Finite Group Databasebeta

← C11×#13039 #14590232

Subgroups — C11×#13039 #14590232

Order 2816.

472 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#510C211yesmaximal, characteristic
2C2×C11×#444C211yesmaximal, characteristic
3C2×C11×#362C211yesmaximal, characteristic, complemented
4C2×C11×#360C211yesmaximal, characteristic
5C11×#1971C211yesmaximal, characteristic, complemented
6C11×#1383C211yesmaximal, characteristic, complemented
7C11×#1375C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9C22×C11×Q16C2211yescharacteristic
10C2×C11×#131—21no—
11C11×#510—22no—
12C11×#510—22no—
13C2×C11×Q32C412yescomplemented
14C2×C11×SD32C412yescomplemented
15C2×C11×M32C2211yescharacteristic
16C2×C11×M32C2211yescharacteristic
17C11×#444—22no—
18C11×#444—22no—
19C2×C11×#108C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#104—21no—
22C2×C11×#103—21no—
23C2×C11×#97C2211yescharacteristic
24C11×#391—21no—
25C11×#362—22no—
26C11×#360—22no—
27C2×C11×#41—21no—
28C22×Q8×C11—21no—
29C11×#135—21no—
30C11×#135—21no—
31C11×#135D412yes—
32C11×#135D412yes—
33C2×C11×Q16—21no—
34C2×C11×Q16—21no—
35C2×C11×Q16—21no—
36C2×C11×Q16—21no—
37C2×C11×Q16—21no—
38C2×C11×Q16C2×C412yes—
39C2×C11×Q16C2×C411yescharacteristic
40C2×C11×SD16—21no—
41C2×C11×D8C2×C411yescharacteristic
42C11×#131—24no—
43C11×#131—42no—
44C2×C11×M16—21no—
45C2×C11×M16—41no—
46C22×C8×C11—41no—
47C22×C8×C11D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C2×C11×C4⋊C4—21no—
50C2×C42×C11D411yescharacteristic
51C11×Q32—24no—
52C11×SD32—24no—
53C11×M32—21no—
54C11×M32—21no—
55C11×M32—21no—
56C11×M32—21no—
57C2×C11×C16—21no—
58C2×C11×C16C2×C412yes—
59C11×#108—21no—
60C11×#108D412yes—
61C11×#106—21no—
62C11×#106—21no—
63C11×#104—24no—
64C11×#103—42no—
65C11×#97—21no—
66C11×#97—21no—
67C11×#95—42no—
68#13039C1111yesmaximal, characteristic, direct product factor, Sylow
69C11×#41—22no—
70C11×#41—22no—
71C11×#41—41no—
72C11×#41—41no—
73C2×Q8×C11—21no—
74C2×Q8×C11—22no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×D4×C11—21no—
81C2×D4×C11—41no—
82C22×C4×C11—21no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C11×Q16—21no—
88C11×Q16—22no—
89C11×Q16—22no—
90C11×Q16—41no—
91C11×Q16—41no—
92C11×Q16C22⋊C412yes—
93C11×SD16—22no—
94C11×SD16—22no—
95C11×D8—21no—
96C11×D8C22⋊C412yes—
97C11×M16—22no—
98C11×M16—44no—
99C11×M16—41no—
100C2×C8×C11—21no—
101C2×C8×C11—21no—
102C2×C8×C11—44no—
103C2×C8×C11—41no—
104C2×C8×C11D812yes—
105C2×C8×C11C22×C411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11#4111yescharacteristic
110C2×C8×C11#4111yescharacteristic
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C42×C11—21no—
114C42×C11—21no—
115C11×C16—22no—
116C11×C16—41no—
117C2×#510C2×C1111yescharacteristic
118C2×#444C2×C1111yescharacteristic
119C2×#362C2×C1111yescharacteristic, complemented
120C2×#360C2×C1111yescharacteristic
121#1971C2×C1111yescharacteristic, complemented
122#1383C2×C1111yescharacteristic, complemented
123#1375C2×C1111yescharacteristic, complemented
124C23×C11—41no—
125C23×C11AGL(1,ℤ/8)11yescharacteristic
126Q8×C11—22no—
127Q8×C11—41no—
128Q8×C11—42no—
129Q8×C11—42no—
130Q8×C11—81no—
131Q8×C11—81no—
132D4×C11—22no—
133D4×C11—42no—
134D4×C11—42no—
135D4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11—82no—
145C2×C4×C11—81no—
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11#13511yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C8×C11—22no—
153C8×C11—42no—
154C8×C11C2×C22⋊C411yescharacteristic
155C8×C11C4×D411yescharacteristic
156C8×C11#12111yescharacteristic
157C8×C11#12311yescharacteristic
158C2×#135C22×C1111yescharacteristic
159C22×Q16C22×C1111yescharacteristic
160C2×#131—21no—
161#510—22no—
162#510—22no—
163C2×Q32C4×C1112yescomplemented
164C2×SD32C4×C1112yescomplemented
165C2×M32C22×C1111yescharacteristic
166C2×M32C22×C1111yescharacteristic
167#444—22no—
168#444—22no—
169C2×#108C22×C1111yescharacteristic
170C2×#106C22×C1111yescharacteristic
171C2×#104—21no—
172C2×#103—21no—
173C2×#97C22×C1111yescharacteristic
174#391—21no—
175#362—22no—
176#360—22no—
177C22×C11—22no—
178C22×C11—42no—
179C22×C11—82no—
180C22×C11#44211yescharacteristic
181C22×C11#44911yescharacteristic
182C22×C11#45911yescharacteristic
183C4×C11—42no—
184C4×C11—81no—
185C4×C11—82no—
186C4×C11—161no—
187C4×C11#38611yescharacteristic
188C4×C11C4×D811yescharacteristic
189C4×C11#44711yescharacteristic
190C4×C11#46311yescharacteristic
191C2×#41—21no—
192C22×Q8—21no—
193#135—21no—
194#135—21no—
195#135D4×C1112yes—
196#135D4×C1112yes—
197C2×Q16—21no—
198C2×Q16—21no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16—21no—
202C2×Q16C2×C4×C1112yes—
203C2×Q16C2×C4×C1111yescharacteristic
204C2×SD16—21no—
205C2×D8C2×C4×C1111yescharacteristic
206#131—24no—
207#131—42no—
208C2×M16—21no—
209C2×M16—41no—
210C22×C8—41no—
211C22×C8D4×C1111yescharacteristic
212C22×C8C23×C1111yescharacteristic
213C2×C4⋊C4—21no—
214C2×C42D4×C1111yescharacteristic
215Q32—24no—
216SD32—24no—
217M32—21no—
218M32—21no—
219M32—21no—
220M32—21no—
221C2×C16—21no—
222C2×C16C2×C4×C1112yes—
223#108—21no—
224#108D4×C1112yes—
225#106—21no—
226#106—21no—
227#104—24no—
228#103—42no—
229#97—21no—
230#97—21no—
231#95—42no—
232C2×C11—21no—
233C2×C11—21no—
234C2×C11—82no—
235C2×C11#187911yescharacteristic
236C2×C11#218012yes—
237#41—22no—
238#41—22no—
239#41—41no—
240#41—41no—
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×D4—21no—
249C2×D4—41no—
250C22×C4—21no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4C2×D4×C1111yescharacteristic
255Q16—22no—
256Q16—21no—
257Q16—22no—
258Q16—41no—
259Q16—41no—
260Q16C11×C22⋊C412yes—
261SD16—22no—
262SD16—22no—
263D8—21no—
264D8C11×C22⋊C412yes—
265M16—22no—
266M16—44no—
267M16—41no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—44no—
271C2×C8—41no—
272C2×C8C11×D812yes—
273C2×C8C22×C4×C1111yescharacteristic
274C2×C8C2×D4×C1111yescharacteristic
275C2×C8C2×D4×C1111yescharacteristic
276C2×C8C2×D4×C1111yescharacteristic
277C2×C8C11×#4111yescharacteristic
278C2×C8C11×#4111yescharacteristic
279C4⋊C4—41no—
280C4⋊C4—41no—
281C42—21no—
282C42—21no—
283C16—22no—
284C16—41no—
285C11#1303911yescharacteristic, direct product factor, Sylow
286C23—41no—
287C23C11×AGL(1,ℤ/8)11yescharacteristic
288Q8—22no—
289Q8—41no—
290Q8—42no—
291Q8—42no—
292Q8—81no—
293Q8—81no—
294D4—22no—
295D4—42no—
296D4—42no—
297D4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—82no—
307C2×C4—81no—
308C2×C4C4×D4×C1111yescharacteristic
309C2×C4C11×#12011yescharacteristic
310C2×C4C11×#12111yescharacteristic
311C2×C4C2×C11×D811yescharacteristic
312C2×C4C11×#13511yescharacteristic
313C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
314C8—22no—
315C8—42no—
316C8C2×C11×C22⋊C411yescharacteristic
317C8C4×D4×C1111yescharacteristic
318C8C11×#12111yescharacteristic
319C8C11×#12311yescharacteristic
320C22—22no—
321C22—42no—
322C22—82no—
323C22C11×#44211yescharacteristic
324C22C11×#44911yescharacteristic
325C22C11×#45911yescharacteristic
326C4—42no—
327C4—81no—
328C4—82no—
329C4—161no—
330C4C11×#38611yescharacteristic
331C4C4×C11×D811yescharacteristic
332C4C11×#44711yescharacteristic
333C4C11×#46311yescharacteristic
334C2—21no—
335C2—21no—
336C2—82no—
337C2C11×#187911yescharacteristic
338C2C11×#218012yes—
subgroupG/H
center, socleC22×C11#442
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
prime radicalC2×C11×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#97 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#362C2semidirect
5. C11×#1971C2semidirect
6. C11×#1383C2semidirect
7. C11×#1375C2semidirect
13. C2×C11×Q32C4semidirect
14. C2×C11×SD32C4semidirect
68. #13039C11direct (N × H)
119. C2×#362C2×C11semidirect
121. #1971C2×C11semidirect
122. #1383C2×C11semidirect
123. #1375C2×C11semidirect
163. C2×Q32C4×C11semidirect
164. C2×SD32C4×C11semidirect
285. C11#13039direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5102
C2×C11×#4442
C2×C11×#3622
C2×C11×#3602
C11×#19712
C11×#13832
C11×#13752
#1303911