Finite Group Databasebeta

← C11×#23310 #14600503

Subgroups — C11×#23310 #14600503

Order 2816.

918 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2388C211yesmaximal, characteristic
2C11×#1955C211yesmaximal, characteristic, complemented
3C11×#1954C212yesmaximal, complemented
4C11×#1924C212yesmaximal, complemented
5C11×#1923C212yesmaximal, complemented
6C11×#1923C212yesmaximal, complemented
7C11×#1869C212yesmaximal, complemented
8C11×#1869C211yesmaximal, characteristic, complemented
9C11×#1780C212yesmaximal, complemented
10C22×C11×#41C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C2×C4×D4×C11C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C4⋊C8C2212yes—
16C2×C11×C22⋊C8C2212yes—
17C2×C11×C22⋊C8C2212yes—
18C2×C11×C22⋊C8C2212yes—
19C2×C11×C22⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2212yes—
21C2×C11×C22⋊C8C2212yes—
22C2×C11×C22⋊C8C2212yes—
23C2×C11×C22⋊C8C2212yes—
24C2×C11×#97C2211yescharacteristic
25C2×C4×C8×C11C2212yes—
26C11×#395C411yescharacteristic
27C11×#394C412yes—
28C11×#394C411yescharacteristic
29C11×#393C411yescharacteristic
30C11×#392C411yescharacteristic
31C11×#392C412yes—
32C4×C11×C22⋊C4C2211yescharacteristic
33C4×C11×C22⋊C4C2212yes—
34C11×#336C2212yes—
35C11×#336C2212yes—
36C11×#336C2212yes—
37C2×C11×#41—41no—
38C2×C11×#41—42no—
39C2×C11×#41—41no—
40C2×C11×#41—42no—
41C22×Q8×C11C2×C411yescharacteristic
42C22×D4×C11C2×C412yes—
43C22×D4×C11C2×C411yescharacteristic
44C22×D4×C11C2×C412yes—
45C22×D4×C11C2×C411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C22×C8×C11—41no—
50C22×C8×C11—42no—
51C22×C8×C11C2312yes—
52C22×C8×C11C2312yes—
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C4×D4×C11—42no—
56C4×D4×C11—41no—
57C4×D4×C11—42no—
58C4×D4×C11—41no—
59C2×C11×C4⋊C4C2×C411yescharacteristic
60C2×C11×C4⋊C4C2×C412yes—
61C2×C11×C22⋊C4C2×C412yes—
62C2×C11×C22⋊C4C2×C412yes—
63C2×C11×C22⋊C4C2×C412yes—
64C2×C11×C22⋊C4C2×C412yes—
65C2×C11×C22⋊C4C2×C411yescharacteristic
66C2×C11×C22⋊C4C2×C412yes—
67C2×C11×C22⋊C4C2×C411yescharacteristic
68C2×C42×C11C2312yes—
69C2×C42×C11C2311yescharacteristic
70C11×C4⋊C8—41no—
71C11×C4⋊C8—42no—
72C11×C22⋊C8—42no—
73C11×C22⋊C8—42no—
74C11×C22⋊C8—42no—
75C11×C22⋊C8—41no—
76C11×C22⋊C8—42no—
77C11×C22⋊C8—42no—
78C11×C22⋊C8—42no—
79C11×C22⋊C8—42no—
80C11×#97—41no—
81C4×C8×C11—42no—
82C11×#95C2×C412yes—
83C11×#95C2×C411yescharacteristic
84C11×#95C2×C411yescharacteristic
85C11×#95C2×C412yes—
86#23310C1111yesmaximal, characteristic, direct product factor, Sylow
87C24×C11C22×C411yescharacteristic
88C24×C11C22×C412yes—
89C24×C11C22×C411yescharacteristic
90C11×#41—44no—
91C11×#41—48no—
92C11×#41—44no—
93C2×Q8×C11—41no—
94C2×Q8×C11—42no—
95C2×D4×C11—24no—
96C2×D4×C11—22no—
97C2×D4×C11—24no—
98C2×D4×C11—42no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—42no—
103C2×D4×C11—42no—
104C2×D4×C11—42no—
105C2×D4×C11—42no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C412yes—
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C22×C412yes—
127C22×C4×C11C2411yescharacteristic
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—44no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—41no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—24no—
145C11×C22⋊C4—42no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—42no—
148C11×C22⋊C4—41no—
149C11×C22⋊C4—42no—
150C42×C11—22no—
151C42×C11—21no—
152C42×C11—22no—
153C42×C11—21no—
154#2388C2×C1111yescharacteristic
155#1955C2×C1111yescharacteristic, complemented
156#1954C2×C1112yescomplemented
157#1924C2×C1112yescomplemented
158#1923C2×C1112yescomplemented
159#1923C2×C1112yescomplemented
160#1869C2×C1112yescomplemented
161#1869C2×C1111yescharacteristic, complemented
162#1780C2×C1112yescomplemented
163C23×C11—21no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—21no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—21no—
179C23×C11#13112yes—
180C23×C11C23×C411yescharacteristic
181Q8×C11—44no—
182D4×C11—48no—
183D4×C11—44no—
184D4×C11—44no—
185D4×C11—48no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11#13114yes—
214C2×C4×C11H(5,𝔽2)11yescharacteristic
215C2×C4×C11H(5,𝔽2)12yes—
216C2×C4×C11H(5,𝔽2)11yescharacteristic
217C2×C4×C11H(5,𝔽2)12yes—
218C8×C11—42no—
219C8×C11—42no—
220C8×C11—42no—
221C8×C11—42no—
222C22×#41C22×C1111yescharacteristic
223C23×C8C22×C1111yescharacteristic
224C2×C4×D4C22×C1112yes—
225C2×C4×D4C22×C1111yescharacteristic
226C2×C4⋊C8C22×C1111yescharacteristic
227C2×C4⋊C8C22×C1112yes—
228C2×C22⋊C8C22×C1112yes—
229C2×C22⋊C8C22×C1112yes—
230C2×C22⋊C8C22×C1112yes—
231C2×C22⋊C8C22×C1111yescharacteristic
232C2×C22⋊C8C22×C1112yes—
233C2×C22⋊C8C22×C1112yes—
234C2×C22⋊C8C22×C1112yes—
235C2×C22⋊C8C22×C1112yes—
236C2×#97C22×C1111yescharacteristic
237C2×C4×C8C22×C1112yes—
238#395C4×C1111yescharacteristic
239#394C4×C1112yes—
240#394C4×C1111yescharacteristic
241#393C4×C1111yescharacteristic
242#392C4×C1111yescharacteristic
243#392C4×C1112yes—
244C4×C22⋊C4C22×C1111yescharacteristic
245C4×C22⋊C4C22×C1112yes—
246#336C22×C1112yes—
247#336C22×C1112yes—
248#336C22×C1112yes—
249C22×C11—22no—
250C22×C11—24no—
251C22×C11—41no—
252C22×C11—41no—
253C22×C11—42no—
254C22×C11—41no—
255C22×C11—42no—
256C22×C11—41no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—41no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11#51811yescharacteristic
267C22×C11#51812yes—
268C22×C11C2×#13111yescharacteristic
269C22×C11C2×#13112yes—
270C22×C11#56811yescharacteristic
271C4×C11—24no—
272C4×C11—41no—
273C4×C11—41no—
274C4×C11—42no—
275C4×C11—41no—
276C4×C11—41no—
277C4×C11—42no—
278C4×C11#56012yes—
279C4×C11#56011yescharacteristic
280C4×C11H(3,𝔽4)11yescharacteristic
281C2×#41—41no—
282C2×#41—42no—
283C2×#41—41no—
284C2×#41—42no—
285C22×Q8C2×C4×C1111yescharacteristic
286C22×D4C2×C4×C1112yes—
287C22×D4C2×C4×C1111yescharacteristic
288C22×D4C2×C4×C1112yes—
289C22×D4C2×C4×C1111yescharacteristic
290C23×C4C23×C1111yescharacteristic
291C23×C4C23×C1112yes—
292C23×C4C23×C1111yescharacteristic
293C22×C8—41no—
294C22×C8—42no—
295C22×C8C23×C1112yes—
296C22×C8C23×C1112yes—
297C22×C8C23×C1112yes—
298C22×C8C23×C1112yes—
299C4×D4—42no—
300C4×D4—41no—
301C4×D4—42no—
302C4×D4—41no—
303C2×C4⋊C4C2×C4×C1111yescharacteristic
304C2×C4⋊C4C2×C4×C1112yes—
305C2×C22⋊C4C2×C4×C1112yes—
306C2×C22⋊C4C2×C4×C1112yes—
307C2×C22⋊C4C2×C4×C1112yes—
308C2×C22⋊C4C2×C4×C1111yescharacteristic
309C2×C22⋊C4C2×C4×C1112yes—
310C2×C22⋊C4C2×C4×C1111yescharacteristic
311C2×C22⋊C4C2×C4×C1112yes—
312C2×C42C23×C1112yes—
313C2×C42C23×C1111yescharacteristic
314C4⋊C8—41no—
315C4⋊C8—42no—
316C22⋊C8—42no—
317C22⋊C8—42no—
318C22⋊C8—42no—
319C22⋊C8—41no—
320C22⋊C8—42no—
321C22⋊C8—42no—
322C22⋊C8—42no—
323C22⋊C8—42no—
324#97—41no—
325C4×C8—42no—
326#95C2×C4×C1112yes—
327#95C2×C4×C1111yescharacteristic
328#95C2×C4×C1111yescharacteristic
329#95C2×C4×C1112yes—
330C2×C11—42no—
331C2×C11—81no—
332C2×C11—82no—
333C2×C11#237511yescharacteristic
334C2×C11#297611yescharacteristic
335C2×C11#297712yes—
336C2×C11#297911yescharacteristic
337C2×C11#298112yes—
338C24C22×C4×C1111yescharacteristic
339C24C22×C4×C1112yes—
340C24C22×C4×C1111yescharacteristic
341#41—44no—
342#41—48no—
343#41—44no—
344C2×Q8—41no—
345C2×Q8—42no—
346C2×D4—24no—
347C2×D4—22no—
348C2×D4—24no—
349C2×D4—42no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—42no—
353C2×D4—42no—
354C2×D4—42no—
355C2×D4—42no—
356C2×D4—41no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4C22×C4×C1111yescharacteristic
372C22×C4C22×C4×C1112yes—
373C22×C4C22×C4×C1111yescharacteristic
374C22×C4C22×C4×C1111yescharacteristic
375C22×C4C22×C4×C1112yes—
376C22×C4C22×C4×C1111yescharacteristic
377C22×C4C22×C4×C1112yes—
378C22×C4C24×C1111yescharacteristic
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—44no—
392C4⋊C4—42no—
393C4⋊C4—41no—
394C22⋊C4—24no—
395C22⋊C4—24no—
396C22⋊C4—41no—
397C22⋊C4—42no—
398C22⋊C4—41no—
399C22⋊C4—42no—
400C22⋊C4—42no—
401C42—22no—
402C42—21no—
403C42—22no—
404C42—21no—
405C11#2331011yescharacteristic, direct product factor, Sylow
406C23—21no—
407C23—22no—
408C23—22no—
409C23—21no—
410C23—21no—
411C23—22no—
412C23—22no—
413C23—22no—
414C23—22no—
415C23—22no—
416C23—22no—
417C23—21no—
418C23—22no—
419C23—22no—
420C23—22no—
421C23—21no—
422C23C11×#13112yes—
423C23C23×C4×C1111yescharacteristic
424Q8—44no—
425D4—48no—
426D4—44no—
427D4—44no—
428D4—48no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4C11×#13114yes—
457C2×C4C11×H(5,𝔽2)11yescharacteristic
458C2×C4C11×H(5,𝔽2)12yes—
459C2×C4C11×H(5,𝔽2)11yescharacteristic
460C2×C4C11×H(5,𝔽2)12yes—
461C8—42no—
462C8—42no—
463C8—42no—
464C8—42no—
465C22—22no—
466C22—24no—
467C22—41no—
468C22—42no—
469C22—41no—
470C22—41no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—41no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—41no—
481C22—42no—
482C22C11×#51811yescharacteristic
483C22C11×#51812yes—
484C22C2×C11×#13111yescharacteristic
485C22C2×C11×#13112yes—
486C22C11×#56811yescharacteristic
487C4—24no—
488C4—41no—
489C4—41no—
490C4—42no—
491C4—41no—
492C4—42no—
493C4—41no—
494C4C11×#56011yescharacteristic
495C4C11×#56012yes—
496C4C11×H(3,𝔽4)11yescharacteristic
497C2—42no—
498C2—81no—
499C2—82no—
500C2C11×#237511yescharacteristic
501C2C11×#297611yescharacteristic
502C2C11×#297712yes—
503C2C11×#297911yescharacteristic
504C2C11×#298112yes—
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC11×#2388C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1955C2semidirect
3. C11×#1954C2semidirect
4. C11×#1924C2semidirect
5. C11×#1923C2semidirect
6. C11×#1923C2semidirect
7. C11×#1869C2semidirect
8. C11×#1869C2semidirect
9. C11×#1780C2semidirect
86. #23310C11direct (N × H)
155. #1955C2×C11semidirect
156. #1954C2×C11semidirect
157. #1924C2×C11semidirect
158. #1923C2×C11semidirect
159. #1923C2×C11semidirect
160. #1869C2×C11semidirect
161. #1869C2×C11semidirect
162. #1780C2×C11semidirect
405. C11#23310direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23882
C11×#19552
C11×#19542
C11×#19242
C11×#19232
C11×#18692
C11×#17802
#2331011