Finite Group Databasebeta

← #30610937

Subgroups — #30610937

Order 15616.

1116 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462498C211yesmaximal, characteristic, complemented
2C4×#14519856C211yesmaximal, characteristic, complemented
3#21461220C214yesmaximal, complemented
4#21461219C212yesmaximal, complemented
5#21461215C212yesmaximal
6#21461191C214yesmaximal, complemented
7C2×#16840291C211yesmaximal, characteristic
8C2×#14519856—21no—
9#16840785C2212yescomplemented
10#16840782—21no—
11#16840780C2212yescomplemented
12#16840779—21no—
13#16840767—21no—
14#16840733C2212yes—
15C4×#11758213—21no—
16C4×C4⋊#6923—21no—
17C4×C4⋊#6923C2212yescomplemented
18C4×C22⋊#6923—21no—
19C4×C22⋊#6923C2212yes—
20#16840698C2212yescomplemented
21C42×#6923—21no—
22#16840616C2218yescomplemented
23#16840613C2218yes—
24#16840291—21no—
25#16840291—21no—
26#16840291—21no—
27#16840291—21no—
28#16840291C412yescomplemented
29#16840291C412yescomplemented
30#16840291C2212yes—
31#16840291C2212yes—
32C2×#14519770—21no—
33C2×#14519769C411yescharacteristic, complemented
34C2×#14519759—21no—
35C2×#14519753C2211yescharacteristic
36C2×#14519748C2211yescharacteristic
37C2×Q8×Dic61C411yescharacteristic, complemented
38C2×D4×Dic61C411yescharacteristic, complemented
39C2×#14519737—21no—
40C2×#14519733—21no—
41C2×C42×D61C2211yescharacteristic
42C2×#124×C61C411yescharacteristic, complemented
43C2×#11758213—22no—
44#14519856—28no—
45C2×C4⋊#6923—22no—
46C2×C22⋊#6923—22no—
47C2×C4×#6923—22no—
48C2×C4×#6923—22no—
49C2×C4×#6923—22no—
50#14519844—22no—
51#14519844—22no—
52#14519834C2314yes—
53C22⋊#92420—22no—
54#14519832—22no—
55C4×#92420—22no—
56(C2×#6923)⋊C4—22no—
57(C2×#6923)⋊C4C2314yes—
58C22×C22⋊D61—21no—
59C23×Dic61—21no—
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63#14519770—22no—
64#14519770—22no—
65#14519770—22no—
66#14519770—22no—
67#14519769—21no—
68#14519769—21no—
69#14519769C2×C412yes—
70#14519769C2×C412yes—
71#14519759—22no—
72#14519759—22no—
73#14519759—22no—
74#14519759—22no—
75#14519753—21no—
76#14519753—21no—
77#14519753C2×C412yes—
78#14519753C2312yes—
79#14519748—21no—
80#14519748—21no—
81#14519748C2×C412yes—
82#14519748C2312yes—
83Q8×Dic61—21no—
84Q8×Dic61—21no—
85Q8×Dic61C2×C412yes—
86Q8×Dic61C2×C412yes—
87D4×Dic61—21no—
88D4×Dic61—21no—
89D4×Dic61C2×C412yes—
90D4×Dic61C2×C412yes—
91#14519737—22no—
92#14519737—22no—
93#14519737—22no—
94#14519737—22no—
95#14519733—22no—
96#14519733—22no—
97#14519733—22no—
98#14519733—22no—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61C2×C411yescharacteristic
101C2×C4⋊Dic61C2×C411yescharacteristic
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×#11758198—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61C2×C411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61C2311yescharacteristic
119C42×D61C2311yescharacteristic
120C22×Q8×C61C2×C411yescharacteristic
121C22×D4×C61C2×C411yescharacteristic
122#124×C61—21no—
123#124×C61—21no—
124#124×C61C2×C412yes—
125#124×C61C2×C412yes—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C42×C61C2×C411yescharacteristic
129C24×C61—21no—
130C23×D61C2×D411yescharacteristic
131C22×#6923—24no—
132C2×Q8×C61—21no—
133C2×Q8×C61—42no—
134C2×Q8×C61C22×C412yes—
135C2×D4×C61—21no—
136C2×D4×C61—42no—
137C2×D4×C61C22×C412yes—
138C22×C4×C61—21no—
139C22×C4×C61C22⋊C411yescharacteristic
140C22×C4×C61C22⋊C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C2×C22⋊D61—22no—
143C2×C22⋊D61—22no—
144C2×C22⋊D61—44no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—44no—
150C22×Dic61C22⋊C411yescharacteristic
151C22×Dic61C22⋊C411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C2×C4×D61—24no—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×C4×D61C22⋊C411yescharacteristic
157C2×C4×D61C22⋊C411yescharacteristic
158C2×C4×D61C22⋊C411yescharacteristic
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22×C411yescharacteristic
161C2×C4×D61C2×D411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61C2×D411yescharacteristic
164C2×C4×D61C2×D411yescharacteristic
165C2×C4×D61C2×D411yescharacteristic
166C2×C4×D61C2×D411yescharacteristic
167C2×C4×D61C2411yescharacteristic
168C22⋊#6923—28no—
169C2×#92420—24no—
170C4⋊#6923—28no—
171C4×#6923—28no—
172C4×#6923—44no—
173C4×#6923—44no—
174#11758213—44no—
175C22⋊C4×C61—22no—
176C22⋊C4×C61—22no—
177C22⋊C4×C61—22no—
178C22⋊C4×C61—22no—
179C42×C61C22⋊C411yescharacteristic
180C42×C61C22⋊C411yescharacteristic
181C42×C61C22×C411yescharacteristic
182C42×C61C22×C411yescharacteristic
183C22⋊Dic61—22no—
184C22⋊Dic61—22no—
185C22⋊Dic61—22no—
186C22⋊Dic61—22no—
187#11758198—22no—
188#11758198—22no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—22no—
192C4⋊Dic61—22no—
193C4⋊Dic61C22×C412yes—
194C4⋊Dic61C22×C412yes—
195#11758196—22no—
196#11758196—22no—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—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×C61—22no—
216C23×C61—42no—
217C23×C61—42no—
218C23×C61—42no—
219C23×C61C2×C22⋊C411yescharacteristic
220C22×D61—22no—
221C22×D61—22no—
222C22×D61—41no—
223C22×D61C2×C22⋊C411yescharacteristic
224C22×D61C22×D411yescharacteristic
225C2×#6923—28no—
226C2×#6923—44no—
227C2×#6923—44no—
228Q8×C61—42no—
229Q8×C61—42no—
230D4×C61—42no—
231D4×C61—42no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—41no—
236C2×C4×C61—42no—
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C23×C411yescharacteristic
243C22⋊D61—44no—
244C22⋊D61—44no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—42no—
250C2×Dic61—42no—
251C2×Dic61—44no—
252C2×Dic61—44no—
253C2×Dic61#10414yes—
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C2×C22⋊C411yescharacteristic
257C2×Dic61C2×C22⋊C411yescharacteristic
258C2×Dic61C2×C22⋊C411yescharacteristic
259C2×Dic61C22×D411yescharacteristic
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—22no—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—41no—
269C4×D61—41no—
270C4×D61—41no—
271C4×D61—41no—
272#92420—44no—
273#17537—611nomaximal, Sylow
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—42no—
277C22×C61—42no—
278C22×C61—42no—
279C22×C61—84no—
280C22×C61C2×#10412yes—
281C22×C61C22×C22⋊C411yescharacteristic
282C2×D61—21no—
283C2×D61—21no—
284C2×D61—21no—
285C2×D61—21no—
286C2×D61—21no—
287C2×D61—44no—
288C2×D61#57512yes—
289#6923—48no—
290C4×C61—21no—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—21no—
294C4×C61—21no—
295C4×C61—42no—
296C4×C61#41012yes—
297Dic61—21no—
298Dic61—21no—
299Dic61—21no—
300Dic61—21no—
301Dic61—42no—
302Dic61—42no—
303Dic61C2×#10412yes—
304Dic61C2×#10412yes—
305C2×#529—611no—
306#2920—611no—
307C4×#117—611no—
308#1509—614no—
309#1508—612no—
310#1507—612no—
311#1500—614no—
312C2×C61—22no—
313C2×C61—82no—
314C2×C61C2×#41011yescharacteristic
315C2×C61#289611yescharacteristic
316C2×C61C22×#10411yescharacteristic
317D61—22no—
318D61—41no—
319#529—612no—
320#529—612no—
321#529—612no—
322#529—612no—
323#529—1221no—
324#529—1221no—
325#529—1221no—
326#529—1221no—
327C2×#126—1221no—
328C2×#125—611no—
329C2×#124#692311yescharacteristic, complemented
330C2×#123—1221no—
331C2×C22⋊Q8—611no—
332C2×#121—611no—
333C2×C4×Q8—611no—
334C2×C4×D4—611no—
335C2×C4×D4—1221no—
336C2×#117—1221no—
337C2×#117—1221no—
338C22×C42—611no—
339#432—612no—
340#432—1221no—
341#431—612no—
342#431—1221no—
343#423—1221no—
344#407—612no—
345C4×M16—1221no—
346C4×C4⋊C4—612no—
347C4×C4⋊C4—1221no—
348C4×C22⋊C4—612no—
349C4×C22⋊C4—1221no—
350#376—612no—
351C43—1221no—
352#328—618no—
353#327—618no—
354C61#1753711yescharacteristic, complemented, Sylow
355C22×Q8C2×#692311yescharacteristic
356C22×D4—1221no—
357C22×D4C2×#692311yescharacteristic
358C23×C4—611no—
359C23×C4—611no—
360C23×C4—611no—
361C23×C4—1221no—
362C2×M16—1222no—
363#126—1222no—
364#126—1222no—
365#126—1222no—
366#126—1222no—
367#125—612no—
368#125—612no—
369#125—1221no—
370#125—1221no—
371#124—21no—
372#124—21no—
373#124C2×#692312yes—
374#124C2×#692312yes—
375#123—1222no—
376#123—1222no—
377#123—1222no—
378#123—1222no—
379C22⋊Q8—612no—
380C22⋊Q8—612no—
381C22⋊Q8—1221no—
382C22⋊Q8—1221no—
383#121—612no—
384#121—612no—
385#121—1221no—
386#121—1221no—
387C4×Q8—612no—
388C4×Q8—612no—
389C4×Q8—1221no—
390C4×Q8—1221no—
391C4×D4—612no—
392C4×D4—612no—
393C4×D4—1221no—
394C4×D4—1221no—
395C4×D4—1222no—
396C4×D4—1222no—
397C4×D4—1222no—
398C4×D4—1222no—
399#117—1222no—
400#117—1222no—
401#117—1222no—
402#117—1222no—
403#117—1228no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1222no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—1221no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—1222no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—1221no—
429C2×C42—1222no—
430C2×C42—1222no—
431C2×C42—1222no—
432C2×C42C2×#692311yescharacteristic
433C4⋊C8—1222no—
434C4⋊C8—1222no—
435C22⋊C8—614no—
436C22⋊C8—1222no—
437#97—1222no—
438C4×C8—1222no—
439#95—614no—
440#95—1222no—
441C24—21no—
442C24—611no—
443C2×Q8—21no—
444C2×Q8—42no—
445C2×Q8C22×#692312yes—
446C2×D4—21no—
447C2×D4—42no—
448C2×D4—1222no—
449C2×D4—1222no—
450C2×D4—2444no—
451C2×D4C22×#692312yes—
452C22×C4—21no—
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—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—1224no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1224no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—2442no—
475C22×C4—2442no—
476C22×C4—2444no—
477C22×C4C22⋊#692311yescharacteristic
478C22×C4C22⋊#692311yescharacteristic
479C22×C4C22×#692311yescharacteristic
480M16—2444no—
481C2×C8—1224no—
482C4⋊C4—612no—
483C4⋊C4—612no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—1222no—
488C4⋊C4—1228no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1222no—
492C4⋊C4—1222no—
493C4⋊C4—1222no—
494C4⋊C4—1222no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—1222no—
500C22⋊C4—1222no—
501C22⋊C4—1222no—
502C22⋊C4—1222no—
503C22⋊C4—1222no—
504C22⋊C4—1222no—
505C22⋊C4—1228no—
506C42—611no—
507C42—611no—
508C42—611no—
509C42—611no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42—611no—
515C42—611no—
516C42—611no—
517C42—611no—
518C42—1222no—
519C42—1222no—
520C42—1228no—
521C42—2444no—
522C42—2444no—
523C42C22⋊#692311yescharacteristic
524C42C22⋊#692311yescharacteristic
525C42C22×#692311yescharacteristic
526C42C22×#692311yescharacteristic
527C23—22no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—611no—
532C23—611no—
533C23—1222no—
534C23—1222no—
535C23—2441no—
536C23C2×C22⋊#692311yescharacteristic
537Q8—42no—
538Q8—42no—
539D4—42no—
540D4—42no—
541D4—2444no—
542D4—2444no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—614no—
549C2×C4—611no—
550C2×C4—611no—
551C2×C4—611no—
552C2×C4—611no—
553C2×C4—611no—
554C2×C4—611no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1228no—
564C2×C4—1222no—
565C2×C4—1222no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2444no—
571C2×C4—2444no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2442no—
575C2×C4—2444no—
576C2×C4—2444no—
577C2×C4—2442no—
578C2×C4C2×C22⋊#692311yescharacteristic
579C2×C4C2×C22⋊#692311yescharacteristic
580C2×C4C2×C22⋊#692311yescharacteristic
581C2×C4C2×C22⋊#692311yescharacteristic
582C2×C4C2×C22⋊#692311yescharacteristic
583C2×C4C23×#692311yescharacteristic
584C8—2444no—
585C22—21no—
586C22—21no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—84no—
591C22—612no—
592C22—1221no—
593C22—1221no—
594C22—1221no—
595C22—1221no—
596C22—1221no—
597C22—2444no—
598C22D61⋊#10412yes—
599C22C22×C22⋊#692311yescharacteristic
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—21no—
605C4—42no—
606C4—612no—
607C4—612no—
608C4—1221no—
609C4—1221no—
610C4—1221no—
611C4—1221no—
612C4—2448no—
613C4—2442no—
614C4—2442no—
615C4#1684074212yes—
616C2—22no—
617C2—82no—
618C2—1222no—
619C2—2441no—
620C2C2×#1684074211yescharacteristic
621C2#2146243911yescharacteristic
622C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#124×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519748C22
cosocleC2×C4×D61C24
hypercenterC2×#124#6923
hypocenterC61#17537
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #21462498C2semidirect
2. C4×#14519856C2semidirect
3. #21461220C2semidirect
4. #21461219C2semidirect
6. #21461191C2semidirect
9. #16840785C22semidirect
11. #16840780C22semidirect
17. C4×C4⋊#6923C22semidirect
20. #16840698C22semidirect
22. #16840616C22semidirect
28. #16840291C4semidirect
29. #16840291C4semidirect
33. C2×#14519769C4semidirect
37. C2×Q8×Dic61C4semidirect
38. C2×D4×Dic61C4semidirect
42. C2×#124×C61C4semidirect
329. C2×#124#6923semidirect
354. C61#17537semidirect

Maximal subgroups

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

subgroupindex
#214624982
C4×#145198562
#214612202
#214612192
#214612152
#214611912
C2×#168402912
#1753761