Finite Group Databasebeta

← C11×#23841 #14601034

Subgroups — C11×#23841 #14601034

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×C4⋊Q8C211yesmaximal, characteristic
2C4×C11×#125C211yesmaximal, characteristic
3C11×#2085C212yesmaximal
4C11×#2084C211yesmaximal, characteristic
5C11×#2083C211yesmaximal, characteristic
6C11×#2059C212yesmaximal
7C11×#2058C211yesmaximal, characteristic
8C11×#2057C211yesmaximal, characteristic
9C11×#1776C212yesmaximal
10C11×#1776C212yesmaximal
11C11×#1745C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#125C2211yescharacteristic
14C2×C4×Q8×C11—21no—
15C2×C11×#107C2212yes—
16C2×C11×#107C2212yes—
17C2×C11×#106C2212yes—
18C2×C11×#106C2212yes—
19C2×C11×#97C2212yes—
20C11×#391—21no—
21C11×#389—21no—
22C11×#389C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#389C2212yes—
25C11×#387—21no—
26C11×#387—21no—
27C11×#384C2211yescharacteristic
28C11×#382C2211yescharacteristic
29C4×C11×C4⋊C4—21no—
30C4×C11×C4⋊C4—21no—
31C4×C11×C4⋊C4—21no—
32C4×C11×C4⋊C4C2211yescharacteristic
33C4×C11×C4⋊C4C2211yescharacteristic
34C4×C11×C4⋊C4C2212yes—
35C43×C11C2211yescharacteristic
36C11×#340C2212yes—
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#336C2211yescharacteristic
41C11×#336C2211yescharacteristic
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×C8×C11C2312yes—
45C22×C8×C11C2312yes—
46C11×C4⋊Q8—24no—
47C11×#125—22no—
48C11×#125—22no—
49C4×Q8×C11—44no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C42×C11—21no—
65C2×C42×C11—21no—
66C2×C42×C11—22no—
67C2×C42×C11D411yescharacteristic
68C2×C42×C11D411yescharacteristic
69C2×C42×C11D411yescharacteristic
70C2×C42×C11D411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C11×#107—24no—
75C11×#107—24no—
76C11×#106—24no—
77C11×#106—24no—
78C11×#97Q818yescomplemented
79C11×#95—21no—
80C11×#95—21no—
81C11×#95—21no—
82C11×#95—21no—
83C11×#95—22no—
84C11×#95—21no—
85C11×#95—21no—
86C11×#95—22no—
87#23841C1111yesmaximal, characteristic, direct product factor, Sylow
88C2×Q8×C11—24no—
89C2×Q8×C11—42no—
90C2×Q8×C11—42no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11C2×Q814yes—
109C2×C8×C11C2×Q814yes—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—42no—
121C11×C4⋊C4—44no—
122C11×C4⋊C4—42no—
123C11×C4⋊C4—42no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4#4112yes—
126C11×C4⋊C4#4114yes—
127C11×C4⋊C4#4112yes—
128C42×C11—22no—
129C42×C11—22no—
130C42×C11—21no—
131C42×C11—21no—
132C42×C11—22no—
133C42×C11—41no—
134C42×C11—41no—
135C42×C11—42no—
136C42×C11—42no—
137C42×C11—44no—
138C42×C11C2×Q814yes—
139C4×C4⋊Q8C2×C1111yescharacteristic
140C4×#125C2×C1111yescharacteristic
141#2085C2×C1112yes—
142#2084C2×C1111yescharacteristic
143#2083C2×C1111yescharacteristic
144#2059C2×C1112yes—
145#2058C2×C1111yescharacteristic
146#2057C2×C1111yescharacteristic
147#1776C2×C1112yes—
148#1776C2×C1112yes—
149#1745C2×C1111yescharacteristic
150C23×C11C22×D411yescharacteristic
151Q8×C11—48no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—24no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11C4⋊Q812yes—
185C2×C4×C11C4⋊Q812yes—
186C2×C4×C11AGL(1,ℤ/8)12yes—
187C2×C4×C11#13712yes—
188C2×C4×C11C22×Q812yes—
189C2×C4×C11C2×#4112yes—
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C8×C11—24no—
193C8×C11—24no—
194C2×C4⋊Q8C22×C1111yescharacteristic
195C2×#125C22×C1111yescharacteristic
196C2×C4×Q8—21no—
197C2×#107C22×C1112yes—
198C2×#107C22×C1112yes—
199C2×#106C22×C1112yes—
200C2×#106C22×C1112yes—
201C2×#97C22×C1112yes—
202#391—21no—
203#389—21no—
204#389C22×C1111yescharacteristic
205#389C22×C1111yescharacteristic
206#389C22×C1112yes—
207#387—21no—
208#387—21no—
209#384C22×C1111yescharacteristic
210#382C22×C1111yescharacteristic
211C4×C4⋊C4—21no—
212C4×C4⋊C4—21no—
213C4×C4⋊C4—21no—
214C4×C4⋊C4C22×C1111yescharacteristic
215C4×C4⋊C4C22×C1111yescharacteristic
216C4×C4⋊C4C22×C1112yes—
217C43C22×C1111yescharacteristic
218#340C22×C1112yes—
219#340C22×C1112yes—
220#340C22×C1112yes—
221#340C22×C1112yes—
222#336C22×C1111yescharacteristic
223#336C22×C1111yescharacteristic
224#336C22×C1112yes—
225C22×C11#52511yescharacteristic
226C22×C11#52511yescharacteristic
227C22×C11C2×C4⋊Q811yescharacteristic
228C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
229C22×C11C2×#13711yescharacteristic
230C22×C11#57511yescharacteristic
231C22×C11#57511yescharacteristic
232C4×C11—22no—
233C4×C11—22no—
234C4×C11—22no—
235C4×C11—22no—
236C4×C11—44no—
237C4×C11—41no—
238C4×C11—42no—
239C4×C11—41no—
240C4×C11—42no—
241C4×C11—81no—
242C4×C11—82no—
243C4×C11—81no—
244C4×C11#53312yes—
245C4×C11#53312yes—
246C22×Q8—21no—
247C22×C8C23×C1112yes—
248C22×C8C23×C1112yes—
249C4⋊Q8—24no—
250#125—22no—
251#125—22no—
252C4×Q8—44no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4C23×C1111yescharacteristic
262C2×C4⋊C4C23×C1111yescharacteristic
263C2×C4⋊C4C23×C1112yes—
264C2×C4⋊C4C23×C1111yescharacteristic
265C2×C4⋊C4C23×C1111yescharacteristic
266C2×C4⋊C4C23×C1112yes—
267C2×C42—22no—
268C2×C42—21no—
269C2×C42—21no—
270C2×C42D4×C1111yescharacteristic
271C2×C42D4×C1111yescharacteristic
272C2×C42D4×C1111yescharacteristic
273C2×C42D4×C1111yescharacteristic
274C2×C42C23×C1111yescharacteristic
275C2×C42C23×C1111yescharacteristic
276C2×C42C23×C1111yescharacteristic
277#107—24no—
278#107—24no—
279#106—24no—
280#106—24no—
281#97Q8×C1118yescomplemented
282#95—21no—
283#95—21no—
284#95—21no—
285#95—21no—
286#95—22no—
287#95—21no—
288#95—21no—
289#95—22no—
290C2×C11#239911yescharacteristic
291C2×C11#311411yescharacteristic
292C2×C11#311511yescharacteristic
293C2×C11#311611yescharacteristic
294C2×C11#311711yescharacteristic
295C2×C11#316511yescharacteristic
296C2×C11#316611yescharacteristic
297C2×Q8—24no—
298C2×Q8—42no—
299C2×Q8—42no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4C2×D4×C1111yescharacteristic
307C22×C4C2×D4×C1111yescharacteristic
308C22×C4C2×D4×C1111yescharacteristic
309C22×C4C2×D4×C1111yescharacteristic
310C22×C4C2×D4×C1111yescharacteristic
311C22×C4C2×D4×C1111yescharacteristic
312C22×C4C24×C1111yescharacteristic
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8C2×Q8×C1114yes—
318C2×C8C2×Q8×C1114yes—
319C4⋊C4—24no—
320C4⋊C4—24no—
321C4⋊C4—24no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—44no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—42no—
333C4⋊C4—42no—
334C4⋊C4C11×#4112yes—
335C4⋊C4C11×#4114yes—
336C4⋊C4C11×#4112yes—
337C42—22no—
338C42—22no—
339C42—21no—
340C42—21no—
341C42—22no—
342C42—41no—
343C42—41no—
344C42—44no—
345C42—42no—
346C42—42no—
347C42C2×Q8×C1114yes—
348C11#2384111yescharacteristic, direct product factor, Sylow
349C23C22×D4×C1111yescharacteristic
350Q8—48no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—24no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4C11×C4⋊Q812yes—
384C2×C4C11×C4⋊Q812yes—
385C2×C4C11×AGL(1,ℤ/8)12yes—
386C2×C4C11×#13712yes—
387C2×C4C22×Q8×C1112yes—
388C2×C4C2×C11×#4112yes—
389C2×C4C2×C11×#4111yescharacteristic
390C2×C4C2×C11×#4111yescharacteristic
391C8—24no—
392C8—24no—
393C22C11×#52511yescharacteristic
394C22C11×#52511yescharacteristic
395C22C2×C11×C4⋊Q811yescharacteristic
396C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
397C22C2×C11×#13711yescharacteristic
398C22C11×#57511yescharacteristic
399C22C11×#57511yescharacteristic
400C4—22no—
401C4—22no—
402C4—22no—
403C4—22no—
404C4—44no—
405C4—41no—
406C4—42no—
407C4—41no—
408C4—42no—
409C4—81no—
410C4—82no—
411C4—81no—
412C4C11×#53312yes—
413C4C11×#53312yes—
414C2C11×#239911yescharacteristic
415C2C11×#311411yescharacteristic
416C2C11×#311511yescharacteristic
417C2C11×#311611yescharacteristic
418C2C11×#311711yescharacteristic
419C2C11×#316511yescharacteristic
420C2C11×#316611yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
78. C11×#97Q8semidirect
87. #23841C11direct (N × H)
281. #97Q8×C11semidirect
348. C11#23841direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×C4⋊Q82
C4×C11×#1252
C11×#20852
C11×#20842
C11×#20832
C11×#20592
C11×#20582
C11×#20572
C11×#17762
C11×#17452
#2384111