Finite Group Databasebeta

← C11×#23934 #14601127

Subgroups — C11×#23934 #14601127

Order 2816.

1272 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic
2C2×C11×#451C212yesmaximal
3C2×C11×#391C211yesmaximal, characteristic
4C11×#2024C212yesmaximal, complemented
5C11×#2016C212yesmaximal, complemented
6C11×#1878C214yesmaximal, complemented
7C11×#1872C212yesmaximal
8C11×#1817C211yesmaximal, characteristic
9C23×Q8×C11C2211yescharacteristic
10C22×C11×Q16C2214yes—
11C11×#533—28no—
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#125—21no—
15C2×C11×C22⋊Q8—21no—
16C2×C11×C22⋊Q8C2212yes—
17C2×C4×Q8×C11—21no—
18C2×C4×Q8×C11C2212yes—
19C2×C11×#117—21no—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C11×#451—28no—
23C2×C11×#103C2214yes—
24C2×C11×#103C2214yes—
25C2×C11×C22⋊C8C2212yes—
26C11×#391—21no—
27C11×#391—21no—
28C11×#391C2212yes—
29C11×#391C2212yes—
30C2×C11×#95—21no—
31C2×C11×#95—21no—
32C11×#340C2214yes—
33C11×#336C2212yes—
34C11×#336C2212yes—
35C22×Q8×C11—24no—
36C22×Q8×C11—21no—
37C22×Q8×C11—21no—
38C22×Q8×C11—24no—
39C22×Q8×C11—42no—
40C22×Q8×C11C2312yes—
41C22×Q8×C11C2312yes—
42C23×C4×C11—21no—
43C23×C4×C11—21no—
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C2×C11×Q16—28no—
48C2×C11×Q16—28no—
49C2×C11×Q16—44no—
50C22×C8×C11C2314yes—
51C11×C4⋊Q8—24no—
52C11×C4⋊Q8—24no—
53C11×#125—28no—
54C11×C22⋊Q8—28no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8D418yes—
57C4×Q8×C11—28no—
58C4×Q8×C11—24no—
59C4×Q8×C11—24no—
60C11×#117—28no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—42no—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C22⋊C4—22no—
71C2×C42×C11—24no—
72C2×C42×C11—22no—
73C2×C42×C11D411yescharacteristic
74C2×C42×C11D411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C11×#103—28no—
78C11×#103—44no—
79C11×C22⋊C8—24no—
80C11×#95—22no—
81C11×#95—22no—
82C11×#95—22no—
83C11×#95—22no—
84#23934C1111yesmaximal, characteristic, direct product factor, Sylow
85C24×C11C2×D411yescharacteristic
86C2×Q8×C11—24no—
87C2×Q8×C11—24no—
88C2×Q8×C11—22no—
89C2×Q8×C11—22no—
90C2×Q8×C11—24no—
91C2×Q8×C11—24no—
92C2×Q8×C11—24no—
93C2×Q8×C11—24no—
94C2×Q8×C11—416no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C2×Q8×C11C2×D414yes—
100C2×Q8×C11#4114yes—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—24no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—41no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11Q1614yescomplemented
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D414yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C11×Q16—416no—
127C2×C8×C11—24no—
128C2×C8×C11—24no—
129C2×C8×C11—24no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—28no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—28no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4C2×D414yes—
139C11×C22⋊C4—28no—
140C42×C11—28no—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11—22no—
144C42×C11—22no—
145C2×#533C2×C1111yescharacteristic
146C2×#451C2×C1112yes—
147C2×#391C2×C1111yescharacteristic
148#2024C2×C1112yescomplemented
149#2016C2×C1112yescomplemented
150#1878C2×C1114yescomplemented
151#1872C2×C1112yes—
152#1817C2×C1111yescharacteristic
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11#12012yes—
158C23×C11C2×Q1612yes—
159C23×C11#13712yes—
160C23×C11C22×D411yescharacteristic
161Q8×C11—28no—
162Q8×C11—28no—
163Q8×C11—48no—
164Q8×C11—48no—
165Q8×C11—44no—
166Q8×C11—44no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—28no—
176C2×C4×C11—28no—
177C2×C4×C11—21no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—44no—
184C2×C4×C11—48no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—84no—
195C2×C4×C11#12012yes—
196C2×C4×C11C2×Q1612yes—
197C2×C4×C11C2×Q1612yes—
198C2×C4×C11#13712yes—
199C2×C4×C11C22×D412yes—
200C2×C4×C11C2×#4112yes—
201C2×C4×C11H(5,𝔽2)12yes—
202C8×C11—44no—
203C23×Q8C22×C1111yescharacteristic
204C22×Q16C22×C1114yes—
205#533—28no—
206C2×C4⋊Q8C22×C1111yescharacteristic
207C2×C4⋊Q8C22×C1111yescharacteristic
208C2×#125—21no—
209C2×C22⋊Q8—21no—
210C2×C22⋊Q8C22×C1112yes—
211C2×C4×Q8—21no—
212C2×C4×Q8C22×C1112yes—
213C2×#117—21no—
214C22×C4⋊C4C22×C1111yescharacteristic
215C22×C42C22×C1111yescharacteristic
216#451—28no—
217C2×#103C22×C1114yes—
218C2×#103C22×C1114yes—
219C2×C22⋊C8C22×C1112yes—
220#391—21no—
221#391—21no—
222#391C22×C1112yes—
223#391C22×C1112yes—
224C2×#95—21no—
225C2×#95—21no—
226#340C22×C1114yes—
227#336C22×C1112yes—
228#336C22×C1112yes—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—22no—
232C22×C11—22no—
233C22×C11—22no—
234C22×C11—22no—
235C22×C11#45114yes—
236C22×C11C2×#12011yescharacteristic
237C22×C11#52511yescharacteristic
238C22×C11#53511yescharacteristic
239C22×C11C22×Q1611yescharacteristic
240C22×C11C2×#13711yescharacteristic
241C22×C11C2×#13711yescharacteristic
242C22×C11#57511yescharacteristic
243C4×C11—22no—
244C4×C11—22no—
245C4×C11—22no—
246C4×C11—22no—
247C4×C11—44no—
248C4×C11—44no—
249C4×C11—41no—
250C4×C11—44no—
251C4×C11—82no—
252C4×C11#54614yes—
253C22×Q8—24no—
254C22×Q8—21no—
255C22×Q8—21no—
256C22×Q8—24no—
257C22×Q8—42no—
258C22×Q8C23×C1112yes—
259C22×Q8C23×C1112yes—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4D4×C1111yescharacteristic
263C23×C4D4×C1111yescharacteristic
264C23×C4C23×C1111yescharacteristic
265C2×Q16—28no—
266C2×Q16—28no—
267C2×Q16—44no—
268C22×C8C23×C1114yes—
269C4⋊Q8—24no—
270C4⋊Q8—24no—
271#125—28no—
272C22⋊Q8—28no—
273C22⋊Q8—24no—
274C22⋊Q8D4×C1118yes—
275C4×Q8—28no—
276C4×Q8—24no—
277C4×Q8—24no—
278#117—28no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4C23×C1112yes—
287C2×C4⋊C4C23×C1112yes—
288C2×C22⋊C4—22no—
289C2×C42—22no—
290C2×C42—24no—
291C2×C42D4×C1111yescharacteristic
292C2×C42D4×C1111yescharacteristic
293C2×C42C23×C1111yescharacteristic
294C2×C42C23×C1111yescharacteristic
295#103—28no—
296#103—44no—
297C22⋊C8—24no—
298#95—22no—
299#95—22no—
300#95—22no—
301#95—22no—
302C2×C11—24no—
303C2×C11#240411yescharacteristic
304C2×C11C2×#45111yescharacteristic
305C2×C11#300711yescharacteristic
306C2×C11#310411yescharacteristic
307C2×C11#311311yescharacteristic
308C2×C11#320911yescharacteristic
309C2×C11#321511yescharacteristic
310C24C2×D4×C1111yescharacteristic
311C2×Q8—24no—
312C2×Q8—24no—
313C2×Q8—22no—
314C2×Q8—22no—
315C2×Q8—24no—
316C2×Q8—24no—
317C2×Q8—24no—
318C2×Q8—24no—
319C2×Q8—416no—
320C2×Q8—42no—
321C2×Q8—42no—
322C2×Q8—42no—
323C2×Q8—42no—
324C2×Q8C2×D4×C1114yes—
325C2×Q8C11×#4114yes—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—41no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4C11×Q1614yescomplemented
344C22×C4C2×D4×C1111yescharacteristic
345C22×C4C2×D4×C1111yescharacteristic
346C22×C4C2×D4×C1114yes—
347C22×C4C2×D4×C1111yescharacteristic
348C22×C4C2×D4×C1111yescharacteristic
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C24×C1111yescharacteristic
351Q16—416no—
352C2×C8—24no—
353C2×C8—24no—
354C2×C8—24no—
355C4⋊C4—24no—
356C4⋊C4—24no—
357C4⋊C4—28no—
358C4⋊C4—24no—
359C4⋊C4—28no—
360C4⋊C4—22no—
361C4⋊C4—24no—
362C4⋊C4—42no—
363C4⋊C4C2×D4×C1114yes—
364C22⋊C4—28no—
365C42—28no—
366C42—22no—
367C42—22no—
368C42—22no—
369C42—22no—
370C11#2393411yescharacteristic, direct product factor, Sylow
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23C11×#12012yes—
376C23C2×C11×Q1612yes—
377C23C11×#13712yes—
378C23C22×D4×C1111yescharacteristic
379Q8—28no—
380Q8—28no—
381Q8—48no—
382Q8—48no—
383Q8—44no—
384Q8—44no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—28no—
394C2×C4—28no—
395C2×C4—21no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—44no—
402C2×C4—48no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—84no—
413C2×C4C11×#12012yes—
414C2×C4C2×C11×Q1612yes—
415C2×C4C2×C11×Q1612yes—
416C2×C4C11×#13712yes—
417C2×C4C22×D4×C1112yes—
418C2×C4C2×C11×#4112yes—
419C2×C4C11×H(5,𝔽2)12yes—
420C8—44no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22C11×#45114yes—
428C22C2×C11×#12011yescharacteristic
429C22C11×#52511yescharacteristic
430C22C11×#53511yescharacteristic
431C22C22×C11×Q1611yescharacteristic
432C22C2×C11×#13711yescharacteristic
433C22C2×C11×#13711yescharacteristic
434C22C11×#57511yescharacteristic
435C4—22no—
436C4—22no—
437C4—22no—
438C4—22no—
439C4—44no—
440C4—44no—
441C4—41no—
442C4—44no—
443C4—82no—
444C4C11×#54614yes—
445C2—24no—
446C2C11×#240411yescharacteristic
447C2C2×C11×#45111yescharacteristic
448C2C11×#300711yescharacteristic
449C2C11×#310411yescharacteristic
450C2C11×#311311yescharacteristic
451C2C11×#320911yescharacteristic
452C2C11×#321511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#2024C2semidirect
5. C11×#2016C2semidirect
6. C11×#1878C2semidirect
84. #23934C11direct (N × H)
118. C22×C4×C11Q16semidirect
148. #2024C2×C11semidirect
149. #2016C2×C11semidirect
150. #1878C2×C11semidirect
343. C22×C4C11×Q16semidirect
370. C11#23934direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C2×C11×#4512
C2×C11×#3912
C11×#20242
C11×#20162
C11×#18782
C11×#18722
C11×#18172
#2393411