Finite Group Databasebeta

← #29695465

Subgroups — #29695465

Order 15616.

1490 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840417C211yesmaximal, characteristic
2C2×D4×#92418C211yesmaximal, characteristic, complemented
3C2×#16839756C212yesmaximal, complemented
4#21446742C211yesmaximal, characteristic, complemented
5#21446620C211yesmaximal, characteristic, complemented
6#21446240C212yesmaximal, complemented
7#21446131C212yesmaximal, complemented
8#21445816C211yesmaximal, characteristic, complemented
9#21445757C212yesmaximal, complemented
10C4×#14519697C211yesmaximal, characteristic, complemented
11C61×#2354C211yesmaximal, characteristic, complemented
12C22×#11758222C2212yes—
13C23×#92418C2212yes—
14#16840417—24no—
15#16840417C418yescomplemented
16C2×#14519777C2211yescharacteristic
17C2×#14519759—22no—
18C2×#14519756C2212yes—
19C2×#14519748—21no—
20C2×C4×D244C2211yescharacteristic
21C2×C4⋊C4×D61—21no—
22D4×#92418—24no—
23C2×C4⋊#92418C2211yescharacteristic
24#16839756—28no—
25C2×#14519700C2212yes—
26C2×#14519700C2212yes—
27C2×#14519700C2212yes—
28C2×#14519700C2212yes—
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2212yes—
31C2×#14519697C2211yescharacteristic
32C2×C22⋊#92418C2212yes—
33C2×C4×#92418C2211yescharacteristic
34#16839524C2211yescharacteristic
35#16839524C2211yescharacteristic
36#16839524C2212yes—
37C2×C4×D4×C61C2211yescharacteristic
38C2×#117×C61C2212yes—
39C61×#390—21no—
40C61×#388—22no—
41C61×#384C2211yescharacteristic
42C61×#380C2212yes—
43C4×C4⋊C4×C61—21no—
44C4×C4⋊C4×C61C2211yescharacteristic
45C2×#11758222—24no—
46C2×#11758222—24no—
47C2×#11758222—24no—
48C2×#11758222—42no—
49C2×#11758222—42no—
50C2×#11758222C2×C418yes—
51C22×Dic122C2312yes—
52C22×D244C2311yescharacteristic
53C22×C22⋊D61—22no—
54C22×C4×D61—21no—
55C22×C4×D61—22no—
56C22×#92418—24no—
57C22×#92418—24no—
58C22×#92418—42no—
59C22×#92418C2311yescharacteristic
60C22×#92418C2312yes—
61C22×#92418C2311yescharacteristic
62#14519777—22no—
63#14519777C2×C414yes—
64#14519759—216no—
65#14519756—24no—
66#14519756C2×C418yes—
67#14519748—28no—
68C4×D244—22no—
69C4×D244C2×C414yes—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—22no—
74C4⋊C4×D61—28no—
75C2×C22⋊Dic61—22no—
76C2×#11758198—21no—
77C4⋊#92418—22no—
78#14519700—24no—
79#14519700—24no—
80#14519700—42no—
81#14519700—42no—
82#14519697—24no—
83#14519697—22no—
84#14519697D414yescomplemented
85C22⋊#92418—24no—
86C4×#92418—22no—
87C22×D4×C61D411yescharacteristic
88C23×C4×C61C2312yes—
89C4×D4×C61C2×C414yes—
90C4×D4×C61D414yes—
91#117×C61—24no—
92#117×C61—42no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61D411yescharacteristic
96C2×C4⋊C4×C61C2311yescharacteristic
97C2×C4⋊C4×C61C2312yes—
98C2×C4⋊C4×C61C2311yescharacteristic
99C2×C22⋊C4×C61—22no—
100C2×C22⋊C4×C61—22no—
101C2×C22⋊C4×C61D412yes—
102C2×C42×C61—21no—
103C2×C42×C61—22no—
104C2×C42×C61C2311yescharacteristic
105#95×C61—22no—
106#95×C61—21no—
107C24×C61C2×D412yes—
108C23×D61—21no—
109C2×D4×C61—22no—
110C2×D4×C61—22no—
111C2×D4×C61C22⋊C414yes—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61—22no—
119C22×C4×C61C22×C414yes—
120C22×C4×C61C2×D412yes—
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D414yes—
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2411yescharacteristic
125C2×C22⋊D61—28no—
126C2×C22⋊D61—44no—
127C2×C22⋊D61—44no—
128C22×Dic61—22no—
129C22×Dic61—21no—
130#11758222—216no—
131#11758222—48no—
132#11758222—48no—
133#11758222—48no—
134C2×D244—21no—
135C2×D244—21no—
136C2×D244—21no—
137C2×D244C22×C412yes—
138C2×D244C2×D412yes—
139C2×D244#4112yes—
140C2×C4×D61—28no—
141C2×C4×D61—24no—
142C2×C4×D61—44no—
143C2×C4×D61—44no—
144C2×C4×D61—42no—
145C2×C4×D61—42no—
146C2×Dic122—22no—
147C2×Dic122—22no—
148C2×Dic122—22no—
149C2×Dic122—22no—
150C2×Dic122—22no—
151C2×Dic122C22×C414yes—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—42no—
158C4⋊C4×C61—81no—
159C4⋊C4×C61C22⋊C414yes—
160C4⋊C4×C61C2×D412yes—
161C22⋊C4×C61—44no—
162C22⋊C4×C61—82no—
163C22⋊C4×C61C22⋊C418yes—
164C42×C61—44no—
165C42×C61—42no—
166C42×C61C22×C412yes—
167C42×C61C2×D412yes—
168C22⋊Dic61—28no—
169#11758198—24no—
170C4⋊Dic61—24no—
171C4⋊Dic61—24no—
172C4⋊Dic61—21no—
173C4⋊Dic61C22×C412yes—
174#11758196—28no—
175C2×#92418—21no—
176C2×#92418—21no—
177C2×#92418—21no—
178C2×#92418—22no—
179C2×#92418—22no—
180C2×#92418—21no—
181C2×#92418—21no—
182C2×#92418—22no—
183C2×#92418—48no—
184C2×#92418C2×D412yes—
185C23×C61—22no—
186C23×C61—22no—
187C23×C61—22no—
188C23×C61—22no—
189C23×C61—22no—
190C23×C61—22no—
191C23×C61C2×C22⋊C414yes—
192C23×C61C22×D411yescharacteristic
193C22×D61—22no—
194C22×D61—22no—
195C22×D61—22no—
196C22×D61—41no—
197C22×D61—41no—
198C22×D61—41no—
199C22×D61—41no—
200D4×C61—28no—
201C2×C4×C61—22no—
202C2×C4×C61—22no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—24no—
206C2×C4×C61—24no—
207C2×C4×C61—24no—
208C2×C4×C61—24no—
209C2×C4×C61—22no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—42no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—42no—
216C2×C4×C61—41no—
217C2×C4×C61—42no—
218C2×C4×C61C2×C22⋊C414yes—
219C2×C4×C61C2×C22⋊C412yes—
220C2×C4×C61C2×C22⋊C412yes—
221C2×C4×C61#13512yes—
222C2×C4×C61#13512yes—
223C2×C4×C61C23×C411yescharacteristic
224C2×C4×C61C22×D411yescharacteristic
225C2×C4×C61C22×D411yescharacteristic
226C2×C4×C61C2×#4111yescharacteristic
227C2×C4×C61H(5,𝔽2)11yescharacteristic
228C2×C4×C61H(5,𝔽2)11yescharacteristic
229C22⋊D61—416no—
230C2×Dic61—22no—
231C2×Dic61—24no—
232C2×Dic61—42no—
233C2×Dic61—42no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236D244—22no—
237D244—22no—
238D244—22no—
239D244C4×D414yes—
240C4×D61—416no—
241C4×D61—48no—
242Dic122—24no—
243Dic122—24no—
244Dic122—42no—
245Dic122—42no—
246#92418—22no—
247#92418—42no—
248#92418—41no—
249#22417—611nomaximal, Sylow
250C22×C61—24no—
251C22×C61—24no—
252C22×C61—24no—
253C22×C61—42no—
254C22×C61—42no—
255C22×C61—42no—
256C22×C61—42no—
257C22×C61C22×C22⋊C411yescharacteristic
258C22×C61D4211yescharacteristic
259C22×C61#54611yescharacteristic
260C22×C61C2×#13511yescharacteristic
261C22×C61C2×#13511yescharacteristic
262C22×C61#57711yescharacteristic
263C22×C61#57811yescharacteristic
264C2×D61—24no—
265C2×D61—42no—
266C2×D61—42no—
267C2×D61—42no—
268C2×D61—42no—
269C2×D61—42no—
270C2×D61—42no—
271C4×C61—24no—
272C4×C61—22no—
273C4×C61—42no—
274C4×C61—82no—
275C4×C61—81no—
276C4×C61#41614yescomplemented
277C4×C61C2×C4×D411yescharacteristic
278C4×C61#51811yescharacteristic
279C4×C61D4211yescharacteristic
280C4×C61#54611yescharacteristic
281Dic61—44no—
282Dic61—42no—
283C2×#547—611no—
284C2×C8×D4—611no—
285C2×#416—612no—
286#2354D6111yescharacteristic, complemented
287#1981—611no—
288#1956—611no—
289#1892—612no—
290#1873—612no—
291#1802—611no—
292#1788—612no—
293C4×#102—611no—
294C2×C61—44no—
295C2×C61D4×C22⋊C411yescharacteristic
296C2×C61C2×#41611yescharacteristic
297C2×C61#289811yescharacteristic
298C2×C61#328311yescharacteristic
299C2×C61#328411yescharacteristic
300C2×C61#330211yescharacteristic
301C2×C61#330311yescharacteristic
302D61—44no—
303C22×#41—612no—
304C23×C8—612no—
305#547—618no—
306#547—1224no—
307C2×C4⋊Q8—611no—
308C2×#123—1222no—
309C2×C22⋊Q8—612no—
310C2×#121—1221no—
311C2×C4×D4—611no—
312C2×C4×D4C2×D6111yescharacteristic
313C2×#117C2×D6112yes—
314C22×C4⋊C4—1221no—
315C8×D4—1224no—
316C2×C4⋊C8—611no—
317#416—1228no—
318C2×#103—612no—
319C2×#103—612no—
320C2×#103—612no—
321C2×#103—612no—
322C2×#102—611no—
323C2×#102—612no—
324C2×#102—611no—
325C2×C22⋊C8—612no—
326C2×C4×C8—611no—
327#390—21no—
328#388—22no—
329#384C2×D6111yescharacteristic
330#380C2×D6112yes—
331C4×C4⋊C4—21no—
332C4×C4⋊C4C2×D6111yescharacteristic
333#340—612no—
334#340—611no—
335#340—611no—
336C61#2241711yescharacteristic, complemented, Sylow
337C2×#41—618no—
338C2×#41—1224no—
339C2×#41—1224no—
340C2×#41—1224no—
341C2×#41—2442no—
342C2×#41—2442no—
343C22×Q8—612no—
344C22×D4—611no—
345C22×D4—1222no—
346C22×D4C22⋊D6111yescharacteristic
347C23×C4—1221no—
348C23×C4—1222no—
349C23×C4C22×D6112yes—
350C22×C8—611no—
351C22×C8—612no—
352C22×C8—611no—
353C22×C8—1224no—
354C22×C8—1224no—
355C22×C8—2442no—
356C4⋊Q8—614no—
357C4⋊Q8—1222no—
358#123—12216no—
359C22⋊Q8—618no—
360C22⋊Q8—1224no—
361#121—1228no—
362C4×D4—614no—
363C4×D4—1222no—
364C4×D4C4×D6114yes—
365C4×D4D24414yes—
366#117—24no—
367#117—42no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—1221no—
372C2×C4⋊C4—1222no—
373C2×C4⋊C4—1221no—
374C2×C4⋊C4—1228no—
375C2×C4⋊C4C22⋊D6111yescharacteristic
376C2×C4⋊C4C22×D6112yes—
377C2×C4⋊C4C22×D6111yescharacteristic
378C2×C4⋊C4C22×D6111yescharacteristic
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—1222no—
382C2×C22⋊C4—1221no—
383C2×C22⋊C4C22⋊D6112yes—
384C2×C42—22no—
385C2×C42—21no—
386C2×C42C22×D6111yescharacteristic
387C4⋊C8—1222no—
388#103—1224no—
389#103—1224no—
390#103—2442no—
391#103—2442no—
392#102—614no—
393#102—1222no—
394#102—1224no—
395C22⋊C8—1224no—
396C4×C8—1222no—
397#95—22no—
398#95—21no—
399C24—1221no—
400C24C2×C22⋊D6112yes—
401#41—12216no—
402#41—2448no—
403#41—2448no—
404#41—2448no—
405C2×Q8—614no—
406C2×Q8—1222no—
407C2×Q8—1222no—
408C2×Q8—1222no—
409C2×Q8—1222no—
410C2×Q8—1222no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—612no—
414C2×D4—612no—
415C2×D4—612no—
416C2×D4—1228no—
417C2×D4—1221no—
418C2×D4—1221no—
419C2×D4—1221no—
420C2×D4—2444no—
421C2×D4—2444no—
422C2×D4#1175819814yes—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—1221no—
431C22×C4—1222no—
432C22×C4—1224no—
433C22×C4—1228no—
434C22×C4—2444no—
435C22×C4—2444no—
436C22×C4—2442no—
437C22×C4—2442no—
438C22×C4C2×C4×D6114yes—
439C22×C4C2×D24414yes—
440C22×C4C2×C22⋊D6112yes—
441C22×C4C2×C22⋊D6111yescharacteristic
442C22×C4C2×C22⋊D6111yescharacteristic
443C22×C4C23×D6111yescharacteristic
444C2×C8—612no—
445C2×C8—1221no—
446C2×C8—1221no—
447C2×C8—1222no—
448C2×C8—1221no—
449C2×C8—1222no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1222no—
453C2×C8—2448no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—42no—
460C4⋊C4—81no—
461C4⋊C4—612no—
462C4⋊C4—1221no—
463C4⋊C4—1228no—
464C4⋊C4—1224no—
465C4⋊C4—1224no—
466C4⋊C4#1175819814yes—
467C4⋊C4D4×D6112yes—
468C22⋊C4—44no—
469C22⋊C4—82no—
470C22⋊C4—1228no—
471C22⋊C4—1224no—
472C22⋊C4#1175819818yes—
473C42—44no—
474C42—42no—
475C42C2×C4×D6112yes—
476C42C2×D24412yes—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—1222no—
484C23—1222no—
485C23—1222no—
486C23—2441no—
487C23—2441no—
488C23—2441no—
489C23—2441no—
490C23C2×#1175819814yes—
491C23C22×C22⋊D6111yescharacteristic
492Q8—1224no—
493Q8—1224no—
494Q8—2442no—
495Q8—2442no—
496D4—28no—
497D4—614no—
498D4—1222no—
499D4—1222no—
500D4—1222no—
501D4—24416no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—1222no—
520C2×C4—1224no—
521C2×C4—24416no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4—2442no—
525C2×C4—2442no—
526C2×C4—2448no—
527C2×C4C2×#1175819812yes—
528C2×C4C2×#1175819814yes—
529C2×C4C2×#1175819812yes—
530C2×C4#1451979712yes—
531C2×C4#1451979712yes—
532C2×C4C22×C4×D6111yescharacteristic
533C2×C4C2×D4×D6111yescharacteristic
534C2×C4C22×D24411yescharacteristic
535C2×C4#41×D6111yescharacteristic
536C2×C4#1451982211yescharacteristic
537C2×C4#1451982311yescharacteristic
538C8—1222no—
539C8—2442no—
540C8—2441no—
541C22—24no—
542C22—24no—
543C22—24no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—1224no—
549C22—2442no—
550C22—2442no—
551C22—2442no—
552C22—2442no—
553C22—2442no—
554C22—2442no—
555C22C22×#1175819811yescharacteristic
556C22D4×C22⋊D6111yescharacteristic
557C22#1684040011yescharacteristic
558C22C2×#1451979711yescharacteristic
559C22C2×#1451979711yescharacteristic
560C22#1684057311yescharacteristic
561C22#1684057711yescharacteristic
562C4—22no—
563C4—24no—
564C4—42no—
565C4—81no—
566C4—82no—
567C4—2444no—
568C4—2442no—
569C4#1683975614yescomplemented
570C4C4×D4×D6111yescharacteristic
571C4#1684023411yescharacteristic
572C4D4×D24411yescharacteristic
573C4#1684040711yescharacteristic
574C2—44no—
575C2—2444no—
576C2D4×#1175819811yescharacteristic
577C2C2×#1683975611yescharacteristic
578C2#2145434911yescharacteristic
579C2#2145753711yescharacteristic
580C2#2145754911yescharacteristic
581C2#2145773011yescharacteristic
582C2#2145774111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2354C2
socleC23×C61C22×D4
prime radicalC2×#16840417C2
cosocleC22×C4×C61C24
hypercenter#2354D61
hypocenterC61#22417
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. C2×D4×#92418C2semidirect
3. C2×#16839756C2semidirect
4. #21446742C2semidirect
5. #21446620C2semidirect
6. #21446240C2semidirect
7. #21446131C2semidirect
8. #21445816C2semidirect
9. #21445757C2semidirect
10. C4×#14519697C2semidirect
11. C61×#2354C2semidirect
15. #16840417C4semidirect
84. #14519697D4semidirect
276. C4×C61#416semidirect
286. #2354D61semidirect
336. C61#22417semidirect
569. C4#16839756semidirect

Maximal subgroups

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

subgroupindex
C2×#168404172
C2×D4×#924182
C2×#168397562
#214467422
#214466202
#214462402
#214461312
#214458162
#214457572
C4×#145196972
C61×#23542
#2241761