Finite Group Databasebeta

← #14650507

Subgroups — #14650507

Order 2816.

508 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079737C211yesmaximal, characteristic
2#13069448C211yesmaximal, characteristic
3#13067288C211yesmaximal, characteristic, complemented
4#13067175C211yesmaximal, characteristic
5#13066474C211yesmaximal, characteristic, complemented
6#13066445C211yesmaximal, characteristic, complemented
7C11×#2327C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8×C11—21no—
10#10623008C2211yescharacteristic
11C11×#391—21no—
12C11×#387—22no—
13C11×#387—22no—
14C11×#382C2211yescharacteristic
15C11×#376C2211yescharacteristic
16#10622701C412yescomplemented
17#10622700—22no—
18#10622691C412yescomplemented
19#10622580—22no—
20C2×#66869—21no—
21C2×#66869—21no—
22#10622538C2211yescharacteristic
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25#10622185—22no—
26#10622089—22no—
27C22×Q8×C11—21no—
28C2×#4339—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8C2×C412yes—
32C11×C4⋊Q8D412yes—
33C4×Q8×C11—42no—
34C4×Q8×C11—42no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4D412yes—
39C2×C42×C11—22no—
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11C2311yescharacteristic
43#66983—21no—
44#66983—21no—
45C2×#4318—21no—
46#66928—21no—
47#66927C2×C411yescharacteristic
48C4×D44—21no—
49C4×D44—21no—
50#66922C2×C411yescharacteristic
51C11×#95—24no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95D412yes—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)—21no—
58#66873—24no—
59#66871—24no—
60#66869—42no—
61#66869—42no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8C2×C412yes—
68#9300—111nomaximal, Sylow
69C2×Q8×C11—22no—
70C2×Q8×C11—22no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C22×C4×C11—21no—
76C22×C4×C11—22no—
77C22×C4×C11—21no—
78C22×C4×C11—22no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C2×C22⋊D11—41no—
83#4339—41no—
84#4339—41no—
85#4339—41no—
86#4339—41no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×C4×D11—41no—
91C2×Dic22—21no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—44no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4C22⋊C414yes—
99C42×C11—21no—
100C42×C11—21no—
101C42×C11—21no—
102C42×C11—44no—
103C42×C11D812yes—
104C42×C11C22×C411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11#4111yescharacteristic
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112#4318—41no—
113#4318—41no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117#3226—111no—
118#2327D1111yescharacteristic, complemented
119#1963—111no—
120#1546—111no—
121#1517—111no—
122#1286—111no—
123#1274—111no—
124C23×C11#12011yescharacteristic
125C22×D11—41no—
126Q8×C11—42no—
127Q8×C11—42no—
128Q8×C11—42no—
129Q8×C11—42no—
130C2×C4×C11—24no—
131C2×C4×C11—22no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—41no—
144C2×C4×C11C2×C22⋊C411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12311yescharacteristic
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11#13511yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C22⋊D11—81no—
155C22⋊D11—81no—
156C2×Dic11—41no—
157D44—42no—
158D44—41no—
159D44—41no—
160D44—81no—
161C4×D11—81no—
162C4×D11—81no—
163Dic22—41no—
164Dic22—41no—
165C11⋊C8—42no—
166C11⋊C8—81no—
167C11⋊C8—81no—
168#532—111no—
169C2×C4⋊Q8C2×D1111yescharacteristic
170C2×C4×Q8—21no—
171#500—112no—
172#486—112no—
173#480—222no—
174#474—222no—
175#431—111no—
176#431—111no—
177#423—111no—
178C2×#104—221no—
179C2×#104—221no—
180#391—21no—
181#387—22no—
182#387—22no—
183#382C2×D1111yescharacteristic
184#376C2×D1111yescharacteristic
185#332—222no—
186#327—222no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11#38611yescharacteristic
190C22×C11#44711yescharacteristic
191C22×C11#44911yescharacteristic
192C2×D11—81no—
193C2×D11—81no—
194C2×D11—81no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—42no—
200C4×C11—44no—
201C4×C11—82no—
202C4×C11—81no—
203C4×C11C4×D811yescharacteristic
204C4×C11#44211yescharacteristic
205C4×C11#45911yescharacteristic
206C4×C11#46311yescharacteristic
207Dic11—81no—
208C2×#41—221no—
209C22×Q8—21no—
210C2×M16—221no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—111no—
214C4⋊Q8C4×D1112yes—
215C4⋊Q8D4412yes—
216#127—111no—
217#124—221no—
218#121—221no—
219#121—221no—
220C4×Q8—42no—
221C4×Q8—42no—
222C4×D4—221no—
223C4×D4—221no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4C22⋊D1112yes—
228C2×C42—22no—
229C2×C42C22⋊D1111yescharacteristic
230C2×C42C22⋊D1111yescharacteristic
231C2×C42C22×D1111yescharacteristic
232#107—224no—
233C4⋊C8—221no—
234C4⋊C8—221no—
235C4⋊C8—221no—
236C4⋊C8—221no—
237#104—442no—
238#104—442no—
239#102—224no—
240C22⋊C8—221no—
241C22⋊C8—221no—
242C4×C8—112no—
243C4×C8—221no—
244#95—24no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95C22⋊D1112yes—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11#187911yescharacteristic
252C2×C11#190511yescharacteristic
253C2×C11#191211yescharacteristic
254D11—161no—
255#41—441no—
256#41—441no—
257#41—441no—
258#41—441no—
259C2×Q8—22no—
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—221no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—441no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—441no—
275C22×C4C2×C22⋊D1111yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278M16—441no—
279M16—441no—
280C2×C8—222no—
281C2×C8—441no—
282C2×C8—441no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—44no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4(C2×D11)⋊C414yes—
292C22⋊C4—441no—
293C22⋊C4—441no—
294C42—21no—
295C42—21no—
296C42—21no—
297C42—44no—
298C42#432312yes—
299C42C2×C4×D1111yescharacteristic
300C42C2×D4411yescharacteristic
301C42#433911yescharacteristic
302C42#433911yescharacteristic
303C11#930011yescharacteristic, complemented, Sylow
304C23—441no—
305C23#6700611yescharacteristic
306Q8—42no—
307Q8—42no—
308Q8—42no—
309Q8—42no—
310Q8—441no—
311Q8—441no—
312D4—442no—
313D4—441no—
314D4—441no—
315D4—881no—
316D4—881no—
317D4—881no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—441no—
333C2×C4—881no—
334C2×C4—881no—
335C2×C4C2×(C2×D11)⋊C411yescharacteristic
336C2×C4C4×C22⋊D1111yescharacteristic
337C2×C4C4×C22⋊D1111yescharacteristic
338C2×C4#6698211yescharacteristic
339C2×C4#6698311yescharacteristic
340C2×C4#6698311yescharacteristic
341C2×C4C2×#432311yescharacteristic
342C2×C4#6698511yescharacteristic
343C2×C4#6700211yescharacteristic
344C2×C4#6700311yescharacteristic
345C8—442no—
346C8—881no—
347C8—881no—
348C22—21no—
349C22—21no—
350C22—881no—
351C22—881no—
352C22—881no—
353C22#1062282611yescharacteristic
354C22#1062283011yescharacteristic
355C22#1062285111yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—42no—
361C4—44no—
362C4—82no—
363C4—81no—
364C4—881no—
365C4C4×#432311yescharacteristic
366C4#1062262711yescharacteristic
367C4#1062262811yescharacteristic
368C4#1062262911yescharacteristic
369C2—21no—
370C2—21no—
371C2—1761no—
372C2#1306896411yescharacteristic
373C2#1306911011yescharacteristic
374C2#1306915311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2327C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#2327D11
hypocenterC11#9300
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2327

Complements

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

NH ≅ G/Ntype
3. #13067288C2semidirect
5. #13066474C2semidirect
6. #13066445C2semidirect
7. C11×#2327C2semidirect
16. #10622701C4semidirect
18. #10622691C4semidirect
118. #2327D11semidirect
303. C11#9300semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130694482
#130672882
#130671752
#130664742
#130664452
C11×#23272
#930011