Finite Group Databasebeta

← C11×#34954 #14612147

Subgroups — C11×#34954 #14612147

Order 2816.

1948 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2593C214yesmaximal, complemented
2C11×#2582C211yesmaximal, characteristic, complemented
3C11×#2571C211yesmaximal, characteristic, complemented
4C11×#2548C212yesmaximal
5C11×#2513C214yesmaximal, complemented
6C11×#2448C214yesmaximal, complemented
7C11×#2395C214yesmaximal, complemented
8C4×C11×#127C211yesmaximal, characteristic
9C4×C11×#124C214yesmaximal, complemented
10C11×#2293C214yesmaximal, complemented
11C42×Q8×C11C212yesmaximal, complemented
12C2×C11×#127C2211yescharacteristic
13C2×C11×#124C2214yes—
14C2×C4×Q8×C11C2212yes—
15C2×C4×Q8×C11C2212yes—
16C2×C4×Q8×C11C2212yes—
17C2×C4×D4×C11C2214yes—
18C2×C4×D4×C11C2212yes—
19C2×C11×#117C2214yes—
20C11×#400C2214yes—
21C11×#399C2214yes—
22C11×#398C2214yes—
23C11×#397C2218yes—
24C11×#397C2214yes—
25C11×#394C2218yes—
26C11×#391C2214yes—
27C11×#390C2214yes—
28C11×#390C2214yes—
29C11×#390C2214yes—
30C11×#390C2214yes—
31C11×#390C2212yes—
32C11×#389C2214yes—
33C11×#389C2214yes—
34C11×#388C2218yes—
35C11×#388C2218yes—
36C11×#388C2218yes—
37C11×#388C2218yes—
38C11×#384C2211yescharacteristic
39C11×#382C2214yes—
40C4×C11×C4⋊C4C2214yes—
41C4×C11×C4⋊C4C2214yes—
42C4×C11×C4⋊C4C2212yes—
43C4×C11×C4⋊C4C2212yes—
44C4×C11×C4⋊C4C2212yes—
45C4×C11×C4⋊C4C2214yes—
46C4×C11×C22⋊C4C2218yes—
47C4×C11×C22⋊C4C2214yes—
48C43×C11C2211yescharacteristic
49C43×C11C2214yes—
50C22×Q8×C11C2312yes—
51C22×D4×C11C2314yes—
52C22×D4×C11C2312yes—
53C23×C4×C11C2314yes—
54C11×#127—24no—
55C11×#124—216no—
56C4×Q8×C11—28no—
57C4×Q8×C11—28no—
58C4×Q8×C11—28no—
59C4×D4×C11—216no—
60C4×D4×C11—44no—
61C11×#117—48no—
62C2×C11×C4⋊C4C2314yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2314yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2314yes—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C22⋊C4C2318yes—
73C2×C11×C22⋊C4C2318yes—
74C2×C11×C22⋊C4C2318yes—
75C2×C11×C22⋊C4C2318yes—
76C2×C11×C22⋊C4C2318yes—
77C2×C11×C22⋊C4C2314yes—
78C2×C42×C11C2312yes—
79C2×C42×C11C2314yes—
80C2×C42×C11C2314yes—
81C2×C42×C11C2314yes—
82C2×C42×C11C2314yes—
83C2×C42×C11C2314yes—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2314yes—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2312yes—
89C11×#95C2314yes—
90C11×#95C2318yes—
91C11×#95C2318yes—
92C11×#95C2314yes—
93C11×#95C2314yes—
94C11×#95C2314yes—
95C11×#95C2314yes—
96#34954C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11C2414yes—
98C2×Q8×C11—24no—
99C2×Q8×C11—24no—
100C2×Q8×C11#4118yes—
101C2×D4×C11—28no—
102C2×D4×C11—28no—
103C2×D4×C11—24no—
104C2×D4×C11—28no—
105C2×D4×C11—42no—
106C2×D4×C11—42no—
107C22×C4×C11—216no—
108C22×C4×C11—28no—
109C22×C4×C11C2414yes—
110C22×C4×C11C2414yes—
111C22×C4×C11C2414yes—
112C22×C4×C11C2411yescharacteristic
113C22×C4×C11C2414yes—
114C22×C4×C11C2414yes—
115C22×C4×C11C2411yescharacteristic
116C22×C4×C11C2412yes—
117C22×C4×C11C2412yes—
118C22×C4×C11C2411yescharacteristic
119C11×C4⋊C4—28no—
120C11×C4⋊C4—28no—
121C11×C4⋊C4—28no—
122C11×C4⋊C4—28no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—44no—
127C11×C4⋊C4—44no—
128C11×C4⋊C4—42no—
129C11×C22⋊C4—216no—
130C11×C22⋊C4—216no—
131C11×C22⋊C4—216no—
132C11×C22⋊C4—48no—
133C11×C22⋊C4—48no—
134C11×C22⋊C4—44no—
135C42×C11—28no—
136C42×C11—24no—
137C42×C11—28no—
138C42×C11—28no—
139C42×C11—28no—
140C42×C11—28no—
141C42×C11—22no—
142C42×C11—41no—
143C42×C11—44no—
144C42×C11#4118yes—
145C42×C11#4114yes—
146#2593C2×C1114yescomplemented
147#2582C2×C1111yescharacteristic, complemented
148#2571C2×C1111yescharacteristic, complemented
149#2548C2×C1112yes—
150#2513C2×C1114yescomplemented
151#2448C2×C1114yescomplemented
152#2395C2×C1114yescomplemented
153C4×#127C2×C1111yescharacteristic
154C4×#124C2×C1114yescomplemented
155#2293C2×C1114yescomplemented
156C42×Q8C2×C1112yescomplemented
157C23×C11—28no—
158C23×C11—28no—
159C23×C11—24no—
160C23×C11—24no—
161C23×C11—24no—
162C23×C11C2511yescharacteristic
163Q8×C11—216no—
164D4×C11—48no—
165D4×C11—416no—
166C2×C4×C11—22no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—21no—
170C2×C4×C11—22no—
171C2×C4×C11—21no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—22no—
178C2×C4×C11—28no—
179C2×C4×C11—21no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—416no—
186C2×C4×C11C2×#4118yes—
187C2×C4×C11C2×#4114yes—
188C2×C4×C11C2×#4112yes—
189C2×C4×C11C2×#4114yes—
190C2×C4×C11C2×#4114yes—
191C2×C4×C11C2×#4114yes—
192C2×C4×C11C2×#4114yes—
193C2×C4×C11H(5,𝔽2)12yes—
194C2×#127C22×C1111yescharacteristic
195C2×#124C22×C1114yes—
196C2×C4×Q8C22×C1112yes—
197C2×C4×Q8C22×C1112yes—
198C2×C4×Q8C22×C1112yes—
199C2×C4×D4C22×C1114yes—
200C2×C4×D4C22×C1112yes—
201C2×#117C22×C1114yes—
202#400C22×C1114yes—
203#399C22×C1114yes—
204#398C22×C1114yes—
205#397C22×C1118yes—
206#397C22×C1114yes—
207#394C22×C1118yes—
208#391C22×C1114yes—
209#390C22×C1112yes—
210#390C22×C1114yes—
211#390C22×C1114yes—
212#390C22×C1114yes—
213#390C22×C1114yes—
214#389C22×C1114yes—
215#389C22×C1114yes—
216#388C22×C1118yes—
217#388C22×C1118yes—
218#388C22×C1118yes—
219#388C22×C1118yes—
220#384C22×C1111yescharacteristic
221#382C22×C1114yes—
222C4×C4⋊C4C22×C1112yes—
223C4×C4⋊C4C22×C1114yes—
224C4×C4⋊C4C22×C1114yes—
225C4×C4⋊C4C22×C1114yes—
226C4×C4⋊C4C22×C1112yes—
227C4×C4⋊C4C22×C1112yes—
228C4×C22⋊C4C22×C1118yes—
229C4×C22⋊C4C22×C1114yes—
230C43C22×C1111yescharacteristic
231C43C22×C1114yes—
232C22×C11—48no—
233C22×C11—44no—
234C22×C11—44no—
235C22×C11—48no—
236C22×C11—44no—
237C22×C11C22×#4111yescharacteristic
238C22×C11C22×#4112yes—
239C22×C11C22×#4112yes—
240C22×C11C2×H(5,𝔽2)11yescharacteristic
241C22×C11#58511yescharacteristic
242C4×C11—28no—
243C4×C11—22no—
244C4×C11—24no—
245C4×C11—44no—
246C4×C11—44no—
247C4×C11—44no—
248C4×C11—44no—
249C4×C11—41no—
250C4×C11#52918yes—
251C4×C11#55914yes—
252C22×Q8C23×C1112yes—
253C22×D4C23×C1114yes—
254C22×D4C23×C1112yes—
255C23×C4C23×C1114yes—
256#127—24no—
257#124—216no—
258C4×Q8—28no—
259C4×Q8—28no—
260C4×Q8—28no—
261C4×D4—216no—
262C4×D4—44no—
263#117—48no—
264C2×C4⋊C4C23×C1114yes—
265C2×C4⋊C4C23×C1112yes—
266C2×C4⋊C4C23×C1114yes—
267C2×C4⋊C4C23×C1112yes—
268C2×C4⋊C4C23×C1112yes—
269C2×C4⋊C4C23×C1114yes—
270C2×C4⋊C4C23×C1114yes—
271C2×C4⋊C4C23×C1114yes—
272C2×C4⋊C4C23×C1114yes—
273C2×C4⋊C4C23×C1112yes—
274C2×C22⋊C4C23×C1118yes—
275C2×C22⋊C4C23×C1118yes—
276C2×C22⋊C4C23×C1118yes—
277C2×C22⋊C4C23×C1118yes—
278C2×C22⋊C4C23×C1114yes—
279C2×C22⋊C4C23×C1118yes—
280C2×C42C23×C1114yes—
281C2×C42C23×C1111yescharacteristic
282C2×C42C23×C1114yes—
283C2×C42C23×C1112yes—
284C2×C42C23×C1114yes—
285C2×C42C23×C1114yes—
286C2×C42C23×C1114yes—
287C2×C42C23×C1111yescharacteristic
288C2×C42C23×C1114yes—
289C2×C42C23×C1112yes—
290C2×C42C23×C1111yescharacteristic
291#95C23×C1114yes—
292#95C23×C1118yes—
293#95C23×C1118yes—
294#95C23×C1114yes—
295#95C23×C1114yes—
296#95C23×C1114yes—
297#95C23×C1114yes—
298C2×C11—84no—
299C2×C11C2×#52912yes—
300C2×C11#346011yescharacteristic
301C2×C11C2×#55911yescharacteristic
302C2×C11#348012yes—
303C2×C11#348311yescharacteristic
304C24C24×C1114yes—
305C2×Q8—24no—
306C2×Q8—24no—
307C2×Q8C11×#4118yes—
308C2×D4—28no—
309C2×D4—28no—
310C2×D4—24no—
311C2×D4—28no—
312C2×D4—42no—
313C2×D4—42no—
314C22×C4—216no—
315C22×C4—28no—
316C22×C4C24×C1114yes—
317C22×C4C24×C1114yes—
318C22×C4C24×C1114yes—
319C22×C4C24×C1111yescharacteristic
320C22×C4C24×C1114yes—
321C22×C4C24×C1114yes—
322C22×C4C24×C1111yescharacteristic
323C22×C4C24×C1112yes—
324C22×C4C24×C1112yes—
325C22×C4C24×C1111yescharacteristic
326C4⋊C4—28no—
327C4⋊C4—28no—
328C4⋊C4—28no—
329C4⋊C4—28no—
330C4⋊C4—24no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—44no—
334C4⋊C4—44no—
335C4⋊C4—42no—
336C22⋊C4—216no—
337C22⋊C4—216no—
338C22⋊C4—216no—
339C22⋊C4—48no—
340C22⋊C4—44no—
341C22⋊C4—48no—
342C42—28no—
343C42—24no—
344C42—28no—
345C42—28no—
346C42—28no—
347C42—28no—
348C42—22no—
349C42—41no—
350C42—44no—
351C42C11×#4118yes—
352C42C11×#4114yes—
353C11#3495411yescharacteristic, direct product factor, Sylow
354C23—28no—
355C23—28no—
356C23—24no—
357C23—24no—
358C23—24no—
359C23C25×C1111yescharacteristic
360Q8—216no—
361D4—48no—
362D4—416no—
363C2×C4—22no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—22no—
375C2×C4—28no—
376C2×C4—21no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—416no—
383C2×C4C2×C11×#4118yes—
384C2×C4C2×C11×#4114yes—
385C2×C4C2×C11×#4112yes—
386C2×C4C2×C11×#4114yes—
387C2×C4C2×C11×#4114yes—
388C2×C4C2×C11×#4114yes—
389C2×C4C2×C11×#4114yes—
390C2×C4C11×H(5,𝔽2)12yes—
391C22—48no—
392C22—44no—
393C22—44no—
394C22—48no—
395C22—44no—
396C22C22×C11×#4111yescharacteristic
397C22C22×C11×#4112yes—
398C22C22×C11×#4112yes—
399C22C2×C11×H(5,𝔽2)11yescharacteristic
400C22C11×#58511yescharacteristic
401C4—28no—
402C4—22no—
403C4—24no—
404C4—44no—
405C4—44no—
406C4—44no—
407C4—44no—
408C4—41no—
409C4C11×#52918yes—
410C4C11×#55914yes—
411C2—84no—
412C2C2×C11×#52912yes—
413C2C11×#346011yescharacteristic
414C2C2×C11×#55911yescharacteristic
415C2C11×#348012yes—
416C2C11×#348311yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC2×C11×#127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2593C2semidirect
2. C11×#2582C2semidirect
3. C11×#2571C2semidirect
5. C11×#2513C2semidirect
6. C11×#2448C2semidirect
7. C11×#2395C2semidirect
9. C4×C11×#124C2semidirect
10. C11×#2293C2semidirect
11. C42×Q8×C11C2semidirect
96. #34954C11direct (N × H)
146. #2593C2×C11semidirect
147. #2582C2×C11semidirect
148. #2571C2×C11semidirect
150. #2513C2×C11semidirect
151. #2448C2×C11semidirect
152. #2395C2×C11semidirect
154. C4×#124C2×C11semidirect
155. #2293C2×C11semidirect
156. C42×Q8C2×C11semidirect
353. C11#34954direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25932
C11×#25822
C11×#25712
C11×#25482
C11×#25132
C11×#24482
C11×#23952
C4×C11×#1272
C4×C11×#1242
C11×#22932
C42×Q8×C112
#3495411