Finite Group Databasebeta

← C11×#9498 #14586691

Subgroups — C11×#9498 #14586691

Order 2816.

900 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 900 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2405C211yesmaximal, characteristic
2C11×#2312C211yesmaximal, characteristic, complemented
3C11×#1819C211yesmaximal, characteristic, complemented
4C11×#1781C212yesmaximal
5C11×#1304C212yesmaximal, complemented
6C23×D4×C11C2211yescharacteristic
7C2×C11×#123—21no—
8C22×C11×C22⋊C4C2211yescharacteristic
9C2×C11×#99—24no—
10C11×#394—22no—
11C11×#388—24no—
12C11×#386—21no—
13C11×#385C412yescomplemented
14C11×#380—21no—
15C11×#379C412yescomplemented
16C11×#379C2212yes—
17C11×#379C2211yescharacteristic
18C11×#379C2212yes—
19C4×C11×C22⋊C4—21no—
20C11×#342—22no—
21C25×C11C2×C411yescharacteristic
22C25×C11C2311yescharacteristic
23C22×D4×C11—21no—
24C22×D4×C11—22no—
25C22×D4×C11—21no—
26C22×D4×C11—22no—
27C22×D4×C11—44no—
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C11×#123—44no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4C2×C412yes—
46C2×C11×C22⋊C4C2×C412yes—
47C2×C11×C22⋊C4D412yes—
48C2×C11×C22⋊C4D414yes—
49C2×C42×C11—22no—
50C11×#99—48no—
51C11×#95—22no—
52C11×#95—22no—
53C11×#95—22no—
54#9498C1111yesmaximal, characteristic, direct product factor, Sylow
55C24×C11—21no—
56C24×C11—22no—
57C24×C11—42no—
58C24×C11—42no—
59C24×C11—42no—
60C24×C11—42no—
61C24×C11—81no—
62C24×C11—81no—
63C24×C11C22×C411yescharacteristic
64C24×C11C2×D411yescharacteristic
65C24×C11C2×D411yescharacteristic
66C24×C11C2×D412yes—
67C24×C11#4112yes—
68C2×D4×C11—28no—
69C2×D4×C11—24no—
70C2×D4×C11—42no—
71C2×D4×C11—44no—
72C2×D4×C11—42no—
73C2×D4×C11—44no—
74C2×D4×C11—42no—
75C2×D4×C11—44no—
76C2×D4×C11—41no—
77C2×D4×C11—42no—
78C2×D4×C11—41no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—22no—
86C22×C4×C11—24no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11—81no—
91C22×C4×C11C22⋊C412yes—
92C22×C4×C11C22⋊C412yes—
93C11×C4⋊C4—44no—
94C11×C4⋊C4—82no—
95C11×C22⋊C4—24no—
96C11×C22⋊C4—24no—
97C11×C22⋊C4—44no—
98C11×C22⋊C4—44no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—44no—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—44no—
103C11×C22⋊C4—44no—
104C11×C22⋊C4—82no—
105C11×C22⋊C4—82no—
106C11×C22⋊C4—81no—
107C11×C22⋊C4—82no—
108C42×C11—82no—
109#2405C2×C1111yescharacteristic
110#2312C2×C1111yescharacteristic, complemented
111#1819C2×C1111yescharacteristic, complemented
112#1781C2×C1112yes—
113#1304C2×C1112yescomplemented
114C23×C11—22no—
115C23×C11—22no—
116C23×C11—22no—
117C23×C11—22no—
118C23×C11—24no—
119C23×C11—22no—
120C23×C11—24no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—42no—
125C23×C11—41no—
126C23×C11—42no—
127C23×C11—41no—
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—42no—
131C23×C11—42no—
132C23×C11—41no—
133C23×C11—42no—
134C23×C11—41no—
135C23×C11—42no—
136C23×C11—82no—
137C23×C11—82no—
138C23×C11—88no—
139C23×C11—88no—
140C23×C11C2×C22⋊C411yescharacteristic
141C23×C11C4×D412yes—
142C23×C11#12011yescharacteristic
143C23×C11#12112yes—
144C23×C11#12311yescharacteristic
145D4×C11—48no—
146D4×C11—44no—
147D4×C11—44no—
148C2×C4×C11—22no—
149C2×C4×C11—24no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—44no—
160C2×C4×C11—42no—
161C2×C4×C11—44no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—44no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11—82no—
168C2×C4×C11—82no—
169C2×C4×C11—82no—
170C23×D4C22×C1111yescharacteristic
171C2×#123—21no—
172C22×C22⋊C4C22×C1111yescharacteristic
173C2×#99—24no—
174#394—22no—
175#388—24no—
176#386—21no—
177#385C4×C1112yescomplemented
178#380—21no—
179#379C4×C1112yescomplemented
180#379C22×C1112yes—
181#379C22×C1111yescharacteristic
182#379C22×C1112yes—
183C4×C22⋊C4—21no—
184#342—22no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—22no—
190C22×C11—22no—
191C22×C11—21no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—21no—
195C22×C11—22no—
196C22×C11—21no—
197C22×C11—22no—
198C22×C11—44no—
199C22×C11—44no—
200C22×C11—44no—
201C22×C11—42no—
202C22×C11—84no—
203C22×C11—82no—
204C22×C11—82no—
205C22×C11—84no—
206C22×C11—84no—
207C22×C11—84no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11#38611yescharacteristic
211C22×C11#41012yes—
212C22×C11B(4,𝔽2)12yes—
213C4×C11—42no—
214C4×C11—42no—
215C4×C11—42no—
216C4×C11—84no—
217C4×C11—82no—
218C4×C11—162no—
219C25C2×C4×C1111yescharacteristic
220C25C23×C1111yescharacteristic
221C22×D4—21no—
222C22×D4—22no—
223C22×D4—21no—
224C22×D4—22no—
225C22×D4—44no—
226C23×C4C2×C4×C1111yescharacteristic
227C23×C4D4×C1111yescharacteristic
228C23×C4D4×C1111yescharacteristic
229#123—44no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4C2×C4×C1112yes—
244C2×C22⋊C4C2×C4×C1112yes—
245C2×C22⋊C4D4×C1112yes—
246C2×C22⋊C4D4×C1114yes—
247C2×C42—22no—
248#99—48no—
249#95—22no—
250#95—22no—
251#95—22no—
252C2×C11—22no—
253C2×C11—22no—
254C2×C11—42no—
255C2×C11—41no—
256C2×C11—42no—
257C2×C11—82no—
258C2×C11#188911yescharacteristic
259C2×C11#189911yescharacteristic
260C2×C11#191311yescharacteristic
261C24—21no—
262C24—22no—
263C24—42no—
264C24—42no—
265C24—42no—
266C24—42no—
267C24—81no—
268C24—81no—
269C24C22×C4×C1111yescharacteristic
270C24C2×D4×C1111yescharacteristic
271C24C2×D4×C1111yescharacteristic
272C24C2×D4×C1112yes—
273C24C11×#4112yes—
274C2×D4—28no—
275C2×D4—24no—
276C2×D4—42no—
277C2×D4—44no—
278C2×D4—42no—
279C2×D4—44no—
280C2×D4—42no—
281C2×D4—44no—
282C2×D4—41no—
283C2×D4—42no—
284C2×D4—41no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—24no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—81no—
297C22×C4C11×C22⋊C412yes—
298C22×C4C11×C22⋊C412yes—
299C4⋊C4—44no—
300C4⋊C4—82no—
301C22⋊C4—24no—
302C22⋊C4—24no—
303C22⋊C4—44no—
304C22⋊C4—42no—
305C22⋊C4—44no—
306C22⋊C4—44no—
307C22⋊C4—42no—
308C22⋊C4—44no—
309C22⋊C4—44no—
310C22⋊C4—82no—
311C22⋊C4—82no—
312C22⋊C4—81no—
313C22⋊C4—82no—
314C42—82no—
315C11#949811yescharacteristic, direct product factor, Sylow
316C23—22no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—24no—
321C23—22no—
322C23—24no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—42no—
327C23—41no—
328C23—42no—
329C23—41no—
330C23—42no—
331C23—42no—
332C23—42no—
333C23—42no—
334C23—41no—
335C23—42no—
336C23—41no—
337C23—42no—
338C23—82no—
339C23—82no—
340C23—88no—
341C23—88no—
342C23C2×C11×C22⋊C411yescharacteristic
343C23C4×D4×C1112yes—
344C23C11×#12011yescharacteristic
345C23C11×#12112yes—
346C23C11×#12311yescharacteristic
347D4—48no—
348D4—44no—
349D4—44no—
350C2×C4—22no—
351C2×C4—24no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—44no—
362C2×C4—42no—
363C2×C4—44no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—44no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—82no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—22no—
377C22—22no—
378C22—21no—
379C22—22no—
380C22—22no—
381C22—21no—
382C22—22no—
383C22—21no—
384C22—22no—
385C22—44no—
386C22—44no—
387C22—44no—
388C22—42no—
389C22—84no—
390C22—82no—
391C22—82no—
392C22—84no—
393C22—84no—
394C22—84no—
395C22—81no—
396C22—81no—
397C22C11×#38611yescharacteristic
398C22C11×#41012yes—
399C22C11×B(4,𝔽2)12yes—
400C4—42no—
401C4—42no—
402C4—42no—
403C4—84no—
404C4—82no—
405C4—162no—
406C2—22no—
407C2—22no—
408C2—42no—
409C2—42no—
410C2—41no—
411C2—82no—
412C2C11×#188911yescharacteristic
413C2C11×#189911yescharacteristic
414C2C11×#191311yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC24C22×C4×C11
Frattini, cosocleC25C23×C11
prime radicalC23×D4×C11C22
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2312C2semidirect
3. C11×#1819C2semidirect
5. C11×#1304C2semidirect
13. C11×#385C4semidirect
15. C11×#379C4semidirect
54. #9498C11direct (N × H)
110. #2312C2×C11semidirect
111. #1819C2×C11semidirect
113. #1304C2×C11semidirect
177. #385C4×C11semidirect
179. #379C4×C11semidirect
315. C11#9498direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#24052
C11×#23122
C11×#18192
C11×#17812
C11×#13042
#949811