Finite Group Databasebeta

← #29686182

Subgroups — #29686182

Order 15616.

1272 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839957C211yesmaximal, characteristic
2C2×#16839842C212yesmaximal, complemented
3#21448381C211yesmaximal, characteristic, complemented
4C4×D4×Dic61C211yesmaximal, characteristic, complemented
5#21446745C211yesmaximal, characteristic, complemented
6#21446575C211yesmaximal, characteristic, complemented
7#21446437C212yesmaximal, complemented
8#21446165C212yesmaximal, complemented
9C4⋊C8×Dic61C211yesmaximal, characteristic, complemented
10#21445633C212yesmaximal, complemented
11C61×#1802C211yesmaximal, characteristic, complemented
12C22×#11758199C2212yes—
13C2×#14519774C2211yescharacteristic
14C2×D4×Dic61C2211yescharacteristic
15C2×D4×Dic61C2211yescharacteristic
16C2×#14519739—21no—
17C2×#14519739—21no—
18C2×#14519739C2212yes—
19C22×C4×Dic61—21no—
20#16839957C418yescomplemented
21#16839842—28no—
22C2×#14519710C2212yes—
23C2×C4⋊#92418C2211yescharacteristic
24C2×#14519699C2212yes—
25C2×#14519699C2212yes—
26C2×#14519697C2212yes—
27C2×C8×Dic61C2212yes—
28#16839663—21no—
29#16839663—21no—
30#16839663C2212yes—
31C4⋊C4×Dic61C2211yescharacteristic
32C4⋊C4×Dic61C2211yescharacteristic
33C4×C4⋊Dic61C2211yescharacteristic
34C22⋊C4×Dic61—21no—
35C22⋊C4×Dic61—21no—
36C4×C22⋊Dic61—21no—
37C42×Dic61C2211yescharacteristic
38#16839524C2212yes—
39#16839516C2212yes—
40C2×C4×D4×C61C2211yescharacteristic
41C2×C4⋊C8×C61C2211yescharacteristic
42C2×#102×C61C2212yes—
43C61×#384C2211yescharacteristic
44C61×#340C2212yes—
45C22×D244—21no—
46C22×D244—21no—
47C22×D244C2312yes—
48C23×Dic61—21no—
49C23×Dic61—21no—
50C22×C4×D61—22no—
51C2×#11758199—24no—
52C2×#11758199—24no—
53C2×#11758199C2×C418yescomplemented
54C22×#92418C2312yes—
55#14519774—22no—
56#14519774C2×C414yescomplemented
57D4×Dic61—22no—
58D4×Dic61—22no—
59D4×Dic61—22no—
60D4×Dic61D414yescomplemented
61#14519739—24no—
62#14519739—24no—
63#14519739—44no—
64#14519739—44no—
65C2×C4⋊Dic61C2311yescharacteristic
66C2×C4⋊Dic61C2311yescharacteristic
67C2×C22⋊Dic61—21no—
68C2×C22⋊Dic61—21no—
69C2×#11758198—22no—
70C2×#11758198—22no—
71C2×#11758198—22no—
72C2×C4×Dic61—21no—
73C2×C4×Dic61—21no—
74C2×C4×Dic61—21no—
75C2×C4×Dic61—44no—
76C2×C4×Dic61D411yescharacteristic
77C2×C4×Dic61D411yescharacteristic
78C2×C4×Dic61D411yescharacteristic
79C2×C4×Dic61D411yescharacteristic
80C2×C4×Dic61C2311yescharacteristic
81C2×C4×Dic61C2311yescharacteristic
82#14519710—24no—
83C4⋊#92418C2×C414yescomplemented
84#14519699—24no—
85#14519699—24no—
86#14519697C2×C418yescomplemented
87C8×Dic61—24no—
88#14519684—21no—
89#14519684—21no—
90#14519684—21no—
91C22×D4×C61C2311yescharacteristic
92C23×C4×C61—21no—
93C22×C8×C61C2312yes—
94C4×D4×C61—22no—
95C4×D4×C61C2×C414yescomplemented
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61C2312yes—
99C2×C4⋊C4×C61C2311yescharacteristic
100C2×C22⋊C4×C61—21no—
101C2×C42×C61C2311yescharacteristic
102C4⋊C8×C61—22no—
103#102×C61—24no—
104C24×C61—21no—
105C23×D61—22no—
106C2×D4×C61—21no—
107C2×D4×C61—21no—
108C2×D4×C61—21no—
109C2×D4×C61C22×C412yes—
110C2×D4×C61C2×D412yes—
111C2×D4×C61#4112yes—
112C22×C4×C61—21no—
113C22×C4×C61—24no—
114C22×C4×C61—22no—
115C22×C4×C61—42no—
116C22×C4×C61—42no—
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2411yescharacteristic
120C22×Dic61—24no—
121C22×Dic61—21no—
122C22×Dic61—21no—
123C22×Dic61—24no—
124C22×Dic61—42no—
125C22×Dic61—42no—
126C22×Dic61—42no—
127C22×Dic61—42no—
128C22×Dic61C2×D411yescharacteristic
129C22×Dic61C2×D411yescharacteristic
130C22×Dic61C2×D411yescharacteristic
131C22×Dic61C2×D411yescharacteristic
132C2×D244—22no—
133C2×D244—22no—
134C2×D244—22no—
135C2×D244—22no—
136C2×D244—24no—
137C2×D244—24no—
138C2×D244—22no—
139C2×D244—42no—
140C2×D244—42no—
141C2×D244—42no—
142C2×D244—42no—
143C2×D244C22×C414yes—
144C2×C4×D61—44no—
145C2×C4×D61—44no—
146C2×C4×D61—44no—
147C2×C8×C61—22no—
148C2×C8×C61—22no—
149C2×C8×C61—22no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—22no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—42no—
154C4⋊C4×C61—42no—
155C4⋊C4×C61C22×C412yes—
156C22⋊C4×C61—24no—
157C42×C61C22×C412yes—
158C42×C61#4112yes—
159C22⋊Dic61—24no—
160C22⋊Dic61—24no—
161#11758199—216no—
162#11758198—44no—
163#11758198—44no—
164#11758198—44no—
165C4⋊Dic61—21no—
166C4⋊Dic61—21no—
167C4⋊Dic61C2×D412yes—
168C4⋊Dic61#4112yes—
169C4×Dic61—22no—
170C4×Dic61—21no—
171C4×Dic61—21no—
172C4×Dic61—22no—
173C4×Dic61—41no—
174C4×Dic61—42no—
175C4×Dic61—42no—
176C4×Dic61—42no—
177C4×Dic61D814yescomplemented
178C4×Dic61C2×D412yes—
179C4×Dic61#4112yes—
180C2×#92418—22no—
181C2×#92418—22no—
182C2×#92418C22×C414yes—
183C23×C61—22no—
184C23×C61—22no—
185C23×C61—22no—
186C23×C61—41no—
187C23×C61—41no—
188C23×C61—41no—
189C23×C61—41no—
190C23×C61C22×D411yescharacteristic
191C22×D61—24no—
192C22×D61—42no—
193C22×D61—42no—
194C22×D61—42no—
195C22×D61—42no—
196C22×D61—42no—
197C22×D61—42no—
198D4×C61—22no—
199D4×C61—22no—
200D4×C61—22no—
201D4×C61C4×D414yescomplemented
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—22no—
205C2×C4×C61—41no—
206C2×C4×C61—41no—
207C2×C4×C61—48no—
208C2×C4×C61—42no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61C4×D412yes—
212C2×C4×C61C4×D412yes—
213C2×C4×C61C2×D812yes—
214C2×C4×C61#13512yes—
215C2×C4×C61C23×C411yescharacteristic
216C2×C4×C61C22×D411yescharacteristic
217C2×C4×C61C2×#4111yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—22no—
226C2×Dic61—21no—
227C2×Dic61—22no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—48no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61—48no—
236C2×Dic61#12112yes—
237C2×Dic61#12112yes—
238C2×Dic61C2×D812yes—
239C2×Dic61C2×D812yes—
240C2×Dic61AGL(1,ℤ/8)12yes—
241D244—24no—
242D244—24no—
243D244—48no—
244D244—42no—
245D244—42no—
246D244—48no—
247C4×D61—88no—
248C8×C61—42no—
249#92418—24no—
250C4×#459—611nomaximal, Sylow
251C22×C61—24no—
252C22×C61—42no—
253C22×C61—42no—
254C22×C61—42no—
255C22×C61—42no—
256C22×C61—42no—
257C22×C61—42no—
258C22×C61C2×C4×D411yescharacteristic
259C22×C61C2×#12111yescharacteristic
260C22×C61#52511yescharacteristic
261C22×C61C22×D811yescharacteristic
262C22×C61C2×#13511yescharacteristic
263C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
264C22×C61#57511yescharacteristic
265C2×D61—44no—
266C2×D61—44no—
267C2×D61—44no—
268C2×D61—82no—
269C2×D61—82no—
270C2×D61—82no—
271C2×D61—82no—
272C4×C61—22no—
273C4×C61—42no—
274C4×C61—82no—
275C4×C61C4×D814yescomplemented
276C4×C61C2×C4×D411yescharacteristic
277C4×C61C4×#4111yescharacteristic
278C4×C61#52911yescharacteristic
279C4×C61#53211yescharacteristic
280Dic61—22no—
281Dic61—22no—
282Dic61—42no—
283Dic61—41no—
284Dic61—42no—
285Dic61#45914yescomplemented
286C2×#459—611no—
287C2×C4×D8—612no—
288C4×#127—611no—
289C42×D4—611no—
290#1982—611no—
291#1947—611no—
292#1925—612no—
293#1879—612no—
294#1802D6111yescharacteristic, complemented
295C4×C4⋊C8—611no—
296C4×#102—612no—
297C2×C61—44no—
298C2×C61C4×#12111yescharacteristic
299C2×C61C2×C4×D811yescharacteristic
300C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
301C2×C61C2×#45911yescharacteristic
302C2×C61#303511yescharacteristic
303C2×C61#310011yescharacteristic
304C2×C61#310611yescharacteristic
305D61—84no—
306C22×D8—612no—
307C2×#127—611no—
308C2×C4×D4—611no—
309C2×C4×D4—611no—
310C2×C4×D4—612no—
311C2×C4×D4—1221no—
312C2×C4×D4—1221no—
313C2×C4×D4C2×D6111yescharacteristic
314C22×C42—1221no—
315#459—618no—
316C4×D8—1228no—
317C2×#107—612no—
318C2×C4⋊C8—611no—
319C2×C4⋊C8C2×D6111yescharacteristic
320C2×#102—612no—
321C2×#102—612no—
322C2×#102—612no—
323C2×#102C2×D6112yes—
324C2×C4×C8—612no—
325#390—612no—
326#390—1221no—
327#390—1221no—
328#384C2×D6111yescharacteristic
329C4×C4⋊C4—611no—
330C4×C4⋊C4—611no—
331C4×C4⋊C4—611no—
332C4×C22⋊C4—1221no—
333C4×C22⋊C4—1221no—
334C4×C22⋊C4—1221no—
335C43—611no—
336#340—612no—
337#340C2×D6112yes—
338#336—612no—
339C61C4×#45911yescharacteristic, complemented, Sylow
340C22×D4—612no—
341C22×D4—1221no—
342C22×D4—1221no—
343C22×D4C22×D6111yescharacteristic
344C23×C4—21no—
345C23×C4—1222no—
346C23×C4—1221no—
347C23×C4—1221no—
348C2×D8—618no—
349C2×D8—1224no—
350C2×D8—1224no—
351C22×C8—612no—
352C22×C8C22×D6112yes—
353#127—614no—
354#127—1222no—
355C4×D4—22no—
356C4×D4—614no—
357C4×D4—1222no—
358C4×D4—1224no—
359C4×D4—1224no—
360C4×D4—1222no—
361C4×D4—1222no—
362C4×D4—2444no—
363C4×D4—2444no—
364C4×D4C4×D6114yescomplemented
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—611no—
368C2×C4⋊C4—611no—
369C2×C4⋊C4C22×D6112yes—
370C2×C4⋊C4C22×D6111yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—1221no—
373C2×C22⋊C4—1221no—
374C2×C22⋊C4—1222no—
375C2×C22⋊C4—1222no—
376C2×C22⋊C4—1222no—
377C2×C42—611no—
378C2×C42—611no—
379C2×C42—611no—
380C2×C42—611no—
381C2×C42—611no—
382C2×C42—611no—
383C2×C42—1221no—
384C2×C42—1221no—
385C2×C42—1221no—
386C2×C42—2444no—
387C2×C42C22×D6111yescharacteristic
388#107—1224no—
389C4⋊C8—22no—
390C4⋊C8—614no—
391#102—24no—
392#102—618no—
393#102—1224no—
394#102—1224no—
395C4×C8—1224no—
396#95—1221no—
397#95—1221no—
398#95—1221no—
399C24—21no—
400C24—1222no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—614no—
405C2×D4—1222no—
406C2×D4—1222no—
407C2×D4—1222no—
408C2×D4—1222no—
409C2×D4—1222no—
410C2×D4—1224no—
411C2×D4—1224no—
412C2×D4—2442no—
413C2×D4—2442no—
414C2×D4—2442no—
415C2×D4—2442no—
416C2×D4C2×C4×D6112yes—
417C2×D4D4×D6112yes—
418C2×D4#1175822612yes—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—22no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—1224no—
429C22×C4—1224no—
430C22×C4—1221no—
431C22×C4—1221no—
432C22×C4—2444no—
433C22×C4—2444no—
434C22×C4—2444no—
435C22×C4—2442no—
436C22×C4—2442no—
437C22×C4—2442no—
438C22×C4—2442no—
439C22×C4D4×D6111yescharacteristic
440C22×C4D4×D6111yescharacteristic
441C22×C4C23×D6111yescharacteristic
442D8—12216no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—614no—
447C2×C8—1222no—
448C2×C8—1222no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—42no—
453C4⋊C4—42no—
454C4⋊C4—612no—
455C4⋊C4—612no—
456C4⋊C4—1221no—
457C4⋊C4—1221no—
458C4⋊C4C2×C4×D6112yes—
459C22⋊C4—24no—
460C22⋊C4—1224no—
461C22⋊C4—1224no—
462C22⋊C4—2444no—
463C22⋊C4—2444no—
464C22⋊C4—2444no—
465C42—612no—
466C42—612no—
467C42—614no—
468C42—1222no—
469C42—1221no—
470C42—1221no—
471C42—1222no—
472C42—2441no—
473C42—2442no—
474C42—2442no—
475C42—2442no—
476C42C2×C4×D6112yes—
477C42#1175822412yes—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—1224no—
486C23—2442no—
487C23—2442no—
488C23—2442no—
489C23—2442no—
490C23—2442no—
491C23—2442no—
492C23C2×D4×D6111yescharacteristic
493D4—22no—
494D4—22no—
495D4—22no—
496D4—1224no—
497D4—1224no—
498D4—2448no—
499D4—2442no—
500D4—2442no—
501D4—2448no—
502D4#1451973914yescomplemented
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—48no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—612no—
513C2×C4—612no—
514C2×C4—612no—
515C2×C4—612no—
516C2×C4—612no—
517C2×C4—1221no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1222no—
522C2×C4—1221no—
523C2×C4—1222no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—4888no—
527C2×C4—2448no—
528C2×C4—2448no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4#1451973712yes—
534C2×C4#1451973712yes—
535C2×C4D8×D6112yes—
536C2×C4#1451979812yes—
537C2×C4C22×C4×D6111yescharacteristic
538C2×C4C2×D4×D6111yescharacteristic
539C2×C4#41×D6111yescharacteristic
540C2×C4#41×D6111yescharacteristic
541C2×C4C2×#1175822411yescharacteristic
542C2×C4C2×#1175822611yescharacteristic
543C8—42no—
544C8—1224no—
545C22—24no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—4882no—
553C22—4882no—
554C22—4882no—
555C22—4882no—
556C22—2444no—
557C22—2444no—
558C22—2444no—
559C22C2×#1451973711yescharacteristic
560C22#121×D6111yescharacteristic
561C22#1684027511yescharacteristic
562C22C2×D8×D6111yescharacteristic
563C22C2×#1451979811yescharacteristic
564C22AGL(1,ℤ/8)×D6111yescharacteristic
565C22#1684056111yescharacteristic
566C4—22no—
567C4—42no—
568C4—82no—
569C4—614no—
570C4—1222no—
571C4—1222no—
572C4—2441no—
573C4—2442no—
574C4—2442no—
575C4#1683984214yescomplemented
576C4C2×#1451973911yescharacteristic
577C4#1684023011yescharacteristic
578C4#1684029811yescharacteristic
579C4#1684030711yescharacteristic
580C2—44no—
581C2—4884no—
582C2#2144832511yescharacteristic
583C2C2×#1683984211yescharacteristic
584C2#2145463211yescharacteristic
585C2#459×D6111yescharacteristic
586C2#2145527511yescharacteristic
587C2#2145582111yescharacteristic
588C2#2145588111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1802C2
socleC23×C61C22×D4
prime radicalC2×#16839957C2
cosocleC22×C4×C61C24
hypercenter#1802D61
hypocenterC61C4×#459
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#16839842C2semidirect
3. #21448381C2semidirect
4. C4×D4×Dic61C2semidirect
5. #21446745C2semidirect
6. #21446575C2semidirect
7. #21446437C2semidirect
8. #21446165C2semidirect
9. C4⋊C8×Dic61C2semidirect
10. #21445633C2semidirect
11. C61×#1802C2semidirect
20. #16839957C4semidirect
53. C2×#11758199C2×C4semidirect
56. #14519774C2×C4semidirect
60. D4×Dic61D4semidirect
83. C4⋊#92418C2×C4semidirect
86. #14519697C2×C4semidirect
95. C4×D4×C61C2×C4semidirect
177. C4×Dic61D8semidirect
201. D4×C61C4×D4semidirect
275. C4×C61C4×D8semidirect
285. Dic61#459semidirect
294. #1802D61semidirect
339. C61C4×#459semidirect
364. C4×D4C4×D61semidirect
502. D4#14519739semidirect
575. C4#16839842semidirect

Maximal subgroups

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

subgroupindex
C2×#168399572
C2×#168398422
#214483812
C4×D4×Dic612
#214467452
#214465752
#214464372
#214461652
C4⋊C8×Dic612
#214456332
C61×#18022
C4×#45961