Finite Group Databasebeta

← #14764095

Subgroups — #14764095

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622739C211yesmaximal, characteristic
2D11×#407C212yesmaximal
3#13068822C214yesmaximal, complemented
4#13068819C214yesmaximal, complemented
5#13068658C211yesmaximal, characteristic, complemented
6#13068656C212yesmaximal, complemented
7C11×#1811C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×#4318C2211yescharacteristic
11C2×M16×D11C2214yes—
12C2×C11×#108C2212yescomplemented
13C11×#407C2212yes—
14#10622820C2212yes—
15#10622739C412yes—
16#10622739C414yes—
17#10622739C412yes—
18#10622739C2214yes—
19C2×#66886C2214yescomplemented
20C2×(C2×D11)⋊C8C2212yes—
21C2×(C2×D11)⋊C8C2212yes—
22C2×#66883C2212yescomplemented
23#10622339—22no—
24#10622339—22no—
25D11×C22⋊C8—22no—
26D11×C22⋊C8—22no—
27C11×#341C2212yescomplemented
28#10622196C2214yescomplemented
29#10622190C2212yescomplemented
30C24×D11Q811yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C23×Dic11Q811yescharacteristic
33C22×C4×D11—42no—
34C22×C4×D11—42no—
35C22×C4×D11C2×C411yescharacteristic
36C22×C4×D11C2×C412yes—
37C22×C4×D11C2×C411yescharacteristic
38C22×C4×D11D411yescharacteristic
39C22×C4×D11D412yes—
40C22×C4×D11D411yescharacteristic
41C22×C4×D11Q812yes—
42C22×C4×D11C2312yes—
43C2×C11×M16—42no—
44C2×C11×M16C2×C412yes—
45C2×C11×M16C2×C412yes—
46C2×C11×M16C2314yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C2×#4318—42no—
50C2×#4318C2×C412yes—
51C2×#4318C2×C412yes—
52C2×#4318C2314yes—
53C22×C11⋊C8C2312yes—
54M16×D11—44no—
55M16×D11—44no—
56C2×#4313—24no—
57C2×C8×D11—24no—
58C11×#108—42no—
59C11×C22⋊C8—22no—
60C11×C22⋊C8—22no—
61C22⋊(C11⋊C8)—22no—
62C22⋊(C11⋊C8)—22no—
63#66886—44no—
64(C2×D11)⋊C8—24no—
65(C2×D11)⋊C8—24no—
66(C2×D11)⋊C8C2×C414yes—
67(C2×D11)⋊C8C2×C414yes—
68(C2×D11)⋊C8C2×C414yes—
69(C2×D11)⋊C8C2×C414yes—
70#66883—42no—
71#21949—111nomaximal, Sylow
72C24×C11C2×Q811yescharacteristic
73C23×D11—44no—
74C23×D11—42no—
75C23×D11C4⋊C411yescharacteristic
76C23×D11C4⋊C412yes—
77C23×D11C4⋊C411yescharacteristic
78C23×D11C2×Q812yes—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×Q811yescharacteristic
86C22×C4×C11C2411yescharacteristic
87C22×Dic11—42no—
88C22×Dic11C4⋊C411yescharacteristic
89C22×Dic11C4⋊C412yes—
90C22×Dic11C4⋊C411yescharacteristic
91C22×Dic11C2×Q812yes—
92C2×C4×D11—24no—
93C2×C4×D11—24no—
94C2×C4×D11—44no—
95C2×C4×D11—41no—
96C2×C4×D11—42no—
97C2×C4×D11—41no—
98C2×C4×D11—41no—
99C2×C4×D11—42no—
100C2×C4×D11—41no—
101C2×C4×D11—42no—
102C2×C4×D11—44no—
103C2×C4×D11—42no—
104C2×C4×D11C4⋊C412yes—
105C2×C4×D11C4⋊C412yes—
106C2×C4×D11C4⋊C412yes—
107C2×C4×D11C4⋊C412yes—
108C2×C4×D11C22×C412yes—
109C2×C4×D11C22×C412yes—
110C2×C4×D11C2×D412yes—
111C2×C4×D11C2×D412yes—
112C11×M16—24no—
113C11×M16—24no—
114C11×M16—42no—
115C11×M16—42no—
116C2×C8×C11—24no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11C22×C412yes—
120C2×C8×C11C22×C412yes—
121#4318—24no—
122#4318—24no—
123#4318—42no—
124#4318—42no—
125C2×C11⋊C8—24no—
126C2×C11⋊C8—24no—
127C2×C11⋊C8C22×C414yes—
128#4313—48no—
129C8×D11—48no—
130C2×#407—112no—
131C2×#407—111no—
132#1855—114no—
133#1855—114no—
134#1811—112no—
135#1811—111no—
136#1811D1111yescharacteristic, complemented
137C23×C11—22no—
138C23×C11—42no—
139C23×C11C2×C4⋊C411yescharacteristic
140C23×C11C2×C4⋊C411yescharacteristic
141C23×C11C22×Q811yescharacteristic
142C22×D11—24no—
143C22×D11—24no—
144C22×D11—24no—
145C22×D11—24no—
146C22×D11—41no—
147C22×D11—42no—
148C22×D11—41no—
149C22×D11—42no—
150C22×D11—42no—
151C22×D11—42no—
152C22×D11—416no—
153C22×D11C2×C4⋊C412yes—
154C22×D11C2×C4⋊C412yes—
155C2×C4×C11—22no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11C2×C4⋊C411yescharacteristic
163C2×C4×C11C2×C4⋊C411yescharacteristic
164C2×C4×C11C23×C411yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11H(5,𝔽2)12yes—
167C2×C4×C11H(5,𝔽2)12yes—
168C2×Dic11—24no—
169C2×Dic11—41no—
170C2×Dic11—42no—
171C2×Dic11—41no—
172C2×Dic11C2×C4⋊C412yes—
173C2×Dic11C2×C4⋊C412yes—
174C4×D11—22no—
175C4×D11—22no—
176C4×D11—22no—
177C4×D11—22no—
178C4×D11—24no—
179C4×D11—24no—
180C4×D11—42no—
181C4×D11—42no—
182C4×D11—42no—
183C4×D11—42no—
184C8×C11—22no—
185C8×C11—22no—
186C8×C11—44no—
187C11⋊C8—24no—
188C11⋊C8—44no—
189C24×C4—111no—
190C22×M16—111no—
191C22×M16—114no—
192C22×M16C2×D1111yescharacteristic
193C2×#108—114no—
194C2×#108—112no—
195C2×#108C2×D1112yescomplemented
196#407—112no—
197#407—114no—
198#407—112no—
199#407—112no—
200#407—114no—
201#407—222no—
202#407—222no—
203#407C2×D1112yes—
204C2×C22⋊C8—112no—
205C2×C22⋊C8—112no—
206C2×C22⋊C8—222no—
207C2×C22⋊C8—222no—
208#341—114no—
209#341—112no—
210#341C2×D1112yescomplemented
211C22×C11—22no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—22no—
215C22×C11—22no—
216C22×C11—44no—
217C22×C11C22×C4⋊C411yescharacteristic
218C22×C11#54312yes—
219C2×D11—22no—
220C2×D11—22no—
221C2×D11—22no—
222C2×D11—22no—
223C2×D11—22no—
224C2×D11—44no—
225C2×D11—48no—
226C2×D11—48no—
227C2×D11—44no—
228C2×D11#43014yes—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11#51811yescharacteristic
232C4×C11#51811yescharacteristic
233C4×C11#53412yes—
234Dic11—22no—
235Dic11—22no—
236C25—111no—
237C23×C4—111no—
238C23×C4—112no—
239C23×C4—111no—
240C23×C4—112no—
241C23×C4—111no—
242C23×C4—111no—
243C23×C4—112no—
244C23×C4—111no—
245C23×C4—112no—
246C23×C4—442no—
247C23×C4—442no—
248C23×C4C22×D1111yescharacteristic
249C2×M16—42no—
250C2×M16—112no—
251C2×M16—112no—
252C2×M16—114no—
253C2×M16—224no—
254C2×M16—442no—
255C2×M16—444no—
256C2×M16—444no—
257C2×M16C4×D1112yes—
258C2×M16C4×D1112yes—
259C2×M16C22×D1114yes—
260C22×C8—112no—
261C22×C8—224no—
262C22×C8C22×D1111yescharacteristic
263C22×C8C22×D1111yescharacteristic
264#108—42no—
265#108—442no—
266#108—444no—
267C22⋊C8—22no—
268C22⋊C8—22no—
269C22⋊C8—114no—
270C22⋊C8—114no—
271C22⋊C8—114no—
272C22⋊C8—114no—
273C22⋊C8—224no—
274C22⋊C8—224no—
275C22⋊C8—222no—
276C22⋊C8—222no—
277C2×C11—22no—
278C2×C11—41no—
279C2×C11—41no—
280C2×C11#231511yescharacteristic
281C2×C11C2×#43012yes—
282D11—24no—
283D11—42no—
284C24—111no—
285C24—112no—
286C24—112no—
287C24—111no—
288C24—442no—
289C24—444no—
290C24Q8×D1111yescharacteristic
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—112no—
294C22×C4—111no—
295C22×C4—112no—
296C22×C4—111no—
297C22×C4—112no—
298C22×C4—112no—
299C22×C4—112no—
300C22×C4—112no—
301C22×C4—112no—
302C22×C4—112no—
303C22×C4—112no—
304C22×C4—112no—
305C22×C4—224no—
306C22×C4—224no—
307C22×C4—441no—
308C22×C4—442no—
309C22×C4—441no—
310C22×C4—441no—
311C22×C4—442no—
312C22×C4—441no—
313C22×C4—442no—
314C22×C4—444no—
315C22×C4—442no—
316C22×C4—444no—
317C22×C4—442no—
318C22×C4C2×C4×D1111yescharacteristic
319C22×C4C2×C4×D1111yescharacteristic
320C22×C4D4×D1111yescharacteristic
321C22×C4D4×D1111yescharacteristic
322C22×C4Q8×D1111yescharacteristic
323C22×C4C23×D1111yescharacteristic
324M16—24no—
325M16—24no—
326M16—42no—
327M16—42no—
328M16—224no—
329M16—224no—
330M16—448no—
331M16—442no—
332M16—442no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—24no—
336C2×C8—114no—
337C2×C8—224no—
338C2×C8—224no—
339C2×C8—448no—
340C2×C8C2×C4×D1112yes—
341C2×C8C2×C4×D1112yes—
342C11#2194911yescharacteristic, complemented, Sylow
343C23—22no—
344C23—42no—
345C23—112no—
346C23—112no—
347C23—224no—
348C23—224no—
349C23—224no—
350C23—224no—
351C23—441no—
352C23—442no—
353C23—441no—
354C23—442no—
355C23—442no—
356C23—442no—
357C23—4416no—
358C23C4⋊C4×D1111yescharacteristic
359C23C4⋊C4×D1111yescharacteristic
360C23C2×Q8×D1111yescharacteristic
361C2×C4—22no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—112no—
369C2×C4—112no—
370C2×C4—224no—
371C2×C4—222no—
372C2×C4—222no—
373C2×C4—222no—
374C2×C4—222no—
375C2×C4—224no—
376C2×C4—224no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—441no—
382C2×C4—442no—
383C2×C4—441no—
384C2×C4C4⋊C4×D1111yescharacteristic
385C2×C4C4⋊C4×D1111yescharacteristic
386C2×C4C22×C4×D1111yescharacteristic
387C2×C4C2×D4×D1111yescharacteristic
388C2×C4#6703712yes—
389C2×C4#6704212yes—
390C8—22no—
391C8—22no—
392C8—44no—
393C8—224no—
394C8—444no—
395C22—22no—
396C22—21no—
397C22—21no—
398C22—22no—
399C22—22no—
400C22—44no—
401C22—114no—
402C22—222no—
403C22—222no—
404C22—222no—
405C22—222no—
406C22—222no—
407C22—448no—
408C22—444no—
409C22—448no—
410C22—444no—
411C22C2×C4⋊C4×D1111yescharacteristic
412C22#1062316512yes—
413C4—21no—
414C4—21no—
415C4—222no—
416C4—222no—
417C4#1062301711yescharacteristic
418C4#1062305211yescharacteristic
419C4#1062313612yes—
420C2—22no—
421C2—41no—
422C2—41no—
423C2—224no—
424C2—442no—
425C2#1307122911yescharacteristic
426C2D11×#43012yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1811C2
socleC22×C11C22×C4⋊C4
prime radicalC24×D11Q8
cosocleC22×C4×C11C24
hypercenter#1811D11
hypocenterC11#21949
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1811

Complements

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

NH ≅ G/Ntype
3. #13068822C2semidirect
4. #13068819C2semidirect
5. #13068658C2semidirect
6. #13068656C2semidirect
7. C11×#1811C2semidirect
12. C2×C11×#108C22semidirect
19. C2×#66886C22semidirect
22. C2×#66883C22semidirect
27. C11×#341C22semidirect
28. #10622196C22semidirect
29. #10622190C22semidirect
136. #1811D11semidirect
195. C2×#108C2×D11semidirect
210. #341C2×D11semidirect
342. C11#21949semidirect

Maximal subgroups

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

subgroupindex
C2×#106227392
D11×#4072
#130688222
#130688192
#130686582
#130686562
C11×#18112
#2194911