Finite Group Databasebeta

← #14649428

Subgroups — #14649428

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 380 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
5C22×C11×C4⋊C8C211yesmaximal, characteristic
6C23×C8×C11—21no—
7C22×C42×C11C2211yescharacteristic
8C2×#66977—21no—
9C2×#66922C2211yescharacteristic
10C2×C11×C4⋊C8—21no—
11C2×C11×C4⋊C8—24no—
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—
27C22×C8×C11—24no—
28C22×C8×C11—22no—
29C22×C8×C11—42no—
30C22×C8×C11—42no—
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#9131—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11—22no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—41no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11D812yes—
72C22×C4×C11SD1612yes—
73C22×C4×C11SD1612yes—
74C22×C4×C11Q1612yes—
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—
86C2×C8×C11—24no—
87C2×C8×C11—48no—
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—42no—
103Dic11⋊C4—44no—
104C2×C11⋊C8—42no—
105C2×C11⋊C8—42no—
106C2×C11⋊C8—42no—
107C22×C4⋊C8D1111yescharacteristic
108#2857—111no—
109#1797—111no—
110C2×#332—112no—
111#1296—112no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11#10112yes—
117C23×C11#10212yes—
118C23×C11#10312yes—
119C23×C11C2×C22⋊C411yescharacteristic
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—24no—
129C2×C4×C11—24no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—44no—
136C2×C4×C11#10212yes—
137C2×C4×C11#10312yes—
138C2×C4×C11C4×D412yes—
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12112yes—
141C2×C4×C11#12311yescharacteristic
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C2×SD1611yescharacteristic
144C2×C4×C11C2×SD1611yescharacteristic
145C2×C4×C11C2×Q1611yescharacteristic
146C2×C4×C11#13512yes—
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155Dic22—81no—
156Dic22—81no—
157Dic22—81no—
158Dic22—81no—
159C8×C11—44no—
160C11⋊C8—82no—
161C23×C8—21no—
162C2×C4⋊Q8—111no—
163C2×C22⋊Q8—221no—
164C22×C42C2×D1111yescharacteristic
165C2×C4⋊C8—21no—
166C2×C4⋊C8—24no—
167C2×C4⋊C8—112no—
168C2×C4⋊C8C2×D1112yes—
169C2×C22⋊C8—221no—
170#391—221no—
171#389—112no—
172#389—221no—
173#384—111no—
174#380—112no—
175#380—221no—
176#336—221no—
177#332—224no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—22no—
183C22×C11—22no—
184C22×C11#33214yescomplemented
185C22×C11#38611yescharacteristic
186C22×C11C2×#10111yescharacteristic
187C22×C11#41311yescharacteristic
188C22×C11C2×#10211yescharacteristic
189C22×C11C2×#10311yescharacteristic
190C22×C11#41611yescharacteristic
191C22×C11#41711yescharacteristic
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—22no—
195C4×C11—41no—
196C4×C11#44711yescharacteristic
197C4×C11#44811yescharacteristic
198C4×C11#46512yes—
199C4×C11#46712yes—
200C4×C11#48011yescharacteristic
201C4×C11#48111yescharacteristic
202Dic11—82no—
203Dic11—82no—
204C22×Q8—221no—
205C23×C4C4×D1111yescharacteristic
206C23×C4D4411yescharacteristic
207C23×C4C22⋊D1111yescharacteristic
208C22×C8—24no—
209C22×C8—22no—
210C22×C8—42no—
211C22×C8—42no—
212C22×C8—222no—
213C4⋊Q8—222no—
214C4⋊Q8—222no—
215C22⋊Q8—442no—
216C22⋊Q8—442no—
217C2×C4⋊C4—112no—
218C2×C4⋊C4—112no—
219C2×C4⋊C4—222no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C22⋊C4—222no—
224C2×C42—22no—
225C2×C42—22no—
226C2×C42C4×D1111yescharacteristic
227C2×C42D4411yescharacteristic
228C2×C42C22⋊D1111yescharacteristic
229C2×C42C22×D1111yescharacteristic
230C4⋊C8—24no—
231C4⋊C8—22no—
232C4⋊C8—222no—
233C4⋊C8—222no—
234C4⋊C8C22⋊D1114yes—
235C22⋊C8—442no—
236#95—222no—
237#95—222no—
238C2×C11—24no—
239C2×C11C2×#33211yescharacteristic
240C2×C11#154011yescharacteristic
241C2×C11#155011yescharacteristic
242C2×C11#155211yescharacteristic
243C2×C11#187411yescharacteristic
244C2×C11#189211yescharacteristic
245C2×C11#190111yescharacteristic
246C24(C2×D11)⋊C411yescharacteristic
247C2×Q8—441no—
248C2×Q8—441no—
249C2×Q8—441no—
250C2×Q8—441no—
251C2×Q8—441no—
252C2×Q8—441no—
253C22×C4—22no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—41no—
262C22×C4—222no—
263C22×C4—222no—
264C22×C4#431412yes—
265C22×C4Dic4412yes—
266C22×C4(C2×D11)⋊C411yescharacteristic
267C22×C4(C2×D11)⋊C411yescharacteristic
268C22×C4(C2×D11)⋊C411yescharacteristic
269C22×C4#432312yes—
270C22×C4#432512yes—
271C22×C4C2×C4×D1111yescharacteristic
272C22×C4C2×D4411yescharacteristic
273C22×C4C2×C22⋊D1111yescharacteristic
274C2×C8—24no—
275C2×C8—48no—
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—442no—
279C2×C8—442no—
280C2×C8—442no—
281C4⋊C4—224no—
282C4⋊C4—442no—
283C4⋊C4—444no—
284C4⋊C4—442no—
285C4⋊C4—442no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C22⋊C4—444no—
289C42—22no—
290C42—21no—
291C42—22no—
292C42—21no—
293C42#433912yes—
294C42C2×C22⋊D1112yes—
295C11#913111yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23#6687312yes—
301C23#6688012yes—
302C23#6688812yes—
303C23C2×(C2×D11)⋊C411yescharacteristic
304Q8—881no—
305Q8—881no—
306Q8—881no—
307Q8—881no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—24no—
315C2×C4—24no—
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—442no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4#6687312yes—
331C2×C4#6688012yes—
332C2×C4C2×#431411yescharacteristic
333C2×C4#6695712yes—
334C2×C4C2×Dic4411yescharacteristic
335C2×C4C4×C22⋊D1112yes—
336C2×C4#6698211yescharacteristic
337C2×C4#6698312yes—
338C2×C4C2×#432311yescharacteristic
339C2×C4#6698511yescharacteristic
340C2×C4C2×#432511yescharacteristic
341C2×C4#6699511yescharacteristic
342C2×C4#6700611yescharacteristic
343C8—44no—
344C8—882no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—22no—
351C22#1062212014yescomplemented
352C22C2×#6687311yescharacteristic
353C22#1062257911yescharacteristic
354C22C2×#6688011yescharacteristic
355C22#1062272611yescharacteristic
356C22#1062274511yescharacteristic
357C22C2×#6688811yescharacteristic
358C22#1062282611yescharacteristic
359C4—22no—
360C4—22no—
361C4—22no—
362C4—41no—
363C4—882no—
364C4—882no—
365C4#1062258011yescharacteristic
366C4#1062258111yescharacteristic
367C4#1062272712yes—
368C4#1062272912yes—
369C4#1062283011yescharacteristic
370C4#1062284011yescharacteristic
371C2—24no—
372C2C2×#1062212011yescharacteristic
373C2#1306726611yescharacteristic
374C2#1306730411yescharacteristic
375C2#1306731411yescharacteristic
376C2#1306893311yescharacteristic
377C2#1306903911yescharacteristic
378C2#1306908411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC22×C11×C4⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC22×C4⋊C8D11
hypocenterC11#9131
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#10622120C2semidirect
4. #13066500C2semidirect
184. C22×C11#332semidirect
295. C11#9131semidirect
351. C22#10622120semidirect

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
C22×C11×C4⋊C82
#913111