Finite Group Databasebeta

← #30616765

Subgroups — #30616765

Order 15616.

1100 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462497C211yesmaximal, characteristic
2C4×D61⋊M16C211yesmaximal, characteristic
3#21462011C212yesmaximal, complemented
4#21461962C212yesmaximal, complemented
5#21461847C214yesmaximal
6C4×#14519838C214yesmaximal, complemented
7C2×#16840316C211yesmaximal, characteristic
8C2×D61⋊M16C2212yes—
9#16840785—21no—
10#16840784—21no—
11#16840781—21no—
12#16840780—21no—
13#16840765C2212yes—
14C2×#14519838C2218yes—
15#16840734C2212yes—
16C4×#11758213—21no—
17C4×#11758213—21no—
18C4×#11758217C2212yes—
19C4×#11758217C2212yes—
20C4×#11758217C2212yes—
21#16840721—21no—
22C4×D61⋊C8—21no—
23#16840642C2218yes—
24#16840316—21no—
25#16840316—21no—
26#16840316—21no—
27#16840316—21no—
28#16840316—21no—
29#16840316—21no—
30#16840316—21no—
31#16840316—21no—
32C2×#14519776C2211yescharacteristic
33C2×#14519775C2211yescharacteristic
34C2×#14519767C412yes—
35C2×#14519757C411yescharacteristic
36C2×#14519755C2212yes—
37C2×#14519753C411yescharacteristic
38C2×C4×Dic122C411yescharacteristic
39C2×C4×Dic122C2212yes—
40C2×#14519734C412yes—
41C2×C42×D61C2211yescharacteristic
42C2×C4×Q8×C61C411yescharacteristic
43C2×#11758213—22no—
44D61⋊M16—28no—
45C2×#11758217C2314yes—
46C2×#11758217C2314yes—
47C2×D61⋊C8—22no—
48#14519844—22no—
49C4⋊#92420—22no—
50#14519838—216no—
51#14519834—22no—
52#14519834—22no—
53#14519832—22no—
54#14519832—22no—
55#14519832—22no—
56C4×#92420—22no—
57C4×#92420—22no—
58C4×#92420—22no—
59C22×Dic122C2×C411yescharacteristic
60C22×Dic122C2312yes—
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64#14519776—21no—
65#14519776—21no—
66#14519776—21no—
67#14519776—21no—
68#14519775—21no—
69#14519775—21no—
70#14519775—21no—
71#14519775—21no—
72#14519767—22no—
73#14519767—22no—
74#14519767—22no—
75#14519767—22no—
76#14519757—21no—
77#14519757—21no—
78#14519757—21no—
79#14519757—21no—
80#14519755—22no—
81#14519755—22no—
82#14519755—22no—
83#14519755—22no—
84#14519753—21no—
85#14519753—21no—
86#14519753—21no—
87#14519753—21no—
88C4×Dic122—21no—
89C4×Dic122—21no—
90C4×Dic122—21no—
91C4×Dic122—21no—
92C4×Dic122—22no—
93C4×Dic122—22no—
94C4×Dic122—22no—
95C4×Dic122—22no—
96#14519734—22no—
97#14519734—22no—
98#14519734—22no—
99#14519734—22no—
100C2×C4⋊Dic61C2×C411yescharacteristic
101C2×C4⋊Dic61C2×C412yes—
102C2×#11758196C2×C412yes—
103C2×#11758196C2×C412yes—
104C2×#11758196C2×C412yes—
105C2×#11758196C2×C412yes—
106C2×#11758196C2312yes—
107C2×#11758198C2×C412yes—
108C2×#11758198C2×C412yes—
109C2×C4×Dic61C2×C412yes—
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61D411yescharacteristic
120C42×D61D411yescharacteristic
121C22×Q8×C61C2×C411yescharacteristic
122C4×Q8×C61—21no—
123C4×Q8×C61—21no—
124C4×Q8×C61—21no—
125C4×Q8×C61—21no—
126C2×C4⋊C4×C61C2×C412yes—
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C42×C61C2×C412yes—
129C2×C42×C61C2×C411yescharacteristic
130C23×D61C22×C411yescharacteristic
131C2×Q8×C61—21no—
132C2×Q8×C61—21no—
133C2×Q8×C61—42no—
134C22×C4×C61C22×C412yes—
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C412yes—
139C22×Dic61C22×C412yes—
140C22×Dic61C22×C411yescharacteristic
141C22×Dic61C22×C412yes—
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C2411yescharacteristic
144C2×C4×D61—24no—
145C2×C4×D61—24no—
146C2×C4×D61—42no—
147C2×C4×D61C22⋊C411yescharacteristic
148C2×C4×D61C22⋊C411yescharacteristic
149C2×C4×D61C22⋊C411yescharacteristic
150C2×C4×D61C22⋊C411yescharacteristic
151C2×C4×D61C22⋊C411yescharacteristic
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61C22⋊C411yescharacteristic
154C2×C4×D61C22⋊C411yescharacteristic
155C2×C4×D61C2×D411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61C2×D411yescharacteristic
158C2×C4×D61C2×D411yescharacteristic
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—22no—
162C2×Dic122—22no—
163C2×Dic122—28no—
164C2×Dic122—42no—
165#11758217—24no—
166#11758217—28no—
167#11758217#4118yes—
168C2×#92420—24no—
169C2×#92420—24no—
170#11758213—28no—
171D61⋊C8—28no—
172C4⋊C4×C61—22no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C42×C61—22no—
177C42×C61—22no—
178C42×C61C22⋊C411yescharacteristic
179C42×C61C22⋊C411yescharacteristic
180C42×C61C22⋊C411yescharacteristic
181C42×C61C22⋊C411yescharacteristic
182#11758198—22no—
183#11758198—22no—
184#11758198—22no—
185#11758198—22no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—22no—
189C4⋊Dic61—22no—
190#11758196—22no—
191#11758196—22no—
192#11758196—22no—
193#11758196—22no—
194#11758196—22no—
195#11758196—22no—
196#11758196—22no—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200C4×Dic61—22no—
201C4×Dic61—22no—
202C4×Dic61C22⋊C411yescharacteristic
203C4×Dic61C22⋊C411yescharacteristic
204C4×Dic61C22⋊C411yescharacteristic
205C4×Dic61C22⋊C411yescharacteristic
206C4×Dic61C2×D411yescharacteristic
207C4×Dic61C2×D411yescharacteristic
208C4×Dic61C2×D411yescharacteristic
209C4×Dic61C2×D411yescharacteristic
210C4×Dic61C2×D411yescharacteristic
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61C2×D411yescharacteristic
213C4×Dic61C2×D411yescharacteristic
214C23×C61C23×C411yescharacteristic
215C22×D61—22no—
216C22×D61—22no—
217C22×D61—41no—
218C22×D61C2×C22⋊C411yescharacteristic
219C22×D61C2×C22⋊C411yescharacteristic
220Q8×C61—42no—
221Q8×C61—42no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—24no—
228C2×C4×C61—42no—
229C2×C4×C61C2×C22⋊C411yescharacteristic
230C2×C4×C61C2×C22⋊C411yescharacteristic
231C2×C4×C61C2×C22⋊C411yescharacteristic
232C2×C4×C61C2×C22⋊C411yescharacteristic
233C2×C4×C61C2×C22⋊C411yescharacteristic
234C2×C4×C61C2×C22⋊C411yescharacteristic
235C2×Dic61—22no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—24no—
239C2×Dic61—41no—
240C2×Dic61—42no—
241C2×Dic61C2×C22⋊C411yescharacteristic
242C2×Dic61C2×C22⋊C411yescharacteristic
243C2×Dic61C2×C22⋊C411yescharacteristic
244C2×Dic61C2×C22⋊C411yescharacteristic
245C2×Dic61C22×D411yescharacteristic
246C2×Dic61C22×D411yescharacteristic
247C2×Dic61C2×#4114yes—
248C4×D61—22no—
249C4×D61—22no—
250C4×D61—22no—
251C4×D61—22no—
252C4×D61—22no—
253C4×D61—22no—
254C4×D61—22no—
255C4×D61—22no—
256C4×D61—22no—
257C4×D61—41no—
258C4×D61—41no—
259C4×D61#10114yescomplemented
260Dic122—42no—
261Dic122—42no—
262Dic122—44no—
263Dic122—44no—
264#92420—28no—
265#92420—44no—
266#21425—611nomaximal, Sylow
267C22×C61—21no—
268C22×C61—21no—
269C22×C61C22×C22⋊C411yescharacteristic
270C22×C61C4×#4112yes—
271C2×D61—21no—
272C2×D61—21no—
273C2×D61—21no—
274C2×D61—21no—
275C2×D61—21no—
276C2×D61—44no—
277C2×D61C2×#10112yes—
278C4×C61—21no—
279C4×C61—21no—
280C4×C61—21no—
281C4×C61—21no—
282C4×C61—42no—
283C4×C61—42no—
284C4×C61C2×#10112yes—
285C4×C61#41312yes—
286Dic61—21no—
287Dic61—21no—
288Dic61—21no—
289Dic61—42no—
290Dic61—42no—
291Dic61C2×#10112yes—
292Dic61#52512yes—
293Dic61#53212yes—
294C2×#533—611no—
295#2920—611no—
296C2×C4×M16—611no—
297#1997—612no—
298#1966—612no—
299#1901—614no—
300C4×#101—614no—
301C2×C61—22no—
302C2×C61#229711yescharacteristic
303C2×C61C22×#10111yescharacteristic
304C2×C61C2×#41311yescharacteristic
305D61—22no—
306D61—41no—
307C22×M16—612no—
308#533—1221no—
309#533—1221no—
310#533—1221no—
311#533—1221no—
312#533—1221no—
313#533—1221no—
314#533—1221no—
315#533—1221no—
316C2×C4⋊Q8—611no—
317C2×C4⋊Q8—611no—
318C2×#125—612no—
319C2×C22⋊Q8—611no—
320C2×C22⋊Q8—612no—
321C2×C22⋊Q8—611no—
322C2×C4×Q8—612no—
323C2×C4×Q8—611no—
324C2×C4×Q8#692311yescharacteristic
325C2×#117—612no—
326C22×C42—611no—
327#432—1221no—
328#432—1221no—
329#431—1221no—
330#431—1221no—
331#423—612no—
332C2×#101—618no—
333#407—612no—
334C4×M16—612no—
335C4×M16—612no—
336C4×M16—612no—
337C4×M16—1221no—
338C4×M16—1221no—
339C2×#97—1221no—
340C2×C4×C8—1221no—
341#343—618no—
342C61#2142511yescharacteristic, complemented, Sylow
343C22×Q8—612no—
344C22×Q8—611no—
345C22×Q8C2×#692311yescharacteristic
346C23×C4—611no—
347C23×C4—611no—
348C23×C4—611no—
349C2×M16—614no—
350C2×M16—614no—
351C2×M16—1228no—
352C2×M16—1222no—
353C22×C8—1222no—
354C4⋊Q8—1221no—
355C4⋊Q8—1221no—
356C4⋊Q8—1221no—
357C4⋊Q8—1221no—
358C4⋊Q8—1221no—
359C4⋊Q8—1221no—
360C4⋊Q8—1221no—
361C4⋊Q8—1221no—
362#125—1222no—
363#125—1222no—
364#125—1222no—
365#125—1222no—
366C22⋊Q8—1222no—
367C22⋊Q8—1222no—
368C22⋊Q8—1222no—
369C22⋊Q8—1222no—
370C22⋊Q8—1221no—
371C22⋊Q8—1221no—
372C22⋊Q8—1221no—
373C22⋊Q8—1221no—
374C22⋊Q8—1221no—
375C22⋊Q8—1221no—
376C22⋊Q8—1221no—
377C22⋊Q8—1221no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8—1222no—
383C4×Q8—1222no—
384C4×Q8—1222no—
385C4×Q8—1222no—
386C4×Q8—1221no—
387C4×Q8—1221no—
388C4×Q8—1221no—
389C4×Q8—1221no—
390#117—1222no—
391#117—1222no—
392#117—1222no—
393#117—1222no—
394C2×C4⋊C4—612no—
395C2×C4⋊C4—612no—
396C2×C4⋊C4—612no—
397C2×C4⋊C4—612no—
398C2×C4⋊C4—612no—
399C2×C4⋊C4—612no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4C2×#692312yes—
402C2×C4⋊C4C2×#692311yescharacteristic
403C2×C22⋊C4—612no—
404C2×C22⋊C4—612no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42—611no—
408C2×C42—611no—
409C2×C42—611no—
410C2×C42—611no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—612no—
417C2×C42C2×#692312yes—
418C2×C42C2×#692311yescharacteristic
419C4⋊C8—1222no—
420C4⋊C8—1222no—
421#101—12216no—
422C22⋊C8—1222no—
423C22⋊C8—1222no—
424#97—1222no—
425#97—1222no—
426#97—1222no—
427C4×C8—1222no—
428C4×C8—1222no—
429C4×C8—1222no—
430C24—611no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—42no—
434C2×Q8—1228no—
435C2×Q8—1222no—
436C2×Q8—1222no—
437C2×Q8—1221no—
438C2×Q8—1221no—
439C2×Q8—2442no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—612no—
456C22×C4—612no—
457C22×C4—1224no—
458C22×C4—1224no—
459C22×C4—2442no—
460C22×C4C22×#692312yes—
461C22×C4C22×#692311yescharacteristic
462C22×C4C22×#692311yescharacteristic
463C22×C4C22×#692311yescharacteristic
464C22×C4C22×#692312yes—
465M16—618no—
466M16—1224no—
467M16—1228no—
468M16—1228no—
469C2×C8—1224no—
470C2×C8—1228no—
471C2×C8—1224no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—1222no—
477C4⋊C4—1222no—
478C4⋊C4—1222no—
479C4⋊C4—1222no—
480C4⋊C4—1222no—
481C4⋊C4—1222no—
482C4⋊C4—1222no—
483C4⋊C4—1222no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—1222no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C22⋊C4—1222no—
491C22⋊C4—1222no—
492C22⋊C4—1222no—
493C22⋊C4—1222no—
494C42—22no—
495C42—22no—
496C42—611no—
497C42—611no—
498C42—611no—
499C42—611no—
500C42—611no—
501C42—611no—
502C42—611no—
503C42—611no—
504C42—611no—
505C42—611no—
506C42—611no—
507C42—611no—
508C42—1222no—
509C42—1222no—
510C42C22⋊#692311yescharacteristic
511C42C22⋊#692311yescharacteristic
512C42C22⋊#692311yescharacteristic
513C42C22⋊#692311yescharacteristic
514C23—611no—
515C23—611no—
516C23—1222no—
517C23—1222no—
518C23—2441no—
519C23C23×#692311yescharacteristic
520Q8—42no—
521Q8—42no—
522Q8—2442no—
523Q8—2444no—
524Q8—2444no—
525Q8—2442no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—42no—
533C2×C4—611no—
534C2×C4—611no—
535C2×C4—611no—
536C2×C4—614no—
537C2×C4—614no—
538C2×C4—611no—
539C2×C4—611no—
540C2×C4—611no—
541C2×C4—1222no—
542C2×C4—1222no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—1222no—
547C2×C4—1222no—
548C2×C4—1222no—
549C2×C4—1222no—
550C2×C4—1222no—
551C2×C4—1222no—
552C2×C4—1222no—
553C2×C4—1224no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2442no—
558C2×C4C2×C22⋊#692311yescharacteristic
559C2×C4C2×C22⋊#692311yescharacteristic
560C2×C4C2×C22⋊#692311yescharacteristic
561C2×C4C2×C22⋊#692311yescharacteristic
562C2×C4C2×C22⋊#692311yescharacteristic
563C2×C4C2×C22⋊#692311yescharacteristic
564C8—1228no—
565C8—2444no—
566C22—21no—
567C22—21no—
568C22—612no—
569C22—1221no—
570C22—1221no—
571C22—1221no—
572C22—1221no—
573C22—1221no—
574C22—2444no—
575C22C22×C22⋊#692311yescharacteristic
576C22#41×#692312yes—
577C4—21no—
578C4—21no—
579C4—21no—
580C4—21no—
581C4—42no—
582C4—42no—
583C4—612no—
584C4—612no—
585C4—612no—
586C4—1221no—
587C4—1221no—
588C4—1221no—
589C4—2442no—
590C4—2442no—
591C4D61⋊#10112yes—
592C4#1684074812yes—
593C2—22no—
594C2—1222no—
595C2—2441no—
596C2#2146228011yescharacteristic
597C2C2×D61⋊#10111yescharacteristic
598C2C2×#1684074811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22×C4
cosocleC22×Dic61C24
hypercenterC2×C4×Q8#6923
hypocenterC61#21425
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #21462011C2semidirect
4. #21461962C2semidirect
6. C4×#14519838C2semidirect
259. C4×D61#101semidirect
342. C61#21425semidirect

Maximal subgroups

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

subgroupindex
#214624972
C4×D61⋊M162
#214620112
#214619622
#214618472
C4×#145198382
C2×#168403162
#2142561