Finite Group Databasebeta

← C11×#34259 #14611452

Subgroups — C11×#34259 #14611452

Order 2816.

5106 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×2−1+4C211yesmaximal, characteristic
2C2×C11×#520C211yesmaximal, characteristic, complemented
3C2×C4×C11×#41C211yesmaximal, characteristic, complemented
4Q8×C11×C22⋊C4C214yesmaximal, complemented
5C11×#2339C2112yesmaximal, complemented
6C11×#2311C213yesmaximal, complemented
7C11×#2310C213yesmaximal, complemented
8C11×#2297C213yesmaximal, complemented
9C2×C11×#391C213yesmaximal, complemented
10C2×C11×2−1+4—28no—
11C2×C11×2−1+4—28no—
12C2×C11×2−1+4C4116yescomplemented
13C22×C11×#41C2213yes—
14C22×C11×#41C2216yes—
15C22×C11×#41C2211yescharacteristic
16C23×Q8×C11C2213yes—
17C23×Q8×C11C2212yes—
18C11×#520—28no—
19C4×C11×#41—28no—
20C2×C4×Q8×C11C2212yes—
21C2×C4×Q8×C11C2212yes—
22C2×C4×D4×C11C2216yes—
23C2×C4×D4×C11C2216yes—
24C2×C11×#117C2213yes—
25C2×C11×#117C2213yes—
26C22×C11×C4⋊C4C2213yes—
27C22×C42×C11C2213yes—
28C11×#391C2213yes—
29C11×#391C2216yes—
30C11×#391C22112yes—
31C11×#391C2213yes—
32C11×#391C22112yes—
33C11×#390C2211yescharacteristic
34C11×#390C2213yes—
35C11×#386C22112yes—
36C11×#386C22112yes—
37C11×#381C22112yes—
38C11×#380C22112yes—
39C4×C11×C22⋊C4C22112yes—
40C2×C11×#95C22112yes—
41C11×2−1+4—2128no—
42C2×C11×#41—224no—
43C2×C11×#41—224no—
44C2×C11×#41—212no—
45C2×C11×#41—212no—
46C2×C11×#41C2×C418yes—
47C2×C11×#41C2×C4148yescomplemented
48C2×C11×#41C2×C4124yescomplemented
49C2×C11×#41D418yes—
50C2×C11×#41D418yes—
51C22×Q8×C11—28no—
52C22×Q8×C11—28no—
53C22×Q8×C11—212no—
54C22×Q8×C11—212no—
55C22×Q8×C11C2×C4116yescomplemented
56C22×Q8×C11C2×C4124yescomplemented
57C22×Q8×C11C2313yes—
58C22×Q8×C11C2316yes—
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2316yes—
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2313yes—
63C23×C4×C11C2316yes—
64C23×C4×C11C2316yes—
65C23×C4×C11C2316yes—
66C23×C4×C11C2316yes—
67C23×C4×C11C2313yes—
68C4×Q8×C11—28no—
69C4×Q8×C11—28no—
70C4×D4×C11—224no—
71C4×D4×C11—224no—
72C11×#117—212no—
73C11×#117—212no—
74C2×C11×C4⋊C4—212no—
75C2×C11×C4⋊C4C2313yes—
76C2×C11×C4⋊C4C2316yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2316yes—
79C2×C11×C22⋊C4C2316yes—
80C2×C11×C22⋊C4C2316yes—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C23112yes—
83C2×C42×C11—212no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2313yes—
86C2×C42×C11C2316yes—
87C2×C42×C11C2316yes—
88C11×#95C23112yes—
89C11×#95C23124yes—
90C11×#95C23112yes—
91#34259C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11C2412yes—
93C24×C11C2413yes—
94C11×#41—2192no—
95C11×#41—296no—
96C11×#41C22⋊C4164yescomplemented
97C2×Q8×C11—264no—
98C2×Q8×C11—296no—
99C2×Q8×C11—26no—
100C2×Q8×C11—212no—
101C2×Q8×C11—212no—
102C2×Q8×C11—26no—
103C2×Q8×C11C22×C4124yes—
104C2×Q8×C11C22×C4112yes—
105C2×Q8×C11C22×C414yes—
106C2×Q8×C11C2×D414yes—
107C2×Q8×C11C2×D414yes—
108C2×D4×C11—212no—
109C2×D4×C11—212no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11C22×C4124yes—
113C2×D4×C11C22×C414yes—
114C2×D4×C11C22×C4112yes—
115C2×D4×C11C2×D4112yes—
116C2×D4×C11C2×D4112yes—
117C22×C4×C11—212no—
118C22×C4×C11—212no—
119C22×C4×C11—212no—
120C22×C4×C11—212no—
121C22×C4×C11—212no—
122C22×C4×C11—212no—
123C22×C4×C11—212no—
124C22×C4×C11—46no—
125C22×C4×C11—412no—
126C22×C4×C11C22×C4124yes—
127C22×C4×C11C22×C4124yes—
128C22×C4×C11C22×C4112yes—
129C22×C4×C11C2×D4112yes—
130C22×C4×C11C2×D4112yes—
131C22×C4×C11C2412yes—
132C22×C4×C11C2416yes—
133C22×C4×C11C2416yes—
134C22×C4×C11C2416yes—
135C22×C4×C11C2412yes—
136C22×C4×C11C2411yescharacteristic
137C22×C4×C11C2413yes—
138C11×C4⋊C4—26no—
139C11×C4⋊C4—212no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—212no—
142C11×C22⋊C4—212no—
143C11×C22⋊C4—212no—
144C11×C22⋊C4—28no—
145C11×C22⋊C4—412no—
146C42×C11—22no—
147C42×C11—26no—
148C42×C11—212no—
149C42×C11—212no—
150C22×2−1+4C2×C1111yescharacteristic
151C2×#520C2×C1111yescharacteristic, complemented
152C2×C4×#41C2×C1111yescharacteristic, complemented
153Q8×C22⋊C4C2×C1114yescomplemented
154#2339C2×C11112yescomplemented
155#2311C2×C1113yescomplemented
156#2310C2×C1113yescomplemented
157#2297C2×C1113yescomplemented
158C2×#391C2×C1113yescomplemented
159C23×C11—26no—
160C23×C11—26no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—24no—
164C23×C11—24no—
165C23×C11C23×C414yes—
166C23×C11C23×C416yes—
167C23×C11C22×D416yes—
168C23×C11C22×D416yes—
169C23×C11C2511yescharacteristic
170Q8×C11—248no—
171Q8×C11—224no—
172Q8×C11C2×C22⋊C4116yes—
173D4×C11—248no—
174D4×C11—28no—
175D4×C11C2×C22⋊C4148yes—
176C2×C4×C11—248no—
177C2×C4×C11—22no—
178C2×C4×C11—26no—
179C2×C4×C11—26no—
180C2×C4×C11—22no—
181C2×C4×C11—248no—
182C2×C4×C11—22no—
183C2×C4×C11—26no—
184C2×C4×C11—26no—
185C2×C4×C11—24no—
186C2×C4×C11—26no—
187C2×C4×C11—26no—
188C2×C4×C11—212no—
189C2×C4×C11—424no—
190C2×C4×C11—812no—
191C2×C4×C11C2×C22⋊C4148yes—
192C2×C4×C11C23×C4112yes—
193C2×C4×C11C23×C416yes—
194C2×C4×C11C23×C412yes—
195C2×C4×C11C22×D412yes—
196C2×C4×C11C22×D416yes—
197C2×C4×C11C22×D416yes—
198C2×C4×C11C22×D412yes—
199C2×C4×C112−1+414yescomplemented
200C2×2−1+4—28no—
201C2×2−1+4—28no—
202C2×2−1+4C4×C11116yescomplemented
203C22×#41C22×C1113yes—
204C22×#41C22×C1116yes—
205C22×#41C22×C1111yescharacteristic
206C23×Q8C22×C1113yes—
207C23×Q8C22×C1112yes—
208#520—28no—
209C4×#41—28no—
210C2×C4×Q8C22×C1112yes—
211C2×C4×Q8C22×C1112yes—
212C2×C4×D4C22×C1116yes—
213C2×C4×D4C22×C1116yes—
214C2×#117C22×C1113yes—
215C2×#117C22×C1113yes—
216C22×C4⋊C4C22×C1113yes—
217C22×C42C22×C1113yes—
218#391C22×C1113yes—
219#391C22×C1116yes—
220#391C22×C11112yes—
221#391C22×C11112yes—
222#391C22×C1113yes—
223#390C22×C1113yes—
224#390C22×C1111yescharacteristic
225#386C22×C11112yes—
226#386C22×C11112yes—
227#381C22×C11112yes—
228#380C22×C11112yes—
229C4×C22⋊C4C22×C11112yes—
230C2×#95C22×C11112yes—
231C22×C11—212no—
232C22×C11—212no—
233C22×C11—26no—
234C22×C11—26no—
235C22×C11—24no—
236C22×C11—28no—
237C22×C11—44no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11C22×C22⋊C4112yes—
241C22×C11C24×C411yescharacteristic
242C22×C11C23×D411yescharacteristic
243C22×C11C23×D411yescharacteristic
244C22×C11C2×2−1+412yes—
245C22×C11#58512yes—
246C4×C11—212no—
247C4×C11—24no—
248C4×C11—46no—
249C4×C11—42no—
250C4×C11—46no—
251C4×C11C22×C22⋊C4112yes—
252C4×C11C22×C22⋊C414yes—
2532−1+4—2128no—
254C2×#41—224no—
255C2×#41—224no—
256C2×#41—212no—
257C2×#41—212no—
258C2×#41C2×C4×C1118yes—
259C2×#41C2×C4×C11148yescomplemented
260C2×#41C2×C4×C11124yescomplemented
261C2×#41D4×C1118yes—
262C2×#41D4×C1118yes—
263C22×Q8—28no—
264C22×Q8—28no—
265C22×Q8—212no—
266C22×Q8—212no—
267C22×Q8C2×C4×C11116yescomplemented
268C22×Q8C2×C4×C11124yescomplemented
269C22×Q8C23×C1113yes—
270C22×Q8C23×C1116yes—
271C22×Q8C23×C1111yescharacteristic
272C22×D4C23×C1116yes—
273C22×D4C23×C1111yescharacteristic
274C22×D4C23×C1113yes—
275C23×C4C23×C1116yes—
276C23×C4C23×C1116yes—
277C23×C4C23×C1116yes—
278C23×C4C23×C1116yes—
279C23×C4C23×C1113yes—
280C4×Q8—28no—
281C4×Q8—28no—
282C4×D4—224no—
283C4×D4—224no—
284#117—212no—
285#117—212no—
286C2×C4⋊C4—212no—
287C2×C4⋊C4C23×C1113yes—
288C2×C4⋊C4C23×C1116yes—
289C2×C4⋊C4C23×C1111yescharacteristic
290C2×C4⋊C4C23×C1116yes—
291C2×C22⋊C4C23×C1116yes—
292C2×C22⋊C4C23×C1116yes—
293C2×C22⋊C4C23×C1114yes—
294C2×C22⋊C4C23×C11112yes—
295C2×C42—212no—
296C2×C42C23×C1113yes—
297C2×C42C23×C1116yes—
298C2×C42C23×C1116yes—
299C2×C42C23×C1111yescharacteristic
300#95C23×C11112yes—
301#95C23×C11124yes—
302#95C23×C11112yes—
303C2×C11—212no—
304C2×C11—44no—
305C2×C11C23×C22⋊C411yescharacteristic
306C2×C11C4×2−1+412yes—
307C2×C11#348912yes—
308C2×C11#349911yescharacteristic
309C2×C11#350011yescharacteristic
310C24C24×C1112yes—
311C24C24×C1113yes—
312#41—2192no—
313#41—296no—
314#41C11×C22⋊C4164yescomplemented
315C2×Q8—264no—
316C2×Q8—296no—
317C2×Q8—26no—
318C2×Q8—212no—
319C2×Q8—212no—
320C2×Q8—26no—
321C2×Q8C22×C4×C11124yes—
322C2×Q8C22×C4×C11112yes—
323C2×Q8C22×C4×C1114yes—
324C2×Q8C2×D4×C1114yes—
325C2×Q8C2×D4×C1114yes—
326C2×D4—212no—
327C2×D4—212no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4C22×C4×C11124yes—
331C2×D4C22×C4×C1114yes—
332C2×D4C22×C4×C11112yes—
333C2×D4C2×D4×C11112yes—
334C2×D4C2×D4×C11112yes—
335C22×C4—212no—
336C22×C4—212no—
337C22×C4—212no—
338C22×C4—212no—
339C22×C4—212no—
340C22×C4—212no—
341C22×C4—212no—
342C22×C4—46no—
343C22×C4—412no—
344C22×C4C22×C4×C11124yes—
345C22×C4C22×C4×C11124yes—
346C22×C4C22×C4×C11112yes—
347C22×C4C2×D4×C11112yes—
348C22×C4C2×D4×C11112yes—
349C22×C4C24×C1112yes—
350C22×C4C24×C1116yes—
351C22×C4C24×C1116yes—
352C22×C4C24×C1116yes—
353C22×C4C24×C1112yes—
354C22×C4C24×C1111yescharacteristic
355C22×C4C24×C1113yes—
356C4⋊C4—26no—
357C4⋊C4—212no—
358C4⋊C4—22no—
359C4⋊C4—212no—
360C22⋊C4—212no—
361C22⋊C4—212no—
362C22⋊C4—28no—
363C22⋊C4—412no—
364C42—22no—
365C42—26no—
366C42—212no—
367C42—212no—
368C11#3425911yescharacteristic, direct product factor, Sylow
369C23—26no—
370C23—26no—
371C23—22no—
372C23—22no—
373C23—24no—
374C23—24no—
375C23C23×C4×C1114yes—
376C23C23×C4×C1116yes—
377C23C22×D4×C1116yes—
378C23C22×D4×C1116yes—
379C23C25×C1111yescharacteristic
380Q8—248no—
381Q8—224no—
382Q8C2×C11×C22⋊C4116yes—
383D4—248no—
384D4—28no—
385D4C2×C11×C22⋊C4148yes—
386C2×C4—248no—
387C2×C4—22no—
388C2×C4—26no—
389C2×C4—26no—
390C2×C4—22no—
391C2×C4—248no—
392C2×C4—22no—
393C2×C4—26no—
394C2×C4—26no—
395C2×C4—24no—
396C2×C4—26no—
397C2×C4—26no—
398C2×C4—212no—
399C2×C4—424no—
400C2×C4—812no—
401C2×C4C2×C11×C22⋊C4148yes—
402C2×C4C23×C4×C11112yes—
403C2×C4C23×C4×C1116yes—
404C2×C4C23×C4×C1112yes—
405C2×C4C22×D4×C1112yes—
406C2×C4C22×D4×C1116yes—
407C2×C4C22×D4×C1116yes—
408C2×C4C22×D4×C1112yes—
409C2×C4C11×2−1+414yescomplemented
410C22—212no—
411C22—212no—
412C22—26no—
413C22—26no—
414C22—24no—
415C22—28no—
416C22—44no—
417C22—42no—
418C22—42no—
419C22C22×C11×C22⋊C4112yes—
420C22C24×C4×C1111yescharacteristic
421C22C23×D4×C1111yescharacteristic
422C22C23×D4×C1111yescharacteristic
423C22C2×C11×2−1+412yes—
424C22C11×#58512yes—
425C4—212no—
426C4—24no—
427C4—46no—
428C4—42no—
429C4—46no—
430C4C22×C11×C22⋊C4112yes—
431C4C22×C11×C22⋊C414yes—
432C2—212no—
433C2—44no—
434C2C23×C11×C22⋊C411yescharacteristic
435C2C4×C11×2−1+412yes—
436C2C11×#348912yes—
437C2C11×#349911yescharacteristic
438C2C11×#350011yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC22×C11×2−1+4C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#520C2semidirect
3. C2×C4×C11×#41C2semidirect
4. Q8×C11×C22⋊C4C2semidirect
5. C11×#2339C2semidirect
6. C11×#2311C2semidirect
7. C11×#2310C2semidirect
8. C11×#2297C2semidirect
9. C2×C11×#391C2semidirect
12. C2×C11×2−1+4C4semidirect
47. C2×C11×#41C2×C4semidirect
48. C2×C11×#41C2×C4semidirect
55. C22×Q8×C11C2×C4semidirect
56. C22×Q8×C11C2×C4semidirect
91. #34259C11direct (N × H)
96. C11×#41C22⋊C4semidirect
151. C2×#520C2×C11semidirect
152. C2×C4×#41C2×C11semidirect
153. Q8×C22⋊C4C2×C11semidirect
154. #2339C2×C11semidirect
155. #2311C2×C11semidirect
156. #2310C2×C11semidirect
157. #2297C2×C11semidirect
158. C2×#391C2×C11semidirect
199. C2×C4×C112−1+4semidirect
202. C2×2−1+4C4×C11semidirect
259. C2×#41C2×C4×C11semidirect
260. C2×#41C2×C4×C11semidirect
267. C22×Q8C2×C4×C11semidirect
268. C22×Q8C2×C4×C11semidirect
314. #41C11×C22⋊C4semidirect
368. C11#34259direct (N × H)
409. C2×C4C11×2−1+4semidirect

Maximal subgroups

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

subgroupindex
C22×C11×2−1+42
C2×C11×#5202
C2×C4×C11×#412
Q8×C11×C22⋊C42
C11×#23392
C11×#23112
C11×#23102
C11×#22972
C2×C11×#3912
#3425911