Finite Group Databasebeta

← C11×#60026 #14637219

Subgroups — C11×#60026 #14637219

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2810C211yesmaximal, characteristic, complemented
2C11×#2750C213yesmaximal, complemented
3C11×#2573C213yesmaximal, complemented
4C11×#2533C213yesmaximal, complemented
5C11×#2497C213yesmaximal, complemented
6C11×#2493C213yesmaximal, complemented
7C11×#2470C213yesmaximal, complemented
8C11×#2457C213yesmaximal
9C11×#2359C213yesmaximal, complemented
10C11×#2353C213yesmaximal, complemented
11C11×#2298C213yesmaximal, complemented
12C2×C11×#123C2213yes—
13C2×C4×D4×C11C2213yes—
14C2×C11×#117C2213yes—
15C11×#401C2211yescharacteristic
16C11×#400C2213yes—
17C11×#400C2213yes—
18C11×#400C2213yes—
19C11×#400C2213yes—
20C11×#400C2213yes—
21C11×#400C2213yes—
22C11×#397C2213yes—
23C11×#396C2213yes—
24C11×#396C2213yes—
25C11×#394C2213yes—
26C11×#392C2211yescharacteristic
27C11×#389C2213yes—
28C11×#389C2213yes—
29C11×#389C2213yes—
30C11×#388C2213yes—
31C11×#388C2213yes—
32C11×#388C2213yes—
33C11×#388C2213yes—
34C11×#388C2213yes—
35C11×#388C2213yes—
36C11×#387C2213yes—
37C11×#387C2213yes—
38C11×#387C2213yes—
39C11×#387C2213yes—
40C11×#387C2213yes—
41C11×#387C2213yes—
42C11×#387C2213yes—
43C11×#387C2213yes—
44C11×#387C2213yes—
45C11×#386C2213yes—
46C11×#386C2213yes—
47C11×#386C2213yes—
48C11×#385C2213yes—
49C11×#385C2213yes—
50C11×#385C2213yes—
51C11×#384C2211yescharacteristic
52C11×#383C2213yes—
53C11×#383C2211yescharacteristic
54C11×#381C2213yes—
55C11×#381C2213yes—
56C11×#380C2213yes—
57C11×#380C2213yes—
58C4×C11×C4⋊C4C2213yes—
59C4×C11×C4⋊C4C2213yes—
60C4×C11×C22⋊C4C2213yes—
61C4×C11×C22⋊C4C2213yes—
62C4×C11×C22⋊C4C2213yes—
63C4×C11×C22⋊C4C2213yes—
64C11×#376C2213yes—
65C2×C11×#95C2213yes—
66C43×C11C2211yescharacteristic
67C22×D4×C11C2313yes—
68C23×C4×C11C2313yes—
69C23×C4×C11C2313yes—
70C23×C4×C11C2313yes—
71C11×#123—212no—
72C4×D4×C11—212no—
73C11×#117—212no—
74C2×C11×C4⋊C4C2313yes—
75C2×C11×C4⋊C4C2313yes—
76C2×C11×C4⋊C4C2313yes—
77C2×C11×C4⋊C4C2313yes—
78C2×C11×C4⋊C4C2313yes—
79C2×C11×C4⋊C4C2313yes—
80C2×C11×C4⋊C4C2313yes—
81C2×C11×C4⋊C4C2313yes—
82C2×C11×C4⋊C4C2313yes—
83C2×C11×C4⋊C4C2313yes—
84C2×C11×C4⋊C4C2313yes—
85C2×C11×C22⋊C4C2313yes—
86C2×C11×C22⋊C4C2313yes—
87C2×C11×C22⋊C4C2313yes—
88C2×C11×C22⋊C4C2313yes—
89C2×C11×C22⋊C4C2313yes—
90C2×C11×C22⋊C4C2313yes—
91C2×C11×C22⋊C4C2313yes—
92C2×C11×C22⋊C4C2313yes—
93C2×C11×C22⋊C4C2313yes—
94C2×C11×C22⋊C4C2313yes—
95C2×C42×C11C2313yes—
96C2×C42×C11C2313yes—
97C2×C42×C11C2313yes—
98C2×C42×C11C2313yes—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2313yes—
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C11×#95C2313yes—
104C11×#95C2313yes—
105C11×#95C2313yes—
106C11×#95C2313yes—
107C11×#95C2313yes—
108C11×#95C2313yes—
109C11×#95C2313yes—
110C11×#95C2313yes—
111C11×#95C2313yes—
112C11×#95C2313yes—
113C11×#95C2313yes—
114C11×#95C2313yes—
115C11×#95C2313yes—
116C11×#95C2313yes—
117C11×#95C2313yes—
118C11×#95C2313yes—
119C11×#95C2313yes—
120C11×#95C2313yes—
121C11×#95C2313yes—
122C11×#95C2313yes—
123C11×#95C2311yescharacteristic
124C11×#95C2311yescharacteristic
125#60026C1111yesmaximal, characteristic, direct product factor, Sylow
126C24×C11C2413yes—
127C2×D4×C11—26no—
128C2×D4×C11—26no—
129C2×D4×C11—43no—
130C22×C4×C11—26no—
131C22×C4×C11—26no—
132C22×C4×C11—26no—
133C22×C4×C11—26no—
134C22×C4×C11—43no—
135C22×C4×C11—43no—
136C22×C4×C11—43no—
137C22×C4×C11—43no—
138C22×C4×C11—43no—
139C22×C4×C11C2413yes—
140C22×C4×C11C2413yes—
141C22×C4×C11C2413yes—
142C22×C4×C11C2413yes—
143C22×C4×C11C2413yes—
144C22×C4×C11C2411yescharacteristic
145C22×C4×C11C2413yes—
146C22×C4×C11C2413yes—
147C22×C4×C11C2413yes—
148C22×C4×C11C2413yes—
149C11×C4⋊C4—26no—
150C11×C4⋊C4—26no—
151C11×C4⋊C4—26no—
152C11×C4⋊C4—26no—
153C11×C4⋊C4—26no—
154C11×C4⋊C4—43no—
155C11×C4⋊C4—43no—
156C11×C4⋊C4—43no—
157C11×C4⋊C4—43no—
158C11×C4⋊C4—43no—
159C11×C4⋊C4—43no—
160C11×C22⋊C4—26no—
161C11×C22⋊C4—26no—
162C11×C22⋊C4—26no—
163C11×C22⋊C4—26no—
164C11×C22⋊C4—43no—
165C11×C22⋊C4—43no—
166C11×C22⋊C4—43no—
167C11×C22⋊C4—43no—
168C11×C22⋊C4—43no—
169C11×C22⋊C4#41112yes—
170C42×C11—26no—
171C42×C11—26no—
172C42×C11—26no—
173C42×C11—43no—
174C42×C11—43no—
175C42×C11—41no—
176C42×C11—41no—
177C42×C11—41no—
178#2810C2×C1111yescharacteristic, complemented
179#2750C2×C1113yescomplemented
180#2573C2×C1113yescomplemented
181#2533C2×C1113yescomplemented
182#2497C2×C1113yescomplemented
183#2493C2×C1113yescomplemented
184#2470C2×C1113yescomplemented
185#2457C2×C1113yes—
186#2359C2×C1113yescomplemented
187#2353C2×C1113yescomplemented
188#2298C2×C1113yescomplemented
189C23×C11—23no—
190C23×C11—23no—
191C23×C11—23no—
192C23×C11—23no—
193C23×C11—23no—
194C23×C11—23no—
195C23×C11C2×#4116yes—
196C23×C11C2511yescharacteristic
197D4×C11—412no—
198C2×C4×C11—23no—
199C2×C4×C11—23no—
200C2×C4×C11—23no—
201C2×C4×C11—23no—
202C2×C4×C11—23no—
203C2×C4×C11—23no—
204C2×C4×C11—23no—
205C2×C4×C11—23no—
206C2×C4×C11—23no—
207C2×C4×C11—23no—
208C2×C4×C11—23no—
209C2×C4×C11—23no—
210C2×C4×C11—23no—
211C2×C4×C11—23no—
212C2×C4×C11—23no—
213C2×C4×C11—23no—
214C2×C4×C11—23no—
215C2×C4×C11—23no—
216C2×C4×C11—23no—
217C2×C4×C11—23no—
218C2×C4×C11—23no—
219C2×C4×C11—23no—
220C2×C4×C11—23no—
221C2×C4×C11—23no—
222C2×C4×C11—23no—
223C2×C4×C11—23no—
224C2×C4×C11—412no—
225C2×C4×C11—86no—
226C2×C4×C11—86no—
227C2×C4×C11C2×#4116yes—
228C2×C4×C11C2×#4116yes—
229C2×#123C22×C1113yes—
230C2×C4×D4C22×C1113yes—
231C2×#117C22×C1113yes—
232#401C22×C1111yescharacteristic
233#400C22×C1113yes—
234#400C22×C1113yes—
235#400C22×C1113yes—
236#400C22×C1113yes—
237#400C22×C1113yes—
238#400C22×C1113yes—
239#397C22×C1113yes—
240#396C22×C1113yes—
241#396C22×C1113yes—
242#394C22×C1113yes—
243#392C22×C1111yescharacteristic
244#389C22×C1113yes—
245#389C22×C1113yes—
246#389C22×C1113yes—
247#388C22×C1113yes—
248#388C22×C1113yes—
249#388C22×C1113yes—
250#388C22×C1113yes—
251#388C22×C1113yes—
252#388C22×C1113yes—
253#387C22×C1113yes—
254#387C22×C1113yes—
255#387C22×C1113yes—
256#387C22×C1113yes—
257#387C22×C1113yes—
258#387C22×C1113yes—
259#387C22×C1113yes—
260#387C22×C1113yes—
261#387C22×C1113yes—
262#386C22×C1113yes—
263#386C22×C1113yes—
264#386C22×C1113yes—
265#385C22×C1113yes—
266#385C22×C1113yes—
267#385C22×C1113yes—
268#384C22×C1111yescharacteristic
269#383C22×C1111yescharacteristic
270#383C22×C1113yes—
271#381C22×C1113yes—
272#381C22×C1113yes—
273#380C22×C1113yes—
274#380C22×C1113yes—
275C4×C4⋊C4C22×C1113yes—
276C4×C4⋊C4C22×C1113yes—
277C4×C22⋊C4C22×C1113yes—
278C4×C22⋊C4C22×C1113yes—
279C4×C22⋊C4C22×C1113yes—
280C4×C22⋊C4C22×C1113yes—
281#376C22×C1113yes—
282C2×#95C22×C1113yes—
283C43C22×C1111yescharacteristic
284C22×C11—26no—
285C22×C11—26no—
286C22×C11—26no—
287C22×C11—43no—
288C22×C11—43no—
289C22×C11—43no—
290C22×C11—43no—
291C22×C11C22×#4113yes—
292C22×C11#58513yes—
293C22×C11#58511yescharacteristic
294C4×C11—26no—
295C4×C11—26no—
296C4×C11—43no—
297C4×C11—43no—
298C4×C11—43no—
299C4×C11—43no—
300C4×C11—43no—
301C4×C11—43no—
302C4×C11—41no—
303C4×C11—43no—
304C22×D4C23×C1113yes—
305C23×C4C23×C1113yes—
306C23×C4C23×C1113yes—
307C23×C4C23×C1113yes—
308#123—212no—
309C4×D4—212no—
310#117—212no—
311C2×C4⋊C4C23×C1113yes—
312C2×C4⋊C4C23×C1113yes—
313C2×C4⋊C4C23×C1113yes—
314C2×C4⋊C4C23×C1113yes—
315C2×C4⋊C4C23×C1113yes—
316C2×C4⋊C4C23×C1113yes—
317C2×C4⋊C4C23×C1113yes—
318C2×C4⋊C4C23×C1113yes—
319C2×C4⋊C4C23×C1113yes—
320C2×C4⋊C4C23×C1113yes—
321C2×C4⋊C4C23×C1113yes—
322C2×C22⋊C4C23×C1113yes—
323C2×C22⋊C4C23×C1113yes—
324C2×C22⋊C4C23×C1113yes—
325C2×C22⋊C4C23×C1113yes—
326C2×C22⋊C4C23×C1113yes—
327C2×C22⋊C4C23×C1113yes—
328C2×C22⋊C4C23×C1113yes—
329C2×C22⋊C4C23×C1113yes—
330C2×C22⋊C4C23×C1113yes—
331C2×C22⋊C4C23×C1113yes—
332C2×C42C23×C1113yes—
333C2×C42C23×C1113yes—
334C2×C42C23×C1113yes—
335C2×C42C23×C1113yes—
336C2×C42C23×C1111yescharacteristic
337C2×C42C23×C1113yes—
338C2×C42C23×C1111yescharacteristic
339C2×C42C23×C1111yescharacteristic
340#95C23×C1113yes—
341#95C23×C1113yes—
342#95C23×C1113yes—
343#95C23×C1113yes—
344#95C23×C1113yes—
345#95C23×C1113yes—
346#95C23×C1113yes—
347#95C23×C1113yes—
348#95C23×C1113yes—
349#95C23×C1113yes—
350#95C23×C1113yes—
351#95C23×C1113yes—
352#95C23×C1113yes—
353#95C23×C1113yes—
354#95C23×C1113yes—
355#95C23×C1113yes—
356#95C23×C1113yes—
357#95C23×C1113yes—
358#95C23×C1113yes—
359#95C23×C1113yes—
360#95C23×C1111yescharacteristic
361#95C23×C1111yescharacteristic
362C2×C11—46no—
363C2×C11#347513yes—
364C2×C11#352113yes—
365C2×C11#356711yescharacteristic
366C24C24×C1113yes—
367C2×D4—26no—
368C2×D4—26no—
369C2×D4—43no—
370C22×C4—26no—
371C22×C4—26no—
372C22×C4—26no—
373C22×C4—26no—
374C22×C4—43no—
375C22×C4—43no—
376C22×C4—43no—
377C22×C4—43no—
378C22×C4—43no—
379C22×C4C24×C1113yes—
380C22×C4C24×C1113yes—
381C22×C4C24×C1113yes—
382C22×C4C24×C1113yes—
383C22×C4C24×C1113yes—
384C22×C4C24×C1111yescharacteristic
385C22×C4C24×C1113yes—
386C22×C4C24×C1113yes—
387C22×C4C24×C1113yes—
388C22×C4C24×C1113yes—
389C4⋊C4—26no—
390C4⋊C4—26no—
391C4⋊C4—26no—
392C4⋊C4—26no—
393C4⋊C4—26no—
394C4⋊C4—43no—
395C4⋊C4—43no—
396C4⋊C4—43no—
397C4⋊C4—43no—
398C4⋊C4—43no—
399C4⋊C4—43no—
400C22⋊C4—26no—
401C22⋊C4—26no—
402C22⋊C4—26no—
403C22⋊C4—26no—
404C22⋊C4—43no—
405C22⋊C4—43no—
406C22⋊C4—43no—
407C22⋊C4—43no—
408C22⋊C4—43no—
409C22⋊C4C11×#41112yes—
410C42—26no—
411C42—26no—
412C42—26no—
413C42—43no—
414C42—43no—
415C42—41no—
416C42—41no—
417C42—41no—
418C11#6002611yescharacteristic, direct product factor, Sylow
419C23—23no—
420C23—23no—
421C23—23no—
422C23—23no—
423C23—23no—
424C23—23no—
425C23C2×C11×#4116yes—
426C23C25×C1111yescharacteristic
427D4—412no—
428C2×C4—23no—
429C2×C4—23no—
430C2×C4—23no—
431C2×C4—23no—
432C2×C4—23no—
433C2×C4—23no—
434C2×C4—23no—
435C2×C4—23no—
436C2×C4—23no—
437C2×C4—23no—
438C2×C4—23no—
439C2×C4—23no—
440C2×C4—23no—
441C2×C4—23no—
442C2×C4—23no—
443C2×C4—23no—
444C2×C4—23no—
445C2×C4—23no—
446C2×C4—23no—
447C2×C4—23no—
448C2×C4—23no—
449C2×C4—23no—
450C2×C4—23no—
451C2×C4—23no—
452C2×C4—23no—
453C2×C4—23no—
454C2×C4—412no—
455C2×C4—86no—
456C2×C4—86no—
457C2×C4C2×C11×#4116yes—
458C2×C4C2×C11×#4116yes—
459C22—26no—
460C22—26no—
461C22—26no—
462C22—43no—
463C22—43no—
464C22—43no—
465C22—43no—
466C22C22×C11×#4113yes—
467C22C11×#58513yes—
468C22C11×#58511yescharacteristic
469C4—26no—
470C4—26no—
471C4—43no—
472C4—43no—
473C4—43no—
474C4—43no—
475C4—43no—
476C4—43no—
477C4—41no—
478C4—43no—
479C2—46no—
480C2C11×#347513yes—
481C2C11×#352113yes—
482C2C11×#356711yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC11×#392C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2810C2semidirect
2. C11×#2750C2semidirect
3. C11×#2573C2semidirect
4. C11×#2533C2semidirect
5. C11×#2497C2semidirect
6. C11×#2493C2semidirect
7. C11×#2470C2semidirect
9. C11×#2359C2semidirect
10. C11×#2353C2semidirect
11. C11×#2298C2semidirect
125. #60026C11direct (N × H)
178. #2810C2×C11semidirect
179. #2750C2×C11semidirect
180. #2573C2×C11semidirect
181. #2533C2×C11semidirect
182. #2497C2×C11semidirect
183. #2493C2×C11semidirect
184. #2470C2×C11semidirect
186. #2359C2×C11semidirect
187. #2353C2×C11semidirect
188. #2298C2×C11semidirect
418. C11#60026direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28102
C11×#27502
C11×#25732
C11×#25332
C11×#24972
C11×#24932
C11×#24702
C11×#24572
C11×#23592
C11×#23532
C11×#22982
#6002611