Finite Group Databasebeta

← #29663508

Subgroups — #29663508

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#21456937C211yesmaximal, characteristic, complemented
3#21456278C211yesmaximal, characteristic, complemented
4#21445308C212yesmaximal, complemented
5#21445284C212yesmaximal, complemented
6#21445184C212yesmaximal, complemented
7#21445160C212yesmaximal, complemented
8#21444571C211yesmaximal, characteristic, complemented
9#21444469C211yesmaximal, characteristic, complemented
10C2×#16839509C211yesmaximal, characteristic, complemented
11C61×#2935C211yesmaximal, characteristic, complemented
12C2×#14519810—21no—
13C2×#14519810—21no—
14#16840312C2211yescharacteristic
15C2×#14519777C2211yescharacteristic
16#16840165—21no—
17#16840156—22no—
18#16840142C2212yes—
19#16840135C2212yes—
20#16840108—21no—
21#16840073—22no—
22#16840042C2212yes—
23#16840042C2212yes—
24#16840042C2212yes—
25#16840039—21no—
26#16839996—22no—
27#16839957C2212yes—
28#16839954—21no—
29#16839815C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31#16839515C2212yes—
32#16839513C2212yes—
33#16839509C2212yes—
34#16839509C2211yescharacteristic
35#16839509C2212yes—
36#16839509C2211yescharacteristic
37#16839505C2211yescharacteristic
38#16839505C2211yescharacteristic
39C2×#131×C61—21no—
40C61×#532C2211yescharacteristic
41C61×#436C2212yes—
42C61×#435—22no—
43C8×D4×C61C2212yes—
44C2×C4⋊C8×C61C2211yescharacteristic
45C61×#408—21no—
46C4×M16×C61C2211yescharacteristic
47C2×#11758222—21no—
48C22×Dic122—21no—
49#14519810—44no—
50#14519810—44no—
51C2×Dic244—22no—
52C2×Dic244—22no—
53C2×#11758190—22no—
54C2×#11758190—22no—
55C2×#11758199—22no—
56C22×#92418—21no—
57#14519777—21no—
58#14519777—21no—
59#14519777—21no—
60#14519777C2312yes—
61#14519777C2311yescharacteristic
62#14519774C2311yescharacteristic
63#14519765—21no—
64#14519751—21no—
65#14519751—21no—
66C4×D244—21no—
67C4×D244—21no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70#14519710—22no—
71#14519710—22no—
72#14519710—22no—
73C4⋊#92418—21no—
74C4⋊#92418C2312yes—
75C4⋊#92418C2311yescharacteristic
76C4⋊#92418C2311yescharacteristic
77#14519698—22no—
78#14519698—22no—
79#14519698—22no—
80#14519697—22no—
81C22⋊#92418—21no—
82C4×#92418—21no—
83C2×#41×C61—21no—
84#131×C61—44no—
85C2×M16×C61—22no—
86C2×M16×C61D411yescharacteristic
87C2×M16×C61D411yescharacteristic
88C22×C8×C61—21no—
89C22×C8×C61—22no—
90C4⋊Q8×C61D411yescharacteristic
91#127×C61D411yescharacteristic
92#124×C61—21no—
93#121×C61—21no—
94#121×C61D412yes—
95C4×D4×C61—21no—
96C4×D4×C61C2312yes—
97C2×C42×C61C2311yescharacteristic
98C4⋊C8×C61—21no—
99C4⋊C8×C61C2311yescharacteristic
100C4⋊C8×C61C2311yescharacteristic
101C22⋊C8×C61—22no—
102C22⋊C8×C61—22no—
103#97×C61D412yes—
104C4×C8×C61C2312yes—
105#41×C61—42no—
106#41×C61—42no—
107C2×Q8×C61—21no—
108C2×D4×C61—22no—
109C2×D4×C61—21no—
110C2×D4×C61—21no—
111C2×D4×C61C2×D412yes—
112C22×C4×C61—22no—
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C2×C22⋊D61—41no—
117C22×Dic61—41no—
118#11758222—42no—
119#11758222—42no—
120C2×D244—21no—
121C2×D244—21no—
122C2×D244—21no—
123C2×C4×D61—41no—
124C2×Dic122—22no—
125C2×Dic122—21no—
126C2×Dic122—42no—
127C2×Dic122—42no—
128C2×Dic122—41no—
129M16×C61—22no—
130M16×C61—44no—
131M16×C61D814yescomplemented
132C2×C8×C61—21no—
133C2×C8×C61—21no—
134C2×C8×C61—42no—
135C2×C8×C61—44no—
136C2×C8×C61C2×D412yes—
137C2×C8×C61C2×D412yes—
138C4⋊C4×C61—21no—
139C4⋊C4×C61C2×D412yes—
140C22⋊C4×C61—22no—
141C22⋊C4×C61—22no—
142C42×C61C2×D411yescharacteristic
143C42×C61C2×D411yescharacteristic
144C42×C61#4111yescharacteristic
145C42×C61C2411yescharacteristic
146#11758199—82no—
147#11758198—41no—
148#11758198—41no—
149C4⋊Dic61—22no—
150C4⋊Dic61—21no—
151C4⋊Dic61—22no—
152C4⋊Dic61—21no—
153C4⋊Dic61—41no—
154C4⋊Dic61—41no—
155C2×#92418—21no—
156C2×#92418—21no—
157C2×#92418—22no—
158C2×#92418—81no—
159Dic244—44no—
160Dic244—44no—
161#11758190—44no—
162#11758190—44no—
163C23×C61—22no—
164C23×C61#12111yescharacteristic
165C22×D61—41no—
166Q8×C61—42no—
167D4×C61—22no—
168D4×C61—22no—
169D4×C61—44no—
170D4×C61—42no—
171D4×C61—81no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—22no—
175C2×C4×C61—41no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61#12111yescharacteristic
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#12111yescharacteristic
181C2×C4×C61C2×D812yes—
182C2×C4×C61AGL(1,ℤ/8)12yes—
183C2×C4×C61C22×D411yescharacteristic
184C2×C4×C61C22×D411yescharacteristic
185C2×C4×C61C2×#4111yescharacteristic
186C22⋊D61—82no—
187C2×Dic61—42no—
188C2×Dic61—41no—
189C2×Dic61—82no—
190D244—41no—
191D244—41no—
192D244—41no—
193D244—41no—
194D244—81no—
195C4×D61—82no—
196Dic122—42no—
197Dic122—41no—
198Dic122—42no—
199Dic122—41no—
200Dic122—82no—
201C8×C61—22no—
202C8×C61—41no—
203C8×C61—41no—
204C8×C61C2×D814yes—
205#92418—41no—
206#92418—42no—
207#92418—41no—
208#19231—611nomaximal, Sylow
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—42no—
212C22×C61—42no—
213C22×C61—42no—
214C22×C61#45912yes—
215C22×C61C2×#12111yescharacteristic
216C2×D61—81no—
217C2×D61—81no—
218C2×D61—81no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—42no—
223C4×C61#45912yes—
224C4×C61C22×D811yescharacteristic
225C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
226C4×C61#57711yescharacteristic
227C4×C61#57811yescharacteristic
228Dic61—82no—
229Dic61—81no—
230#3245—611no—
231#3226—611no—
232#3152—611no—
233#2935D6111yescharacteristic, complemented
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—82no—
243C2×C61C2×#45911yescharacteristic
244C2×C61#306311yescharacteristic
245C2×C61#306911yescharacteristic
246D61—161no—
247C2×#137—1221no—
248C2×#137—1221no—
249C2×#131—21no—
250#532—611no—
251#532C2×D6111yescharacteristic
252C2×C4⋊Q8—611no—
253#500—1221no—
254#497—1222no—
255#494—612no—
256#492—612no—
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#436C2×D6112yes—
267#435—22no—
268C8×D4C2×D6112yes—
269#431—611no—
270C2×C4⋊C8—611no—
271C2×C4⋊C8C2×D6111yescharacteristic
272#408—21no—
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—1221no—
286#137—2444no—
287#137—2444no—
288C2×Q16—1222no—
289C2×Q16—1222no—
290C2×SD16—1222no—
291C2×SD16—1222no—
292C2×D8—1222no—
293#131—44no—
294C2×M16—22no—
295C2×M16C22⋊D6111yescharacteristic
296C2×M16C22⋊D6111yescharacteristic
297C22×C8—21no—
298C22×C8—22no—
299C22×C8—1221no—
300C4⋊Q8—612no—
301C4⋊Q8—611no—
302C4⋊Q8—1221no—
303C4⋊Q8—1221no—
304C4⋊Q8—1221no—
305C4⋊Q8D24411yescharacteristic
306#127—611no—
307#127D24411yescharacteristic
308#124—21no—
309#124—1221no—
310#121—21no—
311#121—1221no—
312#121—1221no—
313#121D24412yes—
314C4×D4—21no—
315C4×D4—1221no—
316C4×D4—1221no—
317C4×D4C22×D6112yes—
318C2×C4⋊C4—1221no—
319C2×C4⋊C4—1221no—
320C2×C42C22×D6111yescharacteristic
321#107—1222no—
322#107—1222no—
323#107—1222no—
324C4⋊C8—21no—
325C4⋊C8—611no—
326C4⋊C8—611no—
327C4⋊C8—612no—
328C4⋊C8—1221no—
329C4⋊C8C22×D6111yescharacteristic
330C4⋊C8C22×D6111yescharacteristic
331#102—1222no—
332#102—1222no—
333#102—1222no—
334#102—1222no—
335C22⋊C8—22no—
336C22⋊C8—22no—
337C22⋊C8—1221no—
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—1221no—
347C2×Q8—1222no—
348C2×Q8—2442no—
349C2×Q8—2442no—
350C2×Q8—2441no—
351C2×D4—22no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—1221no—
355C2×D4—1221no—
356C2×D4—1221no—
357C2×D4—2441no—
358C2×D4C2×D24412yes—
359C22×C4—22no—
360C22×C4—2441no—
361C22×C4—2441no—
362C22×C4C2×D24411yescharacteristic
363C22×C4#1175822211yescharacteristic
364C22×C4C2×C22⋊D6111yescharacteristic
365Q16—2444no—
366Q16—2444no—
367SD16—2444no—
368SD16—2444no—
369D8—4882no—
370M16—22no—
371M16—44no—
372M16#1175819914yescomplemented
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—42no—
376C2×C8—44no—
377C2×C8—1221no—
378C2×C8—1221no—
379C2×C8—1222no—
380C2×C8—4881no—
381C2×C8C2×C22⋊D6112yes—
382C2×C8C2×C22⋊D6112yes—
383C4⋊C4—21no—
384C4⋊C4—1222no—
385C4⋊C4—1221no—
386C4⋊C4—1222no—
387C4⋊C4—1221no—
388C4⋊C4—2441no—
389C4⋊C4—2441no—
390C4⋊C4C2×D24412yes—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—2441no—
394C22⋊C4—2441no—
395C42C2×D24411yescharacteristic
396C42#1175822211yescharacteristic
397C42C2×C22⋊D6111yescharacteristic
398C42C23×D6111yescharacteristic
399C23—22no—
400C23—2441no—
401C23#1451975111yescharacteristic
402Q8—42no—
403Q8—4882no—
404Q8—2442no—
405Q8—2441no—
406Q8—2442no—
407Q8—2441no—
408D4—22no—
409D4—22no—
410D4—44no—
411D4—42no—
412D4—81no—
413D4—4881no—
414D4—4882no—
415D4—2441no—
416D4—2441no—
417D4—2441no—
418D4—2441no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—4882no—
426C2×C4—4882no—
427C2×C4—2441no—
428C2×C4—2442no—
429C2×C4#1451975111yescharacteristic
430C2×C4#1451975111yescharacteristic
431C2×C4#1451975111yescharacteristic
432C2×C4C2×#1175819912yes—
433C2×C4#1451980212yes—
434C2×C4C22×C22⋊D6111yescharacteristic
435C2×C4C22×D24411yescharacteristic
436C2×C4C2×#1175822211yescharacteristic
437C8—22no—
438C8—41no—
439C8—41no—
440C8—2441no—
441C8—2442no—
442C8—2441no—
443C8C2×#1175819914yes—
444C22—21no—
445C22—21no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—4881no—
450C22—4881no—
451C22—4881no—
452C22#1683995712yes—
453C22C2×#1451975111yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—42no—
458C4—4881no—
459C4—4882no—
460C4#1683995712yes—
461C4C22×#1175819911yescharacteristic
462C4C2×#1451980211yescharacteristic
463C4#1684057411yescharacteristic
464C4#1684057911yescharacteristic
465C2—22no—
466C2—82no—
467C2—9761no—
468C2C2×#1683995711yescharacteristic
469C2#2145551011yescharacteristic
470C2#2145555611yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2935C2
socleC22×C61C2×#121
prime radical#21457126C2
hypercenter#2935D61
hypocenterC61#19231
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
2. #21456937C2semidirect
3. #21456278C2semidirect
4. #21445308C2semidirect
5. #21445284C2semidirect
6. #21445184C2semidirect
7. #21445160C2semidirect
8. #21444571C2semidirect
9. #21444469C2semidirect
10. C2×#16839509C2semidirect
11. C61×#2935C2semidirect
131. M16×C61D8semidirect
233. #2935D61semidirect
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
#214569372
#214562782
#214453082
#214452842
#214451842
#214451602
#214445712
#214444692
C2×#168395092
C61×#29352
#1923161