Finite Group Databasebeta

← C11×#19176 #14596369

Subgroups — C11×#19176 #14596369

Order 2816.

618 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3141C211yesmaximal, characteristic
2C11×#3103C211yesmaximal, characteristic
3C2×C11×#477C211yesmaximal, characteristic, complemented
4Q8×C11×M16C211yesmaximal, characteristic, complemented
5C11×#1704C212yesmaximal, complemented
6C11×#1698C212yesmaximal, complemented
7C11×#1684C212yesmaximal, complemented
8C11×#1678C212yesmaximal, complemented
9C11×#1565C211yesmaximal, characteristic, complemented
10C11×#1548C211yesmaximal, characteristic, complemented
11C11×#1547C211yesmaximal, characteristic
12C11×#532C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C11×#489—22no—
16C11×#487C2212yes—
17C11×#486C2212yes—
18C11×#481—21no—
19C11×#477—21no—
20C11×#477—21no—
21C11×#477C2212yes—
22C11×#477C2212yes—
23C11×#475C2211yescharacteristic
24C11×#475C2211yescharacteristic
25C11×#460C2211yescharacteristic
26C11×#460C2211yescharacteristic
27C11×#448—21no—
28C11×#446—22no—
29C11×#446C2212yes—
30C8×Q8×C11C2212yes—
31C4×C11×SD16—21no—
32C4×C11×SD16—21no—
33C11×#431C2211yescharacteristic
34C2×C11×#107—21no—
35C11×#423—21no—
36C11×#423C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C11×#417—21no—
39C11×#417—21no—
40C2×C11×#103—21no—
41C4×C11×M16—21no—
42C4×C11×M16C2211yescharacteristic
43C11×#335C2212yes—
44C11×#334C2212yes—
45C11×#333C2212yes—
46C11×#333C2212yes—
47C11×#332C2212yes—
48C11×#331C2212yes—
49C2×C11×#41—21no—
50C22×Q8×C11—21no—
51C22×Q8×C11D411yescharacteristic
52C2×C11×SD16—21no—
53C2×C11×SD16—21no—
54C2×C11×M16—21no—
55C2×C11×M16D411yescharacteristic
56C2×C11×M16D411yescharacteristic
57C22×C8×C11—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8C2311yescharacteristic
62C11×C4⋊Q8C2312yes—
63C11×#127C2311yescharacteristic
64C11×#124—21no—
65C11×#121—21no—
66C11×#121—21no—
67C4×Q8×C11—21no—
68C4×Q8×C11—21no—
69C4×Q8×C11D411yescharacteristic
70C4×Q8×C11D411yescharacteristic
71C4×Q8×C11C2311yescharacteristic
72C4×Q8×C11C2311yescharacteristic
73C4×D4×C11—21no—
74C4×D4×C11—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C11×#107—22no—
82C11×#107—22no—
83C11×#106—21no—
84C11×#106—21no—
85C11×C4⋊C8—22no—
86C11×C4⋊C8—22no—
87C11×C4⋊C8—21no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8C2312yes—
90C11×C4⋊C8C2312yes—
91C11×C4⋊C8C2311yescharacteristic
92C11×C4⋊C8C2311yescharacteristic
93C11×#103—22no—
94C11×#103—22no—
95C11×#103—21no—
96C11×#103—21no—
97C11×#103—22no—
98C11×#103—22no—
99C11×#102—22no—
100C11×#102—22no—
101C11×#102—21no—
102C11×#102—21no—
103C11×C22⋊C8—21no—
104C11×#97—22no—
105C11×#97D412yes—
106C4×C8×C11—22no—
107C4×C8×C11—21no—
108C4×C8×C11C2312yes—
109#19176C1111yesmaximal, characteristic, direct product factor, Sylow
110C11×#41—42no—
111C11×#41—42no—
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—41no—
117C2×Q8×C11—41no—
118C2×Q8×C11—82no—
119C2×Q8×C11C2×D411yescharacteristic
120C2×Q8×C11C2×D411yescharacteristic
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—41no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11#4111yescharacteristic
132C11×SD16—42no—
133C11×SD16—42no—
134C11×M16—22no—
135C11×M16—22no—
136C11×M16—42no—
137C2×C8×C11—22no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—22no—
141C2×C8×C11—42no—
142C2×C8×C11C2×D412yes—
143C2×C8×C11C2×D412yes—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4C2×D411yescharacteristic
156C11×C4⋊C4C2×D411yescharacteristic
157C11×C22⋊C4—41no—
158C11×C22⋊C4—41no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11C2×D411yescharacteristic
164C42×C11C2×D411yescharacteristic
165C42×C11#4111yescharacteristic
166C42×C11C2411yescharacteristic
167#3141C2×C1111yescharacteristic
168#3103C2×C1111yescharacteristic
169C2×#477C2×C1111yescharacteristic, complemented
170Q8×M16C2×C1111yescharacteristic, complemented
171#1704C2×C1112yescomplemented
172#1698C2×C1112yescomplemented
173#1684C2×C1112yescomplemented
174#1678C2×C1112yescomplemented
175#1565C2×C1111yescharacteristic, complemented
176#1548C2×C1111yescharacteristic, complemented
177#1547C2×C1111yescharacteristic
178C23×C11—41no—
179C23×C11#12111yescharacteristic
180Q8×C11—21no—
181Q8×C11—21no—
182Q8×C11—21no—
183Q8×C11—42no—
184Q8×C11—41no—
185Q8×C11—41no—
186Q8×C11—82no—
187Q8×C11—82no—
188Q8×C11#13712yes—
189D4×C11—41no—
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—41no—
193D4×C11—81no—
194D4×C11—82no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—81no—
206C2×C4×C11—82no—
207C2×C4×C11—82no—
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11#13512yes—
212C2×C4×C11#13712yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C8×C11—22no—
217C8×C11—22no—
218C8×C11—42no—
219C8×C11—41no—
220C8×C11—42no—
221C8×C11—41no—
222#532C22×C1111yescharacteristic
223C2×C4⋊Q8C22×C1111yescharacteristic
224C2×C4×Q8C22×C1111yescharacteristic
225#489—22no—
226#487C22×C1112yes—
227#486C22×C1112yes—
228#481—21no—
229#477—21no—
230#477—21no—
231#477C22×C1112yes—
232#477C22×C1112yes—
233#475C22×C1111yescharacteristic
234#475C22×C1111yescharacteristic
235#460C22×C1111yescharacteristic
236#460C22×C1111yescharacteristic
237#448—21no—
238#446—22no—
239#446C22×C1112yes—
240C8×Q8C22×C1112yes—
241C4×SD16—21no—
242C4×SD16—21no—
243#431C22×C1111yescharacteristic
244C2×#107—21no—
245#423—21no—
246#423C22×C1111yescharacteristic
247C2×C4⋊C8C22×C1111yescharacteristic
248#417—21no—
249#417—21no—
250C2×#103—21no—
251C4×M16—21no—
252C4×M16C22×C1111yescharacteristic
253#335C22×C1112yes—
254#334C22×C1112yes—
255#333C22×C1112yes—
256#333C22×C1112yes—
257#332C22×C1112yes—
258#331C22×C1112yes—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11#46412yes—
265C22×C11C2×#12111yescharacteristic
266C4×C11—21no—
267C4×C11—22no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—41no—
271C4×C11—41no—
272C4×C11—41no—
273C4×C11—81no—
274C4×C11—82no—
275C4×C11#46412yes—
276C4×C11C2×#13511yescharacteristic
277C4×C11C2×#13711yescharacteristic
278C4×C11C2×#13711yescharacteristic
279C4×C11#57511yescharacteristic
280C2×#41—21no—
281C22×Q8—21no—
282C22×Q8D4×C1111yescharacteristic
283C2×SD16—21no—
284C2×SD16—21no—
285C2×M16—21no—
286C2×M16D4×C1111yescharacteristic
287C2×M16D4×C1111yescharacteristic
288C22×C8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8C23×C1112yes—
293C4⋊Q8C23×C1111yescharacteristic
294#127C23×C1111yescharacteristic
295#124—21no—
296#121—21no—
297#121—21no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×Q8D4×C1111yescharacteristic
301C4×Q8D4×C1111yescharacteristic
302C4×Q8C23×C1111yescharacteristic
303C4×Q8C23×C1111yescharacteristic
304C4×D4—21no—
305C4×D4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4D4×C1111yescharacteristic
310C2×C42—21no—
311C2×C42C23×C1111yescharacteristic
312#107—22no—
313#107—22no—
314#106—21no—
315#106—21no—
316C4⋊C8—22no—
317C4⋊C8—22no—
318C4⋊C8—21no—
319C4⋊C8—21no—
320C4⋊C8C23×C1112yes—
321C4⋊C8C23×C1112yes—
322C4⋊C8C23×C1111yescharacteristic
323C4⋊C8C23×C1111yescharacteristic
324#103—22no—
325#103—22no—
326#103—21no—
327#103—21no—
328#103—22no—
329#103—22no—
330#102—22no—
331#102—22no—
332#102—21no—
333#102—21no—
334C22⋊C8—21no—
335#97—22no—
336#97D4×C1112yes—
337C4×C8—22no—
338C4×C8—21no—
339C4×C8C23×C1112yes—
340C2×C11—22no—
341C2×C11—161no—
342C2×C11C2×#46411yescharacteristic
343C2×C11#305611yescharacteristic
344C2×C11#306811yescharacteristic
345#41—42no—
346#41—42no—
347C2×Q8—21no—
348C2×Q8—22no—
349C2×Q8—21no—
350C2×Q8—22no—
351C2×Q8—41no—
352C2×Q8—41no—
353C2×Q8—82no—
354C2×Q8C2×D4×C1111yescharacteristic
355C2×Q8C2×D4×C1111yescharacteristic
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—41no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4C2×D4×C1111yescharacteristic
365C22×C4C2×D4×C1111yescharacteristic
366C22×C4C11×#4111yescharacteristic
367SD16—42no—
368SD16—42no—
369M16—22no—
370M16—22no—
371M16—42no—
372C2×C8—22no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—22no—
376C2×C8—42no—
377C2×C8C2×D4×C1112yes—
378C2×C8C2×D4×C1112yes—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4C2×D4×C1111yescharacteristic
391C4⋊C4C2×D4×C1111yescharacteristic
392C22⋊C4—41no—
393C22⋊C4—41no—
394C42—21no—
395C42—21no—
396C42—21no—
397C42—21no—
398C42C2×D4×C1111yescharacteristic
399C42C2×D4×C1111yescharacteristic
400C42C11×#4111yescharacteristic
401C42C24×C1111yescharacteristic
402C11#1917611yescharacteristic, direct product factor, Sylow
403C23—41no—
404C23C11×#12111yescharacteristic
405Q8—21no—
406Q8—21no—
407Q8—21no—
408Q8—42no—
409Q8—41no—
410Q8—41no—
411Q8—82no—
412Q8—82no—
413Q8C11×#13712yes—
414D4—41no—
415D4—41no—
416D4—41no—
417D4—41no—
418D4—81no—
419D4—82no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—81no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4C11×#12111yescharacteristic
434C2×C4C11×#12111yescharacteristic
435C2×C4C11×#12111yescharacteristic
436C2×C4C11×#13512yes—
437C2×C4C11×#13712yes—
438C2×C4C22×D4×C1111yescharacteristic
439C2×C4C22×D4×C1111yescharacteristic
440C2×C4C2×C11×#4111yescharacteristic
441C8—22no—
442C8—22no—
443C8—42no—
444C8—41no—
445C8—42no—
446C8—41no—
447C22—21no—
448C22—21no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22C11×#46412yes—
453C22C2×C11×#12111yescharacteristic
454C4—21no—
455C4—22no—
456C4—21no—
457C4—21no—
458C4—41no—
459C4—41no—
460C4—41no—
461C4—81no—
462C4—82no—
463C4C11×#46412yes—
464C4C2×C11×#13511yescharacteristic
465C4C2×C11×#13711yescharacteristic
466C4C2×C11×#13711yescharacteristic
467C4C11×#57511yescharacteristic
468C2—22no—
469C2—161no—
470C2C2×C11×#46411yescharacteristic
471C2C11×#305611yescharacteristic
472C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#477C2semidirect
4. Q8×C11×M16C2semidirect
5. C11×#1704C2semidirect
6. C11×#1698C2semidirect
7. C11×#1684C2semidirect
8. C11×#1678C2semidirect
9. C11×#1565C2semidirect
10. C11×#1548C2semidirect
109. #19176C11direct (N × H)
169. C2×#477C2×C11semidirect
170. Q8×M16C2×C11semidirect
171. #1704C2×C11semidirect
172. #1698C2×C11semidirect
173. #1684C2×C11semidirect
174. #1678C2×C11semidirect
175. #1565C2×C11semidirect
176. #1548C2×C11semidirect
402. C11#19176direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31412
C11×#31032
C2×C11×#4772
Q8×C11×M162
C11×#17042
C11×#16982
C11×#16842
C11×#16782
C11×#15652
C11×#15482
C11×#15472
#1917611