Finite Group Databasebeta

← C11×#11070 #14588263

Subgroups — C11×#11070 #14588263

Order 2816.

1202 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2315C211yesmaximal, characteristic
2C2×C11×#381C212yesmaximal
3C2×C11×#381C211yesmaximal, characteristic
4C2×C11×#342C212yesmaximal
5C2×C11×#342C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C22×C11×C22⋊C4C2212yes—
8C22×C11×C22⋊C4C2211yescharacteristic
9C22×C11×C22⋊C4C2212yes—
10C22×C11×C22⋊C4C2211yescharacteristic
11C11×#385—24no—
12C11×#381—24no—
13C11×#381—24no—
14C11×#381—22no—
15C11×#381C414yescomplemented
16C11×#380—22no—
17C2×C11×#95—24no—
18C2×C11×#95—22no—
19C11×#342—22no—
20C11×#342—24no—
21C25×C11C2311yescharacteristic
22C23×C4×C11—21no—
23C23×C4×C11—22no—
24C23×C4×C11—21no—
25C23×C4×C11—22no—
26C23×C4×C11—21no—
27C23×C4×C11—21no—
28C23×C4×C11—22no—
29C23×C4×C11—22no—
30C23×C4×C11—21no—
31C23×C4×C11—22no—
32C23×C4×C11C2×C412yes—
33C23×C4×C11D412yes—
34C23×C4×C11D414yes—
35C23×C4×C11D412yes—
36C23×C4×C11Q812yes—
37C2×C11×C4⋊C4—24no—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4C2×C412yes—
55C2×C11×C22⋊C4C2×C412yes—
56C2×C11×C22⋊C4D414yes—
57C2×C11×C22⋊C4D412yes—
58C11×#95—216no—
59C11×#95—24no—
60C11×#95—28no—
61#11070C1111yesmaximal, characteristic, direct product factor, Sylow
62C24×C11—44no—
63C24×C11C22×C411yescharacteristic
64C24×C11C2×D411yescharacteristic
65C24×C11C2×D412yes—
66C24×C11C2×D411yescharacteristic
67C24×C11C2×D411yescharacteristic
68C24×C11C2×D412yes—
69C24×C11C2×Q811yescharacteristic
70C24×C11#4111yescharacteristic
71C24×C11#4111yescharacteristic
72C24×C11#4112yes—
73C24×C11#4112yes—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—24no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—24no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—24no—
90C22×C4×C11—24no—
91C22×C4×C11—24no—
92C22×C4×C11—24no—
93C22×C4×C11—41no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11—41no—
98C22×C4×C11—42no—
99C22×C4×C11—42no—
100C22×C4×C11—41no—
101C22×C4×C11—42no—
102C22×C4×C11—41no—
103C22×C4×C11—44no—
104C22×C4×C11—48no—
105C22×C4×C11—44no—
106C22×C4×C11—48no—
107C22×C4×C11—42no—
108C22×C4×C11—41no—
109C22×C4×C11—42no—
110C22×C4×C11—41no—
111C22×C4×C11C22⋊C414yes—
112C22×C4×C11C4⋊C414yescomplemented
113C11×C4⋊C4—84no—
114C11×C22⋊C4—24no—
115C11×C22⋊C4—24no—
116C11×C22⋊C4—24no—
117C11×C22⋊C4—24no—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—42no—
120C11×C22⋊C4—42no—
121C11×C22⋊C4—42no—
122C11×C22⋊C4—42no—
123C11×C22⋊C4—42no—
124C11×C22⋊C4—42no—
125C11×C22⋊C4—42no—
126#2315C2×C1111yescharacteristic
127C2×#381C2×C1112yes—
128C2×#381C2×C1111yescharacteristic
129C2×#342C2×C1112yes—
130C2×#342C2×C1111yescharacteristic
131C23×C11—24no—
132C23×C11—28no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—44no—
137C23×C11—42no—
138C23×C11—44no—
139C23×C11—42no—
140C23×C11—42no—
141C23×C11—44no—
142C23×C11C2×C22⋊C411yescharacteristic
143C23×C11C2×C4⋊C411yescharacteristic
144C23×C11#11711yescharacteristic
145C23×C11C4×D412yes—
146C23×C11C4×D412yes—
147C23×C11#12012yes—
148C23×C11#12011yescharacteristic
149C23×C11#12111yescharacteristic
150C23×C11#12112yes—
151C23×C11#12112yes—
152C23×C11#12111yescharacteristic
153C23×C11#12112yes—
154C23×C11C22⋊Q811yescharacteristic
155C23×C11C22⋊Q812yes—
156C23×C11C22⋊Q811yescharacteristic
157C23×C11C22⋊Q812yes—
158C23×C11#12311yescharacteristic
159C23×C11#12312yes—
160C23×C11#12312yes—
161C23×C11#12412yes—
162C23×C11#12411yescharacteristic
163C23×C11#12612yes—
164C23×C11#12711yescharacteristic
165C2×C4×C11—24no—
166C2×C4×C11—28no—
167C2×C4×C11—24no—
168C2×C4×C11—42no—
169C2×C4×C11—44no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—44no—
174C2×C4×C11—44no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—44no—
178C2×C4×C11—44no—
179C2×C4×C11—44no—
180C2×C4×C11—48no—
181C2×C4×C11—48no—
182C2×C4×C11—42no—
183C2×C4×C11—44no—
184C2×C4×C11—44no—
185C2×C4×C11—48no—
186C2×C4×C11—82no—
187C2×C4×C11—84no—
188C2×C4×C11—82no—
189C2×C4×C11—82no—
190C2×C4×C11—84no—
191C2×C4×C11—84no—
192C24×C4C22×C1111yescharacteristic
193C22×C22⋊C4C22×C1112yes—
194C22×C22⋊C4C22×C1111yescharacteristic
195C22×C22⋊C4C22×C1112yes—
196C22×C22⋊C4C22×C1111yescharacteristic
197#385—24no—
198#381—24no—
199#381—24no—
200#381—22no—
201#381C4×C1114yescomplemented
202#380—22no—
203C2×#95—24no—
204C2×#95—22no—
205#342—22no—
206#342—24no—
207C22×C11—22no—
208C22×C11—24no—
209C22×C11—22no—
210C22×C11—24no—
211C22×C11—24no—
212C22×C11—24no—
213C22×C11—22no—
214C22×C11—22no—
215C22×C11—22no—
216C22×C11—24no—
217C22×C11—22no—
218C22×C11—24no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—42no—
222C22×C11—42no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—42no—
226C22×C11—42no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11#38011yescharacteristic
230C22×C11#38512yes—
231C22×C11#38611yescharacteristic
232C22×C11#38812yes—
233C22×C11#39011yescharacteristic
234C22×C11#39211yescharacteristic
235C22×C11#39311yescharacteristic
236C22×C11#39412yes—
237C22×C11#39612yes—
238C22×C11#39711yescharacteristic
239C22×C11#39911yescharacteristic
240C22×C11#45814yes—
241C4×C11—44no—
242C4×C11—44no—
243C4×C11—82no—
244C4×C11—84no—
245C4×C11—84no—
246C25C23×C1111yescharacteristic
247C23×C4—21no—
248C23×C4—22no—
249C23×C4—21no—
250C23×C4—22no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—21no—
256C23×C4—22no—
257C23×C4C2×C4×C1112yes—
258C23×C4D4×C1112yes—
259C23×C4D4×C1114yes—
260C23×C4D4×C1112yes—
261C23×C4Q8×C1112yes—
262C2×C4⋊C4—24no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4C2×C4×C1112yes—
280C2×C22⋊C4C2×C4×C1112yes—
281C2×C22⋊C4D4×C1114yes—
282C2×C22⋊C4D4×C1112yes—
283#95—216no—
284#95—24no—
285#95—28no—
286C2×C11—21no—
287C2×C11—22no—
288C2×C11—21no—
289C2×C11—22no—
290C2×C11—22no—
291C2×C11—22no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11#143911yescharacteristic
295C2×C11#189012yes—
296C2×C11#202212yes—
297C2×C11#203012yes—
298C24—44no—
299C24C22×C4×C1111yescharacteristic
300C24C2×D4×C1111yescharacteristic
301C24C2×D4×C1112yes—
302C24C2×D4×C1111yescharacteristic
303C24C2×D4×C1111yescharacteristic
304C24C2×D4×C1112yes—
305C24C2×Q8×C1111yescharacteristic
306C24C11×#4111yescharacteristic
307C24C11×#4111yescharacteristic
308C24C11×#4112yes—
309C24C11×#4112yes—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—41no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—41no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—41no—
337C22×C4—42no—
338C22×C4—41no—
339C22×C4—44no—
340C22×C4—48no—
341C22×C4—44no—
342C22×C4—48no—
343C22×C4—42no—
344C22×C4—41no—
345C22×C4—42no—
346C22×C4—41no—
347C22×C4C11×C22⋊C414yes—
348C22×C4C11×C4⋊C414yescomplemented
349C4⋊C4—84no—
350C22⋊C4—24no—
351C22⋊C4—24no—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—24no—
355C22⋊C4—42no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C22⋊C4—42no—
360C22⋊C4—42no—
361C22⋊C4—42no—
362C11#1107011yescharacteristic, direct product factor, Sylow
363C23—24no—
364C23—28no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—44no—
369C23—42no—
370C23—44no—
371C23—42no—
372C23—42no—
373C23—44no—
374C23C2×C11×C22⋊C411yescharacteristic
375C23C2×C11×C4⋊C411yescharacteristic
376C23C11×#11711yescharacteristic
377C23C4×D4×C1112yes—
378C23C4×D4×C1112yes—
379C23C11×#12012yes—
380C23C11×#12011yescharacteristic
381C23C11×#12111yescharacteristic
382C23C11×#12112yes—
383C23C11×#12112yes—
384C23C11×#12111yescharacteristic
385C23C11×#12112yes—
386C23C11×C22⋊Q811yescharacteristic
387C23C11×C22⋊Q812yes—
388C23C11×C22⋊Q811yescharacteristic
389C23C11×C22⋊Q812yes—
390C23C11×#12311yescharacteristic
391C23C11×#12312yes—
392C23C11×#12312yes—
393C23C11×#12412yes—
394C23C11×#12411yescharacteristic
395C23C11×#12612yes—
396C23C11×#12711yescharacteristic
397C2×C4—24no—
398C2×C4—28no—
399C2×C4—24no—
400C2×C4—42no—
401C2×C4—44no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—44no—
406C2×C4—44no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—44no—
410C2×C4—44no—
411C2×C4—44no—
412C2×C4—48no—
413C2×C4—48no—
414C2×C4—42no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—48no—
418C2×C4—82no—
419C2×C4—84no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—84no—
423C2×C4—84no—
424C22—22no—
425C22—24no—
426C22—22no—
427C22—24no—
428C22—24no—
429C22—24no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—24no—
434C22—22no—
435C22—24no—
436C22—41no—
437C22—41no—
438C22—42no—
439C22—42no—
440C22—41no—
441C22—41no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22C11×#38011yescharacteristic
447C22C11×#38512yes—
448C22C11×#38611yescharacteristic
449C22C11×#38812yes—
450C22C11×#39011yescharacteristic
451C22C11×#39211yescharacteristic
452C22C11×#39311yescharacteristic
453C22C11×#39412yes—
454C22C11×#39612yes—
455C22C11×#39711yescharacteristic
456C22C11×#39911yescharacteristic
457C22C11×#45814yes—
458C4—44no—
459C4—44no—
460C4—82no—
461C4—84no—
462C4—84no—
463C2—21no—
464C2—22no—
465C2—21no—
466C2—22no—
467C2—22no—
468C2—22no—
469C2—21no—
470C2—21no—
471C2C11×#143911yescharacteristic
472C2C11×#189012yes—
473C2C11×#202212yes—
474C2C11×#203012yes—
subgroupG/H
center, socleC23×C11#120
commutatorC24C22×C4×C11
Frattini, cosocleC25C23×C11
prime radicalC25×C11C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
15. C11×#381C4semidirect
61. #11070C11direct (N × H)
112. C22×C4×C11C4⋊C4semidirect
201. #381C4×C11semidirect
348. C22×C4C11×C4⋊C4semidirect
362. C11#11070direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23152
C2×C11×#3812
C2×C11×#3422
#1107011