Finite Group Databasebeta

← C2×C11×#2628 #14611800

Subgroups — C2×C11×#2628 #14611800

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C22×C11×#117C211yesmaximal, characteristic
3C11×#2628C2116yesmaximal, direct product factor
4C2×C11×#400C212yesmaximal, complemented
5C2×C11×#399C212yesmaximal
6C2×C11×#395C212yesmaximal, complemented
7C2×C11×#393C212yesmaximal
8C2×C11×#389C212yesmaximal, complemented
9C2×C11×#382C211yesmaximal, characteristic, complemented
10C2×C11×#380C212yesmaximal
11C23×Q8×C11C2212yes—
12C24×C4×C11C2211yescharacteristic
13C2×C11×C4⋊Q8—28no—
14C2×C11×C4⋊Q8C2218yescomplemented
15C2×C11×#117—28no—
16C2×C11×#117C2218yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2212yes—
21C22×C11×C4⋊C4C2212yes—
22C22×C11×C4⋊C4C2214yes—
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2214yes—
26C22×C42×C11C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C11×#400C22116yescomplemented
29C11×#399C22116yes—
30C11×#395C22116yescomplemented
31C11×#393C22116yes—
32C11×#389C22116yescomplemented
33C11×#382C2218yescomplemented
34C11×#380C22116yes—
35C2×C11×#95C2212yes—
36C2×C11×#95C2214yes—
37C2×C11×#95C2214yes—
38C2×C11×#95C2212yes—
39C25×C11C2311yescharacteristic
40C22×Q8×C11—28no—
41C22×Q8×C11—48no—
42C22×Q8×C11C2318yes—
43C23×C4×C11—24no—
44C23×C4×C11—24no—
45C23×C4×C11Q818yescomplemented
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2314yes—
49C23×C4×C11C2314yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2314yes—
54C23×C4×C11C2311yescharacteristic
55C11×C4⋊Q8—232no—
56C11×#117—232no—
57C2×C11×C4⋊C4—24no—
58C2×C11×C4⋊C4—24no—
59C2×C11×C4⋊C4—28no—
60C2×C11×C4⋊C4—28no—
61C2×C11×C4⋊C4—28no—
62C2×C11×C4⋊C4—48no—
63C2×C11×C4⋊C4C2314yes—
64C2×C11×C4⋊C4C2314yes—
65C2×C11×C4⋊C4C2318yes—
66C2×C11×C4⋊C4C2318yes—
67C2×C11×C4⋊C4C2318yes—
68C2×C11×C4⋊C4C23116yes—
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4—48no—
72C2×C11×C22⋊C4C2314yes—
73C2×C11×C22⋊C4C2314yes—
74C2×C11×C22⋊C4C23116yes—
75C2×C42×C11—24no—
76C2×C42×C11D418yes—
77C2×C42×C11C2314yes—
78C2×C42×C11C2314yes—
79C11×#95C23116yes—
80C11×#95C2318yes—
81C11×#95C2318yes—
82C11×#95C23116yes—
83C2×#2628C1111yesmaximal, characteristic, direct product factor, Sylow
84C24×C11—22no—
85C24×C11—22no—
86C24×C11—24no—
87C24×C11—24no—
88C24×C11C2×Q814yes—
89C24×C11C2412yes—
90C24×C11C2411yescharacteristic
91C2×Q8×C11—216no—
92C2×Q8×C11—416no—
93C2×Q8×C11—432no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—232no—
99C22×C4×C11—28no—
100C22×C4×C11—28no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—28no—
104C22×C4×C11—28no—
105C22×C4×C11—28no—
106C22×C4×C11—28no—
107C22×C4×C11—24no—
108C22×C4×C11—28no—
109C22×C4×C11—24no—
110C22×C4×C11—28no—
111C22×C4×C11C2×D414yes—
112C22×C4×C11C2×D414yes—
113C22×C4×C11C2×D414yes—
114C22×C4×C11C2×Q814yes—
115C22×C4×C11C2×Q814yes—
116C22×C4×C11C2×Q8116yescomplemented
117C22×C4×C11#4114yes—
118C22×C4×C11C2412yes—
119C22×C4×C11C2418yes—
120C22×C4×C11C2418yes—
121C22×C4×C11C2412yes—
122C22×C4×C11C2412yes—
123C22×C4×C11C2412yes—
124C22×C4×C11C2412yes—
125C22×C4×C11C2412yes—
126C11×C4⋊C4—28no—
127C11×C4⋊C4—28no—
128C11×C4⋊C4—216no—
129C11×C4⋊C4—216no—
130C11×C4⋊C4—216no—
131C11×C4⋊C4—416no—
132C11×C22⋊C4—28no—
133C11×C22⋊C4—28no—
134C11×C22⋊C4—416no—
135C42×C11—28no—
136C42×C11C2×D4116yes—
137C22×C4⋊Q8C2×C1111yescharacteristic, complemented
138C22×#117C2×C1111yescharacteristic
139#2628C2×C11116yesdirect product factor
140C2×#400C2×C1112yescomplemented
141C2×#399C2×C1112yes—
142C2×#395C2×C1112yescomplemented
143C2×#393C2×C1112yes—
144C2×#389C2×C1112yescomplemented
145C2×#382C2×C1111yescharacteristic, complemented
146C2×#380C2×C1112yes—
147C23×C11—28no—
148C23×C11—216no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—24no—
152C23×C11—24no—
153C23×C11—44no—
154C23×C11—44no—
155C23×C11—48no—
156C23×C11C22×D412yes—
157C23×C11C22×Q814yes—
158C23×C11C22×Q812yes—
159C23×C11C2×#4112yes—
160C23×C11H(5,𝔽2)14yes—
161C23×C112−1+414yes—
162C23×C11C2511yescharacteristic
163Q8×C11—432no—
164C2×C4×C11—28no—
165C2×C4×C11—28no—
166C2×C4×C11—28no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—232no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—28no—
175C2×C4×C11—28no—
176C2×C4×C11—28no—
177C2×C4×C11—28no—
178C2×C4×C11—24no—
179C2×C4×C11—28no—
180C2×C4×C11—24no—
181C2×C4×C11—28no—
182C2×C4×C11—44no—
183C2×C4×C11—416no—
184C2×C4×C11—44no—
185C2×C4×C11—416no—
186C2×C4×C11C22⋊Q8116yes—
187C2×C4×C11C22×D414yes—
188C2×C4×C11C22×D414yes—
189C2×C4×C11C22×D414yes—
190C2×C4×C11C22×Q814yes—
191C2×C4×C11C22×Q814yes—
192C2×C4×C11C2×#4114yes—
193C23×Q8C22×C1112yes—
194C24×C4C22×C1111yescharacteristic
195C2×C4⋊Q8—28no—
196C2×C4⋊Q8C22×C1118yescomplemented
197C2×#117—28no—
198C2×#117C22×C1118yes—
199C22×C4⋊C4C22×C1111yescharacteristic
200C22×C4⋊C4C22×C1112yes—
201C22×C4⋊C4C22×C1111yescharacteristic
202C22×C4⋊C4C22×C1112yes—
203C22×C4⋊C4C22×C1112yes—
204C22×C4⋊C4C22×C1114yes—
205C22×C22⋊C4C22×C1111yescharacteristic
206C22×C22⋊C4C22×C1111yescharacteristic
207C22×C22⋊C4C22×C1114yes—
208C22×C42C22×C1111yescharacteristic
209C22×C42C22×C1111yescharacteristic
210#400C22×C11116yescomplemented
211#399C22×C11116yes—
212#395C22×C11116yescomplemented
213#393C22×C11116yes—
214#389C22×C11116yescomplemented
215#382C22×C1118yescomplemented
216#380C22×C11116yes—
217C2×#95C22×C1112yes—
218C2×#95C22×C1114yes—
219C2×#95C22×C1114yes—
220C2×#95C22×C1112yes—
221C22×C11—24no—
222C22×C11—28no—
223C22×C11—416no—
224C22×C11—42no—
225C22×C11—42no—
226C22×C11—44no—
227C22×C11C2×C22⋊Q814yes—
228C22×C11#53514yes—
229C22×C11#53614yes—
230C22×C11#54218yes—
231C22×C11#54418yes—
232C22×C11C23×D411yescharacteristic
233C22×C11C23×Q811yescharacteristic
234C22×C11C22×#4111yescharacteristic
235C22×C11C2×H(5,𝔽2)12yes—
236C22×C11C2×2−1+412yes—
237C4×C11—24no—
238C4×C11—24no—
239C4×C11—24no—
240C4×C11—42no—
241C4×C11—48no—
242C4×C11—42no—
243C4×C11—48no—
244C4×C11C2×C22⋊Q818yes—
245C25C23×C1111yescharacteristic
246C22×Q8—28no—
247C22×Q8—48no—
248C22×Q8C23×C1118yes—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4Q8×C1118yescomplemented
252C23×C4C23×C1111yescharacteristic
253C23×C4C23×C1114yes—
254C23×C4C23×C1114yes—
255C23×C4C23×C1111yescharacteristic
256C23×C4C23×C1111yescharacteristic
257C23×C4C23×C1111yescharacteristic
258C23×C4C23×C1111yescharacteristic
259C23×C4C23×C1114yes—
260C23×C4C23×C1111yescharacteristic
261C4⋊Q8—232no—
262#117—232no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—28no—
266C2×C4⋊C4—28no—
267C2×C4⋊C4—28no—
268C2×C4⋊C4—48no—
269C2×C4⋊C4C23×C1114yes—
270C2×C4⋊C4C23×C1114yes—
271C2×C4⋊C4C23×C1118yes—
272C2×C4⋊C4C23×C1118yes—
273C2×C4⋊C4C23×C1118yes—
274C2×C4⋊C4C23×C11116yes—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—24no—
277C2×C22⋊C4—48no—
278C2×C22⋊C4C23×C1114yes—
279C2×C22⋊C4C23×C1114yes—
280C2×C22⋊C4C23×C11116yes—
281C2×C42—24no—
282C2×C42D4×C1118yes—
283C2×C42C23×C1114yes—
284C2×C42C23×C1114yes—
285#95C23×C11116yes—
286#95C23×C1118yes—
287#95C23×C1118yes—
288#95C23×C11116yes—
289C2×C11—44no—
290C2×C11#262818yesdirect product factor
291C2×C11C22×C22⋊Q811yescharacteristic
292C2×C11C2×#53511yescharacteristic
293C2×C11C2×#53611yescharacteristic
294C2×C11C2×#54212yes—
295C2×C11C2×#54412yes—
296C24—22no—
297C24—22no—
298C24—24no—
299C24—24no—
300C24C2×Q8×C1114yes—
301C24C24×C1112yes—
302C24C24×C1111yescharacteristic
303C2×Q8—216no—
304C2×Q8—416no—
305C2×Q8—432no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—24no—
309C22×C4—24no—
310C22×C4—232no—
311C22×C4—28no—
312C22×C4—28no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—28no—
316C22×C4—28no—
317C22×C4—28no—
318C22×C4—28no—
319C22×C4—24no—
320C22×C4—28no—
321C22×C4—24no—
322C22×C4—28no—
323C22×C4C2×D4×C1114yes—
324C22×C4C2×D4×C1114yes—
325C22×C4C2×D4×C1114yes—
326C22×C4C2×Q8×C1114yes—
327C22×C4C2×Q8×C1114yes—
328C22×C4C2×Q8×C11116yescomplemented
329C22×C4C11×#4114yes—
330C22×C4C24×C1112yes—
331C22×C4C24×C1118yes—
332C22×C4C24×C1118yes—
333C22×C4C24×C1112yes—
334C22×C4C24×C1112yes—
335C22×C4C24×C1112yes—
336C22×C4C24×C1112yes—
337C22×C4C24×C1112yes—
338C4⋊C4—28no—
339C4⋊C4—28no—
340C4⋊C4—216no—
341C4⋊C4—216no—
342C4⋊C4—216no—
343C4⋊C4—416no—
344C22⋊C4—28no—
345C22⋊C4—28no—
346C22⋊C4—416no—
347C42—28no—
348C42C2×D4×C11116yes—
349C11C2×#262811yescharacteristic, direct product factor, Sylow
350C23—28no—
351C23—216no—
352C23—22no—
353C23—22no—
354C23—24no—
355C23—24no—
356C23—44no—
357C23—44no—
358C23—48no—
359C23C22×D4×C1112yes—
360C23C22×Q8×C1114yes—
361C23C22×Q8×C1112yes—
362C23C2×C11×#4112yes—
363C23C11×H(5,𝔽2)14yes—
364C23C11×2−1+414yes—
365C23C25×C1111yescharacteristic
366Q8—432no—
367C2×C4—28no—
368C2×C4—28no—
369C2×C4—28no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—232no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—28no—
378C2×C4—28no—
379C2×C4—28no—
380C2×C4—28no—
381C2×C4—24no—
382C2×C4—28no—
383C2×C4—24no—
384C2×C4—28no—
385C2×C4—44no—
386C2×C4—416no—
387C2×C4—44no—
388C2×C4—416no—
389C2×C4C11×C22⋊Q8116yes—
390C2×C4C22×D4×C1114yes—
391C2×C4C22×D4×C1114yes—
392C2×C4C22×D4×C1114yes—
393C2×C4C22×Q8×C1114yes—
394C2×C4C22×Q8×C1114yes—
395C2×C4C2×C11×#4114yes—
396C22—24no—
397C22—28no—
398C22—42no—
399C22—42no—
400C22—44no—
401C22—416no—
402C22C2×C11×C22⋊Q814yes—
403C22C11×#53514yes—
404C22C11×#53614yes—
405C22C11×#54218yes—
406C22C11×#54418yes—
407C22C23×D4×C1111yescharacteristic
408C22C23×Q8×C1111yescharacteristic
409C22C22×C11×#4111yescharacteristic
410C22C2×C11×H(5,𝔽2)12yes—
411C22C2×C11×2−1+412yes—
412C4—24no—
413C4—24no—
414C4—24no—
415C4—48no—
416C4—42no—
417C4—42no—
418C4—48no—
419C4C2×C11×C22⋊Q818yes—
420C2—44no—
421C2C11×#262818yesdirect product factor
422C2C22×C11×C22⋊Q811yescharacteristic
423C2C2×C11×#53511yescharacteristic
424C2C2×C11×#53611yescharacteristic
425C2C2×C11×#54212yes—
426C2C2×C11×#54412yes—
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×C4⋊Q8C2semidirect
3. C11×#2628C2direct (N × H)
4. C2×C11×#400C2semidirect
6. C2×C11×#395C2semidirect
8. C2×C11×#389C2semidirect
9. C2×C11×#382C2semidirect
14. C2×C11×C4⋊Q8C22semidirect
28. C11×#400C22semidirect
30. C11×#395C22semidirect
32. C11×#389C22semidirect
33. C11×#382C22semidirect
45. C23×C4×C11Q8semidirect
83. C2×#2628C11direct (N × H)
116. C22×C4×C11C2×Q8semidirect
137. C22×C4⋊Q8C2×C11semidirect
139. #2628C2×C11direct (N × H)
140. C2×#400C2×C11semidirect
142. C2×#395C2×C11semidirect
144. C2×#389C2×C11semidirect
145. C2×#382C2×C11semidirect
196. C2×C4⋊Q8C22×C11semidirect
210. #400C22×C11semidirect
212. #395C22×C11semidirect
214. #389C22×C11semidirect
215. #382C22×C11semidirect
251. C23×C4Q8×C11semidirect
290. C2×C11#2628direct (N × H)
328. C22×C4C2×Q8×C11semidirect
349. C11C2×#2628direct (N × H)
421. C2C11×#2628direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊Q82
C22×C11×#1172
C11×#26282
C2×C11×#4002
C2×C11×#3992
C2×C11×#3952
C2×C11×#3932
C2×C11×#3892
C2×C11×#3822
C2×C11×#3802
C2×#262811