Finite Group Databasebeta

← C11×#10190 #14587383

Subgroups — C11×#10190 #14587383

Order 2816.

496 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3230C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic
3C2×C11×#474C211yesmaximal, characteristic
4C11×#1548C211yesmaximal, characteristic, complemented
5C11×#1481C211yesmaximal, characteristic, complemented
6C11×#1460C211yesmaximal, characteristic
7C11×#1301C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C11×#500—21no—
12C11×#487—21no—
13C11×#484—22no—
14C11×#478—22no—
15C11×#477—22no—
16C11×#476—21no—
17C11×#474—22no—
18C11×#474—21no—
19C11×#474—22no—
20C11×#431C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#428—21no—
23C2×C11×#107—21no—
24C11×#423C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#418—21no—
27C2×C11×#102—21no—
28C11×#333—22no—
29C11×Q8⋊C8—22no—
30C11×#323—22no—
31C22×Q8×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C2×C11×M16—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D411yescharacteristic
40C11×C4⋊Q8D412yes—
41C11×C4⋊Q8D411yescharacteristic
42C11×#125—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C11×#117—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C42×C11C2311yescharacteristic
57C11×#107—24no—
58C11×#107—24no—
59C11×#107—22no—
60C11×#106—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66C11×C4⋊C8D412yes—
67C11×#103—24no—
68C11×#102—24no—
69C11×#102—22no—
70C11×#102—22no—
71C11×C22⋊C8—21no—
72C11×C22⋊C8D412yes—
73C4×C8×C11—21no—
74C4×C8×C11—21no—
75#10190C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—41no—
81C2×Q8×C11—82no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11Q1612yes—
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—82no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C11×M16—41no—
97C11×M16—41no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11—41no—
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124#3230C2×C1111yescharacteristic, complemented
125#3077C2×C1111yescharacteristic
126C2×#474C2×C1111yescharacteristic
127#1548C2×C1111yescharacteristic, complemented
128#1481C2×C1111yescharacteristic, complemented
129#1460C2×C1111yescharacteristic
130#1301C2×C1111yescharacteristic, complemented
131C23×C11—22no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—81no—
135C23×C11—81no—
136C23×C11#12111yescharacteristic
137Q8×C11—42no—
138Q8×C11—42no—
139Q8×C11—82no—
140Q8×C11—82no—
141D4×C11—22no—
142D4×C11—22no—
143D4×C11—41no—
144D4×C11—41no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—82no—
152C2×C4×C11—82no—
153C2×C4×C11—82no—
154C2×C4×C11—81no—
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12711yescharacteristic
161C2×C4×C11C2×Q1611yescharacteristic
162C2×C4×C11#13511yescharacteristic
163C2×C4×C11#13711yescharacteristic
164C2×C4×C11#13711yescharacteristic
165C8×C11—42no—
166C8×C11—42no—
167C8×C11—42no—
168C8×C11—81no—
169#533C22×C1111yescharacteristic
170C2×C4⋊Q8C22×C1111yescharacteristic
171C2×C4×D4C22×C1111yescharacteristic
172#500—21no—
173#487—21no—
174#484—22no—
175#478—22no—
176#477—22no—
177#476—21no—
178#474—21no—
179#474—22no—
180#474—22no—
181#431C22×C1111yescharacteristic
182#431C22×C1111yescharacteristic
183#428—21no—
184C2×#107—21no—
185#423C22×C1111yescharacteristic
186C2×C4⋊C8C22×C1111yescharacteristic
187#418—21no—
188C2×#102—21no—
189#333—22no—
190Q8⋊C8—22no—
191#323—22no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—42no—
195C22×C11—82no—
196C22×C11—82no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11#39211yescharacteristic
200C22×C11#46711yescharacteristic
201C22×C11#47011yescharacteristic
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11—82no—
208C4×C11—81no—
209C4×C11#45111yescharacteristic
210C4×C11#45111yescharacteristic
211C4×C11#45211yescharacteristic
212C4×C11#45211yescharacteristic
213C4×C11#47212yes—
214C22×Q8—21no—
215C22×D4D4×C1111yescharacteristic
216C23×C4—21no—
217C2×M16—21no—
218C22×C8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8D4×C1112yes—
223C4⋊Q8D4×C1111yescharacteristic
224C4⋊Q8D4×C1111yescharacteristic
225#125—21no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×D4—21no—
231C4×D4—21no—
232C4×D4—21no—
233C4×D4—21no—
234#117—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4D4×C1111yescharacteristic
238C2×C22⋊C4—21no—
239C2×C42C23×C1111yescharacteristic
240#107—24no—
241#107—22no—
242#107—24no—
243#106—22no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8D4×C1112yes—
249C4⋊C8D4×C1112yes—
250#103—24no—
251#102—24no—
252#102—22no—
253#102—22no—
254C22⋊C8—21no—
255C22⋊C8D4×C1112yes—
256C4×C8—21no—
257C4×C8—21no—
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—82no—
261C2×C11#200111yescharacteristic
262C2×C11#200911yescharacteristic
263C2×C11#201811yescharacteristic
264C24—21no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—22no—
268C2×Q8—41no—
269C2×Q8—82no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4C11×Q1612yes—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—82no—
281C22×C4C2×D4×C1111yescharacteristic
282C22×C4C2×D4×C1111yescharacteristic
283C22×C4C11×#4111yescharacteristic
284M16—41no—
285M16—41no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C4⋊C4—21no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C42—41no—
308C42C2×D4×C1111yescharacteristic
309C42C2×D4×C1111yescharacteristic
310C42C2×D4×C1111yescharacteristic
311C42C2×D4×C1111yescharacteristic
312C11#1019011yescharacteristic, direct product factor, Sylow
313C23—22no—
314C23—41no—
315C23—41no—
316C23—81no—
317C23—81no—
318C23C11×#12111yescharacteristic
319Q8—42no—
320Q8—42no—
321Q8—82no—
322Q8—82no—
323D4—22no—
324D4—22no—
325D4—41no—
326D4—41no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—81no—
337C2×C4C11×#12011yescharacteristic
338C2×C4C11×#12011yescharacteristic
339C2×C4C11×#12011yescharacteristic
340C2×C4C11×#12111yescharacteristic
341C2×C4C11×#12111yescharacteristic
342C2×C4C11×#12711yescharacteristic
343C2×C4C2×C11×Q1611yescharacteristic
344C2×C4C11×#13511yescharacteristic
345C2×C4C11×#13711yescharacteristic
346C2×C4C11×#13711yescharacteristic
347C8—42no—
348C8—42no—
349C8—42no—
350C8—81no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—82no—
355C22—82no—
356C22—81no—
357C22—81no—
358C22C11×#39211yescharacteristic
359C22C11×#46711yescharacteristic
360C22C11×#47011yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—81no—
366C4—82no—
367C4—81no—
368C4C11×#45111yescharacteristic
369C4C11×#45111yescharacteristic
370C4C11×#45211yescharacteristic
371C4C11×#45211yescharacteristic
372C4C11×#47212yes—
373C2—21no—
374C2—21no—
375C2—82no—
376C2C11×#200111yescharacteristic
377C2C11×#200911yescharacteristic
378C2C11×#201811yescharacteristic
subgroupG/H
center, socleC22×C11#392
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
1. C11×#3230C2semidirect
4. C11×#1548C2semidirect
5. C11×#1481C2semidirect
7. C11×#1301C2semidirect
75. #10190C11direct (N × H)
124. #3230C2×C11semidirect
127. #1548C2×C11semidirect
128. #1481C2×C11semidirect
130. #1301C2×C11semidirect
312. C11#10190direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32302
C11×#30772
C2×C11×#4742
C11×#15482
C11×#14812
C11×#14602
C11×#13012
#1019011