Finite Group Databasebeta

← C11×#18197 #14595390

Subgroups — C11×#18197 #14595390

Order 2816.

1174 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×#3501C211yesmaximal, characteristic
2C2×C11×#451C212yesmaximal, complemented
3C11×#2409C211yesmaximal, characteristic
4C11×#1605C214yesmaximal, complemented
5C11×#1602C214yesmaximal, complemented
6C11×#1520C212yesmaximal, complemented
7C11×#1459C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C22×C11×Q16—22no—
10C11×#554—24no—
11C11×#554—22no—
12D4×Q8×C11—22no—
13C11×#544C2212yes—
14C11×#543—21no—
15C11×#543C2212yes—
16C11×#533—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2212yes—
20C11×#518—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C11×#451—24no—
23C11×#451C2218yes—
24C2×C11×#103—22no—
25C2×C11×C22⋊C8C2212yes—
26C11×#395C2212yes—
27C11×#393C2212yes—
28C11×#391—21no—
29C11×#386—21no—
30C11×#385—21no—
31C11×#380C2211yescharacteristic
32C11×#328C2218yes—
33C11×#324C2212yes—
34C11×#323C2212yes—
35C22×Q8×C11—21no—
36C22×Q8×C11—21no—
37C22×Q8×C11—22no—
38C22×Q8×C11—22no—
39C22×Q8×C11—44no—
40C22×Q8×C11D412yes—
41C22×Q8×C11C2312yes—
42C22×D4×C11D411yescharacteristic
43C23×C4×C11—21no—
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C2×C11×Q16—28no—
47C2×C11×Q16—48no—
48C22×C8×C11—22no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—24no—
52C11×#125—22no—
53C11×#125—24no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8—24no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—44no—
65C11×C22⋊Q8D414yes—
66C11×C22⋊Q8C2314yes—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×D4×C11—24no—
70C4×D4×C11—24no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C11×#117—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4D412yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C11×C22⋊C4C2311yescharacteristic
87C2×C42×C11D411yescharacteristic
88C11×#103—28no—
89C11×C22⋊C8—22no—
90C11×C22⋊C8C2314yes—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95C2312yes—
94#18197C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11C2×D411yescharacteristic
96C24×C11C2×D411yescharacteristic
97C2×Q8×C11—24no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11—28no—
102C2×Q8×C11—24no—
103C2×Q8×C11—44no—
104C2×Q8×C11—42no—
105C2×Q8×C11—44no—
106C2×Q8×C11—44no—
107C2×Q8×C11—48no—
108C2×Q8×C11—41no—
109C2×Q8×C11—41no—
110C2×Q8×C11—82no—
111C2×Q8×C11C2×D414yes—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11Q1614yescomplemented
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—42no—
124C22×C4×C11—44no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2411yescharacteristic
134C11×Q16—416no—
135C2×C8×C11—24no—
136C2×C8×C11—44no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—44no—
149C11×C4⋊C4C2×D414yes—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—44no—
156C11×C22⋊C4—42no—
157C42×C11—24no—
158C42×C11—21no—
159C42×C11—21no—
160#3501C2×C1111yescharacteristic
161C2×#451C2×C1112yescomplemented
162#2409C2×C1111yescharacteristic
163#1605C2×C1114yescomplemented
164#1602C2×C1114yescomplemented
165#1520C2×C1112yescomplemented
166#1459C2×C1111yescharacteristic
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11#12012yes—
174C23×C11C2×Q1612yes—
175C23×C11C2×Q1612yescomplemented
176C23×C11#13712yes—
177C23×C11C22×D411yescharacteristic
178Q8×C11—28no—
179Q8×C11—44no—
180Q8×C11—44no—
181Q8×C11—44no—
182Q8×C11—44no—
183Q8×C11—44no—
184Q8×C11—82no—
185Q8×C11—82no—
186D4×C11—28no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—21no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—21no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—48no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—81no—
208C2×C4×C11—82no—
209C2×C4×C11—82no—
210C2×C4×C11—82no—
211C2×C4×C11—82no—
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11C2×Q1612yescomplemented
215C2×C4×C11C22×D412yes—
216C8×C11—44no—
217C23×Q8C22×C1111yescharacteristic
218C22×Q16—22no—
219#554—24no—
220#554—22no—
221D4×Q8—22no—
222#544C22×C1112yes—
223#543—21no—
224#543C22×C1112yes—
225#533—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C22×C1112yes—
229#518—21no—
230C2×C4×D4C22×C1111yescharacteristic
231#451—24no—
232#451C22×C1118yes—
233C2×#103—22no—
234C2×C22⋊C8C22×C1112yes—
235#395C22×C1112yes—
236#393C22×C1112yes—
237#391—21no—
238#386—21no—
239#385—21no—
240#380C22×C1111yescharacteristic
241#328C22×C1118yes—
242#324C22×C1112yes—
243#323C22×C1112yes—
244C22×C11—21no—
245C22×C11—22no—
246C22×C11—21no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—42no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—41no—
253C22×C11—41no—
254C22×C11—81no—
255C22×C11#45114yes—
256C22×C11C2×#12011yescharacteristic
257C22×C11C22×Q1611yescharacteristic
258C22×C11C2×#13711yescharacteristic
259C4×C11—22no—
260C4×C11—21no—
261C4×C11—22no—
262C4×C11—41no—
263C4×C11—44no—
264C4×C11—44no—
265C4×C11—41no—
266C4×C11—44no—
267C4×C11—82no—
268C4×C11B(4,𝔽2)12yes—
269C22×Q8—21no—
270C22×Q8—21no—
271C22×Q8—22no—
272C22×Q8—22no—
273C22×Q8—44no—
274C22×Q8D4×C1112yes—
275C22×Q8C23×C1112yes—
276C22×D4D4×C1111yescharacteristic
277C23×C4—21no—
278C23×C4D4×C1111yescharacteristic
279C23×C4C23×C1111yescharacteristic
280C2×Q16—28no—
281C2×Q16—48no—
282C22×C8—22no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—24no—
286#125—22no—
287#125—24no—
288C22⋊Q8—22no—
289C22⋊Q8—22no—
290C22⋊Q8—24no—
291C22⋊Q8—24no—
292C22⋊Q8—24no—
293C22⋊Q8—22no—
294C22⋊Q8—22no—
295C22⋊Q8—22no—
296C22⋊Q8—22no—
297C22⋊Q8—24no—
298C22⋊Q8—44no—
299C22⋊Q8D4×C1114yes—
300C22⋊Q8C23×C1114yes—
301C4×Q8—22no—
302C4×Q8—22no—
303C4×D4—24no—
304C4×D4—24no—
305C4×D4—22no—
306C4×D4—22no—
307#117—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4D4×C1112yes—
314C2×C4⋊C4C23×C1111yescharacteristic
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4D4×C1111yescharacteristic
320C2×C22⋊C4C23×C1111yescharacteristic
321C2×C42D4×C1111yescharacteristic
322#103—28no—
323C22⋊C8—22no—
324C22⋊C8C23×C1114yes—
325#95—22no—
326#95—22no—
327#95C23×C1112yes—
328C2×C11—21no—
329C2×C11—21no—
330C2×C11—24no—
331C2×C11—42no—
332C2×C11C2×#45111yescharacteristic
333C2×C11#302211yescharacteristic
334C2×C11C2×B(4,𝔽2)11yescharacteristic
335C24C2×D4×C1111yescharacteristic
336C24C2×D4×C1111yescharacteristic
337C2×Q8—24no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—28no—
342C2×Q8—24no—
343C2×Q8—44no—
344C2×Q8—42no—
345C2×Q8—44no—
346C2×Q8—44no—
347C2×Q8—48no—
348C2×Q8—41no—
349C2×Q8—41no—
350C2×Q8—82no—
351C2×Q8C2×D4×C1114yes—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4C11×Q1614yescomplemented
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—42no—
364C22×C4—44no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4C2×D4×C1111yescharacteristic
368C22×C4C2×D4×C1112yes—
369C22×C4C2×D4×C1111yescharacteristic
370C22×C4C2×D4×C1111yescharacteristic
371C22×C4C2×D4×C1111yescharacteristic
372C22×C4C2×D4×C1112yes—
373C22×C4C24×C1111yescharacteristic
374Q16—416no—
375C2×C8—24no—
376C2×C8—44no—
377C4⋊C4—22no—
378C4⋊C4—24no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—24no—
382C4⋊C4—22no—
383C4⋊C4—24no—
384C4⋊C4—22no—
385C4⋊C4—24no—
386C4⋊C4—22no—
387C4⋊C4—42no—
388C4⋊C4—44no—
389C4⋊C4C2×D4×C1114yes—
390C22⋊C4—24no—
391C22⋊C4—24no—
392C22⋊C4—22no—
393C22⋊C4—24no—
394C22⋊C4—22no—
395C22⋊C4—44no—
396C22⋊C4—42no—
397C42—24no—
398C42—21no—
399C42—21no—
400C11#1819711yescharacteristic, direct product factor, Sylow
401C23—21no—
402C23—21no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23C11×#12012yes—
408C23C2×C11×Q1612yes—
409C23C2×C11×Q1612yescomplemented
410C23C11×#13712yes—
411C23C22×D4×C1111yescharacteristic
412Q8—28no—
413Q8—44no—
414Q8—44no—
415Q8—44no—
416Q8—44no—
417Q8—44no—
418Q8—82no—
419Q8—82no—
420D4—28no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—21no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—21no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—48no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—81no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4C11×#12011yescharacteristic
447C2×C4C11×#12011yescharacteristic
448C2×C4C2×C11×Q1612yescomplemented
449C2×C4C22×D4×C1112yes—
450C8—44no—
451C22—21no—
452C22—22no—
453C22—21no—
454C22—22no—
455C22—22no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—41no—
460C22—41no—
461C22—81no—
462C22C11×#45114yes—
463C22C2×C11×#12011yescharacteristic
464C22C22×C11×Q1611yescharacteristic
465C22C2×C11×#13711yescharacteristic
466C4—22no—
467C4—22no—
468C4—21no—
469C4—41no—
470C4—44no—
471C4—44no—
472C4—41no—
473C4—44no—
474C4—82no—
475C4C11×B(4,𝔽2)12yes—
476C2—21no—
477C2—21no—
478C2—24no—
479C2—42no—
480C2C2×C11×#45111yescharacteristic
481C2C11×#302211yescharacteristic
482C2C2×C11×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#451C2semidirect
4. C11×#1605C2semidirect
5. C11×#1602C2semidirect
6. C11×#1520C2semidirect
94. #18197C11direct (N × H)
114. C2×D4×C11Q16semidirect
161. C2×#451C2×C11semidirect
163. #1605C2×C11semidirect
164. #1602C2×C11semidirect
165. #1520C2×C11semidirect
175. C23×C11C2×Q16semidirect
214. C2×C4×C11C2×Q16semidirect
354. C2×D4C11×Q16semidirect
400. C11#18197direct (N × H)
409. C23C2×C11×Q16semidirect
448. C2×C4C2×C11×Q16semidirect

Maximal subgroups

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

subgroupindex
C11×#35012
C2×C11×#4512
C11×#24092
C11×#16052
C11×#16022
C11×#15202
C11×#14592
#1819711