Finite Group Databasebeta

← #29699185

Subgroups — #29699185

Order 15616.

858 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839849C211yesmaximal, characteristic
2#21448780C211yesmaximal, characteristic, complemented
3#21448728C211yesmaximal, characteristic
4#21446510C211yesmaximal, characteristic, complemented
5#21446508C211yesmaximal, characteristic, complemented
6#21446399C211yesmaximal, characteristic, complemented
7#21446154C211yesmaximal, characteristic
8#21446152C211yesmaximal, characteristic
9#21445948C211yesmaximal, characteristic, complemented
10#21445833C211yesmaximal, characteristic, complemented
11#21445828C211yesmaximal, characteristic
12#21445685C211yesmaximal, characteristic, complemented
13#21445647C211yesmaximal, characteristic
14#21445643C211yesmaximal, characteristic
15C61×#1919C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C2×#14519742C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519739C2211yescharacteristic
20C2×#14519739C2211yescharacteristic
21#16839849C418yescomplemented
22C2×#14519706C2211yescharacteristic
23C2×#14519702C2211yescharacteristic
24C2×#14519700C2211yescharacteristic
25C2×#14519700C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519688C2211yescharacteristic
30C2×#14519687C2211yescharacteristic
31C2×C8×Dic61C2211yescharacteristic
32#16839668C2211yescharacteristic
33#16839667C2211yescharacteristic
34#16839661C2211yescharacteristic
35#16839646—21no—
36#16839644—21no—
37#16839636—21no—
38#16839633—21no—
39#16839629—21no—
40#16839627C2211yescharacteristic
41#16839627C2211yescharacteristic
42#16839619—21no—
43C4⋊C4×Dic61C2211yescharacteristic
44C4×#11758196C2211yescharacteristic
45#16839608—21no—
46#95×D61—21no—
47#16839525C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53C2×#106×C61C2211yescharacteristic
54C61×#389C2211yescharacteristic
55C4×C4⋊C4×C61C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C22×Dic122C2311yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C4×D61—21no—
63C22×C4×D61—21no—
64C22×C4×D61—21no—
65C2×#11758190—22no—
66C2×#11758190—22no—
67C2×#11758190C2×C414yes—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70#14519742—22no—
71#14519742C2×C414yescomplemented
72C4×D244—22no—
73C4×D244—41no—
74#14519739—22no—
75#14519739—22no—
76#14519739—41no—
77#14519739C2×C414yes—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—21no—
82C2×#11758196D411yescharacteristic
83C2×#11758196D411yescharacteristic
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61C2311yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91#14519706—22no—
92#14519702—41no—
93#14519700—41no—
94#14519700C2×C414yescomplemented
95#14519699—22no—
96#14519697—22no—
97#14519697C2×C414yes—
98#14519688—41no—
99#14519687—41no—
100C8×Dic61C2×C414yescomplemented
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684D411yescharacteristic
112#14519684D411yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C42×C61—21no—
121C2×C42×C61C2311yescharacteristic
122#106×C61C2×C414yescomplemented
123#95×C61—21no—
124#95×C61—21no—
125C23×D61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2411yescharacteristic
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61C2×D411yescharacteristic
137C22×Dic61C2×D411yescharacteristic
138C22×Dic61C2×D411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140C2×D244—21no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244C22×C412yes—
144C2×D244#4112yes—
145C2×D244#4112yes—
146C2×C4×D61—24no—
147C2×C4×D61—42no—
148C2×C4×D61—42no—
149C2×C4×D61—42no—
150C2×C4×D61—42no—
151C2×C4×D61—81no—
152C2×C4×D61—81no—
153C2×C4×D61—81no—
154C2×C4×D61—81no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122C22×C412yes—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61C22×C412yes—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—81no—
174C4⋊C4×C61C22×C412yes—
175C4⋊C4×C61C22×C412yes—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—42no—
179#11758198—24no—
180#11758198—42no—
181#11758198—42no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—81no—
187#11758196—24no—
188#11758196—41no—
189#11758196—41no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—24no—
193C4×Dic61—42no—
194C4×Dic61C22×C412yes—
195C4×Dic61#4112yes—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C22×C412yes—
202#11758190—28no—
203C23×C61C22×D411yescharacteristic
204C22×D61—22no—
205C22×D61—22no—
206C22×D61—22no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—41no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61C23×C411yescharacteristic
230C2×C4×C61C2×#4111yescharacteristic
231C2×C4×C61C2×#4111yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61H(5,𝔽2)11yescharacteristic
234C2×C4×C612−1+411yescharacteristic
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—22no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61C4×D412yes—
255C2×Dic61C4×D412yes—
256D244—22no—
257D244—22no—
258D244—22no—
259D244#11714yes—
260C4×D61—84no—
261C4×D61—84no—
262C4×D61—84no—
263Dic122—22no—
264Dic122—22no—
265Dic122—41no—
266Dic122—41no—
267C8×C61—22no—
268C8×C61—41no—
269#92418—22no—
270#92418—41no—
271#22760—611nomaximal, Sylow
272C22×C61C2×C4×D411yescharacteristic
273C22×C61#54611yescharacteristic
274C22×C61#54811yescharacteristic
275C22×C61#57511yescharacteristic
276C22×C61#57511yescharacteristic
277C22×C61#57711yescharacteristic
278C22×C61#57711yescharacteristic
279C2×D61—24no—
280C2×D61—42no—
281C2×D61—42no—
282C2×D61—42no—
283C2×D61—42no—
284C2×D61—42no—
285C2×D61—42no—
286C4×C61—42no—
287C4×C61—42no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—81no—
291C4×C61—81no—
292C4×C61C2×#11711yescharacteristic
293C4×C61#52011yescharacteristic
294C4×C61#55211yescharacteristic
295C4×C61#55311yescharacteristic
296Dic61—22no—
297Dic61—22no—
298Dic61—42no—
299Dic61—41no—
300Dic61—41no—
301Dic61—81no—
302Dic61—81no—
303C2×C4×SD16—611no—
304#2356—611no—
305#2349—611no—
306#1935—611no—
307#1935—611no—
308#1919—611no—
309#1919D6111yescharacteristic, complemented
310#1877—611no—
311#1877—611no—
312#1835—611no—
313#1805—611no—
314#1804—611no—
315#1770—611no—
316#1762—611no—
317#1762—611no—
318C2×C61#235211yescharacteristic
319C2×C61#294311yescharacteristic
320C2×C61#294911yescharacteristic
321C2×C61#332311yescharacteristic
322C2×C61#332311yescharacteristic
323C2×C61#337611yescharacteristic
324C2×C61#337611yescharacteristic
325D61—44no—
326C22×SD16—611no—
327C2×C4×Q8—611no—
328C2×C4×D4—611no—
329C2×C4×D4—611no—
330C2×C4×D4—611no—
331C4×SD16—618no—
332C2×#106C2×D6111yescharacteristic
333C2×C4⋊C8—611no—
334C2×#103—611no—
335C2×#103—611no—
336C2×#103—611no—
337C2×#102—611no—
338C2×#102—611no—
339C2×#102—611no—
340C2×#97—611no—
341C2×#97—611no—
342C2×C4×C8—611no—
343#391—611no—
344#391—611no—
345#389—611no—
346#389C2×D6111yescharacteristic
347#387—1221no—
348#387—1221no—
349#385—1221no—
350#385—1221no—
351#383—1221no—
352#382—611no—
353#382—611no—
354#380—1221no—
355C4×C4⋊C4—611no—
356C4×C4⋊C4—611no—
357C4×C4⋊C4C2×D6111yescharacteristic
358#376—1221no—
359C2×#95—1221no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340—611no—
364#340—611no—
365#340C2×D6111yescharacteristic
366#340C2×D6111yescharacteristic
367#340C2×D6111yescharacteristic
368#336—611no—
369#336C2×D6111yescharacteristic
370C61#2276011yescharacteristic, complemented, Sylow
371C22×Q8—611no—
372C22×D4—611no—
373C23×C4—1221no—
374C23×C4—1221no—
375C23×C4—1221no—
376C2×SD16—614no—
377C2×SD16—1222no—
378C2×SD16—1222no—
379C22×C8—611no—
380C22×C8—611no—
381C22×C8C22×D6111yescharacteristic
382C22×C8C22×D6111yescharacteristic
383C4×Q8—614no—
384C4×Q8—1222no—
385C4×D4—614no—
386C4×D4—1222no—
387C4×D4—1222no—
388C4×D4—1222no—
389C4×D4—2441no—
390C4×D4—2441no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4—1221no—
398C2×C4⋊C4C22×D6111yescharacteristic
399C2×C4⋊C4C22×D6111yescharacteristic
400C2×C4⋊C4C22×D6111yescharacteristic
401C2×C4⋊C4C22×D6111yescharacteristic
402C2×C22⋊C4—1221no—
403C2×C22⋊C4—1221no—
404C2×C22⋊C4—1221no—
405C2×C42—21no—
406C2×C42—611no—
407C2×C42—611no—
408C2×C42—1221no—
409C2×C42—1221no—
410C2×C42C22×D6111yescharacteristic
411#106C4×D6114yescomplemented
412C4⋊C8—1222no—
413#103—614no—
414#103—2441no—
415#103—2441no—
416#102—614no—
417#102—1222no—
418#102—1222no—
419#97—2441no—
420#97—2441no—
421C4×C8—614no—
422#95—21no—
423#95—21no—
424#95—611no—
425#95—611no—
426#95—1221no—
427#95—1221no—
428#95—1221no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433#95—1221no—
434#95—1221no—
435#95—1221no—
436C24—1221no—
437C2×Q8—612no—
438C2×Q8—1221no—
439C2×Q8—1221no—
440C2×Q8—1221no—
441C2×Q8—1221no—
442C2×Q8—1221no—
443C2×D4—612no—
444C2×D4—612no—
445C2×D4—612no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—1221no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—1224no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—4881no—
462C22×C4—4881no—
463C22×C4—4881no—
464C22×C4—4881no—
465C22×C4—2442no—
466C22×C4—2442no—
467C22×C4—2442no—
468C22×C4—2442no—
469C22×C4D4×D6111yescharacteristic
470C22×C4D4×D6111yescharacteristic
471C22×C4C23×D6111yescharacteristic
472SD16—1228no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—612no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8C2×C4×D6112yes—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—81no—
492C4⋊C4—1224no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—4881no—
498C4⋊C4—2441no—
499C4⋊C4—2441no—
500C4⋊C4C2×C4×D6112yes—
501C4⋊C4C2×C4×D6112yes—
502C22⋊C4—1224no—
503C22⋊C4—2442no—
504C22⋊C4—2442no—
505C42—21no—
506C42—21no—
507C42—42no—
508C42—612no—
509C42—612no—
510C42—1224no—
511C42—1221no—
512C42—1221no—
513C42—2442no—
514C23—1222no—
515C23—1222no—
516C23—1222no—
517C23—2441no—
518C23—2441no—
519C23—2441no—
520C23—2441no—
521C23C2×D4×D6111yescharacteristic
522Q8—1222no—
523Q8—1222no—
524Q8—2441no—
525Q8—2441no—
526D4—614no—
527D4—1222no—
528D4—1222no—
529D4—1222no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—612no—
549C2×C4—612no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1222no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—4884no—
562C2×C4—4884no—
563C2×C4—4884no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4C22×C4×D6111yescharacteristic
573C2×C4#41×D6111yescharacteristic
574C2×C4#41×D6111yescharacteristic
575C2×C4#41×D6111yescharacteristic
576C2×C4#1451982311yescharacteristic
577C2×C4#1451982511yescharacteristic
578C8—22no—
579C8—41no—
580C8—1222no—
581C8—2441no—
582C22—1224no—
583C22—2442no—
584C22—2442no—
585C22—2442no—
586C22—2442no—
587C22—2442no—
588C22—2442no—
589C22C4×D4×D6111yescharacteristic
590C22#1684040411yescharacteristic
591C22#1684042211yescharacteristic
592C22#1684055811yescharacteristic
593C22#1684056111yescharacteristic
594C22#1684056811yescharacteristic
595C22#1684056911yescharacteristic
596C4—42no—
597C4—42no—
598C4—41no—
599C4—41no—
600C4—81no—
601C4—81no—
602C4—1222no—
603C4—1222no—
604C4—4881no—
605C4—4881no—
606C4—2442no—
607C4—2441no—
608C4—2441no—
609C4#117×D6111yescharacteristic
610C4#1684024411yescharacteristic
611C4#1684044411yescharacteristic
612C4#1684046311yescharacteristic
613C2—2444no—
614C2#2144874311yescharacteristic
615C2#2145461411yescharacteristic
616C2#2145467311yescharacteristic
617C2#2145803311yescharacteristic
618C2#2145803811yescharacteristic
619C2#2145864911yescharacteristic
620C2#2145865311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1919C2
socleC23×C61C22×D4
prime radicalC22×D244C23
cosocleC22×C4×C61C24
hypercenter#1919D61
hypocenterC61#22760
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
2. #21448780C2semidirect
4. #21446510C2semidirect
5. #21446508C2semidirect
6. #21446399C2semidirect
9. #21445948C2semidirect
10. #21445833C2semidirect
12. #21445685C2semidirect
15. C61×#1919C2semidirect
21. #16839849C4semidirect
71. #14519742C2×C4semidirect
94. #14519700C2×C4semidirect
100. C8×Dic61C2×C4semidirect
122. #106×C61C2×C4semidirect
309. #1919D61semidirect
370. C61#22760semidirect
411. #106C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398492
#214487802
#214487282
#214465102
#214465082
#214463992
#214461542
#214461522
#214459482
#214458332
#214458282
#214456852
#214456472
#214456432
C61×#19192
#2276061