Finite Group Databasebeta

← C11×#23462 #14600655

Subgroups — C11×#23462 #14600655

Order 2816.

1214 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#544C211yesmaximal, characteristic, complemented
2C11×#2896C212yesmaximal
3C11×#2311C211yesmaximal, characteristic
4C11×#2028C214yesmaximal, complemented
5C11×#2027C214yesmaximal, complemented
6C2×C11×#343C211yesmaximal, characteristic, complemented
7C11×#1733C212yesmaximal, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2212yes—
10C11×#544—24no—
11C11×#544—22no—
12C11×#544C2214yes—
13C2×C11×C4⋊Q8—22no—
14C2×C11×#125—22no—
15C2×C11×C22⋊Q8—22no—
16C2×C11×#117C2212yes—
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#419C2214yes—
20C11×#418C2214yes—
21C11×#417—22no—
22C11×#417—22no—
23C11×#416—24no—
24C11×#391C2212yes—
25C11×#390C2212yes—
26C11×#386—22no—
27C11×#380—22no—
28C11×#343C2214yes—
29C11×#339C2218yes—
30C2×C11×#41—22no—
31C2×C11×#41—22no—
32C2×C11×#41—22no—
33C2×C11×#41—24no—
34C2×C11×#41Q814yescomplemented
35C22×Q8×C11—22no—
36C22×Q8×C11C2311yescharacteristic
37C22×D4×C11—21no—
38C22×D4×C11C2311yescharacteristic
39C23×C4×C11—21no—
40C23×C4×C11D412yes—
41C23×C4×C11C2311yescharacteristic
42C2×C11×M16—22no—
43C2×C11×M16—24no—
44C2×C11×M16—24no—
45C2×C11×M16C2314yes—
46C22×C8×C11—22no—
47C11×C4⋊Q8—28no—
48C11×C4⋊Q8—28no—
49C11×#125—28no—
50C11×#125—28no—
51C11×C22⋊Q8—28no—
52C11×C22⋊Q8—28no—
53C11×#117—22no—
54C11×#117—22no—
55C11×#117—24no—
56C11×#117D414yes—
57C11×#117C2314yes—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—24no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D412yes—
64C2×C11×C4⋊C4D412yes—
65C2×C11×C4⋊C4D412yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—24no—
70C2×C42×C11—22no—
71C2×C42×C11C2312yes—
72C11×#103—24no—
73C11×#103—24no—
74C11×#102—24no—
75C11×#102—24no—
76C11×#95—24no—
77#23462C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—21no—
79C24×C11C2×D411yescharacteristic
80C11×#41—28no—
81C11×#41—28no—
82C11×#41—44no—
83C11×#41—44no—
84C2×Q8×C11—28no—
85C2×Q8×C11—21no—
86C2×Q8×C11—22no—
87C2×Q8×C11—22no—
88C2×Q8×C11—84no—
89C2×Q8×C11C2×Q812yescomplemented
90C2×D4×C11—24no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—21no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—42no—
97C2×D4×C11C2×Q812yescomplemented
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—82no—
108C22×C4×C11C2×D414yes—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×Q812yes—
113C22×C4×C11#4114yes—
114C22×C4×C11#4112yes—
115C22×C4×C11C2411yescharacteristic
116C11×M16—24no—
117C11×M16—24no—
118C11×M16—44no—
119C2×C8×C11—24no—
120C2×C8×C11—44no—
121C11×C4⋊C4—28no—
122C11×C4⋊C4—216no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4C2×D414yes—
129C11×C4⋊C4C2×D414yes—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—42no—
133C11×C22⋊C4—84no—
134C42×C11—24no—
135C42×C11—24no—
136C42×C11—24no—
137C2×#544C2×C1111yescharacteristic, complemented
138#2896C2×C1112yes—
139#2311C2×C1111yescharacteristic
140#2028C2×C1114yescomplemented
141#2027C2×C1114yescomplemented
142C2×#343C2×C1111yescharacteristic, complemented
143#1733C2×C1112yescomplemented
144C23×C11—22no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11#12011yescharacteristic
152C23×C11#12011yescharacteristic
153C23×C11C22⋊Q812yes—
154C23×C11#12412yes—
155C23×C11C22×D411yescharacteristic
156Q8×C11—24no—
157Q8×C11—42no—
158Q8×C11—88no—
159D4×C11—24no—
160D4×C11—44no—
161D4×C11—44no—
162D4×C11—42no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—22no—
167C2×C4×C11—44no—
168C2×C4×C11—44no—
169C2×C4×C11—44no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—48no—
173C2×C4×C11—44no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—82no—
178C2×C4×C11#12012yes—
179C2×C4×C11C22⋊Q814yes—
180C2×C4×C11C22⋊Q814yes—
181C2×C4×C11C22⋊Q812yes—
182C2×C4×C11#12414yes—
183C2×C4×C11#12414yes—
184C2×C4×C11#12412yes—
185C2×C4×C11C22×D412yes—
186C2×C4×C11C22×Q811yescharacteristic
187C2×C4×C11C2×#4112yes—
188C2×C4×C11C2×#4111yescharacteristic
189C8×C11—44no—
190C22×#41C22×C1111yescharacteristic
191C22×M16C22×C1112yes—
192#544—24no—
193#544—22no—
194#544C22×C1114yes—
195C2×C4⋊Q8—22no—
196C2×#125—22no—
197C2×C22⋊Q8—22no—
198C2×#117C22×C1112yes—
199C2×#117C22×C1111yescharacteristic
200C22×C4⋊C4C22×C1111yescharacteristic
201#419C22×C1114yes—
202#418C22×C1114yes—
203#417—22no—
204#417—22no—
205#416—24no—
206#391C22×C1112yes—
207#390C22×C1112yes—
208#386—22no—
209#380—22no—
210#343C22×C1114yes—
211#339C22×C1118yes—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—42no—
219C22×C11—42no—
220C22×C11—44no—
221C22×C11—42no—
222C22×C11—82no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11#39312yes—
226C22×C11#39312yes—
227C22×C11C2×#12011yescharacteristic
228C22×C11C2×C22⋊Q811yescharacteristic
229C22×C11C2×#12411yescharacteristic
230C4×C11—42no—
231C4×C11—44no—
232C4×C11—44no—
233C4×C11—44no—
234C4×C11—82no—
235C4×C11#39314yes—
236C4×C11C2×C22⋊Q812yes—
237C4×C11C2×#12412yes—
238C2×#41—22no—
239C2×#41—22no—
240C2×#41—22no—
241C2×#41—24no—
242C2×#41Q8×C1114yescomplemented
243C22×Q8—22no—
244C22×Q8C23×C1111yescharacteristic
245C22×D4—21no—
246C22×D4C23×C1111yescharacteristic
247C23×C4—21no—
248C23×C4D4×C1112yes—
249C23×C4C23×C1111yescharacteristic
250C2×M16—22no—
251C2×M16—24no—
252C2×M16—24no—
253C2×M16C23×C1114yes—
254C22×C8—22no—
255C4⋊Q8—28no—
256C4⋊Q8—28no—
257#125—28no—
258#125—28no—
259C22⋊Q8—28no—
260C22⋊Q8—28no—
261#117—22no—
262#117—22no—
263#117—24no—
264#117D4×C1114yes—
265#117C23×C1114yes—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4D4×C1112yes—
272C2×C4⋊C4D4×C1112yes—
273C2×C4⋊C4D4×C1112yes—
274C2×C4⋊C4C23×C1112yes—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—24no—
278C2×C42—22no—
279C2×C42C23×C1112yes—
280#103—24no—
281#103—24no—
282#102—24no—
283#102—24no—
284#95—24no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—22no—
288C2×C11—22no—
289C2×C11—82no—
290C2×C11C2×#39311yescharacteristic
291C2×C11#301911yescharacteristic
292C2×C11#302011yescharacteristic
293C24—21no—
294C24C2×D4×C1111yescharacteristic
295#41—28no—
296#41—28no—
297#41—44no—
298#41—44no—
299C2×Q8—28no—
300C2×Q8—21no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—84no—
304C2×Q8C2×Q8×C1112yescomplemented
305C2×D4—24no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—42no—
312C2×D4C2×Q8×C1112yescomplemented
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—24no—
319C22×C4—22no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—82no—
323C22×C4C2×D4×C1114yes—
324C22×C4C2×D4×C1111yescharacteristic
325C22×C4C2×D4×C1112yes—
326C22×C4C2×D4×C1112yes—
327C22×C4C2×Q8×C1112yes—
328C22×C4C11×#4114yes—
329C22×C4C11×#4112yes—
330C22×C4C24×C1111yescharacteristic
331M16—24no—
332M16—24no—
333M16—44no—
334C2×C8—24no—
335C2×C8—44no—
336C4⋊C4—28no—
337C4⋊C4—216no—
338C4⋊C4—24no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—24no—
342C4⋊C4—42no—
343C4⋊C4C2×D4×C1114yes—
344C4⋊C4C2×D4×C1114yes—
345C22⋊C4—24no—
346C22⋊C4—24no—
347C22⋊C4—42no—
348C22⋊C4—84no—
349C42—24no—
350C42—24no—
351C42—24no—
352C11#2346211yescharacteristic, direct product factor, Sylow
353C23—22no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—42no—
358C23—41no—
359C23—41no—
360C23C11×#12011yescharacteristic
361C23C11×#12011yescharacteristic
362C23C11×C22⋊Q812yes—
363C23C11×#12412yes—
364C23C22×D4×C1111yescharacteristic
365Q8—24no—
366Q8—42no—
367Q8—88no—
368D4—24no—
369D4—44no—
370D4—44no—
371D4—42no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—22no—
376C2×C4—44no—
377C2×C4—44no—
378C2×C4—44no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—48no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—82no—
387C2×C4C11×#12012yes—
388C2×C4C11×C22⋊Q814yes—
389C2×C4C11×C22⋊Q814yes—
390C2×C4C11×C22⋊Q812yes—
391C2×C4C11×#12414yes—
392C2×C4C11×#12414yes—
393C2×C4C11×#12412yes—
394C2×C4C22×D4×C1112yes—
395C2×C4C22×Q8×C1111yescharacteristic
396C2×C4C2×C11×#4112yes—
397C2×C4C2×C11×#4111yescharacteristic
398C8—44no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—42no—
406C22—42no—
407C22—44no—
408C22—42no—
409C22—82no—
410C22—81no—
411C22—81no—
412C22C11×#39312yes—
413C22C11×#39312yes—
414C22C2×C11×#12011yescharacteristic
415C22C2×C11×C22⋊Q811yescharacteristic
416C22C2×C11×#12411yescharacteristic
417C4—42no—
418C4—44no—
419C4—44no—
420C4—44no—
421C4—82no—
422C4C11×#39314yes—
423C4C2×C11×C22⋊Q812yes—
424C4C2×C11×#12412yes—
425C2—21no—
426C2—21no—
427C2—22no—
428C2—22no—
429C2—82no—
430C2C2×C11×#39311yescharacteristic
431C2C11×#301911yescharacteristic
432C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×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
1. C2×C11×#544C2semidirect
4. C11×#2028C2semidirect
5. C11×#2027C2semidirect
6. C2×C11×#343C2semidirect
7. C11×#1733C2semidirect
34. C2×C11×#41Q8semidirect
77. #23462C11direct (N × H)
89. C2×Q8×C11C2×Q8semidirect
97. C2×D4×C11C2×Q8semidirect
137. C2×#544C2×C11semidirect
140. #2028C2×C11semidirect
141. #2027C2×C11semidirect
142. C2×#343C2×C11semidirect
143. #1733C2×C11semidirect
242. C2×#41Q8×C11semidirect
304. C2×Q8C2×Q8×C11semidirect
312. C2×D4C2×Q8×C11semidirect
352. C11#23462direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5442
C11×#28962
C11×#23112
C11×#20282
C11×#20272
C2×C11×#3432
C11×#17332
#2346211