Finite Group Databasebeta

← C2×C11×#3385 #14638552

Subgroups — C2×C11×#3385 #14638552

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q82×C11C211yesmaximal, characteristic, complemented
2C2×C11×#554C211yesmaximal, characteristic
3C11×#3385C2116yesmaximal, direct product factor
4C2×C11×#501C212yesmaximal, complemented
5C2×C11×#500C211yesmaximal, characteristic, complemented
6C2×C11×#479C212yesmaximal, complemented
7C2×C11×#477C211yesmaximal, characteristic, complemented
8C2×C11×#476C211yesmaximal, characteristic
9C2×C11×#474C212yesmaximal
10C2×C11×#446C211yesmaximal, characteristic, complemented
11C2×C11×#440C212yesmaximal
12C2×C4×C11×SD16C211yesmaximal, characteristic
13C22×C11×SD16C2211yescharacteristic
14Q82×C11—24no—
15Q82×C11C2218yescomplemented
16C11×#554—24no—
17C11×#554C2218yes—
18C2×C11×C4⋊Q8—21no—
19C2×C11×C4⋊Q8—22no—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C11×C4⋊Q8C2212yes—
23C2×C11×#125C2212yes—
24C2×C11×C22⋊Q8—21no—
25C2×C11×C22⋊Q8—22no—
26C2×C4×Q8×C11—21no—
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×Q8×C11C2212yes—
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C2×C4×D4×C11C2212yes—
32C22×C11×C4⋊C4—21no—
33C11×#501C22116yescomplemented
34C11×#500C2218yescomplemented
35C11×#479C22116yescomplemented
36C11×#477C2218yescomplemented
37C11×#476C2218yes—
38C11×#474C22116yes—
39C11×#446C2218yescomplemented
40C11×#440C22116yes—
41C4×C11×SD16C2218yes—
42C2×C11×#107C2212yes—
43C2×C11×#107C2212yes—
44C2×C11×#107C2212yes—
45C2×C11×#106C2211yescharacteristic
46C2×C11×#106C2212yes—
47C2×C11×C4⋊C8C2212yes—
48C2×C11×C4⋊C8C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2212yes—
51C2×C11×#102C2211yescharacteristic
52C2×C11×#102C2212yes—
53C2×C11×#97C2212yes—
54C2×C4×C8×C11C2211yescharacteristic
55C22×Q8×C11—21no—
56C22×Q8×C11—21no—
57C22×Q8×C11—22no—
58C22×Q8×C11D411yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11—22no—
63C2×C11×SD16Q818yescomplemented
64C2×C11×SD16C2314yes—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2312yes—
67C22×C8×C11C2311yescharacteristic
68C11×C4⋊Q8—28no—
69C11×C4⋊Q8—216no—
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8—24no—
72C11×C4⋊Q8—22no—
73C11×C4⋊Q8C2314yes—
74C11×C4⋊Q8C2314yes—
75C11×C4⋊Q8C2318yes—
76C11×#125—24no—
77C11×#125C2318yes—
78C11×C22⋊Q8—28no—
79C11×C22⋊Q8—216no—
80C4×Q8×C11—28no—
81C4×Q8×C11—24no—
82C4×Q8×C11—22no—
83C4×Q8×C11D414yes—
84C4×Q8×C11C2314yes—
85C4×Q8×C11C2318yes—
86C4×Q8×C11C2314yes—
87C4×D4×C11—24no—
88C4×D4×C11—22no—
89C4×D4×C11C2314yes—
90C4×D4×C11C2318yes—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—28no—
99C2×C11×C4⋊C4D411yescharacteristic
100C2×C11×C4⋊C4D412yes—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2312yes—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—22no—
107C2×C42×C11—22no—
108C2×C42×C11—21no—
109C2×C42×C11C2312yes—
110C2×C42×C11C2311yescharacteristic
111C11×#107C2318yes—
112C11×#107C2318yes—
113C11×#107C2318yes—
114C11×#106C2314yes—
115C11×#106C2318yes—
116C11×C4⋊C8C2318yes—
117C11×C4⋊C8C2314yes—
118C11×#103C2314yes—
119C11×#103C2318yes—
120C11×#102C2314yes—
121C11×#102C2318yes—
122C11×#97C2318yes—
123C4×C8×C11C2314yes—
124C2×#3385C1111yesmaximal, characteristic, direct product factor, Sylow
125C24×C11—21no—
126C2×Q8×C11—24no—
127C2×Q8×C11—21no—
128C2×Q8×C11—24no—
129C2×Q8×C11—24no—
130C2×Q8×C11—28no—
131C2×Q8×C11—22no—
132C2×Q8×C11—84no—
133C2×Q8×C11—82no—
134C2×Q8×C11—82no—
135C2×Q8×C11C2×D414yes—
136C2×Q8×C11C2×Q814yes—
137C2×Q8×C11C2412yes—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11C2×Q814yes—
141C2×D4×C11C2412yes—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—24no—
148C22×C4×C11—28no—
149C22×C4×C11—44no—
150C22×C4×C11—84no—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C11×SD16C2×Q8116yescomplemented
157C2×C8×C11—22no—
158C2×C8×C11—24no—
159C2×C8×C11C2×Q814yes—
160C2×C8×C11C2412yes—
161C2×C8×C11C2414yes—
162C2×C8×C11C2412yes—
163C11×C4⋊C4—28no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—28no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—28no—
169C11×C4⋊C4—28no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4C2×D414yes—
175C11×C4⋊C4C2×D418yes—
176C11×C4⋊C4C2412yes—
177C11×C4⋊C4C2414yes—
178C11×C4⋊C4C2412yes—
179C11×C4⋊C4C2414yes—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—28no—
182C42×C11—28no—
183C42×C11—24no—
184C42×C11C2×D414yes—
185C42×C11C2×D412yes—
186C42×C11C2412yes—
187C42×C11C2414yes—
188C2×Q82C2×C1111yescharacteristic, complemented
189C2×#554C2×C1111yescharacteristic
190#3385C2×C11116yesdirect product factor
191C2×#501C2×C1112yescomplemented
192C2×#500C2×C1111yescharacteristic, complemented
193C2×#479C2×C1112yescomplemented
194C2×#477C2×C1111yescharacteristic, complemented
195C2×#476C2×C1111yescharacteristic
196C2×#474C2×C1112yes—
197C2×#446C2×C1111yescharacteristic, complemented
198C2×#440C2×C1112yes—
199C2×C4×SD16C2×C1111yescharacteristic
200C23×C11—24no—
201C23×C11—22no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11C22×D411yescharacteristic
205Q8×C11—24no—
206Q8×C11—28no—
207Q8×C11—22no—
208Q8×C11—88no—
209Q8×C11—84no—
210Q8×C11—84no—
211Q8×C11C22×Q814yes—
212D4×C11—24no—
213D4×C11—22no—
214D4×C11C22×Q814yes—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—42no—
225C2×C4×C11—44no—
226C2×C4×C11—42no—
227C2×C4×C11—44no—
228C2×C4×C11—48no—
229C2×C4×C11—88no—
230C2×C4×C11#13714yes—
231C2×C4×C11C22×D414yes—
232C2×C4×C11C22×D412yes—
233C2×C4×C11C22×D414yes—
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D412yes—
236C2×C4×C11C22×Q812yes—
237C2×C4×C112−1+412yes—
238C2×C4×C11C2511yescharacteristic
239C8×C11—22no—
240C8×C11—24no—
241C8×C11C22×Q814yes—
242C22×SD16C22×C1111yescharacteristic
243Q82—24no—
244Q82C22×C1118yescomplemented
245#554—24no—
246#554C22×C1118yes—
247C2×C4⋊Q8—21no—
248C2×C4⋊Q8—22no—
249C2×C4⋊Q8C22×C1111yescharacteristic
250C2×C4⋊Q8C22×C1111yescharacteristic
251C2×C4⋊Q8C22×C1112yes—
252C2×#125C22×C1112yes—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8—22no—
255C2×C4×Q8—21no—
256C2×C4×Q8C22×C1111yescharacteristic
257C2×C4×Q8C22×C1112yes—
258C2×C4×Q8C22×C1111yescharacteristic
259C2×C4×D4C22×C1111yescharacteristic
260C2×C4×D4C22×C1112yes—
261C22×C4⋊C4—21no—
262#501C22×C11116yescomplemented
263#500C22×C1118yescomplemented
264#479C22×C11116yescomplemented
265#477C22×C1118yescomplemented
266#476C22×C1118yes—
267#474C22×C11116yes—
268#446C22×C1118yescomplemented
269#440C22×C11116yes—
270C4×SD16C22×C1118yes—
271C2×#107C22×C1112yes—
272C2×#107C22×C1112yes—
273C2×#107C22×C1112yes—
274C2×#106C22×C1112yes—
275C2×#106C22×C1111yescharacteristic
276C2×C4⋊C8C22×C1111yescharacteristic
277C2×C4⋊C8C22×C1112yes—
278C2×#103C22×C1112yes—
279C2×#103C22×C1111yescharacteristic
280C2×#102C22×C1111yescharacteristic
281C2×#102C22×C1112yes—
282C2×#97C22×C1112yes—
283C2×C4×C8C22×C1111yescharacteristic
284C22×C11—24no—
285C22×C11—48no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11D4×Q812yes—
289C22×C11C2×#13712yes—
290C22×C11#57612yes—
291C22×C11C23×D411yescharacteristic
292C4×C11—24no—
293C4×C11—24no—
294C4×C11—24no—
295C4×C11—22no—
296C4×C11—42no—
297C4×C11—44no—
298C4×C11—42no—
299C4×C11—44no—
300C4×C11D4×Q812yes—
301C4×C11C2×#13714yes—
302C4×C11C23×Q811yescharacteristic
303C4×C11C2×2−1+411yescharacteristic
304C22×Q8—21no—
305C22×Q8—21no—
306C22×Q8—22no—
307C22×Q8D4×C1111yescharacteristic
308C22×Q8C23×C1111yescharacteristic
309C22×D4C23×C1111yescharacteristic
310C23×C4—21no—
311C23×C4—22no—
312C2×SD16Q8×C1118yescomplemented
313C2×SD16C23×C1114yes—
314C22×C8C23×C1111yescharacteristic
315C22×C8C23×C1112yes—
316C22×C8C23×C1111yescharacteristic
317C4⋊Q8—28no—
318C4⋊Q8—216no—
319C4⋊Q8—22no—
320C4⋊Q8—24no—
321C4⋊Q8—22no—
322C4⋊Q8C23×C1114yes—
323C4⋊Q8C23×C1118yes—
324C4⋊Q8C23×C1114yes—
325#125—24no—
326#125C23×C1118yes—
327C22⋊Q8—28no—
328C22⋊Q8—216no—
329C4×Q8—28no—
330C4×Q8—24no—
331C4×Q8—22no—
332C4×Q8D4×C1114yes—
333C4×Q8C23×C1114yes—
334C4×Q8C23×C1118yes—
335C4×Q8C23×C1114yes—
336C4×D4—24no—
337C4×D4—22no—
338C4×D4C23×C1114yes—
339C4×D4C23×C1118yes—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4D4×C1111yescharacteristic
349C2×C4⋊C4D4×C1112yes—
350C2×C4⋊C4C23×C1111yescharacteristic
351C2×C4⋊C4C23×C1112yes—
352C2×C4⋊C4C23×C1111yescharacteristic
353C2×C4⋊C4C23×C1112yes—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—22no—
356C2×C42—22no—
357C2×C42—21no—
358C2×C42C23×C1112yes—
359C2×C42C23×C1111yescharacteristic
360#107C23×C1118yes—
361#107C23×C1118yes—
362#107C23×C1118yes—
363#106C23×C1114yes—
364#106C23×C1118yes—
365C4⋊C8C23×C1118yes—
366C4⋊C8C23×C1114yes—
367#103C23×C1114yes—
368#103C23×C1118yes—
369#102C23×C1114yes—
370#102C23×C1118yes—
371#97C23×C1118yes—
372C4×C8C23×C1114yes—
373C2×C11—44no—
374C2×C11#338514yesdirect product factor
375C2×C11C2×D4×Q811yescharacteristic
376C2×C11C22×#13711yescharacteristic
377C2×C11C2×#57611yescharacteristic
378C24—21no—
379C2×Q8—24no—
380C2×Q8—21no—
381C2×Q8—24no—
382C2×Q8—24no—
383C2×Q8—28no—
384C2×Q8—22no—
385C2×Q8—84no—
386C2×Q8—82no—
387C2×Q8—82no—
388C2×Q8C2×D4×C1114yes—
389C2×Q8C2×Q8×C1114yes—
390C2×Q8C24×C1112yes—
391C2×D4—21no—
392C2×D4—22no—
393C2×D4C2×Q8×C1114yes—
394C2×D4C24×C1112yes—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—28no—
402C22×C4—44no—
403C22×C4—84no—
404C22×C4C2×D4×C1112yes—
405C22×C4C2×D4×C1111yescharacteristic
406C22×C4C2×D4×C1112yes—
407C22×C4C2×D4×C1111yescharacteristic
408C22×C4C24×C1111yescharacteristic
409SD16C2×Q8×C11116yescomplemented
410C2×C8—22no—
411C2×C8—24no—
412C2×C8C2×Q8×C1114yes—
413C2×C8C24×C1112yes—
414C2×C8C24×C1114yes—
415C2×C8C24×C1112yes—
416C4⋊C4—28no—
417C4⋊C4—24no—
418C4⋊C4—28no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—28no—
422C4⋊C4—28no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4C2×D4×C1114yes—
428C4⋊C4C2×D4×C1118yes—
429C4⋊C4C24×C1112yes—
430C4⋊C4C24×C1114yes—
431C4⋊C4C24×C1112yes—
432C4⋊C4C24×C1114yes—
433C22⋊C4—24no—
434C22⋊C4—28no—
435C42—28no—
436C42—24no—
437C42C2×D4×C1114yes—
438C42C2×D4×C1112yes—
439C42C24×C1112yes—
440C42C24×C1114yes—
441C11C2×#338511yescharacteristic, direct product factor, Sylow
442C23—24no—
443C23—22no—
444C23—42no—
445C23—42no—
446C23C22×D4×C1111yescharacteristic
447Q8—24no—
448Q8—28no—
449Q8—22no—
450Q8—88no—
451Q8—84no—
452Q8—84no—
453Q8C22×Q8×C1114yes—
454D4—24no—
455D4—22no—
456D4C22×Q8×C1114yes—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—42no—
467C2×C4—44no—
468C2×C4—42no—
469C2×C4—44no—
470C2×C4—48no—
471C2×C4—88no—
472C2×C4C11×#13714yes—
473C2×C4C22×D4×C1114yes—
474C2×C4C22×D4×C1112yes—
475C2×C4C22×D4×C1114yes—
476C2×C4C22×D4×C1111yescharacteristic
477C2×C4C22×D4×C1112yes—
478C2×C4C22×Q8×C1112yes—
479C2×C4C11×2−1+412yes—
480C2×C4C25×C1111yescharacteristic
481C8—22no—
482C8—24no—
483C8C22×Q8×C1114yes—
484C22—24no—
485C22—42no—
486C22—42no—
487C22—48no—
488C22D4×Q8×C1112yes—
489C22C2×C11×#13712yes—
490C22C11×#57612yes—
491C22C23×D4×C1111yescharacteristic
492C4—24no—
493C4—24no—
494C4—24no—
495C4—22no—
496C4—42no—
497C4—44no—
498C4—42no—
499C4—44no—
500C4D4×Q8×C1112yes—
501C4C2×C11×#13714yes—
502C4C23×Q8×C1111yescharacteristic
503C4C2×C11×2−1+411yescharacteristic
504C2—44no—
505C2C11×#338514yesdirect product factor
506C2C2×D4×Q8×C1111yescharacteristic
507C2C22×C11×#13711yescharacteristic
508C2C2×C11×#57611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×Q82×C11C2semidirect
3. C11×#3385C2direct (N × H)
4. C2×C11×#501C2semidirect
5. C2×C11×#500C2semidirect
6. C2×C11×#479C2semidirect
7. C2×C11×#477C2semidirect
10. C2×C11×#446C2semidirect
15. Q82×C11C22semidirect
33. C11×#501C22semidirect
34. C11×#500C22semidirect
35. C11×#479C22semidirect
36. C11×#477C22semidirect
39. C11×#446C22semidirect
63. C2×C11×SD16Q8semidirect
124. C2×#3385C11direct (N × H)
156. C11×SD16C2×Q8semidirect
188. C2×Q82C2×C11semidirect
190. #3385C2×C11direct (N × H)
191. C2×#501C2×C11semidirect
192. C2×#500C2×C11semidirect
193. C2×#479C2×C11semidirect
194. C2×#477C2×C11semidirect
197. C2×#446C2×C11semidirect
244. Q82C22×C11semidirect
262. #501C22×C11semidirect
263. #500C22×C11semidirect
264. #479C22×C11semidirect
265. #477C22×C11semidirect
268. #446C22×C11semidirect
312. C2×SD16Q8×C11semidirect
374. C2×C11#3385direct (N × H)
409. SD16C2×Q8×C11semidirect
441. C11C2×#3385direct (N × H)
505. C2C11×#3385direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q82×C112
C2×C11×#5542
C11×#33852
C2×C11×#5012
C2×C11×#5002
C2×C11×#4792
C2×C11×#4772
C2×C11×#4762
C2×C11×#4742
C2×C11×#4462
C2×C11×#4402
C2×C4×C11×SD162
C2×#338511