Finite Group Databasebeta

← C11×#22232 #14599425

Subgroups — C11×#22232 #14599425

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#490C211yesmaximal, characteristic
2C11×#2330C211yesmaximal, characteristic, complemented
3C11×#2328C211yesmaximal, characteristic
4C11×#1991C211yesmaximal, characteristic, complemented
5C11×#1957C211yesmaximal, characteristic
6C11×#1926C212yesmaximal, complemented
7C11×#1925C212yesmaximal, complemented
8C11×#1864C212yesmaximal, complemented
9C11×#1862C212yesmaximal, complemented
10C11×#1847C211yesmaximal, characteristic, complemented
11C11×#1746C211yesmaximal, characteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C2×C11×#125C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C11×#490C418yescomplemented
17C2×C11×#107C2212yes—
18C2×C11×#106C2212yes—
19C2×C11×#102C2212yes—
20C2×C11×#102C2212yes—
21C2×C11×#102C2212yes—
22C2×C11×#102C2212yes—
23C2×C11×#97C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#389—22no—
28C11×#389C2212yes—
29C11×#387—22no—
30C11×#386—22no—
31C11×#386—22no—
32C11×#384C2211yescharacteristic
33C11×#382C2211yescharacteristic
34C4×C11×C4⋊C4C2212yes—
35C11×#376C2211yescharacteristic
36C11×#340C2212yes—
37C11×#340C2212yes—
38C11×#336C2212yes—
39C11×#336C2212yes—
40C22×D4×C11—22no—
41C22×D4×C11C2311yescharacteristic
42C22×D4×C11C2311yescharacteristic
43C23×C4×C11—21no—
44C23×C4×C11—21no—
45C22×C8×C11C2312yes—
46C22×C8×C11C2312yes—
47C11×#127—22no—
48C11×#127C2×C414yes—
49C11×#125—22no—
50C11×#125C2×C414yescomplemented
51C4×D4×C11—42no—
52C4×D4×C11—42no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C42×C11—22no—
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C11×#107—42no—
69C11×#106—42no—
70C11×#102—42no—
71C11×#102—42no—
72C11×#102C2×C418yescomplemented
73C11×#102C2×C418yescomplemented
74C11×#97C2×C414yescomplemented
75C4×C8×C11—22no—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—22no—
79C11×#95D412yes—
80C11×#95D412yes—
81#22232C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11—21no—
83C24×C11—21no—
84C2×D4×C11—28no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—82no—
92C2×D4×C11—82no—
93C2×D4×C11C22×C412yes—
94C2×D4×C11C22×C412yes—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11—82no—
102C22×C4×C11—82no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2411yescharacteristic
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11C22×C414yes—
114C11×C4⋊C4—28no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—82no—
121C11×C4⋊C4—82no—
122C11×C4⋊C4C22×C414yes—
123C11×C22⋊C4—42no—
124C11×C22⋊C4—42no—
125C11×C22⋊C4—82no—
126C11×C22⋊C4—82no—
127C42×C11—22no—
128C42×C11—22no—
129C42×C11—82no—
130C42×C11C22×C412yes—
131C42×C11#4112yes—
132C2×#490C2×C1111yescharacteristic
133#2330C2×C1111yescharacteristic, complemented
134#2328C2×C1111yescharacteristic
135#1991C2×C1111yescharacteristic, complemented
136#1957C2×C1111yescharacteristic
137#1926C2×C1112yescomplemented
138#1925C2×C1112yescomplemented
139#1864C2×C1112yescomplemented
140#1862C2×C1112yescomplemented
141#1847C2×C1111yescharacteristic, complemented
142#1746C2×C1111yescharacteristic, complemented
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—42no—
150C23×C11—42no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11C22×D411yescharacteristic
154D4×C11—24no—
155D4×C11—24no—
156D4×C11—42no—
157D4×C11—42no—
158D4×C11—88no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—24no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—84no—
179C2×C4×C11—84no—
180C2×C4×C11C4×D414yes—
181C2×C4×C11C23×C411yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11H(5,𝔽2)12yes—
184C2×C4×C112−1+412yes—
185C8×C11—24no—
186C8×C11—42no—
187C2×#127C22×C1111yescharacteristic
188C2×#125C22×C1111yescharacteristic
189C2×C4×D4C22×C1111yescharacteristic
190C2×C4×D4C22×C1111yescharacteristic
191#490C4×C1118yescomplemented
192C2×#107C22×C1112yes—
193C2×#106C22×C1112yes—
194C2×#102C22×C1112yes—
195C2×#102C22×C1112yes—
196C2×#102C22×C1112yes—
197C2×#102C22×C1112yes—
198C2×#97C22×C1111yescharacteristic
199C2×C4×C8C22×C1111yescharacteristic
200#390C22×C1111yescharacteristic
201#390C22×C1111yescharacteristic
202#389—22no—
203#389C22×C1112yes—
204#387—22no—
205#386—22no—
206#386—22no—
207#384C22×C1111yescharacteristic
208#382C22×C1111yescharacteristic
209C4×C4⋊C4C22×C1112yes—
210#376C22×C1111yescharacteristic
211#340C22×C1112yes—
212#340C22×C1112yes—
213#336C22×C1112yes—
214#336C22×C1112yes—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—44no—
218C22×C11—44no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11—82no—
224C22×C11—82no—
225C22×C11C2×C4×D411yescharacteristic
226C22×C11#53511yescharacteristic
227C22×C11#53611yescharacteristic
228C22×C11#57612yes—
229C22×C11#57712yes—
230C4×C11—24no—
231C4×C11—44no—
232C4×C11—41no—
233C4×C11—41no—
234C4×C11—42no—
235C4×C11—82no—
236C4×C11—81no—
237C4×C11—81no—
238C4×C11#52012yes—
239C4×C11#54212yes—
240C22×D4—22no—
241C22×D4C23×C1111yescharacteristic
242C22×D4C23×C1111yescharacteristic
243C23×C4—21no—
244C23×C4—21no—
245C22×C8C23×C1112yes—
246C22×C8C23×C1112yes—
247#127—22no—
248#127C2×C4×C1114yes—
249#125—22no—
250#125C2×C4×C1114yescomplemented
251C4×D4—42no—
252C4×D4—42no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4C23×C1111yescharacteristic
257C2×C4⋊C4C23×C1111yescharacteristic
258C2×C4⋊C4C23×C1112yes—
259C2×C4⋊C4C23×C1112yes—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—22no—
264C2×C42—22no—
265C2×C42C23×C1111yescharacteristic
266C2×C42C23×C1111yescharacteristic
267C2×C42C23×C1111yescharacteristic
268#107—42no—
269#106—42no—
270#102—42no—
271#102—42no—
272#102C2×C4×C1118yescomplemented
273#102C2×C4×C1118yescomplemented
274#97C2×C4×C1114yescomplemented
275C4×C8—22no—
276#95—22no—
277#95—22no—
278#95—22no—
279#95D4×C1112yes—
280#95D4×C1112yes—
281C2×C11—82no—
282C2×C11—82no—
283C2×C11#232611yescharacteristic
284C2×C11#294612yes—
285C2×C11#322011yescharacteristic
286C2×C11#322211yescharacteristic
287C2×C11#324112yes—
288C24—21no—
289C24—21no—
290C2×D4—28no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—82no—
298C2×D4—82no—
299C2×D4C22×C4×C1112yes—
300C2×D4C22×C4×C1112yes—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—82no—
308C22×C4—82no—
309C22×C4C2×D4×C1111yescharacteristic
310C22×C4C2×D4×C1112yes—
311C22×C4C2×D4×C1111yescharacteristic
312C22×C4C2×D4×C1112yes—
313C22×C4C24×C1111yescharacteristic
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8C22×C4×C1114yes—
320C4⋊C4—28no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—82no—
327C4⋊C4—82no—
328C4⋊C4C22×C4×C1114yes—
329C22⋊C4—42no—
330C22⋊C4—42no—
331C22⋊C4—82no—
332C22⋊C4—82no—
333C42—22no—
334C42—22no—
335C42—82no—
336C42C22×C4×C1112yes—
337C42C11×#4112yes—
338C11#2223211yescharacteristic, direct product factor, Sylow
339C23—22no—
340C23—22no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—42no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23C22×D4×C1111yescharacteristic
350D4—24no—
351D4—24no—
352D4—42no—
353D4—42no—
354D4—88no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—84no—
375C2×C4—84no—
376C2×C4C4×D4×C1114yes—
377C2×C4C23×C4×C1111yescharacteristic
378C2×C4C2×C11×#4111yescharacteristic
379C2×C4C11×H(5,𝔽2)12yes—
380C2×C4C11×2−1+412yes—
381C8—24no—
382C8—42no—
383C22—44no—
384C22—44no—
385C22—42no—
386C22—42no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—82no—
392C22—82no—
393C22C2×C4×D4×C1111yescharacteristic
394C22C11×#53511yescharacteristic
395C22C11×#53611yescharacteristic
396C22C11×#57612yes—
397C22C11×#57712yes—
398C4—24no—
399C4—44no—
400C4—41no—
401C4—41no—
402C4—42no—
403C4—81no—
404C4—82no—
405C4—81no—
406C4C11×#52012yes—
407C4C11×#54212yes—
408C2—82no—
409C2—82no—
410C2C11×#232611yescharacteristic
411C2C11×#294612yes—
412C2C11×#322011yescharacteristic
413C2C11×#322211yescharacteristic
414C2C11×#324112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C11×#376 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2330C2semidirect
4. C11×#1991C2semidirect
6. C11×#1926C2semidirect
7. C11×#1925C2semidirect
8. C11×#1864C2semidirect
9. C11×#1862C2semidirect
10. C11×#1847C2semidirect
11. C11×#1746C2semidirect
16. C11×#490C4semidirect
50. C11×#125C2×C4semidirect
72. C11×#102C2×C4semidirect
73. C11×#102C2×C4semidirect
74. C11×#97C2×C4semidirect
81. #22232C11direct (N × H)
133. #2330C2×C11semidirect
135. #1991C2×C11semidirect
137. #1926C2×C11semidirect
138. #1925C2×C11semidirect
139. #1864C2×C11semidirect
140. #1862C2×C11semidirect
141. #1847C2×C11semidirect
142. #1746C2×C11semidirect
191. #490C4×C11semidirect
250. #125C2×C4×C11semidirect
272. #102C2×C4×C11semidirect
273. #102C2×C4×C11semidirect
274. #97C2×C4×C11semidirect
338. C11#22232direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4902
C11×#23302
C11×#23282
C11×#19912
C11×#19572
C11×#19262
C11×#19252
C11×#18642
C11×#18622
C11×#18472
C11×#17462
#2223211