Finite Group Databasebeta

← #14649678

Subgroups — #14649678

Order 2816.

566 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078413C211yesmaximal, characteristic
2#13071526C211yesmaximal, characteristic
3#13067181C211yesmaximal, characteristic, complemented
4#13067116C211yesmaximal, characteristic, complemented
5#13066518C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#1478C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C2×D4×Dic11—21no—
10#10623001C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#431C2211yescharacteristic
13#10622828—21no—
14#10622825—21no—
15C2×C11⋊#95—21no—
16#10622622—22no—
17#10622621C412yescomplemented
18#10622620C412yescomplemented
19#10622598—21no—
20#10622577—21no—
21#10622563—22no—
22#10622549C2211yescharacteristic
23C4×C4⋊Dic11C2211yescharacteristic
24#10622537C2211yescharacteristic
25C11×D4⋊C8—22no—
26#10622105—21no—
27#10622105—21no—
28#10622105—22no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C23×Dic11—22no—
32C4×D4×C11—21no—
33C4×D4×C11—21no—
34C4×D4×C11C2×C412yes—
35C4×D4×C11D412yes—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C42×C11C2311yescharacteristic
39C2×C22⋊Dic11—22no—
40D4×Dic11—42no—
41D4×Dic11—42no—
42#66979—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—22no—
46#66977—21no—
47#66977—21no—
48C2×C4×Dic11—21no—
49C2×#4318—21no—
50#66923—21no—
51#66922C2×C411yescharacteristic, complemented
52#66922C2×C411yescharacteristic, complemented
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60C4×C8×C11—21no—
61#66896—22no—
62#66896—22no—
63C11⋊#95—22no—
64C11⋊#95—21no—
65C11⋊#95D411yescharacteristic
66C11⋊#95D411yescharacteristic
67C11⋊#95D412yes—
68#66872—22no—
69#66871—22no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)C2×C412yescomplemented
72#9175—111nomaximal, Sylow
73C24×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11C22⋊C412yes—
78C2×D4×C11SD1612yes—
79C2×D4×C11Q1612yes—
80C22×C4×C11—21no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—82no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×Dic11—21no—
88C22×Dic11—22no—
89C22×Dic11—21no—
90C22×Dic11—44no—
91C22×Dic11—44no—
92C22×Dic11—82no—
93C2×Dic22—21no—
94C2×Dic22—21no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4C22⋊C412yes—
99C11×C22⋊C4—22no—
100C11×C22⋊C4—22no—
101C42×C11C22×C411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11#4111yescharacteristic
104C42×C11#4111yescharacteristic
105C22⋊Dic11—44no—
106C22⋊Dic11—41no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—42no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—82no—
115Dic11⋊C4—41no—
116Dic11⋊C4—41no—
117C4×Dic11—41no—
118C4×Dic11—41no—
119C4×Dic11—41no—
120#4318—41no—
121#4318—41no—
122C2×C11⋊C8—22no—
123#3077—111no—
124#2349—111no—
125#1518—111no—
126#1503—111no—
127#1478D1111yescharacteristic
128#1303—111no—
129#1286—111no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—22no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11#12011yescharacteristic
136D4×C11—22no—
137D4×C11—22no—
138D4×C11—22no—
139D4×C11#10314yes—
140C2×C4×C11—22no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—82no—
145C2×C4×C11—82no—
146C2×C4×C11C2×C22⋊C411yescharacteristic
147C2×C4×C11C4×D411yescharacteristic
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12311yescharacteristic
152C2×C4×C11C2×SD1611yescharacteristic
153C2×C4×C11C2×Q1611yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C2×Dic11—22no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—42no—
167C2×Dic11—88no—
168Dic22—81no—
169Dic22—81no—
170C8×C11—81no—
171C8×C11—81no—
172C11⋊C8—42no—
173#533—111no—
174C2×C4×D4—221no—
175C2×C4×D4C2×D1111yescharacteristic
176#478—222no—
177#476—112no—
178#474—112no—
179#431C2×D1111yescharacteristic
180#431C2×D1111yescharacteristic
181#428—221no—
182#423—111no—
183#418—221no—
184#389—221no—
185#385—222no—
186#382—111no—
187#380—221no—
188C4×C4⋊C4—111no—
189C2×#95—221no—
190#328—221no—
191#328—221no—
192#328—222no—
193D4⋊C8—22no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—24no—
197C22×C11—44no—
198C22×C11—44no—
199C22×C11—42no—
200C22×C11—42no—
201C22×C11#38611yescharacteristic
202C22×C11#45011yescharacteristic
203C22×C11#45111yescharacteristic
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—42no—
209C4×C11C2×#10311yescharacteristic
210C4×C11#41711yescharacteristic
211C4×C11#48311yescharacteristic
212C4×C11#48411yescharacteristic
213Dic11—42no—
214Dic11—81no—
215Dic11—82no—
216Dic11—81no—
217Dic11—81no—
218C22×D4D4411yescharacteristic
219C23×C4—21no—
220C23×C4—222no—
221C2×M16—221no—
222C4⋊Q8—111no—
223C4⋊Q8—111no—
224#125—221no—
225C22⋊Q8—221no—
226C22⋊Q8—221no—
227C4×Q8—221no—
228C4×Q8—221no—
229C4×D4—21no—
230C4×D4—21no—
231C4×D4—442no—
232C4×D4—442no—
233C4×D4C4×D1112yes—
234C4×D4C22⋊D1112yes—
235#117—221no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C4⋊C4—222no—
239C2×C4⋊C4D4411yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—222no—
242C2×C42—221no—
243C2×C42C22×D1111yescharacteristic
244#107—222no—
245#106—222no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—112no—
249C4⋊C8—221no—
250#102—222no—
251#102—222no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C4×C8—21no—
255C4×C8—21no—
256#95—111no—
257#95—111no—
258#95—112no—
259#95—222no—
260#95—221no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—44no—
264C2×C11#187211yescharacteristic
265C2×C11#190411yescharacteristic
266C2×C11#190611yescharacteristic
267C24—21no—
268C2×Q8—221no—
269C2×Q8—221no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4#431412yes—
274C2×D4Dic4412yes—
275C2×D4(C2×D11)⋊C412yes—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—82no—
280C22×C4—221no—
281C22×C4—222no—
282C22×C4—221no—
283C22×C4—444no—
284C22×C4—444no—
285C22×C4—882no—
286C22×C4C2×D4411yescharacteristic
287C22×C4D4×D1111yescharacteristic
288C22×C4D4×D1111yescharacteristic
289M16—441no—
290M16—441no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—222no—
294C4⋊C4—21no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—442no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C4⋊C4—882no—
305C4⋊C4(C2×D11)⋊C412yes—
306C22⋊C4—22no—
307C22⋊C4—22no—
308C22⋊C4—444no—
309C22⋊C4—441no—
310C42—441no—
311C42—441no—
312C42—441no—
313C42C2×C4×D1111yescharacteristic
314C42#434111yescharacteristic
315C42#434111yescharacteristic
316C42C2×C22⋊D1111yescharacteristic
317C11#917511yescharacteristic, complemented, Sylow
318C23—22no—
319C23—22no—
320C23—22no—
321C23—42no—
322C23—42no—
323C23#6693511yescharacteristic
324Q8—881no—
325Q8—881no—
326D4—22no—
327D4—22no—
328D4—22no—
329D4#6688014yes—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—222no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—442no—
347C2×C4—888no—
348C2×C4(C22⋊D11)⋊C411yescharacteristic
349C2×C4(C22⋊D11)⋊C411yescharacteristic
350C2×C4#6693911yescharacteristic
351C2×C4C2×#431411yescharacteristic
352C2×C4C2×Dic4411yescharacteristic
353C2×C4#6696111yescharacteristic
354C2×C4#6696211yescharacteristic
355C2×C4C2×(C2×D11)⋊C411yescharacteristic
356C2×C4#6699211yescharacteristic
357C2×C4#6699211yescharacteristic
358C8—81no—
359C8—81no—
360C8—442no—
361C22—21no—
362C22—21no—
363C22—24no—
364C22—44no—
365C22—44no—
366C22—42no—
367C22—42no—
368C22#1062234411yescharacteristic
369C22#1062235211yescharacteristic
370C22#1062257111yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—442no—
377C4—882no—
378C4—881no—
379C4—881no—
380C4—881no—
381C4#1062233411yescharacteristic
382C4#1062233511yescharacteristic
383C4C2×#6688011yescharacteristic
384C4#1062274611yescharacteristic
385C2—21no—
386C2—21no—
387C2—44no—
388C2#1306892111yescharacteristic
389C2#1306910111yescharacteristic
390C2#1306911511yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1478C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#1478D11
hypocenterC11#9175
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
3. #13067181C2semidirect
4. #13067116C2semidirect
5. #13066518C2semidirect
6. #13066475C2semidirect
17. #10622621C4semidirect
18. #10622620C4semidirect
51. #66922C2×C4semidirect
52. #66922C2×C4semidirect
71. C4⋊(C11⋊C8)C2×C4semidirect
317. C11#9175semidirect

Maximal subgroups

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

subgroupindex
#130784132
#130715262
#130671812
#130671162
#130665182
#130664752
C11×#14782
#917511