Finite Group Databasebeta

← C11×#10939 #14588132

Subgroups — C11×#10939 #14588132

Order 2816.

1058 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#100C212yesmaximal
2C11×#2873C211yesmaximal, characteristic, complemented
3C11×#2309C211yesmaximal, characteristic
4C2×C11×#344C212yesmaximal, complemented
5C11×#1742C211yesmaximal, characteristic, complemented
6C23×D4×C11C2211yescharacteristic
7C22×C11×M16C2212yes—
8C22×C11×M16C2212yes—
9C2×C11×#117C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C2×C11×#100—24no—
12C2×C11×#100—24no—
13C2×C11×#100C418yescomplemented
14C11×#405—24no—
15C4×C11×M16—22no—
16C11×#390—22no—
17C11×#390—22no—
18C11×#379C414yes—
19C11×#344—24no—
20C11×#343—22no—
21C25×C11C2×C412yes—
22C22×D4×C11—21no—
23C22×D4×C11—21no—
24C22×D4×C11—22no—
25C22×D4×C11—22no—
26C22×D4×C11—22no—
27C22×D4×C11—22no—
28C22×D4×C11—22no—
29C22×D4×C11C2×C414yes—
30C23×C4×C11C2311yescharacteristic
31C2×C11×M16—22no—
32C2×C11×M16—22no—
33C2×C11×M16—22no—
34C2×C11×M16—22no—
35C2×C11×M16—22no—
36C2×C11×M16—22no—
37C2×C11×M16—22no—
38C2×C11×M16—22no—
39C2×C11×M16C2×C414yes—
40C2×C11×M16C2×C414yes—
41C2×C11×M16D414yes—
42C2×C11×M16D414yes—
43C22×C8×C11—22no—
44C22×C8×C11—22no—
45C11×#117—22no—
46C11×#117—22no—
47C11×#117—22no—
48C11×#117—22no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D412yes—
51C2×C11×C22⋊C4—28no—
52C2×C11×C22⋊C4C2×C412yes—
53C2×C11×C22⋊C4C2×C412yes—
54C2×C42×C11—21no—
55C2×C42×C11D412yes—
56C11×#100—216no—
57C11×#97—24no—
58C4×C8×C11—24no—
59#10939C1111yesmaximal, characteristic, direct product factor, Sylow
60C24×C11—22no—
61C24×C11—22no—
62C24×C11—24no—
63C24×C11—24no—
64C24×C11—84no—
65C24×C11C4214yes—
66C24×C11C22×C411yescharacteristic
67C2×D4×C11—24no—
68C2×D4×C11—24no—
69C2×D4×C11—24no—
70C2×D4×C11—24no—
71C2×D4×C11—24no—
72C2×D4×C11—24no—
73C2×D4×C11—41no—
74C2×D4×C11—42no—
75C2×D4×C11—42no—
76C2×D4×C11—42no—
77C2×D4×C11—42no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—42no—
81C2×D4×C11—42no—
82C2×D4×C11—41no—
83C22×C4×C11—22no—
84C22×C4×C11C22⋊C414yes—
85C22×C4×C11C22×C412yes—
86C22×C4×C11C2×D412yes—
87C22×C4×C11C2×D412yes—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4112yes—
91C22×C4×C11#4112yes—
92C22×C4×C11#4112yes—
93C11×M16—24no—
94C11×M16—24no—
95C11×M16—24no—
96C11×M16—24no—
97C11×M16—24no—
98C11×M16—42no—
99C11×M16—42no—
100C11×M16C22⋊C418yescomplemented
101C2×C8×C11—24no—
102C2×C8×C11—24no—
103C2×C8×C11—24no—
104C2×C8×C11—24no—
105C2×C8×C11—42no—
106C2×C8×C11—42no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—42no—
109C11×C22⋊C4—24no—
110C11×C22⋊C4—24no—
111C11×C22⋊C4—88no—
112C42×C11—22no—
113C42×C11—22no—
114C42×C11—41no—
115C42×C11—41no—
116C22×#100C2×C1112yes—
117#2873C2×C1111yescharacteristic, complemented
118#2309C2×C1111yescharacteristic
119C2×#344C2×C1112yescomplemented
120#1742C2×C1111yescharacteristic, complemented
121C23×C11—24no—
122C23×C11—28no—
123C23×C11—42no—
124C23×C11—48no—
125C23×C11—42no—
126C23×C11—44no—
127C23×C11—42no—
128C23×C11—88no—
129C23×C11—84no—
130C23×C11—84no—
131C23×C11—88no—
132C23×C11C2×C4211yescharacteristic
133C23×C11C2×C22⋊C411yescharacteristic
134C23×C11#11711yescharacteristic
135C23×C11C4×D412yes—
136C23×C11C4×D412yes—
137D4×C11—44no—
138D4×C11—44no—
139D4×C11—44no—
140D4×C11—44no—
141C2×C4×C11—24no—
142C2×C4×C11—44no—
143C2×C4×C11—44no—
144C2×C4×C11—42no—
145C2×C4×C11C2×C22⋊C412yes—
146C2×C4×C11#11712yes—
147C2×C4×C11C4×D412yes—
148C2×C4×C11C4×D412yes—
149C2×C4×C11C4×D412yes—
150C2×C4×C11C4×D412yes—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12112yes—
153C2×C4×C11#12112yes—
154C2×C4×C11#12112yes—
155C2×C4×C11#12312yes—
156C2×C4×C11#12311yescharacteristic
157C2×C4×C11#12411yescharacteristic
158C2×C4×C11#12412yes—
159C2×C4×C11#12612yes—
160C2×C4×C11#12711yescharacteristic
161C8×C11—28no—
162C8×C11—44no—
163C23×D4C22×C1111yescharacteristic
164C22×M16C22×C1112yes—
165C22×M16C22×C1112yes—
166C2×#117C22×C1111yescharacteristic
167C2×#117C22×C1111yescharacteristic
168C2×#100—24no—
169C2×#100—24no—
170C2×#100C4×C1118yescomplemented
171#405—24no—
172C4×M16—22no—
173#390—22no—
174#390—22no—
175#379C4×C1114yes—
176#344—24no—
177#343—22no—
178C22×C11—22no—
179C22×C11—24no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—42no—
183C22×C11—48no—
184C22×C11—44no—
185C22×C11—88no—
186C22×C11—84no—
187C22×C11—88no—
188C22×C11—84no—
189C22×C11C4×C22⋊C412yes—
190C22×C11C4×C22⋊C411yescharacteristic
191C22×C11#38611yescharacteristic
192C22×C11#38812yes—
193C22×C11#39011yescharacteristic
194C4×C11—44no—
195C4×C11—82no—
196C4×C11#38612yes—
197C4×C11#38812yes—
198C4×C11#38812yes—
199C4×C11#39012yes—
200C25C2×C4×C1112yes—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—22no—
204C22×D4—22no—
205C22×D4—22no—
206C22×D4—22no—
207C22×D4—22no—
208C22×D4C2×C4×C1114yes—
209C23×C4C23×C1111yescharacteristic
210C2×M16—22no—
211C2×M16—22no—
212C2×M16—22no—
213C2×M16—22no—
214C2×M16—22no—
215C2×M16—22no—
216C2×M16—22no—
217C2×M16—22no—
218C2×M16C2×C4×C1114yes—
219C2×M16C2×C4×C1114yes—
220C2×M16D4×C1114yes—
221C2×M16D4×C1114yes—
222C22×C8—22no—
223C22×C8—22no—
224#117—22no—
225#117—22no—
226#117—22no—
227#117—22no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4D4×C1112yes—
230C2×C22⋊C4—28no—
231C2×C22⋊C4C2×C4×C1112yes—
232C2×C22⋊C4C2×C4×C1112yes—
233C2×C42—21no—
234C2×C42D4×C1112yes—
235#100—216no—
236#97—24no—
237C4×C8—24no—
238C2×C11—21no—
239C2×C11—21no—
240C2×C11—22no—
241C2×C11—22no—
242C2×C11—84no—
243C2×C11#143711yescharacteristic
244C2×C11#191412yes—
245C24—22no—
246C24—22no—
247C24—24no—
248C24—24no—
249C24—84no—
250C24C42×C1114yes—
251C24C22×C4×C1111yescharacteristic
252C2×D4—24no—
253C2×D4—24no—
254C2×D4—24no—
255C2×D4—24no—
256C2×D4—24no—
257C2×D4—24no—
258C2×D4—41no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—42no—
262C2×D4—42no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—41no—
268C22×C4—22no—
269C22×C4C11×C22⋊C414yes—
270C22×C4C22×C4×C1112yes—
271C22×C4C2×D4×C1112yes—
272C22×C4C2×D4×C1112yes—
273C22×C4C2×D4×C1111yescharacteristic
274C22×C4C2×D4×C1111yescharacteristic
275C22×C4C11×#4112yes—
276C22×C4C11×#4112yes—
277C22×C4C11×#4112yes—
278M16—24no—
279M16—24no—
280M16—24no—
281M16—24no—
282M16—24no—
283M16—42no—
284M16—42no—
285M16C11×C22⋊C418yescomplemented
286C2×C8—24no—
287C2×C8—24no—
288C2×C8—24no—
289C2×C8—24no—
290C2×C8—42no—
291C2×C8—42no—
292C4⋊C4—24no—
293C4⋊C4—42no—
294C22⋊C4—24no—
295C22⋊C4—24no—
296C22⋊C4—88no—
297C42—22no—
298C42—22no—
299C42—41no—
300C42—41no—
301C11#1093911yescharacteristic, direct product factor, Sylow
302C23—24no—
303C23—28no—
304C23—42no—
305C23—48no—
306C23—42no—
307C23—44no—
308C23—42no—
309C23—88no—
310C23—84no—
311C23—84no—
312C23—88no—
313C23C2×C42×C1111yescharacteristic
314C23C2×C11×C22⋊C411yescharacteristic
315C23C11×#11711yescharacteristic
316C23C4×D4×C1112yes—
317C23C4×D4×C1112yes—
318D4—44no—
319D4—44no—
320D4—44no—
321D4—44no—
322C2×C4—24no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—42no—
326C2×C4C2×C11×C22⋊C412yes—
327C2×C4C11×#11712yes—
328C2×C4C4×D4×C1112yes—
329C2×C4C4×D4×C1112yes—
330C2×C4C4×D4×C1112yes—
331C2×C4C4×D4×C1112yes—
332C2×C4C11×#12011yescharacteristic
333C2×C4C11×#12112yes—
334C2×C4C11×#12112yes—
335C2×C4C11×#12112yes—
336C2×C4C11×#12312yes—
337C2×C4C11×#12311yescharacteristic
338C2×C4C11×#12411yescharacteristic
339C2×C4C11×#12412yes—
340C2×C4C11×#12612yes—
341C2×C4C11×#12711yescharacteristic
342C8—28no—
343C8—44no—
344C22—22no—
345C22—24no—
346C22—41no—
347C22—41no—
348C22—42no—
349C22—48no—
350C22—44no—
351C22—88no—
352C22—84no—
353C22—88no—
354C22—84no—
355C22C4×C11×C22⋊C412yes—
356C22C4×C11×C22⋊C411yescharacteristic
357C22C11×#38611yescharacteristic
358C22C11×#38812yes—
359C22C11×#39011yescharacteristic
360C4—44no—
361C4—82no—
362C4C11×#38612yes—
363C4C11×#38812yes—
364C4C11×#38812yes—
365C4C11×#39012yes—
366C2—21no—
367C2—21no—
368C2—22no—
369C2—22no—
370C2—84no—
371C2C11×#143711yescharacteristic
372C2C11×#191412yes—
subgroupG/H
center, socleC22×C11#386
commutatorC23C2×C42×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2873C2semidirect
4. C2×C11×#344C2semidirect
5. C11×#1742C2semidirect
13. C2×C11×#100C4semidirect
59. #10939C11direct (N × H)
100. C11×M16C22⋊C4semidirect
117. #2873C2×C11semidirect
119. C2×#344C2×C11semidirect
120. #1742C2×C11semidirect
170. C2×#100C4×C11semidirect
285. M16C11×C22⋊C4semidirect
301. C11#10939direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1002
C11×#28732
C11×#23092
C2×C11×#3442
C11×#17422
#1093911