Finite Group Databasebeta

← C11×#10177 #14587370

Subgroups — C11×#10177 #14587370

Order 2816.

614 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3205C211yesmaximal, characteristic
2C11×#3037C211yesmaximal, characteristic, complemented
3C2×C11×#460C211yesmaximal, characteristic, complemented
4C11×#1545C211yesmaximal, characteristic, complemented
5C11×#1480C211yesmaximal, characteristic, complemented
6C11×#1461C211yesmaximal, characteristic, complemented
7C11×#1301C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C22×C11×SD16—21no—
10C11×#532C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C11×#493—21no—
14C11×#486—21no—
15C11×#464—22no—
16C11×#462—21no—
17C11×#460—22no—
18C11×#460—21no—
19C11×#460—22no—
20C11×#459—22no—
21C11×#447—22no—
22C11×#431C2211yescharacteristic
23C11×#431C2211yescharacteristic
24C11×#423C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#417—21no—
27C2×C11×#102—21no—
28C11×#331—22no—
29C11×D4⋊C8—22no—
30C11×#324—22no—
31C2×C11×#41—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C11×#137—42no—
37C11×#137—42no—
38C2×C11×Q16—22no—
39C2×C11×SD16—24no—
40C2×C11×SD16—22no—
41C2×C11×SD16—42no—
42C2×C11×SD16—42no—
43C2×C11×D8—24no—
44C2×C11×M16—21no—
45C22×C8×C11—21no—
46C11×C4⋊Q8D411yescharacteristic
47C11×#127—21no—
48C11×#127—21no—
49C11×#127—21no—
50C11×#127D411yescharacteristic
51C11×#127D412yes—
52C11×#124—21no—
53C11×#121—21no—
54C11×#121—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8D412yes—
70C11×C4⋊C8D412yes—
71C11×#103—22no—
72C11×#102—24no—
73C11×#102—22no—
74C11×#102—24no—
75C11×C22⋊C8—21no—
76C11×C22⋊C8D412yes—
77C4×C8×C11—21no—
78C4×C8×C11—21no—
79#10177C1111yesmaximal, characteristic, direct product factor, Sylow
80C24×C11—41no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—41no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11D812yescomplemented
92C2×D4×C11—21no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—22no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C2×D4×C11—41no—
104C2×D4×C11—41no—
105C2×D4×C11—41no—
106C2×D4×C11—82no—
107C2×D4×C11—82no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—41no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C11×Q16—44no—
115C11×SD16—48no—
116C11×SD16—44no—
117C11×D8—84no—
118C11×M16—41no—
119C11×M16—41no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—41no—
124C2×C8×C11—41no—
125C2×C8×C11—41no—
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×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C42×C11—41no—
135C42×C11—41no—
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140#3205C2×C1111yescharacteristic
141#3037C2×C1111yescharacteristic, complemented
142C2×#460C2×C1111yescharacteristic, complemented
143#1545C2×C1111yescharacteristic, complemented
144#1480C2×C1111yescharacteristic, complemented
145#1461C2×C1111yescharacteristic, complemented
146#1301C2×C1111yescharacteristic, complemented
147C23×C11—41no—
148C23×C11—42no—
149C23×C11—82no—
150C23×C11—82no—
151C23×C11—81no—
152C23×C11—81no—
153C23×C11#12111yescharacteristic
154Q8×C11—22no—
155Q8×C11—22no—
156Q8×C11—41no—
157Q8×C11—41no—
158Q8×C11—41no—
159Q8×C11—41no—
160D4×C11—42no—
161D4×C11—44no—
162D4×C11—42no—
163D4×C11—41no—
164D4×C11—42no—
165D4×C11—41no—
166D4×C11—42no—
167D4×C11—82no—
168D4×C11—82no—
169D4×C11—81no—
170D4×C11—81no—
171D4×C11—81no—
172D4×C11—81no—
173D4×C11—82no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11—81no—
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12011yescharacteristic
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12711yescharacteristic
190C2×C4×C11C2×D811yescharacteristic
191C2×C4×C11#13511yescharacteristic
192C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
194C8×C11—42no—
195C8×C11—42no—
196C8×C11—42no—
197C8×C11—81no—
198C2×#137—21no—
199C22×SD16—21no—
200#532C22×C1111yescharacteristic
201C2×#127C22×C1111yescharacteristic
202C2×C4×Q8C22×C1111yescharacteristic
203#493—21no—
204#486—21no—
205#464—22no—
206#462—21no—
207#460—22no—
208#460—21no—
209#460—22no—
210#459—22no—
211#447—22no—
212#431C22×C1111yescharacteristic
213#431C22×C1111yescharacteristic
214#423C22×C1111yescharacteristic
215C2×C4⋊C8C22×C1111yescharacteristic
216#417—21no—
217C2×#102—21no—
218#331—22no—
219D4⋊C8—22no—
220#324—22no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—81no—
224C22×C11—82no—
225C22×C11—82no—
226C22×C11—81no—
227C22×C11—81no—
228C22×C11—82no—
229C22×C11—162no—
230C22×C11—162no—
231C22×C11#39211yescharacteristic
232C22×C11#46611yescharacteristic
233C22×C11#46911yescharacteristic
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—42no—
238C4×C11—81no—
239C4×C11—81no—
240C4×C11#44711yescharacteristic
241C4×C11#44711yescharacteristic
242C4×C11#44911yescharacteristic
243C4×C11#44911yescharacteristic
244C4×C11#47112yes—
245C2×#41—21no—
246C22×Q8D4×C1111yescharacteristic
247C22×D4—21no—
248C22×D4—21no—
249C22×D4—21no—
250#137—42no—
251#137—42no—
252C2×Q16—22no—
253C2×SD16—24no—
254C2×SD16—22no—
255C2×SD16—42no—
256C2×SD16—42no—
257C2×D8—24no—
258C2×M16—21no—
259C22×C8—21no—
260C4⋊Q8D4×C1111yescharacteristic
261#127—21no—
262#127—21no—
263#127—21no—
264#127D4×C1112yes—
265#127D4×C1111yescharacteristic
266#124—21no—
267#121—21no—
268#121—21no—
269C4×Q8—21no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×Q8—21no—
273C4×D4—21no—
274C4×D4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4D4×C1111yescharacteristic
277C2×C42—21no—
278C2×C42C23×C1111yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8D4×C1112yes—
284C4⋊C8D4×C1112yes—
285#103—22no—
286#102—24no—
287#102—22no—
288#102—24no—
289C22⋊C8—21no—
290C22⋊C8D4×C1112yes—
291C4×C8—21no—
292C4×C8—21no—
293C2×C11—21no—
294C2×C11—21no—
295C2×C11—161no—
296C2×C11—162no—
297C2×C11#199911yescharacteristic
298C2×C11#200811yescharacteristic
299C2×C11#201911yescharacteristic
300C24—41no—
301#41—41no—
302#41—41no—
303#41—41no—
304#41—41no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8C11×D812yescomplemented
312C2×D4—21no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—22no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—82no—
327C2×D4—82no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—41no—
331C22×C4C2×D4×C1111yescharacteristic
332C22×C4C2×D4×C1111yescharacteristic
333C22×C4C11×#4111yescharacteristic
334Q16—44no—
335SD16—48no—
336SD16—44no—
337D8—84no—
338M16—41no—
339M16—41no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C42—41no—
355C42—41no—
356C42C2×D4×C1111yescharacteristic
357C42C2×D4×C1111yescharacteristic
358C42C2×D4×C1111yescharacteristic
359C42C2×D4×C1111yescharacteristic
360C11#1017711yescharacteristic, direct product factor, Sylow
361C23—41no—
362C23—42no—
363C23—82no—
364C23—82no—
365C23—81no—
366C23—81no—
367C23C11×#12111yescharacteristic
368Q8—22no—
369Q8—22no—
370Q8—41no—
371Q8—41no—
372Q8—41no—
373Q8—41no—
374D4—42no—
375D4—44no—
376D4—42no—
377D4—41no—
378D4—42no—
379D4—41no—
380D4—42no—
381D4—82no—
382D4—82no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387D4—82no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4C11×#12011yescharacteristic
399C2×C4C11×#12011yescharacteristic
400C2×C4C11×#12011yescharacteristic
401C2×C4C11×#12111yescharacteristic
402C2×C4C11×#12111yescharacteristic
403C2×C4C11×#12711yescharacteristic
404C2×C4C2×C11×D811yescharacteristic
405C2×C4C11×#13511yescharacteristic
406C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
407C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
408C8—42no—
409C8—42no—
410C8—42no—
411C8—81no—
412C22—21no—
413C22—21no—
414C22—81no—
415C22—82no—
416C22—82no—
417C22—81no—
418C22—81no—
419C22—82no—
420C22—162no—
421C22—162no—
422C22C11×#39211yescharacteristic
423C22C11×#46611yescharacteristic
424C22C11×#46911yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—42no—
429C4—81no—
430C4—81no—
431C4C11×#44711yescharacteristic
432C4C11×#44711yescharacteristic
433C4C11×#44911yescharacteristic
434C4C11×#44911yescharacteristic
435C4C11×#47112yes—
436C2—21no—
437C2—21no—
438C2—162no—
439C2—161no—
440C2C11×#199911yescharacteristic
441C2C11×#200811yescharacteristic
442C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3205C2
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×#3037C2semidirect
3. C2×C11×#460C2semidirect
4. C11×#1545C2semidirect
5. C11×#1480C2semidirect
6. C11×#1461C2semidirect
7. C11×#1301C2semidirect
79. #10177C11direct (N × H)
91. C2×Q8×C11D8semidirect
141. #3037C2×C11semidirect
142. C2×#460C2×C11semidirect
143. #1545C2×C11semidirect
144. #1480C2×C11semidirect
145. #1461C2×C11semidirect
146. #1301C2×C11semidirect
311. C2×Q8C11×D8semidirect
360. C11#10177direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32052
C11×#30372
C2×C11×#4602
C11×#15452
C11×#14802
C11×#14612
C11×#13012
#1017711