Finite Group Databasebeta

← #29692136

Subgroups — #29692136

Order 15616.

836 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840051C211yesmaximal, characteristic
2C4×#14519776C211yesmaximal, characteristic, complemented
3#21448277C211yesmaximal, characteristic
4#21446765C211yesmaximal, characteristic, complemented
5#21446576C211yesmaximal, characteristic, complemented
6#21446563C211yesmaximal, characteristic, complemented
7#21446561C211yesmaximal, characteristic, complemented
8#21446517C211yesmaximal, characteristic
9#21446514C211yesmaximal, characteristic
10#21446440C211yesmaximal, characteristic
11#21446439C211yesmaximal, characteristic
12#21446401C211yesmaximal, characteristic, complemented
13#21445818C211yesmaximal, characteristic
14#21445671C211yesmaximal, characteristic, complemented
15C61×#1920C211yesmaximal, characteristic, complemented
16C2×#14519776C2211yescharacteristic
17C2×C4×Dic122—21no—
18C2×#14519739C2211yescharacteristic
19C2×#14519735—21no—
20#16840051C418yescomplemented
21C2×#14519711C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519687C2211yescharacteristic
31C2×#14519687C2211yescharacteristic
32#16839666—21no—
33#16839664C2211yescharacteristic
34#16839663C2211yescharacteristic
35#16839661C2211yescharacteristic
36#16839661C2211yescharacteristic
37#16839659—21no—
38#16839658C2211yescharacteristic
39#16839654—21no—
40#16839652—21no—
41#16839631C2211yescharacteristic
42C4⋊C4×Dic61C2211yescharacteristic
43C4×#11758196—21no—
44C4×C4⋊Dic61C2211yescharacteristic
45#16839609—21no—
46C42×Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839517C2211yescharacteristic
53C2×#106×C61C2211yescharacteristic
54C61×#389C2211yescharacteristic
55C4×C4⋊C4×C61C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C22×Dic122—21no—
61C22×D244C2311yescharacteristic
62C22×C4×D61—21no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519776—22no—
66#14519776C2×C414yes—
67C4×Dic122—44no—
68#14519739—22no—
69#14519739C2×C414yes—
70#14519735—44no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61D411yescharacteristic
88C2×C4×Dic61D411yescharacteristic
89C2×C4×Dic61D411yescharacteristic
90C2×C4×Dic61D411yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93#14519711—41no—
94#14519710—41no—
95#14519708C2×C414yes—
96#14519706—22no—
97#14519706C2×C414yes—
98#14519699—41no—
99#14519699C2×C414yes—
100#14519697—41no—
101#14519697C2×C414yes—
102#14519687—41no—
103#14519687—41no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C42×C61—21no—
117C2×C42×C61C2311yescharacteristic
118#106×C61C2×C414yes—
119#95×C61—21no—
120#95×C61—21no—
121C23×D61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2411yescharacteristic
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61C2×D411yescharacteristic
133C22×Dic61C2×D411yescharacteristic
134C22×Dic61C2×D411yescharacteristic
135C22×Dic61C2×D411yescharacteristic
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—21no—
139C2×D244—21no—
140C2×D244—21no—
141C2×D244C22×C412yes—
142C2×C4×D61—24no—
143C2×C4×D61—42no—
144C2×C4×D61—42no—
145C2×Dic122—24no—
146C2×Dic122—42no—
147C2×Dic122—42no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61C22×C412yes—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—42no—
161C4⋊C4×C61C22×C412yes—
162C4⋊C4×C61C22×C412yes—
163C42×C61—21no—
164C42×C61—21no—
165C42×C61—42no—
166#11758198—24no—
167#11758198—42no—
168#11758198—42no—
169#11758198—42no—
170#11758198—42no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—42no—
177C4⋊Dic61—42no—
178C4⋊Dic61C22×C412yes—
179#11758196—24no—
180#11758196—42no—
181#11758196—42no—
182#11758196—42no—
183C4×Dic61—22no—
184C4×Dic61—21no—
185C4×Dic61—21no—
186C4×Dic61—22no—
187C4×Dic61—22no—
188C4×Dic61—41no—
189C4×Dic61—42no—
190C4×Dic61—42no—
191C4×Dic61C22×C412yes—
192C4×Dic61#4112yes—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418C22×C412yes—
199C23×C61C22×D411yescharacteristic
200C22×D61—22no—
201C22×D61—41no—
202C22×D61—41no—
203C22×D61—41no—
204C22×D61—41no—
205C22×D61—41no—
206C22×D61—41no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—22no—
210C2×C4×C61—22no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61AGL(1,ℤ/8)12yes—
225C2×C4×C61C23×C411yescharacteristic
226C2×C4×C61C2×#4111yescharacteristic
227C2×C4×C61H(5,𝔽2)11yescharacteristic
228C2×C4×C612−1+411yescharacteristic
229C2×C4×C612−1+411yescharacteristic
230C2×C4×C612−1+411yescharacteristic
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—22no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61C4×D412yes—
249C2×Dic61C4×D412yes—
250C2×Dic61AGL(1,ℤ/8)12yes—
251C2×Dic61#13712yes—
252D244—22no—
253D244—22no—
254D244—41no—
255D244—41no—
256C4×D61—48no—
257Dic122—48no—
258C8×C61—22no—
259C8×C61—41no—
260#92418—22no—
261#92418—41no—
262#22117—611nomaximal, Sylow
263C22×C61C2×C4×D411yescharacteristic
264C22×C61#53611yescharacteristic
265C22×C61#53711yescharacteristic
266C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
268C22×C61C2×#13711yescharacteristic
269C22×C61#57511yescharacteristic
270C2×D61—42no—
271C2×D61—42no—
272C2×D61—42no—
273C2×D61—81no—
274C2×D61—81no—
275C2×D61—81no—
276C2×D61—81no—
277C4×C61—22no—
278C4×C61—42no—
279C4×C61—42no—
280C4×C61—41no—
281C4×C61—81no—
282C4×C61—81no—
283C4×C61#51911yescharacteristic
284C4×C61#52011yescharacteristic
285C4×C61#54111yescharacteristic
286C4×C61#54211yescharacteristic
287Dic61—22no—
288Dic61—42no—
289Dic61—41no—
290Dic61—41no—
291Dic61—81no—
292Dic61—81no—
293Dic61#44014yes—
294C2×#476—611no—
295C4×C4⋊Q8—611no—
296#2293—611no—
297#1987—611no—
298#1947—611no—
299#1944—611no—
300#1944—611no—
301#1936—611no—
302#1936—611no—
303#1925—611no—
304#1925—611no—
305#1920—611no—
306#1920D6111yescharacteristic, complemented
307#1802—611no—
308#1767—611no—
309C2×C61#232311yescharacteristic
310C2×C61C2×#44011yescharacteristic
311C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
312C2×C61#323511yescharacteristic
313C2×C61#323811yescharacteristic
314C2×C61#325211yescharacteristic
315C2×C61#325311yescharacteristic
316D61—82no—
317C2×C4⋊Q8—611no—
318C2×C4×Q8—1221no—
319C2×C4×D4—611no—
320C2×#117—1221no—
321#476—618no—
322C2×#107—611no—
323C2×#107—611no—
324C2×#106—611no—
325C2×#106C2×D6111yescharacteristic
326C2×C4⋊C8—611no—
327C2×C4⋊C8—611no—
328C2×#102—611no—
329C2×#102—611no—
330C2×#102—611no—
331C2×#102—611no—
332C2×#97—611no—
333C2×#97—611no—
334#391—1221no—
335#390—611no—
336#390—611no—
337#389—611no—
338#389—611no—
339#389—611no—
340#389—1221no—
341#389C2×D6111yescharacteristic
342#388—1221no—
343#388—1221no—
344#384—611no—
345C4×C4⋊C4—611no—
346C4×C4⋊C4—611no—
347C4×C4⋊C4—1221no—
348C4×C4⋊C4C2×D6111yescharacteristic
349C4×C22⋊C4—1221no—
350C43—611no—
351#340—611no—
352#340—611no—
353#340—611no—
354#340—611no—
355#340—611no—
356#340C2×D6111yescharacteristic
357#340C2×D6111yescharacteristic
358#340C2×D6111yescharacteristic
359#336—611no—
360#336C2×D6111yescharacteristic
361C61#2211711yescharacteristic, complemented, Sylow
362C22×Q8—1221no—
363C22×D4—611no—
364C23×C4—1221no—
365C22×C8—611no—
366C22×C8—611no—
367C22×C8C22×D6111yescharacteristic
368C22×C8C22×D6111yescharacteristic
369C4⋊Q8—614no—
370C4⋊Q8—1222no—
371C4×Q8—2444no—
372C4×D4—614no—
373C4×D4—1222no—
374#117—2444no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4—1221no—
385C2×C4⋊C4C22×D6111yescharacteristic
386C2×C4⋊C4C22×D6111yescharacteristic
387C2×C4⋊C4C22×D6111yescharacteristic
388C2×C4⋊C4C22×D6111yescharacteristic
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C22⋊C4—1221no—
392C2×C22⋊C4—1221no—
393C2×C22⋊C4—1221no—
394C2×C42—21no—
395C2×C42—611no—
396C2×C42—611no—
397C2×C42—611no—
398C2×C42—611no—
399C2×C42—611no—
400C2×C42—611no—
401C2×C42—1221no—
402C2×C42—1221no—
403C2×C42C22×D6111yescharacteristic
404#107—2441no—
405#107—2441no—
406#106—614no—
407#106C4×D6114yes—
408C4⋊C8—614no—
409C4⋊C8—1222no—
410#102—614no—
411#102—614no—
412#102—2441no—
413#102—2441no—
414#97—2441no—
415#97—2441no—
416#95—21no—
417#95—21no—
418#95—1221no—
419#95—1221no—
420#95—1221no—
421#95—1221no—
422#95—1221no—
423C24—1221no—
424C2×Q8—1224no—
425C2×Q8—2442no—
426C2×Q8—2442no—
427C2×D4—612no—
428C2×D4—1221no—
429C2×D4—1221no—
430C2×D4—1221no—
431C2×D4—1221no—
432C2×D4—1221no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—1224no—
442C22×C4—1221no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—2442no—
446C22×C4—2442no—
447C22×C4D4×D6111yescharacteristic
448C22×C4D4×D6111yescharacteristic
449C22×C4C23×D6111yescharacteristic
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—612no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8C2×C4×D6112yes—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—612no—
470C4⋊C4—1224no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—2442no—
477C4⋊C4—2442no—
478C4⋊C4—2442no—
479C4⋊C4—2442no—
480C4⋊C4—2442no—
481C4⋊C4C2×C4×D6112yes—
482C4⋊C4C2×C4×D6112yes—
483C22⋊C4—1224no—
484C22⋊C4—2442no—
485C22⋊C4—2442no—
486C22⋊C4—2442no—
487C22⋊C4—2442no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—612no—
492C42—612no—
493C42—1222no—
494C42—1222no—
495C42—1221no—
496C42—1221no—
497C42—1222no—
498C42—2441no—
499C42—2442no—
500C42—2442no—
501C23—1222no—
502C23—2441no—
503C23—2441no—
504C23—2441no—
505C23—2441no—
506C23—2441no—
507C23—2441no—
508C23C2×D4×D6111yescharacteristic
509Q8—2448no—
510D4—1222no—
511D4—1222no—
512D4—2441no—
513D4—2441no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—612no—
532C2×C4—612no—
533C2×C4—612no—
534C2×C4—612no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1222no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—2448no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4#1451980412yes—
554C2×C4C22×C4×D6111yescharacteristic
555C2×C4#41×D6111yescharacteristic
556C2×C4#1451982311yescharacteristic
557C2×C4#1451982411yescharacteristic
558C2×C4#1451982411yescharacteristic
559C2×C4#1451982511yescharacteristic
560C8—22no—
561C8—41no—
562C8—1222no—
563C8—2441no—
564C22—4881no—
565C22—4881no—
566C22—4881no—
567C22—4881no—
568C22—2442no—
569C22—2442no—
570C22—2442no—
571C22C4×D4×D6111yescharacteristic
572C22#1684033411yescharacteristic
573C22#1684034211yescharacteristic
574C22AGL(1,ℤ/8)×D6111yescharacteristic
575C22C2×#1451980411yescharacteristic
576C22#137×D6111yescharacteristic
577C22#1684055911yescharacteristic
578C4—22no—
579C4—42no—
580C4—42no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4—614no—
585C4—1222no—
586C4—4881no—
587C4—4881no—
588C4—2442no—
589C4—2441no—
590C4—2441no—
591C4#1684023811yescharacteristic
592C4#1684024211yescharacteristic
593C4#1684037111yescharacteristic
594C4#1684037811yescharacteristic
595C2—4882no—
596C2#2144850011yescharacteristic
597C2#440×D6111yescharacteristic
598C2C4×#1451980411yescharacteristic
599C2#2145701411yescharacteristic
600C2#2145704311yescharacteristic
601C2#2145719111yescharacteristic
602C2#2145719911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1920C2
socleC23×C61C22×D4
prime radicalC22×D244C23
cosocleC22×C4×C61C24
hypercenter#1920D61
hypocenterC61#22117
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
2. C4×#14519776C2semidirect
4. #21446765C2semidirect
5. #21446576C2semidirect
6. #21446563C2semidirect
7. #21446561C2semidirect
12. #21446401C2semidirect
14. #21445671C2semidirect
15. C61×#1920C2semidirect
20. #16840051C4semidirect
306. #1920D61semidirect
361. C61#22117semidirect

Maximal subgroups

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

subgroupindex
C2×#168400512
C4×#145197762
#214482772
#214467652
#214465762
#214465632
#214465612
#214465172
#214465142
#214464402
#214464392
#214464012
#214458182
#214456712
C61×#19202
#2211761