Finite Group Databasebeta

← #14764435

Subgroups — #14764435

Order 2816.

800 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071053C211yesmaximal, characteristic
2#13069225C212yesmaximal, complemented
3#13069170C212yesmaximal, complemented
4#13068905C212yesmaximal
5#13068792C212yesmaximal, complemented
6#13068760C211yesmaximal, characteristic, complemented
7#13068734C211yesmaximal, characteristic, complemented
8#13068687C211yesmaximal, characteristic, complemented
9#13068373C211yesmaximal, characteristic, complemented
10D11×#336C211yesmaximal, characteristic, complemented
11C11×#1798C211yesmaximal, characteristic, complemented
12C2×C11×#117C2211yescharacteristic
13C2×C4×C22⋊D11C2211yescharacteristic
14C22×C8×D11C2212yes—
15C2×C42×D11C2211yescharacteristic
16C2×C11×C4⋊C8C2212yes—
17C2×C11×C22⋊C8C2212yes—
18C4×C22⋊Dic11C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2212yes—
20C2×(C2×D11)⋊C8C2212yes—
21C2×Dic11⋊C8C2212yes—
22C2×C8×Dic11C2212yes—
23#10622602C412yes—
24#10622591C412yes—
25#10622569C412yes—
26#10622557C412yes—
27C4×(C2×D11)⋊C4C2211yescharacteristic
28#10622545C2211yescharacteristic
29C4×Dic11⋊C4C2211yescharacteristic
30C11×#336C2211yescharacteristic
31C11×#336C2211yescharacteristic
32#10622188C2212yes—
33#10622188C2212yes—
34#10622188C2212yes—
35#10622188C2212yes—
36#10622162C2211yescharacteristic
37#10622162C2211yescharacteristic
38#10622162C2212yes—
39C23×C4×C11C2311yescharacteristic
40C22×C22⋊D11C2×C411yescharacteristic
41C22×C4×D11C2×C412yes—
42C22×C4×D11C2311yescharacteristic
43C22×C8×C11C2312yes—
44C22×C8×C11C2312yes—
45C11×#117—42no—
46C2×C11×C4⋊C4C2×C412yes—
47C2×C11×C22⋊C4C2×C412yes—
48C2×C42×C11C2311yescharacteristic
49C2×C42×C11C2311yescharacteristic
50C2×C22⋊Dic11C2×C411yescharacteristic
51C2×C22⋊Dic11C2×C412yes—
52C4×C22⋊D11—24no—
53C2×(C2×D11)⋊C4C2×C412yes—
54C2×(C2×D11)⋊C4C2×C411yescharacteristic
55C2×Dic11⋊C4C2×C412yes—
56C2×Dic11⋊C4C2×C411yescharacteristic
57C2×C4×Dic11C2×C412yes—
58C2×C4×Dic11C2311yescharacteristic
59C2×C4×Dic11C2311yescharacteristic
60C2×C4×Dic11C2311yescharacteristic
61C22×C11⋊C8C2312yes—
62C22×C11⋊C8C2312yes—
63C2×C8×D11—24no—
64C2×C8×D11—42no—
65C2×C8×D11—42no—
66C42×D11—42no—
67C11×C4⋊C8—42no—
68C11×C22⋊C8—42no—
69C11⋊#95C2×C412yes—
70C11⋊#95C2×C412yes—
71C11⋊#95C2×C412yes—
72C11⋊#95C2×C412yes—
73C11⋊#95C2×C412yes—
74C22⋊(C11⋊C8)—42no—
75(C2×D11)⋊C8—24no—
76Dic11⋊C8—42no—
77C8×Dic11—42no—
78#21997—111nomaximal, Sylow
79C24×C11C22×C411yescharacteristic
80C23×D11C22×C411yescharacteristic
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11C22×C412yes—
86C22×C4×C11C22×C412yes—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C2411yescharacteristic
89C2×C22⋊D11—22no—
90C2×C22⋊D11—24no—
91C22×Dic11C22×C411yescharacteristic
92C22×Dic11C22×C412yes—
93C22×Dic11C22×C411yescharacteristic
94C22×Dic11C22×C411yescharacteristic
95C22×Dic11C22×C412yes—
96C2×C4×D11—24no—
97C2×C4×D11—24no—
98C2×C4×D11—22no—
99C2×C4×D11—21no—
100C2×C4×D11—21no—
101C2×C4×D11—42no—
102C2×C4×D11#4114yes—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C11×C4⋊C4—42no—
110C11×C22⋊C4—42no—
111C42×C11—22no—
112C42×C11—22no—
113C22⋊Dic11—22no—
114C22⋊Dic11—24no—
115(C2×D11)⋊C4—22no—
116(C2×D11)⋊C4—24no—
117Dic11⋊C4—22no—
118Dic11⋊C4—24no—
119C4×Dic11—22no—
120C4×Dic11—22no—
121C4×Dic11—21no—
122C4×Dic11—21no—
123C4×Dic11—42no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C8×D11—48no—
131#2290—111no—
132#1923—112no—
133#1916—112no—
134#1869—112no—
135#1850—112no—
136#1840—111no—
137#1832—111no—
138#1818—111no—
139#1798D1111yescharacteristic, complemented
140C4×C22⋊C8—111no—
141C2×#336—111no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11C23×C411yescharacteristic
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—22no—
151C22×D11#11712yes—
152C22×D11#13114yes—
153C2×C4×C11—21no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11C2×#4112yes—
165C2×C4×C11H(5,𝔽2)11yescharacteristic
166C2×C4×C11H(5,𝔽2)12yes—
167C2×C4×C112−1+411yescharacteristic
168C22⋊D11—44no—
169C2×Dic11—22no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—22no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11#11712yes—
181C2×Dic11#13114yes—
182C4×D11—24no—
183C4×D11—24no—
184C4×D11—48no—
185C8×C11—42no—
186C8×C11—42no—
187C11⋊C8—42no—
188C11⋊C8—42no—
189C23×C8—112no—
190C2×C4×D4—111no—
191C2×#117C2×D1111yescharacteristic
192C22×C42—111no—
193C2×C4⋊C8—112no—
194C2×C4⋊C8C2×D1112yes—
195C2×C22⋊C8—112no—
196C2×C22⋊C8—112no—
197C2×C22⋊C8C2×D1112yes—
198C2×C4×C8—112no—
199#388—112no—
200#387—112no—
201#386—112no—
202#385—112no—
203C4×C4⋊C4—111no—
204C4×C22⋊C4—111no—
205C4×C22⋊C4—111no—
206#376—111no—
207#336—112no—
208#336—112no—
209#336—112no—
210#336—112no—
211#336—111no—
212#336—111no—
213#336—112no—
214#336C2×D1111yescharacteristic
215#336C2×D1111yescharacteristic
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11C2×#11711yescharacteristic
222C22×C11#51811yescharacteristic
223C22×C11#52011yescharacteristic
224C22×C11C2×#13112yes—
225C22×C11C2×#13112yes—
226C2×D11—22no—
227C2×D11—22no—
228C2×D11—24no—
229C2×D11—24no—
230C2×D11#43314yes—
231C4×C11—41no—
232C4×C11—42no—
233C4×C11—42no—
234C4×C11#53812yes—
235C4×C11#53912yes—
236Dic11—22no—
237Dic11—24no—
238Dic11—41no—
239Dic11—41no—
240Dic11—42no—
241C22×D4—111no—
242C23×C4—111no—
243C23×C4—112no—
244C23×C4C22×D1111yescharacteristic
245C22×C8—112no—
246C22×C8—112no—
247C22×C8—224no—
248C22×C8—442no—
249C22×C8—442no—
250C22×C8C22×D1112yes—
251C22×C8C22×D1112yes—
252C4×D4—224no—
253#117—42no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4—112no—
256C2×C4⋊C4C4×D1112yes—
257C2×C22⋊C4—111no—
258C2×C22⋊C4—112no—
259C2×C22⋊C4—111no—
260C2×C22⋊C4—112no—
261C2×C22⋊C4C4×D1112yes—
262C2×C42—111no—
263C2×C42—111no—
264C2×C42—111no—
265C2×C42—112no—
266C2×C42—442no—
267C2×C42C22×D1111yescharacteristic
268C2×C42C22×D1111yescharacteristic
269C4⋊C8—42no—
270C4⋊C8—442no—
271C22⋊C8—42no—
272C22⋊C8—224no—
273C22⋊C8—442no—
274C4×C8—442no—
275#95—112no—
276#95—112no—
277#95—112no—
278#95—112no—
279#95—112no—
280C2×C11—81no—
281C2×C11#231811yescharacteristic
282C2×C11C2×#43311yescharacteristic
283C2×C11#292211yescharacteristic
284C2×C11#297712yes—
285C2×C11#299412yes—
286D11—24no—
287C24—111no—
288C24C2×C4×D1111yescharacteristic
289C2×D4—222no—
290C2×D4—224no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—112no—
296C22×C4—111no—
297C22×C4—114no—
298C22×C4—112no—
299C22×C4—111no—
300C22×C4—111no—
301C22×C4—224no—
302C22×C4—224no—
303C22×C4—222no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—442no—
307C22×C4C2×C4×D1112yes—
308C22×C4C2×C4×D1112yes—
309C22×C4C2×C4×D1111yescharacteristic
310C22×C4C23×D1111yescharacteristic
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—222no—
318C2×C8—222no—
319C2×C8—222no—
320C2×C8—222no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8—448no—
324C4⋊C4—42no—
325C4⋊C4—222no—
326C4⋊C4—224no—
327C22⋊C4—42no—
328C22⋊C4—222no—
329C22⋊C4—224no—
330C22⋊C4—222no—
331C22⋊C4—224no—
332C42—22no—
333C42—22no—
334C42—222no—
335C42—221no—
336C42—221no—
337C42—222no—
338C42—442no—
339C11#2199711yescharacteristic, complemented, Sylow
340C23—21no—
341C23—22no—
342C23—22no—
343C23—21no—
344C23—21no—
345C23—114no—
346C23—112no—
347C23—221no—
348C23—222no—
349C23—221no—
350C23C22×C4×D1111yescharacteristic
351D4—444no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—114no—
364C2×C4—112no—
365C2×C4—222no—
366C2×C4—221no—
367C2×C4—222no—
368C2×C4—221no—
369C2×C4—224no—
370C2×C4—224no—
371C2×C4—222no—
372C2×C4—222no—
373C2×C4—222no—
374C2×C4—222no—
375C2×C4—222no—
376C2×C4—221no—
377C2×C4—221no—
378C2×C4—448no—
379C2×C4#6703711yescharacteristic
380C2×C4#6703712yes—
381C2×C4#6704011yescharacteristic
382C2×C4#41×D1112yes—
383C8—42no—
384C8—42no—
385C8—442no—
386C8—442no—
387C22—41no—
388C22—42no—
389C22—41no—
390C22—42no—
391C22—41no—
392C22—114no—
393C22—222no—
394C22—224no—
395C22—222no—
396C22—224no—
397C22#1062301711yescharacteristic
398C22#1062303511yescharacteristic
399C22D11×#11711yescharacteristic
400C22D11×#13112yes—
401C22D11×#13112yes—
402C4—41no—
403C4—42no—
404C4—42no—
405C4—222no—
406C4—224no—
407C4—441no—
408C4—442no—
409C4—441no—
410C4#1062314412yes—
411C4#1062316912yes—
412C2—81no—
413C2—224no—
414C2#1307125111yescharacteristic
415C2D11×#43311yescharacteristic
416C2#1307725711yescharacteristic
417C2#1307766812yes—
418C2#1307777412yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1798C2
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1798D11
hypocenterC11#21997
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. #13069225C2semidirect
3. #13069170C2semidirect
5. #13068792C2semidirect
6. #13068760C2semidirect
7. #13068734C2semidirect
8. #13068687C2semidirect
9. #13068373C2semidirect
10. D11×#336C2semidirect
11. C11×#1798C2semidirect
139. #1798D11semidirect
339. C11#21997semidirect

Maximal subgroups

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

subgroupindex
#130710532
#130692252
#130691702
#130689052
#130687922
#130687602
#130687342
#130686872
#130683732
D11×#3362
C11×#17982
#2199711