Finite Group Databasebeta

← C22×C11×#352 #14610535

Subgroups — C22×C11×#352 #14610535

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#123C211yesmaximal, characteristic
2C22×C11×#100C211yesmaximal, characteristic
3C22×C11×#99C211yesmaximal, characteristic
4C2×C11×#352C2112yesmaximal, direct product factor
5C23×D4×C11C2211yescharacteristic
6C24×C4×C11C411yescharacteristic, complemented
7C22×C11×M16—21no—
8C2×C11×#123—23no—
9C2×C11×#123—23no—
10C2×C11×#123C416yescomplemented
11C2×C11×#123C2216yes—
12C22×C11×C4⋊C4—21no—
13C22×C11×C22⋊C4—21no—
14C22×C11×C22⋊C4—21no—
15C22×C11×C22⋊C4C411yescharacteristic, complemented
16C2×C11×#100—23no—
17C2×C11×#100C2216yes—
18C2×C11×#99—23no—
19C2×C11×#99C2216yes—
20C11×#352C22116yesdirect product factor
21C25×C11C2×C411yescharacteristic
22C25×C11D411yescharacteristic
23C22×D4×C11—43no—
24C22×D4×C11—41no—
25C22×D4×C11C2×C413yes—
26C22×D4×C11D413yes—
27C22×D4×C11D413yes—
28C22×D4×C11C2313yes—
29C23×C4×C11—23no—
30C23×C4×C11—21no—
31C23×C4×C11—21no—
32C23×C4×C11—43no—
33C23×C4×C11—41no—
34C23×C4×C11—41no—
35C23×C4×C11C2×C416yescomplemented
36C23×C4×C11D411yescharacteristic
37C2×C11×M16—26no—
38C2×C11×M16—43no—
39C22×C8×C11—41no—
40C11×#123—212no—
41C11×#123—26no—
42C11×#123—26no—
43C11×#123C2×C4112yescomplemented
44C11×#123C2314yes—
45C2×C11×C4⋊C4—26no—
46C2×C11×C4⋊C4—26no—
47C2×C11×C22⋊C4—26no—
48C2×C11×C22⋊C4—23no—
49C2×C11×C22⋊C4—26no—
50C2×C11×C22⋊C4—26no—
51C2×C11×C22⋊C4—43no—
52C2×C11×C22⋊C4C2×C416yescomplemented
53C11×#100—26no—
54C11×#100C2314yes—
55C11×#99—26no—
56C11×#99C2314yes—
57C22×#352C1111yesmaximal, characteristic, direct product factor, Sylow
58C24×C11—23no—
59C24×C11—21no—
60C24×C11—21no—
61C24×C11—23no—
62C24×C11—44no—
63C24×C11—44no—
64C24×C11C22⋊C413yes—
65C24×C11C22⋊C413yes—
66C24×C11C22⋊C411yescharacteristic
67C24×C11C22×C413yes—
68C24×C11C2×D413yes—
69C2×D4×C11—43no—
70C2×D4×C11—43no—
71C2×D4×C11—43no—
72C2×D4×C11—43no—
73C2×D4×C11—43no—
74C2×D4×C11—43no—
75C2×D4×C11—43no—
76C2×D4×C11—43no—
77C2×D4×C11C22⋊C416yes—
78C2×D4×C11C22×C413yes—
79C2×D4×C11C2×D413yes—
80C2×D4×C11C2×D413yes—
81C2×D4×C11C2411yescharacteristic
82C22×C4×C11—23no—
83C22×C4×C11—21no—
84C22×C4×C11—26no—
85C22×C4×C11—26no—
86C22×C4×C11—26no—
87C22×C4×C11—44no—
88C22×C4×C11—46no—
89C22×C4×C11—46no—
90C22×C4×C11—43no—
91C22×C4×C11—41no—
92C22×C4×C11—46no—
93C22×C4×C11—46no—
94C22×C4×C11—46no—
95C22×C4×C11—84no—
96C22×C4×C11C22⋊C413yes—
97C22×C4×C11C22×C414yescomplemented
98C22×C4×C11C2×D413yes—
99C11×M16—24no—
100C11×M16—46no—
101C2×C8×C11—46no—
102C11×C4⋊C4—212no—
103C11×C4⋊C4—24no—
104C11×C22⋊C4—212no—
105C11×C22⋊C4—26no—
106C11×C22⋊C4—24no—
107C11×C22⋊C4—24no—
108C11×C22⋊C4—46no—
109C11×C22⋊C4C22×C414yescomplemented
110C22×#123C2×C1111yescharacteristic
111C22×#100C2×C1111yescharacteristic
112C22×#99C2×C1111yescharacteristic
113C2×#352C2×C11112yesdirect product factor
114C23×C11—24no—
115C23×C11—23no—
116C23×C11—23no—
117C23×C11—23no—
118C23×C11—23no—
119C23×C11—23no—
120C23×C11—23no—
121C23×C11—23no—
122C23×C11—23no—
123C23×C11—46no—
124C23×C11—46no—
125C23×C11—412no—
126C23×C11—46no—
127C23×C11—46no—
128C23×C11—44no—
129C23×C11—44no—
130C23×C11—86no—
131C23×C11#9913yes—
132C23×C11#9911yescharacteristic
133C23×C11C2×C22⋊C413yes—
134C23×C11C2×C22⋊C413yes—
135C23×C11C2×C22⋊C413yes—
136C23×C11C23×C411yescharacteristic
137C23×C11C22×D411yescharacteristic
138D4×C11—46no—
139D4×C11—43no—
140D4×C11—43no—
141D4×C11—43no—
142D4×C11—41no—
143C2×C4×C11—23no—
144C2×C4×C11—23no—
145C2×C4×C11—23no—
146C2×C4×C11—23no—
147C2×C4×C11—24no—
148C2×C4×C11—24no—
149C2×C4×C11—412no—
150C2×C4×C11—412no—
151C2×C4×C11—46no—
152C2×C4×C11—46no—
153C2×C4×C11—44no—
154C2×C4×C11—44no—
155C2×C4×C11—812no—
156C2×C4×C11C2×C22⋊C413yes—
157C2×C4×C11C22×D411yescharacteristic
158C8×C11—44no—
159C23×D4C22×C1111yescharacteristic
160C24×C4C4×C1111yescharacteristic, complemented
161C22×M16—21no—
162C2×#123—23no—
163C2×#123—23no—
164C2×#123C4×C1116yescomplemented
165C2×#123C22×C1116yes—
166C22×C4⋊C4—21no—
167C22×C22⋊C4—21no—
168C22×C22⋊C4—21no—
169C22×C22⋊C4C4×C1111yescharacteristic, complemented
170C2×#100—23no—
171C2×#100C22×C1116yes—
172C2×#99—23no—
173C2×#99C22×C1116yes—
174#352C22×C11116yesdirect product factor
175C22×C11—26no—
176C22×C11—26no—
177C22×C11—23no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—23no—
181C22×C11—43no—
182C22×C11—43no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—46no—
186C22×C11—46no—
187C22×C11—46no—
188C22×C11—46no—
189C22×C11—46no—
190C22×C11—46no—
191C22×C11—83no—
192C22×C11—83no—
193C22×C11#35214yesdirect product factor
194C22×C11C2×#9913yes—
195C22×C11C2×#9913yes—
196C22×C11C22×C22⋊C411yescharacteristic
197C4×C11—23no—
198C4×C11—21no—
199C4×C11—44no—
200C4×C11—44no—
201C4×C11—84no—
202C25C2×C4×C1111yescharacteristic
203C25D4×C1111yescharacteristic
204C22×D4—41no—
205C22×D4—43no—
206C22×D4C2×C4×C1113yes—
207C22×D4D4×C1113yes—
208C22×D4D4×C1113yes—
209C22×D4C23×C1113yes—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—23no—
213C23×C4—43no—
214C23×C4—41no—
215C23×C4—41no—
216C23×C4C2×C4×C1116yescomplemented
217C23×C4D4×C1111yescharacteristic
218C2×M16—26no—
219C2×M16—43no—
220C22×C8—41no—
221#123—212no—
222#123—26no—
223#123—26no—
224#123C2×C4×C11112yescomplemented
225#123C23×C1114yes—
226C2×C4⋊C4—26no—
227C2×C4⋊C4—26no—
228C2×C22⋊C4—26no—
229C2×C22⋊C4—23no—
230C2×C22⋊C4—26no—
231C2×C22⋊C4—26no—
232C2×C22⋊C4—43no—
233C2×C22⋊C4C2×C4×C1116yescomplemented
234#100—26no—
235#100C23×C1114yes—
236#99—26no—
237#99C23×C1114yes—
238C2×C11—21no—
239C2×C11—23no—
240C2×C11—41no—
241C2×C11—43no—
242C2×C11—41no—
243C2×C11—43no—
244C2×C11C2×#35216yesdirect product factor
245C2×C11C22×#9911yescharacteristic
246C24—23no—
247C24—21no—
248C24—21no—
249C24—23no—
250C24—44no—
251C24—44no—
252C24C11×C22⋊C411yescharacteristic
253C24C11×C22⋊C413yes—
254C24C11×C22⋊C413yes—
255C24C22×C4×C1113yes—
256C24C2×D4×C1113yes—
257C2×D4—43no—
258C2×D4—43no—
259C2×D4—43no—
260C2×D4—43no—
261C2×D4—43no—
262C2×D4—43no—
263C2×D4—43no—
264C2×D4—43no—
265C2×D4C11×C22⋊C416yes—
266C2×D4C22×C4×C1113yes—
267C2×D4C2×D4×C1113yes—
268C2×D4C2×D4×C1113yes—
269C2×D4C24×C1111yescharacteristic
270C22×C4—21no—
271C22×C4—23no—
272C22×C4—26no—
273C22×C4—26no—
274C22×C4—26no—
275C22×C4—46no—
276C22×C4—46no—
277C22×C4—44no—
278C22×C4—43no—
279C22×C4—41no—
280C22×C4—46no—
281C22×C4—46no—
282C22×C4—46no—
283C22×C4—84no—
284C22×C4C11×C22⋊C413yes—
285C22×C4C22×C4×C1114yescomplemented
286C22×C4C2×D4×C1113yes—
287M16—24no—
288M16—46no—
289C2×C8—46no—
290C4⋊C4—212no—
291C4⋊C4—24no—
292C22⋊C4—212no—
293C22⋊C4—26no—
294C22⋊C4—24no—
295C22⋊C4—24no—
296C22⋊C4—46no—
297C22⋊C4C22×C4×C1114yescomplemented
298C11C22×#35211yescharacteristic, direct product factor, Sylow
299C23—24no—
300C23—23no—
301C23—23no—
302C23—23no—
303C23—23no—
304C23—23no—
305C23—23no—
306C23—23no—
307C23—23no—
308C23—46no—
309C23—46no—
310C23—412no—
311C23—46no—
312C23—46no—
313C23—44no—
314C23—44no—
315C23—86no—
316C23C11×#9913yes—
317C23C11×#9911yescharacteristic
318C23C2×C11×C22⋊C413yes—
319C23C2×C11×C22⋊C413yes—
320C23C2×C11×C22⋊C413yes—
321C23C23×C4×C1111yescharacteristic
322C23C22×D4×C1111yescharacteristic
323D4—46no—
324D4—43no—
325D4—43no—
326D4—43no—
327D4—41no—
328C2×C4—23no—
329C2×C4—23no—
330C2×C4—23no—
331C2×C4—23no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—412no—
335C2×C4—412no—
336C2×C4—46no—
337C2×C4—46no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—812no—
341C2×C4C2×C11×C22⋊C413yes—
342C2×C4C22×D4×C1111yescharacteristic
343C8—44no—
344C22—26no—
345C22—26no—
346C22—23no—
347C22—21no—
348C22—21no—
349C22—23no—
350C22—43no—
351C22—43no—
352C22—41no—
353C22—41no—
354C22—46no—
355C22—46no—
356C22—46no—
357C22—46no—
358C22—46no—
359C22—46no—
360C22—83no—
361C22—83no—
362C22C11×#35214yesdirect product factor
363C22C2×C11×#9913yes—
364C22C2×C11×#9913yes—
365C22C22×C11×C22⋊C411yescharacteristic
366C4—21no—
367C4—23no—
368C4—44no—
369C4—44no—
370C4—84no—
371C2—21no—
372C2—23no—
373C2—41no—
374C2—43no—
375C2—41no—
376C2—43no—
377C2C2×C11×#35216yesdirect product factor
378C2C22×C11×#9911yescharacteristic
subgroupG/H
center, socleC23×C11#99
commutatorC23C23×C4×C11
Frattini, cosocleC2×D4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C11 ◁ C23×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C11×#352C2direct (N × H)
6. C24×C4×C11C4semidirect
10. C2×C11×#123C4semidirect
15. C22×C11×C22⋊C4C4semidirect
20. C11×#352C22direct (N × H)
35. C23×C4×C11C2×C4semidirect
43. C11×#123C2×C4semidirect
52. C2×C11×C22⋊C4C2×C4semidirect
57. C22×#352C11direct (N × H)
97. C22×C4×C11C22×C4semidirect
109. C11×C22⋊C4C22×C4semidirect
113. C2×#352C2×C11direct (N × H)
160. C24×C4C4×C11semidirect
164. C2×#123C4×C11semidirect
169. C22×C22⋊C4C4×C11semidirect
174. #352C22×C11direct (N × H)
193. C22×C11#352direct (N × H)
216. C23×C4C2×C4×C11semidirect
224. #123C2×C4×C11semidirect
233. C2×C22⋊C4C2×C4×C11semidirect
244. C2×C11C2×#352direct (N × H)
285. C22×C4C22×C4×C11semidirect
297. C22⋊C4C22×C4×C11semidirect
298. C11C22×#352direct (N × H)
362. C22C11×#352direct (N × H)
377. C2C2×C11×#352direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1232
C22×C11×#1002
C22×C11×#992
C2×C11×#3522
C22×#35211