Finite Group Databasebeta

← C11×#9971 #14587164

Subgroups — C11×#9971 #14587164

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#483C211yesmaximal, characteristic, complemented
2C2×C11×#480C211yesmaximal, characteristic
3C11×#2639C211yesmaximal, characteristic
4C2×C11×#328C211yesmaximal, characteristic, complemented
5C2×C11×#327C211yesmaximal, characteristic
6C11×#1445C211yesmaximal, characteristic, complemented
7C11×#1280C211yesmaximal, characteristic, complemented
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×C11×#121C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C11×#483—22no—
12C11×#483—22no—
13C11×#480—22no—
14C11×#480—22no—
15C2×C11×#107—21no—
16C2×C11×#106—21no—
17C2×C11×#103—21no—
18C2×C11×#102—21no—
19C2×C11×C22⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C11×#400—21no—
22C11×#397—21no—
23C11×#394—21no—
24C11×#393—21no—
25C11×#386—22no—
26C2×C11×#95—22no—
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C11×#328—22no—
30C11×#327—22no—
31C22×Q8×C11D411yescharacteristic
32C22×D4×C11—21no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C23×C4×C11—21no—
36C23×C4×C11D412yes—
37C23×C4×C11C2311yescharacteristic
38C22×C8×C11—21no—
39C22×C8×C11—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C11×#121—21no—
45C11×#121—21no—
46C11×#121—21no—
47C11×#121—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C11×#107—24no—
62C11×#106—24no—
63C11×#103—24no—
64C11×#102—24no—
65C11×C22⋊C8—21no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8D412yes—
68C11×C22⋊C8D412yes—
69C11×#95—22no—
70C11×#95—22no—
71C11×#95—21no—
72C11×#95—21no—
73C11×#95—21no—
74C11×#95—21no—
75C11×#95—44no—
76#9971C1111yesmaximal, characteristic, direct product factor, Sylow
77C24×C11—21no—
78C24×C11C2×D411yescharacteristic
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—42no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—42no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—42no—
88C2×D4×C11—42no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11—42no—
100C22×C4×C11—41no—
101C22×C4×C11—42no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—42no—
117C2×C8×C11—42no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—82no—
133C11×C22⋊C4—82no—
134C2×#483C2×C1111yescharacteristic, complemented
135C2×#480C2×C1111yescharacteristic
136#2639C2×C1111yescharacteristic
137C2×#328C2×C1111yescharacteristic, complemented
138C2×#327C2×C1111yescharacteristic
139#1445C2×C1111yescharacteristic, complemented
140#1280C2×C1111yescharacteristic, complemented
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—22no—
144C23×C11—41no—
145C23×C11—42no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—42no—
149C23×C11#12011yescharacteristic
150C23×C11#12111yescharacteristic
151C23×C11#12711yescharacteristic
152C23×C11#13512yes—
153C23×C11AGL(1,ℤ/8)12yes—
154Q8×C11—42no—
155Q8×C11—81no—
156D4×C11—42no—
157D4×C11—81no—
158D4×C11—82no—
159D4×C11—81no—
160D4×C11—81no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—44no—
168C2×C4×C11—42no—
169C2×C4×C11—44no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—44no—
182C2×C4×C11—82no—
183C2×C4×C11—81no—
184C2×C4×C11—82no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11—81no—
188C2×C4×C11—82no—
189C2×C4×C11#12011yescharacteristic
190C2×C4×C11#12011yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C8×C11—42no—
194C8×C11—42no—
195C2×C22⋊Q8C22×C1111yescharacteristic
196C2×#121C22×C1111yescharacteristic
197C22×C4⋊C4C22×C1111yescharacteristic
198#483—22no—
199#483—22no—
200#480—22no—
201#480—22no—
202C2×#107—21no—
203C2×#106—21no—
204C2×#103—21no—
205C2×#102—21no—
206C2×C22⋊C8C22×C1111yescharacteristic
207C2×C22⋊C8C22×C1111yescharacteristic
208#400—21no—
209#397—21no—
210#394—21no—
211#393—21no—
212#386—22no—
213C2×#95—22no—
214C2×#95C22×C1111yescharacteristic
215C2×#95C22×C1111yescharacteristic
216#328—22no—
217#327—22no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—82no—
227C22×C11—82no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11#39211yescharacteristic
232C22×C11#44912yes—
233C22×C11#45511yescharacteristic
234C22×C11#45611yescharacteristic
235C22×C11#45812yes—
236C22×C11#46312yes—
237C22×C11#49511yescharacteristic
238C22×C11#49611yescharacteristic
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—82no—
244C4×C11—82no—
245C4×C11—81no—
246C4×C11—82no—
247C4×C11—81no—
248C4×C11—81no—
249C22×Q8D4×C1111yescharacteristic
250C22×D4—21no—
251C22×D4D4×C1111yescharacteristic
252C23×C4—21no—
253C23×C4—21no—
254C23×C4D4×C1112yes—
255C23×C4C23×C1111yescharacteristic
256C22×C8—21no—
257C22×C8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262#121—21no—
263#121—21no—
264#121—21no—
265#121—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4D4×C1112yes—
273C2×C4⋊C4D4×C1111yescharacteristic
274C2×C4⋊C4D4×C1111yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—22no—
279#107—24no—
280#106—24no—
281#103—24no—
282#102—24no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8D4×C1112yes—
286C22⋊C8D4×C1112yes—
287#95—22no—
288#95—22no—
289#95—21no—
290#95—21no—
291#95—21no—
292#95—21no—
293#95—44no—
294C2×C11—21no—
295C2×C11—22no—
296C2×C11—21no—
297C2×C11—161no—
298C2×C11#160912yes—
299C2×C11#161212yes—
300C2×C11#200711yescharacteristic
301C2×C11#201211yescharacteristic
302C2×C11#202211yescharacteristic
303C24—21no—
304C24C2×D4×C1111yescharacteristic
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—42no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—42no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—42no—
314C2×D4—42no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—41no—
327C22×C4—42no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4C2×D4×C1111yescharacteristic
335C22×C4C2×D4×C1111yescharacteristic
336C22×C4C2×D4×C1111yescharacteristic
337C22×C4C2×D4×C1111yescharacteristic
338C22×C4C2×D4×C1111yescharacteristic
339C22×C4C11×#4111yescharacteristic
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—42no—
343C2×C8—42no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—82no—
359C22⋊C4—82no—
360C11#997111yescharacteristic, direct product factor, Sylow
361C23—21no—
362C23—21no—
363C23—22no—
364C23—41no—
365C23—42no—
366C23—41no—
367C23—41no—
368C23—42no—
369C23C11×#12011yescharacteristic
370C23C11×#12111yescharacteristic
371C23C11×#12711yescharacteristic
372C23C11×#13512yes—
373C23C11×AGL(1,ℤ/8)12yes—
374Q8—42no—
375Q8—81no—
376D4—42no—
377D4—81no—
378D4—81no—
379D4—81no—
380D4—82no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—44no—
402C2×C4—82no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4C11×#12011yescharacteristic
410C2×C4C11×#12011yescharacteristic
411C2×C4C11×#12111yescharacteristic
412C2×C4C11×#12111yescharacteristic
413C8—42no—
414C8—42no—
415C22—22no—
416C22—22no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—22no—
422C22—22no—
423C22—82no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—82no—
428C22C11×#39211yescharacteristic
429C22C11×#44912yes—
430C22C11×#45511yescharacteristic
431C22C11×#45611yescharacteristic
432C22C11×#45812yes—
433C22C11×#46312yes—
434C22C11×#49511yescharacteristic
435C22C11×#49611yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—82no—
441C4—82no—
442C4—81no—
443C4—82no—
444C4—81no—
445C4—81no—
446C2—21no—
447C2—21no—
448C2—22no—
449C2—161no—
450C2C11×#160912yes—
451C2C11×#161212yes—
452C2C11×#200711yescharacteristic
453C2C11×#201211yescharacteristic
454C2C11×#202211yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC2×C11×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#483C2semidirect
4. C2×C11×#328C2semidirect
6. C11×#1445C2semidirect
7. C11×#1280C2semidirect
76. #9971C11direct (N × H)
134. C2×#483C2×C11semidirect
137. C2×#328C2×C11semidirect
139. #1445C2×C11semidirect
140. #1280C2×C11semidirect
360. C11#9971direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4832
C2×C11×#4802
C11×#26392
C2×C11×#3282
C2×C11×#3272
C11×#14452
C11×#12802
#997111