Finite Group Databasebeta

← #14652912

Subgroups — #14652912

Order 2816.

764 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076961C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic, complemented
3C2×#10622089C214yesmaximal, complemented
4C11×#1434C211yesmaximal, characteristic, complemented
5C22×C42×C11C2211yescharacteristic
6C2×#66983—21no—
7C2×#66983—21no—
8C2×#66983C2212yes—
9C2×#66927C411yescharacteristic, complemented
10C2×C11×#95—21no—
11C2×C11×#95—21no—
12C2×C11×#95C2212yes—
13C2×C22⋊(C11⋊C8)C2212yes—
14#10622552—21no—
15#10622552—21no—
16#10622552C412yescomplemented
17#10622548C411yescharacteristic, complemented
18C2×C4⋊(C11⋊C8)—21no—
19#10622162—21no—
20#10622089—28no—
21C23×C4×C11—22no—
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C22×C22⋊D11—22no—
26C22×D44—21no—
27C22×D44—21no—
28C22×D44C2×C412yes—
29C2×C42×C11—42no—
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34#66983—24no—
35#66983—24no—
36#66983—44no—
37#66983—42no—
38#66983—42no—
39C2×(C2×D11)⋊C4—22no—
40C2×(C2×D11)⋊C4—22no—
41C2×(C2×D11)⋊C4—22no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11C2×C412yes—
45C22×C11⋊C8—22no—
46#66927—42no—
47C11×#95—22no—
48C11×#95—42no—
49C11×#95—42no—
50C11×#95D414yescomplemented
51C22⋊(C11⋊C8)—24no—
52C4⋊(C11⋊C8)—42no—
53#9715—111nomaximal, Sylow
54C24×C11C2×D411yescharacteristic
55C23×D11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—24no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11—42no—
69C22×C4×C11—42no—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11D812yes—
75C22×C4×C11SD1612yes—
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D412yes—
79C22×C4×C11#4112yes—
80C2×C22⋊D11—44no—
81C2×C22⋊D11—42no—
82C2×C22⋊D11—42no—
83C2×C22⋊D11—44no—
84C22×Dic11—22no—
85C2×D44—24no—
86C2×D44—42no—
87C2×D44—42no—
88C2×D44—42no—
89C2×D44—42no—
90C2×D44—42no—
91C2×D44—42no—
92C2×D44—42no—
93C2×D44—42no—
94C42×C11—22no—
95C42×C11—22no—
96C42×C11—41no—
97C42×C11—41no—
98(C2×D11)⋊C4—44no—
99(C2×D11)⋊C4—44no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102C4⋊Dic11—24no—
103C4⋊Dic11—42no—
104C4⋊Dic11—42no—
105C2×C11⋊C8—42no—
106C2×C11⋊C8—42no—
107C2×C11⋊C8—42no—
108#2856—111no—
109#1797—111no—
110C2×#327—114no—
111#1434D1111yescharacteristic, complemented
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11C2×C22⋊C411yescharacteristic
117C23×C11#12112yes—
118C23×C11C2×D811yescharacteristic
119C23×C11C2×SD1611yescharacteristic
120C23×C11AGL(1,ℤ/8)12yes—
121C22×D11—42no—
122C22×D11—42no—
123C22×D11—42no—
124C22×D11—42no—
125C22×D11—42no—
126C22×D11—42no—
127C22×D11—42no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—44no—
146C2×C4×C11—44no—
147C2×C4×C11—44no—
148C2×C4×C11—44no—
149C2×C4×C11—82no—
150C2×C4×C11—82no—
151C2×C4×C11—82no—
152C2×C4×C11—82no—
153C2×C4×C11#9912yes—
154C2×C4×C11#10212yes—
155C2×C4×C11#10212yes—
156C2×C4×C11C4×D412yes—
157C2×C4×C11#12411yescharacteristic
158C2×C4×C11#12711yescharacteristic
159C22⋊D11—84no—
160C22⋊D11—84no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164D44—84no—
165D44—84no—
166D44—84no—
167C11⋊C8—82no—
168C2×#127—111no—
169C2×#121—112no—
170C2×#121—221no—
171C2×#121—221no—
172C22×C42C2×D1111yescharacteristic
173C2×C4⋊C8—221no—
174C2×C22⋊C8—112no—
175#390—112no—
176#390—221no—
177#390—221no—
178#384—111no—
179C2×#95—21no—
180C2×#95—21no—
181C2×#95C2×D1112yes—
182#336—221no—
183#327—228no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11#39011yescharacteristic
193C22×C11C2×#9911yescharacteristic
194C22×C11#41011yescharacteristic
195C22×C11C2×#10211yescharacteristic
196C22×C11#41811yescharacteristic
197C22×C11#42111yescharacteristic
198C22×C11#42111yescharacteristic
199C22×C11#45912yes—
200C22×C11#46012yes—
201C2×D11—82no—
202C2×D11—82no—
203C2×D11—82no—
204C2×D11—82no—
205C2×D11—82no—
206C2×D11—82no—
207C2×D11—82no—
208C4×C11—22no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—22no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—41no—
215C4×C11—84no—
216Dic11—82no—
217C22×D4—112no—
218C22×D4—222no—
219C22×D4—221no—
220C22×D4—221no—
221C23×C4—22no—
222C23×C4C22⋊D1111yescharacteristic
223C23×C4C22⋊D1111yescharacteristic
224C23×C4C22×D1111yescharacteristic
225C22×C8—222no—
226#127—442no—
227#121—224no—
228#121—224no—
229#121—444no—
230#121—442no—
231#121—442no—
232C2×C4⋊C4—112no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C22⋊C4—222no—
236C2×C22⋊C4—222no—
237C2×C22⋊C4—222no—
238C2×C42—42no—
239C2×C42C4×D1111yescharacteristic
240C2×C42C4×D1111yescharacteristic
241C2×C42D4411yescharacteristic
242C2×C42D4411yescharacteristic
243C4⋊C8—442no—
244C22⋊C8—224no—
245#95—22no—
246#95—42no—
247#95—42no—
248#95D4414yescomplemented
249C2×C11—22no—
250C2×C11—22no—
251C2×C11#151011yescharacteristic
252C2×C11#151411yescharacteristic
253C2×C11#151711yescharacteristic
254C2×C11#151911yescharacteristic
255C2×C11#196311yescharacteristic
256C2×C11#196411yescharacteristic
257C2×C11#198211yescharacteristic
258D11—162no—
259C24—222no—
260C24C2×C22⋊D1111yescharacteristic
261C2×D4—224no—
262C2×D4—442no—
263C2×D4—442no—
264C2×D4—442no—
265C2×D4—442no—
266C2×D4—442no—
267C2×D4—442no—
268C2×D4—444no—
269C2×D4—442no—
270C2×D4—442no—
271C2×D4—444no—
272C2×D4—442no—
273C2×D4—442no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—24no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—222no—
289C22×C4(C2×D11)⋊C411yescharacteristic
290C22×C4(C2×D11)⋊C411yescharacteristic
291C22×C4(C2×D11)⋊C411yescharacteristic
292C22×C4(C2×D11)⋊C411yescharacteristic
293C22×C4#432312yes—
294C22×C4#432512yes—
295C22×C4C2×C4×D1111yescharacteristic
296C22×C4C2×D4411yescharacteristic
297C22×C4C2×D4412yes—
298C22×C4#433912yes—
299C2×C8—442no—
300C2×C8—442no—
301C2×C8—442no—
302C4⋊C4—224no—
303C4⋊C4—442no—
304C4⋊C4—442no—
305C22⋊C4—444no—
306C22⋊C4—444no—
307C22⋊C4—442no—
308C22⋊C4—442no—
309C42—22no—
310C42—22no—
311C42—41no—
312C42—41no—
313C11#971511yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—442no—
319C23—442no—
320C23—442no—
321C23—442no—
322C23—442no—
323C23—442no—
324C23—442no—
325C23C2×(C2×D11)⋊C411yescharacteristic
326C23#6698312yes—
327C23C2×#432311yescharacteristic
328C23C2×#432511yescharacteristic
329C23#6700212yes—
330D4—884no—
331D4—884no—
332D4—884no—
333D4—884no—
334D4—884no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—44no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—82no—
359C2×C4—82no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4#6687012yes—
364C2×C4#6687312yes—
365C2×C4#6687312yes—
366C2×C4C4×D4412yes—
367C2×C4#6692711yescharacteristic
368C2×C4#6692811yescharacteristic
369C8—882no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—882no—
379C22—882no—
380C22—882no—
381C22—882no—
382C22—882no—
383C22—882no—
384C22—882no—
385C22#1062255211yescharacteristic
386C22C2×#6687011yescharacteristic
387C22C2×#6687311yescharacteristic
388C22#1062261411yescharacteristic
389C22#1062261811yescharacteristic
390C22#1062261811yescharacteristic
391C22#1062261911yescharacteristic
392C22#1062262812yes—
393C22#1062264012yes—
394C4—22no—
395C4—21no—
396C4—22no—
397C4—21no—
398C4—22no—
399C4—22no—
400C4—41no—
401C4—84no—
402C4—882no—
403C2—22no—
404C2—22no—
405C2—1762no—
406C2#1306714411yescharacteristic
407C2#1306716211yescharacteristic
408C2#1306717511yescharacteristic
409C2#1306718311yescharacteristic
410C2#1306944811yescharacteristic
411C2#1306945211yescharacteristic
412C2#1306954311yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1434C2
socleC23×C11C2×C22⋊C4
prime radical#13076961C2
cosocleC23×C4×C11C23
hypercenter#1434D11
hypocenterC11#9715
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. #13068596C2semidirect
3. C2×#10622089C2semidirect
4. C11×#1434C2semidirect
9. C2×#66927C4semidirect
16. #10622552C4semidirect
17. #10622548C4semidirect
50. C11×#95D4semidirect
111. #1434D11semidirect
248. #95D44semidirect
313. C11#9715semidirect

Maximal subgroups

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

subgroupindex
#130769612
#130685962
C2×#106220892
C11×#14342
#971511