Finite Group Databasebeta

← #14652899

Subgroups — #14652899

Order 2816.

856 conjugacy classes of subgroups.

The subgroup lattice has 420 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
4C4×C11×#95C211yesmaximal, characteristic, complemented
5C22×C42×C11—21no—
6C22×C42×C11C2211yescharacteristic
7C2×#66983—21no—
8C2×#66983—21no—
9C2×#66983C2212yes—
10C2×#66927C411yescharacteristic, complemented
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—24no—
30C2×C42×C11—42no—
31C2×C42×C11—42no—
32C2×C42×C11—42no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37#66983—24no—
38#66983—24no—
39#66983—44no—
40#66983—42no—
41#66983—42no—
42C2×(C2×D11)⋊C4—22no—
43C2×(C2×D11)⋊C4—22no—
44C2×(C2×D11)⋊C4—22no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11C2×C412yes—
48C22×C11⋊C8—22no—
49#66927—42no—
50C11×#95—24no—
51C11×#95—22no—
52C11×#95D414yescomplemented
53C22⋊(C11⋊C8)—24no—
54C4⋊(C11⋊C8)—42no—
55#9712—111nomaximal, Sylow
56C24×C11C2×D411yescharacteristic
57C23×D11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—24no—
61C22×C4×C11—24no—
62C22×C4×C11—24no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11—42no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11—42no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11D812yes—
77C22×C4×C11SD1612yes—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D412yes—
81C22×C4×C11#4112yes—
82C2×C22⋊D11—44no—
83C2×C22⋊D11—42no—
84C2×C22⋊D11—42no—
85C2×C22⋊D11—44no—
86C22×Dic11—22no—
87C2×D44—24no—
88C2×D44—42no—
89C2×D44—42no—
90C2×D44—42no—
91C2×D44—42no—
92C2×D44—42no—
93C2×D44—42no—
94C2×D44—42no—
95C2×D44—42no—
96C42×C11—22no—
97C42×C11—22no—
98C42×C11—41no—
99C42×C11—41no—
100C42×C11—48no—
101(C2×D11)⋊C4—44no—
102(C2×D11)⋊C4—44no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—42no—
105C4⋊Dic11—24no—
106C4⋊Dic11—42no—
107C4⋊Dic11—42no—
108C2×C11⋊C8—42no—
109C2×C11⋊C8—42no—
110C2×C11⋊C8—42no—
111#2856—111no—
112#1797—111no—
113C2×#327—114no—
114C4×#95D1111yescharacteristic, complemented
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11C2×C22⋊C411yescharacteristic
120C23×C11#12112yes—
121C23×C11C2×D811yescharacteristic
122C23×C11C2×SD1611yescharacteristic
123C23×C11AGL(1,ℤ/8)12yes—
124C22×D11—42no—
125C22×D11—42no—
126C22×D11—42no—
127C22×D11—42no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—42no—
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—24no—
140C2×C4×C11—24no—
141C2×C4×C11—28no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—44no—
148C2×C4×C11—44no—
149C2×C4×C11—44no—
150C2×C4×C11—44no—
151C2×C4×C11—44no—
152C2×C4×C11—44no—
153C2×C4×C11—44no—
154C2×C4×C11#9912yes—
155C2×C4×C11#10212yes—
156C2×C4×C11#10212yes—
157C2×C4×C11#10412yes—
158C2×C4×C11#10412yes—
159C2×C4×C11C4×D412yes—
160C2×C4×C11#12411yescharacteristic
161C2×C4×C11#12711yescharacteristic
162C22⋊D11—84no—
163C22⋊D11—84no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167D44—84no—
168D44—84no—
169D44—84no—
170C11⋊C8—82no—
171C2×#127—111no—
172C2×#121—112no—
173C2×#121—221no—
174C2×#121—221no—
175C22×C42—21no—
176C22×C42C2×D1111yescharacteristic
177C2×C4⋊C8—221no—
178C2×C22⋊C8—112no—
179#390—112no—
180#390—221no—
181#390—221no—
182#384—111no—
183C2×#95—21no—
184C2×#95C2×D1112yes—
185#336—221no—
186#327—228no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11#39011yescharacteristic
196C22×C11C2×#9911yescharacteristic
197C22×C11#41011yescharacteristic
198C22×C11C2×#10211yescharacteristic
199C22×C11#41811yescharacteristic
200C22×C11C2×#10411yescharacteristic
201C22×C11C2×#10411yescharacteristic
202C22×C11#45912yes—
203C22×C11#46012yes—
204C2×D11—82no—
205C2×D11—82no—
206C2×D11—82no—
207C2×D11—82no—
208C2×D11—82no—
209C2×D11—82no—
210C2×D11—82no—
211C4×C11—22no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—22no—
215C4×C11—22no—
216C4×C11—48no—
217C4×C11—41no—
218C4×C11#32714yescomplemented
219Dic11—82no—
220C22×D4—112no—
221C22×D4—222no—
222C22×D4—221no—
223C22×D4—221no—
224C23×C4—22no—
225C23×C4C22⋊D1111yescharacteristic
226C23×C4C22⋊D1111yescharacteristic
227C23×C4C22×D1111yescharacteristic
228C22×C8—222no—
229#127—442no—
230#121—224no—
231#121—224no—
232#121—444no—
233#121—442no—
234#121—442no—
235C2×C4⋊C4—112no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C22⋊C4—222no—
239C2×C22⋊C4—222no—
240C2×C22⋊C4—222no—
241C2×C42—24no—
242C2×C42—42no—
243C2×C42—42no—
244C2×C42—42no—
245C2×C42C4×D1111yescharacteristic
246C2×C42C4×D1111yescharacteristic
247C2×C42D4411yescharacteristic
248C2×C42D4411yescharacteristic
249C4⋊C8—442no—
250C22⋊C8—224no—
251#95—24no—
252#95—22no—
253#95D4414yescomplemented
254C2×C11—22no—
255C2×C11—22no—
256C2×C11C2×#32711yescharacteristic
257C2×C11#150211yescharacteristic
258C2×C11#150511yescharacteristic
259C2×C11#150711yescharacteristic
260C2×C11#196211yescharacteristic
261C2×C11#196411yescharacteristic
262C2×C11#198211yescharacteristic
263D11—162no—
264C24—222no—
265C24C2×C22⋊D1111yescharacteristic
266C2×D4—224no—
267C2×D4—442no—
268C2×D4—442no—
269C2×D4—442no—
270C2×D4—442no—
271C2×D4—444no—
272C2×D4—442no—
273C2×D4—442no—
274C2×D4—444no—
275C2×D4—442no—
276C2×D4—442no—
277C2×D4—442no—
278C2×D4—442no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—222no—
294C22×C4(C2×D11)⋊C411yescharacteristic
295C22×C4(C2×D11)⋊C411yescharacteristic
296C22×C4(C2×D11)⋊C411yescharacteristic
297C22×C4(C2×D11)⋊C411yescharacteristic
298C22×C4#432312yes—
299C22×C4#432512yes—
300C22×C4C2×C4×D1111yescharacteristic
301C22×C4C2×D4411yescharacteristic
302C22×C4C2×D4412yes—
303C22×C4#433912yes—
304C2×C8—442no—
305C2×C8—442no—
306C2×C8—442no—
307C4⋊C4—224no—
308C4⋊C4—442no—
309C4⋊C4—442no—
310C22⋊C4—444no—
311C22⋊C4—444no—
312C22⋊C4—442no—
313C22⋊C4—442no—
314C42—22no—
315C42—22no—
316C42—41no—
317C42—41no—
318C42—48no—
319C11#971211yescharacteristic, complemented, Sylow
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—442no—
325C23—442no—
326C23—442no—
327C23—442no—
328C23—442no—
329C23—442no—
330C23—442no—
331C23C2×(C2×D11)⋊C411yescharacteristic
332C23#6698312yes—
333C23C2×#432311yescharacteristic
334C23C2×#432511yescharacteristic
335C23#6700212yes—
336D4—884no—
337D4—884no—
338D4—884no—
339D4—884no—
340D4—884no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—28no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—44no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4#6686912yes—
368C2×C4#6686912yes—
369C2×C4#6687012yes—
370C2×C4#6687312yes—
371C2×C4#6687312yes—
372C2×C4C4×D4412yes—
373C2×C4#6692711yescharacteristic
374C2×C4#6692811yescharacteristic
375C8—882no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—882no—
385C22—882no—
386C22—882no—
387C22—882no—
388C22—882no—
389C22—882no—
390C22—882no—
391C22C2×#6686911yescharacteristic
392C22C2×#6686911yescharacteristic
393C22#1062255211yescharacteristic
394C22C2×#6687011yescharacteristic
395C22C2×#6687311yescharacteristic
396C22#1062261411yescharacteristic
397C22#1062261911yescharacteristic
398C22#1062262812yes—
399C22#1062264012yes—
400C4—22no—
401C4—22no—
402C4—21no—
403C4—22no—
404C4—21no—
405C4—48no—
406C4—41no—
407C4—882no—
408C4#1062208914yescomplemented
409C2—22no—
410C2—22no—
411C2—1762no—
412C2C2×#1062208911yescharacteristic
413C2#1306711011yescharacteristic
414C2#1306712311yescharacteristic
415C2#1306713111yescharacteristic
416C2#1306944411yescharacteristic
417C2#1306945211yescharacteristic
418C2#1306954311yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC4×C11×#95C2
socleC23×C11C2×C22⋊C4
prime radical#13076961C2
cosocleC23×C4×C11C23
hypercenterC4×#95D11
hypocenterC11#9712
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. #13068596C2semidirect
3. C2×#10622089C2semidirect
4. C4×C11×#95C2semidirect
10. C2×#66927C4semidirect
16. #10622552C4semidirect
17. #10622548C4semidirect
52. C11×#95D4semidirect
114. C4×#95D11semidirect
218. C4×C11#327semidirect
253. #95D44semidirect
319. C11#9712semidirect
408. C4#10622089semidirect

Maximal subgroups

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

subgroupindex
#130769612
#130685962
C2×#106220892
C4×C11×#952
#971211