Finite Group Databasebeta

← C11×#23613 #14600806

Subgroups — C11×#23613 #14600806

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#427C211yesmaximal, characteristic
2C2×C11×#424C211yesmaximal, characteristic
3C2×C11×#419C211yesmaximal, characteristic
4C22×C11×#103C211yesmaximal, characteristic
5C11×#2317C211yesmaximal, characteristic
6C11×#2310C211yesmaximal, characteristic
7C11×#2068C214yesmaximal, complemented
8C11×#2066C214yesmaximal, complemented
9C11×#1736C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C11×#427—24no—
18C2×C11×#107C2212yes—
19C2×C11×#106C2212yes—
20C11×#424—24no—
21C2×C11×C4⋊C8C2212yes—
22C2×C11×C4⋊C8C2212yes—
23C11×#419—24no—
24C2×C11×#103—24no—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×#103C2214yes—
28C11×#391—21no—
29C11×#391—21no—
30C11×#391C2214yes—
31C11×#389C2214yes—
32C11×#385—22no—
33C11×#384—21no—
34C11×#382—21no—
35C11×#381—22no—
36C11×#340C2214yes—
37C22×Q8×C11—21no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11Q814yes—
44C22×Q8×C11C2312yes—
45C23×C4×C11—21no—
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C22×C8×C11—22no—
52C22×C8×C11—22no—
53C22×C8×C11D414yes—
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C11×#117—22no—
58C11×#117—22no—
59C11×#117—22no—
60C11×#117—22no—
61C11×#117—22no—
62C11×#117D414yes—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4D412yes—
75C2×C42×C11—21no—
76C2×C42×C11—21no—
77C2×C42×C11C2312yes—
78C11×#107—24no—
79C11×#106—24no—
80C11×C4⋊C8—24no—
81C11×C4⋊C8—24no—
82C11×#103—24no—
83C11×#103—24no—
84C11×#103—28no—
85C11×#95—24no—
86C11×#95—24no—
87C11×#95—24no—
88#23613C1111yesmaximal, characteristic, direct product factor, Sylow
89C24×C11C2×D411yescharacteristic
90C2×Q8×C11—24no—
91C2×Q8×C11—22no—
92C2×Q8×C11—28no—
93C2×Q8×C11—28no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C2×Q8×C11—44no—
101C2×Q8×C11—44no—
102C2×Q8×C11C2×Q814yes—
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—82no—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×Q812yes—
118C22×C4×C11#4112yes—
119C22×C4×C11#4112yes—
120C22×C4×C11#4112yes—
121C22×C4×C11C2411yescharacteristic
122C11×M16—44no—
123C2×C8×C11—28no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—22no—
131C2×C8×C11C2×D412yes—
132C2×C8×C11C2×D412yes—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—84no—
142C11×C4⋊C4C2×D414yes—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—24no—
145C11×C22⋊C4—42no—
146C42×C11—24no—
147C42×C11—22no—
148C42×C11—22no—
149C42×C11—42no—
150C2×#427C2×C1111yescharacteristic
151C2×#424C2×C1111yescharacteristic
152C2×#419C2×C1111yescharacteristic
153C22×#103C2×C1111yescharacteristic
154#2317C2×C1111yescharacteristic
155#2310C2×C1111yescharacteristic
156#2068C2×C1114yescomplemented
157#2066C2×C1114yescomplemented
158#1736C2×C1111yescharacteristic
159C23×C11—22no—
160C23×C11—22no—
161C23×C11#12112yes—
162C23×C11#12112yes—
163C23×C11C22⋊Q812yes—
164C23×C11C22×D411yescharacteristic
165Q8×C11—24no—
166Q8×C11—24no—
167Q8×C11—42no—
168Q8×C11—42no—
169Q8×C11—48no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—48no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—44no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—84no—
187C2×C4×C11#12114yes—
188C2×C4×C11#12112yes—
189C2×C4×C11#12112yes—
190C2×C4×C11C22⋊Q814yes—
191C2×C4×C11C22⋊Q814yes—
192C2×C4×C11C22⋊Q812yes—
193C2×C4×C11#12614yes—
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C22×Q811yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C8×C11—22no—
201C8×C11—22no—
202C8×C11—42no—
203C23×Q8C22×C1111yescharacteristic
204C22×M16C22×C1111yescharacteristic
205C23×C8C22×C1111yescharacteristic
206C2×#117C22×C1111yescharacteristic
207C2×#117C22×C1111yescharacteristic
208C2×#117C22×C1111yescharacteristic
209C22×C4⋊C4C22×C1111yescharacteristic
210#427—24no—
211C2×#107C22×C1112yes—
212C2×#106C22×C1112yes—
213#424—24no—
214C2×C4⋊C8C22×C1112yes—
215C2×C4⋊C8C22×C1112yes—
216#419—24no—
217C2×#103—24no—
218C2×#103C22×C1112yes—
219C2×#103C22×C1114yes—
220C2×#103C22×C1112yes—
221#391—21no—
222#391—21no—
223#391C22×C1114yes—
224#389C22×C1114yes—
225#385—22no—
226#384—21no—
227#382—21no—
228#381—22no—
229#340C22×C1114yes—
230C22×C11—24no—
231C22×C11—24no—
232C22×C11—22no—
233C22×C11—22no—
234C22×C11#39614yes—
235C22×C11C2×#12111yescharacteristic
236C22×C11C2×#12111yescharacteristic
237C22×C11C2×C22⋊Q811yescharacteristic
238C22×C11#57712yes—
239C22×C11#57812yes—
240C4×C11—44no—
241C4×C11—44no—
242C4×C11—42no—
243C4×C11—42no—
244C4×C11—82no—
245C4×C11—82no—
246C4×C11#39614yes—
247C4×C11C2×#12111yescharacteristic
248C4×C11C2×C22⋊Q811yescharacteristic
249C4×C11C2×C22⋊Q811yescharacteristic
250C4×C11C2×#12611yescharacteristic
251C22×Q8—21no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8Q8×C1114yes—
258C22×Q8C23×C1112yes—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4C23×C1111yescharacteristic
262C2×M16—22no—
263C2×M16—22no—
264C2×M16—22no—
265C22×C8—22no—
266C22×C8—22no—
267C22×C8D4×C1114yes—
268C22×C8C23×C1112yes—
269C22×C8C23×C1111yescharacteristic
270C22×C8C23×C1111yescharacteristic
271#117—22no—
272#117—22no—
273#117—22no—
274#117—22no—
275#117—22no—
276#117D4×C1114yes—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4D4×C1111yescharacteristic
282C2×C4⋊C4D4×C1111yescharacteristic
283C2×C4⋊C4C23×C1112yes—
284C2×C4⋊C4C23×C1112yes—
285C2×C4⋊C4C23×C1112yes—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4D4×C1112yes—
289C2×C42—21no—
290C2×C42—21no—
291C2×C42C23×C1112yes—
292#107—24no—
293#106—24no—
294C4⋊C8—24no—
295C4⋊C8—24no—
296#103—24no—
297#103—24no—
298#103—28no—
299#95—24no—
300#95—24no—
301#95—24no—
302C2×C11—24no—
303C2×C11C2×#39611yescharacteristic
304C2×C11#304612yes—
305C2×C11#305711yescharacteristic
306C2×C11#305911yescharacteristic
307C2×C11#308212yes—
308C24C2×D4×C1111yescharacteristic
309C2×Q8—24no—
310C2×Q8—22no—
311C2×Q8—28no—
312C2×Q8—28no—
313C2×Q8—22no—
314C2×Q8—22no—
315C2×Q8—22no—
316C2×Q8—22no—
317C2×Q8—42no—
318C2×Q8—42no—
319C2×Q8—44no—
320C2×Q8—44no—
321C2×Q8C2×Q8×C1114yes—
322C22×C4—24no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—82no—
331C22×C4C2×D4×C1112yes—
332C22×C4C2×D4×C1112yes—
333C22×C4C2×D4×C1111yescharacteristic
334C22×C4C2×D4×C1112yes—
335C22×C4C2×D4×C1112yes—
336C22×C4C2×Q8×C1112yes—
337C22×C4C11×#4112yes—
338C22×C4C11×#4112yes—
339C22×C4C11×#4112yes—
340C22×C4C24×C1111yescharacteristic
341M16—44no—
342C2×C8—28no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8C2×D4×C1112yes—
351C2×C8C2×D4×C1112yes—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—42no—
360C4⋊C4—84no—
361C4⋊C4C2×D4×C1114yes—
362C22⋊C4—24no—
363C22⋊C4—24no—
364C22⋊C4—42no—
365C42—24no—
366C42—22no—
367C42—22no—
368C42—42no—
369C11#2361311yescharacteristic, direct product factor, Sylow
370C23—22no—
371C23—22no—
372C23C11×#12112yes—
373C23C11×#12112yes—
374C23C11×C22⋊Q812yes—
375C23C22×D4×C1111yescharacteristic
376Q8—24no—
377Q8—24no—
378Q8—42no—
379Q8—42no—
380Q8—48no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—48no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—84no—
398C2×C4C11×#12114yes—
399C2×C4C11×#12112yes—
400C2×C4C11×#12112yes—
401C2×C4C11×C22⋊Q814yes—
402C2×C4C11×C22⋊Q814yes—
403C2×C4C11×C22⋊Q812yes—
404C2×C4C11×#12614yes—
405C2×C4C22×D4×C1111yescharacteristic
406C2×C4C22×D4×C1111yescharacteristic
407C2×C4C22×Q8×C1111yescharacteristic
408C2×C4C2×C11×#4111yescharacteristic
409C2×C4C2×C11×#4111yescharacteristic
410C2×C4C2×C11×#4111yescharacteristic
411C8—22no—
412C8—22no—
413C8—42no—
414C22—24no—
415C22—22no—
416C22—22no—
417C22—24no—
418C22C11×#39614yes—
419C22C2×C11×#12111yescharacteristic
420C22C2×C11×#12111yescharacteristic
421C22C2×C11×C22⋊Q811yescharacteristic
422C22C11×#57712yes—
423C22C11×#57812yes—
424C4—44no—
425C4—44no—
426C4—42no—
427C4—42no—
428C4—82no—
429C4—82no—
430C4C11×#39614yes—
431C4C2×C11×#12111yescharacteristic
432C4C2×C11×C22⋊Q811yescharacteristic
433C4C2×C11×C22⋊Q811yescharacteristic
434C4C2×C11×#12611yescharacteristic
435C2—24no—
436C2C2×C11×#39611yescharacteristic
437C2C11×#304612yes—
438C2C11×#305711yescharacteristic
439C2C11×#305911yescharacteristic
440C2C11×#308212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
7. C11×#2068C2semidirect
8. C11×#2066C2semidirect
88. #23613C11direct (N × H)
156. #2068C2×C11semidirect
157. #2066C2×C11semidirect
369. C11#23613direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4272
C2×C11×#4242
C2×C11×#4192
C22×C11×#1032
C11×#23172
C11×#23102
C11×#20682
C11×#20662
C11×#17362
#2361311