Finite Group Databasebeta

← C11×#13223 #14590416

Subgroups — C11×#13223 #14590416

Order 2816.

724 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2541C211yesmaximal, characteristic
2C2×C11×#353C214yesmaximal, complemented
3C11×#1799C211yesmaximal, characteristic, complemented
4C4×C11×#99C211yesmaximal, characteristic, complemented
5C2×C11×#127C411yescharacteristic, complemented
6C2×C11×#127C2212yes—
7C2×C11×#121—21no—
8C2×C11×#121—21no—
9C2×C4×D4×C11C2211yescharacteristic
10C2×C11×#99C2212yes—
11C2×C11×#99C2212yes—
12C11×#392—21no—
13C11×#392—21no—
14C11×#390C412yescomplemented
15C11×#380—21no—
16C4×C11×C4⋊C4C411yescharacteristic, complemented
17C4×C11×C22⋊C4—21no—
18C11×#353—28no—
19C11×#342—21no—
20C11×#342—21no—
21C22×D4×C11—22no—
22C22×D4×C11—22no—
23C22×D4×C11—21no—
24C22×D4×C11—21no—
25C22×D4×C11C2×C412yes—
26C22×D4×C11C2311yescharacteristic
27C23×C4×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C11×#127—24no—
30C11×#127—24no—
31C11×#127—41no—
32C11×#127—41no—
33C11×#121—44no—
34C11×#121—44no—
35C4×D4×C11—41no—
36C4×D4×C11—41no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—41no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4D411yescharacteristic
45C2×C11×C22⋊C4D411yescharacteristic
46C2×C42×C11—41no—
47C2×C42×C11C2×C412yes—
48C2×C42×C11C2×C411yescharacteristic
49C11×#99—22no—
50C11×#99—24no—
51C11×#99D414yescomplemented
52C11×#95—21no—
53C11×#95—41no—
54C11×#95—41no—
55#13223C1111yesmaximal, characteristic, direct product factor, Sylow
56C24×C11—22no—
57C24×C11C2×D411yescharacteristic
58C24×C11C2×D411yescharacteristic
59C2×D4×C11—24no—
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C2×D4×C11—42no—
63C2×D4×C11—42no—
64C2×D4×C11—44no—
65C2×D4×C11—44no—
66C2×D4×C11—42no—
67C2×D4×C11—42no—
68C2×D4×C11—42no—
69C2×D4×C11—44no—
70C2×D4×C11—42no—
71C2×D4×C11—42no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—82no—
75C2×D4×C11—82no—
76C2×D4×C11—82no—
77C2×D4×C11C2×D412yes—
78C2×D4×C11#4112yes—
79C22×C4×C11—22no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11C22⋊C411yescharacteristic
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22⋊C411yescharacteristic
92C22×C4×C11C22×C411yescharacteristic
93C11×C4⋊C4—24no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—82no—
96C11×C22⋊C4—24no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—44no—
100C11×C22⋊C4—44no—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—42no—
104C42×C11—21no—
105C42×C11—21no—
106C42×C11—24no—
107C42×C11—82no—
108#2541C2×C1111yescharacteristic
109C2×#353C2×C1114yescomplemented
110#1799C2×C1111yescharacteristic, complemented
111C4×#99C2×C1111yescharacteristic, complemented
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—42no—
121C23×C11—42no—
122C23×C11—42no—
123C23×C11—42no—
124C23×C11—42no—
125C23×C11—42no—
126C23×C11—42no—
127C23×C11C2×C22⋊C411yescharacteristic
128C23×C11#12112yes—
129C23×C11#12411yescharacteristic
130C23×C11#12711yescharacteristic
131D4×C11—42no—
132D4×C11—42no—
133D4×C11—84no—
134D4×C11—82no—
135D4×C11—88no—
136D4×C11—84no—
137D4×C11—84no—
138D4×C11—84no—
139D4×C11—82no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—22no—
143C2×C4×C11—24no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—44no—
155C2×C4×C11—81no—
156C2×C4×C11—81no—
157C2×C4×C11—82no—
158C2×C4×C11—82no—
159C2×C4×C11—82no—
160C2×C4×C11—82no—
161C2×C4×C11—82no—
162C2×C4×C11#9911yescharacteristic
163C2×C4×C11#9911yescharacteristic
164C2×C4×C11C4×D412yes—
165C2×#127C4×C1111yescharacteristic, complemented
166C2×#127C22×C1112yes—
167C2×#121—21no—
168C2×#121—21no—
169C2×C4×D4C22×C1111yescharacteristic
170C2×#99C22×C1112yes—
171C2×#99C22×C1112yes—
172#392—21no—
173#392—21no—
174#390C4×C1112yescomplemented
175#380—21no—
176C4×C4⋊C4C4×C1111yescharacteristic, complemented
177C4×C22⋊C4—21no—
178#353—28no—
179#342—21no—
180#342—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—22no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—42no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—82no—
196C22×C11—82no—
197C22×C11—82no—
198C22×C11—82no—
199C22×C11—82no—
200C22×C11—82no—
201C22×C11—82no—
202C22×C11#39011yescharacteristic
203C22×C11C2×#9911yescharacteristic
204C22×C11#41011yescharacteristic
205C4×C11—21no—
206C4×C11—22no—
207C4×C11—44no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11—84no—
212C4×C11—162no—
213C4×C11#35312yescomplemented
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4C2×C4×C1112yes—
219C22×D4C23×C1111yescharacteristic
220C23×C4D4×C1111yescharacteristic
221C23×C4D4×C1111yescharacteristic
222#127—24no—
223#127—24no—
224#127—41no—
225#127—41no—
226#121—44no—
227#121—44no—
228C4×D4—41no—
229C4×D4—41no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—41no—
232C2×C4⋊C4C2×C4×C1111yescharacteristic
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4D4×C1111yescharacteristic
238C2×C22⋊C4D4×C1111yescharacteristic
239C2×C42—41no—
240C2×C42C2×C4×C1112yes—
241C2×C42C2×C4×C1111yescharacteristic
242#99—22no—
243#99—24no—
244#99D4×C1114yescomplemented
245#95—21no—
246#95—41no—
247#95—41no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11—42no—
251C2×C11—41no—
252C2×C11—41no—
253C2×C11—162no—
254C2×C11#196411yescharacteristic
255C2×C11C2×#35311yescharacteristic
256C2×C11#212811yescharacteristic
257C24—22no—
258C24C2×D4×C1111yescharacteristic
259C24C2×D4×C1111yescharacteristic
260C2×D4—24no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—44no—
268C2×D4—44no—
269C2×D4—42no—
270C2×D4—44no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—82no—
276C2×D4—82no—
277C2×D4—82no—
278C2×D4C2×D4×C1112yes—
279C2×D4C11×#4112yes—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4C11×C22⋊C411yescharacteristic
290C22×C4C11×C22⋊C411yescharacteristic
291C22×C4C11×C22⋊C411yescharacteristic
292C22×C4C11×C22⋊C411yescharacteristic
293C22×C4C22×C4×C1111yescharacteristic
294C4⋊C4—24no—
295C4⋊C4—41no—
296C4⋊C4—82no—
297C22⋊C4—24no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—44no—
301C22⋊C4—44no—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C22⋊C4—42no—
305C42—21no—
306C42—21no—
307C42—24no—
308C42—82no—
309C11#1322311yescharacteristic, direct product factor, Sylow
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23C2×C11×C22⋊C411yescharacteristic
326C23C11×#12112yes—
327C23C11×#12411yescharacteristic
328C23C11×#12711yescharacteristic
329D4—42no—
330D4—42no—
331D4—84no—
332D4—82no—
333D4—88no—
334D4—84no—
335D4—84no—
336D4—84no—
337D4—82no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—44no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—82no—
359C2×C4—82no—
360C2×C4C11×#9911yescharacteristic
361C2×C4C11×#9911yescharacteristic
362C2×C4C4×D4×C1112yes—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—21no—
367C22—21no—
368C22—42no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—81no—
376C22—81no—
377C22—82no—
378C22—82no—
379C22—82no—
380C22—82no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22C11×#39011yescharacteristic
385C22C2×C11×#9911yescharacteristic
386C22C11×#41011yescharacteristic
387C4—21no—
388C4—22no—
389C4—44no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—84no—
394C4—162no—
395C4C11×#35312yescomplemented
396C2—21no—
397C2—21no—
398C2—42no—
399C2—41no—
400C2—41no—
401C2—162no—
402C2C11×#196411yescharacteristic
403C2C2×C11×#35311yescharacteristic
404C2C11×#212811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC22×D4C23×C11
prime radicalC11×#2541C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#353C2semidirect
3. C11×#1799C2semidirect
4. C4×C11×#99C2semidirect
5. C2×C11×#127C4semidirect
14. C11×#390C4semidirect
16. C4×C11×C4⋊C4C4semidirect
51. C11×#99D4semidirect
55. #13223C11direct (N × H)
109. C2×#353C2×C11semidirect
110. #1799C2×C11semidirect
111. C4×#99C2×C11semidirect
165. C2×#127C4×C11semidirect
174. #390C4×C11semidirect
176. C4×C4⋊C4C4×C11semidirect
213. C4×C11#353semidirect
244. #99D4×C11semidirect
309. C11#13223direct (N × H)
395. C4C11×#353semidirect

Maximal subgroups

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

subgroupindex
C11×#25412
C2×C11×#3532
C11×#17992
C4×C11×#992
#1322311