Finite Group Databasebeta

← C11×#18294 #14595487

Subgroups — C11×#18294 #14595487

Order 2816.

1002 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#544C211yesmaximal, characteristic, complemented
2C11×#3187C212yesmaximal
3C11×#2618C211yesmaximal, characteristic
4C11×#1611C214yesmaximal, complemented
5C11×#1599C214yesmaximal, complemented
6C11×#1520C212yesmaximal, complemented
7C2×C11×#324C211yesmaximal, characteristic, complemented
8C11×#544—24no—
9C11×#544—22no—
10C11×#544C2214yes—
11C2×C11×C4⋊Q8—22no—
12C2×C11×#125—22no—
13C2×C11×#123—21no—
14C2×C11×C22⋊Q8—21no—
15C2×C11×C22⋊Q8C2212yes—
16C2×C11×#121C2211yescharacteristic
17C2×C11×#117—21no—
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#483C2214yes—
20C11×#481—22no—
21C11×#465—24no—
22C11×#450C2214yes—
23C11×#448—22no—
24C2×C11×C22⋊C8C2212yes—
25C11×#398C2212yes—
26C11×#396—22no—
27C11×#394C2212yes—
28C11×#386—21no—
29C11×#380C2211yescharacteristic
30C11×#328C2218yes—
31C11×#324C2214yes—
32C22×Q8×C11—21no—
33C22×Q8×C11D412yes—
34C22×D4×C11—21no—
35C22×D4×C11C2311yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C2×C11×SD16—24no—
40C22×C8×C11—22no—
41C11×C4⋊Q8—28no—
42C11×C4⋊Q8—28no—
43C11×#125—28no—
44C11×#125—28no—
45C11×#123—44no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8—22no—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8D414yes—
51C11×C22⋊Q8C2314yes—
52C11×#121—22no—
53C11×#121—22no—
54C11×#117—24no—
55C11×#117—24no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4D412yes—
66C2×C11×C4⋊C4D412yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C42×C11—22no—
75C11×#106—24no—
76C11×#103—24no—
77C11×#102—24no—
78C11×C22⋊C8—22no—
79C11×C22⋊C8C2314yes—
80C11×#95—22no—
81C11×#95C2312yes—
82#18294C1111yesmaximal, characteristic, direct product factor, Sylow
83C24×C11—21no—
84C24×C11C2×D411yescharacteristic
85C2×Q8×C11—24no—
86C2×Q8×C11—22no—
87C2×Q8×C11—82no—
88C2×Q8×C11—82no—
89C2×Q8×C11C2×D414yes—
90C2×D4×C11—22no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—42no—
94C2×D4×C11—42no—
95C2×D4×C11—81no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—81no—
106C22×C4×C11—81no—
107C22×C4×C11SD1614yescomplemented
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2411yescharacteristic
114C11×SD16—84no—
115C2×C8×C11—24no—
116C2×C8×C11—82no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—28no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—24no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—44no—
128C11×C4⋊C4—81no—
129C11×C4⋊C4C2×D414yes—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—42no—
133C11×C22⋊C4—42no—
134C11×C22⋊C4—44no—
135C11×C22⋊C4—82no—
136C42×C11—28no—
137C2×#544C2×C1111yescharacteristic, complemented
138#3187C2×C1112yes—
139#2618C2×C1111yescharacteristic
140#1611C2×C1114yescomplemented
141#1599C2×C1114yescomplemented
142#1520C2×C1112yescomplemented
143C2×#324C2×C1111yescharacteristic, complemented
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11#12011yescharacteristic
152C23×C11#12011yescharacteristic
153C23×C11C2×SD1612yes—
154C23×C11#13712yes—
155C23×C11C22×D411yescharacteristic
156Q8×C11—44no—
157Q8×C11—82no—
158Q8×C11—84no—
159D4×C11—44no—
160D4×C11—82no—
161D4×C11—82no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—22no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—44no—
174C2×C4×C11—42no—
175C2×C4×C11—44no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—81no—
184C2×C4×C11#12012yes—
185C2×C4×C11C2×SD1614yes—
186C2×C4×C11C22×D412yes—
187C8×C11—44no—
188#544—24no—
189#544—22no—
190#544C22×C1114yes—
191C2×C4⋊Q8—22no—
192C2×#125—22no—
193C2×#123—21no—
194C2×C22⋊Q8—21no—
195C2×C22⋊Q8C22×C1112yes—
196C2×#121C22×C1111yescharacteristic
197C2×#117—21no—
198C22×C4⋊C4C22×C1111yescharacteristic
199#483C22×C1114yes—
200#481—22no—
201#465—24no—
202#450C22×C1114yes—
203#448—22no—
204C2×C22⋊C8C22×C1112yes—
205#398C22×C1112yes—
206#396—22no—
207#394C22×C1112yes—
208#386—21no—
209#380C22×C1111yescharacteristic
210#328C22×C1118yes—
211#324C22×C1114yes—
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—82no—
221C22×C11—82no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11#44812yes—
226C22×C11#44812yes—
227C22×C11C2×#12011yescharacteristic
228C22×C11C22×SD1611yescharacteristic
229C22×C11C2×#13711yescharacteristic
230C4×C11—24no—
231C4×C11—22no—
232C4×C11—22no—
233C4×C11—44no—
234C4×C11—42no—
235C4×C11—44no—
236C4×C11—82no—
237C4×C11—81no—
238C22×Q8—21no—
239C22×Q8D4×C1112yes—
240C22×D4—21no—
241C22×D4C23×C1111yescharacteristic
242C23×C4D4×C1111yescharacteristic
243C23×C4D4×C1111yescharacteristic
244C23×C4C23×C1111yescharacteristic
245C2×SD16—24no—
246C22×C8—22no—
247C4⋊Q8—28no—
248C4⋊Q8—28no—
249#125—28no—
250#125—28no—
251#123—44no—
252C22⋊Q8—24no—
253C22⋊Q8—24no—
254C22⋊Q8—22no—
255C22⋊Q8—22no—
256C22⋊Q8D4×C1114yes—
257C22⋊Q8C23×C1114yes—
258#121—22no—
259#121—22no—
260#117—24no—
261#117—24no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4D4×C1112yes—
272C2×C4⋊C4D4×C1112yes—
273C2×C4⋊C4C23×C1111yescharacteristic
274C2×C4⋊C4C23×C1112yes—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C42—22no—
281#106—24no—
282#103—24no—
283#102—24no—
284C22⋊C8—22no—
285C22⋊C8C23×C1114yes—
286#95—22no—
287#95C23×C1112yes—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—22no—
291C2×C11—22no—
292C2×C11—161no—
293C2×C11C2×#44811yescharacteristic
294C2×C11#302011yescharacteristic
295C2×C11#302611yescharacteristic
296C24—21no—
297C24C2×D4×C1111yescharacteristic
298C2×Q8—24no—
299C2×Q8—22no—
300C2×Q8—82no—
301C2×Q8—82no—
302C2×Q8C2×D4×C1114yes—
303C2×D4—22no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—42no—
307C2×D4—42no—
308C2×D4—81no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—81no—
319C22×C4—81no—
320C22×C4C11×SD1614yescomplemented
321C22×C4C2×D4×C1112yes—
322C22×C4C2×D4×C1112yes—
323C22×C4C2×D4×C1111yescharacteristic
324C22×C4C2×D4×C1112yes—
325C22×C4C2×D4×C1112yes—
326C22×C4C24×C1111yescharacteristic
327SD16—84no—
328C2×C8—24no—
329C2×C8—82no—
330C4⋊C4—24no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—28no—
334C4⋊C4—24no—
335C4⋊C4—24no—
336C4⋊C4—22no—
337C4⋊C4—24no—
338C4⋊C4—24no—
339C4⋊C4—22no—
340C4⋊C4—44no—
341C4⋊C4—81no—
342C4⋊C4C2×D4×C1114yes—
343C22⋊C4—24no—
344C22⋊C4—24no—
345C22⋊C4—42no—
346C22⋊C4—42no—
347C22⋊C4—44no—
348C22⋊C4—82no—
349C42—28no—
350C11#1829411yescharacteristic, direct product factor, Sylow
351C23—41no—
352C23—41no—
353C23—42no—
354C23—42no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23C11×#12011yescharacteristic
359C23C11×#12011yescharacteristic
360C23C2×C11×SD1612yes—
361C23C11×#13712yes—
362C23C22×D4×C1111yescharacteristic
363Q8—44no—
364Q8—82no—
365Q8—84no—
366D4—44no—
367D4—82no—
368D4—82no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—44no—
381C2×C4—42no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4C11×#12012yes—
392C2×C4C2×C11×SD1614yes—
393C2×C4C22×D4×C1112yes—
394C8—44no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—42no—
402C22—42no—
403C22—82no—
404C22—82no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22C11×#44812yes—
409C22C11×#44812yes—
410C22C2×C11×#12011yescharacteristic
411C22C22×C11×SD1611yescharacteristic
412C22C2×C11×#13711yescharacteristic
413C4—24no—
414C4—22no—
415C4—22no—
416C4—44no—
417C4—42no—
418C4—44no—
419C4—82no—
420C4—81no—
421C2—21no—
422C2—21no—
423C2—22no—
424C2—22no—
425C2—161no—
426C2C2×C11×#44811yescharacteristic
427C2C11×#302011yescharacteristic
428C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ 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×#1611C2semidirect
5. C11×#1599C2semidirect
6. C11×#1520C2semidirect
7. C2×C11×#324C2semidirect
82. #18294C11direct (N × H)
107. C22×C4×C11SD16semidirect
137. C2×#544C2×C11semidirect
140. #1611C2×C11semidirect
141. #1599C2×C11semidirect
142. #1520C2×C11semidirect
143. C2×#324C2×C11semidirect
320. C22×C4C11×SD16semidirect
350. C11#18294direct (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×#31872
C11×#26182
C11×#16112
C11×#15992
C11×#15202
C2×C11×#3242
#1829411