Finite Group Databasebeta

← #29667673

Subgroups — #29667673

Order 15616.

814 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456379C211yesmaximal, characteristic, complemented
2#21456378C211yesmaximal, characteristic, complemented
3#21456374C211yesmaximal, characteristic, complemented
4#21456329C211yesmaximal, characteristic, complemented
5#21456245C211yesmaximal, characteristic
6#21445422C211yesmaximal, characteristic, complemented
7#21445419C211yesmaximal, characteristic, complemented
8#21445415C211yesmaximal, characteristic, complemented
9#21445414C211yesmaximal, characteristic, complemented
10#21445410C211yesmaximal, characteristic, complemented
11#21445409C211yesmaximal, characteristic, complemented
12#21445407C211yesmaximal, characteristic, complemented
13#21445405C211yesmaximal, characteristic, complemented
14C2×C8×#92418C211yesmaximal, characteristic, complemented
15C61×#3167C211yesmaximal, characteristic, complemented
16C2×#14519797—22no—
17#16840319C2211yescharacteristic
18#16840312C2211yescharacteristic
19#16840165C2211yescharacteristic
20#16840165C2211yescharacteristic
21#16840161—22no—
22#16840160C2211yescharacteristic
23#16840158C2211yescharacteristic
24#16840158C2211yescharacteristic
25#16840158C2211yescharacteristic
26#16840158C2211yescharacteristic
27#16840144—22no—
28#16840141C2211yescharacteristic
29#16840138C2211yescharacteristic
30#16840136C2211yescharacteristic
31#16840136C2211yescharacteristic
32#16840135C2211yescharacteristic
33#16840134C2211yescharacteristic
34#16840134C2211yescharacteristic
35#16840114C2211yescharacteristic
36#16840113C2211yescharacteristic
37#16840112C2211yescharacteristic
38#16840110C2211yescharacteristic
39#16840109C2211yescharacteristic
40#16840108C2211yescharacteristic
41#16839993—22no—
42#16839991—22no—
43#16839989—22no—
44C4×#11758190—22no—
45C4×#11758201—22no—
46C4×#11758200—22no—
47#16839798—22no—
48C2×C4×#92418C2211yescharacteristic
49C2×C4×#92418C2211yescharacteristic
50C8×#92418C2211yescharacteristic
51C8×#92418C2211yescharacteristic
52C8×#92418C2211yescharacteristic
53C8×#92418C2211yescharacteristic
54C61×#533C2211yescharacteristic
55C61×#532C2211yescharacteristic
56C61×#498C2211yescharacteristic
57C61×#492C2211yescharacteristic
58C61×#487C2211yescharacteristic
59C61×#486C2211yescharacteristic
60C61×#465—22no—
61C4×SD16×C61—22no—
62C2×C4×C8×C61C2211yescharacteristic
63C2×#11758222—21no—
64#14519797—48no—
65C2×#11758202—22no—
66C2×#11758190—22no—
67C2×#11758200—22no—
68C2×#11758200—22no—
69C2×#11758201—22no—
70C2×#11758201—22no—
71C2×#11758199—22no—
72C22×#92418D412yes—
73C22×#92418D412yes—
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519774C2311yescharacteristic
78#14519769—21no—
79#14519765—21no—
80#14519756—21no—
81#14519756—21no—
82#14519751—21no—
83#14519751—21no—
84C4×Dic122—21no—
85C4×Dic122—21no—
86C4×D244—21no—
87C4×D244—21no—
88#14519736—21no—
89#14519710—22no—
90#14519710—22no—
91#14519709—22no—
92#14519708—22no—
93#14519708—22no—
94#14519708—22no—
95#14519708—22no—
96#14519702—22no—
97#14519701—22no—
98#14519700—22no—
99#14519699—22no—
100#14519698—22no—
101#14519697—22no—
102C4×#92418D412yes—
103C4×#92418D412yes—
104C4×#92418C2311yescharacteristic
105C4×#92418C2311yescharacteristic
106C4×#92418C2311yescharacteristic
107C4×#92418C2311yescharacteristic
108C2×#41×C61—21no—
109C2×SD16×C61—22no—
110C22×C8×C61D412yes—
111C4⋊Q8×C61C2311yescharacteristic
112C4⋊Q8×C61C2311yescharacteristic
113C4⋊Q8×C61C2311yescharacteristic
114#127×C61C2311yescharacteristic
115#125×C61—21no—
116#124×C61—21no—
117C22⋊Q8×C61—21no—
118C22⋊Q8×C61—21no—
119#121×C61—21no—
120#121×C61—21no—
121C4×Q8×C61—21no—
122C4×Q8×C61—21no—
123C4×D4×C61—21no—
124C4×D4×C61—21no—
125#117×C61—21no—
126C2×C42×C61C2311yescharacteristic
127#106×C61—22no—
128#103×C61—22no—
129#102×C61—22no—
130C4×C8×C61D412yes—
131C4×C8×C61C2311yescharacteristic
132C4×C8×C61C2311yescharacteristic
133#41×C61—44no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61—41no—
141C22×C4×C61—41no—
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C2×C22⋊D61—41no—
146#11758222—44no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244—21no—
150C2×C4×D61—41no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154SD16×C61—44no—
155C2×C8×C61—24no—
156C2×C8×C61C2×D412yes—
157C2×C8×C61C2×D412yes—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—41no—
165C4⋊C4×C61—41no—
166C22⋊C4×C61—41no—
167C22⋊C4×C61—41no—
168C22⋊C4×C61—41no—
169C42×C61—41no—
170C42×C61C2×D411yescharacteristic
171C42×C61C2×D411yescharacteristic
172C42×C61C2×D411yescharacteristic
173C42×C61C2411yescharacteristic
174C22⋊Dic61—41no—
175#11758202—44no—
176#11758201—44no—
177#11758201—44no—
178#11758200—44no—
179#11758200—44no—
180#11758199—44no—
181#11758198—41no—
182#11758198—41no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189#11758196—41no—
190#11758196—41no—
191C4×Dic61—41no—
192C2×#92418—24no—
193C2×#92418SD1618yescomplemented
194C2×#92418C2×D412yes—
195C2×#92418C2×D412yes—
196C2×#92418C2×D412yes—
197C2×#92418C2×D412yes—
198#11758190—44no—
199C23×C61—41no—
200C23×C61#12711yescharacteristic
201C22×D61—41no—
202Q8×C61—42no—
203Q8×C61—42no—
204Q8×C61—42no—
205D4×C61—42no—
206D4×C61—42no—
207D4×C61—42no—
208D4×C61—82no—
209C2×C4×C61—22no—
210C2×C4×C61—22no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—82no—
215C2×C4×C61#12711yescharacteristic
216C2×C4×C61#12711yescharacteristic
217C2×C4×C61#12711yescharacteristic
218C2×C4×C61C2×SD1614yes—
219C2×C4×C61C22×D411yescharacteristic
220C2×C4×C61C22×D411yescharacteristic
221C2×C4×C61C22×D411yescharacteristic
222C22⋊D61—82no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226D244—42no—
227D244—42no—
228D244—42no—
229C4×D61—82no—
230Dic122—42no—
231Dic122—42no—
232Dic122—42no—
233C8×C61—22no—
234C8×C61#13514yescomplemented
235#92418—22no—
236#92418C2×SD1614yes—
237#92418C2×SD1614yes—
238#92418#13514yescomplemented
239#19596—611nomaximal, Sylow
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—81no—
243C22×C61—81no—
244C22×C61—81no—
245C22×C61#49212yes—
246C22×C61C2×#12711yescharacteristic
247C2×D61—81no—
248C2×D61—81no—
249C2×D61—81no—
250C4×C61—21no—
251C4×C61—21no—
252C4×C61—81no—
253C4×C61—81no—
254C4×C61—81no—
255C4×C61#49212yes—
256C4×C61C22×SD1612yes—
257C4×C61C2×#13512yes—
258C4×C61C2×#13512yes—
259Dic61—81no—
260Dic61—81no—
261Dic61—81no—
262#3167—611no—
263#3167—611no—
264#3167—611no—
265#3167D6111yescharacteristic, complemented
266#3160—611no—
267#3147—611no—
268#1708—611no—
269#1708—611no—
270#1707—611no—
271#1707—611no—
272#1706—611no—
273#1706—611no—
274#1705—611no—
275#1705—611no—
276C2×C82—611no—
277C2×C61—22no—
278C2×C61—161no—
279C2×C61C2×#49211yescharacteristic
280C2×C61#314711yescharacteristic
281C2×C61#314711yescharacteristic
282D61—161no—
283C2×#135—1222no—
284#533—611no—
285#533C2×D6111yescharacteristic
286#532—611no—
287#532C2×D6111yescharacteristic
288#500—611no—
289#500—611no—
290#499—1222no—
291#498—611no—
292#498—611no—
293#498—611no—
294#498—611no—
295#498—611no—
296#498C2×D6111yescharacteristic
297#495—1222no—
298#494—611no—
299#493—611no—
300#492—611no—
301#492—611no—
302#492—611no—
303#492—611no—
304#492—611no—
305#492C2×D6111yescharacteristic
306#487—611no—
307#487—611no—
308#487—611no—
309#487C2×D6111yescharacteristic
310#486—611no—
311#486—611no—
312#486—611no—
313#486C2×D6111yescharacteristic
314#465—22no—
315#465—1222no—
316#465—1222no—
317#465—1222no—
318C4×SD16—22no—
319C4×SD16—1222no—
320C4×SD16—1222no—
321C4×SD16—1222no—
322#427—1222no—
323C2×C4×C8—611no—
324C2×C4×C8—611no—
325C2×C4×C8C2×D6111yescharacteristic
326C82—611no—
327C82—611no—
328C82—611no—
329C82—611no—
330C61#1959611yescharacteristic, complemented, Sylow
331C2×#41—21no—
332C2×#41—1221no—
333#135—2448no—
334C2×Q16—1222no—
335C2×SD16—22no—
336C2×SD16—1222no—
337C2×SD16—1222no—
338C2×SD16—1222no—
339C2×SD16—1222no—
340C2×SD16—1222no—
341C2×D8—1222no—
342C22×C8—612no—
343C22×C8—612no—
344C22×C8C22⋊D6112yes—
345C4⋊Q8—611no—
346C4⋊Q8—611no—
347C4⋊Q8—611no—
348C4⋊Q8C22×D6111yescharacteristic
349C4⋊Q8C22×D6111yescharacteristic
350C4⋊Q8C22×D6111yescharacteristic
351#127—611no—
352#127C22×D6111yescharacteristic
353#125—21no—
354#125—1221no—
355#124—21no—
356#124—1221no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—1221no—
360C22⋊Q8—1221no—
361#121—21no—
362#121—21no—
363#121—1221no—
364#121—1221no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—1221no—
368C4×Q8—1221no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—1221no—
372C4×D4—1221no—
373#117—21no—
374#117—1221no—
375C2×C42C22×D6111yescharacteristic
376#107—1222no—
377#107—1222no—
378#106—22no—
379#106—1222no—
380#106—1222no—
381#106—1222no—
382#106—1222no—
383#106—1222no—
384#103—22no—
385#103—1222no—
386#103—1222no—
387#103—1222no—
388#102—22no—
389#102—1222no—
390#102—1222no—
391#102—1222no—
392C4×C8—612no—
393C4×C8—612no—
394C4×C8—611no—
395C4×C8—611no—
396C4×C8—611no—
397C4×C8—611no—
398C4×C8C22⋊D6112yes—
399C4×C8C22×D6111yescharacteristic
400C4×C8C22×D6111yescharacteristic
401#41—44no—
402#41—2444no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—1221no—
407C2×Q8—1221no—
408C2×Q8—1221no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—41no—
413C2×D4—1221no—
414C2×D4—1221no—
415C2×D4—1221no—
416C2×D4—2441no—
417C22×C4—41no—
418C22×C4—2441no—
419C22×C4D4×D6111yescharacteristic
420C22×C4D4×D6111yescharacteristic
421C22×C4C2×C22⋊D6111yescharacteristic
422Q16—2444no—
423SD16—44no—
424SD16—2444no—
425SD16—2444no—
426SD16—2444no—
427SD16—2444no—
428SD16—2444no—
429D8—2444no—
430C2×C8—24no—
431C2×C8—612no—
432C2×C8—612no—
433C2×C8—612no—
434C2×C8—618no—
435C2×C8—612no—
436C2×C8—1224no—
437C2×C8C2×C22⋊D6112yes—
438C2×C8C2×C22⋊D6112yes—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4—1221no—
448C4⋊C4—1221no—
449C4⋊C4—1221no—
450C4⋊C4—1221no—
451C4⋊C4—1221no—
452C4⋊C4—1221no—
453C4⋊C4—2441no—
454C4⋊C4—2441no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—2441no—
459C22⋊C4—2441no—
460C22⋊C4—2441no—
461C42—41no—
462C42—2441no—
463C42D4×D6111yescharacteristic
464C42D4×D6111yescharacteristic
465C42C2×C22⋊D6111yescharacteristic
466C42C23×D6111yescharacteristic
467C23—41no—
468C23—2441no—
469C23#1451977311yescharacteristic
470Q8—42no—
471Q8—42no—
472Q8—42no—
473Q8—2442no—
474Q8—2442no—
475Q8—2442no—
476D4—42no—
477D4—42no—
478D4—42no—
479D4—82no—
480D4—4882no—
481D4—2442no—
482D4—2442no—
483D4—2442no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—82no—
490C2×C4—4882no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4#1451977311yescharacteristic
495C2×C4#1451977311yescharacteristic
496C2×C4#1451977311yescharacteristic
497C2×C4SD16×D6114yes—
498C2×C4C2×D4×D6111yescharacteristic
499C2×C4C2×D4×D6111yescharacteristic
500C2×C4C22×C22⋊D6111yescharacteristic
501C8—22no—
502C8—614no—
503C8—614no—
504C8—614no—
505C8—1222no—
506C8#1451979714yescomplemented
507C22—21no—
508C22—21no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—4881no—
513C22—4881no—
514C22—4881no—
515C22#1684013312yes—
516C22C2×#1451977311yescharacteristic
517C4—21no—
518C4—21no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—4881no—
523C4—4881no—
524C4—4881no—
525C4#1684013312yes—
526C4C2×SD16×D6112yes—
527C4#135×D6112yes—
528C4C2×#1451979712yes—
529C2—22no—
530C2—161no—
531C2—9761no—
532C2C2×#1684013311yescharacteristic
533C2#2145624311yescharacteristic
534C2#2145624511yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3167C2
socleC22×C61C2×#127
prime radical#21456245C2
hypercenter#3167D61
hypocenterC61#19596
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #21456379C2semidirect
2. #21456378C2semidirect
3. #21456374C2semidirect
4. #21456329C2semidirect
6. #21445422C2semidirect
7. #21445419C2semidirect
8. #21445415C2semidirect
9. #21445414C2semidirect
10. #21445410C2semidirect
11. #21445409C2semidirect
12. #21445407C2semidirect
13. #21445405C2semidirect
14. C2×C8×#92418C2semidirect
15. C61×#3167C2semidirect
193. C2×#92418SD16semidirect
234. C8×C61#135semidirect
238. #92418#135semidirect
265. #3167D61semidirect
330. C61#19596semidirect
506. C8#14519797semidirect

Maximal subgroups

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

subgroupindex
#214563792
#214563782
#214563742
#214563292
#214562452
#214454222
#214454192
#214454152
#214454142
#214454102
#214454092
#214454072
#214454052
C2×C8×#924182
C61×#31672
#1959661