Finite Group Databasebeta

← #29689017

Subgroups — #29689017

Order 15616.

1914 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519752C211yesmaximal, characteristic
2C2×C22⋊C8×D61C211yesmaximal, characteristic, complemented
3#380×D61C211yesmaximal, characteristic, complemented
4#21446246C214yesmaximal, complemented
5#21446135C214yesmaximal, complemented
6#21445905C211yesmaximal, characteristic, complemented
7#21445751C211yesmaximal, characteristic, complemented
8#21445749C211yesmaximal, characteristic, complemented
9C61×#1823C211yesmaximal, characteristic, complemented
10C23×D244—21no—
11C23×D244C2211yescharacteristic
12C23×C4×D61C2211yescharacteristic
13C22×C8×D61C2212yescomplemented
14C2×#14519752—21no—
15C2×#14519752—21no—
16C2×#14519752—24no—
17C2×#14519752C418yescomplemented
18C2×#14519752C2212yes—
19C2×#14519752C2212yes—
20C2×C4⋊C4×D61C2212yescomplemented
21C22×#11758198—21no—
22C2×C22⋊C4×D61—21no—
23C2×#14519699C2214yescomplemented
24C2×#14519697C2214yescomplemented
25C2×C22⋊#92418C2211yescharacteristic
26C2×#14519689C2212yescomplemented
27C22⋊C8×D61—24no—
28#16839622C2211yescharacteristic
29#16839621—21no—
30#16839620—21no—
31#16839619C2212yescomplemented
32#95×D61—21no—
33#16839524C2214yescomplemented
34C22×C4⋊C4×C61C2211yescharacteristic
35C2×C22⋊C8×C61C2211yescharacteristic
36C61×#380C2211yescharacteristic
37C61×#340C2214yescomplemented
38C24×D61—21no—
39C24×D61D411yescharacteristic
40C22×D244—28no—
41C22×D244—22no—
42C22×D244—22no—
43C22×D244—21no—
44C22×D244—22no—
45C22×D244—44no—
46C22×D244—44no—
47C22×D244—44no—
48C22×D244C2×C414yescomplemented
49C22×D244C2312yes—
50C23×Dic61D411yescharacteristic
51C22×C4×D61—22no—
52C22×C4×D61—44no—
53C22×C4×D61C2×C414yes—
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D414yes—
57C22×C4×D61C2311yescharacteristic
58C22×C4×D61C2311yescharacteristic
59C22×#92418C2312yes—
60C2×C8×D61—24no—
61C2×C8×D61—44no—
62#14519752—28no—
63#14519752—28no—
64#14519752—24no—
65#14519752—24no—
66#14519752C2×C418yes—
67#14519752C2×C418yescomplemented
68C2×C4⋊Dic61C2312yes—
69C2×#11758196—22no—
70C4⋊C4×D61—44no—
71C2×C22⋊Dic61—21no—
72C2×#11758198—28no—
73C2×#11758198—22no—
74C2×#11758198—22no—
75C2×#11758198—22no—
76C22⋊C4×D61—44no—
77#14519699—44no—
78#14519697—44no—
79C22⋊#92418—22no—
80#14519689—24no—
81#14519684—21no—
82#14519684—22no—
83C23×C4×C61—21no—
84C23×C4×C61C2311yescharacteristic
85C22×C8×C61C2312yes—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61C2×C414yescomplemented
89C2×C4⋊C4×C61C2312yes—
90C2×C4⋊C4×C61C2312yes—
91C2×C22⋊C4×C61—21no—
92C22⋊C8×C61—22no—
93#95×C61—21no—
94C24×C61C2×D411yescharacteristic
95C23×D61—24no—
96C23×D61—22no—
97C23×D61—42no—
98C23×D61—42no—
99C23×D61—44no—
100C23×D61—44no—
101C23×D61—42no—
102C23×D61—42no—
103C23×D61C22⋊C414yes—
104C23×D61D814yes—
105C23×D61SD1614yes—
106C23×D61C2×D411yescharacteristic
107C23×D61C2×D411yescharacteristic
108C22×C4×C61—24no—
109C22×C4×C61—24no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—42no—
113C22×C4×C61—42no—
114C22×C4×C61C22×C412yes—
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D412yes—
117C22×C4×C61C2411yescharacteristic
118C22×Dic61—22no—
119C22×Dic61—42no—
120C22×Dic61C22⋊C414yes—
121C22×Dic61C2×D411yescharacteristic
122C22×Dic61C2×D411yescharacteristic
123C2×D244—24no—
124C2×D244—24no—
125C2×D244—28no—
126C2×D244—28no—
127C2×D244—24no—
128C2×D244—22no—
129C2×D244—48no—
130C2×D244—44no—
131C2×D244—48no—
132C2×D244—432no—
133C2×D244—44no—
134C2×D244—44no—
135C2×D244—44no—
136C2×D244—44no—
137C2×D244C22×C414yes—
138C2×C4×D61—24no—
139C2×C4×D61—24no—
140C2×C4×D61—48no—
141C2×C4×D61—48no—
142C2×C4×D61—42no—
143C2×C4×D61—42no—
144C2×C4×D61—44no—
145C2×C4×D61—44no—
146C2×C4×D61—44no—
147C2×C4×D61C22⋊C414yes—
148C2×C4×D61C22⋊C414yes—
149C2×C4×D61C22×C412yes—
150C2×C4×D61C22×C412yes—
151C2×C4×D61C2×D412yes—
152C2×C4×D61C2×D412yes—
153C2×C8×C61—22no—
154C2×C8×C61—24no—
155C4⋊C4×C61—24no—
156C4⋊C4×C61—22no—
157C4⋊C4×C61—24no—
158C4⋊C4×C61C22×C414yes—
159C22⋊C4×C61—42no—
160C22⋊Dic61—42no—
161#11758198—28no—
162#11758198—28no—
163#11758198—44no—
164C4⋊Dic61—24no—
165#11758196—44no—
166C2×#92418—22no—
167C2×#92418—24no—
168C8×D61—48no—
169C23×C61—22no—
170C23×C61—22no—
171C23×C61C2×C22⋊C412yes—
172C23×C61C2×D812yes—
173C23×C61C2×SD1612yes—
174C23×C61C22×D411yescharacteristic
175C22×D61—22no—
176C22×D61—22no—
177C22×D61—22no—
178C22×D61—22no—
179C22×D61—24no—
180C22×D61—44no—
181C22×D61—44no—
182C22×D61—48no—
183C22×D61—48no—
184C22×D61—48no—
185C22×D61—48no—
186C22×D61—44no—
187C22×D61—42no—
188C22×D61—42no—
189C22×D61—44no—
190C22×D61—48no—
191C22×D61—88no—
192C22×D61—88no—
193C22×D61#102116yescomplemented
194C22×D61C2×C22⋊C412yes—
195C22×D61C2×C22⋊C412yes—
196C22×D61C2×D812yes—
197C22×D61C2×D812yes—
198C22×D61C2×SD1612yes—
199C22×D61C2×SD1612yes—
200C2×C4×C61—22no—
201C2×C4×C61—24no—
202C2×C4×C61—24no—
203C2×C4×C61—24no—
204C2×C4×C61—42no—
205C2×C4×C61—42no—
206C2×C4×C61—48no—
207C2×C4×C61—42no—
208C2×C4×C61—42no—
209C2×C4×C61—42no—
210C2×C4×C61C2×C22⋊C412yes—
211C2×C4×C61C23×C411yescharacteristic
212C2×C4×C61C22×D411yescharacteristic
213C2×C4×C61H(5,𝔽2)14yes—
214C2×Dic61—22no—
215C2×Dic61—22no—
216C2×Dic61—44no—
217C2×Dic61—42no—
218C2×Dic61—42no—
219C2×Dic61—42no—
220C2×Dic61C2×C22⋊C412yes—
221C2×Dic61C2×C22⋊C412yes—
222D244—24no—
223D244—24no—
224D244—48no—
225D244—416no—
226D244—416no—
227D244—44no—
228C4×D61—24no—
229C4×D61—24no—
230C4×D61—24no—
231C4×D61—24no—
232C4×D61—44no—
233C4×D61—44no—
234C4×D61—88no—
235C8×C61—42no—
236#92418—42no—
237#21758—611nomaximal, Sylow
238C22×C61—22no—
239C22×C61—22no—
240C22×C61—24no—
241C22×C61—24no—
242C22×C61C2×#10214yes—
243C22×C61C22×C22⋊C411yescharacteristic
244C22×C61#53412yes—
245C22×C61C22×D811yescharacteristic
246C22×C61C22×SD1611yescharacteristic
247C22×C61#57512yes—
248C2×D61—22no—
249C2×D61—22no—
250C2×D61—22no—
251C2×D61—22no—
252C2×D61—24no—
253C2×D61—24no—
254C2×D61—24no—
255C2×D61—24no—
256C2×D61—416no—
257C2×D61—44no—
258C2×D61—44no—
259C2×D61—44no—
260C2×D61—816no—
261C2×D61—84no—
262C2×D61—84no—
263C2×D61C2×#10214yes—
264C2×D61C2×#10214yes—
265C4×C61—22no—
266C4×C61—44no—
267C4×C61—82no—
268C4×C61#51812yes—
269C4×C61#53412yes—
270Dic61—22no—
271Dic61—22no—
272Dic61—82no—
273C22×#121—611no—
274C22×C22⋊C8—611no—
275C2×#380—611no—
276#1893—614no—
277#1874—614no—
278#1823—611no—
279#1823D6111yescharacteristic, complemented
280#1786—611no—
281#1786—611no—
282C2×C61—24no—
283C2×C61#230811yescharacteristic
284C2×C61C22×#10211yescharacteristic
285C2×C61#289611yescharacteristic
286C2×C61#318612yes—
287C2×C61#318712yes—
288D61—24no—
289D61—24no—
290D61—84no—
291C23×D4—611no—
292C23×D4—1221no—
293C24×C4—611no—
294C23×C8—612no—
295C2×#121—618no—
296C2×#121—612no—
297C2×#121—612no—
298C2×#121—1221no—
299C2×#121—1221no—
300C2×#121—1224no—
301C22×C4⋊C4—612no—
302C22×C4⋊C4C2×D6111yescharacteristic
303C22×C22⋊C4—1221no—
304C22×C22⋊C4—1221no—
305C2×#102—614no—
306C2×#102—614no—
307C2×C22⋊C8—611no—
308C2×C22⋊C8—612no—
309C2×C22⋊C8—1224no—
310C2×C22⋊C8C2×D6111yescharacteristic
311#380—611no—
312#380—612no—
313#380—1221no—
314#380—1221no—
315#380C2×D6111yescharacteristic
316C2×#95—1221no—
317#340—614no—
318#340C2×D6114yescomplemented
319C61#2175811yescharacteristic, complemented, Sylow
320C25—611no—
321C25—1221no—
322C22×D4—614no—
323C22×D4—612no—
324C22×D4—1222no—
325C22×D4—1222no—
326C22×D4—1228no—
327C22×D4—1222no—
328C22×D4—1221no—
329C22×D4—2444no—
330C22×D4—2444no—
331C22×D4—2444no—
332C23×C4—21no—
333C23×C4—611no—
334C23×C4—611no—
335C23×C4—611no—
336C23×C4—614no—
337C23×C4—611no—
338C23×C4—611no—
339C23×C4—614no—
340C23×C4—1222no—
341C23×C4—2444no—
342C23×C4C22×D6111yescharacteristic
343C22×C8—612no—
344C22×C8—1224no—
345C22×C8—2444no—
346C22×C8C22×D6112yes—
347#121—618no—
348#121—618no—
349#121—1224no—
350#121—1224no—
351#121—1228no—
352#121—1228no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—612no—
356C2×C4⋊C4—1222no—
357C2×C4⋊C4—2444no—
358C2×C4⋊C4C4×D6114yescomplemented
359C2×C4⋊C4C22×D6112yes—
360C2×C4⋊C4C22×D6112yes—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—1222no—
363C2×C22⋊C4—1222no—
364C2×C22⋊C4—1228no—
365C2×C22⋊C4—1222no—
366C2×C22⋊C4—1221no—
367C2×C22⋊C4—2444no—
368#102—2444no—
369#102—2444no—
370C22⋊C8—22no—
371C22⋊C8—1224no—
372C22⋊C8—1222no—
373#95—21no—
374#95—1222no—
375#95—1221no—
376C24—611no—
377C24—611no—
378C24—614no—
379C24—614no—
380C24—614no—
381C24—1222no—
382C24—1224no—
383C24—2442no—
384C24—2442no—
385C24—2444no—
386C24—2444no—
387C24—2442no—
388C24—2442no—
389C24D4×D6111yescharacteristic
390C2×D4—614no—
391C2×D4—1228no—
392C2×D4—1228no—
393C2×D4—1222no—
394C2×D4—1224no—
395C2×D4—1224no—
396C2×D4—1224no—
397C2×D4—2448no—
398C2×D4—2444no—
399C2×D4—2448no—
400C2×D4—24432no—
401C2×D4—2444no—
402C2×D4—2444no—
403C2×D4—2444no—
404C2×D4—2444no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—611no—
412C22×C4—611no—
413C22×C4—614no—
414C22×C4—612no—
415C22×C4—612no—
416C22×C4—612no—
417C22×C4—612no—
418C22×C4—614no—
419C22×C4—614no—
420C22×C4—1224no—
421C22×C4—1224no—
422C22×C4—1222no—
423C22×C4—2448no—
424C22×C4—2448no—
425C22×C4—2442no—
426C22×C4—2442no—
427C22×C4—2444no—
428C22×C4—2444no—
429C22×C4—2444no—
430C22×C4—2442no—
431C22×C4C2×C4×D6112yes—
432C22×C4D4×D6112yes—
433C22×C4D4×D6111yescharacteristic
434C22×C4C23×D6111yescharacteristic
435C2×C8—22no—
436C2×C8—24no—
437C2×C8—1222no—
438C2×C8—1224no—
439C2×C8—2448no—
440C4⋊C4—22no—
441C4⋊C4—24no—
442C4⋊C4—24no—
443C4⋊C4—1224no—
444C4⋊C4—2444no—
445C4⋊C4C2×C4×D6114yes—
446C22⋊C4—42no—
447C22⋊C4—1228no—
448C22⋊C4—1228no—
449C22⋊C4—2444no—
450C22⋊C4—2442no—
451C23—22no—
452C23—22no—
453C23—612no—
454C23—612no—
455C23—612no—
456C23—612no—
457C23—612no—
458C23—612no—
459C23—6116no—
460C23—1222no—
461C23—1222no—
462C23—1222no—
463C23—1222no—
464C23—1224no—
465C23—4888no—
466C23—4888no—
467C23—2444no—
468C23—2444no—
469C23—2448no—
470C23—2448no—
471C23—2448no—
472C23—2448no—
473C23—2448no—
474C23—2442no—
475C23—2442no—
476C23—2444no—
477C23—2444no—
478C23C22⋊C4×D6112yes—
479C23D8×D6112yes—
480C23SD16×D6112yes—
481C23C2×D4×D6111yescharacteristic
482D4—1224no—
483D4—1224no—
484D4—2448no—
485D4—24416no—
486D4—24416no—
487D4—2444no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—48no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—612no—
499C2×C4—612no—
500C2×C4—1222no—
501C2×C4—1222no—
502C2×C4—1224no—
503C2×C4—1224no—
504C2×C4—1224no—
505C2×C4—1224no—
506C2×C4—4888no—
507C2×C4—2444no—
508C2×C4—2444no—
509C2×C4—2444no—
510C2×C4—2442no—
511C2×C4—2442no—
512C2×C4—2442no—
513C2×C4C22⋊C4×D6112yes—
514C2×C4C22×C4×D6111yescharacteristic
515C2×C4C2×D4×D6111yescharacteristic
516C2×C4#1451982314yes—
517C8—42no—
518C8—2442no—
519C22—22no—
520C22—24no—
521C22—24no—
522C22—22no—
523C22—614no—
524C22—614no—
525C22—1222no—
526C22—1222no—
527C22—1224no—
528C22—1224no—
529C22—1224no—
530C22—1224no—
531C22—1222no—
532C22—1222no—
533C22—48816no—
534C22—4884no—
535C22—4884no—
536C22—24416no—
537C22—2444no—
538C22—2444no—
539C22—2444no—
540C22#102×D6114yes—
541C22C2×C22⋊C4×D6111yescharacteristic
542C22#1684032312yes—
543C22C2×D8×D6111yescharacteristic
544C22C2×SD16×D6111yescharacteristic
545C22#1684056112yes—
546C4—22no—
547C4—44no—
548C4—82no—
549C4—1222no—
550C4—1222no—
551C4—4882no—
552C4#1684023612yes—
553C4#1684032312yes—
554C2—24no—
555C2—1224no—
556C2—1224no—
557C2—4884no—
558C2#2144839611yescharacteristic
559C2C2×#102×D6111yescharacteristic
560C2#2145433711yescharacteristic
561C2#2145656912yes—
562C2#2145657512yes—
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1823C2
socleC23×C61C22×D4
prime radicalC22×#14519752C2
cosocleC22×C4×C61C24
hypercenter#1823D61
hypocenterC61#21758
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C8×D61C2semidirect
3. #380×D61C2semidirect
4. #21446246C2semidirect
5. #21446135C2semidirect
6. #21445905C2semidirect
7. #21445751C2semidirect
8. #21445749C2semidirect
9. C61×#1823C2semidirect
13. C22×C8×D61C22semidirect
17. C2×#14519752C4semidirect
20. C2×C4⋊C4×D61C22semidirect
23. C2×#14519699C22semidirect
24. C2×#14519697C22semidirect
26. C2×#14519689C22semidirect
31. #16839619C22semidirect
33. #16839524C22semidirect
37. C61×#340C22semidirect
48. C22×D244C2×C4semidirect
67. #14519752C2×C4semidirect
88. C2×C4⋊C4×C61C2×C4semidirect
193. C22×D61#102semidirect
279. #1823D61semidirect
318. #340C2×D61semidirect
319. C61#21758semidirect
358. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197522
C2×C22⋊C8×D612
#380×D612
#214462462
#214461352
#214459052
#214457512
#214457492
C61×#18232
#2175861