Finite Group Databasebeta

← #14723261

Subgroups — #14723261

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077723C212yesmaximal, complemented
2C4×#66965C211yesmaximal, characteristic
3#13067440C211yesmaximal, characteristic, complemented
4#13067436C211yesmaximal, characteristic, complemented
5#13067434C211yesmaximal, characteristic, complemented
6#13067419C212yesmaximal, complemented
7C8×#4324C212yesmaximal, complemented
8D11×#334C211yesmaximal, characteristic, complemented
9#13067000C212yesmaximal, complemented
10#13066901C211yesmaximal, characteristic, complemented
11C11×#1580C211yesmaximal, characteristic, complemented
12C2×#66965C411yescharacteristic
13C4×#4341C2212yes—
14C4×C11×D8C2211yescharacteristic
15C8×D4×C11C2212yes—
16D8×Dic11C411yescharacteristic
17C8×C22⋊D11—22no—
18C2×Dic11⋊C8—22no—
19C4×#4324C2212yes—
20D4×C11⋊C8C2212yes—
21#10622493C411yescharacteristic
22#10622486C411yescharacteristic
23D11×C4⋊C8C2212yes—
24#10622443C2212yes—
25#10622385C412yes—
26#10622371C412yes—
27(C22⋊D11)⋊C8—22no—
28#10622331—22no—
29C4×Dic44C2211yescharacteristic
30#10622298C2211yescharacteristic
31#10622298C2211yescharacteristic
32C4×C8×D11C2211yescharacteristic
33C8×Dic22C2212yes—
34C11×#334C2211yescharacteristic
35C11×D4⋊C8C2212yes—
36C11×#322C2211yescharacteristic
37D4⋊(C11⋊C8)C2212yes—
38#10622122C2212yes—
39#10622118C2212yes—
40#10622095C2211yescharacteristic
41#10622094C2212yes—
42#10622093C2211yescharacteristic
43C8×C11⋊C8C2211yescharacteristic
44C8×C11⋊C8C2211yescharacteristic
45C2×#4341C2×C412yes—
46C2×C11×D8C2×C411yescharacteristic
47C22×C8×C11—22no—
48C4×D4×C11C2312yes—
49D4×Dic11C2×C412yes—
50C2×#4324C2×C412yes—
51C4×C22⋊D11—22no—
52C2×C4×Dic11—22no—
53C22×C11⋊C8—22no—
54#66965C818yescomplemented
55C2×Dic44C2×C411yescharacteristic
56C2×C8×D11—22no—
57C2×C8×D11C2×C411yescharacteristic
58C2×C8×D11C2×C411yescharacteristic
59#66945C2×C412yes—
60#66940C2×C412yes—
61(C22⋊D11)⋊C4—22no—
62#66930—22no—
63C42×D11C2311yescharacteristic
64C4×Dic22C2312yes—
65C11×#107C2×C411yescharacteristic
66C11×C4⋊C8C2312yes—
67C11×#102C2×C412yes—
68C11×C22⋊C8—22no—
69C4×C8×C11C2311yescharacteristic
70C4×C8×C11C2311yescharacteristic
71C4×C8×C11C2311yescharacteristic
72#66896C2×C412yes—
73C22⋊(C11⋊C8)—22no—
74(C2×D11)⋊C8—21no—
75(C2×D11)⋊C8D412yes—
76#66882C2×C411yescharacteristic
77#66880C2×C412yes—
78Dic11⋊C8—22no—
79Dic11⋊C8—22no—
80Dic11⋊C8—21no—
81Dic11⋊C8—22no—
82Dic11⋊C8D412yes—
83C8×Dic11—22no—
84C8×Dic11—22no—
85C8×Dic11C2×C411yescharacteristic
86C8×Dic11C2×C411yescharacteristic
87#66874C2×C412yes—
88#66872C2×C412yes—
89C4⋊(C11⋊C8)C2312yes—
90C4×C11⋊C8C2311yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92C4×C11⋊C8C2311yescharacteristic
93#17858—111nomaximal, Sylow
94C2×D4×C11C22×C412yes—
95C22×C4×C11—22no—
96C2×C22⋊D11—22no—
97C22×Dic11—22no—
98C22×Dic11—22no—
99#4341—24no—
100#4341C2×C818yescomplemented
101C2×C4×D11C22×C411yescharacteristic
102C2×C4×D11C2×D411yescharacteristic
103C2×C4×D11#4111yescharacteristic
104C2×Dic22C22×C412yes—
105C11×D8C2×C814yescomplemented
106C2×C8×C11—22no—
107C2×C8×C11—21no—
108C2×C8×C11—82no—
109C2×C8×C11C22×C411yescharacteristic
110C2×C8×C11C22×C411yescharacteristic
111C2×C8×C11C2×D412yes—
112C11×C4⋊C4C22×C412yes—
113C11×C22⋊C4—22no—
114C42×C11C2411yescharacteristic
115C22⋊Dic11—22no—
116#4324C2×C818yescomplemented
117(C2×D11)⋊C4—22no—
118C4⋊Dic11C22×C412yes—
119Dic11⋊C4—22no—
120Dic11⋊C4—22no—
121C4×Dic11—22no—
122C4×Dic11—22no—
123C4×Dic11—22no—
124C4×Dic11C22×C411yescharacteristic
125C4×Dic11C2×D411yescharacteristic
126C4×Dic11#4111yescharacteristic
127C2×C11⋊C8—22no—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—82no—
130C2×C11⋊C8C22×C411yescharacteristic
131C2×C11⋊C8C22×C411yescharacteristic
132C2×C11⋊C8C2×D412yes—
133Dic44C2×C814yescomplemented
134C8×D11—22no—
135C8×D11—82no—
136C8×D11C2×C814yescomplemented
137#2988—112no—
138C4×#135—111no—
139#1580—111no—
140#1580D1111yescharacteristic, complemented
141#1579—111no—
142#1579—111no—
143C8×SD16—112no—
144C8×SD16—112no—
145C2×#334—111no—
146#1477—112no—
147#1450—111no—
148C23×C11—22no—
149C22×D11C4×D411yescharacteristic
150D4×C11—22no—
151D4×C11C22×C814yes—
152C2×C4×C11—22no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11C23×C411yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C2×C4×C11C2×#4111yescharacteristic
158C22⋊D11—28no—
159C2×Dic11—22no—
160C2×Dic11—28no—
161C2×Dic11—22no—
162C2×Dic11—82no—
163C2×Dic11C4×D411yescharacteristic
164C2×Dic11C4×D411yescharacteristic
165C2×Dic11C4×D411yescharacteristic
166C4×D11—22no—
167C4×D11—41no—
168C4×D11C22×C812yes—
169C4×D11#13112yes—
170Dic22—22no—
171Dic22C22×C814yes—
172C8×C11—21no—
173C8×C11—22no—
174C8×C11—41no—
175C8×C11—42no—
176C8×C11C22×C812yes—
177C11⋊C8—21no—
178C11⋊C8—22no—
179C11⋊C8—41no—
180C11⋊C8—42no—
181C11⋊C8C22×C812yes—
182C2×#135—111no—
183C4×#41—112no—
184C8×Q8—112no—
185C8×Q8—112no—
186C4×Q16—111no—
187C4×Q16—111no—
188C4×SD16—112no—
189C4×SD16—112no—
190C4×D8—111no—
191C4×D8C2×D1111yescharacteristic
192C8×D4—112no—
193C8×D4—222no—
194C8×D4—222no—
195C8×D4C2×D1112yes—
196#431—111no—
197#431—111no—
198#431—222no—
199#427—111no—
200C2×C4⋊C8—112no—
201C2×C4⋊C8—222no—
202#416—112no—
203C2×C4×C8—111no—
204#334—112no—
205#334—111no—
206#334C2×D1111yescharacteristic
207Q8⋊C8—112no—
208Q8⋊C8—112no—
209D4⋊C8—112no—
210D4⋊C8C2×D1112yes—
211#322—111no—
212#322C2×D1111yescharacteristic
213C82—111no—
214C82—111no—
215C22×C11—24no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11C2×C4×D411yescharacteristic
219C2×D11—21no—
220C2×D11—21no—
221C2×D11C8×D412yes—
222C4×C11—21no—
223C4×C11—42no—
224C4×C11C23×C811yescharacteristic
225C4×C11C2×#13111yescharacteristic
226C4×C11#57712yes—
227Dic11—24no—
228Dic11—21no—
229Dic11—21no—
230Dic11—42no—
231Dic11C8×D412yes—
232C2×#41—112no—
233#135—118no—
234C2×Q16—111no—
235C2×SD16—112no—
236C2×D8C4×D1111yescharacteristic
237C22×C8—22no—
238C22×C8—111no—
239C22×C8—111no—
240C22×C8—222no—
241C22×C8—222no—
242C4×Q8—112no—
243C4×Q8—112no—
244C4×D4—112no—
245C4×D4—222no—
246C4×D4—222no—
247C4×D4C22×D1112yes—
248#117—112no—
249#117—222no—
250C2×C42—111no—
251C2×C42—222no—
252#107—111no—
253#107C4×D1111yescharacteristic
254#106—112no—
255C4⋊C8—112no—
256C4⋊C8—112no—
257C4⋊C8—222no—
258C4⋊C8—221no—
259C4⋊C8—222no—
260C4⋊C8—222no—
261C4⋊C8C22×D1112yes—
262#103—112no—
263#103—112no—
264#102—112no—
265#102C4×D1112yes—
266C22⋊C8—22no—
267C22⋊C8—112no—
268C22⋊C8—221no—
269C22⋊C8—222no—
270C4×C8—111no—
271C4×C8—111no—
272C4×C8—111no—
273C4×C8—111no—
274C4×C8—111no—
275C4×C8—222no—
276C4×C8—222no—
277C4×C8C22×D1111yescharacteristic
278C4×C8C22×D1111yescharacteristic
279C4×C8C22×D1111yescharacteristic
280C2×C11—44no—
281C2×C11C2×C8×D411yescharacteristic
282C2×C11#295211yescharacteristic
283C2×C11#295711yescharacteristic
284D11—22no—
285#41—118no—
286#41—224no—
287C2×Q8—112no—
288C2×D4—222no—
289C2×D4C2×C4×D1112yes—
290C22×C4—22no—
291C22×C4—111no—
292C22×C4—111no—
293C22×C4—111no—
294C22×C4—222no—
295C22×C4—222no—
296Q16—114no—
297SD16—118no—
298D8C8×D1114yescomplemented
299C2×C8—22no—
300C2×C8—21no—
301C2×C8—82no—
302C2×C8—111no—
303C2×C8—114no—
304C2×C8—111no—
305C2×C8—112no—
306C2×C8—222no—
307C2×C8—222no—
308C2×C8—221no—
309C2×C8—882no—
310C2×C8—882no—
311C2×C8C2×C4×D1111yescharacteristic
312C2×C8C2×C4×D1111yescharacteristic
313C2×C8D4×D1112yes—
314C4⋊C4—112no—
315C4⋊C4—222no—
316C4⋊C4—222no—
317C4⋊C4C2×C4×D1112yes—
318C22⋊C4—22no—
319C22⋊C4—222no—
320C22⋊C4—222no—
321C42—111no—
322C42—111no—
323C42—111no—
324C42—222no—
325C42—222no—
326C42—222no—
327C42C23×D1111yescharacteristic
328C11#1785811yescharacteristic, complemented, Sylow
329C23—22no—
330C23—111no—
331Q8—114no—
332Q8—222no—
333D4—22no—
334D4—228no—
335D4C2×C8×D1114yes—
336C2×C4—22no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—111no—
340C2×C4—112no—
341C2×C4—112no—
342C2×C4—111no—
343C2×C4—111no—
344C2×C4—228no—
345C2×C4—222no—
346C2×C4—222no—
347C2×C4—222no—
348C2×C4—441no—
349C2×C4—882no—
350C2×C4C22×C4×D1111yescharacteristic
351C2×C4C2×D4×D1111yescharacteristic
352C2×C4#41×D1111yescharacteristic
353C8—21no—
354C8—22no—
355C8—41no—
356C8—42no—
357C8—112no—
358C8—221no—
359C8—222no—
360C8—441no—
361C8—442no—
362C8C2×C8×D1112yes—
363C22—24no—
364C22—42no—
365C22—42no—
366C22—112no—
367C22—221no—
368C22—221no—
369C22C4×D4×D1111yescharacteristic
370C4—21no—
371C4—42no—
372C4—112no—
373C4—221no—
374C4—224no—
375C4—221no—
376C4—442no—
377C4C22×C8×D1111yescharacteristic
378C4D11×#13111yescharacteristic
379C4#1062330612yes—
380C2—44no—
381C2—222no—
382C2C8×D4×D1111yescharacteristic
383C2#1307749811yescharacteristic
384C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC11×#1580C2
socleC22×C11C2×C4×D4
prime radicalC2×#66965C4
cosocleC42×C11C24
hypercenter#1580D11
hypocenterC11#17858
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1580

Complements

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

NH ≅ G/Ntype
1. #13077723C2semidirect
3. #13067440C2semidirect
4. #13067436C2semidirect
5. #13067434C2semidirect
6. #13067419C2semidirect
7. C8×#4324C2semidirect
8. D11×#334C2semidirect
9. #13067000C2semidirect
10. #13066901C2semidirect
11. C11×#1580C2semidirect
54. #66965C8semidirect
100. #4341C2×C8semidirect
105. C11×D8C2×C8semidirect
116. #4324C2×C8semidirect
133. Dic44C2×C8semidirect
136. C8×D11C2×C8semidirect
140. #1580D11semidirect
298. D8C8×D11semidirect
328. C11#17858semidirect

Maximal subgroups

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

subgroupindex
#130777232
C4×#669652
#130674402
#130674362
#130674342
#130674192
C8×#43242
D11×#3342
#130670002
#130669012
C11×#15802
#1785811