Finite Group Databasebeta

← #14655522

Subgroups — #14655522

Order 2816.

690 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 111 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#13079541C211yesmaximal, characteristic, complemented
2#13079068C211yesmaximal, characteristic
3C2×#10622698C211yesmaximal, characteristic, complemented
4#13067285C211yesmaximal, characteristic, complemented
5#13067066C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C11×#1997C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4325—22no—
10C2×#66961—22no—
11#10623008C2211yescharacteristic
12C2×#66927C2211yescharacteristic
13C11×#423C2211yescharacteristic
14C4×C11×M16C2211yescharacteristic
15#10622840—22no—
16#10622698—22no—
17#10622698—21no—
18#10622698—22no—
19#10622696—22no—
20#10622694—21no—
21#10622538C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622325—22no—
24#10622308—21no—
25#10622306—21no—
26C11×#343—22no—
27#10622123—22no—
28#10622121—22no—
29C22×Q8×C11D412yes—
30C2×#4339—21no—
31C22×D44—21no—
32C22×D44—21no—
33C22×D44—21no—
34C2×C11×M16—21no—
35C2×C11×M16D412yes—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C42×C11C2311yescharacteristic
43C2×#4325—28no—
44C2×#4325—24no—
45C2×#4325—48no—
46#66983—21no—
47#66983—21no—
48C22×C11⋊C8—21no—
49#66961—44no—
50#66961—44no—
51C2×D88—24no—
52C2×#4314—24no—
53#66928—21no—
54#66927—21no—
55#66927—21no—
56#66927—21no—
57#66927D412yes—
58#66927D411yescharacteristic
59C4×D44—21no—
60C4×D44—21no—
61#66922D411yescharacteristic
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×#97—21no—
65C4×C8×C11—21no—
66#66899—24no—
67C22⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8D412yes—
72#10146—111nomaximal, Sylow
73C23×D11—41no—
74C2×Q8×C11—22no—
75C2×Q8×C11—22no—
76C2×Q8×C11—44no—
77C22×C4×C11—22no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C2×C22⋊D11—41no—
82#4339—42no—
83#4339—42no—
84C2×D44—21no—
85C2×D44—22no—
86C2×D44—22no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—22no—
90C2×D44—44no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—42no—
95C2×D44—42no—
96C2×D44—82no—
97C2×C4×D11—41no—
98C2×Dic22—21no—
99C11×M16—22no—
100C11×M16—42no—
101C11×M16SD1614yescomplemented
102C2×C8×C11—22no—
103C2×C8×C11—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112#4325—416no—
113#4325—84no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C2×C11⋊C8—24no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121D88—48no—
122#4314—48no—
123#3206—111no—
124#3151—111no—
125C2×#492—111no—
126#1997D1111yescharacteristic, complemented
127#1545—111no—
128#1492—111no—
129#1278—111no—
130C23×C11#12111yescharacteristic
131C22×D11—41no—
132C22×D11—42no—
133C22×D11—82no—
134C22×D11—82no—
135C22×D11—82no—
136Q8×C11—44no—
137Q8×C11—44no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—42no—
141C2×C4×C11—82no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12711yescharacteristic
148C2×C4×C11C2×SD1612yes—
149C2×C4×C11AGL(1,ℤ/8)12yes—
150C22⋊D11—82no—
151C2×Dic11—41no—
152D44—44no—
153D44—44no—
154D44—42no—
155D44—42no—
156D44—42no—
157D44—82no—
158D44—82no—
159D44—82no—
160D44—81no—
161D44—81no—
162C4×D11—81no—
163C4×D11—81no—
164Dic22—42no—
165C8×C11—24no—
166C8×C11—81no—
167C11⋊C8—24no—
168C11⋊C8—42no—
169C2×AGL(1,ℤ/8)—222no—
170C22×SD16—222no—
171#532—111no—
172C2×C4⋊Q8C2×D1111yescharacteristic
173C2×#127—111no—
174#496—222no—
175#493—221no—
176#492—221no—
177#492—222no—
178#492—222no—
179#492—221no—
180#487—221no—
181#461—222no—
182#448—222no—
183#431—111no—
184#423C2×D1111yescharacteristic
185C4×M16C2×D1111yescharacteristic
186C2×C4×C8—111no—
187#343—22no—
188#331—222no—
189D4⋊C8—222no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11#39211yescharacteristic
193C22×C11#46012yes—
194C2×D11—82no—
195C2×D11—81no—
196C2×D11—82no—
197C2×D11—81no—
198C2×D11—82no—
199C2×D11—81no—
200C2×D11—164no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—82no—
204C4×C11#45012yes—
205C4×C11#45312yes—
206C4×C11#47112yes—
207C4×C11#49211yescharacteristic
208C4×C11#49611yescharacteristic
209Dic11—81no—
210C2×#41—221no—
211C22×Q8D4412yes—
212C22×D4—221no—
213C22×D4—221no—
214C22×D4—221no—
215AGL(1,ℤ/8)—444no—
216AGL(1,ℤ/8)—444no—
217C2×SD16—224no—
218C2×SD16—228no—
219C2×SD16—224no—
220C2×SD16—448no—
221C2×D8—224no—
222C2×M16—21no—
223C2×M16C22⋊D1112yes—
224C22×C8—221no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—111no—
230#127—112no—
231#127—111no—
232#127—221no—
233#127—221no—
234#127—221no—
235#124—221no—
236#121—221no—
237#121—221no—
238C4×D4—221no—
239C4×D4—221no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C42C22×D1111yescharacteristic
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—112no—
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#200211yescharacteristic
255C2×C11#201411yescharacteristic
256C2×C11#201911yescharacteristic
257D11—161no—
258D11—162no—
259C24—441no—
260#41—442no—
261#41—442no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—44no—
265C2×Q8—221no—
266C2×D4—221no—
267C2×D4—222no—
268C2×D4—221no—
269C2×D4—222no—
270C2×D4—221no—
271C2×D4—222no—
272C2×D4—444no—
273C2×D4—441no—
274C2×D4—441no—
275C2×D4—441no—
276C2×D4—441no—
277C2×D4—442no—
278C2×D4—442no—
279C2×D4—882no—
280C22×C4—22no—
281C22×C4—441no—
282C22×C4C2×D4411yescharacteristic
283C22×C4#433911yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285SD16—448no—
286SD16—4416no—
287SD16—884no—
288D8—448no—
289M16—22no—
290M16—42no—
291M16#432514yescomplemented
292C2×C8—22no—
293C2×C8—41no—
294C2×C8—224no—
295C2×C8—222no—
296C2×C8—222no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C42D4×D1111yescharacteristic
306C42D4×D1111yescharacteristic
307C42D4×D1111yescharacteristic
308C42D4×D1111yescharacteristic
309C11#1014611yescharacteristic, complemented, Sylow
310C23—441no—
311C23—442no—
312C23—882no—
313C23—882no—
314C23—882no—
315C23#6698311yescharacteristic
316Q8—44no—
317Q8—44no—
318Q8—442no—
319D4—444no—
320D4—442no—
321D4—442no—
322D4—442no—
323D4—444no—
324D4—882no—
325D4—882no—
326D4—882no—
327D4—882no—
328D4—881no—
329D4—881no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—42no—
333C2×C4—82no—
334C2×C4—441no—
335C2×C4—881no—
336C2×C4—881no—
337C2×C4#6693511yescharacteristic
338C2×C4#6693511yescharacteristic
339C2×C4#6693711yescharacteristic
340C2×C4#6693711yescharacteristic
341C2×C4#6699011yescharacteristic
342C2×C4#6699311yescharacteristic
343C2×C4C2×#432512yes—
344C2×C4#6700212yes—
345C8—24no—
346C8—81no—
347C8—224no—
348C8—442no—
349C22—21no—
350C22—21no—
351C22—882no—
352C22—881no—
353C22—881no—
354C22—882no—
355C22—881no—
356C22—882no—
357C22—1764no—
358C22#1062257311yescharacteristic
359C22#1062264012yes—
360C4—21no—
361C4—21no—
362C4—82no—
363C4—881no—
364C4#1062236012yes—
365C4#1062236712yes—
366C4#1062265912yes—
367C4#1062267111yescharacteristic
368C4#1062269811yescharacteristic
369C2—22no—
370C2—1762no—
371C2—1761no—
372C2#1306963311yescharacteristic
373C2#1306970311yescharacteristic
374C2#1306972911yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1997C2
socleC22×C11#392
prime radical#13079068C2
hypercenter#1997D11
hypocenterC11#10146
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
1. #13079541C2semidirect
3. C2×#10622698C2semidirect
4. #13067285C2semidirect
5. #13067066C2semidirect
6. #13066454C2semidirect
7. C11×#1997C2semidirect
101. C11×M16SD16semidirect
126. #1997D11semidirect
291. M16#4325semidirect
309. C11#10146semidirect

Maximal subgroups

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

subgroupindex
#130795412
#130790682
C2×#106226982
#130672852
#130670662
#130664542
C11×#19972
#1014611