Finite Group Databasebeta

← C11×#34498 #14611691

Subgroups — C11×#34498 #14611691

Order 2816.

2340 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#559C211yesmaximal, characteristic
2C11×#2376C214yesmaximal, complemented
3C11×#2367C214yesmaximal, complemented
4C11×#2366C211yesmaximal, characteristic
5Q8×C11×C4⋊C4C212yesmaximal, complemented
6D4×C11×C4⋊C4C214yesmaximal, complemented
7C11×#2326C214yesmaximal, complemented
8C11×#2322C214yesmaximal, complemented
9C11×#2319C214yesmaximal, complemented
10C4×C11×#127C211yesmaximal, characteristic
11C11×#2295C212yesmaximal, complemented
12C11×#559C4116yescomplemented
13C2×C11×#127C2211yescharacteristic
14C2×C11×#124C2214yes—
15C2×C11×#123C2214yes—
16C2×C4×Q8×C11C2214yes—
17C2×C4×Q8×C11C2212yes—
18C2×C4×D4×C11C2212yes—
19C2×C4×D4×C11C2214yes—
20C2×C4×D4×C11C2214yes—
21C2×C4×D4×C11C2214yes—
22C22×C11×C4⋊C4C2214yes—
23C11×#391C2212yes—
24C11×#391C2212yes—
25C11×#390C2214yes—
26C11×#390C2212yes—
27C11×#390C2214yes—
28C11×#389C2212yes—
29C11×#389C2212yes—
30C11×#389C2214yes—
31C11×#389C2218yes—
32C11×#388C2218yes—
33C11×#388C2218yes—
34C11×#388C2218yes—
35C11×#387C2214yes—
36C11×#387C2214yes—
37C11×#386C2214yes—
38C11×#385C2214yes—
39C11×#385C2218yes—
40C11×#385C2218yes—
41C11×#384C2211yescharacteristic
42C11×#384C2214yes—
43C11×#381C2214yes—
44C11×#380C2218yes—
45C4×C11×C4⋊C4C2214yes—
46C4×C11×C4⋊C4C2212yes—
47C4×C11×C4⋊C4C2214yes—
48C4×C11×C22⋊C4C2214yes—
49C11×#376C2214yes—
50C43×C11C2211yescharacteristic
51C22×Q8×C11C2312yes—
52C22×D4×C11C2314yes—
53C22×D4×C11C2312yes—
54C23×C4×C11C2314yes—
55C23×C4×C11C2314yes—
56C23×C4×C11C2314yes—
57C11×#127C2×C418yes—
58C11×#124C2×C4132yescomplemented
59C11×#123C2×C4132yescomplemented
60C4×Q8×C11—48no—
61C4×Q8×C11C2×C4116yescomplemented
62C4×D4×C11—48no—
63C4×D4×C11—48no—
64C4×D4×C11—44no—
65C4×D4×C11C2×C4132yescomplemented
66C2×C11×C4⋊C4—48no—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2318yes—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2314yes—
74C2×C11×C4⋊C4C2318yes—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C22⋊C4C2314yes—
78C2×C11×C22⋊C4C2318yes—
79C2×C11×C22⋊C4C2318yes—
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C2318yes—
83C2×C42×C11C2312yes—
84C2×C42×C11C2312yes—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2314yes—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2318yes—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2314yes—
91C11×#95C2314yes—
92C11×#95C2314yes—
93C11×#95C2314yes—
94C11×#95C2314yes—
95C11×#95C2314yes—
96C11×#95C2318yes—
97C11×#95C2314yes—
98C11×#95C2314yes—
99#34498C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11C2414yes—
101C2×Q8×C11—24no—
102C2×Q8×C11—24no—
103C2×Q8×C11C22×C418yes—
104C2×D4×C11—28no—
105C2×D4×C11—28no—
106C2×D4×C11—42no—
107C2×D4×C11—42no—
108C2×D4×C11C22×C4116yes—
109C2×D4×C11C22×C418yes—
110C22×C4×C11—28no—
111C22×C4×C11—44no—
112C22×C4×C11—44no—
113C22×C4×C11—44no—
114C22×C4×C11—48no—
115C22×C4×C11—48no—
116C22×C4×C11C22×C4116yes—
117C22×C4×C11C2411yescharacteristic
118C22×C4×C11C2414yes—
119C22×C4×C11C2412yes—
120C22×C4×C11C2414yes—
121C22×C4×C11C2414yes—
122C22×C4×C11C2414yes—
123C22×C4×C11C2411yescharacteristic
124C22×C4×C11C2414yes—
125C22×C4×C11C2411yescharacteristic
126C22×C4×C11C2412yes—
127C11×C4⋊C4—28no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—28no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—48no—
132C11×C4⋊C4—44no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—48no—
135C11×C4⋊C4C22×C418yes—
136C11×C4⋊C4C22×C4116yes—
137C11×C22⋊C4—44no—
138C11×C22⋊C4—48no—
139C11×C22⋊C4—48no—
140C11×C22⋊C4—44no—
141C11×C22⋊C4C22×C4132yes—
142C11×C22⋊C4C22×C4116yes—
143C42×C11—22no—
144C42×C11—24no—
145C42×C11—28no—
146C42×C11—24no—
147C42×C11—41no—
148C42×C11—48no—
149C42×C11C22×C4116yes—
150C42×C11C22×C414yes—
151C2×#559C2×C1111yescharacteristic
152#2376C2×C1114yescomplemented
153#2367C2×C1114yescomplemented
154#2366C2×C1111yescharacteristic
155Q8×C4⋊C4C2×C1112yescomplemented
156D4×C4⋊C4C2×C1114yescomplemented
157#2326C2×C1114yescomplemented
158#2322C2×C1114yescomplemented
159#2319C2×C1114yescomplemented
160C4×#127C2×C1111yescharacteristic
161#2295C2×C1112yescomplemented
162C23×C11—28no—
163C23×C11—24no—
164C23×C11—28no—
165C23×C11—24no—
166C23×C11C23×C418yes—
167C23×C11C2511yescharacteristic
168Q8×C11—216no—
169D4×C11—232no—
170D4×C11—48no—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—21no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—24no—
182C2×C4×C11—28no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—24no—
189C2×C4×C11—22no—
190C2×C4×C11—24no—
191C2×C4×C11—416no—
192C2×C4×C11—88no—
193C2×C4×C11—88no—
194C2×C4×C11C23×C418yes—
195C2×C4×C11C23×C418yes—
196C2×C4×C11C23×C412yes—
197C2×C4×C11C23×C414yes—
198C2×C4×C11H(5,𝔽2)12yes—
199C2×C4×C11H(5,𝔽2)14yes—
200C2×C4×C112−1+414yes—
201#559C4×C11116yescomplemented
202C2×#127C22×C1111yescharacteristic
203C2×#124C22×C1114yes—
204C2×#123C22×C1114yes—
205C2×C4×Q8C22×C1114yes—
206C2×C4×Q8C22×C1112yes—
207C2×C4×D4C22×C1112yes—
208C2×C4×D4C22×C1114yes—
209C2×C4×D4C22×C1114yes—
210C2×C4×D4C22×C1114yes—
211C22×C4⋊C4C22×C1114yes—
212#391C22×C1112yes—
213#391C22×C1112yes—
214#390C22×C1114yes—
215#390C22×C1112yes—
216#390C22×C1114yes—
217#389C22×C1112yes—
218#389C22×C1114yes—
219#389C22×C1118yes—
220#389C22×C1112yes—
221#388C22×C1118yes—
222#388C22×C1118yes—
223#388C22×C1118yes—
224#387C22×C1114yes—
225#387C22×C1114yes—
226#386C22×C1114yes—
227#385C22×C1114yes—
228#385C22×C1118yes—
229#385C22×C1118yes—
230#384C22×C1111yescharacteristic
231#384C22×C1114yes—
232#381C22×C1114yes—
233#380C22×C1118yes—
234C4×C4⋊C4C22×C1114yes—
235C4×C4⋊C4C22×C1114yes—
236C4×C4⋊C4C22×C1112yes—
237C4×C22⋊C4C22×C1114yes—
238#376C22×C1114yes—
239C43C22×C1111yescharacteristic
240C22×C11—216no—
241C22×C11—28no—
242C22×C11—44no—
243C22×C11—44no—
244C22×C11—48no—
245C22×C11C24×C411yescharacteristic
246C22×C11C2×H(5,𝔽2)12yes—
247C22×C11C2×H(5,𝔽2)11yescharacteristic
248C22×C11C2×2−1+412yes—
249C22×C11#58511yescharacteristic
250C4×C11—28no—
251C4×C11—28no—
252C4×C11—22no—
253C4×C11—22no—
254C4×C11—44no—
255C4×C11—44no—
256C4×C11—41no—
257C4×C11—44no—
258C4×C11—42no—
259C4×C11#52018yes—
260C22×Q8C23×C1112yes—
261C22×D4C23×C1114yes—
262C22×D4C23×C1112yes—
263C23×C4C23×C1114yes—
264C23×C4C23×C1114yes—
265C23×C4C23×C1114yes—
266#127C2×C4×C1118yes—
267#124C2×C4×C11132yescomplemented
268#123C2×C4×C11132yescomplemented
269C4×Q8—48no—
270C4×Q8C2×C4×C11116yescomplemented
271C4×D4—48no—
272C4×D4—48no—
273C4×D4—44no—
274C4×D4C2×C4×C11132yescomplemented
275C2×C4⋊C4—48no—
276C2×C4⋊C4C23×C1114yes—
277C2×C4⋊C4C23×C1112yes—
278C2×C4⋊C4C23×C1114yes—
279C2×C4⋊C4C23×C1112yes—
280C2×C4⋊C4C23×C1118yes—
281C2×C4⋊C4C23×C1112yes—
282C2×C4⋊C4C23×C1118yes—
283C2×C4⋊C4C23×C1114yes—
284C2×C4⋊C4C23×C1112yes—
285C2×C4⋊C4C23×C1114yes—
286C2×C22⋊C4C23×C1118yes—
287C2×C22⋊C4C23×C1118yes—
288C2×C22⋊C4C23×C1114yes—
289C2×C22⋊C4C23×C1114yes—
290C2×C22⋊C4C23×C1118yes—
291C2×C22⋊C4C23×C1114yes—
292C2×C42C23×C1112yes—
293C2×C42C23×C1111yescharacteristic
294C2×C42C23×C1114yes—
295C2×C42C23×C1112yes—
296C2×C42C23×C1118yes—
297C2×C42C23×C1111yescharacteristic
298C2×C42C23×C1114yes—
299C2×C42C23×C1111yescharacteristic
300#95C23×C1114yes—
301#95C23×C1114yes—
302#95C23×C1114yes—
303#95C23×C1114yes—
304#95C23×C1114yes—
305#95C23×C1118yes—
306#95C23×C1114yes—
307#95C23×C1114yes—
308C2×C11—48no—
309C2×C11C2×#52012yes—
310C2×C11C4×H(5,𝔽2)11yescharacteristic
311C2×C11#354311yescharacteristic
312C2×C11#355011yescharacteristic
313C2×C11#355412yes—
314C24C24×C1114yes—
315C2×Q8—24no—
316C2×Q8—24no—
317C2×Q8C22×C4×C1118yes—
318C2×D4—28no—
319C2×D4—28no—
320C2×D4—42no—
321C2×D4—42no—
322C2×D4C22×C4×C11116yes—
323C2×D4C22×C4×C1118yes—
324C22×C4—28no—
325C22×C4—44no—
326C22×C4—44no—
327C22×C4—44no—
328C22×C4—48no—
329C22×C4—48no—
330C22×C4C22×C4×C11116yes—
331C22×C4C24×C1111yescharacteristic
332C22×C4C24×C1114yes—
333C22×C4C24×C1112yes—
334C22×C4C24×C1114yes—
335C22×C4C24×C1114yes—
336C22×C4C24×C1114yes—
337C22×C4C24×C1111yescharacteristic
338C22×C4C24×C1114yes—
339C22×C4C24×C1111yescharacteristic
340C22×C4C24×C1112yes—
341C4⋊C4—28no—
342C4⋊C4—24no—
343C4⋊C4—28no—
344C4⋊C4—24no—
345C4⋊C4—48no—
346C4⋊C4—42no—
347C4⋊C4—48no—
348C4⋊C4—44no—
349C4⋊C4C22×C4×C1118yes—
350C4⋊C4C22×C4×C11116yes—
351C22⋊C4—48no—
352C22⋊C4—48no—
353C22⋊C4—44no—
354C22⋊C4—44no—
355C22⋊C4C22×C4×C11132yes—
356C22⋊C4C22×C4×C11116yes—
357C42—22no—
358C42—24no—
359C42—28no—
360C42—24no—
361C42—48no—
362C42—41no—
363C42C22×C4×C11116yes—
364C42C22×C4×C1114yes—
365C11#3449811yescharacteristic, direct product factor, Sylow
366C23—28no—
367C23—24no—
368C23—28no—
369C23—24no—
370C23C23×C4×C1118yes—
371C23C25×C1111yescharacteristic
372Q8—216no—
373D4—232no—
374D4—48no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—24no—
380C2×C4—21no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—28no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—416no—
396C2×C4—88no—
397C2×C4—88no—
398C2×C4C23×C4×C1118yes—
399C2×C4C23×C4×C1118yes—
400C2×C4C23×C4×C1112yes—
401C2×C4C23×C4×C1114yes—
402C2×C4C11×H(5,𝔽2)12yes—
403C2×C4C11×H(5,𝔽2)14yes—
404C2×C4C11×2−1+414yes—
405C22—216no—
406C22—28no—
407C22—44no—
408C22—44no—
409C22—48no—
410C22C24×C4×C1111yescharacteristic
411C22C2×C11×H(5,𝔽2)12yes—
412C22C2×C11×H(5,𝔽2)11yescharacteristic
413C22C2×C11×2−1+412yes—
414C22C11×#58511yescharacteristic
415C4—28no—
416C4—28no—
417C4—22no—
418C4—22no—
419C4—44no—
420C4—44no—
421C4—41no—
422C4—44no—
423C4—42no—
424C4C11×#52018yes—
425C2—48no—
426C2C2×C11×#52012yes—
427C2C4×C11×H(5,𝔽2)11yescharacteristic
428C2C11×#354311yescharacteristic
429C2C11×#355011yescharacteristic
430C2C11×#355412yes—
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC2×C11×#127C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2376C2semidirect
3. C11×#2367C2semidirect
5. Q8×C11×C4⋊C4C2semidirect
6. D4×C11×C4⋊C4C2semidirect
7. C11×#2326C2semidirect
8. C11×#2322C2semidirect
9. C11×#2319C2semidirect
11. C11×#2295C2semidirect
12. C11×#559C4semidirect
58. C11×#124C2×C4semidirect
59. C11×#123C2×C4semidirect
61. C4×Q8×C11C2×C4semidirect
65. C4×D4×C11C2×C4semidirect
99. #34498C11direct (N × H)
152. #2376C2×C11semidirect
153. #2367C2×C11semidirect
155. Q8×C4⋊C4C2×C11semidirect
156. D4×C4⋊C4C2×C11semidirect
157. #2326C2×C11semidirect
158. #2322C2×C11semidirect
159. #2319C2×C11semidirect
161. #2295C2×C11semidirect
201. #559C4×C11semidirect
267. #124C2×C4×C11semidirect
268. #123C2×C4×C11semidirect
270. C4×Q8C2×C4×C11semidirect
274. C4×D4C2×C4×C11semidirect
365. C11#34498direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5592
C11×#23762
C11×#23672
C11×#23662
Q8×C11×C4⋊C42
D4×C11×C4⋊C42
C11×#23262
C11×#23222
C11×#23192
C4×C11×#1272
C11×#22952
#3449811