Finite Group Databasebeta

← C11×#11242 #14588435

Subgroups — C11×#11242 #14588435

Order 2816.

682 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#108C211yesmaximal, characteristic
2C2×C11×#424C211yesmaximal, characteristic
3C2×C11×#343C212yesmaximal
4C11×#1736C212yesmaximal
5C2×C11×#340C211yesmaximal, characteristic
6C22×C11×M16C2211yescharacteristic
7C22×C11×M16C2212yes—
8C23×C8×C11C2211yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C22×C11×C4⋊C4C2212yes—
11C2×C11×#108—24no—
12C2×C11×#108—22no—
13C11×#424—22no—
14C11×#424C414yescomplemented
15C2×C11×C4⋊C8—22no—
16C11×#343—24no—
17C11×#340—22no—
18C11×#340—22no—
19C11×#340—22no—
20C23×C4×C11—22no—
21C23×C4×C11C2311yescharacteristic
22C2×C11×M16—21no—
23C2×C11×M16—22no—
24C2×C11×M16—22no—
25C2×C11×M16—22no—
26C2×C11×M16—22no—
27C2×C11×M16—22no—
28C2×C11×M16—22no—
29C2×C11×M16—22no—
30C2×C11×M16C2×C412yes—
31C2×C11×M16D414yes—
32C22×C8×C11—22no—
33C22×C8×C11—22no—
34C22×C8×C11—22no—
35C22×C8×C11—21no—
36C22×C8×C11C2×C412yes—
37C22×C8×C11D412yes—
38C22×C8×C11D412yes—
39C11×#117—21no—
40C11×#117—21no—
41C11×#117C2×C412yes—
42C11×#117Q812yes—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C4⋊C4Q814yes—
51C2×C11×C22⋊C4—21no—
52C2×C42×C11—21no—
53C11×#108—28no—
54C11×C4⋊C8—28no—
55#11242C1111yesmaximal, characteristic, direct product factor, Sylow
56C24×C11#4111yescharacteristic
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—24no—
60C22×C4×C11—42no—
61C22×C4×C11—42no—
62C22×C4×C11—82no—
63C22×C4×C11—82no—
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D412yes—
69C22×C4×C11C2×Q811yescharacteristic
70C22×C4×C11C2×Q812yes—
71C22×C4×C11#4112yes—
72C22×C4×C11#4112yes—
73C22×C4×C11#4111yescharacteristic
74C11×M16—24no—
75C11×M16—24no—
76C11×M16—24no—
77C11×M16—41no—
78C11×M16—41no—
79C11×M16—42no—
80C11×M16—42no—
81C2×C8×C11—22no—
82C2×C8×C11—24no—
83C2×C8×C11—22no—
84C2×C8×C11—24no—
85C2×C8×C11—24no—
86C2×C8×C11—22no—
87C2×C8×C11—42no—
88C2×C8×C11—42no—
89C2×C8×C11—42no—
90C2×C8×C11C22⋊C414yes—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4—24no—
95C11×C4⋊C4—42no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4C4⋊C412yes—
98C11×C4⋊C4C4⋊C412yes—
99C11×C22⋊C4—22no—
100C11×C22⋊C4—22no—
101C42×C11—22no—
102C42×C11—22no—
103C22×#108C2×C1111yescharacteristic
104C2×#424C2×C1111yescharacteristic
105C2×#343C2×C1112yes—
106#1736C2×C1112yes—
107C2×#340C2×C1111yescharacteristic
108C23×C11—22no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11#11711yescharacteristic
112C23×C11#12111yescharacteristic
113C23×C11C22⋊Q811yescharacteristic
114C23×C11C22⋊Q812yes—
115C23×C11#12612yes—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—42no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—44no—
122C2×C4×C11—84no—
123C2×C4×C11—82no—
124C2×C4×C11—82no—
125C2×C4×C11—84no—
126C2×C4×C11C2×C22⋊C411yescharacteristic
127C2×C4×C11C2×C4⋊C411yescharacteristic
128C2×C4×C11C4×D412yes—
129C2×C4×C11C4×Q812yes—
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12112yes—
132C2×C4×C11#12112yes—
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11C22⋊Q812yes—
135C2×C4×C11C22⋊Q812yes—
136C2×C4×C11C22⋊Q811yescharacteristic
137C2×C4×C11#12311yescharacteristic
138C2×C4×C11#12312yes—
139C2×C4×C11#12411yescharacteristic
140C2×C4×C11#12512yes—
141C2×C4×C11#12512yes—
142C2×C4×C11C4⋊Q812yes—
143C2×C4×C11C4⋊Q811yescharacteristic
144C8×C11—24no—
145C8×C11—42no—
146C8×C11—44no—
147C22×M16C22×C1111yescharacteristic
148C22×M16C22×C1112yes—
149C23×C8C22×C1111yescharacteristic
150C2×#117C22×C1111yescharacteristic
151C22×C4⋊C4C22×C1112yes—
152C2×#108—24no—
153C2×#108—22no—
154#424—22no—
155#424C4×C1114yescomplemented
156C2×C4⋊C8—22no—
157#343—24no—
158#340—22no—
159#340—22no—
160#340—22no—
161C22×C11—22no—
162C22×C11—22no—
163C22×C11—22no—
164C22×C11—22no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11#38011yescharacteristic
170C22×C11#38712yes—
171C22×C11#39511yescharacteristic
172C22×C11#39612yes—
173C22×C11#40011yescharacteristic
174C22×C11#47112yes—
175C22×C11#47211yescharacteristic
176C22×C11#47311yescharacteristic
177C4×C11—42no—
178C4×C11—42no—
179C4×C11—84no—
180C4×C11#38611yescharacteristic
181C4×C11#38912yes—
182C4×C11#39111yescharacteristic
183C4×C11#39411yescharacteristic
184C4×C11#39812yes—
185C4×C11#39811yescharacteristic
186C23×C4—22no—
187C23×C4C23×C1111yescharacteristic
188C2×M16—21no—
189C2×M16—22no—
190C2×M16—22no—
191C2×M16—22no—
192C2×M16—22no—
193C2×M16—22no—
194C2×M16—22no—
195C2×M16—22no—
196C2×M16C2×C4×C1112yes—
197C2×M16D4×C1114yes—
198C22×C8—22no—
199C22×C8—22no—
200C22×C8—22no—
201C22×C8—21no—
202C22×C8C2×C4×C1112yes—
203C22×C8D4×C1112yes—
204C22×C8D4×C1112yes—
205#117—21no—
206#117—21no—
207#117C2×C4×C1112yes—
208#117Q8×C1112yes—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4D4×C1111yescharacteristic
215C2×C4⋊C4D4×C1111yescharacteristic
216C2×C4⋊C4Q8×C1114yes—
217C2×C22⋊C4—21no—
218C2×C42—21no—
219#108—28no—
220C4⋊C8—28no—
221C2×C11—22no—
222C2×C11—21no—
223C2×C11—21no—
224C2×C11#144111yescharacteristic
225C2×C11#181511yescharacteristic
226C2×C11#181611yescharacteristic
227C2×C11#206312yes—
228C2×C11#206412yes—
229C24C11×#4111yescharacteristic
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—24no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—82no—
236C22×C4—82no—
237C22×C4C22×C4×C1111yescharacteristic
238C22×C4C2×D4×C1111yescharacteristic
239C22×C4C2×D4×C1111yescharacteristic
240C22×C4C2×D4×C1111yescharacteristic
241C22×C4C2×D4×C1112yes—
242C22×C4C2×Q8×C1111yescharacteristic
243C22×C4C2×Q8×C1112yes—
244C22×C4C11×#4112yes—
245C22×C4C11×#4112yes—
246C22×C4C11×#4111yescharacteristic
247M16—24no—
248M16—24no—
249M16—24no—
250M16—41no—
251M16—41no—
252M16—42no—
253M16—42no—
254C2×C8—24no—
255C2×C8—22no—
256C2×C8—24no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—24no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8C11×C22⋊C414yes—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—24no—
267C4⋊C4—24no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4C11×C4⋊C412yes—
271C4⋊C4C11×C4⋊C412yes—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C42—22no—
275C42—22no—
276C11#1124211yescharacteristic, direct product factor, Sylow
277C23—22no—
278C23—21no—
279C23—21no—
280C23C11×#11711yescharacteristic
281C23C11×#12111yescharacteristic
282C23C11×C22⋊Q811yescharacteristic
283C23C11×C22⋊Q812yes—
284C23C11×#12612yes—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—44no—
291C2×C4—84no—
292C2×C4—82no—
293C2×C4—82no—
294C2×C4—84no—
295C2×C4C2×C11×C22⋊C411yescharacteristic
296C2×C4C2×C11×C4⋊C411yescharacteristic
297C2×C4C4×D4×C1112yes—
298C2×C4C4×Q8×C1112yes—
299C2×C4C11×#12011yescharacteristic
300C2×C4C11×#12112yes—
301C2×C4C11×#12112yes—
302C2×C4C11×#12111yescharacteristic
303C2×C4C11×C22⋊Q812yes—
304C2×C4C11×C22⋊Q812yes—
305C2×C4C11×C22⋊Q811yescharacteristic
306C2×C4C11×#12311yescharacteristic
307C2×C4C11×#12312yes—
308C2×C4C11×#12411yescharacteristic
309C2×C4C11×#12512yes—
310C2×C4C11×#12512yes—
311C2×C4C11×C4⋊Q812yes—
312C2×C4C11×C4⋊Q811yescharacteristic
313C8—24no—
314C8—42no—
315C8—44no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22C11×#38011yescharacteristic
325C22C11×#38712yes—
326C22C11×#39511yescharacteristic
327C22C11×#39612yes—
328C22C11×#40011yescharacteristic
329C22C11×#47112yes—
330C22C11×#47211yescharacteristic
331C22C11×#47311yescharacteristic
332C4—42no—
333C4—42no—
334C4—84no—
335C4C11×#38611yescharacteristic
336C4C11×#38912yes—
337C4C11×#39111yescharacteristic
338C4C11×#39411yescharacteristic
339C4C11×#39812yes—
340C4C11×#39811yescharacteristic
341C2—22no—
342C2—21no—
343C2—21no—
344C2C11×#144111yescharacteristic
345C2C11×#181511yescharacteristic
346C2C11×#181611yescharacteristic
347C2C11×#206312yes—
348C2C11×#206412yes—
subgroupG/H
center, socleC23×C11#121
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
14. C11×#424C4semidirect
55. #11242C11direct (N × H)
155. #424C4×C11semidirect
276. C11#11242direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1082
C2×C11×#4242
C2×C11×#3432
C11×#17362
C2×C11×#3402
#1124211