Finite Group Databasebeta

← C2×C11×#1638 #14595686

Subgroups — C2×C11×#1638 #14595686

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#556C211yesmaximal, characteristic
2C2×C11×#487C211yesmaximal, characteristic, complemented
3C2×C11×#477C211yesmaximal, characteristic, complemented
4C2×C11×#476C211yesmaximal, characteristic
5C11×#1638C218yesmaximal, direct product factor
6C2×C11×#332C211yesmaximal, characteristic, complemented
7C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×C11×D4⋊C8C211yesmaximal, characteristic
9C11×#556—22no—
10C11×#556—22no—
11C11×#556—22no—
12C11×#556C2214yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—22no—
16C2×C11×#124—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117—21no—
22C11×#487—22no—
23C11×#487C2214yescomplemented
24C11×#477—22no—
25C11×#477C2214yescomplemented
26C11×#476—22no—
27C11×#476C2214yes—
28C2×C11×#107—21no—
29C2×C11×#106—21no—
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×#103—21no—
33C2×C11×#103—22no—
34C2×C11×#102—21no—
35C2×C4×C8×C11C2211yescharacteristic
36C11×#332C2214yescomplemented
37C11×Q8⋊C8C2214yescomplemented
38C11×D4⋊C8C2214yes—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11D411yescharacteristic
42C22×D4×C11D411yescharacteristic
43C23×C4×C11—21no—
44C22×C8×C11—21no—
45C22×C8×C11—21no—
46C22×C8×C11—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8D412yes—
53C11×C4⋊Q8C2312yes—
54C11×C4⋊Q8C2312yes—
55C11×#126—28no—
56C11×#126—28no—
57C11×#124—24no—
58C11×#124—24no—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8—24no—
61C4×Q8×C11—24no—
62C4×Q8×C11—24no—
63C4×Q8×C11—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11D412yes—
66C4×Q8×C11C2312yes—
67C4×D4×C11—21no—
68C4×D4×C11—21no—
69C4×D4×C11D412yes—
70C4×D4×C11C2312yes—
71C11×#117—24no—
72C11×#117—24no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D412yes—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—21no—
84C2×C42×C11—22no—
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87C11×#107—24no—
88C11×#106—24no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8C2312yes—
92C11×C4⋊C8C2312yes—
93C11×#103—24no—
94C11×#103—28no—
95C11×#102—24no—
96C4×C8×C11—21no—
97C4×C8×C11C2312yes—
98C2×#1638C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—44no—
107C2×Q8×C11—41no—
108C2×Q8×C11—42no—
109C2×Q8×C11—42no—
110C2×Q8×C11C2×D412yes—
111C2×D4×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11C2×D412yes—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—42no—
131C2×C8×C11—42no—
132C2×C8×C11—42no—
133C11×C4⋊C4—28no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4C2×D414yes—
146C11×C4⋊C4C2×D412yes—
147C11×C4⋊C4C2×D412yes—
148C11×C22⋊C4—28no—
149C11×C22⋊C4—28no—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—22no—
152C42×C11—28no—
153C42×C11—22no—
154C42×C11—22no—
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11C2411yescharacteristic
159C2×#556C2×C1111yescharacteristic
160C2×#487C2×C1111yescharacteristic, complemented
161C2×#477C2×C1111yescharacteristic, complemented
162C2×#476C2×C1111yescharacteristic
163#1638C2×C1118yesdirect product factor
164C2×#332C2×C1111yescharacteristic, complemented
165C2×Q8⋊C8C2×C1111yescharacteristic, complemented
166C2×D4⋊C8C2×C1111yescharacteristic
167C23×C11—22no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11#12011yescharacteristic
172Q8×C11—22no—
173Q8×C11—22no—
174Q8×C11—44no—
175Q8×C11—42no—
176Q8×C11—42no—
177Q8×C11—42no—
178Q8×C11—44no—
179Q8×C11—82no—
180D4×C11—22no—
181D4×C11—22no—
182D4×C11—42no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—44no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—44no—
195C2×C4×C11—42no—
196C2×C4×C11—82no—
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11#12011yescharacteristic
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11#13512yes—
201C2×C4×C11#13512yes—
202C2×C4×C11#13712yes—
203C2×C4×C11#13712yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C8×C11—42no—
208C8×C11—42no—
209C8×C11—42no—
210#556—22no—
211#556—22no—
212#556—22no—
213#556C22×C1114yes—
214C2×C4⋊Q8C22×C1111yescharacteristic
215C2×C4⋊Q8C22×C1111yescharacteristic
216C2×#126—22no—
217C2×#124—21no—
218C2×C22⋊Q8—21no—
219C2×C4×Q8—21no—
220C2×C4×Q8C22×C1111yescharacteristic
221C2×C4×D4C22×C1111yescharacteristic
222C2×#117—21no—
223#487—22no—
224#487C22×C1114yescomplemented
225#477—22no—
226#477C22×C1114yescomplemented
227#476—22no—
228#476C22×C1114yes—
229C2×#107—21no—
230C2×#106—21no—
231C2×C4⋊C8C22×C1111yescharacteristic
232C2×C4⋊C8C22×C1111yescharacteristic
233C2×#103—21no—
234C2×#103—22no—
235C2×#102—21no—
236C2×C4×C8C22×C1111yescharacteristic
237#332C22×C1114yescomplemented
238Q8⋊C8C22×C1114yescomplemented
239D4⋊C8C22×C1114yes—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—42no—
243C22×C11—84no—
244C22×C11#45212yes—
245C22×C11#45212yes—
246C22×C11#45412yes—
247C22×C11C2×#12011yescharacteristic
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—42no—
251C4×C11—42no—
252C4×C11—44no—
253C4×C11—42no—
254C4×C11—82no—
255C4×C11#45212yes—
256C4×C11#45212yes—
257C4×C11C2×#13511yescharacteristic
258C4×C11C2×#13511yescharacteristic
259C4×C11C2×#13711yescharacteristic
260C4×C11C2×#13711yescharacteristic
261C22×Q8—21no—
262C22×Q8—21no—
263C22×Q8D4×C1111yescharacteristic
264C22×D4D4×C1111yescharacteristic
265C23×C4—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8—21no—
272C4⋊Q8—21no—
273C4⋊Q8—21no—
274C4⋊Q8D4×C1112yes—
275C4⋊Q8C23×C1112yes—
276C4⋊Q8C23×C1112yes—
277#126—28no—
278#126—28no—
279#124—24no—
280#124—24no—
281C22⋊Q8—24no—
282C22⋊Q8—24no—
283C4×Q8—24no—
284C4×Q8—24no—
285C4×Q8—21no—
286C4×Q8—21no—
287C4×Q8D4×C1112yes—
288C4×Q8C23×C1112yes—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4D4×C1112yes—
292C4×D4C23×C1112yes—
293#117—24no—
294#117—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4D4×C1111yescharacteristic
301C2×C4⋊C4D4×C1111yescharacteristic
302C2×C4⋊C4D4×C1112yes—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—21no—
306C2×C42—22no—
307C2×C42—21no—
308C2×C42C23×C1111yescharacteristic
309#107—24no—
310#106—24no—
311C4⋊C8—21no—
312C4⋊C8—21no—
313C4⋊C8C23×C1112yes—
314C4⋊C8C23×C1112yes—
315#103—24no—
316#103—28no—
317#102—24no—
318C4×C8—21no—
319C4×C8C23×C1112yes—
320C2×C11—82no—
321C2×C11#163814yesdirect product factor
322C2×C11C2×#45211yescharacteristic
323C2×C11C2×#45211yescharacteristic
324C2×C11C2×#45411yescharacteristic
325C24—21no—
326C2×Q8—21no—
327C2×Q8—22no—
328C2×Q8—22no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—44no—
333C2×Q8—41no—
334C2×Q8—42no—
335C2×Q8—42no—
336C2×Q8C2×D4×C1112yes—
337C2×D4—21no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4C2×D4×C1112yes—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—41no—
350C22×C4C2×D4×C1111yescharacteristic
351C22×C4C2×D4×C1111yescharacteristic
352C22×C4C2×D4×C1111yescharacteristic
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—42no—
357C2×C8—42no—
358C2×C8—42no—
359C4⋊C4—28no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4C2×D4×C1114yes—
372C4⋊C4C2×D4×C1112yes—
373C4⋊C4C2×D4×C1112yes—
374C22⋊C4—28no—
375C22⋊C4—28no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C42—28no—
379C42—22no—
380C42—22no—
381C42C2×D4×C1111yescharacteristic
382C42C2×D4×C1111yescharacteristic
383C42C2×D4×C1111yescharacteristic
384C42C24×C1111yescharacteristic
385C11C2×#163811yescharacteristic, direct product factor, Sylow
386C23—22no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23C11×#12011yescharacteristic
391Q8—22no—
392Q8—22no—
393Q8—44no—
394Q8—42no—
395Q8—42no—
396Q8—42no—
397Q8—44no—
398Q8—82no—
399D4—22no—
400D4—22no—
401D4—42no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—82no—
416C2×C4C11×#12011yescharacteristic
417C2×C4C11×#12011yescharacteristic
418C2×C4C11×#12011yescharacteristic
419C2×C4C11×#13512yes—
420C2×C4C11×#13512yes—
421C2×C4C11×#13712yes—
422C2×C4C11×#13712yes—
423C2×C4C22×D4×C1111yescharacteristic
424C2×C4C22×D4×C1111yescharacteristic
425C2×C4C22×D4×C1111yescharacteristic
426C8—42no—
427C8—42no—
428C8—42no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—84no—
433C22C11×#45212yes—
434C22C11×#45212yes—
435C22C11×#45412yes—
436C22C2×C11×#12011yescharacteristic
437C4—21no—
438C4—21no—
439C4—42no—
440C4—42no—
441C4—44no—
442C4—42no—
443C4—82no—
444C4C11×#45212yes—
445C4C11×#45212yes—
446C4C2×C11×#13511yescharacteristic
447C4C2×C11×#13511yescharacteristic
448C4C2×C11×#13711yescharacteristic
449C4C2×C11×#13711yescharacteristic
450C2—82no—
451C2C11×#163814yesdirect product factor
452C2C2×C11×#45211yescharacteristic
453C2C2×C11×#45211yescharacteristic
454C2C2×C11×#45411yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#487C2semidirect
3. C2×C11×#477C2semidirect
5. C11×#1638C2direct (N × H)
6. C2×C11×#332C2semidirect
7. C2×C11×Q8⋊C8C2semidirect
23. C11×#487C22semidirect
25. C11×#477C22semidirect
36. C11×#332C22semidirect
37. C11×Q8⋊C8C22semidirect
98. C2×#1638C11direct (N × H)
160. C2×#487C2×C11semidirect
161. C2×#477C2×C11semidirect
163. #1638C2×C11direct (N × H)
164. C2×#332C2×C11semidirect
165. C2×Q8⋊C8C2×C11semidirect
224. #487C22×C11semidirect
226. #477C22×C11semidirect
237. #332C22×C11semidirect
238. Q8⋊C8C22×C11semidirect
321. C2×C11#1638direct (N × H)
385. C11C2×#1638direct (N × H)
451. C2C11×#1638direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5562
C2×C11×#4872
C2×C11×#4772
C2×C11×#4762
C11×#16382
C2×C11×#3322
C2×C11×Q8⋊C82
C2×C11×D4⋊C82
C2×#163811