Finite Group Databasebeta

← #14650478

Subgroups — #14650478

Order 2816.

470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079762C211yesmaximal, characteristic
2#13071335C211yesmaximal, characteristic
3#13069597C211yesmaximal, characteristic
4#13067287C211yesmaximal, characteristic
5#13067181C211yesmaximal, characteristic
6#13066475C211yesmaximal, characteristic
7C11×#1274C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×C4×Dic22—21no—
11C11×#431C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#376C2211yescharacteristic
14#10622549C2211yescharacteristic
15#10622542—21no—
16#10622537C2211yescharacteristic
17#10622464—22no—
18#10622334—22no—
19#10622294C412yescomplemented
20#10622293C412yescomplemented
21#10622266—22no—
22#10622266—22no—
23#10622161—21no—
24#10622161—21no—
25#10622124—22no—
26#10622105—22no—
27C22×Dic22—21no—
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11C2311yescharacteristic
31#66979—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11D412yes—
35#66977—21no—
36#66977—21no—
37C2×Dic11⋊C4—22no—
38C2×C4×Dic11—22no—
39C2×#4318—21no—
40#66923—21no—
41#66922—21no—
42#66922—21no—
43#66922C2×C411yescharacteristic
44#66922C2×C411yescharacteristic
45#66922C2×C412yes—
46#66922D412yes—
47C4×Dic22—21no—
48C4×Dic22—21no—
49C4×Dic22—42no—
50C4×Dic22—42no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8—21no—
55C4×C8×C11—21no—
56C4×C8×C11C2×C412yes—
57C11×#95—21no—
58C11×#95—21no—
59C11⋊#95—24no—
60C11⋊#95—21no—
61C11⋊#95D412yes—
62#66881—24no—
63#66880—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#9296—111nomaximal, Sylow
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—22no—
73C22×Dic11—22no—
74C2×Dic22—21no—
75C2×Dic22—22no—
76C2×Dic22—21no—
77C2×Dic22—22no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×Dic22—41no—
82C2×C8×C11—22no—
83C2×C8×C11—41no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11SD1612yes—
88C42×C11C22×C411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11#4111yescharacteristic
91C42×C11#4111yescharacteristic
92C22⋊Dic11—41no—
93C4⋊Dic11—21no—
94C4⋊Dic11—22no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—22no—
99C4⋊Dic11—22no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C4⋊Dic11C22⋊C414yes—
103Dic11⋊C4—44no—
104Dic11⋊C4—41no—
105Dic11⋊C4—41no—
106C4×Dic11—44no—
107C4×Dic11—41no—
108#4318—41no—
109#4318—41no—
110C2×C11⋊C8—41no—
111#3229—111no—
112#2327—111no—
113#1995—111no—
114#1546—111no—
115#1518—111no—
116#1286—111no—
117#1274D1111yescharacteristic
118C23×C11#12011yescharacteristic
119C2×C4×C11—22no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11C2×C22⋊C411yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11C2×SD1611yescharacteristic
134C2×C4×C11#13511yescharacteristic
135C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C2×Dic11—24no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—42no—
145Dic22—42no—
146Dic22—42no—
147Dic22—42no—
148Dic22—42no—
149Dic22—42no—
150Dic22—81no—
151C8×C11—42no—
152C8×C11—81no—
153C11⋊C8—81no—
154#533—111no—
155C2×C4⋊Q8—111no—
156C2×C4×Q8—221no—
157#498—112no—
158#487—112no—
159#483—222no—
160#475—222no—
161#431C2×D1111yescharacteristic
162#431C2×D1111yescharacteristic
163#423—111no—
164#391—221no—
165#387—222no—
166#387—222no—
167#382—111no—
168#376C2×D1111yescharacteristic
169#339—221no—
170#339—221no—
171#332—222no—
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—42no—
183C4×C11—81no—
184C4×C11C4×SD1611yescharacteristic
185C4×C11#44011yescharacteristic
186C4×C11#46111yescharacteristic
187C4×C11#46311yescharacteristic
188Dic11—44no—
189Dic11—82no—
190Dic11—81no—
191Dic11—81no—
192C22×Q8—221no—
193C2×M16—221no—
194C4⋊Q8—112no—
195C4⋊Q8—111no—
196C4⋊Q8—111no—
197C4⋊Q8—112no—
198C4⋊Q8—221no—
199C4⋊Q8—221no—
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—112no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—222no—
211C2×C4⋊C4—221no—
212C2×C42—222no—
213C2×C42D4411yescharacteristic
214C2×C42D4411yescharacteristic
215C2×C42C22×D1111yescharacteristic
216#106—224no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—221no—
220C4⋊C8—221no—
221#103—224no—
222C22⋊C8—21no—
223C22⋊C8—21no—
224C4×C8—21no—
225C4×C8C4×D1112yes—
226#95—21no—
227#95—21no—
228#95—112no—
229#95—224no—
230#95—221no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#187711yescharacteristic
234C2×C11#190511yescharacteristic
235C2×C11#191211yescharacteristic
236C2×Q8—222no—
237C2×Q8—222no—
238C2×Q8—221no—
239C2×Q8—221no—
240C2×Q8—441no—
241C2×Q8—441no—
242C2×Q8—441no—
243C2×Q8—441no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—222no—
247C22×C4—222no—
248C22×C4C2×D4411yescharacteristic
249C22×C4D4×D1111yescharacteristic
250C22×C4D4×D1111yescharacteristic
251M16—441no—
252M16—441no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—441no—
256C4⋊C4—114no—
257C4⋊C4—222no—
258C4⋊C4—222no—
259C4⋊C4—222no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—444no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C4⋊C4—441no—
269C22⋊C4—441no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—444no—
274C42—441no—
275C42#431412yes—
276C42C2×C4×D1111yescharacteristic
277C42#433911yescharacteristic
278C42D4×D1111yescharacteristic
279C42#434311yescharacteristic
280C11#929611yescharacteristic, complemented, Sylow
281C23#6693511yescharacteristic
282Q8—442no—
283Q8—442no—
284Q8—442no—
285Q8—442no—
286Q8—442no—
287Q8—881no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—224no—
297C2×C4—442no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—442no—
304C2×C4C4×D4411yescharacteristic
305C2×C4C22⋊C4×D1111yescharacteristic
306C2×C4#6693711yescharacteristic
307C2×C4#6694611yescharacteristic
308C2×C4#6694711yescharacteristic
309C2×C4#6694811yescharacteristic
310C2×C4C2×#431411yescharacteristic
311C2×C4#6695711yescharacteristic
312C2×C4#6696111yescharacteristic
313C2×C4#6696211yescharacteristic
314C8—42no—
315C8—81no—
316C8—881no—
317C22—21no—
318C22—21no—
319C22#1062227811yescharacteristic
320C22#1062234411yescharacteristic
321C22#1062234611yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—81no—
328C4—444no—
329C4—882no—
330C4—881no—
331C4—881no—
332C4C4×#431411yescharacteristic
333C4#1062232311yescharacteristic
334C4#1062245411yescharacteristic
335C4#1062245711yescharacteristic
336C2—21no—
337C2—21no—
338C2#1306894911yescharacteristic
339C2#1306911111yescharacteristic
340C2#1306915211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1274C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1274D11
hypocenterC11#9296
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
19. #10622294C4semidirect
20. #10622293C4semidirect
280. C11#9296semidirect

Maximal subgroups

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

subgroupindex
#130797622
#130713352
#130695972
#130672872
#130671812
#130664752
C11×#12742
#929611