Finite Group Databasebeta

← C2×C11×#1701 #14596333

Subgroups — C2×C11×#1701 #14596333

Order 2816.

810 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#486C211yesmaximal, characteristic, complemented
2C2×C11×#461C211yesmaximal, characteristic, complemented
3C2×C11×#459C211yesmaximal, characteristic
4C2×C11×#436C211yesmaximal, characteristic, complemented
5C11×#1701C218yesmaximal, direct product factor
6C2×C11×#334C211yesmaximal, characteristic, complemented
7C2×C11×#332C211yesmaximal, characteristic, complemented
8C2×C11×#331C211yesmaximal, characteristic, complemented
9C22×C11×SD16—21no—
10C22×C11×D8—21no—
11C22×C11×M16—21no—
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C11×#486—22no—
16C11×#486C2214yescomplemented
17C11×#461—22no—
18C11×#461C2214yescomplemented
19C11×#459—22no—
20C11×#459C2214yes—
21C11×#436—22no—
22C11×#436C2214yescomplemented
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103—21no—
27C2×C11×#102—21no—
28C2×C11×#102—21no—
29C2×C11×#102—21no—
30C2×C11×C22⋊C8—21no—
31C2×C4×C8×C11C2211yescharacteristic
32C11×#334C2214yescomplemented
33C11×#332C2214yescomplemented
34C11×#331C2214yescomplemented
35C22×Q8×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11D411yescharacteristic
40C23×C4×C11—21no—
41C2×C11×SD16—24no—
42C2×C11×SD16—44no—
43C2×C11×D8—24no—
44C2×C11×D8—44no—
45C2×C11×M16—24no—
46C2×C11×M16—44no—
47C22×C8×C11—21no—
48C22×C8×C11—21no—
49C22×C8×C11—21no—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11D411yescharacteristic
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8C2312yes—
56C11×#127—21no—
57C11×#127—21no—
58C11×#127—21no—
59C11×#127C2312yes—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11D412yes—
63C4×D4×C11C2312yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C42×C11C2311yescharacteristic
69C11×C4⋊C8—21no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8—21no—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×C4⋊C8C2312yes—
75C11×#103—24no—
76C11×#102—24no—
77C11×#102—24no—
78C11×#102—24no—
79C11×C22⋊C8—24no—
80C4×C8×C11D412yes—
81C4×C8×C11C2312yes—
82C2×#1701C1111yesmaximal, characteristic, direct product factor, Sylow
83C24×C11—21no—
84C24×C11—41no—
85C2×Q8×C11—22no—
86C2×Q8×C11—41no—
87C2×Q8×C11—42no—
88C2×Q8×C11—42no—
89C2×D4×C11—21no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—42no—
101C2×D4×C11—42no—
102C2×D4×C11—82no—
103C2×D4×C11C2×D412yes—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—41no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C11×SD16—48no—
114C11×D8—48no—
115C11×M16—48no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—42no—
122C2×C8×C11—42no—
123C2×C8×C11—42no—
124C2×C8×C11C2×D412yes—
125C2×C8×C11C2×D412yes—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4C2×D412yes—
132C11×C22⋊C4—22no—
133C11×C22⋊C4—22no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138C2×#486C2×C1111yescharacteristic, complemented
139C2×#461C2×C1111yescharacteristic, complemented
140C2×#459C2×C1111yescharacteristic
141C2×#436C2×C1111yescharacteristic, complemented
142#1701C2×C1118yesdirect product factor
143C2×#334C2×C1111yescharacteristic, complemented
144C2×#332C2×C1111yescharacteristic, complemented
145C2×#331C2×C1111yescharacteristic, complemented
146C23×C11—22no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—42no—
150C23×C11—42no—
151C23×C11—82no—
152C23×C11—82no—
153C23×C11—82no—
154C23×C11#12111yescharacteristic
155Q8×C11—42no—
156Q8×C11—42no—
157Q8×C11—82no—
158D4×C11—22no—
159D4×C11—22no—
160D4×C11—42no—
161D4×C11—42no—
162D4×C11—42no—
163D4×C11—42no—
164D4×C11—42no—
165D4×C11—82no—
166D4×C11—82no—
167D4×C11—82no—
168D4×C11—82no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—44no—
175C2×C4×C11—42no—
176C2×C4×C11—82no—
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#13512yes—
181C2×C4×C11AGL(1,ℤ/8)12yes—
182C2×C4×C11AGL(1,ℤ/8)12yes—
183C2×C4×C11AGL(1,ℤ/8)12yes—
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C8×C11—22no—
188C8×C11—22no—
189C8×C11—42no—
190C8×C11—42no—
191C8×C11—42no—
192C22×SD16—21no—
193C22×D8—21no—
194C22×M16—21no—
195C2×C4⋊Q8C22×C1111yescharacteristic
196C2×#127C22×C1111yescharacteristic
197C2×C4×D4C22×C1111yescharacteristic
198#486—22no—
199#486C22×C1114yescomplemented
200#461—22no—
201#461C22×C1114yescomplemented
202#459—22no—
203#459C22×C1114yes—
204#436—22no—
205#436C22×C1114yescomplemented
206C2×C4⋊C8C22×C1111yescharacteristic
207C2×C4⋊C8C22×C1111yescharacteristic
208C2×C4⋊C8C22×C1111yescharacteristic
209C2×#103—21no—
210C2×#102—21no—
211C2×#102—21no—
212C2×#102—21no—
213C2×C22⋊C8—21no—
214C2×C4×C8C22×C1111yescharacteristic
215#334C22×C1114yescomplemented
216#332C22×C1114yescomplemented
217#331C22×C1114yescomplemented
218C22×C11—42no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—84no—
222C22×C11—82no—
223C22×C11—82no—
224C22×C11—82no—
225C22×C11—164no—
226C22×C11#46312yes—
227C22×C11#46912yes—
228C22×C11#47112yes—
229C22×C11C2×#12111yescharacteristic
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—42no—
233C4×C11—82no—
234C4×C11#46312yes—
235C4×C11#46912yes—
236C4×C11C2×#13511yescharacteristic
237C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
238C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
239C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
240C22×Q8—21no—
241C22×D4—21no—
242C22×D4—21no—
243C22×D4—21no—
244C22×D4D4×C1111yescharacteristic
245C23×C4—21no—
246C2×SD16—24no—
247C2×SD16—44no—
248C2×D8—24no—
249C2×D8—44no—
250C2×M16—24no—
251C2×M16—44no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8D4×C1111yescharacteristic
256C22×C8D4×C1111yescharacteristic
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8C23×C1112yes—
261#127—21no—
262#127—21no—
263#127—21no—
264#127C23×C1112yes—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4D4×C1112yes—
268C4×D4C23×C1112yes—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4D4×C1111yescharacteristic
272C2×C22⋊C4—21no—
273C2×C42C23×C1111yescharacteristic
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8C23×C1112yes—
278C4⋊C8C23×C1112yes—
279C4⋊C8C23×C1112yes—
280#103—24no—
281#102—24no—
282#102—24no—
283#102—24no—
284C22⋊C8—24no—
285C4×C8D4×C1112yes—
286C4×C8C23×C1112yes—
287C2×C11—82no—
288C2×C11—162no—
289C2×C11#170114yesdirect product factor
290C2×C11C2×#46311yescharacteristic
291C2×C11C2×#46911yescharacteristic
292C2×C11C2×#47111yescharacteristic
293C24—21no—
294C24—41no—
295C2×Q8—22no—
296C2×Q8—41no—
297C2×Q8—42no—
298C2×Q8—42no—
299C2×D4—21no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—22no—
304C2×D4—22no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—42no—
309C2×D4—42no—
310C2×D4—42no—
311C2×D4—42no—
312C2×D4—82no—
313C2×D4C2×D4×C1112yes—
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—41no—
320C22×C4C2×D4×C1111yescharacteristic
321C22×C4C2×D4×C1111yescharacteristic
322C22×C4C11×#4111yescharacteristic
323SD16—48no—
324D8—48no—
325M16—48no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—42no—
332C2×C8—42no—
333C2×C8—42no—
334C2×C8C2×D4×C1112yes—
335C2×C8C2×D4×C1112yes—
336C4⋊C4—21no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4C2×D4×C1112yes—
342C22⋊C4—22no—
343C22⋊C4—22no—
344C42C2×D4×C1111yescharacteristic
345C42C2×D4×C1111yescharacteristic
346C42C11×#4111yescharacteristic
347C42C24×C1111yescharacteristic
348C11C2×#170111yescharacteristic, direct product factor, Sylow
349C23—22no—
350C23—42no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—82no—
355C23—82no—
356C23—82no—
357C23C11×#12111yescharacteristic
358Q8—42no—
359Q8—42no—
360Q8—82no—
361D4—22no—
362D4—22no—
363D4—42no—
364D4—42no—
365D4—42no—
366D4—42no—
367D4—42no—
368D4—82no—
369D4—82no—
370D4—82no—
371D4—82no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—44no—
378C2×C4—42no—
379C2×C4—82no—
380C2×C4C11×#12111yescharacteristic
381C2×C4C11×#12111yescharacteristic
382C2×C4C11×#12111yescharacteristic
383C2×C4C11×#13512yes—
384C2×C4C11×AGL(1,ℤ/8)12yes—
385C2×C4C11×AGL(1,ℤ/8)12yes—
386C2×C4C11×AGL(1,ℤ/8)12yes—
387C2×C4C22×D4×C1111yescharacteristic
388C2×C4C22×D4×C1111yescharacteristic
389C2×C4C2×C11×#4111yescharacteristic
390C8—22no—
391C8—22no—
392C8—42no—
393C8—42no—
394C8—42no—
395C22—42no—
396C22—42no—
397C22—42no—
398C22—84no—
399C22—82no—
400C22—82no—
401C22—82no—
402C22—164no—
403C22C11×#46312yes—
404C22C11×#46912yes—
405C22C11×#47112yes—
406C22C2×C11×#12111yescharacteristic
407C4—21no—
408C4—21no—
409C4—42no—
410C4—82no—
411C4C11×#46312yes—
412C4C11×#46912yes—
413C4C2×C11×#13511yescharacteristic
414C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
415C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
416C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
417C2—82no—
418C2—162no—
419C2C11×#170114yesdirect product factor
420C2C2×C11×#46311yescharacteristic
421C2C2×C11×#46911yescharacteristic
422C2C2×C11×#47111yescharacteristic
subgroupG/H
center, socleC23×C11#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#459C2
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
1. C2×C11×#486C2semidirect
2. C2×C11×#461C2semidirect
4. C2×C11×#436C2semidirect
5. C11×#1701C2direct (N × H)
6. C2×C11×#334C2semidirect
7. C2×C11×#332C2semidirect
8. C2×C11×#331C2semidirect
16. C11×#486C22semidirect
18. C11×#461C22semidirect
22. C11×#436C22semidirect
32. C11×#334C22semidirect
33. C11×#332C22semidirect
34. C11×#331C22semidirect
82. C2×#1701C11direct (N × H)
138. C2×#486C2×C11semidirect
139. C2×#461C2×C11semidirect
141. C2×#436C2×C11semidirect
142. #1701C2×C11direct (N × H)
143. C2×#334C2×C11semidirect
144. C2×#332C2×C11semidirect
145. C2×#331C2×C11semidirect
199. #486C22×C11semidirect
201. #461C22×C11semidirect
205. #436C22×C11semidirect
215. #334C22×C11semidirect
216. #332C22×C11semidirect
217. #331C22×C11semidirect
289. C2×C11#1701direct (N × H)
348. C11C2×#1701direct (N × H)
419. C2C11×#1701direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4862
C2×C11×#4612
C2×C11×#4592
C2×C11×#4362
C11×#17012
C2×C11×#3342
C2×C11×#3322
C2×C11×#3312
C2×#170111