Finite Group Databasebeta

← #14763274

Subgroups — #14763274

Order 2816.

1042 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66943C211yesmaximal, characteristic
2C2×#10622331C211yesmaximal, characteristic
3#13071011C211yesmaximal, characteristic
4#13069579C214yesmaximal, complemented
5#13069570C214yesmaximal, complemented
6#13068706C211yesmaximal, characteristic
7#13068703C211yesmaximal, characteristic
8#13068700C211yesmaximal, characteristic
9C11×#1824C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic11—21no—
12C22×C4⋊Dic11C2211yescharacteristic
13C22×Dic11⋊C4—21no—
14C22×C4×Dic11C2211yescharacteristic
15C2×#66943—21no—
16C2×#66943—21no—
17C2×#66943—24no—
18C2×#66943C418yescomplemented
19C2×#66943C2212yes—
20C2×#66943C2212yes—
21C2×C11×C22⋊C8C2211yescharacteristic
22C11×#380C2211yescharacteristic
23#10622825C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25C2×Dic11⋊C8C2212yes—
26C2×C8×Dic11C2212yes—
27#10622590C2212yes—
28C4⋊C4×Dic11C2212yes—
29#10622556—21no—
30C22⋊C4×Dic11—21no—
31#10622331—24no—
32#10622264—21no—
33#10622261—21no—
34C11×#340C2214yes—
35#10622189C2214yes—
36#10622167C2214yes—
37#10622167C2214yes—
38C23×C4×C11—21no—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11—21no—
41C23×Dic11D411yescharacteristic
42C23×Dic11D411yescharacteristic
43C22×C8×C11C2312yes—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4C2×C414yes—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C22⋊C4—21no—
50C2×C22⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11—28no—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11C2×C414yes—
57C2×C4⋊Dic11C2312yes—
58C2×C4⋊Dic11C2312yes—
59C2×Dic11⋊C4—28no—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11C2×C414yes—
64C2×C4×Dic11D411yescharacteristic
65C2×C4×Dic11D411yescharacteristic
66C2×C4×Dic11D414yes—
67C2×C4×Dic11C2311yescharacteristic
68C2×C4×Dic11C2311yescharacteristic
69C22×C11⋊C8C2312yes—
70#66943—28no—
71#66943—28no—
72#66943—24no—
73#66943—24no—
74#66943C2×C418yes—
75#66943C2×C418yes—
76C11×C22⋊C8—22no—
77C11×#95—21no—
78C11⋊#95—21no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C22⋊(C11⋊C8)—22no—
83Dic11⋊C8—24no—
84C8×Dic11—24no—
85#21836—111nomaximal, Sylow
86C24×C11C2×D411yescharacteristic
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—44no—
92C22×C4×C11C22×C412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2411yescharacteristic
96C22×Dic11—24no—
97C22×Dic11—22no—
98C22×Dic11—22no—
99C22×Dic11—22no—
100C22×Dic11—22no—
101C22×Dic11—42no—
102C22×Dic11—42no—
103C22×Dic11—42no—
104C22×Dic11C22⋊C414yes—
105C22×Dic11C22⋊C414yes—
106C22×Dic11C2×D411yescharacteristic
107C22×Dic11C2×D411yescharacteristic
108C22×Dic11C2×D411yescharacteristic
109C22×Dic11C2×D411yescharacteristic
110C2×C8×C11—22no—
111C2×C8×C11—24no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4C22×C414yes—
116C11×C22⋊C4—42no—
117C22⋊Dic11—42no—
118C4⋊Dic11—28no—
119C4⋊Dic11—28no—
120C4⋊Dic11—24no—
121C4⋊Dic11—22no—
122C4⋊Dic11—24no—
123C4⋊Dic11C22×C414yes—
124Dic11⋊C4—28no—
125Dic11⋊C4—28no—
126C4×Dic11—44no—
127C4×Dic11C22⋊C414yes—
128C4×Dic11C22⋊C414yes—
129C4×Dic11C22×C412yes—
130C4×Dic11C22×C412yes—
131C4×Dic11C2×D412yes—
132C4×Dic11C2×D412yes—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—24no—
135C22×#125—111no—
136C2×#431—111no—
137#2283—111no—
138#1991—114no—
139#1989—114no—
140#1824—111no—
141#1824D1111yescharacteristic
142#1823—111no—
143#1823—111no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11C2×C22⋊C412yes—
147C23×C11#13512yes—
148C23×C11#13512yes—
149C23×C11C22×D411yescharacteristic
150C2×C4×C11—22no—
151C2×C4×C11—24no—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—48no—
155C2×C4×C11—44no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11C2×C22⋊C412yes—
160C2×C4×C11C23×C411yescharacteristic
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C112−1+414yes—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—22no—
168C2×Dic11—22no—
169C2×Dic11—28no—
170C2×Dic11—24no—
171C2×Dic11—44no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—48no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11C2×C22⋊C412yes—
179C2×Dic11C2×C22⋊C412yes—
180C2×Dic11C2×C22⋊C412yes—
181C2×Dic11C2×C22⋊C412yes—
182C8×C11—42no—
183C11⋊C8—42no—
184C2×#125—112no—
185C2×#125—112no—
186C2×#125—118no—
187C2×#125—221no—
188C2×#125—221no—
189C2×#125—224no—
190C22×C4⋊C4—111no—
191C22×C4⋊C4—221no—
192C22×C4⋊C4—221no—
193C22×C4⋊C4C2×D1111yescharacteristic
194C22×C42—111no—
195#431—224no—
196C2×C4⋊C8—112no—
197C2×C22⋊C8—111no—
198C2×C22⋊C8C2×D1111yescharacteristic
199C2×C4×C8—112no—
200#383—221no—
201#382—112no—
202#381—221no—
203#380—111no—
204#380C2×D1111yescharacteristic
205C4×C4⋊C4—112no—
206C4×C22⋊C4—221no—
207#376—221no—
208#340—114no—
209#340—114no—
210#340—114no—
211#340C2×D1114yes—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—24no—
215C22×C11—24no—
216C22×C11#41614yes—
217C22×C11C22×C22⋊C411yescharacteristic
218C22×C11#53612yes—
219C22×C11C2×#13511yescharacteristic
220C22×C11C2×#13511yescharacteristic
221C22×C11#57512yes—
222C4×C11—22no—
223C4×C11—44no—
224C4×C11—82no—
225C4×C11#51912yes—
226C4×C11#53612yes—
227Dic11—22no—
228Dic11—22no—
229Dic11—22no—
230Dic11—22no—
231Dic11—44no—
232Dic11—82no—
233C23×C4—21no—
234C23×C4—111no—
235C23×C4—111no—
236C23×C4—221no—
237C23×C4C22×D1111yescharacteristic
238C22×C8—112no—
239C22×C8C22×D1112yes—
240#125—118no—
241#125—118no—
242#125—228no—
243#125—228no—
244#125—224no—
245#125—224no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—114no—
249C2×C4⋊C4—112no—
250C2×C4⋊C4—112no—
251C2×C4⋊C4—228no—
252C2×C4⋊C4—222no—
253C2×C4⋊C4—222no—
254C2×C4⋊C4—228no—
255C2×C4⋊C4—222no—
256C2×C4⋊C4—222no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—222no—
259C2×C4⋊C4C4×D1114yes—
260C2×C4⋊C4C22×D1112yes—
261C2×C4⋊C4C22×D1112yes—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—221no—
264C2×C42—114no—
265C2×C42—111no—
266C2×C42—111no—
267C2×C42—114no—
268C2×C42—111no—
269C2×C42—111no—
270C2×C42—222no—
271C4⋊C8—224no—
272C22⋊C8—22no—
273C22⋊C8—222no—
274C4×C8—224no—
275#95—21no—
276#95—222no—
277#95—222no—
278#95—222no—
279#95—221no—
280C2×C11—24no—
281C2×C11#231011yescharacteristic
282C2×C11C2×#41611yescharacteristic
283C2×C11#289611yescharacteristic
284C2×C11#323212yes—
285C2×C11#323212yes—
286C24D4×D1111yescharacteristic
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—44no—
292C22×C4—114no—
293C22×C4—111no—
294C22×C4—111no—
295C22×C4—111no—
296C22×C4—111no—
297C22×C4—114no—
298C22×C4—222no—
299C22×C4—222no—
300C22×C4—224no—
301C22×C4—222no—
302C22×C4—222no—
303C22×C4—442no—
304C22×C4—442no—
305C22×C4—442no—
306C22×C4C2×C4×D1112yes—
307C22×C4D4×D1111yescharacteristic
308C22×C4D4×D1112yes—
309C22×C4C23×D1111yescharacteristic
310C2×C8—22no—
311C2×C8—24no—
312C2×C8—222no—
313C2×C8—224no—
314C4⋊C4—24no—
315C4⋊C4—22no—
316C4⋊C4—24no—
317C4⋊C4—114no—
318C4⋊C4—228no—
319C4⋊C4—228no—
320C4⋊C4—228no—
321C4⋊C4—228no—
322C4⋊C4—224no—
323C4⋊C4—222no—
324C4⋊C4—224no—
325C4⋊C4C2×C4×D1114yes—
326C22⋊C4—42no—
327C22⋊C4—442no—
328C42—114no—
329C42—114no—
330C42—112no—
331C42—112no—
332C42—112no—
333C42—112no—
334C42—444no—
335C11#2183611yescharacteristic, complemented, Sylow
336C23—22no—
337C23—22no—
338C23C22⋊C4×D1112yes—
339C23#6696912yes—
340C23#6697212yes—
341C23C2×D4×D1111yescharacteristic
342C2×C4—22no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—48no—
347C2×C4—44no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—112no—
352C2×C4—112no—
353C2×C4—112no—
354C2×C4—112no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—228no—
362C2×C4—224no—
363C2×C4—444no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—448no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4—442no—
370C2×C4C22⋊C4×D1112yes—
371C2×C4C22×C4×D1111yescharacteristic
372C2×C4C2×D4×D1111yescharacteristic
373C2×C4#6704314yes—
374C8—42no—
375C8—442no—
376C22—22no—
377C22—22no—
378C22—24no—
379C22—24no—
380C22#1062241714yes—
381C22C2×C22⋊C4×D1111yescharacteristic
382C22#1062317912yes—
383C22C2×#6696911yescharacteristic
384C22C2×#6697211yescharacteristic
385C22#1062330412yes—
386C4—22no—
387C4—44no—
388C4—82no—
389C4—222no—
390C4—222no—
391C4—222no—
392C4—222no—
393C4—444no—
394C4—882no—
395C4#1062304712yes—
396C4#1062317912yes—
397C2—24no—
398C2#1307120111yescharacteristic
399C2C2×#1062241711yescharacteristic
400C2#1307713011yescharacteristic
401C2#1307978312yes—
402C2#1307978912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1824C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1824D11
hypocenterC11#21836
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
4. #13069579C2semidirect
5. #13069570C2semidirect
18. C2×#66943C4semidirect
335. C11#21836semidirect

Maximal subgroups

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

subgroupindex
C22×#669432
C2×#106223312
#130710112
#130695792
#130695702
#130687062
#130687032
#130687002
C11×#18242
#2183611