Finite Group Databasebeta

← #14649523

Subgroups — #14649523

Order 2816.

1088 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076898C211yesmaximal, characteristic
2#13068526C211yesmaximal, characteristic, complemented
3C2×#10622089C212yesmaximal, complemented
4#13066495C212yesmaximal, complemented
5C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
6C24×C4×C11C2211yescharacteristic
7C22×C11×C22⋊C4—21no—
8C22×C42×C11—21no—
9C2×#67006—21no—
10C2×#66983C412yescomplemented
11C2×#66983C2211yescharacteristic
12C4×C11×C22⋊C4—24no—
13C2×C11×#95C2212yes—
14#10622826—21no—
15#10622826—22no—
16#10622825C412yescomplemented
17#10622825C2211yescharacteristic
18C2×C22⋊(C11⋊C8)—22no—
19C2×C22⋊(C11⋊C8)C2212yes—
20#10622089—24no—
21C25×C11D411yescharacteristic
22C23×C4×C11—22no—
23C23×C4×C11—22no—
24C23×C4×C11—22no—
25C23×C4×C11—44no—
26C23×C4×C11C2×C412yes—
27C23×C4×C11D412yes—
28C23×C4×C11D411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C22×C22⋊D11—22no—
31C22×C22⋊D11—21no—
32C22×D44C2×C411yescharacteristic
33C2×C11×C22⋊C4—28no—
34C2×C11×C22⋊C4—24no—
35C2×C42×C11—24no—
36C2×C42×C11—44no—
37#67006—44no—
38C2×C22⋊Dic11—22no—
39C2×C22⋊Dic11—21no—
40#66983—22no—
41#66983—22no—
42#66983—44no—
43C2×(C2×D11)⋊C4—22no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×C4⋊Dic11C2×C412yes—
47C22×C11⋊C8—22no—
48C11×#95—22no—
49C11×#95D414yescomplemented
50C11⋊#95—22no—
51C11⋊#95—21no—
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—22no—
54C22⋊(C11⋊C8)—44no—
55#9150—111nomaximal, Sylow
56C24×C11—24no—
57C24×C11—21no—
58C24×C11—21no—
59C24×C11—22no—
60C24×C11—22no—
61C24×C11—42no—
62C24×C11C22⋊C412yes—
63C24×C11C2×D411yescharacteristic
64C23×D11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—24no—
68C22×C4×C11—28no—
69C22×C4×C11—24no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—24no—
73C22×C4×C11—24no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—48no—
78C22×C4×C11—48no—
79C22×C4×C11—44no—
80C22×C4×C11—42no—
81C22×C4×C11—42no—
82C22×C4×C11C22⋊C412yes—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D412yes—
86C22×C4×C11#4112yes—
87C2×C22⋊D11—44no—
88C2×C22⋊D11—44no—
89C2×C22⋊D11—44no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11—41no—
92C2×C22⋊D11—42no—
93C2×C22⋊D11—42no—
94C22×Dic11—21no—
95C22×Dic11—22no—
96C2×D44—22no—
97C2×D44—42no—
98C11×C22⋊C4—216no—
99C42×C11—48no—
100C22⋊Dic11—44no—
101C22⋊Dic11—42no—
102(C2×D11)⋊C4—44no—
103(C2×D11)⋊C4—42no—
104C4⋊Dic11—22no—
105C4⋊Dic11—42no—
106C2×C11⋊C8—44no—
107C2×C11⋊C8—42no—
108#2847—111no—
109C2×C4×C22⋊C4D1111yescharacteristic, complemented
110#1779—111no—
111C2×#327—112no—
112#1294—112no—
113C23×C11—22no—
114C23×C11—22no—
115C23×C11—24no—
116C23×C11—24no—
117C23×C11—22no—
118C23×C11—22no—
119C23×C11—22no—
120C23×C11—22no—
121C23×C11—22no—
122C23×C11—22no—
123C23×C11—48no—
124C23×C11—48no—
125C23×C11—42no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11#10414yes—
130C23×C11C2×C22⋊C411yescharacteristic
131C23×C11#12011yescharacteristic
132C23×C11#12311yescharacteristic
133C23×C11#13512yes—
134C23×C11AGL(1,ℤ/8)12yes—
135C22×D11—41no—
136C22×D11—42no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—42no—
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—28no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—48no—
150C2×C4×C11—48no—
151C2×C4×C11—44no—
152C2×C4×C11—48no—
153C2×C4×C11—48no—
154C2×C4×C11—44no—
155C2×C4×C11#9914yes—
156C2×C4×C11C4×D412yes—
157C2×C4×C11#12112yes—
158C22⋊D11—88no—
159C22⋊D11—82no—
160C22⋊D11—82no—
161C2×Dic11—41no—
162C2×Dic11—42no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167D44—82no—
168C11⋊C8—82no—
169C24×C4C2×D1111yescharacteristic
170C2×#121—111no—
171C2×#121—112no—
172C2×#120—221no—
173C22×C22⋊C4—21no—
174C22×C42—21no—
175C2×C22⋊C8—112no—
176C2×C22⋊C8—222no—
177#386—222no—
178#386—221no—
179#380—111no—
180#380—112no—
181C4×C22⋊C4—24no—
182C2×#95C2×D1112yes—
183#327—224no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—24no—
189C22×C11—24no—
190C22×C11—24no—
191C22×C11—24no—
192C22×C11—24no—
193C22×C11—48no—
194C22×C11—48no—
195C22×C11—42no—
196C22×C11—42no—
197C22×C11—42no—
198C22×C11—42no—
199C22×C11#38611yescharacteristic
200C22×C11C2×#9912yes—
201C22×C11#41611yescharacteristic
202C22×C11#41811yescharacteristic
203C22×C11C2×#10412yes—
204C22×C11#44912yes—
205C22×C11#48212yes—
206C2×D11—81no—
207C2×D11—81no—
208C2×D11—81no—
209C2×D11—82no—
210C2×D11—82no—
211C4×C11—24no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—48no—
215Dic11—81no—
216Dic11—82no—
217C25C22⋊D1111yescharacteristic
218C22×D4—111no—
219C22×D4—222no—
220C22×D4—221no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—44no—
225C23×C4C4×D1112yes—
226C23×C4D4412yes—
227C23×C4C22⋊D1111yescharacteristic
228C23×C4C22×D1111yescharacteristic
229C22×C8—222no—
230#121—222no—
231#121—222no—
232#121—444no—
233#120—444no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4—112no—
236C2×C22⋊C4—24no—
237C2×C22⋊C4—28no—
238C2×C22⋊C4—222no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—222no—
241C2×C22⋊C4—221no—
242C2×C42—24no—
243C2×C42—44no—
244C22⋊C8—222no—
245C22⋊C8—222no—
246C22⋊C8—444no—
247#95—22no—
248#95—222no—
249#95—221no—
250#95C22⋊D1114yescomplemented
251C2×C11—22no—
252C2×C11—22no—
253C2×C11—44no—
254C2×C11#150112yes—
255C2×C11#150712yes—
256C2×C11#187511yescharacteristic
257C2×C11#189611yescharacteristic
258C2×C11#189811yescharacteristic
259D11—161no—
260C24—24no—
261C24—21no—
262C24—21no—
263C24—22no—
264C24—22no—
265C24—42no—
266C24—221no—
267C24(C2×D11)⋊C412yes—
268C24C2×C22⋊D1111yescharacteristic
269C2×D4—222no—
270C2×D4—442no—
271C2×D4—444no—
272C2×D4—444no—
273C2×D4—444no—
274C2×D4—441no—
275C2×D4—442no—
276C2×D4—442no—
277C2×D4—441no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—24no—
281C22×C4—28no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—48no—
291C22×C4—48no—
292C22×C4—44no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—222no—
296C22×C4—221no—
297C22×C4(C2×D11)⋊C412yes—
298C22×C4C2×C4×D1111yescharacteristic
299C22×C4C2×D4411yescharacteristic
300C22×C4#433912yes—
301C22×C4C2×C22⋊D1112yes—
302C2×C8—444no—
303C2×C8—442no—
304C4⋊C4—222no—
305C4⋊C4—442no—
306C22⋊C4—216no—
307C22⋊C4—444no—
308C22⋊C4—442no—
309C22⋊C4—444no—
310C22⋊C4—442no—
311C42—48no—
312C11#915011yescharacteristic, complemented, Sylow
313C23—22no—
314C23—22no—
315C23—24no—
316C23—24no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—48no—
324C23—48no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23—42no—
329C23—442no—
330C23—442no—
331C23—441no—
332C23—441no—
333C23—441no—
334C23#6686914yes—
335C23C2×(C2×D11)⋊C411yescharacteristic
336C23#6698211yescharacteristic
337C23#6700212yes—
338C23#6700312yes—
339C23#6700611yescharacteristic
340D4—882no—
341D4—888no—
342D4—882no—
343D4—882no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—28no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—48no—
354C2×C4—48no—
355C2×C4—44no—
356C2×C4—48no—
357C2×C4—48no—
358C2×C4—44no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—441no—
362C2×C4—442no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4#6687014yes—
366C2×C4C4×C22⋊D1112yes—
367C2×C4#6698312yes—
368C8—882no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—24no—
374C22—24no—
375C22—24no—
376C22—24no—
377C22—24no—
378C22—48no—
379C22—48no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—881no—
385C22—881no—
386C22—882no—
387C22—882no—
388C22—881no—
389C22C2×#6686912yes—
390C22C2×#6687012yes—
391C22#1062261411yescharacteristic
392C22#1062261511yescharacteristic
393C22#1062261612yes—
394C22#1062282611yescharacteristic
395C22#1062285112yes—
396C4—22no—
397C4—24no—
398C4—22no—
399C4—48no—
400C4—882no—
401C4—881no—
402C2—22no—
403C2—22no—
404C2—44no—
405C2—1761no—
406C2#1306710512yes—
407C2#1306713112yes—
408C2#1306893811yescharacteristic
409C2#1306905911yescharacteristic
410C2#1306906911yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C4×C11×C22⋊C4C2
socleC23×C11C2×C22⋊C4
prime radical#13076898C2
cosocleC23×C4×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#9150
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13068526C2semidirect
3. C2×#10622089C2semidirect
4. #13066495C2semidirect
5. C2×C4×C11×C22⋊C4C2semidirect
10. C2×#66983C4semidirect
16. #10622825C4semidirect
49. C11×#95D4semidirect
109. C2×C4×C22⋊C4D11semidirect
250. #95C22⋊D11semidirect
312. C11#9150semidirect

Maximal subgroups

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

subgroupindex
#130768982
#130685262
C2×#106220892
#130664952
C2×C4×C11×C22⋊C42
#915011