Finite Group Databasebeta

← C11×#19429 #14596622

Subgroups — C11×#19429 #14596622

Order 2816.

618 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3230C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic
3C2×C11×#476C211yesmaximal, characteristic
4C11×#2975C211yesmaximal, characteristic
5C11×#1703C214yesmaximal, complemented
6C11×#1695C214yesmaximal, complemented
7C11×#1570C211yesmaximal, characteristic, complemented
8C11×#1548C211yesmaximal, characteristic, complemented
9C11×#1542C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C11×#500C2212yescomplemented
14C11×#487C2212yescomplemented
15C11×#484—22no—
16C11×#478—22no—
17C11×#477—22no—
18C11×#476—22no—
19C11×#476C2212yes—
20C11×#476C2214yes—
21C11×#474C2212yes—
22C11×#436—22no—
23C11×#436C2214yes—
24C11×#431C2211yescharacteristic
25C11×#431C2211yescharacteristic
26C11×#428—21no—
27C2×C11×#106—21no—
28C11×#423C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C11×#418—21no—
31C2×C11×#102—21no—
32C11×#407—22no—
33C11×#334C2214yescomplemented
34C11×#333C2212yescomplemented
35C11×#333C2214yescomplemented
36C11×#332C2212yescomplemented
37C22×Q8×C11—21no—
38C22×D4×C11D411yescharacteristic
39C23×C4×C11—21no—
40C2×C11×M16—21no—
41C2×C11×M16—24no—
42C22×C8×C11—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8C2311yescharacteristic
47C11×C4⋊Q8C2311yescharacteristic
48C11×C4⋊Q8C2312yes—
49C11×#125—21no—
50C11×C22⋊Q8—21no—
51C11×C22⋊Q8—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11D412yes—
57C4×D4×C11C2312yes—
58C11×#117—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C22⋊C4—21no—
63C2×C42×C11C2311yescharacteristic
64C11×#107—24no—
65C11×#107—22no—
66C11×#106—24no—
67C11×#106—22no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8D412yes—
71C11×C4⋊C8C2312yes—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×#103—24no—
75C11×#102—24no—
76C11×#102—22no—
77C11×#102—22no—
78C11×C22⋊C8—21no—
79C11×C22⋊C8—24no—
80C11×C22⋊C8D412yes—
81C4×C8×C11—21no—
82C4×C8×C11C2312yes—
83#19429C1111yesmaximal, characteristic, direct product factor, Sylow
84C24×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—22no—
88C2×Q8×C11—41no—
89C2×Q8×C11—82no—
90C2×D4×C11—21no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11C2×D412yes—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—41no—
98C22×C4×C11—82no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C11×M16—42no—
103C11×M16—84no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—42no—
108C2×C8×C11C2×D414yes—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4C2×D412yes—
121C11×C22⋊C4—22no—
122C11×C22⋊C4—22no—
123C11×C22⋊C4—41no—
124C42×C11—41no—
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11#4111yescharacteristic
128C42×C11C2411yescharacteristic
129#3230C2×C1111yescharacteristic, complemented
130#3077C2×C1111yescharacteristic
131C2×#476C2×C1111yescharacteristic
132#2975C2×C1111yescharacteristic
133#1703C2×C1114yescomplemented
134#1695C2×C1114yescomplemented
135#1570C2×C1111yescharacteristic, complemented
136#1548C2×C1111yescharacteristic, complemented
137#1542C2×C1111yescharacteristic, complemented
138C23×C11—22no—
139C23×C11—42no—
140C23×C11—81no—
141C23×C11—81no—
142C23×C11#12111yescharacteristic
143Q8×C11—42no—
144Q8×C11—81no—
145Q8×C11—82no—
146Q8×C11—82no—
147D4×C11—22no—
148D4×C11—22no—
149D4×C11—42no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—44no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—82no—
158C2×C4×C11—81no—
159C2×C4×C11—82no—
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#13712yes—
164C2×C4×C11#13712yes—
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C2×#4111yescharacteristic
168C8×C11—24no—
169C8×C11—42no—
170C8×C11—42no—
171C8×C11—42no—
172#533C22×C1111yescharacteristic
173C2×C4⋊Q8C22×C1111yescharacteristic
174C2×C4×D4C22×C1111yescharacteristic
175#500C22×C1112yescomplemented
176#487C22×C1112yescomplemented
177#484—22no—
178#478—22no—
179#477—22no—
180#476—22no—
181#476C22×C1112yes—
182#476C22×C1114yes—
183#474C22×C1112yes—
184#436—22no—
185#436C22×C1114yes—
186#431C22×C1111yescharacteristic
187#431C22×C1111yescharacteristic
188#428—21no—
189C2×#106—21no—
190#423C22×C1111yescharacteristic
191C2×C4⋊C8C22×C1111yescharacteristic
192#418—21no—
193C2×#102—21no—
194#407—22no—
195#334C22×C1114yescomplemented
196#333C22×C1112yescomplemented
197#333C22×C1114yescomplemented
198#332C22×C1112yescomplemented
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—42no—
202C22×C11—42no—
203C22×C11—42no—
204C22×C11—84no—
205C22×C11#47012yes—
206C22×C11C2×#12111yescharacteristic
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—42no—
211C4×C11—81no—
212C4×C11—82no—
213C4×C11—81no—
214C4×C11#47012yes—
215C4×C11C2×#13711yescharacteristic
216C4×C11C2×#13711yescharacteristic
217C4×C11#57712yes—
218C22×Q8—21no—
219C22×D4D4×C1111yescharacteristic
220C23×C4—21no—
221C2×M16—21no—
222C2×M16—24no—
223C22×C8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8C23×C1112yes—
228C4⋊Q8C23×C1111yescharacteristic
229C4⋊Q8C23×C1111yescharacteristic
230#125—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4D4×C1112yes—
238C4×D4C23×C1112yes—
239#117—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4D4×C1111yescharacteristic
243C2×C22⋊C4—21no—
244C2×C42C23×C1111yescharacteristic
245#107—24no—
246#107—22no—
247#106—24no—
248#106—22no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8D4×C1112yes—
252C4⋊C8C23×C1112yes—
253C4⋊C8C23×C1112yes—
254C4⋊C8C23×C1112yes—
255#103—24no—
256#102—24no—
257#102—22no—
258#102—22no—
259C22⋊C8—21no—
260C22⋊C8—24no—
261C22⋊C8D4×C1112yes—
262C4×C8—21no—
263C4×C8C23×C1112yes—
264C2×C11—22no—
265C2×C11—82no—
266C2×C11#304211yescharacteristic
267C2×C11C2×#47011yescharacteristic
268C2×C11#306811yescharacteristic
269C24—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—82no—
275C2×D4—21no—
276C2×D4—22no—
277C2×D4—22no—
278C2×D4C2×D4×C1112yes—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—41no—
283C22×C4—82no—
284C22×C4C2×D4×C1111yescharacteristic
285C22×C4C2×D4×C1111yescharacteristic
286C22×C4C11×#4111yescharacteristic
287M16—42no—
288M16—84no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—42no—
293C2×C8C2×D4×C1114yes—
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4C2×D4×C1112yes—
306C22⋊C4—22no—
307C22⋊C4—22no—
308C22⋊C4—41no—
309C42—41no—
310C42C2×D4×C1111yescharacteristic
311C42C2×D4×C1111yescharacteristic
312C42C11×#4111yescharacteristic
313C42C24×C1111yescharacteristic
314C11#1942911yescharacteristic, direct product factor, Sylow
315C23—22no—
316C23—42no—
317C23—81no—
318C23—81no—
319C23C11×#12111yescharacteristic
320Q8—42no—
321Q8—81no—
322Q8—82no—
323Q8—82no—
324D4—22no—
325D4—22no—
326D4—42no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—44no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—81no—
336C2×C4—82no—
337C2×C4C11×#12111yescharacteristic
338C2×C4C11×#12111yescharacteristic
339C2×C4C11×#12111yescharacteristic
340C2×C4C11×#13712yes—
341C2×C4C11×#13712yes—
342C2×C4C22×D4×C1111yescharacteristic
343C2×C4C22×D4×C1111yescharacteristic
344C2×C4C2×C11×#4111yescharacteristic
345C8—24no—
346C8—42no—
347C8—42no—
348C8—42no—
349C22—21no—
350C22—21no—
351C22—42no—
352C22—42no—
353C22—42no—
354C22—84no—
355C22C11×#47012yes—
356C22C2×C11×#12111yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—42no—
361C4—81no—
362C4—82no—
363C4—81no—
364C4C11×#47012yes—
365C4C2×C11×#13711yescharacteristic
366C4C2×C11×#13711yescharacteristic
367C4C11×#57712yes—
368C2—22no—
369C2—82no—
370C2C11×#304211yescharacteristic
371C2C2×C11×#47011yescharacteristic
372C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3230C2semidirect
5. C11×#1703C2semidirect
6. C11×#1695C2semidirect
7. C11×#1570C2semidirect
8. C11×#1548C2semidirect
9. C11×#1542C2semidirect
13. C11×#500C22semidirect
14. C11×#487C22semidirect
33. C11×#334C22semidirect
34. C11×#333C22semidirect
35. C11×#333C22semidirect
36. C11×#332C22semidirect
83. #19429C11direct (N × H)
129. #3230C2×C11semidirect
133. #1703C2×C11semidirect
134. #1695C2×C11semidirect
135. #1570C2×C11semidirect
136. #1548C2×C11semidirect
137. #1542C2×C11semidirect
175. #500C22×C11semidirect
176. #487C22×C11semidirect
195. #334C22×C11semidirect
196. #333C22×C11semidirect
197. #333C22×C11semidirect
198. #332C22×C11semidirect
314. C11#19429direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32302
C11×#30772
C2×C11×#4762
C11×#29752
C11×#17032
C11×#16952
C11×#15702
C11×#15482
C11×#15422
#1942911