Finite Group Databasebeta

← #14649685

Subgroups — #14649685

Order 2816.

490 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078421C211yesmaximal, characteristic
2#13071537C211yesmaximal, characteristic
3#13067181C211yesmaximal, characteristic
4#13067116C211yesmaximal, characteristic
5#13066518C211yesmaximal, characteristic
6#13066475C211yesmaximal, characteristic
7C11×#1479C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×Q8×Dic11—21no—
10#10623001C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#431C2211yescharacteristic
13#10622838—21no—
14#10622635—22no—
15#10622634C412yescomplemented
16#10622633C412yescomplemented
17#10622598—21no—
18#10622598—22no—
19#10622577—21no—
20#10622549—21no—
21#10622549C2211yescharacteristic
22C4×C4⋊Dic11—21no—
23C4×C4⋊Dic11C2211yescharacteristic
24#10622537C2211yescharacteristic
25C11×Q8⋊C8—22no—
26#10622105—21no—
27#10622105—21no—
28#10622105—22no—
29C22×Q8×C11D411yescharacteristic
30C4×Q8×C11—21no—
31C4×Q8×C11—21no—
32C4×Q8×C11C2×C412yes—
33C4×Q8×C11D412yes—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C42×C11—21no—
37C2×C42×C11C2311yescharacteristic
38Q8×Dic11—42no—
39Q8×Dic11—42no—
40#66979—21no—
41C2×C4⋊Dic11—22no—
42C2×C4⋊Dic11—22no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45#66977—21no—
46#66977—21no—
47C2×C4×Dic11—22no—
48C2×C4×Dic11—21no—
49C2×#4318—21no—
50#66923—21no—
51#66922C2×C411yescharacteristic
52#66922C2×C411yescharacteristic
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#66899—22no—
62#66899—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×C412yes—
72#9176—111nomaximal, Sylow
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11—21no—
76C2×Q8×C11C22⋊C412yes—
77C2×Q8×C11SD1612yes—
78C2×Q8×C11Q1612yes—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—22no—
87C2×Dic22—21no—
88C2×Dic22—21no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4C22⋊C412yes—
95C42×C11—22no—
96C42×C11—22no—
97C42×C11C22×C411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101C22⋊Dic11—41no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—44no—
107C4⋊Dic11—42no—
108C4⋊Dic11—44no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111Dic11⋊C4—41no—
112Dic11⋊C4—41no—
113C4×Dic11—44no—
114C4×Dic11—41no—
115C4×Dic11—41no—
116C4×Dic11—41no—
117#4318—41no—
118#4318—41no—
119C2×C11⋊C8—22no—
120#3078—111no—
121#2351—111no—
122#1518—111no—
123#1503—111no—
124#1479D1111yescharacteristic
125#1303—111no—
126#1286—111no—
127C23×C11#12011yescharacteristic
128Q8×C11—22no—
129Q8×C11—22no—
130Q8×C11—22no—
131Q8×C11#10314yes—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11C2×C22⋊C411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12311yescharacteristic
145C2×C4×C11C2×SD1611yescharacteristic
146C2×C4×C11C2×Q1611yescharacteristic
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C2×Dic11—22no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154C2×Dic11—41no—
155C2×Dic11—42no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—42no—
159C2×Dic11—41no—
160Dic22—81no—
161Dic22—81no—
162C8×C11—81no—
163C8×C11—81no—
164C11⋊C8—42no—
165#533—111no—
166C2×C4×Q8—221no—
167C2×C4×Q8C2×D1111yescharacteristic
168#479—222no—
169#477—112no—
170#475—112no—
171#431C2×D1111yescharacteristic
172#431C2×D1111yescharacteristic
173#428—221no—
174#423—111no—
175#419—221no—
176#389—222no—
177#389—221no—
178#382—111no—
179#382—221no—
180C4×C4⋊C4—111no—
181C4×C4⋊C4—221no—
182#328—221no—
183#328—221no—
184#328—222no—
185Q8⋊C8—22no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11#38611yescharacteristic
189C22×C11#45011yescharacteristic
190C22×C11#45111yescharacteristic
191C4×C11—24no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—42no—
197C4×C11C2×#10311yescharacteristic
198C4×C11#41711yescharacteristic
199C4×C11#48311yescharacteristic
200C4×C11#48411yescharacteristic
201Dic11—42no—
202Dic11—82no—
203Dic11—81no—
204Dic11—81no—
205Dic11—81no—
206C22×Q8D4411yescharacteristic
207C2×M16—221no—
208C4⋊Q8—111no—
209C4⋊Q8—111no—
210#125—221no—
211C22⋊Q8—221no—
212C22⋊Q8—221no—
213C4×Q8—21no—
214C4×Q8—21no—
215C4×Q8—221no—
216C4×Q8—221no—
217C4×Q8—442no—
218C4×Q8—442no—
219C4×Q8C4×D1112yes—
220C4×Q8C22⋊D1112yes—
221#117—221no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—222no—
224C2×C4⋊C4—222no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4D4411yescharacteristic
228C2×C42—21no—
229C2×C42—222no—
230C2×C42—221no—
231C2×C42C22×D1111yescharacteristic
232#107—222no—
233#106—222no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—112no—
237C4⋊C8—221no—
238#103—222no—
239#103—222no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C4×C8—21no—
243C4×C8—21no—
244#95—111no—
245#95—111no—
246#95—112no—
247#95—222no—
248#95—221no—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11#187211yescharacteristic
252C2×C11#190511yescharacteristic
253C2×C11#190611yescharacteristic
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—221no—
258C2×Q8—221no—
259C2×Q8#431412yes—
260C2×Q8Dic4412yes—
261C2×Q8(C2×D11)⋊C412yes—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—222no—
267C22×C4C2×D4411yescharacteristic
268C22×C4D4×D1111yescharacteristic
269C22×C4D4×D1111yescharacteristic
270M16—441no—
271M16—441no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—222no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—444no—
283C4⋊C4—442no—
284C4⋊C4—444no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4(C2×D11)⋊C412yes—
290C22⋊C4—441no—
291C42—22no—
292C42—22no—
293C42—444no—
294C42—441no—
295C42—441no—
296C42—441no—
297C42C2×C4×D1111yescharacteristic
298C42#434111yescharacteristic
299C42#434111yescharacteristic
300C42C2×C22⋊D1111yescharacteristic
301C11#917611yescharacteristic, complemented, Sylow
302C23#6693511yescharacteristic
303Q8—22no—
304Q8—22no—
305Q8—22no—
306Q8—881no—
307Q8—881no—
308Q8#6688014yes—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—222no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—442no—
321C2×C4—441no—
322C2×C4—442no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—442no—
326C2×C4—441no—
327C2×C4(C22⋊D11)⋊C411yescharacteristic
328C2×C4(C22⋊D11)⋊C411yescharacteristic
329C2×C4#6693911yescharacteristic
330C2×C4C2×#431411yescharacteristic
331C2×C4C2×Dic4411yescharacteristic
332C2×C4#6696111yescharacteristic
333C2×C4#6696211yescharacteristic
334C2×C4C2×(C2×D11)⋊C411yescharacteristic
335C2×C4#6699211yescharacteristic
336C2×C4#6699211yescharacteristic
337C8—81no—
338C8—81no—
339C8—442no—
340C22—21no—
341C22—21no—
342C22#1062234411yescharacteristic
343C22#1062235211yescharacteristic
344C22#1062257111yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—24no—
350C4—42no—
351C4—442no—
352C4—882no—
353C4—881no—
354C4—881no—
355C4—881no—
356C4#1062233411yescharacteristic
357C4#1062233511yescharacteristic
358C4C2×#6688011yescharacteristic
359C4#1062274611yescharacteristic
360C2—21no—
361C2—21no—
362C2#1306892111yescharacteristic
363C2#1306910811yescharacteristic
364C2#1306911511yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1479C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1479D11
hypocenterC11#9176
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
15. #10622634C4semidirect
16. #10622633C4semidirect
301. C11#9176semidirect

Maximal subgroups

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

subgroupindex
#130784212
#130715372
#130671812
#130671162
#130665182
#130664752
C11×#14792
#917611