Finite Group Databasebeta

← #14725468

Subgroups — #14725468

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077746C212yesmaximal, complemented
2C4×#66957C211yesmaximal, characteristic
3#13067500C212yesmaximal, complemented
4#13067493C214yesmaximal, complemented
5#13067422C212yesmaximal, complemented
6#13067053C212yesmaximal, complemented
7C8×#4318C211yesmaximal, characteristic, complemented
8C11×#1567C211yesmaximal, characteristic, complemented
9C2×#66957C411yescharacteristic
10C4×#4339C2212yes—
11C11×#423C2212yes—
12C2×C4×C8×C11C2211yescharacteristic
13#10622741—24no—
14#10622726C412yes—
15#10622719C411yescharacteristic
16#10622538C2211yescharacteristic
17C4×#4318C2211yescharacteristic
18#10622451C2214yes—
19#10622450—22no—
20#10622446—22no—
21#10622443C2214yes—
22C4×Dic44C411yescharacteristic
23C4×Dic44C2211yescharacteristic
24C4×D88C411yescharacteristic
25C4×D88C2211yescharacteristic
26C4×#4314C412yes—
27C4×#4314C2212yes—
28C11×#335C2212yes—
29C11×#335C2212yes—
30#10622122C2214yes—
31#10622121C2214yes—
32#10622092C2212yes—
33C8×C11⋊C8C2212yes—
34C2×#4339C2×C412yes—
35C2×C11×M16—22no—
36C22×C8×C11C2×C411yescharacteristic
37C22×C8×C11C2×C411yescharacteristic
38C2×C42×C11C2311yescharacteristic
39C4×C22⋊D11—22no—
40C4×C22⋊D11—22no—
41#66979C2×C412yes—
42C2×#4318—21no—
43C2×Dic44C2×C411yescharacteristic
44#66957—24no—
45C2×D88C2×C411yescharacteristic
46C2×#4314C2×C412yes—
47C2×#4313—24no—
48C4×D44C2×C412yes—
49C4×D44C2312yes—
50#66925—22no—
51C42×D11—22no—
52C4×Dic22C2×C412yes—
53C4×Dic22C2312yes—
54C11×C4⋊C8—22no—
55C11×C4⋊C8C2314yes—
56C4×C8×C11C2×C411yescharacteristic
57C4×C8×C11C2×C411yescharacteristic
58C4×C8×C11C2311yescharacteristic
59C4×C8×C11C2311yescharacteristic
60C22⋊(C11⋊C8)D412yes—
61#66885C2×C412yes—
62#66885C2×C412yes—
63(C2×D11)⋊C8—24no—
64#66882C2×C411yescharacteristic
65#66882C2×C411yescharacteristic
66#66881C2×C412yes—
67#66880C2×C412yes—
68#66880C2×C412yes—
69Dic11⋊C8—24no—
70C8×Dic11—24no—
71C4⋊(C11⋊C8)D411yescharacteristic
72C4⋊(C11⋊C8)D411yescharacteristic
73#66867—21no—
74C4×C11⋊C8C2312yes—
75C4×C11⋊C8C2312yes—
76#18059—111nomaximal, Sylow
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C2×C22⋊D11—22no—
81#4339—24no—
82#4339—42no—
83C2×D44C22×C412yes—
84C2×C4×D11—22no—
85C2×C4×D11—22no—
86C2×C4×D11—22no—
87C2×Dic22C22×C412yes—
88C11×M16—82no—
89C2×C8×C11—22no—
90C2×C8×C11—24no—
91C2×C8×C11—41no—
92C2×C8×C11C22×C411yescharacteristic
93C2×C8×C11C22×C411yescharacteristic
94C2×C8×C11C22×C411yescharacteristic
95C2×C8×C11C22×C411yescharacteristic
96C42×C11C22×C411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11#4111yescharacteristic
99C42×C11C2411yescharacteristic
100C22⋊Dic11—22no—
101(C2×D11)⋊C4—22no—
102(C2×D11)⋊C4—22no—
103C4⋊Dic11C22×C412yes—
104C4⋊Dic11C22×C412yes—
105Dic11⋊C4—22no—
106Dic11⋊C4—22no—
107C4×Dic11—22no—
108C4×Dic11—22no—
109C4×Dic11—22no—
110#4318—24no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8C2×D412yes—
113C2×C11⋊C8C2×D412yes—
114Dic44M1614yescomplemented
115D88—22no—
116#4314—24no—
117#4313—84no—
118#2991—112no—
119C4×#135—111no—
120#1589—112no—
121#1588—114no—
122C8×Q16—112no—
123#1567D1111yescharacteristic, complemented
124#1489—112no—
125C8×M16—111no—
126C23×C11C4×D411yescharacteristic
127C22×D11—22no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—22no—
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11C4×D411yescharacteristic
135C2×C4×C11C4×D411yescharacteristic
136C2×C4×C11C23×C411yescharacteristic
137C2×C4×C11C22×D411yescharacteristic
138C2×C4×C11C2×#4111yescharacteristic
139C22⋊D11—44no—
140C2×Dic11—22no—
141C2×Dic11—22no—
142C2×Dic11—22no—
143D44—22no—
144D44—22no—
145C4×D11—44no—
146C4×D11—42no—
147C4×D11—42no—
148C4×D11—44no—
149Dic22—22no—
150Dic22C2×M1614yes—
151C8×C11—21no—
152C8×C11—21no—
153C8×C11—21no—
154C8×C11—44no—
155C8×C11C2×M1612yes—
156C11⋊C8—24no—
157C11⋊C8—22no—
158C11⋊C8—22no—
159C2×#135—111no—
160C4×#41—112no—
161C8×Q8—114no—
162C4×Q16—111no—
163C4×Q16—111no—
164C4×SD16—112no—
165C4×SD16—112no—
166C4×D8—111no—
167C4×D8—111no—
168#436—114no—
169#436—224no—
170#431—111no—
171#431—222no—
172#427—111no—
173#423—222no—
174#423C2×D1112yes—
175#416—112no—
176C4×M16—111no—
177C2×C4×C8C2×D1111yescharacteristic
178#335C2×D1112yes—
179#335C2×D1112yes—
180Q8⋊C8—114no—
181D4⋊C8—114no—
182#322—112no—
183C82—112no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11C2×C4×D411yescharacteristic
188C2×D11—42no—
189C2×D11—42no—
190C2×D11—42no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11#44312yes—
195C4×C11C22×M1611yescharacteristic
196C4×C11#56811yescharacteristic
197C4×C11#57611yescharacteristic
198C4×C11#57811yescharacteristic
199Dic11—24no—
200Dic11—42no—
201Dic11—42no—
202C2×#41—112no—
203#135—224no—
204C2×Q16—111no—
205C2×SD16—112no—
206C2×D8—111no—
207C2×M16—22no—
208C2×M16—224no—
209C2×M16—221no—
210C22×C8C4×D1111yescharacteristic
211C22×C8C4×D1111yescharacteristic
212C4×Q8—112no—
213C4×Q8—112no—
214C4×D4—112no—
215C4×D4—112no—
216C4×D4—222no—
217C4×D4—222no—
218#117—112no—
219#117—222no—
220C2×C42—222no—
221C2×C42C22×D1111yescharacteristic
222#107—111no—
223#107—111no—
224#106—112no—
225C4⋊C8—22no—
226C4⋊C8—111no—
227C4⋊C8—111no—
228C4⋊C8—224no—
229C4⋊C8C22×D1114yes—
230#103—112no—
231#103—112no—
232#102—112no—
233#102—112no—
234C22⋊C8—112no—
235C22⋊C8—224no—
236#97—221no—
237C4×C8—112no—
238C4×C8—112no—
239C4×C8—224no—
240C4×C8C4×D1111yescharacteristic
241C4×C8C4×D1111yescharacteristic
242C4×C8C22×D1111yescharacteristic
243C4×C8C22×D1111yescharacteristic
244C2×C11—41no—
245C2×C11D4×M1611yescharacteristic
246C2×C11#295111yescharacteristic
247C2×C11C2×#44311yescharacteristic
248D11—82no—
249#41—224no—
250#41—442no—
251C2×Q8—112no—
252C2×D4—112no—
253C2×D4—222no—
254C22×C4—222no—
255C22×C4—222no—
256C22×C4—222no—
257C22×C4C2×C4×D1111yescharacteristic
258C22×C4D4×D1111yescharacteristic
259C22×C4#434311yescharacteristic
260Q16—114no—
261SD16—224no—
262D8—222no—
263M16—82no—
264M16—224no—
265M16—884no—
266C2×C8—22no—
267C2×C8—24no—
268C2×C8—41no—
269C2×C8—112no—
270C2×C8—112no—
271C2×C8—222no—
272C2×C8C2×C4×D1111yescharacteristic
273C2×C8C2×C4×D1111yescharacteristic
274C2×C8C2×C4×D1111yescharacteristic
275C2×C8C2×C4×D1111yescharacteristic
276C4⋊C4—112no—
277C4⋊C4—112no—
278C4⋊C4—222no—
279C4⋊C4—222no—
280C22⋊C4—222no—
281C22⋊C4—222no—
282C22⋊C4—222no—
283C42—222no—
284C42—222no—
285C42—222no—
286C42C2×C4×D1111yescharacteristic
287C42D4×D1111yescharacteristic
288C42#434311yescharacteristic
289C42C23×D1111yescharacteristic
290C11#1805911yescharacteristic, complemented, Sylow
291C23—222no—
292C23#6694611yescharacteristic
293Q8—114no—
294Q8—222no—
295D4—222no—
296D4—222no—
297D4—444no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—222no—
304C2×C4—222no—
305C2×C4—222no—
306C2×C4—444no—
307C2×C4—444no—
308C2×C4—442no—
309C2×C4—442no—
310C2×C4#6694611yescharacteristic
311C2×C4#6694611yescharacteristic
312C2×C4#6694611yescharacteristic
313C2×C4C22×C4×D1111yescharacteristic
314C2×C4C2×D4×D1111yescharacteristic
315C2×C4C2×#434311yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—44no—
320C8—224no—
321C8—222no—
322C8—222no—
323C8M16×D1112yes—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—442no—
328C22—442no—
329C22—442no—
330C22C2×#6694611yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—224no—
335C4—442no—
336C4—442no—
337C4#1062250812yes—
338C4C2×M16×D1111yescharacteristic
339C4#1062327611yescharacteristic
340C4#1062328811yescharacteristic
341C4#1062329711yescharacteristic
342C2—41no—
343C2—882no—
344C2#1307735111yescharacteristic
345C2#1307749011yescharacteristic
346C2C2×#1062250811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1567C2
socleC22×C11C2×C4×D4
prime radicalC2×#66957C4
cosocleC42×C11C24
hypercenter#1567D11
hypocenterC11#18059
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1567

Complements

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

NH ≅ G/Ntype
1. #13077746C2semidirect
3. #13067500C2semidirect
4. #13067493C2semidirect
5. #13067422C2semidirect
6. #13067053C2semidirect
7. C8×#4318C2semidirect
8. C11×#1567C2semidirect
114. Dic44M16semidirect
123. #1567D11semidirect
290. C11#18059semidirect

Maximal subgroups

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

subgroupindex
#130777462
C4×#669572
#130675002
#130674932
#130674222
#130670532
C8×#43182
C11×#15672
#1805911