Finite Group Databasebeta

← #14650477

Subgroups — #14650477

Order 2816.

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

normal subgroups only

This group has 470 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#13079760C211yesmaximal, characteristic
2#13071336C211yesmaximal, characteristic
3#13069596C211yesmaximal, characteristic
4#13067181C211yesmaximal, characteristic
5#13066476C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic
7C11×#1546C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×Q8×Dic11—21no—
10#10623001C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622843—21no—
14#10622707—22no—
15#10622706C412yescomplemented
16#10622692C412yescomplemented
17#10622594—22no—
18#10622594—22no—
19#10622584—22no—
20#10622549C2211yescharacteristic
21#10622545C2211yescharacteristic
22#10622538C2211yescharacteristic
23C11×#332—22no—
24#10622193—21no—
25#10622193—21no—
26#10622105—22no—
27C22×Q8×C11—21no—
28C2×C11×M16—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8C2×C412yes—
32C11×C4⋊Q8D412yes—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D412yes—
35C2×C42×C11C2311yescharacteristic
36Q8×Dic11—42no—
37Q8×Dic11—42no—
38#66979—21no—
39C2×C4⋊Dic11—22no—
40C2×C4⋊Dic11—21no—
41#66977—21no—
42#66977—21no—
43C2×C4×Dic11—22no—
44C2×C4×Dic11D411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46#66923—21no—
47#66922C2×C411yescharacteristic
48#66922C2×C411yescharacteristic
49C4×Dic22—21no—
50C4×Dic22—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C22⋊C8—21no—
55C4×C8×C11—21no—
56C11⋊#95—24no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95D412yes—
61C22⋊(C11⋊C8)—21no—
62#66874—24no—
63#66872—24no—
64C4⋊(C11⋊C8)—21no—
65C4×C11⋊C8C2×C412yes—
66#9296—111nomaximal, Sylow
67C2×Q8×C11—22no—
68C2×Q8×C11—22no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C22×C4×C11—22no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—22no—
80C2×Dic22—21no—
81C2×Dic22—21no—
82C11×M16—41no—
83C11×M16—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4C22⋊C414yes—
90C42×C11C22×C411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11#4111yescharacteristic
93C42×C11#4111yescharacteristic
94C22⋊Dic11—41no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—44no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102Dic11⋊C4—41no—
103Dic11⋊C4—41no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—44no—
108C4×Dic11—41no—
109C4×Dic11SD1612yes—
110C2×C11⋊C8—22no—
111#3229—111no—
112#2327—111no—
113#1995—111no—
114#1546D1111yescharacteristic
115#1518—111no—
116#1286—111no—
117#1274—111no—
118C23×C11#12011yescharacteristic
119Q8×C11—42no—
120Q8×C11—42no—
121Q8×C11—42no—
122Q8×C11—42no—
123C2×C4×C11—24no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11C2×C22⋊C411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12311yescharacteristic
134C2×C4×C11C2×SD1611yescharacteristic
135C2×C4×C11#13511yescharacteristic
136C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C2×Dic11—22no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—42no—
143C2×Dic11—41no—
144C2×Dic11—42no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—42no—
148C2×Dic11—41no—
149Dic22—42no—
150Dic22—81no—
151C8×C11—81no—
152C8×C11—81no—
153C11⋊C8—42no—
154#533—111no—
155C2×C4⋊Q8C2×D1111yescharacteristic
156C2×C4×Q8—221no—
157#498—112no—
158#487—112no—
159#483—222no—
160#475—222no—
161#431—111no—
162#431C2×D1111yescharacteristic
163#423C2×D1111yescharacteristic
164#391—221no—
165#387—222no—
166#387—222no—
167#382—111no—
168#376—111no—
169#339—221no—
170#339—221no—
171#332—22no—
172#328—222no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11#38611yescharacteristic
176C22×C11#45011yescharacteristic
177C22×C11#45211yescharacteristic
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—44no—
183C4×C11C4×SD1611yescharacteristic
184C4×C11#44011yescharacteristic
185C4×C11#46111yescharacteristic
186C4×C11#46311yescharacteristic
187Dic11—42no—
188Dic11—82no—
189Dic11—81no—
190Dic11—81no—
191Dic11—81no—
192C22×Q8—21no—
193C2×M16—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—111no—
197C4⋊Q8—111no—
198C4⋊Q8C4×D1112yes—
199C4⋊Q8C22⋊D1112yes—
200#125—221no—
201C22⋊Q8—221no—
202C22⋊Q8—221no—
203C4×Q8—221no—
204C4×Q8—221no—
205C4×Q8—442no—
206C4×Q8—442no—
207#117—221no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—222no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4D4412yes—
212C2×C42—111no—
213C2×C42—111no—
214C2×C42—222no—
215C2×C42C22×D1111yescharacteristic
216#106—224no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—221no—
221#103—224no—
222C22⋊C8—21no—
223C22⋊C8—221no—
224C4×C8—21no—
225C4×C8—112no—
226#95—112no—
227#95—224no—
228#95—221no—
229#95—221no—
230#95—221no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#187711yescharacteristic
234C2×C11#190511yescharacteristic
235C2×C11#191211yescharacteristic
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—221no—
243C2×Q8—221no—
244C22×C4—22no—
245C22×C4—221no—
246C22×C4—222no—
247C22×C4—221no—
248C22×C4C2×D4411yescharacteristic
249C22×C4D4×D1111yescharacteristic
250C22×C4D4×D1111yescharacteristic
251M16—41no—
252M16—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—222no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—444no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C4⋊C4(C2×D11)⋊C414yes—
269C22⋊C4—441no—
270C42—112no—
271C42—221no—
272C42—221no—
273C42—221no—
274C42—444no—
275C42—441no—
276C42C2×C4×D1111yescharacteristic
277C42#434111yescharacteristic
278C42#434111yescharacteristic
279C42C2×C22⋊D1111yescharacteristic
280C11#929611yescharacteristic, complemented, Sylow
281C23#6693511yescharacteristic
282Q8—42no—
283Q8—42no—
284Q8—42no—
285Q8—42no—
286Q8—442no—
287Q8—881no—
288C2×C4—24no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—222no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—442no—
297C2×C4—441no—
298C2×C4—442no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—442no—
303C2×C4—441no—
304C2×C4(C22⋊D11)⋊C411yescharacteristic
305C2×C4(C22⋊D11)⋊C411yescharacteristic
306C2×C4#6693911yescharacteristic
307C2×C4#6696411yescharacteristic
308C2×C4#6696511yescharacteristic
309C2×C4SD16×D1111yescharacteristic
310C2×C4#6696811yescharacteristic
311C2×C4C2×(C2×D11)⋊C411yescharacteristic
312C2×C4#6699211yescharacteristic
313C2×C4#6699211yescharacteristic
314C8—81no—
315C8—81no—
316C8—442no—
317C22—21no—
318C22—21no—
319C22#1062238911yescharacteristic
320C22#1062239611yescharacteristic
321C22#1062257111yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—44no—
327C4—442no—
328C4—882no—
329C4—881no—
330C4—881no—
331C4—881no—
332C4#1062237011yescharacteristic
333C4#1062237111yescharacteristic
334C4#1062276611yescharacteristic
335C4#1062277511yescharacteristic
336C2—21no—
337C2—21no—
338C2#1306894811yescharacteristic
339C2#1306910811yescharacteristic
340C2#1306915111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1546C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1546D11
hypocenterC11#9296
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
15. #10622706C4semidirect
16. #10622692C4semidirect
280. C11#9296semidirect

Maximal subgroups

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

subgroupindex
#130797602
#130713362
#130695962
#130671812
#130664762
#130664442
C11×#15462
#929611