Finite Group Databasebeta

← C11×#11072 #14588265

Subgroups — C11×#11072 #14588265

Order 2816.

934 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#421C212yesmaximal
2C11×#2316C211yesmaximal, characteristic, complemented
3C11×#2311C211yesmaximal, characteristic
4C2×C11×#343C211yesmaximal, characteristic, complemented
5C2×C11×H(3,ℤ/4)C212yesmaximal, complemented
6C22×C11×#41C2211yescharacteristic
7C22×C11×M16C2212yes—
8C2×C11×#117C2211yescharacteristic
9C2×C11×#117C2212yes—
10C22×C11×C4⋊C4C2211yescharacteristic
11C11×#421—24no—
12C11×#421—24no—
13C2×C11×#104—24no—
14C11×#391C412yescomplemented
15C11×#390C412yescomplemented
16C11×#389—24no—
17C11×#386—22no—
18C11×#380—22no—
19C11×#380—22no—
20C11×#343—22no—
21C11×H(3,ℤ/4)—24no—
22C2×C11×#41—21no—
23C2×C11×#41—21no—
24C2×C11×#41—22no—
25C2×C11×#41—22no—
26C2×C11×#41—22no—
27C2×C11×#41—22no—
28C2×C11×#41D412yes—
29C2×C11×#41Q812yes—
30C22×Q8×C11C2×C411yescharacteristic
31C22×D4×C11—21no—
32C22×D4×C11C2×C411yescharacteristic
33C23×C4×C11—21no—
34C23×C4×C11D412yes—
35C23×C4×C11C2311yescharacteristic
36C2×C11×M16—22no—
37C2×C11×M16—22no—
38C2×C11×M16—22no—
39C2×C11×M16—22no—
40C2×C11×M16—22no—
41C2×C11×M16D414yes—
42C22×C8×C11—22no—
43C11×#117—22no—
44C11×#117—22no—
45C11×#117—22no—
46C11×#117—22no—
47C11×#117—22no—
48C11×#117—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4C2×C412yes—
55C2×C11×C4⋊C4D412yes—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—24no—
59C2×C42×C11C2×C412yes—
60C2×C42×C11D414yes—
61C11×#104—216no—
62C11×#95—24no—
63C11×#95—24no—
64#11072C1111yesmaximal, characteristic, direct product factor, Sylow
65C24×C11—21no—
66C24×C11C2×D411yescharacteristic
67C11×#41—24no—
68C11×#41—24no—
69C11×#41—24no—
70C11×#41—24no—
71C11×#41—42no—
72C11×#41—42no—
73C11×#41—42no—
74C11×#41—42no—
75C2×Q8×C11—21no—
76C2×Q8×C11—22no—
77C2×Q8×C11—22no—
78C2×Q8×C11C4⋊C412yescomplemented
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—21no—
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11C4⋊C412yescomplemented
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—24no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—82no—
99C22×C4×C11C22⋊C414yes—
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×Q811yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C22×C4×C11#4112yes—
109C22×C4×C11#4112yes—
110C11×M16—24no—
111C11×M16—24no—
112C11×M16—42no—
113C11×M16—42no—
114C2×C8×C11—24no—
115C2×C8×C11—42no—
116C2×C8×C11—42no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4—42no—
121C11×C4⋊C4—42no—
122C11×C4⋊C4—84no—
123C11×C22⋊C4—42no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—42no—
127C11×C22⋊C4—84no—
128C42×C11—24no—
129C42×C11—24no—
130C42×C11—24no—
131C2×#421C2×C1112yes—
132#2316C2×C1111yescharacteristic, complemented
133#2311C2×C1111yescharacteristic
134C2×#343C2×C1111yescharacteristic, complemented
135C2×H(3,ℤ/4)C2×C1112yescomplemented
136C23×C11—22no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—42no—
140C23×C11—42no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11C2×C22⋊C411yescharacteristic
144C23×C11#12011yescharacteristic
145C23×C11#12111yescharacteristic
146C23×C11C22⋊Q811yescharacteristic
147C23×C11#12311yescharacteristic
148C23×C11#12411yescharacteristic
149C23×C11#12711yescharacteristic
150Q8×C11—24no—
151Q8×C11—42no—
152D4×C11—24no—
153D4×C11—42no—
154D4×C11—42no—
155D4×C11—42no—
156D4×C11—42no—
157D4×C11—42no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—44no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—44no—
164C2×C4×C11—44no—
165C2×C4×C11—44no—
166C2×C4×C11—42no—
167C2×C4×C11—44no—
168C2×C4×C11—44no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—44no—
172C2×C4×C11—82no—
173C2×C4×C11C2×C4⋊C411yescharacteristic
174C2×C4×C11#11711yescharacteristic
175C2×C4×C11C4×D412yes—
176C2×C4×C11C4×D412yes—
177C2×C4×C11#12012yes—
178C2×C4×C11#12112yes—
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12112yes—
181C2×C4×C11#12112yes—
182C2×C4×C11C22⋊Q812yes—
183C2×C4×C11C22⋊Q812yes—
184C2×C4×C11C22⋊Q811yescharacteristic
185C2×C4×C11#12312yes—
186C2×C4×C11#12312yes—
187C2×C4×C11#12412yes—
188C2×C4×C11#12612yes—
189C8×C11—44no—
190C22×#41C22×C1111yescharacteristic
191C22×M16C22×C1112yes—
192C2×#117C22×C1111yescharacteristic
193C2×#117C22×C1112yes—
194C22×C4⋊C4C22×C1111yescharacteristic
195#421—24no—
196#421—24no—
197C2×#104—24no—
198#391C4×C1112yescomplemented
199#390C4×C1112yescomplemented
200#389—24no—
201#386—22no—
202#380—22no—
203#380—22no—
204#343—22no—
205H(3,ℤ/4)—24no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—44no—
217C22×C11—42no—
218C22×C11—82no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11#38011yescharacteristic
222C22×C11#38611yescharacteristic
223C22×C11#39011yescharacteristic
224C22×C11#39211yescharacteristic
225C22×C11#39311yescharacteristic
226C22×C11#39711yescharacteristic
227C22×C11#39911yescharacteristic
228C4×C11—44no—
229C4×C11—42no—
230C4×C11—84no—
231C4×C11—82no—
232C4×C11#38512yes—
233C4×C11#38812yes—
234C4×C11#39412yes—
235C4×C11#39612yes—
236C2×#41—21no—
237C2×#41—21no—
238C2×#41—22no—
239C2×#41—22no—
240C2×#41—22no—
241C2×#41—22no—
242C2×#41D4×C1112yes—
243C2×#41Q8×C1112yes—
244C22×Q8C2×C4×C1111yescharacteristic
245C22×D4—21no—
246C22×D4C2×C4×C1111yescharacteristic
247C23×C4—21no—
248C23×C4D4×C1112yes—
249C23×C4C23×C1111yescharacteristic
250C2×M16—22no—
251C2×M16—22no—
252C2×M16—22no—
253C2×M16—22no—
254C2×M16—22no—
255C2×M16D4×C1114yes—
256C22×C8—22no—
257#117—22no—
258#117—22no—
259#117—22no—
260#117—22no—
261#117—22no—
262#117—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4C2×C4×C1112yes—
269C2×C4⋊C4D4×C1112yes—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—24no—
273C2×C42C2×C4×C1112yes—
274C2×C42D4×C1114yes—
275#104—216no—
276#95—24no—
277#95—24no—
278C2×C11—21no—
279C2×C11—21no—
280C2×C11—21no—
281C2×C11—21no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—82no—
285C2×C11#143911yescharacteristic
286C2×C11#191111yescharacteristic
287C2×C11#191211yescharacteristic
288C24—21no—
289C24C2×D4×C1111yescharacteristic
290#41—24no—
291#41—24no—
292#41—24no—
293#41—24no—
294#41—42no—
295#41—42no—
296#41—42no—
297#41—42no—
298C2×Q8—21no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8C11×C4⋊C412yescomplemented
302C2×D4—22no—
303C2×D4—22no—
304C2×D4—21no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4C11×C4⋊C412yescomplemented
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—24no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—82no—
322C22×C4C11×C22⋊C414yes—
323C22×C4C22×C4×C1111yescharacteristic
324C22×C4C2×D4×C1111yescharacteristic
325C22×C4C2×D4×C1112yes—
326C22×C4C2×D4×C1112yes—
327C22×C4C2×D4×C1111yescharacteristic
328C22×C4C2×Q8×C1111yescharacteristic
329C22×C4C11×#4111yescharacteristic
330C22×C4C11×#4111yescharacteristic
331C22×C4C11×#4112yes—
332C22×C4C11×#4112yes—
333M16—24no—
334M16—24no—
335M16—42no—
336M16—42no—
337C2×C8—24no—
338C2×C8—42no—
339C2×C8—42no—
340C4⋊C4—24no—
341C4⋊C4—24no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—42no—
345C4⋊C4—84no—
346C22⋊C4—42no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—42no—
350C22⋊C4—84no—
351C42—24no—
352C42—24no—
353C42—24no—
354C11#1107211yescharacteristic, direct product factor, Sylow
355C23—22no—
356C23—41no—
357C23—41no—
358C23—42no—
359C23—42no—
360C23—41no—
361C23—41no—
362C23C2×C11×C22⋊C411yescharacteristic
363C23C11×#12011yescharacteristic
364C23C11×#12111yescharacteristic
365C23C11×C22⋊Q811yescharacteristic
366C23C11×#12311yescharacteristic
367C23C11×#12411yescharacteristic
368C23C11×#12711yescharacteristic
369Q8—24no—
370Q8—42no—
371D4—24no—
372D4—42no—
373D4—42no—
374D4—42no—
375D4—42no—
376D4—42no—
377C2×C4—22no—
378C2×C4—24no—
379C2×C4—44no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—44no—
383C2×C4—44no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—44no—
391C2×C4—82no—
392C2×C4C2×C11×C4⋊C411yescharacteristic
393C2×C4C11×#11711yescharacteristic
394C2×C4C4×D4×C1112yes—
395C2×C4C4×D4×C1112yes—
396C2×C4C11×#12012yes—
397C2×C4C11×#12112yes—
398C2×C4C11×#12111yescharacteristic
399C2×C4C11×#12112yes—
400C2×C4C11×#12112yes—
401C2×C4C11×C22⋊Q812yes—
402C2×C4C11×C22⋊Q812yes—
403C2×C4C11×C22⋊Q811yescharacteristic
404C2×C4C11×#12312yes—
405C2×C4C11×#12312yes—
406C2×C4C11×#12412yes—
407C2×C4C11×#12612yes—
408C8—44no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—44no—
420C22—42no—
421C22—82no—
422C22—81no—
423C22—81no—
424C22C11×#38011yescharacteristic
425C22C11×#38611yescharacteristic
426C22C11×#39011yescharacteristic
427C22C11×#39211yescharacteristic
428C22C11×#39311yescharacteristic
429C22C11×#39711yescharacteristic
430C22C11×#39911yescharacteristic
431C4—44no—
432C4—42no—
433C4—84no—
434C4—82no—
435C4C11×#38512yes—
436C4C11×#38812yes—
437C4C11×#39412yes—
438C4C11×#39612yes—
439C2—21no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—21no—
444C2—21no—
445C2—82no—
446C2C11×#143911yescharacteristic
447C2C11×#191111yescharacteristic
448C2C11×#191211yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2316C2semidirect
4. C2×C11×#343C2semidirect
5. C2×C11×H(3,ℤ/4)C2semidirect
14. C11×#391C4semidirect
15. C11×#390C4semidirect
64. #11072C11direct (N × H)
78. C2×Q8×C11C4⋊C4semidirect
88. C2×D4×C11C4⋊C4semidirect
132. #2316C2×C11semidirect
134. C2×#343C2×C11semidirect
135. C2×H(3,ℤ/4)C2×C11semidirect
198. #391C4×C11semidirect
199. #390C4×C11semidirect
301. C2×Q8C11×C4⋊C4semidirect
311. C2×D4C11×C4⋊C4semidirect
354. C11#11072direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4212
C11×#23162
C11×#23112
C2×C11×#3432
C2×C11×H(3,ℤ/4)2
#1107211