Finite Group Databasebeta

← C2×C11×#1653 #14595693

Subgroups — C2×C11×#1653 #14595693

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#557C211yesmaximal, characteristic
2C2×C11×#498C211yesmaximal, characteristic
3C2×C11×#475C211yesmaximal, characteristic
4C2×C11×#462C211yesmaximal, characteristic
5C11×#1653C218yesmaximal, direct product factor
6C2×C11×#332C211yesmaximal, characteristic
7C2×C11×Q8⋊C8C211yesmaximal, characteristic
8C2×C11×Q8⋊C8C211yesmaximal, characteristic
9C22×C11×Q16—21no—
10C11×#557—22no—
11C11×#557—22no—
12C11×#557—22no—
13C11×#557C2214yes—
14C2×C11×C4⋊Q8—21no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125—22no—
18C2×C11×#125—21no—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C11×#498—22no—
24C11×#498C2214yes—
25C11×#475—22no—
26C11×#475C2214yes—
27C11×#462—22no—
28C11×#462C2214yes—
29C2×C11×#106—22no—
30C2×C11×#106—21no—
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×C11×#103—21no—
34C2×C11×#103—21no—
35C2×C4×C8×C11C2211yescharacteristic
36C11×#332C2214yes—
37C11×Q8⋊C8C2214yes—
38C11×Q8⋊C8C2214yes—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11D411yescharacteristic
42C22×Q8×C11D411yescharacteristic
43C2×C11×Q16—24no—
44C2×C11×Q16—44no—
45C22×C8×C11—21no—
46C22×C8×C11—21no—
47C22×C8×C11—21no—
48C11×C4⋊Q8—24no—
49C11×C4⋊Q8—24no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8D412yes—
56C11×C4⋊Q8C2312yes—
57C11×C4⋊Q8C2312yes—
58C11×#125—28no—
59C11×#125—24no—
60C11×#125—28no—
61C11×#125—24no—
62C4×Q8×C11—24no—
63C4×Q8×C11—24no—
64C4×Q8×C11—24no—
65C4×Q8×C11—24no—
66C4×Q8×C11—21no—
67C4×Q8×C11—21no—
68C4×Q8×C11—21no—
69C4×Q8×C11—21no—
70C4×Q8×C11D412yes—
71C4×Q8×C11D412yes—
72C4×Q8×C11C2312yes—
73C4×Q8×C11C2312yes—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4D412yes—
85C2×C42×C11—22no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C11×#106—28no—
90C11×#106—24no—
91C11×C4⋊C8—21no—
92C11×C4⋊C8—21no—
93C11×C4⋊C8C2312yes—
94C11×C4⋊C8C2312yes—
95C11×#103—24no—
96C11×#103—24no—
97C4×C8×C11—21no—
98C4×C8×C11C2312yes—
99C2×#1653C1111yesmaximal, characteristic, direct product factor, Sylow
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—41no—
109C2×Q8×C11—42no—
110C2×Q8×C11—42no—
111C2×Q8×C11—42no—
112C2×Q8×C11—42no—
113C2×Q8×C11SD1614yes—
114C2×Q8×C11C2×D412yes—
115C2×Q8×C11C2×D412yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—41no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C11×Q16—48no—
126C2×C8×C11—24no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—42no—
131C2×C8×C11—42no—
132C11×C4⋊C4—28no—
133C11×C4⋊C4—28no—
134C11×C4⋊C4—28no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4—41no—
148C11×C4⋊C4C2×D412yes—
149C11×C4⋊C4C2×D412yes—
150C11×C4⋊C4C2×D414yes—
151C42×C11—28no—
152C42×C11—22no—
153C42×C11—22no—
154C42×C11—22no—
155C42×C11—22no—
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11C2411yescharacteristic
160C2×#557C2×C1111yescharacteristic
161C2×#498C2×C1111yescharacteristic
162C2×#475C2×C1111yescharacteristic
163C2×#462C2×C1111yescharacteristic
164#1653C2×C1118yesdirect product factor
165C2×#332C2×C1111yescharacteristic
166C2×Q8⋊C8C2×C1111yescharacteristic
167C2×Q8⋊C8C2×C1111yescharacteristic
168C23×C11#12011yescharacteristic
169Q8×C11—22no—
170Q8×C11—24no—
171Q8×C11—22no—
172Q8×C11—22no—
173Q8×C11—42no—
174Q8×C11—42no—
175Q8×C11—42no—
176Q8×C11—44no—
177Q8×C11—42no—
178Q8×C11—42no—
179Q8×C11—82no—
180Q8×C11C2×SD1614yes—
181C2×C4×C11—22no—
182C2×C4×C11—24no—
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—44no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—82no—
194C2×C4×C11#12011yescharacteristic
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11#12011yescharacteristic
197C2×C4×C11C2×SD1612yes—
198C2×C4×C11#13512yes—
199C2×C4×C11#13712yes—
200C2×C4×C11#13712yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C8×C11—24no—
205C8×C11—42no—
206C8×C11—42no—
207C22×Q16—21no—
208#557—22no—
209#557—22no—
210#557—22no—
211#557C22×C1114yes—
212C2×C4⋊Q8—21no—
213C2×C4⋊Q8C22×C1111yescharacteristic
214C2×C4⋊Q8C22×C1111yescharacteristic
215C2×#125—22no—
216C2×#125—21no—
217C2×C4×Q8—21no—
218C2×C4×Q8—21no—
219C2×C4×Q8C22×C1111yescharacteristic
220C2×C4×Q8C22×C1111yescharacteristic
221#498—22no—
222#498C22×C1114yes—
223#475—22no—
224#475C22×C1114yes—
225#462—22no—
226#462C22×C1114yes—
227C2×#106—21no—
228C2×#106—22no—
229C2×C4⋊C8C22×C1111yescharacteristic
230C2×C4⋊C8C22×C1111yescharacteristic
231C2×#103—21no—
232C2×#103—21no—
233C2×C4×C8C22×C1111yescharacteristic
234#332C22×C1114yes—
235Q8⋊C8C22×C1114yes—
236Q8⋊C8C22×C1114yes—
237C22×C11#44812yes—
238C22×C11#45212yes—
239C22×C11#45612yes—
240C22×C11C2×#12011yescharacteristic
241C4×C11—24no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—42no—
245C4×C11—44no—
246C4×C11—42no—
247C4×C11—42no—
248C4×C11—82no—
249C4×C11#44812yes—
250C4×C11#45212yes—
251C4×C11C22×SD1611yescharacteristic
252C4×C11C2×#13511yescharacteristic
253C4×C11C2×#13711yescharacteristic
254C4×C11C2×#13711yescharacteristic
255C22×Q8—21no—
256C22×Q8—21no—
257C22×Q8D4×C1111yescharacteristic
258C22×Q8D4×C1111yescharacteristic
259C2×Q16—24no—
260C2×Q16—44no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C4⋊Q8—24no—
265C4⋊Q8—24no—
266C4⋊Q8—21no—
267C4⋊Q8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8D4×C1112yes—
272C4⋊Q8C23×C1112yes—
273C4⋊Q8C23×C1112yes—
274#125—28no—
275#125—24no—
276#125—28no—
277#125—24no—
278C4×Q8—24no—
279C4×Q8—24no—
280C4×Q8—24no—
281C4×Q8—24no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×Q8—21no—
285C4×Q8—21no—
286C4×Q8D4×C1112yes—
287C4×Q8D4×C1112yes—
288C4×Q8C23×C1112yes—
289C4×Q8C23×C1112yes—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4D4×C1111yescharacteristic
299C2×C4⋊C4D4×C1111yescharacteristic
300C2×C4⋊C4D4×C1112yes—
301C2×C42—22no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42C23×C1111yescharacteristic
305#106—24no—
306#106—28no—
307C4⋊C8—21no—
308C4⋊C8—21no—
309C4⋊C8C23×C1112yes—
310C4⋊C8C23×C1112yes—
311#103—24no—
312#103—24no—
313C4×C8—21no—
314C4×C8C23×C1112yes—
315C2×C11#165314yesdirect product factor
316C2×C11C2×#44811yescharacteristic
317C2×C11C2×#45211yescharacteristic
318C2×C11C2×#45611yescharacteristic
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—22no—
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—22no—
326C2×Q8—22no—
327C2×Q8—41no—
328C2×Q8—42no—
329C2×Q8—42no—
330C2×Q8—42no—
331C2×Q8—42no—
332C2×Q8C11×SD1614yes—
333C2×Q8C2×D4×C1112yes—
334C2×Q8C2×D4×C1112yes—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—41no—
341C22×C4C2×D4×C1111yescharacteristic
342C22×C4C2×D4×C1111yescharacteristic
343C22×C4C2×D4×C1111yescharacteristic
344Q16—48no—
345C2×C8—24no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—42no—
350C2×C8—42no—
351C4⋊C4—28no—
352C4⋊C4—28no—
353C4⋊C4—28no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4C2×D4×C1112yes—
368C4⋊C4C2×D4×C1112yes—
369C4⋊C4C2×D4×C1114yes—
370C42—28no—
371C42—22no—
372C42—22no—
373C42—22no—
374C42—22no—
375C42C2×D4×C1111yescharacteristic
376C42C2×D4×C1111yescharacteristic
377C42C2×D4×C1111yescharacteristic
378C42C24×C1111yescharacteristic
379C11C2×#165311yescharacteristic, direct product factor, Sylow
380C23C11×#12011yescharacteristic
381Q8—22no—
382Q8—24no—
383Q8—22no—
384Q8—22no—
385Q8—42no—
386Q8—42no—
387Q8—42no—
388Q8—44no—
389Q8—42no—
390Q8—42no—
391Q8—82no—
392Q8C2×C11×SD1614yes—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—42no—
401C2×C4—44no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—82no—
406C2×C4C11×#12011yescharacteristic
407C2×C4C11×#12011yescharacteristic
408C2×C4C11×#12011yescharacteristic
409C2×C4C2×C11×SD1612yes—
410C2×C4C11×#13512yes—
411C2×C4C11×#13712yes—
412C2×C4C11×#13712yes—
413C2×C4C22×D4×C1111yescharacteristic
414C2×C4C22×D4×C1111yescharacteristic
415C2×C4C22×D4×C1111yescharacteristic
416C8—24no—
417C8—42no—
418C8—42no—
419C22C11×#44812yes—
420C22C11×#45212yes—
421C22C11×#45612yes—
422C22C2×C11×#12011yescharacteristic
423C4—24no—
424C4—21no—
425C4—21no—
426C4—42no—
427C4—44no—
428C4—42no—
429C4—42no—
430C4—82no—
431C4C11×#44812yes—
432C4C11×#45212yes—
433C4C22×C11×SD1611yescharacteristic
434C4C2×C11×#13511yescharacteristic
435C4C2×C11×#13711yescharacteristic
436C4C2×C11×#13711yescharacteristic
437C2C11×#165314yesdirect product factor
438C2C2×C11×#44811yescharacteristic
439C2C2×C11×#45211yescharacteristic
440C2C2×C11×#45611yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#120
commutator, Frattini, cosocleC42C24×C11
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
5. C11×#1653C2direct (N × H)
99. C2×#1653C11direct (N × H)
164. #1653C2×C11direct (N × H)
315. C2×C11#1653direct (N × H)
379. C11C2×#1653direct (N × H)
437. C2C11×#1653direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5572
C2×C11×#4982
C2×C11×#4752
C2×C11×#4622
C11×#16532
C2×C11×#3322
C2×C11×Q8⋊C82
C2×#165311