Finite Group Databasebeta

← C11×#10263 #14587456

Subgroups — C11×#10263 #14587456

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#486C211yesmaximal, characteristic
2C2×C11×#462C211yesmaximal, characteristic, complemented
3C2×C11×#460C211yesmaximal, characteristic
4C11×#1984C211yesmaximal, characteristic, complemented
5C2×C11×#332C211yesmaximal, characteristic, complemented
6C2×C11×#331C211yesmaximal, characteristic
7C11×#1277C211yesmaximal, characteristic, complemented
8C22×C11×Q16—21no—
9C22×C11×SD16—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C11×#486—22no—
14C11×#486—22no—
15C11×#462—22no—
16C11×#462—22no—
17C11×#460—22no—
18C11×#460—22no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103—21no—
23C2×C11×#102—22no—
24C2×C11×#102—21no—
25C2×C4×C8×C11C2211yescharacteristic
26C11×#336—22no—
27C11×#332—22no—
28C11×#331—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11D411yescharacteristic
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C2×C11×Q16—24no—
35C2×C11×Q16—42no—
36C2×C11×Q16—42no—
37C2×C11×SD16—24no—
38C2×C11×SD16—42no—
39C2×C11×SD16—42no—
40C22×C8×C11—21no—
41C22×C8×C11—21no—
42C22×C8×C11—21no—
43C22×C8×C11D412yes—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8D412yes—
48C11×#127—21no—
49C11×#127—21no—
50C11×#127—21no—
51C11×#127D412yes—
52C4×Q8×C11—21no—
53C4×Q8×C11—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×C4⋊C8D412yes—
68C11×#103—24no—
69C11×#102—24no—
70C11×#102—28no—
71C4×C8×C11—21no—
72C4×C8×C11—21no—
73#10263C1111yesmaximal, characteristic, direct product factor, Sylow
74C24×C11—41no—
75C2×Q8×C11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11D812yes—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—42no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—42no—
99C2×D4×C11—82no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C11×Q16—48no—
107C11×SD16—48no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C2×C8×C11—42no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C42×C11—41no—
128C42×C11—41no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C2×#486C2×C1111yescharacteristic
134C2×#462C2×C1111yescharacteristic, complemented
135C2×#460C2×C1111yescharacteristic
136#1984C2×C1111yescharacteristic, complemented
137C2×#332C2×C1111yescharacteristic, complemented
138C2×#331C2×C1111yescharacteristic
139#1277C2×C1111yescharacteristic, complemented
140C23×C11—42no—
141C23×C11—82no—
142C23×C11—81no—
143C23×C11—81no—
144C23×C11—82no—
145C23×C11#12111yescharacteristic
146Q8×C11—22no—
147Q8×C11—22no—
148Q8×C11—41no—
149Q8×C11—41no—
150Q8×C11—42no—
151Q8×C11—42no—
152Q8×C11—81no—
153Q8×C11—81no—
154D4×C11—42no—
155D4×C11—42no—
156D4×C11—44no—
157D4×C11—82no—
158D4×C11—82no—
159D4×C11—81no—
160D4×C11—81no—
161D4×C11—81no—
162D4×C11—81no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12711yescharacteristic
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11#13511yescharacteristic
180C2×C4×C11#13512yes—
181C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C11#13712yes—
184C8×C11—42no—
185C8×C11—42no—
186C8×C11—42no—
187C8×C11—81no—
188C22×Q16—21no—
189C22×SD16—21no—
190C2×C4⋊Q8C22×C1111yescharacteristic
191C2×#127C22×C1111yescharacteristic
192C2×C4×Q8C22×C1111yescharacteristic
193#486—22no—
194#486—22no—
195#462—22no—
196#462—22no—
197#460—22no—
198#460—22no—
199C2×C4⋊C8C22×C1111yescharacteristic
200C2×C4⋊C8C22×C1111yescharacteristic
201C2×C4⋊C8C22×C1111yescharacteristic
202C2×#103—21no—
203C2×#102—22no—
204C2×#102—21no—
205C2×C4×C8C22×C1111yescharacteristic
206#336—22no—
207#332—22no—
208#331—22no—
209C22×C11—82no—
210C22×C11—82no—
211C22×C11—82no—
212C22×C11—162no—
213C22×C11—162no—
214C22×C11#39211yescharacteristic
215C22×C11#46412yes—
216C22×C11#46611yescharacteristic
217C22×C11#46911yescharacteristic
218C22×C11#47112yes—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—42no—
222C4×C11—82no—
223C4×C11—81no—
224C4×C11#44711yescharacteristic
225C4×C11#44711yescharacteristic
226C4×C11#44911yescharacteristic
227C4×C11#44911yescharacteristic
228C4×C11#45212yes—
229C4×C11#49511yescharacteristic
230C4×C11#49711yescharacteristic
231C22×Q8—21no—
232C22×Q8D4×C1111yescharacteristic
233C22×D4—21no—
234C22×D4—21no—
235C22×D4—21no—
236C2×Q16—24no—
237C2×Q16—42no—
238C2×Q16—42no—
239C2×SD16—24no—
240C2×SD16—42no—
241C2×SD16—42no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8D4×C1112yes—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8D4×C1112yes—
250#127—21no—
251#127—21no—
252#127—21no—
253#127D4×C1112yes—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4D4×C1111yescharacteristic
262C2×C42—21no—
263C2×C42C23×C1111yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8D4×C1112yes—
269C4⋊C8D4×C1112yes—
270#103—24no—
271#102—24no—
272#102—28no—
273C4×C8—21no—
274C4×C8—21no—
275C2×C11—162no—
276C2×C11#168212yes—
277C2×C11#170212yes—
278C2×C11#199911yescharacteristic
279C2×C11#201511yescharacteristic
280C2×C11#201911yescharacteristic
281C24—41no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8C11×D812yes—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—42no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—42no—
306C2×D4—82no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4C2×D4×C1111yescharacteristic
311C22×C4C2×D4×C1111yescharacteristic
312C22×C4C11×#4111yescharacteristic
313Q16—48no—
314SD16—48no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—42no—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—22no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C42—41no—
335C42—41no—
336C42C2×D4×C1111yescharacteristic
337C42C2×D4×C1111yescharacteristic
338C42C2×D4×C1111yescharacteristic
339C42C2×D4×C1111yescharacteristic
340C11#1026311yescharacteristic, direct product factor, Sylow
341C23—42no—
342C23—82no—
343C23—81no—
344C23—81no—
345C23—82no—
346C23C11×#12111yescharacteristic
347Q8—22no—
348Q8—22no—
349Q8—41no—
350Q8—41no—
351Q8—42no—
352Q8—42no—
353Q8—81no—
354Q8—81no—
355D4—42no—
356D4—42no—
357D4—44no—
358D4—82no—
359D4—82no—
360D4—81no—
361D4—81no—
362D4—81no—
363D4—81no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4C11×#12011yescharacteristic
374C2×C4C11×#12011yescharacteristic
375C2×C4C11×#12011yescharacteristic
376C2×C4C11×#12111yescharacteristic
377C2×C4C11×#12111yescharacteristic
378C2×C4C11×#12711yescharacteristic
379C2×C4C2×C11×D811yescharacteristic
380C2×C4C11×#13512yes—
381C2×C4C11×#13511yescharacteristic
382C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
383C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
384C2×C4C11×#13712yes—
385C8—42no—
386C8—42no—
387C8—42no—
388C8—81no—
389C22—82no—
390C22—82no—
391C22—82no—
392C22—162no—
393C22—162no—
394C22C11×#39211yescharacteristic
395C22C11×#46412yes—
396C22C11×#46611yescharacteristic
397C22C11×#46911yescharacteristic
398C22C11×#47112yes—
399C4—21no—
400C4—21no—
401C4—42no—
402C4—82no—
403C4—81no—
404C4C11×#44711yescharacteristic
405C4C11×#44711yescharacteristic
406C4C11×#44911yescharacteristic
407C4C11×#44911yescharacteristic
408C4C11×#45212yes—
409C4C11×#49511yescharacteristic
410C4C11×#49711yescharacteristic
411C2—162no—
412C2C11×#168212yes—
413C2C11×#170212yes—
414C2C11×#199911yescharacteristic
415C2C11×#201511yescharacteristic
416C2C11×#201911yescharacteristic
subgroupG/H
center, socleC23×C11#121
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#127C22
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
2. C2×C11×#462C2semidirect
4. C11×#1984C2semidirect
5. C2×C11×#332C2semidirect
7. C11×#1277C2semidirect
73. #10263C11direct (N × H)
134. C2×#462C2×C11semidirect
136. #1984C2×C11semidirect
137. C2×#332C2×C11semidirect
139. #1277C2×C11semidirect
340. C11#10263direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4862
C2×C11×#4622
C2×C11×#4602
C11×#19842
C2×C11×#3322
C2×C11×#3312
C11×#12772
#1026311