Finite Group Databasebeta

← C11×#10938 #14588131

Subgroups — C11×#10938 #14588131

Order 2816.

1234 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#99C212yesmaximal
2C11×#2308C211yesmaximal, characteristic
3C11×#2273C211yesmaximal, characteristic, complemented
4C2×C11×#342C212yesmaximal, complemented
5C2×C11×#342C211yesmaximal, characteristic, complemented
6C23×D4×C11C2211yescharacteristic
7C22×C11×C22⋊C4C2211yescharacteristic
8C22×C11×C22⋊C4C2212yes—
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C11×C22⋊C4C2212yes—
11C2×C11×#99—24no—
12C2×C11×#99—24no—
13C2×C11×#99C418yescomplemented
14C11×#386—22no—
15C11×#386—22no—
16C11×#381C412yescomplemented
17C11×#379C412yescomplemented
18C4×C11×C22⋊C4—22no—
19C4×C11×C22⋊C4—24no—
20C11×#342—22no—
21C11×#342—24no—
22C25×C11C2×C411yescharacteristic
23C25×C11C2311yescharacteristic
24C22×D4×C11—21no—
25C22×D4×C11—21no—
26C22×D4×C11—22no—
27C22×D4×C11—22no—
28C22×D4×C11—22no—
29C22×D4×C11—22no—
30C22×D4×C11—22no—
31C22×D4×C11C2×C414yes—
32C23×C4×C11—22no—
33C23×C4×C11—21no—
34C23×C4×C11—22no—
35C23×C4×C11C2×C411yescharacteristic
36C23×C4×C11D412yes—
37C2×C11×C22⋊C4—22no—
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—24no—
51C2×C11×C22⋊C4C2×C412yes—
52C2×C11×C22⋊C4C2×C414yes—
53C2×C11×C22⋊C4C2×C412yes—
54C2×C11×C22⋊C4C2×C414yes—
55C2×C11×C22⋊C4D412yes—
56C2×C11×C22⋊C4D414yes—
57C2×C11×C22⋊C4D414yes—
58C2×C42×C11—24no—
59C11×#99—216no—
60C11×#95—24no—
61C11×#95—24no—
62#10938C1111yesmaximal, characteristic, direct product factor, Sylow
63C24×C11—21no—
64C24×C11—21no—
65C24×C11—22no—
66C24×C11—22no—
67C24×C11—82no—
68C24×C11—82no—
69C24×C11C4212yescomplemented
70C24×C11C22×C411yescharacteristic
71C24×C11C22×C412yes—
72C24×C11C2×D411yescharacteristic
73C24×C11C2×D412yes—
74C24×C11C2×D411yescharacteristic
75C24×C11C2×D412yes—
76C24×C11#4112yes—
77C24×C11#4112yes—
78C24×C11#4112yes—
79C2×D4×C11—24no—
80C2×D4×C11—24no—
81C2×D4×C11—24no—
82C2×D4×C11—24no—
83C2×D4×C11—24no—
84C2×D4×C11—24no—
85C2×D4×C11—41no—
86C2×D4×C11—42no—
87C2×D4×C11—42no—
88C2×D4×C11—42no—
89C2×D4×C11—41no—
90C2×D4×C11—42no—
91C2×D4×C11—42no—
92C2×D4×C11—41no—
93C2×D4×C11—42no—
94C2×D4×C11—41no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—24no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11—82no—
111C22×C4×C11—84no—
112C22×C4×C11—82no—
113C22×C4×C11—84no—
114C22×C4×C11C4212yescomplemented
115C22×C4×C11C22⋊C414yes—
116C11×C22⋊C4—24no—
117C11×C22⋊C4—24no—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—42no—
125C11×C22⋊C4—42no—
126C11×C22⋊C4—42no—
127C11×C22⋊C4—84no—
128C11×C22⋊C4C22⋊C418yescomplemented
129C42×C11—84no—
130C22×#99C2×C1112yes—
131#2308C2×C1111yescharacteristic
132#2273C2×C1111yescharacteristic, complemented
133C2×#342C2×C1112yescomplemented
134C2×#342C2×C1111yescharacteristic, complemented
135C23×C11—22no—
136C23×C11—24no—
137C23×C11—42no—
138C23×C11—44no—
139C23×C11—42no—
140C23×C11—44no—
141C23×C11—42no—
142C23×C11—44no—
143C23×C11—41no—
144C23×C11—42no—
145C23×C11—41no—
146C23×C11—84no—
147C23×C11—82no—
148C23×C11—82no—
149C23×C11—82no—
150C23×C11—82no—
151C23×C11—82no—
152C23×C11—82no—
153C23×C11—84no—
154C23×C11C2×C4211yescharacteristic
155C23×C11C2×C22⋊C411yescharacteristic
156C23×C11C2×C22⋊C412yes—
157C23×C11#11711yescharacteristic
158C23×C11#11712yes—
159C23×C11C4×D412yes—
160C23×C11C4×D412yes—
161C23×C11C4×D412yes—
162C23×C11C4×D412yes—
163C23×C11C4×D412yes—
164C23×C11C4×D412yes—
165C23×C11#12011yescharacteristic
166C23×C11#12112yes—
167C23×C11#12112yes—
168C23×C11#12112yes—
169C23×C11#12311yescharacteristic
170C23×C11#12312yes—
171C23×C11#12412yes—
172C23×C11#12411yescharacteristic
173C23×C11#12612yes—
174C23×C11#12711yescharacteristic
175D4×C11—44no—
176D4×C11—44no—
177D4×C11—44no—
178D4×C11—44no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—28no—
182C2×C4×C11—24no—
183C2×C4×C11—48no—
184C2×C4×C11—44no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—44no—
189C2×C4×C11—44no—
190C2×C4×C11—42no—
191C2×C4×C11—44no—
192C2×C4×C11—82no—
193C2×C4×C11—84no—
194C2×C4×C11—84no—
195C2×C4×C11—84no—
196C2×C4×C11—82no—
197C2×C4×C11—82no—
198C2×C4×C11—84no—
199C2×C4×C11—84no—
200C23×D4C22×C1111yescharacteristic
201C22×C22⋊C4C22×C1111yescharacteristic
202C22×C22⋊C4C22×C1112yes—
203C22×C22⋊C4C22×C1111yescharacteristic
204C22×C22⋊C4C22×C1112yes—
205C2×#99—24no—
206C2×#99—24no—
207C2×#99C4×C1118yescomplemented
208#386—22no—
209#386—22no—
210#381C4×C1112yescomplemented
211#379C4×C1112yescomplemented
212C4×C22⋊C4—22no—
213C4×C22⋊C4—24no—
214#342—22no—
215#342—24no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—24no—
219C22×C11—22no—
220C22×C11—24no—
221C22×C11—42no—
222C22×C11—42no—
223C22×C11—42no—
224C22×C11—41no—
225C22×C11—42no—
226C22×C11—41no—
227C22×C11—41no—
228C22×C11—41no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—42no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—44no—
238C22×C11—42no—
239C22×C11—84no—
240C22×C11—82no—
241C22×C11—84no—
242C22×C11—82no—
243C22×C11C4×C22⋊C411yescharacteristic
244C22×C11C4×C22⋊C412yes—
245C22×C11#38612yes—
246C22×C11#38611yescharacteristic
247C22×C11#38812yes—
248C22×C11#38812yes—
249C22×C11#38812yes—
250C22×C11#39011yescharacteristic
251C22×C11#39012yes—
252C4×C11—48no—
253C4×C11—44no—
254C4×C11—42no—
255C4×C11—82no—
256C4×C11—84no—
257C25C2×C4×C1111yescharacteristic
258C25C23×C1111yescharacteristic
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4C2×C4×C1114yes—
267C23×C4—22no—
268C23×C4—21no—
269C23×C4—22no—
270C23×C4C2×C4×C1111yescharacteristic
271C23×C4D4×C1112yes—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4C2×C4×C1112yes—
287C2×C22⋊C4C2×C4×C1114yes—
288C2×C22⋊C4C2×C4×C1112yes—
289C2×C22⋊C4C2×C4×C1114yes—
290C2×C22⋊C4D4×C1112yes—
291C2×C22⋊C4D4×C1114yes—
292C2×C22⋊C4D4×C1114yes—
293C2×C42—24no—
294#99—216no—
295#95—24no—
296#95—24no—
297C2×C11—22no—
298C2×C11—21no—
299C2×C11—22no—
300C2×C11—21no—
301C2×C11—22no—
302C2×C11—22no—
303C2×C11—22no—
304C2×C11—22no—
305C2×C11—82no—
306C2×C11#143711yescharacteristic
307C2×C11#191312yes—
308C24—21no—
309C24—21no—
310C24—22no—
311C24—22no—
312C24—82no—
313C24—82no—
314C24C42×C1112yescomplemented
315C24C22×C4×C1111yescharacteristic
316C24C22×C4×C1112yes—
317C24C2×D4×C1111yescharacteristic
318C24C2×D4×C1112yes—
319C24C2×D4×C1111yescharacteristic
320C24C2×D4×C1112yes—
321C24C11×#4112yes—
322C24C11×#4112yes—
323C24C11×#4112yes—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—24no—
327C2×D4—24no—
328C2×D4—24no—
329C2×D4—24no—
330C2×D4—41no—
331C2×D4—42no—
332C2×D4—42no—
333C2×D4—42no—
334C2×D4—41no—
335C2×D4—42no—
336C2×D4—42no—
337C2×D4—41no—
338C2×D4—42no—
339C2×D4—41no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—24no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—82no—
356C22×C4—84no—
357C22×C4—82no—
358C22×C4—84no—
359C22×C4C42×C1112yescomplemented
360C22×C4C11×C22⋊C414yes—
361C22⋊C4—24no—
362C22⋊C4—24no—
363C22⋊C4—24no—
364C22⋊C4—24no—
365C22⋊C4—24no—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—24no—
369C22⋊C4—42no—
370C22⋊C4—42no—
371C22⋊C4—42no—
372C22⋊C4—84no—
373C22⋊C4C11×C22⋊C418yescomplemented
374C42—84no—
375C11#1093811yescharacteristic, direct product factor, Sylow
376C23—22no—
377C23—24no—
378C23—42no—
379C23—44no—
380C23—42no—
381C23—44no—
382C23—42no—
383C23—44no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—84no—
388C23—82no—
389C23—82no—
390C23—82no—
391C23—82no—
392C23—82no—
393C23—82no—
394C23—84no—
395C23C2×C42×C1111yescharacteristic
396C23C2×C11×C22⋊C411yescharacteristic
397C23C2×C11×C22⋊C412yes—
398C23C11×#11711yescharacteristic
399C23C11×#11712yes—
400C23C4×D4×C1112yes—
401C23C4×D4×C1112yes—
402C23C4×D4×C1112yes—
403C23C4×D4×C1112yes—
404C23C4×D4×C1112yes—
405C23C4×D4×C1112yes—
406C23C11×#12011yescharacteristic
407C23C11×#12112yes—
408C23C11×#12112yes—
409C23C11×#12112yes—
410C23C11×#12311yescharacteristic
411C23C11×#12312yes—
412C23C11×#12412yes—
413C23C11×#12411yescharacteristic
414C23C11×#12612yes—
415C23C11×#12711yescharacteristic
416D4—44no—
417D4—44no—
418D4—44no—
419D4—44no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—28no—
424C2×C4—48no—
425C2×C4—44no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—44no—
430C2×C4—44no—
431C2×C4—42no—
432C2×C4—44no—
433C2×C4—82no—
434C2×C4—84no—
435C2×C4—84no—
436C2×C4—84no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—84no—
440C2×C4—84no—
441C22—22no—
442C22—22no—
443C22—24no—
444C22—22no—
445C22—24no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—41no—
450C22—42no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—42no—
462C22—44no—
463C22—42no—
464C22—84no—
465C22—82no—
466C22—84no—
467C22—82no—
468C22C4×C11×C22⋊C411yescharacteristic
469C22C4×C11×C22⋊C412yes—
470C22C11×#38612yes—
471C22C11×#38611yescharacteristic
472C22C11×#38812yes—
473C22C11×#38812yes—
474C22C11×#38812yes—
475C22C11×#39011yescharacteristic
476C22C11×#39012yes—
477C4—48no—
478C4—44no—
479C4—42no—
480C4—82no—
481C4—84no—
482C2—22no—
483C2—21no—
484C2—22no—
485C2—21no—
486C2—22no—
487C2—22no—
488C2—22no—
489C2—22no—
490C2—82no—
491C2C11×#143711yescharacteristic
492C2C11×#191312yes—
subgroupG/H
center, socleC22×C11#386
commutatorC23C2×C42×C11
Frattini, cosocleC25C23×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2273C2semidirect
4. C2×C11×#342C2semidirect
5. C2×C11×#342C2semidirect
13. C2×C11×#99C4semidirect
16. C11×#381C4semidirect
17. C11×#379C4semidirect
62. #10938C11direct (N × H)
69. C24×C11C42semidirect
114. C22×C4×C11C42semidirect
128. C11×C22⋊C4C22⋊C4semidirect
132. #2273C2×C11semidirect
133. C2×#342C2×C11semidirect
134. C2×#342C2×C11semidirect
207. C2×#99C4×C11semidirect
210. #381C4×C11semidirect
211. #379C4×C11semidirect
314. C24C42×C11semidirect
359. C22×C4C42×C11semidirect
373. C22⋊C4C11×C22⋊C4semidirect
375. C11#10938direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#992
C11×#23082
C11×#22732
C2×C11×#3422
#1093811