Finite Group Databasebeta

← #29663502

Subgroups — #29663502

Order 15616.

726 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457126C211yesmaximal, characteristic
2#21456940C211yesmaximal, characteristic, complemented
3#21454565C211yesmaximal, characteristic, complemented
4#21445305C212yesmaximal, complemented
5#21445281C212yesmaximal, complemented
6#21445181C212yesmaximal, complemented
7#21445157C212yesmaximal, complemented
8#21444571C211yesmaximal, characteristic, complemented
9#21444468C211yesmaximal, characteristic, complemented
10C2×#16839508C211yesmaximal, characteristic, complemented
11C61×#3152C211yesmaximal, characteristic, complemented
12C2×#14519785—21no—
13#16840312C2211yescharacteristic
14#16840165—21no—
15#16840110—21no—
16#16840075—22no—
17#16840042—21no—
18#16840039C2212yes—
19#16840039C2212yes—
20#16840039C2212yes—
21#16839996—22no—
22#16839957—21no—
23#16839954C2212yes—
24#16839841C2212yes—
25#16839835—22no—
26C8×D244C2212yes—
27#16839815C2211yescharacteristic
28C2×C4⋊#92418C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30#16839730—21no—
31#16839515C2212yes—
32#16839513C2212yes—
33#16839508C2212yes—
34#16839508C2211yescharacteristic
35#16839508C2212yes—
36#16839508C2211yescharacteristic
37#16839506C2211yescharacteristic
38#16839506C2211yescharacteristic
39C2×#137×C61—21no—
40C2×#137×C61—21no—
41C61×#532C2211yescharacteristic
42C2×C4⋊Q8×C61C2211yescharacteristic
43C61×#497—22no—
44C61×#494C2212yes—
45C61×#492C2212yes—
46C4×M16×C61C2211yescharacteristic
47C2×#11758222—21no—
48C2×#11758199—22no—
49#14519785—44no—
50C2×#11758189—22no—
51C22×#92418—21no—
52C22×#92418—21no—
53C2×C8×D61—22no—
54#14519777D411yescharacteristic
55#14519774D411yescharacteristic
56#14519765—21no—
57#14519751—21no—
58#14519751D412yes—
59C4×D244—21no—
60C4×D244C2312yes—
61#14519710—22no—
62#14519710—22no—
63#14519710—22no—
64C4⋊#92418—21no—
65C4⋊#92418—21no—
66C4⋊#92418C2312yes—
67C4⋊#92418C2311yescharacteristic
68C4⋊#92418C2311yescharacteristic
69C4⋊#92418C2311yescharacteristic
70C4⋊#92418C2311yescharacteristic
71#14519698—22no—
72#14519697—22no—
73#14519697—22no—
74#14519697—22no—
75C22⋊#92418—21no—
76#14519689—22no—
77#14519689—22no—
78C4×#92418—21no—
79C2×#41×C61—21no—
80C22×Q8×C61—21no—
81#137×C61—44no—
82#137×C61—44no—
83C2×Q16×C61—22no—
84C2×Q16×C61—22no—
85C2×SD16×C61—22no—
86C2×SD16×C61—22no—
87C2×M16×C61D411yescharacteristic
88C2×M16×C61D411yescharacteristic
89C4⋊Q8×C61—21no—
90C4⋊Q8×C61—21no—
91C4⋊Q8×C61—21no—
92C4⋊Q8×C61C2312yes—
93C4⋊Q8×C61C2311yescharacteristic
94#127×C61C2311yescharacteristic
95#124×C61—21no—
96#121×C61—21no—
97#121×C61—21no—
98C4×D4×C61—21no—
99C4×D4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C42×C61C2311yescharacteristic
103#97×C61D412yes—
104C4×C8×C61C2312yes—
105#41×C61—42no—
106#41×C61—42no—
107C2×Q8×C61—21no—
108C2×Q8×C61—22no—
109C2×Q8×C61—41no—
110C2×Q8×C61—42no—
111C2×Q8×C61—42no—
112C2×D4×C61—21no—
113C2×D4×C61—21no—
114C2×D4×C61—21no—
115C2×D4×C61—41no—
116C22×C4×C61—41no—
117C22×C4×C61—41no—
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61#4111yescharacteristic
121C2×C22⋊D61—22no—
122#11758222—42no—
123#11758222—42no—
124C2×D244—21no—
125C2×D244—21no—
126C2×D244C2×D412yes—
127C2×C4×D61—22no—
128C2×Dic122—21no—
129Q16×C61—44no—
130Q16×C61—44no—
131SD16×C61—44no—
132SD16×C61—44no—
133M16×C61—22no—
134M16×C61D814yescomplemented
135C2×C8×C61C2×D412yes—
136C2×C8×C61C2×D412yes—
137C4⋊C4×C61—22no—
138C4⋊C4×C61—21no—
139C4⋊C4×C61—22no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—41no—
142C4⋊C4×C61—41no—
143C22⋊C4×C61—41no—
144C22⋊C4×C61—41no—
145C42×C61C2×D411yescharacteristic
146C42×C61C2×D411yescharacteristic
147C42×C61#4111yescharacteristic
148C42×C61C2411yescharacteristic
149#11758199—82no—
150#11758198—22no—
151#11758198—22no—
152C4⋊Dic61—21no—
153C4⋊Dic61C2×D412yes—
154C2×#92418—21no—
155C2×#92418—21no—
156C2×#92418—21no—
157C2×#92418—21no—
158C2×#92418—22no—
159C2×#92418—42no—
160C2×#92418—81no—
161#11758189—44no—
162C8×D61—44no—
163C23×C61—41no—
164C23×C61#12111yescharacteristic
165C22×D61—22no—
166Q8×C61—42no—
167Q8×C61—41no—
168Q8×C61—42no—
169Q8×C61—41no—
170Q8×C61—82no—
171D4×C61—41no—
172D4×C61—41no—
173D4×C61—41no—
174D4×C61—41no—
175D4×C61—81no—
176D4×C61—82no—
177C2×C4×C61—21no—
178C2×C4×C61—21no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—42no—
182C2×C4×C61—82no—
183C2×C4×C61—82no—
184C2×C4×C61#12111yescharacteristic
185C2×C4×C61#12111yescharacteristic
186C2×C4×C61#12111yescharacteristic
187C2×C4×C61C2×D812yes—
188C2×C4×C61AGL(1,ℤ/8)12yes—
189C2×C4×C61C22×D411yescharacteristic
190C2×C4×C61C22×D411yescharacteristic
191C2×C4×C61C2×#4111yescharacteristic
192C22⋊D61—44no—
193C2×Dic61—22no—
194D244—22no—
195D244—22no—
196D244—42no—
197D244—81no—
198C4×D61—42no—
199C4×D61—42no—
200Dic122—42no—
201C8×C61—22no—
202C8×C61C2×D814yes—
203#92418—41no—
204#92418—41no—
205#92418—41no—
206#92418—42no—
207#92418—41no—
208#19231—611nomaximal, Sylow
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61#45912yes—
215C22×C61C2×#12111yescharacteristic
216C2×D61—42no—
217C2×D61—42no—
218C2×D61—42no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—81no—
223C4×C61—82no—
224C4×C61#45912yes—
225C4×C61C22×D811yescharacteristic
226C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
227C4×C61#57711yescharacteristic
228C4×C61#57811yescharacteristic
229Dic61—42no—
230#3245—611no—
231#3226—611no—
232#3152D6111yescharacteristic, complemented
233#2935—611no—
234#1689—612no—
235#1685—612no—
236#1669—612no—
237#1665—612no—
238#1565—611no—
239#1540—611no—
240C2×#332—611no—
241C2×C61—22no—
242C2×C61—161no—
243C2×C61C2×#45911yescharacteristic
244C2×C61#306311yescharacteristic
245C2×C61#306911yescharacteristic
246D61—82no—
247C2×#137—21no—
248C2×#137—21no—
249C2×#131—1221no—
250#532—611no—
251#532C2×D6111yescharacteristic
252C2×C4⋊Q8C2×D6111yescharacteristic
253#500—1221no—
254#497—22no—
255#494C2×D6112yes—
256#492C2×D6112yes—
257#486—1221no—
258#480—1222no—
259#474—612no—
260#474—612no—
261#474—612no—
262#474—1221no—
263#466—1222no—
264#459—612no—
265#459—1221no—
266#436—612no—
267#435—1222no—
268C8×D4—612no—
269#431—611no—
270C2×C4⋊C8—611no—
271C2×C4⋊C8—611no—
272#408—1221no—
273C4×M16C2×D6111yescharacteristic
274#335—612no—
275#334—612no—
276#332—612no—
277#332—612no—
278#332—611no—
279#332—611no—
280#331—611no—
281#331—611no—
282C61#1923111yescharacteristic, complemented, Sylow
283C2×#41—21no—
284C2×#41—1221no—
285C22×Q8—21no—
286#137—44no—
287#137—44no—
288C2×Q16—22no—
289C2×Q16—22no—
290C2×SD16—22no—
291C2×SD16—22no—
292C2×D8—1222no—
293#131—2444no—
294C2×M16—1222no—
295C2×M16C22⋊D6111yescharacteristic
296C2×M16C22⋊D6111yescharacteristic
297C22×C8—1221no—
298C22×C8—1221no—
299C22×C8—1222no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—611no—
304C4⋊Q8C22×D6112yes—
305C4⋊Q8C22×D6111yescharacteristic
306#127—611no—
307#127C22×D6111yescharacteristic
308#124—21no—
309#124—1221no—
310#121—21no—
311#121—21no—
312#121—612no—
313#121—1221no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—612no—
317C4×D4—1221no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C42C22×D6111yescharacteristic
321#107—1222no—
322#107—1222no—
323#107—1222no—
324C4⋊C8—611no—
325C4⋊C8—611no—
326C4⋊C8—611no—
327C4⋊C8—611no—
328C4⋊C8—612no—
329C4⋊C8—1221no—
330C4⋊C8—1221no—
331#102—1222no—
332#102—1222no—
333#102—1222no—
334#102—1222no—
335C22⋊C8—1221no—
336C22⋊C8—1222no—
337C22⋊C8—1222no—
338#97C22⋊D6112yes—
339C4×C8—1221no—
340C4×C8C22×D6112yes—
341#41—42no—
342#41—42no—
343#41—2442no—
344#41—2442no—
345C2×Q8—21no—
346C2×Q8—22no—
347C2×Q8—41no—
348C2×Q8—42no—
349C2×Q8—42no—
350C2×Q8—1221no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—41no—
355C2×D4—612no—
356C2×D4—1222no—
357C2×D4—1221no—
358C2×D4—1221no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—1222no—
362C22×C4D4×D6111yescharacteristic
363C22×C4#1175822411yescharacteristic
364C22×C4C2×C22⋊D6111yescharacteristic
365Q16—44no—
366Q16—44no—
367SD16—44no—
368SD16—44no—
369D8—4882no—
370M16—22no—
371M16—2444no—
372M16#1175819914yescomplemented
373C2×C8—1221no—
374C2×C8—1221no—
375C2×C8—1222no—
376C2×C8—1221no—
377C2×C8—1221no—
378C2×C8—4881no—
379C2×C8—2442no—
380C2×C8—2444no—
381C2×C8C2×C22⋊D6112yes—
382C2×C8C2×C22⋊D6112yes—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—612no—
390C4⋊C4—1221no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—1222no—
394C22⋊C4—1222no—
395C42D4×D6111yescharacteristic
396C42#1175822411yescharacteristic
397C42C2×C22⋊D6111yescharacteristic
398C42C23×D6111yescharacteristic
399C23—41no—
400C23—1222no—
401C23#1451974811yescharacteristic
402Q8—42no—
403Q8—41no—
404Q8—42no—
405Q8—41no—
406Q8—82no—
407Q8—2442no—
408D4—41no—
409D4—41no—
410D4—41no—
411D4—41no—
412D4—81no—
413D4—82no—
414D4—1222no—
415D4—1222no—
416D4—4881no—
417D4—2444no—
418D4—2442no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—1222no—
427C2×C4—2442no—
428C2×C4—2442no—
429C2×C4#1451974811yescharacteristic
430C2×C4#1451974811yescharacteristic
431C2×C4#1451974811yescharacteristic
432C2×C4C2×#1175819912yes—
433C2×C4#1451980312yes—
434C2×C4C2×D4×D6111yescharacteristic
435C2×C4C22×C22⋊D6111yescharacteristic
436C2×C4C2×#1175822411yescharacteristic
437C8—22no—
438C8—2441no—
439C8—2441no—
440C8—2441no—
441C8—2442no—
442C8—2441no—
443C8C2×#1175819914yes—
444C22—21no—
445C22—21no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—2442no—
450C22—2442no—
451C22—2442no—
452C22#1683995412yes—
453C22C2×#1451974811yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—81no—
458C4—82no—
459C4—2442no—
460C4#1683995412yes—
461C4C22×#1175819911yescharacteristic
462C4C2×#1451980311yescharacteristic
463C4#1684057111yescharacteristic
464C4#1684057811yescharacteristic
465C2—22no—
466C2—161no—
467C2—4882no—
468C2C2×#1683995411yescharacteristic
469C2#2145550411yescharacteristic
470C2#2145555211yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3152C2
socleC22×C61C2×#121
prime radical#21457126C2
hypercenter#3152D61
hypocenterC61#19231
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3152

Complements

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

NH ≅ G/Ntype
2. #21456940C2semidirect
3. #21454565C2semidirect
4. #21445305C2semidirect
5. #21445281C2semidirect
6. #21445181C2semidirect
7. #21445157C2semidirect
8. #21444571C2semidirect
9. #21444468C2semidirect
10. C2×#16839508C2semidirect
11. C61×#3152C2semidirect
134. M16×C61D8semidirect
232. #3152D61semidirect
282. C61#19231semidirect
372. M16#11758199semidirect

Maximal subgroups

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

subgroupindex
#214571262
#214569402
#214545652
#214453052
#214452812
#214451812
#214451572
#214445712
#214444682
C2×#168395082
C61×#31522
#1923161