Finite Group Databasebeta

← #14738988

Subgroups — #14738988

Order 2816.

674 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#13079760C211yesmaximal, characteristic, complemented
2#13078413C211yesmaximal, characteristic
3#13077640C211yesmaximal, characteristic
4#13068041C214yesmaximal, complemented
5#13067989C214yesmaximal, complemented
6#13067386C211yesmaximal, characteristic, complemented
7#13067288C211yesmaximal, characteristic, complemented
8#13067274C211yesmaximal, characteristic, complemented
9C2×C11×#461C211yesmaximal, characteristic
10C22×C11×SD16—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13#10623001C2211yescharacteristic
14C11×#461—22no—
15C11×#461C2214yes—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#103—21no—
18#10622828—21no—
19C2×C22⋊(C11⋊C8)—22no—
20#10622707—22no—
21#10622706C2212yescomplemented
22#10622692C2212yescomplemented
23D4×C11⋊C8—22no—
24D4×C11⋊C8C2214yes—
25#10622622—22no—
26#10622621C2212yes—
27#10622620C2212yes—
28#10622584—22no—
29#10622577—21no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622185C2214yescomplemented
34#10622124C2212yescomplemented
35#10622119C2212yescomplemented
36#10622118C2214yescomplemented
37C22×Q8×C11—21no—
38C22×D4×C11D411yescharacteristic
39C23×C4×C11—21no—
40C2×C11×SD16—24no—
41C2×C11×SD16—44no—
42C22×C8×C11—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8C2312yes—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11D412yes—
50C4×D4×C11C2312yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C22⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56#66979—21no—
57#66977—21no—
58#66977—21no—
59C2×#4318—21no—
60C22×C11⋊C8—24no—
61#66923—21no—
62#66922C2311yescharacteristic
63#66922C2311yescharacteristic
64C4×Dic22—21no—
65C4×Dic22—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8C2312yes—
68C11×#103—24no—
69#66896—22no—
70#66896—22no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—24no—
73C22⋊(C11⋊C8)D412yes—
74#66874—24no—
75#66872—22no—
76#66872—24no—
77#66871—22no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)D412yes—
80C4⋊(C11⋊C8)C2312yes—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8—21no—
83C4×C11⋊C8C2312yes—
84#19390—111nomaximal, Sylow
85C24×C11—21no—
86C2×Q8×C11—22no—
87C2×Q8×C11—41no—
88C2×Q8×C11—42no—
89C2×Q8×C11—42no—
90C2×D4×C11—21no—
91C2×D4×C11—22no—
92C2×D4×C11SD1614yes—
93C2×D4×C11C2×D412yes—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—41no—
98C22×C4×C11—82no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C2×Dic22—21no—
103C2×Dic22—21no—
104C11×SD16—48no—
105C2×C8×C11—22no—
106C2×C8×C11—42no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4C2×D412yes—
113C11×C22⋊C4—22no—
114C11×C22⋊C4—22no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118C42×C11C2411yescharacteristic
119C22⋊Dic11—41no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126C4×Dic11—41no—
127#4318—42no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—84no—
131C2×C11⋊C8C2×D414yes—
132#3229—111no—
133#3077—111no—
134C2×#461D1111yescharacteristic
135#2972—111no—
136#1679—114no—
137#1671—114no—
138#1570—111no—
139#1546—111no—
140#1542—111no—
141C23×C11—22no—
142C23×C11—24no—
143C23×C11—81no—
144C23×C11—81no—
145C23×C11#12111yescharacteristic
146Q8×C11—42no—
147Q8×C11—42no—
148Q8×C11—82no—
149D4×C11—22no—
150D4×C11—24no—
151D4×C11C2×SD1614yes—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—41no—
155C2×C4×C11—44no—
156C2×C4×C11—42no—
157C2×C4×C11—82no—
158C2×C4×C11—81no—
159C2×C4×C11—82no—
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11C2×SD1612yes—
164C2×C4×C11#13512yes—
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C2×#4111yescharacteristic
168C2×Dic11—41no—
169C2×Dic11—41no—
170Dic22—42no—
171Dic22—81no—
172C8×C11—42no—
173C11⋊C8—24no—
174C11⋊C8—42no—
175C11⋊C8—42no—
176C22×SD16—21no—
177#533—111no—
178C2×C4⋊Q8C2×D1111yescharacteristic
179C2×C4×D4C2×D1111yescharacteristic
180#498—112no—
181#487—112no—
182#483—222no—
183#478—222no—
184#476—112no—
185#475—222no—
186#474—112no—
187#461—22no—
188#461C2×D1114yes—
189C8×D4—114no—
190C8×D4—222no—
191#431—111no—
192#431—111no—
193#428—221no—
194#423—111no—
195C2×C4⋊C8C2×D1111yescharacteristic
196#418—221no—
197C2×#103—21no—
198C2×C22⋊C8—222no—
199#334—114no—
200#333—112no—
201#332—114no—
202#332—112no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—24no—
206C22×C11—42no—
207C22×C11—42no—
208C22×C11—84no—
209C22×C11#46512yes—
210C22×C11C2×#12111yescharacteristic
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—42no—
215C4×C11—82no—
216C4×C11#46512yes—
217C4×C11C22×SD1611yescharacteristic
218C4×C11C2×#13511yescharacteristic
219C4×C11#57712yes—
220Dic11—81no—
221Dic11—81no—
222C22×Q8—21no—
223C22×D4C22⋊D1111yescharacteristic
224C23×C4—21no—
225C2×SD16—24no—
226C2×SD16—44no—
227C2×M16—221no—
228C22×C8—21no—
229C22×C8—224no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—111no—
234C4⋊Q8—111no—
235C4⋊Q8C22×D1112yes—
236#125—221no—
237C22⋊Q8—221no—
238C22⋊Q8—221no—
239C4×Q8—221no—
240C4×Q8—221no—
241C4×D4—21no—
242C4×D4—21no—
243C4×D4C22⋊D1112yes—
244C4×D4C22×D1112yes—
245#117—221no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C22⋊D1111yescharacteristic
249C2×C22⋊C4—21no—
250C2×C42C22×D1111yescharacteristic
251#107—222no—
252#106—224no—
253#106—222no—
254C4⋊C8—21no—
255C4⋊C8—112no—
256C4⋊C8—112no—
257C4⋊C8—112no—
258C4⋊C8—221no—
259C4⋊C8C22×D1112yes—
260#103—24no—
261#103—224no—
262#102—222no—
263#102—222no—
264C22⋊C8—112no—
265C22⋊C8—224no—
266C22⋊C8—221no—
267C4×C8—112no—
268C4×C8—221no—
269C2×C11—22no—
270C2×C11—44no—
271C2×C11#304211yescharacteristic
272C2×C11C2×#46511yescharacteristic
273C2×C11#306911yescharacteristic
274C24—21no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—42no—
278C2×Q8—42no—
279C2×Q8—221no—
280C2×Q8—221no—
281C2×D4—21no—
282C2×D4—22no—
283C2×D4#432414yes—
284C2×D4C2×C22⋊D1112yes—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—41no—
289C22×C4—82no—
290C22×C4D4×D1111yescharacteristic
291C22×C4#434111yescharacteristic
292C22×C4C2×C22⋊D1111yescharacteristic
293SD16—48no—
294M16—442no—
295C2×C8—22no—
296C2×C8—42no—
297C2×C8—114no—
298C2×C8—222no—
299C2×C8—222no—
300C2×C8—884no—
301C4⋊C4—21no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—221no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C4⋊C4C2×C22⋊D1112yes—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—441no—
316C42—441no—
317C42D4×D1111yescharacteristic
318C42#434111yescharacteristic
319C42C2×C22⋊D1111yescharacteristic
320C42C23×D1111yescharacteristic
321C11#1939011yescharacteristic, complemented, Sylow
322C23—22no—
323C23—24no—
324C23—81no—
325C23—81no—
326C23#6699211yescharacteristic
327Q8—42no—
328Q8—42no—
329Q8—82no—
330Q8—442no—
331Q8—881no—
332D4—22no—
333D4—24no—
334D4C2×#432414yes—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—44no—
339C2×C4—42no—
340C2×C4—82no—
341C2×C4—81no—
342C2×C4—82no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4C2×#432412yes—
346C2×C4#6699211yescharacteristic
347C2×C4#6699211yescharacteristic
348C2×C4#6699211yescharacteristic
349C2×C4#6700312yes—
350C2×C4C2×D4×D1111yescharacteristic
351C2×C4C2×#434111yescharacteristic
352C2×C4C22×C22⋊D1111yescharacteristic
353C8—42no—
354C8—224no—
355C8—442no—
356C8—442no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—42no—
361C22—42no—
362C22—84no—
363C22#1062265412yes—
364C22C2×#6699211yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—42no—
369C4—82no—
370C4—881no—
371C4—881no—
372C4#1062265412yes—
373C4#1062329312yes—
374C4C22×#432411yescharacteristic
375C4C2×#6700311yescharacteristic
376C2—22no—
377C2—44no—
378C2#1307812511yescharacteristic
379C2C2×#1062265411yescharacteristic
380C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#461C2
socleC22×C11C2×#121
prime radicalC22×D4×C11D4
hypercenterC2×#461D11
hypocenterC11#19390
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. #13079760C2semidirect
4. #13068041C2semidirect
5. #13067989C2semidirect
6. #13067386C2semidirect
7. #13067288C2semidirect
8. #13067274C2semidirect
21. #10622706C22semidirect
22. #10622692C22semidirect
33. #10622185C22semidirect
34. #10622124C22semidirect
35. #10622119C22semidirect
36. #10622118C22semidirect
321. C11#19390semidirect

Maximal subgroups

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

subgroupindex
#130797602
#130784132
#130776402
#130680412
#130679892
#130673862
#130672882
#130672742
C2×C11×#4612
#1939011