Finite Group Databasebeta

← #30610685

Subgroups — #30610685

Order 15616.

1036 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462498C211yesmaximal, characteristic, complemented
2D61⋊#423C211yesmaximal, characteristic, complemented
3#21461175C214yesmaximal, complemented
4#21461147C212yesmaximal, complemented
5#21461144C212yesmaximal, complemented
6#21461135C214yesmaximal, complemented
7C2×#16840291C211yesmaximal, characteristic
8C2×D61⋊M16—21no—
9#16840785—21no—
10#16840782—21no—
11#16840780C2212yescomplemented
12#16840779C2212yes—
13#16840767—21no—
14#16840767—21no—
15#16840766C2212yescomplemented
16#16840765—21no—
17#16840765C2212yes—
18D61⋊(C4⋊C8)—21no—
19D61⋊(C4⋊C8)C2212yescomplemented
20#16840733—21no—
21C4×#11758213C2212yescomplemented
22Q8⋊#92420C2218yescomplemented
23D4⋊#92420C2218yescomplemented
24#16840291—21no—
25#16840291—21no—
26#16840291—21no—
27#16840291—21no—
28#16840291C412yes—
29#16840291C412yes—
30#16840291C2212yes—
31#16840291C2212yes—
32C2×#14519770—21no—
33C2×#14519769C411yescharacteristic
34C2×#14519759—21no—
35C2×#14519753C411yescharacteristic
36C2×#14519748C411yescharacteristic
37C2×Q8×Dic61C2211yescharacteristic
38C2×D4×Dic61C2211yescharacteristic
39C2×#14519737—21no—
40C2×#14519733—21no—
41C2×C42×D61C2211yescharacteristic
42C2×#124×C61C411yescharacteristic
43C2×#11758213—22no—
44C2×#11758213—22no—
45D61⋊M16—44no—
46C2×#11758217—22no—
47C2×D61⋊C8—22no—
48#14519844—22no—
49#14519844—22no—
50#14519844—22no—
51#14519844—22no—
52C4⋊#92420—22no—
53C4⋊#92420C2314yes—
54#14519834—22no—
55C22⋊#92420—22no—
56#14519832—22no—
57C4×#92420C2314yes—
58C22×C22⋊D61—21no—
59C23×Dic61—21no—
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
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#14519753C2×C412yes—
79#14519748—21no—
80#14519748—21no—
81#14519748C2×C412yes—
82#14519748C2×C412yes—
83Q8×Dic61—21no—
84Q8×Dic61—21no—
85Q8×Dic61C2×C412yes—
86Q8×Dic61C2312yes—
87D4×Dic61—21no—
88D4×Dic61—21no—
89D4×Dic61C2×C412yes—
90D4×Dic61C2312yes—
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×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
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×D61C22⋊C411yescharacteristic
131C2×Q8×C61—21no—
132C2×Q8×C61—42no—
133C2×Q8×C61C22×C412yes—
134C2×D4×C61—21no—
135C2×D4×C61—42no—
136C2×D4×C61C22×C412yes—
137C22×C4×C61—21no—
138C22×C4×C61C22⋊C411yescharacteristic
139C22×C4×C61C22⋊C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C2×C22⋊D61—22no—
142C2×C22⋊D61—22no—
143C2×C22⋊D61—44no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—42no—
149C22×Dic61—42no—
150C22×Dic61C22⋊C411yescharacteristic
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—42no—
156C2×C4×D61—42no—
157C2×C4×D61C22⋊C411yescharacteristic
158C2×C4×D61C22⋊C411yescharacteristic
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22⋊C411yescharacteristic
161C2×C4×D61C22⋊C411yescharacteristic
162C2×C4×D61C22⋊C411yescharacteristic
163C2×C4×D61C22×C411yescharacteristic
164C2×C4×D61C22×C411yescharacteristic
165C2×C4×D61C2×D411yescharacteristic
166C2×C4×D61C2×D411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169#11758217—44no—
170C2×#92420—24no—
171C2×#92420—24no—
172#11758213—44no—
173#11758213—44no—
174D61⋊C8—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×Dic61C2×D411yescharacteristic
209C4×Dic61C2×D411yescharacteristic
210C4×Dic61C2×D411yescharacteristic
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61C2×D411yescharacteristic
213C4×Dic61C2×D411yescharacteristic
214C4×Dic61C2411yescharacteristic
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×D61C2×C22⋊C411yescharacteristic
225Q8×C61—24no—
226Q8×C61—42no—
227D4×C61—24no—
228D4×C61—42no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—41no—
233C2×C4×C61—42no—
234C2×C4×C61C2×C22⋊C411yescharacteristic
235C2×C4×C61C2×C22⋊C411yescharacteristic
236C2×C4×C61C2×C22⋊C411yescharacteristic
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C23×C411yescharacteristic
240C22⋊D61—44no—
241C22⋊D61—44no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61—42no—
249C2×Dic61—42no—
250C2×Dic61—44no—
251C2×Dic61C2×C22⋊C411yescharacteristic
252C2×Dic61C2×C22⋊C411yescharacteristic
253C2×Dic61C2×C22⋊C411yescharacteristic
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61AGL(1,ℤ/8)12yes—
256C2×Dic61#13712yes—
257C2×Dic61C22×D411yescharacteristic
258C2×Dic61C22×D411yescharacteristic
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—21no—
264C4×D61—21no—
265C4×D61—21no—
266C4×D61—21no—
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—41no—
270C4×D61—41no—
271C4×D61—41no—
272C4×D61—41no—
273#92420—44no—
274#92420—44no—
275#17492—611nomaximal, Sylow
276C22×C61—21no—
277C22×C61—21no—
278C22×C61—42no—
279C22×C61—42no—
280C22×C61—42no—
281C22×C61—84no—
282C22×C61#41712yes—
283C22×C61C22×C22⋊C411yescharacteristic
284C2×D61—21no—
285C2×D61—21no—
286C2×D61—21no—
287C2×D61—21no—
288C2×D61—21no—
289C2×D61—44no—
290C2×D61#42112yes—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—21no—
294C4×C61—21no—
295C4×C61—21no—
296C4×C61—42no—
297C4×C61#56812yes—
298Dic61—21no—
299Dic61—21no—
300Dic61—21no—
301Dic61—21no—
302Dic61—42no—
303Dic61—42no—
304Dic61#41712yes—
305Dic61C2×AGL(1,ℤ/8)11yescharacteristic
306Dic61C2×#13711yescharacteristic
307C2×#529—611no—
308#2920—611no—
309C2×#423—611no—
310#1495—614no—
311#1487—612no—
312#1486—612no—
313#1483—614no—
314C2×C61—22no—
315C2×C61—82no—
316C2×C61#287911yescharacteristic
317C2×C61C2×#41711yescharacteristic
318C2×C61C2×#42111yescharacteristic
319D61—22no—
320D61—41no—
321C22×M16—1221no—
322#529—612no—
323#529—612no—
324#529—612no—
325#529—612no—
326#529—1221no—
327#529—1221no—
328#529—1221no—
329#529—1221no—
330C2×#126—1221no—
331C2×#125—611no—
332C2×#124#692311yescharacteristic
333C2×#123—1221no—
334C2×C22⋊Q8—611no—
335C2×#121—611no—
336C2×C4×Q8—611no—
337C2×C4×D4—611no—
338C2×C4×D4—1221no—
339C2×#117—1221no—
340C22×C42—611no—
341#432—1221no—
342#432—1221no—
343#431—612no—
344#431—612no—
345#423—612no—
346#423—612no—
347#423—1221no—
348#423—1221no—
349#423—1221no—
350C2×C4⋊C8—612no—
351C2×C4⋊C8—1221no—
352#407—1221no—
353C4×M16—612no—
354Q8⋊C8—618no—
355D4⋊C8—618no—
356C61#1749211yescharacteristic, complemented, Sylow
357C22×Q8C2×#692311yescharacteristic
358C22×D4—1221no—
359C22×D4C2×#692311yescharacteristic
360C23×C4—611no—
361C23×C4—611no—
362C23×C4—611no—
363C23×C4—1221no—
364C2×M16—1222no—
365C2×M16—1222no—
366C2×M16—1222no—
367C2×M16—2444no—
368C22×C8—1222no—
369#126—1222no—
370#126—1222no—
371#126—1222no—
372#126—1222no—
373#125—612no—
374#125—612no—
375#125—1221no—
376#125—1221no—
377#124—21no—
378#124—21no—
379#124C2×#692312yes—
380#124C2×#692312yes—
381#123—1222no—
382#123—1222no—
383#123—1222no—
384#123—1222no—
385C22⋊Q8—612no—
386C22⋊Q8—612no—
387C22⋊Q8—1221no—
388C22⋊Q8—1221no—
389#121—612no—
390#121—612no—
391#121—1221no—
392#121—1221no—
393C4×Q8—612no—
394C4×Q8—612no—
395C4×Q8—1221no—
396C4×Q8—1221no—
397C4×D4—612no—
398C4×D4—612no—
399C4×D4—1221no—
400C4×D4—1221no—
401C4×D4—1222no—
402C4×D4—1222no—
403C4×D4—1222no—
404C4×D4—1222no—
405#117—1222no—
406#117—1222no—
407#117—1222no—
408#117—1222no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4—1221no—
419C2×C22⋊C4—1221no—
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—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—1221no—
432C2×C42C2×#692311yescharacteristic
433C4⋊C8—614no—
434C4⋊C8—1222no—
435C4⋊C8—1222no—
436C4⋊C8—1222no—
437C4⋊C8—1222no—
438C4⋊C8—1222no—
439C22⋊C8—1222no—
440C22⋊C8—1222no—
441#97—1222no—
442C4×C8—614no—
443C24—21no—
444C24—611no—
445C2×Q8—21no—
446C2×Q8—42no—
447C2×Q8C22×#692312yes—
448C2×D4—21no—
449C2×D4—42no—
450C2×D4—1222no—
451C2×D4—1222no—
452C2×D4—2444no—
453C2×D4C22×#692312yes—
454C22×C4—21no—
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—611no—
469C22×C4—611no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—2442no—
477C22×C4—2442no—
478C22×C4—2442no—
479C22×C4—2442no—
480C22×C4C22⋊#692311yescharacteristic
481C22×C4C22⋊#692311yescharacteristic
482C22×C4C22×#692311yescharacteristic
483M16—2444no—
484M16—2444no—
485M16—2444no—
486C2×C8—1224no—
487C2×C8—1224no—
488C2×C8—2444no—
489C4⋊C4—612no—
490C4⋊C4—612no—
491C4⋊C4—1222no—
492C4⋊C4—1222no—
493C4⋊C4—1222no—
494C4⋊C4—1222no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4—1222no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—1222no—
506C22⋊C4—1222no—
507C22⋊C4—1222no—
508C22⋊C4—1222no—
509C22⋊C4—1222no—
510C22⋊C4—1222no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42—611no—
515C42—611no—
516C42—611no—
517C42—611no—
518C42—611no—
519C42—611no—
520C42—611no—
521C42—611no—
522C42—611no—
523C42—1222no—
524C42—1222no—
525C42C22⋊#692311yescharacteristic
526C42C22⋊#692311yescharacteristic
527C42C22×#692311yescharacteristic
528C42C22×#692311yescharacteristic
529C23—22no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—611no—
534C23—611no—
535C23—1222no—
536C23—1222no—
537C23—2441no—
538C23C2×C22⋊#692311yescharacteristic
539Q8—24no—
540Q8—42no—
541D4—24no—
542D4—42no—
543D4—2444no—
544D4—2444no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—612no—
551C2×C4—612no—
552C2×C4—611no—
553C2×C4—611no—
554C2×C4—611no—
555C2×C4—611no—
556C2×C4—611no—
557C2×C4—611no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4—2444no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2442no—
580C2×C4—2442no—
581C2×C4C2×C22⋊#692311yescharacteristic
582C2×C4C2×C22⋊#692311yescharacteristic
583C2×C4C2×C22⋊#692311yescharacteristic
584C2×C4C2×C22⋊#692311yescharacteristic
585C2×C4C2×C22⋊#692311yescharacteristic
586C2×C4C23×#692311yescharacteristic
587C8—2444no—
588C8—2444no—
589C22—21no—
590C22—21no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—84no—
595C22—612no—
596C22—1221no—
597C22—1221no—
598C22—1221no—
599C22—1221no—
600C22—1221no—
601C22—2444no—
602C22#1684075312yes—
603C22C22×C22⋊#692311yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—21no—
609C4—42no—
610C4—611no—
611C4—611no—
612C4—612no—
613C4—1221no—
614C4—1221no—
615C4—1221no—
616C4—1221no—
617C4—2442no—
618C4—2442no—
619C4#1684084012yes—
620C2—22no—
621C2—82no—
622C2—1222no—
623C2—2441no—
624C2#2146240511yescharacteristic
625C2C2×#1684075311yescharacteristic
626C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#124×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519748C4
cosocleC4×Dic61C24
hypercenterC2×#124#6923
hypocenterC61#17492
LCSG ▷ C2×C4×C61 ▷ C2×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. D61⋊#423C2semidirect
3. #21461175C2semidirect
4. #21461147C2semidirect
5. #21461144C2semidirect
6. #21461135C2semidirect
11. #16840780C22semidirect
15. #16840766C22semidirect
19. D61⋊(C4⋊C8)C22semidirect
21. C4×#11758213C22semidirect
22. Q8⋊#92420C22semidirect
23. D4⋊#92420C22semidirect
356. C61#17492semidirect

Maximal subgroups

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

subgroupindex
#214624982
D61⋊#4232
#214611752
#214611472
#214611442
#214611352
C2×#168402912
#1749261