Finite Group Databasebeta

← C4×C11×#510 #14610646

Subgroups — C4×C11×#510 #14610646

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#510C211yesmaximal, characteristic
2C4×C11×#135C211yesmaximal, characteristic
3C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
4C11×#2176C212yesmaximal, complemented
5C11×#2175C212yesmaximal, complemented
6C4×C11×Q32C212yesmaximal, complemented
7C4×C11×SD32C212yesmaximal, complemented
8C11×#2159C211yesmaximal, characteristic, complemented
9C11×#2141C211yesmaximal, characteristic, complemented
10C11×#2139C211yesmaximal, characteristic
11C4×C11×M32C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C22×C11×Q16C2211yescharacteristic
14C4×C11×#41—21no—
15C2×C4×Q8×C11—21no—
16C11×#510C418yesdirect product factor
17C2×C11×Q32C2212yes—
18C2×C11×SD32C2212yes—
19C2×C11×M32C2211yescharacteristic
20C2×C11×M32C2211yescharacteristic
21C4×C11×Q16—21no—
22C4×C11×Q16—21no—
23C4×C11×Q16C2212yes—
24C4×C11×Q16C2212yes—
25C4×C11×Q16C2211yescharacteristic
26C4×C11×Q16C2211yescharacteristic
27C4×C11×SD16—21no—
28C4×C11×SD16—21no—
29C4×C11×D8C2211yescharacteristic
30C4×C11×D8C2211yescharacteristic
31C11×#427C2211yescharacteristic
32C2×C11×#107C2211yescharacteristic
33C11×#416—21no—
34C2×C11×#103—21no—
35C2×C4×C8×C11C2211yescharacteristic
36C11×#367C2212yes—
37C11×#366C2212yes—
38C11×#358C2212yes—
39C11×#358C2212yes—
40C11×#358C2212yes—
41C11×#357C2212yes—
42C11×#346C2212yes—
43C4×C11×C16C2212yes—
44C2×C11×#41—21no—
45C22×Q8×C11—21no—
46C11×#135—22no—
47C11×#135C2×C414yes—
48C2×C11×Q16—21no—
49C2×C11×Q16—22no—
50C2×C11×Q16C2×C414yescomplemented
51C2×C11×Q16C2312yes—
52C2×C11×Q16C2311yescharacteristic
53C2×C11×SD16—21no—
54C2×C11×D8C2311yescharacteristic
55C22×C8×C11D411yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C4×Q8×C11—41no—
62C4×Q8×C11—41no—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C4×D4×C11—41no—
66C4×D4×C11—41no—
67C11×#117—21no—
68C11×#117—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—41no—
71C2×C42×C11—41no—
72C2×C42×C11—41no—
73C2×C42×C11D411yescharacteristic
74C11×Q32C2×C418yescomplemented
75C11×SD32C2×C418yescomplemented
76C11×M32—22no—
77C11×M32C2×C414yescomplemented
78C2×C11×C16C2312yes—
79C2×C11×C16C2312yes—
80C11×#107—21no—
81C11×#107C2312yes—
82C11×#107C2311yescharacteristic
83C11×#107C2311yescharacteristic
84C11×#106—21no—
85C11×#103—22no—
86C11×#103—22no—
87C11×#103—21no—
88C11×#103—21no—
89C11×#102—21no—
90C11×#102—21no—
91C4×C8×C11D411yescharacteristic
92C4×C8×C11D411yescharacteristic
93C4×C8×C11C2311yescharacteristic
94C4×C8×C11C2311yescharacteristic
95C4×#510C1111yesmaximal, characteristic, direct product factor, Sylow
96C11×#41—24no—
97C11×#41—42no—
98C2×Q8×C11—24no—
99C2×Q8×C11—21no—
100C2×Q8×C11—22no—
101C2×Q8×C11—41no—
102C2×Q8×C11—42no—
103C2×D4×C11—21no—
104C2×D4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11D811yescharacteristic
111C22×C4×C11D811yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C11×Q16—24no—
114C11×Q16—22no—
115C11×Q16—21no—
116C11×Q16C22×C414yes—
117C11×Q16C22×C412yes—
118C11×SD16—24no—
119C11×D8—21no—
120C11×D8C22×C412yes—
121C2×C8×C11—22no—
122C2×C8×C11C22×C412yes—
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11#4112yes—
127C2×C8×C11C2411yescharacteristic
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C42×C11—41no—
140C42×C11—41no—
141C42×C11—42no—
142C42×C11—41no—
143C42×C11—42no—
144C42×C11D811yescharacteristic
145C42×C11D811yescharacteristic
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C11×C16—22no—
149C11×C16C22×C414yes—
150C2×#510C2×C1111yescharacteristic
151C4×#135C2×C1111yescharacteristic
152C2×C4×Q16C2×C1111yescharacteristic, complemented
153#2176C2×C1112yescomplemented
154#2175C2×C1112yescomplemented
155C4×Q32C2×C1112yescomplemented
156C4×SD32C2×C1112yescomplemented
157#2159C2×C1111yescharacteristic, complemented
158#2141C2×C1111yescharacteristic, complemented
159#2139C2×C1111yescharacteristic
160C4×M32C2×C1111yescharacteristic, complemented
161C23×C11—41no—
162C23×C11C2×D811yescharacteristic
163Q8×C11—22no—
164Q8×C11—24no—
165Q8×C11—42no—
166Q8×C11—41no—
167Q8×C11—44no—
168D4×C11—22no—
169D4×C11—44no—
170D4×C11—41no—
171C2×C4×C11—22no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—44no—
176C2×C4×C11—44no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—82no—
181C2×C4×C11—82no—
182C2×C4×C11—82no—
183C2×C4×C11C4×D412yes—
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11C2×D811yescharacteristic
186C2×C4×C11C2×D811yescharacteristic
187C2×C4×C11C2×D811yescharacteristic
188C2×C4×C11C2×D811yescharacteristic
189C2×C4×C11#13512yes—
190C2×C4×C11C22×D411yescharacteristic
191C8×C11—21no—
192C8×C11—21no—
193C8×C11C4×D412yes—
194C8×C11C23×C411yescharacteristic
195C8×C11C2×#4111yescharacteristic
196C2×#135C22×C1111yescharacteristic
197C22×Q16C22×C1111yescharacteristic
198C4×#41—21no—
199C2×C4×Q8—21no—
200#510C4×C1118yesdirect product factor
201C2×Q32C22×C1112yes—
202C2×SD32C22×C1112yes—
203C2×M32C22×C1111yescharacteristic
204C2×M32C22×C1111yescharacteristic
205C4×Q16—21no—
206C4×Q16—21no—
207C4×Q16C22×C1112yes—
208C4×Q16C22×C1112yes—
209C4×Q16C22×C1111yescharacteristic
210C4×Q16C22×C1111yescharacteristic
211C4×SD16—21no—
212C4×SD16—21no—
213C4×D8C22×C1111yescharacteristic
214C4×D8C22×C1111yescharacteristic
215#427C22×C1111yescharacteristic
216C2×#107C22×C1111yescharacteristic
217#416—21no—
218C2×#103—21no—
219C2×C4×C8C22×C1111yescharacteristic
220#367C22×C1112yes—
221#366C22×C1112yes—
222#358C22×C1112yes—
223#358C22×C1112yes—
224#358C22×C1112yes—
225#357C22×C1112yes—
226#346C22×C1112yes—
227C4×C16C22×C1112yes—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—42no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11C4×D812yes—
234C22×C11C22×D811yescharacteristic
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—42no—
239C4×C11—44no—
240C4×C11—81no—
241C4×C11—81no—
242C4×C11—82no—
243C4×C11C4×D812yes—
244C4×C11#51012yesdirect product factor
245C4×C11C2×C4×D411yescharacteristic
246C4×C11C2×#13511yescharacteristic
247C2×#41—21no—
248C22×Q8—21no—
249#135—22no—
250#135C2×C4×C1114yes—
251C2×Q16—21no—
252C2×Q16—22no—
253C2×Q16C2×C4×C1114yescomplemented
254C2×Q16C23×C1112yes—
255C2×Q16C23×C1111yescharacteristic
256C2×SD16—21no—
257C2×D8C23×C1111yescharacteristic
258C22×C8D4×C1111yescharacteristic
259C22×C8C23×C1111yescharacteristic
260C4×Q8—22no—
261C4×Q8—22no—
262C4×Q8—21no—
263C4×Q8—21no—
264C4×Q8—41no—
265C4×Q8—41no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—41no—
269C4×D4—41no—
270#117—21no—
271#117—41no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—41no—
274C2×C42—41no—
275C2×C42—41no—
276C2×C42D4×C1111yescharacteristic
277Q32C2×C4×C1118yescomplemented
278SD32C2×C4×C1118yescomplemented
279M32—22no—
280M32C2×C4×C1114yescomplemented
281C2×C16C23×C1112yes—
282C2×C16C23×C1112yes—
283#107—21no—
284#107C23×C1112yes—
285#107C23×C1111yescharacteristic
286#107C23×C1111yescharacteristic
287#106—21no—
288#103—22no—
289#103—22no—
290#103—21no—
291#103—21no—
292#102—21no—
293#102—21no—
294C4×C8D4×C1111yescharacteristic
295C4×C8D4×C1111yescharacteristic
296C4×C8C23×C1111yescharacteristic
297C4×C8C23×C1111yescharacteristic
298C2×C11—22no—
299C2×C11—82no—
300C2×C11C2×C4×D811yescharacteristic
301C2×C11C2×#51011yescharacteristic
302C2×C11#341411yescharacteristic
303#41—24no—
304#41—42no—
305C2×Q8—24no—
306C2×Q8—21no—
307C2×Q8—22no—
308C2×Q8—41no—
309C2×Q8—42no—
310C2×D4—21no—
311C2×D4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4C11×D811yescharacteristic
318C22×C4C11×D811yescharacteristic
319C22×C4C2×D4×C1111yescharacteristic
320Q16—24no—
321Q16—22no—
322Q16—21no—
323Q16C22×C4×C1114yes—
324Q16C22×C4×C1112yes—
325SD16—24no—
326D8—21no—
327D8C22×C4×C1112yes—
328C2×C8—22no—
329C2×C8C22×C4×C1112yes—
330C2×C8C2×D4×C1111yescharacteristic
331C2×C8C2×D4×C1111yescharacteristic
332C2×C8C2×D4×C1111yescharacteristic
333C2×C8C11×#4112yes—
334C2×C8C24×C1111yescharacteristic
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—22no—
338C4⋊C4—41no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C42—41no—
347C42—41no—
348C42—41no—
349C42—42no—
350C42—42no—
351C42C11×D811yescharacteristic
352C42C11×D811yescharacteristic
353C42C2×D4×C1111yescharacteristic
354C42C2×D4×C1111yescharacteristic
355C16—22no—
356C16C22×C4×C1114yes—
357C11C4×#51011yescharacteristic, direct product factor, Sylow
358C23—41no—
359C23C2×C11×D811yescharacteristic
360Q8—22no—
361Q8—24no—
362Q8—42no—
363Q8—41no—
364Q8—44no—
365D4—22no—
366D4—44no—
367D4—41no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4C4×D4×C1112yes—
381C2×C4C2×C11×D811yescharacteristic
382C2×C4C2×C11×D811yescharacteristic
383C2×C4C2×C11×D811yescharacteristic
384C2×C4C2×C11×D811yescharacteristic
385C2×C4C2×C11×D811yescharacteristic
386C2×C4C11×#13512yes—
387C2×C4C22×D4×C1111yescharacteristic
388C8—21no—
389C8—21no—
390C8C4×D4×C1112yes—
391C8C23×C4×C1111yescharacteristic
392C8C2×C11×#4111yescharacteristic
393C22—21no—
394C22—21no—
395C22—42no—
396C22—81no—
397C22—81no—
398C22C4×C11×D812yes—
399C22C22×C11×D811yescharacteristic
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—44no—
405C4—81no—
406C4—81no—
407C4—82no—
408C4C4×C11×D812yes—
409C4C11×#51012yesdirect product factor
410C4C2×C4×D4×C1111yescharacteristic
411C4C2×C11×#13511yescharacteristic
412C2—22no—
413C2—82no—
414C2C2×C4×C11×D811yescharacteristic
415C2C2×C11×#51011yescharacteristic
416C2C11×#341411yescharacteristic
subgroupG/H
centerC2×C4×C11C2×D8
commutatorC8C23×C4×C11
Frattini, cosocleC2×C8C24×C11
socleC22×C11C22×D8
prime radicalC2×C11×#135C22
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C11×Q16C2semidirect
4. C11×#2176C2semidirect
5. C11×#2175C2semidirect
6. C4×C11×Q32C2semidirect
7. C4×C11×SD32C2semidirect
8. C11×#2159C2semidirect
9. C11×#2141C2semidirect
11. C4×C11×M32C2semidirect
16. C11×#510C4direct (N × H)
50. C2×C11×Q16C2×C4semidirect
74. C11×Q32C2×C4semidirect
75. C11×SD32C2×C4semidirect
77. C11×M32C2×C4semidirect
95. C4×#510C11direct (N × H)
152. C2×C4×Q16C2×C11semidirect
153. #2176C2×C11semidirect
154. #2175C2×C11semidirect
155. C4×Q32C2×C11semidirect
156. C4×SD32C2×C11semidirect
157. #2159C2×C11semidirect
158. #2141C2×C11semidirect
160. C4×M32C2×C11semidirect
200. #510C4×C11direct (N × H)
244. C4×C11#510direct (N × H)
253. C2×Q16C2×C4×C11semidirect
277. Q32C2×C4×C11semidirect
278. SD32C2×C4×C11semidirect
280. M32C2×C4×C11semidirect
357. C11C4×#510direct (N × H)
409. C4C11×#510direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5102
C4×C11×#1352
C2×C4×C11×Q162
C11×#21762
C11×#21752
C4×C11×Q322
C4×C11×SD322
C11×#21592
C11×#21412
C11×#21392
C4×C11×M322
C4×#51011