Finite Group Databasebeta

← C11×#21762 #14598955

Subgroups — C11×#21762 #14598955

Order 2816.

1498 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
1C22×C11×C22⋊Q8C211yesmaximal, characteristic
2C22×C11×C22⋊C8C211yesmaximal, characteristic
3C11×#2280C211yesmaximal, characteristic
4C11×#1892C214yesmaximal, complemented
5C11×#1873C214yesmaximal, complemented
6C11×#1823C212yesmaximal, complemented
7C11×#1787C212yesmaximal, complemented
8C23×Q8×C11C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C23×C8×C11C2212yes—
11C2×C11×C22⋊Q8—24no—
12C2×C11×C22⋊Q8—21no—
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8C418yescomplemented
15C2×C11×C22⋊Q8C2212yes—
16C2×C11×C22⋊Q8C2212yes—
17C2×C11×#117C2212yes—
18C22×C11×C4⋊C4—21no—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4—21no—
21C2×C11×#103C2218yescomplemented
22C2×C11×C22⋊C8—24no—
23C2×C11×C22⋊C8C2212yes—
24C2×C11×C22⋊C8C2212yes—
25C11×#381—21no—
26C11×#380C2212yes—
27C11×#380C2212yes—
28C11×#379—21no—
29C4×C11×C22⋊C4—21no—
30C4×C11×C22⋊C4—21no—
31C11×#340C2218yescomplemented
32C25×C11D411yescharacteristic
33C22×Q8×C11—22no—
34C22×Q8×C11—21no—
35C22×Q8×C11—44no—
36C22×Q8×C11C2×C414yes—
37C22×Q8×C11C2312yes—
38C23×C4×C11—21no—
39C23×C4×C11—21no—
40C23×C4×C11—44no—
41C23×C4×C11C2×C414yes—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D414yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C22×C8×C11—24no—
50C22×C8×C11—44no—
51C22×C8×C11C2314yes—
52C11×C22⋊Q8—28no—
53C11×C22⋊Q8—28no—
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8C2×C418yes—
57C11×C22⋊Q8C2×C418yes—
58C11×#117—44no—
59C2×C11×C4⋊C4—28no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4C2×C414yes—
65C2×C11×C4⋊C4C2314yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4—28no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C42×C11—22no—
74C11×#103—48no—
75C11×C22⋊C8—24no—
76C11×C22⋊C8—24no—
77C11×#95—22no—
78C11×#95—22no—
79#21762C1111yesmaximal, characteristic, direct product factor, Sylow
80C24×C11—24no—
81C24×C11—24no—
82C24×C11—42no—
83C24×C11C22⋊C414yes—
84C24×C11C2×D411yescharacteristic
85C24×C11C2×D411yescharacteristic
86C24×C11C2×D411yescharacteristic
87C2×Q8×C11—24no—
88C2×Q8×C11—22no—
89C2×Q8×C11—28no—
90C2×Q8×C11—48no—
91C2×Q8×C11—44no—
92C2×Q8×C11—48no—
93C2×Q8×C11C22×C414yes—
94C22×C4×C11—24no—
95C22×C4×C11—24no—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—24no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—24no—
102C22×C4×C11—48no—
103C22×C4×C11—48no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—44no—
108C22×C4×C11—44no—
109C22×C4×C11C22⋊C414yes—
110C22×C4×C11C22⋊C414yes—
111C22×C4×C11C22⋊C414yes—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2411yescharacteristic
122C2×C8×C11—24no—
123C2×C8×C11—28no—
124C2×C8×C11—48no—
125C11×C4⋊C4—28no—
126C11×C4⋊C4—28no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—28no—
130C11×C4⋊C4C22×C414yes—
131C11×C22⋊C4—28no—
132C11×C22⋊C4—28no—
133C11×C22⋊C4—44no—
134C11×C22⋊C4—44no—
135C11×C22⋊C4—44no—
136C42×C11—44no—
137C22×C22⋊Q8C2×C1111yescharacteristic
138C22×C22⋊C8C2×C1111yescharacteristic
139#2280C2×C1111yescharacteristic
140#1892C2×C1114yescomplemented
141#1873C2×C1114yescomplemented
142#1823C2×C1112yescomplemented
143#1787C2×C1112yescomplemented
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—28no—
152C23×C11—28no—
153C23×C11—44no—
154C23×C11—416no—
155C23×C11C2×C22⋊C412yes—
156C23×C11C2×C22⋊C412yes—
157C23×C11C2×C22⋊C412yes—
158C23×C11#13514yes—
159C23×C11#13714yes—
160C23×C11C22×D411yescharacteristic
161Q8×C11—28no—
162Q8×C11—48no—
163Q8×C11—44no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—44no—
176C2×C4×C11—44no—
177C2×C4×C11—44no—
178C2×C4×C11—48no—
179C2×C4×C11—44no—
180C2×C4×C11—44no—
181C2×C4×C11—48no—
182C2×C4×C11—44no—
183C2×C4×C11—44no—
184C2×C4×C11—44no—
185C2×C4×C11C2×C22⋊C412yes—
186C2×C4×C11C2×C22⋊C412yes—
187C2×C4×C11C2×C22⋊C412yes—
188C2×C4×C11C23×C411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11H(5,𝔽2)14yes—
191C8×C11—44no—
192C23×Q8C22×C1111yescharacteristic
193C24×C4C22×C1111yescharacteristic
194C23×C8C22×C1112yes—
195C2×C22⋊Q8—24no—
196C2×C22⋊Q8—21no—
197C2×C22⋊Q8—21no—
198C2×C22⋊Q8C4×C1118yescomplemented
199C2×C22⋊Q8C22×C1112yes—
200C2×C22⋊Q8C22×C1112yes—
201C2×#117C22×C1112yes—
202C22×C4⋊C4—21no—
203C22×C4⋊C4C22×C1111yescharacteristic
204C22×C22⋊C4—21no—
205C2×#103C22×C1118yescomplemented
206C2×C22⋊C8—24no—
207C2×C22⋊C8C22×C1112yes—
208C2×C22⋊C8C22×C1112yes—
209#381—21no—
210#380C22×C1112yes—
211#380C22×C1112yes—
212#379—21no—
213C4×C22⋊C4—21no—
214C4×C22⋊C4—21no—
215#340C22×C1118yescomplemented
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—28no—
221C22×C11—28no—
222C22×C11—22no—
223C22×C11—22no—
224C22×C11—22no—
225C22×C11—416no—
226C22×C11—44no—
227C22×C11#41614yes—
228C22×C11#41914yes—
229C22×C11C22×C22⋊C411yescharacteristic
230C22×C11#53412yes—
231C22×C11C2×#13512yes—
232C22×C11C2×#13712yes—
233C4×C11—22no—
234C4×C11—22no—
235C4×C11—22no—
236C4×C11—44no—
237C4×C11—44no—
238C4×C11—84no—
239C4×C11#51812yes—
240C4×C11#53412yes—
241C25D4×C1111yescharacteristic
242C22×Q8—22no—
243C22×Q8—21no—
244C22×Q8—44no—
245C22×Q8C2×C4×C1114yes—
246C22×Q8C23×C1112yes—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—44no—
250C23×C4C2×C4×C1114yes—
251C23×C4D4×C1111yescharacteristic
252C23×C4D4×C1111yescharacteristic
253C23×C4D4×C1111yescharacteristic
254C23×C4D4×C1114yes—
255C23×C4C23×C1111yescharacteristic
256C23×C4C23×C1111yescharacteristic
257C23×C4C23×C1111yescharacteristic
258C22×C8—24no—
259C22×C8—44no—
260C22×C8C23×C1114yes—
261C22⋊Q8—28no—
262C22⋊Q8—28no—
263C22⋊Q8—24no—
264C22⋊Q8—24no—
265C22⋊Q8C2×C4×C1118yes—
266C22⋊Q8C2×C4×C1118yes—
267#117—44no—
268C2×C4⋊C4—28no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4C2×C4×C1114yes—
274C2×C4⋊C4C23×C1114yes—
275C2×C4⋊C4C23×C1112yes—
276C2×C22⋊C4—28no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C42—22no—
283#103—48no—
284C22⋊C8—24no—
285C22⋊C8—24no—
286#95—22no—
287#95—22no—
288C2×C11—24no—
289C2×C11—24no—
290C2×C11—42no—
291C2×C11#230811yescharacteristic
292C2×C11C2×#41611yescharacteristic
293C2×C11C2×#41911yescharacteristic
294C2×C11#319014yes—
295C24—24no—
296C24—24no—
297C24—42no—
298C24C11×C22⋊C414yes—
299C24C2×D4×C1111yescharacteristic
300C24C2×D4×C1111yescharacteristic
301C24C2×D4×C1111yescharacteristic
302C2×Q8—24no—
303C2×Q8—22no—
304C2×Q8—28no—
305C2×Q8—48no—
306C2×Q8—44no—
307C2×Q8—48no—
308C2×Q8C22×C4×C1114yes—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—24no—
317C22×C4—48no—
318C22×C4—48no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—44no—
323C22×C4—44no—
324C22×C4C11×C22⋊C414yes—
325C22×C4C11×C22⋊C414yes—
326C22×C4C11×C22⋊C414yes—
327C22×C4C22×C4×C1112yes—
328C22×C4C22×C4×C1112yes—
329C22×C4C22×C4×C1112yes—
330C22×C4C2×D4×C1111yescharacteristic
331C22×C4C2×D4×C1111yescharacteristic
332C22×C4C2×D4×C1111yescharacteristic
333C22×C4C2×D4×C1112yes—
334C22×C4C2×D4×C1112yes—
335C22×C4C2×D4×C1112yes—
336C22×C4C24×C1111yescharacteristic
337C2×C8—24no—
338C2×C8—28no—
339C2×C8—48no—
340C4⋊C4—28no—
341C4⋊C4—28no—
342C4⋊C4—24no—
343C4⋊C4—22no—
344C4⋊C4—28no—
345C4⋊C4C22×C4×C1114yes—
346C22⋊C4—28no—
347C22⋊C4—28no—
348C22⋊C4—44no—
349C22⋊C4—44no—
350C22⋊C4—44no—
351C42—44no—
352C11#2176211yescharacteristic, direct product factor, Sylow
353C23—22no—
354C23—22no—
355C23—22no—
356C23—22no—
357C23—22no—
358C23—28no—
359C23—28no—
360C23—22no—
361C23—22no—
362C23—44no—
363C23—416no—
364C23C2×C11×C22⋊C412yes—
365C23C2×C11×C22⋊C412yes—
366C23C2×C11×C22⋊C412yes—
367C23C11×#13514yes—
368C23C11×#13714yes—
369C23C22×D4×C1111yescharacteristic
370Q8—28no—
371Q8—48no—
372Q8—44no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—24no—
384C2×C4—44no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—48no—
388C2×C4—44no—
389C2×C4—48no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4C2×C11×C22⋊C412yes—
395C2×C4C2×C11×C22⋊C412yes—
396C2×C4C2×C11×C22⋊C412yes—
397C2×C4C23×C4×C1111yescharacteristic
398C2×C4C22×D4×C1111yescharacteristic
399C2×C4C11×H(5,𝔽2)14yes—
400C8—44no—
401C22—22no—
402C22—22no—
403C22—28no—
404C22—28no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—416no—
411C22—44no—
412C22C11×#41614yes—
413C22C11×#41914yes—
414C22C22×C11×C22⋊C411yescharacteristic
415C22C11×#53412yes—
416C22C2×C11×#13512yes—
417C22C2×C11×#13712yes—
418C4—22no—
419C4—22no—
420C4—22no—
421C4—44no—
422C4—44no—
423C4—84no—
424C4C11×#51812yes—
425C4C11×#53412yes—
426C2—24no—
427C2—24no—
428C2—42no—
429C2C11×#230811yescharacteristic
430C2C2×C11×#41611yescharacteristic
431C2C2×C11×#41911yescharacteristic
432C2C11×#319014yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC25×C11D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1892C2semidirect
5. C11×#1873C2semidirect
6. C11×#1823C2semidirect
7. C11×#1787C2semidirect
14. C2×C11×C22⋊Q8C4semidirect
21. C2×C11×#103C22semidirect
31. C11×#340C22semidirect
79. #21762C11direct (N × H)
140. #1892C2×C11semidirect
141. #1873C2×C11semidirect
142. #1823C2×C11semidirect
143. #1787C2×C11semidirect
198. C2×C22⋊Q8C4×C11semidirect
205. C2×#103C22×C11semidirect
215. #340C22×C11semidirect
352. C11#21762direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊Q82
C22×C11×C22⋊C82
C11×#22802
C11×#18922
C11×#18732
C11×#18232
C11×#17872
#2176211