Finite Group Databasebeta

← C11×#23670 #14600863

Subgroups — C11×#23670 #14600863

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#428C211yesmaximal, characteristic
2C2×C11×#423C211yesmaximal, characteristic
3C11×#2296C211yesmaximal, characteristic
4C2×C11×#389C211yesmaximal, characteristic
5C11×#2088C212yesmaximal, complemented
6C11×#2088C212yesmaximal, complemented
7C11×#2087C212yesmaximal, complemented
8C11×#2086C212yesmaximal, complemented
9C11×#1736C211yesmaximal, characteristic
10C11×#1736C211yesmaximal, characteristic
11C11×#1736C211yesmaximal, characteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C11×C4⋊C4—21no—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C11×#428—24no—
21C2×C11×#107C2212yes—
22C2×C11×#106C2212yes—
23C11×#423—24no—
24C2×C11×C4⋊C8C2212yes—
25C2×C11×C4⋊C8C2212yes—
26C11×#389—21no—
27C11×#389—21no—
28C11×#389C2212yes—
29C11×#389C2212yes—
30C11×#389C2211yescharacteristic
31C11×#389C2211yescharacteristic
32C11×#389C2211yescharacteristic
33C11×#389C2211yescharacteristic
34C11×#385—21no—
35C11×#385—21no—
36C4×C11×C4⋊C4—21no—
37C4×C11×C4⋊C4—21no—
38C2×C11×#95—21no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C23×C4×C11—21no—
46C23×C4×C11—21no—
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C2×C11×M16—22no—
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C2×C11×M16—22no—
55C2×C11×M16D414yes—
56C22×C8×C11C2312yes—
57C22×C8×C11C2312yes—
58C11×#117—22no—
59C11×#117—22no—
60C11×#117—22no—
61C11×#117Q814yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—44no—
74C2×C11×C4⋊C4Q814yes—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—22no—
84C2×C42×C11—21no—
85C2×C42×C11—22no—
86C2×C42×C11—21no—
87C2×C42×C11D411yescharacteristic
88C2×C42×C11D411yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C11×#107—24no—
92C11×#106—24no—
93C11×C4⋊C8—24no—
94C11×C4⋊C8—24no—
95C11×#95—22no—
96C11×#95—22no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101#23670C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11C2×D411yescharacteristic
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—24no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—41no—
115C22×C4×C11—41no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×Q812yes—
128C22×C4×C11C2×Q812yes—
129C22×C4×C11#4112yes—
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×C4×C11C2411yescharacteristic
133C11×M16—28no—
134C11×M16—44no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11C2×D414yes—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—44no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—44no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4C2×Q814yes—
159C11×C4⋊C4C2×Q812yes—
160C11×C4⋊C4C2×Q812yes—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—42no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—24no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—42no—
171C2×#428C2×C1111yescharacteristic
172C2×#423C2×C1111yescharacteristic
173#2296C2×C1111yescharacteristic
174C2×#389C2×C1111yescharacteristic
175#2088C2×C1112yescomplemented
176#2088C2×C1112yescomplemented
177#2087C2×C1112yescomplemented
178#2086C2×C1112yescomplemented
179#1736C2×C1111yescharacteristic
180#1736C2×C1111yescharacteristic
181#1736C2×C1111yescharacteristic
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11#12112yes—
187C23×C11C22⋊Q812yes—
188C23×C11C22⋊Q812yes—
189C23×C11C22×D411yescharacteristic
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—24no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—44no—
204C2×C4×C11—44no—
205C2×C4×C11—48no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—84no—
222C2×C4×C11#12112yes—
223C2×C4×C11C22⋊Q812yes—
224C2×C4×C11C22⋊Q812yes—
225C2×C4×C11#12314yes—
226C2×C4×C11#12514yes—
227C2×C4×C11#12514yes—
228C2×C4×C11C4⋊Q814yes—
229C2×C4×C11AGL(1,ℤ/8)12yes—
230C2×C4×C11#13712yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×Q811yescharacteristic
233C2×C4×C11C22×Q811yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C8×C11—24no—
238C8×C11—42no—
239C22×M16C22×C1111yescharacteristic
240C22×M16C22×C1111yescharacteristic
241C2×#117C22×C1111yescharacteristic
242C2×#117C22×C1111yescharacteristic
243C22×C4⋊C4—21no—
244C22×C4⋊C4C22×C1111yescharacteristic
245C22×C4⋊C4C22×C1111yescharacteristic
246C22×C42C22×C1111yescharacteristic
247#428—24no—
248C2×#107C22×C1112yes—
249C2×#106C22×C1112yes—
250#423—24no—
251C2×C4⋊C8C22×C1112yes—
252C2×C4⋊C8C22×C1112yes—
253#389—21no—
254#389—21no—
255#389C22×C1111yescharacteristic
256#389C22×C1112yes—
257#389C22×C1111yescharacteristic
258#389C22×C1112yes—
259#389C22×C1111yescharacteristic
260#389C22×C1111yescharacteristic
261#385—21no—
262#385—21no—
263C4×C4⋊C4—21no—
264C4×C4⋊C4—21no—
265C2×#95—21no—
266#340C22×C1112yes—
267#340C22×C1112yes—
268#340C22×C1112yes—
269#340C22×C1112yes—
270#340C22×C1112yes—
271#340C22×C1112yes—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11#39814yes—
279C22×C11C2×#12111yescharacteristic
280C22×C11C2×C22⋊Q811yescharacteristic
281C22×C11C2×C22⋊Q811yescharacteristic
282C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C11C2×#13711yescharacteristic
284C22×C11#57511yescharacteristic
285C22×C11#57511yescharacteristic
286C4×C11—22no—
287C4×C11—22no—
288C4×C11—44no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—41no—
292C4×C11—41no—
293C4×C11—81no—
294C4×C11—82no—
295C4×C11—81no—
296C4×C11#39814yes—
297C4×C11C2×#12311yescharacteristic
298C4×C11C2×#12511yescharacteristic
299C4×C11C2×#12511yescharacteristic
300C4×C11C2×C4⋊Q811yescharacteristic
301C23×C4—21no—
302C23×C4—21no—
303C23×C4D4×C1111yescharacteristic
304C23×C4D4×C1111yescharacteristic
305C23×C4C23×C1111yescharacteristic
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—22no—
310C2×M16—22no—
311C2×M16D4×C1114yes—
312C22×C8C23×C1112yes—
313C22×C8C23×C1112yes—
314#117—22no—
315#117—22no—
316#117—22no—
317#117Q8×C1114yes—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4Q8×C1114yes—
331C2×C4⋊C4C23×C1112yes—
332C2×C4⋊C4C23×C1111yescharacteristic
333C2×C4⋊C4C23×C1111yescharacteristic
334C2×C4⋊C4C23×C1112yes—
335C2×C4⋊C4C23×C1111yescharacteristic
336C2×C4⋊C4C23×C1111yescharacteristic
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C42—21no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—21no—
343C2×C42D4×C1111yescharacteristic
344C2×C42D4×C1111yescharacteristic
345C2×C42C23×C1111yescharacteristic
346C2×C42C23×C1111yescharacteristic
347#107—24no—
348#106—24no—
349C4⋊C8—24no—
350C4⋊C8—24no—
351#95—22no—
352#95—22no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95—21no—
357C2×C11—24no—
358C2×C11C2×#39811yescharacteristic
359C2×C11#305511yescharacteristic
360C2×C11#305611yescharacteristic
361C2×C11#307711yescharacteristic
362C2×C11#307811yescharacteristic
363C2×C11#307911yescharacteristic
364C2×C11#308011yescharacteristic
365C24C2×D4×C1111yescharacteristic
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—24no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4C2×D4×C1111yescharacteristic
385C22×C4C2×D4×C1111yescharacteristic
386C22×C4C2×D4×C1111yescharacteristic
387C22×C4C2×D4×C1111yescharacteristic
388C22×C4C2×D4×C1111yescharacteristic
389C22×C4C2×D4×C1112yes—
390C22×C4C2×Q8×C1112yes—
391C22×C4C2×Q8×C1112yes—
392C22×C4C11×#4112yes—
393C22×C4C11×#4112yes—
394C22×C4C11×#4112yes—
395C22×C4C24×C1111yescharacteristic
396M16—28no—
397M16—44no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8C2×D4×C1114yes—
404C4⋊C4—24no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—44no—
415C4⋊C4—42no—
416C4⋊C4—42no—
417C4⋊C4—42no—
418C4⋊C4—44no—
419C4⋊C4—42no—
420C4⋊C4—42no—
421C4⋊C4C2×Q8×C1114yes—
422C4⋊C4C2×Q8×C1112yes—
423C4⋊C4C2×Q8×C1112yes—
424C22⋊C4—24no—
425C22⋊C4—42no—
426C42—22no—
427C42—22no—
428C42—24no—
429C42—21no—
430C42—21no—
431C42—21no—
432C42—21no—
433C42—42no—
434C11#2367011yescharacteristic, direct product factor, Sylow
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23C11×#12112yes—
440C23C11×C22⋊Q812yes—
441C23C11×C22⋊Q812yes—
442C23C22×D4×C1111yescharacteristic
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—44no—
457C2×C4—44no—
458C2×C4—48no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—84no—
475C2×C4C11×#12112yes—
476C2×C4C11×C22⋊Q812yes—
477C2×C4C11×C22⋊Q812yes—
478C2×C4C11×#12314yes—
479C2×C4C11×#12514yes—
480C2×C4C11×#12514yes—
481C2×C4C11×C4⋊Q814yes—
482C2×C4C11×AGL(1,ℤ/8)12yes—
483C2×C4C11×#13712yes—
484C2×C4C22×D4×C1111yescharacteristic
485C2×C4C22×Q8×C1111yescharacteristic
486C2×C4C22×Q8×C1111yescharacteristic
487C2×C4C2×C11×#4111yescharacteristic
488C2×C4C2×C11×#4111yescharacteristic
489C2×C4C2×C11×#4111yescharacteristic
490C8—24no—
491C8—42no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22C11×#39814yes—
499C22C2×C11×#12111yescharacteristic
500C22C2×C11×C22⋊Q811yescharacteristic
501C22C2×C11×C22⋊Q811yescharacteristic
502C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
503C22C2×C11×#13711yescharacteristic
504C22C11×#57511yescharacteristic
505C22C11×#57511yescharacteristic
506C4—22no—
507C4—22no—
508C4—41no—
509C4—41no—
510C4—44no—
511C4—42no—
512C4—42no—
513C4—82no—
514C4—81no—
515C4—81no—
516C4C11×#39814yes—
517C4C2×C11×#12311yescharacteristic
518C4C2×C11×#12511yescharacteristic
519C4C2×C11×#12511yescharacteristic
520C4C2×C11×C4⋊Q811yescharacteristic
521C2—24no—
522C2C2×C11×#39811yescharacteristic
523C2C11×#305511yescharacteristic
524C2C11×#305611yescharacteristic
525C2C11×#307711yescharacteristic
526C2C11×#307811yescharacteristic
527C2C11×#307911yescharacteristic
528C2C11×#308011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
5. C11×#2088C2semidirect
6. C11×#2088C2semidirect
7. C11×#2087C2semidirect
8. C11×#2086C2semidirect
101. #23670C11direct (N × H)
175. #2088C2×C11semidirect
176. #2088C2×C11semidirect
177. #2087C2×C11semidirect
178. #2086C2×C11semidirect
434. C11#23670direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4282
C2×C11×#4232
C11×#22962
C2×C11×#3892
C11×#20882
C11×#20872
C11×#20862
C11×#17362
#2367011