Finite Group Databasebeta

← #14737303

Subgroups — #14737303

Order 2816.

704 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079531C211yesmaximal, characteristic
2#13078992C211yesmaximal, characteristic, complemented
3#13077360C211yesmaximal, characteristic, complemented
4#13068179C212yesmaximal, complemented
5#13068151C212yesmaximal, complemented
6#13068055C212yesmaximal, complemented
7#13068027C212yesmaximal, complemented
8#13067366C211yesmaximal, characteristic, complemented
9#13067273C211yesmaximal, characteristic, complemented
10C2×#10622123C211yesmaximal, characteristic, complemented
11C11×#3246C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×#67001—21no—
15C2×#66927C2211yescharacteristic
16C11×#476C2212yescomplemented
17C11×#475—21no—
18C11×#465—22no—
19C11×#461C2212yescomplemented
20C11×#460—21no—
21C2×C11×C4⋊C8C2211yescharacteristic
22#10622847—21no—
23#10622701—21no—
24#10622701C2212yes—
25#10622701C2212yes—
26#10622686—21no—
27#10622680—22no—
28#10622649—22no—
29#10622628C2212yes—
30#10622628C2212yes—
31#10622625C2212yescomplemented
32#10622624—22no—
33D4×C11⋊C8C2212yescomplemented
34#10622614—21no—
35#10622614—21no—
36#10622538C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622185C2211yescharacteristic, complemented
40#10622185C2211yescharacteristic, complemented
41#10622184C2211yescharacteristic, complemented
42#10622184C2211yescharacteristic, complemented
43#10622123C2212yes—
44#10622123C2212yes—
45#10622118C2212yescomplemented
46#10622117C2212yescomplemented
47C2×C11×#41—21no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44—21no—
51C2×C11×SD16—22no—
52C22×C8×C11—21no—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8C2311yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×#127D411yescharacteristic
57C11×#125—21no—
58C11×#124—21no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8—21no—
61C11×#121—21no—
62C11×#121D412yes—
63C4×Q8×C11—21no—
64C4×Q8×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11C2312yes—
67C11×#117—21no—
68C2×C42×C11C2311yescharacteristic
69#67001—44no—
70C2×#4323—22no—
71C2×#4323—22no—
72C2×#4318—22no—
73C2×#4318D411yescharacteristic
74C2×#4318D411yescharacteristic
75C22×C11⋊C8—21no—
76C22×C11⋊C8—22no—
77#66927—21no—
78#66927—21no—
79#66927—21no—
80#66927C2312yes—
81C11×#106—22no—
82C11×C4⋊C8—21no—
83C11×C4⋊C8C2312yes—
84C11×#103—22no—
85C11×#102—22no—
86C22⋊(C11⋊C8)—21no—
87C22⋊(C11⋊C8)—22no—
88C22⋊(C11⋊C8)—22no—
89#66873—22no—
90#66873—22no—
91#66873—22no—
92#66873—22no—
93#66873—22no—
94#66873—22no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)C2311yescharacteristic
97C4⋊(C11⋊C8)C2311yescharacteristic
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2311yescharacteristic
100#66867D412yes—
101C4×C11⋊C8—21no—
102C4×C11⋊C8C2312yes—
103#19234—111nomaximal, Sylow
104C23×D11—41no—
105C11×#41—42no—
106C11×#41—42no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11C2×D412yes—
114C22×C4×C11—22no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—41no—
122C2×D44—41no—
123C2×D44—41no—
124C2×D44—42no—
125C2×D44—42no—
126C2×D44—81no—
127C2×D44—81no—
128C2×D44—82no—
129C11×SD16—82no—
130C2×C8×C11—22no—
131C2×C8×C11—81no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4C2×D412yes—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—41no—
143C42×C11—41no—
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11#4111yescharacteristic
147C42×C11C2411yescharacteristic
148#4323—82no—
149#4323—82no—
150#4318—22no—
151#4318—22no—
152#4318—44no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—44no—
158C2×C11⋊C8—42no—
159C2×C11⋊C8C2×D412yes—
160C2×C11⋊C8C2×D412yes—
161#3246D1111yescharacteristic, complemented
162#3205—111no—
163#3138—111no—
164#2935—111no—
165#1701—112no—
166#1697—112no—
167#1681—112no—
168#1677—112no—
169#1565—111no—
170#1542—111no—
171C2×#331—111no—
172C23×C11—22no—
173C23×C11#12111yescharacteristic
174C22×D11—42no—
175C22×D11—82no—
176C22×D11—82no—
177C22×D11—82no—
178Q8×C11—42no—
179Q8×C11—41no—
180Q8×C11—41no—
181Q8×C11—81no—
182D4×C11—22no—
183D4×C11—22no—
184D4×C11—44no—
185D4×C11—42no—
186D4×C11—81no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#13512yes—
199C2×C4×C11AGL(1,ℤ/8)12yes—
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203D44—42no—
204D44—42no—
205D44—42no—
206D44—42no—
207D44—82no—
208D44—82no—
209D44—82no—
210D44—82no—
211C8×C11—42no—
212C11⋊C8—22no—
213C11⋊C8—22no—
214C11⋊C8—41no—
215C11⋊C8—41no—
216C11⋊C8—41no—
217C11⋊C8—41no—
218C2×#131—221no—
219#533C2×D1111yescharacteristic
220#532C2×D1111yescharacteristic
221C2×#127—111no—
222#493—221no—
223#490—222no—
224#486—112no—
225#486—112no—
226#486—221no—
227#476C2×D1112yescomplemented
228#475—21no—
229#465—22no—
230#461C2×D1112yescomplemented
231#460—21no—
232#459—112no—
233#459—112no—
234#447—222no—
235#436—112no—
236#435—222no—
237C8×D4—112no—
238#431—111no—
239C2×C4⋊C8—111no—
240C2×C4⋊C8C2×D1111yescharacteristic
241#418—221no—
242#418—221no—
243#408—221no—
244C4×M16—111no—
245#335—112no—
246#334—112no—
247#333—111no—
248#333—111no—
249#332—111no—
250#332—111no—
251#331—112no—
252#331—112no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11#46312yes—
259C22×C11C2×#12111yescharacteristic
260C2×D11—82no—
261C2×D11—82no—
262C2×D11—82no—
263C2×D11—164no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—42no—
268C4×C11—81no—
269C4×C11—81no—
270C4×C11#46312yes—
271C4×C11C2×#13511yescharacteristic
272C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
273C4×C11#57611yescharacteristic
274C4×C11#57711yescharacteristic
275C2×#41—21no—
276C22×D4—221no—
277C22×D4—221no—
278C22×D4—221no—
279C2×SD16—22no—
280C2×D8—222no—
281C2×D8—222no—
282#131—444no—
283C2×M16—111no—
284C2×M16—111no—
285C2×M16—222no—
286C22×C8—21no—
287C22×C8—222no—
288C22×C8—221no—
289C4⋊Q8C22⋊D1111yescharacteristic
290C4⋊Q8C22×D1111yescharacteristic
291C4⋊Q8C22×D1111yescharacteristic
292#127—112no—
293#127—221no—
294#127—221no—
295#127—221no—
296#127C22⋊D1111yescharacteristic
297#125—21no—
298#124—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301#121—21no—
302#121C22⋊D1112yes—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×D4—21no—
306C4×D4C22×D1112yes—
307#117—21no—
308C2×C42C22×D1111yescharacteristic
309#106—22no—
310C4⋊C8—21no—
311C4⋊C8—111no—
312C4⋊C8—111no—
313C4⋊C8—111no—
314C4⋊C8—111no—
315C4⋊C8—221no—
316C4⋊C8C22×D1112yes—
317#103—22no—
318#102—22no—
319#102—222no—
320#102—222no—
321#102—222no—
322#102—222no—
323#102—222no—
324#102—222no—
325C22⋊C8—222no—
326C22⋊C8—222no—
327C22⋊C8—221no—
328#97—112no—
329C4×C8—112no—
330C4×C8—221no—
331C2×C11—22no—
332C2×C11—82no—
333C2×C11C2×#46311yescharacteristic
334C2×C11#306211yescharacteristic
335C2×C11#306811yescharacteristic
336D11—162no—
337C24—441no—
338#41—42no—
339#41—42no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×D4—22no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—222no—
347C2×D4—222no—
348C2×D4—222no—
349C2×D4—442no—
350C2×D4—442no—
351C2×D4—441no—
352C2×D4—441no—
353C2×D4—441no—
354C2×D4—881no—
355C2×D4—881no—
356C2×D4—882no—
357C2×D4C2×C22⋊D1112yes—
358C22×C4—22no—
359C22×C4D4×D1111yescharacteristic
360C22×C4#434111yescharacteristic
361C22×C4C2×C22⋊D1111yescharacteristic
362SD16—82no—
363D8—882no—
364D8—882no—
365M16—222no—
366M16—222no—
367M16—444no—
368C2×C8—22no—
369C2×C8—81no—
370C2×C8—112no—
371C2×C8—112no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8—221no—
376C2×C8—444no—
377C2×C8—442no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4C2×C22⋊D1112yes—
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—41no—
389C42—41no—
390C42D4×D1111yescharacteristic
391C42#434111yescharacteristic
392C42C2×C22⋊D1111yescharacteristic
393C42C23×D1111yescharacteristic
394C11#1923411yescharacteristic, complemented, Sylow
395C23—22no—
396C23—442no—
397C23—882no—
398C23—882no—
399C23—882no—
400C23#6699211yescharacteristic
401Q8—42no—
402Q8—41no—
403Q8—41no—
404Q8—81no—
405D4—22no—
406D4—22no—
407D4—44no—
408D4—42no—
409D4—81no—
410D4—442no—
411D4—442no—
412D4—442no—
413D4—442no—
414D4—882no—
415D4—882no—
416D4—882no—
417D4—882no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4#6696712yes—
427C2×C4#6696912yes—
428C2×C4#6699211yescharacteristic
429C2×C4#6699211yescharacteristic
430C2×C4#6699211yescharacteristic
431C2×C4C2×D4×D1111yescharacteristic
432C2×C4C2×#434111yescharacteristic
433C2×C4C22×C22⋊D1111yescharacteristic
434C8—42no—
435C8—222no—
436C8—222no—
437C8—441no—
438C8—441no—
439C8—441no—
440C8—441no—
441C22—21no—
442C22—21no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—882no—
447C22—882no—
448C22—882no—
449C22—1764no—
450C22#1062277812yes—
451C22C2×#6699211yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—42no—
456C4—81no—
457C4—81no—
458C4#1062277812yes—
459C4C2×#6696711yescharacteristic
460C4C2×#6696911yescharacteristic
461C4#1062336611yescharacteristic
462C4#1062336811yescharacteristic
463C2—22no—
464C2—82no—
465C2—1762no—
466C2C2×#1062277811yescharacteristic
467C2#1307829811yescharacteristic
468C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3246C2
socleC22×C11C2×#121
prime radical#13079531C2
hypercenter#3246D11
hypocenterC11#19234
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3246

Complements

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

NH ≅ G/Ntype
2. #13078992C2semidirect
3. #13077360C2semidirect
4. #13068179C2semidirect
5. #13068151C2semidirect
6. #13068055C2semidirect
7. #13068027C2semidirect
8. #13067366C2semidirect
9. #13067273C2semidirect
10. C2×#10622123C2semidirect
11. C11×#3246C2semidirect
16. C11×#476C22semidirect
19. C11×#461C22semidirect
31. #10622625C22semidirect
33. D4×C11⋊C8C22semidirect
39. #10622185C22semidirect
40. #10622185C22semidirect
41. #10622184C22semidirect
42. #10622184C22semidirect
45. #10622118C22semidirect
46. #10622117C22semidirect
161. #3246D11semidirect
227. #476C2×D11semidirect
230. #461C2×D11semidirect
394. C11#19234semidirect

Maximal subgroups

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

subgroupindex
#130795312
#130789922
#130773602
#130681792
#130681512
#130680552
#130680272
#130673662
#130672732
C2×#106221232
C11×#32462
#1923411