Finite Group Databasebeta

← #29665500

Subgroups — #29665500

Order 15616.

694 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456937C211yesmaximal, characteristic, complemented
2#21455307C211yesmaximal, characteristic, complemented
3#21455268C211yesmaximal, characteristic
4#21454928C211yesmaximal, characteristic, complemented
5#21445262C212yesmaximal, complemented
6#21445255C212yesmaximal, complemented
7#21445212C212yesmaximal, complemented
8#21445207C212yesmaximal, complemented
9#21444595C211yesmaximal, characteristic, complemented
10C2×#16839507C211yesmaximal, characteristic, complemented
11C61×#1547C211yesmaximal, characteristic, complemented
12C2×#14519810—21no—
13C2×#14519797—21no—
14C2×#14519777C2211yescharacteristic
15C4×#11758222C2211yescharacteristic
16#16840165C2212yes—
17#16840108C2212yes—
18#16840073—22no—
19#16840042—21no—
20#16840042—21no—
21#16839981—21no—
22#16839974—21no—
23#16839973—21no—
24#16839973C2212yes—
25#16839969C2211yescharacteristic
26#16839968—21no—
27#16839968C2212yes—
28#16839964C2211yescharacteristic
29#16839959C2211yescharacteristic
30#16839954C2211yescharacteristic
31#16839886C2212yes—
32#16839827C2212yes—
33C8×C22⋊D61—22no—
34#16839815C2211yescharacteristic
35#16839814—21no—
36C2×C4⋊#92418C2211yescharacteristic
37C4⋊C8×D61—21no—
38#16839772—21no—
39#16839758—21no—
40#16839514C2212yes—
41#16839514C2212yes—
42#16839507C2212yes—
43#16839507C2212yes—
44C61×#532C2211yescharacteristic
45C61×#423C2211yescharacteristic
46C2×C4⋊C8×C61C2211yescharacteristic
47C61×#332C2212yes—
48C61×#331C2212yes—
49C2×#11758222D411yescharacteristic
50C22×Dic122—21no—
51#14519810—44no—
52#14519797—44no—
53C2×Dic244—22no—
54C2×#11758202—21no—
55C2×#11758190—22no—
56C2×#11758200—21no—
57C2×#11758201—21no—
58C2×#11758199—21no—
59C22×#92418—21no—
60C2×C8×D61—22no—
61#14519777—21no—
62#14519777—21no—
63#14519777—21no—
64#14519777C2312yes—
65C4×Dic122D411yescharacteristic
66C4×Dic122C2311yescharacteristic
67C4×D244D411yescharacteristic
68C4×D244C2311yescharacteristic
69C4×C22⋊D61—21no—
70C4×C22⋊D61—21no—
71#14519736D411yescharacteristic
72#14519734—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—21no—
75C42×D61—21no—
76#14519710—22no—
77#14519710—22no—
78C4⋊#92418—21no—
79C4⋊#92418D411yescharacteristic
80C4⋊#92418D411yescharacteristic
81C4⋊#92418C2311yescharacteristic
82C4⋊#92418C2311yescharacteristic
83#14519706—22no—
84#14519702—22no—
85#14519702—22no—
86#14519701—21no—
87#14519701—21no—
88#14519698—21no—
89#14519698—21no—
90#14519698—22no—
91#14519698—22no—
92C22⋊#92418D412yes—
93#14519689—22no—
94C4×#92418C2312yes—
95C8×Dic61—22no—
96C2×#41×C61—21no—
97C2×M16×C61—21no—
98C22×C8×C61—21no—
99C4⋊Q8×C61C2311yescharacteristic
100#127×C61C2311yescharacteristic
101#124×C61—21no—
102#121×C61—21no—
103#121×C61—21no—
104C4×D4×C61—21no—
105C4×D4×C61—21no—
106C2×C42×C61C2311yescharacteristic
107C4⋊C8×C61—21no—
108C4⋊C8×C61—21no—
109C4⋊C8×C61C2312yes—
110C4⋊C8×C61C2312yes—
111#41×C61—42no—
112#41×C61—42no—
113C2×Q8×C61—21no—
114C2×D4×C61—21no—
115C2×D4×C61—21no—
116C2×D4×C61—21no—
117C2×D4×C61—41no—
118C22×C4×C61—41no—
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61#4111yescharacteristic
122C2×C22⋊D61—21no—
123C22×Dic61—41no—
124#11758222—22no—
125#11758222D814yes—
126C2×D244C2×D411yescharacteristic
127C2×C4×D61—21no—
128C2×C4×D61—21no—
129C2×C4×D61—21no—
130C2×Dic122—22no—
131C2×Dic122—42no—
132C2×Dic122—42no—
133C2×Dic122—41no—
134C2×Dic122C2×D411yescharacteristic
135M16×C61—42no—
136C2×C8×C61—22no—
137C2×C8×C61—22no—
138C2×C8×C61—81no—
139C4⋊C4×C61—21no—
140C4⋊C4×C61—21no—
141C22⋊C4×C61—41no—
142C22⋊C4×C61—41no—
143C42×C61C2×D411yescharacteristic
144C42×C61C2×D411yescharacteristic
145C42×C61#4111yescharacteristic
146C42×C61C2411yescharacteristic
147C22⋊Dic61—21no—
148#11758202—42no—
149#11758201—42no—
150#11758200—42no—
151#11758199—42no—
152#11758198—21no—
153#11758198—21no—
154C4⋊Dic61—22no—
155C4⋊Dic61—22no—
156C4⋊Dic61—41no—
157C4⋊Dic61—41no—
158C4⋊Dic61C2×D411yescharacteristic
159C4⋊Dic61C2×D411yescharacteristic
160#11758196—21no—
161#11758196—21no—
162C4×Dic61—21no—
163C4×Dic61—21no—
164C4×Dic61—21no—
165C2×#92418—21no—
166C2×#92418—21no—
167C2×#92418—42no—
168C2×#92418C2×D412yes—
169C2×#92418C2×D412yes—
170Dic244—44no—
171#11758190—44no—
172C8×D61—82no—
173C23×C61—41no—
174C23×C61#12111yescharacteristic
175C22×D61—21no—
176Q8×C61—41no—
177Q8×C61—41no—
178D4×C61—41no—
179D4×C61—41no—
180D4×C61—41no—
181D4×C61—41no—
182D4×C61—81no—
183D4×C61—82no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—82no—
189C2×C4×C61#12111yescharacteristic
190C2×C4×C61#12111yescharacteristic
191C2×C4×C61#12111yescharacteristic
192C2×C4×C61C2×D812yes—
193C2×C4×C61#13512yes—
194C2×C4×C61C22×D411yescharacteristic
195C2×C4×C61C22×D411yescharacteristic
196C2×C4×C61C2×#4111yescharacteristic
197C22⋊D61—24no—
198C2×Dic61—21no—
199C2×Dic61—21no—
200C2×Dic61—21no—
201C2×Dic61—42no—
202C2×Dic61—82no—
203D244—21no—
204D244C2×D812yes—
205C4×D61—24no—
206C4×D61—41no—
207C4×D61—41no—
208C4×D61—81no—
209Dic122—21no—
210Dic122—42no—
211Dic122—42no—
212Dic122—82no—
213Dic122C2×D812yes—
214C8×C61—42no—
215C8×C61—42no—
216#92418—22no—
217#92418—22no—
218#92418—41no—
219#92418—41no—
220#19416—611nomaximal, Sylow
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—81no—
224C22×C61—81no—
225C22×C61—81no—
226C22×C61#46612yes—
227C22×C61C2×#12111yescharacteristic
228C2×D61—22no—
229C2×D61—41no—
230C2×D61—41no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—81no—
235C4×C61#46612yes—
236C4×C61C22×D811yescharacteristic
237C4×C61C2×#13511yescharacteristic
238C4×C61#57711yescharacteristic
239C4×C61#57811yescharacteristic
240Dic61—22no—
241Dic61—41no—
242Dic61—41no—
243Dic61—82no—
244#3226—611no—
245#3039—611no—
246#3035—611no—
247#2988—611no—
248#1682—612no—
249#1681—612no—
250#1674—612no—
251#1673—612no—
252#1571—611no—
253#1547D6111yescharacteristic, complemented
254C2×#332—611no—
255C2×C61—22no—
256C2×C61—161no—
257C2×C61#304611yescharacteristic
258C2×C61C2×#46611yescharacteristic
259C2×C61#306911yescharacteristic
260D61—42no—
261C2×#137—1221no—
262C2×#135—1221no—
263#532C2×D6111yescharacteristic
264C2×C4⋊Q8—611no—
265C4×#41—611no—
266#500—612no—
267#486—612no—
268#480—1222no—
269#474—1221no—
270#474—1221no—
271#464—1221no—
272#463—1221no—
273#462—611no—
274#462—612no—
275#462—1221no—
276#461—611no—
277#461—612no—
278#461—1221no—
279#460—611no—
280#459—611no—
281C8×Q8—612no—
282C8×D4—612no—
283C8×D4—1222no—
284#431—611no—
285#431—1221no—
286#423C2×D6111yescharacteristic
287C2×C4⋊C8—611no—
288C2×C4⋊C8—1221no—
289C2×C4⋊C8C2×D6111yescharacteristic
290#419—1221no—
291#416—1221no—
292#335—612no—
293#335—612no—
294#332—612no—
295#332—612no—
296#332C2×D6112yes—
297#331C2×D6112yes—
298C61#1941611yescharacteristic, complemented, Sylow
299C2×#41—21no—
300C2×#41—611no—
301C22×Q8—1221no—
302#137—2444no—
303#135—2444no—
304C2×Q16—1222no—
305C2×Q16—1221no—
306C2×SD16—1222no—
307C2×SD16—1221no—
308C2×SD16—1221no—
309C2×D8—1221no—
310C2×M16—21no—
311C22×C8—21no—
312C22×C8—1222no—
313C22×C8—1221no—
314C4⋊Q8—612no—
315C4⋊Q8—1221no—
316C4⋊Q8—1221no—
317C4⋊Q8—1221no—
318C4⋊Q8C22×D6111yescharacteristic
319#127C22×D6111yescharacteristic
320#124—21no—
321#121—21no—
322#121—21no—
323C4×Q8—611no—
324C4×Q8—611no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—611no—
328C4×D4—611no—
329C4×D4—1221no—
330C4×D4—1221no—
331#117—611no—
332#117—1221no—
333C2×C4⋊C4—1221no—
334C2×C4⋊C4—1221no—
335C2×C42—1221no—
336C2×C42C22×D6111yescharacteristic
337#107—1222no—
338#107—1222no—
339C4⋊C8—21no—
340C4⋊C8—21no—
341C4⋊C8—611no—
342C4⋊C8—611no—
343C4⋊C8—611no—
344C4⋊C8—611no—
345C4⋊C8—1222no—
346C4⋊C8—1221no—
347C4⋊C8C22×D6112yes—
348C4⋊C8C22×D6112yes—
349#103—1222no—
350#103—1222no—
351#103—1221no—
352#103—1221no—
353#102—1221no—
354#102—1221no—
355#102—1222no—
356#102—1222no—
357C22⋊C8—612no—
358C22⋊C8—1222no—
359C4×C8—612no—
360C4×C8—1222no—
361#41—42no—
362#41—42no—
363#41—614no—
364#41—1222no—
365C2×Q8—21no—
366C2×Q8—611no—
367C2×Q8—1222no—
368C2×Q8—2442no—
369C2×Q8—2442no—
370C2×Q8—2441no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—41no—
375C2×D4—611no—
376C2×D4—1221no—
377C22×C4—41no—
378C22×C4—1221no—
379C22×C4—1221no—
380C22×C4—1221no—
381C22×C4—2441no—
382C22×C4#1175822211yescharacteristic
383C22×C4D4×D6111yescharacteristic
384C22×C4D4×D6111yescharacteristic
385Q16—2444no—
386Q16—2442no—
387SD16—2444no—
388SD16—2442no—
389SD16—2442no—
390D8—2442no—
391M16—42no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—81no—
395C2×C8—612no—
396C2×C8—612no—
397C2×C8—1221no—
398C2×C8—1221no—
399C2×C8—4882no—
400C2×C8—2442no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—611no—
404C4⋊C4—611no—
405C4⋊C4—1221no—
406C4⋊C4—1221no—
407C4⋊C4—1222no—
408C4⋊C4—1222no—
409C4⋊C4—2441no—
410C4⋊C4—2441no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—1221no—
414C22⋊C4—1221no—
415C22⋊C4—1221no—
416C42—1221no—
417C42—1221no—
418C42—1221no—
419C42#1175822211yescharacteristic
420C42D4×D6111yescharacteristic
421C42D4×D6111yescharacteristic
422C42C23×D6111yescharacteristic
423C23—41no—
424C23—1221no—
425C23#1451975011yescharacteristic
426Q8—41no—
427Q8—41no—
428Q8—612no—
429Q8—1221no—
430Q8—4882no—
431Q8—2442no—
432Q8—2442no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—81no—
438D4—82no—
439D4—612no—
440D4—1224no—
441D4—1221no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—82no—
447C2×C4—1221no—
448C2×C4—1224no—
449C2×C4—1221no—
450C2×C4—1221no—
451C2×C4—4881no—
452C2×C4—4882no—
453C2×C4—2442no—
454C2×C4—2441no—
455C2×C4—2441no—
456C2×C4#1451975011yescharacteristic
457C2×C4#1451975011yescharacteristic
458C2×C4#1451975011yescharacteristic
459C2×C4D8×D6112yes—
460C2×C4#1451979812yes—
461C2×C4C2×D4×D6111yescharacteristic
462C2×C4C2×D4×D6111yescharacteristic
463C2×C4C2×#1175822211yescharacteristic
464C8—42no—
465C8—42no—
466C8—1222no—
467C8—1222no—
468C8—2441no—
469C8—2441no—
470C22—21no—
471C22—21no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—1222no—
476C22—2441no—
477C22—2441no—
478C22#1683999712yes—
479C22C2×#1451975011yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—81no—
484C4—1222no—
485C4—4882no—
486C4—2441no—
487C4—2441no—
488C4#1683999712yes—
489C4C2×D8×D6111yescharacteristic
490C4C2×#1451979811yescharacteristic
491C4#1684057211yescharacteristic
492C4#1684057811yescharacteristic
493C2—22no—
494C2—161no—
495C2—2442no—
496C2#2145536811yescharacteristic
497C2C2×#1683999711yescharacteristic
498C2#2145555911yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1547C2
socleC22×C61C2×#121
prime radical#21455268C2
hypercenter#1547D61
hypocenterC61#19416
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
1. #21456937C2semidirect
2. #21455307C2semidirect
4. #21454928C2semidirect
5. #21445262C2semidirect
6. #21445255C2semidirect
7. #21445212C2semidirect
8. #21445207C2semidirect
9. #21444595C2semidirect
10. C2×#16839507C2semidirect
11. C61×#1547C2semidirect
253. #1547D61semidirect
298. C61#19416semidirect

Maximal subgroups

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

subgroupindex
#214569372
#214553072
#214552682
#214549282
#214452622
#214452552
#214452122
#214452072
#214445952
C2×#168395072
C61×#15472
#1941661