Finite Group Databasebeta

← #29573335

Subgroups — #29573335

Order 15616.

1158 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#95×D61C211yesmaximal, characteristic
2#21445728C212yesmaximal
3#21443662C211yesmaximal, characteristic, complemented
4#21443661C212yesmaximal, complemented
5C61×#1280C211yesmaximal, characteristic, complemented
6C23×C4×D61C411yescharacteristic
7C23×C4×D61C411yescharacteristic
8C23×C4×D61C2211yescharacteristic
9C2×C22⋊#92418C2212yes—
10C2×#14519689—22no—
11C2×#14519689—22no—
12C2×#14519684C411yescharacteristic
13C2×#14519684C411yescharacteristic
14C2×#14519684C2211yescharacteristic
15#95×D61—22no—
16#95×D61—22no—
17C2×C22⋊C8×C61C2212yes—
18C2×#95×C61C2211yescharacteristic
19C24×D61C2×C411yescharacteristic
20C23×Dic61C2×C411yescharacteristic
21C23×Dic61C2×C411yescharacteristic
22C23×Dic61C2×C411yescharacteristic
23C22×C4×D61—21no—
24C22×C4×D61—21no—
25C22×C4×D61—21no—
26C22×C4×D61—21no—
27C22×C4×D61—22no—
28C22×C4×D61—22no—
29C22×C4×D61—22no—
30C22×C4×D61—21no—
31C22×C4×D61—21no—
32C22×C4×D61—22no—
33C22×C4×D61—42no—
34C22×C4×D61—42no—
35C22×C4×D61—42no—
36C22×C4×D61—42no—
37C22×C4×D61—42no—
38C22×C4×D61—42no—
39C22×C4×D61C814yescomplemented
40C22×C4×D61D412yes—
41C22×C4×D61D412yes—
42C22×#92418—22no—
43C22⋊#92418—22no—
44C22⋊#92418—22no—
45#14519689—44no—
46#14519689—44no—
47#14519684—22no—
48#14519684—22no—
49#14519684—22no—
50C23×C4×C61C2×C411yescharacteristic
51C23×C4×C61C2×C411yescharacteristic
52C23×C4×C61C2311yescharacteristic
53C22×C8×C61—22no—
54C22⋊C8×C61—22no—
55C22⋊C8×C61—22no—
56#95×C61—22no—
57C24×C61C22×C411yescharacteristic
58C23×D61—21no—
59C23×D61—21no—
60C23×D61—21no—
61C23×D61—21no—
62C23×D61—22no—
63C23×D61—22no—
64C23×D61—22no—
65C23×D61—22no—
66C23×D61C22⋊C411yescharacteristic
67C23×D61C22⋊C411yescharacteristic
68C23×D61C2×C812yes—
69C23×D61M1612yes—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—41no—
75C22×C4×C61—41no—
76C22×C4×C61—41no—
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61C2×C812yes—
81C22×C4×C61M1612yes—
82C22×C4×C61C2×D412yes—
83C22×C4×C61#4112yes—
84C22×C4×C61#4111yescharacteristic
85C22×C4×C61#4111yescharacteristic
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—41no—
93C22×Dic61—41no—
94C22×Dic61—41no—
95C22×Dic61—41no—
96C22×Dic61—41no—
97C22×Dic61—41no—
98C22×Dic61C22⋊C412yes—
99C22×Dic61C2×C812yes—
100C22×Dic61M1612yes—
101C2×C4×D61—24no—
102C2×C4×D61—24no—
103C2×C4×D61—24no—
104C2×C4×D61—24no—
105C2×C4×D61—24no—
106C2×C4×D61—24no—
107C2×C4×D61—22no—
108C2×C4×D61—22no—
109C2×C4×D61—22no—
110C2×C4×D61—22no—
111C2×C4×D61—42no—
112C2×C4×D61—42no—
113C2×C4×D61—44no—
114C2×C4×D61—48no—
115C2×C4×D61—44no—
116C2×C4×D61—48no—
117C2×C4×D61—42no—
118C2×C4×D61—42no—
119C2×C4×D61—42no—
120C2×C4×D61—42no—
121C2×C4×D61—48no—
122C2×C4×D61—48no—
123C2×C4×D61—42no—
124C2×C4×D61—42no—
125C2×C4×D61—42no—
126C2×C4×D61—42no—
127C2×C4×D61—48no—
128C2×C8×C61—42no—
129C2×C8×C61—42no—
130C2×C8×C61—42no—
131C2×#92418—42no—
132C2×#92418—42no—
133C2×#92418—42no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61C2×C22⋊C411yescharacteristic
139C23×C61#11711yescharacteristic
140C23×C61#11711yescharacteristic
141C23×C61C22×C811yescharacteristic
142C23×C61C2×M1611yescharacteristic
143C23×C61C2×M1611yescharacteristic
144C23×C61C2×M1611yescharacteristic
145C22×D61—24no—
146C22×D61—24no—
147C22×D61—24no—
148C22×D61—24no—
149C22×D61—24no—
150C22×D61—24no—
151C22×D61—24no—
152C22×D61—24no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61—21no—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—22no—
162C22×D61—22no—
163C22×D61—22no—
164C22×D61—22no—
165C22×D61—24no—
166C22×D61—24no—
167C22×D61—24no—
168C22×D61—24no—
169C22×D61C22⋊C812yes—
170C22×D61C22⋊C812yes—
171C22×D61#9912yes—
172C22×D61#9912yes—
173C22×D61#10012yes—
174C22×D61#10112yes—
175C2×C4×C61—22no—
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—41no—
180C2×C4×C61—42no—
181C2×C4×C61—41no—
182C2×C4×C61—42no—
183C2×C4×C61—42no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—42no—
189C2×C4×C61—42no—
190C2×C4×C61#12312yes—
191C2×C4×C61#12312yes—
192C2×Dic61—22no—
193C2×Dic61—22no—
194C2×Dic61—22no—
195C2×Dic61—22no—
196C2×Dic61—22no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61—41no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—42no—
206C2×Dic61—42no—
207C4×D61—44no—
208C4×D61—44no—
209C4×D61—44no—
210C4×D61—44no—
211C4×D61—48no—
212C4×D61—48no—
213C4×D61—48no—
214C4×D61—48no—
215C8×C61—82no—
216#92418—82no—
217#8698—611nomaximal, Sylow
218C22×C61—21no—
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61#38111yescharacteristic
231C22×C61C2×C22⋊C811yescharacteristic
232C22×C61#40711yescharacteristic
233C22×C61C2×#9911yescharacteristic
234C22×C61C2×#9911yescharacteristic
235C22×C61C2×#10011yescharacteristic
236C22×C61C2×#10111yescharacteristic
237C22×C61#43111yescharacteristic
238C22×C61#43111yescharacteristic
239C22×C61#43211yescharacteristic
240C22×C61#43211yescharacteristic
241C2×D61—28no—
242C2×D61—28no—
243C2×D61—28no—
244C2×D61—28no—
245C2×D61—22no—
246C2×D61—22no—
247C2×D61—22no—
248C2×D61—22no—
249C2×D61—22no—
250C2×D61—22no—
251C2×D61—22no—
252C2×D61—22no—
253C2×D61—22no—
254C2×D61—22no—
255C2×D61—22no—
256C2×D61—22no—
257C2×D61#32314yes—
258C2×D61#32414yes—
259C4×C61—22no—
260C4×C61—22no—
261C4×C61—42no—
262C4×C61—42no—
263Dic61—42no—
264Dic61—42no—
265Dic61—42no—
266C22×#95—611no—
267#1779—612no—
268#1280—612no—
269#1280—611no—
270#1280D6111yescharacteristic, complemented
271C2×C61—21no—
272C2×C61—21no—
273C2×C61—21no—
274C2×C61—21no—
275C2×C61C2×#32311yescharacteristic
276C2×C61C2×#32411yescharacteristic
277C2×C61#146211yescharacteristic
278C2×C61#146311yescharacteristic
279C2×C61#181711yescharacteristic
280C2×C61#181911yescharacteristic
281C2×C61#182111yescharacteristic
282D61—24no—
283D61—24no—
284C24×C4—611no—
285C24×C4—611no—
286C24×C4—611no—
287C2×C22⋊C8—612no—
288C2×C22⋊C8—1222no—
289C2×C22⋊C8—1222no—
290C2×C22⋊C8C2×D6112yes—
291C2×#95—611no—
292C2×#95—611no—
293C2×#95—611no—
294C2×#95—1222no—
295C2×#95—1222no—
296C2×#95C2×D6111yescharacteristic
297C61#869811yescharacteristic, complemented, Sylow
298C25—611no—
299C23×C4—611no—
300C23×C4—611no—
301C23×C4—611no—
302C23×C4—612no—
303C23×C4—612no—
304C23×C4—614no—
305C23×C4—1222no—
306C23×C4—1222no—
307C23×C4—1221no—
308C23×C4—1221no—
309C23×C4—1221no—
310C23×C4—1221no—
311C23×C4—1222no—
312C23×C4—1222no—
313C23×C4—1221no—
314C23×C4—1221no—
315C23×C4—2442no—
316C23×C4—2442no—
317C23×C4—2442no—
318C23×C4—2442no—
319C23×C4—2442no—
320C23×C4—2442no—
321C23×C4C4×D6111yescharacteristic
322C23×C4C4×D6111yescharacteristic
323C23×C4C22×D6111yescharacteristic
324C22×C8—22no—
325C22×C8—1222no—
326C22⋊C8—22no—
327C22⋊C8—22no—
328C22⋊C8—1222no—
329C22⋊C8—1222no—
330C22⋊C8—2444no—
331C22⋊C8—2444no—
332#95—22no—
333#95—1222no—
334#95—1222no—
335#95—1222no—
336C24—611no—
337C24—611no—
338C24—612no—
339C24—612no—
340C24—1222no—
341C24—1222no—
342C24—1222no—
343C24—1222no—
344C24—1221no—
345C24—1221no—
346C24—1221no—
347C24—1221no—
348C24C2×C4×D6111yescharacteristic
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—612no—
360C22×C4—612no—
361C22×C4—612no—
362C22×C4—1224no—
363C22×C4—1224no—
364C22×C4—1224no—
365C22×C4—1224no—
366C22×C4—1224no—
367C22×C4—1224no—
368C22×C4—1221no—
369C22×C4—1221no—
370C22×C4—1221no—
371C22×C4—1221no—
372C22×C4—1221no—
373C22×C4—1221no—
374C22×C4—1222no—
375C22×C4—1222no—
376C22×C4—1222no—
377C22×C4—1222no—
378C22×C4—2442no—
379C22×C4—2442no—
380C22×C4—2442no—
381C22×C4—2442no—
382C22×C4—2442no—
383C22×C4—2442no—
384C22×C4—2448no—
385C22×C4—2444no—
386C22×C4—2444no—
387C22×C4—2448no—
388C22×C4—2448no—
389C22×C4—2442no—
390C22×C4—2442no—
391C22×C4—2442no—
392C22×C4—2442no—
393C22×C4—2448no—
394C22×C4—2448no—
395C22×C4—2441no—
396C22×C4—2441no—
397C22×C4—2441no—
398C22×C4—2441no—
399C22×C4—2441no—
400C22×C4—2441no—
401C22×C4C8×D6112yes—
402C22×C4#1175818912yes—
403C22×C4#1175822212yes—
404C22×C4D4×D6112yes—
405C22×C4#1175822411yescharacteristic
406C22×C4#1175822611yescharacteristic
407C2×C8—42no—
408C2×C8—42no—
409C2×C8—42no—
410C2×C8—2442no—
411C2×C8—2442no—
412C2×C8—2442no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—612no—
418C23—612no—
419C23—612no—
420C23—612no—
421C23—612no—
422C23—612no—
423C23—1224no—
424C23—1224no—
425C23—1224no—
426C23—1224no—
427C23—1224no—
428C23—1224no—
429C23—1224no—
430C23—1224no—
431C23—1224no—
432C23—1224no—
433C23—1224no—
434C23—1224no—
435C23—1221no—
436C23—1221no—
437C23—1221no—
438C23—1221no—
439C23—1221no—
440C23—1221no—
441C23—1222no—
442C23—1222no—
443C23—1222no—
444C23—1222no—
445C23—1221no—
446C23—1221no—
447C23C22⋊C4×D6111yescharacteristic
448C23#1451973411yescharacteristic
449C23#1451973511yescharacteristic
450C23C2×C8×D6111yescharacteristic
451C23M16×D6111yescharacteristic
452C23M16×D6111yescharacteristic
453C23C2×#1175818911yescharacteristic
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—1222no—
470C2×C4—1222no—
471C2×C4—1222no—
472C2×C4—1222no—
473C2×C4—1222no—
474C2×C4—2444no—
475C2×C4—2444no—
476C2×C4—2444no—
477C2×C4—2444no—
478C2×C4—2448no—
479C2×C4—2448no—
480C2×C4—2448no—
481C2×C4—2448no—
482C2×C4—2442no—
483C2×C4—2442no—
484C2×C4—2442no—
485C2×C4—2442no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2442no—
491C2×C4—2442no—
492C2×C4#1451975912yes—
493C2×C4#1451976212yes—
494C8—82no—
495C8—4882no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—614no—
509C22—614no—
510C22—1228no—
511C22—1228no—
512C22—1228no—
513C22—1228no—
514C22—1222no—
515C22—1222no—
516C22—1222no—
517C22—1222no—
518C22—1222no—
519C22—1222no—
520C22—1222no—
521C22—1222no—
522C22—1222no—
523C22—1222no—
524C22—1222no—
525C22—1222no—
526C22#1683962411yescharacteristic
527C22C22⋊C8×D6111yescharacteristic
528C22#1683972411yescharacteristic
529C22#99×D6111yescharacteristic
530C22#99×D6111yescharacteristic
531C22#100×D6111yescharacteristic
532C22#101×D6111yescharacteristic
533C22#1683981311yescharacteristic
534C22#1683981411yescharacteristic
535C22#1683981711yescharacteristic
536C22#1683981811yescharacteristic
537C4—22no—
538C4—22no—
539C4—42no—
540C4—42no—
541C4—2442no—
542C4—2442no—
543C4—2442no—
544C2—21no—
545C2—21no—
546C2—21no—
547C2—21no—
548C2—1224no—
549C2—1224no—
550C2#323×D6111yescharacteristic
551C2#324×D6111yescharacteristic
552C2#2144414411yescharacteristic
553C2#2144414711yescharacteristic
554C2#2144588611yescharacteristic
555C2#2144589211yescharacteristic
556C2#2144589811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC23×C61C22×C8
FrattiniC23×C4C22×D61
FittingC61×#1280C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC23×C4×C61C23
hypercenter#1280D61
hypocenterC61#8698
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
3. #21443662C2semidirect
4. #21443661C2semidirect
5. C61×#1280C2semidirect
39. C22×C4×D61C8semidirect
270. #1280D61semidirect
297. C61#8698semidirect

Maximal subgroups

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

subgroupindex
C2×#95×D612
#214457282
#214436622
#214436612
C61×#12802
#869861