Finite Group Databasebeta

← C11×#22034 #14599227

Subgroups — C11×#22034 #14599227

Order 2816.

1176 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#435C211yesmaximal, characteristic, complemented
2C22×C11×C22⋊C8C211yesmaximal, characteristic, complemented
3C4×C11×#120C211yesmaximal, characteristic
4C11×#1955C212yesmaximal, complemented
5C11×#1924C212yesmaximal, complemented
6C11×#1924C212yesmaximal, complemented
7C11×#1870C212yesmaximal, complemented
8C11×#1869C211yesmaximal, characteristic, complemented
9C11×#1850C211yesmaximal, characteristic, complemented
10C11×#1779C211yesmaximal, characteristic, complemented
11C11×#1752C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic, complemented
14C23×C8×C11C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C2×C11×#120C411yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2212yes—
19C11×#435—24no—
20C2×C11×C4⋊C8C2211yescharacteristic, complemented
21C2×C11×C4⋊C8C2212yescomplemented
22C2×C11×C22⋊C8—24no—
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2212yes—
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2212yes—
27C2×C11×C22⋊C8C2212yes—
28C2×C11×C22⋊C8C2212yes—
29C2×C11×C22⋊C8C2211yescharacteristic, complemented
30C2×C11×C22⋊C8C2212yescomplemented
31C2×C11×#97C2211yescharacteristic, complemented
32C2×C11×#97C2212yescomplemented
33C11×#386C411yescharacteristic
34C11×#386C412yes—
35C11×#385C411yescharacteristic
36C11×#385C412yes—
37C11×#379C411yescharacteristic
38C4×C11×C22⋊C4C2212yes—
39C4×C11×C22⋊C4C2211yescharacteristic
40C11×#336C2212yescomplemented
41C11×#336C2212yescomplemented
42C11×#336C2212yescomplemented
43C25×C11C2×C411yescharacteristic
44C22×D4×C11C2×C411yescharacteristic
45C22×D4×C11C2×C412yes—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—42no—
49C23×C4×C11—42no—
50C23×C4×C11C2×C411yescharacteristic
51C23×C4×C11C2×C412yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C2×C11×M16—22no—
56C2×C11×M16—42no—
57C22×C8×C11—22no—
58C22×C8×C11—42no—
59C22×C8×C11—42no—
60C22×C8×C11D414yescomplemented
61C22×C8×C11C2312yes—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2312yes—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#120—24no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—42no—
71C4×D4×C11—42no—
72C2×C11×C4⋊C4C2×C411yescharacteristic
73C2×C11×C4⋊C4C2×C412yes—
74C2×C11×C22⋊C4C2×C411yescharacteristic
75C2×C11×C22⋊C4C2×C412yes—
76C2×C11×C22⋊C4C2×C411yescharacteristic
77C2×C11×C22⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4C2×C411yescharacteristic
79C2×C11×C22⋊C4C2×C412yes—
80C2×C11×C22⋊C4C2×C412yes—
81C2×C11×C22⋊C4C2×C412yes—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2312yes—
84C11×C4⋊C8—22no—
85C11×C4⋊C8—42no—
86C11×C22⋊C8—22no—
87C11×C22⋊C8—22no—
88C11×C22⋊C8—24no—
89C11×C22⋊C8—24no—
90C11×C22⋊C8—22no—
91C11×C22⋊C8—42no—
92C11×C22⋊C8—42no—
93C11×C22⋊C8—42no—
94C11×#97—22no—
95C11×#97—42no—
96C11×#95C2×C412yes—
97C11×#95C2×C412yes—
98C11×#95C2×C412yes—
99#22034C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—42no—
103C24×C11—42no—
104C24×C11M1614yescomplemented
105C24×C11C22×C411yescharacteristic
106C24×C11C22×C412yes—
107C24×C11C22×C411yescharacteristic
108C2×D4×C11—22no—
109C2×D4×C11—24no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—42no—
113C2×D4×C11—42no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—44no—
132C22×C4×C11—44no—
133C22×C4×C11—48no—
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C412yes—
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11#4112yes—
143C22×C4×C11C2411yescharacteristic
144C11×M16—44no—
145C2×C8×C11—21no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—44no—
158C2×C8×C11—44no—
159C2×C8×C11C2×D412yes—
160C2×C8×C11C2×D412yes—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—42no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—42no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—42no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—22no—
174C42×C11—22no—
175C2×#435C2×C1111yescharacteristic, complemented
176C22×C22⋊C8C2×C1111yescharacteristic, complemented
177C4×#120C2×C1111yescharacteristic
178#1955C2×C1112yescomplemented
179#1924C2×C1112yescomplemented
180#1924C2×C1112yescomplemented
181#1870C2×C1112yescomplemented
182#1869C2×C1111yescharacteristic, complemented
183#1850C2×C1111yescharacteristic, complemented
184#1779C2×C1111yescharacteristic, complemented
185#1752C2×C1111yescharacteristic, complemented
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—28no—
195C23×C11—21no—
196C23×C11—22no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—22no—
200C23×C11—48no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11—48no—
204C23×C11C4×D412yes—
205C23×C11C2×M1614yes—
206C23×C11C2×M1612yes—
207C23×C11#13112yes—
208C23×C11C23×C411yescharacteristic
209D4×C11—48no—
210D4×C11—44no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—48no—
232C2×C4×C11—44no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11C4×D412yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)12yes—
244C2×C4×C11H(5,𝔽2)12yes—
245C8×C11—22no—
246C8×C11—22no—
247C8×C11—41no—
248C8×C11—41no—
249C8×C11—42no—
250C8×C11—42no—
251C24×C4C22×C1111yescharacteristic
252C22×M16C22×C1111yescharacteristic, complemented
253C23×C8C22×C1111yescharacteristic
254C23×C8C22×C1111yescharacteristic
255C2×#120C4×C1111yescharacteristic
256C2×C4×D4C22×C1111yescharacteristic
257C2×C4×D4C22×C1112yes—
258#435—24no—
259C2×C4⋊C8C22×C1111yescharacteristic, complemented
260C2×C4⋊C8C22×C1112yescomplemented
261C2×C22⋊C8—24no—
262C2×C22⋊C8C22×C1111yescharacteristic
263C2×C22⋊C8C22×C1112yes—
264C2×C22⋊C8C22×C1112yes—
265C2×C22⋊C8C22×C1111yescharacteristic
266C2×C22⋊C8C22×C1112yes—
267C2×C22⋊C8C22×C1112yes—
268C2×C22⋊C8C22×C1111yescharacteristic, complemented
269C2×C22⋊C8C22×C1112yescomplemented
270C2×#97C22×C1111yescharacteristic, complemented
271C2×#97C22×C1112yescomplemented
272#386C4×C1112yes—
273#386C4×C1111yescharacteristic
274#385C4×C1111yescharacteristic
275#385C4×C1112yes—
276#379C4×C1111yescharacteristic
277C4×C22⋊C4C22×C1111yescharacteristic
278C4×C22⋊C4C22×C1112yes—
279#336C22×C1112yescomplemented
280#336C22×C1112yescomplemented
281#336C22×C1112yescomplemented
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—24no—
287C22×C11—24no—
288C22×C11—24no—
289C22×C11—416no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—41no—
295C22×C11—41no—
296C22×C11—41no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11#43514yes—
300C22×C11C2×C4×D411yescharacteristic
301C22×C11#51812yes—
302C22×C11C22×M1611yescharacteristic
303C22×C11C2×#13111yescharacteristic
304C22×C11#56812yes—
305C4×C11—22no—
306C4×C11—41no—
307C4×C11—42no—
308C4×C11—41no—
309C4×C11—41no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11#53411yescharacteristic
313C4×C11#53511yescharacteristic
314C4×C11#53812yes—
315C25C2×C4×C1111yescharacteristic
316C22×D4C2×C4×C1111yescharacteristic
317C22×D4C2×C4×C1112yes—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—42no—
321C23×C4—42no—
322C23×C4C2×C4×C1111yescharacteristic
323C23×C4C2×C4×C1112yes—
324C23×C4C23×C1111yescharacteristic
325C23×C4C23×C1112yes—
326C23×C4C23×C1111yescharacteristic
327C2×M16—22no—
328C2×M16—42no—
329C22×C8—22no—
330C22×C8—42no—
331C22×C8—42no—
332C22×C8D4×C1114yescomplemented
333C22×C8C23×C1112yes—
334C22×C8C23×C1111yescharacteristic
335C22×C8C23×C1112yes—
336C22×C8C23×C1111yescharacteristic
337C22×C8C23×C1111yescharacteristic
338C22×C8C23×C1111yescharacteristic
339#120—24no—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—42no—
343C4×D4—42no—
344C2×C4⋊C4C2×C4×C1111yescharacteristic
345C2×C4⋊C4C2×C4×C1112yes—
346C2×C22⋊C4C2×C4×C1111yescharacteristic
347C2×C22⋊C4C2×C4×C1111yescharacteristic
348C2×C22⋊C4C2×C4×C1112yes—
349C2×C22⋊C4C2×C4×C1111yescharacteristic
350C2×C22⋊C4C2×C4×C1111yescharacteristic
351C2×C22⋊C4C2×C4×C1112yes—
352C2×C22⋊C4C2×C4×C1112yes—
353C2×C22⋊C4C2×C4×C1112yes—
354C2×C42C23×C1111yescharacteristic
355C2×C42C23×C1112yes—
356C4⋊C8—22no—
357C4⋊C8—42no—
358C22⋊C8—22no—
359C22⋊C8—22no—
360C22⋊C8—24no—
361C22⋊C8—24no—
362C22⋊C8—22no—
363C22⋊C8—42no—
364C22⋊C8—42no—
365C22⋊C8—42no—
366#97—22no—
367#97—42no—
368#95C2×C4×C1112yes—
369#95C2×C4×C1112yes—
370#95C2×C4×C1112yes—
371C2×C11—24no—
372C2×C11—44no—
373C2×C11—81no—
374C2×C11#232111yescharacteristic
375C2×C11C2×#43511yescharacteristic
376C2×C11#293011yescharacteristic
377C2×C11#297312yes—
378C2×C11#297612yes—
379C24—22no—
380C24—22no—
381C24—42no—
382C24—42no—
383C24C11×M1614yescomplemented
384C24C22×C4×C1111yescharacteristic
385C24C22×C4×C1112yes—
386C24C22×C4×C1111yescharacteristic
387C2×D4—22no—
388C2×D4—24no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—42no—
392C2×D4—42no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—44no—
411C22×C4—44no—
412C22×C4—48no—
413C22×C4C22×C4×C1111yescharacteristic
414C22×C4C22×C4×C1112yes—
415C22×C4C22×C4×C1111yescharacteristic
416C22×C4C22×C4×C1112yes—
417C22×C4C22×C4×C1112yes—
418C22×C4C22×C4×C1111yescharacteristic
419C22×C4C22×C4×C1111yescharacteristic
420C22×C4C2×D4×C1112yes—
421C22×C4C11×#4112yes—
422C22×C4C24×C1111yescharacteristic
423M16—44no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—21no—
427C2×C8—22no—
428C2×C8—21no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—44no—
437C2×C8—44no—
438C2×C8C2×D4×C1112yes—
439C2×C8C2×D4×C1112yes—
440C4⋊C4—22no—
441C4⋊C4—42no—
442C22⋊C4—22no—
443C22⋊C4—24no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—42no—
448C22⋊C4—42no—
449C22⋊C4—42no—
450C42—21no—
451C42—21no—
452C42—22no—
453C42—22no—
454C11#2203411yescharacteristic, direct product factor, Sylow
455C23—22no—
456C23—22no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—28no—
464C23—21no—
465C23—22no—
466C23—21no—
467C23—21no—
468C23—22no—
469C23—48no—
470C23—44no—
471C23—44no—
472C23—48no—
473C23C4×D4×C1112yes—
474C23C2×C11×M1614yes—
475C23C2×C11×M1612yes—
476C23C11×#13112yes—
477C23C23×C4×C1111yescharacteristic
478D4—48no—
479D4—44no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—48no—
501C2×C4—44no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4C4×D4×C1112yes—
510C2×C4C22×D4×C1111yescharacteristic
511C2×C4C2×C11×#4111yescharacteristic
512C2×C4C11×H(5,𝔽2)12yes—
513C2×C4C11×H(5,𝔽2)12yes—
514C8—22no—
515C8—22no—
516C8—41no—
517C8—42no—
518C8—41no—
519C8—42no—
520C22—22no—
521C22—24no—
522C22—24no—
523C22—22no—
524C22—24no—
525C22—24no—
526C22—24no—
527C22—416no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—41no—
533C22—41no—
534C22—42no—
535C22—42no—
536C22—41no—
537C22C11×#43514yes—
538C22C2×C4×D4×C1111yescharacteristic
539C22C11×#51812yes—
540C22C22×C11×M1611yescharacteristic
541C22C2×C11×#13111yescharacteristic
542C22C11×#56812yes—
543C4—22no—
544C4—41no—
545C4—41no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—41no—
550C4C11×#53411yescharacteristic
551C4C11×#53511yescharacteristic
552C4C11×#53812yes—
553C2—24no—
554C2—44no—
555C2—81no—
556C2C11×#232111yescharacteristic
557C2C2×C11×#43511yescharacteristic
558C2C11×#293011yescharacteristic
559C2C11×#297312yes—
560C2C11×#297612yes—
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC2×C11×#120C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#435C2semidirect
2. C22×C11×C22⋊C8C2semidirect
4. C11×#1955C2semidirect
5. C11×#1924C2semidirect
6. C11×#1924C2semidirect
7. C11×#1870C2semidirect
8. C11×#1869C2semidirect
9. C11×#1850C2semidirect
10. C11×#1779C2semidirect
11. C11×#1752C2semidirect
13. C22×C11×M16C22semidirect
20. C2×C11×C4⋊C8C22semidirect
21. C2×C11×C4⋊C8C22semidirect
29. C2×C11×C22⋊C8C22semidirect
30. C2×C11×C22⋊C8C22semidirect
31. C2×C11×#97C22semidirect
32. C2×C11×#97C22semidirect
40. C11×#336C22semidirect
41. C11×#336C22semidirect
42. C11×#336C22semidirect
60. C22×C8×C11D4semidirect
99. #22034C11direct (N × H)
104. C24×C11M16semidirect
175. C2×#435C2×C11semidirect
176. C22×C22⋊C8C2×C11semidirect
178. #1955C2×C11semidirect
179. #1924C2×C11semidirect
180. #1924C2×C11semidirect
181. #1870C2×C11semidirect
182. #1869C2×C11semidirect
183. #1850C2×C11semidirect
184. #1779C2×C11semidirect
185. #1752C2×C11semidirect
252. C22×M16C22×C11semidirect
259. C2×C4⋊C8C22×C11semidirect
260. C2×C4⋊C8C22×C11semidirect
268. C2×C22⋊C8C22×C11semidirect
269. C2×C22⋊C8C22×C11semidirect
270. C2×#97C22×C11semidirect
271. C2×#97C22×C11semidirect
279. #336C22×C11semidirect
280. #336C22×C11semidirect
281. #336C22×C11semidirect
332. C22×C8D4×C11semidirect
383. C24C11×M16semidirect
454. C11#22034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4352
C22×C11×C22⋊C82
C4×C11×#1202
C11×#19552
C11×#19242
C11×#18702
C11×#18692
C11×#18502
C11×#17792
C11×#17522
#2203411