Finite Group Databasebeta

← #14649751

Subgroups — #14649751

Order 2816.

580 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 103 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#13074500C211yesmaximal, characteristic
2C4×#66898C211yesmaximal, characteristic, complemented
3#13067133C212yesmaximal, complemented
4#13066470C212yesmaximal, complemented
5C11×#2975C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C11×#436—24no—
9C11×#431—21no—
10C11×#407—21no—
11C11×#407C2212yes—
12#10622836—21no—
13C2×#66898—21no—
14#10622826—21no—
15#10622824C2211yescharacteristic
16C4×C22⋊Dic11C2212yes—
17#10622604C411yescharacteristic, complemented
18#10622599C411yescharacteristic, complemented
19#10622573C411yescharacteristic, complemented
20#10622572—21no—
21#10622562C411yescharacteristic, complemented
22#10622553—21no—
23#10622164—21no—
24#10622108—24no—
25C22×D4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11—21no—
29C22×C22⋊D11—21no—
30C22×D44C2×C411yescharacteristic
31C2×C11×M16—22no—
32C2×C11×M16—22no—
33C4×D4×C11—22no—
34C4×D4×C11—22no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C22⋊Dic11—22no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42#66983—22no—
43#66983—22no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×C4⋊Dic11C2×C411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11—22no—
51C11×C4⋊C8—22no—
52C11×C22⋊C8—22no—
53C11×C22⋊C8—22no—
54C11×C22⋊C8D414yescomplemented
55C4×C8×C11—22no—
56#66898—24no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—22no—
61C11⋊#95C2×C411yescharacteristic
62C11⋊#95C2×C411yescharacteristic
63#9186—111nomaximal, Sylow
64C24×C11C22⋊C411yescharacteristic
65C24×C11C2×D411yescharacteristic
66C23×D11—21no—
67C2×D4×C11—22no—
68C2×D4×C11—22no—
69C2×D4×C11—41no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—81no—
73C22×C4×C11—81no—
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D412yes—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4112yes—
81C2×C22⋊D11—42no—
82C2×C22⋊D11—42no—
83C2×C22⋊D11—81no—
84C2×C22⋊D11—81no—
85C2×C22⋊D11—81no—
86C2×C22⋊D11—81no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—42no—
91C2×D44—22no—
92C2×D44—81no—
93C11×M16—82no—
94C11×M16—82no—
95C2×C8×C11—24no—
96C11×C4⋊C4—22no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—22no—
99C42×C11—21no—
100C42×C11—21no—
101C22⋊Dic11—24no—
102C22⋊Dic11—42no—
103C22⋊Dic11—81no—
104C22⋊Dic11—81no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—81no—
109(C2×D11)⋊C4—81no—
110C4⋊Dic11—22no—
111Dic11⋊C4—81no—
112C4×Dic11—82no—
113#2975D1111yescharacteristic, complemented
114#2635—111no—
115C4×#99—111no—
116#1507—112no—
117#1284—112no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11C2×C22⋊C411yescharacteristic
128C23×C11#12112yes—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—41no—
136D4×C11—44no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—81no—
149C2×C4×C11#10412yes—
150C2×C4×C11C4×D412yes—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12311yescharacteristic
153C22⋊D11—84no—
154C22⋊D11—84no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—44no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—82no—
166C2×Dic11—82no—
167D44—82no—
168C8×C11—44no—
169C2×#121—111no—
170C2×C4×D4C2×D1111yescharacteristic
171#436—24no—
172#431—21no—
173C2×#99—221no—
174#407—21no—
175#407C2×D1112yes—
176#400—111no—
177#399—111no—
178#394—111no—
179#394—221no—
180#392—111no—
181#392—221no—
182#388—221no—
183#386—221no—
184#381—111no—
185C4×C22⋊C4—112no—
186#342—221no—
187#327—224no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—22no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—42no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11#38611yescharacteristic
201C22×C11C2×#10411yescharacteristic
202C22×C11#42111yescharacteristic
203C2×D11—81no—
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C2×D11—81no—
209C2×D11—81no—
210C4×C11—22no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—22no—
214C4×C11—41no—
215C4×C11—41no—
216Dic11—81no—
217Dic11—81no—
218Dic11—84no—
219Dic11—81no—
220C22×D4—111no—
221C22×D4—221no—
222C22×D4—221no—
223C22×D4D4411yescharacteristic
224C23×C4C22⋊D1111yescharacteristic
225C23×C4C22×D1111yescharacteristic
226C2×M16—22no—
227C2×M16—22no—
228#121—222no—
229#121—222no—
230C4×D4—22no—
231C4×D4—22no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4C4×D1111yescharacteristic
235C2×C22⋊C4—222no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4C4×D1111yescharacteristic
243C2×C22⋊C4D4411yescharacteristic
244C2×C42—222no—
245C2×C42C22⋊D1111yescharacteristic
246C4⋊C8—22no—
247#99—224no—
248C22⋊C8—22no—
249C22⋊C8—22no—
250C22⋊C8C22⋊D1114yescomplemented
251C4×C8—22no—
252#95—111no—
253#95—111no—
254#95—221no—
255#95—221no—
256#95—221no—
257#95—222no—
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—42no—
261C2×C11—81no—
262C2×C11#187111yescharacteristic
263C2×C11#191011yescharacteristic
264C2×C11#191311yescharacteristic
265D11—161no—
266C24—221no—
267C24(C2×D11)⋊C411yescharacteristic
268C24C2×D4411yescharacteristic
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—41no—
272C2×D4—222no—
273C2×D4—442no—
274C2×D4—442no—
275C2×D4—881no—
276C2×D4—881no—
277C2×D4—881no—
278C2×D4—881no—
279C2×D4—881no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—81no—
283C22×C4—81no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—442no—
288C22×C4(C2×D11)⋊C411yescharacteristic
289C22×C4(C2×D11)⋊C411yescharacteristic
290C22×C4(C2×D11)⋊C411yescharacteristic
291C22×C4C2×C4×D1111yescharacteristic
292C22×C4#433912yes—
293C22×C4C2×C22⋊D1112yes—
294C22×C4C2×C22⋊D1111yescharacteristic
295M16—82no—
296M16—82no—
297C2×C8—24no—
298C4⋊C4—22no—
299C4⋊C4—222no—
300C4⋊C4—881no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—224no—
304C22⋊C4—442no—
305C22⋊C4—442no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C22⋊C4—881no—
309C22⋊C4—881no—
310C22⋊C4—881no—
311C22⋊C4—881no—
312C42—21no—
313C42—21no—
314C42—882no—
315C11#918611yescharacteristic, complemented, Sylow
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—441no—
326C23—441no—
327C23—441no—
328C23—441no—
329C23—441no—
330C23—441no—
331C23—441no—
332C23C2×(C2×D11)⋊C411yescharacteristic
333C23#6698312yes—
334D4—44no—
335D4—882no—
336D4—884no—
337D4—884no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—444no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—882no—
361C2×C4—882no—
362C2×C4#6688912yes—
363C2×C4C4×C22⋊D1112yes—
364C2×C4#6698211yescharacteristic
365C2×C4#6700611yescharacteristic
366C8—44no—
367C22—21no—
368C22—21no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—42no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—881no—
380C22—881no—
381C22—881no—
382C22—881no—
383C22—881no—
384C22—881no—
385C22—881no—
386C22C2×#6688911yescharacteristic
387C22#1062275211yescharacteristic
388C22#1062282611yescharacteristic
389C4—21no—
390C4—21no—
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—881no—
396C4—881no—
397C4—884no—
398C4—881no—
399C2—21no—
400C2—21no—
401C2—42no—
402C2—81no—
403C2—1761no—
404C2#1306891811yescharacteristic
405C2#1306914311yescharacteristic
406C2#1306915811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2975C2
socleC22×C11#386
prime radical#13074500C2
cosocleC23×C4×C11C23
hypercenter#2975D11
hypocenterC11#9186
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2975

Complements

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

NH ≅ G/Ntype
2. C4×#66898C2semidirect
3. #13067133C2semidirect
4. #13066470C2semidirect
5. C11×#2975C2semidirect
17. #10622604C4semidirect
18. #10622599C4semidirect
19. #10622573C4semidirect
21. #10622562C4semidirect
54. C11×C22⋊C8D4semidirect
113. #2975D11semidirect
250. C22⋊C8C22⋊D11semidirect
315. C11#9186semidirect

Maximal subgroups

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

subgroupindex
#130745002
C4×#668982
#130671332
#130664702
C11×#29752
#918611