Finite Group Databasebeta

← C11×#34594 #14611787

Subgroups — C11×#34594 #14611787

Order 2816.

2362 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#529C212yesmaximal, complemented
2C11×#2664C214yesmaximal, complemented
3C11×#2662C214yesmaximal, complemented
4C11×#2659C211yesmaximal, characteristic, complemented
5C11×#2656C211yesmaximal, characteristic
6C11×#2639C212yesmaximal, complemented
7C11×#2618C214yesmaximal, complemented
8C11×#2396C214yesmaximal, complemented
9C11×#2392C214yesmaximal, complemented
10C4×C11×#121C214yesmaximal, complemented
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C11×#529—216no—
13C2×C11×#126C2214yes—
14C2×C11×#125C2212yes—
15C2×C11×#124C2212yes—
16C2×C11×#123C2214yes—
17C2×C11×C22⋊Q8C2212yes—
18C2×C11×#121C2212yes—
19C2×C11×#121C2214yes—
20C2×C4×Q8×C11C2212yes—
21C2×C4×D4×C11C2212yes—
22C2×C4×D4×C11C2214yes—
23C2×C4×D4×C11C2214yes—
24C2×C11×#117C2214yes—
25C22×C11×C4⋊C4C2212yes—
26C22×C42×C11C2212yes—
27C22×C42×C11C2211yescharacteristic
28C11×#400C2214yes—
29C11×#399C2214yes—
30C11×#398C2214yes—
31C11×#398C2218yes—
32C11×#397C2214yes—
33C11×#396C2218yes—
34C11×#396C2218yes—
35C11×#395C2214yes—
36C11×#394C2214yes—
37C11×#394C2218yes—
38C11×#393C2214yes—
39C11×#392C2214yes—
40C11×#390C2214yes—
41C11×#389C2214yes—
42C11×#388C2218yes—
43C11×#386C2218yes—
44C11×#380C2214yes—
45C4×C11×C4⋊C4C2214yes—
46C4×C11×C4⋊C4C2214yes—
47C4×C11×C4⋊C4C2214yes—
48C4×C11×C22⋊C4C2218yes—
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51C22×Q8×C11C2312yes—
52C22×D4×C11C2314yes—
53C22×D4×C11C2312yes—
54C22×D4×C11C2314yes—
55C23×C4×C11C2314yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C11×#126—216no—
62C11×#125—28no—
63C11×#124—28no—
64C11×#123—216no—
65C11×C22⋊Q8—28no—
66C11×#121—28no—
67C11×#121—216no—
68C4×Q8×C11—28no—
69C4×D4×C11—216no—
70C4×D4×C11—28no—
71C4×D4×C11—48no—
72C11×#117—216no—
73C2×C11×C4⋊C4—28no—
74C2×C11×C4⋊C4C2318yes—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C22⋊C4C2314yes—
85C2×C11×C22⋊C4C2314yes—
86C2×C11×C22⋊C4C2318yes—
87C2×C11×C22⋊C4C2314yes—
88C2×C11×C22⋊C4C2314yes—
89C2×C11×C22⋊C4C2314yes—
90C2×C11×C22⋊C4C2318yes—
91C2×C11×C22⋊C4C2318yes—
92C2×C42×C11—44no—
93C2×C42×C11D418yescomplemented
94C2×C42×C11C2314yes—
95C2×C42×C11C2314yes—
96C2×C42×C11C2314yes—
97C2×C42×C11C2312yes—
98C2×C42×C11C2312yes—
99C11×#95C2314yes—
100C11×#95C2314yes—
101C11×#95C2318yes—
102C11×#95C2318yes—
103C11×#95C2318yes—
104#34594C1111yesmaximal, characteristic, direct product factor, Sylow
105C24×C11C2414yes—
106C24×C11C2411yescharacteristic
107C2×Q8×C11—24no—
108C2×Q8×C11—44no—
109C2×D4×C11—28no—
110C2×D4×C11—216no—
111C2×D4×C11—24no—
112C2×D4×C11—28no—
113C2×D4×C11—44no—
114C2×D4×C11—44no—
115C2×D4×C11—44no—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—28no—
121C22×C4×C11—28no—
122C22×C4×C11—28no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C2×D414yes—
129C22×C4×C11C2×D414yes—
130C22×C4×C11C2×D414yes—
131C22×C4×C11#4118yes—
132C22×C4×C11C2414yes—
133C22×C4×C11C2414yes—
134C22×C4×C11C2414yes—
135C22×C4×C11C2414yes—
136C22×C4×C11C2412yes—
137C22×C4×C11C2411yescharacteristic
138C22×C4×C11C2412yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2411yescharacteristic
141C11×C4⋊C4—28no—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—28no—
147C11×C4⋊C4—216no—
148C11×C4⋊C4—28no—
149C11×C4⋊C4—44no—
150C11×C4⋊C4—44no—
151C11×C22⋊C4—28no—
152C11×C22⋊C4—28no—
153C11×C22⋊C4—28no—
154C11×C22⋊C4—28no—
155C11×C22⋊C4—28no—
156C11×C22⋊C4—216no—
157C11×C22⋊C4—48no—
158C11×C22⋊C4—48no—
159C42×C11—28no—
160C42×C11—28no—
161C42×C11—44no—
162C42×C11C2×D418yes—
163C42×C11C2×D418yes—
164C2×#529C2×C1112yescomplemented
165#2664C2×C1114yescomplemented
166#2662C2×C1114yescomplemented
167#2659C2×C1111yescharacteristic, complemented
168#2656C2×C1111yescharacteristic
169#2639C2×C1112yescomplemented
170#2618C2×C1114yescomplemented
171#2396C2×C1114yescomplemented
172#2392C2×C1114yescomplemented
173C4×#121C2×C1114yescomplemented
174C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—22no—
178C23×C11—24no—
179C23×C11—28no—
180C23×C11—24no—
181C23×C11—24no—
182C23×C11—28no—
183C23×C11C22×D412yes—
184C23×C11C2×#4114yes—
185C23×C11C2511yescharacteristic
186Q8×C11—48no—
187D4×C11—48no—
188D4×C11—416no—
189D4×C11—416no—
190C2×C4×C11—28no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—28no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—28no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—28no—
208C2×C4×C11—44no—
209C2×C4×C11—48no—
210C2×C4×C11—48no—
211C2×C4×C11—416no—
212C2×C4×C11C22×D414yes—
213C2×C4×C11C22×D412yes—
214C2×C4×C11C22×D414yes—
215C2×C4×C11C22×D412yes—
216C2×C4×C11C2×#4118yes—
217C2×C4×C11H(5,𝔽2)12yes—
218C2×C4×C112−1+412yes—
219#529—216no—
220C2×#126C22×C1114yes—
221C2×#125C22×C1112yes—
222C2×#124C22×C1112yes—
223C2×#123C22×C1114yes—
224C2×C22⋊Q8C22×C1112yes—
225C2×#121C22×C1114yes—
226C2×#121C22×C1112yes—
227C2×C4×Q8C22×C1112yes—
228C2×C4×D4C22×C1112yes—
229C2×C4×D4C22×C1114yes—
230C2×C4×D4C22×C1114yes—
231C2×#117C22×C1114yes—
232C22×C4⋊C4C22×C1112yes—
233C22×C42C22×C1112yes—
234C22×C42C22×C1111yescharacteristic
235#400C22×C1114yes—
236#399C22×C1114yes—
237#398C22×C1118yes—
238#398C22×C1114yes—
239#397C22×C1114yes—
240#396C22×C1118yes—
241#396C22×C1118yes—
242#395C22×C1114yes—
243#394C22×C1118yes—
244#394C22×C1114yes—
245#393C22×C1114yes—
246#392C22×C1114yes—
247#390C22×C1114yes—
248#389C22×C1114yes—
249#388C22×C1118yes—
250#386C22×C1118yes—
251#380C22×C1114yes—
252C4×C4⋊C4C22×C1114yes—
253C4×C4⋊C4C22×C1114yes—
254C4×C4⋊C4C22×C1114yes—
255C4×C22⋊C4C22×C1118yes—
256C2×#95C22×C1111yescharacteristic
257C2×#95C22×C1111yescharacteristic
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—24no—
261C22×C11—24no—
262C22×C11—44no—
263C22×C11—44no—
264C22×C11—44no—
265C22×C11—48no—
266C22×C11—48no—
267C22×C11#53214yes—
268C22×C11C23×D411yescharacteristic
269C22×C11C22×#4112yes—
270C22×C11C2×H(5,𝔽2)11yescharacteristic
271C22×C11C2×2−1+411yescharacteristic
272C22×C11#58512yes—
273C4×C11—24no—
274C4×C11—22no—
275C4×C11—24no—
276C4×C11—28no—
277C4×C11—44no—
278C4×C11—44no—
279C4×C11—44no—
280C4×C11—44no—
281C4×C11#53714yes—
282C22×Q8C23×C1112yes—
283C22×D4C23×C1114yes—
284C22×D4C23×C1112yes—
285C22×D4C23×C1114yes—
286C23×C4C23×C1114yes—
287C23×C4C23×C1111yescharacteristic
288C23×C4C23×C1111yescharacteristic
289C23×C4C23×C1112yes—
290C23×C4C23×C1111yescharacteristic
291C23×C4C23×C1112yes—
292#126—216no—
293#125—28no—
294#124—28no—
295#123—216no—
296C22⋊Q8—28no—
297#121—28no—
298#121—216no—
299C4×Q8—28no—
300C4×D4—216no—
301C4×D4—28no—
302C4×D4—48no—
303#117—216no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4C23×C1118yes—
306C2×C4⋊C4C23×C1114yes—
307C2×C4⋊C4C23×C1114yes—
308C2×C4⋊C4C23×C1112yes—
309C2×C4⋊C4C23×C1114yes—
310C2×C4⋊C4C23×C1112yes—
311C2×C4⋊C4C23×C1114yes—
312C2×C4⋊C4C23×C1114yes—
313C2×C4⋊C4C23×C1114yes—
314C2×C4⋊C4C23×C1114yes—
315C2×C22⋊C4C23×C1114yes—
316C2×C22⋊C4C23×C1114yes—
317C2×C22⋊C4C23×C1114yes—
318C2×C22⋊C4C23×C1114yes—
319C2×C22⋊C4C23×C1114yes—
320C2×C22⋊C4C23×C1118yes—
321C2×C22⋊C4C23×C1118yes—
322C2×C22⋊C4C23×C1118yes—
323C2×C42—44no—
324C2×C42D4×C1118yescomplemented
325C2×C42C23×C1114yes—
326C2×C42C23×C1114yes—
327C2×C42C23×C1114yes—
328C2×C42C23×C1112yes—
329C2×C42C23×C1112yes—
330#95C23×C1114yes—
331#95C23×C1114yes—
332#95C23×C1118yes—
333#95C23×C1118yes—
334#95C23×C1118yes—
335C2×C11—24no—
336C2×C11—84no—
337C2×C11C2×#53211yescharacteristic
338C2×C11C2×#53711yescharacteristic
339C2×C11#344911yescharacteristic
340C2×C11#345912yes—
341C2×C11#346112yes—
342C24C24×C1114yes—
343C24C24×C1111yescharacteristic
344C2×Q8—24no—
345C2×Q8—44no—
346C2×D4—28no—
347C2×D4—216no—
348C2×D4—24no—
349C2×D4—28no—
350C2×D4—44no—
351C2×D4—44no—
352C2×D4—44no—
353C22×C4—24no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—24no—
357C22×C4—28no—
358C22×C4—28no—
359C22×C4—28no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4C2×D4×C1114yes—
366C22×C4C2×D4×C1114yes—
367C22×C4C2×D4×C1114yes—
368C22×C4C11×#4118yes—
369C22×C4C24×C1114yes—
370C22×C4C24×C1114yes—
371C22×C4C24×C1114yes—
372C22×C4C24×C1114yes—
373C22×C4C24×C1112yes—
374C22×C4C24×C1111yescharacteristic
375C22×C4C24×C1112yes—
376C22×C4C24×C1114yes—
377C22×C4C24×C1111yescharacteristic
378C4⋊C4—28no—
379C4⋊C4—28no—
380C4⋊C4—24no—
381C4⋊C4—28no—
382C4⋊C4—24no—
383C4⋊C4—28no—
384C4⋊C4—216no—
385C4⋊C4—28no—
386C4⋊C4—44no—
387C4⋊C4—44no—
388C22⋊C4—28no—
389C22⋊C4—28no—
390C22⋊C4—28no—
391C22⋊C4—28no—
392C22⋊C4—28no—
393C22⋊C4—216no—
394C22⋊C4—48no—
395C22⋊C4—48no—
396C42—28no—
397C42—28no—
398C42—44no—
399C42C2×D4×C1118yes—
400C42C2×D4×C1118yes—
401C11#3459411yescharacteristic, direct product factor, Sylow
402C23—21no—
403C23—21no—
404C23—22no—
405C23—24no—
406C23—28no—
407C23—24no—
408C23—24no—
409C23—28no—
410C23C22×D4×C1112yes—
411C23C2×C11×#4114yes—
412C23C25×C1111yescharacteristic
413Q8—48no—
414D4—48no—
415D4—416no—
416D4—416no—
417C2×C4—28no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—28no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—28no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—28no—
435C2×C4—44no—
436C2×C4—48no—
437C2×C4—48no—
438C2×C4—416no—
439C2×C4C22×D4×C1114yes—
440C2×C4C22×D4×C1112yes—
441C2×C4C22×D4×C1114yes—
442C2×C4C22×D4×C1112yes—
443C2×C4C2×C11×#4118yes—
444C2×C4C11×H(5,𝔽2)12yes—
445C2×C4C11×2−1+412yes—
446C22—22no—
447C22—22no—
448C22—24no—
449C22—24no—
450C22—44no—
451C22—44no—
452C22—44no—
453C22—48no—
454C22—48no—
455C22C11×#53214yes—
456C22C23×D4×C1111yescharacteristic
457C22C22×C11×#4112yes—
458C22C2×C11×H(5,𝔽2)11yescharacteristic
459C22C2×C11×2−1+411yescharacteristic
460C22C11×#58512yes—
461C4—24no—
462C4—22no—
463C4—24no—
464C4—28no—
465C4—44no—
466C4—44no—
467C4—44no—
468C4—44no—
469C4C11×#53714yes—
470C2—24no—
471C2—84no—
472C2C2×C11×#53211yescharacteristic
473C2C2×C11×#53711yescharacteristic
474C2C11×#344911yescharacteristic
475C2C11×#345912yes—
476C2C11×#346112yes—
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC11×#2656C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#529C2semidirect
2. C11×#2664C2semidirect
3. C11×#2662C2semidirect
4. C11×#2659C2semidirect
6. C11×#2639C2semidirect
7. C11×#2618C2semidirect
8. C11×#2396C2semidirect
9. C11×#2392C2semidirect
10. C4×C11×#121C2semidirect
11. C2×C4×C11×C4⋊C4C2semidirect
93. C2×C42×C11D4semidirect
104. #34594C11direct (N × H)
164. C2×#529C2×C11semidirect
165. #2664C2×C11semidirect
166. #2662C2×C11semidirect
167. #2659C2×C11semidirect
169. #2639C2×C11semidirect
170. #2618C2×C11semidirect
171. #2396C2×C11semidirect
172. #2392C2×C11semidirect
173. C4×#121C2×C11semidirect
174. C2×C4×C4⋊C4C2×C11semidirect
324. C2×C42D4×C11semidirect
401. C11#34594direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5292
C11×#26642
C11×#26622
C11×#26592
C11×#26562
C11×#26392
C11×#26182
C11×#23962
C11×#23922
C4×C11×#1212
C2×C4×C11×C4⋊C42
#3459411