Finite Group Databasebeta

← C11×#10052 #14587245

Subgroups — C11×#10052 #14587245

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#486C211yesmaximal, characteristic, complemented
2C2×C11×#459C211yesmaximal, characteristic
3C11×#2542C211yesmaximal, characteristic, complemented
4C11×#1982C211yesmaximal, characteristic, complemented
5C2×C11×#332C211yesmaximal, characteristic, complemented
6C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
7C11×#1279C211yesmaximal, characteristic, complemented
8C22×C11×D8—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C11×C22⋊Q8—22no—
12C2×C4×D4×C11C2211yescharacteristic
13C11×#486—22no—
14C11×#486—22no—
15C11×#459—22no—
16C11×#459—22no—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102—21no—
20C2×C11×#102—22no—
21C2×C11×#102—22no—
22C2×C4×C8×C11C2211yescharacteristic
23C11×#399—22no—
24C11×#390—21no—
25C11×#384—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#332—22no—
28C11×D4⋊C8—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C2×C11×D8—24no—
36C2×C11×D8—42no—
37C2×C11×D8—42no—
38C22×C8×C11—21no—
39C22×C8×C11—21no—
40C22×C8×C11—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×#127—21no—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127D412yes—
49C11×C22⋊Q8—44no—
50C11×C22⋊Q8—44no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4D412yes—
59C2×C11×C4⋊C4D412yes—
60C2×C11×C22⋊C4—24no—
61C2×C11×C22⋊C4—21no—
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yes—
68C11×#102—24no—
69C11×#102—28no—
70C11×#102—44no—
71C4×C8×C11—21no—
72C4×C8×C11D412yes—
73C11×#95—21no—
74#10052C1111yesmaximal, characteristic, direct product factor, Sylow
75C24×C11—21no—
76C24×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—42no—
80C2×Q8×C11—42no—
81C2×D4×C11—21no—
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11—21no—
85C2×D4×C11—22no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—44no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—42no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—42no—
98C2×D4×C11—41no—
99C2×D4×C11SD1612yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C11×D8—48no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—42no—
114C2×C8×C11—41no—
115C2×C8×C11—42no—
116C2×C8×C11—41no—
117C2×C8×C11—41no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—48no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4D814yescomplemented
127C11×C22⋊C4—48no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C42×C11—41no—
131C42×C11—41no—
132C42×C11C2×D411yescharacteristic
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11#4111yescharacteristic
136C2×#486C2×C1111yescharacteristic, complemented
137C2×#459C2×C1111yescharacteristic
138#2542C2×C1111yescharacteristic, complemented
139#1982C2×C1111yescharacteristic, complemented
140C2×#332C2×C1111yescharacteristic, complemented
141C2×D4⋊C8C2×C1111yescharacteristic, complemented
142#1279C2×C1111yescharacteristic, complemented
143C23×C11—22no—
144C23×C11—41no—
145C23×C11—42no—
146C23×C11—41no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—82no—
150C23×C11—81no—
151C23×C11—81no—
152C23×C11—82no—
153C23×C11#12011yescharacteristic
154Q8×C11—82no—
155Q8×C11—81no—
156Q8×C11—81no—
157D4×C11—22no—
158D4×C11—22no—
159D4×C11—44no—
160D4×C11—42no—
161D4×C11—41no—
162D4×C11—42no—
163D4×C11—44no—
164D4×C11—41no—
165D4×C11—82no—
166D4×C11—81no—
167D4×C11—81no—
168D4×C11—81no—
169D4×C11—81no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—44no—
177C2×C4×C11—42no—
178C2×C4×C11—82no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12711yescharacteristic
187C2×C4×C11C2×D812yes—
188C2×C4×C11C2×SD1611yescharacteristic
189C2×C4×C11#13511yescharacteristic
190C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C11AGL(1,ℤ/8)12yes—
192C2×C4×C11#13711yescharacteristic
193C8×C11—42no—
194C8×C11—42no—
195C8×C11—81no—
196C22×D8—21no—
197C2×C4⋊Q8C22×C1111yescharacteristic
198C2×#127C22×C1111yescharacteristic
199C2×C22⋊Q8—22no—
200C2×C4×D4C22×C1111yescharacteristic
201#486—22no—
202#486—22no—
203#459—22no—
204#459—22no—
205C2×C4⋊C8C22×C1111yescharacteristic
206C2×C4⋊C8C22×C1111yescharacteristic
207C2×#102—22no—
208C2×#102—21no—
209C2×#102—22no—
210C2×C4×C8C22×C1111yescharacteristic
211#399—22no—
212#390—21no—
213#384—21no—
214C4×C4⋊C4C22×C1111yescharacteristic
215#332—22no—
216D4⋊C8—22no—
217C22×C11—44no—
218C22×C11—42no—
219C22×C11—82no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—82no—
223C22×C11—82no—
224C22×C11—82no—
225C22×C11—162no—
226C22×C11—162no—
227C22×C11#39211yescharacteristic
228C22×C11#44712yes—
229C22×C11#44811yescharacteristic
230C22×C11#44911yescharacteristic
231C22×C11#45412yes—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—44no—
235C4×C11—81no—
236C4×C11—82no—
237C4×C11#45011yescharacteristic
238C4×C11#45211yescharacteristic
239C4×C11#45912yes—
240C4×C11#46511yescharacteristic
241C4×C11#46811yescharacteristic
242C4×C11#49311yescharacteristic
243C4×C11#49611yescharacteristic
244C22×Q8—21no—
245C22×D4—21no—
246C22×D4—21no—
247C22×D4—21no—
248C22×D4D4×C1111yescharacteristic
249C23×C4—21no—
250C2×D8—24no—
251C2×D8—42no—
252C2×D8—42no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260#127—21no—
261#127—21no—
262#127—21no—
263#127D4×C1112yes—
264C22⋊Q8—44no—
265C22⋊Q8—44no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4D4×C1111yescharacteristic
273C2×C4⋊C4D4×C1112yes—
274C2×C4⋊C4D4×C1112yes—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—21no—
277C2×C42—21no—
278C2×C42C23×C1111yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8D4×C1112yes—
283#102—24no—
284#102—28no—
285#102—44no—
286C4×C8—21no—
287C4×C8D4×C1112yes—
288#95—21no—
289C2×C11—82no—
290C2×C11—162no—
291C2×C11#162512yes—
292C2×C11#162712yes—
293C2×C11#200011yescharacteristic
294C2×C11#200311yescharacteristic
295C2×C11#201111yescharacteristic
296C24—21no—
297C24—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—42no—
301C2×Q8—42no—
302C2×D4—21no—
303C2×D4—22no—
304C2×D4—22no—
305C2×D4—21no—
306C2×D4—22no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—44no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—42no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—42no—
319C2×D4—41no—
320C2×D4C11×SD1612yes—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4C2×D4×C1111yescharacteristic
329C22×C4C2×D4×C1111yescharacteristic
330C22×C4C2×D4×C1111yescharacteristic
331D8—48no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—42no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—42no—
339C4⋊C4—22no—
340C4⋊C4—21no—
341C4⋊C4—22no—
342C4⋊C4—21no—
343C4⋊C4—22no—
344C4⋊C4—48no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4C11×D814yescomplemented
348C22⋊C4—48no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C42—41no—
352C42—41no—
353C42C2×D4×C1111yescharacteristic
354C42C2×D4×C1111yescharacteristic
355C42C2×D4×C1111yescharacteristic
356C42C11×#4111yescharacteristic
357C11#1005211yescharacteristic, direct product factor, Sylow
358C23—22no—
359C23—41no—
360C23—42no—
361C23—41no—
362C23—42no—
363C23—42no—
364C23—82no—
365C23—81no—
366C23—81no—
367C23—82no—
368C23C11×#12011yescharacteristic
369Q8—81no—
370Q8—81no—
371Q8—82no—
372D4—22no—
373D4—22no—
374D4—44no—
375D4—42no—
376D4—41no—
377D4—42no—
378D4—44no—
379D4—41no—
380D4—82no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385C2×C4—22no—
386C2×C4—24no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—42no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—82no—
396C2×C4C11×#12011yescharacteristic
397C2×C4C11×#12011yescharacteristic
398C2×C4C11×#12111yescharacteristic
399C2×C4C11×#12111yescharacteristic
400C2×C4C11×#12111yescharacteristic
401C2×C4C11×#12711yescharacteristic
402C2×C4C2×C11×D812yes—
403C2×C4C2×C11×SD1611yescharacteristic
404C2×C4C11×#13511yescharacteristic
405C2×C4C11×AGL(1,ℤ/8)12yes—
406C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
407C2×C4C11×#13711yescharacteristic
408C8—42no—
409C8—42no—
410C8—81no—
411C22—44no—
412C22—42no—
413C22—82no—
414C22—81no—
415C22—81no—
416C22—82no—
417C22—82no—
418C22—82no—
419C22—162no—
420C22—162no—
421C22C11×#39211yescharacteristic
422C22C11×#44712yes—
423C22C11×#44811yescharacteristic
424C22C11×#44911yescharacteristic
425C22C11×#45412yes—
426C4—21no—
427C4—21no—
428C4—44no—
429C4—81no—
430C4—82no—
431C4C11×#45011yescharacteristic
432C4C11×#45211yescharacteristic
433C4C11×#45912yes—
434C4C11×#46511yescharacteristic
435C4C11×#46811yescharacteristic
436C4C11×#49311yescharacteristic
437C4C11×#49611yescharacteristic
438C2—82no—
439C2—162no—
440C2C11×#162512yes—
441C2C11×#162712yes—
442C2C11×#200011yescharacteristic
443C2C11×#200311yescharacteristic
444C2C11×#201111yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#459C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#486C2semidirect
3. C11×#2542C2semidirect
4. C11×#1982C2semidirect
5. C2×C11×#332C2semidirect
6. C2×C11×D4⋊C8C2semidirect
7. C11×#1279C2semidirect
74. #10052C11direct (N × H)
126. C11×C4⋊C4D8semidirect
136. C2×#486C2×C11semidirect
138. #2542C2×C11semidirect
139. #1982C2×C11semidirect
140. C2×#332C2×C11semidirect
141. C2×D4⋊C8C2×C11semidirect
142. #1279C2×C11semidirect
347. C4⋊C4C11×D8semidirect
357. C11#10052direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4862
C2×C11×#4592
C11×#25422
C11×#19822
C2×C11×#3322
C2×C11×D4⋊C82
C11×#12792
#1005211