Finite Group Databasebeta

← #14660273

Subgroups — #14660273

Order 2816.

1778 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66897C212yesmaximal, complemented
2C2×#10622820C212yesmaximal, complemented
3C2×#10622168C212yesmaximal, complemented
4C22×C11×#121C211yesmaximal, characteristic
5C23×D4×C11C412yes—
6C23×D4×C11C2211yescharacteristic
7C24×C4×C11C2211yescharacteristic
8C2×C11×#121—24no—
9C2×C11×#121—24no—
10C2×C11×#121—24no—
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C412yes—
13C22×#4318C2214yes—
14C2×#66897—24no—
15C2×#66897—28no—
16#10622820—28no—
17C2×C22⋊(C11⋊C8)—24no—
18#10622168—24no—
19C25×C11C2×C411yescharacteristic
20C25×C11C2×C412yes—
21C22×D4×C11—24no—
22C22×D4×C11—24no—
23C22×D4×C11—24no—
24C22×D4×C11—24no—
25C22×D4×C11—22no—
26C22×D4×C11—22no—
27C22×D4×C11—24no—
28C22×D4×C11—48no—
29C22×D4×C11D414yes—
30C23×C4×C11—24no—
31C23×C4×C11—22no—
32C23×C4×C11—22no—
33C23×C4×C11—24no—
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11C2×C412yes—
36C23×C4×C11D414yes—
37C23×C4×C11C2311yescharacteristic
38C11×#121—232no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4D414yes—
42C2×C11×C22⋊C4—24no—
43C2×C11×C22⋊C4—24no—
44C2×C11×C22⋊C4—24no—
45C2×#4318—24no—
46C2×#4318—24no—
47C2×#4318—24no—
48C2×#4318—24no—
49C2×#4318—24no—
50C2×#4318D418yescomplemented
51C22×C11⋊C8—24no—
52#66897—216no—
53C22⋊(C11⋊C8)—216no—
54#10967—111nomaximal, Sylow
55C24×C11—24no—
56C24×C11—21no—
57C24×C11—21no—
58C24×C11—22no—
59C24×C11—22no—
60C24×C11—24no—
61C24×C11—28no—
62C24×C11—42no—
63C24×C11—44no—
64C24×C11—44no—
65C24×C11C22⋊C412yes—
66C24×C11C22⋊C414yes—
67C24×C11C22×C411yescharacteristic
68C2×D4×C11—216no—
69C2×D4×C11—24no—
70C2×D4×C11—28no—
71C2×D4×C11—28no—
72C2×D4×C11—24no—
73C2×D4×C11—416no—
74C2×D4×C11—48no—
75C2×D4×C11—416no—
76C2×D4×C11—48no—
77C2×D4×C11—42no—
78C2×D4×C11—44no—
79C2×D4×C11—44no—
80C2×D4×C11—42no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—28no—
90C22×C4×C11—28no—
91C22×C4×C11—24no—
92C22×C4×C11—42no—
93C22×C4×C11—44no—
94C22×C4×C11—44no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—44no—
99C22×C4×C11C22⋊C412yes—
100C22×C4×C11C22⋊C414yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D414yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11#4114yes—
106C11×C4⋊C4—28no—
107C11×C22⋊C4—216no—
108#4318—28no—
109#4318—28no—
110#4318—44no—
111#4318—44no—
112C2×C11⋊C8—28no—
113C2×C11⋊C8—44no—
114C2×C11⋊C8—44no—
115C22×#121D1111yescharacteristic
116C22×#100—112no—
117C2×#407—112no—
118C2×#343—112no—
119C23×C11—22no—
120C23×C11—22no—
121C23×C11—24no—
122C23×C11—24no—
123C23×C11—22no—
124C23×C11—24no—
125C23×C11—22no—
126C23×C11—24no—
127C23×C11—24no—
128C23×C11—28no—
129C23×C11—416no—
130C23×C11—42no—
131C23×C11—42no—
132C23×C11—44no—
133C23×C11—44no—
134C23×C11—44no—
135C23×C11—44no—
136C23×C11—42no—
137C23×C11—42no—
138C23×C11—44no—
139C23×C11—44no—
140C23×C11—44no—
141C23×C11—44no—
142C23×C11—816no—
143C23×C11#10014yescomplemented
144C23×C11C2×C22⋊C411yescharacteristic
145C23×C11C2×C22⋊C411yescharacteristic
146C23×C11C2×C22⋊C411yescharacteristic
147C23×C11C4×D414yes—
148D4×C11—432no—
149D4×C11—48no—
150D4×C11—48no—
151C2×C4×C11—22no—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—44no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—44no—
158C2×C4×C11—48no—
159C2×C4×C11—48no—
160C2×C4×C11—44no—
161C2×C4×C11#12012yes—
162C2×C4×C11#12012yes—
163C2×C4×C11#12014yes—
164C2×C4×C11#12114yes—
165C2×C4×C11#12114yes—
166C2×C4×C11#12114yes—
167C2×C4×C11#12312yes—
168C2×C4×C11#12312yes—
169C2×C4×C11#12412yes—
170C2×C4×C11#12712yes—
171C11⋊C8—48no—
172C23×D4Dic1112yes—
173C23×D4C2×D1111yescharacteristic
174C24×C4C2×D1111yescharacteristic
175C22×M16—114no—
176C2×#121—24no—
177C2×#121—24no—
178C2×#121—24no—
179C22×C4⋊C4C2×D1111yescharacteristic
180C22×C22⋊C4Dic1112yes—
181C2×#100—228no—
182C2×#100—224no—
183#407—228no—
184C2×C22⋊C8—224no—
185#343—224no—
186C22×C11—28no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—28no—
192C22×C11—24no—
193C22×C11—48no—
194C22×C11—48no—
195C22×C11—44no—
196C22×C11—42no—
197C22×C11—42no—
198C22×C11—44no—
199C22×C11—44no—
200C22×C11—44no—
201C22×C11—88no—
202C22×C11—88no—
203C22×C11—88no—
204C22×C11#37911yescharacteristic
205C22×C11#38612yes—
206C22×C11#38612yes—
207C22×C11#39012yes—
208C22×C11C2×#10012yes—
209C22×C11#41312yes—
210C4×C11—42no—
211C4×C11—44no—
212C4×C11#39214yes—
213C4×C11#39414yes—
214C25C2×Dic1111yescharacteristic
215C25C2×Dic1112yes—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—48no—
224C22×D4C22⋊D1114yes—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4C2×Dic1111yescharacteristic
230C23×C4C2×Dic1112yes—
231C23×C4C22⋊D1114yes—
232C23×C4C22×D1111yescharacteristic
233C2×M16—118no—
234C2×M16—224no—
235C2×M16—224no—
236C2×M16—224no—
237C2×M16—224no—
238C2×M16—224no—
239C22×C8—224no—
240#121—232no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4C22⋊D1114yes—
244C2×C22⋊C4—24no—
245C2×C22⋊C4—24no—
246C2×C22⋊C4—24no—
247#100—2216no—
248C22⋊C8—2216no—
249C2×C11—22no—
250C2×C11—22no—
251C2×C11—44no—
252C2×C11—84no—
253C2×C11#143811yescharacteristic
254C2×C11#178311yescharacteristic
255C2×C11#178511yescharacteristic
256C2×C11#190014yes—
257C24—24no—
258C24—21no—
259C24—21no—
260C24—24no—
261C24—22no—
262C24—22no—
263C24—28no—
264C24—42no—
265C24—44no—
266C24—44no—
267C24C22⋊Dic1112yes—
268C24C22⋊Dic1114yes—
269C24C22×Dic1111yescharacteristic
270C2×D4—216no—
271C2×D4—24no—
272C2×D4—24no—
273C2×D4—28no—
274C2×D4—28no—
275C2×D4—416no—
276C2×D4—48no—
277C2×D4—416no—
278C2×D4—48no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4—42no—
282C2×D4—44no—
283C2×D4—44no—
284C2×D4—42no—
285C22×C4—24no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—28no—
293C22×C4—28no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—44no—
298C22×C4—44no—
299C22×C4—42no—
300C22×C4—44no—
301C22×C4C22⋊Dic1112yes—
302C22×C4C22⋊Dic1114yes—
303C22×C4D4×D1114yes—
304C22×C4#434114yes—
305C22×C4C2×C22⋊D1112yes—
306C22×C4C2×C22⋊D1112yes—
307C22×C4C2×C22⋊D1112yes—
308M16—228no—
309M16—228no—
310M16—444no—
311M16—444no—
312C2×C8—228no—
313C2×C8—444no—
314C2×C8—444no—
315C4⋊C4—28no—
316C22⋊C4—216no—
317C11#1096711yescharacteristic, complemented, Sylow
318C23—22no—
319C23—22no—
320C23—24no—
321C23—24no—
322C23—22no—
323C23—24no—
324C23—24no—
325C23—22no—
326C23—24no—
327C23—28no—
328C23—416no—
329C23—42no—
330C23—42no—
331C23—44no—
332C23—44no—
333C23—44no—
334C23—44no—
335C23—42no—
336C23—42no—
337C23—44no—
338C23—44no—
339C23—44no—
340C23—44no—
341C23—816no—
342C23#6689714yescomplemented
343C23D4×Dic1114yes—
344C23C2×C22⋊Dic1111yescharacteristic
345C23C2×C22⋊Dic1111yescharacteristic
346C23C2×C22⋊Dic1111yescharacteristic
347D4—432no—
348D4—48no—
349D4—48no—
350C2×C4—24no—
351C2×C4—22no—
352C2×C4—24no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—48no—
358C2×C4—48no—
359C2×C4—44no—
360C2×C4#6698812yes—
361C2×C4#6698812yes—
362C2×C4#6698912yes—
363C2×C4#6699012yes—
364C2×C4#6699012yes—
365C2×C4#6699114yes—
366C2×C4#6699214yes—
367C2×C4#6699214yes—
368C2×C4#6699312yes—
369C2×C4#6700614yes—
370C8—448no—
371C22—21no—
372C22—21no—
373C22—28no—
374C22—21no—
375C22—21no—
376C22—28no—
377C22—24no—
378C22—48no—
379C22—48no—
380C22—42no—
381C22—44no—
382C22—42no—
383C22—44no—
384C22—44no—
385C22—44no—
386C22—88no—
387C22—88no—
388C22—88no—
389C22C2×#6689712yes—
390C22#1062283312yes—
391C22#1062283312yes—
392C22#1062283412yes—
393C22#1062285012yes—
394C22#1062286011yescharacteristic
395C4—42no—
396C4—44no—
397C4#1062283514yes—
398C4#1062283614yes—
399C2—22no—
400C2—22no—
401C2—44no—
402C2—84no—
403C2#1306685711yescharacteristic
404C2#1306853711yescharacteristic
405C2#1306854411yescharacteristic
406C2#1306908014yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC22×C11×#121C2
socleC23×C11C2×C22⋊C4
cosocleC23×C4×C11C23
hypercenterC22×#121D11
hypocenterC11#10967
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66897C2semidirect
2. C2×#10622820C2semidirect
3. C2×#10622168C2semidirect
50. C2×#4318D4semidirect
143. C23×C11#100semidirect
317. C11#10967semidirect
342. C23#66897semidirect

Maximal subgroups

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

subgroupindex
C22×#668972
C2×#106228202
C2×#106221682
C22×C11×#1212
#1096711