Finite Group Databasebeta

← C11×#21877 #14599070

Subgroups — C11×#21877 #14599070

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#539C211yesmaximal, characteristic
2C11×#2316C211yesmaximal, characteristic, complemented
3C11×#2313C211yesmaximal, characteristic, complemented
4C11×#1996C212yesmaximal, complemented
5C11×#1964C212yesmaximal
6C11×#1899C214yesmaximal, complemented
7C11×#1799C214yesmaximal, complemented
8C11×#539—24no—
9C11×#539—24no—
10C2×C11×#126C412yescomplemented
11C2×C11×#125C412yescomplemented
12C2×C11×#123C412yescomplemented
13C2×C11×#123C2212yes—
14C2×C11×C22⋊Q8C412yescomplemented
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11C2212yes—
18C2×C11×#117C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×C11×#99C2218yes—
21C11×#389—24no—
22C11×#387—24no—
23C11×#381C2212yes—
24C11×#380C2212yes—
25C11×#380C2212yes—
26C11×#380C2212yes—
27C4×C11×C22⋊C4C2212yes—
28C11×#342C2218yes—
29C22×Q8×C11C2×C411yescharacteristic
30C22×D4×C11C2×C411yescharacteristic
31C22×D4×C11C2312yes—
32C23×C4×C11C2×C412yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C11×#126—28no—
37C11×#125—28no—
38C11×#123—24no—
39C11×#123—24no—
40C11×#123—28no—
41C11×C22⋊Q8—22no—
42C11×C22⋊Q8—22no—
43C11×C22⋊Q8—28no—
44C11×#121—22no—
45C11×#121—22no—
46C4×D4×C11—24no—
47C4×D4×C11—24no—
48C11×#117—44no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2×C412yes—
54C2×C11×C4⋊C4C2×C411yescharacteristic
55C2×C11×C4⋊C4C2×C412yes—
56C2×C11×C4⋊C4C2×C412yes—
57C2×C11×C4⋊C4C2×C411yescharacteristic
58C2×C11×C4⋊C4C2×C412yes—
59C2×C11×C4⋊C4C2×C412yes—
60C2×C11×C4⋊C4C2×C412yes—
61C2×C11×C4⋊C4D414yes—
62C2×C11×C4⋊C4D414yes—
63C2×C11×C22⋊C4C2×C412yes—
64C2×C11×C22⋊C4C2×C412yes—
65C2×C11×C22⋊C4C2×C412yes—
66C2×C11×C22⋊C4C2×C412yes—
67C2×C11×C22⋊C4C2314yes—
68C2×C11×C22⋊C4C2314yes—
69C2×C11×C22⋊C4C2312yes—
70C2×C42×C11—22no—
71C2×C42×C11—22no—
72C2×C42×C11C2×C412yes—
73C11×#99—48no—
74C11×#95—22no—
75C11×#95—22no—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—24no—
79#21877C1111yesmaximal, characteristic, direct product factor, Sylow
80C24×C11C22×C412yes—
81C24×C11C2411yescharacteristic
82C2×Q8×C11—22no—
83C2×Q8×C11—81no—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—24no—
87C2×D4×C11—24no—
88C2×D4×C11—22no—
89C2×D4×C11—81no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—24no—
93C22×C4×C11—24no—
94C22×C4×C11—24no—
95C22×C4×C11—81no—
96C22×C4×C11—81no—
97C22×C4×C11—82no—
98C22×C4×C11C22×C412yes—
99C22×C4×C11C22×C412yes—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C22×C411yescharacteristic
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—44no—
118C11×C4⋊C4—82no—
119C11×C4⋊C4—82no—
120C11×C4⋊C4—82no—
121C11×C4⋊C4C22⋊C418yes—
122C11×C4⋊C4C22⋊C418yes—
123C11×C22⋊C4—22no—
124C11×C22⋊C4—22no—
125C11×C22⋊C4—24no—
126C11×C22⋊C4—24no—
127C11×C22⋊C4—24no—
128C11×C22⋊C4—24no—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—28no—
131C11×C22⋊C4—24no—
132C42×C11—24no—
133C42×C11—44no—
134C42×C11—82no—
135C2×#539C2×C1111yescharacteristic
136#2316C2×C1111yescharacteristic, complemented
137#2313C2×C1111yescharacteristic, complemented
138#1996C2×C1112yescomplemented
139#1964C2×C1112yes—
140#1899C2×C1114yescomplemented
141#1799C2×C1114yescomplemented
142C23×C11—22no—
143C23×C11—24no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11C23×C411yescharacteristic
149C23×C11C22×D411yescharacteristic
150C23×C11C22×D411yescharacteristic
151C23×C11H(5,𝔽2)12yes—
152C23×C112−1+412yes—
153Q8×C11—82no—
154D4×C11—42no—
155D4×C11—42no—
156D4×C11—44no—
157D4×C11—82no—
158C2×C4×C11—24no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—24no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—24no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—44no—
176C2×C4×C11—44no—
177C2×C4×C11—44no—
178C2×C4×C11—44no—
179C2×C4×C11—44no—
180C2×C4×C11—44no—
181C2×C4×C11—84no—
182C2×C4×C11C2×C22⋊C414yes—
183C2×C4×C11C2×C22⋊C414yes—
184C2×C4×C11C2×C22⋊C412yes—
185C2×C4×C11C2×C22⋊C412yes—
186#539—24no—
187#539—24no—
188C2×#126C4×C1112yescomplemented
189C2×#125C4×C1112yescomplemented
190C2×#123C4×C1112yescomplemented
191C2×#123C22×C1112yes—
192C2×C22⋊Q8C4×C1112yescomplemented
193C2×C22⋊Q8C22×C1111yescharacteristic
194C2×#121C22×C1111yescharacteristic
195C2×C4×D4C22×C1112yes—
196C2×#117C22×C1112yes—
197C22×C4⋊C4C22×C1111yescharacteristic
198C2×#99C22×C1118yes—
199#389—24no—
200#387—24no—
201#381C22×C1112yes—
202#380C22×C1112yes—
203#380C22×C1112yes—
204#380C22×C1112yes—
205C4×C22⋊C4C22×C1112yes—
206#342C22×C1118yes—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11—84no—
219C22×C11C22×C22⋊C411yescharacteristic
220C22×C11#52012yes—
221C22×C11#53511yescharacteristic
222C22×C11#53611yescharacteristic
223C22×C11#53712yes—
224C4×C11—24no—
225C4×C11—24no—
226C4×C11—22no—
227C4×C11—22no—
228C4×C11—42no—
229C4×C11—42no—
230C4×C11—42no—
231C4×C11—84no—
232C4×C11—84no—
233C22×Q8C2×C4×C1111yescharacteristic
234C22×D4C2×C4×C1111yescharacteristic
235C22×D4C23×C1112yes—
236C23×C4C2×C4×C1112yes—
237C23×C4C23×C1111yescharacteristic
238C23×C4C23×C1111yescharacteristic
239C23×C4C23×C1111yescharacteristic
240#126—28no—
241#125—28no—
242#123—24no—
243#123—24no—
244#123—28no—
245C22⋊Q8—22no—
246C22⋊Q8—22no—
247C22⋊Q8—28no—
248#121—22no—
249#121—22no—
250C4×D4—24no—
251C4×D4—24no—
252#117—44no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4C2×C4×C1112yes—
258C2×C4⋊C4C2×C4×C1111yescharacteristic
259C2×C4⋊C4C2×C4×C1112yes—
260C2×C4⋊C4C2×C4×C1112yes—
261C2×C4⋊C4C2×C4×C1111yescharacteristic
262C2×C4⋊C4C2×C4×C1112yes—
263C2×C4⋊C4C2×C4×C1112yes—
264C2×C4⋊C4C2×C4×C1112yes—
265C2×C4⋊C4D4×C1114yes—
266C2×C4⋊C4D4×C1114yes—
267C2×C22⋊C4C2×C4×C1112yes—
268C2×C22⋊C4C2×C4×C1112yes—
269C2×C22⋊C4C2×C4×C1112yes—
270C2×C22⋊C4C2×C4×C1112yes—
271C2×C22⋊C4C23×C1114yes—
272C2×C22⋊C4C23×C1114yes—
273C2×C22⋊C4C23×C1112yes—
274C2×C42—22no—
275C2×C42—22no—
276C2×C42C2×C4×C1112yes—
277#99—48no—
278#95—22no—
279#95—22no—
280#95—22no—
281#95—22no—
282#95—24no—
283C2×C11—21no—
284C2×C11—22no—
285C2×C11—22no—
286C2×C11—21no—
287C2×C11—82no—
288C2×C11#231111yescharacteristic
289C2×C11#288311yescharacteristic
290C2×C11#288411yescharacteristic
291C24C22×C4×C1112yes—
292C24C24×C1111yescharacteristic
293C2×Q8—22no—
294C2×Q8—81no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—24no—
298C2×D4—24no—
299C2×D4—22no—
300C2×D4—81no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—81no—
307C22×C4—81no—
308C22×C4—82no—
309C22×C4C22×C4×C1112yes—
310C22×C4C22×C4×C1112yes—
311C22×C4C22×C4×C1112yes—
312C22×C4C22×C4×C1112yes—
313C22×C4C22×C4×C1112yes—
314C22×C4C22×C4×C1111yescharacteristic
315C22×C4C22×C4×C1111yescharacteristic
316C22×C4C2×D4×C1112yes—
317C22×C4C2×D4×C1112yes—
318C22×C4C2×D4×C1112yes—
319C22×C4C2×D4×C1112yes—
320C22×C4C2×D4×C1112yes—
321C22×C4C2×D4×C1112yes—
322C4⋊C4—24no—
323C4⋊C4—22no—
324C4⋊C4—24no—
325C4⋊C4—24no—
326C4⋊C4—22no—
327C4⋊C4—24no—
328C4⋊C4—44no—
329C4⋊C4—82no—
330C4⋊C4—82no—
331C4⋊C4—82no—
332C4⋊C4C11×C22⋊C418yes—
333C4⋊C4C11×C22⋊C418yes—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—24no—
337C22⋊C4—24no—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—28no—
342C22⋊C4—24no—
343C42—24no—
344C42—44no—
345C42—82no—
346C11#2187711yescharacteristic, direct product factor, Sylow
347C23—22no—
348C23—24no—
349C23—41no—
350C23—41no—
351C23—42no—
352C23—42no—
353C23C23×C4×C1111yescharacteristic
354C23C22×D4×C1111yescharacteristic
355C23C22×D4×C1111yescharacteristic
356C23C11×H(5,𝔽2)12yes—
357C23C11×2−1+412yes—
358Q8—82no—
359D4—42no—
360D4—42no—
361D4—44no—
362D4—82no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—24no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—24no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—44no—
381C2×C4—44no—
382C2×C4—44no—
383C2×C4—44no—
384C2×C4—44no—
385C2×C4—44no—
386C2×C4—84no—
387C2×C4C2×C11×C22⋊C414yes—
388C2×C4C2×C11×C22⋊C414yes—
389C2×C4C2×C11×C22⋊C412yes—
390C2×C4C2×C11×C22⋊C412yes—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—42no—
398C22—42no—
399C22—42no—
400C22—42no—
401C22—42no—
402C22—84no—
403C22C22×C11×C22⋊C411yescharacteristic
404C22C11×#52012yes—
405C22C11×#53511yescharacteristic
406C22C11×#53611yescharacteristic
407C22C11×#53712yes—
408C4—24no—
409C4—24no—
410C4—22no—
411C4—22no—
412C4—42no—
413C4—42no—
414C4—42no—
415C4—84no—
416C4—84no—
417C2—21no—
418C2—22no—
419C2—22no—
420C2—21no—
421C2—82no—
422C2C11×#231111yescharacteristic
423C2C11×#288311yescharacteristic
424C2C11×#288411yescharacteristic
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2316C2semidirect
3. C11×#2313C2semidirect
4. C11×#1996C2semidirect
6. C11×#1899C2semidirect
7. C11×#1799C2semidirect
10. C2×C11×#126C4semidirect
11. C2×C11×#125C4semidirect
12. C2×C11×#123C4semidirect
14. C2×C11×C22⋊Q8C4semidirect
79. #21877C11direct (N × H)
136. #2316C2×C11semidirect
137. #2313C2×C11semidirect
138. #1996C2×C11semidirect
140. #1899C2×C11semidirect
141. #1799C2×C11semidirect
188. C2×#126C4×C11semidirect
189. C2×#125C4×C11semidirect
190. C2×#123C4×C11semidirect
192. C2×C22⋊Q8C4×C11semidirect
346. C11#21877direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5392
C11×#23162
C11×#23132
C11×#19962
C11×#19642
C11×#18992
C11×#17992
#2187711