Finite Group Databasebeta

← #14655519

Subgroups — #14655519

Order 2816.

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

normal subgroups only

This group has 690 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#13079538C211yesmaximal, characteristic, complemented
2C2×#10622689C211yesmaximal, characteristic, complemented
3#13069605C211yesmaximal, characteristic, complemented
4#13067284C211yesmaximal, characteristic, complemented
5#13067067C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C11×#3151C211yesmaximal, characteristic
8C2×C11×AGL(1,ℤ/8)—22no—
9C11×#532C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C22×#4324—22no—
12C2×#66922C2211yescharacteristic
13C11×#496—22no—
14C11×#493—21no—
15C11×#492—21no—
16C4×C11×M16C2211yescharacteristic
17#10622706—21no—
18#10622689—22no—
19#10622689—21no—
20#10622689—22no—
21#10622653—22no—
22#10622632—22no—
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26#10622192—22no—
27#10622182—22no—
28D4⋊(C11⋊C8)—22no—
29C2×C11×#41—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×Dic22D412yes—
34C11×AGL(1,ℤ/8)—44no—
35C11×AGL(1,ℤ/8)—44no—
36C2×C11×SD16—24no—
37C2×C11×D8—24no—
38C2×C11×M16D412yes—
39C11×C4⋊Q8D411yescharacteristic
40C11×#127—21no—
41C11×#127—21no—
42C11×#127—21no—
43C11×#127D411yescharacteristic
44C11×#127D412yes—
45C11×#124—21no—
46C11×#121—21no—
47C11×#121—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4324—28no—
52C2×#4324—24no—
53C2×#4324—48no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×#4318—21no—
57C22×C11⋊C8—21no—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922—21no—
62C11×#97—21no—
63C4×C8×C11—21no—
64C22⋊(C11⋊C8)—21no—
65#66874—24no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8D412yes—
72#10146—111nomaximal, Sylow
73C24×C11—41no—
74C11×#41—42no—
75C11×#41—42no—
76C2×Q8×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—22no—
79C2×D4×C11—21no—
80C2×D4×C11—22no—
81C2×D4×C11—21no—
82C2×D4×C11—22no—
83C2×D4×C11—44no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—42no—
89C2×D4×C11—42no—
90C2×D4×C11—82no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×Dic11—22no—
96C2×Dic22—22no—
97C2×Dic22—22no—
98C2×Dic22—44no—
99C11×SD16—48no—
100C11×D8—48no—
101C11×M16—22no—
102C11×M16SD1614yescomplemented
103C2×C8×C11—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112#4324—416no—
113#4324—84no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118#4318—42no—
119C2×C11⋊C8—24no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—41no—
123#3206—111no—
124#3151D1111yescharacteristic
125C2×#492—111no—
126#1997—111no—
127#1545—111no—
128#1492—111no—
129#1278—111no—
130C23×C11—41no—
131C23×C11—42no—
132C23×C11—82no—
133C23×C11—82no—
134C23×C11—82no—
135C23×C11#12111yescharacteristic
136Q8×C11—42no—
137D4×C11—44no—
138D4×C11—42no—
139D4×C11—44no—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11—82no—
143D4×C11—82no—
144D4×C11—82no—
145D4×C11—82no—
146D4×C11—81no—
147D4×C11—81no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—81no—
152C2×C4×C11—81no—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12711yescharacteristic
159C2×C4×C11C2×SD1612yes—
160C2×C4×C11AGL(1,ℤ/8)12yes—
161C2×Dic11—42no—
162C2×Dic11—82no—
163Dic22—44no—
164Dic22—44no—
165C8×C11—24no—
166C11⋊C8—24no—
167C11⋊C8—42no—
168C11⋊C8—81no—
169C2×AGL(1,ℤ/8)—22no—
170C22×SD16—222no—
171#532C2×D1111yescharacteristic
172C2×C4⋊Q8—111no—
173C2×#127C2×D1111yescharacteristic
174#496—22no—
175#493—21no—
176#492—21no—
177#492—222no—
178#492—222no—
179#492—221no—
180#487—221no—
181#461—222no—
182#448—222no—
183#431—111no—
184#423—111no—
185C4×M16C2×D1111yescharacteristic
186C2×C4×C8—111no—
187#343—222no—
188#331—222no—
189D4⋊C8—222no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—82no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—82no—
196C22×C11—81no—
197C22×C11—82no—
198C22×C11—164no—
199C22×C11#39211yescharacteristic
200C22×C11#46012yes—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—81no—
204C4×C11#45012yes—
205C4×C11#45312yes—
206C4×C11#47112yes—
207C4×C11#49211yescharacteristic
208C4×C11#49611yescharacteristic
209Dic11—82no—
210C2×#41—21no—
211C22×Q8—112no—
212C22×D4—21no—
213C22×D4—21no—
214C22×D4—21no—
215AGL(1,ℤ/8)—44no—
216AGL(1,ℤ/8)—44no—
217C2×SD16—24no—
218C2×SD16—228no—
219C2×SD16—224no—
220C2×SD16—448no—
221C2×D8—24no—
222C2×M16—221no—
223C2×M16C22⋊D1112yes—
224C22×C8—221no—
225C4⋊Q8—221no—
226C4⋊Q8—221no—
227C4⋊Q8—221no—
228C4⋊Q8—221no—
229C4⋊Q8C22⋊D1111yescharacteristic
230#127—21no—
231#127—21no—
232#127—21no—
233#127C22⋊D1112yes—
234#127C22⋊D1111yescharacteristic
235#124—21no—
236#121—21no—
237#121—21no—
238C4×D4—21no—
239C4×D4—21no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C42C22×D1111yescharacteristic
243C4⋊C8—112no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246#103—224no—
247C22⋊C8—221no—
248#97—21no—
249C4×C8—21no—
250C4×C8—112no—
251C4×C8—221no—
252C4×C8—221no—
253C2×C11—22no—
254C2×C11—161no—
255C2×C11—162no—
256C2×C11#200211yescharacteristic
257C2×C11#201411yescharacteristic
258C2×C11#201911yescharacteristic
259C24—41no—
260#41—42no—
261#41—42no—
262C2×Q8—21no—
263C2×Q8—222no—
264C2×Q8—222no—
265C2×Q8—444no—
266C2×D4—21no—
267C2×D4—22no—
268C2×D4—21no—
269C2×D4—22no—
270C2×D4—21no—
271C2×D4—22no—
272C2×D4—44no—
273C2×D4—41no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—82no—
280C22×C4—41no—
281C22×C4—222no—
282C22×C4D4×D1111yescharacteristic
283C22×C4#434111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285SD16—48no—
286SD16—4416no—
287SD16—884no—
288D8—48no—
289M16—22no—
290M16—442no—
291M16#432414yescomplemented
292C2×C8—22no—
293C2×C8—224no—
294C2×C8—222no—
295C2×C8—222no—
296C2×C8—441no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—441no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C42D4×D1111yescharacteristic
306C42D4×D1111yescharacteristic
307C42C2×C22⋊D1111yescharacteristic
308C42C2×C22⋊D1111yescharacteristic
309C11#1014611yescharacteristic, complemented, Sylow
310C23—41no—
311C23—42no—
312C23—82no—
313C23—82no—
314C23—82no—
315C23#6699111yescharacteristic
316Q8—42no—
317Q8—444no—
318Q8—444no—
319D4—44no—
320D4—42no—
321D4—42no—
322D4—42no—
323D4—44no—
324D4—82no—
325D4—82no—
326D4—82no—
327D4—82no—
328D4—81no—
329D4—81no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—442no—
336C2×C4—882no—
337C2×C4#6698512yes—
338C2×C4C2×#432412yes—
339C2×C4#6699011yescharacteristic
340C2×C4#6699011yescharacteristic
341C2×C4#6699211yescharacteristic
342C2×C4#6699211yescharacteristic
343C2×C4#6699311yescharacteristic
344C2×C4#6700611yescharacteristic
345C8—24no—
346C8—224no—
347C8—442no—
348C8—881no—
349C22—21no—
350C22—21no—
351C22—82no—
352C22—81no—
353C22—81no—
354C22—82no—
355C22—81no—
356C22—82no—
357C22—164no—
358C22#1062268812yes—
359C22#1062283611yescharacteristic
360C4—21no—
361C4—21no—
362C4—81no—
363C4—882no—
364C4#1062268711yescharacteristic
365C4#1062268911yescharacteristic
366C4#1062281112yes—
367C4#1062281312yes—
368C4#1062283112yes—
369C2—22no—
370C2—162no—
371C2—161no—
372C2#1306962811yescharacteristic
373C2#1306970411yescharacteristic
374C2#1306973011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3151C2
socleC22×C11#392
hypercenter#3151D11
hypocenterC11#10146
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3151

Complements

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

NH ≅ G/Ntype
1. #13079538C2semidirect
2. C2×#10622689C2semidirect
3. #13069605C2semidirect
4. #13067284C2semidirect
5. #13067067C2semidirect
6. #13066454C2semidirect
102. C11×M16SD16semidirect
291. M16#4324semidirect
309. C11#10146semidirect

Maximal subgroups

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

subgroupindex
#130795382
C2×#106226892
#130696052
#130672842
#130670672
#130664542
C11×#31512
#1014611