Finite Group Databasebeta

← #14651655

Subgroups — #14651655

Order 2816.

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

normal subgroups only

This group has 600 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#13077035C211yesmaximal, characteristic, complemented
2#13074182C211yesmaximal, characteristic
3#13067058C212yesmaximal, complemented
4#13066482C212yesmaximal, complemented
5C11×#1464C211yesmaximal, characteristic, complemented
6C2×C11×#117C2211yescharacteristic
7C22×#4318—21no—
8C2×C4×D44C2211yescharacteristic
9C11×#432C2212yes—
10#10622826—21no—
11#10622610—24no—
12#10622604C411yescharacteristic
13#10622602—21no—
14#10622599C411yescharacteristic
15#10622573C411yescharacteristic
16#10622569—21no—
17#10622562C411yescharacteristic
18#10622553—21no—
19#10622550C2211yescharacteristic
20C4×#4318—21no—
21C4×#4318C2212yes—
22C11×#324—21no—
23C11×#323—21no—
24#10622121—24no—
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×D44C2×C411yescharacteristic
28C22×C4×D11—21no—
29C11×#117—22no—
30C11×#117—22no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×#4318—24no—
45C2×#4318—24no—
46C2×#4318—22no—
47C2×#4318—22no—
48C22×C11⋊C8—22no—
49C4×D44—22no—
50C4×D44—22no—
51C11×C4⋊C8—22no—
52C11×C22⋊C8—22no—
53C11×#97—22no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95C2×C411yescharacteristic
59C11⋊#95C2×C411yescharacteristic
60#66867—22no—
61#66867—22no—
62C4×C11⋊C8—22no—
63C4×C11⋊C8D414yescomplemented
64#9492—111nomaximal, Sylow
65C24×C11C22⋊C411yescharacteristic
66C23×D11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—42no—
78C2×C22⋊D11—42no—
79C2×C22⋊D11—81no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C2×D44—22no—
84C2×D44—42no—
85C2×C4×D11—42no—
86C2×C4×D11—81no—
87C2×C4×D11—81no—
88C2×C8×C11—42no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—22no—
93C42×C11—21no—
94C42×C11—21no—
95C42×C11C2×D412yes—
96C42×C11#4112yes—
97C22⋊Dic11—81no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—81no—
103C4⋊Dic11—22no—
104Dic11⋊C4—81no—
105#4318—28no—
106#4318—24no—
107#4318—24no—
108C2×C11⋊C8—28no—
109C2×C11⋊C8—24no—
110#2873—111no—
111#2598—111no—
112#1490—112no—
113#1464D1111yescharacteristic, complemented
114#1288—112no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11#10412yes—
120C23×C11C2×C22⋊C411yescharacteristic
121C22×D11—22no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—24no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11#10412yes—
142C2×C4×C11C4×D412yes—
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12112yes—
145C2×C4×C11#12311yescharacteristic
146C22⋊D11—84no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156D44—24no—
157D44—42no—
158C4×D11—84no—
159C8×C11—82no—
160C11⋊C8—28no—
161C22×M16—221no—
162C2×C4×D4—111no—
163C2×#117C2×D1111yescharacteristic
164#432C2×D1112yes—
165#405—224no—
166C4×M16—112no—
167C4×M16—221no—
168#400—111no—
169#399—111no—
170#394—111no—
171#392—111no—
172#388—221no—
173#386—221no—
174#386—221no—
175#385—221no—
176#383—111no—
177D4⋊C8—224no—
178#324—21no—
179#323—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—22no—
183C22×C11—42no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—81no—
187C22×C11#38611yescharacteristic
188C22×C11C2×#10411yescharacteristic
189C22×C11C2×#10411yescharacteristic
190C2×D11—42no—
191C2×D11—42no—
192C2×D11—42no—
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C4×C11—22no—
198C4×C11—22no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—22no—
202C4×C11—41no—
203C4×C11—41no—
204Dic11—81no—
205Dic11—81no—
206Dic11—81no—
207C22×D4—111no—
208C22×D4—221no—
209C23×C4—221no—
210C23×C4D4411yescharacteristic
211C2×M16—222no—
212C2×M16—224no—
213C2×M16—224no—
214C2×M16—222no—
215C22×C8—222no—
216C4×D4—222no—
217C4×D4—222no—
218#117—22no—
219#117—22no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4C4×D1111yescharacteristic
223C2×C4⋊C4C22⋊D1111yescharacteristic
224C2×C22⋊C4—221no—
225C2×C22⋊C4—221no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4C4×D1111yescharacteristic
230C2×C22⋊C4C22⋊D1111yescharacteristic
231C2×C42D4411yescharacteristic
232C2×C42C22×D1111yescharacteristic
233C4⋊C8—22no—
234C22⋊C8—22no—
235#97—22no—
236#97—222no—
237#97—222no—
238C4×C8—114no—
239C4×C8—222no—
240#95—111no—
241#95—111no—
242#95—221no—
243#95—221no—
244#95—221no—
245#95—221no—
246C2×C11—21no—
247C2×C11—21no—
248C2×C11—42no—
249C2×C11#189111yescharacteristic
250C2×C11#189611yescharacteristic
251C2×C11#191011yescharacteristic
252D11—82no—
253C24—221no—
254C24(C2×D11)⋊C411yescharacteristic
255C2×D4—222no—
256C2×D4—442no—
257C2×D4—442no—
258C2×D4—442no—
259C2×D4—881no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—442no—
268C22×C4—881no—
269C22×C4—881no—
270C22×C4(C2×D11)⋊C411yescharacteristic
271C22×C4(C2×D11)⋊C411yescharacteristic
272C22×C4(C2×D11)⋊C411yescharacteristic
273C22×C4C2×C4×D1111yescharacteristic
274C22×C4C2×D4411yescharacteristic
275C22×C4C2×C22⋊D1111yescharacteristic
276M16—228no—
277M16—224no—
278M16—224no—
279C2×C8—42no—
280C2×C8—228no—
281C2×C8—224no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—222no—
285C4⋊C4—881no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—442no—
289C22⋊C4—442no—
290C22⋊C4—441no—
291C22⋊C4—441no—
292C22⋊C4—881no—
293C22⋊C4—881no—
294C42—21no—
295C42—21no—
296C42D4×D1112yes—
297C42#434112yes—
298C11#949211yescharacteristic, complemented, Sylow
299C23—21no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23—222no—
304C23—441no—
305C23—441no—
306C23—441no—
307C23—441no—
308C23—441no—
309C23—441no—
310C23#6688912yes—
311C23C2×(C2×D11)⋊C411yescharacteristic
312D4—224no—
313D4—442no—
314D4—884no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—884no—
338C2×C4#6688912yes—
339C2×C4(C22⋊D11)⋊C412yes—
340C2×C4#6693511yescharacteristic
341C2×C4#6693911yescharacteristic
342C2×C4#6699212yes—
343C8—82no—
344C8—228no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—42no—
349C22—41no—
350C22—41no—
351C22—81no—
352C22—442no—
353C22—442no—
354C22—442no—
355C22—881no—
356C22—881no—
357C22—881no—
358C22—881no—
359C22#1062257111yescharacteristic
360C22C2×#6688911yescharacteristic
361C22C2×#6688911yescharacteristic
362C4—21no—
363C4—22no—
364C4—21no—
365C4—22no—
366C4—22no—
367C4—41no—
368C4—41no—
369C4—881no—
370C4—881no—
371C4—881no—
372C2—21no—
373C2—21no—
374C2—42no—
375C2—882no—
376C2#1306903211yescharacteristic
377C2#1306905711yescharacteristic
378C2#1306914111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1464C2
socleC22×C11#386
prime radical#10622573C4
cosocleC2×C42×C11C23
hypercenter#1464D11
hypocenterC11#9492
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
1. #13077035C2semidirect
3. #13067058C2semidirect
4. #13066482C2semidirect
5. C11×#1464C2semidirect
63. C4×C11⋊C8D4semidirect
113. #1464D11semidirect
298. C11#9492semidirect

Maximal subgroups

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

subgroupindex
#130770352
#130741822
#130670582
#130664822
C11×#14642
#949211