Finite Group Databasebeta

← #14758368

Subgroups — #14758368

Order 2816.

1382 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66922C211yesmaximal, characteristic
2#13071023C211yesmaximal, characteristic
3#13069589C214yesmaximal, complemented
4#13069577C214yesmaximal, complemented
5#13068336C214yesmaximal
6C2×C4×C11×M16C211yesmaximal, characteristic
7C23×Dic22—21no—
8C22×C11×M16C2212yes—
9C22×C42×C11C2211yescharacteristic
10C2×#66979C2212yes—
11C22×C4⋊Dic11—21no—
12C22×C4⋊Dic11C2212yes—
13C2×#66922—21no—
14C2×#66922—21no—
15C2×#66922—24no—
16C2×#66922C418yescomplemented
17C2×#66922C2212yes—
18C2×#66922C2212yes—
19C4×C11×M16—24no—
20C2×C11×#97C2212yes—
21C2×C4×C8×C11C2212yes—
22#10622825—21no—
23#10622825—21no—
24#10622549C2212yes—
25#10622548C2212yes—
26C4×C4⋊Dic11—21no—
27C4×C4⋊Dic11—21no—
28#10622189C22116yes—
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C23×Dic11—22no—
33C22×Dic22—28no—
34C22×Dic22—22no—
35C22×Dic22—22no—
36C22×Dic22—48no—
37C2×C11×M16—24no—
38C2×C11×M16—24no—
39C2×C11×M16Q818yescomplemented
40C22×C8×C11C2314yes—
41C2×C42×C11C2×C414yes—
42C2×C42×C11D411yescharacteristic
43C2×C42×C11D411yescharacteristic
44C2×C42×C11D414yes—
45C2×C42×C11C2311yescharacteristic
46C2×C42×C11C2311yescharacteristic
47C2×C22⋊Dic11—22no—
48#66979—28no—
49C2×C4⋊Dic11—28no—
50C2×C4⋊Dic11—22no—
51C2×C4⋊Dic11—24no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11C2×C418yes—
57C2×C4⋊Dic11C2314yes—
58C2×C4⋊Dic11C2314yes—
59C2×C4×Dic11—22no—
60#66922—28no—
61#66922—28no—
62#66922—24no—
63#66922—24no—
64#66922C2×C418yes—
65#66922C2×C418yes—
66C11×#97—24no—
67C4×C8×C11—24no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70#21324—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C22×C4×C11—24no—
73C22×C4×C11—24no—
74C22×C4×C11C22⋊C414yes—
75C22×C4×C11C22⋊C414yes—
76C22×C4×C11C22×C412yes—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2×Q814yes—
84C22×C4×C11#4114yes—
85C22×C4×C11C2411yescharacteristic
86C22×Dic11—28no—
87C22×Dic11—24no—
88C22×Dic11—24no—
89C22×Dic11—48no—
90C2×Dic22—28no—
91C2×Dic22—28no—
92C2×Dic22—48no—
93C2×Dic22—432no—
94C2×Dic22—48no—
95C11×M16—216no—
96C2×C8×C11—24no—
97C2×C8×C11—24no—
98C2×C8×C11C2×Q818yescomplemented
99C42×C11C22⋊C414yes—
100C42×C11C22⋊C414yes—
101C42×C11C22×C412yes—
102C42×C11C22×C412yes—
103C42×C11C2×D412yes—
104C42×C11C2×D412yes—
105C22⋊Dic11—44no—
106C4⋊Dic11—28no—
107C4⋊Dic11—28no—
108C4⋊Dic11—28no—
109C4⋊Dic11—24no—
110C4⋊Dic11—28no—
111C4⋊Dic11—44no—
112C4⋊Dic11—44no—
113C4⋊Dic11C22×C418yes—
114C4×Dic11—44no—
115C22×C4⋊Q8—111no—
116C2×C4×M16D1111yescharacteristic
117#2285—111no—
118#1993—114no—
119#1990—114no—
120#1736—114no—
121C23×C11—22no—
122C23×C11—22no—
123C23×C11C2×C22⋊C412yes—
124C23×C11#12412yes—
125C23×C11C4⋊Q812yes—
126C23×C11C22×D411yescharacteristic
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—28no—
130C2×C4×C11—28no—
131C2×C4×C11C2×C22⋊C412yes—
132C2×C4×C11C2×C22⋊C412yes—
133C2×C4×C11C2×C22⋊C412yes—
134C2×C4×C11C2×C22⋊C412yes—
135C2×C4×C11C2×C22⋊C412yes—
136C2×C4×C11C4×Q818yes—
137C2×C4×C11C22⋊Q818yes—
138C2×C4×C11#12412yes—
139C2×C4×C11C4⋊Q812yes—
140C2×C4×C11AGL(1,ℤ/8)14yes—
141C2×C4×C11#13714yes—
142C2×C4×C11C23×C411yescharacteristic
143C2×C4×C11C22×D411yescharacteristic
144C2×C4×C11C22×Q812yes—
145C2×C4×C11C2×#4112yes—
146C2×Dic11—28no—
147C2×Dic11—416no—
148C2×Dic11—48no—
149C2×Dic11—44no—
150C2×Dic11—44no—
151C2×Dic11—44no—
152Dic22—416no—
153Dic22—416no—
154C8×C11—28no—
155C23×Q8—221no—
156C22×M16C2×D1112yes—
157C2×C4⋊Q8—112no—
158C2×C4⋊Q8—112no—
159C2×C4⋊Q8—118no—
160C2×C4⋊Q8—221no—
161C2×C4⋊Q8—221no—
162C2×C4⋊Q8—224no—
163C2×#117—112no—
164C22×C4⋊C4—112no—
165C22×C4⋊C4—221no—
166C22×C42C2×D1111yescharacteristic
167C4×M16—24no—
168C2×#97C2×D1112yes—
169C2×C4×C8C2×D1112yes—
170#384—112no—
171#382—112no—
172#380—221no—
173#380—221no—
174C4×C4⋊C4—221no—
175C4×C4⋊C4—221no—
176#340—1116no—
177C22×C11—24no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—24no—
181C22×C11#39114yes—
182C22×C11C22×C22⋊C411yescharacteristic
183C22×C11C2×#12411yescharacteristic
184C22×C11C2×C4⋊Q811yescharacteristic
185C22×C11C2×AGL(1,ℤ/8)12yes—
186C22×C11C2×#13712yes—
187C4×C11—22no—
188C4×C11—22no—
189C4×C11#39114yes—
190C4×C11#41814yes—
191C4×C11#41914yes—
192C4×C11C2×C4×Q812yes—
193C4×C11C2×C22⋊Q812yes—
194Dic11—48no—
195Dic11—84no—
196C22×Q8—228no—
197C22×Q8—222no—
198C22×Q8—222no—
199C22×Q8—448no—
200C23×C4—222no—
201C23×C4D4411yescharacteristic
202C23×C4D4411yescharacteristic
203C23×C4C22×D1111yescharacteristic
204C2×M16—24no—
205C2×M16—24no—
206C2×M16Dic2218yescomplemented
207C22×C8C22×D1114yes—
208C4⋊Q8—118no—
209C4⋊Q8—118no—
210C4⋊Q8—228no—
211C4⋊Q8—228no—
212C4⋊Q8—224no—
213C4⋊Q8—224no—
214#117—228no—
215C2×C4⋊C4—118no—
216C2×C4⋊C4—114no—
217C2×C4⋊C4—114no—
218C2×C4⋊C4—228no—
219C2×C4⋊C4—222no—
220C2×C4⋊C4—222no—
221C2×C4⋊C4—222no—
222C2×C4⋊C4—224no—
223C2×C4⋊C4—222no—
224C2×C4⋊C4—222no—
225C2×C22⋊C4—222no—
226C2×C42—222no—
227C2×C42C4×D1114yes—
228C2×C42D4411yescharacteristic
229C2×C42D4411yescharacteristic
230C2×C42C22⋊D1114yes—
231C2×C42C22×D1111yescharacteristic
232C2×C42C22×D1111yescharacteristic
233#97—24no—
234C4×C8—24no—
235#95—222no—
236#95—222no—
237C2×C11—24no—
238C2×C11C2×#39111yescharacteristic
239C2×C11C2×#41811yescharacteristic
240C2×C11C2×#41911yescharacteristic
241C2×C11#314112yes—
242C2×C11#316512yes—
243C24C2×D4411yescharacteristic
244C2×Q8—228no—
245C2×Q8—228no—
246C2×Q8—448no—
247C2×Q8—4432no—
248C2×Q8—448no—
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—228no—
252C22×C4—224no—
253C22×C4—224no—
254C22×C4—448no—
255C22×C4(C2×D11)⋊C414yes—
256C22×C4(C2×D11)⋊C414yes—
257C22×C4C2×Dic2214yes—
258C22×C4C2×C4×D1112yes—
259C22×C4C2×D4411yescharacteristic
260C22×C4C2×D4411yescharacteristic
261C22×C4C2×D4411yescharacteristic
262C22×C4C2×D4411yescharacteristic
263C22×C4C2×D4411yescharacteristic
264C22×C4#433914yes—
265C22×C4C2×C22⋊D1112yes—
266C22×C4C23×D1111yescharacteristic
267M16—216no—
268C2×C8—24no—
269C2×C8—24no—
270C2×C8C2×Dic2218yescomplemented
271C4⋊C4—118no—
272C4⋊C4—228no—
273C4⋊C4—228no—
274C4⋊C4—228no—
275C4⋊C4—224no—
276C4⋊C4—228no—
277C4⋊C4—444no—
278C4⋊C4—444no—
279C22⋊C4—444no—
280C42—444no—
281C42(C2×D11)⋊C414yes—
282C42(C2×D11)⋊C414yes—
283C42C2×C4×D1112yes—
284C42C2×C4×D1112yes—
285C42C2×C22⋊D1112yes—
286C42C2×C22⋊D1112yes—
287C11#2132411yescharacteristic, complemented, Sylow
288C23—22no—
289C23—22no—
290C23#6692212yes—
291C23#6692812yes—
292C23C2×(C2×D11)⋊C412yes—
293C23C22×D4411yescharacteristic
294Q8—4416no—
295Q8—4416no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—28no—
299C2×C4—28no—
300C2×C4—228no—
301C2×C4—4416no—
302C2×C4—448no—
303C2×C4—444no—
304C2×C4—444no—
305C2×C4—444no—
306C2×C4C4×Dic2218yes—
307C2×C4#6692212yes—
308C2×C4#6692812yes—
309C2×C4#6696114yes—
310C2×C4#6696214yes—
311C2×C4#6697718yes—
312C2×C4C2×(C2×D11)⋊C412yes—
313C2×C4C2×(C2×D11)⋊C412yes—
314C2×C4C2×(C2×D11)⋊C412yes—
315C2×C4C2×(C2×D11)⋊C412yes—
316C2×C4C2×(C2×D11)⋊C412yes—
317C2×C4C22×Dic2212yes—
318C2×C4C22×C4×D1111yescharacteristic
319C2×C4C2×#433912yes—
320C2×C4C22×C22⋊D1111yescharacteristic
321C8—28no—
322C22—24no—
323C22—22no—
324C22—22no—
325C22—24no—
326C22#1062254214yes—
327C22C2×#6692211yescharacteristic
328C22C2×#6692811yescharacteristic
329C22C2×#6696112yes—
330C22C2×#6696212yes—
331C22C22×(C2×D11)⋊C411yescharacteristic
332C4—22no—
333C4—22no—
334C4—448no—
335C4—884no—
336C4#1062254214yes—
337C4#1062273314yes—
338C4#1062274414yes—
339C4C2×C4×Dic2212yes—
340C4C2×#6697712yes—
341C2—24no—
342C2C2×#1062254211yescharacteristic
343C2C2×#1062274411yescharacteristic
344C2C2×#1062273311yescharacteristic
345C2#1307901012yes—
346C2#1307916212yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×M16C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×C4×M16D11
hypocenterC11#21324
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
3. #13069589C2semidirect
4. #13069577C2semidirect
16. C2×#66922C4semidirect
39. C2×C11×M16Q8semidirect
98. C2×C8×C11C2×Q8semidirect
206. C2×M16Dic22semidirect
270. C2×C8C2×Dic22semidirect
287. C11#21324semidirect

Maximal subgroups

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

subgroupindex
C22×#669222
#130710232
#130695892
#130695772
#130683362
C2×C4×C11×M162
#2132411