Finite Group Databasebeta

← #29709888

Subgroups — #29709888

Order 15616.

1098 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×#16839801C211yesmaximal, characteristic, complemented
2C2×#106×D61C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic
4C2×#16839755C211yesmaximal, characteristic
5#21448440C211yesmaximal, characteristic, complemented
6#21448409C211yesmaximal, characteristic
7#21447368C211yesmaximal, characteristic, complemented
8#21447366C211yesmaximal, characteristic, complemented
9#21447363C211yesmaximal, characteristic, complemented
10#21447359C211yesmaximal, characteristic, complemented
11#21447350C211yesmaximal, characteristic, complemented
12#21447340C211yesmaximal, characteristic, complemented
13#21447338C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, characteristic, complemented
15C61×#2094C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519735C2211yescharacteristic
20C2×#14519734C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23#16839801—24no—
24C2×#14519711C2211yescharacteristic
25C2×#14519710C2211yescharacteristic
26C2×#14519709C2211yescharacteristic
27C2×#14519708C2211yescharacteristic
28C2×#14519708C2211yescharacteristic
29C2×#14519708C2211yescharacteristic
30#106×D61—24no—
31#16839760—24no—
32#16839755—24no—
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39#16839668C2211yescharacteristic
40#16839667C2211yescharacteristic
41#16839665C2211yescharacteristic
42#16839657—22no—
43#16839638—22no—
44#16839633—22no—
45#16839631C2211yescharacteristic
46#16839628C2211yescharacteristic
47#16839627C2211yescharacteristic
48#16839620—22no—
49#16839517C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#106×C61C2211yescharacteristic
53C2×#106×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C61×#384C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C2×#11758224—22no—
60C2×#11758224—22no—
61C2×#11758224—22no—
62C2×#11758224—22no—
63C2×#11758224—22no—
64C2×#11758224Q814yes—
65C22×Dic122C2311yescharacteristic
66C22×C22⋊D61—21no—
67C23×Dic61—21no—
68C22×C4×D61—21no—
69C22×C4×D61—21no—
70C22×C4×D61C2311yescharacteristic
71C2×#11758189—22no—
72C2×#11758189—22no—
73C2×#11758189D414yes—
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C2×C8×D61—22no—
77C2×C8×D61—22no—
78C2×C8×D61D414yes—
79#14519735—22no—
80#14519735—22no—
81#14519734—22no—
82#14519734—22no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—22no—
89C2×#11758196D412yes—
90C4⋊C4×D61—22no—
91C4⋊C4×D61—22no—
92C4⋊C4×D61—22no—
93C4⋊C4×D61—22no—
94C2×C22⋊Dic61—22no—
95C2×#11758198—21no—
96C2×#11758198D412yes—
97C2×C4×Dic61—21no—
98C2×C4×Dic61C2311yescharacteristic
99#14519711—22no—
100#14519710—22no—
101#14519709—22no—
102#14519708—22no—
103#14519708—22no—
104#14519708—22no—
105#14519702—22no—
106#14519702—22no—
107#14519700—22no—
108#14519700—22no—
109#14519698—22no—
110#14519698—22no—
111#14519684—22no—
112#14519684—22no—
113#14519684—22no—
114#14519684—22no—
115C22×D4×C61C2311yescharacteristic
116C22×C8×C61C2311yescharacteristic
117C22×C8×C61C2311yescharacteristic
118C2×C4⋊C4×C61—22no—
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C22⋊C4×C61—22no—
123C2×C42×C61C2311yescharacteristic
124#106×C61—22no—
125#106×C61—22no—
126#102×C61—22no—
127#102×C61—22no—
128C24×C61—21no—
129C23×D61C2×D411yescharacteristic
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61C2×Q812yes—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61C2×D412yes—
140C22×C4×C61C2411yescharacteristic
141C2×C22⋊D61—24no—
142C2×C22⋊D61—42no—
143C2×C22⋊D61—42no—
144C22×Dic61—21no—
145C22×Dic61—24no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—42no—
150C22×Dic61—42no—
151C22×Dic61C2×D412yes—
152C22×Dic61C2×D411yescharacteristic
153#11758224—28no—
154#11758224—28no—
155#11758224—44no—
156#11758224—44no—
157C2×C4×D61—42no—
158C2×C4×D61—42no—
159C2×C4×D61—82no—
160C2×C4×D61—82no—
161C2×C4×D61C2×D412yes—
162C2×C4×D61C2×D412yes—
163C2×C4×D61C2×Q812yes—
164C2×C4×D61#4112yes—
165C2×C4×D61#4112yes—
166C2×C4×D61#4112yes—
167C2×Dic122—21no—
168C2×Dic122—21no—
169C2×Dic122—21no—
170C2×Dic122—21no—
171C2×Dic122—21no—
172C2×Dic122C2×Q812yes—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61C2×D412yes—
178C2×C8×C61C2×D412yes—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—82no—
186C22⋊C4×C61—82no—
187C42×C61—21no—
188C42×C61—21no—
189C22⋊Dic61—82no—
190#11758198—24no—
191#11758198—42no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198#11758196—24no—
199#11758196—42no—
200#11758196—42no—
201#11758196—82no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—42no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418C2×D412yes—
210C2×#92418C2×D412yes—
211#11758189—28no—
212C8×D61—28no—
213C23×C61—22no—
214C23×C61—41no—
215C23×C61—41no—
216C23×C61—42no—
217C23×C61—42no—
218C23×C61C22×D411yescharacteristic
219C22×D61—22no—
220C22×D61—22no—
221C22×D61C22⋊Q812yes—
222C22×D61#12312yes—
223C22×D61#12712yes—
224D4×C61—22no—
225D4×C61—22no—
226D4×C61—41no—
227D4×C61—41no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C22×Q811yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C22⋊D61—48no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—48no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61—42no—
257C2×Dic61C22⋊Q812yes—
258C2×Dic61#12312yes—
259C2×Dic61#12712yes—
260C4×D61—84no—
261C4×D61—84no—
262C4×D61C22⋊Q814yes—
263C4×D61C22⋊Q814yes—
264C4×D61#12314yes—
265C4×D61#12314yes—
266Dic122—22no—
267Dic122—22no—
268Dic122—41no—
269Dic122—41no—
270C8×C61—22no—
271C8×C61—22no—
272#92418—22no—
273#92418—22no—
274#23738—611nomaximal, Sylow
275C22×C61—44no—
276C22×C61—42no—
277C22×C61—82no—
278C22×C61—81no—
279C22×C61—81no—
280C22×C61C2×C22⋊Q811yescharacteristic
281C22×C61C2×#12311yescharacteristic
282C22×C61C2×#12711yescharacteristic
283C22×C61#57712yes—
284C22×C61#57712yes—
285C2×D61—24no—
286C2×D61—24no—
287C2×D61—22no—
288C2×D61—22no—
289C2×D61#39914yes—
290C4×C61—42no—
291C4×C61—81no—
292C4×C61—81no—
293C4×C61—81no—
294C4×C61C2×C22⋊Q811yescharacteristic
295C4×C61C2×C22⋊Q811yescharacteristic
296C4×C61C2×#12311yescharacteristic
297C4×C61C2×#12311yescharacteristic
298Dic61—42no—
299Dic61—42no—
300Dic61—81no—
301Dic61—81no—
302Dic61—81no—
303Dic61#39914yes—
304C2×#428—611no—
305C22×#106—611no—
306C2×#417—611no—
307C2×#416—611no—
308#2317—611no—
309#2311—611no—
310#2097—611no—
311#2097—611no—
312#2096—611no—
313#2096—611no—
314#2094—611no—
315#2094D6111yescharacteristic, complemented
316#2092—611no—
317#2092—611no—
318#1729—611no—
319C2×C61—82no—
320C2×C61C2×#39911yescharacteristic
321C2×C61#308412yes—
322C2×C61#309912yes—
323C2×C61#315411yescharacteristic
324C2×C61#315411yescharacteristic
325D61—24no—
326C22×#41—611no—
327C22×M16—611no—
328C23×C8—611no—
329C2×#117—611no—
330C2×#117—611no—
331C22×C4⋊C4—611no—
332C22×C4⋊C4—611no—
333#428—1224no—
334C2×#107—611no—
335C2×#107—611no—
336C2×#106—611no—
337C2×#106—611no—
338C2×#106—611no—
339C2×#106—611no—
340C2×#106—1224no—
341C2×#106C2×D6111yescharacteristic
342C2×#106C2×D6111yescharacteristic
343#417—1224no—
344#416—1224no—
345C2×#103—611no—
346C2×#103—611no—
347C2×#103—611no—
348C2×#103—611no—
349C2×#102—611no—
350C2×#102—611no—
351C2×#102C2×D6111yescharacteristic
352C2×#102C2×D6111yescharacteristic
353#391—611no—
354#391—611no—
355#390—611no—
356#390C2×D6111yescharacteristic
357#389—1222no—
358#386—1222no—
359#385—1222no—
360#384—611no—
361#384C2×D6111yescharacteristic
362#382—611no—
363#382—611no—
364#380—1222no—
365#336—611no—
366#336—611no—
367#336—611no—
368#336C2×D6111yescharacteristic
369C61#2373811yescharacteristic, complemented, Sylow
370C2×#41—614no—
371C2×#41—1222no—
372C2×#41—1222no—
373C2×#41—1222no—
374C2×#41—1222no—
375C2×#41—1222no—
376C22×Q8—611no—
377C22×D4—1221no—
378C22×D4C22×D6111yescharacteristic
379C23×C4—611no—
380C23×C4—1221no—
381C23×C4—1221no—
382C23×C4—1221no—
383C2×M16—614no—
384C2×M16—1222no—
385C2×M16—1222no—
386C22×C8—611no—
387C22×C8—611no—
388C22×C8—614no—
389C22×C8—1222no—
390C22×C8—1222no—
391C22×C8C22×D6111yescharacteristic
392C22×C8C22×D6111yescharacteristic
393#117—1222no—
394#117—1222no—
395#117—1222no—
396#117—1222no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—612no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—1222no—
403C2×C4⋊C4—1222no—
404C2×C4⋊C4—1222no—
405C2×C4⋊C4—1222no—
406C2×C4⋊C4—1222no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4C22×D6111yescharacteristic
410C2×C4⋊C4C22×D6111yescharacteristic
411C2×C4⋊C4C22×D6111yescharacteristic
412C2×C22⋊C4—22no—
413C2×C22⋊C4—612no—
414C2×C22⋊C4—1222no—
415C2×C22⋊C4—1221no—
416C2×C42—611no—
417C2×C42—1221no—
418C2×C42C22×D6111yescharacteristic
419#107—1222no—
420#107—1222no—
421#106—22no—
422#106—22no—
423#106—1222no—
424#106—1222no—
425#106—1222no—
426#106—1222no—
427#103—1222no—
428#103—1222no—
429#103—1222no—
430#103—1222no—
431#102—22no—
432#102—22no—
433#102—1222no—
434#102—1222no—
435#95—1222no—
436#95—1222no—
437#95—1222no—
438#95—1222no—
439C24—21no—
440C24—611no—
441#41—1228no—
442#41—1228no—
443#41—2444no—
444#41—2444no—
445C2×Q8—612no—
446C2×Q8—1221no—
447C2×Q8—1221no—
448C2×Q8—1221no—
449C2×Q8—1221no—
450C2×Q8—1221no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—1224no—
457C2×D4—2442no—
458C2×D4—2442no—
459C2×D4Q8×D6112yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—611no—
464C22×C4—612no—
465C22×C4—612no—
466C22×C4—612no—
467C22×C4—612no—
468C22×C4—612no—
469C22×C4—612no—
470C22×C4—612no—
471C22×C4—1224no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—4882no—
477C22×C4—4882no—
478C22×C4—2442no—
479C22×C4—2442no—
480C22×C4—2442no—
481C22×C4—2442no—
482C22×C4D4×D6112yes—
483C22×C4C23×D6111yescharacteristic
484M16—1228no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—612no—
490C2×C8—612no—
491C2×C8—1228no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8D4×D6112yes—
497C2×C8D4×D6112yes—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—82no—
505C4⋊C4—1224no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—4882no—
513C4⋊C4—2442no—
514C4⋊C4—2442no—
515C22⋊C4—82no—
516C22⋊C4—1224no—
517C22⋊C4—4882no—
518C22⋊C4—2442no—
519C42—21no—
520C42—21no—
521C42—1221no—
522C42—1221no—
523C42—2442no—
524C23—22no—
525C23—41no—
526C23—41no—
527C23—42no—
528C23—42no—
529C23—612no—
530C23—612no—
531C23—612no—
532C23—1222no—
533C23—1222no—
534C23C2×D4×D6111yescharacteristic
535Q8—1222no—
536Q8—1222no—
537Q8—2441no—
538Q8—2441no—
539D4—22no—
540D4—22no—
541D4—41no—
542D4—41no—
543D4—2448no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—612no—
554C2×C4—612no—
555C2×C4—612no—
556C2×C4—614no—
557C2×C4—614no—
558C2×C4—614no—
559C2×C4—614no—
560C2×C4—1222no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—4884no—
565C2×C4—4884no—
566C2×C4—2448no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2442no—
571C2×C4—2442no—
572C2×C4—2442no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4C2×D4×D6111yescharacteristic
576C2×C4C2×D4×D6111yescharacteristic
577C2×C4C2×Q8×D6111yescharacteristic
578C2×C4#41×D6111yescharacteristic
579C2×C4#41×D6111yescharacteristic
580C2×C4#41×D6111yescharacteristic
581C8—22no—
582C8—22no—
583C8—1222no—
584C8—1222no—
585C22—44no—
586C22—42no—
587C22—81no—
588C22—81no—
589C22—82no—
590C22—614no—
591C22—1224no—
592C22—1222no—
593C22—1222no—
594C22—1224no—
595C22C22⋊Q8×D6111yescharacteristic
596C22#123×D6111yescharacteristic
597C22#127×D6111yescharacteristic
598C22#1684056812yes—
599C22#1684057212yes—
600C4—42no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4—614no—
605C4—4881no—
606C4—4881no—
607C4—4881no—
608C4—2442no—
609C4—2442no—
610C4C22⋊Q8×D6111yescharacteristic
611C4C22⋊Q8×D6111yescharacteristic
612C4#123×D6111yescharacteristic
613C4#123×D6111yescharacteristic
614C2—82no—
615C2—1224no—
616C2#399×D6111yescharacteristic
617C2#2145567612yes—
618C2#2145580912yes—
619C2#2145628811yescharacteristic
620C2#2145629211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2094C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
hypercenter#2094D61
hypocenterC61#23738
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2094

Complements

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

NH ≅ G/Ntype
1. C2×#16839801C2semidirect
2. C2×#106×D61C2semidirect
5. #21448440C2semidirect
7. #21447368C2semidirect
8. #21447366C2semidirect
9. #21447363C2semidirect
10. #21447359C2semidirect
11. #21447350C2semidirect
12. #21447340C2semidirect
13. #21447338C2semidirect
14. #21445514C2semidirect
15. C61×#2094C2semidirect
315. #2094D61semidirect
369. C61#23738semidirect

Maximal subgroups

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

subgroupindex
C2×#168398012
C2×#106×D612
C2×#168397602
C2×#168397552
#214484402
#214484092
#214473682
#214473662
#214473632
#214473592
#214473502
#214473402
#214473382
#214455142
C61×#20942
#2373861