Finite Group Databasebeta

← #29721318

Subgroups — #29721318

Order 15616.

912 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840039C211yesmaximal, characteristic, complemented
2C2×#16839819C211yesmaximal, characteristic, complemented
3C4×#14519751C211yesmaximal, characteristic
4#21447250C212yesmaximal, complemented
5#21447008C212yesmaximal
6#21446772C211yesmaximal, characteristic, complemented
7#21446580C211yesmaximal, characteristic, complemented
8#21446559C212yesmaximal, complemented
9#21446515C212yesmaximal, complemented
10#21445816C211yesmaximal, characteristic, complemented
11C61×#2857C211yesmaximal, characteristic, complemented
12C2×#14519751C2211yescharacteristic
13C2×C4×D244C2211yescharacteristic
14C2×C4×C22⋊D61—21no—
15#16840039—24no—
16#16839819—24no—
17C2×#14519710C2212yes—
18C2×#14519708C2212yes—
19C2×C4⋊#92418C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519697C2212yes—
22C2×#14519697C2212yes—
23C2×C22⋊#92418C2212yes—
24C2×#14519688C2212yes—
25#16839664C2211yescharacteristic
26#16839660C2211yescharacteristic
27#16839653—21no—
28#16839641—21no—
29#16839622C2211yescharacteristic
30C4×C4⋊Dic61C2211yescharacteristic
31C4×#11758198—21no—
32#16839524C2212yes—
33#16839524C2212yes—
34#16839524C2212yes—
35#16839524C2212yes—
36C2×C4⋊Q8×C61C2211yescharacteristic
37C2×C22⋊Q8×C61—21no—
38C22×C42×C61C2211yescharacteristic
39C61×#391—21no—
40C61×#389—21no—
41C61×#389C2212yes—
42C61×#384C2211yescharacteristic
43C61×#380—21no—
44C61×#380C2212yes—
45C22×D244C2311yescharacteristic
46C22×C22⋊D61—21no—
47C22×C4×D61—21no—
48C22×#92418C2312yes—
49C22×#92418C2312yes—
50#14519751—22no—
51#14519751—22no—
52C4×D244—22no—
53C4×D244—22no—
54C4×C22⋊D61—44no—
55C2×C4⋊Dic61C2311yescharacteristic
56C2×C4⋊Dic61C2311yescharacteristic
57C2×C4⋊Dic61C2311yescharacteristic
58C2×#11758196—21no—
59C2×C22⋊Dic61—21no—
60C2×#11758198—21no—
61C2×#11758198—21no—
62C2×#11758198—21no—
63C2×#11758198—21no—
64C2×C4×Dic61—21no—
65#14519710—24no—
66#14519708—24no—
67C4⋊#92418—22no—
68C4⋊#92418D414yescomplemented
69#14519697—24no—
70#14519697—24no—
71C22⋊#92418—24no—
72#14519688—24no—
73#14519684—21no—
74#14519684—21no—
75#14519684—21no—
76C22×Q8×C61—21no—
77C23×C4×C61D411yescharacteristic
78C23×C4×C61D411yescharacteristic
79C23×C4×C61C2311yescharacteristic
80C4⋊Q8×C61—22no—
81C4⋊Q8×C61—22no—
82C22⋊Q8×C61—44no—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—22no—
87C2×C4⋊C4×C61C2312yes—
88C2×C4⋊C4×C61C2312yes—
89C2×C22⋊C4×C61—22no—
90C2×C42×C61—22no—
91C2×C42×C61—22no—
92C2×C42×C61D411yescharacteristic
93C2×C42×C61D411yescharacteristic
94C2×C42×C61C2311yescharacteristic
95C2×C42×C61C2311yescharacteristic
96#95×C61—22no—
97#95×C61—22no—
98C24×C61C2×D411yescharacteristic
99C23×D61—21no—
100C2×Q8×C61—42no—
101C2×Q8×C61—42no—
102C2×Q8×C61—42no—
103C22×C4×C61—22no—
104C22×C4×C61—22no—
105C22×C4×C61—22no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—41no—
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2411yescharacteristic
123C2×C22⋊D61—24no—
124C2×C22⋊D61—42no—
125C2×C22⋊D61—42no—
126C22×Dic61—21no—
127C22×Dic61—21no—
128C22×Dic61—21no—
129C2×D244—21no—
130C2×D244—21no—
131C2×D244—21no—
132C2×D244—21no—
133C2×D244—21no—
134C2×D244#4112yes—
135C2×C4×D61—42no—
136C2×C4×D61—42no—
137C2×C4×D61—42no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—22no—
140C4⋊C4×C61—22no—
141C4⋊C4×C61—22no—
142C4⋊C4×C61—42no—
143C4⋊C4×C61—44no—
144C4⋊C4×C61—42no—
145C4⋊C4×C61—42no—
146C22⋊C4×C61—44no—
147C42×C61—22no—
148C42×C61—22no—
149C42×C61—21no—
150C42×C61—21no—
151C42×C61C2×D412yes—
152C42×C61#4112yes—
153C22⋊Dic61—42no—
154#11758198—24no—
155#11758198—42no—
156#11758198—42no—
157#11758198—42no—
158C4⋊Dic61—21no—
159C4⋊Dic61—21no—
160C4⋊Dic61—21no—
161C4⋊Dic61—21no—
162C4⋊Dic61—21no—
163C4⋊Dic61#4112yes—
164#11758196—42no—
165C4×Dic61—42no—
166C2×#92418—22no—
167C2×#92418—22no—
168C2×#92418—22no—
169C2×#92418—22no—
170C2×#92418—22no—
171C2×#92418C2×D414yes—
172C23×C61—21no—
173C23×C61—21no—
174C23×C61—21no—
175C23×C61—21no—
176C23×C61—21no—
177C23×C61—21no—
178C23×C61#13712yes—
179C23×C61C22×D411yescharacteristic
180C22×D61—22no—
181C22×D61—41no—
182C22×D61—41no—
183C22×D61—41no—
184C22×D61—41no—
185C22×D61—41no—
186C22×D61—41no—
187Q8×C61—84no—
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—21no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—21no—
199C2×C4×C61—44no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—44no—
205C2×C4×C61—42no—
206C2×C4×C61—42no—
207C2×C4×C61—42no—
208C2×C4×C61—42no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61#12112yes—
212C2×C4×C61#12112yes—
213C2×C4×C61AGL(1,ℤ/8)12yes—
214C2×C4×C61AGL(1,ℤ/8)12yes—
215C2×C4×C61C22×D411yescharacteristic
216C2×C4×C61C2×#4111yescharacteristic
217C2×C4×C61C2×#4111yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C2×C4×C612−1+411yescharacteristic
220C2×C4×C612−1+411yescharacteristic
221C22⋊D61—48no—
222C2×Dic61—22no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61—41no—
227C2×Dic61—41no—
228C2×Dic61—41no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231D244—22no—
232D244—22no—
233D244—41no—
234D244—41no—
235C4×D61—84no—
236#92418—24no—
237#92418—42no—
238#24709—611nomaximal, Sylow
239C22×C61—22no—
240C22×C61—22no—
241C22×C61—22no—
242C22×C61—41no—
243C22×C61—41no—
244C22×C61—41no—
245C22×C61—41no—
246C22×C61C2×#12111yescharacteristic
247C22×C61#52511yescharacteristic
248C22×C61#53611yescharacteristic
249C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
250C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
251C22×C61C2×#13711yescharacteristic
252C22×C61#57511yescharacteristic
253C2×D61—42no—
254C2×D61—42no—
255C2×D61—42no—
256C2×D61—81no—
257C2×D61—81no—
258C2×D61—81no—
259C2×D61—81no—
260C4×C61—22no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61—41no—
264C4×C61—82no—
265C4×C61—82no—
266C4×C61#46914yes—
267C4×C61#54711yescharacteristic
268C4×C61#54811yescharacteristic
269C4×C61#55211yescharacteristic
270C4×C61#55611yescharacteristic
271Dic61—42no—
272Dic61—81no—
273Dic61—81no—
274C2×#474—611no—
275C2×#432—611no—
276#2857D6111yescharacteristic, complemented
277C4×#121—611no—
278#2076—612no—
279#2034—612no—
280#1988—611no—
281#1948—611no—
282#1944—612no—
283#1936—612no—
284#1802—611no—
285C2×C61—42no—
286C2×C61#241511yescharacteristic
287C2×C61C2×#46911yescharacteristic
288C2×C61#305611yescharacteristic
289C2×C61#311011yescharacteristic
290C2×C61#311511yescharacteristic
291C2×C61#323511yescharacteristic
292C2×C61#323911yescharacteristic
293D61—82no—
294C2×C4⋊Q8C2×D6111yescharacteristic
295C2×C22⋊Q8—21no—
296C2×#121—611no—
297C2×C4×D4—611no—
298C2×C4×D4—1221no—
299C22×C42C2×D6111yescharacteristic
300#474—1224no—
301#432—1224no—
302C2×#107—612no—
303C2×#106—612no—
304C2×C4⋊C8—611no—
305C2×C4⋊C8—611no—
306C2×#102—612no—
307C2×#102—612no—
308C2×C22⋊C8—612no—
309C2×#97—612no—
310#391—21no—
311#390—611no—
312#389—21no—
313#389—611no—
314#389C2×D6112yes—
315#388—1221no—
316#386—1221no—
317#384C2×D6111yescharacteristic
318#380—21no—
319#380—611no—
320#380C2×D6112yes—
321C4×C4⋊C4—611no—
322C4×C22⋊C4—1221no—
323#340—612no—
324#340—612no—
325#340—612no—
326#340—612no—
327C61#2470911yescharacteristic, complemented, Sylow
328C22×Q8—21no—
329C22×D4—611no—
330C22×D4—1221no—
331C23×C4—1221no—
332C23×C4C22⋊D6111yescharacteristic
333C23×C4C22⋊D6111yescharacteristic
334C23×C4C22×D6111yescharacteristic
335C22×C8—612no—
336C22×C8—612no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C22⋊Q8—44no—
340#121—1222no—
341#121—1222no—
342C4×D4—1222no—
343C4×D4—1222no—
344C4×D4—2444no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—611no—
350C2×C4⋊C4—611no—
351C2×C4⋊C4—611no—
352C2×C4⋊C4—1221no—
353C2×C4⋊C4C22×D6112yes—
354C2×C4⋊C4C22×D6112yes—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—1221no—
357C2×C22⋊C4—1221no—
358C2×C22⋊C4—1221no—
359C2×C22⋊C4—1221no—
360C2×C22⋊C4—1221no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—1221no—
364C2×C42C22⋊D6111yescharacteristic
365C2×C42C22⋊D6111yescharacteristic
366C2×C42C22×D6111yescharacteristic
367C2×C42C22×D6111yescharacteristic
368#107—1224no—
369#106—1224no—
370C4⋊C8—614no—
371C4⋊C8—1222no—
372#102—1224no—
373#102—1224no—
374C22⋊C8—1224no—
375#97—1224no—
376#95—22no—
377#95—22no—
378#95—1221no—
379#95—1221no—
380#95—1221no—
381C24—1221no—
382C24C2×C22⋊D6111yescharacteristic
383C2×Q8—42no—
384C2×Q8—42no—
385C2×Q8—42no—
386C2×D4—612no—
387C2×D4—1224no—
388C2×D4—1221no—
389C2×D4—1221no—
390C2×D4—1221no—
391C2×D4—1221no—
392C2×D4—1221no—
393C2×D4—2442no—
394C2×D4—2442no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—41no—
409C22×C4—1221no—
410C22×C4—1221no—
411C22×C4—1221no—
412C22×C4—2442no—
413C22×C4—2442no—
414C22×C4—2442no—
415C22×C4C2×C22⋊D6111yescharacteristic
416C22×C4C2×C22⋊D6111yescharacteristic
417C22×C4C2×C22⋊D6111yescharacteristic
418C22×C4C2×C22⋊D6111yescharacteristic
419C22×C4C2×C22⋊D6111yescharacteristic
420C22×C4C23×D6111yescharacteristic
421C2×C8—614no—
422C2×C8—1222no—
423C2×C8—1222no—
424C2×C8—1222no—
425C2×C8—1222no—
426C2×C8—1222no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—44no—
432C4⋊C4—42no—
433C4⋊C4—42no—
434C4⋊C4—42no—
435C4⋊C4—612no—
436C4⋊C4—1221no—
437C4⋊C4—1221no—
438C4⋊C4—1221no—
439C4⋊C4—1221no—
440C4⋊C4—1221no—
441C4⋊C4—2442no—
442C22⋊C4—44no—
443C22⋊C4—1224no—
444C22⋊C4—2442no—
445C22⋊C4—2442no—
446C22⋊C4—2442no—
447C22⋊C4—2442no—
448C42—21no—
449C42—21no—
450C42—22no—
451C42—22no—
452C42—2442no—
453C42D4×D6112yes—
454C42#1175822412yes—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—1222no—
462C23—2441no—
463C23—2441no—
464C23—2441no—
465C23—2441no—
466C23—2441no—
467C23—2441no—
468C23#1451980812yes—
469C23C22×C22⋊D6111yescharacteristic
470Q8—84no—
471D4—1222no—
472D4—1222no—
473D4—2448no—
474D4—2441no—
475D4—2441no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—44no—
488C2×C4—41no—
489C2×C4—44no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—1222no—
500C2×C4—4884no—
501C2×C4—2441no—
502C2×C4—2441no—
503C2×C4—2441no—
504C2×C4—2441no—
505C2×C4—2441no—
506C2×C4—2441no—
507C2×C4—2441no—
508C2×C4—2441no—
509C2×C4#1451974912yes—
510C2×C4#1451974912yes—
511C2×C4#1451980212yes—
512C2×C4#1451980312yes—
513C2×C4C2×D4×D6111yescharacteristic
514C2×C4#41×D6111yescharacteristic
515C2×C4#41×D6111yescharacteristic
516C2×C4C2×#1175822411yescharacteristic
517C2×C4#1451982511yescharacteristic
518C2×C4#1451982511yescharacteristic
519C8—1224no—
520C8—2442no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—4881no—
529C22—4881no—
530C22—4881no—
531C22—4881no—
532C22—2442no—
533C22—2442no—
534C22—2442no—
535C22C2×#1451974911yescharacteristic
536C22#1684026911yescharacteristic
537C22#1684033611yescharacteristic
538C22C2×#1451980211yescharacteristic
539C22C2×#1451980311yescharacteristic
540C22C2×#1451980811yescharacteristic
541C22#1684056011yescharacteristic
542C4—22no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—82no—
547C4—82no—
548C4—4881no—
549C4—4881no—
550C4—2442no—
551C4#1684001314yes—
552C4#1684041411yescharacteristic
553C4#1684042211yescharacteristic
554C4#1684044611yescharacteristic
555C4#1684048311yescharacteristic
556C2—42no—
557C2—4882no—
558C2#2144924911yescharacteristic
559C2C2×#1684001311yescharacteristic
560C2#2145544511yescharacteristic
561C2#2145591411yescharacteristic
562C2#2145596411yescharacteristic
563C2#2145701711yescharacteristic
564C2#2145704911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2857C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#2857D61
hypocenterC61#24709
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
1. C2×#16840039C2semidirect
2. C2×#16839819C2semidirect
4. #21447250C2semidirect
6. #21446772C2semidirect
7. #21446580C2semidirect
8. #21446559C2semidirect
9. #21446515C2semidirect
10. #21445816C2semidirect
11. C61×#2857C2semidirect
68. C4⋊#92418D4semidirect
276. #2857D61semidirect
327. C61#24709semidirect

Maximal subgroups

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

subgroupindex
C2×#168400392
C2×#168398192
C4×#145197512
#214472502
#214470082
#214467722
#214465802
#214465592
#214465152
#214458162
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