Finite Group Databasebeta

← #14670641

Subgroups — #14670641

Order 2816.

456 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081719C211yesmaximal, characteristic, complemented
2#13077517C211yesmaximal, characteristic
3#13070243C211yesmaximal, characteristic, complemented
4#13070229C211yesmaximal, characteristic, complemented
5#13066704C211yesmaximal, characteristic, complemented
6#13066703C211yesmaximal, characteristic, complemented
7C2×C11×#350C211yesmaximal, characteristic, complemented
8C2×C11×#131C2211yescharacteristic
9#10623353C411yescharacteristic
10C2×#66954C2211yescharacteristic
11C2×C11×M32C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13#10622849C411yescharacteristic
14#10622758—22no—
15#10622757—22no—
16#10622753—22no—
17#10622753—22no—
18#10622752C411yescharacteristic
19#10622737C411yescharacteristic
20#10622714C2211yescharacteristic
21C2×#66876—22no—
22C2×#66876C2211yescharacteristic
23C2×#66876C2211yescharacteristic
24C11×#350—22no—
25#10622146—22no—
26(C2×D11)⋊C16—22no—
27C2×C11×#41C2×C411yescharacteristic
28C2×#4339C2×C411yescharacteristic
29C11×#131—21no—
30C11×#131—21no—
31C11×#131D412yes—
32C11×#131D412yes—
33C2×C11×M16—21no—
34C2×C11×M16C2×C411yescharacteristic
35C22×C8×C11—21no—
36C22×C8×C11C2311yescharacteristic
37#67004C812yes—
38#67003—22no—
39#67002C812yes—
40#66995—21no—
41#66985—21no—
42#66979C2×C411yescharacteristic
43C2×#4318C2×C411yescharacteristic
44C2×#4318C2×C411yescharacteristic
45#66954—21no—
46#66954—21no—
47#66954—21no—
48#66954—21no—
49C2×#4313—21no—
50C2×C8×D11—21no—
51C11×M32—21no—
52C11×M32—21no—
53C2×C11×C16—21no—
54C2×C11×C16—21no—
55C2×C11×C16—21no—
56C2×C11×C16—21no—
57#66901—22no—
58#66889—22no—
59#66886—22no—
60#66879—21no—
61C8×Dic11—21no—
62#66876—24no—
63#66876—21no—
64#66876—21no—
65#66876—21no—
66#66876D412yes—
67C2×C11⋊C16—24no—
68C2×C11⋊C16—21no—
69C2×C11⋊C16D412yes—
70#12979—111nomaximal, Sylow
71C11×#41—21no—
72C11×#41—21no—
73C11×#41C22⋊C412yes—
74C11×#41C2×C812yes—
75C2×Q8×C11M1611yescharacteristic
76C2×D4×C11—21no—
77C2×D4×C11M1611yescharacteristic
78C22×C4×C11—21no—
79C22×C4×C11C22×C411yescharacteristic
80C2×C22⋊D11—21no—
81#4339—21no—
82#4339—21no—
83#4339—21no—
84#4339—21no—
85C2×D44C2×C811yescharacteristic
86C2×C4×D11—21no—
87C2×Dic22C2×C811yescharacteristic
88C11×M16—22no—
89C11×M16—22no—
90C11×M16—21no—
91C11×M16C22⋊C412yes—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—21no—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11#4111yescharacteristic
100C2×C8×C11#4111yescharacteristic
101C22⋊Dic11—21no—
102#4326—22no—
103#4325—22no—
104#4324—22no—
105#4323—22no—
106C4⋊Dic11—21no—
107C4×Dic11—21no—
108#4318—21no—
109#4318—21no—
110#4318—21no—
111#4318C2×C812yes—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—21no—
114#4313—41no—
115#4313—41no—
116C8×D11—41no—
117C8×D11—41no—
118C11×C16—41no—
119C11×C16—41no—
120C11⋊C16—22no—
121C11⋊C16—22no—
122#3407—111no—
123#2955—111no—
124#2117—111no—
125C2×#350D1111yescharacteristic, complemented
126#2113—111no—
127#1379—111no—
128#1378—111no—
129C23×C11—21no—
130C23×C11#13111yescharacteristic
131C22×D11—21no—
132Q8×C11—21no—
133Q8×C11C22⋊C812yes—
134D4×C11—22no—
135D4×C11—22no—
136D4×C11—21no—
137D4×C11C22⋊C812yes—
138C2×C4×C11—21no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11C2×C22⋊C411yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C22×C811yescharacteristic
145C2×C4×C11C2×M1611yescharacteristic
146C2×C4×C11#13111yescharacteristic
147C22⋊D11—41no—
148C22⋊D11—41no—
149C2×Dic11—21no—
150C2×Dic11—41no—
151D44—21no—
152D44—21no—
153C4×D11—41no—
154C4×D11—41no—
155Dic22—21no—
156Dic22—21no—
157C8×C11—22no—
158C8×C11#12011yescharacteristic
159C8×C11#12111yescharacteristic
160C8×C11#12111yescharacteristic
161C8×C11#12311yescharacteristic
162C11⋊C8—22no—
163C11⋊C8—41no—
164#575—111no—
165C2×#131—111no—
166C2×#131C2×D1111yescharacteristic
167#504—222no—
168#504—222no—
169C2×M32—111no—
170C2×M32—111no—
171C2×M32—222no—
172C2×M32C2×D1111yescharacteristic
173C22×C16C2×D1111yescharacteristic
174#444—222no—
175#443—222no—
176#430—111no—
177#421—111no—
178#421—111no—
179#405—111no—
180#350—22no—
181#350—222no—
182C22⋊C16—222no—
183C22×C11—22no—
184C22×C11—41no—
185C22×C11—81no—
186C22×C11#40811yescharacteristic
187C22×C11C8×D411yescharacteristic
188C22×C11#43511yescharacteristic
189C2×D11—42no—
190C2×D11—41no—
191C4×C11—22no—
192C4×C11#38611yescharacteristic
193C4×C11C2×C22⋊C811yescharacteristic
194C4×C11C8×D411yescharacteristic
195C4×C11#43511yescharacteristic
196Dic11—41no—
197Dic11—81no—
198C2×#41—111no—
199C2×#41C4×D1111yescharacteristic
200#137—112no—
201#137—221no—
202AGL(1,ℤ/8)—112no—
203AGL(1,ℤ/8)—221no—
204#135—222no—
205#131—21no—
206#131—21no—
207#131—221no—
208#131—221no—
209#131—221no—
210#131—221no—
211#131D4412yes—
212#131C22⋊D1112yes—
213C2×M16—21no—
214C2×M16—111no—
215C2×M16—111no—
216C2×M16—221no—
217C2×M16C4×D1111yescharacteristic
218C22×C8—21no—
219C22×C8—221no—
220C22×C8C22×D1111yescharacteristic
221#117—111no—
222M32—21no—
223M32—21no—
224M32—112no—
225M32—224no—
226M32—221no—
227M32—221no—
228M32—221no—
229C2×C16—21no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—112no—
234C2×C16—224no—
235C2×C16—221no—
236#108—222no—
237#104—222no—
238#104—222no—
239#97—221no—
240C4×C8—221no—
241C2×C11—21no—
242C2×C11—21no—
243C2×C11—21no—
244C2×C11—42no—
245C2×C11#186911yescharacteristic
246D11—81no—
247#41—21no—
248#41—21no—
249#41—221no—
250#41—221no—
251#41—221no—
252#41—221no—
253#41C8×D1112yes—
254#41(C2×D11)⋊C412yes—
255C2×Q8—111no—
256C2×Q8#431311yescharacteristic
257C2×D4—21no—
258C2×D4—111no—
259C2×D4—221no—
260C2×D4#431311yescharacteristic
261C22×C4—21no—
262C22×C4—221no—
263C22×C4C2×C4×D1111yescharacteristic
264Q16—222no—
265SD16—222no—
266SD16—222no—
267D8—222no—
268M16—21no—
269M16—22no—
270M16—22no—
271M16—112no—
272M16—221no—
273M16—221no—
274M16—221no—
275M16—441no—
276M16—441no—
277M16(C2×D11)⋊C412yes—
278C2×C8—21no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—221no—
282C2×C8—221no—
283C2×C8—441no—
284C2×C8—441no—
285C2×C8C2×D4411yescharacteristic
286C2×C8D4×D1111yescharacteristic
287C2×C8D4×D1111yescharacteristic
288C2×C8#434111yescharacteristic
289C2×C8#434111yescharacteristic
290C2×C8C2×C22⋊D1111yescharacteristic
291C4⋊C4—221no—
292C22⋊C4—221no—
293C42—221no—
294C16—41no—
295C16—41no—
296C16—222no—
297C16—222no—
298C11#1297911yescharacteristic, complemented, Sylow
299C23—21no—
300C23—221no—
301C23#6696011yescharacteristic
302Q8—21no—
303Q8—221no—
304Q8—221no—
305Q8(C2×D11)⋊C812yes—
306D4—22no—
307D4—22no—
308D4—21no—
309D4—221no—
310D4—221no—
311D4—441no—
312D4—441no—
313D4(C2×D11)⋊C812yes—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—221no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4(C22⋊D11)⋊C411yescharacteristic
322C2×C4(C22⋊D11)⋊C411yescharacteristic
323C2×C4C2×C8×D1111yescharacteristic
324C2×C4C2×#431311yescharacteristic
325C2×C4#6696011yescharacteristic
326C2×C4C2×(C2×D11)⋊C411yescharacteristic
327C8—22no—
328C8—222no—
329C8—441no—
330C8#6693511yescharacteristic
331C8#6693911yescharacteristic
332C8#6699211yescharacteristic
333C8#6699211yescharacteristic
334C22—22no—
335C22—41no—
336C22—81no—
337C22—442no—
338C22—441no—
339C22(C22⋊D11)⋊C811yescharacteristic
340C22#1062234311yescharacteristic
341C22#1062274211yescharacteristic
342C4—22no—
343C4—441no—
344C4—881no—
345C4(C22⋊D11)⋊C811yescharacteristic
346C4#1062234311yescharacteristic
347C4#1062257111yescharacteristic
348C4C2×(C2×D11)⋊C811yescharacteristic
349C2—21no—
350C2—21no—
351C2—21no—
352C2—42no—
353C2—881no—
354C2#1306890611yescharacteristic
subgroupG/H
centerC8#66935
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC2×C11×#350C2
socleC2×C11#1869
prime radical#10623353C4
cosocleC22×C8×C11C23
hypercenterC2×#350D11
hypocenterC11#12979
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
1. #13081719C2semidirect
3. #13070243C2semidirect
4. #13070229C2semidirect
5. #13066704C2semidirect
6. #13066703C2semidirect
7. C2×C11×#350C2semidirect
125. C2×#350D11semidirect
298. C11#12979semidirect

Maximal subgroups

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

subgroupindex
#130817192
#130775172
#130702432
#130702292
#130667042
#130667032
C2×C11×#3502
#1297911