Finite Group Databasebeta

← #14670729

Subgroups — #14670729

Order 2816.

476 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078336C211yesmaximal, characteristic
2#13077227C211yesmaximal, characteristic, complemented
3#13070345C211yesmaximal, characteristic, complemented
4C2×#10622148C211yesmaximal, characteristic, complemented
5#13066728C211yesmaximal, characteristic, complemented
6#13066710C211yesmaximal, characteristic, complemented
7C2×C11×#350C211yesmaximal, characteristic, complemented
8C2×C11×#131C2211yescharacteristic
9#10623353—21no—
10#10623350—21no—
11C2×#66957C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13C22×C11×C16C2211yescharacteristic
14#10622756C412yes—
15#10622755C412yes—
16#10622754—22no—
17#10622745—21no—
18#10622738—21no—
19#10622738—22no—
20C2×#66883—22no—
21C2×#66883C2211yescharacteristic
22C2×#66883C2211yescharacteristic
23C2×#66883C2211yescharacteristic
24C11×#350—22no—
25#10622148—22no—
26#10622148—22no—
27C2×C11×#41D411yescharacteristic
28C2×#4339—21no—
29C11×#131—21no—
30C11×#131—21no—
31C11×#131C2×C412yes—
32C11×#131D412yes—
33C2×C11×M16—21no—
34C2×C11×M16D411yescharacteristic
35C22×C8×C11—21no—
36C22×C8×C11C2311yescharacteristic
37#67004—22no—
38#67003—42no—
39#67002—22no—
40#67001—42no—
41#67001—42no—
42#66995—41no—
43#66985—41no—
44C2×#4318—24no—
45C2×#4318—21no—
46C2×#4318—21no—
47C2×#4318—21no—
48C2×Dic44C2×C411yescharacteristic
49#66957—21no—
50#66957—21no—
51#66957—21no—
52#66957—21no—
53C2×D88C2×C411yescharacteristic
54C2×#4314—21no—
55C11×M32—21no—
56C11×M32—21no—
57C2×C11×C16—21no—
58C2×C11×C16—21no—
59C2×C11×C16—21no—
60C2×C11×C16—21no—
61#66888—22no—
62#66887—22no—
63#66883—24no—
64#66883—21no—
65#66883—21no—
66#66883—21no—
67#66883C2×C412yes—
68#66883D412yes—
69#66883D412yes—
70#12995—111nomaximal, Sylow
71C11×#41—21no—
72C11×#41—21no—
73C11×#41C22⋊C412yes—
74C11×#41D812yes—
75C2×Q8×C11SD1611yescharacteristic
76C2×D4×C11—21no—
77C2×D4×C11SD1611yescharacteristic
78C22×C4×C11—21no—
79C22×C4×C11C2×D411yescharacteristic
80C2×C22⋊D11—41no—
81#4339—41no—
82#4339—41no—
83#4339—41no—
84#4339—41no—
85C2×D44—21no—
86C2×C4×D11—41no—
87C2×Dic22—21no—
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×C11C22×C411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11#4111yescharacteristic
100C2×C8×C11#4111yescharacteristic
101#4326—42no—
102#4325—42no—
103#4324—42no—
104#4323—42no—
105#4318—22no—
106#4318—22no—
107#4318—22no—
108#4318—44no—
109#4318—41no—
110#4318—41no—
111#4318—41no—
112C2×C11⋊C8—44no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116Dic44—21no—
117Dic44—21no—
118D88—21no—
119D88—21no—
120#4314—41no—
121#4314—41no—
122C11×C16—41no—
123C11×C16—41no—
124#3067—111no—
125#2916—111no—
126#2143—111no—
127C2×#359—111no—
128C2×#350D1111yescharacteristic, complemented
129#1388—111no—
130#1381—111no—
131C23×C11—21no—
132C23×C11#13711yescharacteristic
133C22×D11—41no—
134Q8×C11—21no—
135Q8×C11#10212yes—
136D4×C11—22no—
137D4×C11—22no—
138D4×C11—21no—
139D4×C11#10212yes—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11C2×C22⋊C411yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12311yescharacteristic
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C2×SD1611yescharacteristic
148C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
149C22⋊D11—81no—
150C22⋊D11—81no—
151C2×Dic11—41no—
152D44—41no—
153D44—41no—
154C4×D11—81no—
155C4×D11—81no—
156Dic22—41no—
157Dic22—41no—
158C8×C11—22no—
159C8×C11C4×D411yescharacteristic
160C8×C11C4×D411yescharacteristic
161C8×C11#12111yescharacteristic
162C8×C11#12111yescharacteristic
163C11⋊C8—42no—
164C11⋊C8—42no—
165C11⋊C8—42no—
166#575—221no—
167C2×#135—111no—
168#568—221no—
169C2×#131C2×D1111yescharacteristic
170C2×M32C2×D1111yescharacteristic
171C22×C16C2×D1111yescharacteristic
172#473—112no—
173#472—112no—
174#471—222no—
175#430—222no—
176#430—221no—
177C2×#108—111no—
178C2×#108—111no—
179C2×#108—111no—
180C2×#108—222no—
181#413—221no—
182#359—222no—
183#359—222no—
184#350—22no—
185C22×C11—22no—
186C22×C11—41no—
187C22×C11—81no—
188C22×C11#41711yescharacteristic
189C22×C11#44811yescharacteristic
190C22×C11#48011yescharacteristic
191C2×D11—81no—
192C2×D11—161no—
193C4×C11—22no—
194C4×C11#38611yescharacteristic
195C4×C11C2×#10211yescharacteristic
196C4×C11#44711yescharacteristic
197C4×C11#48111yescharacteristic
198Dic11—81no—
199C2×#41—221no—
200C2×#41D4411yescharacteristic
201#137—222no—
202#137—441no—
203AGL(1,ℤ/8)—222no—
204AGL(1,ℤ/8)—441no—
205#135—221no—
206#135—221no—
207#135—221no—
208#135—221no—
209#135—442no—
210C2×Q16—111no—
211C2×SD16—221no—
212C2×D8—111no—
213#131—21no—
214#131—21no—
215#131—442no—
216#131—442no—
217#131C4×D1112yes—
218#131C22⋊D1112yes—
219C2×M16—21no—
220C2×M16—224no—
221C2×M16—221no—
222C2×M16—221no—
223C2×M16—221no—
224C2×M16D4411yescharacteristic
225C22×C8—21no—
226C22×C8C22×D1111yescharacteristic
227M32—21no—
228M32—21no—
229C2×C16—21no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233#108—112no—
234#108—112no—
235#108—112no—
236#108—224no—
237#108—221no—
238#108—221no—
239#108—221no—
240#101—222no—
241#100—222no—
242C2×C11—21no—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11—42no—
246C2×C11#187411yescharacteristic
247D11—161no—
248#41—21no—
249#41—21no—
250#41—441no—
251#41—441no—
252#41—441no—
253#41—441no—
254#41D8812yes—
255#41(C2×D11)⋊C412yes—
256C2×Q8—221no—
257C2×Q8#431411yescharacteristic
258C2×D4—21no—
259C2×D4—221no—
260C2×D4—441no—
261C2×D4#431411yescharacteristic
262C22×C4—21no—
263C22×C4—441no—
264C22×C4C2×D4411yescharacteristic
265Q16—221no—
266Q16—221no—
267Q16—442no—
268SD16—442no—
269SD16—442no—
270SD16—441no—
271SD16—441no—
272D8—221no—
273D8—221no—
274D8—442no—
275M16—21no—
276M16—22no—
277M16—22no—
278M16—222no—
279M16—222no—
280M16—222no—
281M16—444no—
282M16—441no—
283M16—441no—
284M16—441no—
285M16(C2×D11)⋊C412yes—
286C2×C8—21no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—444no—
290C2×C8—441no—
291C2×C8—441no—
292C2×C8—441no—
293C2×C8C2×C4×D1111yescharacteristic
294C2×C8D4×D1111yescharacteristic
295C2×C8D4×D1111yescharacteristic
296C2×C8#434111yescharacteristic
297C2×C8#434111yescharacteristic
298C2×C8C2×C22⋊D1111yescharacteristic
299C16—41no—
300C16—41no—
301C11#1299511yescharacteristic, complemented, Sylow
302C23—21no—
303C23—441no—
304C23#6696211yescharacteristic
305Q8—21no—
306Q8—441no—
307Q8—441no—
308Q8#6688512yes—
309D4—22no—
310D4—22no—
311D4—21no—
312D4—441no—
313D4—441no—
314D4—881no—
315D4—881no—
316D4#6688512yes—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—441no—
321C2×C4—881no—
322C2×C4—881no—
323C2×C4#6693511yescharacteristic
324C2×C4#6693911yescharacteristic
325C2×C4C2×#431411yescharacteristic
326C2×C4C2×D8811yescharacteristic
327C2×C4#6696111yescharacteristic
328C2×C4C2×(C2×D11)⋊C411yescharacteristic
329C8—22no—
330C8—442no—
331C8—442no—
332C8—442no—
333C8(C22⋊D11)⋊C411yescharacteristic
334C8(C22⋊D11)⋊C411yescharacteristic
335C8#6699211yescharacteristic
336C8#6699211yescharacteristic
337C22—22no—
338C22—41no—
339C22—81no—
340C22—881no—
341C22—1761no—
342C22#1062234911yescharacteristic
343C22#1062235111yescharacteristic
344C22#1062274611yescharacteristic
345C4—22no—
346C4—881no—
347C4#1062234511yescharacteristic
348C4#1062234811yescharacteristic
349C4#1062257111yescharacteristic
350C4C2×#6688511yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—1761no—
356C2#1306893111yescharacteristic
subgroupG/H
centerC4#10622345
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#350C2
socleC2×C11#1874
prime radical#13078336C2
cosocleC22×C8×C11C23
hypercenterC2×#350D11
hypocenterC11#12995
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#131 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
2. #13077227C2semidirect
3. #13070345C2semidirect
4. C2×#10622148C2semidirect
5. #13066728C2semidirect
6. #13066710C2semidirect
7. C2×C11×#350C2semidirect
128. C2×#350D11semidirect
301. C11#12995semidirect

Maximal subgroups

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

subgroupindex
#130783362
#130772272
#130703452
C2×#106221482
#130667282
#130667102
C2×C11×#3502
#1299511