Finite Group Databasebeta

← C11×#9074 #14586267

Subgroups — C11×#9074 #14586267

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#431C211yesmaximal, characteristic, complemented
2C4×C11×#121C211yesmaximal, characteristic
3C11×#1797C211yesmaximal, characteristic, complemented
4C2×C11×D4⋊C8C212yesmaximal, complemented
5C11×#1279C212yesmaximal, complemented
6C2×C11×#121C411yescharacteristic
7C2×C4×D4×C11—21no—
8C2×C4×D4×C11C2211yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C11×#431—24no—
11C2×C11×C4⋊C8—21no—
12C2×C11×C4⋊C8C2212yes—
13C2×C11×C22⋊C8—21no—
14C2×C11×C22⋊C8—21no—
15C2×C4×C8×C11C2212yes—
16C11×#390C411yescharacteristic
17C11×#389C411yescharacteristic
18C11×#388—21no—
19C11×#386—21no—
20C11×#380C411yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C4×C11×C22⋊C4—21no—
23C11×#336—21no—
24C11×D4⋊C8—24no—
25C22×D4×C11—21no—
26C22×D4×C11C2×C411yescharacteristic
27C23×C4×C11—21no—
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C22×C8×C11—22no—
32C22×C8×C11—22no—
33C11×#121—22no—
34C11×#121C814yescomplemented
35C4×D4×C11—22no—
36C4×D4×C11—22no—
37C4×D4×C11—44no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C11×C4⋊C4C2×C411yescharacteristic
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C42×C11—22no—
48C2×C42×C11—22no—
49C2×C42×C11—21no—
50C2×C42×C11C2×C411yescharacteristic
51C2×C42×C11D411yescharacteristic
52C2×C42×C11D411yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C11×C4⋊C8—24no—
55C11×C4⋊C8—22no—
56C11×C4⋊C8—22no—
57C11×C22⋊C8—24no—
58C11×C22⋊C8—42no—
59C4×C8×C11—22no—
60C4×C8×C11D414yescomplemented
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—21no—
64#9074C1111yesmaximal, characteristic, direct product factor, Sylow
65C24×C11—21no—
66C24×C11C22⋊C411yescharacteristic
67C2×D4×C11—24no—
68C2×D4×C11—22no—
69C2×D4×C11—21no—
70C2×D4×C11—22no—
71C2×D4×C11—42no—
72C2×D4×C11—42no—
73C2×D4×C11C2×C812yes—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—22no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—22no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11C22⋊C411yescharacteristic
92C22×C4×C11C22⋊C411yescharacteristic
93C22×C4×C11C22⋊C411yescharacteristic
94C22×C4×C11C2×C812yes—
95C22×C4×C11M1612yes—
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C2×C8×C11—24no—
100C2×C8×C11—42no—
101C2×C8×C11—42no—
102C2×C8×C11—42no—
103C2×C8×C11—42no—
104C2×C8×C11—42no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—42no—
109C11×C4⋊C4C2×C812yes—
110C11×C22⋊C4—24no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—42no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11—22no—
117C42×C11—21no—
118C42×C11—22no—
119C42×C11—21no—
120C42×C11—42no—
121C42×C11C2×D412yes—
122C42×C11#4112yes—
123C2×#431C2×C1111yescharacteristic, complemented
124C4×#121C2×C1111yescharacteristic
125#1797C2×C1111yescharacteristic, complemented
126C2×D4⋊C8C2×C1112yescomplemented
127#1279C2×C1112yescomplemented
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—22no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11C22⋊C812yes—
142C23×C11C2×C22⋊C411yescharacteristic
143D4×C11—24no—
144D4×C11—48no—
145D4×C11—42no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—22no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—82no—
172C2×C4×C11—82no—
173C2×C4×C11C22⋊C812yes—
174C2×C4×C11C4×D412yes—
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12112yes—
177C2×C4×C11#12311yescharacteristic
178C2×C4×C11C22×C811yescharacteristic
179C2×C4×C11C2×M1611yescharacteristic
180C2×C4×C11#13112yes—
181C2×C4×C11AGL(1,ℤ/8)12yes—
182C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C11#13711yescharacteristic
184C8×C11—44no—
185C8×C11—82no—
186C2×#121C4×C1111yescharacteristic
187C2×C4×D4—21no—
188C2×C4×D4C22×C1111yescharacteristic
189C22×C42C22×C1111yescharacteristic
190#431—24no—
191C2×C4⋊C8—21no—
192C2×C4⋊C8C22×C1112yes—
193C2×C22⋊C8—21no—
194C2×C22⋊C8—21no—
195C2×C4×C8C22×C1112yes—
196#390C4×C1111yescharacteristic
197#389C4×C1111yescharacteristic
198#388—21no—
199#386—21no—
200#380C4×C1111yescharacteristic
201C4×C4⋊C4C22×C1111yescharacteristic
202C4×C22⋊C4—21no—
203#336—21no—
204D4⋊C8—24no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—42no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11#38611yescharacteristic
220C22×C11C2×C22⋊C811yescharacteristic
221C22×C11#40811yescharacteristic
222C22×C11#41711yescharacteristic
223C22×C11#41811yescharacteristic
224C22×C11#42111yescharacteristic
225C22×C11#42111yescharacteristic
226C4×C11—22no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—41no—
230C4×C11—41no—
231C4×C11—42no—
232C4×C11—81no—
233C4×C11—81no—
234C4×C11C8×D412yes—
235C4×C11#43512yes—
236C4×C11#46812yes—
237C4×C11#46912yes—
238C22×D4—21no—
239C22×D4C2×C4×C1111yescharacteristic
240C23×C4—21no—
241C23×C4C2×C4×C1111yescharacteristic
242C23×C4D4×C1111yescharacteristic
243C23×C4D4×C1111yescharacteristic
244C22×C8—22no—
245C22×C8—22no—
246#121—22no—
247#121C8×C1114yescomplemented
248C4×D4—22no—
249C4×D4—22no—
250C4×D4—44no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C2×C4×C1111yescharacteristic
253C2×C4⋊C4C2×C4×C1111yescharacteristic
254C2×C4⋊C4C2×C4×C1111yescharacteristic
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C42—22no—
261C2×C42—22no—
262C2×C42—21no—
263C2×C42C2×C4×C1111yescharacteristic
264C2×C42D4×C1111yescharacteristic
265C2×C42D4×C1111yescharacteristic
266C2×C42C23×C1111yescharacteristic
267C4⋊C8—24no—
268C4⋊C8—22no—
269C4⋊C8—22no—
270C22⋊C8—24no—
271C22⋊C8—42no—
272C4×C8—22no—
273C4×C8D4×C1114yescomplemented
274#95—21no—
275#95—21no—
276#95—21no—
277C2×C11—42no—
278C2×C11—82no—
279C2×C11#147711yescharacteristic
280C2×C11#147811yescharacteristic
281C2×C11#149511yescharacteristic
282C2×C11#149611yescharacteristic
283C2×C11#186911yescharacteristic
284C2×C11#189511yescharacteristic
285C2×C11#189711yescharacteristic
286C24—21no—
287C24C11×C22⋊C411yescharacteristic
288C2×D4—24no—
289C2×D4—22no—
290C2×D4—21no—
291C2×D4—22no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4C2×C8×C1112yes—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4C11×C22⋊C411yescharacteristic
313C22×C4C11×C22⋊C411yescharacteristic
314C22×C4C11×C22⋊C411yescharacteristic
315C22×C4C2×C8×C1112yes—
316C22×C4C11×M1612yes—
317C22×C4C22×C4×C1111yescharacteristic
318C22×C4C2×D4×C1111yescharacteristic
319C22×C4C2×D4×C1111yescharacteristic
320C2×C8—24no—
321C2×C8—42no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—42no—
326C4⋊C4—21no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—42no—
330C4⋊C4C2×C8×C1112yes—
331C22⋊C4—24no—
332C22⋊C4—42no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C42—22no—
338C42—21no—
339C42—22no—
340C42—21no—
341C42—42no—
342C42C2×D4×C1112yes—
343C42C11×#4112yes—
344C11#907411yescharacteristic, direct product factor, Sylow
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—22no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23C11×C22⋊C812yes—
359C23C2×C11×C22⋊C411yescharacteristic
360D4—24no—
361D4—48no—
362D4—42no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4C11×C22⋊C812yes—
391C2×C4C4×D4×C1112yes—
392C2×C4C11×#12011yescharacteristic
393C2×C4C11×#12112yes—
394C2×C4C11×#12311yescharacteristic
395C2×C4C22×C8×C1111yescharacteristic
396C2×C4C2×C11×M1611yescharacteristic
397C2×C4C11×#13112yes—
398C2×C4C11×AGL(1,ℤ/8)12yes—
399C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
400C2×C4C11×#13711yescharacteristic
401C8—44no—
402C8—82no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22C11×#38611yescharacteristic
418C22C2×C11×C22⋊C811yescharacteristic
419C22C11×#40811yescharacteristic
420C22C11×#41711yescharacteristic
421C22C11×#41811yescharacteristic
422C22C11×#42111yescharacteristic
423C22C11×#42111yescharacteristic
424C4—22no—
425C4—21no—
426C4—21no—
427C4—41no—
428C4—41no—
429C4—42no—
430C4—81no—
431C4—81no—
432C4C8×D4×C1112yes—
433C4C11×#43512yes—
434C4C11×#46812yes—
435C4C11×#46912yes—
436C2—42no—
437C2—82no—
438C2C11×#147711yescharacteristic
439C2C11×#147811yescharacteristic
440C2C11×#149511yescharacteristic
441C2C11×#149611yescharacteristic
442C2C11×#186911yescharacteristic
443C2C11×#189511yescharacteristic
444C2C11×#189711yescharacteristic
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC2×C4C22×C8×C11
Frattini, cosocleC2×C42C23×C11
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#431C2semidirect
3. C11×#1797C2semidirect
4. C2×C11×D4⋊C8C2semidirect
5. C11×#1279C2semidirect
34. C11×#121C8semidirect
60. C4×C8×C11D4semidirect
64. #9074C11direct (N × H)
123. C2×#431C2×C11semidirect
125. #1797C2×C11semidirect
126. C2×D4⋊C8C2×C11semidirect
127. #1279C2×C11semidirect
247. #121C8×C11semidirect
273. C4×C8D4×C11semidirect
344. C11#9074direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4312
C4×C11×#1212
C11×#17972
C2×C11×D4⋊C82
C11×#12792
#907411