Finite Group Databasebeta

← C11×#9968 #14587161

Subgroups — C11×#9968 #14587161

Order 2816.

772 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 138 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×#481C212yesmaximal, complemented
2C11×#2656C211yesmaximal, characteristic
3C2×C11×#327C212yesmaximal, complemented
4C11×#1445C211yesmaximal, characteristic, complemented
5C11×#1280C211yesmaximal, characteristic, complemented
6C2×C11×#121—22no—
7C2×C11×#121C2212yes—
8C22×C11×C4⋊C4C2211yescharacteristic
9C11×#481—24no—
10C11×#481—24no—
11C2×C11×#106—22no—
12C2×C11×#102—22no—
13C2×C11×C22⋊C8C2212yes—
14C11×#399—22no—
15C11×#392—22no—
16C2×C11×#95—22no—
17C2×C11×#95C2211yescharacteristic
18C2×C11×#95C2211yescharacteristic
19C11×#327—24no—
20C22×D4×C11—22no—
21C22×D4×C11—22no—
22C22×D4×C11D412yes—
23C23×C4×C11—21no—
24C23×C4×C11—21no—
25C23×C4×C11D412yes—
26C23×C4×C11C2311yescharacteristic
27C22×C8×C11—22no—
28C11×#121—22no—
29C11×#121—22no—
30C11×#121—22no—
31C11×#121—22no—
32C11×#121—44no—
33C11×#121—44no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4D412yes—
39C2×C11×C4⋊C4D412yescomplemented
40C2×C11×C22⋊C4—24no—
41C2×C11×C22⋊C4—22no—
42C11×#106—28no—
43C11×#102—28no—
44C11×C22⋊C8—22no—
45C11×C22⋊C8D414yescomplemented
46C11×#95—22no—
47C11×#95—22no—
48C11×#95—44no—
49#9968C1111yesmaximal, characteristic, direct product factor, Sylow
50C24×C11—22no—
51C24×C11C2×D411yescharacteristic
52C2×D4×C11—22no—
53C2×D4×C11—22no—
54C2×D4×C11—44no—
55C2×D4×C11—44no—
56C2×D4×C11—42no—
57C2×D4×C11—42no—
58C2×D4×C11—44no—
59C2×D4×C11—44no—
60C2×D4×C11—82no—
61C2×D4×C11—82no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—42no—
68C22×C4×C11—42no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11—41no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—42no—
78C22×C4×C11SD1614yes—
79C22×C4×C11C2×D412yes—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D412yes—
82C22×C4×C11#4111yescharacteristic
83C2×C8×C11—24no—
84C2×C8×C11—44no—
85C11×C4⋊C4—24no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—44no—
89C11×C4⋊C4—42no—
90C11×C22⋊C4—48no—
91C11×C22⋊C4—42no—
92C11×C22⋊C4—42no—
93C2×#481C2×C1112yescomplemented
94#2656C2×C1111yescharacteristic
95C2×#327C2×C1112yescomplemented
96#1445C2×C1111yescharacteristic, complemented
97#1280C2×C1111yescharacteristic, complemented
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—22no—
101C23×C11—42no—
102C23×C11—44no—
103C23×C11—42no—
104C23×C11—42no—
105C23×C11—44no—
106C23×C11#12011yescharacteristic
107C23×C11#12111yescharacteristic
108C23×C11#12711yescharacteristic
109C23×C11C2×SD1612yes—
110C23×C11AGL(1,ℤ/8)12yes—
111D4×C11—44no—
112D4×C11—82no—
113D4×C11—88no—
114D4×C11—84no—
115D4×C11—82no—
116D4×C11—82no—
117C2×C4×C11—24no—
118C2×C4×C11—24no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—44no—
125C2×C4×C11—44no—
126C2×C4×C11—42no—
127C2×C4×C11—44no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—44no—
131C2×C4×C11—82no—
132C2×C4×C11—82no—
133C2×C4×C11—81no—
134C2×C4×C11—82no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11#12012yes—
139C2×C4×C11#12112yes—
140C8×C11—44no—
141C2×#121—22no—
142C2×#121C22×C1112yes—
143C22×C4⋊C4C22×C1111yescharacteristic
144#481—24no—
145#481—24no—
146C2×#106—22no—
147C2×#102—22no—
148C2×C22⋊C8C22×C1112yes—
149#399—22no—
150#392—22no—
151C2×#95—22no—
152C2×#95C22×C1111yescharacteristic
153C2×#95C22×C1111yescharacteristic
154#327—24no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—84no—
164C22×C11—84no—
165C22×C11—82no—
166C22×C11—82no—
167C22×C11—82no—
168C22×C11#39211yescharacteristic
169C22×C11#45012yes—
170C22×C11#45311yescharacteristic
171C22×C11#45411yescharacteristic
172C22×C11#45812yes—
173C22×C11#46012yes—
174C22×C11#49211yescharacteristic
175C22×C11#49611yescharacteristic
176C4×C11—22no—
177C4×C11—22no—
178C4×C11—44no—
179C4×C11—82no—
180C4×C11—82no—
181C4×C11—82no—
182C22×D4—22no—
183C22×D4—22no—
184C22×D4D4×C1112yes—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4D4×C1112yes—
188C23×C4C23×C1111yescharacteristic
189C22×C8—22no—
190#121—22no—
191#121—22no—
192#121—22no—
193#121—22no—
194#121—44no—
195#121—44no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4D4×C1112yes—
201C2×C4⋊C4D4×C1112yescomplemented
202C2×C22⋊C4—24no—
203C2×C22⋊C4—22no—
204#106—28no—
205#102—28no—
206C22⋊C8—22no—
207C22⋊C8D4×C1114yescomplemented
208#95—22no—
209#95—22no—
210#95—44no—
211C2×C11—21no—
212C2×C11—22no—
213C2×C11—21no—
214C2×C11—162no—
215C2×C11#161312yes—
216C2×C11#161612yes—
217C2×C11#200611yescharacteristic
218C2×C11#201411yescharacteristic
219C2×C11#202211yescharacteristic
220C24—22no—
221C24C2×D4×C1111yescharacteristic
222C2×D4—22no—
223C2×D4—22no—
224C2×D4—44no—
225C2×D4—44no—
226C2×D4—42no—
227C2×D4—42no—
228C2×D4—44no—
229C2×D4—44no—
230C2×D4—82no—
231C2×D4—82no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—41no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—42no—
248C22×C4C11×SD1614yes—
249C22×C4C2×D4×C1112yes—
250C22×C4C2×D4×C1111yescharacteristic
251C22×C4C2×D4×C1112yes—
252C22×C4C11×#4111yescharacteristic
253C2×C8—24no—
254C2×C8—44no—
255C4⋊C4—24no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—44no—
259C4⋊C4—42no—
260C22⋊C4—48no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C11#996811yescharacteristic, direct product factor, Sylow
264C23—21no—
265C23—21no—
266C23—22no—
267C23—42no—
268C23—44no—
269C23—42no—
270C23—42no—
271C23—44no—
272C23C11×#12011yescharacteristic
273C23C11×#12111yescharacteristic
274C23C11×#12711yescharacteristic
275C23C2×C11×SD1612yes—
276C23C11×AGL(1,ℤ/8)12yes—
277D4—44no—
278D4—82no—
279D4—88no—
280D4—82no—
281D4—82no—
282D4—84no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—42no—
293C2×C4—44no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—82no—
298C2×C4—82no—
299C2×C4—81no—
300C2×C4—82no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4C11×#12012yes—
305C2×C4C11×#12112yes—
306C8—44no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—84no—
316C22—84no—
317C22—82no—
318C22—82no—
319C22—82no—
320C22C11×#39211yescharacteristic
321C22C11×#45012yes—
322C22C11×#45311yescharacteristic
323C22C11×#45411yescharacteristic
324C22C11×#45812yes—
325C22C11×#46012yes—
326C22C11×#49211yescharacteristic
327C22C11×#49611yescharacteristic
328C4—22no—
329C4—22no—
330C4—44no—
331C4—82no—
332C4—82no—
333C4—82no—
334C2—21no—
335C2—21no—
336C2—22no—
337C2—162no—
338C2C11×#161312yes—
339C2C11×#161612yes—
340C2C11×#200611yescharacteristic
341C2C11×#201411yescharacteristic
342C2C11×#202211yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC11×#2656C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#481C2semidirect
3. C2×C11×#327C2semidirect
4. C11×#1445C2semidirect
5. C11×#1280C2semidirect
39. C2×C11×C4⋊C4D4semidirect
45. C11×C22⋊C8D4semidirect
49. #9968C11direct (N × H)
93. C2×#481C2×C11semidirect
95. C2×#327C2×C11semidirect
96. #1445C2×C11semidirect
97. #1280C2×C11semidirect
201. C2×C4⋊C4D4×C11semidirect
207. C22⋊C8D4×C11semidirect
263. C11#9968direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4812
C11×#26562
C2×C11×#3272
C11×#14452
C11×#12802
#996811