Finite Group Databasebeta

← #29740191

Subgroups — #29740191

Order 15616.

800 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839970C211yesmaximal, characteristic
2C2×#16839854C211yesmaximal, characteristic
3#21449598C211yesmaximal, characteristic
4Q8×C4⋊Dic61C211yesmaximal, characteristic
5#21447357C211yesmaximal, characteristic
6#21447316C211yesmaximal, characteristic
7#21447229C211yesmaximal, characteristic
8#21447064C211yesmaximal, characteristic
9#21446497C211yesmaximal, characteristic
10#21446375C211yesmaximal, characteristic
11#21446162C211yesmaximal, characteristic
12#21446160C211yesmaximal, characteristic
13#21446074C211yesmaximal, characteristic
14#21446071C211yesmaximal, characteristic
15C61×#1878C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C2×#14519775C2211yescharacteristic
18C2×Q8×Dic61C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×#14519742C2211yescharacteristic
21#16839970—24no—
22#16839854—24no—
23C2×#14519710C2211yescharacteristic
24C2×#14519710C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33#16839703—21no—
34#16839696—21no—
35#16839669C2211yescharacteristic
36#16839668C2211yescharacteristic
37#16839661—21no—
38#16839661—21no—
39#16839661C2211yescharacteristic
40#16839661C2211yescharacteristic
41#16839658C2211yescharacteristic
42#16839645—21no—
43#16839644—21no—
44#16839632—21no—
45#16839632C2211yescharacteristic
46C4×C4⋊Dic61—21no—
47C4×C4⋊Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×Q16×C61C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C61×#391C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C2×#11758202—22no—
63C2×#11758202—22no—
64C2×#11758202D414yes—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519775—22no—
68#14519775—41no—
69Q8×Dic61—22no—
70Q8×Dic61—22no—
71Q8×Dic61—41no—
72Q8×Dic61—41no—
73#14519742—22no—
74#14519742—41no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61D411yescharacteristic
82C2×C4⋊Dic61D411yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61C2311yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95#14519710—22no—
96#14519710—41no—
97#14519706—22no—
98#14519702—22no—
99#14519702—22no—
100#14519701—22no—
101#14519701—22no—
102#14519701—41no—
103#14519700—22no—
104C8×Dic61—22no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684D411yescharacteristic
113#14519684D411yescharacteristic
114C22×Q8×C61C2311yescharacteristic
115C22×Q8×C61C2311yescharacteristic
116C2×Q16×C61—22no—
117C2×Q16×C61—22no—
118C2×Q16×C61—22no—
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C4×Q8×C61—22no—
122C4×Q8×C61—22no—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C42×C61—21no—
127C2×C42×C61C2311yescharacteristic
128#103×C61—22no—
129#103×C61—22no—
130#95×C61—21no—
131#95×C61—21no—
132C2×Q8×C61—21no—
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61—21no—
141C2×Q8×C61C2×D412yes—
142C2×Q8×C61#4112yes—
143C2×Q8×C61#4112yes—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2411yescharacteristic
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122C2×D412yes—
165Q16×C61—44no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C4⋊C4×C61—24no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61#4112yes—
177C42×C61—24no—
178C42×C61—21no—
179C42×C61—21no—
180#11758202—28no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—41no—
188C4⋊Dic61—42no—
189C4⋊Dic61—42no—
190C4⋊Dic61—42no—
191C4⋊Dic61—81no—
192C4⋊Dic61—81no—
193C4⋊Dic61—81no—
194C4⋊Dic61Q1614yescomplemented
195#11758196—42no—
196#11758196—42no—
197#11758196—42no—
198#11758196—42no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61—42no—
204C4×Dic61—42no—
205C4×Dic61—42no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418C2×D412yes—
212C23×C61C22×D411yescharacteristic
213Q8×C61—22no—
214Q8×C61—22no—
215Q8×C61—22no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61#12314yes—
221C2×C4×C61—21no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—22no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61C2×Q1612yes—
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61H(5,𝔽2)11yescharacteristic
244C2×C4×C612−1+411yescharacteristic
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—22no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61C2×Q1612yes—
268C2×Dic61C2×Q1612yes—
269Dic122—22no—
270Dic122—22no—
271Dic122—41no—
272Dic122—41no—
273C8×C61—41no—
274C8×C61—41no—
275#92418—22no—
276#92418—41no—
277#26171—611nomaximal, Sylow
278C22×C61#52511yescharacteristic
279C22×C61D4211yescharacteristic
280C22×C61#54811yescharacteristic
281C22×C61C22×Q1611yescharacteristic
282C22×C61#57511yescharacteristic
283C22×C61#57711yescharacteristic
284C22×C61#57811yescharacteristic
285C4×C61—22no—
286C4×C61—24no—
287C4×C61—41no—
288C4×C61—42no—
289C4×C61—81no—
290C4×C61—81no—
291C4×C61C2×#12311yescharacteristic
292C4×C61#53911yescharacteristic
293C4×C61#54711yescharacteristic
294C4×C61#55311yescharacteristic
295Dic61—22no—
296Dic61—22no—
297Dic61—42no—
298Dic61—41no—
299Dic61—41no—
300Dic61—81no—
301Dic61—81no—
302Dic61—81no—
303C2×#462—611no—
304C2×C4×Q16—611no—
305#2446—611no—
306Q8×C4⋊C4—611no—
307#2095—611no—
308#2087—611no—
309#2072—611no—
310#2043—611no—
311#1933—611no—
312#1916—611no—
313#1878—611no—
314#1878—611no—
315#1878D6111yescharacteristic
316#1863—611no—
317#1863—611no—
318C2×C61#244311yescharacteristic
319C2×C61#310411yescharacteristic
320C2×C61#312011yescharacteristic
321C2×C61#327111yescharacteristic
322C2×C61D4×Q1611yescharacteristic
323C2×C61#336311yescharacteristic
324C2×C61#337711yescharacteristic
325C22×Q16—611no—
326C22×Q16C2×D6111yescharacteristic
327C2×C4⋊Q8—611no—
328C2×C4×Q8—611no—
329C2×C4×Q8—611no—
330C2×C4×Q8—611no—
331C2×C4×Q8C2×D6111yescharacteristic
332#462—1224no—
333C4×Q16—1224no—
334C2×#107—611no—
335C2×#107—611no—
336C2×C4⋊C8—611no—
337C2×#103—611no—
338C2×#103—611no—
339C2×#103—611no—
340C2×#103—611no—
341C2×#103—611no—
342C2×#103—611no—
343C2×#103C2×D6111yescharacteristic
344C2×#103C2×D6111yescharacteristic
345C2×C4×C8—611no—
346#400—1221no—
347#398—1221no—
348#391—611no—
349#391—611no—
350#391C2×D6111yescharacteristic
351#389—611no—
352#389—611no—
353#389—611no—
354#389—1221no—
355#389—1221no—
356#387—1221no—
357#387—1221no—
358#384—611no—
359#384—1221no—
360C4×C4⋊C4—611no—
361C4×C4⋊C4—1221no—
362#340—611no—
363#340—611no—
364#340—611no—
365#340C2×D6111yescharacteristic
366#336—611no—
367#336—611no—
368#336—611no—
369#336C2×D6111yescharacteristic
370C61#2617111yescharacteristic, complemented, Sylow
371C22×Q8—611no—
372C22×Q8C22×D6111yescharacteristic
373C22×Q8C22×D6111yescharacteristic
374C2×Q16—22no—
375C2×Q16—22no—
376C2×Q16—22no—
377C2×Q16—614no—
378C2×Q16—1222no—
379C2×Q16—1222no—
380C22×C8—611no—
381C22×C8—611no—
382C22×C8C22×D6111yescharacteristic
383C22×C8C22×D6111yescharacteristic
384C4⋊Q8—1222no—
385C4⋊Q8—2441no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×Q8—1222no—
389C4×Q8—1222no—
390C4×Q8—1222no—
391C4×Q8—2441no—
392C4×Q8—2441no—
393C4×Q8—2441no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4C22×D6111yescharacteristic
411C2×C4⋊C4C22×D6111yescharacteristic
412C2×C42—21no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—1221no—
416C2×C42—1221no—
417C2×C42—1221no—
418C2×C42C22×D6111yescharacteristic
419#107—1222no—
420#107—2441no—
421C4⋊C8—1222no—
422#103—22no—
423#103—22no—
424#103—1222no—
425#103—1222no—
426#103—1222no—
427#103—1222no—
428#103—1222no—
429#103—2441no—
430C4×C8—1222no—
431#95—21no—
432#95—21no—
433#95—611no—
434#95—611no—
435#95—1221no—
436#95—1221no—
437#95—1221no—
438#95—1221no—
439#95—1221no—
440#95—1221no—
441#95—1221no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—612no—
452C2×Q8—1221no—
453C2×Q8—1221no—
454C2×Q8—1221no—
455C2×Q8—1221no—
456C2×Q8—1221no—
457C2×Q8#1175822212yes—
458C2×Q8D4×D6112yes—
459C2×Q8#1175822412yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4D4×D6111yescharacteristic
473C22×C4D4×D6111yescharacteristic
474C22×C4C23×D6111yescharacteristic
475Q16—44no—
476Q16—1228no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—612no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C4⋊C4—24no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—614no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—4881no—
501C4⋊C4—4881no—
502C4⋊C4—4881no—
503C4⋊C4—2441no—
504C4⋊C4—2442no—
505C4⋊C4—2442no—
506C4⋊C4—2442no—
507C4⋊C4—2442no—
508C4⋊C4—2442no—
509C4⋊C4—2442no—
510C4⋊C4—2442no—
511C4⋊C4#1175822412yes—
512C42—24no—
513C42—21no—
514C42—21no—
515C42—1221no—
516C42—1221no—
517C42—1221no—
518C42—1221no—
519C42—2442no—
520C42—2442no—
521C42—2442no—
522C23C2×D4×D6111yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—22no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—1222no—
531Q8—1222no—
532Q8—2441no—
533Q8—2441no—
534Q8#1451975914yes—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—612no—
553C2×C4—612no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1222no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4Q16×D6112yes—
577C2×C4C2×D4×D6111yescharacteristic
578C2×C4C2×#1175822411yescharacteristic
579C2×C4C2×#1175822411yescharacteristic
580C2×C4C2×#1175822211yescharacteristic
581C2×C4#1451982311yescharacteristic
582C2×C4#1451982411yescharacteristic
583C8—41no—
584C8—41no—
585C8—1222no—
586C8—2441no—
587C22#1684026811yescharacteristic
588C22#1684039611yescharacteristic
589C22#1684042111yescharacteristic
590C22C2×Q16×D6111yescharacteristic
591C22#1684056111yescharacteristic
592C22#1684056911yescharacteristic
593C22#1684057811yescharacteristic
594C4—24no—
595C4—22no—
596C4—41no—
597C4—42no—
598C4—81no—
599C4—81no—
600C4—1222no—
601C4—1222no—
602C4—4881no—
603C4—4881no—
604C4—4881no—
605C4—2441no—
606C4—2441no—
607C4—2442no—
608C4C2×#1451975911yescharacteristic
609C4#1684035611yescharacteristic
610C4#1684041211yescharacteristic
611C4#1684045811yescharacteristic
612C2#2144956011yescharacteristic
613C2#2145585311yescharacteristic
614C2#2145602611yescharacteristic
615C2#2145741011yescharacteristic
616C2#2145756611yescharacteristic
617C2#2145849511yescharacteristic
618C2#2145866611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1878C2
socle, prime radicalC23×C61C22×D4
hypercenter#1878D61
hypocenterC61#26171
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
194. C4⋊Dic61Q16semidirect
370. C61#26171semidirect

Maximal subgroups

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

subgroupindex
C2×#168399702
C2×#168398542
#214495982
Q8×C4⋊Dic612
#214473572
#214473162
#214472292
#214470642
#214464972
#214463752
#214461622
#214461602
#214460742
#214460712
C61×#18782
#2617161