Finite Group Databasebeta

← #14764313

Subgroups — #14764313

Order 2816.

850 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622298C211yesmaximal, characteristic
2#13071021C211yesmaximal, characteristic
3#13071021C211yesmaximal, characteristic
4#13069383C214yesmaximal, complemented
5#13068816C214yesmaximal
6#13068775C211yesmaximal, characteristic, complemented
7#13068773C211yesmaximal, characteristic, complemented
8#13068743C211yesmaximal, characteristic, complemented
9C11×#1834C211yesmaximal, characteristic, complemented
10C2×#66945—21no—
11C2×#66945C2212yes—
12C2×C42×D11C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C11×#384C2211yescharacteristic
15C11×#384C2211yescharacteristic
16C2×(C2×D11)⋊C8C2212yes—
17C2×#66881C2214yes—
18C2×Dic11⋊C8C2212yes—
19#10622600—21no—
20#10622600—21no—
21#10622600—21no—
22#10622600C2212yes—
23#10622590—21no—
24#10622590C2212yes—
25C4⋊C4×Dic11—21no—
26C4⋊C4×Dic11—21no—
27C4⋊C4×Dic11—21no—
28C4⋊C4×Dic11C2212yes—
29C2×#66871C2214yes—
30#10622548C2211yescharacteristic
31#10622548C2211yescharacteristic
32C2×C4×C11⋊C8C2211yescharacteristic
33#10622298C418yescomplemented
34C11×#340C2214yes—
35#10622167C2214yes—
36C22×C4×D11D411yescharacteristic
37C22×C4×D11D411yescharacteristic
38C22×C4×D11C2311yescharacteristic
39C22×C8×C11C2312yes—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4C2312yes—
45C2×C11×C4⋊C4C2312yes—
46C2×C42×C11C2311yescharacteristic
47C2×(C2×D11)⋊C4—22no—
48C2×(C2×D11)⋊C4—22no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11C2312yes—
54C2×C4⋊Dic11C2312yes—
55C2×C4×Dic11—22no—
56C2×C4×Dic11—22no—
57C2×C4×Dic11D411yescharacteristic
58C2×C4×Dic11D411yescharacteristic
59C2×C4×Dic11C2311yescharacteristic
60C22×C11⋊C8C2312yes—
61#66945—44no—
62#66945—44no—
63C42×D11C2×C414yes—
64C42×D11Q814yes—
65C4×C8×C11C2×C414yes—
66C11⋊#95—22no—
67C11⋊#95—22no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70(C2×D11)⋊C8C2×C418yes—
71#66881—44no—
72Dic11⋊C8C2×C418yes—
73#66871—44no—
74C4×C11⋊C8C2×C414yes—
75#21984—111nomaximal, Sylow
76C23×D11C2×D411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2411yescharacteristic
82C22×Dic11—22no—
83C22×Dic11—22no—
84C22×Dic11C2×D411yescharacteristic
85C22×Dic11C2×D411yescharacteristic
86C22×Dic11C2×D411yescharacteristic
87C2×C4×D11—22no—
88C2×C4×D11—22no—
89C2×C4×D11—22no—
90C2×C4×D11—22no—
91C2×C4×D11—22no—
92C2×C4×D11—22no—
93C2×C4×D11C4⋊C414yes—
94C2×C4×D11C4⋊C414yes—
95C2×C4×D11C22×C412yes—
96C2×C4×D11C2×Q812yes—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11C22×C414yes—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—42no—
104C11×C4⋊C4—42no—
105C11×C4⋊C4—42no—
106C42×C11C22×C412yes—
107C42×C11C2×Q812yes—
108(C2×D11)⋊C4—44no—
109(C2×D11)⋊C4—44no—
110C4⋊Dic11—24no—
111C4⋊Dic11—24no—
112C4⋊Dic11—42no—
113C4⋊Dic11—42no—
114C4⋊Dic11—42no—
115C4⋊Dic11—42no—
116C4×Dic11—44no—
117C4×Dic11—44no—
118C4×Dic11C4⋊C414yes—
119C4×Dic11C4⋊C414yes—
120C4×Dic11C22×C412yes—
121C4×Dic11C2×Q812yes—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8C22×C414yes—
125C2×#431—111no—
126#2285—111no—
127#2285—111no—
128#1949—114no—
129#1854—114no—
130#1845—111no—
131#1844—111no—
132#1834—111no—
133#1834D1111yescharacteristic, complemented
134C23×C11C22×D411yescharacteristic
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—21no—
141C22×D11C2×C4⋊C412yes—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11C2×C4⋊C412yes—
149C2×C4×C11C2×C4⋊C412yes—
150C2×C4×C11#13512yes—
151C2×C4×C11#13512yes—
152C2×C4×C11AGL(1,ℤ/8)12yes—
153C2×C4×C11#13712yes—
154C2×C4×C11C23×C411yescharacteristic
155C2×C4×C11C22×Q811yescharacteristic
156C2×C4×C11H(5,𝔽2)12yes—
157C2×C4×C112−1+412yes—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11C2×C4⋊C412yes—
171C2×Dic11C2×C4⋊C412yes—
172C2×Dic11C2×C4⋊C412yes—
173C4×D11—24no—
174C4×D11—24no—
175C4×D11—28no—
176C4×D11—28no—
177C8×C11—24no—
178C11⋊C8—24no—
179C2×#117—112no—
180C2×#117—221no—
181C22×C42—111no—
182#431—118no—
183C2×#107—114no—
184C2×#106—114no—
185C2×C4⋊C8—112no—
186C2×C22⋊C8—112no—
187C2×C4×C8—111no—
188C2×C4×C8C2×D1111yescharacteristic
189#384—111no—
190#384—111no—
191#384C2×D1111yescharacteristic
192#384C2×D1111yescharacteristic
193#382—112no—
194#382—221no—
195#380—112no—
196#380—221no—
197#380—221no—
198#380—221no—
199C4×C4⋊C4—112no—
200C4×C4⋊C4—221no—
201C4×C4⋊C4—221no—
202C4×C4⋊C4—221no—
203#340—114no—
204#340C2×D1114yes—
205C22×C11C22×C4⋊C411yescharacteristic
206C22×C11#53511yescharacteristic
207C22×C11#53611yescharacteristic
208C22×C11C2×#13511yescharacteristic
209C22×C11C2×#13511yescharacteristic
210C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
211C22×C11C2×#13711yescharacteristic
212C2×D11—22no—
213C2×D11—22no—
214C2×D11—22no—
215C2×D11—41no—
216C2×D11—41no—
217C2×D11—41no—
218C2×D11—41no—
219C4×C11—82no—
220C4×C11—82no—
221C4×C11#42714yes—
222C4×C11#42814yes—
223C4×C11#52012yes—
224C4×C11#54412yes—
225Dic11—22no—
226Dic11—22no—
227Dic11—22no—
228Dic11—82no—
229Dic11—82no—
230C23×C4—111no—
231C23×C4—111no—
232C23×C4—111no—
233C22×C8—112no—
234C22×C8C22×D1112yes—
235#117—444no—
236#117—444no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—112no—
242C2×C4⋊C4—112no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4C22×D1112yes—
248C2×C4⋊C4C22×D1112yes—
249C2×C22⋊C4—222no—
250C2×C22⋊C4—222no—
251C2×C42—111no—
252C2×C42—111no—
253C2×C42—111no—
254C2×C42—114no—
255C2×C42—114no—
256C2×C42—222no—
257C2×C42—222no—
258C2×C42C22×D1111yescharacteristic
259#107—444no—
260#106—444no—
261C4⋊C8—118no—
262C22⋊C8—118no—
263C4×C8—114no—
264C4×C8C4×D1114yes—
265#95—222no—
266#95—222no—
267#95—222no—
268#95—222no—
269C2×C11#231711yescharacteristic
270C2×C11C2×#42711yescharacteristic
271C2×C11C2×#42811yescharacteristic
272C2×C11#320711yescharacteristic
273C2×C11#321011yescharacteristic
274C2×C11#322811yescharacteristic
275C2×C11#323111yescharacteristic
276D11—42no—
277C24—111no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—111no—
281C22×C4—111no—
282C22×C4—111no—
283C22×C4—114no—
284C22×C4—114no—
285C22×C4—112no—
286C22×C4—112no—
287C22×C4—222no—
288C22×C4—222no—
289C22×C4—222no—
290C22×C4—222no—
291C22×C4—222no—
292C22×C4—222no—
293C22×C4—222no—
294C22×C4—222no—
295C22×C4D4×D1111yescharacteristic
296C22×C4D4×D1111yescharacteristic
297C22×C4C23×D1111yescharacteristic
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—114no—
301C2×C8—222no—
302C2×C8—222no—
303C2×C8C2×C4×D1114yes—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C4⋊C4—42no—
309C4⋊C4—42no—
310C4⋊C4—224no—
311C4⋊C4—224no—
312C4⋊C4—442no—
313C4⋊C4—442no—
314C4⋊C4—442no—
315C4⋊C4—442no—
316C22⋊C4—444no—
317C22⋊C4—444no—
318C42—114no—
319C42—114no—
320C42—112no—
321C42—112no—
322C42—444no—
323C42—444no—
324C42C2×C4×D1112yes—
325C42Q8×D1112yes—
326C11#2198411yescharacteristic, complemented, Sylow
327C23—112no—
328C23—221no—
329C23—221no—
330C23—221no—
331C23—221no—
332C23—221no—
333C23—221no—
334C23C2×D4×D1111yescharacteristic
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—112no—
342C2×C4—112no—
343C2×C4—112no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—228no—
351C2×C4—228no—
352C2×C4—224no—
353C2×C4—224no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4C4⋊C4×D1112yes—
361C2×C4C4⋊C4×D1112yes—
362C2×C4#6696412yes—
363C2×C4#6696912yes—
364C2×C4#6696912yes—
365C2×C4#6697112yes—
366C2×C4C22×C4×D1111yescharacteristic
367C2×C4C2×Q8×D1111yescharacteristic
368C2×C4#6704212yes—
369C2×C4#6704312yes—
370C8—24no—
371C8—224no—
372C22—222no—
373C22—222no—
374C22—222no—
375C22—441no—
376C22—441no—
377C22—441no—
378C22—441no—
379C22C2×C4⋊C4×D1111yescharacteristic
380C22#1062320511yescharacteristic
381C22#1062320611yescharacteristic
382C22C2×#6696411yescharacteristic
383C22C2×#6696911yescharacteristic
384C22C2×#6696911yescharacteristic
385C22C2×#6697111yescharacteristic
386C4—82no—
387C4—82no—
388C4—222no—
389C4—222no—
390C4—222no—
391C4—882no—
392C4—882no—
393C4#1062247314yes—
394C4#1062249414yes—
395C4#1062305412yes—
396C4#1062322012yes—
397C2—442no—
398C2#1307124111yescharacteristic
399C2C2×#1062247311yescharacteristic
400C2C2×#1062249411yescharacteristic
401C2#1307955011yescharacteristic
402C2#1307957511yescharacteristic
403C2#1307974911yescharacteristic
404C2#1307977011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1834C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1834D11
hypocenterC11#21984
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
4. #13069383C2semidirect
6. #13068775C2semidirect
7. #13068773C2semidirect
8. #13068743C2semidirect
9. C11×#1834C2semidirect
33. #10622298C4semidirect
133. #1834D11semidirect
326. C11#21984semidirect

Maximal subgroups

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

subgroupindex
C2×#106222982
#130710212
#130693832
#130688162
#130687752
#130687732
#130687432
C11×#18342
#2198411