Finite Group Databasebeta

← C11×#10257 #14587450

Subgroups — C11×#10257 #14587450

Order 2816.

528 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3246C211yesmaximal, characteristic
2C11×#3078C211yesmaximal, characteristic, complemented
3C11×#3037C211yesmaximal, characteristic
4C11×#1984C211yesmaximal, characteristic, complemented
5C11×#1493C211yesmaximal, characteristic, complemented
6C11×#1492C211yesmaximal, characteristic
7C11×#1292C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C11×#533C2211yescharacteristic
10C11×#532C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C11×#479—22no—
13C11×#477—21no—
14C11×#476—21no—
15C11×#475—21no—
16C11×#475—21no—
17C11×#465—22no—
18C11×#464—22no—
19C11×#462—21no—
20C11×#461—21no—
21C11×#460—21no—
22C11×#460—21no—
23C11×#428—21no—
24C11×#423C2211yescharacteristic
25C11×#423C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#419—21no—
28C11×#417—21no—
29C2×C4×C8×C11C2211yescharacteristic
30C11×#336—22no—
31C11×Q8⋊C8—22no—
32C11×D4⋊C8—22no—
33C2×C11×#41—21no—
34C22×Q8×C11D411yescharacteristic
35C11×#137—42no—
36C11×#137—42no—
37C2×C11×Q16—22no—
38C2×C11×SD16—22no—
39C2×C11×SD16—22no—
40C2×C11×M16—21no—
41C2×C11×M16—21no—
42C22×C8×C11—21no—
43C22×C8×C11D412yes—
44C11×C4⋊Q8D411yescharacteristic
45C11×C4⋊Q8D411yescharacteristic
46C11×C4⋊Q8D411yescharacteristic
47C11×#127D411yescharacteristic
48C11×#125—21no—
49C11×#124—21no—
50C11×C22⋊Q8—21no—
51C11×C22⋊Q8—21no—
52C11×#121—21no—
53C11×#121—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C11×#117—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67C11×#107—22no—
68C11×#106—22no—
69C11×#106—22no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8—21no—
72C11×C4⋊C8—21no—
73C11×C4⋊C8—21no—
74C11×C4⋊C8D412yes—
75C11×C4⋊C8D412yes—
76C11×#103—22no—
77C11×#103—22no—
78C11×#103—22no—
79C11×#103—22no—
80C11×#102—22no—
81C11×#102—22no—
82C4×C8×C11—21no—
83C4×C8×C11—21no—
84#10257C1111yesmaximal, characteristic, direct product factor, Sylow
85C11×#41—41no—
86C11×#41—41no—
87C11×#41—41no—
88C11×#41—41no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11SD1612yescomplemented
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—41no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—41no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C11×Q16—44no—
109C11×SD16—44no—
110C11×SD16—82no—
111C11×M16—41no—
112C11×M16—41no—
113C11×M16—41no—
114C11×M16—41no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—42no—
120C2×C8×C11—41no—
121C2×C8×C11—41no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C42×C11—41no—
138C42×C11—41no—
139C42×C11—41no—
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144#3246C2×C1111yescharacteristic
145#3078C2×C1111yescharacteristic, complemented
146#3037C2×C1111yescharacteristic
147#1984C2×C1111yescharacteristic, complemented
148#1493C2×C1111yescharacteristic, complemented
149#1492C2×C1111yescharacteristic
150#1292C2×C1111yescharacteristic, complemented
151C23×C11—41no—
152C23×C11#12111yescharacteristic
153Q8×C11—22no—
154Q8×C11—22no—
155Q8×C11—42no—
156Q8×C11—41no—
157Q8×C11—41no—
158Q8×C11—41no—
159Q8×C11—41no—
160Q8×C11—41no—
161Q8×C11—41no—
162D4×C11—42no—
163D4×C11—41no—
164D4×C11—41no—
165D4×C11—41no—
166D4×C11—41no—
167D4×C11—81no—
168D4×C11—81no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—22no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12711yescharacteristic
188C2×C4×C11C2×SD1611yescharacteristic
189C2×C4×C11#13511yescharacteristic
190C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C11#13711yescharacteristic
192C8×C11—42no—
193C8×C11—42no—
194C8×C11—42no—
195C8×C11—42no—
196C2×#137—21no—
197#533C22×C1111yescharacteristic
198#532C22×C1111yescharacteristic
199C2×C4×Q8C22×C1111yescharacteristic
200#479—22no—
201#477—21no—
202#476—21no—
203#475—21no—
204#475—21no—
205#465—22no—
206#464—22no—
207#462—21no—
208#461—21no—
209#460—21no—
210#460—21no—
211#428—21no—
212#423C22×C1111yescharacteristic
213#423C22×C1111yescharacteristic
214C2×C4⋊C8C22×C1111yescharacteristic
215#419—21no—
216#417—21no—
217C2×C4×C8C22×C1111yescharacteristic
218#336—22no—
219Q8⋊C8—22no—
220D4⋊C8—22no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11#39211yescharacteristic
227C22×C11#46511yescharacteristic
228C22×C11#46811yescharacteristic
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—42no—
233C4×C11—81no—
234C4×C11—81no—
235C4×C11—81no—
236C4×C11—81no—
237C4×C11#44811yescharacteristic
238C4×C11#44911yescharacteristic
239C4×C11#45011yescharacteristic
240C4×C11#45211yescharacteristic
241C4×C11#45511yescharacteristic
242C4×C11#45611yescharacteristic
243C2×#41—21no—
244C22×Q8D4×C1111yescharacteristic
245#137—42no—
246#137—42no—
247C2×Q16—22no—
248C2×SD16—22no—
249C2×SD16—22no—
250C2×M16—21no—
251C2×M16—21no—
252C22×C8—21no—
253C22×C8D4×C1112yes—
254C4⋊Q8D4×C1111yescharacteristic
255C4⋊Q8D4×C1111yescharacteristic
256C4⋊Q8D4×C1111yescharacteristic
257#127D4×C1111yescharacteristic
258#125—21no—
259#124—21no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262#121—21no—
263#121—21no—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×Q8—21no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×Q8—21no—
270C4×D4—21no—
271C4×D4—21no—
272#117—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4D4×C1111yescharacteristic
275C2×C42—21no—
276C2×C42C23×C1111yescharacteristic
277#107—22no—
278#106—22no—
279#106—22no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8D4×C1112yes—
285C4⋊C8D4×C1112yes—
286#103—22no—
287#103—22no—
288#103—22no—
289#103—22no—
290#102—22no—
291#102—22no—
292C4×C8—21no—
293C4×C8—21no—
294C2×C11—21no—
295C2×C11—21no—
296C2×C11—161no—
297C2×C11#200011yescharacteristic
298C2×C11#200711yescharacteristic
299C2×C11#201711yescharacteristic
300#41—41no—
301#41—41no—
302#41—41no—
303#41—41no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8C11×SD1612yescomplemented
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4C2×D4×C1111yescharacteristic
321C22×C4C2×D4×C1111yescharacteristic
322C22×C4C11×#4111yescharacteristic
323Q16—44no—
324SD16—44no—
325SD16—82no—
326M16—41no—
327M16—41no—
328M16—41no—
329M16—41no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—42no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C42—41no—
353C42—41no—
354C42—41no—
355C42C2×D4×C1111yescharacteristic
356C42C2×D4×C1111yescharacteristic
357C42C2×D4×C1111yescharacteristic
358C42C2×D4×C1111yescharacteristic
359C11#1025711yescharacteristic, direct product factor, Sylow
360C23—41no—
361C23C11×#12111yescharacteristic
362Q8—22no—
363Q8—22no—
364Q8—42no—
365Q8—41no—
366Q8—41no—
367Q8—41no—
368Q8—41no—
369Q8—41no—
370Q8—41no—
371D4—42no—
372D4—41no—
373D4—41no—
374D4—41no—
375D4—41no—
376D4—81no—
377D4—81no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4C11×#12011yescharacteristic
392C2×C4C11×#12011yescharacteristic
393C2×C4C11×#12011yescharacteristic
394C2×C4C11×#12111yescharacteristic
395C2×C4C11×#12111yescharacteristic
396C2×C4C11×#12711yescharacteristic
397C2×C4C2×C11×SD1611yescharacteristic
398C2×C4C11×#13511yescharacteristic
399C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
400C2×C4C11×#13711yescharacteristic
401C8—42no—
402C8—42no—
403C8—42no—
404C8—42no—
405C22—21no—
406C22—21no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22C11×#39211yescharacteristic
411C22C11×#46511yescharacteristic
412C22C11×#46811yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—81no—
418C4—81no—
419C4—81no—
420C4—81no—
421C4C11×#44811yescharacteristic
422C4C11×#44911yescharacteristic
423C4C11×#45011yescharacteristic
424C4C11×#45211yescharacteristic
425C4C11×#45511yescharacteristic
426C4C11×#45611yescharacteristic
427C2—21no—
428C2—21no—
429C2—161no—
430C2C11×#200011yescharacteristic
431C2C11×#200711yescharacteristic
432C2C11×#201711yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3078C2semidirect
4. C11×#1984C2semidirect
5. C11×#1493C2semidirect
7. C11×#1292C2semidirect
84. #10257C11direct (N × H)
97. C2×Q8×C11SD16semidirect
145. #3078C2×C11semidirect
147. #1984C2×C11semidirect
148. #1493C2×C11semidirect
150. #1292C2×C11semidirect
312. C2×Q8C11×SD16semidirect
359. C11#10257direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32462
C11×#30782
C11×#30372
C11×#19842
C11×#14932
C11×#14922
C11×#12922
#1025711