Finite Group Databasebeta

← #30616713

Subgroups — #30616713

Order 15616.

1142 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D61⋊M16C211yesmaximal, characteristic
2#21462266C211yesmaximal, characteristic
3#21462003C212yesmaximal, complemented
4#21461950C212yesmaximal, complemented
5#21461834C214yesmaximal
6C4×#14519840C214yesmaximal, complemented
7#533×D61C211yesmaximal, characteristic
8C2×D61⋊M16C2212yes—
9C2×#14519840C2218yes—
10C4×#11758213—21no—
11C4×#11758213—21no—
12C4×#11758217—21no—
13C4×#11758217—21no—
14#16840721C2212yes—
15C4×D61⋊C8C2212yes—
16#16840707—21no—
17#16840706C2212yes—
18#16840705—21no—
19#16840704C2212yes—
20C4×C4⋊#6923C2212yes—
21C4×C22⋊#6923—21no—
22#16840698—21no—
23#16840635C2218yes—
24#16840319C411yescharacteristic, complemented
25#16840318—21no—
26#16840317C411yescharacteristic, complemented
27#16840317C411yescharacteristic, complemented
28#16840316—21no—
29#16840316C412yescomplemented
30#16840315—21no—
31#16840314—21no—
32#16840314C412yescomplemented
33C4⋊Q8×D61C2211yescharacteristic
34C4⋊Q8×D61C2211yescharacteristic
35#125×D61—21no—
36C22⋊Q8×D61—21no—
37C22⋊Q8×D61C2212yes—
38C4×Q8×D61—21no—
39C4×Q8×D61C2212yes—
40#117×D61—21no—
41C2×C42×D61C2211yescharacteristic
42C61×#533C411yescharacteristic, complemented
43C2×#11758213—22no—
44D61⋊M16—28no—
45C2×#11758217—22no—
46C2×D61⋊C8C2314yes—
47C2×C4⋊#6923C2314yes—
48C2×C22⋊#6923—22no—
49C2×C4×#6923—22no—
50#14519840—216no—
51#14519832—22no—
52#14519832—22no—
53C4×#92420—22no—
54C4×#92420—22no—
55(C2×#6923)⋊C4—22no—
56(C2×#6923)⋊C4—22no—
57(C2×#6923)⋊C4—22no—
58(C2×#6923)⋊C4—22no—
59C2×Q8×D61—21no—
60C2×Q8×D61C2312yes—
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64#14519777C2×C411yescharacteristic
65#14519777C2×C411yescharacteristic
66#14519776—21no—
67#14519776—21no—
68#14519776—21no—
69#14519776C2×C412yes—
70#14519775—21no—
71#14519775C2×C412yes—
72#14519769—21no—
73#14519768—21no—
74#14519768—21no—
75#14519767—22no—
76#14519767—22no—
77#14519757—21no—
78#14519757C2×C412yes—
79#14519756—21no—
80#14519756C2×C412yes—
81#14519755—22no—
82#14519755—22no—
83#14519754—22no—
84#14519754—22no—
85#14519753—21no—
86#14519753C2×C412yes—
87Q8×Dic61—21no—
88Q8×Dic61C2×C412yes—
89C4×Dic122—21no—
90C4×Dic122—22no—
91C4×Dic122—22no—
92C4×Dic122C2×C412yes—
93#14519742—21no—
94#14519742—22no—
95#14519742—22no—
96#14519742C2×C412yes—
97#14519736—21no—
98#14519735—21no—
99#14519735—21no—
100#14519734—22no—
101#14519733—22no—
102C4⋊C4×D61—21no—
103C4⋊C4×D61—21no—
104C4⋊C4×D61—21no—
105C4⋊C4×D61—22no—
106C4⋊C4×D61—22no—
107C4⋊C4×D61C2312yes—
108C22⋊C4×D61—22no—
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C42×D61—22no—
113C42×D61C2×C411yescharacteristic
114C42×D61C2×C411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61C2311yescharacteristic
120C42×D61C2311yescharacteristic
121C4⋊Q8×C61C2×C411yescharacteristic
122C4⋊Q8×C61C2×C411yescharacteristic
123#125×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61C2×C412yes—
126C4×Q8×C61—21no—
127C4×Q8×C61C2×C412yes—
128#117×C61—21no—
129C2×C42×C61C2×C411yescharacteristic
130C23×D61C2×D411yescharacteristic
131C22×#6923—24no—
132C2×Q8×C61—21no—
133C2×Q8×C61C22×C412yes—
134C22×C4×C61C22⋊C411yescharacteristic
135C22×C4×C61C22⋊C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×Dic61C22⋊C411yescharacteristic
138C22×Dic61C22⋊C411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140Q8×D61—28no—
141Q8×D61—44no—
142C2×C4×D61—24no—
143C2×C4×D61—24no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
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×D61C2×D411yescharacteristic
153C2×C4×D61C2×D411yescharacteristic
154C2×C4×D61C2×D411yescharacteristic
155C2×C4×D61C2×D411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61C2×D411yescharacteristic
158C2×C4×D61C2411yescharacteristic
159C2×Dic122—21no—
160C2×Dic122—22no—
161C2×Dic122—22no—
162C2×Dic122C22×C412yes—
163C22⋊#6923—44no—
164#11758217—28no—
165C2×#92420—24no—
166C4⋊#6923—28no—
167C4×#6923—44no—
168#11758213—28no—
169D61⋊C8—24no—
170D61⋊C8#4118yes—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—22no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61C22×C412yes—
177C22⋊C4×C61—22no—
178C42×C61—22no—
179C42×C61C22⋊C411yescharacteristic
180C42×C61C22⋊C411yescharacteristic
181C42×C61C22×C411yescharacteristic
182C42×C61C22×C411yescharacteristic
183C22⋊Dic61—22no—
184#11758198—22no—
185#11758198—22no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—22no—
190C4⋊Dic61—22no—
191C4⋊Dic61C22×C412yes—
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×Dic61—22no—
203C4×Dic61C22⋊C411yescharacteristic
204C4×Dic61C22⋊C411yescharacteristic
205C4×Dic61C22⋊C411yescharacteristic
206C4×Dic61C22⋊C411yescharacteristic
207C4×Dic61C22⋊C411yescharacteristic
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22×C411yescharacteristic
210C4×Dic61C22×C411yescharacteristic
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61C2×D411yescharacteristic
213C4×Dic61C2×D411yescharacteristic
214C4×Dic61C2×D411yescharacteristic
215C23×C61C2×C22⋊C411yescharacteristic
216C22×D61—22no—
217C22×D61—22no—
218C22×D61—22no—
219C22×D61C2×C22⋊C411yescharacteristic
220C22×D61C22×D411yescharacteristic
221C2×#6923—44no—
222C2×#6923—44no—
223C2×#6923—44no—
224Q8×C61—24no—
225Q8×C61—42no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—41no—
231C2×C4×C61C2×C22⋊C411yescharacteristic
232C2×C4×C61C2×C22⋊C411yescharacteristic
233C2×C4×C61C2×C22⋊C411yescharacteristic
234C2×C4×C61C2×C22⋊C411yescharacteristic
235C2×C4×C61C2×C22⋊C411yescharacteristic
236C2×C4×C61C23×C411yescharacteristic
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—41no—
242C2×Dic61C2×C22⋊C411yescharacteristic
243C2×Dic61C2×C22⋊C411yescharacteristic
244C2×Dic61C2×C22⋊C411yescharacteristic
245C2×Dic61C2×C22⋊C411yescharacteristic
246C2×Dic61C2×C22⋊C411yescharacteristic
247C2×Dic61C22×D411yescharacteristic
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—41no—
257C4×D61—41no—
258C4×D61—44no—
259C4×D61—44no—
260C4×D61#13714yes—
261C4×D61C2×#4114yes—
262Dic122—24no—
263Dic122—44no—
264Dic122—42no—
265Dic122—44no—
266#92420—28no—
267#21404—611nomaximal, Sylow
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61C22×C22⋊C411yescharacteristic
272C2×D61—21no—
273C2×D61—21no—
274C2×D61—21no—
275C2×D61—44no—
276C2×D61#53212yes—
277C2×D61C2×#13712yes—
278C2×D61#57512yes—
279#6923—84no—
280C4×C61—21no—
281C4×C61—21no—
282C4×C61—21no—
283C4×C61—21no—
284C4×C61—42no—
285C4×C61—42no—
286C4×C61#41912yes—
287C4×C61C4×#4112yes—
288Dic61—21no—
289Dic61—21no—
290Dic61—21no—
291Dic61—21no—
292Dic61—42no—
293Dic61—42no—
294Dic61#41912yes—
295Dic61#52512yes—
296C2×#533—611no—
297C2×C4×M16—611no—
298#2283—611no—
299#1993—612no—
300#1960—612no—
301#1894—614no—
302C4×#103—614no—
303C2×C61—41no—
304C2×C61#229711yescharacteristic
305C2×C61C2×#41911yescharacteristic
306C2×C61#289611yescharacteristic
307D61—41no—
308D61#317214yes—
309C22×M16—612no—
310#533—611no—
311#533—611no—
312#533—612no—
313#533—612no—
314#533—611no—
315#533—1221no—
316#533—1221no—
317#533—1221no—
318#533—1221no—
319#533#692311yescharacteristic, complemented
320C2×C4⋊Q8—611no—
321C2×C4⋊Q8—611no—
322C2×#125—1221no—
323C2×C22⋊Q8—612no—
324C2×C22⋊Q8—1221no—
325C2×C4×Q8—612no—
326C2×C4×Q8—1221no—
327C2×#117—1221no—
328C22×C42—611no—
329C2×#103—618no—
330C4×M16—1221no—
331C4×M16—1221no—
332C4×M16—1221no—
333C4×M16—1221no—
334C2×#97—612no—
335C2×C4×C8—612no—
336#383—1221no—
337#382—612no—
338#381—1221no—
339#380—612no—
340C4×C4⋊C4—612no—
341C4×C22⋊C4—1221no—
342#376—1221no—
343#340—618no—
344C61#2140411yescharacteristic, complemented, Sylow
345C22×Q8—612no—
346C22×Q8—1221no—
347C23×C4—611no—
348C23×C4—611no—
349C23×C4—611no—
350C2×M16—1228no—
351C2×M16—1222no—
352C2×M16—1222no—
353C22×C8—614no—
354C4⋊Q8—612no—
355C4⋊Q8—612no—
356C4⋊Q8—611no—
357C4⋊Q8—611no—
358C4⋊Q8—1221no—
359C4⋊Q8—1221no—
360C4⋊Q8—1221no—
361C4⋊Q8—1221no—
362C4⋊Q8C2×#692311yescharacteristic
363C4⋊Q8C2×#692311yescharacteristic
364#125—21no—
365#125—1222no—
366#125—1222no—
367#125—1221no—
368#125—1221no—
369#125—1221no—
370C22⋊Q8—21no—
371C22⋊Q8—612no—
372C22⋊Q8—612no—
373C22⋊Q8—612no—
374C22⋊Q8—1222no—
375C22⋊Q8—1222no—
376C22⋊Q8—1222no—
377C22⋊Q8—1222no—
378C22⋊Q8—1221no—
379C22⋊Q8—1221no—
380C22⋊Q8—1221no—
381C22⋊Q8C2×#692312yes—
382C4×Q8—21no—
383C4×Q8—612no—
384C4×Q8—612no—
385C4×Q8—612no—
386C4×Q8—1222no—
387C4×Q8—1222no—
388C4×Q8—1222no—
389C4×Q8—1221no—
390C4×Q8—1222no—
391C4×Q8—1221no—
392C4×Q8—1221no—
393C4×Q8C2×#692312yes—
394#117—21no—
395#117—1222no—
396#117—1222no—
397#117—1221no—
398#117—1221no—
399#117—1221no—
400C2×C4⋊C4—612no—
401C2×C4⋊C4—614no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1222no—
405C2×C4⋊C4—1222no—
406C2×C4⋊C4—1221no—
407C2×C22⋊C4—1222no—
408C2×C22⋊C4—1222no—
409C2×C42—611no—
410C2×C42—611no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—611no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—611no—
420C2×C42—1222no—
421C2×C42—1222no—
422C2×C42C2×#692311yescharacteristic
423#103—12216no—
424#97—1222no—
425#97—1222no—
426C4×C8—1222no—
427C4×C8—1222no—
428#95—1222no—
429#95—1222no—
430#95—1222no—
431#95—1222no—
432C24—611no—
433C2×Q8—21no—
434C2×Q8—612no—
435C2×Q8—1222no—
436C2×Q8—1222no—
437C2×Q8—1228no—
438C2×Q8—1221no—
439C2×Q8—2444no—
440C2×Q8C22×#692312yes—
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—611no—
456C22×C4—1224no—
457C22×C4—1224no—
458C22×C4—1222no—
459C22×C4—1222no—
460C22×C4—1224no—
461C22×C4—2442no—
462C22×C4C22⋊#692311yescharacteristic
463C22×C4C22⋊#692311yescharacteristic
464C22×C4C22×#692311yescharacteristic
465M16—1228no—
466M16—1228no—
467C2×C8—618no—
468C2×C8—1224no—
469C2×C8—1224no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—612no—
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—1228no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4C22×#692312yes—
491C22⋊C4—22no—
492C22⋊C4—1222no—
493C22⋊C4—1222no—
494C22⋊C4—1222no—
495C22⋊C4—2444no—
496C42—22no—
497C42—611no—
498C42—611no—
499C42—611no—
500C42—611no—
501C42—611no—
502C42—611no—
503C42—611no—
504C42—611no—
505C42—611no—
506C42—611no—
507C42—611no—
508C42—611no—
509C42—1222no—
510C42—1222no—
511C42—1222no—
512C42—2444no—
513C42C22⋊#692311yescharacteristic
514C42C22⋊#692311yescharacteristic
515C42C22×#692311yescharacteristic
516C42C22×#692311yescharacteristic
517C23—611no—
518C23—611no—
519C23—1222no—
520C23—1222no—
521C23—1222no—
522C23C2×C22⋊#692311yescharacteristic
523Q8—24no—
524Q8—42no—
525Q8—1224no—
526Q8—2442no—
527Q8—2444no—
528Q8—2444no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—611no—
535C2×C4—611no—
536C2×C4—614no—
537C2×C4—614no—
538C2×C4—611no—
539C2×C4—611no—
540C2×C4—611no—
541C2×C4—611no—
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—1222no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2444no—
557C2×C4—2444no—
558C2×C4—2441no—
559C2×C4—2444no—
560C2×C4—2444no—
561C2×C4—2444no—
562C2×C4C2×C22⋊#692311yescharacteristic
563C2×C4C2×C22⋊#692311yescharacteristic
564C2×C4C2×C22⋊#692311yescharacteristic
565C2×C4C2×C22⋊#692311yescharacteristic
566C2×C4C2×C22⋊#692311yescharacteristic
567C2×C4C23×#692311yescharacteristic
568C8—1228no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—612no—
573C22—612no—
574C22—612no—
575C22—1221no—
576C22—1221no—
577C22—1221no—
578C22—2444no—
579C22C22×C22⋊#692311yescharacteristic
580C4—21no—
581C4—21no—
582C4—21no—
583C4—21no—
584C4—42no—
585C4—42no—
586C4—612no—
587C4—612no—
588C4—1221no—
589C4—1221no—
590C4—1221no—
591C4—1221no—
592C4—4884no—
593C4—2442no—
594C4—2442no—
595C4#1684075512yes—
596C4#41×#692312yes—
597C2—41no—
598C2—614no—
599C2—2441no—
600C2#2146228011yescharacteristic
601C2C2×#1684075511yescharacteristic
602C2#2146243911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#533C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenter#533#6923
hypocenterC61#21404
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #21462003C2semidirect
4. #21461950C2semidirect
6. C4×#14519840C2semidirect
24. #16840319C4semidirect
26. #16840317C4semidirect
27. #16840317C4semidirect
29. #16840316C4semidirect
32. #16840314C4semidirect
42. C61×#533C4semidirect
319. #533#6923semidirect
344. C61#21404semidirect

Maximal subgroups

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

subgroupindex
C4×D61⋊M162
#214622662
#214620032
#214619502
#214618342
C4×#145198402
#533×D612
#2140461