Finite Group Databasebeta

← #29571474

Subgroups — #29571474

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840314C211yesmaximal, characteristic
2#21445885C211yesmaximal, characteristic
3C2×#16839500C211yesmaximal, characteristic
4C2×#16839499C211yesmaximal, characteristic
5C2×#16839498C211yesmaximal, characteristic
6#21444043C211yesmaximal, characteristic
7C2×C61×#328C211yesmaximal, characteristic
8#16840314—22no—
9#16840314—22no—
10#16840314—22no—
11#16840314—22no—
12C2×#14519776C411yescharacteristic, complemented
13C2×#14519775C411yescharacteristic, complemented
14C2×#14519767—21no—
15C2×#14519756C2211yescharacteristic
16C2×#14519754—21no—
17C2×Q8×Dic61C411yescharacteristic, complemented
18C2×#14519742—21no—
19C2×#14519742C411yescharacteristic, complemented
20C2×#14519733—21no—
21C22×C4×Dic61C2211yescharacteristic
22C2×C22⋊#92418C2211yescharacteristic
23C2×#14519684—21no—
24C2×#14519684—21no—
25C2×#14519684C2211yescharacteristic
26#16839516—21no—
27#16839516—21no—
28#16839500—22no—
29#16839499—22no—
30#16839498—22no—
31C2×C22⋊Q8×C61C2211yescharacteristic
32C2×C22⋊C8×C61C2211yescharacteristic
33C2×#95×C61C2211yescharacteristic
34C61×#328—22no—
35C22×Dic122—21no—
36C22×Dic122C2×C411yescharacteristic
37C23×Dic61—21no—
38C23×Dic61D411yescharacteristic
39C23×Dic61D411yescharacteristic
40C22×#92418—21no—
41#14519776—22no—
42#14519776—22no—
43#14519775—22no—
44#14519775—22no—
45#14519767—24no—
46#14519767—24no—
47#14519756—21no—
48#14519756—21no—
49#14519756D412yes—
50#14519756D412yes—
51#14519754—24no—
52#14519754—24no—
53Q8×Dic61—22no—
54Q8×Dic61—22no—
55#14519742—24no—
56#14519742—24no—
57#14519742—22no—
58#14519742—22no—
59#14519733—24no—
60#14519733—24no—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61C2×C411yescharacteristic
63C2×#11758196—21no—
64C2×#11758196—21no—
65C2×#11758196—21no—
66C2×#11758196—21no—
67C2×#11758196—21no—
68C2×C22⋊Dic61—21no—
69C2×C4×Dic61—21no—
70C2×C4×Dic61—21no—
71C2×C4×Dic61—21no—
72C2×C4×Dic61—21no—
73C2×C4×Dic61—21no—
74C2×C4×Dic61—21no—
75C2×C4×Dic61C2×C411yescharacteristic
76C2×C4×Dic61C2×C411yescharacteristic
77C2×C4×Dic61D411yescharacteristic
78C2×C4×Dic61D411yescharacteristic
79C22⋊#92418—21no—
80C22⋊#92418—21no—
81#14519684—24no—
82#14519684—21no—
83#14519684—21no—
84#14519684—42no—
85C22×Q8×C61C2×C411yescharacteristic
86C23×C4×C61—21no—
87C23×C4×C61C2311yescharacteristic
88C22×C8×C61—21no—
89C22⋊Q8×C61—21no—
90C22⋊Q8×C61—21no—
91C22⋊Q8×C61D412yes—
92C22⋊Q8×C61D412yes—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61C2×C411yescharacteristic
95C2×C22⋊C4×C61—21no—
96C22⋊C8×C61—21no—
97C22⋊C8×C61—21no—
98#95×C61—21no—
99#95×C61—21no—
100C24×C61C2×D411yescharacteristic
101C2×Q8×C61—21no—
102C2×Q8×C61—41no—
103C2×Q8×C61—41no—
104C2×Q8×C61C22⋊C412yes—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—22no—
108C22×C4×C61—41no—
109C22×C4×C61—41no—
110C22×C4×C61—41no—
111C22×C4×C61—41no—
112C22×C4×C61—41no—
113C22×C4×C61—41no—
114C22×C4×C61—41no—
115C22×C4×C61—41no—
116C22×C4×C61C22×C411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C22×Dic61—21no—
123C22×Dic61—21no—
124C22×Dic61—21no—
125C22×Dic61—21no—
126C22×Dic61—21no—
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61—22no—
131C22×Dic61—22no—
132C22×Dic61—41no—
133C22×Dic61—41no—
134C22×Dic61—41no—
135C22×Dic61—41no—
136C22×Dic61—41no—
137C22×Dic61—41no—
138C22×Dic61—41no—
139C22×Dic61C22⋊C411yescharacteristic
140C22×Dic61C22⋊C411yescharacteristic
141C22×Dic61C22⋊C411yescharacteristic
142C22×Dic61C22⋊C411yescharacteristic
143C22×Dic61SD1612yes—
144C22×Dic61Q1612yes—
145C2×Dic122—24no—
146C2×Dic122—21no—
147C2×Dic122—42no—
148C2×Dic122—42no—
149C2×Dic122—41no—
150C2×Dic122—41no—
151C2×Dic122C22⋊C412yes—
152C2×C8×C61—41no—
153C2×C8×C61—41no—
154C2×C8×C61—41no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—22no—
157C4⋊C4×C61—22no—
158C4⋊C4×C61C22⋊C412yes—
159C22⋊C4×C61—22no—
160C22⋊C4×C61—22no—
161C22⋊Dic61—22no—
162C22⋊Dic61—22no—
163C4⋊Dic61—24no—
164C4⋊Dic61—21no—
165C4⋊Dic61C22⋊C412yes—
166#11758196—24no—
167#11758196—24no—
168#11758196—24no—
169#11758196—24no—
170#11758196—22no—
171#11758196—22no—
172C4×Dic61—24no—
173C4×Dic61—24no—
174C4×Dic61—21no—
175C4×Dic61—21no—
176C4×Dic61—21no—
177C4×Dic61—21no—
178C4×Dic61—21no—
179C4×Dic61—21no—
180C4×Dic61—21no—
181C4×Dic61—21no—
182C2×#92418—41no—
183C2×#92418—41no—
184C2×#92418—41no—
185C23×C61—21no—
186C23×C61—21no—
187C23×C61—21no—
188C23×C61—21no—
189C23×C61C2×C22⋊C411yescharacteristic
190C23×C61#12011yescharacteristic
191C23×C61#12011yescharacteristic
192C23×C61C2×SD1611yescharacteristic
193C23×C61C2×Q1611yescharacteristic
194C23×C61#13711yescharacteristic
195C23×C61#13711yescharacteristic
196Q8×C61—42no—
197Q8×C61—42no—
198C2×C4×C61—21no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61—41no—
207C2×C4×C61—41no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—42no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61—81no—
216C2×C4×C61—81no—
217C2×C4×C61—81no—
218C2×C4×C61—81no—
219C2×C4×C61C2×C22⋊C411yescharacteristic
220C2×C4×C61C2×C22⋊C411yescharacteristic
221C2×C4×C61#12011yescharacteristic
222C2×C4×C61#12011yescharacteristic
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—22no—
230C2×Dic61—22no—
231C2×Dic61—22no—
232C2×Dic61—22no—
233C2×Dic61—21no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—42no—
239C2×Dic61—42no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246C2×Dic61—42no—
247C2×Dic61—81no—
248C2×Dic61—81no—
249C2×Dic61—81no—
250C2×Dic61—81no—
251C2×Dic61#10312yes—
252C2×Dic61#10312yes—
253C2×Dic61#10412yes—
254Dic122—48no—
255Dic122—42no—
256Dic122—42no—
257C8×C61—81no—
258#92418—81no—
259#8333—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—21no—
272C22×C61#37911yescharacteristic
273C22×C61#41011yescharacteristic
274C22×C61#41011yescharacteristic
275C22×C61C2×#10311yescharacteristic
276C22×C61#41911yescharacteristic
277C22×C61C2×#10411yescharacteristic
278C22×C61#42111yescharacteristic
279C22×C61#44811yescharacteristic
280C22×C61#44811yescharacteristic
281C22×C61#45111yescharacteristic
282C22×C61#45111yescharacteristic
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—42no—
288C4×C61—42no—
289C4×C61—82no—
290Dic61—22no—
291Dic61—22no—
292Dic61—22no—
293Dic61—42no—
294Dic61—42no—
295Dic61—41no—
296Dic61—82no—
297C2×#533—611no—
298#1817—611no—
299C2×#328—611no—
300C2×#328—611no—
301C2×#328—611no—
302C2×#328D6111yescharacteristic
303#1434—611no—
304C2×C61—21no—
305C2×C61—21no—
306C2×C61—21no—
307C2×C61—21no—
308C2×C61#150311yescharacteristic
309C2×C61#150611yescharacteristic
310C2×C61#151511yescharacteristic
311C2×C61#151811yescharacteristic
312C2×C61#178211yescharacteristic
313C2×C61#178711yescharacteristic
314C2×C61#178911yescharacteristic
315#533—1222no—
316#533—1222no—
317#533—1222no—
318#533—1222no—
319C2×C4⋊Q8—611no—
320C2×C4⋊Q8—611no—
321C2×#125—1221no—
322C2×C22⋊Q8—611no—
323C2×C22⋊Q8—1221no—
324C2×C22⋊Q8C2×D6111yescharacteristic
325C2×C4×Q8—611no—
326C2×C4×Q8—611no—
327C2×C4×Q8—1221no—
328C2×#117—1221no—
329C22×C42—611no—
330C2×C22⋊C8—611no—
331C2×C22⋊C8C2×D6111yescharacteristic
332C2×#95—611no—
333C2×#95—1221no—
334C2×#95—1221no—
335C2×#95C2×D6111yescharacteristic
336#336—1221no—
337#336—1221no—
338#328—22no—
339#328—1222no—
340#328—1222no—
341#328—1222no—
342C61#833311yescharacteristic, complemented, Sylow
343C22×Q8—611no—
344C22×Q8—1221no—
345C22×Q8C4×D6111yescharacteristic
346C23×C4—21no—
347C23×C4—611no—
348C23×C4—611no—
349C23×C4—1221no—
350C23×C4C22×D6111yescharacteristic
351C22×C8—21no—
352C22×C8—1221no—
353C4⋊Q8—1222no—
354C4⋊Q8—1222no—
355C4⋊Q8—1222no—
356C4⋊Q8—1222no—
357#125—1224no—
358#125—1224no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—612no—
362C22⋊Q8—612no—
363C22⋊Q8—1224no—
364C22⋊Q8—1224no—
365C22⋊Q8—1221no—
366C22⋊Q8—1221no—
367C22⋊Q8D24412yes—
368C22⋊Q8C22⋊D6112yes—
369C4×Q8—1222no—
370C4×Q8—1224no—
371C4×Q8—1224no—
372C4×Q8—1222no—
373C4×Q8—1222no—
374C4×Q8—1222no—
375#117—1224no—
376#117—1224no—
377C2×C4⋊C4—21no—
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⋊C4C4×D6111yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—1221no—
388C2×C42—611no—
389C2×C42—611no—
390C2×C42—611no—
391C2×C42—611no—
392C2×C42—1221no—
393C2×C42—1221no—
394C2×C42—1221no—
395C2×C42—1221no—
396C2×C42—1221no—
397C2×C42—1221no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400C22⋊C8—1221no—
401C22⋊C8—1221no—
402#95—21no—
403#95—21no—
404#95—1224no—
405#95—1221no—
406#95—1221no—
407#95—2442no—
408C24D4×D6111yescharacteristic
409C2×Q8—21no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8—612no—
413C2×Q8—1224no—
414C2×Q8—1221no—
415C2×Q8—2441no—
416C2×Q8—2441no—
417C2×Q8—2442no—
418C2×Q8—2442no—
419C2×Q8#1175819812yes—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—612no—
435C22×C4—612no—
436C22×C4—611no—
437C22×C4—1222no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1221no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1222no—
447C22×C4—2441no—
448C22×C4—2441no—
449C22×C4—2441no—
450C22×C4—2441no—
451C22×C4—2441no—
452C22×C4—2441no—
453C22×C4—2441no—
454C22×C4C2×C4×D6111yescharacteristic
455C22×C4C2×D24411yescharacteristic
456C22×C4D4×D6111yescharacteristic
457C22×C4D4×D6111yescharacteristic
458C22×C4D4×D6111yescharacteristic
459C22×C4C2×C22⋊D6111yescharacteristic
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—2441no—
464C2×C8—2441no—
465C2×C8—2441no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—612no—
470C4⋊C4—1224no—
471C4⋊C4—1224no—
472C4⋊C4—1224no—
473C4⋊C4—1224no—
474C4⋊C4—1224no—
475C4⋊C4—1221no—
476C4⋊C4—1222no—
477C4⋊C4—1222no—
478C4⋊C4#1175819812yes—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—1222no—
482C22⋊C4—1222no—
483C42—1224no—
484C42—1224no—
485C42—1221no—
486C42—1221no—
487C42—1221no—
488C42—1221no—
489C42—1221no—
490C42—1221no—
491C42—1221no—
492C42—1221no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23C22⋊C4×D6111yescharacteristic
498C23#1451974511yescharacteristic
499C23#1451974711yescharacteristic
500C23SD16×D6111yescharacteristic
501C23Q16×D6111yescharacteristic
502C23#1451980611yescharacteristic
503C23#1451980911yescharacteristic
504Q8—42no—
505Q8—42no—
506Q8—2442no—
507Q8—2442no—
508Q8—2448no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—81no—
527C2×C4—81no—
528C2×C4—81no—
529C2×C4—81no—
530C2×C4—612no—
531C2×C4—612no—
532C2×C4—612no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1222no—
540C2×C4—1222no—
541C2×C4—1222no—
542C2×C4—1222no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1222no—
547C2×C4—1222no—
548C2×C4—4881no—
549C2×C4—4881no—
550C2×C4—4881no—
551C2×C4—4881no—
552C2×C4—2442no—
553C2×C4—2442no—
554C2×C4—2442no—
555C2×C4—2442no—
556C2×C4—2442no—
557C2×C4—2441no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4—2441no—
561C2×C4C22⋊C4×D6111yescharacteristic
562C2×C4C2×#1175819811yescharacteristic
563C2×C4#1451974511yescharacteristic
564C2×C4#1451974711yescharacteristic
565C8—81no—
566C8—4881no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22#1683961711yescharacteristic
580C22#1683973411yescharacteristic
581C22#1683973411yescharacteristic
582C22#103×D6111yescharacteristic
583C22#1683976911yescharacteristic
584C22#104×D6111yescharacteristic
585C22#1683977711yescharacteristic
586C22#1683989911yescharacteristic
587C22#1683990211yescharacteristic
588C22#1683991611yescharacteristic
589C22#1683991911yescharacteristic
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—42no—
595C4—42no—
596C4—82no—
597C4—1222no—
598C4—1222no—
599C4—1222no—
600C4—4882no—
601C4—2442no—
602C4—2441no—
603C4—2442no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2#2144431611yescharacteristic
609C2#2144432911yescharacteristic
610C2#2144436811yescharacteristic
611C2#2144438111yescharacteristic
612C2#2144573511yescharacteristic
613C2#2144575211yescharacteristic
614C2#2144576111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#328C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenterC2×#328D61
hypocenterC61#8333
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
12. C2×#14519776C4semidirect
13. C2×#14519775C4semidirect
17. C2×Q8×Dic61C4semidirect
19. C2×#14519742C4semidirect
342. C61#8333semidirect

Maximal subgroups

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

subgroupindex
C2×#168403142
#214458852
C2×#168395002
C2×#168394992
C2×#168394982
#214440432
C2×C61×#3282
#833361