Finite Group Databasebeta

← C11×#9335 #14586528

Subgroups — C11×#9335 #14586528

Order 2816.

400 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 114 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×#3234C211yesmaximal, characteristic
2C11×#2980C211yesmaximal, characteristic
3C11×#1553C211yesmaximal, characteristic
4C11×#1534C211yesmaximal, characteristic, complemented
5C11×#1470C211yesmaximal, characteristic, complemented
6C11×#1308C211yesmaximal, characteristic, complemented
7C11×#1287C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10C11×#501—21no—
11C11×#490—21no—
12C11×#481C412yes—
13C11×#480C412yes—
14C11×#478—22no—
15C11×#435—22no—
16C11×#435—22no—
17C11×#432C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C11×#432C2211yescharacteristic
20C11×#432C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#408—22no—
23C11×#332—21no—
24C11×#331—21no—
25C11×#330—22no—
26C11×#324—22no—
27C2×C11×#41—21no—
28C2×C11×M16—22no—
29C22×C8×C11—22no—
30C11×C4⋊Q8D411yescharacteristic
31C11×#127D411yescharacteristic
32C11×#125—21no—
33C11×#125—21no—
34C11×#125—21no—
35C11×#125—21no—
36C11×#124—21no—
37C11×#121—21no—
38C11×#121C2×C412yes—
39C4×D4×C11—21no—
40C4×D4×C11D412yes—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4C2×C411yescharacteristic
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C11×#107—22no—
47C11×#106—22no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×#102—22no—
54C11×#102—22no—
55C11×C22⋊C8—24no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8C2×C412yes—
60C11×C22⋊C8D412yes—
61C11×#97—21no—
62C11×#97—21no—
63C11×#97—21no—
64C11×#97D412yes—
65C4×C8×C11—21no—
66#9335C1111yesmaximal, characteristic, direct product factor, Sylow
67C11×#41—81no—
68C11×#41—81no—
69C2×Q8×C11—21no—
70C2×D4×C11—22no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11C22⋊C412yes—
74C22×C4×C11—22no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C11×M16—82no—
81C2×C8×C11—22no—
82C2×C8×C11—22no—
83C2×C8×C11—22no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C2×C8×C11—82no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4C22⋊C412yes—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—22no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103#3234C2×C1111yescharacteristic
104#2980C2×C1111yescharacteristic
105#1553C2×C1111yescharacteristic
106#1534C2×C1111yescharacteristic, complemented
107#1470C2×C1111yescharacteristic, complemented
108#1308C2×C1111yescharacteristic, complemented
109#1287C2×C1111yescharacteristic, complemented
110C23×C11—22no—
111C23×C11C4×D411yescharacteristic
112Q8×C11—81no—
113D4×C11—42no—
114D4×C11—81no—
115D4×C11—81no—
116D4×C11—82no—
117C2×C4×C11—22no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—81no—
127C2×C4×C11C2×C22⋊C411yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C8×C11—42no—
134C8×C11—42no—
135C8×C11—42no—
136C8×C11—81no—
137C8×C11—81no—
138#532C22×C1111yescharacteristic
139C2×#125C22×C1111yescharacteristic
140#501—21no—
141#490—21no—
142#481C4×C1112yes—
143#480C4×C1112yes—
144#478—22no—
145#435—22no—
146#435—22no—
147#432C22×C1111yescharacteristic
148#432C22×C1111yescharacteristic
149#432C22×C1111yescharacteristic
150#432C22×C1111yescharacteristic
151#431C22×C1111yescharacteristic
152#408—22no—
153#332—21no—
154#331—21no—
155#330—22no—
156#324—22no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—42no—
161C22×C11—42no—
162C22×C11—42no—
163C22×C11#38611yescharacteristic
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—42no—
171C4×C11—81no—
172C4×C11—81no—
173C2×#41—21no—
174C2×M16—22no—
175C22×C8—22no—
176C4⋊Q8D4×C1111yescharacteristic
177#127D4×C1111yescharacteristic
178#125—21no—
179#125—21no—
180#125—21no—
181#125—21no—
182#124—21no—
183#121—21no—
184#121C2×C4×C1112yes—
185C4×D4—21no—
186C4×D4D4×C1112yes—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4C2×C4×C1111yescharacteristic
190C2×C4⋊C4C2×C4×C1111yescharacteristic
191C2×C42C23×C1111yescharacteristic
192#107—22no—
193#106—22no—
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199#102—22no—
200#102—22no—
201C22⋊C8—24no—
202C22⋊C8—21no—
203C22⋊C8—21no—
204C22⋊C8—21no—
205C22⋊C8C2×C4×C1112yes—
206C22⋊C8D4×C1112yes—
207#97—21no—
208#97—21no—
209#97—21no—
210#97D4×C1112yes—
211C4×C8—21no—
212C2×C11—41no—
213C2×C11—82no—
214C2×C11#188111yescharacteristic
215C2×C11#190411yescharacteristic
216C2×C11#191511yescharacteristic
217#41—81no—
218#41—81no—
219C2×Q8—21no—
220C2×D4—22no—
221C2×D4—21no—
222C2×D4—21no—
223C2×D4C11×C22⋊C412yes—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4C22×C4×C1111yescharacteristic
228C22×C4C2×D4×C1111yescharacteristic
229C22×C4C11×#4111yescharacteristic
230M16—82no—
231C2×C8—22no—
232C2×C8—22no—
233C2×C8—22no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—82no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4C11×C22⋊C412yes—
247C22⋊C4—22no—
248C22⋊C4—22no—
249C42C2×D4×C1111yescharacteristic
250C42C2×D4×C1111yescharacteristic
251C42C2×D4×C1111yescharacteristic
252C42C11×#4111yescharacteristic
253C11#933511yescharacteristic, direct product factor, Sylow
254C23—22no—
255C23C4×D4×C1111yescharacteristic
256Q8—81no—
257D4—42no—
258D4—81no—
259D4—81no—
260D4—82no—
261C2×C4—22no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—81no—
271C2×C4C2×C11×C22⋊C411yescharacteristic
272C2×C4C4×D4×C1111yescharacteristic
273C2×C4C11×#12011yescharacteristic
274C2×C4C11×#12111yescharacteristic
275C2×C4C11×#12111yescharacteristic
276C2×C4C11×#12311yescharacteristic
277C8—42no—
278C8—42no—
279C8—42no—
280C8—81no—
281C8—81no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22C11×#38611yescharacteristic
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—42no—
296C4—81no—
297C4—81no—
298C2—41no—
299C2—82no—
300C2C11×#188111yescharacteristic
301C2C11×#190411yescharacteristic
302C2C11×#191511yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1534C2semidirect
5. C11×#1470C2semidirect
6. C11×#1308C2semidirect
7. C11×#1287C2semidirect
66. #9335C11direct (N × H)
106. #1534C2×C11semidirect
107. #1470C2×C11semidirect
108. #1308C2×C11semidirect
109. #1287C2×C11semidirect
253. C11#9335direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32342
C11×#29802
C11×#15532
C11×#15342
C11×#14702
C11×#13082
C11×#12872
#933511