Finite Group Databasebeta

← C11×#10058 #14587251

Subgroups — C11×#10058 #14587251

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#487C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic
3C11×#2547C211yesmaximal, characteristic
4C11×#1987C211yesmaximal, characteristic, complemented
5C2×C11×#332C211yesmaximal, characteristic, complemented
6C2×C11×D4⋊C8C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#124—21no—
11C2×C4×D4×C11C2211yescharacteristic
12C11×#487—22no—
13C11×#487—22no—
14C11×#476—22no—
15C11×#476—22no—
16C2×C11×#106—21no—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#103—22no—
20C2×C11×#102—21no—
21C2×C4×C8×C11C2211yescharacteristic
22C11×#397—22no—
23C11×#391—21no—
24C11×#380—22no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C11×#340—22no—
27C11×#332—22no—
28C11×D4⋊C8—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8D412yes—
44C11×#124—42no—
45C11×#124—42no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D412yes—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D412yes—
56C2×C11×C22⋊C4—24no—
57C2×C11×C22⋊C4—21no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C11×#106—24no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×#103—28no—
66C11×#102—24no—
67C4×C8×C11—21no—
68C4×C8×C11D412yes—
69C11×#95—24no—
70C11×#95—21no—
71#10058C1111yesmaximal, characteristic, direct product factor, Sylow
72C24×C11—21no—
73C2×Q8×C11—22no—
74C2×Q8×C11—44no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11SD1612yes—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11—42no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C2×C8×C11—42no—
105C2×C8×C11—41no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C22⋊C4—48no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11—41no—
122C42×C11—41no—
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127C2×#487C2×C1111yescharacteristic, complemented
128C2×#476C2×C1111yescharacteristic
129#2547C2×C1111yescharacteristic
130#1987C2×C1111yescharacteristic, complemented
131C2×#332C2×C1111yescharacteristic, complemented
132C2×D4⋊C8C2×C1111yescharacteristic
133#1279C2×C1111yescharacteristic, complemented
134C23×C11—22no—
135C23×C11—41no—
136C23×C11—42no—
137C23×C11—41no—
138C23×C11—42no—
139C23×C11#12011yescharacteristic
140Q8×C11—44no—
141Q8×C11—82no—
142Q8×C11—81no—
143Q8×C11—81no—
144Q8×C11—81no—
145Q8×C11—81no—
146D4×C11—22no—
147D4×C11—22no—
148D4×C11—41no—
149D4×C11—41no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—82no—
161C2×C4×C11—82no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12711yescharacteristic
170C2×C4×C11C2×SD1611yescharacteristic
171C2×C4×C11#13511yescharacteristic
172C2×C4×C11#13512yes—
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C11#13711yescharacteristic
175C2×C4×C11#13712yes—
176C8×C11—42no—
177C8×C11—42no—
178C8×C11—81no—
179C2×C4⋊Q8C22×C1111yescharacteristic
180C2×C4⋊Q8C22×C1111yescharacteristic
181C2×#124—21no—
182C2×C4×D4C22×C1111yescharacteristic
183#487—22no—
184#487—22no—
185#476—22no—
186#476—22no—
187C2×#106—21no—
188C2×C4⋊C8C22×C1111yescharacteristic
189C2×C4⋊C8C22×C1111yescharacteristic
190C2×#103—22no—
191C2×#102—21no—
192C2×C4×C8C22×C1111yescharacteristic
193#397—22no—
194#391—21no—
195#380—22no—
196C4×C4⋊C4C22×C1111yescharacteristic
197#340—22no—
198#332—22no—
199D4⋊C8—22no—
200C22×C11—44no—
201C22×C11—42no—
202C22×C11—82no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11#39211yescharacteristic
206C22×C11#45011yescharacteristic
207C22×C11#45212yes—
208C22×C11#45211yescharacteristic
209C22×C11#45412yes—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—82no—
213C4×C11—82no—
214C4×C11—82no—
215C4×C11—81no—
216C4×C11#44811yescharacteristic
217C4×C11#44911yescharacteristic
218C4×C11#46412yes—
219C4×C11#46511yescharacteristic
220C4×C11#46811yescharacteristic
221C4×C11#49511yescharacteristic
222C4×C11#49711yescharacteristic
223C22×Q8—21no—
224C22×Q8—21no—
225C22×D4D4×C1111yescharacteristic
226C23×C4—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8D4×C1112yes—
238#124—42no—
239#124—42no—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4—21no—
243C4×D4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4D4×C1111yescharacteristic
248C2×C4⋊C4D4×C1112yes—
249C2×C4⋊C4D4×C1112yes—
250C2×C22⋊C4—24no—
251C2×C22⋊C4—21no—
252C2×C42—21no—
253C2×C42C23×C1111yescharacteristic
254#106—24no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8D4×C1112yes—
259#103—28no—
260#102—24no—
261C4×C8—21no—
262C4×C8D4×C1112yes—
263#95—24no—
264#95—21no—
265C2×C11—82no—
266C2×C11#163512yes—
267C2×C11#163812yes—
268C2×C11#200011yescharacteristic
269C2×C11#200311yescharacteristic
270C2×C11#201511yescharacteristic
271C24—21no—
272C2×Q8—22no—
273C2×Q8—44no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4C11×SD1612yes—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4C2×D4×C1111yescharacteristic
296C22×C4C2×D4×C1111yescharacteristic
297C22×C4C2×D4×C1111yescharacteristic
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—42no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—42no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—21no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C22⋊C4—48no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C42—41no—
321C42—41no—
322C42C2×D4×C1111yescharacteristic
323C42C2×D4×C1111yescharacteristic
324C42C2×D4×C1111yescharacteristic
325C42C11×#4111yescharacteristic
326C11#1005811yescharacteristic, direct product factor, Sylow
327C23—22no—
328C23—41no—
329C23—42no—
330C23—41no—
331C23—42no—
332C23C11×#12011yescharacteristic
333Q8—44no—
334Q8—82no—
335Q8—81no—
336Q8—81no—
337Q8—81no—
338Q8—81no—
339D4—22no—
340D4—22no—
341D4—41no—
342D4—41no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—82no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—82no—
357C2×C4C11×#12011yescharacteristic
358C2×C4C11×#12011yescharacteristic
359C2×C4C11×#12111yescharacteristic
360C2×C4C11×#12111yescharacteristic
361C2×C4C11×#12111yescharacteristic
362C2×C4C11×#12711yescharacteristic
363C2×C4C2×C11×SD1611yescharacteristic
364C2×C4C11×#13512yes—
365C2×C4C11×#13511yescharacteristic
366C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
367C2×C4C11×#13712yes—
368C2×C4C11×#13711yescharacteristic
369C8—42no—
370C8—42no—
371C8—81no—
372C22—44no—
373C22—42no—
374C22—82no—
375C22—81no—
376C22—81no—
377C22C11×#39211yescharacteristic
378C22C11×#45011yescharacteristic
379C22C11×#45212yes—
380C22C11×#45211yescharacteristic
381C22C11×#45412yes—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—82no—
386C4—82no—
387C4—81no—
388C4C11×#44811yescharacteristic
389C4C11×#44911yescharacteristic
390C4C11×#46412yes—
391C4C11×#46511yescharacteristic
392C4C11×#46811yescharacteristic
393C4C11×#49511yescharacteristic
394C4C11×#49711yescharacteristic
395C2—82no—
396C2C11×#163512yes—
397C2C11×#163812yes—
398C2C11×#200011yescharacteristic
399C2C11×#200311yescharacteristic
400C2C11×#201511yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#487C2semidirect
4. C11×#1987C2semidirect
5. C2×C11×#332C2semidirect
7. C11×#1279C2semidirect
71. #10058C11direct (N × H)
127. C2×#487C2×C11semidirect
130. #1987C2×C11semidirect
131. C2×#332C2×C11semidirect
133. #1279C2×C11semidirect
326. C11#10058direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4872
C2×C11×#4762
C11×#25472
C11×#19872
C2×C11×#3322
C2×C11×D4⋊C82
C11×#12792
#1005811