Finite Group Databasebeta

← C11×#13418 #14590611

Subgroups — C11×#13418 #14590611

Order 2816.

422 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3156C211yesmaximal, characteristic
2C11×#2148C211yesmaximal, characteristic
3C2×C11×#362C211yesmaximal, characteristic, complemented
4C2×C11×#362C211yesmaximal, characteristic, complemented
5C11×#2143C211yesmaximal, characteristic
6C11×#1953C211yesmaximal, characteristic, complemented
7C11×#1378C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C2×C11×#135C2211yescharacteristic
10C22×C11×Q16C2211yescharacteristic
11C11×#536—21no—
12C2×C11×M32C2211yescharacteristic
13C2×C11×M32C2211yescharacteristic
14C11×#497—22no—
15C11×#495—21no—
16C11×#494—21no—
17C11×#430—21no—
18C2×C11×#108C2211yescharacteristic
19C2×C11×#108C2211yescharacteristic
20C11×#405C2211yescharacteristic
21C11×#362—22no—
22C11×#362—21no—
23C11×#362—22no—
24C11×#361—21no—
25C11×#359—22no—
26C11×#344—21no—
27C2×C11×#41—21no—
28C22×Q8×C11—21no—
29C11×#137—42no—
30C11×#137—42no—
31C11×#135—21no—
32C11×#135—21no—
33C11×#135—21no—
34C11×#135—21no—
35C2×C11×Q16—22no—
36C2×C11×Q16—21no—
37C2×C11×Q16—21no—
38C2×C11×Q16—21no—
39C2×C11×Q16—21no—
40C2×C11×Q16—21no—
41C2×C11×Q16D411yescharacteristic
42C2×C11×Q16D412yes—
43C2×C11×SD16—22no—
44C2×C11×SD16—21no—
45C2×C11×D8D411yescharacteristic
46C2×C11×M16—21no—
47C2×C11×M16—21no—
48C2×C11×M16D411yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C11×C4⋊Q8—22no—
51C11×#124—22no—
52C11×#123—42no—
53C11×C22⋊Q8—42no—
54C11×#117D411yescharacteristic
55C11×M32—21no—
56C11×M32—21no—
57C11×M32—21no—
58C11×M32—21no—
59C2×C11×C16—21no—
60C2×C11×C16—21no—
61C11×#108—21no—
62C11×#108—21no—
63C11×#108—21no—
64C11×#108—42no—
65C11×#108D412yes—
66C11×#97—21no—
67C4×C8×C11—21no—
68#13418C1111yesmaximal, characteristic, direct product factor, Sylow
69C11×#41—41no—
70C11×#41—41no—
71C11×#41—41no—
72C11×#41—41no—
73C2×Q8×C11—22no—
74C2×Q8×C11—21no—
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—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C11×Q16—22no—
86C11×Q16—21no—
87C11×Q16—22no—
88C11×Q16—21no—
89C11×Q16—44no—
90C11×Q16—41no—
91C11×Q16—41no—
92C11×SD16—44no—
93C11×SD16—41no—
94C11×SD16—41no—
95C11×D8—21no—
96C11×D8—21no—
97C11×M16—22no—
98C11×M16—21no—
99C11×M16—41no—
100C11×M16—41no—
101C11×M16—41no—
102C11×M16D812yes—
103C2×C8×C11—21no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11#4111yescharacteristic
110C2×C8×C11#4111yescharacteristic
111C2×C8×C11#4111yescharacteristic
112C11×C4⋊C4—21no—
113C11×C4⋊C4—44no—
114C11×C22⋊C4—44no—
115C11×C22⋊C4SD1612yes—
116C42×C11—21no—
117C11×C16—41no—
118C11×C16—41no—
119#3156C2×C1111yescharacteristic
120#2148C2×C1111yescharacteristic
121C2×#362C2×C1111yescharacteristic, complemented
122C2×#362C2×C1111yescharacteristic, complemented
123#2143C2×C1111yescharacteristic
124#1953C2×C1111yescharacteristic, complemented
125#1378C2×C1111yescharacteristic, complemented
126C23×C11—41no—
127C23×C11C2×SD1611yescharacteristic
128Q8×C11—41no—
129Q8×C11—42no—
130Q8×C11—42no—
131Q8×C11—41no—
132Q8×C11—81no—
133Q8×C11—81no—
134D4×C11—41no—
135D4×C11—41no—
136D4×C11—81no—
137D4×C11—81no—
138C2×C4×C11—22no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12411yescharacteristic
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C8×C11—22no—
152C8×C11—42no—
153C8×C11—81no—
154C8×C11#12111yescharacteristic
155C8×C11#12111yescharacteristic
156C8×C11#12311yescharacteristic
157C8×C11#12311yescharacteristic
158C2×#137—21no—
159C2×#135C22×C1111yescharacteristic
160C22×Q16C22×C1111yescharacteristic
161#536—21no—
162C2×M32C22×C1111yescharacteristic
163C2×M32C22×C1111yescharacteristic
164#497—22no—
165#495—21no—
166#494—21no—
167#430—21no—
168C2×#108C22×C1111yescharacteristic
169C2×#108C22×C1111yescharacteristic
170#405C22×C1111yescharacteristic
171#362—22no—
172#362—21no—
173#362—22no—
174#361—21no—
175#359—22no—
176#344—21no—
177C22×C11—41no—
178C22×C11—82no—
179C22×C11—81no—
180C22×C11#45011yescharacteristic
181C22×C11#46011yescharacteristic
182C22×C11#48611yescharacteristic
183C4×C11—42no—
184C4×C11—81no—
185C4×C11—82no—
186C4×C11#39411yescharacteristic
187C4×C11#44711yescharacteristic
188C4×C11#45911yescharacteristic
189C4×C11#49011yescharacteristic
190C2×#41—21no—
191C22×Q8—21no—
192#137—42no—
193#137—42no—
194#135—21no—
195#135—21no—
196#135—21no—
197#135—21no—
198C2×Q16—22no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16—21no—
202C2×Q16—21no—
203C2×Q16—21no—
204C2×Q16D4×C1112yes—
205C2×Q16D4×C1111yescharacteristic
206C2×SD16—22no—
207C2×SD16—21no—
208C2×D8D4×C1111yescharacteristic
209C2×M16—21no—
210C2×M16—21no—
211C2×M16D4×C1111yescharacteristic
212C22×C8C23×C1111yescharacteristic
213C4⋊Q8—22no—
214#124—22no—
215#123—42no—
216C22⋊Q8—42no—
217#117D4×C1111yescharacteristic
218M32—21no—
219M32—21no—
220M32—21no—
221M32—21no—
222C2×C16—21no—
223C2×C16—21no—
224#108—21no—
225#108—21no—
226#108—21no—
227#108—42no—
228#108D4×C1112yes—
229#97—21no—
230C4×C8—21no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11—21no—
234C2×C11—161no—
235C2×C11#204111yescharacteristic
236#41—41no—
237#41—41no—
238#41—41no—
239#41—41no—
240C2×Q8—22no—
241C2×Q8—21no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×D4—21no—
248C2×D4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4C2×D4×C1111yescharacteristic
252Q16—22no—
253Q16—21no—
254Q16—22no—
255Q16—21no—
256Q16—44no—
257Q16—41no—
258Q16—41no—
259SD16—44no—
260SD16—41no—
261SD16—41no—
262D8—21no—
263D8—21no—
264M16—21no—
265M16—22no—
266M16—41no—
267M16—41no—
268M16—41no—
269M16C11×D812yes—
270C2×C8—21no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8C2×D4×C1111yescharacteristic
274C2×C8C2×D4×C1111yescharacteristic
275C2×C8C2×D4×C1111yescharacteristic
276C2×C8C11×#4111yescharacteristic
277C2×C8C11×#4111yescharacteristic
278C2×C8C11×#4111yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—44no—
281C22⋊C4—44no—
282C22⋊C4C11×SD1612yes—
283C42—21no—
284C16—41no—
285C16—41no—
286C11#1341811yescharacteristic, direct product factor, Sylow
287C23—41no—
288C23C2×C11×SD1611yescharacteristic
289Q8—41no—
290Q8—42no—
291Q8—42no—
292Q8—41no—
293Q8—81no—
294Q8—81no—
295D4—41no—
296D4—41no—
297D4—81no—
298D4—81no—
299C2×C4—22no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4C11×#12011yescharacteristic
307C2×C4C11×#12111yescharacteristic
308C2×C4C11×#12411yescharacteristic
309C2×C4C2×C11×D811yescharacteristic
310C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
311C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
312C8—22no—
313C8—42no—
314C8—81no—
315C8C11×#12111yescharacteristic
316C8C11×#12111yescharacteristic
317C8C11×#12311yescharacteristic
318C8C11×#12311yescharacteristic
319C22—41no—
320C22—82no—
321C22—81no—
322C22C11×#45011yescharacteristic
323C22C11×#46011yescharacteristic
324C22C11×#48611yescharacteristic
325C4—42no—
326C4—81no—
327C4—82no—
328C4C11×#39411yescharacteristic
329C4C11×#44711yescharacteristic
330C4C11×#45911yescharacteristic
331C4C11×#49011yescharacteristic
332C2—21no—
333C2—21no—
334C2—21no—
335C2—161no—
336C2C11×#204111yescharacteristic
subgroupG/H
center, socleC2×C11#2041
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC2×C11×#135C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#362C2semidirect
4. C2×C11×#362C2semidirect
6. C11×#1953C2semidirect
7. C11×#1378C2semidirect
68. #13418C11direct (N × H)
121. C2×#362C2×C11semidirect
122. C2×#362C2×C11semidirect
124. #1953C2×C11semidirect
125. #1378C2×C11semidirect
286. C11#13418direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31562
C11×#21482
C2×C11×#3622
C11×#21432
C11×#19532
C11×#13782
#1341811