Finite Group Databasebeta

← #14656749

Subgroups — #14656749

Order 2816.

684 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 113 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#13074730C211yesmaximal, characteristic
2#13068552C212yesmaximal
3#13066886C211yesmaximal, characteristic
4#13066496C212yesmaximal
5C11×#1280C211yesmaximal, characteristic
6C23×Dic22C2211yescharacteristic
7C2×#66977—21no—
8C2×C11×C22⋊C8C2212yes—
9C2×C11×#95C2211yescharacteristic
10#10622825—21no—
11#10622825C2212yes—
12C2×C11⋊#95—21no—
13C2×C11⋊#95—21no—
14C2×C11⋊#95C2211yescharacteristic
15C2×#66880—22no—
16C2×#66880—22no—
17#10622274—22no—
18#10622269—22no—
19C23×C4×C11D411yescharacteristic
20C23×C4×C11D411yescharacteristic
21C23×C4×C11C2311yescharacteristic
22C23×Dic11—21no—
23C23×Dic11—21no—
24C22×Dic22—22no—
25C22×Dic22—22no—
26C22×Dic22—21no—
27C22×Dic22—21no—
28C22×Dic22—42no—
29C22×Dic22—42no—
30C22×Dic22Q812yescomplemented
31C22×C8×C11—22no—
32C2×C22⋊Dic11—22no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11D412yes—
37C2×C4⋊Dic11D412yes—
38#66977—42no—
39#66977—42no—
40C2×Dic11⋊C4—22no—
41C11×C22⋊C8—22no—
42C11×C22⋊C8—22no—
43C11×#95—22no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95—42no—
48C11⋊#95—42no—
49#66880—44no—
50#66880—44no—
51#10341—111nomaximal, Sylow
52C24×C11C2×D411yescharacteristic
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11SD1612yes—
64C22×C4×C11Q1612yes—
65C22×C4×C11C2×D412yes—
66C22×C4×C11C2×Q811yescharacteristic
67C22×C4×C11#4112yes—
68C22×C4×C11#4111yescharacteristic
69C22×Dic11—22no—
70C22×Dic11—22no—
71C22×Dic11—22no—
72C22×Dic11—22no—
73C22×Dic11—22no—
74C22×Dic11—22no—
75C22×Dic11—41no—
76C22×Dic11—41no—
77C22×Dic11—41no—
78C22×Dic11—41no—
79C22×Dic11—41no—
80C22×Dic11—41no—
81C22×Dic11—41no—
82C22×Dic11—41no—
83C22×Dic11—41no—
84C22×Dic11—41no—
85C2×Dic22—24no—
86C2×Dic22—24no—
87C2×Dic22—24no—
88C2×Dic22—42no—
89C2×Dic22—42no—
90C2×Dic22—42no—
91C2×Dic22—44no—
92C2×Dic22—48no—
93C2×Dic22—44no—
94C2×Dic22—42no—
95C2×Dic22—81no—
96C2×Dic22—81no—
97C2×C8×C11—42no—
98C2×C8×C11—42no—
99C2×C8×C11—42no—
100C22⋊Dic11—42no—
101C22⋊Dic11—42no—
102C4⋊Dic11—42no—
103C4⋊Dic11—42no—
104C4⋊Dic11—42no—
105C4⋊Dic11—81no—
106C4⋊Dic11—81no—
107Dic11⋊C4—44no—
108#2659—111no—
109#1787—112no—
110#1446—111no—
111#1294—112no—
112#1280D1111yescharacteristic
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11#12011yescharacteristic
118C23×C11C22⋊Q811yescharacteristic
119C23×C11#12411yescharacteristic
120C23×C11C2×SD1611yescharacteristic
121C23×C11C2×Q1611yescharacteristic
122C23×C11AGL(1,ℤ/8)11yescharacteristic
123C23×C11#13711yescharacteristic
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—41no—
129C2×C4×C11—42no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11C22⋊Q812yes—
140C2×C4×C11#12412yes—
141C2×Dic11—24no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—42no—
157C2×Dic11—81no—
158C2×Dic11—81no—
159C2×Dic11—81no—
160C2×Dic11—81no—
161Dic22—28no—
162Dic22—44no—
163Dic22—44no—
164Dic22—44no—
165Dic22—84no—
166C8×C11—82no—
167C23×Q8—111no—
168C2×C22⋊Q8—221no—
169C2×#103—222no—
170C2×#103—222no—
171C2×C22⋊C8C2×D1112yes—
172#398—222no—
173#395—222no—
174#380—112no—
175#380—221no—
176C2×#95—111no—
177C2×#95—221no—
178C2×#95—221no—
179C2×#95C2×D1111yescharacteristic
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11#39311yescharacteristic
193C22×C11#45011yescharacteristic
194C22×C11#45111yescharacteristic
195C22×C11#45511yescharacteristic
196C22×C11#45611yescharacteristic
197C22×C11B(4,𝔽2)11yescharacteristic
198C22×C11B(4,𝔽2)11yescharacteristic
199C22×C11#47511yescharacteristic
200C22×C11#47711yescharacteristic
201C22×C11#48711yescharacteristic
202C22×C11#48911yescharacteristic
203C4×C11—22no—
204C4×C11—22no—
205C4×C11—42no—
206C4×C11—42no—
207Dic11—44no—
208Dic11—82no—
209Dic11—82no—
210Dic11—82no—
211C22×Q8—112no—
212C22×Q8—221no—
213C22×Q8—221no—
214C22×Q8—222no—
215C22×Q8—222no—
216C22×Q8—442no—
217C22×Q8—442no—
218C23×C4—221no—
219C23×C4—221no—
220C23×C4D4411yescharacteristic
221C23×C4D4411yescharacteristic
222C23×C4C22×D1111yescharacteristic
223C22×C8—22no—
224C22⋊Q8—442no—
225C22⋊Q8—442no—
226C2×C4⋊C4—112no—
227C2×C4⋊C4—112no—
228C2×C4⋊C4—222no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C22⋊C4—222no—
233#103—444no—
234#103—444no—
235C22⋊C8—22no—
236C22⋊C8—22no—
237#95—22no—
238#95—222no—
239#95—222no—
240#95—222no—
241#95—442no—
242#95—442no—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11—21no—
246C2×C11—21no—
247C2×C11#160111yescharacteristic
248C2×C11#160211yescharacteristic
249C2×C11#160411yescharacteristic
250C2×C11#160511yescharacteristic
251C2×C11#202411yescharacteristic
252C2×C11#202811yescharacteristic
253C2×C11#202911yescharacteristic
254C24C2×D4411yescharacteristic
255C2×Q8—224no—
256C2×Q8—224no—
257C2×Q8—224no—
258C2×Q8—442no—
259C2×Q8—442no—
260C2×Q8—442no—
261C2×Q8—444no—
262C2×Q8—444no—
263C2×Q8—448no—
264C2×Q8—442no—
265C2×Q8—881no—
266C2×Q8—881no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—222no—
278C22×C4—222no—
279C22×C4—222no—
280C22×C4—222no—
281C22×C4—222no—
282C22×C4—222no—
283C22×C4—441no—
284C22×C4—441no—
285C22×C4—441no—
286C22×C4—441no—
287C22×C4—441no—
288C22×C4—441no—
289C22×C4—441no—
290C22×C4—441no—
291C22×C4—441no—
292C22×C4—441no—
293C22×C4#431412yes—
294C22×C4Dic4412yes—
295C22×C4#433912yes—
296C22×C4D4×D1112yes—
297C22×C4#434111yescharacteristic
298C22×C4Q8×D1111yescharacteristic
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—42no—
302C4⋊C4—442no—
303C4⋊C4—442no—
304C4⋊C4—444no—
305C4⋊C4—442no—
306C4⋊C4—881no—
307C4⋊C4—881no—
308C22⋊C4—442no—
309C22⋊C4—442no—
310C11#1034111yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23#6692811yescharacteristic
316C23#6693511yescharacteristic
317C23#6695011yescharacteristic
318C23C2×#431411yescharacteristic
319C23C2×Dic4411yescharacteristic
320C23#6696111yescharacteristic
321C23#6696211yescharacteristic
322Q8—228no—
323Q8—444no—
324Q8—444no—
325Q8—444no—
326Q8—884no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—224no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—881no—
359C2×C4—881no—
360C2×C4—881no—
361C2×C4—881no—
362C2×C4#6693812yes—
363C2×C4#6694912yes—
364C8—82no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22#1062228611yescharacteristic
378C22#1062229411yescharacteristic
379C22#1062232711yescharacteristic
380C22#1062234411yescharacteristic
381C22#1062235211yescharacteristic
382C22#1062235411yescharacteristic
383C22#1062235411yescharacteristic
384C22#1062235911yescharacteristic
385C22#1062236511yescharacteristic
386C22#1062246311yescharacteristic
387C22#1062246411yescharacteristic
388C4—22no—
389C4—22no—
390C4—42no—
391C4—42no—
392C4—444no—
393C4—882no—
394C4—882no—
395C4—882no—
396C2—21no—
397C2—21no—
398C2—21no—
399C2—21no—
400C2#1306757011yescharacteristic
401C2#1306757511yescharacteristic
402C2#1306758711yescharacteristic
403C2#1306759211yescharacteristic
404C2#1306975811yescharacteristic
405C2#1306977811yescharacteristic
406C2#1306978111yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1280C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1280D11
hypocenterC11#10341
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
30. C22×Dic22Q8semidirect
310. C11#10341semidirect

Maximal subgroups

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

subgroupindex
#130747302
#130685522
#130668862
#130664962
C11×#12802
#1034111