Finite Group Databasebeta

← C11×#19155 #14596348

Subgroups — C11×#19155 #14596348

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3131C211yesmaximal, characteristic
2C11×#3104C211yesmaximal, characteristic, complemented
3C11×#3103C211yesmaximal, characteristic
4C2×C11×#446C211yesmaximal, characteristic, complemented
5C11×#1704C212yesmaximal, complemented
6C11×#1702C212yesmaximal, complemented
7C11×#1700C212yesmaximal, complemented
8C11×#1698C212yesmaximal, complemented
9C11×#1564C211yesmaximal, characteristic, complemented
10C11×#1542C211yesmaximal, characteristic, complemented
11C11×#1540C211yesmaximal, characteristic
12C11×#533C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C11×#488—21no—
16C11×#488—21no—
17C11×#487C2211yescharacteristic
18C11×#487C2211yescharacteristic
19C11×#486C2211yescharacteristic
20C11×#486C2211yescharacteristic
21C11×#484—21no—
22C11×#481—21no—
23C11×#477C2212yes—
24C11×#475C2212yes—
25C11×#462C2212yes—
26C11×#460C2212yes—
27C11×#451—21no—
28C11×#448—21no—
29C11×#446—21no—
30C11×#446—21no—
31C11×#446C2212yes—
32C11×#446C2212yes—
33C4×C11×Q16—22no—
34C4×C11×SD16—22no—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C2×C11×C4⋊C8—21no—
38C2×C11×C4⋊C8C2211yescharacteristic
39C11×#416—21no—
40C11×#416—21no—
41C2×C11×#97—21no—
42C2×C4×C8×C11C2211yescharacteristic
43C11×#335C2212yes—
44C11×#334C2212yes—
45C11×#333C2212yes—
46C11×#332C2212yes—
47C11×#332C2212yes—
48C11×#331C2212yes—
49C2×C11×#41—21no—
50C22×Q8×C11D411yescharacteristic
51C2×C11×Q16—22no—
52C2×C11×SD16—22no—
53C22×C8×C11—21no—
54C22×C8×C11D411yescharacteristic
55C22×C8×C11D411yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×C4⋊Q8C2311yescharacteristic
58C11×C4⋊Q8C2311yescharacteristic
59C11×#127C2311yescharacteristic
60C11×#125—21no—
61C11×#124—21no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—21no—
64C11×#121—21no—
65C11×#121—21no—
66C4×Q8×C11—21no—
67C4×Q8×C11—21no—
68C4×Q8×C11—21no—
69C4×Q8×C11—21no—
70C4×Q8×C11D412yes—
71C4×Q8×C11C2312yes—
72C4×D4×C11—21no—
73C4×D4×C11—21no—
74C11×#117—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C11×#107—22no—
80C11×#106—22no—
81C11×C4⋊C8—22no—
82C11×C4⋊C8—22no—
83C11×C4⋊C8—21no—
84C11×C4⋊C8C2312yes—
85C11×C4⋊C8C2312yes—
86C11×C4⋊C8C2312yes—
87C11×#103—22no—
88C11×#103—22no—
89C11×#103—21no—
90C11×#103—21no—
91C11×#103—21no—
92C11×#103—21no—
93C11×#103—22no—
94C11×#102—21no—
95C11×#102—21no—
96C11×#102—21no—
97C11×#102—21no—
98C11×#102—22no—
99C11×C22⋊C8—21no—
100C11×C22⋊C8—21no—
101C11×#97—22no—
102C11×#97—22no—
103C4×C8×C11—21no—
104C4×C8×C11—21no—
105C4×C8×C11D411yescharacteristic
106C4×C8×C11D411yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109#19155C1111yesmaximal, characteristic, direct product factor, Sylow
110C11×#41—42no—
111C11×#41—42no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—42no—
117C2×Q8×C11C2×D412yes—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—41no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—41no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11#4111yescharacteristic
128C11×Q16—44no—
129C11×SD16—44no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—42no—
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2×D411yescharacteristic
140C11×C4⋊C4—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4C2×D412yes—
152C11×C22⋊C4—41no—
153C11×C22⋊C4—41no—
154C11×C22⋊C4—41no—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11—41no—
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11#4111yescharacteristic
161C42×C11C2411yescharacteristic
162#3131C2×C1111yescharacteristic
163#3104C2×C1111yescharacteristic, complemented
164#3103C2×C1111yescharacteristic
165C2×#446C2×C1111yescharacteristic, complemented
166#1704C2×C1112yescomplemented
167#1702C2×C1112yescomplemented
168#1700C2×C1112yescomplemented
169#1698C2×C1112yescomplemented
170#1564C2×C1111yescharacteristic, complemented
171#1542C2×C1111yescharacteristic, complemented
172#1540C2×C1111yescharacteristic
173C23×C11—41no—
174C23×C11#12111yescharacteristic
175Q8×C11—22no—
176Q8×C11—22no—
177Q8×C11—42no—
178Q8×C11—41no—
179Q8×C11—41no—
180Q8×C11—42no—
181Q8×C11—81no—
182D4×C11—41no—
183D4×C11—41no—
184D4×C11—42no—
185D4×C11—81no—
186D4×C11—82no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—82no—
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#13512yes—
201C2×C4×C11#13712yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C8×C11—21no—
206C8×C11—21no—
207C8×C11—21no—
208C8×C11—21no—
209C8×C11—42no—
210C8×C11—42no—
211C8×C11—42no—
212#533C22×C1111yescharacteristic
213#532C22×C1111yescharacteristic
214C2×C4×Q8C22×C1111yescharacteristic
215#488—21no—
216#488—21no—
217#487C22×C1111yescharacteristic
218#487C22×C1111yescharacteristic
219#486C22×C1111yescharacteristic
220#486C22×C1111yescharacteristic
221#484—21no—
222#481—21no—
223#477C22×C1112yes—
224#475C22×C1112yes—
225#462C22×C1112yes—
226#460C22×C1112yes—
227#451—21no—
228#448—21no—
229#446—21no—
230#446—21no—
231#446C22×C1112yes—
232#446C22×C1112yes—
233C4×Q16—22no—
234C4×SD16—22no—
235#431C22×C1111yescharacteristic
236#431C22×C1111yescharacteristic
237C2×C4⋊C8—21no—
238C2×C4⋊C8C22×C1111yescharacteristic
239#416—21no—
240#416—21no—
241C2×#97—21no—
242C2×C4×C8C22×C1111yescharacteristic
243#335C22×C1112yes—
244#334C22×C1112yes—
245#333C22×C1112yes—
246#332C22×C1112yes—
247#332C22×C1112yes—
248#331C22×C1112yes—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—81no—
252C22×C11—81no—
253C22×C11—81no—
254C22×C11#46412yes—
255C22×C11C2×#12111yescharacteristic
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—81no—
262C4×C11—81no—
263C4×C11—81no—
264C4×C11#46412yes—
265C4×C11C2×#13511yescharacteristic
266C4×C11C2×#13711yescharacteristic
267C4×C11#57512yes—
268C2×#41—21no—
269C22×Q8D4×C1111yescharacteristic
270C2×Q16—22no—
271C2×SD16—22no—
272C22×C8—21no—
273C22×C8D4×C1111yescharacteristic
274C22×C8D4×C1111yescharacteristic
275C4⋊Q8C23×C1111yescharacteristic
276C4⋊Q8C23×C1111yescharacteristic
277C4⋊Q8C23×C1111yescharacteristic
278#127C23×C1111yescharacteristic
279#125—21no—
280#124—21no—
281C22⋊Q8—21no—
282C22⋊Q8—21no—
283#121—21no—
284#121—21no—
285C4×Q8—21no—
286C4×Q8—21no—
287C4×Q8—21no—
288C4×Q8—21no—
289C4×Q8D4×C1112yes—
290C4×Q8C23×C1112yes—
291C4×D4—21no—
292C4×D4—21no—
293#117—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4D4×C1111yescharacteristic
296C2×C42—21no—
297C2×C42C23×C1111yescharacteristic
298#107—22no—
299#106—22no—
300C4⋊C8—22no—
301C4⋊C8—22no—
302C4⋊C8—21no—
303C4⋊C8C23×C1112yes—
304C4⋊C8C23×C1112yes—
305C4⋊C8C23×C1112yes—
306#103—22no—
307#103—22no—
308#103—21no—
309#103—21no—
310#103—21no—
311#103—21no—
312#103—22no—
313#102—21no—
314#102—21no—
315#102—21no—
316#102—21no—
317#102—22no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320#97—22no—
321#97—22no—
322C4×C8—21no—
323C4×C8—21no—
324C4×C8D4×C1111yescharacteristic
325C4×C8D4×C1111yescharacteristic
326C4×C8C23×C1111yescharacteristic
327C4×C8C23×C1111yescharacteristic
328C2×C11—22no—
329C2×C11—161no—
330C2×C11C2×#46411yescharacteristic
331C2×C11#305411yescharacteristic
332C2×C11#306711yescharacteristic
333#41—42no—
334#41—42no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—42no—
340C2×Q8C2×D4×C1112yes—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—41no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—41no—
348C22×C4C2×D4×C1111yescharacteristic
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C11×#4111yescharacteristic
351Q16—44no—
352SD16—44no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—42no—
359C2×C8C2×D4×C1111yescharacteristic
360C2×C8C2×D4×C1111yescharacteristic
361C2×C8C2×D4×C1111yescharacteristic
362C2×C8C2×D4×C1111yescharacteristic
363C4⋊C4—22no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4C2×D4×C1112yes—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C42—22no—
379C42—22no—
380C42—41no—
381C42C2×D4×C1111yescharacteristic
382C42C2×D4×C1111yescharacteristic
383C42C11×#4111yescharacteristic
384C42C24×C1111yescharacteristic
385C11#1915511yescharacteristic, direct product factor, Sylow
386C23—41no—
387C23C11×#12111yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—42no—
391Q8—41no—
392Q8—41no—
393Q8—42no—
394Q8—81no—
395D4—41no—
396D4—41no—
397D4—42no—
398D4—81no—
399D4—82no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—82no—
410C2×C4C11×#12111yescharacteristic
411C2×C4C11×#12111yescharacteristic
412C2×C4C11×#12111yescharacteristic
413C2×C4C11×#13512yes—
414C2×C4C11×#13712yes—
415C2×C4C22×D4×C1111yescharacteristic
416C2×C4C22×D4×C1111yescharacteristic
417C2×C4C2×C11×#4111yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—21no—
422C8—42no—
423C8—42no—
424C8—42no—
425C22—21no—
426C22—21no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22C11×#46412yes—
431C22C2×C11×#12111yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—42no—
436C4—42no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4C11×#46412yes—
441C4C2×C11×#13511yescharacteristic
442C4C2×C11×#13711yescharacteristic
443C4C11×#57512yes—
444C2—22no—
445C2—161no—
446C2C2×C11×#46411yescharacteristic
447C2C11×#305411yescharacteristic
448C2C11×#306711yescharacteristic
subgroupG/H
centerC2×C4×C11#121
commutator, Frattini, cosocleC42C24×C11
socleC22×C11C2×#121
prime radicalC11×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3104C2semidirect
4. C2×C11×#446C2semidirect
5. C11×#1704C2semidirect
6. C11×#1702C2semidirect
7. C11×#1700C2semidirect
8. C11×#1698C2semidirect
9. C11×#1564C2semidirect
10. C11×#1542C2semidirect
109. #19155C11direct (N × H)
163. #3104C2×C11semidirect
165. C2×#446C2×C11semidirect
166. #1704C2×C11semidirect
167. #1702C2×C11semidirect
168. #1700C2×C11semidirect
169. #1698C2×C11semidirect
170. #1564C2×C11semidirect
171. #1542C2×C11semidirect
385. C11#19155direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31312
C11×#31042
C11×#31032
C2×C11×#4462
C11×#17042
C11×#17022
C11×#17002
C11×#16982
C11×#15642
C11×#15422
C11×#15402
#1915511