Finite Group Databasebeta

← C11×#33671 #14610864

Subgroups — C11×#33671 #14610864

Order 2816.

554 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3168C211yesmaximal, characteristic, complemented
2C4×C11×#135C211yesmaximal, characteristic, complemented
3C11×#2237C211yesmaximal, characteristic, complemented
4C11×#2234C211yesmaximal, characteristic, complemented
5C11×#2229C211yesmaximal, characteristic, complemented
6C11×#2228C211yesmaximal, characteristic, complemented
7C11×#2211C211yesmaximal, characteristic, complemented
8C11×#2210C211yesmaximal, characteristic, complemented
9C11×#2189C211yesmaximal, characteristic, complemented
10C11×#2186C211yesmaximal, characteristic
11C11×#2177C211yesmaximal, characteristic, complemented
12C11×#2176C211yesmaximal, characteristic, complemented
13C11×#2175C211yesmaximal, characteristic, complemented
14C11×#2175C211yesmaximal, characteristic, complemented
15C11×#2163C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C11×#529—21no—
18C4×C11×#41—21no—
19C2×C11×Q32C2211yescharacteristic
20C2×C11×SD32C2211yescharacteristic
21C2×C11×SD32C2211yescharacteristic
22C2×C11×D16C2211yescharacteristic
23C11×#499C2211yescharacteristic
24C11×#495C2211yescharacteristic
25C11×#488—21no—
26C11×#467C2211yescharacteristic
27C11×#466C2211yescharacteristic
28C11×#465—21no—
29C4×C11×Q16C2211yescharacteristic
30C4×C11×Q16C2211yescharacteristic
31C4×C11×Q16C2211yescharacteristic
32C4×C11×SD16—21no—
33C4×C11×SD16—21no—
34C4×C11×SD16—21no—
35C4×C11×D8C2211yescharacteristic
36C4×C11×D8C2211yescharacteristic
37C4×C11×D8C2211yescharacteristic
38C11×#427C2211yescharacteristic
39C11×#416—21no—
40C2×C4×C8×C11C2211yescharacteristic
41C11×#367C2211yescharacteristic
42C11×#367C2211yescharacteristic
43C11×#366C2211yescharacteristic
44C11×#366C2211yescharacteristic
45C11×C4⋊C16C2211yescharacteristic
46C11×C4⋊C16C2211yescharacteristic
47C11×#358C2211yescharacteristic
48C11×#358C2211yescharacteristic
49C11×#358C2211yescharacteristic
50C11×#358C2211yescharacteristic
51C11×#357C2211yescharacteristic
52C11×#357C2211yescharacteristic
53C11×#357C2211yescharacteristic
54C11×#357C2211yescharacteristic
55C11×C22⋊C16C2211yescharacteristic
56C11×C22⋊C16C2211yescharacteristic
57C11×#346C2211yescharacteristic
58C11×#346C2211yescharacteristic
59C2×C11×#41—21no—
60C11×#135—22no—
61C11×#135—22no—
62C2×C11×Q16C2311yescharacteristic
63C2×C11×Q16C2311yescharacteristic
64C2×C11×SD16—21no—
65C2×C11×SD16—21no—
66C2×C11×D8C2311yescharacteristic
67C2×C11×D8C2311yescharacteristic
68C22×C8×C11D411yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×#126—41no—
71C11×#125—21no—
72C11×#124—21no—
73C11×#123—41no—
74C11×C22⋊Q8—21no—
75C11×#121—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11—41no—
83C4×D4×C11—41no—
84C4×D4×C11—41no—
85C11×#117—21no—
86C11×#117—41no—
87C11×#117—41no—
88C2×C42×C11—41no—
89C2×C42×C11D411yescharacteristic
90C11×Q32—22no—
91C11×SD32—22no—
92C11×SD32—22no—
93C11×D16—22no—
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C2×C11×C16C2311yescharacteristic
98C11×#107C2311yescharacteristic
99C11×#107C2311yescharacteristic
100C11×#107C2311yescharacteristic
101C11×#107C2311yescharacteristic
102C11×#106—21no—
103C11×#106—21no—
104C11×#103—21no—
105C11×#103—21no—
106C11×#103—21no—
107C11×#103—21no—
108C11×#102—21no—
109C11×#102—21no—
110C11×#102—21no—
111C11×#102—21no—
112C4×C8×C11D411yescharacteristic
113C4×C8×C11D411yescharacteristic
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116#33671C1111yesmaximal, characteristic, direct product factor, Sylow
117C11×#41—24no—
118C11×#41—42no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C22×C4×C11—41no—
126C22×C4×C11—41no—
127C22×C4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11D811yescharacteristic
130C22×C4×C11D811yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C11×Q16—21no—
133C11×Q16—21no—
134C11×Q16—21no—
135C11×Q16#4112yes—
136C11×SD16—24no—
137C11×SD16—42no—
138C11×D8—21no—
139C11×D8—21no—
140C11×D8—21no—
141C11×D8#4112yes—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—41no—
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2411yescharacteristic
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4—41no—
159C11×C22⋊C4—41no—
160C11×C22⋊C4—41no—
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C11×C22⋊C4—41no—
164C11×C22⋊C4—41no—
165C11×C22⋊C4—41no—
166C11×C22⋊C4—41no—
167C42×C11—41no—
168C42×C11—41no—
169C42×C11—41no—
170C42×C11—41no—
171C42×C11D811yescharacteristic
172C42×C11D811yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C11×C16—21no—
176C11×C16—21no—
177C11×C16—21no—
178C11×C16—21no—
179#3168C2×C1111yescharacteristic, complemented
180C4×#135C2×C1111yescharacteristic, complemented
181#2237C2×C1111yescharacteristic, complemented
182#2234C2×C1111yescharacteristic, complemented
183#2229C2×C1111yescharacteristic, complemented
184#2228C2×C1111yescharacteristic, complemented
185#2211C2×C1111yescharacteristic, complemented
186#2210C2×C1111yescharacteristic, complemented
187#2189C2×C1111yescharacteristic, complemented
188#2186C2×C1111yescharacteristic
189#2177C2×C1111yescharacteristic, complemented
190#2176C2×C1111yescharacteristic, complemented
191#2175C2×C1111yescharacteristic, complemented
192#2175C2×C1111yescharacteristic, complemented
193#2163C2×C1111yescharacteristic, complemented
194C23×C11—41no—
195C23×C11—41no—
196C23×C11C2×D811yescharacteristic
197Q8×C11—22no—
198Q8×C11—41no—
199Q8×C11—41no—
200Q8×C11—41no—
201D4×C11—22no—
202D4×C11—44no—
203D4×C11—41no—
204D4×C11—41no—
205D4×C11—41no—
206D4×C11—82no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—44no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—82no—
219C2×C4×C11—82no—
220C2×C4×C11—82no—
221C2×C4×C11C2×D811yescharacteristic
222C2×C4×C11C2×D811yescharacteristic
223C2×C4×C11C2×D811yescharacteristic
224C2×C4×C11C2×D811yescharacteristic
225C2×C4×C11C2×D811yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C8×C11—21no—
228C8×C11—21no—
229C8×C11—21no—
230C8×C11C2×#4111yescharacteristic
231C8×C11C2×#4111yescharacteristic
232C2×#135C22×C1111yescharacteristic
233#529—21no—
234C4×#41—21no—
235C2×Q32C22×C1111yescharacteristic
236C2×SD32C22×C1111yescharacteristic
237C2×SD32C22×C1111yescharacteristic
238C2×D16C22×C1111yescharacteristic
239#499C22×C1111yescharacteristic
240#495C22×C1111yescharacteristic
241#488—21no—
242#467C22×C1111yescharacteristic
243#466C22×C1111yescharacteristic
244#465—21no—
245C4×Q16C22×C1111yescharacteristic
246C4×Q16C22×C1111yescharacteristic
247C4×Q16C22×C1111yescharacteristic
248C4×SD16—21no—
249C4×SD16—21no—
250C4×SD16—21no—
251C4×D8C22×C1111yescharacteristic
252C4×D8C22×C1111yescharacteristic
253C4×D8C22×C1111yescharacteristic
254#427C22×C1111yescharacteristic
255#416—21no—
256C2×C4×C8C22×C1111yescharacteristic
257#367C22×C1111yescharacteristic
258#367C22×C1111yescharacteristic
259#366C22×C1111yescharacteristic
260#366C22×C1111yescharacteristic
261C4⋊C16C22×C1111yescharacteristic
262C4⋊C16C22×C1111yescharacteristic
263#358C22×C1111yescharacteristic
264#358C22×C1111yescharacteristic
265#358C22×C1111yescharacteristic
266#358C22×C1111yescharacteristic
267#357C22×C1111yescharacteristic
268#357C22×C1111yescharacteristic
269#357C22×C1111yescharacteristic
270#357C22×C1111yescharacteristic
271C22⋊C16C22×C1111yescharacteristic
272C22⋊C16C22×C1111yescharacteristic
273#346C22×C1111yescharacteristic
274#346C22×C1111yescharacteristic
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—42no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11C22×D811yescharacteristic
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—42no—
291C4×C11—81no—
292C4×C11—81no—
293C4×C11—81no—
294C4×C11—81no—
295C4×C11—81no—
296C4×C11#52511yescharacteristic
297C4×C11#57511yescharacteristic
298C2×#41—21no—
299#135—22no—
300#135—22no—
301C2×Q16C23×C1111yescharacteristic
302C2×Q16C23×C1111yescharacteristic
303C2×SD16—21no—
304C2×SD16—21no—
305C2×D8C23×C1111yescharacteristic
306C2×D8C23×C1111yescharacteristic
307C22×C8D4×C1111yescharacteristic
308C22×C8C23×C1111yescharacteristic
309#126—41no—
310#125—21no—
311#124—21no—
312#123—41no—
313C22⋊Q8—21no—
314#121—21no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×Q8—21no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—41no—
322C4×D4—41no—
323C4×D4—41no—
324#117—21no—
325#117—41no—
326#117—41no—
327C2×C42—41no—
328C2×C42D4×C1111yescharacteristic
329Q32—22no—
330SD32—22no—
331SD32—22no—
332D16—22no—
333C2×C16C23×C1111yescharacteristic
334C2×C16C23×C1111yescharacteristic
335C2×C16C23×C1111yescharacteristic
336C2×C16C23×C1111yescharacteristic
337#107C23×C1111yescharacteristic
338#107C23×C1111yescharacteristic
339#107C23×C1111yescharacteristic
340#107C23×C1111yescharacteristic
341#106—21no—
342#106—21no—
343#103—21no—
344#103—21no—
345#103—21no—
346#103—21no—
347#102—21no—
348#102—21no—
349#102—21no—
350#102—21no—
351C4×C8D4×C1111yescharacteristic
352C4×C8D4×C1111yescharacteristic
353C4×C8C23×C1111yescharacteristic
354C4×C8C23×C1111yescharacteristic
355C2×C11—41no—
356C2×C11—82no—
357C2×C11—161no—
358C2×C11#310011yescharacteristic
359C2×C11#341411yescharacteristic
360C2×C11#341411yescharacteristic
361#41—24no—
362#41—42no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4C11×D811yescharacteristic
374C22×C4C11×D811yescharacteristic
375C22×C4C2×D4×C1111yescharacteristic
376Q16—21no—
377Q16—21no—
378Q16—21no—
379Q16C11×#4112yes—
380SD16—24no—
381SD16—42no—
382D8—21no—
383D8—21no—
384D8—21no—
385D8C11×#4112yes—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—41no—
389C2×C8C2×D4×C1111yescharacteristic
390C2×C8C2×D4×C1111yescharacteristic
391C2×C8C2×D4×C1111yescharacteristic
392C2×C8C24×C1111yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C42—41no—
412C42—41no—
413C42—41no—
414C42—41no—
415C42C11×D811yescharacteristic
416C42C11×D811yescharacteristic
417C42C2×D4×C1111yescharacteristic
418C42C2×D4×C1111yescharacteristic
419C16—21no—
420C16—21no—
421C16—21no—
422C16—21no—
423C11#3367111yescharacteristic, direct product factor, Sylow
424C23—41no—
425C23—41no—
426C23C2×C11×D811yescharacteristic
427Q8—22no—
428Q8—41no—
429Q8—41no—
430Q8—41no—
431D4—22no—
432D4—44no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—82no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—44no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—82no—
451C2×C4C2×C11×D811yescharacteristic
452C2×C4C2×C11×D811yescharacteristic
453C2×C4C2×C11×D811yescharacteristic
454C2×C4C2×C11×D811yescharacteristic
455C2×C4C2×C11×D811yescharacteristic
456C2×C4C22×D4×C1111yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8C2×C11×#4111yescharacteristic
461C8C2×C11×#4111yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22C22×C11×D811yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—81no—
479C4—81no—
480C4—81no—
481C4—81no—
482C4—81no—
483C4C11×#52511yescharacteristic
484C4C11×#57511yescharacteristic
485C2—41no—
486C2—82no—
487C2—161no—
488C2C11×#310011yescharacteristic
489C2C11×#341411yescharacteristic
490C2C11×#341411yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
prime radicalC11×#2186C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3168C2semidirect
2. C4×C11×#135C2semidirect
3. C11×#2237C2semidirect
4. C11×#2234C2semidirect
5. C11×#2229C2semidirect
6. C11×#2228C2semidirect
7. C11×#2211C2semidirect
8. C11×#2210C2semidirect
9. C11×#2189C2semidirect
11. C11×#2177C2semidirect
12. C11×#2176C2semidirect
13. C11×#2175C2semidirect
14. C11×#2175C2semidirect
15. C11×#2163C2semidirect
116. #33671C11direct (N × H)
179. #3168C2×C11semidirect
180. C4×#135C2×C11semidirect
181. #2237C2×C11semidirect
182. #2234C2×C11semidirect
183. #2229C2×C11semidirect
184. #2228C2×C11semidirect
185. #2211C2×C11semidirect
186. #2210C2×C11semidirect
187. #2189C2×C11semidirect
189. #2177C2×C11semidirect
190. #2176C2×C11semidirect
191. #2175C2×C11semidirect
192. #2175C2×C11semidirect
193. #2163C2×C11semidirect
423. C11#33671direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31682
C4×C11×#1352
C11×#22372
C11×#22342
C11×#22292
C11×#22282
C11×#22112
C11×#22102
C11×#21892
C11×#21862
C11×#21772
C11×#21762
C11×#21752
C11×#21632
#3367111