Finite Group Databasebeta

← #14723451

Subgroups — #14723451

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#13077696C211yesmaximal, characteristic, complemented
2C2×C4×#4324C211yesmaximal, characteristic
3#13067492C214yesmaximal, complemented
4#13067457C214yesmaximal, complemented
5#13067362C211yesmaximal, characteristic, complemented
6#13067010C211yesmaximal, characteristic, complemented
7#13067007C211yesmaximal, characteristic
8#13066909C211yesmaximal, characteristic, complemented
9C11×#2975C211yesmaximal, characteristic
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4324C411yescharacteristic
12C2×C4×Dic22C2211yescharacteristic
13C11×#436—22no—
14C11×#436C2214yes—
15C11×#431C2211yescharacteristic
16C11×#431C2211yescharacteristic
17C11×#407—22no—
18C2×#66896C411yescharacteristic
19C4×#4324C412yes—
20C4×#4324C412yes—
21C4×#4324C2212yes—
22C4×#4324C2212yes—
23C2×#66874C411yescharacteristic
24C2×#66872C411yescharacteristic
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×C4×C11⋊C8C2211yescharacteristic
28#10622443—22no—
29#10622331—22no—
30C8×Dic22C2214yescomplemented
31D4⋊(C11⋊C8)C2214yes—
32#10622122C2214yescomplemented
33#10622118C2212yescomplemented
34#10622117C2212yescomplemented
35#10622093C2212yescomplemented
36#10622092C2212yescomplemented
37C22×D4×C11C2×C411yescharacteristic
38C23×C4×C11—21no—
39C22×Dic22C2×C411yescharacteristic
40C2×C11×M16—24no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11C2×C412yes—
44C4×D4×C11C2312yes—
45C2×C11×C4⋊C4C2×C411yescharacteristic
46C2×C11×C22⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4324—24no—
49C2×#4324C2×C412yes—
50C2×#4324C2×C412yes—
51C2×C4⋊Dic11C2×C411yescharacteristic
52C2×Dic11⋊C4—21no—
53C2×C4×Dic11—21no—
54C22×C11⋊C8C2×C411yescharacteristic
55C22×C11⋊C8C2×C411yescharacteristic
56C4×Dic22—21no—
57C4×Dic22—21no—
58C4×Dic22C2×C412yes—
59C4×Dic22C2312yes—
60C11×C4⋊C8D412yes—
61C11×C4⋊C8C2312yes—
62C11×C22⋊C8—21no—
63C11×C22⋊C8—24no—
64C11×C22⋊C8D412yes—
65C4×C8×C11—21no—
66C4×C8×C11C2312yes—
67#66896C2×C412yes—
68#66896C2×C412yes—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71Dic11⋊C8—24no—
72C8×Dic11—24no—
73#66874C2×C412yes—
74#66874C2×C412yes—
75#66872C2×C412yes—
76#66872C2×C412yes—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)C2312yes—
79C4×C11⋊C8—21no—
80C4×C11⋊C8C2×C411yescharacteristic
81C4×C11⋊C8C2×C411yescharacteristic
82C4×C11⋊C8C2312yes—
83C4×C11⋊C8C2311yescharacteristic
84C4×C11⋊C8C2311yescharacteristic
85#17878—111nomaximal, Sylow
86C24×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11C22×C412yes—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—82no—
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×Dic11—21no—
99C22×Dic11—21no—
100C2×Dic22—21no—
101C2×Dic22—22no—
102C2×Dic22M1614yescomplemented
103C2×Dic22C22×C412yes—
104C11×M16—84no—
105C2×C8×C11—22no—
106C2×C8×C11C2×D414yes—
107C11×C4⋊C4—21no—
108C11×C4⋊C4C22×C412yes—
109C11×C22⋊C4—22no—
110C11×C22⋊C4—22no—
111C42×C11C22×C411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114C42×C11C2411yescharacteristic
115#4324—24no—
116#4324—24no—
117C4⋊Dic11—21no—
118C4⋊Dic11C22×C412yes—
119Dic11⋊C4—22no—
120Dic11⋊C4—22no—
121C4×Dic11—22no—
122C4×Dic11—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8C22×C411yescharacteristic
128C2×C11⋊C8C22×C411yescharacteristic
129C2×C11⋊C8C22×C411yescharacteristic
130C2×C11⋊C8C22×C411yescharacteristic
131#2982—111no—
132#2975D1111yescharacteristic
133C2×C4×SD16—111no—
134#1588—114no—
135#1583—114no—
136#1564—111no—
137#1479—111no—
138#1478—111no—
139#1452—111no—
140C23×C11—22no—
141C23×C11—42no—
142C23×C11—81no—
143C23×C11—81no—
144C23×C11C4×D411yescharacteristic
145D4×C11—22no—
146D4×C11—22no—
147D4×C11—42no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—44no—
152C2×C4×C11—82no—
153C2×C4×C11—81no—
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11C2×M1612yes—
158C2×C4×C11#13112yes—
159C2×C4×C11C23×C411yescharacteristic
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C2×#4111yescharacteristic
162C2×Dic11—22no—
163C2×Dic11—24no—
164C2×Dic11—22no—
165C2×Dic11—81no—
166Dic22—22no—
167Dic22—24no—
168Dic22C2×M1614yes—
169C8×C11—24no—
170C8×C11—42no—
171C11⋊C8—21no—
172C11⋊C8—21no—
173C11⋊C8—21no—
174C11⋊C8—21no—
175C11⋊C8—42no—
176C11⋊C8—42no—
177C22×SD16—111no—
178C2×C4×Q8—111no—
179C2×C4×D4C2×D1111yescharacteristic
180C8×Q8—114no—
181C8×Q8—222no—
182C4×SD16—112no—
183C4×SD16—112no—
184C4×SD16—112no—
185C4×SD16—112no—
186#436—22no—
187#436C2×D1114yes—
188#431—111no—
189#431—111no—
190#431—222no—
191#431C2×D1111yescharacteristic
192#431C2×D1111yescharacteristic
193C2×#106—111no—
194C2×#103—111no—
195C2×#102—111no—
196#407—22no—
197C2×C4×C8—111no—
198#335—112no—
199#334—112no—
200Q8⋊C8—114no—
201D4⋊C8—114no—
202#322—112no—
203#322—112no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—42no—
207C22×C11—42no—
208C22×C11—42no—
209C22×C11—84no—
210C22×C11#43512yes—
211C22×C11C2×C4×D411yescharacteristic
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11#43512yes—
217C4×C11C22×M1611yescharacteristic
218C4×C11C2×#13111yescharacteristic
219C4×C11#57712yes—
220Dic11—24no—
221Dic11—42no—
222C22×Q8—111no—
223C22×D4C4×D1111yescharacteristic
224C23×C4—21no—
225C2×SD16—112no—
226C2×SD16—112no—
227C2×SD16—224no—
228C2×M16—24no—
229C22×C8—111no—
230C22×C8—111no—
231C4×Q8—112no—
232C4×Q8—112no—
233C4×Q8—221no—
234C4×Q8—221no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4C4×D1112yes—
238C4×D4C22×D1112yes—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4C4×D1111yescharacteristic
242C2×C22⋊C4—21no—
243C2×C42—221no—
244C2×C42C22×D1111yescharacteristic
245#106—112no—
246#106—112no—
247C4⋊C8—112no—
248C4⋊C8—224no—
249C4⋊C8—221no—
250C4⋊C8C22⋊D1112yes—
251C4⋊C8C22×D1112yes—
252#103—112no—
253#103—112no—
254#102—112no—
255#102—112no—
256C22⋊C8—21no—
257C22⋊C8—24no—
258C22⋊C8—221no—
259C22⋊C8—221no—
260C22⋊C8C22⋊D1112yes—
261C4×C8—21no—
262C4×C8—111no—
263C4×C8—111no—
264C4×C8—111no—
265C4×C8—111no—
266C4×C8—112no—
267C4×C8—224no—
268C4×C8—221no—
269C4×C8C22×D1112yes—
270C2×C11—22no—
271C2×C11—82no—
272C2×C11C2×#43511yescharacteristic
273C2×C11#294911yescharacteristic
274C2×C11#295711yescharacteristic
275C24—21no—
276C2×Q8—114no—
277C2×Q8—112no—
278C2×Q8—222no—
279C2×Q8—221no—
280C2×D4—22no—
281C2×D4—22no—
282C2×D4—21no—
283C2×D4C2×C4×D1112yes—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—82no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4C2×C4×D1111yescharacteristic
291C22×C4#433911yescharacteristic
292C22×C4C2×C22⋊D1111yescharacteristic
293SD16—224no—
294SD16—224no—
295M16—84no—
296C2×C8—22no—
297C2×C8—111no—
298C2×C8—111no—
299C2×C8—111no—
300C2×C8—111no—
301C2×C8—222no—
302C2×C8—222no—
303C2×C8—222no—
304C2×C8—222no—
305C2×C8C2×C22⋊D1114yes—
306C4⋊C4—21no—
307C4⋊C4—112no—
308C4⋊C4—221no—
309C4⋊C4—222no—
310C4⋊C4—222no—
311C4⋊C4C2×C4×D1112yes—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C42—222no—
315C42—222no—
316C42C2×C4×D1111yescharacteristic
317C42#433911yescharacteristic
318C42C2×C22⋊D1111yescharacteristic
319C42C23×D1111yescharacteristic
320C11#1787811yescharacteristic, complemented, Sylow
321C23—22no—
322C23—42no—
323C23—81no—
324C23—81no—
325C23C4×C22⋊D1111yescharacteristic
326Q8—114no—
327Q8—224no—
328Q8—222no—
329D4—22no—
330D4—22no—
331D4—42no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—44no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4—224no—
339C2×C4—222no—
340C2×C4—222no—
341C2×C4—881no—
342C2×C4M16×D1112yes—
343C2×C4#6696012yes—
344C2×C4C4×C22⋊D1111yescharacteristic
345C2×C4C4×C22⋊D1111yescharacteristic
346C2×C4C4×C22⋊D1111yescharacteristic
347C2×C4C22×C4×D1111yescharacteristic
348C2×C4C2×#433911yescharacteristic
349C2×C4C22×C22⋊D1111yescharacteristic
350C8—24no—
351C8—42no—
352C8—221no—
353C8—221no—
354C8—221no—
355C8—221no—
356C8—442no—
357C8—442no—
358C22—21no—
359C22—21no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—84no—
364C22#1062274012yes—
365C22C2×C4×C22⋊D1111yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—224no—
371C4—442no—
372C4#1062274012yes—
373C4C2×M16×D1111yescharacteristic
374C4C2×#6696011yescharacteristic
375C4#1062336712yes—
376C2—22no—
377C2—82no—
378C2C2×#1062274011yescharacteristic
379C2#1307747311yescharacteristic
380C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2975C2
socleC22×C11C2×C4×D4
prime radicalC22×D4×C11C2×C4
cosocleC42×C11C24
hypercenter#2975D11
hypocenterC11#17878
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2975

Complements

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

NH ≅ G/Ntype
1. #13077696C2semidirect
3. #13067492C2semidirect
4. #13067457C2semidirect
5. #13067362C2semidirect
6. #13067010C2semidirect
8. #13066909C2semidirect
30. C8×Dic22C22semidirect
32. #10622122C22semidirect
33. #10622118C22semidirect
34. #10622117C22semidirect
35. #10622093C22semidirect
36. #10622092C22semidirect
102. C2×Dic22M16semidirect
320. C11#17878semidirect

Maximal subgroups

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

subgroupindex
#130776962
C2×C4×#43242
#130674922
#130674572
#130673622
#130670102
#130670072
#130669092
C11×#29752
#1787811