Finite Group Databasebeta

← C11×#14290 #14591483

Subgroups — C11×#14290 #14591483

Order 2816.

2302 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#121C211yesmaximal, characteristic
2C2×C11×#381C211yesmaximal, characteristic, complemented
3C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
4C11×#1445C212yesmaximal, complemented
5C11×#1438C214yesmaximal, complemented
6C11×#1438C212yesmaximal, complemented
7C11×#1437C214yesmaximal, complemented
8C23×D4×C11C2212yes—
9C23×D4×C11C2211yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C2×C11×#121—24no—
12C2×C11×#121—24no—
13C2×C11×#121C418yescomplemented
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C11×C22⋊C4C2218yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C42×C11C2212yes—
20C11×#381—24no—
21C4×C11×C22⋊C4—24no—
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2218yes—
26C25×C11C2312yes—
27C25×C11C2311yescharacteristic
28C22×D4×C11—24no—
29C22×D4×C11—24no—
30C22×D4×C11—22no—
31C22×D4×C11—22no—
32C22×D4×C11—44no—
33C22×D4×C11—48no—
34C22×D4×C11C2×C418yes—
35C22×D4×C11C2×C414yes—
36C23×C4×C11—44no—
37C23×C4×C11C2×C414yes—
38C23×C4×C11D414yes—
39C23×C4×C11D414yes—
40C23×C4×C11C2314yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2314yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C11×#121—232no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4C2×C414yes—
49C2×C11×C22⋊C4—24no—
50C2×C11×C22⋊C4—24no—
51C2×C11×C22⋊C4—24no—
52C2×C11×C22⋊C4—28no—
53C2×C11×C22⋊C4—24no—
54C2×C11×C22⋊C4—216no—
55C2×C11×C22⋊C4—48no—
56C2×C11×C22⋊C4—48no—
57C2×C11×C22⋊C4—44no—
58C2×C11×C22⋊C4C2×C418yes—
59C2×C42×C11—24no—
60C2×C42×C11—44no—
61C11×#95—24no—
62C11×#95—24no—
63C11×#95—24no—
64C11×#95—48no—
65#14290C1111yesmaximal, characteristic, direct product factor, Sylow
66C24×C11—24no—
67C24×C11—24no—
68C24×C11—24no—
69C24×C11—22no—
70C24×C11—22no—
71C24×C11—28no—
72C24×C11—28no—
73C24×C11—28no—
74C24×C11C22×C414yes—
75C24×C11C22×C412yes—
76C24×C11C2×D412yes—
77C24×C11C2×D412yes—
78C24×C11C2411yescharacteristic
79C2×D4×C11—216no—
80C2×D4×C11—28no—
81C2×D4×C11—48no—
82C2×D4×C11—416no—
83C2×D4×C11—48no—
84C2×D4×C11—48no—
85C2×D4×C11—416no—
86C2×D4×C11—416no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—24no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—24no—
93C22×C4×C11—28no—
94C22×C4×C11—28no—
95C22×C4×C11—28no—
96C22×C4×C11—24no—
97C22×C4×C11—28no—
98C22×C4×C11—24no—
99C22×C4×C11—28no—
100C22×C4×C11—24no—
101C22×C4×C11—48no—
102C22×C4×C11—48no—
103C22×C4×C11—48no—
104C22×C4×C11C22⋊C4116yescomplemented
105C22×C4×C11C22×C414yes—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C22×C412yes—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11#4118yes—
113C11×C4⋊C4—28no—
114C11×C22⋊C4—216no—
115C11×C22⋊C4—216no—
116C11×C22⋊C4—432no—
117C11×C22⋊C4—48no—
118C42×C11—48no—
119C22×#121C2×C1111yescharacteristic
120C2×#381C2×C1111yescharacteristic, complemented
121C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
122#1445C2×C1112yescomplemented
123#1438C2×C1114yescomplemented
124#1438C2×C1112yescomplemented
125#1437C2×C1114yescomplemented
126C23×C11—24no—
127C23×C11—24no—
128C23×C11—24no—
129C23×C11—24no—
130C23×C11—24no—
131C23×C11—24no—
132C23×C11—24no—
133C23×C11—24no—
134C23×C11—24no—
135C23×C11—24no—
136C23×C11—28no—
137C23×C11—28no—
138C23×C11—28no—
139C23×C11—48no—
140C23×C11—48no—
141C23×C11—44no—
142C23×C11—44no—
143C23×C11—44no—
144C23×C11—44no—
145C23×C11—44no—
146C23×C11—44no—
147C23×C11—48no—
148C23×C11—48no—
149C23×C11—416no—
150C23×C11C2×C22⋊C414yes—
151C23×C11C23×C411yescharacteristic
152C23×C11C22×D411yescharacteristic
153C23×C11C22×D411yescharacteristic
154C23×C11C2×#4114yes—
155C23×C11H(5,𝔽2)14yes—
156C23×C11H(5,𝔽2)14yes—
157D4×C11—416no—
158D4×C11—432no—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—28no—
167C2×C4×C11—28no—
168C2×C4×C11—216no—
169C2×C4×C11—416no—
170C2×C4×C11—44no—
171C2×C4×C11—44no—
172C2×C4×C11—44no—
173C2×C4×C11—44no—
174C2×C4×C11—48no—
175C2×C4×C11—44no—
176C2×C4×C11—44no—
177C2×C4×C11—44no—
178C2×C4×C11—48no—
179C2×C4×C11—48no—
180C2×C4×C11C2×C22⋊C414yes—
181C2×C4×C11C2×C22⋊C414yes—
182C23×D4C22×C1112yes—
183C23×D4C22×C1111yescharacteristic
184C24×C4C22×C1111yescharacteristic
185C2×#121—24no—
186C2×#121—24no—
187C2×#121C4×C1118yescomplemented
188C22×C4⋊C4C22×C1111yescharacteristic
189C22×C22⋊C4C22×C1112yes—
190C22×C22⋊C4C22×C1112yes—
191C22×C22⋊C4C22×C1118yes—
192C22×C22⋊C4C22×C1112yes—
193C22×C42C22×C1112yes—
194#381—24no—
195C4×C22⋊C4—24no—
196C2×#95C22×C1112yes—
197C2×#95C22×C1112yes—
198C2×#95C22×C1112yes—
199C2×#95C22×C1118yes—
200C22×C11—24no—
201C22×C11—24no—
202C22×C11—24no—
203C22×C11—48no—
204C22×C11—48no—
205C22×C11—48no—
206C22×C11—44no—
207C22×C11—44no—
208C22×C11—416no—
209C22×C11—44no—
210C22×C11—88no—
211C22×C11—88no—
212C22×C11C22×C22⋊C411yescharacteristic
213C22×C11C4×#4112yes—
214C22×C11#51812yes—
215C22×C11#51812yes—
216C22×C11#52512yes—
217C22×C11#53212yes—
218C22×C11#53412yes—
219C22×C11#53412yes—
220C22×C11#53512yes—
221C22×C11#53512yes—
222C22×C11#53818yes—
223C22×C11#54018yes—
224C4×C11—24no—
225C4×C11—24no—
226C4×C11—44no—
227C4×C11—48no—
228C4×C11—84no—
229C25C23×C1112yes—
230C25C23×C1111yescharacteristic
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—44no—
236C22×D4—48no—
237C22×D4C2×C4×C1118yes—
238C22×D4C2×C4×C1114yes—
239C23×C4—44no—
240C23×C4C2×C4×C1114yes—
241C23×C4D4×C1114yes—
242C23×C4D4×C1114yes—
243C23×C4C23×C1114yes—
244C23×C4C23×C1112yes—
245C23×C4C23×C1114yes—
246C23×C4C23×C1111yescharacteristic
247C23×C4C23×C1111yescharacteristic
248#121—232no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4C2×C4×C1114yes—
252C2×C22⋊C4—24no—
253C2×C22⋊C4—24no—
254C2×C22⋊C4—24no—
255C2×C22⋊C4—28no—
256C2×C22⋊C4—24no—
257C2×C22⋊C4—216no—
258C2×C22⋊C4—48no—
259C2×C22⋊C4—48no—
260C2×C22⋊C4—44no—
261C2×C22⋊C4C2×C4×C1118yes—
262C2×C42—24no—
263C2×C42—44no—
264#95—24no—
265#95—24no—
266#95—24no—
267#95—48no—
268C2×C11—44no—
269C2×C11—84no—
270C2×C11#229711yescharacteristic
271C2×C11#230811yescharacteristic
272C2×C11#230911yescharacteristic
273C2×C11#233314yes—
274C2×C11#263514yes—
275C2×C11#266114yes—
276C24—24no—
277C24—24no—
278C24—24no—
279C24—22no—
280C24—22no—
281C24—28no—
282C24—28no—
283C24—28no—
284C24C22×C4×C1114yes—
285C24C22×C4×C1112yes—
286C24C2×D4×C1112yes—
287C24C2×D4×C1112yes—
288C24C24×C1111yescharacteristic
289C2×D4—216no—
290C2×D4—28no—
291C2×D4—48no—
292C2×D4—416no—
293C2×D4—48no—
294C2×D4—48no—
295C2×D4—416no—
296C2×D4—416no—
297C22×C4—24no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—24no—
303C22×C4—28no—
304C22×C4—28no—
305C22×C4—28no—
306C22×C4—24no—
307C22×C4—28no—
308C22×C4—24no—
309C22×C4—28no—
310C22×C4—24no—
311C22×C4—48no—
312C22×C4—48no—
313C22×C4—48no—
314C22×C4C11×C22⋊C4116yescomplemented
315C22×C4C22×C4×C1114yes—
316C22×C4C22×C4×C1112yes—
317C22×C4C22×C4×C1112yes—
318C22×C4C2×D4×C1112yes—
319C22×C4C2×D4×C1112yes—
320C22×C4C2×D4×C1112yes—
321C22×C4C2×D4×C1112yes—
322C22×C4C11×#4118yes—
323C4⋊C4—28no—
324C22⋊C4—216no—
325C22⋊C4—216no—
326C22⋊C4—432no—
327C22⋊C4—48no—
328C42—48no—
329C11#1429011yescharacteristic, direct product factor, Sylow
330C23—24no—
331C23—24no—
332C23—24no—
333C23—24no—
334C23—24no—
335C23—24no—
336C23—24no—
337C23—24no—
338C23—24no—
339C23—24no—
340C23—28no—
341C23—28no—
342C23—28no—
343C23—48no—
344C23—48no—
345C23—44no—
346C23—44no—
347C23—44no—
348C23—44no—
349C23—44no—
350C23—44no—
351C23—48no—
352C23—48no—
353C23—416no—
354C23C2×C11×C22⋊C414yes—
355C23C23×C4×C1111yescharacteristic
356C23C22×D4×C1111yescharacteristic
357C23C22×D4×C1111yescharacteristic
358C23C2×C11×#4114yes—
359C23C11×H(5,𝔽2)14yes—
360C23C11×H(5,𝔽2)14yes—
361D4—416no—
362D4—432no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—28no—
371C2×C4—28no—
372C2×C4—216no—
373C2×C4—416no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—44no—
377C2×C4—44no—
378C2×C4—48no—
379C2×C4—44no—
380C2×C4—44no—
381C2×C4—44no—
382C2×C4—48no—
383C2×C4—48no—
384C2×C4C2×C11×C22⋊C414yes—
385C2×C4C2×C11×C22⋊C414yes—
386C22—24no—
387C22—24no—
388C22—24no—
389C22—48no—
390C22—48no—
391C22—48no—
392C22—44no—
393C22—44no—
394C22—44no—
395C22—416no—
396C22—88no—
397C22—88no—
398C22C22×C11×C22⋊C411yescharacteristic
399C22C4×C11×#4112yes—
400C22C11×#51812yes—
401C22C11×#51812yes—
402C22C11×#52512yes—
403C22C11×#53212yes—
404C22C11×#53412yes—
405C22C11×#53412yes—
406C22C11×#53512yes—
407C22C11×#53512yes—
408C22C11×#53818yes—
409C22C11×#54018yes—
410C4—24no—
411C4—24no—
412C4—48no—
413C4—44no—
414C4—84no—
415C2—44no—
416C2—84no—
417C2C11×#229711yescharacteristic
418C2C11×#230811yescharacteristic
419C2C11×#230911yescharacteristic
420C2C11×#233314yes—
421C2C11×#263514yes—
422C2C11×#266114yes—
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC22×C11×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#381C2semidirect
3. C2×C4×C11×C22⋊C4C2semidirect
4. C11×#1445C2semidirect
5. C11×#1438C2semidirect
6. C11×#1438C2semidirect
7. C11×#1437C2semidirect
13. C2×C11×#121C4semidirect
65. #14290C11direct (N × H)
104. C22×C4×C11C22⋊C4semidirect
120. C2×#381C2×C11semidirect
121. C2×C4×C22⋊C4C2×C11semidirect
122. #1445C2×C11semidirect
123. #1438C2×C11semidirect
124. #1438C2×C11semidirect
125. #1437C2×C11semidirect
187. C2×#121C4×C11semidirect
314. C22×C4C11×C22⋊C4semidirect
329. C11#14290direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1212
C2×C11×#3812
C2×C4×C11×C22⋊C42
C11×#14452
C11×#14382
C11×#14372
#1429011