Finite Group Databasebeta

← #14651439

Subgroups — #14651439

Order 2816.

490 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 91 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#13077644C211yesmaximal, characteristic
2#13073817C211yesmaximal, characteristic
3#13067243C211yesmaximal, characteristic, complemented
4#13066956C211yesmaximal, characteristic
5#13066473C211yesmaximal, characteristic, complemented
6#13066471C211yesmaximal, characteristic, complemented
7C11×#1534C211yesmaximal, characteristic, complemented
8C2×C11×#125C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12#10622607—21no—
13#10622607—21no—
14#10622602—21no—
15#10622602—21no—
16#10622601C411yescharacteristic
17#10622601C411yescharacteristic
18#10622590C411yescharacteristic
19#10622589C411yescharacteristic
20C4×C4⋊Dic11C2211yescharacteristic
21#10622539C2211yescharacteristic
22#10622539C2211yescharacteristic
23#10622449—22no—
24#10622339—21no—
25D11×C22⋊C8—21no—
26#10622319—22no—
27C11×#330—22no—
28#10622181—22no—
29#10622106—21no—
30#10622106—21no—
31C22×D44C2×C411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C22×C4×D11D411yescharacteristic
34C11×#125—21no—
35C11×#125—21no—
36C11×#125—21no—
37C11×#125—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C11×C4⋊C4C2×C411yescharacteristic
42C2×C42×C11C2311yescharacteristic
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4D411yescharacteristic
48C2×(C2×D11)⋊C4D411yescharacteristic
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11C2×C411yescharacteristic
51C2×Dic11⋊C4—21no—
52C2×Dic11⋊C4—21no—
53C2×C4×Dic11C2×C411yescharacteristic
54C2×C4×Dic11C2×C411yescharacteristic
55C2×#4313—22no—
56C2×C8×D11—22no—
57C4×D44—21no—
58C4×D44—21no—
59C4×D44—21no—
60C4×D44—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×#97—21no—
66C11×#97D412yes—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72(C2×D11)⋊C8—22no—
73(C2×D11)⋊C8—22no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76#66867—21no—
77#66867D412yes—
78#9449—111nomaximal, Sylow
79C23×D11C22⋊C411yescharacteristic
80C23×D11C22⋊C411yescharacteristic
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11C22⋊C411yescharacteristic
89C22×Dic11C22⋊C411yescharacteristic
90C2×D44—22no—
91C2×D44—21no—
92C2×D44—21no—
93C2×D44—41no—
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×C4×D11—21no—
98C2×C4×D11—81no—
99C2×C4×D11—81no—
100C2×C8×C11—22no—
101C2×C8×C11—41no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113C42×C11#4111yescharacteristic
114(C2×D11)⋊C4—21no—
115(C2×D11)⋊C4—21no—
116(C2×D11)⋊C4—21no—
117(C2×D11)⋊C4—21no—
118(C2×D11)⋊C4—42no—
119(C2×D11)⋊C4—42no—
120(C2×D11)⋊C4—81no—
121(C2×D11)⋊C4—81no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—42no—
125Dic11⋊C4—81no—
126Dic11⋊C4—81no—
127C4×Dic11—41no—
128C4×Dic11—41no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—41no—
131#4313—82no—
132C8×D11—82no—
133#2973—111no—
134#2566—111no—
135#1534—111no—
136#1534D1111yescharacteristic, complemented
137#1466—111no—
138#1285—111no—
139#1285—111no—
140C23×C11C2×C22⋊C411yescharacteristic
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—21no—
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—41no—
147C22×D11—41no—
148C22×D11—41no—
149C22×D11—41no—
150C22×D11#10112yes—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11C4×D411yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12311yescharacteristic
167C2×Dic11—22no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177D44—42no—
178D44—42no—
179C4×D11—42no—
180C4×D11—42no—
181C4×D11—81no—
182C4×D11—81no—
183C8×C11—42no—
184C8×C11—81no—
185C11⋊C8—42no—
186C11⋊C8—81no—
187C2×#125C2×D1111yescharacteristic
188C2×C4×D4—111no—
189#435—222no—
190#435—222no—
191#432—111no—
192#432—111no—
193#432C2×D1111yescharacteristic
194#432C2×D1111yescharacteristic
195#407—221no—
196C2×C22⋊C8—221no—
197#396—221no—
198#396—221no—
199#390—111no—
200#390—111no—
201#385—221no—
202#385—221no—
203#384—111no—
204#382—111no—
205C4×C4⋊C4—111no—
206#330—22no—
207#330—222no—
208#323—221no—
209#323—221no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11#38611yescharacteristic
213C22×C11C2×#10111yescharacteristic
214C22×C11#41311yescharacteristic
215C2×D11—22no—
216C2×D11—41no—
217C2×D11—41no—
218C2×D11—42no—
219C2×D11—42no—
220C2×D11—41no—
221C2×D11—41no—
222C2×D11—41no—
223C2×D11—81no—
224C2×D11—81no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—81no—
232C4×C11—81no—
233Dic11—42no—
234Dic11—41no—
235Dic11—41no—
236Dic11—81no—
237C22×D4—111no—
238C23×C4—111no—
239C23×C4—111no—
240C2×M16—222no—
241C22×C8—222no—
242#125—21no—
243#125—21no—
244#125—21no—
245#125—21no—
246C4×D4—221no—
247C4×D4—221no—
248C4×D4—221no—
249C4×D4—221no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4C4×D1111yescharacteristic
257C2×C4⋊C4C4×D1111yescharacteristic
258C2×C22⋊C4—111no—
259C2×C22⋊C4—111no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—221no—
264C2×C42—111no—
265C2×C42—111no—
266C2×C42C22×D1111yescharacteristic
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—221no—
270C4⋊C8—221no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—222no—
274C22⋊C8—222no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277#97—21no—
278#97—112no—
279#97—221no—
280#97C22⋊D1112yes—
281#95—221no—
282#95—221no—
283#95—221no—
284C2×C11—21no—
285C2×C11—21no—
286C2×C11#188411yescharacteristic
287C2×C11#190111yescharacteristic
288C2×C11#191111yescharacteristic
289D11—42no—
290D11—81no—
291C24—111no—
292C24—111no—
293C2×D4—222no—
294C2×D4—221no—
295C2×D4—221no—
296C2×D4—441no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—111no—
300C22×C4—111no—
301C22×C4—221no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—881no—
308C22×C4—881no—
309C22×C4C2×C4×D1111yescharacteristic
310C22×C4D4×D1111yescharacteristic
311C22×C4D4×D1111yescharacteristic
312M16—882no—
313C2×C8—22no—
314C2×C8—41no—
315C2×C8—222no—
316C2×C8—441no—
317C2×C8—882no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—221no—
327C4⋊C4—221no—
328C4⋊C4—442no—
329C4⋊C4—881no—
330C4⋊C4—881no—
331C22⋊C4—221no—
332C22⋊C4—221no—
333C22⋊C4—221no—
334C22⋊C4—221no—
335C22⋊C4—442no—
336C22⋊C4—442no—
337C22⋊C4—881no—
338C22⋊C4—881no—
339C42—441no—
340C42—441no—
341C42#433911yescharacteristic
342C42D4×D1111yescharacteristic
343C42#434111yescharacteristic
344C42C2×C22⋊D1111yescharacteristic
345C11#944911yescharacteristic, complemented, Sylow
346C23—112no—
347C23—221no—
348C23—221no—
349C23—221no—
350C23—221no—
351C23—221no—
352C23—441no—
353C23—441no—
354C23—441no—
355C23—441no—
356C23C22⋊C4×D1111yescharacteristic
357D4—442no—
358D4—442no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—222no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—442no—
373C2×C4—442no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—881no—
382C2×C4—881no—
383C2×C4(C22⋊D11)⋊C411yescharacteristic
384C2×C4#6693611yescharacteristic
385C2×C4#6693711yescharacteristic
386C2×C4C4×C22⋊D1111yescharacteristic
387C2×C4#6699011yescharacteristic
388C2×C4#6699111yescharacteristic
389C8—42no—
390C8—81no—
391C8—442no—
392C8—881no—
393C22—21no—
394C22—21no—
395C22—222no—
396C22—442no—
397C22—442no—
398C22—441no—
399C22—441no—
400C22—441no—
401C22—441no—
402C22—441no—
403C22—881no—
404C22—881no—
405C22D11×#10111yescharacteristic
406C22#1062236411yescharacteristic
407C22#1062256911yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—81no—
415C4—81no—
416C4—442no—
417C4—441no—
418C4—441no—
419C4—881no—
420C2—21no—
421C2—21no—
422C2—442no—
423C2—881no—
424C2#1306899611yescharacteristic
425C2#1306908111yescharacteristic
426C2#1306914511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1534C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1534D11
hypocenterC11#9449
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1534

Complements

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

NH ≅ G/Ntype
3. #13067243C2semidirect
5. #13066473C2semidirect
6. #13066471C2semidirect
7. C11×#1534C2semidirect
136. #1534D11semidirect
345. C11#9449semidirect

Maximal subgroups

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

subgroupindex
#130776442
#130738172
#130672432
#130669562
#130664732
#130664712
C11×#15342
#944911