Finite Group Databasebeta

← C11×#10270 #14587463

Subgroups — C11×#10270 #14587463

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#487C211yesmaximal, characteristic, complemented
2C2×C11×#474C211yesmaximal, characteristic
3C2×C11×#461C211yesmaximal, characteristic
4C11×#1954C211yesmaximal, characteristic
5C2×C11×#332C211yesmaximal, characteristic, complemented
6C2×C11×#332C211yesmaximal, characteristic, complemented
7C11×#1277C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C11×#487—22no—
13C11×#487—22no—
14C11×#474—22no—
15C11×#474—22no—
16C11×#461—22no—
17C11×#461—22no—
18C2×C11×#107—21no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103—22no—
23C2×C11×#103—21no—
24C2×C11×#102—21no—
25C2×C11×C22⋊C8—22no—
26C2×C4×C8×C11C2211yescharacteristic
27C11×#332—22no—
28C11×#332—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C2×C11×SD16—24no—
34C2×C11×SD16—42no—
35C2×C11×SD16—42no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C22×C8×C11D412yes—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8D412yes—
47C11×C4⋊Q8D412yes—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C42×C11C2311yescharacteristic
59C11×#107—24no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×C4⋊C8D412yes—
66C11×#103—24no—
67C11×#103—28no—
68C11×#102—24no—
69C11×C22⋊C8—44no—
70C4×C8×C11—21no—
71C4×C8×C11—21no—
72#10270C1111yesmaximal, characteristic, direct product factor, Sylow
73C24×C11—21no—
74C2×Q8×C11—22no—
75C2×Q8×C11—22no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—42no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—42no—
83C2×Q8×C11—41no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11SD1612yes—
90C22×C4×C11—21no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C11×SD16—48no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C2×C8×C11—41no—
111C2×C8×C11—42no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C2×#487C2×C1111yescharacteristic, complemented
129C2×#474C2×C1111yescharacteristic
130C2×#461C2×C1111yescharacteristic
131#1954C2×C1111yescharacteristic
132C2×#332C2×C1111yescharacteristic, complemented
133C2×#332C2×C1111yescharacteristic, complemented
134#1277C2×C1111yescharacteristic, complemented
135C23×C11—22no—
136C23×C11—41no—
137C23×C11—42no—
138C23×C11—41no—
139C23×C11—42no—
140C23×C11#12111yescharacteristic
141Q8×C11—44no—
142Q8×C11—42no—
143Q8×C11—42no—
144Q8×C11—81no—
145Q8×C11—81no—
146Q8×C11—81no—
147Q8×C11—81no—
148D4×C11—22no—
149D4×C11—22no—
150D4×C11—41no—
151D4×C11—41no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—82no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11—82no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12711yescharacteristic
169C2×C4×C11C2×SD1611yescharacteristic
170C2×C4×C11#13511yescharacteristic
171C2×C4×C11#13512yes—
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11AGL(1,ℤ/8)12yes—
174C2×C4×C11#13711yescharacteristic
175C8×C11—42no—
176C8×C11—42no—
177C8×C11—42no—
178C8×C11—81no—
179C22×SD16—21no—
180C2×C4⋊Q8C22×C1111yescharacteristic
181C2×C4⋊Q8C22×C1111yescharacteristic
182C2×C4×D4C22×C1111yescharacteristic
183#487—22no—
184#487—22no—
185#474—22no—
186#474—22no—
187#461—22no—
188#461—22no—
189C2×#107—21no—
190C2×C4⋊C8C22×C1111yescharacteristic
191C2×C4⋊C8C22×C1111yescharacteristic
192C2×C4⋊C8C22×C1111yescharacteristic
193C2×#103—22no—
194C2×#103—21no—
195C2×#102—21no—
196C2×C22⋊C8—22no—
197C2×C4×C8C22×C1111yescharacteristic
198#332—22no—
199#332—22no—
200C22×C11—44no—
201C22×C11—42no—
202C22×C11—82no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11#39211yescharacteristic
206C22×C11#46312yes—
207C22×C11#46511yescharacteristic
208C22×C11#46811yescharacteristic
209C22×C11#47312yes—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—82no—
213C4×C11—81no—
214C4×C11—82no—
215C4×C11#44811yescharacteristic
216C4×C11#44911yescharacteristic
217C4×C11#44912yes—
218C4×C11#45011yescharacteristic
219C4×C11#45211yescharacteristic
220C4×C11#49511yescharacteristic
221C4×C11#49611yescharacteristic
222C22×Q8—21no—
223C22×Q8—21no—
224C22×D4D4×C1111yescharacteristic
225C23×C4—21no—
226C2×SD16—24no—
227C2×SD16—42no—
228C2×SD16—42no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8D4×C1112yes—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8D4×C1112yes—
240C4⋊Q8D4×C1112yes—
241C4×D4—21no—
242C4×D4—21no—
243C4×D4—21no—
244C4×D4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4D4×C1111yescharacteristic
250C2×C22⋊C4—21no—
251C2×C42C23×C1111yescharacteristic
252#107—24no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8D4×C1112yes—
258C4⋊C8D4×C1112yes—
259#103—24no—
260#103—28no—
261#102—24no—
262C22⋊C8—44no—
263C4×C8—21no—
264C4×C8—21no—
265C2×C11—82no—
266C2×C11#167912yes—
267C2×C11#169912yes—
268C2×C11#200011yescharacteristic
269C2×C11#201211yescharacteristic
270C2×C11#202011yescharacteristic
271C24—21no—
272C2×Q8—22no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—42no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—42no—
281C2×Q8—41no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4C11×SD1612yes—
288C22×C4—21no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4C2×D4×C1111yescharacteristic
296C22×C4C2×D4×C1111yescharacteristic
297C22×C4C11×#4111yescharacteristic
298SD16—48no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—42no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C42C2×D4×C1111yescharacteristic
323C42C2×D4×C1111yescharacteristic
324C42C2×D4×C1111yescharacteristic
325C42C2×D4×C1111yescharacteristic
326C11#1027011yescharacteristic, direct product factor, Sylow
327C23—22no—
328C23—41no—
329C23—42no—
330C23—41no—
331C23—42no—
332C23C11×#12111yescharacteristic
333Q8—44no—
334Q8—42no—
335Q8—42no—
336Q8—81no—
337Q8—81no—
338Q8—81no—
339Q8—81no—
340D4—22no—
341D4—22no—
342D4—41no—
343D4—41no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—82no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—82no—
355C2×C4C11×#12011yescharacteristic
356C2×C4C11×#12011yescharacteristic
357C2×C4C11×#12011yescharacteristic
358C2×C4C11×#12111yescharacteristic
359C2×C4C11×#12111yescharacteristic
360C2×C4C11×#12711yescharacteristic
361C2×C4C2×C11×SD1611yescharacteristic
362C2×C4C11×#13512yes—
363C2×C4C11×#13511yescharacteristic
364C2×C4C11×AGL(1,ℤ/8)12yes—
365C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
366C2×C4C11×#13711yescharacteristic
367C8—42no—
368C8—42no—
369C8—42no—
370C8—81no—
371C22—44no—
372C22—42no—
373C22—82no—
374C22—81no—
375C22—81no—
376C22C11×#39211yescharacteristic
377C22C11×#46312yes—
378C22C11×#46511yescharacteristic
379C22C11×#46811yescharacteristic
380C22C11×#47312yes—
381C4—21no—
382C4—21no—
383C4—82no—
384C4—81no—
385C4—82no—
386C4C11×#44811yescharacteristic
387C4C11×#44911yescharacteristic
388C4C11×#44912yes—
389C4C11×#45011yescharacteristic
390C4C11×#45211yescharacteristic
391C4C11×#49511yescharacteristic
392C4C11×#49611yescharacteristic
393C2—82no—
394C2C11×#167912yes—
395C2C11×#169912yes—
396C2C11×#200011yescharacteristic
397C2C11×#201211yescharacteristic
398C2C11×#202011yescharacteristic
subgroupG/H
center, socleC23×C11#121
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
5. C2×C11×#332C2semidirect
6. C2×C11×#332C2semidirect
7. C11×#1277C2semidirect
72. #10270C11direct (N × H)
128. C2×#487C2×C11semidirect
132. C2×#332C2×C11semidirect
133. C2×#332C2×C11semidirect
134. #1277C2×C11semidirect
326. C11#10270direct (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×#4742
C2×C11×#4612
C11×#19542
C2×C11×#3322
C11×#12772
#1027011