Finite Group Databasebeta

← #14655673

Subgroups — #14655673

Order 2816.

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

normal subgroups only

This group has 642 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#13079531C211yesmaximal, characteristic
2C2×#10622701C211yesmaximal, characteristic, complemented
3#13069456C211yesmaximal, characteristic, complemented
4#13067288C211yesmaximal, characteristic, complemented
5#13067067C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C11×#3152C211yesmaximal, characteristic, complemented
8C2×C11×#137—22no—
9C11×#532C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66927C2211yescharacteristic
12C11×#497—22no—
13C11×#494—21no—
14C11×#492—21no—
15C4×C11×M16C2211yescharacteristic
16C2×#66887—22no—
17#10622701—22no—
18#10622701—21no—
19#10622701—22no—
20#10622686—21no—
21#10622649—22no—
22#10622628—22no—
23C2×#66873—22no—
24#10622538C2211yescharacteristic
25#10622537C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27#10622185—22no—
28D4⋊(C11⋊C8)—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×D44—21no—
32C22×D44—21no—
33C22×D44D412yes—
34C11×#137—44no—
35C11×#137—44no—
36C2×C11×Q16—24no—
37C2×C11×SD16—24no—
38C2×C11×M16D412yes—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8D411yescharacteristic
43C11×C4⋊Q8D412yes—
44C11×#127D411yescharacteristic
45C11×#124—21no—
46C11×#121—21no—
47C11×#121—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4323—24no—
54C2×#4318—21no—
55C22×C11⋊C8—21no—
56#66927—21no—
57#66927—21no—
58#66927—21no—
59#66927—21no—
60C11×#97—21no—
61C4×C8×C11—21no—
62C22⋊(C11⋊C8)—21no—
63#66887—44no—
64#66873—28no—
65#66873—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#10168—111nomaximal, Sylow
73C23×D11—22no—
74C11×#41—42no—
75C11×#41—42no—
76C2×Q8×C11—21no—
77C2×Q8×C11—22no—
78C2×Q8×C11—41no—
79C2×Q8×C11—42no—
80C2×Q8×C11—42no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C2×D44—22no—
91C2×D44—22no—
92C2×D44—44no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44—42no—
98C2×D44—42no—
99C2×D44—82no—
100C11×Q16—48no—
101C11×SD16—48no—
102C11×M16—22no—
103C11×M16D814yescomplemented
104C2×C8×C11—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117#4323—84no—
118#4318—42no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—42no—
122C2×C11⋊C8—41no—
123#3205—111no—
124#3152D1111yescharacteristic, complemented
125C2×#486—111no—
126#1965—111no—
127#1546—111no—
128#1492—111no—
129#1278—111no—
130C23×C11—41no—
131C23×C11#12111yescharacteristic
132C22×D11—42no—
133C22×D11—44no—
134C22×D11—82no—
135C22×D11—82no—
136Q8×C11—44no—
137Q8×C11—42no—
138Q8×C11—81no—
139Q8×C11—81no—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11—42no—
143D4×C11—82no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—82no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12711yescharacteristic
157C2×C4×C11C2×D812yes—
158C2×C4×C11AGL(1,ℤ/8)12yes—
159D44—44no—
160D44—44no—
161D44—82no—
162D44—82no—
163D44—82no—
164D44—81no—
165D44—81no—
166C8×C11—24no—
167C11⋊C8—42no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170C2×#137—22no—
171#532C2×D1111yescharacteristic
172C2×C4⋊Q8C2×D1111yescharacteristic
173C2×#127—111no—
174#497—22no—
175#494—21no—
176#493—221no—
177#492—21no—
178#486—222no—
179#486—222no—
180#486—221no—
181#459—222no—
182#447—222no—
183#431—111no—
184#423—111no—
185C2×#102—222no—
186C2×#100—222no—
187C4×M16C2×D1111yescharacteristic
188C2×C4×C8—111no—
189#332—222no—
190D4⋊C8—222no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11#39211yescharacteristic
197C22×C11#45912yes—
198C2×D11—82no—
199C2×D11—82no—
200C2×D11—82no—
201C2×D11—164no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—81no—
205C4×C11—82no—
206C4×C11#44712yes—
207C4×C11#45512yes—
208C4×C11#47112yes—
209C4×C11#49311yescharacteristic
210C4×C11#49611yescharacteristic
211C2×#41—21no—
212C22×Q8—21no—
213C22×D4—112no—
214C22×D4—221no—
215C22×D4—221no—
216#137—44no—
217#137—44no—
218C2×Q16—24no—
219C2×SD16—24no—
220C2×D8—224no—
221C2×M16—221no—
222C2×M16C22⋊D1112yes—
223C22×C8—221no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8C22⋊D1112yes—
228C4⋊Q8C22⋊D1111yescharacteristic
229#127—221no—
230#127—221no—
231#127—221no—
232#127—221no—
233#127C22⋊D1111yescharacteristic
234#124—21no—
235#121—21no—
236#121—21no—
237C4×D4—21no—
238C4×D4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C42C22×D1111yescharacteristic
242C4⋊C8—112no—
243C4⋊C8—221no—
244C4⋊C8—221no—
245#102—228no—
246#102—224no—
247#100—444no—
248C22⋊C8—221no—
249#97—21no—
250C4×C8—21no—
251C4×C8—112no—
252C4×C8—221no—
253C4×C8—221no—
254C2×C11—22no—
255C2×C11—161no—
256C2×C11#200411yescharacteristic
257C2×C11#201111yescharacteristic
258C2×C11#201911yescharacteristic
259D11—162no—
260C24—222no—
261#41—42no—
262#41—42no—
263C2×Q8—21no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—222no—
273C2×D4—222no—
274C2×D4—444no—
275C2×D4—442no—
276C2×D4—442no—
277C2×D4—441no—
278C2×D4—441no—
279C2×D4—441no—
280C2×D4—441no—
281C2×D4—882no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4D4×D1111yescharacteristic
285C22×C4#434111yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287Q16—48no—
288SD16—48no—
289D8—884no—
290M16—22no—
291M16—442no—
292M16#432314yescomplemented
293C2×C8—22no—
294C2×C8—222no—
295C2×C8—222no—
296C2×C8—442no—
297C2×C8—441no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C42D4×D1111yescharacteristic
307C42D4×D1111yescharacteristic
308C42C2×C22⋊D1111yescharacteristic
309C42C2×C22⋊D1111yescharacteristic
310C11#1016811yescharacteristic, complemented, Sylow
311C23—41no—
312C23—442no—
313C23—444no—
314C23—882no—
315C23—882no—
316C23#6699111yescharacteristic
317Q8—44no—
318Q8—42no—
319Q8—81no—
320Q8—81no—
321D4—42no—
322D4—42no—
323D4—42no—
324D4—82no—
325D4—444no—
326D4—444no—
327D4—882no—
328D4—882no—
329D4—882no—
330D4—881no—
331D4—881no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4C2×#432312yes—
340C2×C4#6698512yes—
341C2×C4#6699011yescharacteristic
342C2×C4#6699011yescharacteristic
343C2×C4#6699211yescharacteristic
344C2×C4#6699211yescharacteristic
345C2×C4#6699311yescharacteristic
346C2×C4#6700611yescharacteristic
347C8—24no—
348C8—442no—
349C8—442no—
350C8—881no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—882no—
357C22—882no—
358C22—882no—
359C22—1764no—
360C22#1062268512yes—
361C22#1062283611yescharacteristic
362C4—21no—
363C4—21no—
364C4—81no—
365C4—82no—
366C4#1062268611yescharacteristic
367C4#1062268711yescharacteristic
368C4#1062281512yes—
369C4#1062281612yes—
370C4#1062283012yes—
371C2—22no—
372C2—161no—
373C2—1762no—
374C2#1306964211yescharacteristic
375C2#1306968711yescharacteristic
376C2#1306972711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3152C2
socleC22×C11#392
prime radical#13079531C2
hypercenter#3152D11
hypocenterC11#10168
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3152

Complements

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

NH ≅ G/Ntype
2. C2×#10622701C2semidirect
3. #13069456C2semidirect
4. #13067288C2semidirect
5. #13067067C2semidirect
6. #13066454C2semidirect
7. C11×#3152C2semidirect
103. C11×M16D8semidirect
124. #3152D11semidirect
292. M16#4323semidirect
310. C11#10168semidirect

Maximal subgroups

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

subgroupindex
#130795312
C2×#106227012
#130694562
#130672882
#130670672
#130664542
C11×#31522
#1016811