Finite Group Databasebeta

← #14670944

Subgroups — #14670944

Order 2816.

476 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
1C2×#10622809C211yesmaximal, characteristic
2C2×#10622203C211yesmaximal, characteristic, complemented
3#13070328C211yesmaximal, characteristic
4#13069478C211yesmaximal, characteristic, complemented
5#13066725C211yesmaximal, characteristic, complemented
6#13066697C211yesmaximal, characteristic, complemented
7C2×C11×#510C211yesmaximal, characteristic
8C2×C11×#135C2211yescharacteristic
9C22×C11×Q16C2211yescharacteristic
10C2×#67001—21no—
11C11×#510—22no—
12C11×#510C414yescomplemented
13C2×C11×Q32—21no—
14C2×C11×SD32—21no—
15C2×C11×M32C2211yescharacteristic
16C2×#66901—21no—
17#10622843—21no—
18C2×#66899—21no—
19#10622809—22no—
20#10622809—22no—
21C2×#66883C2211yescharacteristic
22C2×#66882C2211yescharacteristic
23C2×C8×Dic11C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25#10622203—22no—
26#10622202—21no—
27#10622200—21no—
28C2×C11×#41—21no—
29C22×Q8×C11—21no—
30C11×#135—21no—
31C11×#135—21no—
32C11×#135C2×C412yes—
33C11×#135D412yes—
34C2×C11×Q16—21no—
35C2×C11×Q16—21no—
36C2×C11×Q16—21no—
37C2×C11×Q16—21no—
38C2×C11×Q16—21no—
39C2×C11×Q16C2×C412yes—
40C2×C11×Q16D411yescharacteristic
41C2×C11×SD16—21no—
42C2×C11×D8D411yescharacteristic
43C22×C8×C11C2311yescharacteristic
44#67001—24no—
45#67001—42no—
46C2×C4⋊Dic11—21no—
47C2×C4×Dic11D411yescharacteristic
48C2×#4318—21no—
49C2×#4318—41no—
50C22×C11⋊C8—41no—
51C22×C11⋊C8D411yescharacteristic
52C11×Q32—24no—
53C11×SD32—24no—
54C11×M32—21no—
55C11×M32C2×C412yes—
56C2×C11×C16—21no—
57#66901—24no—
58#66899—41no—
59#66899—41no—
60C11⋊#95—42no—
61#66883—21no—
62#66883D412yes—
63#66882—21no—
64#66882—21no—
65C8×Dic11—21no—
66C8×Dic11—21no—
67#66876—21no—
68#66876—21no—
69C2×C11⋊C16—21no—
70#13028—111nomaximal, Sylow
71C11×#41—22no—
72C11×#41—22no—
73C11×#41—41no—
74C11×#41—41no—
75C2×Q8×C11—22no—
76C2×Q8×C11—21no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×D4×C11—21no—
83C2×D4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×Dic11—21no—
88C22×Dic11—41no—
89C11×Q16—21no—
90C11×Q16—22no—
91C11×Q16—22no—
92C11×Q16—41no—
93C11×Q16—41no—
94C11×Q16C22⋊C412yes—
95C11×SD16—22no—
96C11×SD16—22no—
97C11×D8—21no—
98C11×D8C22⋊C412yes—
99C2×C8×C11C22×C411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11#4111yescharacteristic
104C2×C8×C11#4111yescharacteristic
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109#4318—22no—
110#4318—44no—
111#4318—41no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—21no—
114C2×C11⋊C8—44no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8D811yescharacteristic
117C2×C11⋊C8D811yescharacteristic
118C11×C16—22no—
119C11⋊C16—41no—
120C2×#510D1111yescharacteristic
121C2×#443—111no—
122C2×#362—111no—
123#2139—111no—
124#1969—111no—
125#1387—111no—
126#1376—111no—
127C23×C11—41no—
128C23×C11AGL(1,ℤ/8)11yescharacteristic
129Q8×C11—22no—
130Q8×C11—41no—
131Q8×C11—42no—
132Q8×C11—42no—
133Q8×C11—81no—
134Q8×C11—81no—
135D4×C11—22no—
136D4×C11—42no—
137D4×C11—42no—
138D4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×Dic11—22no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—82no—
155C2×Dic11—81no—
156C8×C11C2×C22⋊C411yescharacteristic
157C8×C11C4×D411yescharacteristic
158C8×C11#12111yescharacteristic
159C8×C11#12311yescharacteristic
160C11⋊C8—21no—
161C11⋊C8—21no—
162C11⋊C8—42no—
163C2×#135C2×D1111yescharacteristic
164C22×Q16C2×D1111yescharacteristic
165C2×#131—221no—
166#510—22no—
167#510Dic1114yescomplemented
168C2×Q32—21no—
169C2×SD32—21no—
170C2×M32—111no—
171C2×M32C2×D1111yescharacteristic
172#443—222no—
173#443—222no—
174C2×#108—111no—
175C2×#107—111no—
176C2×#104—221no—
177C2×#103—221no—
178C2×C4×C8—111no—
179#391—221no—
180#362—222no—
181#358—221no—
182#357—221no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—42no—
186C22×C11—81no—
187C22×C11—81no—
188C22×C11#44211yescharacteristic
189C22×C11#44911yescharacteristic
190C22×C11#45911yescharacteristic
191C4×C11—42no—
192C4×C11—82no—
193C4×C11#38611yescharacteristic
194C4×C11C4×D811yescharacteristic
195C4×C11#44711yescharacteristic
196C4×C11#46311yescharacteristic
197Dic11—42no—
198Dic11—161no—
199C2×#41—21no—
200C22×Q8—21no—
201#135—21no—
202#135—21no—
203#135C2×Dic1112yes—
204#135C22⋊D1112yes—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16—21no—
210C2×Q16C2×Dic1112yes—
211C2×Q16C22⋊D1111yescharacteristic
212C2×SD16—21no—
213C2×D8C22⋊D1111yescharacteristic
214#131—224no—
215#131—442no—
216C2×M16—221no—
217C2×M16—441no—
218C22×C8—111no—
219C22×C8—441no—
220C22×C8C22×D1111yescharacteristic
221C2×C4⋊C4—221no—
222C2×C42—111no—
223Q32—24no—
224SD32—24no—
225M32—21no—
226M32—221no—
227M32—221no—
228M32C2×Dic1112yes—
229C2×C16—21no—
230C2×C16—221no—
231#108—112no—
232#108—221no—
233#107—221no—
234#107—221no—
235#104—224no—
236#103—441no—
237#103—441no—
238C4×C8—221no—
239C4×C8—221no—
240#95—442no—
241C2×C11—21no—
242C2×C11—21no—
243C2×C11—82no—
244C2×C11#187911yescharacteristic
245C2×C11#221211yescharacteristic
246C2×C11#221411yescharacteristic
247#41—22no—
248#41—22no—
249#41—41no—
250#41—41no—
251C2×Q8—22no—
252C2×Q8—21no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×D4—21no—
259C2×D4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—221no—
263C22×C4—441no—
264C22×C4D4×D1111yescharacteristic
265Q16—22no—
266Q16—21no—
267Q16—22no—
268Q16—41no—
269Q16—41no—
270Q16C22⋊Dic1112yes—
271SD16—22no—
272SD16—22no—
273D8—21no—
274D8C22⋊Dic1112yes—
275M16—222no—
276M16—444no—
277M16—441no—
278C2×C8—111no—
279C2×C8—111no—
280C2×C8—221no—
281C2×C8—221no—
282C2×C8—444no—
283C2×C8—441no—
284C2×C8D4×D1111yescharacteristic
285C2×C8#434111yescharacteristic
286C2×C8#434111yescharacteristic
287C2×C8C22×Dic1111yescharacteristic
288C2×C8C2×C22⋊D1111yescharacteristic
289C2×C8C2×C22⋊D1111yescharacteristic
290C4⋊C4—441no—
291C4⋊C4—441no—
292C42—221no—
293C42—221no—
294C16—22no—
295C16—441no—
296C11#1302811yescharacteristic, complemented, Sylow
297C23—41no—
298C23#6696411yescharacteristic
299Q8—22no—
300Q8—41no—
301Q8—42no—
302Q8—42no—
303Q8—81no—
304Q8—81no—
305D4—22no—
306D4—42no—
307D4—42no—
308D4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—222no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—882no—
319C2×C4—881no—
320C2×C4D8×D1111yescharacteristic
321C2×C4#6696411yescharacteristic
322C2×C4#6696511yescharacteristic
323C2×C4D4×Dic1111yescharacteristic
324C2×C4#6699011yescharacteristic
325C2×C4#6699211yescharacteristic
326C8—221no—
327C8—221no—
328C8—442no—
329C8D4×Dic1111yescharacteristic
330C8#6698811yescharacteristic
331C8#6699211yescharacteristic
332C8C2×C22⋊Dic1111yescharacteristic
333C22—21no—
334C22—21no—
335C22—42no—
336C22—81no—
337C22—81no—
338C22#1062276311yescharacteristic
339C22#1062276511yescharacteristic
340C22#1062277111yescharacteristic
341C4—42no—
342C4—82no—
343C4—442no—
344C4—1761no—
345C4D8×Dic1111yescharacteristic
346C4#1062276611yescharacteristic
347C4#1062276911yescharacteristic
348C4#1062283311yescharacteristic
349C2—21no—
350C2—21no—
351C2—82no—
352C2#1306896611yescharacteristic
353C2#1307068711yescharacteristic
354C2#1307069511yescharacteristic
subgroupG/H
centerC22#10622763
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#510C2
socleC22×C11#459
prime radicalC2×C11×#135C22
cosocleC22×C8×C11C23
hypercenterC2×#510D11
hypocenterC11#13028
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

Complements

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

NH ≅ G/Ntype
2. C2×#10622203C2semidirect
4. #13069478C2semidirect
5. #13066725C2semidirect
6. #13066697C2semidirect
12. C11×#510C4semidirect
167. #510Dic11semidirect
296. C11#13028semidirect

Maximal subgroups

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

subgroupindex
C2×#106228092
C2×#106222032
#130703282
#130694782
#130667252
#130666972
C2×C11×#5102
#1302811