Finite Group Databasebeta

← #14741696

Subgroups — #14741696

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079739C211yesmaximal, characteristic
2#13079176C211yesmaximal, characteristic
3#13079012C211yesmaximal, characteristic
4#13078998C211yesmaximal, characteristic, complemented
5C2×#10622694C211yesmaximal, characteristic, complemented
6#13068272C212yesmaximal, complemented
7#13068265C212yesmaximal, complemented
8#13068229C212yesmaximal, complemented
9#13068225C212yesmaximal, complemented
10#13066897C211yesmaximal, characteristic, complemented
11C11×#3230C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14#10623008C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C11×#500C2212yes—
17C11×#487C2212yes—
18C11×#484—22no—
19C11×#477—22no—
20C11×#431C2211yescharacteristic
21C2×#66899—22no—
22#10622706C2212yes—
23#10622706C2212yes—
24#10622706C2212yes—
25#10622702—22no—
26#10622701C2211yescharacteristic
27#10622701C2212yes—
28#10622698C2211yescharacteristic
29#10622694—22no—
30#10622694C2211yescharacteristic
31#10622694C2212yes—
32#10622694C2212yes—
33#10622692C2211yescharacteristic
34#10622682—22no—
35#10622661—22no—
36C4×#4325—22no—
37#10622617—22no—
38#10622579—22no—
39C4×#4318C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622459—22no—
42#10622349—22no—
43#10622307C2212yes—
44#10622295C2212yes—
45#10622092C2212yes—
46C8×C11⋊C8C2212yes—
47C22×Q8×C11—21no—
48C2×#4339—21no—
49C22×Dic22—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8C2311yescharacteristic
54C11×C4⋊Q8C2312yes—
55C11×C4⋊Q8C2311yescharacteristic
56C11×#125—21no—
57C11×C22⋊Q8—21no—
58C11×C22⋊Q8—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C11×#117—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65C2×#4325—22no—
66#66983—21no—
67#66983—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×#4318D412yes—
71C22×C11⋊C8D412yes—
72#66928—21no—
73#66927C2311yescharacteristic
74C4×D44—21no—
75C4×D44—21no—
76#66922—21no—
77#66922—21no—
78#66922—21no—
79#66922C2312yes—
80#66922C2311yescharacteristic
81C11×#107—24no—
82C11×C4⋊C8D412yes—
83C11×#103—24no—
84C11×C22⋊C8D412yes—
85C4×C8×C11C2312yes—
86#66899—24no—
87#66899—24no—
88#66899—22no—
89#66885—24no—
90#66882—24no—
91#66874—24no—
92#66874—24no—
93#66874—24no—
94#66873—24no—
95#66873—22no—
96#66872—22no—
97#66867D412yes—
98C4×C11⋊C8D412yes—
99C4×C11⋊C8C2311yescharacteristic
100C4×C11⋊C8C2311yescharacteristic
101C4×C11⋊C8C2312yes—
102#19628—111nomaximal, Sylow
103C2×Q8×C11—22no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—44no—
107C2×Q8×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C2×C22⋊D11—41no—
113C22×Dic11—41no—
114#4339—44no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×C4×D11—41no—
119C2×Dic22—22no—
120C2×Dic22—21no—
121C2×Dic22—41no—
122C2×Dic22—44no—
123C2×C8×C11C2×D414yes—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C22⋊C4—41no—
135C42×C11—41no—
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11C2411yescharacteristic
140#4325—44no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—41no—
148C4⋊Dic11—41no—
149#4318—24no—
150C2×C11⋊C8—42no—
151C2×C11⋊C8C2×D412yes—
152C2×C11⋊C8C2×D412yes—
153C2×C11⋊C8C2×D414yes—
154#3230D1111yescharacteristic, complemented
155#3226—111no—
156#3167—111no—
157#3141—111no—
158#3139—111no—
159C2×#487—111no—
160#1719—112no—
161#1718—112no—
162#1711—112no—
163#1710—112no—
164C8×M16—111no—
165C23×C11#12711yescharacteristic
166C22×D11—41no—
167Q8×C11—42no—
168Q8×C11—44no—
169Q8×C11—42no—
170Q8×C11—82no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—82no—
177C2×C4×C11#12711yescharacteristic
178C2×C4×C11#12711yescharacteristic
179C2×C4×C11#12711yescharacteristic
180C2×C4×C11#13514yes—
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C22⋊D11—82no—
185C2×Dic11—42no—
186C2×Dic11—41no—
187C2×Dic11—82no—
188D44—42no—
189D44—42no—
190D44—42no—
191C4×D11—82no—
192Dic22—44no—
193Dic22—42no—
194Dic22—82no—
195C8×C11—24no—
196C11⋊C8—24no—
197C11⋊C8—22no—
198C11⋊C8—22no—
199#533C2×D1111yescharacteristic
200#532—111no—
201C2×C4⋊Q8—111no—
202C2×C4⋊Q8C2×D1111yescharacteristic
203#500—112no—
204#500C2×D1112yes—
205#498—111no—
206#492—111no—
207#491—222no—
208#489—222no—
209#487—112no—
210#487—112no—
211#487—112no—
212#487—112no—
213#487—112no—
214#487—111no—
215#487—222no—
216#487C2×D1112yes—
217#486—112no—
218#486—111no—
219#486—112no—
220#484—22no—
221#480—222no—
222#477—22no—
223#474—222no—
224#465—222no—
225C4×SD16—222no—
226#431C2×D1111yescharacteristic
227#419—222no—
228#417—222no—
229C2×#103—222no—
230C4×M16—111no—
231C2×C4×C8—111no—
232#322—112no—
233C82—112no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11#49512yes—
237C22×C11C2×#12711yescharacteristic
238C2×D11—81no—
239C2×D11—81no—
240C2×D11—81no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—82no—
244C4×C11—81no—
245C4×C11—81no—
246C4×C11#49512yes—
247C4×C11C2×#13512yes—
248C4×C11#57512yes—
249C4×C11#57812yes—
250Dic11—82no—
251Dic11—81no—
252C2×#41—221no—
253C22×Q8—21no—
254C22×Q8—221no—
255C2×SD16—222no—
256C2×M16—112no—
257C22×C8—112no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8—112no—
262C4⋊Q8—111no—
263C4⋊Q8—221no—
264C4⋊Q8—221no—
265C4⋊Q8—221no—
266C4⋊Q8C22×D1112yes—
267C4⋊Q8C22×D1111yescharacteristic
268C4⋊Q8C22×D1111yescharacteristic
269#127—111no—
270#125—21no—
271#124—221no—
272C22⋊Q8—21no—
273C22⋊Q8—21no—
274#121—221no—
275#121—221no—
276C4×Q8—21no—
277C4×Q8—21no—
278C4×D4—221no—
279C4×D4—221no—
280#117—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4—221no—
285C2×C42C22×D1111yescharacteristic
286#107—24no—
287#107—224no—
288#106—222no—
289C4⋊C8C22⋊D1112yes—
290#103—24no—
291#103—224no—
292#103—224no—
293#103—224no—
294#103—224no—
295#103—224no—
296#103—222no—
297#102—224no—
298#102—222no—
299#102—224no—
300C22⋊C8C22⋊D1112yes—
301#97—112no—
302C4×C8—112no—
303C4×C8—111no—
304C4×C8—112no—
305C4×C8—111no—
306C4×C8C22×D1112yes—
307C2×C11—22no—
308C2×C11C2×#49511yescharacteristic
309C2×C11#315311yescharacteristic
310C2×C11#315611yescharacteristic
311D11—161no—
312#41—444no—
313C2×Q8—22no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—44no—
317C2×Q8—41no—
318C2×Q8—221no—
319C2×Q8—222no—
320C2×Q8—441no—
321C2×Q8—444no—
322C2×D4—221no—
323C2×D4—221no—
324C2×D4—221no—
325C2×D4—441no—
326C22×C4—41no—
327C22×C4—441no—
328C22×C4—441no—
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332SD16—444no—
333M16—224no—
334C2×C8—112no—
335C2×C8—112no—
336C2×C8—114no—
337C2×C8—442no—
338C2×C8C2×C22⋊D1114yes—
339C4⋊C4—22no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—222no—
350C4⋊C4—221no—
351C4⋊C4—222no—
352C4⋊C4—221no—
353C4⋊C4—441no—
354C4⋊C4—441no—
355C22⋊C4—41no—
356C22⋊C4—441no—
357C22⋊C4—441no—
358C42—41no—
359C42D4×D1111yescharacteristic
360C42D4×D1111yescharacteristic
361C42C2×C22⋊D1111yescharacteristic
362C42C23×D1111yescharacteristic
363C11#1962811yescharacteristic, complemented, Sylow
364C23—441no—
365C23#6699311yescharacteristic
366Q8—42no—
367Q8—44no—
368Q8—42no—
369Q8—82no—
370Q8—444no—
371Q8—442no—
372Q8—882no—
373D4—442no—
374D4—442no—
375D4—442no—
376D4—882no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—441no—
384C2×C4—442no—
385C2×C4—882no—
386C2×C4—882no—
387C2×C4#6697214yes—
388C2×C4#6699311yescharacteristic
389C2×C4#6699311yescharacteristic
390C2×C4#6699311yescharacteristic
391C2×C4C2×D4×D1111yescharacteristic
392C2×C4C2×D4×D1111yescharacteristic
393C2×C4C22×C22⋊D1111yescharacteristic
394C8—24no—
395C8—224no—
396C8—222no—
397C8—222no—
398C22—21no—
399C22—21no—
400C22—881no—
401C22—881no—
402C22—881no—
403C22#1062280412yes—
404C22C2×#6699311yescharacteristic
405C4—21no—
406C4—21no—
407C4—82no—
408C4—81no—
409C4—81no—
410C4—881no—
411C4—882no—
412C4#1062280412yes—
413C4C2×#6697212yes—
414C4#1062330412yes—
415C4#1062336912yes—
416C2—22no—
417C2—1761no—
418C2C2×#1062280411yescharacteristic
419C2#1307907811yescharacteristic
420C2#1307910711yescharacteristic
subgroupG/H
centerC22C2×#66993
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3230C2
socleC22×C11C2×#127
prime radical#10623008C22
hypercenter#3230D11
hypocenterC11#19628
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
4. #13078998C2semidirect
5. C2×#10622694C2semidirect
6. #13068272C2semidirect
7. #13068265C2semidirect
8. #13068229C2semidirect
9. #13068225C2semidirect
10. #13066897C2semidirect
11. C11×#3230C2semidirect
154. #3230D11semidirect
363. C11#19628semidirect

Maximal subgroups

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

subgroupindex
#130797392
#130791762
#130790122
#130789982
C2×#106226942
#130682722
#130682652
#130682292
#130682252
#130668972
C11×#32302
#1962811