Finite Group Databasebeta

← #14655617

Subgroups — #14655617

Order 2816.

578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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#13067297C211yesmaximal, characteristic, complemented
5#13067067C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C11×#3141C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66927C2211yescharacteristic
11C11×#489—22no—
12C11×#487—21no—
13C11×#486—21no—
14C11×#417—22no—
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#10622184—22no—
28D4⋊(C11⋊C8)—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×D44—21no—
32C22×D44—21no—
33C22×D44D412yes—
34C2×C11×M16D412yes—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D412yes—
39C11×C4⋊Q8D411yescharacteristic
40C11×#127D411yescharacteristic
41C11×#124—21no—
42C11×#121—21no—
43C11×#121—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4323—24no—
50C2×#4318—21no—
51C22×C11⋊C8—21no—
52#66927—21no—
53#66927—21no—
54#66927—21no—
55#66927—21no—
56C11×#103—24no—
57C11×#102—24no—
58C11×#97—21no—
59C4×C8×C11—21no—
60C22⋊(C11⋊C8)—21no—
61#66887—44no—
62#66873—28no—
63#66873—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)D412yes—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10160—111nomaximal, Sylow
71C23×D11—22no—
72C11×#41—42no—
73C11×#41—42no—
74C2×Q8×C11—21no—
75C2×Q8×C11—22no—
76C2×Q8×C11—41no—
77C2×Q8×C11—82no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C2×D44—22no—
88C2×D44—22no—
89C2×D44—44no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—42no—
95C2×D44—42no—
96C2×D44—82no—
97C11×M16—22no—
98C11×M16—22no—
99C2×C8×C11—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112#4323—84no—
113#4318—42no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—42no—
117C2×C11⋊C8—41no—
118#3205—111no—
119#3141D1111yescharacteristic, complemented
120C2×#486—111no—
121#1965—111no—
122#1548—111no—
123#1492—111no—
124#1278—111no—
125C23×C11—41no—
126C23×C11#12111yescharacteristic
127C22×D11—42no—
128C22×D11—44no—
129C22×D11—82no—
130C22×D11—82no—
131Q8×C11—42no—
132Q8×C11—82no—
133Q8×C11—82no—
134D4×C11—42no—
135D4×C11—42no—
136D4×C11—42no—
137D4×C11—82no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—82no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12711yescharacteristic
151C2×C4×C11#13512yes—
152C2×C4×C11AGL(1,ℤ/8)12yes—
153D44—44no—
154D44—44no—
155D44—82no—
156D44—82no—
157D44—82no—
158D44—81no—
159D44—81no—
160C8×C11—42no—
161C11⋊C8—42no—
162C11⋊C8—42no—
163C11⋊C8—81no—
164#532C2×D1111yescharacteristic
165C2×C4⋊Q8C2×D1111yescharacteristic
166C2×#127—111no—
167#493—221no—
168#489—22no—
169#487—21no—
170#486—21no—
171#486—222no—
172#486—222no—
173#486—221no—
174#459—222no—
175#447—222no—
176#431—111no—
177#423—111no—
178#417—22no—
179C2×#102—222no—
180C2×#100—222no—
181C4×M16C2×D1111yescharacteristic
182C2×C4×C8—111no—
183#333—222no—
184D4⋊C8—222no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11#39211yescharacteristic
191C22×C11#46312yes—
192C2×D11—82no—
193C2×D11—82no—
194C2×D11—82no—
195C2×D11—164no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—81no—
199C4×C11—82no—
200C4×C11#44912yes—
201C4×C11#45512yes—
202C4×C11#47212yes—
203C4×C11#49511yescharacteristic
204C4×C11#49611yescharacteristic
205C2×#41—21no—
206C22×Q8—21no—
207C22×D4—112no—
208C22×D4—221no—
209C22×D4—221no—
210C2×D8—224no—
211C2×M16—221no—
212C2×M16C22⋊D1112yes—
213C22×C8—221no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8C22⋊D1112yes—
218C4⋊Q8C22⋊D1111yescharacteristic
219#127—221no—
220#127—221no—
221#127—221no—
222#127—221no—
223#127C22⋊D1111yescharacteristic
224#124—21no—
225#121—21no—
226#121—21no—
227C4×D4—21no—
228C4×D4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C42C22×D1111yescharacteristic
232C4⋊C8—112no—
233C4⋊C8—221no—
234C4⋊C8—221no—
235#103—24no—
236#102—24no—
237#102—228no—
238#102—224no—
239#100—444no—
240C22⋊C8—221no—
241#97—21no—
242C4×C8—21no—
243C4×C8—112no—
244C4×C8—221no—
245C4×C8—221no—
246C2×C11—22no—
247C2×C11—161no—
248C2×C11#200411yescharacteristic
249C2×C11#201211yescharacteristic
250C2×C11#201811yescharacteristic
251D11—162no—
252C24—222no—
253#41—42no—
254#41—42no—
255C2×Q8—22no—
256C2×Q8—21no—
257C2×Q8—41no—
258C2×Q8—82no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—222no—
264C2×D4—222no—
265C2×D4—444no—
266C2×D4—441no—
267C2×D4—441no—
268C2×D4—441no—
269C2×D4—442no—
270C2×D4—442no—
271C2×D4—441no—
272C2×D4—882no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4D4×D1111yescharacteristic
276C22×C4#434111yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278D8—884no—
279M16—22no—
280M16—22no—
281M16—442no—
282C2×C8—22no—
283C2×C8—222no—
284C2×C8—222no—
285C2×C8—442no—
286C2×C8—441no—
287C4⋊C4—22no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—22no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C42D4×D1111yescharacteristic
296C42D4×D1111yescharacteristic
297C42C2×C22⋊D1111yescharacteristic
298C42C2×C22⋊D1111yescharacteristic
299C11#1016011yescharacteristic, complemented, Sylow
300C23—41no—
301C23—442no—
302C23—444no—
303C23—882no—
304C23—882no—
305C23#6699111yescharacteristic
306Q8—42no—
307Q8—82no—
308Q8—82no—
309D4—42no—
310D4—42no—
311D4—42no—
312D4—82no—
313D4—444no—
314D4—444no—
315D4—882no—
316D4—882no—
317D4—882no—
318D4—881no—
319D4—881no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—82no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4#6699011yescharacteristic
328C2×C4#6699011yescharacteristic
329C2×C4#6699211yescharacteristic
330C2×C4#6699211yescharacteristic
331C2×C4#6699311yescharacteristic
332C2×C4#6700212yes—
333C2×C4#6700312yes—
334C2×C4#6700611yescharacteristic
335C8—42no—
336C8—442no—
337C8—442no—
338C8—881no—
339C22—21no—
340C22—21no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—882no—
345C22—882no—
346C22—882no—
347C22—1764no—
348C22#1062267012yes—
349C22#1062283611yescharacteristic
350C4—21no—
351C4—21no—
352C4—81no—
353C4—82no—
354C4#1062267111yescharacteristic
355C4#1062267211yescharacteristic
356C4#1062281212yes—
357C4#1062281512yes—
358C4#1062285112yes—
359C2—22no—
360C2—161no—
361C2—1762no—
362C2#1306964211yescharacteristic
363C2#1306969311yescharacteristic
364C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3141C2
socleC22×C11#392
prime radical#13079531C2
hypercenter#3141D11
hypocenterC11#10160
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. C2×#10622701C2semidirect
3. #13069456C2semidirect
4. #13067297C2semidirect
5. #13067067C2semidirect
6. #13066454C2semidirect
7. C11×#3141C2semidirect
119. #3141D11semidirect
299. C11#10160semidirect

Maximal subgroups

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

subgroupindex
#130795312
C2×#106227012
#130694562
#130672972
#130670672
#130664542
C11×#31412
#1016011