Finite Group Databasebeta

← #14782829

Subgroups — #14782829

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622493C211yesmaximal, characteristic
2C2×D11×C4⋊C8C211yesmaximal, characteristic
3#13071097C212yesmaximal
4#13070119C212yesmaximal, complemented
5#13070117C212yesmaximal, complemented
6#13070111C211yesmaximal, characteristic, complemented
7#13070109C211yesmaximal, characteristic, complemented
8#13070105C211yesmaximal, characteristic, complemented
9#13068331C211yesmaximal, characteristic
10#13068331C212yesmaximal
11C11×#2086C211yesmaximal, characteristic, complemented
12C22×C8×D11C2211yescharacteristic
13C22×C8×D11C2211yescharacteristic
14C2×#66945C2212yes—
15C2×#66945C2212yes—
16C2×C42×D11C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C11×#389C2212yes—
20C2×#66882C2211yescharacteristic
21C2×Dic11⋊C8C2211yescharacteristic
22C2×Dic11⋊C8C2211yescharacteristic
23#10622602—22no—
24#10622598C2212yes—
25C4⋊C4×Dic11—22no—
26#10622586C2212yes—
27C2×#66872C2212yes—
28#10622541C2212yes—
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30#10622493—24no—
31D11×C4⋊C8—24no—
32#10622281—22no—
33#10622262—22no—
34C11×#340C2211yescharacteristic
35C11×#340C2212yes—
36#10622189C2211yescharacteristic
37#10622189C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41C22×C4×D11D411yescharacteristic
42C22×C4×D11D411yescharacteristic
43C22×C4×D11C2311yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C42×C11C2311yescharacteristic
50C2×(C2×D11)⋊C4—22no—
51C2×(C2×D11)⋊C4—22no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11C2312yes—
54C2×C4⋊Dic11C2312yes—
55C2×Dic11⋊C4—22no—
56C2×Dic11⋊C4—22no—
57C2×C4×Dic11—22no—
58C2×C4×Dic11—22no—
59C2×C4×Dic11D411yescharacteristic
60C2×C4×Dic11D411yescharacteristic
61C2×C4×Dic11C2311yescharacteristic
62C22×C11⋊C8C2311yescharacteristic
63C22×C11⋊C8C2311yescharacteristic
64C2×C8×D11—24no—
65C2×C8×D11—22no—
66C2×C8×D11—24no—
67C2×C8×D11D414yes—
68#66945—24no—
69#66945—24no—
70#66945—24no—
71#66945Q818yes—
72C42×D11—22no—
73C42×D11—22no—
74C11×#107—22no—
75C11×C4⋊C8—22no—
76C11×#95—22no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80#66882—22no—
81Dic11⋊C8—22no—
82Dic11⋊C8—22no—
83#66872—24no—
84C4⋊(C11⋊C8)—22no—
85#23666—111nomaximal, Sylow
86C23×D11C2×D411yescharacteristic
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2411yescharacteristic
92C22×Dic11—22no—
93C22×Dic11—22no—
94C22×Dic11C2×D411yescharacteristic
95C22×Dic11C2×D411yescharacteristic
96C22×Dic11C2×D411yescharacteristic
97C2×C4×D11—22no—
98C2×C4×D11—22no—
99C2×C4×D11—22no—
100C2×C4×D11—22no—
101C2×C4×D11—42no—
102C2×C4×D11C2×D412yes—
103C2×C4×D11C2×Q814yes—
104C2×C4×D11#4112yes—
105C2×C4×D11#4114yes—
106C2×C8×C11—21no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11C2×D412yes—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—44no—
114C11×C4⋊C4C2×Q814yes—
115C42×C11—21no—
116C42×C11—21no—
117(C2×D11)⋊C4—28no—
118(C2×D11)⋊C4—44no—
119C4⋊Dic11—22no—
120C4⋊Dic11—22no—
121C4⋊Dic11—22no—
122C4⋊Dic11—44no—
123C4⋊Dic11C2×Q814yes—
124Dic11⋊C4—44no—
125Dic11⋊C4—44no—
126C4×Dic11—22no—
127C4×Dic11—22no—
128C4×Dic11—28no—
129C4×Dic11—21no—
130C4×Dic11—21no—
131C4×Dic11—44no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8C2×D412yes—
136C8×D11—28no—
137C8×D11—44no—
138C2×#427—111no—
139C22×C4⋊C8—111no—
140#2296—112no—
141#2088—112no—
142#2088—112no—
143#2087—111no—
144#2087—111no—
145#2086—111no—
146#2086D1111yescharacteristic, complemented
147#1735—111no—
148#1735—112no—
149C23×C11C22×D411yescharacteristic
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—22no—
153C22×D11#12112yes—
154C22×D11C22⋊Q814yes—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—24no—
159C2×C4×C11—22no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11#13512yes—
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C22×Q812yes—
168C2×C4×C11C2×#4112yes—
169C2×C4×C11C2×#4111yescharacteristic
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—24no—
174C2×Dic11—22no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11#12112yes—
181C2×Dic11C22⋊Q814yes—
182C2×Dic11#13512yes—
183C4×D11—28no—
184C4×D11—44no—
185C4×D11#12314yes—
186C4×D11#12518yes—
187C4×D11C4⋊Q814yes—
188C8×C11—22no—
189C8×C11—41no—
190C11⋊C8—22no—
191C11⋊C8—41no—
192C23×C8—111no—
193C23×C8—111no—
194C2×#117—112no—
195C2×#117—112no—
196C22×C42—111no—
197#427—224no—
198C2×#107—111no—
199C2×#107C2×D1111yescharacteristic
200C2×#106—112no—
201C2×C4⋊C8—111no—
202C2×C4⋊C8—111no—
203C2×C4⋊C8—111no—
204C2×C4⋊C8—224no—
205C2×C4⋊C8C2×D1111yescharacteristic
206#389—112no—
207#389—112no—
208#389—112no—
209#389C2×D1112yes—
210#385—222no—
211#385—222no—
212C4×C4⋊C4—222no—
213C4×C4⋊C4—222no—
214#340—111no—
215#340—112no—
216#340—112no—
217#340—112no—
218#340—112no—
219#340C2×D1111yescharacteristic
220#340C2×D1112yes—
221C22×C11C2×#12111yescharacteristic
222C22×C11C2×C22⋊Q812yes—
223C22×C11C2×#13511yescharacteristic
224C22×C11C2×#13511yescharacteristic
225C22×C11#57512yes—
226C2×D11—24no—
227C2×D11—24no—
228C2×D11—22no—
229C2×D11—22no—
230C2×D11#39814yes—
231C4×C11—22no—
232C4×C11—44no—
233C4×C11—41no—
234C4×C11—82no—
235C4×C11C2×#12311yescharacteristic
236C4×C11C2×#12512yes—
237C4×C11C2×C4⋊Q811yescharacteristic
238Dic11—22no—
239Dic11—44no—
240Dic11—41no—
241Dic11—82no—
242Dic11#39814yes—
243C23×C4—111no—
244C23×C4—111no—
245C23×C4—111no—
246C22×C8—111no—
247C22×C8—114no—
248C22×C8—111no—
249C22×C8—224no—
250C22×C8—224no—
251C22×C8—222no—
252C22×C8C22×D1111yescharacteristic
253C22×C8C22×D1111yescharacteristic
254#117—118no—
255#117—224no—
256#117—224no—
257#117—224no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—112no—
260C2×C4⋊C4—112no—
261C2×C4⋊C4—222no—
262C2×C4⋊C4—222no—
263C2×C4⋊C4—222no—
264C2×C4⋊C4C22×D1112yes—
265C2×C4⋊C4C22×D1112yes—
266C2×C22⋊C4—222no—
267C2×C22⋊C4—222no—
268C2×C42—111no—
269C2×C42—111no—
270C2×C42—111no—
271C2×C42—222no—
272C2×C42—222no—
273C2×C42—222no—
274C2×C42—222no—
275C2×C42C22×D1111yescharacteristic
276#107—22no—
277#107—222no—
278#106—224no—
279C4⋊C8—22no—
280C4⋊C8—222no—
281C4⋊C8—222no—
282C4⋊C8—222no—
283#95—22no—
284#95—222no—
285#95—222no—
286#95—222no—
287C2×C11C2×#39811yescharacteristic
288C2×C11#305011yescharacteristic
289C2×C11#305411yescharacteristic
290C2×C11#307612yes—
291C2×C11#307612yes—
292D11—24no—
293C24—111no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—111no—
297C22×C4—112no—
298C22×C4—114no—
299C22×C4—112no—
300C22×C4—114no—
301C22×C4—111no—
302C22×C4—111no—
303C22×C4—222no—
304C22×C4—222no—
305C22×C4—222no—
306C22×C4—222no—
307C22×C4—222no—
308C22×C4—222no—
309C22×C4—442no—
310C22×C4D4×D1111yescharacteristic
311C22×C4D4×D1111yescharacteristic
312C22×C4C23×D1111yescharacteristic
313C2×C8—22no—
314C2×C8—21no—
315C2×C8—22no—
316C2×C8—112no—
317C2×C8—228no—
318C2×C8—222no—
319C2×C8—221no—
320C2×C8—222no—
321C2×C8—444no—
322C2×C8D4×D1112yes—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—44no—
327C4⋊C4—114no—
328C4⋊C4—222no—
329C4⋊C4—222no—
330C4⋊C4—222no—
331C4⋊C4—444no—
332C4⋊C4—444no—
333C4⋊C4—444no—
334C4⋊C4Q8×D1114yes—
335C22⋊C4—228no—
336C22⋊C4—444no—
337C42—21no—
338C42—21no—
339C42—222no—
340C42—222no—
341C42—228no—
342C42—221no—
343C42—221no—
344C42—444no—
345C11#2366611yescharacteristic, complemented, Sylow
346C23—112no—
347C23—114no—
348C23—221no—
349C23—221no—
350C23—222no—
351C23C2×D4×D1111yescharacteristic
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—24no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—112no—
363C2×C4—114no—
364C2×C4—114no—
365C2×C4—114no—
366C2×C4—118no—
367C2×C4—112no—
368C2×C4—228no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—222no—
372C2×C4—221no—
373C2×C4—224no—
374C2×C4—444no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4#6696512yes—
381C2×C4C2×D4×D1111yescharacteristic
382C2×C4C2×Q8×D1112yes—
383C2×C4#41×D1112yes—
384C2×C4#41×D1111yescharacteristic
385C8—22no—
386C8—41no—
387C8—222no—
388C8—441no—
389C22—114no—
390C22—224no—
391C22—224no—
392C22—222no—
393C22—222no—
394C22D11×#12111yescharacteristic
395C22D11×C22⋊Q812yes—
396C22C2×#6696511yescharacteristic
397C22D11×#13511yescharacteristic
398C22#1062330812yes—
399C4—22no—
400C4—44no—
401C4—41no—
402C4—82no—
403C4—114no—
404C4—222no—
405C4—444no—
406C4—441no—
407C4—882no—
408C4D11×#12311yescharacteristic
409C4D11×#12512yes—
410C4D11×C4⋊Q811yescharacteristic
411C2—224no—
412C2D11×#39811yescharacteristic
413C2#1307819511yescharacteristic
414C2#1307822711yescharacteristic
415C2#1307839712yes—
416C2#1307840312yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2086C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2086D11
hypocenterC11#23666
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2086

Complements

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

NH ≅ G/Ntype
4. #13070119C2semidirect
5. #13070117C2semidirect
6. #13070111C2semidirect
7. #13070109C2semidirect
8. #13070105C2semidirect
11. C11×#2086C2semidirect
146. #2086D11semidirect
345. C11#23666semidirect

Maximal subgroups

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

subgroupindex
C2×#106224932
C2×D11×C4⋊C82
#130710972
#130701192
#130701172
#130701112
#130701092
#130701052
#130683312
C11×#20862
#2366611