Finite Group Databasebeta

← #14680195

Subgroups — #14680195

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊Dic11C211yesmaximal, characteristic
2C2×#10622559C212yesmaximal
3C2×#10622824C211yesmaximal, characteristic
4#13066880C214yesmaximal, complemented
5#13066872C214yesmaximal, complemented
6#13066838C212yesmaximal
7C2×C11×#381C211yesmaximal, characteristic
8C24×C4×C11C2211yescharacteristic
9C24×Dic11C2212yes—
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×C22⋊Dic11C2212yes—
13C22×C4⋊Dic11—24no—
14C22×C4⋊Dic11—28no—
15C22×C4⋊Dic11C2214yes—
16C22×Dic11⋊C4C2214yes—
17C11×#381—24no—
18C2×C11×#95C2212yes—
19C2×C11×#95C2212yes—
20#10622824C418yescomplemented
21C2×C11⋊#95C2214yes—
22C2×C11⋊#95C2218yes—
23C2×C11⋊#95C2214yes—
24#10622559—28no—
25C25×C11C2311yescharacteristic
26C23×C4×C11—24no—
27C23×C4×C11—24no—
28C23×C4×C11C2×C414yes—
29C23×C4×C11D414yes—
30C23×C4×C11Q814yes—
31C23×C4×C11C2311yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C23×C4×C11C2312yes—
34C23×C4×C11C2312yes—
35C23×Dic11—24no—
36C23×Dic11—24no—
37C23×Dic11—48no—
38C23×Dic11D418yes—
39C23×Dic11C2314yes—
40C23×Dic11C2314yes—
41C2×C11×C22⋊C4—24no—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4—24no—
45C2×C22⋊Dic11—24no—
46C2×C22⋊Dic11—24no—
47C2×C22⋊Dic11C2×C418yes—
48C2×C4⋊Dic11—232no—
49C2×C4⋊Dic11—28no—
50C2×C4⋊Dic11—216no—
51C2×Dic11⋊C4—28no—
52C2×Dic11⋊C4—48no—
53C11×#95—24no—
54C11×#95—24no—
55C11⋊#95—28no—
56C11⋊#95—48no—
57C11⋊#95C2×C4116yescomplemented
58#14263—111nomaximal, Sylow
59C24×C11—24no—
60C24×C11—24no—
61C24×C11C22×C412yes—
62C24×C11C2×D412yes—
63C24×C11C2×D414yes—
64C24×C11C2×Q812yes—
65C24×C11#4114yes—
66C24×C11C2411yescharacteristic
67C22×C4×C11—216no—
68C22×C4×C11—28no—
69C22×C4×C11—216no—
70C22×C4×C11—28no—
71C22×C4×C11—24no—
72C22×C4×C11—24no—
73C22×C4×C11—22no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—24no—
83C22×C4×C11C4⋊C4116yescomplemented
84C22×C4×C11C22×C414yes—
85C22×C4×C11C2×D414yes—
86C22×C4×C11C2×Q814yes—
87C22×Dic11—216no—
88C22×Dic11—24no—
89C22×Dic11—24no—
90C22×Dic11—24no—
91C22×Dic11—24no—
92C22×Dic11—28no—
93C22×Dic11—28no—
94C22×Dic11—28no—
95C22×Dic11—28no—
96C22×Dic11—416no—
97C22×Dic11—416no—
98C22×Dic11—416no—
99C22×Dic11C22×C418yes—
100C22×Dic11C2×D418yes—
101C11×C22⋊C4—44no—
102C11×C22⋊C4—44no—
103C22⋊Dic11—216no—
104C4⋊Dic11—232no—
105Dic11⋊C4—416no—
106C23×C4⋊C4—111no—
107C2×#385—112no—
108C2×#381—111no—
109C2×#381D1111yescharacteristic
110#1444—114no—
111#1442—114no—
112C22⋊#95—112no—
113C23×C11—28no—
114C23×C11—28no—
115C23×C11—24no—
116C23×C11—24no—
117C23×C11—28no—
118C23×C11—216no—
119C23×C11—28no—
120C23×C11C2×C4⋊C414yes—
121C23×C11C4×D418yes—
122C23×C11#12014yes—
123C23×C11C22⋊Q818yes—
124C23×C11#12314yes—
125C23×C11C23×C411yescharacteristic
126C23×C11C22×D412yes—
127C23×C11C22×D411yescharacteristic
128C23×C11C22×Q811yescharacteristic
129C23×C11C2×#4112yes—
130C23×C11H(5,𝔽2)14yes—
131C23×C112−1+414yes—
132C2×C4×C11—28no—
133C2×C4×C11—24no—
134C2×C4×C11—28no—
135C2×C4×C11—24no—
136C2×C4×C11—232no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—44no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—44no—
146C2×C4×C11—48no—
147C2×C4×C11C2×C4⋊C418yes—
148C2×Dic11—28no—
149C2×Dic11—216no—
150C2×Dic11—28no—
151C2×Dic11—28no—
152C2×Dic11—28no—
153C2×Dic11—432no—
154C2×Dic11—44no—
155C2×Dic11—48no—
156C2×Dic11—48no—
157C2×Dic11—44no—
158C2×Dic11—48no—
159C24×C4—112no—
160C24×C4C2×D1111yescharacteristic
161C22×C4⋊C4—114no—
162C22×C4⋊C4—114no—
163C22×C4⋊C4—228no—
164C22×C4⋊C4—224no—
165C22×C22⋊C4—112no—
166C22×C22⋊C4C2×D1111yescharacteristic
167C22×C22⋊C4C2×D1111yescharacteristic
168#385—228no—
169#381—24no—
170#381—118no—
171C2×#95—114no—
172C2×#95—114no—
173C2×#95—118no—
174C2×#95C2×D1112yes—
175C2×#95C2×D1112yes—
176C22×C11—28no—
177C22×C11—216no—
178C22×C11—24no—
179C22×C11—24no—
180C22×C11—28no—
181C22×C11—216no—
182C22×C11#38518yes—
183C22×C11C22×C4⋊C411yescharacteristic
184C22×C11C2×C4×D412yes—
185C22×C11#52014yes—
186C22×C11C2×#12011yescharacteristic
187C22×C11C2×C22⋊Q812yes—
188C22×C11C2×#12311yescharacteristic
189C22×C11#53414yes—
190C22×C11#53512yes—
191C22×C11#53612yes—
192C22×C11#53614yes—
193C22×C11#53918yes—
194C22×C11#54414yes—
195C4×C11—28no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11—82no—
199Dic11—48no—
200Dic11—48no—
201C25C22×D1111yescharacteristic
202C23×C4—24no—
203C23×C4—24no—
204C23×C4—114no—
205C23×C4—114no—
206C23×C4—118no—
207C23×C4—224no—
208C23×C4—224no—
209C23×C4—448no—
210C23×C4Dic2214yes—
211C23×C4C4×D1114yes—
212C23×C4C22⋊D1114yes—
213C23×C4C22×D1111yescharacteristic
214C23×C4C22×D1111yescharacteristic
215C23×C4C22×D1112yes—
216C23×C4C22×D1112yes—
217C2×C4⋊C4—2216no—
218C2×C4⋊C4—2232no—
219C2×C4⋊C4—228no—
220C2×C4⋊C4—228no—
221C2×C4⋊C4—448no—
222C2×C22⋊C4—24no—
223C2×C22⋊C4—24no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—118no—
227C2×C22⋊C4—224no—
228C2×C22⋊C4—224no—
229#95—24no—
230#95—24no—
231#95—1116no—
232#95—228no—
233#95—448no—
234C2×C11—28no—
235C2×C11C2×#38511yescharacteristic
236C2×C11#231712yes—
237C2×C11#232214yes—
238C2×C11#261311yescharacteristic
239C2×C11#261411yescharacteristic
240C2×C11#262312yes—
241C2×C11#262714yes—
242C24—24no—
243C24—24no—
244C24C2×Dic2212yes—
245C24C2×C4×D1112yes—
246C24D4×D1114yes—
247C24#434114yes—
248C24C2×C22⋊D1112yes—
249C24C23×D1111yescharacteristic
250C22×C4—216no—
251C22×C4—216no—
252C22×C4—28no—
253C22×C4—28no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—118no—
267C22×C4—118no—
268C22×C4—2216no—
269C22×C4—224no—
270C22×C4—224no—
271C22×C4—224no—
272C22×C4—228no—
273C22×C4—228no—
274C22×C4—228no—
275C22×C4—228no—
276C22×C4—224no—
277C22×C4—4416no—
278C22×C4—4416no—
279C22×C4—4416no—
280C22×C4Dic11⋊C4116yescomplemented
281C22×C4C2×Dic2214yes—
282C22×C4C2×C4×D1114yes—
283C22×C4C2×C22⋊D1114yes—
284C4⋊C4—2232no—
285C4⋊C4—4416no—
286C22⋊C4—44no—
287C22⋊C4—44no—
288C22⋊C4—2216no—
289C11#1426311yescharacteristic, complemented, Sylow
290C23—28no—
291C23—28no—
292C23—24no—
293C23—24no—
294C23—28no—
295C23—28no—
296C23—216no—
297C23#6693118yes—
298C23(C22⋊D11)⋊C418yes—
299C23C2×Dic11⋊C414yes—
300C23#6698814yes—
301C23#6699014yes—
302C23C22×Dic2211yescharacteristic
303C23C22×C4×D1111yescharacteristic
304C23C2×D4×D1112yes—
305C23C2×#434112yes—
306C23#6704214yes—
307C23#6704314yes—
308C23C22×C22⋊D1111yescharacteristic
309C2×C4—28no—
310C2×C4—28no—
311C2×C4—232no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—48no—
324C2×C4—228no—
325C2×C4—2216no—
326C2×C4—228no—
327C2×C4—228no—
328C2×C4—228no—
329C2×C4—4432no—
330C2×C4—448no—
331C2×C4—444no—
332C2×C4—444no—
333C2×C4—448no—
334C2×C4—448no—
335C2×C4C2×Dic11⋊C418yes—
336C22—216no—
337C22—28no—
338C22—24no—
339C22—24no—
340C22—216no—
341C22—28no—
342C22#1062255918yes—
343C22C2×#6693112yes—
344C22C2×(C22⋊D11)⋊C412yes—
345C22#1062305014yes—
346C22#1062305414yes—
347C22#1062317914yes—
348C22#1062318414yes—
349C22#1062319618yes—
350C22C22×Dic11⋊C411yescharacteristic
351C22C2×#6698811yescharacteristic
352C22C2×#6699011yescharacteristic
353C22#1062335612yes—
354C22#1062336112yes—
355C4—28no—
356C4—81no—
357C4—81no—
358C4—82no—
359C4—448no—
360C4—448no—
361C2—28no—
362C2C2×#1062255911yescharacteristic
363C2#1307123612yes—
364C2#1307128214yes—
365C2#1307433211yescharacteristic
366C2#1307433711yescharacteristic
367C2#1307439812yes—
368C2#1307443314yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#381C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#381D11
hypocenterC11#14263
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
4. #13066880C2semidirect
5. #13066872C2semidirect
20. #10622824C4semidirect
57. C11⋊#95C2×C4semidirect
83. C22×C4×C11C4⋊C4semidirect
280. C22×C4Dic11⋊C4semidirect
289. C11#14263semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊Dic112
C2×#106225592
C2×#106228242
#130668802
#130668722
#130668382
C2×C11×#3812
#1426311