Finite Group Databasebeta

← C11×#10048 #14587241

Subgroups — C11×#10048 #14587241

Order 2816.

746 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
1C2×C11×#492C211yesmaximal, characteristic, complemented
2C2×C11×#459C211yesmaximal, characteristic
3C11×#2563C211yesmaximal, characteristic, complemented
4C11×#1982C211yesmaximal, characteristic, complemented
5C2×C11×#333C211yesmaximal, characteristic, complemented
6C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
7C11×#1279C211yesmaximal, characteristic, complemented
8C22×C11×SD16—22no—
9C22×C11×D8—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C11×#492—22no—
14C11×#492—22no—
15C11×#459—22no—
16C11×#459—22no—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102—21no—
20C2×C11×#102—22no—
21C2×C4×C8×C11C2211yescharacteristic
22C11×#393—22no—
23C11×#390—21no—
24C11×#382—21no—
25C11×#380—22no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#333—22no—
28C11×D4⋊C8—22no—
29C22×Q8×C11D412yes—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C2×C11×SD16—28no—
36C2×C11×SD16—48no—
37C2×C11×D8—24no—
38C2×C11×D8—42no—
39C2×C11×D8—42no—
40C22×C8×C11—21no—
41C22×C8×C11—21no—
42C22×C8×C11—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×#127—21no—
48C11×#127—21no—
49C11×#127—21no—
50C11×#127D412yes—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4D412yes—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—24no—
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×#102—24no—
68C11×#102—44no—
69C4×C8×C11—21no—
70C4×C8×C11D412yes—
71C11×#95—24no—
72C11×#95—21no—
73#10048C1111yesmaximal, characteristic, direct product factor, Sylow
74C24×C11—21no—
75C24×C11—41no—
76C2×Q8×C11—22no—
77C2×Q8×C11—22no—
78C2×Q8×C11—44no—
79C2×D4×C11—21no—
80C2×D4×C11—22no—
81C2×D4×C11—22no—
82C2×D4×C11—21no—
83C2×D4×C11—22no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—44no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—42no—
94C2×D4×C11—42no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11SD1612yescomplemented
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C11×SD16—416no—
109C11×D8—48no—
110C2×C8×C11—24no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C2×C8×C11—42no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—84no—
128C42×C11—41no—
129C42×C11—41no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11#4111yescharacteristic
134C2×#492C2×C1111yescharacteristic, complemented
135C2×#459C2×C1111yescharacteristic
136#2563C2×C1111yescharacteristic, complemented
137#1982C2×C1111yescharacteristic, complemented
138C2×#333C2×C1111yescharacteristic, complemented
139C2×D4⋊C8C2×C1111yescharacteristic, complemented
140#1279C2×C1111yescharacteristic, complemented
141C23×C11—22no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11—41no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—81no—
148C23×C11—81no—
149C23×C11—82no—
150C23×C11—82no—
151C23×C11#12011yescharacteristic
152Q8×C11—44no—
153Q8×C11—82no—
154D4×C11—22no—
155D4×C11—22no—
156D4×C11—44no—
157D4×C11—42no—
158D4×C11—41no—
159D4×C11—42no—
160D4×C11—44no—
161D4×C11—41no—
162D4×C11—82no—
163D4×C11—81no—
164D4×C11—81no—
165D4×C11—81no—
166D4×C11—81no—
167C2×C4×C11—22no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—44no—
175C2×C4×C11—82no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12711yescharacteristic
184C2×C4×C11C2×SD1611yescharacteristic
185C2×C4×C11#13511yescharacteristic
186C2×C4×C11#13512yes—
187C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C11AGL(1,ℤ/8)12yes—
189C2×C4×C11#13711yescharacteristic
190C8×C11—24no—
191C8×C11—42no—
192C8×C11—81no—
193C22×SD16—22no—
194C22×D8—21no—
195C2×C4⋊Q8C22×C1111yescharacteristic
196C2×#127C22×C1111yescharacteristic
197C2×C4×D4C22×C1111yescharacteristic
198#492—22no—
199#492—22no—
200#459—22no—
201#459—22no—
202C2×C4⋊C8C22×C1111yescharacteristic
203C2×C4⋊C8C22×C1111yescharacteristic
204C2×#102—21no—
205C2×#102—22no—
206C2×C4×C8C22×C1111yescharacteristic
207#393—22no—
208#390—21no—
209#382—21no—
210#380—22no—
211C4×C4⋊C4C22×C1111yescharacteristic
212#333—22no—
213D4⋊C8—22no—
214C22×C11—44no—
215C22×C11—42no—
216C22×C11—82no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11—162no—
223C22×C11—162no—
224C22×C11#39211yescharacteristic
225C22×C11#44811yescharacteristic
226C22×C11#44912yes—
227C22×C11#44911yescharacteristic
228C22×C11#45312yes—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—82no—
232C4×C11—82no—
233C4×C11—81no—
234C4×C11#45011yescharacteristic
235C4×C11#45211yescharacteristic
236C4×C11#46312yes—
237C4×C11#46511yescharacteristic
238C4×C11#46811yescharacteristic
239C4×C11#49511yescharacteristic
240C4×C11#49611yescharacteristic
241C22×Q8D4×C1112yes—
242C22×D4—21no—
243C22×D4—21no—
244C22×D4—21no—
245C22×D4D4×C1111yescharacteristic
246C23×C4—21no—
247C2×SD16—28no—
248C2×SD16—48no—
249C2×D8—24no—
250C2×D8—42no—
251C2×D8—42no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259#127—21no—
260#127—21no—
261#127—21no—
262#127D4×C1112yes—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4D4×C1111yescharacteristic
270C2×C4⋊C4D4×C1112yes—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—24no—
273C2×C42—21no—
274C2×C42C23×C1111yescharacteristic
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8D4×C1112yes—
279#102—24no—
280#102—44no—
281C4×C8—21no—
282C4×C8D4×C1112yes—
283#95—24no—
284#95—21no—
285C2×C11—82no—
286C2×C11—162no—
287C2×C11#162212yes—
288C2×C11#162412yes—
289C2×C11#200011yescharacteristic
290C2×C11#200211yescharacteristic
291C2×C11#201211yescharacteristic
292C24—21no—
293C24—41no—
294C2×Q8—22no—
295C2×Q8—22no—
296C2×Q8—44no—
297C2×D4—21no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—21no—
301C2×D4—22no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—44no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—42no—
311C2×D4—41no—
312C2×D4—42no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4C11×SD1612yescomplemented
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4C2×D4×C1111yescharacteristic
324C22×C4C2×D4×C1111yescharacteristic
325C22×C4C2×D4×C1111yescharacteristic
326SD16—416no—
327D8—48no—
328C2×C8—24no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—42no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—84no—
346C42—41no—
347C42—41no—
348C42C2×D4×C1111yescharacteristic
349C42C2×D4×C1111yescharacteristic
350C42C2×D4×C1111yescharacteristic
351C42C11×#4111yescharacteristic
352C11#1004811yescharacteristic, direct product factor, Sylow
353C23—22no—
354C23—41no—
355C23—42no—
356C23—41no—
357C23—42no—
358C23—42no—
359C23—81no—
360C23—81no—
361C23—82no—
362C23—82no—
363C23C11×#12011yescharacteristic
364Q8—44no—
365Q8—82no—
366D4—22no—
367D4—22no—
368D4—44no—
369D4—42no—
370D4—41no—
371D4—42no—
372D4—44no—
373D4—41no—
374D4—82no—
375D4—81no—
376D4—81no—
377D4—81no—
378D4—81no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—82no—
390C2×C4C11×#12011yescharacteristic
391C2×C4C11×#12011yescharacteristic
392C2×C4C11×#12111yescharacteristic
393C2×C4C11×#12111yescharacteristic
394C2×C4C11×#12111yescharacteristic
395C2×C4C11×#12711yescharacteristic
396C2×C4C2×C11×SD1611yescharacteristic
397C2×C4C11×#13512yes—
398C2×C4C11×#13511yescharacteristic
399C2×C4C11×AGL(1,ℤ/8)12yes—
400C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
401C2×C4C11×#13711yescharacteristic
402C8—24no—
403C8—42no—
404C8—81no—
405C22—44no—
406C22—42no—
407C22—82no—
408C22—81no—
409C22—81no—
410C22—82no—
411C22—82no—
412C22—82no—
413C22—162no—
414C22—162no—
415C22C11×#39211yescharacteristic
416C22C11×#44811yescharacteristic
417C22C11×#44912yes—
418C22C11×#44911yescharacteristic
419C22C11×#45312yes—
420C4—21no—
421C4—21no—
422C4—82no—
423C4—82no—
424C4—81no—
425C4C11×#45011yescharacteristic
426C4C11×#45211yescharacteristic
427C4C11×#46312yes—
428C4C11×#46511yescharacteristic
429C4C11×#46811yescharacteristic
430C4C11×#49511yescharacteristic
431C4C11×#49611yescharacteristic
432C2—82no—
433C2—162no—
434C2C11×#162212yes—
435C2C11×#162412yes—
436C2C11×#200011yescharacteristic
437C2C11×#200211yescharacteristic
438C2C11×#201211yescharacteristic
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×#492C2semidirect
3. C11×#2563C2semidirect
4. C11×#1982C2semidirect
5. C2×C11×#333C2semidirect
6. C2×C11×D4⋊C8C2semidirect
7. C11×#1279C2semidirect
73. #10048C11direct (N × H)
97. C2×D4×C11SD16semidirect
134. C2×#492C2×C11semidirect
136. #2563C2×C11semidirect
137. #1982C2×C11semidirect
138. C2×#333C2×C11semidirect
139. C2×D4⋊C8C2×C11semidirect
140. #1279C2×C11semidirect
315. C2×D4C11×SD16semidirect
352. C11#10048direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4922
C2×C11×#4592
C11×#25632
C11×#19822
C2×C11×#3332
C2×C11×D4⋊C82
C11×#12792
#1004811