Finite Group Databasebeta

← #14670646

Subgroups — #14670646

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#13081718C211yesmaximal, characteristic, complemented
2#13077517C211yesmaximal, characteristic
3C2×#10622153C211yesmaximal, characteristic, complemented
4#13070230C211yesmaximal, characteristic, complemented
5#13066706C211yesmaximal, characteristic, complemented
6#13066703C211yesmaximal, characteristic, complemented
7C11×#2117C211yesmaximal, characteristic, complemented
8C2×C11×#131C2211yescharacteristic
9#10623353C411yescharacteristic
10C2×#66954C2211yescharacteristic
11C2×C11×M32C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13#10622849C411yescharacteristic
14#10622758—22no—
15#10622757—22no—
16#10622752C411yescharacteristic
17#10622737C411yescharacteristic
18#10622714C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20C22×C11⋊C16C2211yescharacteristic
21#10622520—22no—
22D11×M32—22no—
23#10622514—22no—
24C11×#350—22no—
25C22⋊(C11⋊C16)—22no—
26#10622153—22no—
27C2×C11×#41C2×C411yescharacteristic
28C2×#4339C2×C411yescharacteristic
29C11×#131—21no—
30C11×#131—21no—
31C11×#131—21no—
32C11×#131—21no—
33C2×C11×M16—21no—
34C2×C11×M16C2×C411yescharacteristic
35C22×C8×C11—21no—
36C22×C8×C11C2311yescharacteristic
37#67004—21no—
38#67003—22no—
39#67002—21no—
40#66995C812yes—
41#66985C812yes—
42#66979C2×C411yescharacteristic
43C2×#4318C2×C411yescharacteristic
44C2×#4318C2×C411yescharacteristic
45#66954—21no—
46#66954—21no—
47#66954D412yes—
48#66954D412yes—
49C2×#4313—21no—
50C2×C8×D11—21no—
51C11×M32—21no—
52C11×M32—21no—
53C11×M32—21no—
54C11×M32D412yes—
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—21no—
63#66876—21no—
64C2×C11⋊C16—21no—
65C2×C11⋊C16—21no—
66C2×C11⋊C16—21no—
67C2×C11⋊C16D412yes—
68#66862—24no—
69C16×D11—24no—
70#12979—111nomaximal, Sylow
71C11×#41—21no—
72C11×#41—21no—
73C11×#41—21no—
74C11×#41—21no—
75C2×Q8×C11C2×C811yescharacteristic
76C2×D4×C11—21no—
77C2×D4×C11C2×C811yescharacteristic
78C22×C4×C11—21no—
79C22×C4×C11C22×C411yescharacteristic
80C2×C22⋊D11—21no—
81#4339—21no—
82#4339—21no—
83#4339C22⋊C412yes—
84#4339C2×C812yes—
85C2×D44M1611yescharacteristic
86C2×C4×D11—21no—
87C2×Dic22M1611yescharacteristic
88C11×M16—21no—
89C11×M16—21no—
90C11×M16—41no—
91C11×M16—41no—
92C2×C8×C11—21no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
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#4318C22⋊C412yes—
111#4318C2×C812yes—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—21no—
114#4313—22no—
115#4313—22no—
116C8×D11—22no—
117C8×D11—22no—
118C11×C16—22no—
119C11×C16—41no—
120C11⋊C16—22no—
121C11⋊C16—41no—
122#3407—111no—
123#2955—111no—
124#2117D1111yescharacteristic, complemented
125C2×#350—111no—
126#2113—111no—
127#1379—111no—
128#1378—111no—
129C23×C11—21no—
130C23×C11#13111yescharacteristic
131C22×D11—21no—
132Q8×C11—21no—
133Q8×C11—21no—
134D4×C11—21no—
135D4×C11—21no—
136D4×C11—41no—
137D4×C11—41no—
138C2×C4×C11—21no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
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—22no—
148C22⋊D11—22no—
149C2×Dic11—21no—
150C2×Dic11—41no—
151D44—21no—
152D44C22⋊C812yes—
153C4×D11—22no—
154C4×D11—22no—
155Dic22—21no—
156Dic22C22⋊C812yes—
157C8×C11—41no—
158C8×C11#12011yescharacteristic
159C8×C11#12111yescharacteristic
160C8×C11#12111yescharacteristic
161C8×C11#12311yescharacteristic
162C11⋊C8—22no—
163C11⋊C8—22no—
164#575—111no—
165C2×#131—111no—
166C2×#131C2×D1111yescharacteristic
167#504—222no—
168#504—222no—
169C2×M32—111no—
170C2×M32—222no—
171C2×M32C2×D1111yescharacteristic
172C2×M32C2×D1111yescharacteristic
173C22×C16—111no—
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—41no—
184C22×C11—42no—
185C22×C11—41no—
186C22×C11#40811yescharacteristic
187C22×C11C8×D411yescharacteristic
188C22×C11#43511yescharacteristic
189C2×D11—22no—
190C2×D11—81no—
191C4×C11—41no—
192C4×C11#38611yescharacteristic
193C4×C11C2×C22⋊C811yescharacteristic
194C4×C11C8×D411yescharacteristic
195C4×C11#43511yescharacteristic
196Dic11—22no—
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—21no—
208#131—21no—
209#131—112no—
210#131—112no—
211#131—221no—
212#131—221no—
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—21no—
225M32—224no—
226M32—221no—
227M32—221no—
228M32C22⋊D1112yes—
229C2×C16—21no—
230C2×C16—21no—
231C2×C16—112no—
232C2×C16—224no—
233C2×C16—221no—
234C2×C16—221no—
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—81no—
245C2×C11#186911yescharacteristic
246D11—42no—
247#41—21no—
248#41—21no—
249#41—21no—
250#41—21no—
251#41—112no—
252#41—112no—
253#41—221no—
254#41—221no—
255C2×Q8—111no—
256C2×Q8C8×D1111yescharacteristic
257C2×D4—21no—
258C2×D4—111no—
259C2×D4—221no—
260C2×D4C8×D1111yescharacteristic
261C22×C4—21no—
262C22×C4—221no—
263C22×C4C2×C4×D1111yescharacteristic
264Q16—222no—
265SD16—222no—
266SD16—222no—
267D8—222no—
268M16—21no—
269M16—21no—
270M16—41no—
271M16—41no—
272M16—112no—
273M16—112no—
274M16—221no—
275M16—221no—
276M16—222no—
277M16—222no—
278C2×C8—21no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—221no—
282C2×C8—221no—
283C2×C8—222no—
284C2×C8—222no—
285C2×C8#433911yescharacteristic
286C2×C8D4×D1111yescharacteristic
287C2×C8D4×D1111yescharacteristic
288C2×C8D4×D1111yescharacteristic
289C2×C8#434111yescharacteristic
290C2×C8C2×C22⋊D1111yescharacteristic
291C4⋊C4—221no—
292C22⋊C4—221no—
293C42—221no—
294C16—22no—
295C16—41no—
296C16—222no—
297C16—441no—
298C11#1297911yescharacteristic, complemented, Sylow
299C23—21no—
300C23—221no—
301C23#6696011yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—112no—
305Q8—221no—
306D4—21no—
307D4—21no—
308D4—41no—
309D4—41no—
310D4—112no—
311D4—222no—
312D4—222no—
313D4—221no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—221no—
318C2×C4—222no—
319C2×C4—222no—
320C2×C4—441no—
321C2×C4C22⋊C4×D1111yescharacteristic
322C2×C4(C22⋊D11)⋊C411yescharacteristic
323C2×C4C2×C8×D1111yescharacteristic
324C2×C4#6695411yescharacteristic
325C2×C4M16×D1111yescharacteristic
326C2×C4C4×C22⋊D1111yescharacteristic
327C8—41no—
328C8—222no—
329C8—222no—
330C8#6693611yescharacteristic
331C8#6693711yescharacteristic
332C8#6699011yescharacteristic
333C8#6699111yescharacteristic
334C22—41no—
335C22—42no—
336C22—41no—
337C22—222no—
338C22—881no—
339C22(C22⋊D11)⋊C811yescharacteristic
340C22#1062234011yescharacteristic
341C22#1062274011yescharacteristic
342C4—41no—
343C4—222no—
344C4—881no—
345C4D11×C22⋊C811yescharacteristic
346C4#1062234111yescharacteristic
347C4#1062256911yescharacteristic
348C4C8×C22⋊D1111yescharacteristic
349C2—21no—
350C2—21no—
351C2—21no—
352C2—81no—
353C2—442no—
354C2#1306890511yescharacteristic
subgroupG/H
centerC8#66990
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC11×#2117C2
socleC2×C11#1869
prime radical#10623353C4
cosocleC22×C8×C11C23
hypercenter#2117D11
hypocenterC11#12979
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
1. #13081718C2semidirect
3. C2×#10622153C2semidirect
4. #13070230C2semidirect
5. #13066706C2semidirect
6. #13066703C2semidirect
7. C11×#2117C2semidirect
124. #2117D11semidirect
298. C11#12979semidirect

Maximal subgroups

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

subgroupindex
#130817182
#130775172
C2×#106221532
#130702302
#130667062
#130667032
C11×#21172
#1297911