Finite Group Databasebeta

← #14758140

Subgroups — #14758140

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071259C212yesmaximal, complemented
2#13069493C211yesmaximal, characteristic
3#13069483C211yesmaximal, characteristic
4#13069360C211yesmaximal, characteristic, complemented
5#13069345C211yesmaximal, characteristic, complemented
6#13069315C212yesmaximal, complemented
7#13069301C212yesmaximal, complemented
8#13068513C211yesmaximal, characteristic, complemented
9C4×#66896C212yesmaximal, complemented
10#13068304C211yesmaximal, characteristic, complemented
11C2×C11×#442C211yesmaximal, characteristic
12C22×C11×D8C2211yescharacteristic
13C2×C4×D4×C11C2212yes—
14C11×#442C418yescomplemented
15C2×C11×#106C2211yescharacteristic
16C2×C11×#102C2212yes—
17C2×C11×#97C2211yescharacteristic
18#10622834C2212yes—
19#10622834C2212yes—
20C2×#66896C2212yes—
21C2×#66896C2212yes—
22#10622825—22no—
23#10622824—22no—
24C2×#66882C2211yescharacteristic
25C2×#66881C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622598C2212yes—
31#10622598C2212yes—
32#10622564—22no—
33#10622564—22no—
34C4×C4⋊Dic11C2212yes—
35#10622545C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622189C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40C22×D4×C11C2312yes—
41C23×C4×C11—22no—
42C2×C11×D8—22no—
43C2×C11×D8—22no—
44C2×C11×D8C2×C414yes—
45C22×C8×C11C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C4×D4×C11—24no—
48C4×D4×C11C2×C418yes—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C22⋊C4—22no—
51C2×C42×C11C2311yescharacteristic
52C2×C22⋊Dic11—22no—
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—22no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11C2312yes—
59C2×C4⋊Dic11C2312yes—
60C2×C4×Dic11—22no—
61C2×C4×Dic11C2311yescharacteristic
62C2×C4×Dic11C2311yescharacteristic
63C22×C11⋊C8C2311yescharacteristic
64C22×C11⋊C8C2311yescharacteristic
65C11×#106C2×C414yes—
66C11×#102C2×C418yes—
67C11×#97C2×C414yes—
68#66896—24no—
69#66896—24no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95D412yes—
74C11⋊#95D412yes—
75#66882—22no—
76#66881—22no—
77#66879—22no—
78#66879—22no—
79C8×Dic11—22no—
80C8×Dic11—22no—
81C4×C11⋊C8—22no—
82#21290—111nomaximal, Sylow
83C24×C11—22no—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11C22×C414yes—
90C22×C4×C11—22no—
91C22×C4×C11—28no—
92C22×C4×C11—82no—
93C22×C4×C11—82no—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2411yescharacteristic
96C22×Dic11—22no—
97C22×Dic11—22no—
98C22×Dic11C2×D411yescharacteristic
99C22×Dic11C2×D412yes—
100C22×Dic11C2×D411yescharacteristic
101C11×D8—28no—
102C2×C8×C11—21no—
103C2×C8×C11—21no—
104C2×C8×C11C22×C412yes—
105C2×C8×C11C22×C412yes—
106C2×C8×C11#4112yes—
107C2×C8×C11#4112yes—
108C11×C4⋊C4—22no—
109C11×C4⋊C4C22×C414yes—
110C11×C22⋊C4—28no—
111C42×C11C22×C412yes—
112C42×C11#4112yes—
113C22⋊Dic11—82no—
114C22⋊Dic11—82no—
115C22⋊Dic11—82no—
116C22⋊Dic11—82no—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—22no—
120C4⋊Dic11—22no—
121C4⋊Dic11—82no—
122C4⋊Dic11—82no—
123C4×Dic11—21no—
124C4×Dic11—21no—
125C4×Dic11—21no—
126C4×Dic11—21no—
127C4×Dic11—82no—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8#4112yes—
133C2×C11⋊C8#4112yes—
134C2×#442D1111yescharacteristic
135#2319—112no—
136#1972—111no—
137#1970—111no—
138#1944—111no—
139#1941—111no—
140#1936—112no—
141#1934—112no—
142#1776—111no—
143C4×#102—112no—
144#1726—111no—
145C23×C11—24no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—42no—
150C23×C11—42no—
151C23×C11—42no—
152C23×C11C22×D411yescharacteristic
153D4×C11—24no—
154D4×C11—24no—
155D4×C11—42no—
156D4×C11—42no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—88no—
163C2×C4×C11C4×D414yes—
164C2×C4×C11C23×C411yescharacteristic
165C2×C4×C11C2×#4111yescharacteristic
166C2×C4×C11C2×#4111yescharacteristic
167C2×C4×C11C2×#4111yescharacteristic
168C2×C4×C11C2×#4111yescharacteristic
169C2×C4×C11C2×#4111yescharacteristic
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—22no—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C8×C11—22no—
184C8×C11#11714yes—
185C11⋊C8—22no—
186C11⋊C8—22no—
187C22×D8C2×D1111yescharacteristic
188C2×C4×D4C2×D1112yes—
189#442Dic1118yescomplemented
190C2×#107—111no—
191C2×#106—111no—
192C2×#106C2×D1111yescharacteristic
193C2×#102—112no—
194C2×#102—112no—
195C2×#102C2×D1112yes—
196C2×#97—111no—
197C2×#97—111no—
198C2×#97C2×D1111yescharacteristic
199C2×C4×C8—111no—
200C2×C4×C8—111no—
201C2×C4×C8—111no—
202#390—112no—
203#390—112no—
204#389—112no—
205#389—112no—
206#388—222no—
207#388—222no—
208#381—222no—
209#380—222no—
210C4×C4⋊C4—112no—
211#376—111no—
212#340—112no—
213#340—112no—
214#340—112no—
215C22×C11—44no—
216C22×C11—44no—
217C22×C11—44no—
218C22×C11—82no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11C2×C4×D411yescharacteristic
223C22×C11#53211yescharacteristic
224C22×C11#53211yescharacteristic
225C22×C11#57612yes—
226C22×C11#57712yes—
227C4×C11—24no—
228C4×C11—44no—
229C4×C11C2×#11711yescharacteristic
230C4×C11C4×#4111yescharacteristic
231C4×C11#52911yescharacteristic
232C4×C11#52911yescharacteristic
233Dic11—41no—
234Dic11—41no—
235Dic11—42no—
236Dic11—82no—
237Dic11—82no—
238C22×D4C22×D1112yes—
239C23×C4—22no—
240C2×D8—22no—
241C2×D8—22no—
242C2×D8C2×Dic1114yes—
243C22×C8—111no—
244C22×C8—111no—
245C22×C8C22×D1111yescharacteristic
246C22×C8C22×D1111yescharacteristic
247C4×D4—24no—
248C4×D4C2×Dic1118yes—
249C2×C4⋊C4—112no—
250C2×C4⋊C4—112no—
251C2×C4⋊C4—222no—
252C2×C4⋊C4—222no—
253C2×C4⋊C4C22×D1112yes—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—222no—
256C2×C22⋊C4—222no—
257C2×C22⋊C4—222no—
258C2×C22⋊C4—222no—
259C2×C42—111no—
260C2×C42—111no—
261C2×C42—222no—
262C2×C42C22×D1111yescharacteristic
263#107—222no—
264#106—222no—
265#106C2×Dic1114yes—
266#102—224no—
267#102—224no—
268#102C2×Dic1118yes—
269#97—222no—
270#97—222no—
271#97C2×Dic1114yes—
272C4×C8—222no—
273C4×C8—222no—
274C4×C8—222no—
275#95—112no—
276#95—112no—
277#95—222no—
278#95—222no—
279#95—222no—
280C2×C11—84no—
281C2×C11#229311yescharacteristic
282C2×C11#294612yes—
283C2×C11#317311yescharacteristic
284C2×C11#317611yescharacteristic
285C2×C11#317912yes—
286C24—22no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4C22×Dic1114yes—
293C22×C4—22no—
294C22×C4—28no—
295C22×C4—82no—
296C22×C4—82no—
297C22×C4—111no—
298C22×C4—112no—
299C22×C4—111no—
300C22×C4—222no—
301C22×C4—222no—
302C22×C4D4×D1112yes—
303C22×C4C23×D1111yescharacteristic
304D8—28no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—112no—
308C2×C8—112no—
309C2×C8—221no—
310C2×C8—221no—
311C2×C8—221no—
312C2×C8—221no—
313C2×C8#433912yes—
314C2×C8#433912yes—
315C2×C8C22×Dic1112yes—
316C2×C8C22×Dic1112yes—
317C4⋊C4—22no—
318C4⋊C4—222no—
319C4⋊C4—222no—
320C4⋊C4—222no—
321C4⋊C4—222no—
322C4⋊C4—882no—
323C4⋊C4—882no—
324C4⋊C4C22×Dic1114yes—
325C22⋊C4—28no—
326C22⋊C4—882no—
327C22⋊C4—882no—
328C22⋊C4—882no—
329C22⋊C4—882no—
330C42—221no—
331C42—221no—
332C42—221no—
333C42—221no—
334C42—882no—
335C42#434112yes—
336C42C22×Dic1112yes—
337C11#2129011yescharacteristic, complemented, Sylow
338C23—24no—
339C23—42no—
340C23—42no—
341C23—42no—
342C23—42no—
343C23—42no—
344C23—42no—
345C23C2×D4×D1111yescharacteristic
346D4—24no—
347D4—24no—
348D4—42no—
349D4—42no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—24no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—88no—
356C2×C4—222no—
357C2×C4—222no—
358C2×C4—222no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—221no—
362C2×C4—221no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4D4×Dic1114yes—
370C2×C4C2×#433911yescharacteristic
371C2×C4C2×#433911yescharacteristic
372C2×C4C2×#434111yescharacteristic
373C2×C4#41×D1111yescharacteristic
374C2×C4#41×D1111yescharacteristic
375C2×C4C23×Dic1111yescharacteristic
376C8—22no—
377C8—222no—
378C8—222no—
379C8#6697914yes—
380C22—44no—
381C22—44no—
382C22—44no—
383C22—82no—
384C22—82no—
385C22—82no—
386C22—82no—
387C22#1062307911yescharacteristic
388C22#1062307911yescharacteristic
389C22#1062330512yes—
390C22#1062330612yes—
391C22C2×D4×Dic1111yescharacteristic
392C4—24no—
393C4—44no—
394C4—442no—
395C4—441no—
396C4—441no—
397C4—882no—
398C4—882no—
399C4#1062308811yescharacteristic
400C4#1062308811yescharacteristic
401C4C2×#6697911yescharacteristic
402C4#41×Dic1111yescharacteristic
403C2—84no—
404C2#1307108111yescharacteristic
405C2#1307744912yes—
406C2#1307923111yescharacteristic
407C2#1307926411yescharacteristic
408C2#1307930512yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#442C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
cosocleC22×C4×C11C24
hypercenterC2×#442D11
hypocenterC11#21290
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. #13071259C2semidirect
4. #13069360C2semidirect
5. #13069345C2semidirect
6. #13069315C2semidirect
7. #13069301C2semidirect
8. #13068513C2semidirect
9. C4×#66896C2semidirect
10. #13068304C2semidirect
14. C11×#442C4semidirect
189. #442Dic11semidirect
337. C11#21290semidirect

Maximal subgroups

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

subgroupindex
#130712592
#130694932
#130694832
#130693602
#130693452
#130693152
#130693012
#130685132
C4×#668962
#130683042
C2×C11×#4422
#2129011