Finite Group Databasebeta

← C11×#23102 #14600295

Subgroups — C11×#23102 #14600295

Order 2816.

814 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#462C211yesmaximal, characteristic
2C11×#2365C211yesmaximal, characteristic
3C11×#2355C211yesmaximal, characteristic
4C11×#1971C212yesmaximal
5C11×#1956C211yesmaximal, characteristic
6C11×#1948C211yesmaximal, characteristic
7C11×#1927C212yesmaximal
8C11×#1878C212yesmaximal
9C11×#1770C211yesmaximal, characteristic
10C11×#1763C212yesmaximal
11C4×C11×#103C211yesmaximal, characteristic
12C22×C11×Q16C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2212yes—
15C2×C4×Q8×C11C2211yescharacteristic
16C11×#462C418yescomplemented
17C2×C11×#106C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#103C2211yescharacteristic
20C2×C11×#103C2212yes—
21C2×C11×#103C2211yescharacteristic
22C2×C11×#103C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#97C2212yes—
25C2×C4×C8×C11C2211yescharacteristic
26C11×#391C2212yes—
27C11×#391C2212yes—
28C11×#389—21no—
29C11×#387—22no—
30C11×#387—22no—
31C11×#384C2211yescharacteristic
32C11×#382—21no—
33C4×C11×C4⋊C4—21no—
34C4×C11×C4⋊C4—21no—
35C4×C11×C4⋊C4C2212yes—
36C4×C11×C4⋊C4C2211yescharacteristic
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#340C2212yes—
39C11×#340C2211yescharacteristic
40C11×#340C2211yescharacteristic
41C11×#336C2212yes—
42C22×Q8×C11C2311yescharacteristic
43C22×Q8×C11C2312yes—
44C2×C11×Q16—42no—
45C2×C11×Q16—42no—
46C2×C11×Q16C2×C418yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2312yes—
49C22×C8×C11C2311yescharacteristic
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8C2×C414yes—
52C4×Q8×C11—22no—
53C4×Q8×C11—24no—
54C4×Q8×C11—42no—
55C4×Q8×C11C2×C414yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11—21no—
70C2×C42×C11—22no—
71C2×C42×C11—22no—
72C2×C42×C11C2312yes—
73C2×C42×C11C2311yescharacteristic
74C11×#106—42no—
75C11×C4⋊C8C2×C414yes—
76C11×#103—24no—
77C11×#103—22no—
78C11×#103—22no—
79C11×#103—42no—
80C11×#103C2×C418yes—
81C11×#97—42no—
82C4×C8×C11—22no—
83C11×#95—22no—
84C11×#95—22no—
85C11×#95—22no—
86C11×#95—21no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95D412yes—
90#23102C1111yesmaximal, characteristic, direct product factor, Sylow
91C2×Q8×C11—21no—
92C2×Q8×C11—22no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11C22×C414yes—
102C2×Q8×C11C22×C412yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C11×Q16—48no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—21no—
122C2×C8×C11C22×C414yes—
123C2×C8×C11#4112yes—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—44no—
136C11×C4⋊C4—42no—
137C11×C4⋊C4—81no—
138C11×C4⋊C4C22×C412yes—
139C11×C4⋊C4#4112yes—
140C42×C11—24no—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11—44no—
144C42×C11—42no—
145C42×C11—82no—
146C42×C11C22×C412yes—
147C42×C11#4112yes—
148C2×#462C2×C1111yescharacteristic
149#2365C2×C1111yescharacteristic
150#2355C2×C1111yescharacteristic
151#1971C2×C1112yes—
152#1956C2×C1111yescharacteristic
153#1948C2×C1111yescharacteristic
154#1927C2×C1112yes—
155#1878C2×C1112yes—
156#1770C2×C1111yescharacteristic
157#1763C2×C1112yes—
158C4×#103C2×C1111yescharacteristic
159C23×C11C22×D411yescharacteristic
160Q8×C11—22no—
161Q8×C11—24no—
162Q8×C11—22no—
163Q8×C11—24no—
164Q8×C11—41no—
165Q8×C11—42no—
166Q8×C11—41no—
167Q8×C11—42no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—24no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11C4×D412yes—
195C2×C4×C11C4×D412yes—
196C2×C4×C11#13712yes—
197C2×C4×C11#13712yes—
198C2×C4×C11C23×C411yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11H(5,𝔽2)11yescharacteristic
203C2×C4×C11H(5,𝔽2)11yescharacteristic
204C8×C11—24no—
205C8×C11—22no—
206C8×C11—41no—
207C22×Q16C22×C1112yes—
208C2×C4⋊Q8C22×C1111yescharacteristic
209C2×C4×Q8C22×C1112yes—
210C2×C4×Q8C22×C1111yescharacteristic
211#462C4×C1118yescomplemented
212C2×#106C22×C1112yes—
213C2×C4⋊C8C22×C1111yescharacteristic
214C2×#103C22×C1111yescharacteristic
215C2×#103C22×C1112yes—
216C2×#103C22×C1111yescharacteristic
217C2×#103C22×C1112yes—
218C2×#103C22×C1112yes—
219C2×#97C22×C1112yes—
220C2×C4×C8C22×C1111yescharacteristic
221#391C22×C1112yes—
222#391C22×C1112yes—
223#389—21no—
224#387—22no—
225#387—22no—
226#384C22×C1111yescharacteristic
227#382—21no—
228C4×C4⋊C4—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4C22×C1112yes—
231C4×C4⋊C4C22×C1111yescharacteristic
232C4×C4⋊C4C22×C1111yescharacteristic
233#340C22×C1112yes—
234#340C22×C1111yescharacteristic
235#340C22×C1111yescharacteristic
236#336C22×C1112yes—
237C22×C11C2×C4×D411yescharacteristic
238C22×C11#54611yescharacteristic
239C22×C11#55011yescharacteristic
240C22×C11C2×#13711yescharacteristic
241C22×C11C2×#13711yescharacteristic
242C22×C11#57711yescharacteristic
243C22×C11#57811yescharacteristic
244C4×C11—22no—
245C4×C11—42no—
246C4×C11—42no—
247C4×C11—42no—
248C4×C11—42no—
249C4×C11—44no—
250C4×C11—42no—
251C4×C11—81no—
252C4×C11—82no—
253C4×C11#44114yes—
254C4×C11C4×#4111yescharacteristic
255C4×C11#51811yescharacteristic
256C4×C11#55311yescharacteristic
257C4×C11#55511yescharacteristic
258C22×Q8C23×C1112yes—
259C22×Q8C23×C1111yescharacteristic
260C2×Q16—42no—
261C2×Q16—42no—
262C2×Q16C2×C4×C1118yes—
263C22×C8C23×C1111yescharacteristic
264C22×C8C23×C1112yes—
265C22×C8C23×C1111yescharacteristic
266C4⋊Q8—22no—
267C4⋊Q8C2×C4×C1114yes—
268C4×Q8—22no—
269C4×Q8—24no—
270C4×Q8—42no—
271C4×Q8C2×C4×C1114yes—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4D4×C1111yescharacteristic
279C2×C4⋊C4D4×C1111yescharacteristic
280C2×C4⋊C4C23×C1112yes—
281C2×C4⋊C4C23×C1111yescharacteristic
282C2×C4⋊C4C23×C1111yescharacteristic
283C2×C4⋊C4C23×C1111yescharacteristic
284C2×C42—21no—
285C2×C42—22no—
286C2×C42—21no—
287C2×C42—22no—
288C2×C42C23×C1112yes—
289C2×C42C23×C1111yescharacteristic
290#106—42no—
291C4⋊C8C2×C4×C1114yes—
292#103—24no—
293#103—22no—
294#103—22no—
295#103—42no—
296#103C2×C4×C1118yes—
297#97—42no—
298C4×C8—22no—
299#95—22no—
300#95—22no—
301#95—22no—
302#95—21no—
303#95—22no—
304#95—22no—
305#95D4×C1112yes—
306C2×C11#236311yescharacteristic
307C2×C11C2×#44111yescharacteristic
308C2×C11#294711yescharacteristic
309C2×C11#332811yescharacteristic
310C2×C11#333111yescharacteristic
311C2×C11#339811yescharacteristic
312C2×C11#340011yescharacteristic
313C2×Q8—21no—
314C2×Q8—22no—
315C2×Q8—21no—
316C2×Q8—22no—
317C2×Q8—21no—
318C2×Q8—22no—
319C2×Q8—22no—
320C2×Q8—22no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8C22×C4×C1114yes—
324C2×Q8C22×C4×C1112yes—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—22no—
331C22×C4C2×D4×C1112yes—
332C22×C4C2×D4×C1112yes—
333C22×C4C2×D4×C1111yescharacteristic
334C22×C4C2×D4×C1111yescharacteristic
335C22×C4C24×C1111yescharacteristic
336Q16—48no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8C22×C4×C1114yes—
345C2×C8C11×#4112yes—
346C4⋊C4—24no—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—22no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—21no—
357C4⋊C4—44no—
358C4⋊C4—42no—
359C4⋊C4—81no—
360C4⋊C4C22×C4×C1112yes—
361C4⋊C4C11×#4112yes—
362C42—24no—
363C42—22no—
364C42—22no—
365C42—44no—
366C42—42no—
367C42—82no—
368C42C22×C4×C1112yes—
369C42C11×#4112yes—
370C11#2310211yescharacteristic, direct product factor, Sylow
371C23C22×D4×C1111yescharacteristic
372Q8—22no—
373Q8—24no—
374Q8—22no—
375Q8—24no—
376Q8—41no—
377Q8—42no—
378Q8—41no—
379Q8—42no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—24no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4C4×D4×C1112yes—
407C2×C4C4×D4×C1112yes—
408C2×C4C11×#13712yes—
409C2×C4C11×#13712yes—
410C2×C4C23×C4×C1111yescharacteristic
411C2×C4C2×C11×#4111yescharacteristic
412C2×C4C2×C11×#4111yescharacteristic
413C2×C4C2×C11×#4111yescharacteristic
414C2×C4C11×H(5,𝔽2)11yescharacteristic
415C2×C4C11×H(5,𝔽2)11yescharacteristic
416C8—24no—
417C8—22no—
418C8—41no—
419C22C2×C4×D4×C1111yescharacteristic
420C22C11×#54611yescharacteristic
421C22C11×#55011yescharacteristic
422C22C2×C11×#13711yescharacteristic
423C22C2×C11×#13711yescharacteristic
424C22C11×#57711yescharacteristic
425C22C11×#57811yescharacteristic
426C4—22no—
427C4—42no—
428C4—42no—
429C4—42no—
430C4—42no—
431C4—42no—
432C4—44no—
433C4—81no—
434C4—82no—
435C4C11×#44114yes—
436C4C4×C11×#4111yescharacteristic
437C4C11×#51811yescharacteristic
438C4C11×#55311yescharacteristic
439C4C11×#55511yescharacteristic
440C2C11×#236311yescharacteristic
441C2C2×C11×#44111yescharacteristic
442C2C11×#294711yescharacteristic
443C2C11×#332811yescharacteristic
444C2C11×#333111yescharacteristic
445C2C11×#339811yescharacteristic
446C2C11×#340011yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
16. C11×#462C4semidirect
90. #23102C11direct (N × H)
211. #462C4×C11semidirect
370. C11#23102direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4622
C11×#23652
C11×#23552
C11×#19712
C11×#19562
C11×#19482
C11×#19272
C11×#18782
C11×#17702
C11×#17632
C4×C11×#1032
#2310211