Finite Group Databasebeta

← C2×C11×#3218 #14637979

Subgroups — C2×C11×#3218 #14637979

Order 2816.

2146 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×C11×#529C211yesmaximal, characteristic
3C11×#3218C2116yesmaximal, direct product factor
4C2×C11×#497C212yesmaximal, complemented
5C2×C11×#491C212yesmaximal, complemented
6C2×C11×#462C212yesmaximal, complemented
7C2×C11×#461C212yesmaximal, complemented
8C2×C11×#451C212yesmaximal, complemented
9C2×C11×#448C212yesmaximal
10C2×C11×#432C211yesmaximal, characteristic, complemented
11C23×Q8×C11C2212yes—
12C22×C11×Q16C2214yes—
13C22×C11×SD16C2214yes—
14C2×C11×C4⋊Q8—21no—
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8—24no—
17C2×C11×C4⋊Q8C2212yes—
18C2×C11×C4⋊Q8C2212yes—
19C2×C11×C4⋊Q8C2218yescomplemented
20C11×#529—24no—
21C11×#529C2218yes—
22C2×C11×#126—21no—
23C2×C11×#125C2211yescharacteristic
24C2×C11×#124C2211yescharacteristic
25C2×C11×#123—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11—21no—
30C2×C4×D4×C11C2211yescharacteristic
31C2×C11×#117—21no—
32C22×C11×C4⋊C4—21no—
33C22×C11×C4⋊C4—21no—
34C22×C42×C11C2211yescharacteristic
35C11×#497C22116yescomplemented
36C11×#491C22116yescomplemented
37C11×#462C22116yescomplemented
38C11×#461C22116yescomplemented
39C11×#451C22116yescomplemented
40C11×#448C22116yes—
41C11×#432C2218yescomplemented
42C2×C11×C4⋊C8C2212yes—
43C2×C11×#103C2214yes—
44C2×C11×#103C2214yes—
45C2×C11×C22⋊C8C2212yes—
46C2×C11×#97C2212yes—
47C22×Q8×C11—24no—
48C22×Q8×C11—22no—
49C22×Q8×C11—48no—
50C22×Q8×C11C2311yescharacteristic
51C22×Q8×C11C2314yes—
52C22×Q8×C11C2318yes—
53C22×D4×C11—21no—
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11—22no—
56C23×C4×C11—21no—
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C2×C11×Q16—48no—
61C2×C11×Q16C23116yes—
62C2×C11×SD16—48no—
63C2×C11×SD16C23116yes—
64C22×C8×C11C2314yes—
65C11×C4⋊Q8—24no—
66C11×C4⋊Q8—24no—
67C11×C4⋊Q8—28no—
68C11×C4⋊Q8—28no—
69C11×C4⋊Q8C2318yes—
70C11×C4⋊Q8C2318yes—
71C11×#126—28no—
72C11×#125—22no—
73C11×#125C2314yes—
74C11×#124—22no—
75C11×#124C2314yes—
76C11×#123—28no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8C2314yes—
79C11×#121—22no—
80C11×#121C2314yes—
81C4×Q8×C11—22no—
82C4×Q8×C11C2314yes—
83C4×D4×C11—28no—
84C4×D4×C11—22no—
85C4×D4×C11C2314yes—
86C11×#117—28no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—28no—
92C2×C11×C4⋊C4—28no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C42×C11—21no—
105C2×C42×C11D411yescharacteristic
106C2×C42×C11D411yescharacteristic
107C2×C42×C11D414yes—
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2314yes—
111C11×C4⋊C8C2318yes—
112C11×#103C23116yes—
113C11×#103C23116yes—
114C11×C22⋊C8C2318yes—
115C11×#97C2318yes—
116C2×#3218C1111yesmaximal, characteristic, direct product factor, Sylow
117C24×C11—21no—
118C24×C11C2×D411yescharacteristic
119C2×Q8×C11—21no—
120C2×Q8×C11—28no—
121C2×Q8×C11—24no—
122C2×Q8×C11—28no—
123C2×Q8×C11—24no—
124C2×Q8×C11—28no—
125C2×Q8×C11—416no—
126C2×Q8×C11—48no—
127C2×Q8×C11—416no—
128C2×Q8×C11C2418yes—
129C2×Q8×C11C2412yes—
130C2×D4×C11—24no—
131C2×D4×C11—21no—
132C2×D4×C11—24no—
133C2×D4×C11—44no—
134C2×D4×C11C2412yes—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—28no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—48no—
145C22×C4×C11—44no—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2412yes—
155C22×C4×C11C2411yescharacteristic
156C11×Q16—416no—
157C11×SD16—416no—
158C2×C8×C11—28no—
159C2×C8×C11C2418yes—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—28no—
162C11×C4⋊C4—28no—
163C11×C4⋊C4—28no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C2412yes—
171C11×C4⋊C4C2412yes—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—24no—
177C42×C11—24no—
178C42×C11C2×D414yes—
179C42×C11C2×D412yes—
180C42×C11C2×D412yes—
181C42×C11C2×D414yes—
182C42×C11C2412yes—
183C42×C11C2412yes—
184C22×C4⋊Q8C2×C1111yescharacteristic, complemented
185C2×#529C2×C1111yescharacteristic
186#3218C2×C11116yesdirect product factor
187C2×#497C2×C1112yescomplemented
188C2×#491C2×C1112yescomplemented
189C2×#462C2×C1112yescomplemented
190C2×#461C2×C1112yescomplemented
191C2×#451C2×C1112yescomplemented
192C2×#448C2×C1112yes—
193C2×#432C2×C1111yescharacteristic, complemented
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11#13714yes—
201C23×C11C22×D412yes—
202C23×C11C22×D411yescharacteristic
203Q8×C11—28no—
204Q8×C11—24no—
205Q8×C11—28no—
206Q8×C11—416no—
207Q8×C11—42no—
208Q8×C11—48no—
209D4×C11—24no—
210D4×C11—48no—
211D4×C11—42no—
212C2×C4×C11—22no—
213C2×C4×C11—28no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—28no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—28no—
224C2×C4×C11—416no—
225C2×C4×C11—48no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—48no—
230C2×C4×C11#13714yes—
231C2×C4×C11C22×D412yes—
232C2×C4×C11C22×D412yes—
233C2×C4×C11C22×D412yes—
234C2×C4×C11C22×D412yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D412yes—
237C2×C4×C11H(5,𝔽2)14yes—
238C2×C4×C11C2511yescharacteristic
239C8×C11—28no—
240C23×Q8C22×C1112yes—
241C22×Q16C22×C1114yes—
242C22×SD16C22×C1114yes—
243C2×C4⋊Q8—21no—
244C2×C4⋊Q8—21no—
245C2×C4⋊Q8—24no—
246C2×C4⋊Q8C22×C1112yes—
247C2×C4⋊Q8C22×C1112yes—
248C2×C4⋊Q8C22×C1118yescomplemented
249#529—24no—
250#529C22×C1118yes—
251C2×#126—21no—
252C2×#125C22×C1111yescharacteristic
253C2×#124C22×C1111yescharacteristic
254C2×#123—21no—
255C2×C22⋊Q8C22×C1111yescharacteristic
256C2×#121C22×C1111yescharacteristic
257C2×C4×Q8C22×C1111yescharacteristic
258C2×C4×D4—21no—
259C2×C4×D4C22×C1111yescharacteristic
260C2×#117—21no—
261C22×C4⋊C4—21no—
262C22×C4⋊C4—21no—
263C22×C42C22×C1111yescharacteristic
264#497C22×C11116yescomplemented
265#491C22×C11116yescomplemented
266#462C22×C11116yescomplemented
267#461C22×C11116yescomplemented
268#451C22×C11116yescomplemented
269#448C22×C11116yes—
270#432C22×C1118yescomplemented
271C2×C4⋊C8C22×C1112yes—
272C2×#103C22×C1114yes—
273C2×#103C22×C1114yes—
274C2×C22⋊C8C22×C1112yes—
275C2×#97C22×C1112yes—
276C22×C11—22no—
277C22×C11—28no—
278C22×C11—22no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—84no—
283C22×C11#53512yes—
284C22×C11C2×#13714yes—
285C22×C11C2×#13712yes—
286C22×C11C2×#13712yes—
287C22×C11C23×D411yescharacteristic
288C4×C11—22no—
289C4×C11—22no—
290C4×C11—22no—
291C4×C11—22no—
292C4×C11—48no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11#53512yes—
297C4×C11C2×#13714yes—
298C4×C11C2×H(5,𝔽2)12yes—
299C22×Q8—22no—
300C22×Q8—24no—
301C22×Q8—48no—
302C22×Q8C23×C1111yescharacteristic
303C22×Q8C23×C1114yes—
304C22×Q8C23×C1118yes—
305C22×D4—21no—
306C22×D4C23×C1111yescharacteristic
307C23×C4—22no—
308C23×C4—21no—
309C23×C4D4×C1111yescharacteristic
310C23×C4D4×C1111yescharacteristic
311C23×C4C23×C1111yescharacteristic
312C2×Q16—48no—
313C2×Q16C23×C11116yes—
314C2×SD16—48no—
315C2×SD16C23×C11116yes—
316C22×C8C23×C1114yes—
317C4⋊Q8—24no—
318C4⋊Q8—24no—
319C4⋊Q8—28no—
320C4⋊Q8—28no—
321C4⋊Q8C23×C1118yes—
322C4⋊Q8C23×C1118yes—
323#126—28no—
324#125—22no—
325#125C23×C1114yes—
326#124—22no—
327#124C23×C1114yes—
328#123—28no—
329C22⋊Q8—22no—
330C22⋊Q8C23×C1114yes—
331#121—22no—
332#121C23×C1114yes—
333C4×Q8—22no—
334C4×Q8C23×C1114yes—
335C4×D4—28no—
336C4×D4—22no—
337C4×D4C23×C1114yes—
338#117—28no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4C23×C1111yescharacteristic
350C2×C4⋊C4C23×C1111yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C42—21no—
357C2×C42D4×C1111yescharacteristic
358C2×C42D4×C1111yescharacteristic
359C2×C42D4×C1114yes—
360C2×C42C23×C1111yescharacteristic
361C2×C42C23×C1111yescharacteristic
362C2×C42C23×C1114yes—
363C4⋊C8C23×C1118yes—
364#103C23×C11116yes—
365#103C23×C11116yes—
366C22⋊C8C23×C1118yes—
367#97C23×C1118yes—
368C2×C11—24no—
369C2×C11—82no—
370C2×C11#321814yesdirect product factor
371C2×C11C2×#53511yescharacteristic
372C2×C11C22×#13711yescharacteristic
373C2×C11C22×#13711yescharacteristic
374C24—21no—
375C24C2×D4×C1111yescharacteristic
376C2×Q8—21no—
377C2×Q8—28no—
378C2×Q8—24no—
379C2×Q8—28no—
380C2×Q8—24no—
381C2×Q8—28no—
382C2×Q8—416no—
383C2×Q8—48no—
384C2×Q8—416no—
385C2×Q8C24×C1118yes—
386C2×Q8C24×C1112yes—
387C2×D4—24no—
388C2×D4—21no—
389C2×D4—24no—
390C2×D4—44no—
391C2×D4C24×C1112yes—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—28no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—48no—
402C22×C4—44no—
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C2×D4×C1112yes—
405C22×C4C2×D4×C1111yescharacteristic
406C22×C4C2×D4×C1111yescharacteristic
407C22×C4C2×D4×C1111yescharacteristic
408C22×C4C2×D4×C1114yes—
409C22×C4C2×D4×C1114yes—
410C22×C4C2×D4×C1111yescharacteristic
411C22×C4C24×C1112yes—
412C22×C4C24×C1111yescharacteristic
413Q16—416no—
414SD16—416no—
415C2×C8—28no—
416C2×C8C24×C1118yes—
417C4⋊C4—28no—
418C4⋊C4—28no—
419C4⋊C4—28no—
420C4⋊C4—28no—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4C24×C1112yes—
428C4⋊C4C24×C1112yes—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C42—24no—
435C42C2×D4×C1114yes—
436C42C2×D4×C1112yes—
437C42C2×D4×C1112yes—
438C42C2×D4×C1114yes—
439C42C24×C1112yes—
440C42C24×C1112yes—
441C11C2×#321811yescharacteristic, direct product factor, Sylow
442C23—22no—
443C23—22no—
444C23—22no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23C11×#13714yes—
449C23C22×D4×C1112yes—
450C23C22×D4×C1111yescharacteristic
451Q8—28no—
452Q8—24no—
453Q8—28no—
454Q8—416no—
455Q8—42no—
456Q8—48no—
457D4—24no—
458D4—48no—
459D4—42no—
460C2×C4—22no—
461C2×C4—28no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—28no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—28no—
472C2×C4—416no—
473C2×C4—48no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—48no—
478C2×C4C11×#13714yes—
479C2×C4C22×D4×C1112yes—
480C2×C4C22×D4×C1112yes—
481C2×C4C22×D4×C1112yes—
482C2×C4C22×D4×C1112yes—
483C2×C4C22×D4×C1111yescharacteristic
484C2×C4C22×D4×C1112yes—
485C2×C4C11×H(5,𝔽2)14yes—
486C2×C4C25×C1111yescharacteristic
487C8—28no—
488C22—22no—
489C22—28no—
490C22—22no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—84no—
495C22C11×#53512yes—
496C22C2×C11×#13714yes—
497C22C2×C11×#13712yes—
498C22C2×C11×#13712yes—
499C22C23×D4×C1111yescharacteristic
500C4—22no—
501C4—22no—
502C4—22no—
503C4—22no—
504C4—48no—
505C4—42no—
506C4—42no—
507C4—42no—
508C4C11×#53512yes—
509C4C2×C11×#13714yes—
510C4C2×C11×H(5,𝔽2)12yes—
511C2—24no—
512C2—82no—
513C2C11×#321814yesdirect product factor
514C2C2×C11×#53511yescharacteristic
515C2C22×C11×#13711yescharacteristic
516C2C22×C11×#13711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×C4⋊Q8C2semidirect
3. C11×#3218C2direct (N × H)
4. C2×C11×#497C2semidirect
5. C2×C11×#491C2semidirect
6. C2×C11×#462C2semidirect
7. C2×C11×#461C2semidirect
8. C2×C11×#451C2semidirect
10. C2×C11×#432C2semidirect
19. C2×C11×C4⋊Q8C22semidirect
35. C11×#497C22semidirect
36. C11×#491C22semidirect
37. C11×#462C22semidirect
38. C11×#461C22semidirect
39. C11×#451C22semidirect
41. C11×#432C22semidirect
116. C2×#3218C11direct (N × H)
184. C22×C4⋊Q8C2×C11semidirect
186. #3218C2×C11direct (N × H)
187. C2×#497C2×C11semidirect
188. C2×#491C2×C11semidirect
189. C2×#462C2×C11semidirect
190. C2×#461C2×C11semidirect
191. C2×#451C2×C11semidirect
193. C2×#432C2×C11semidirect
248. C2×C4⋊Q8C22×C11semidirect
264. #497C22×C11semidirect
265. #491C22×C11semidirect
266. #462C22×C11semidirect
267. #461C22×C11semidirect
268. #451C22×C11semidirect
270. #432C22×C11semidirect
370. C2×C11#3218direct (N × H)
441. C11C2×#3218direct (N × H)
513. C2C11×#3218direct (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
C2×C11×#5292
C11×#32182
C2×C11×#4972
C2×C11×#4912
C2×C11×#4622
C2×C11×#4612
C2×C11×#4512
C2×C11×#4482
C2×C11×#4322
C2×#321811