Finite Group Databasebeta

← C11×#23619 #14600812

Subgroups — C11×#23619 #14600812

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#428C211yesmaximal, characteristic
2C2×C11×#423C211yesmaximal, characteristic
3C2×C11×#419C211yesmaximal, characteristic
4C2×C11×#419C211yesmaximal, characteristic
5C11×#2296C211yesmaximal, characteristic
6C2×C11×#391C211yesmaximal, characteristic
7C11×#2068C214yesmaximal, complemented
8C11×#2066C214yesmaximal, complemented
9C11×#1736C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C11×#428—24no—
18C2×C11×#107C2212yes—
19C2×C11×#106C2212yes—
20C11×#423—24no—
21C2×C11×C4⋊C8C2214yes—
22C11×#419—24no—
23C11×#419—24no—
24C2×C11×#103C2212yes—
25C2×C11×#103C2214yes—
26C2×C11×#103C2212yes—
27C11×#391—21no—
28C11×#391—21no—
29C11×#391C2214yes—
30C11×#389C2212yes—
31C11×#389C2212yes—
32C11×#385—22no—
33C4×C11×C4⋊C4—21no—
34C4×C11×C4⋊C4—21no—
35C2×C11×#95—22no—
36C11×#340C2214yes—
37C22×Q8×C11—21no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11Q814yes—
44C22×Q8×C11C2312yes—
45C23×C4×C11—21no—
46C23×C4×C11—21no—
47C23×C4×C11D412yes—
48C23×C4×C11C2311yescharacteristic
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C2×C11×M16D414yes—
55C22×C8×C11C2312yes—
56C22×C8×C11C2312yes—
57C11×#117—22no—
58C11×#117—22no—
59C11×#117—22no—
60C11×#117D414yes—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C42×C11—22no—
73C2×C42×C11—21no—
74C2×C42×C11—22no—
75C2×C42×C11—21no—
76C2×C42×C11D411yescharacteristic
77C2×C42×C11D411yescharacteristic
78C2×C42×C11C2312yes—
79C11×#107—24no—
80C11×#106—24no—
81C11×C4⋊C8—28no—
82C11×#103—28no—
83C11×#103—24no—
84C11×#103—24no—
85C11×#95—24no—
86C11×#95—24no—
87C11×#95—22no—
88C11×#95—22no—
89#23619C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11C2×D411yescharacteristic
91C2×Q8×C11—24no—
92C2×Q8×C11—22no—
93C2×Q8×C11—28no—
94C2×Q8×C11—28no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—42no—
100C2×Q8×C11—42no—
101C2×Q8×C11—44no—
102C2×Q8×C11—44no—
103C2×Q8×C11C2×Q814yes—
104C22×C4×C11—24no—
105C22×C4×C11—24no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—24no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11—44no—
116C22×C4×C11—42no—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×Q812yes—
123C22×C4×C11#4112yes—
124C22×C4×C11#4112yes—
125C22×C4×C11#4112yes—
126C22×C4×C11C2411yescharacteristic
127C11×M16—28no—
128C11×M16—44no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11C2×D414yes—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—44no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—44no—
144C11×C4⋊C4C2×D412yes—
145C11×C4⋊C4C2×D412yes—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—42no—
148C42×C11—22no—
149C42×C11—22no—
150C42×C11—24no—
151C42×C11—22no—
152C42×C11—22no—
153C42×C11—42no—
154C2×#428C2×C1111yescharacteristic
155C2×#423C2×C1111yescharacteristic
156C2×#419C2×C1111yescharacteristic
157C2×#419C2×C1111yescharacteristic
158#2296C2×C1111yescharacteristic
159C2×#391C2×C1111yescharacteristic
160#2068C2×C1114yescomplemented
161#2066C2×C1114yescomplemented
162#1736C2×C1111yescharacteristic
163C23×C11—22no—
164C23×C11—22no—
165C23×C11#12112yes—
166C23×C11#12112yes—
167C23×C11C22⋊Q812yes—
168C23×C11C22×D411yescharacteristic
169Q8×C11—24no—
170Q8×C11—24no—
171Q8×C11—42no—
172Q8×C11—42no—
173Q8×C11—48no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—24no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—48no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—48no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—44no—
193C2×C4×C11—84no—
194C2×C4×C11#12114yes—
195C2×C4×C11#12112yes—
196C2×C4×C11#12112yes—
197C2×C4×C11C22⋊Q814yes—
198C2×C4×C11C22⋊Q814yes—
199C2×C4×C11C22⋊Q812yes—
200C2×C4×C11#12614yes—
201C2×C4×C11#13714yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×Q811yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C8×C11—24no—
209C8×C11—42no—
210C23×Q8C22×C1111yescharacteristic
211C22×M16C22×C1111yescharacteristic
212C22×M16C22×C1111yescharacteristic
213C2×#117C22×C1111yescharacteristic
214C2×#117C22×C1111yescharacteristic
215C22×C4⋊C4C22×C1111yescharacteristic
216C22×C42C22×C1111yescharacteristic
217#428—24no—
218C2×#107C22×C1112yes—
219C2×#106C22×C1112yes—
220#423—24no—
221C2×C4⋊C8C22×C1114yes—
222#419—24no—
223#419—24no—
224C2×#103C22×C1112yes—
225C2×#103C22×C1114yes—
226C2×#103C22×C1112yes—
227#391—21no—
228#391—21no—
229#391C22×C1114yes—
230#389C22×C1112yes—
231#389C22×C1112yes—
232#385—22no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C2×#95—22no—
236#340C22×C1114yes—
237C22×C11—24no—
238C22×C11—22no—
239C22×C11—22no—
240C22×C11—24no—
241C22×C11#39614yes—
242C22×C11C2×#12111yescharacteristic
243C22×C11C2×#12111yescharacteristic
244C22×C11C2×C22⋊Q811yescharacteristic
245C22×C11C2×#13712yes—
246C22×C11#57512yes—
247C4×C11—24no—
248C4×C11—44no—
249C4×C11—42no—
250C4×C11—42no—
251C4×C11—42no—
252C4×C11—82no—
253C4×C11—82no—
254C4×C11#39614yes—
255C4×C11C2×#12111yescharacteristic
256C4×C11C2×C22⋊Q811yescharacteristic
257C4×C11C2×C22⋊Q811yescharacteristic
258C4×C11C2×#12611yescharacteristic
259C22×Q8—21no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8Q8×C1114yes—
266C22×Q8C23×C1112yes—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4D4×C1112yes—
270C23×C4C23×C1111yescharacteristic
271C2×M16—22no—
272C2×M16—22no—
273C2×M16—22no—
274C2×M16—22no—
275C2×M16—22no—
276C2×M16D4×C1114yes—
277C22×C8C23×C1112yes—
278C22×C8C23×C1112yes—
279#117—22no—
280#117—22no—
281#117—22no—
282#117D4×C1114yes—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4C23×C1112yes—
289C2×C4⋊C4C23×C1112yes—
290C2×C4⋊C4C23×C1111yescharacteristic
291C2×C4⋊C4C23×C1111yescharacteristic
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C42—21no—
295C2×C42—22no—
296C2×C42—22no—
297C2×C42—21no—
298C2×C42D4×C1111yescharacteristic
299C2×C42D4×C1111yescharacteristic
300C2×C42C23×C1112yes—
301#107—24no—
302#106—24no—
303C4⋊C8—28no—
304#103—28no—
305#103—24no—
306#103—24no—
307#95—24no—
308#95—24no—
309#95—22no—
310#95—22no—
311C2×C11—24no—
312C2×C11C2×#39611yescharacteristic
313C2×C11#303911yescharacteristic
314C2×C11#304011yescharacteristic
315C2×C11#305612yes—
316C2×C11#307812yes—
317C24C2×D4×C1111yescharacteristic
318C2×Q8—24no—
319C2×Q8—22no—
320C2×Q8—28no—
321C2×Q8—28no—
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—22no—
326C2×Q8—42no—
327C2×Q8—42no—
328C2×Q8—44no—
329C2×Q8—44no—
330C2×Q8C2×Q8×C1114yes—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—24no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—44no—
343C22×C4—42no—
344C22×C4C2×D4×C1112yes—
345C22×C4C2×D4×C1112yes—
346C22×C4C2×D4×C1111yescharacteristic
347C22×C4C2×D4×C1112yes—
348C22×C4C2×D4×C1112yes—
349C22×C4C2×Q8×C1112yes—
350C22×C4C11×#4112yes—
351C22×C4C11×#4112yes—
352C22×C4C11×#4112yes—
353C22×C4C24×C1111yescharacteristic
354M16—28no—
355M16—44no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8C2×D4×C1114yes—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—44no—
369C4⋊C4—42no—
370C4⋊C4—44no—
371C4⋊C4C2×D4×C1112yes—
372C4⋊C4C2×D4×C1112yes—
373C22⋊C4—24no—
374C22⋊C4—42no—
375C42—22no—
376C42—22no—
377C42—24no—
378C42—22no—
379C42—22no—
380C42—42no—
381C11#2361911yescharacteristic, direct product factor, Sylow
382C23—22no—
383C23—22no—
384C23C11×#12112yes—
385C23C11×#12112yes—
386C23C11×C22⋊Q812yes—
387C23C22×D4×C1111yescharacteristic
388Q8—24no—
389Q8—24no—
390Q8—42no—
391Q8—42no—
392Q8—48no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—48no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—48no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—44no—
412C2×C4—84no—
413C2×C4C11×#12114yes—
414C2×C4C11×#12112yes—
415C2×C4C11×#12112yes—
416C2×C4C11×C22⋊Q814yes—
417C2×C4C11×C22⋊Q814yes—
418C2×C4C11×C22⋊Q812yes—
419C2×C4C11×#12614yes—
420C2×C4C11×#13714yes—
421C2×C4C22×D4×C1111yescharacteristic
422C2×C4C22×D4×C1111yescharacteristic
423C2×C4C22×Q8×C1111yescharacteristic
424C2×C4C2×C11×#4111yescharacteristic
425C2×C4C2×C11×#4111yescharacteristic
426C2×C4C2×C11×#4111yescharacteristic
427C8—24no—
428C8—42no—
429C22—22no—
430C22—22no—
431C22—24no—
432C22—24no—
433C22C11×#39614yes—
434C22C2×C11×#12111yescharacteristic
435C22C2×C11×#12111yescharacteristic
436C22C2×C11×C22⋊Q811yescharacteristic
437C22C2×C11×#13712yes—
438C22C11×#57512yes—
439C4—24no—
440C4—44no—
441C4—42no—
442C4—42no—
443C4—42no—
444C4—82no—
445C4—82no—
446C4C11×#39614yes—
447C4C2×C11×#12111yescharacteristic
448C4C2×C11×C22⋊Q811yescharacteristic
449C4C2×C11×C22⋊Q811yescharacteristic
450C4C2×C11×#12611yescharacteristic
451C2—24no—
452C2C2×C11×#39611yescharacteristic
453C2C11×#303911yescharacteristic
454C2C11×#304011yescharacteristic
455C2C11×#305612yes—
456C2C11×#307812yes—
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
7. C11×#2068C2semidirect
8. C11×#2066C2semidirect
89. #23619C11direct (N × H)
160. #2068C2×C11semidirect
161. #2066C2×C11semidirect
381. C11#23619direct (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
C2×C11×#4192
C11×#22962
C2×C11×#3912
C11×#20682
C11×#20662
C11×#17362
#2361911