Finite Group Databasebeta

← #30606297

Subgroups — #30606297

Order 15616.

854 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#410C211yesmaximal, characteristic
2#21462280C211yesmaximal, characteristic
3#21460912C214yesmaximal, complemented
4#410×D61C211yesmaximal, characteristic
5C2×#14519856—21no—
6C2×#14519856C411yescharacteristic, complemented
7C22×C4×#6923C411yescharacteristic, complemented
8#16840743C412yescomplemented
9#16840742—21no—
10#16840741—21no—
11#16840741C412yescomplemented
12D61⋊#99—21no—
13D61⋊#99C2212yes—
14(C2×#6923)⋊Q8C412yescomplemented
15#16840714C2212yes—
16#16840710—21no—
17#16840710—21no—
18C4×C22⋊#6923—21no—
19C4×C22⋊#6923—21no—
20C2×#41×D61C2211yescharacteristic
21#117×D61—21no—
22#16839736C411yescharacteristic, complemented
23#16839735—21no—
24#16839734—21no—
25#16839734C412yescomplemented
26#99×D61—21no—
27#99×D61C2212yes—
28C61×#410C411yescharacteristic, complemented
29C23×#6923—21no—
30#14519856—22no—
31#14519856—22no—
32#14519856—41no—
33#14519856—41no—
34#14519856—41no—
35#14519856—41no—
36C2×C4⋊#6923—41no—
37C2×C4⋊#6923C2×C412yes—
38C2×C22⋊#6923—22no—
39C2×C22⋊#6923—21no—
40C2×C22⋊#6923—22no—
41C2×C22⋊#6923—22no—
42C2×C4×#6923—21no—
43C2×C4×#6923—21no—
44C2×C4×#6923—41no—
45C2×C4×#6923—41no—
46C2×C4×#6923—41no—
47C2×C4×#6923C2×C412yes—
48#14519836—22no—
49#14519836C2×C414yescomplemented
50#14519835—22no—
51#14519835—22no—
52(C2×#6923)⋊C4—22no—
53(C2×#6923)⋊C4—22no—
54C2×#11758226C2×C411yescharacteristic
55C2×#11758222C2×C411yescharacteristic
56C2×#11758222D411yescharacteristic
57C2×#11758222Q811yescharacteristic
58C2×#11758224C2×C411yescharacteristic
59C2×#11758224D411yescharacteristic
60C2×#11758224Q811yescharacteristic
61#41×D61—41no—
62#41×D61—41no—
63#41×D61—41no—
64#41×D61—41no—
65C2×Q8×D61C2×C411yescharacteristic
66C2×D4×D61D411yescharacteristic
67C2×D4×D61D411yescharacteristic
68C2×D4×D61C2311yescharacteristic
69C22×C4×D61C2×C411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72#14519736—21no—
73#14519735—41no—
74#14519734—41no—
75#14519733—22no—
76C4⋊C4×D61—41no—
77C22⋊C4×D61—22no—
78C42×D61—41no—
79#14519692—21no—
80#14519692C2×C412yescomplemented
81#14519691—22no—
82#14519691—22no—
83C2×#41×C61C2×C411yescharacteristic
84#117×C61—21no—
85#99×C61—21no—
86#99×C61C2×C412yescomplemented
87C23×D61C22⋊C411yescharacteristic
88C23×D61C2×D411yescharacteristic
89C23×D61C2×D411yescharacteristic
90C22×#6923—22no—
91C22×#6923—22no—
92C22×#6923—44no—
93C22×#6923—42no—
94C22×#6923—42no—
95#41×C61—41no—
96#41×C61—41no—
97C2×Q8×C61C4211yescharacteristic
98C2×D4×C61C22⋊C411yescharacteristic
99C2×D4×C61C4⋊C411yescharacteristic
100C2×D4×C61C22×C411yescharacteristic
101C22×C4×C61C4211yescharacteristic
102C22×C4×C61C22⋊C411yescharacteristic
103C22×C4×C61C4⋊C411yescharacteristic
104C2×C22⋊D61C22⋊C411yescharacteristic
105C2×C22⋊D61C22⋊C411yescharacteristic
106C2×C22⋊D61C4⋊C411yescharacteristic
107C2×C22⋊D61C4⋊C411yescharacteristic
108C2×C22⋊D61C2×D411yescharacteristic
109C2×C22⋊D61C2×Q811yescharacteristic
110C22×Dic61C22⋊C411yescharacteristic
111C22×Dic61C4⋊C411yescharacteristic
112C22×Dic61C4⋊C411yescharacteristic
113#11758226—41no—
114#11758226—41no—
115Q8×D61—41no—
116Q8×D61—41no—
117#11758224—41no—
118#11758224—41no—
119#11758224—41no—
120#11758224—41no—
121#11758224—41no—
122#11758224—41no—
123D4×D61—41no—
124D4×D61—41no—
125D4×D61—41no—
126D4×D61—41no—
127D4×D61—41no—
128D4×D61—41no—
129#11758222—41no—
130#11758222—41no—
131#11758222—41no—
132#11758222—41no—
133#11758222—41no—
134#11758222—41no—
135C2×D244C22⋊C411yescharacteristic
136C2×D244C4⋊C411yescharacteristic
137C2×D244C22×C411yescharacteristic
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61—21no—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61—42no—
151C2×C4×D61C4211yescharacteristic
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61C22⋊C411yescharacteristic
154C2×C4×D61C22⋊C411yescharacteristic
155C2×C4×D61C22⋊C411yescharacteristic
156C2×C4×D61C22⋊C411yescharacteristic
157C2×C4×D61C4⋊C411yescharacteristic
158C2×C4×D61C4⋊C411yescharacteristic
159C2×C4×D61C4⋊C411yescharacteristic
160C2×C4×D61C22×C411yescharacteristic
161C2×Dic122C4211yescharacteristic
162C2×Dic122C4⋊C411yescharacteristic
163C2×Dic122C4⋊C411yescharacteristic
164C22⋊#6923—24no—
165C22⋊#6923—44no—
166C22⋊#6923—44no—
167C22⋊#6923—42no—
168C22⋊#6923—42no—
169C4⋊#6923—42no—
170C4⋊#6923—42no—
171C4⋊#6923—42no—
172C4×#6923—42no—
173C4×#6923—42no—
174C4×#6923—42no—
175C4×#6923—41no—
176C4×#6923—41no—
177C4×#6923—41no—
178C4×#6923—41no—
179C4⋊C4×C61—41no—
180C22⋊C4×C61—22no—
181C42×C61—41no—
182C22⋊Dic61—22no—
183#11758198—42no—
184C4⋊Dic61—41no—
185#11758196—42no—
186C4×Dic61—42no—
187C4×Dic61—41no—
188C23×C61#9511yescharacteristic
189C23×C61C2×C22⋊C411yescharacteristic
190C23×C61C2×C4⋊C411yescharacteristic
191C22×D61—21no—
192C22×D61—21no—
193C22×D61—21no—
194C22×D61—21no—
195C22×D61—21no—
196C22×D61—21no—
197C22×D61—42no—
198C22×D61—42no—
199C22×D61—42no—
200C22×D61#9511yescharacteristic
201C22×D61C2×C22⋊C411yescharacteristic
202C22×D61C2×C22⋊C411yescharacteristic
203C22×D61C2×C4⋊C411yescharacteristic
204C2×#6923—24no—
205C2×#6923—42no—
206C2×#6923—48no—
207C2×#6923—42no—
208C2×#6923—44no—
209C2×#6923—42no—
210C2×#6923—42no—
211C2×#6923—42no—
212C2×#6923—84no—
213Q8×C61—41no—
214D4×C61—41no—
215D4×C61—41no—
216D4×C61—41no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—42no—
224C2×C4×C61#9511yescharacteristic
225C2×C4×C61#9511yescharacteristic
226C2×C4×C61#9511yescharacteristic
227C2×C4×C61C2×C4211yescharacteristic
228C22⋊D61—41no—
229C22⋊D61—41no—
230C22⋊D61—41no—
231C22⋊D61—41no—
232C22⋊D61—41no—
233C22⋊D61—41no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—42no—
241C2×Dic61#9511yescharacteristic
242C2×Dic61#9511yescharacteristic
243C2×Dic61#9511yescharacteristic
244C2×Dic61C2×C4⋊C411yescharacteristic
245D244—41no—
246D244—41no—
247D244—41no—
248C4×D61—21no—
249C4×D61—21no—
250C4×D61—21no—
251C4×D61—21no—
252C4×D61—21no—
253C4×D61—21no—
254C4×D61—21no—
255C4×D61—21no—
256C4×D61—21no—
257C4×D61—21no—
258C4×D61—21no—
259C4×D61—21no—
260C4×D61—21no—
261C4×D61—21no—
262C4×D61—21no—
263C4×D61—21no—
264C4×D61—21no—
265C4×D61—21no—
266C4×D61—84no—
267C4×D61#9911yescharacteristic
268C4×D61#9911yescharacteristic
269C4×D61#9911yescharacteristic
270C4×D61#9911yescharacteristic
271Dic122—41no—
272Dic122—41no—
273Dic122—41no—
274#12581—611nomaximal, Sylow
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—21no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61C2×#9511yescharacteristic
282C2×D61—22no—
283C2×D61—21no—
284C2×D61—21no—
285C2×D61—21no—
286C2×D61—42no—
287C2×D61—42no—
288C2×D61—42no—
289C2×D61—42no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—81no—
294C2×D61—81no—
295C2×D61C2×#9911yescharacteristic
296C2×D61C2×#9911yescharacteristic
297#6923—44no—
298#6923—84no—
299#6923—82no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—21no—
303C4×C61—82no—
304C4×C61#34211yescharacteristic
305C4×C61#34211yescharacteristic
306Dic61—21no—
307Dic61—21no—
308Dic61—21no—
309Dic61—82no—
310Dic61#34211yescharacteristic
311Dic61#34211yescharacteristic
312C2×#410—611no—
313C2×#410—611no—
314#2297—611no—
315#1393—614no—
316C2×C61—21no—
317C2×C61—41no—
318C2×C61—41no—
319C2×C61—41no—
320C2×C61C2×#34211yescharacteristic
321D61—21no—
322D61—41no—
323D61—41no—
324D61—41no—
325D61#212612yes—
326C22×#41—611no—
327C2×#117—611no—
328C2×#117—1221no—
329C2×#117—1221no—
330C22×C42—611no—
331#410—612no—
332#410—612no—
333#410—611no—
334#410—612no—
335#410—1221no—
336#410—1221no—
337#410—1221no—
338#410—1221no—
339#410#692311yescharacteristic, complemented
340C2×#99—612no—
341C2×#99—612no—
342C2×#99—1221no—
343C2×#99—1221no—
344#391—612no—
345#390—612no—
346#386—1221no—
347#386—1221no—
348C4×C22⋊C4—1221no—
349C4×C22⋊C4—1221no—
350C61#1258111yescharacteristic, complemented, Sylow
351C2×#41—611no—
352C2×#41—611no—
353C2×#41—611no—
354C2×#41—611no—
355C2×#41—611no—
356C2×#41—611no—
357C2×#41—611no—
358C2×#41—2441no—
359C2×#41—2441no—
360C2×#41—2441no—
361C2×#41—2441no—
362C2×#41C2×#692311yescharacteristic
363C22×Q8—611no—
364C22×D4—611no—
365C22×D4—611no—
366C22×D4—611no—
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—611no—
370C23×C4—1221no—
371#117—21no—
372#117—1222no—
373#117—1222no—
374#117—1222no—
375#117—1221no—
376#117—2441no—
377#117—2441no—
378#117—2441no—
379#117—2441no—
380#117—2441no—
381#117—2441no—
382C2×C4⋊C4—612no—
383C2×C4⋊C4—2441no—
384C2×C4⋊C4—2441no—
385C2×C22⋊C4—1222no—
386C2×C22⋊C4—1222no—
387C2×C22⋊C4—1221no—
388C2×C22⋊C4—1222no—
389C2×C22⋊C4—1222no—
390C2×C42—612no—
391C2×C42—1221no—
392C2×C42—1221no—
393C2×C42—2441no—
394C2×C42—2441no—
395C2×C42—2441no—
396C2×C42—2441no—
397#99—21no—
398#99—614no—
399#99—612no—
400#99—1222no—
401#99—1222no—
402#99—1222no—
403#99—1222no—
404#99—1222no—
405#99—1221no—
406#99C2×#692312yescomplemented
407#95—1222no—
408#95—1222no—
409C24—611no—
410C24—611no—
411C24—611no—
412#41—41no—
413#41—41no—
414#41—2441no—
415#41—2441no—
416#41—2441no—
417#41—2441no—
418#41—2441no—
419#41—2441no—
420#41—2441no—
421#41—2441no—
422#41—2441no—
423#41—2441no—
424#41—2441no—
425#41—2441no—
426#41—2441no—
427#41—2441no—
428C2×Q8—611no—
429C2×Q8—611no—
430C2×Q8—611no—
431C2×Q8—2441no—
432C2×Q8—2441no—
433C2×Q8C4×#692311yescharacteristic
434C2×D4—611no—
435C2×D4—611no—
436C2×D4—611no—
437C2×D4—611no—
438C2×D4—611no—
439C2×D4—611no—
440C2×D4—611no—
441C2×D4—611no—
442C2×D4—611no—
443C2×D4—2441no—
444C2×D4—2441no—
445C2×D4—2441no—
446C2×D4—2441no—
447C2×D4—2441no—
448C2×D4—2441no—
449C2×D4C4⋊#692311yescharacteristic
450C2×D4C22⋊#692311yescharacteristic
451C2×D4C22×#692311yescharacteristic
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—2442no—
480C22×C4—2444no—
481C22×C4—2442no—
482C22×C4—2442no—
483C22×C4C4×#692311yescharacteristic
484C22×C4C4⋊#692311yescharacteristic
485C22×C4C22⋊#692311yescharacteristic
486C4⋊C4—41no—
487C4⋊C4—2441no—
488C4⋊C4—2442no—
489C4⋊C4—2442no—
490C4⋊C4—2442no—
491C4⋊C4—2442no—
492C22⋊C4—22no—
493C22⋊C4—1224no—
494C22⋊C4—1222no—
495C22⋊C4—2442no—
496C22⋊C4—2444no—
497C22⋊C4—2444no—
498C22⋊C4—2442no—
499C22⋊C4—2442no—
500C42—41no—
501C42—2441no—
502C42—2442no—
503C42—2441no—
504C42—2441no—
505C42—2441no—
506C42—2441no—
507C42—2442no—
508C42—2442no—
509C42—2442no—
510C23—611no—
511C23—611no—
512C23—611no—
513C23—611no—
514C23—1221no—
515C23—1221no—
516C23—1221no—
517C23—1221no—
518C23—1221no—
519C23—1221no—
520C23—2442no—
521C23—2442no—
522C23—2442no—
523C23(C2×#6923)⋊C411yescharacteristic
524C23C2×C22⋊#692311yescharacteristic
525C23C2×C4⋊#692311yescharacteristic
526Q8—41no—
527Q8—2441no—
528Q8—2441no—
529Q8—2441no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—2441no—
534D4—2441no—
535D4—2441no—
536D4—2441no—
537D4—2441no—
538D4—2441no—
539D4—2441no—
540D4—2441no—
541D4—2441no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—42no—
549C2×C4—611no—
550C2×C4—611no—
551C2×C4—611no—
552C2×C4—611no—
553C2×C4—611no—
554C2×C4—611no—
555C2×C4—611no—
556C2×C4—611no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—1224no—
582C2×C4—4884no—
583C2×C4—4884no—
584C2×C4—2442no—
585C2×C4—2442no—
586C2×C4—2444no—
587C2×C4—2442no—
588C2×C4—2442no—
589C2×C4—2442no—
590C2×C4—2442no—
591C2×C4—2448no—
592C2×C4(C2×#6923)⋊C411yescharacteristic
593C2×C4(C2×#6923)⋊C411yescharacteristic
594C2×C4(C2×#6923)⋊C411yescharacteristic
595C2×C4C2×C4×#692311yescharacteristic
596C22—21no—
597C22—21no—
598C22—21no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—611no—
603C22—611no—
604C22—1222no—
605C22—1221no—
606C22—1221no—
607C22—1221no—
608C22—4881no—
609C22—4881no—
610C22—2441no—
611C22—2441no—
612C22—2441no—
613C22—2442no—
614C22—2442no—
615C22—2442no—
616C22—2442no—
617C22C2×(C2×#6923)⋊C411yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—82no—
622C4—611no—
623C4—611no—
624C4—1221no—
625C4—1221no—
626C4—1221no—
627C4—4882no—
628C4—4882no—
629C4—4884no—
630C4—2444no—
631C4#1684063911yescharacteristic
632C4#1684063911yescharacteristic
633C2—21no—
634C2—41no—
635C2—41no—
636C2—41no—
637C2—612no—
638C2—1221no—
639C2—2441no—
640C2—2441no—
641C2—2441no—
642C2C2×#1684063911yescharacteristic
subgroupG/H
centerC4#16840639
commutatorC2×C4×C61C2×C42
FrattiniC2×D4C22×#6923
FittingC61×#410C4
socleC2×C61C2×#342
prime radicalC2×#41×D61C22
cosocleC2×D4×D61C23
hypercenter#410#6923
hypocenterC61#12581
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #21460912C2semidirect
6. C2×#14519856C4semidirect
7. C22×C4×#6923C4semidirect
8. #16840743C4semidirect
11. #16840741C4semidirect
14. (C2×#6923)⋊Q8C4semidirect
22. #16839736C4semidirect
25. #16839734C4semidirect
28. C61×#410C4semidirect
49. #14519836C2×C4semidirect
80. #14519692C2×C4semidirect
86. #99×C61C2×C4semidirect
339. #410#6923semidirect
350. C61#12581semidirect
406. #99C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4102
#214622802
#214609122
#410×D612
#1258161