Finite Group Databasebeta

← #14764288

Subgroups — #14764288

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071023C211yesmaximal, characteristic
2C2×#10622548C211yesmaximal, characteristic
3#13069380C214yesmaximal, complemented
4#13068811C214yesmaximal
5#13068773C212yesmaximal, complemented
6#13068744C212yesmaximal, complemented
7C2×C11×#431C211yesmaximal, characteristic
8C22×C42×C11C2211yescharacteristic
9C2×#66979—21no—
10C22×C4⋊Dic11—21no—
11C22×C4⋊Dic11—21no—
12C22×C4⋊Dic11C2212yes—
13C11×#431C418yescomplemented
14C2×C11×C4⋊C8C2212yes—
15C2×C11×C22⋊C8C2212yes—
16C2×C4×C8×C11C2212yes—
17#10622825—21no—
18#10622825C2212yes—
19C2×#66881C2218yes—
20#10622549—21no—
21#10622548—21no—
22#10622548—21no—
23#10622548C2212yes—
24#10622548C2212yes—
25#10622548C2211yescharacteristic
26#10622548C2211yescharacteristic
27C4×C4⋊Dic11—21no—
28C4×C4⋊Dic11C2212yes—
29#10622189C2218yes—
30C23×C4×C11D411yescharacteristic
31C23×C4×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C23×Dic11—22no—
34C22×C8×C11C2314yes—
35C2×C42×C11C2×C414yes—
36C2×C42×C11D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C42×C11Q814yes—
39C2×C42×C11C2311yescharacteristic
40C2×C42×C11C2311yescharacteristic
41C2×C22⋊Dic11—22no—
42#66979—44no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—22no—
46C2×C4⋊Dic11—22no—
47C2×C4⋊Dic11—22no—
48C2×C4⋊Dic11—22no—
49C2×C4⋊Dic11—22no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—44no—
53C2×C4⋊Dic11—44no—
54C2×C4⋊Dic11—44no—
55C2×C4⋊Dic11C2312yes—
56C2×C4⋊Dic11C2312yes—
57C2×C4⋊Dic11C2314yes—
58C2×C4×Dic11—22no—
59C11×C4⋊C8C2×C418yescomplemented
60C11×C22⋊C8C2×C418yes—
61C4×C8×C11C2×C418yescomplemented
62C11⋊#95—22no—
63C11⋊#95—22no—
64#66881—48no—
65#21981—111nomaximal, Sylow
66C24×C11C2×D411yescharacteristic
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11C4⋊C414yes—
72C22×C4×C11C4⋊C414yes—
73C22×C4×C11SD1614yes—
74C22×C4×C11SD1614yes—
75C22×C4×C11C22×C412yes—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×Q812yes—
82C22×C4×C11C2411yescharacteristic
83C22×Dic11—22no—
84C22×Dic11—22no—
85C22×Dic11—24no—
86C22×Dic11—44no—
87C22×Dic11—44no—
88C22×Dic11—44no—
89C2×C8×C11—24no—
90C2×C8×C11—24no—
91C2×C8×C11C22×C418yes—
92C42×C11C4⋊C414yes—
93C42×C11C4⋊C414yes—
94C42×C11C22×C412yes—
95C42×C11C22×C412yes—
96C42×C11C2×Q812yes—
97C42×C11C2×Q812yes—
98C22⋊Dic11—44no—
99C4⋊Dic11—24no—
100C4⋊Dic11—28no—
101C4⋊Dic11—24no—
102C4⋊Dic11—44no—
103C4⋊Dic11—44no—
104C4⋊Dic11—44no—
105C4⋊Dic11—44no—
106C4⋊Dic11—42no—
107C4⋊Dic11—42no—
108C4⋊Dic11—42no—
109C4⋊Dic11—44no—
110C4⋊Dic11—42no—
111C4×Dic11—44no—
112C2×#431D1111yescharacteristic
113#2285—111no—
114C2×#384—111no—
115#1948—114no—
116#1853—114no—
117#1844—112no—
118#1834—112no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11C2×C4⋊C412yes—
124C23×C11C2×SD1612yes—
125C23×C11C2×SD1612yes—
126C23×C11C22×D411yescharacteristic
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—24no—
132C2×C4×C11—24no—
133C2×C4×C11—28no—
134C2×C4×C11#106116yescomplemented
135C2×C4×C11C2×C4⋊C412yes—
136C2×C4×C11C2×C4⋊C412yes—
137C2×C4×C11C2×C4⋊C412yes—
138C2×C4×C11C2×C4⋊C412yes—
139C2×C4×C11C2×C4⋊C412yes—
140C2×C4×C11C2×SD1612yes—
141C2×C4×C11C2×SD1612yes—
142C2×C4×C11C2×SD1612yes—
143C2×C4×C11C2×SD1612yes—
144C2×C4×C11AGL(1,ℤ/8)12yes—
145C2×C4×C11#13712yes—
146C2×C4×C11C23×C411yescharacteristic
147C2×C4×C11C22×Q811yescharacteristic
148C2×C4×C11H(5,𝔽2)12yes—
149C2×C4×C112−1+412yes—
150C2×Dic11—44no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—44no—
156C2×Dic11—44no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—88no—
160C8×C11—28no—
161C2×#117—221no—
162C22×C4⋊C4—112no—
163C22×C4⋊C4—221no—
164C22×C4⋊C4—221no—
165C22×C42C2×D1111yescharacteristic
166#431Dic1118yescomplemented
167C2×#106—118no—
168C2×C4⋊C8C2×D1112yes—
169C2×C22⋊C8C2×D1112yes—
170C2×C4×C8C2×D1112yes—
171#384—111no—
172#384—112no—
173#384—111no—
174#384—112no—
175#384—221no—
176#384—221no—
177#382—221no—
178#380—112no—
179#380—221no—
180C4×C4⋊C4—112no—
181C4×C4⋊C4—221no—
182#340—118no—
183C22×C11—22no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11C2×#10614yes—
190C22×C11C22×C4⋊C411yescharacteristic
191C22×C11#53511yescharacteristic
192C22×C11#53611yescharacteristic
193C22×C11C22×SD1611yescharacteristic
194C22×C11C22×SD1611yescharacteristic
195C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
196C22×C11C2×#13711yescharacteristic
197C4×C11—22no—
198C4×C11—22no—
199C4×C11C2×#10614yes—
200C4×C11C2×#10614yes—
201C4×C11#42814yes—
202C4×C11#52012yes—
203C4×C11#54412yes—
204Dic11—82no—
205Dic11—84no—
206Dic11—82no—
207C23×C4—222no—
208C23×C4D4411yescharacteristic
209C23×C4D4411yescharacteristic
210C23×C4C22×D1111yescharacteristic
211C22×C8C22×D1114yes—
212#117—444no—
213C2×C4⋊C4—114no—
214C2×C4⋊C4—112no—
215C2×C4⋊C4—112no—
216C2×C4⋊C4—222no—
217C2×C4⋊C4—222no—
218C2×C4⋊C4—222no—
219C2×C4⋊C4—222no—
220C2×C4⋊C4—222no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—444no—
226C2×C4⋊C4—444no—
227C2×C4⋊C4—444no—
228C2×C22⋊C4—222no—
229C2×C42—222no—
230C2×C42Dic2214yes—
231C2×C42D4411yescharacteristic
232C2×C42D4411yescharacteristic
233C2×C42C2×Dic1114yes—
234C2×C42C22×D1111yescharacteristic
235C2×C42C22×D1111yescharacteristic
236#106—448no—
237C4⋊C8C2×Dic1118yescomplemented
238C22⋊C8C2×Dic1118yes—
239C4×C8C2×Dic1118yescomplemented
240#95—222no—
241#95—222no—
242C2×C11—24no—
243C2×C11#231711yescharacteristic
244C2×C11C22×#10611yescharacteristic
245C2×C11C2×#42811yescharacteristic
246C2×C11#320611yescharacteristic
247C2×C11#320811yescharacteristic
248C2×C11#322711yescharacteristic
249C2×C11#322911yescharacteristic
250C24C2×D4411yescharacteristic
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—222no—
256C22×C4—222no—
257C22×C4—224no—
258C22×C4—444no—
259C22×C4—444no—
260C22×C4—444no—
261C22×C4#431414yes—
262C22×C4#431414yes—
263C22×C4C4⋊Dic1114yes—
264C22×C4C4⋊Dic1114yes—
265C22×C4C2×Dic2212yes—
266C22×C4C2×D4411yescharacteristic
267C22×C4C2×D4411yescharacteristic
268C22×C4C2×D4411yescharacteristic
269C22×C4C2×D4411yescharacteristic
270C22×C4C2×D4411yescharacteristic
271C22×C4C22×Dic1112yes—
272C22×C4C23×D1111yescharacteristic
273C2×C8—24no—
274C2×C8—24no—
275C2×C8C22×Dic1118yes—
276C4⋊C4—224no—
277C4⋊C4—228no—
278C4⋊C4—224no—
279C4⋊C4—444no—
280C4⋊C4—444no—
281C4⋊C4—444no—
282C4⋊C4—444no—
283C4⋊C4—442no—
284C4⋊C4—442no—
285C4⋊C4—444no—
286C4⋊C4—442no—
287C4⋊C4—442no—
288C22⋊C4—444no—
289C42—444no—
290C42C4⋊Dic1114yes—
291C42C4⋊Dic1114yes—
292C42C2×Dic2212yes—
293C42C2×Dic2212yes—
294C42C22×Dic1112yes—
295C42C22×Dic1112yes—
296C11#2198111yescharacteristic, complemented, Sylow
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23C2×#431412yes—
302C23C2×#431412yes—
303C23C2×C4⋊Dic1112yes—
304C23C22×D4411yescharacteristic
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—28no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4—444no—
315C2×C4—444no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—444no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4—888no—
322C2×C4#66881116yescomplemented
323C2×C4C2×#431412yes—
324C2×C4C2×#431412yes—
325C2×C4C2×#431412yes—
326C2×C4C2×#431412yes—
327C2×C4#6696112yes—
328C2×C4#6696212yes—
329C2×C4C2×C4⋊Dic1112yes—
330C2×C4C2×C4⋊Dic1112yes—
331C2×C4C2×C4⋊Dic1112yes—
332C2×C4C2×C4⋊Dic1112yes—
333C2×C4C2×C4⋊Dic1112yes—
334C2×C4C22×Dic2211yescharacteristic
335C2×C4#6704212yes—
336C2×C4#6704312yes—
337C2×C4C23×Dic1111yescharacteristic
338C8—28no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22C2×#6688114yes—
346C22#1062305611yescharacteristic
347C22#1062305711yescharacteristic
348C22C22×#431411yescharacteristic
349C22C22×#431411yescharacteristic
350C22C2×#6696111yescharacteristic
351C22C2×#6696211yescharacteristic
352C22C22×C4⋊Dic1111yescharacteristic
353C4—22no—
354C4—22no—
355C4—884no—
356C4—882no—
357C4—882no—
358C4C2×#6688114yes—
359C4C2×#6688114yes—
360C4#1062273414yes—
361C4#1062305012yes—
362C4#1062335812yes—
363C2—24no—
364C2#1307123911yescharacteristic
365C2C22×#6688111yescharacteristic
366C2C2×#1062273411yescharacteristic
367C2#1307954311yescharacteristic
368C2#1307955911yescharacteristic
369C2#1307974611yescharacteristic
370C2#1307976211yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#431C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#431D11
hypocenterC11#21981
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
3. #13069380C2semidirect
5. #13068773C2semidirect
6. #13068744C2semidirect
13. C11×#431C4semidirect
59. C11×C4⋊C8C2×C4semidirect
61. C4×C8×C11C2×C4semidirect
134. C2×C4×C11#106semidirect
166. #431Dic11semidirect
237. C4⋊C8C2×Dic11semidirect
239. C4×C8C2×Dic11semidirect
296. C11#21981semidirect
322. C2×C4#66881semidirect

Maximal subgroups

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

subgroupindex
#130710232
C2×#106225482
#130693802
#130688112
#130687732
#130687442
C2×C11×#4312
#2198111