Finite Group Databasebeta

← C11×#10448 #14587641

Subgroups — C11×#10448 #14587641

Order 2816.

408 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#474C211yesmaximal, characteristic
2C11×#1800C211yesmaximal, characteristic
3C11×#1570C211yesmaximal, characteristic, complemented
4C11×#1549C211yesmaximal, characteristic, complemented
5C11×#1548C211yesmaximal, characteristic, complemented
6C11×#1478C211yesmaximal, characteristic
7C11×#1301C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C11×#474—22no—
11C11×#474—22no—
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C2×C11×#107—21no—
15C11×#423C2211yescharacteristic
16C11×#423C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#102—21no—
19C2×C11×#100—21no—
20C11×#343—21no—
21C11×#334—22no—
22C11×#333—22no—
23C11×#332—22no—
24C11×D4⋊C8—22no—
25C22×Q8×C11—21no—
26C22×D4×C11D411yescharacteristic
27C23×C4×C11—21no—
28C2×C11×M16—21no—
29C2×C11×M16—21no—
30C22×C8×C11—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8D412yes—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C22⋊C4—21no—
43C2×C42×C11C2311yescharacteristic
44C11×#107—24no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8D412yes—
52C11×C4⋊C8D412yes—
53C11×#102—24no—
54C11×#100—42no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C4×C8×C11—21no—
58C4×C8×C11—21no—
59#10448C1111yesmaximal, characteristic, direct product factor, Sylow
60C24×C11—21no—
61C2×Q8×C11—22no—
62C2×Q8×C11—41no—
63C2×Q8×C11—82no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11SD1612yes—
70C22×C4×C11—21no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—82no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C11×M16—41no—
79C11×M16—41no—
80C11×M16—41no—
81C11×M16—41no—
82C2×C8×C11—22no—
83C2×C8×C11—22no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101C2×#474C2×C1111yescharacteristic
102#1800C2×C1111yescharacteristic
103#1570C2×C1111yescharacteristic, complemented
104#1549C2×C1111yescharacteristic, complemented
105#1548C2×C1111yescharacteristic, complemented
106#1478C2×C1111yescharacteristic
107#1301C2×C1111yescharacteristic, complemented
108C23×C11—22no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11—81no—
112C23×C11—81no—
113C23×C11#12311yescharacteristic
114Q8×C11—82no—
115Q8×C11—82no—
116D4×C11—22no—
117D4×C11—22no—
118D4×C11—41no—
119D4×C11—41no—
120C2×C4×C11—22no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—42no—
124C2×C4×C11—82no—
125C2×C4×C11—82no—
126C2×C4×C11—82no—
127C2×C4×C11—81no—
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11#12411yescharacteristic
134C2×C4×C11C2×SD1611yescharacteristic
135C2×C4×C11#13511yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C8×C11—42no—
139C8×C11—42no—
140C8×C11—81no—
141C8×C11—81no—
142C8×C11—81no—
143C2×C4⋊Q8C22×C1111yescharacteristic
144C2×C4×D4C22×C1111yescharacteristic
145#474—22no—
146#474—22no—
147#431C22×C1111yescharacteristic
148#431C22×C1111yescharacteristic
149C2×#107—21no—
150#423C22×C1111yescharacteristic
151#423C22×C1111yescharacteristic
152C2×C4⋊C8C22×C1111yescharacteristic
153C2×#102—21no—
154C2×#100—21no—
155#343—21no—
156#334—22no—
157#333—22no—
158#332—22no—
159D4⋊C8—22no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—42no—
163C22×C11—82no—
164C22×C11—82no—
165C22×C11—81no—
166C22×C11—81no—
167C22×C11#39411yescharacteristic
168C22×C11#48311yescharacteristic
169C22×C11#48511yescharacteristic
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—81no—
174C4×C11—82no—
175C4×C11#44811yescharacteristic
176C4×C11#45211yescharacteristic
177C4×C11#46511yescharacteristic
178C4×C11#47011yescharacteristic
179C4×C11#47212yes—
180C22×Q8—21no—
181C22×D4D4×C1111yescharacteristic
182C23×C4—21no—
183C2×M16—21no—
184C2×M16—21no—
185C22×C8—21no—
186C4⋊Q8—21no—
187C4⋊Q8—21no—
188C4⋊Q8—21no—
189C4⋊Q8D4×C1112yes—
190C4×D4—21no—
191C4×D4—21no—
192C4×D4—21no—
193C4×D4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4D4×C1111yescharacteristic
197C2×C22⋊C4—21no—
198C2×C42C23×C1111yescharacteristic
199#107—24no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8D4×C1112yes—
207C4⋊C8D4×C1112yes—
208#102—24no—
209#100—42no—
210C22⋊C8—21no—
211C22⋊C8—21no—
212C4×C8—21no—
213C4×C8—21no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11—82no—
217C2×C11#203511yescharacteristic
218C2×C11#204511yescharacteristic
219C2×C11#204911yescharacteristic
220C24—21no—
221C2×Q8—22no—
222C2×Q8—41no—
223C2×Q8—82no—
224C2×D4—21no—
225C2×D4—21no—
226C2×D4—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4C11×SD1612yes—
230C22×C4—21no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—82no—
235C22×C4C2×D4×C1111yescharacteristic
236C22×C4C11×#4111yescharacteristic
237C22×C4C11×#4111yescharacteristic
238M16—41no—
239M16—41no—
240M16—41no—
241M16—41no—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C4⋊C4—22no—
250C4⋊C4—21no—
251C4⋊C4—22no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C42C2×D4×C1111yescharacteristic
258C42C2×D4×C1111yescharacteristic
259C42C2×D4×C1111yescharacteristic
260C42C11×#4111yescharacteristic
261C11#1044811yescharacteristic, direct product factor, Sylow
262C23—22no—
263C23—41no—
264C23—41no—
265C23—81no—
266C23—81no—
267C23C11×#12311yescharacteristic
268Q8—82no—
269Q8—82no—
270D4—22no—
271D4—22no—
272D4—41no—
273D4—41no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4—82no—
281C2×C4—81no—
282C2×C4C11×#12011yescharacteristic
283C2×C4C11×#12111yescharacteristic
284C2×C4C11×#12111yescharacteristic
285C2×C4C11×#12111yescharacteristic
286C2×C4C11×#12311yescharacteristic
287C2×C4C11×#12411yescharacteristic
288C2×C4C2×C11×SD1611yescharacteristic
289C2×C4C11×#13511yescharacteristic
290C2×C4C11×#13711yescharacteristic
291C2×C4C11×#13711yescharacteristic
292C8—42no—
293C8—42no—
294C8—81no—
295C8—81no—
296C8—81no—
297C22—21no—
298C22—21no—
299C22—42no—
300C22—82no—
301C22—82no—
302C22—81no—
303C22—81no—
304C22C11×#39411yescharacteristic
305C22C11×#48311yescharacteristic
306C22C11×#48511yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—81no—
311C4—82no—
312C4C11×#44811yescharacteristic
313C4C11×#45211yescharacteristic
314C4C11×#46511yescharacteristic
315C4C11×#47011yescharacteristic
316C4C11×#47212yes—
317C2—21no—
318C2—21no—
319C2—82no—
320C2C11×#203511yescharacteristic
321C2C11×#204511yescharacteristic
322C2C11×#204911yescharacteristic
subgroupG/H
center, socleC22×C11#394
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1570C2semidirect
4. C11×#1549C2semidirect
5. C11×#1548C2semidirect
7. C11×#1301C2semidirect
59. #10448C11direct (N × H)
103. #1570C2×C11semidirect
104. #1549C2×C11semidirect
105. #1548C2×C11semidirect
107. #1301C2×C11semidirect
261. C11#10448direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4742
C11×#18002
C11×#15702
C11×#15492
C11×#15482
C11×#14782
C11×#13012
#1044811