Finite Group Databasebeta

← C11×#19054 #14596247

Subgroups — C11×#19054 #14596247

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3550C211yesmaximal, characteristic, complemented
2C11×#3235C212yesmaximal, complemented
3C11×#3150C211yesmaximal, characteristic
4C11×#1660C214yesmaximal, complemented
5C11×#1657C214yesmaximal, complemented
6C11×#1536C211yesmaximal, characteristic, complemented
7C11×#1531C212yesmaximal, complemented
8C2×C11×#135—22no—
9C11×#563C2214yes—
10C11×#559—21no—
11Q82×C11—21no—
12C11×#556—22no—
13D4×Q8×C11—22no—
14C11×#542—24no—
15C11×#536—22no—
16C11×#533C2212yes—
17C11×#532C2211yescharacteristic
18C11×#532C2211yescharacteristic
19C11×#501C2214yes—
20C11×#497—21no—
21C11×#497C2212yes—
22C11×#496—21no—
23C11×#496C2212yes—
24C11×#490C2214yes—
25C11×#482—24no—
26C11×#476—22no—
27C11×#474—22no—
28C11×#432C2212yes—
29C2×C11×#97C2211yescharacteristic
30C11×#330C2218yes—
31C11×#329C2214yes—
32C2×C11×#41—21no—
33C2×C11×#41D412yes—
34C22×Q8×C11—22no—
35C11×#135—48no—
36C2×C11×Q16—22no—
37C2×C11×SD16—22no—
38C2×C11×SD16—22no—
39C2×C11×D8—22no—
40C22×C8×C11—21no—
41C11×C4⋊Q8—24no—
42C11×C4⋊Q8—24no—
43C11×C4⋊Q8D411yescharacteristic
44C11×C4⋊Q8D412yes—
45C11×C4⋊Q8D412yes—
46C11×C4⋊Q8C2311yescharacteristic
47C11×#127D411yescharacteristic
48C11×#127C2311yescharacteristic
49C11×#126—28no—
50C11×#125C2314yes—
51C11×#124—24no—
52C11×#124—24no—
53C11×#124—21no—
54C11×#124C2312yes—
55C11×#123—24no—
56C11×#123—24no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—28no—
61C11×#121—22no—
62C11×#121—22no—
63C4×Q8×C11—24no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×D4×C11—24no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C11×#117—22no—
70C11×#117D414yes—
71C2×C42×C11C2311yescharacteristic
72C11×#107—24no—
73C11×#106—24no—
74C11×C4⋊C8—22no—
75C11×#102—24no—
76C11×#102—24no—
77C11×C22⋊C8—22no—
78C11×#97—21no—
79C11×#97C2314yes—
80C11×#97C2312yes—
81#19054C1111yesmaximal, characteristic, direct product factor, Sylow
82C11×#41—44no—
83C11×#41—44no—
84C2×Q8×C11—24no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11—21no—
88C2×Q8×C11—84no—
89C2×Q8×C11C2×D412yes—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—21no—
94C2×D4×C11—41no—
95C2×D4×C11C2×D412yes—
96C22×C4×C11—24no—
97C22×C4×C11—22no—
98C22×C4×C11—41no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D412yes—
101C11×Q16—44no—
102C11×SD16—44no—
103C11×SD16—44no—
104C11×D8—44no—
105C2×C8×C11—24no—
106C2×C8×C11—22no—
107C2×C8×C11—24no—
108C11×C4⋊C4—28no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4C2×D414yes—
116C11×C4⋊C4C2×D414yes—
117C11×C22⋊C4—24no—
118C11×C22⋊C4—28no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—42no—
122C42×C11—24no—
123C42×C11—24no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D412yes—
126C42×C11C2411yescharacteristic
127#3550C2×C1111yescharacteristic, complemented
128#3235C2×C1112yescomplemented
129#3150C2×C1111yescharacteristic
130#1660C2×C1114yescomplemented
131#1657C2×C1114yescomplemented
132#1536C2×C1111yescharacteristic, complemented
133#1531C2×C1112yescomplemented
134C23×C11—22no—
135C23×C11—41no—
136C23×C11#12011yescharacteristic
137Q8×C11—42no—
138Q8×C11—44no—
139Q8×C11—42no—
140Q8×C11—44no—
141Q8×C11—84no—
142D4×C11—42no—
143D4×C11—44no—
144D4×C11—42no—
145D4×C11—44no—
146D4×C11—82no—
147D4×C11—82no—
148C2×C4×C11—22no—
149C2×C4×C11—24no—
150C2×C4×C11—22no—
151C2×C4×C11—24no—
152C2×C4×C11—42no—
153C2×C4×C11—44no—
154C2×C4×C11—41no—
155C2×C4×C11—84no—
156C2×C4×C11—82no—
157C2×C4×C11#12012yes—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11C22×D412yes—
160C2×C4×C11C22×D411yescharacteristic
161C8×C11—24no—
162C8×C11—44no—
163C2×#135—22no—
164#563C22×C1114yes—
165#559—21no—
166Q82—21no—
167#556—22no—
168D4×Q8—22no—
169#542—24no—
170#536—22no—
171#533C22×C1112yes—
172#532C22×C1111yescharacteristic
173#532C22×C1111yescharacteristic
174#501C22×C1114yes—
175#497—21no—
176#497C22×C1112yes—
177#496—21no—
178#496C22×C1112yes—
179#490C22×C1114yes—
180#482—24no—
181#476—22no—
182#474—22no—
183#432C22×C1112yes—
184C2×#97C22×C1111yescharacteristic
185#330C22×C1118yes—
186#329C22×C1114yes—
187C22×C11—21no—
188C22×C11—22no—
189C22×C11—42no—
190C22×C11—44no—
191C22×C11—81no—
192C22×C11—82no—
193C22×C11C2×#12011yescharacteristic
194C4×C11—21no—
195C4×C11—22no—
196C4×C11—22no—
197C4×C11—42no—
198C4×C11—44no—
199C4×C11—44no—
200C4×C11—81no—
201C4×C11#45312yes—
202C2×#41—21no—
203C2×#41D4×C1112yes—
204C22×Q8—22no—
205#135—48no—
206C2×Q16—22no—
207C2×SD16—22no—
208C2×SD16—22no—
209C2×D8—22no—
210C22×C8—21no—
211C4⋊Q8—24no—
212C4⋊Q8—24no—
213C4⋊Q8D4×C1111yescharacteristic
214C4⋊Q8D4×C1112yes—
215C4⋊Q8D4×C1112yes—
216C4⋊Q8C23×C1111yescharacteristic
217#127D4×C1111yescharacteristic
218#127C23×C1111yescharacteristic
219#126—28no—
220#125C23×C1114yes—
221#124—24no—
222#124—24no—
223#124—21no—
224#124C23×C1112yes—
225#123—24no—
226#123—24no—
227C22⋊Q8—24no—
228C22⋊Q8—22no—
229C22⋊Q8—22no—
230C22⋊Q8—28no—
231#121—22no—
232#121—22no—
233C4×Q8—24no—
234C4×Q8—22no—
235C4×Q8—22no—
236C4×D4—24no—
237C4×D4—22no—
238C4×D4—22no—
239#117—22no—
240#117D4×C1114yes—
241C2×C42C23×C1111yescharacteristic
242#107—24no—
243#106—24no—
244C4⋊C8—22no—
245#102—24no—
246#102—24no—
247C22⋊C8—22no—
248#97—21no—
249#97C23×C1114yes—
250#97C23×C1112yes—
251C2×C11—41no—
252C2×C11—82no—
253C2×C11—161no—
254C2×C11C2×#45311yescharacteristic
255C2×C11#302012yes—
256#41—44no—
257#41—44no—
258C2×Q8—24no—
259C2×Q8—22no—
260C2×Q8—22no—
261C2×Q8—21no—
262C2×Q8—84no—
263C2×Q8C2×D4×C1112yes—
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4C2×D4×C1112yes—
270C22×C4—24no—
271C22×C4—22no—
272C22×C4—41no—
273C22×C4C2×D4×C1111yescharacteristic
274C22×C4C2×D4×C1112yes—
275Q16—44no—
276SD16—44no—
277SD16—44no—
278D8—44no—
279C2×C8—24no—
280C2×C8—22no—
281C2×C8—24no—
282C4⋊C4—28no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—24no—
287C4⋊C4—24no—
288C4⋊C4—22no—
289C4⋊C4C2×D4×C1114yes—
290C4⋊C4C2×D4×C1114yes—
291C22⋊C4—24no—
292C22⋊C4—28no—
293C22⋊C4—24no—
294C22⋊C4—24no—
295C22⋊C4—42no—
296C42—24no—
297C42—24no—
298C42C2×D4×C1111yescharacteristic
299C42C2×D4×C1112yes—
300C42C24×C1111yescharacteristic
301C11#1905411yescharacteristic, direct product factor, Sylow
302C23—22no—
303C23—41no—
304C23C11×#12011yescharacteristic
305Q8—42no—
306Q8—44no—
307Q8—42no—
308Q8—44no—
309Q8—84no—
310D4—42no—
311D4—44no—
312D4—42no—
313D4—44no—
314D4—82no—
315D4—82no—
316C2×C4—22no—
317C2×C4—24no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—41no—
323C2×C4—84no—
324C2×C4—82no—
325C2×C4C11×#12012yes—
326C2×C4C11×#12011yescharacteristic
327C2×C4C22×D4×C1112yes—
328C2×C4C22×D4×C1111yescharacteristic
329C8—24no—
330C8—44no—
331C22—21no—
332C22—22no—
333C22—42no—
334C22—44no—
335C22—81no—
336C22—82no—
337C22C2×C11×#12011yescharacteristic
338C4—21no—
339C4—22no—
340C4—22no—
341C4—42no—
342C4—44no—
343C4—44no—
344C4—81no—
345C4C11×#45312yes—
346C2—41no—
347C2—82no—
348C2—161no—
349C2C2×C11×#45311yescharacteristic
350C2C11×#302012yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3150C2
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×#3550C2semidirect
2. C11×#3235C2semidirect
4. C11×#1660C2semidirect
5. C11×#1657C2semidirect
6. C11×#1536C2semidirect
7. C11×#1531C2semidirect
81. #19054C11direct (N × H)
127. #3550C2×C11semidirect
128. #3235C2×C11semidirect
130. #1660C2×C11semidirect
131. #1657C2×C11semidirect
132. #1536C2×C11semidirect
133. #1531C2×C11semidirect
301. C11#19054direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35502
C11×#32352
C11×#31502
C11×#16602
C11×#16572
C11×#15362
C11×#15312
#1905411