4⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—22no—
57#9139—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—22no—
69C22×C4×C11—41no—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11D812yes—
74C22×C4×C11SD1612yes—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×Dic11—22no—
79C22×Dic11—22no—
80C2×Dic22—41no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C2×Dic22—41no—
84C2×Dic22—41no—
85C2×Dic22—41no—
86C11×M16—48no—
87C2×C8×C11—24no—
88C2×C8×C11—42no—
89C2×C8×C11—42no—
90C42×C11—22no—
91C42×C11—21no—
92C42×C11—22no—
93C42×C11—21no—
94C42×C11C2×D412yes—
95C42×C11#4112yes—
96C22⋊Dic11—44no—
97C4⋊Dic11—24no—
98C4⋊Dic11—42no—
99C4⋊Dic11—42no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104Dic11⋊C4—44no—
105C2×C11⋊C8—42no—
106C2×C11⋊C8—42no—
107C2×C11⋊C8—42no—
108C2×#423D1111yescharacteristic
109#2857—111no—
110#1797—111no—
111C2×#332—112no—
112#1296—112no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11#10212yes—
120C23×C11C2×C22⋊C411yescharacteristic
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—44no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11#10112yes—
138C2×C4×C11#10212yes—
139C2×C4×C11C4×D412yes—
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12112yes—
142C2×C4×C11#12311yescharacteristic
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×SD1611yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11#13712yes—
148C2×C4×C11#13711yescharacteristic
149C2×C4×C11#13711yescharacteristic
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156Dic22—81no—
157Dic22—81no—
158Dic22—81no—
159Dic22—81no—
160C8×C11—44no—
161C11⋊C8—82no—
162C22×M16—21no—
163C2×C4⋊Q8—111no—
164C2×C22⋊Q8—221no—
165C22×C42C2×D1111yescharacteristic
166#423—24no—
167C2×C4⋊C8—21no—
168C2×C4⋊C8—112no—
169C2×C4⋊C8C2×D1112yes—
170C2×C22⋊C8—221no—
171#391—221no—
172#389—112no—
173#389—221no—
174#384—111no—
175#380—112no—
176#380—221no—
177#336—221no—
178#332—224no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11#38611yescharacteristic
187C22×C11C2×#10111yescharacteristic
188C22×C11#41311yescharacteristic
189C22×C11C2×#10211yescharacteristic
190C22×C11#41711yescharacteristic
191C22×C11#41711yescharacteristic
192C22×C11#41911yescharacteristic
193C4×C11—22no—
194C4×C11—22no—
195C4×C11—22no—
196C4×C11—41no—
197C4×C11#44711yescharacteristic
198C4×C11#44811yescharacteristic
199C4×C11#46812yes—
200C4×C11#47012yes—
201C4×C11#48011yescharacteristic
202C4×C11#48111yescharacteristic
203Dic11—82no—
204Dic11—82no—
205C22×Q8—221no—
206C23×C4C4×D1111yescharacteristic
207C23×C4D4411yescharacteristic
208C23×C4C22⋊D1111yescharacteristic
209C2×M16—24no—
210C2×M16—42no—
211C2×M16—42no—
212C22×C8—22no—
213C22×C8—222no—
214C4⋊Q8—222no—
215C4⋊Q8—222no—
216C22⋊Q8—442no—
217C22⋊Q8—442no—
218C2×C4⋊C4—112no—
219C2×C4⋊C4—112no—
220C2×C4⋊C4—222no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C22⋊C4—222no—
225C2×C42—22no—
226C2×C42—22no—
227C2×C42C4×D1111yescharacteristic
228C2×C42D4411yescharacteristic
229C2×C42C22⋊D1111yescharacteristic
230C2×C42C22×D1111yescharacteristic
231C4⋊C8—24no—
232C4⋊C8—22no—
233C4⋊C8—222no—
234C4⋊C8—222no—
235C4⋊C8C22⋊D1114yes—
236C22⋊C8—442no—
237#95—222no—
238#95—222no—
239C2×C11—42no—
240C2×C11#154611yescharacteristic
241C2×C11#154711yescharacteristic
242C2×C11#155911yescharacteristic
243C2×C11#156111yescharacteristic
244C2×C11#187411yescharacteristic
245C2×C11#189411yescharacteristic
246C2×C11#190111yescharacteristic
247C24(C2×D11)⋊C411yescharacteristic
248C2×Q8—441no—
249C2×Q8—441no—
250C2×Q8—441no—
251C2×Q8—441no—
252C2×Q8—441no—
253C2×Q8—441no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4—222no—
266C22×C4—222no—
267C22×C4(C2×D11)⋊C411yescharacteristic
268C22×C4(C2×D11)⋊C411yescharacteristic
269C22×C4(C2×D11)⋊C411yescharacteristic
270C22×C4#432312yes—
271C22×C4#432512yes—
272C22×C4C2×C4×D1111yescharacteristic
273C22×C4C2×D4411yescharacteristic
274C22×C4C2×C22⋊D1111yescharacteristic
275M16—48no—
276C2×C8—24no—
277C2×C8—42no—
278C2×C8—42no—
279C2×C8—442no—
280C2×C8—442no—
281C2×C8—442no—
282C4⋊C4—224no—
283C4⋊C4—442no—
284C4⋊C4—444no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—442no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C22⋊C4—444no—
291C42—22no—
292C42—21no—
293C42—22no—
294C42—21no—
295C42#433912yes—
296C42C2×C22⋊D1112yes—
297C11#913911yescharacteristic, complemented, Sylow
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23#6687312yes—
305C23C2×(C2×D11)⋊C411yescharacteristic
306Q8—881no—
307Q8—881no—
308Q8—881no—
309Q8—881no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—44no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4—442no—
332C2×C4#6687312yes—
333C2×C4#6688812yes—
334C2×C4#6696111yescharacteristic
335C2×C4#6696212yes—
336C2×C4#6696211yescharacteristic
337C2×C4C4×C22⋊D1112yes—
338C2×C4#6698211yescharacteristic
339C2×C4#6698312yes—
340C2×C4C2×#432311yescharacteristic
341C2×C4#6698511yescharacteristic
342C2×C4C2×#432511yescharacteristic
343C2×C4#6699511yescharacteristic
344C2×C4#6700611yescharacteristic
345C8—44no—
346C8—882no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22C2×#6687311yescharacteristic
355C22#1062257911yescharacteristic
356C22#1062273311yescharacteristic
357C22#1062274511yescharacteristic
358C22#1062274611yescharacteristic
359C22C2×#6688811yescharacteristic
360C22#1062282611yescharacteristic
361C4—22no—
362C4—22no—
363C4—22no—
364C4—41no—
365C4—882no—
366C4—882no—
367C4#1062258011yescharacteristic
368C4#1062258111yescharacteristic
369C4#1062274712yes—
370C4#1062275012yes—
371C4#1062283011yescharacteristic
372C4#1062284011yescharacteristic
373C2—42no—
374C2#1306728911yescharacteristic
375C2#1306729411yescharacteristic
376C2#1306734411yescharacteristic
377C2#1306735311yescharacteristic
378C2#1306893311yescharacteristic
379C2#1306904911yescharacteristic
380C2#1306908411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#423C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#423D11
hypocenterC11#9139
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
3. C2×#10622120C2semidirect
4. #13066500C2semidirect
297. C11#9139semidirect

Maximal subgroups

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

subgroupindex
#130769682
#130685962
C2×#106221202
#130665002
C2×C11×#4232
#913911