Finite Group Databasebeta

← C11×#10066 #14587259

Subgroups — C11×#10066 #14587259

Order 2816.

634 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#500C211yesmaximal, characteristic, complemented
2C2×C11×#461C211yesmaximal, characteristic
3C11×#2547C211yesmaximal, characteristic
4C11×#1988C211yesmaximal, characteristic, complemented
5C2×C11×#332C211yesmaximal, characteristic, complemented
6C2×C11×D4⋊C8C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#124—21no—
12C2×C4×D4×C11C2211yescharacteristic
13C11×#500—22no—
14C11×#500—22no—
15C11×#461—22no—
16C11×#461—22no—
17C2×C11×#107—22no—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#103—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—
33C2×C11×SD16—24no—
34C2×C11×SD16—42no—
35C2×C11×SD16—42no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C11×C4⋊Q8—21no—
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×#124—42no—
48C11×#124—42no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D412yes—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4D412yes—
59C2×C11×C22⋊C4—24no—
60C2×C11×C22⋊C4—21no—
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C11×#107—28no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yes—
68C11×#103—24no—
69C4×C8×C11—21no—
70C4×C8×C11D412yes—
71C11×#95—24no—
72C11×#95—21no—
73#10066C1111yesmaximal, characteristic, direct product factor, Sylow
74C24×C11—21no—
75C2×Q8×C11—22no—
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×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11D812yes—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C11×SD16—48no—
105C2×C8×C11—24no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C2×C8×C11—42no—
111C2×C8×C11—41no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C22⋊C4—48no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C42×C11—41no—
128C42×C11—41no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11#4111yescharacteristic
133C2×#500C2×C1111yescharacteristic, complemented
134C2×#461C2×C1111yescharacteristic
135#2547C2×C1111yescharacteristic
136#1988C2×C1111yescharacteristic, complemented
137C2×#332C2×C1111yescharacteristic, complemented
138C2×D4⋊C8C2×C1111yescharacteristic
139#1279C2×C1111yescharacteristic, complemented
140C23×C11—22no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11#12011yescharacteristic
146Q8×C11—42no—
147Q8×C11—42no—
148Q8×C11—81no—
149Q8×C11—81no—
150Q8×C11—81no—
151Q8×C11—81no—
152Q8×C11—81no—
153Q8×C11—81no—
154D4×C11—22no—
155D4×C11—22no—
156D4×C11—41no—
157D4×C11—41no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11—82no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12711yescharacteristic
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11#13511yescharacteristic
181C2×C4×C11#13512yes—
182C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C11#13712yes—
185C8×C11—24no—
186C8×C11—42no—
187C8×C11—81no—
188C22×SD16—21no—
189C2×C4⋊Q8C22×C1111yescharacteristic
190C2×C4⋊Q8C22×C1111yescharacteristic
191C2×#124—21no—
192C2×C4×D4C22×C1111yescharacteristic
193#500—22no—
194#500—22no—
195#461—22no—
196#461—22no—
197C2×#107—22no—
198C2×C4⋊C8C22×C1111yescharacteristic
199C2×C4⋊C8C22×C1111yescharacteristic
200C2×#103—21no—
201C2×C4×C8C22×C1111yescharacteristic
202#397—22no—
203#391—21no—
204#380—22no—
205C4×C4⋊C4C22×C1111yescharacteristic
206#340—22no—
207#332—22no—
208D4⋊C8—22no—
209C22×C11—44no—
210C22×C11—42no—
211C22×C11—82no—
212C22×C11—81no—
213C22×C11—81no—
214C22×C11#39211yescharacteristic
215C22×C11#44711yescharacteristic
216C22×C11#44911yescharacteristic
217C22×C11#45212yes—
218C22×C11#45612yes—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—82no—
222C4×C11—82no—
223C4×C11—82no—
224C4×C11—81no—
225C4×C11#44711yescharacteristic
226C4×C11#44911yescharacteristic
227C4×C11#46412yes—
228C4×C11#46611yescharacteristic
229C4×C11#46911yescharacteristic
230C4×C11#49511yescharacteristic
231C4×C11#49711yescharacteristic
232C22×Q8—21no—
233C22×Q8—21no—
234C22×D4D4×C1111yescharacteristic
235C23×C4—21no—
236C2×SD16—24no—
237C2×SD16—42no—
238C2×SD16—42no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8D4×C1112yes—
250#124—42no—
251#124—42no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4D4×C1111yescharacteristic
260C2×C4⋊C4D4×C1112yes—
261C2×C4⋊C4D4×C1112yes—
262C2×C22⋊C4—24no—
263C2×C22⋊C4—21no—
264C2×C42—21no—
265C2×C42C23×C1111yescharacteristic
266#107—28no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8D4×C1112yes—
271#103—24no—
272C4×C8—21no—
273C4×C8D4×C1112yes—
274#95—24no—
275#95—21no—
276C2×C11—82no—
277C2×C11#164712yes—
278C2×C11#165012yes—
279C2×C11#199911yescharacteristic
280C2×C11#200511yescharacteristic
281C2×C11#201511yescharacteristic
282C24—21no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4C11×D812yes—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4C2×D4×C1111yescharacteristic
310C22×C4C2×D4×C1111yescharacteristic
311C22×C4C2×D4×C1111yescharacteristic
312SD16—48no—
313C2×C8—24no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—42no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—21no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C22⋊C4—48no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C42—41no—
336C42—41no—
337C42C2×D4×C1111yescharacteristic
338C42C2×D4×C1111yescharacteristic
339C42C2×D4×C1111yescharacteristic
340C42C11×#4111yescharacteristic
341C11#1006611yescharacteristic, direct product factor, Sylow
342C23—22no—
343C23—41no—
344C23—41no—
345C23—42no—
346C23—42no—
347C23C11×#12011yescharacteristic
348Q8—42no—
349Q8—42no—
350Q8—81no—
351Q8—81no—
352Q8—81no—
353Q8—81no—
354Q8—81no—
355Q8—81no—
356D4—22no—
357D4—22no—
358D4—41no—
359D4—41no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—82no—
375C2×C4C11×#12011yescharacteristic
376C2×C4C11×#12011yescharacteristic
377C2×C4C11×#12111yescharacteristic
378C2×C4C11×#12111yescharacteristic
379C2×C4C11×#12111yescharacteristic
380C2×C4C11×#12711yescharacteristic
381C2×C4C2×C11×D811yescharacteristic
382C2×C4C11×#13512yes—
383C2×C4C11×#13511yescharacteristic
384C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
385C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
386C2×C4C11×#13712yes—
387C8—24no—
388C8—42no—
389C8—81no—
390C22—44no—
391C22—42no—
392C22—82no—
393C22—81no—
394C22—81no—
395C22C11×#39211yescharacteristic
396C22C11×#44711yescharacteristic
397C22C11×#44911yescharacteristic
398C22C11×#45212yes—
399C22C11×#45612yes—
400C4—21no—
401C4—21no—
402C4—82no—
403C4—82no—
404C4—82no—
405C4—81no—
406C4C11×#44711yescharacteristic
407C4C11×#44911yescharacteristic
408C4C11×#46412yes—
409C4C11×#46611yescharacteristic
410C4C11×#46911yescharacteristic
411C4C11×#49511yescharacteristic
412C4C11×#49711yescharacteristic
413C2—82no—
414C2C11×#164712yes—
415C2C11×#165012yes—
416C2C11×#199911yescharacteristic
417C2C11×#200511yescharacteristic
418C2C11×#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×#500C2semidirect
4. C11×#1988C2semidirect
5. C2×C11×#332C2semidirect
7. C11×#1279C2semidirect
73. #10066C11direct (N × H)
133. C2×#500C2×C11semidirect
136. #1988C2×C11semidirect
137. C2×#332C2×C11semidirect
139. #1279C2×C11semidirect
341. C11#10066direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5002
C2×C11×#4612
C11×#25472
C11×#19882
C2×C11×#3322
C2×C11×D4⋊C82
C11×#12792
#1006611