Finite Group Databasebeta

← #14649524

Subgroups — #14649524

Order 2816.

1088 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
2#13068526C211yesmaximal, characteristic, complemented
3C2×#10622175C212yesmaximal, complemented
4#13066494C212yesmaximal, complemented
5C11×#2847C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C2×C11×#121C412yescomplemented
8C2×C11×#121C2211yescharacteristic
9C2×C11×#120—21no—
10C22×C22⋊Dic11—21no—
11C22×C4×Dic11—21no—
12C11×#386—21no—
13C11×#386—22no—
14C11×#380C412yescomplemented
15C11×#380C2211yescharacteristic
16C4×C22⋊Dic11—24no—
17C2×C11⋊#95C2212yes—
18C2×C22⋊(C11⋊C8)—22no—
19C2×C22⋊(C11⋊C8)C2212yes—
20#10622175—24no—
21C25×C11D411yescharacteristic
22C22×D4×C11—22no—
23C22×D4×C11—21no—
24C22×D4×C11C2×C411yescharacteristic
25C23×C4×C11—22no—
26C23×C4×C11—22no—
27C23×C4×C11—44no—
28C23×C4×C11C2×C412yes—
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D412yes—
31C23×C4×C11C2311yescharacteristic
32C23×Dic11—22no—
33C11×#121—22no—
34C11×#121—22no—
35C11×#121—44no—
36C11×#120—44no—
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C4⋊C4C2×C412yes—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—21no—
43C2×C22⋊Dic11—24no—
44C2×C22⋊Dic11—28no—
45C2×C4×Dic11—24no—
46C2×C4×Dic11—44no—
47C22×C11⋊C8—22no—
48C11×#95—22no—
49C11×#95—21no—
50C11⋊#95—22no—
51C11⋊#95D414yescomplemented
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—21no—
62C24×C11—42no—
63C24×C11C22⋊C412yes—
64C24×C11C2×D411yescharacteristic
65C2×D4×C11—22no—
66C2×D4×C11—42no—
67C2×D4×C11—44no—
68C2×D4×C11—44no—
69C2×D4×C11—44no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—42no—
73C2×D4×C11—42no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—24no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—42no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11—48no—
87C22×C4×C11—48no—
88C22×C4×C11C22⋊C412yes—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D412yes—
92C22×C4×C11#4112yes—
93C22×Dic11—28no—
94C22×Dic11—24no—
95C22×Dic11—44no—
96C22×Dic11—42no—
97C22×Dic11—42no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—42no—
100C11×C22⋊C4—44no—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—44no—
103C11×C22⋊C4—42no—
104C22⋊Dic11—216no—
105C4×Dic11—48no—
106C2×C11⋊C8—44no—
107C2×C11⋊C8—42no—
108#2847D1111yescharacteristic
109C2×C4×C22⋊C4—111no—
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—41no—
130C23×C11—42no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—42no—
134C23×C11#10414yes—
135C23×C11C2×C22⋊C411yescharacteristic
136C23×C11#12011yescharacteristic
137C23×C11#12311yescharacteristic
138C23×C11#13512yes—
139C23×C11AGL(1,ℤ/8)12yes—
140D4×C11—82no—
141D4×C11—88no—
142D4×C11—82no—
143D4×C11—82no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—48no—
153C2×C4×C11—48no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11#9914yes—
161C2×C4×C11C4×D412yes—
162C2×C4×C11#12112yes—
163C2×Dic11—28no—
164C2×Dic11—44no—
165C2×Dic11—48no—
166C2×Dic11—48no—
167C2×Dic11—44no—
168C11⋊C8—82no—
169C24×C4C2×D1111yescharacteristic
170C2×#121Dic1112yescomplemented
171C2×#121C2×D1111yescharacteristic
172C2×#120—21no—
173C22×C22⋊C4—221no—
174C22×C42—221no—
175C2×C22⋊C8—112no—
176C2×C22⋊C8—222no—
177#386—21no—
178#386—22no—
179#380Dic1112yescomplemented
180#380C2×D1111yescharacteristic
181C4×C22⋊C4—224no—
182C2×#95—112no—
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—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—82no—
203C22×C11—82no—
204C22×C11#38611yescharacteristic
205C22×C11C2×#9912yes—
206C22×C11#41611yescharacteristic
207C22×C11#41811yescharacteristic
208C22×C11C2×#10412yes—
209C22×C11#44912yes—
210C22×C11#48212yes—
211C4×C11—24no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—81no—
215C4×C11—82no—
216Dic11—48no—
217C25C22⋊D1111yescharacteristic
218C22×D4—22no—
219C22×D4—21no—
220C22×D4C2×Dic1111yescharacteristic
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—44no—
224C23×C4—222no—
225C23×C4C2×Dic1112yes—
226C23×C4C22⋊D1111yescharacteristic
227C23×C4C22⋊D1112yes—
228C23×C4C22×D1111yescharacteristic
229C22×C8—222no—
230#121—22no—
231#121—22no—
232#121—44no—
233#120—44no—
234C2×C4⋊C4C2×Dic1111yescharacteristic
235C2×C4⋊C4C2×Dic1112yes—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—224no—
241C2×C22⋊C4—228no—
242C2×C42—224no—
243C2×C42—444no—
244C22⋊C8—222no—
245C22⋊C8—222no—
246C22⋊C8—444no—
247#95—22no—
248#95—21no—
249#95—114no—
250#95—222no—
251C2×C11—22no—
252C2×C11—22no—
253C2×C11—44no—
254C2×C11—161no—
255C2×C11#150112yes—
256C2×C11#150712yes—
257C2×C11#187511yescharacteristic
258C2×C11#189611yescharacteristic
259C2×C11#189811yescharacteristic
260C24—24no—
261C24—21no—
262C24—21no—
263C24—22no—
264C24—22no—
265C24—21no—
266C24—42no—
267C24C22⋊Dic1112yes—
268C24C2×C22⋊D1111yescharacteristic
269C2×D4—22no—
270C2×D4—42no—
271C2×D4—44no—
272C2×D4—44no—
273C2×D4—44no—
274C2×D4—42no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—42no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—48no—
291C22×C4—48no—
292C22×C4—228no—
293C22×C4—224no—
294C22×C4—444no—
295C22×C4—442no—
296C22×C4—442no—
297C22×C4C22⋊Dic1112yes—
298C22×C4D4×D1112yes—
299C22×C4#434112yes—
300C22×C4C22×Dic1111yescharacteristic
301C22×C4C2×C22⋊D1111yescharacteristic
302C2×C8—444no—
303C2×C8—442no—
304C4⋊C4—22no—
305C4⋊C4—42no—
306C22⋊C4—44no—
307C22⋊C4—42no—
308C22⋊C4—44no—
309C22⋊C4—42no—
310C22⋊C4—2216no—
311C42—448no—
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—41no—
330C23—42no—
331C23—41no—
332C23—41no—
333C23—42no—
334C23#6690114yes—
335C23#6698512yes—
336C23#6698811yescharacteristic
337C23#6699011yescharacteristic
338C23#6700312yes—
339C23C2×C22⋊Dic1111yescharacteristic
340D4—82no—
341D4—88no—
342D4—82no—
343D4—82no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—48no—
353C2×C4—48no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—228no—
361C2×C4—444no—
362C2×C4—448no—
363C2×C4—448no—
364C2×C4—444no—
365C2×C4#6689814yes—
366C2×C4D4×Dic1112yes—
367C2×C4#6699212yes—
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—81no—
385C22—81no—
386C22—82no—
387C22—82no—
388C22—81no—
389C22#1062264812yes—
390C22#1062265012yes—
391C22#1062282811yescharacteristic
392C22C2×#6689812yes—
393C22#1062283311yescharacteristic
394C22#1062284611yescharacteristic
395C22C2×#6690112yes—
396C4—22no—
397C4—24no—
398C4—22no—
399C4—82no—
400C4—81no—
401C4—448no—
402C2—22no—
403C2—22no—
404C2—44no—
405C2—161no—
406C2#1306710712yes—
407C2#1306713212yes—
408C2#1306893911yescharacteristic
409C2#1306906011yescharacteristic
410C2#1306907011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC11×#2847C2
socleC23×C11C2×C22⋊C4
cosocleC23×C4×C11C23
hypercenter#2847D11
hypocenterC11#9150
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊Dic11C2semidirect
2. #13068526C2semidirect
3. C2×#10622175C2semidirect
4. #13066494C2semidirect
7. C2×C11×#121C4semidirect
14. C11×#380C4semidirect
51. C11⋊#95D4semidirect
170. C2×#121Dic11semidirect
179. #380Dic11semidirect
312. C11#9150semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Dic112
#130685262
C2×#106221752
#130664942
C11×#28472
#915011