Finite Group Databasebeta

← C2×C11×#1933 #14598274

Subgroups — C2×C11×#1933 #14598274

Order 2816.

1246 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#103C211yesmaximal, characteristic
2C22×C11×#103C211yesmaximal, characteristic
3C22×C4×C8×C11C211yesmaximal, characteristic
4C2×C11×#391C211yesmaximal, characteristic
5C2×C11×#389C211yesmaximal, characteristic
6C11×#1933C218yesmaximal, direct product factor
7C2×C11×#340C211yesmaximal, characteristic
8C2×C11×#340C211yesmaximal, characteristic
9C23×Q8×C11C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C22×C11×C4⋊C4—21no—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C2×C11×#103—24no—
18C2×C11×#103C418yescomplemented
19C2×C11×#103C2214yes—
20C2×C11×#103C2214yes—
21C2×C4×C8×C11—24no—
22C2×C4×C8×C11C2214yes—
23C11×#391—22no—
24C11×#391C2214yes—
25C11×#389—22no—
26C11×#389C2214yes—
27C2×C11×#95—21no—
28C2×C11×#95—21no—
29C2×C11×#95—21no—
30C11×#340C2214yes—
31C11×#340C2214yes—
32C22×Q8×C11—21no—
33C22×Q8×C11—22no—
34C22×Q8×C11—22no—
35C22×Q8×C11—22no—
36C22×Q8×C11—22no—
37C22×Q8×C11—22no—
38C22×Q8×C11C2×C414yes—
39C22×Q8×C11C2312yes—
40C23×C4×C11—21no—
41C23×C4×C11—21no—
42C23×C4×C11—21no—
43C23×C4×C11—21no—
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C22×C8×C11—22no—
48C22×C8×C11—22no—
49C22×C8×C11—22no—
50C22×C8×C11—22no—
51C22×C8×C11C2×C414yes—
52C22×C8×C11D414yes—
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—44no—
65C2×C11×C4⋊C4C2×C414yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C42×C11—22no—
70C2×C42×C11—22no—
71C2×C42×C11D412yes—
72C2×C42×C11C2312yes—
73C11×#103—28no—
74C11×#103C2×C4116yescomplemented
75C4×C8×C11—28no—
76C11×#95—24no—
77C11×#95—24no—
78C11×#95—24no—
79C2×#1933C1111yesmaximal, characteristic, direct product factor, Sylow
80C24×C11C2×D411yescharacteristic
81C2×Q8×C11—24no—
82C2×Q8×C11—22no—
83C2×Q8×C11—28no—
84C2×Q8×C11—28no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11—22no—
88C2×Q8×C11—22no—
89C2×Q8×C11—42no—
90C2×Q8×C11—44no—
91C2×Q8×C11—42no—
92C2×Q8×C11—44no—
93C2×Q8×C11C22×C414yes—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11SD1614yes—
115C22×C4×C11Q1614yes—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11#4112yes—
122C22×C4×C11#4112yes—
123C22×C4×C11#4112yes—
124C22×C4×C11#4112yes—
125C22×C4×C11C2411yescharacteristic
126C2×C8×C11—28no—
127C2×C8×C11—28no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11C22×C414yes—
133C2×C8×C11C2×D414yes—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—48no—
143C11×C4⋊C4C22×C414yes—
144C42×C11—24no—
145C42×C11—22no—
146C42×C11—22no—
147C22×#103C2×C1111yescharacteristic
148C22×#103C2×C1111yescharacteristic
149C22×C4×C8C2×C1111yescharacteristic
150C2×#391C2×C1111yescharacteristic
151C2×#389C2×C1111yescharacteristic
152#1933C2×C1118yesdirect product factor
153C2×#340C2×C1111yescharacteristic
154C2×#340C2×C1111yescharacteristic
155C23×C11C4×D412yes—
156C23×C11#12112yes—
157C23×C11#12412yes—
158C23×C11C2×SD1612yes—
159C23×C11C2×Q1612yes—
160C23×C11#13512yes—
161C23×C11#13512yes—
162C23×C11C22×D411yescharacteristic
163Q8×C11—24no—
164Q8×C11—24no—
165Q8×C11—42no—
166Q8×C11—42no—
167Q8×C11—48no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—28no—
173C2×C4×C11—28no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—48no—
181C2×C4×C11—48no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—84no—
189C2×C4×C11—84no—
190C2×C4×C11#11714yes—
191C2×C4×C11C4×D414yes—
192C2×C4×C11C4×D412yes—
193C2×C4×C11#12112yes—
194C2×C4×C11#12314yes—
195C2×C4×C11#12412yes—
196C2×C4×C11#12614yes—
197C2×C4×C11C2×SD1614yes—
198C2×C4×C11C2×Q1614yes—
199C2×C4×C11C23×C411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C8×C11—24no—
206C8×C11—24no—
207C23×Q8C22×C1111yescharacteristic
208C23×C8C22×C1111yescharacteristic
209C23×C8C22×C1111yescharacteristic
210C22×C4⋊C4—21no—
211C22×C4⋊C4C22×C1111yescharacteristic
212C22×C4⋊C4C22×C1111yescharacteristic
213C22×C4⋊C4C22×C1111yescharacteristic
214C22×C42C22×C1111yescharacteristic
215C2×#103—24no—
216C2×#103C4×C1118yescomplemented
217C2×#103C22×C1114yes—
218C2×#103C22×C1114yes—
219C2×C4×C8—24no—
220C2×C4×C8C22×C1114yes—
221#391—22no—
222#391C22×C1114yes—
223#389—22no—
224#389C22×C1114yes—
225C2×#95—21no—
226C2×#95—21no—
227C2×#95—21no—
228#340C22×C1114yes—
229#340C22×C1114yes—
230C22×C11#38814yes—
231C22×C11C4×SD1614yes—
232C22×C11C4×Q1614yes—
233C22×C11#46514yes—
234C22×C11#46714yes—
235C22×C11#48714yes—
236C22×C11#48814yes—
237C22×C11C2×C4×D411yescharacteristic
238C22×C11C2×#12111yescharacteristic
239C22×C11C2×#12411yescharacteristic
240C22×C11C22×SD1611yescharacteristic
241C22×C11C22×Q1611yescharacteristic
242C22×C11C2×#13511yescharacteristic
243C22×C11C2×#13511yescharacteristic
244C4×C11—24no—
245C4×C11—24no—
246C4×C11—44no—
247C4×C11—44no—
248C4×C11—82no—
249C4×C11—82no—
250C4×C11#38814yes—
251C4×C11C2×#11711yescharacteristic
252C4×C11C2×C4×D411yescharacteristic
253C4×C11C2×#12311yescharacteristic
254C4×C11C2×#12611yescharacteristic
255C22×Q8—21no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8C2×C4×C1114yes—
262C22×Q8C23×C1112yes—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4D4×C1111yescharacteristic
268C23×C4D4×C1111yescharacteristic
269C23×C4C23×C1111yescharacteristic
270C22×C8—22no—
271C22×C8—22no—
272C22×C8—22no—
273C22×C8—22no—
274C22×C8C2×C4×C1114yes—
275C22×C8D4×C1114yes—
276C22×C8C23×C1112yes—
277C22×C8C23×C1112yes—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4C2×C4×C1114yes—
289C2×C4⋊C4C23×C1112yes—
290C2×C4⋊C4C23×C1112yes—
291C2×C4⋊C4C23×C1112yes—
292C2×C42—22no—
293C2×C42—22no—
294C2×C42D4×C1112yes—
295C2×C42C23×C1112yes—
296#103—28no—
297#103C2×C4×C11116yescomplemented
298C4×C8—28no—
299#95—24no—
300#95—24no—
301#95—24no—
302C2×C11#193318yesdirect product factor
303C2×C11C2×#38811yescharacteristic
304C2×C11C2×C4×SD1611yescharacteristic
305C2×C11C2×C4×Q1611yescharacteristic
306C2×C11C2×#46511yescharacteristic
307C2×C11C2×#46711yescharacteristic
308C2×C11C2×#48711yescharacteristic
309C2×C11C2×#48811yescharacteristic
310C24C2×D4×C1111yescharacteristic
311C2×Q8—24no—
312C2×Q8—22no—
313C2×Q8—28no—
314C2×Q8—28no—
315C2×Q8—22no—
316C2×Q8—22no—
317C2×Q8—22no—
318C2×Q8—22no—
319C2×Q8—42no—
320C2×Q8—44no—
321C2×Q8—42no—
322C2×Q8—44no—
323C2×Q8C22×C4×C1114yes—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4C11×SD1614yes—
345C22×C4C11×Q1614yes—
346C22×C4C22×C4×C1112yes—
347C22×C4C2×D4×C1112yes—
348C22×C4C2×D4×C1112yes—
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C2×D4×C1112yes—
351C22×C4C11×#4112yes—
352C22×C4C11×#4112yes—
353C22×C4C11×#4112yes—
354C22×C4C11×#4112yes—
355C22×C4C24×C1111yescharacteristic
356C2×C8—28no—
357C2×C8—28no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8C22×C4×C1114yes—
363C2×C8C2×D4×C1114yes—
364C4⋊C4—24no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—42no—
371C4⋊C4—42no—
372C4⋊C4—48no—
373C4⋊C4C22×C4×C1114yes—
374C42—24no—
375C42—22no—
376C42—22no—
377C11C2×#193311yescharacteristic, direct product factor, Sylow
378C23C4×D4×C1112yes—
379C23C11×#12112yes—
380C23C11×#12412yes—
381C23C2×C11×SD1612yes—
382C23C2×C11×Q1612yes—
383C23C11×#13512yes—
384C23C11×#13512yes—
385C23C22×D4×C1111yescharacteristic
386Q8—24no—
387Q8—24no—
388Q8—42no—
389Q8—48no—
390Q8—42no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—28no—
396C2×C4—28no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—42no—
400C2×C4—48no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—48no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—84no—
412C2×C4—84no—
413C2×C4C11×#11714yes—
414C2×C4C4×D4×C1114yes—
415C2×C4C4×D4×C1112yes—
416C2×C4C11×#12112yes—
417C2×C4C11×#12314yes—
418C2×C4C11×#12412yes—
419C2×C4C11×#12614yes—
420C2×C4C2×C11×SD1614yes—
421C2×C4C2×C11×Q1614yes—
422C2×C4C23×C4×C1111yescharacteristic
423C2×C4C22×D4×C1111yescharacteristic
424C2×C4C2×C11×#4111yescharacteristic
425C2×C4C2×C11×#4111yescharacteristic
426C2×C4C2×C11×#4111yescharacteristic
427C2×C4C2×C11×#4111yescharacteristic
428C8—24no—
429C8—24no—
430C22C11×#38814yes—
431C22C4×C11×SD1614yes—
432C22C4×C11×Q1614yes—
433C22C11×#46514yes—
434C22C11×#46714yes—
435C22C11×#48714yes—
436C22C11×#48814yes—
437C22C2×C4×D4×C1111yescharacteristic
438C22C2×C11×#12111yescharacteristic
439C22C2×C11×#12411yescharacteristic
440C22C22×C11×SD1611yescharacteristic
441C22C22×C11×Q1611yescharacteristic
442C22C2×C11×#13511yescharacteristic
443C22C2×C11×#13511yescharacteristic
444C4—24no—
445C4—24no—
446C4—44no—
447C4—44no—
448C4—82no—
449C4—82no—
450C4C11×#38814yes—
451C4C2×C11×#11711yescharacteristic
452C4C2×C4×D4×C1111yescharacteristic
453C4C2×C11×#12311yescharacteristic
454C4C2×C11×#12611yescharacteristic
455C2C11×#193318yesdirect product factor
456C2C2×C11×#38811yescharacteristic
457C2C2×C4×C11×SD1611yescharacteristic
458C2C2×C4×C11×Q1611yescharacteristic
459C2C2×C11×#46511yescharacteristic
460C2C2×C11×#46711yescharacteristic
461C2C2×C11×#48711yescharacteristic
462C2C2×C11×#48811yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C11C2×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
6. C11×#1933C2direct (N × H)
18. C2×C11×#103C4semidirect
74. C11×#103C2×C4semidirect
79. C2×#1933C11direct (N × H)
152. #1933C2×C11direct (N × H)
216. C2×#103C4×C11semidirect
297. #103C2×C4×C11semidirect
302. C2×C11#1933direct (N × H)
377. C11C2×#1933direct (N × H)
455. C2C11×#1933direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1032
C22×C4×C8×C112
C2×C11×#3912
C2×C11×#3892
C11×#19332
C2×C11×#3402
C2×#193311