Finite Group Databasebeta

← #14655523

Subgroups — #14655523

Order 2816.

690 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 107 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
2#13079069C211yesmaximal, characteristic
3C2×#10622306C211yesmaximal, characteristic, complemented
4#13069604C211yesmaximal, characteristic, complemented
5#13067285C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C11×#1492C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×#67002—22no—
10C22×#4314—22no—
11C2×#66927C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C11×#423C2211yescharacteristic
14C2×C4×C8×C11C2211yescharacteristic
15#10622706—21no—
16#10622698—21no—
17#10622689—21no—
18#10622686—21no—
19#10622671—22no—
20#10622653—22no—
21#10622632—22no—
22#10622538C2211yescharacteristic
23C4×#4318C2211yescharacteristic
24#10622306—22no—
25#10622306—22no—
26C11×D4⋊C8—22no—
27#10622192—22no—
28#10622123—22no—
29C2×C11×#41—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44—21no—
33C22×Dic22D412yes—
34C2×C11×M16—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8D411yescharacteristic
37C11×#127D411yescharacteristic
38C11×#124—21no—
39C11×#121—21no—
40C11×#121—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C2×C42×C11C2311yescharacteristic
44#67002—44no—
45#67002—44no—
46C2×#4325—24no—
47C2×#4324—24no—
48C2×#4323—24no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×#4318D412yes—
52C2×#4314—28no—
53C2×#4314—48no—
54#66927—21no—
55#66927—21no—
56#66927—21no—
57#66927D412yes—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C4×C8×C11—21no—
65C4×C8×C11D412yes—
66C22⋊(C11⋊C8)—21no—
67#66874—24no—
68C4⋊(C11⋊C8)D412yes—
69#66867—21no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#10146—111nomaximal, Sylow
73C23×D11—41no—
74C11×#41—42no—
75C11×#41—42no—
76C2×Q8×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—22no—
86C2×D44—22no—
87C2×D44—22no—
88C2×D44—22no—
89C2×D44—44no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—42no—
94C2×D44—42no—
95C2×D44—82no—
96C2×Dic22—22no—
97C2×Dic22—22no—
98C2×Dic22—44no—
99C11×M16—42no—
100C2×C8×C11—24no—
101C2×C8×C11—22no—
102C2×C8×C11—41no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111#4325—48no—
112#4324—84no—
113#4323—48no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118#4318—22no—
119#4318SD1614yescomplemented
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122#4314—416no—
123#3206—111no—
124#3151—111no—
125C2×#492—111no—
126#1997—111no—
127#1545—111no—
128#1492D1111yescharacteristic, complemented
129#1278—111no—
130C23×C11—41no—
131C23×C11#12111yescharacteristic
132C22×D11—42no—
133C22×D11—82no—
134C22×D11—82no—
135C22×D11—82no—
136Q8×C11—42no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—82no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12711yescharacteristic
152C2×C4×C11C2×SD1612yes—
153C2×C4×C11AGL(1,ℤ/8)12yes—
154C2×Dic11—42no—
155C2×Dic11—82no—
156D44—44no—
157D44—44no—
158D44—82no—
159D44—82no—
160D44—82no—
161D44—81no—
162D44—81no—
163Dic22—44no—
164Dic22—44no—
165C8×C11—24no—
166C8×C11—81no—
167C11⋊C8—24no—
168C11⋊C8—42no—
169C2×AGL(1,ℤ/8)—222no—
170C22×SD16—222no—
171#532C2×D1111yescharacteristic
172C2×C4⋊Q8—111no—
173C2×#127—111no—
174#496—222no—
175#493—221no—
176#492—222no—
177#492—221no—
178#492—221no—
179#492—222no—
180#487—221no—
181#461—222no—
182#448—222no—
183#431—111no—
184#423C2×D1111yescharacteristic
185C4×M16—111no—
186C2×C4×C8C2×D1111yescharacteristic
187#343—222no—
188#331—222no—
189D4⋊C8—22no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11#39211yescharacteristic
196C22×C11#46012yes—
197C2×D11—82no—
198C2×D11—82no—
199C2×D11—82no—
200C2×D11—164no—
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—221no—
213C22×D4—221no—
214C22×D4—221no—
215AGL(1,ℤ/8)—444no—
216AGL(1,ℤ/8)—444no—
217C2×SD16—228no—
218C2×SD16—224no—
219C2×SD16—224no—
220C2×SD16—448no—
221C2×D8—224no—
222C2×M16—21no—
223C2×M16—112no—
224C22×C8—21no—
225C4⋊Q8—221no—
226C4⋊Q8—221no—
227C4⋊Q8—221no—
228C4⋊Q8—221no—
229C4⋊Q8D4411yescharacteristic
230#127—112no—
231#127—221no—
232#127—221no—
233#127—221no—
234#127D4411yescharacteristic
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—21no—
244C4⋊C8—21no—
245C4⋊C8—112no—
246#103—224no—
247C22⋊C8—221no—
248#97—221no—
249C4×C8—21no—
250C4×C8—221no—
251C4×C8—221no—
252C4×C8C22⋊D1112yes—
253C2×C11—22no—
254C2×C11—161no—
255C2×C11#200211yescharacteristic
256C2×C11#201411yescharacteristic
257C2×C11#201911yescharacteristic
258D11—162no—
259C24—441no—
260#41—42no—
261#41—42no—
262C2×Q8—21no—
263C2×Q8—222no—
264C2×Q8—222no—
265C2×Q8—444no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—41no—
270C2×D4—222no—
271C2×D4—222no—
272C2×D4—222no—
273C2×D4—444no—
274C2×D4—441no—
275C2×D4—442no—
276C2×D4—442no—
277C2×D4—441no—
278C2×D4—441no—
279C2×D4—882no—
280C22×C4—41no—
281C22×C4—222no—
282C22×C4#433911yescharacteristic
283C22×C4D4×D1111yescharacteristic
284C22×C4D4×D1111yescharacteristic
285SD16—4416no—
286SD16—448no—
287SD16—884no—
288D8—448no—
289M16—42no—
290M16—114no—
291M16—222no—
292C2×C8—24no—
293C2×C8—22no—
294C2×C8—41no—
295C2×C8—222no—
296C2×C8—222no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—441no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C42C2×D4411yescharacteristic
306C42D4×D1111yescharacteristic
307C42D4×D1111yescharacteristic
308C42C2×C22⋊D1111yescharacteristic
309C11#1014611yescharacteristic, complemented, Sylow
310C23—41no—
311C23—442no—
312C23—882no—
313C23—882no—
314C23—882no—
315C23#6693711yescharacteristic
316Q8—42no—
317Q8—444no—
318Q8—444no—
319D4—42no—
320D4—42no—
321D4—42no—
322D4—82no—
323D4—444no—
324D4—444no—
325D4—882no—
326D4—882no—
327D4—881no—
328D4—881no—
329D4—882no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—442no—
336C2×C4—882no—
337C2×C4#6693511yescharacteristic
338C2×C4#6693511yescharacteristic
339C2×C4#6693711yescharacteristic
340C2×C4#6696412yes—
341C2×C4SD16×D1112yes—
342C2×C4#6698311yescharacteristic
343C2×C4#6699011yescharacteristic
344C2×C4#6699311yescharacteristic
345C8—24no—
346C8—81no—
347C8—224no—
348C8—442no—
349C22—21no—
350C22—21no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—882no—
355C22—882no—
356C22—882no—
357C22—1764no—
358C22#1062237512yes—
359C22#1062257311yescharacteristic
360C4—21no—
361C4—21no—
362C4—81no—
363C4—882no—
364C4#1062238912yes—
365C4#1062243512yes—
366C4#1062275412yes—
367C4#1062276711yescharacteristic
368C4#1062278811yescharacteristic
369C2—22no—
370C2—161no—
371C2—1762no—
372C2#1306963011yescharacteristic
373C2#1306970511yescharacteristic
374C2#1306973111yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1492C2
socleC22×C11#392
prime radical#13079069C2
hypercenter#1492D11
hypocenterC11#10146
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
1. #13079538C2semidirect
3. C2×#10622306C2semidirect
4. #13069604C2semidirect
5. #13067285C2semidirect
6. #13066453C2semidirect
7. C11×#1492C2semidirect
119. #4318SD16semidirect
128. #1492D11semidirect
309. C11#10146semidirect

Maximal subgroups

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

subgroupindex
#130795382
#130790692
C2×#106223062
#130696042
#130672852
#130664532
C11×#14922
#1014611