Finite Group Databasebeta

← #14656432

Subgroups — #14656432

Order 2816.

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

normal subgroups only

This group has 678 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#13079739C211yesmaximal, characteristic, complemented
2#13079536C211yesmaximal, characteristic
3#13076973C211yesmaximal, characteristic, complemented
4#13069444C211yesmaximal, characteristic, complemented
5#13067287C211yesmaximal, characteristic, complemented
6#13067283C211yesmaximal, characteristic, complemented
7C11×#1276C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C2×#66928—22no—
10C2×#66927C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C43×C11C2211yescharacteristic
15#10622552—22no—
16#10622552—22no—
17C2×#66869—22no—
18#10622537C2211yescharacteristic
19#10622459—22no—
20#10622456—22no—
21#10622349—22no—
22#10622345—22no—
23#10622308—21no—
24#10622307—21no—
25#10622307—21no—
26#10622295—21no—
27#10622124—22no—
28#10622123—22no—
29C2×#4339—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44D412yes—
33C22×Dic22—21no—
34C2×C42×C11—21no—
35C2×C42×C11—21no—
36C2×C42×C11D412yes—
37C2×C42×C11C2311yescharacteristic
38#66983—21no—
39#66983—21no—
40C2×(C2×D11)⋊C4—28no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D412yes—
43C2×#4318—21no—
44C2×D88—24no—
45#66928—21no—
46#66928—44no—
47#66928—44no—
48#66927—21no—
49#66927—21no—
50#66927—21no—
51#66927—21no—
52#66927D411yescharacteristic
53C4×D44—21no—
54C4×D44—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922D411yescharacteristic
60C11×C4⋊C8D412yes—
61C11×C4⋊C8D412yes—
62C11×C22⋊C8—21no—
63C11×C22⋊C8—21no—
64C4×C8×C11—21no—
65C4×C8×C11—21no—
66#66885—24no—
67#66885—24no—
68#66882—24no—
69#66869—44no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72#10284—111nomaximal, Sylow
73C23×D11—22no—
74C22×C4×C11—22no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C2×C22⋊D11—41no—
79C22×Dic11—22no—
80#4339—42no—
81#4339—42no—
82C2×D44—21no—
83C2×D44—22no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—22no—
87C2×D44—44no—
88C2×D44—44no—
89C2×D44—41no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—42no—
94C2×D44—42no—
95C2×C4×D11—41no—
96C2×Dic22—21no—
97C2×Dic22—41no—
98C2×Dic22—41no—
99C2×Dic22—42no—
100C2×Dic22—42no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C42×C11—22no—
104C42×C11—42no—
105C42×C11—42no—
106C42×C11D814yescomplemented
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111(C2×D11)⋊C4—416no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114C4⋊Dic11—21no—
115C4⋊Dic11—22no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120#4318—42no—
121C2×C11⋊C8—41no—
122D88—84no—
123#3226—111no—
124#3205—111no—
125#2858—111no—
126#1962—111no—
127#1546—111no—
128#1545—111no—
129#1276D1111yescharacteristic, complemented
130C23×C11#12011yescharacteristic
131C22×D11—44no—
132C22×D11—44no—
133C22×D11—41no—
134C22×D11—42no—
135C22×D11—44no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—24no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12711yescharacteristic
147C2×C4×C11C2×D812yes—
148C2×C4×C11AGL(1,ℤ/8)12yes—
149C22⋊D11—82no—
150C2×Dic11—42no—
151C2×Dic11—41no—
152C2×Dic11—44no—
153D44—42no—
154D44—42no—
155D44—44no—
156D44—42no—
157D44—82no—
158D44—82no—
159D44—82no—
160D44—82no—
161D44—81no—
162D44—81no—
163C4×D11—81no—
164C4×D11—81no—
165Dic22—42no—
166Dic22—82no—
167Dic22—81no—
168Dic22—81no—
169C8×C11—42no—
170C8×C11—42no—
171C11⋊C8—81no—
172#532—111no—
173C2×C4⋊Q8—111no—
174C2×#127—111no—
175C2×#124—222no—
176#500—221no—
177#493—221no—
178#486—221no—
179#486—221no—
180#480—222no—
181#474—222no—
182#459—222no—
183#447—222no—
184#431C2×D1111yescharacteristic
185#431C2×D1111yescharacteristic
186#423—111no—
187C2×#104—222no—
188#390—222no—
189#390—222no—
190C43C2×D1111yescharacteristic
191#332—222no—
192#331—222no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11#39211yescharacteristic
196C22×C11#44712yes—
197C2×D11—88no—
198C2×D11—82no—
199C2×D11—81no—
200C2×D11—82no—
201C2×D11—81no—
202C2×D11—82no—
203C2×D11—81no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—44no—
207C4×C11#45412yes—
208C4×C11#45512yes—
209C4×C11#45912yes—
210C4×C11#49311yescharacteristic
211C4×C11#49611yescharacteristic
212Dic11—81no—
213Dic11—82no—
214C2×#41—221no—
215C22×Q8—221no—
216C22×D4—112no—
217C22×D4—221no—
218C22×D4—221no—
219C2×D8—224no—
220C2×M16—221no—
221C4⋊Q8—111no—
222C4⋊Q8—221no—
223C4⋊Q8—221no—
224C4⋊Q8—221no—
225C4⋊Q8—221no—
226#127—111no—
227#127—221no—
228#127—221no—
229#127—221no—
230#127—221no—
231#124—221no—
232#124—444no—
233#124—444no—
234#121—221no—
235#121—221no—
236C4×D4—221no—
237C4×D4—221no—
238C2×C4⋊C4—112no—
239C2×C4⋊C4—221no—
240C2×C22⋊C4—228no—
241C2×C42—21no—
242C2×C42—21no—
243C2×C42D4412yes—
244C2×C42C22×D1111yescharacteristic
245#107—224no—
246C4⋊C8—221no—
247C4⋊C8—221no—
248C4⋊C8D4412yes—
249C4⋊C8D4412yes—
250#104—444no—
251#102—224no—
252#102—224no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255C4×C8—21no—
256C4×C8—21no—
257C2×C11—22no—
258C2×C11#200311yescharacteristic
259C2×C11#200411yescharacteristic
260C2×C11#201111yescharacteristic
261D11—161no—
262D11—162no—
263C24—222no—
264#41—442no—
265#41—442no—
266C2×Q8—221no—
267C2×Q8—441no—
268C2×Q8—441no—
269C2×Q8—442no—
270C2×Q8—442no—
271C2×D4—221no—
272C2×D4—222no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—222no—
276C2×D4—444no—
277C2×D4—444no—
278C2×D4—441no—
279C2×D4—441no—
280C2×D4—441no—
281C2×D4—441no—
282C2×D4—441no—
283C2×D4—442no—
284C2×D4—442no—
285C22×C4—22no—
286C22×C4—222no—
287C22×C4—441no—
288C22×C4C2×D4411yescharacteristic
289C22×C4D4×D1111yescharacteristic
290C22×C4D4×D1111yescharacteristic
291D8—884no—
292M16—442no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—441no—
296C4⋊C4—221no—
297C4⋊C4—222no—
298C4⋊C4—221no—
299C4⋊C4—222no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C22⋊C4—4416no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C42—22no—
306C42—42no—
307C42—42no—
308C42D8814yescomplemented
309C42C2×D4411yescharacteristic
310C42C2×D4411yescharacteristic
311C42D4×D1111yescharacteristic
312C42#434311yescharacteristic
313C11#1028411yescharacteristic, complemented, Sylow
314C23—444no—
315C23—444no—
316C23—441no—
317C23—442no—
318C23—444no—
319C23#6693511yescharacteristic
320Q8—442no—
321Q8—881no—
322Q8—881no—
323Q8—882no—
324D4—442no—
325D4—444no—
326D4—442no—
327D4—442no—
328D4—882no—
329D4—882no—
330D4—882no—
331D4—881no—
332D4—881no—
333D4—882no—
334D4—882no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—441no—
341C2×C4—442no—
342C2×C4—444no—
343C2×C4—881no—
344C2×C4—881no—
345C2×C4#6692711yescharacteristic
346C2×C4#6693511yescharacteristic
347C2×C4#6693511yescharacteristic
348C2×C4#6694811yescharacteristic
349C2×C4#6694811yescharacteristic
350C2×C4#6694811yescharacteristic
351C2×C4C2×D8812yes—
352C2×C4#6696112yes—
353C8—42no—
354C8—42no—
355C8—881no—
356C22—21no—
357C22—21no—
358C22—888no—
359C22—881no—
360C22—882no—
361C22—882no—
362C22—881no—
363C22—881no—
364C22—882no—
365C22#1062228411yescharacteristic
366C22#1062234512yes—
367C4—21no—
368C4—21no—
369C4—44no—
370C4—882no—
371C4—881no—
372C4#1062230811yescharacteristic
373C4#1062232511yescharacteristic
374C4#1062243812yes—
375C4#1062244012yes—
376C4#1062245612yes—
377C2—22no—
378C2—1762no—
379C2—1761no—
380C2#1306964111yescharacteristic
381C2#1306964811yescharacteristic
382C2#1306968911yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1276C2
socleC22×C11#392
prime radical#13079536C2
hypercenter#1276D11
hypocenterC11#10284
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
1. #13079739C2semidirect
3. #13076973C2semidirect
4. #13069444C2semidirect
5. #13067287C2semidirect
6. #13067283C2semidirect
7. C11×#1276C2semidirect
106. C42×C11D8semidirect
129. #1276D11semidirect
308. C42D88semidirect
313. C11#10284semidirect

Maximal subgroups

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

subgroupindex
#130797392
#130795362
#130769732
#130694442
#130672872
#130672832
C11×#12762
#1028411