Finite Group Databasebeta

← C11×#34208 #14611401

Subgroups — C11×#34208 #14611401

Order 2816.

3054 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#532C211yesmaximal, characteristic
2C2×C11×#520C212yesmaximal, complemented
3C11×#2364C218yesmaximal, complemented
4C11×#2352C218yesmaximal, complemented
5C11×#2328C212yesmaximal, complemented
6C11×#2327C212yesmaximal, complemented
7C11×#2311C212yesmaximal, complemented
8C4×C11×#124C214yesmaximal, complemented
9C2×C11×#382C211yesmaximal, characteristic, complemented
10C4×C11×#117C211yesmaximal, characteristic, complemented
11C22×C11×#41C2212yes—
12C11×#532C4116yescomplemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124C2212yes—
16C2×C11×#121C2214yes—
17C11×#520—216no—
18C2×C4×Q8×C11C2214yes—
19C2×C4×D4×C11C2214yes—
20C2×C4×D4×C11C2218yes—
21C2×C4×D4×C11C2214yes—
22C2×C11×#117C2214yes—
23C2×C11×#117C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C22×C11×C4⋊C4C2212yes—
26C22×C11×C4⋊C4C2214yes—
27C22×C42×C11C2211yescharacteristic
28C11×#391C2214yes—
29C11×#390C2214yes—
30C11×#388C22116yes—
31C11×#387C22116yes—
32C11×#386C2218yes—
33C11×#386C22116yes—
34C11×#382C2212yes—
35C11×#382C2212yes—
36C11×#382C2214yes—
37C11×#380C2218yes—
38C4×C11×C4⋊C4C2214yes—
39C4×C11×C22⋊C4C2214yes—
40C4×C11×C22⋊C4C22116yes—
41C11×#376C2212yes—
42C2×C11×#95C2214yes—
43C43×C11C2212yes—
44C2×C11×#41—28no—
45C2×C11×#41—28no—
46C2×C11×#41C2×C4116yescomplemented
47C22×Q8×C11C2312yes—
48C22×D4×C11C2314yes—
49C22×D4×C11C2312yes—
50C22×D4×C11C2314yes—
51C23×C4×C11C2314yes—
52C23×C4×C11C2314yes—
53C23×C4×C11C2318yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C11×C4⋊Q8C2×C418yescomplemented
57C11×#127C2×C418yescomplemented
58C11×#124C2×C4116yescomplemented
59C11×#121C2×C4132yescomplemented
60C4×Q8×C11—216no—
61C4×D4×C11—232no—
62C4×D4×C11—216no—
63C4×D4×C11C2×C4132yescomplemented
64C11×#117—24no—
65C11×#117—216no—
66C11×#117D418yescomplemented
67C2×C11×C4⋊C4—28no—
68C2×C11×C4⋊C4—216no—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C4⋊C4C2318yes—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2314yes—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C22⋊C4C2312yes—
76C2×C11×C22⋊C4C2318yes—
77C2×C11×C22⋊C4C23116yes—
78C2×C11×C22⋊C4C2318yes—
79C2×C11×C22⋊C4C2312yes—
80C2×C42×C11C2×C418yescomplemented
81C2×C42×C11C2312yes—
82C2×C42×C11C2318yes—
83C2×C42×C11C2318yes—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2312yes—
87C2×C42×C11C2312yes—
88C11×#95C2318yes—
89C11×#95C2318yes—
90C11×#95C2318yes—
91C11×#95C23116yes—
92#34208C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11C2414yes—
94C24×C11C2411yescharacteristic
95C11×#41—264no—
96C2×Q8×C11—24no—
97C2×Q8×C11—24no—
98C2×Q8×C11C22×C418yes—
99C2×D4×C11—28no—
100C2×D4×C11—28no—
101C2×D4×C11—24no—
102C2×D4×C11—24no—
103C2×D4×C11—48no—
104C2×D4×C11C22×C4116yes—
105C2×D4×C11C22×C418yes—
106C2×D4×C11C22×C4116yes—
107C22×C4×C11—28no—
108C22×C4×C11—28no—
109C22×C4×C11—28no—
110C22×C4×C11—216no—
111C22×C4×C11—44no—
112C22×C4×C11—416no—
113C22×C4×C11—48no—
114C22×C4×C11C22×C4116yes—
115C22×C4×C11C22×C418yes—
116C22×C4×C11C22×C414yes—
117C22×C4×C11C2×D414yes—
118C22×C4×C11#4114yes—
119C22×C4×C11C2414yes—
120C22×C4×C11C2418yes—
121C22×C4×C11C2412yes—
122C22×C4×C11C2412yes—
123C22×C4×C11C2414yes—
124C22×C4×C11C2414yes—
125C22×C4×C11C2411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C11×C4⋊C4—28no—
128C11×C4⋊C4—216no—
129C11×C4⋊C4—28no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4C22×C4116yes—
132C11×C4⋊C4C2×D418yes—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—216no—
135C11×C22⋊C4—416no—
136C11×C22⋊C4C22×C4132yes—
137C11×C22⋊C4C2×D418yes—
138C42×C11—216no—
139C42×C11—24no—
140C42×C11—48no—
141C42×C11C22×C418yes—
142C42×C11C22×C414yes—
143C42×C11C22×C414yes—
144C42×C11C2×D418yes—
145C2×#532C2×C1111yescharacteristic
146C2×#520C2×C1112yescomplemented
147#2364C2×C1118yescomplemented
148#2352C2×C1118yescomplemented
149#2328C2×C1112yescomplemented
150#2327C2×C1112yescomplemented
151#2311C2×C1112yescomplemented
152C4×#124C2×C1114yescomplemented
153C2×#382C2×C1111yescharacteristic, complemented
154C4×#117C2×C1111yescharacteristic, complemented
155C23×C11—24no—
156C23×C11—24no—
157C23×C11—24no—
158C23×C11—28no—
159C23×C11—28no—
160C23×C11C23×C418yes—
161C23×C11C23×C412yes—
162C23×C11C22×D412yes—
163C23×C11C2×#4112yes—
164C23×C11C2511yescharacteristic
165Q8×C11—216no—
166D4×C11—232no—
167D4×C11—216no—
168D4×C11—416no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—28no—
173C2×C4×C11—24no—
174C2×C4×C11—232no—
175C2×C4×C11—28no—
176C2×C4×C11—24no—
177C2×C4×C11—28no—
178C2×C4×C11—216no—
179C2×C4×C11—48no—
180C2×C4×C11—816no—
181C2×C4×C11—88no—
182C2×C4×C11C4×D4116yes—
183C2×C4×C11C23×C414yes—
184C2×C4×C11C23×C414yes—
185C2×C4×C11C23×C418yes—
186C2×C4×C11C23×C412yes—
187C2×C4×C11C23×C412yes—
188C2×C4×C11C22×D418yes—
189C2×C4×C11C22×D412yes—
190C2×C4×C11C22×D412yes—
191C2×C4×C11C2×#4112yes—
192C2×C4×C11C2×#4112yes—
193C22×#41C22×C1112yes—
194#532C4×C11116yescomplemented
195C2×C4⋊Q8C22×C1111yescharacteristic
196C2×#127C22×C1111yescharacteristic
197C2×#124C22×C1112yes—
198C2×#121C22×C1114yes—
199#520—216no—
200C2×C4×Q8C22×C1114yes—
201C2×C4×D4C22×C1114yes—
202C2×C4×D4C22×C1118yes—
203C2×C4×D4C22×C1114yes—
204C2×#117C22×C1111yescharacteristic
205C2×#117C22×C1114yes—
206C2×#117C22×C1111yescharacteristic
207C22×C4⋊C4C22×C1112yes—
208C22×C4⋊C4C22×C1114yes—
209C22×C42C22×C1111yescharacteristic
210#391C22×C1114yes—
211#390C22×C1114yes—
212#388C22×C11116yes—
213#387C22×C11116yes—
214#386C22×C1118yes—
215#386C22×C11116yes—
216#382C22×C1112yes—
217#382C22×C1114yes—
218#382C22×C1112yes—
219#380C22×C1118yes—
220C4×C4⋊C4C22×C1114yes—
221C4×C22⋊C4C22×C11116yes—
222C4×C22⋊C4C22×C1114yes—
223#376C22×C1112yes—
224C2×#95C22×C1114yes—
225C43C22×C1112yes—
226C22×C11—24no—
227C22×C11—24no—
228C22×C11—24no—
229C22×C11—28no—
230C22×C11—216no—
231C22×C11—44no—
232C22×C11—44no—
233C22×C11—48no—
234C22×C11C2×C4×D414yes—
235C22×C11C24×C411yescharacteristic
236C22×C11C23×D411yescharacteristic
237C22×C11C22×#4111yescharacteristic
238C22×C11#58514yes—
239C4×C11—28no—
240C4×C11—24no—
241C4×C11—24no—
242C4×C11—28no—
243C4×C11—48no—
244C4×C11—44no—
245C4×C11C2×C4×D414yes—
246C4×C11C2×C4×D414yes—
247C2×#41—28no—
248C2×#41—28no—
249C2×#41C2×C4×C11116yescomplemented
250C22×Q8C23×C1112yes—
251C22×D4C23×C1114yes—
252C22×D4C23×C1112yes—
253C22×D4C23×C1114yes—
254C23×C4C23×C1114yes—
255C23×C4C23×C1114yes—
256C23×C4C23×C1118yes—
257C23×C4C23×C1112yes—
258C23×C4C23×C1111yescharacteristic
259C4⋊Q8C2×C4×C1118yescomplemented
260#127C2×C4×C1118yescomplemented
261#124C2×C4×C11116yescomplemented
262#121C2×C4×C11132yescomplemented
263C4×Q8—216no—
264C4×D4—232no—
265C4×D4—216no—
266C4×D4C2×C4×C11132yescomplemented
267#117—24no—
268#117—216no—
269#117D4×C1118yescomplemented
270C2×C4⋊C4—28no—
271C2×C4⋊C4—216no—
272C2×C4⋊C4C23×C1114yes—
273C2×C4⋊C4C23×C1114yes—
274C2×C4⋊C4C23×C1118yes—
275C2×C4⋊C4C23×C1112yes—
276C2×C4⋊C4C23×C1114yes—
277C2×C4⋊C4C23×C1112yes—
278C2×C22⋊C4C23×C1118yes—
279C2×C22⋊C4C23×C1112yes—
280C2×C22⋊C4C23×C11116yes—
281C2×C22⋊C4C23×C1118yes—
282C2×C22⋊C4C23×C1112yes—
283C2×C42C2×C4×C1118yescomplemented
284C2×C42C23×C1118yes—
285C2×C42C23×C1112yes—
286C2×C42C23×C1118yes—
287C2×C42C23×C1112yes—
288C2×C42C23×C1111yescharacteristic
289C2×C42C23×C1111yescharacteristic
290C2×C42C23×C1112yes—
291#95C23×C1118yes—
292#95C23×C1118yes—
293#95C23×C1118yes—
294#95C23×C11116yes—
295C2×C11—24no—
296C2×C11—48no—
297C2×C11C22×C4×D411yescharacteristic
298C2×C11#342812yes—
299C2×C11#350012yes—
300C2×C11#351212yes—
301C24C24×C1114yes—
302C24C24×C1111yescharacteristic
303#41—264no—
304C2×Q8—24no—
305C2×Q8—24no—
306C2×Q8C22×C4×C1118yes—
307C2×D4—28no—
308C2×D4—28no—
309C2×D4—24no—
310C2×D4—24no—
311C2×D4—48no—
312C2×D4C22×C4×C11116yes—
313C2×D4C22×C4×C1118yes—
314C2×D4C22×C4×C11116yes—
315C22×C4—28no—
316C22×C4—28no—
317C22×C4—28no—
318C22×C4—216no—
319C22×C4—44no—
320C22×C4—416no—
321C22×C4—48no—
322C22×C4C22×C4×C11116yes—
323C22×C4C22×C4×C1118yes—
324C22×C4C22×C4×C1114yes—
325C22×C4C2×D4×C1114yes—
326C22×C4C11×#4114yes—
327C22×C4C24×C1114yes—
328C22×C4C24×C1118yes—
329C22×C4C24×C1112yes—
330C22×C4C24×C1112yes—
331C22×C4C24×C1114yes—
332C22×C4C24×C1114yes—
333C22×C4C24×C1111yescharacteristic
334C22×C4C24×C1111yescharacteristic
335C4⋊C4—28no—
336C4⋊C4—216no—
337C4⋊C4—28no—
338C4⋊C4—24no—
339C4⋊C4C22×C4×C11116yes—
340C4⋊C4C2×D4×C1118yes—
341C22⋊C4—24no—
342C22⋊C4—216no—
343C22⋊C4—416no—
344C22⋊C4C22×C4×C11132yes—
345C22⋊C4C2×D4×C1118yes—
346C42—216no—
347C42—24no—
348C42—48no—
349C42C22×C4×C1118yes—
350C42C22×C4×C1114yes—
351C42C22×C4×C1114yes—
352C42C2×D4×C1118yes—
353C11#3420811yescharacteristic, direct product factor, Sylow
354C23—24no—
355C23—24no—
356C23—24no—
357C23—28no—
358C23—28no—
359C23C23×C4×C1118yes—
360C23C23×C4×C1112yes—
361C23C22×D4×C1112yes—
362C23C2×C11×#4112yes—
363C23C25×C1111yescharacteristic
364Q8—216no—
365D4—232no—
366D4—216no—
367D4—416no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—28no—
372C2×C4—24no—
373C2×C4—232no—
374C2×C4—28no—
375C2×C4—24no—
376C2×C4—28no—
377C2×C4—216no—
378C2×C4—48no—
379C2×C4—816no—
380C2×C4—88no—
381C2×C4C4×D4×C11116yes—
382C2×C4C23×C4×C1114yes—
383C2×C4C23×C4×C1114yes—
384C2×C4C23×C4×C1118yes—
385C2×C4C23×C4×C1112yes—
386C2×C4C23×C4×C1112yes—
387C2×C4C22×D4×C1118yes—
388C2×C4C22×D4×C1112yes—
389C2×C4C22×D4×C1112yes—
390C2×C4C2×C11×#4112yes—
391C2×C4C2×C11×#4112yes—
392C22—24no—
393C22—24no—
394C22—24no—
395C22—28no—
396C22—216no—
397C22—44no—
398C22—44no—
399C22—48no—
400C22C2×C4×D4×C1114yes—
401C22C24×C4×C1111yescharacteristic
402C22C23×D4×C1111yescharacteristic
403C22C22×C11×#4111yescharacteristic
404C22C11×#58514yes—
405C4—28no—
406C4—24no—
407C4—24no—
408C4—28no—
409C4—48no—
410C4—44no—
411C4C2×C4×D4×C1114yes—
412C4C2×C4×D4×C1114yes—
413C2—24no—
414C2—48no—
415C2C22×C4×D4×C1111yescharacteristic
416C2C11×#342812yes—
417C2C11×#350012yes—
418C2C11×#351212yes—
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC2×C11×#532C2
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. C11×#2364C2semidirect
4. C11×#2352C2semidirect
5. C11×#2328C2semidirect
6. C11×#2327C2semidirect
7. C11×#2311C2semidirect
8. C4×C11×#124C2semidirect
9. C2×C11×#382C2semidirect
10. C4×C11×#117C2semidirect
12. C11×#532C4semidirect
46. C2×C11×#41C2×C4semidirect
56. C11×C4⋊Q8C2×C4semidirect
57. C11×#127C2×C4semidirect
58. C11×#124C2×C4semidirect
59. C11×#121C2×C4semidirect
63. C4×D4×C11C2×C4semidirect
66. C11×#117D4semidirect
80. C2×C42×C11C2×C4semidirect
92. #34208C11direct (N × H)
146. C2×#520C2×C11semidirect
147. #2364C2×C11semidirect
148. #2352C2×C11semidirect
149. #2328C2×C11semidirect
150. #2327C2×C11semidirect
151. #2311C2×C11semidirect
152. C4×#124C2×C11semidirect
153. C2×#382C2×C11semidirect
154. C4×#117C2×C11semidirect
194. #532C4×C11semidirect
249. C2×#41C2×C4×C11semidirect
259. C4⋊Q8C2×C4×C11semidirect
260. #127C2×C4×C11semidirect
261. #124C2×C4×C11semidirect
262. #121C2×C4×C11semidirect
266. C4×D4C2×C4×C11semidirect
269. #117D4×C11semidirect
283. C2×C42C2×C4×C11semidirect
353. C11#34208direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5322
C2×C11×#5202
C11×#23642
C11×#23522
C11×#23282
C11×#23272
C11×#23112
C4×C11×#1242
C2×C11×#3822
C4×C11×#1172
#3420811