Finite Group Databasebeta

← C11×#11796 #14588989

Subgroups — C11×#11796 #14588989

Order 2816.

1068 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C2×C11×#392C211yesmaximal, characteristic
2C11×#1819C211yesmaximal, characteristic, complemented
3C11×#1462C211yesmaximal, characteristic, complemented
4C11×#1343C214yesmaximal, complemented
5C23×D4×C11—21no—
6C23×D4×C11C411yescharacteristic, complemented
7C22×C11×C22⋊C4—21no—
8C22×C11×C22⋊C4C2211yescharacteristic
9C11×#407—21no—
10C11×#392—21no—
11C11×#392—21no—
12C11×#392C412yescomplemented
13C11×#392C2212yes—
14C11×#379—21no—
15C2×C11×#95C411yescharacteristic, complemented
16C11×#342—21no—
17C11×#342C2212yescomplemented
18C11×#323—21no—
19C11×#323C2212yescomplemented
20C25×C11—21no—
21C25×C11D411yescharacteristic
22C22×D4×C11—22no—
23C22×D4×C11—22no—
24C22×D4×C11—21no—
25C22×D4×C11—41no—
26C22×D4×C11—41no—
27C22×D4×C11—44no—
28C22×D4×C11—44no—
29C22×D4×C11—44no—
30C22×D4×C11—44no—
31C22×D4×C11C2×C412yes—
32C23×C4×C11—21no—
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11D411yescharacteristic
35C2×C11×M16—41no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—41no—
40C2×C11×C22⋊C4—41no—
41C2×C11×C22⋊C4—44no—
42C2×C11×C22⋊C4—41no—
43C2×C11×C22⋊C4—41no—
44C2×C11×C22⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4D411yescharacteristic
46C2×C11×C22⋊C4D411yescharacteristic
47C2×C11×C22⋊C4C2311yescharacteristic
48C11×C22⋊C8—22no—
49C11×C22⋊C8—41no—
50C11×#95—21no—
51C11×#95C2×C412yes—
52#11796C1111yesmaximal, characteristic, direct product factor, Sylow
53C24×C11—24no—
54C24×C11—22no—
55C24×C11—22no—
56C24×C11—21no—
57C24×C11—21no—
58C24×C11—41no—
59C24×C11—42no—
60C24×C11—42no—
61C24×C11—42no—
62C24×C11—42no—
63C24×C11—42no—
64C24×C11—42no—
65C24×C11—42no—
66C24×C11—41no—
67C24×C11—41no—
68C24×C11C22⋊C411yescharacteristic
69C24×C11C22⋊C411yescharacteristic
70C24×C11C2×D411yescharacteristic
71C2×D4×C11—44no—
72C2×D4×C11—44no—
73C2×D4×C11—42no—
74C2×D4×C11—42no—
75C2×D4×C11—44no—
76C2×D4×C11—44no—
77C2×D4×C11—44no—
78C2×D4×C11—44no—
79C2×D4×C11—48no—
80C2×D4×C11—432no—
81C2×D4×C11—44no—
82C2×D4×C11—44no—
83C2×D4×C11—44no—
84C2×D4×C11—44no—
85C22×C4×C11—24no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11C22⋊C411yescharacteristic
97C22×C4×C11C22⋊C411yescharacteristic
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C11×M16—82no—
101C2×C8×C11—42no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—44no—
107C11×C22⋊C4—44no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4—42no—
110C11×C22⋊C4—82no—
111C11×C22⋊C4—82no—
112C2×#392C2×C1111yescharacteristic
113#1819C2×C1111yescharacteristic, complemented
114#1462C2×C1111yescharacteristic, complemented
115#1343C2×C1114yescomplemented
116C23×C11—22no—
117C23×C11—22no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—24no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—42no—
133C23×C11—48no—
134C23×C11—48no—
135C23×C11—42no—
136C23×C11—44no—
137C23×C11—42no—
138C23×C11—48no—
139C23×C11—42no—
140C23×C11—44no—
141C23×C11—42no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11—81no—
146C23×C11—81no—
147C23×C11—84no—
148C23×C11—84no—
149C23×C11—84no—
150C23×C11—82no—
151C23×C11—82no—
152C23×C11—82no—
153C23×C11—82no—
154C23×C11#9911yescharacteristic
155C23×C11#9911yescharacteristic
156C23×C11C2×C22⋊C411yescharacteristic
157C23×C11AGL(1,ℤ/8)12yes—
158D4×C11—44no—
159D4×C11—416no—
160D4×C11—416no—
161D4×C11—48no—
162D4×C11—44no—
163C2×C4×C11—24no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—48no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—81no—
179C2×C4×C11—82no—
180C2×C4×C11—82no—
181C2×C4×C11—82no—
182C8×C11—82no—
183C23×D4—21no—
184C23×D4C4×C1111yescharacteristic, complemented
185C22×C22⋊C4—21no—
186C22×C22⋊C4C22×C1111yescharacteristic
187#407—21no—
188#392—21no—
189#392—21no—
190#392C4×C1112yescomplemented
191#392C22×C1112yes—
192#379—21no—
193C2×#95C4×C1111yescharacteristic, complemented
194#342—21no—
195#342C22×C1112yescomplemented
196#323—21no—
197#323C22×C1112yescomplemented
198C22×C11—24no—
199C22×C11—24no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—22no—
207C22×C11—42no—
208C22×C11—42no—
209C22×C11—44no—
210C22×C11—44no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—44no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—81no—
218C22×C11—84no—
219C22×C11—84no—
220C22×C11—81no—
221C22×C11—82no—
222C22×C11—82no—
223C22×C11—88no—
224C22×C11—88no—
225C22×C11—82no—
226C22×C11—82no—
227C22×C11AΣL(1,𝔽16)12yes—
228C22×C11#35312yes—
229C22×C11C2×#9911yescharacteristic
230C22×C11#41811yescharacteristic
231C22×C11#42111yescharacteristic
232C4×C11—44no—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11—41no—
236C4×C11—41no—
237C4×C11—162no—
238C25—21no—
239C25D4×C1111yescharacteristic
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—21no—
243C22×D4—41no—
244C22×D4—41no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4C2×C4×C1112yes—
250C23×C4—21no—
251C23×C4C2×C4×C1111yescharacteristic
252C23×C4D4×C1111yescharacteristic
253C2×M16—41no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—41no—
258C2×C22⋊C4—41no—
259C2×C22⋊C4—44no—
260C2×C22⋊C4—41no—
261C2×C22⋊C4—41no—
262C2×C22⋊C4C2×C4×C1111yescharacteristic
263C2×C22⋊C4D4×C1111yescharacteristic
264C2×C22⋊C4D4×C1111yescharacteristic
265C2×C22⋊C4C23×C1111yescharacteristic
266C22⋊C8—22no—
267C22⋊C8—41no—
268#95—21no—
269#95C2×C4×C1112yes—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—22no—
273C2×C11—22no—
274C2×C11—42no—
275C2×C11—81no—
276C2×C11—84no—
277C2×C11#151011yescharacteristic
278C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
279C2×C11C2×#35311yescharacteristic
280C24—24no—
281C24—22no—
282C24—22no—
283C24—21no—
284C24—21no—
285C24—41no—
286C24—42no—
287C24—42no—
288C24—42no—
289C24—42no—
290C24—42no—
291C24—42no—
292C24—42no—
293C24—41no—
294C24—41no—
295C24C11×C22⋊C411yescharacteristic
296C24C11×C22⋊C411yescharacteristic
297C24C2×D4×C1111yescharacteristic
298C2×D4—42no—
299C2×D4—44no—
300C2×D4—44no—
301C2×D4—42no—
302C2×D4—44no—
303C2×D4—44no—
304C2×D4—44no—
305C2×D4—44no—
306C2×D4—44no—
307C2×D4—48no—
308C2×D4—432no—
309C2×D4—44no—
310C2×D4—44no—
311C2×D4—44no—
312C22×C4—24no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4C11×C22⋊C411yescharacteristic
324C22×C4C11×C22⋊C411yescharacteristic
325C22×C4C22×C4×C1111yescharacteristic
326C22×C4C2×D4×C1111yescharacteristic
327M16—82no—
328C2×C8—42no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—44no—
334C22⋊C4—44no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—82no—
338C22⋊C4—82no—
339C11#1179611yescharacteristic, direct product factor, Sylow
340C23—22no—
341C23—22no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—24no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—48no—
358C23—48no—
359C23—42no—
360C23—42no—
361C23—44no—
362C23—48no—
363C23—42no—
364C23—44no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—81no—
370C23—81no—
371C23—84no—
372C23—84no—
373C23—84no—
374C23—82no—
375C23—82no—
376C23—82no—
377C23—82no—
378C23C11×#9911yescharacteristic
379C23C11×#9911yescharacteristic
380C23C2×C11×C22⋊C411yescharacteristic
381C23C11×AGL(1,ℤ/8)12yes—
382D4—44no—
383D4—416no—
384D4—416no—
385D4—44no—
386D4—48no—
387C2×C4—24no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—48no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—81no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—82no—
406C8—82no—
407C22—24no—
408C22—24no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—22no—
416C22—42no—
417C22—42no—
418C22—44no—
419C22—44no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—44no—
425C22—41no—
426C22—81no—
427C22—84no—
428C22—84no—
429C22—81no—
430C22—82no—
431C22—82no—
432C22—88no—
433C22—88no—
434C22—82no—
435C22—82no—
436C22C11×AΣL(1,𝔽16)12yes—
437C22C11×#35312yes—
438C22C2×C11×#9911yescharacteristic
439C22C11×#41811yescharacteristic
440C22C11×#42111yescharacteristic
441C4—44no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—41no—
446C4—162no—
447C2—21no—
448C2—21no—
449C2—22no—
450C2—22no—
451C2—42no—
452C2—81no—
453C2—84no—
454C2C11×#151011yescharacteristic
455C2C2×C11×AΣL(1,𝔽16)11yescharacteristic
456C2C2×C11×#35311yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC2×C11×#392C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C11 ◁ C22×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1819C2semidirect
3. C11×#1462C2semidirect
4. C11×#1343C2semidirect
6. C23×D4×C11C4semidirect
12. C11×#392C4semidirect
15. C2×C11×#95C4semidirect
17. C11×#342C22semidirect
19. C11×#323C22semidirect
52. #11796C11direct (N × H)
113. #1819C2×C11semidirect
114. #1462C2×C11semidirect
115. #1343C2×C11semidirect
184. C23×D4C4×C11semidirect
190. #392C4×C11semidirect
193. C2×#95C4×C11semidirect
195. #342C22×C11semidirect
197. #323C22×C11semidirect
339. C11#11796direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3922
C11×#18192
C11×#14622
C11×#13432
#1179611