Finite Group Databasebeta

← #14651242

Subgroups — #14651242

Order 2816.

552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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#13071216C211yesmaximal, 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
10C11×#407C2211yescharacteristic
11C4×C11×C22⋊C4C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13C4×C22⋊Dic11C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622571—21no—
16#10622571—21no—
17#10622556—21no—
18#10622555—21no—
19#10622553—22no—
20#10622546—22no—
21#10622285C412yescomplemented
22#10622272C412yescomplemented
23#10622265—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—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—22no—
51C2×Dic11⋊C4C2×C412yes—
52C2×Dic11⋊C4D412yes—
53C2×C4×Dic11—21no—
54C2×#4318—21no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×#95C2×C412yes—
58C11×#95D412yes—
59C11⋊#95—22no—
60C11⋊#95—24no—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C11⋊#95D412yes—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66#9414—111nomaximal, Sylow
67C24×C11C2×D411yescharacteristic
68C23×D11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—81no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C2×C22⋊D11—44no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—41no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—22no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—42no—
88C22×Dic11—81no—
89C22×Dic11C22⋊C412yes—
90C22×Dic11C22⋊C412yes—
91C2×D44—21no—
92C2×D44—21no—
93C2×D44—81no—
94C11×M16—81no—
95C2×C8×C11—41no—
96C11×C22⋊C4—42no—
97C11×C22⋊C4—42no—
98C42×C11—81no—
99C42×C11—81no—
100C22⋊Dic11—42no—
101(C2×D11)⋊C4—44no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—82no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107Dic11⋊C4—22no—
108Dic11⋊C4—22no—
109Dic11⋊C4—22no—
110Dic11⋊C4—22no—
111Dic11⋊C4—82no—
112C4×Dic11—81no—
113#4318—81no—
114C2×C11⋊C8—41no—
115#2591—111no—
116#2313—111no—
117#1507—111no—
118#1507—111no—
119#1463—111no—
120#1297—111no—
121#1297D1111yescharacteristic, complemented
122C23×C11—22no—
123C23×C11—22no—
124C23×C11—41no—
125C23×C11C2×C22⋊C411yescharacteristic
126C23×C11#12011yescharacteristic
127C23×C11#12311yescharacteristic
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—41no—
131C22×D11—42no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C22⋊D11—82no—
149C22⋊D11—82no—
150C2×Dic11—22no—
151C2×Dic11—22no—
152C2×Dic11—22no—
153C2×Dic11—22no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—41no—
162C2×Dic11—42no—
163C2×Dic11—81no—
164D44—81no—
165D44—81no—
166C8×C11—81no—
167C11⋊C8—81no—
168C2×#121—111no—
169C22×C4⋊C4—111no—
170#407—111no—
171#407C2×D1111yescharacteristic
172#400—112no—
173#394—112no—
174#388—222no—
175#387—222no—
176#387—222no—
177#386—221no—
178#386—221no—
179#381—221no—
180#380—221no—
181C4×C22⋊C4—111no—
182C4×C22⋊C4C2×D1111yescharacteristic
183C4×C22⋊C4C2×D1111yescharacteristic
184#327—222no—
185#327—222no—
186#324—222no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—44no—
195C22×C11#38611yescharacteristic
196C22×C11#42112yes—
197C22×C11#45412yes—
198C2×D11—84no—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—81no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—82no—
207C4×C11—82no—
208Dic11—42no—
209Dic11—42no—
210Dic11—82no—
211Dic11—81no—
212C22×D4—111no—
213C22×D4—221no—
214C23×C4—111no—
215C23×C4—111no—
216C23×C4C22×D1111yescharacteristic
217C2×M16—21no—
218C2×M16—221no—
219#121—221no—
220#121—221no—
221#121—221no—
222#121—221no—
223C2×C4⋊C4—112no—
224C2×C4⋊C4—112no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—222no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—222no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—222no—
237C2×C42—21no—
238C2×C42—21no—
239C2×C42—221no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—221no—
243C22⋊C8—221no—
244#95—112no—
245#95—222no—
246#95—222no—
247#95—222no—
248#95—224no—
249#95C4×D1112yes—
250#95D4412yes—
251C2×C11—22no—
252C2×C11—22no—
253C2×C11—41no—
254C2×C11#188811yescharacteristic
255C2×C11#189711yescharacteristic
256C2×C11#191311yescharacteristic
257D11—161no—
258C24—221no—
259C24D4×D1111yescharacteristic
260C2×D4—221no—
261C2×D4—221no—
262C2×D4—444no—
263C2×D4—441no—
264C2×D4—441no—
265C2×D4—881no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—81no—
269C22×C4—112no—
270C22×C4—112no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—222no—
277C22×C4—442no—
278C22×C4—881no—
279C22×C4C2×C4×D1111yescharacteristic
280C22×C4C2×D4411yescharacteristic
281C22×C4#433911yescharacteristic
282C22×C4D4×D1111yescharacteristic
283C22×C4D4×D1111yescharacteristic
284C22×C4#434311yescharacteristic
285M16—81no—
286M16—881no—
287C2×C8—41no—
288C2×C8—441no—
289C4⋊C4—222no—
290C4⋊C4—222no—
291C4⋊C4—222no—
292C4⋊C4—222no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—882no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C22⋊C4—444no—
299C22⋊C4—442no—
300C22⋊C4—441no—
301C22⋊C4—441no—
302C22⋊C4—882no—
303C42—81no—
304C42—81no—
305C42—881no—
306C11#941411yescharacteristic, complemented, Sylow
307C23—22no—
308C23—22no—
309C23—41no—
310C23—442no—
311C23—442no—
312C23—441no—
313C23—442no—
314C23C22⋊C4×D1111yescharacteristic
315C23#6693511yescharacteristic
316C23#6694711yescharacteristic
317D4—881no—
318D4—881no—
319D4—882no—
320D4—882no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—222no—
334C2×C4—222no—
335C2×C4—222no—
336C2×C4—222no—
337C2×C4—442no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—441no—
345C2×C4—442no—
346C2×C4—881no—
347C2×C4C4×D4411yescharacteristic
348C2×C4#6693711yescharacteristic
349C2×C4#6694611yescharacteristic
350C2×C4#6694811yescharacteristic
351C8—81no—
352C8—881no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22—884no—
362C22—881no—
363C22—881no—
364C22—881no—
365C22#1062227811yescharacteristic
366C22#1062243412yes—
367C22#1062244012yes—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—82no—
374C4—442no—
375C4—442no—
376C4—882no—
377C4—881no—
378C2—22no—
379C2—22no—
380C2—41no—
381C2—1761no—
382C2#1306901811yescharacteristic
383C2#1306906311yescharacteristic
384C2#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#9414
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. #13071216C2semidirect
5. #13066945C2semidirect
6. #13066502C2semidirect
7. C11×#1297C2semidirect
21. #10622285C4semidirect
22. #10622272C4semidirect
121. #1297D11semidirect
306. C11#9414semidirect

Maximal subgroups

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

subgroupindex
#130740912
#130712162
#130671332
#130671312
#130669452
#130665022
C11×#12972
#941411