Finite Group Databasebeta

← #14655505

Subgroups — #14655505

Order 2816.

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

normal subgroups only

This group has 758 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, complemented
2C2×#10622686C211yesmaximal, characteristic, complemented
3#13069456C211yesmaximal, characteristic, complemented
4#13067284C211yesmaximal, characteristic, complemented
5#13067067C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C11×#3151C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—22no—
9C11×#532C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C22×#4323—22no—
12C2×#66927C2211yescharacteristic
13C11×#496—22no—
14C11×#493—21no—
15C11×#492—21no—
16C4×C11×M16C2211yescharacteristic
17C2×#66887—22no—
18#10622701—21no—
19#10622686—21no—
20#10622686—22no—
21#10622686—22no—
22#10622649—22no—
23#10622628—22no—
24#10622538C2211yescharacteristic
25#10622537C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27#10622182—22no—
28D4⋊(C11⋊C8)—22no—
29C2×C11×#41—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D44—21no—
34C22×D44—21no—
35C22×D44D412yes—
36C11×AGL(1,ℤ/8)—44no—
37C11×AGL(1,ℤ/8)—44no—
38C2×C11×SD16—24no—
39C2×C11×D8—24no—
40C2×C11×M16D412yes—
41C11×C4⋊Q8D411yescharacteristic
42C11×#127—21no—
43C11×#127—21no—
44C11×#127—21no—
45C11×#127D411yescharacteristic
46C11×#127D412yes—
47C11×#124—21no—
48C11×#121—21no—
49C11×#121—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4323—28no—
54C2×#4323—24no—
55C2×#4323—48no—
56C2×#4318—21no—
57C22×C11⋊C8—21no—
58#66927—21no—
59#66927—21no—
60#66927—21no—
61#66927—21no—
62C11×#97—21no—
63C4×C8×C11—21no—
64C22⋊(C11⋊C8)—21no—
65#66887—44no—
66#66873—24no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)D412yes—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72C4×C11⋊C8D412yes—
73#10144—111nomaximal, Sylow
74C24×C11—41no—
75C23×D11—22no—
76C11×#41—42no—
77C11×#41—42no—
78C2×Q8×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—22no—
81C2×D4×C11—21no—
82C2×D4×C11—22no—
83C2×D4×C11—21no—
84C2×D4×C11—22no—
85C2×D4×C11—44no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—42no—
91C2×D4×C11—42no—
92C2×D4×C11—82no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C2×D44—22no—
98C2×D44—22no—
99C2×D44—44no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—41no—
104C2×D44—42no—
105C2×D44—42no—
106C2×D44—82no—
107C11×SD16—48no—
108C11×D8—48no—
109C11×M16—22no—
110C11×M16D814yescomplemented
111C2×C8×C11—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120#4323—416no—
121#4323—84no—
122#4318—42no—
123C2×C11⋊C8—24no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—41no—
127#3205—111no—
128#3151D1111yescharacteristic, complemented
129C2×#493—111no—
130#1965—111no—
131#1545—111no—
132#1492—111no—
133#1278—111no—
134C23×C11—41no—
135C23×C11—42no—
136C23×C11—82no—
137C23×C11—82no—
138C23×C11—82no—
139C23×C11#12111yescharacteristic
140C22×D11—42no—
141C22×D11—44no—
142C22×D11—82no—
143C22×D11—82no—
144Q8×C11—42no—
145D4×C11—44no—
146D4×C11—42no—
147D4×C11—44no—
148D4×C11—42no—
149D4×C11—42no—
150D4×C11—82no—
151D4×C11—82no—
152D4×C11—82no—
153D4×C11—82no—
154D4×C11—81no—
155D4×C11—81no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12711yescharacteristic
167C2×C4×C11C2×D812yes—
168C2×C4×C11AGL(1,ℤ/8)12yes—
169D44—44no—
170D44—44no—
171D44—82no—
172D44—82no—
173D44—82no—
174D44—81no—
175D44—81no—
176C8×C11—24no—
177C11⋊C8—24no—
178C11⋊C8—42no—
179C11⋊C8—81no—
180C2×AGL(1,ℤ/8)—22no—
181C22×D8—222no—
182#532C2×D1111yescharacteristic
183C2×#127—111no—
184C2×#127C2×D1111yescharacteristic
185#496—22no—
186#493—21no—
187#493—222no—
188#493—222no—
189#493—221no—
190#492—21no—
191#486—221no—
192#459—222no—
193#447—222no—
194#431—111no—
195#423—111no—
196C2×#100—222no—
197C4×M16C2×D1111yescharacteristic
198C2×C4×C8—111no—
199#331—222no—
200D4⋊C8—222no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—82no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—82no—
207C22×C11—81no—
208C22×C11—82no—
209C22×C11—164no—
210C22×C11#39211yescharacteristic
211C22×C11#45912yes—
212C2×D11—82no—
213C2×D11—82no—
214C2×D11—82no—
215C2×D11—164no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—81no—
219C4×C11#44712yes—
220C4×C11#45312yes—
221C4×C11#47212yes—
222C4×C11#49311yescharacteristic
223C4×C11#49611yescharacteristic
224C2×#41—21no—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—112no—
229C22×D4—221no—
230C22×D4—221no—
231AGL(1,ℤ/8)—44no—
232AGL(1,ℤ/8)—44no—
233C2×SD16—24no—
234C2×D8—24no—
235C2×D8—228no—
236C2×D8—224no—
237C2×D8—448no—
238C2×M16—221no—
239C2×M16C22⋊D1112yes—
240C22×C8—221no—
241C4⋊Q8C22⋊D1111yescharacteristic
242#127—21no—
243#127—21no—
244#127—21no—
245#127—221no—
246#127—221no—
247#127—221no—
248#127—221no—
249#127C22⋊D1112yes—
250#127C22⋊D1111yescharacteristic
251#124—21no—
252#121—21no—
253#121—21no—
254C4×D4—21no—
255C4×D4—21no—
256C2×C42C22×D1111yescharacteristic
257C4⋊C8—112no—
258C4⋊C8—221no—
259C4⋊C8—221no—
260#102—224no—
261#100—444no—
262C22⋊C8—221no—
263#97—21no—
264C4×C8—21no—
265C4×C8—112no—
266C4×C8—221no—
267C4×C8—221no—
268C2×C11—22no—
269C2×C11—161no—
270C2×C11—162no—
271C2×C11#200211yescharacteristic
272C2×C11#201111yescharacteristic
273C2×C11#201811yescharacteristic
274D11—162no—
275C24—41no—
276C24—222no—
277#41—42no—
278#41—42no—
279C2×Q8—21no—
280C2×D4—21no—
281C2×D4—22no—
282C2×D4—21no—
283C2×D4—22no—
284C2×D4—21no—
285C2×D4—22no—
286C2×D4—44no—
287C2×D4—41no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—82no—
294C2×D4—222no—
295C2×D4—222no—
296C2×D4—444no—
297C2×D4—442no—
298C2×D4—442no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—441no—
302C2×D4—441no—
303C2×D4—882no—
304C22×C4—41no—
305C22×C4D4×D1111yescharacteristic
306C22×C4#434111yescharacteristic
307C22×C4C2×C22⋊D1111yescharacteristic
308SD16—48no—
309D8—48no—
310D8—4416no—
311D8—884no—
312M16—22no—
313M16—442no—
314M16#432314yescomplemented
315C2×C8—22no—
316C2×C8—224no—
317C2×C8—222no—
318C2×C8—222no—
319C2×C8—441no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C42D4×D1111yescharacteristic
325C42D4×D1111yescharacteristic
326C42C2×C22⋊D1111yescharacteristic
327C42C2×C22⋊D1111yescharacteristic
328C11#1014411yescharacteristic, complemented, Sylow
329C23—41no—
330C23—42no—
331C23—82no—
332C23—82no—
333C23—82no—
334C23—442no—
335C23—444no—
336C23—882no—
337C23—882no—
338C23#6699111yescharacteristic
339Q8—42no—
340D4—44no—
341D4—42no—
342D4—42no—
343D4—42no—
344D4—44no—
345D4—82no—
346D4—82no—
347D4—82no—
348D4—82no—
349D4—81no—
350D4—81no—
351D4—444no—
352D4—444no—
353D4—882no—
354D4—882no—
355D4—882no—
356D4—881no—
357D4—881no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4C2×#432312yes—
364C2×C4#6698512yes—
365C2×C4#6699011yescharacteristic
366C2×C4#6699011yescharacteristic
367C2×C4#6699211yescharacteristic
368C2×C4#6699211yescharacteristic
369C2×C4#6699311yescharacteristic
370C2×C4#6700611yescharacteristic
371C8—24no—
372C8—224no—
373C8—442no—
374C8—881no—
375C22—21no—
376C22—21no—
377C22—82no—
378C22—81no—
379C22—81no—
380C22—82no—
381C22—81no—
382C22—82no—
383C22—164no—
384C22—882no—
385C22—882no—
386C22—882no—
387C22—1764no—
388C22#1062268512yes—
389C22#1062283611yescharacteristic
390C4—21no—
391C4—21no—
392C4—81no—
393C4#1062268611yescharacteristic
394C4#1062268711yescharacteristic
395C4#1062281112yes—
396C4#1062281212yes—
397C4#1062283012yes—
398C2—22no—
399C2—162no—
400C2—161no—
401C2—1762no—
402C2#1306962811yescharacteristic
403C2#1306968711yescharacteristic
404C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3151C2
socleC22×C11#392
hypercenter#3151D11
hypocenterC11#10144
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. #13079531C2semidirect
2. C2×#10622686C2semidirect
3. #13069456C2semidirect
4. #13067284C2semidirect
5. #13067067C2semidirect
6. #13066454C2semidirect
7. C11×#3151C2semidirect
110. C11×M16D8semidirect
128. #3151D11semidirect
314. M16#4323semidirect
328. C11#10144semidirect

Maximal subgroups

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

subgroupindex
#130795312
C2×#106226862
#130694562
#130672842
#130670672
#130664542
C11×#31512
#1014411