Finite Group Databasebeta

← #14651222

Subgroups — #14651222

Order 2816.

644 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 97 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#13074091C211yesmaximal, characteristic
2#13070971C211yesmaximal, characteristic, complemented
3#13067133C211yesmaximal, characteristic
4#13067131C211yesmaximal, characteristic
5#13066945C211yesmaximal, characteristic, complemented
6#13066502C211yesmaximal, characteristic, complemented
7C11×#1297C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C22×Dic11⋊C4C2211yescharacteristic
10C2×#66930—21no—
11C11×#407C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13C4×C11×C22⋊C4C2211yescharacteristic
14C4×C22⋊Dic11C2211yescharacteristic
15#10622820C2211yescharacteristic
16#10622571—21no—
17#10622571—21no—
18C22⋊C4×Dic11—21no—
19#10622553—22no—
20C4×Dic11⋊C4—22no—
21#10622285C412yescomplemented
22#10622272C412yescomplemented
23#10622262—22no—
24#10622108—22no—
25#10622107—22no—
26#10622089—22no—
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11—21no—
29C23×Dic11D411yescharacteristic
30C23×Dic11D411yescharacteristic
31C22×D44C2×C411yescharacteristic
32C2×C11×M16—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C42×C11—21no—
36C2×C42×C11—21no—
37C2×C22⋊Dic11—21no—
38#66983—21no—
39#66983—21no—
40#66983—21no—
41#66983—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—22no—
44C2×(C2×D11)⋊C4—22no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×Dic11⋊C4—22no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4C2×C412yes—
52C2×Dic11⋊C4D412yes—
53C2×C4×Dic11—22no—
54C2×C4×Dic11—22no—
55C2×C4×Dic11—21no—
56C2×#4318—21no—
57#66930—28no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95C2×C412yes—
61C11×#95D412yes—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C11⋊#95D412yes—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68#9410—111nomaximal, Sylow
69C24×C11C2×D411yescharacteristic
70C23×D11—21no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—81no—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C2×C22⋊D11—44no—
81C2×C22⋊D11—41no—
82C2×C22⋊D11—41no—
83C22×Dic11—24no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—22no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—81no—
91C22×Dic11C22⋊C412yes—
92C22×Dic11C22⋊C412yes—
93C2×D44—21no—
94C2×D44—21no—
95C2×D44—81no—
96C11×M16—81no—
97C2×C8×C11—41no—
98C11×C22⋊C4—24no—
99C11×C22⋊C4—42no—
100C42×C11—81no—
101C42×C11—81no—
102C22⋊Dic11—24no—
103(C2×D11)⋊C4—44no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—82no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109Dic11⋊C4—28no—
110Dic11⋊C4—22no—
111Dic11⋊C4—22no—
112Dic11⋊C4—22no—
113Dic11⋊C4—22no—
114C4×Dic11—28no—
115C4×Dic11—81no—
116C4×Dic11—82no—
117#4318—81no—
118C2×C11⋊C8—41no—
119#2591—111no—
120#2274—111no—
121#1507—111no—
122#1507—111no—
123#1463—111no—
124#1297—111no—
125#1297D1111yescharacteristic, complemented
126C23×C11—22no—
127C23×C11—22no—
128C23×C11—41no—
129C23×C11C2×C22⋊C411yescharacteristic
130C23×C11#12011yescharacteristic
131C23×C11#12311yescharacteristic
132C22×D11—42no—
133C22×D11—42no—
134C22×D11—41no—
135C22×D11—42no—
136C2×C4×C11—24no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C22⋊D11—82no—
153C22⋊D11—82no—
154C2×Dic11—22no—
155C2×Dic11—22no—
156C2×Dic11—24no—
157C2×Dic11—22no—
158C2×Dic11—22no—
159C2×Dic11—24no—
160C2×Dic11—22no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—41no—
167C2×Dic11—81no—
168C2×Dic11#10414yes—
169D44—81no—
170D44—81no—
171C8×C11—81no—
172C11⋊C8—81no—
173C2×#121—111no—
174C2×#117—221no—
175C22×C4⋊C4—111no—
176#407—111no—
177#407C2×D1111yescharacteristic
178#400—112no—
179#394—112no—
180#388—222no—
181#386—221no—
182#386—221no—
183C4×C4⋊C4—222no—
184C4×C4⋊C4—222no—
185C4×C22⋊C4—111no—
186C4×C22⋊C4—221no—
187C4×C22⋊C4C2×D1111yescharacteristic
188C4×C22⋊C4C2×D1111yescharacteristic
189#327—222no—
190#327—222no—
191#324—222no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—44no—
200C22×C11#38611yescharacteristic
201C22×C11C2×#10412yes—
202C22×C11#45412yes—
203C2×D11—84no—
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—44no—
212C4×C11—82no—
213Dic11—24no—
214Dic11—44no—
215Dic11—42no—
216Dic11—81no—
217C22×D4—111no—
218C22×D4—221no—
219C23×C4—111no—
220C23×C4—111no—
221C23×C4C22×D1111yescharacteristic
222C2×M16—21no—
223C2×M16—221no—
224#121—221no—
225#121—221no—
226#121—221no—
227#121—221no—
228#117—228no—
229C2×C4⋊C4—112no—
230C2×C4⋊C4—112no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—222no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—221no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—222no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—222no—
243C2×C42—21no—
244C2×C42—21no—
245C2×C42—222no—
246C2×C42—222no—
247C2×C42—221no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8—221no—
251C22⋊C8—221no—
252#95—112no—
253#95—222no—
254#95—222no—
255#95—222no—
256#95C4×D1112yes—
257#95D4412yes—
258C2×C11—22no—
259C2×C11—22no—
260C2×C11—41no—
261C2×C11#188811yescharacteristic
262C2×C11#189611yescharacteristic
263C2×C11#191311yescharacteristic
264D11—161no—
265C24—221no—
266C24D4×D1111yescharacteristic
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—444no—
270C2×D4—441no—
271C2×D4—441no—
272C2×D4—881no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—81no—
276C22×C4—112no—
277C22×C4—112no—
278C22×C4—224no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—222no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—881no—
286C22×C4C2×C4×D1111yescharacteristic
287C22×C4C2×D4411yescharacteristic
288C22×C4#433911yescharacteristic
289C22×C4D4×D1111yescharacteristic
290C22×C4D4×D1111yescharacteristic
291C22×C4#434311yescharacteristic
292M16—81no—
293M16—881no—
294C2×C8—41no—
295C2×C8—441no—
296C4⋊C4—228no—
297C4⋊C4—222no—
298C4⋊C4—222no—
299C4⋊C4—222no—
300C4⋊C4—222no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C22⋊C4—24no—
304C22⋊C4—42no—
305C22⋊C4—224no—
306C22⋊C4—444no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C22⋊C4—882no—
310C42—81no—
311C42—81no—
312C42—228no—
313C42—881no—
314C42—882no—
315C11#941011yescharacteristic, complemented, Sylow
316C23—22no—
317C23—22no—
318C23—41no—
319C23—442no—
320C23—442no—
321C23—441no—
322C23—442no—
323C23C22⋊C4×D1111yescharacteristic
324C23#6693511yescharacteristic
325C23#6694711yescharacteristic
326D4—881no—
327D4—881no—
328D4—882no—
329D4—882no—
330C2×C4—24no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—114no—
343C2×C4—222no—
344C2×C4—222no—
345C2×C4—224no—
346C2×C4—222no—
347C2×C4—222no—
348C2×C4—224no—
349C2×C4—222no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4—442no—
355C2×C4—441no—
356C2×C4—881no—
357C2×C4C4×D4411yescharacteristic
358C2×C4#6693711yescharacteristic
359C2×C4#6694611yescharacteristic
360C2×C4#6694811yescharacteristic
361C8—81no—
362C8—881no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—44no—
371C22—884no—
372C22—881no—
373C22—881no—
374C22—881no—
375C22#1062227811yescharacteristic
376C22D11×#10412yes—
377C22#1062244012yes—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—44no—
383C4—82no—
384C4—224no—
385C4—444no—
386C4—442no—
387C4—881no—
388C2—22no—
389C2—22no—
390C2—41no—
391C2—1761no—
392C2#1306901811yescharacteristic
393C2#1306905811yescharacteristic
394C2#1306915711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1297C2
socleC22×C11#386
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1297D11
hypocenterC11#9410
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
2. #13070971C2semidirect
5. #13066945C2semidirect
6. #13066502C2semidirect
7. C11×#1297C2semidirect
21. #10622285C4semidirect
22. #10622272C4semidirect
125. #1297D11semidirect
315. C11#9410semidirect

Maximal subgroups

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

subgroupindex
#130740912
#130709712
#130671332
#130671312
#130669452
#130665022
C11×#12972
#941011