Finite Group Databasebeta

← #14738471

Subgroups — #14738471

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079623C211yesmaximal, characteristic, complemented
2#13079191C211yesmaximal, characteristic
3#13077551C211yesmaximal, characteristic, complemented
4#13068132C212yesmaximal, complemented
5#13068098C212yesmaximal, complemented
6#13068062C212yesmaximal, complemented
7#13068058C212yesmaximal, complemented
8#13067377C211yesmaximal, characteristic, complemented
9#13067339C211yesmaximal, characteristic, complemented
10#13067338C211yesmaximal, characteristic, complemented
11C11×#3216C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#532C2211yescharacteristic
14#10623008C2211yescharacteristic
15C11×#497—21no—
16C11×#489—21no—
17C11×#462C2212yes—
18C11×#460C2212yes—
19C11×#452—22no—
20C11×#432C2211yescharacteristic
21#10622702—21no—
22#10622701C2211yescharacteristic
23#10622699—21no—
24#10622691C2211yescharacteristic
25#10622686C2211yescharacteristic
26#10622683C2211yescharacteristic
27#10622660—22no—
28#10622651—21no—
29#10622651—21no—
30#10622644C2212yes—
31#10622640C2212yes—
32#10622637—21no—
33#10622637C2212yes—
34Q8×C11⋊C8—21no—
35Q8×C11⋊C8C2212yes—
36C4×#4323—21no—
37C4×#4323—21no—
38#10622612—21no—
39#10622610—21no—
40#10622539C2211yescharacteristic
41#10622537C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622185C2212yes—
44#10622182C2212yes—
45#10622123C2212yes—
46#10622120C2212yes—
47#10622118C2212yes—
48#10622117C2212yes—
49C2×C11×#41—21no—
50C2×#4339—21no—
51C2×C11×Q16—22no—
52C2×C11×SD16—22no—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×#127C2311yescharacteristic
57C11×#125—21no—
58C11×#124—21no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8D412yes—
61C11×#121—21no—
62C11×#121—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11C2312yes—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C11×#117—21no—
68C2×C42×C11C2311yescharacteristic
69C2×#4326—22no—
70C2×#4325—22no—
71C2×#4323—21no—
72C2×#4323—21no—
73#66983—21no—
74#66983—21no—
75C2×#4318—21no—
76C22×C11⋊C8D411yescharacteristic
77C22×C11⋊C8D411yescharacteristic
78#66928—21no—
79#66927C2311yescharacteristic
80C4×D44—21no—
81C4×D44—21no—
82#66922C2311yescharacteristic
83C11×C4⋊C8C2312yes—
84C11×#103—22no—
85C11×#102—22no—
86C11×C22⋊C8—21no—
87C11×#97—21no—
88#66896—21no—
89#66896—21no—
90C22⋊(C11⋊C8)—21no—
91#66874—22no—
92#66873—22no—
93#66873—21no—
94#66873—21no—
95#66871—21no—
96#66871—21no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)—22no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2312yes—
102#66867—21no—
103#66867—22no—
104C4×C11⋊C8—22no—
105C4×C11⋊C8D411yescharacteristic
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8C2311yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109#19347—111nomaximal, Sylow
110C11×#41—82no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11C2×D412yes—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—41no—
118C22×C4×C11—41no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C2×C22⋊D11—41no—
123#4339—82no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44—21no—
127C2×C4×D11—41no—
128C2×Dic22—21no—
129C11×Q16—82no—
130C11×SD16—82no—
131C2×C8×C11—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4C2×D412yes—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—41no—
142C11×C22⋊C4—41no—
143C42×C11—22no—
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11#4111yescharacteristic
147C42×C11C2411yescharacteristic
148#4326—82no—
149#4325—82no—
150#4323—42no—
151#4323—42no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156#4318—42no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—41no—
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165#3216—111no—
166#3216D1111yescharacteristic, complemented
167#3169—111no—
168#2960—111no—
169#1694—112no—
170#1688—112no—
171#1682—112no—
172#1682—112no—
173#1568—111no—
174#1557—111no—
175#1557—111no—
176C23×C11—41no—
177C23×C11#12111yescharacteristic
178C22×D11—41no—
179Q8×C11—22no—
180Q8×C11—22no—
181Q8×C11—42no—
182Q8×C11—42no—
183D4×C11—41no—
184D4×C11—41no—
185D4×C11—42no—
186D4×C11—81no—
187D4×C11—82no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—82no—
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C22⋊D11—82no—
203C2×Dic11—41no—
204D44—41no—
205D44—41no—
206D44—42no—
207D44—81no—
208C4×D11—82no—
209Dic22—42no—
210C8×C11—42no—
211C11⋊C8—21no—
212C11⋊C8—21no—
213C11⋊C8—21no—
214C11⋊C8—42no—
215C11⋊C8—42no—
216C11⋊C8#13712yes—
217#533C2×D1111yescharacteristic
218#532—111no—
219#532C2×D1111yescharacteristic
220#500—111no—
221#497—21no—
222#497—221no—
223#493—111no—
224#489—21no—
225#489—221no—
226#486—111no—
227#486—111no—
228#466—221no—
229#466—221no—
230#462—112no—
231#462C2×D1112yes—
232#460—112no—
233#460C2×D1112yes—
234#452—22no—
235#452—222no—
236#446—112no—
237#446—221no—
238C8×Q8—112no—
239C8×Q8—221no—
240C4×D8—221no—
241C4×D8—221no—
242#432—111no—
243#432C2×D1111yescharacteristic
244#424—221no—
245#423—111no—
246#405—221no—
247C2×C4×C8—111no—
248#335—112no—
249#334—112no—
250#332—112no—
251#332—112no—
252#331—112no—
253#331—112no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11C2×#12111yescharacteristic
261C2×D11—81no—
262C2×D11—81no—
263C2×D11—81no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—81no—
271C4×C11C2×#13711yescharacteristic
272C4×C11#57511yescharacteristic
273C4×C11#57612yes—
274Dic11—81no—
275C2×#41—21no—
276C2×#41—221no—
277C2×Q16—22no—
278C2×Q16—222no—
279C2×SD16—22no—
280C2×SD16—222no—
281C2×D8—221no—
282C2×D8—221no—
283C2×M16—221no—
284C22×C8—111no—
285C22×C8—111no—
286C4⋊Q8—111no—
287C4⋊Q8C22⋊D1111yescharacteristic
288C4⋊Q8C22⋊D1111yescharacteristic
289C4⋊Q8C22×D1111yescharacteristic
290#127—111no—
291#127C22×D1111yescharacteristic
292#125—21no—
293#124—21no—
294#124—221no—
295C22⋊Q8—21no—
296C22⋊Q8C22⋊D1112yes—
297#121—21no—
298#121—21no—
299#121—221no—
300#121—221no—
301C4×Q8—21no—
302C4×Q8C22×D1112yes—
303C4×D4—21no—
304C4×D4—21no—
305C4×D4—221no—
306C4×D4—221no—
307#117—21no—
308C2×C42C22×D1111yescharacteristic
309#107—221no—
310#107—221no—
311C4⋊C8—112no—
312C4⋊C8—112no—
313C4⋊C8—222no—
314C4⋊C8—222no—
315C4⋊C8—221no—
316C4⋊C8C22×D1112yes—
317#103—22no—
318#103—222no—
319#102—22no—
320#102—221no—
321#102—221no—
322#102—221no—
323#102—221no—
324#102—222no—
325C22⋊C8—21no—
326C22⋊C8—221no—
327#97—21no—
328#97—222no—
329#97—221no—
330C4×C8—111no—
331C4×C8—111no—
332C4×C8—111no—
333C4×C8—111no—
334C4×C8—222no—
335C2×C11—41no—
336C2×C11—161no—
337C2×C11#303711yescharacteristic
338C2×C11#305811yescharacteristic
339C2×C11#306711yescharacteristic
340D11—161no—
341#41—82no—
342#41—882no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—221no—
346C2×Q8C2×C22⋊D1112yes—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—41no—
351C2×D4—221no—
352C2×D4—221no—
353C2×D4—221no—
354C2×D4—441no—
355C22×C4—41no—
356C22×C4—441no—
357C22×C4D4×D1111yescharacteristic
358C22×C4#434111yescharacteristic
359C22×C4C2×C22⋊D1111yescharacteristic
360Q16—82no—
361Q16—882no—
362SD16—82no—
363SD16—882no—
364D8—442no—
365D8—442no—
366M16—442no—
367C2×C8—22no—
368C2×C8—111no—
369C2×C8—111no—
370C2×C8—111no—
371C2×C8—111no—
372C2×C8—222no—
373C2×C8—222no—
374C2×C8—222no—
375C2×C8—441no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—221no—
384C4⋊C4—221no—
385C4⋊C4C2×C22⋊D1112yes—
386C22⋊C4—22no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C42—22no—
392C42D4×D1111yescharacteristic
393C42#434111yescharacteristic
394C42C2×C22⋊D1111yescharacteristic
395C42C23×D1111yescharacteristic
396C11#1934711yescharacteristic, complemented, Sylow
397C23—41no—
398C23—441no—
399C23#6699211yescharacteristic
400Q8—22no—
401Q8—22no—
402Q8—42no—
403Q8—42no—
404Q8—442no—
405D4—41no—
406D4—41no—
407D4—42no—
408D4—81no—
409D4—82no—
410D4—441no—
411D4—441no—
412D4—442no—
413D4—881no—
414D4—882no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—82no—
423C2×C4—441no—
424C2×C4—882no—
425C2×C4#6699211yescharacteristic
426C2×C4#6699211yescharacteristic
427C2×C4#6699211yescharacteristic
428C2×C4C2×D4×D1111yescharacteristic
429C2×C4C2×#434111yescharacteristic
430C2×C4C22×C22⋊D1111yescharacteristic
431C8—42no—
432C8—112no—
433C8—221no—
434C8—221no—
435C8—221no—
436C8—442no—
437C8—442no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—881no—
445C22—881no—
446C22—881no—
447C22C2×#6699211yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—42no—
453C4—42no—
454C4—81no—
455C4—881no—
456C4D11×#13711yescharacteristic
457C4#1062330811yescharacteristic
458C4#1062336612yes—
459C2—41no—
460C2—161no—
461C2—1761no—
462C2#1307808511yescharacteristic
463C2#1307826111yescharacteristic
464C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3216C2
socleC22×C11C2×#121
prime radical#13079191C2
hypercenter#3216D11
hypocenterC11#19347
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3216

Complements

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

NH ≅ G/Ntype
1. #13079623C2semidirect
3. #13077551C2semidirect
4. #13068132C2semidirect
5. #13068098C2semidirect
6. #13068062C2semidirect
7. #13068058C2semidirect
8. #13067377C2semidirect
9. #13067339C2semidirect
10. #13067338C2semidirect
11. C11×#3216C2semidirect
166. #3216D11semidirect
396. C11#19347semidirect

Maximal subgroups

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

subgroupindex
#130796232
#130791912
#130775512
#130681322
#130680982
#130680622
#130680582
#130673772
#130673392
#130673382
C11×#32162
#1934711