Finite Group Databasebeta

← #29571436

Subgroups — #29571436

Order 15616.

1006 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840241C211yesmaximal, characteristic
2#21444215C211yesmaximal, characteristic, complemented
3#21444213C211yesmaximal, characteristic, complemented
4#21444210C211yesmaximal, characteristic, complemented
5#21444131C211yesmaximal, characteristic, complemented
6#21444131C211yesmaximal, characteristic, complemented
7C61×#1478C211yesmaximal, characteristic, complemented
8C22×#11758224C411yescharacteristic
9#16840241—22no—
10#16840241—22no—
11#16840241—22no—
12#16840241—22no—
13C2×C4×Dic122C2211yescharacteristic
14C2×#14519742C411yescharacteristic
15C2×D4×Dic61C411yescharacteristic
16C2×C4×C22⋊D61—21no—
17C2×#14519737—21no—
18C2×#14519734C2211yescharacteristic
19C2×#14519733—21no—
20C22×#11758196—21no—
21C2×C4⋊C4×D61C411yescharacteristic
22#16839815C2211yescharacteristic
23#16839815C2211yescharacteristic
24#16839494—22no—
25#16839492—22no—
26D4⋊#92418—22no—
27#16839487—21no—
28#16839487—21no—
29#16839485—21no—
30#16839485—21no—
31C2×C4×D4×C61C2211yescharacteristic
32C61×#431C2211yescharacteristic
33C61×#431C2211yescharacteristic
34C61×D4⋊C8—22no—
35C2×#11758224—22no—
36C2×#11758224—22no—
37C2×#11758224—22no—
38C2×#11758224—22no—
39C2×#11758224—22no—
40C2×#11758224C814yescomplemented
41C22×Dic122C2×C411yescharacteristic
42C22×C22⋊D61—21no—
43C23×Dic61—21no—
44C23×Dic61—21no—
45C22×C4×D61—21no—
46C22×C4×D61C2×C411yescharacteristic
47C4×Dic122—21no—
48C4×Dic122—21no—
49C4×Dic122D412yes—
50C4×Dic122D412yes—
51#14519742—22no—
52#14519742—22no—
53D4×Dic61—22no—
54D4×Dic61—22no—
55C4×C22⋊D61—24no—
56C4×C22⋊D61—24no—
57#14519737—24no—
58#14519737—24no—
59#14519734—21no—
60#14519734—21no—
61#14519734—21no—
62#14519734—21no—
63#14519733—24no—
64#14519733—24no—
65C2×C4⋊Dic61C2×C411yescharacteristic
66C2×#11758196—24no—
67C2×#11758196—24no—
68C2×#11758196—21no—
69C2×#11758196—21no—
70C2×#11758196—21no—
71C2×#11758196D411yescharacteristic
72C2×#11758196D411yescharacteristic
73C4⋊C4×D61—22no—
74C4⋊C4×D61—22no—
75C2×C22⋊Dic61—21no—
76C2×#11758198D411yescharacteristic
77C2×#11758198D411yescharacteristic
78C2×C4×Dic61—21no—
79C2×C4×Dic61—21no—
80C2×C4×Dic61C2×C411yescharacteristic
81C4⋊#92418—21no—
82C4⋊#92418—21no—
83C22⋊#92418—21no—
84C22⋊#92418—21no—
85C4×#92418—21no—
86C4×#92418—21no—
87C22×D4×C61C2×C411yescharacteristic
88C23×C4×C61—21no—
89C4×D4×C61—21no—
90C4×D4×C61—21no—
91C4×D4×C61D412yes—
92C4×D4×C61D412yes—
93C2×C4⋊C4×C61C2×C411yescharacteristic
94C2×C22⋊C4×C61—21no—
95C2×C42×C61C2311yescharacteristic
96C4⋊C8×C61—21no—
97C4⋊C8×C61—21no—
98C22⋊C8×C61—21no—
99C22⋊C8×C61—21no—
100C4×C8×C61—21no—
101C4×C8×C61—21no—
102C24×C61—21no—
103C23×D61C22⋊C411yescharacteristic
104C2×D4×C61—21no—
105C2×D4×C61—21no—
106C2×D4×C61—21no—
107C2×D4×C61C22⋊C412yes—
108C2×D4×C61C2×C812yes—
109C2×D4×C61M1612yes—
110C22×C4×C61—21no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—82no—
114C22×C4×C61C22×C411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C2×C22⋊D61—24no—
118C2×C22⋊D61—24no—
119C2×C22⋊D61—24no—
120C22×Dic61—24no—
121C22×Dic61—24no—
122C22×Dic61—21no—
123C22×Dic61—24no—
124C22×Dic61—21no—
125C22×Dic61—24no—
126C22×Dic61—82no—
127C22×Dic61C22⋊C411yescharacteristic
128C22×Dic61C22⋊C411yescharacteristic
129C22×Dic61C22⋊C411yescharacteristic
130#11758224—28no—
131#11758224—28no—
132#11758224—28no—
133#11758224—28no—
134C2×C4×D61—21no—
135C2×C4×D61—21no—
136C2×C4×D61—21no—
137C2×C4×D61—21no—
138C2×C4×D61—24no—
139C2×C4×D61—82no—
140C2×C4×D61C2×C812yes—
141C2×C4×D61M1612yes—
142C2×Dic122—21no—
143C2×Dic122—21no—
144C2×Dic122—21no—
145C2×Dic122C22⋊C412yes—
146C2×Dic122C2×C812yes—
147C2×Dic122M1612yes—
148C2×C8×C61—41no—
149C2×C8×C61—41no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61C22⋊C412yes—
152C22⋊C4×C61—22no—
153C22⋊C4×C61—22no—
154C42×C61C2×D411yescharacteristic
155C42×C61C2×D411yescharacteristic
156C42×C61C2×D411yescharacteristic
157C42×C61C2×D411yescharacteristic
158C22⋊Dic61—24no—
159#11758198—21no—
160#11758198—21no—
161#11758198—21no—
162#11758198—21no—
163C4⋊Dic61—21no—
164C4⋊Dic61C22⋊C412yes—
165#11758196—24no—
166#11758196—24no—
167#11758196—21no—
168#11758196—21no—
169#11758196—22no—
170#11758196—22no—
171#11758196—21no—
172#11758196—21no—
173C4×Dic61—24no—
174C4×Dic61—21no—
175C4×Dic61—21no—
176C4×Dic61—22no—
177C4×Dic61—22no—
178C2×#92418—41no—
179C2×#92418—41no—
180C23×C61—22no—
181C23×C61—22no—
182C23×C61—22no—
183C23×C61—42no—
184C23×C61—42no—
185C23×C61C2×C22⋊C411yescharacteristic
186C22×D61—21no—
187C22×D61—21no—
188C22×D61—41no—
189C22×D61—41no—
190C22×D61C22⋊C812yes—
191D4×C61—22no—
192D4×C61—22no—
193D4×C61—22no—
194D4×C61C22⋊C814yes—
195C2×C4×C61—22no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—42no—
199C2×C4×C61—82no—
200C2×C4×C61—82no—
201C2×C4×C61C2×C22⋊C411yescharacteristic
202C2×C4×C61C2×C22⋊C411yescharacteristic
203C2×C4×C61#12011yescharacteristic
204C2×C4×C61#12011yescharacteristic
205C2×C4×C61#12011yescharacteristic
206C2×C4×C61#12011yescharacteristic
207C2×C4×C61C22×C811yescharacteristic
208C2×C4×C61C2×M1611yescharacteristic
209C2×C4×C61C2×M1611yescharacteristic
210C2×C4×C61C2×M1611yescharacteristic
211C22⋊D61—216no—
212C2×Dic61—216no—
213C2×Dic61—22no—
214C2×Dic61—21no—
215C2×Dic61—22no—
216C2×Dic61—22no—
217C2×Dic61—21no—
218C2×Dic61—21no—
219C2×Dic61—21no—
220C2×Dic61—22no—
221C2×Dic61—42no—
222C2×Dic61—41no—
223C2×Dic61—41no—
224C2×Dic61—84no—
225C2×Dic61C22⋊C812yes—
226C4×D61—22no—
227C4×D61—22no—
228C4×D61—22no—
229C4×D61—22no—
230C4×D61—84no—
231Dic122—22no—
232Dic122—22no—
233Dic122—22no—
234Dic122C22⋊C814yes—
235C8×C61—81no—
236C8×C61—81no—
237#92418—81no—
238#92418—81no—
239#8324—611nomaximal, Sylow
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—24no—
243C22×C61—44no—
244C22×C61—44no—
245C22×C61—42no—
246C22×C61—42no—
247C22×C61#37911yescharacteristic
248C22×C61C2×C22⋊C811yescharacteristic
249C22×C61#40711yescharacteristic
250C2×D61—22no—
251C2×D61—42no—
252C2×D61—41no—
253C2×D61—41no—
254C2×D61—42no—
255C4×C61—21no—
256C4×C61—21no—
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—42no—
260C4×C61C2×C22⋊C811yescharacteristic
261C4×C61C2×C22⋊C811yescharacteristic
262C4×C61#40711yescharacteristic
263C4×C61#40711yescharacteristic
264Dic61—24no—
265Dic61—22no—
266Dic61—42no—
267Dic61—41no—
268Dic61—41no—
269C2×#520—611no—
270#1479—611no—
271#1479—611no—
272#1478—611no—
273#1478D6111yescharacteristic, complemented
274#1458—611no—
275#1458—611no—
276C2×C61—21no—
277C2×C61—21no—
278C2×C61—44no—
279C2×C61#177911yescharacteristic
280C2×C61#179511yescharacteristic
281C2×C61#179611yescharacteristic
282D61—42no—
283C22×#41—611no—
284#520—1222no—
285#520—1222no—
286#520—1222no—
287#520—1222no—
288C2×C4×Q8—611no—
289C2×C4×Q8—611no—
290C2×C4×D4—611no—
291C2×C4×D4—1221no—
292C2×C4×D4—1221no—
293C2×C4×D4C2×D6111yescharacteristic
294C2×#117—611no—
295C2×#117—1221no—
296C22×C4⋊C4—611no—
297C22×C4⋊C4—1221no—
298#431—611no—
299#431—611no—
300#431C2×D6111yescharacteristic
301#431C2×D6111yescharacteristic
302Q8⋊C8—1222no—
303Q8⋊C8—1222no—
304D4⋊C8—22no—
305D4⋊C8—1222no—
306#324—1221no—
307#324—1221no—
308#323—1221no—
309#323—1221no—
310C61#832411yescharacteristic, complemented, Sylow
311C2×#41—614no—
312C2×#41—1222no—
313C2×#41—1222no—
314C2×#41—1222no—
315C2×#41—1222no—
316C2×#41—1222no—
317C22×Q8—611no—
318C22×D4—1221no—
319C22×D4C4×D6111yescharacteristic
320C23×C4—21no—
321C23×C4—611no—
322C23×C4—1221no—
323C23×C4—1221no—
324C23×C4—1221no—
325C4×Q8—612no—
326C4×Q8—612no—
327C4×Q8—1222no—
328C4×Q8—1222no—
329C4×Q8—1221no—
330C4×Q8—1221no—
331C4×D4—21no—
332C4×D4—21no—
333C4×D4—1224no—
334C4×D4—1224no—
335C4×D4—1222no—
336C4×D4—1224no—
337C4×D4—1224no—
338C4×D4—1222no—
339C4×D4D24412yes—
340C4×D4C22⋊D6112yes—
341#117—1224no—
342#117—1224no—
343#117—1221no—
344#117—1221no—
345#117—1221no—
346#117—1221no—
347C2×C4⋊C4—611no—
348C2×C4⋊C4—611no—
349C2×C4⋊C4—611no—
350C2×C4⋊C4—1222no—
351C2×C4⋊C4—1221no—
352C2×C4⋊C4—1221no—
353C2×C4⋊C4—1224no—
354C2×C4⋊C4—1224no—
355C2×C4⋊C4—1221no—
356C2×C4⋊C4—1222no—
357C2×C4⋊C4C4×D6111yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—611no—
360C2×C22⋊C4—611no—
361C2×C22⋊C4—1221no—
362C2×C42—611no—
363C2×C42—1221no—
364C2×C42—1221no—
365C2×C42C22×D6111yescharacteristic
366C4⋊C8—21no—
367C4⋊C8—21no—
368C4⋊C8—1221no—
369C4⋊C8—1221no—
370C22⋊C8—21no—
371C22⋊C8—21no—
372C22⋊C8—1221no—
373C22⋊C8—1221no—
374C4×C8—21no—
375C4×C8—21no—
376C4×C8—1221no—
377C4×C8—1221no—
378C24—21no—
379C24—611no—
380#41—1228no—
381#41—1228no—
382#41—1228no—
383#41—1228no—
384C2×Q8—612no—
385C2×Q8—612no—
386C2×Q8—612no—
387C2×Q8—1221no—
388C2×Q8—1221no—
389C2×Q8—1221no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—1224no—
394C2×D4—1224no—
395C2×D4—1224no—
396C2×D4C8×D6112yes—
397C2×D4#1175818912yes—
398C2×D4#1175819812yes—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—82no—
403C22×C4—611no—
404C22×C4—612no—
405C22×C4—612no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—1224no—
409C22×C4—1224no—
410C22×C4—1224no—
411C22×C4—1224no—
412C22×C4—1221no—
413C22×C4—1221no—
414C22×C4—1221no—
415C22×C4—1221no—
416C22×C4—1221no—
417C22×C4—1224no—
418C22×C4—1221no—
419C22×C4—4882no—
420C22×C4—4882no—
421C22×C4C2×C4×D6111yescharacteristic
422C22×C4D4×D6111yescharacteristic
423C22×C4D4×D6111yescharacteristic
424C2×C8—41no—
425C2×C8—41no—
426C2×C8—2441no—
427C2×C8—2441no—
428C4⋊C4—21no—
429C4⋊C4—612no—
430C4⋊C4—1224no—
431C4⋊C4—1224no—
432C4⋊C4—1221no—
433C4⋊C4—1221no—
434C4⋊C4—1221no—
435C4⋊C4—1222no—
436C4⋊C4—1221no—
437C4⋊C4—1221no—
438C4⋊C4—1222no—
439C4⋊C4#1175819812yes—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—1224no—
443C22⋊C4—1221no—
444C22⋊C4—1221no—
445C22⋊C4—1221no—
446C22⋊C4—1221no—
447C42—1224no—
448C42—1221no—
449C42—1221no—
450C42—1222no—
451C42—1222no—
452C42C2×D24411yescharacteristic
453C42D4×D6111yescharacteristic
454C42D4×D6111yescharacteristic
455C42C2×C22⋊D6111yescharacteristic
456C23—22no—
457C23—22no—
458C23—22no—
459C23—42no—
460C23—42no—
461C23—612no—
462C23—1221no—
463C23—1221no—
464C23—2441no—
465C23—2441no—
466C23C22⋊C4×D6111yescharacteristic
467Q8—614no—
468Q8—1222no—
469Q8—1222no—
470Q8—1222no—
471D4—22no—
472D4—22no—
473D4—22no—
474D4—12216no—
475D4#1451968914yes—
476C2×C4—22no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4—612no—
483C2×C4—12216no—
484C2×C4—1222no—
485C2×C4—1221no—
486C2×C4—1222no—
487C2×C4—1222no—
488C2×C4—1221no—
489C2×C4—1222no—
490C2×C4—1222no—
491C2×C4—1222no—
492C2×C4—1222no—
493C2×C4—1221no—
494C2×C4—1222no—
495C2×C4—1221no—
496C2×C4—4884no—
497C2×C4—4884no—
498C2×C4—2442no—
499C2×C4—2441no—
500C2×C4—2441no—
501C2×C4C22⋊C4×D6111yescharacteristic
502C2×C4C2×#1175819811yescharacteristic
503C2×C4#1451974511yescharacteristic
504C2×C4#1451974511yescharacteristic
505C2×C4#1451974711yescharacteristic
506C2×C4#1451974711yescharacteristic
507C2×C4C2×C8×D6111yescharacteristic
508C2×C4M16×D6111yescharacteristic
509C2×C4M16×D6111yescharacteristic
510C2×C4C2×#1175818911yescharacteristic
511C8—81no—
512C8—81no—
513C8—4881no—
514C8—4881no—
515C22—21no—
516C22—21no—
517C22—24no—
518C22—44no—
519C22—44no—
520C22—42no—
521C22—42no—
522C22—1222no—
523C22—2442no—
524C22—2442no—
525C22—2441no—
526C22—2441no—
527C22#1683961711yescharacteristic
528C22C22⋊C8×D6111yescharacteristic
529C22#1683972411yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—21no—
534C4—42no—
535C4—1222no—
536C4—1224no—
537C4—2441no—
538C4—2442no—
539C4—2441no—
540C4C22⋊C8×D6111yescharacteristic
541C4C2×#1451968911yescharacteristic
542C4#1683972411yescharacteristic
543C4#1683972511yescharacteristic
544C2—21no—
545C2—21no—
546C2—44no—
547C2—2442no—
548C2#2144572811yescharacteristic
549C2#2144578611yescharacteristic
550C2#2144579311yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1478C2
socleC22×C61#379
prime radicalC22×#11758224C4
cosocleC2×C42×C61C23
hypercenter#1478D61
hypocenterC61#8324
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #21444215C2semidirect
3. #21444213C2semidirect
4. #21444210C2semidirect
5. #21444131C2semidirect
6. #21444131C2semidirect
7. C61×#1478C2semidirect
40. C2×#11758224C8semidirect
273. #1478D61semidirect
310. C61#8324semidirect

Maximal subgroups

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

subgroupindex
C2×#168402412
#214442152
#214442132
#214442102
#214441312
C61×#14782
#832461