Finite Group Databasebeta

← #30610940

Subgroups — #30610940

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#21462496C211yesmaximal, characteristic, complemented
2C4×#14519856C211yesmaximal, characteristic, complemented
3#21461223C214yesmaximal, complemented
4#21461219C212yesmaximal, complemented
5#21461216C212yesmaximal
6#21461192C214yesmaximal, complemented
7C2×#16840299C211yesmaximal, characteristic
8C2×#14519856—21no—
9#16840784C2212yescomplemented
10#16840783—21no—
11#16840781C2212yescomplemented
12#16840778—21no—
13#16840766—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#16840614C2218yes—
24#16840299—21no—
25#16840299—21no—
26#16840299—21no—
27#16840299—21no—
28#16840299C412yescomplemented
29#16840299C412yescomplemented
30#16840299C2212yes—
31#16840299C2212yes—
32C2×#14519772—21no—
33C2×#14519768C411yescharacteristic, complemented
34C2×#14519766C411yescharacteristic, complemented
35C2×#14519762—21no—
36C2×#14519753C2211yescharacteristic
37C2×#14519752C2211yescharacteristic
38C2×C4×D244—21no—
39C2×C4×D244C411yescharacteristic, complemented
40C2×#14519734—21no—
41C2×C42×D61C2211yescharacteristic
42C2×C4×Q8×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—
50C4⋊#92420—22no—
51C4⋊#92420—22no—
52#14519834C2314yes—
53C22⋊#92420—22no—
54#14519832—22no—
55C4×#92420—22no—
56(C2×#6923)⋊C4—22no—
57(C2×#6923)⋊C4C2314yes—
58C22×D244—21no—
59C22×D244C2×C411yescharacteristic
60C22×C4×D61—21no—
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64#14519772—22no—
65#14519772—22no—
66#14519772—22no—
67#14519772—22no—
68#14519768—21no—
69#14519768—21no—
70#14519768C2×C412yes—
71#14519768C2×C412yes—
72#14519766—21no—
73#14519766—21no—
74#14519766C2×C412yes—
75#14519766C2×C412yes—
76#14519762—22no—
77#14519762—22no—
78#14519762—22no—
79#14519762—22no—
80#14519753—21no—
81#14519753—21no—
82#14519753C2×C412yes—
83#14519753C2312yes—
84#14519752—21no—
85#14519752—21no—
86#14519752C2×C412yes—
87#14519752C2312yes—
88C4×D244—22no—
89C4×D244—22no—
90C4×D244—22no—
91C4×D244—22no—
92C4×D244—21no—
93C4×D244—21no—
94C4×D244C2×C412yes—
95C4×D244C2×C412yes—
96#14519734—22no—
97#14519734—22no—
98#14519734—22no—
99#14519734—22no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61C2×C411yescharacteristic
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—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
121C4×Q8×C61—21no—
122C4×Q8×C61—21no—
123C4×Q8×C61C2×C412yes—
124C4×Q8×C61C2×C412yes—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C42×C61—21no—
128C2×C42×C61C2×C411yescharacteristic
129C23×D61—21no—
130C23×D61C2×D411yescharacteristic
131C22×#6923—24no—
132C2×Q8×C61—21no—
133C2×Q8×C61—42no—
134C2×Q8×C61C22×C412yes—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61C22⋊C411yescharacteristic
138C22×C4×C61C22⋊C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×Dic61—21no—
141C22×Dic61C22⋊C411yescharacteristic
142C22×Dic61C22⋊C411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144C2×D244—22no—
145C2×D244—22no—
146C2×D244—21no—
147C2×D244—44no—
148C2×D244—42no—
149C2×D244C22×C412yes—
150C2×C4×D61—24no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—42no—
154C2×C4×D61—42no—
155C2×C4×D61—44no—
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—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61C22×C412yes—
179C42×C61—22no—
180C42×C61—22no—
181C42×C61C22⋊C411yescharacteristic
182C42×C61C22⋊C411yescharacteristic
183C42×C61C22×C411yescharacteristic
184C42×C61C22×C411yescharacteristic
185#11758198—22no—
186#11758198—22no—
187#11758198—22no—
188#11758198—22no—
189#11758198—22no—
190#11758198—22no—
191#11758198—22no—
192#11758198—22no—
193#11758198—22no—
194#11758198—22no—
195C4⋊Dic61—21no—
196C4⋊Dic61—22no—
197C4⋊Dic61—22no—
198C4⋊Dic61C22×C412yes—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—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×D61—41no—
220C22×D61—42no—
221C22×D61—42no—
222C22×D61—42no—
223C22×D61C2×C22⋊C411yescharacteristic
224C22×D61C22×D411yescharacteristic
225C2×#6923—28no—
226C2×#6923—44no—
227C2×#6923—44no—
228Q8×C61—42no—
229Q8×C61—42no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—41no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61#10414yes—
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
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—42no—
248C2×Dic61C2×C22⋊C411yescharacteristic
249C2×Dic61C2×C22⋊C411yescharacteristic
250C2×Dic61C2×C22⋊C411yescharacteristic
251C2×Dic61C2×C22⋊C411yescharacteristic
252C2×Dic61C2×C22⋊C411yescharacteristic
253C2×Dic61C22×D411yescharacteristic
254D244—42no—
255D244—44no—
256D244—44no—
257D244—42no—
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—22no—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—41no—
267C4×D61—41no—
268C4×D61—41no—
269C4×D61—41no—
270C4×D61—44no—
271C4×D61—44no—
272#92420—44no—
273#17537—611nomaximal, Sylow
274C22×C61—21no—
275C22×C61—21no—
276C22×C61C2×#10412yes—
277C22×C61C22×C22⋊C411yescharacteristic
278C2×D61—21no—
279C2×D61—21no—
280C2×D61—21no—
281C2×D61—21no—
282C2×D61—21no—
283C2×D61—44no—
284C2×D61—42no—
285C2×D61—42no—
286C2×D61—42no—
287C2×D61—84no—
288C2×D61#57512yes—
289#6923—48no—
290C4×C61—21no—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—42no—
294C4×C61—42no—
295C4×C61#41012yes—
296C4×C61C2×#10412yes—
297C4×C61C2×#10412yes—
298Dic61—21no—
299Dic61—21no—
300Dic61—21no—
301Dic61—21no—
302Dic61—21no—
303Dic61—21no—
304Dic61—42no—
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×C61C2×#41011yescharacteristic
314C2×C61#289611yescharacteristic
315C2×C61C22×#10411yescharacteristic
316D61—22no—
317D61—41no—
318D61—82no—
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—611no—
330C2×#123—1221no—
331C2×C22⋊Q8—611no—
332C2×#121—611no—
333C2×C4×Q8#692311yescharacteristic, complemented
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—611no—
357C22×D4—1221no—
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—612no—
372#124—612no—
373#124—1221no—
374#124—1221no—
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—21no—
388C4×Q8—21no—
389C4×Q8C2×#692312yes—
390C4×Q8C2×#692312yes—
391C4×D4—612no—
392C4×D4—612no—
393C4×D4—1222no—
394C4×D4—1222no—
395C4×D4—1222no—
396C4×D4—1222no—
397C4×D4—1221no—
398C4×D4—1221no—
399#117—1222no—
400#117—1222no—
401#117—1222no—
402#117—1222no—
403#117—1228no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1222no—
410C2×C4⋊C4C2×#692311yescharacteristic
411C2×C22⋊C4—1221no—
412C2×C22⋊C4—1221no—
413C2×C22⋊C4—1221no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1222no—
416C2×C22⋊C4—1221no—
417C2×C42—21no—
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—611no—
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—611no—
442C24—1221no—
443C2×Q8—21no—
444C2×Q8—42no—
445C2×Q8C22×#692312yes—
446C2×D4—612no—
447C2×D4—1222no—
448C2×D4—1222no—
449C2×D4—1221no—
450C2×D4—2442no—
451C2×D4—2444no—
452C22×C4—21no—
453C22×C4—21no—
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—611no—
469C22×C4—1224no—
470C22×C4—1224no—
471C22×C4—1221no—
472C22×C4—1222no—
473C22×C4—1222no—
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—22no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—612no—
486C4⋊C4—1222no—
487C4⋊C4—1222no—
488C4⋊C4—1222no—
489C4⋊C4—1222no—
490C4⋊C4—1222no—
491C4⋊C4—1222no—
492C4⋊C4—1228no—
493C4⋊C4—1221no—
494C4⋊C4C22×#692312yes—
495C22⋊C4—1222no—
496C22⋊C4—1222no—
497C22⋊C4—1222no—
498C22⋊C4—1222no—
499C22⋊C4—1222no—
500C22⋊C4—1222no—
501C22⋊C4—1222no—
502C22⋊C4—1222no—
503C22⋊C4—1228no—
504C22⋊C4—1222no—
505C22⋊C4—1222no—
506C42—22no—
507C42—22no—
508C42—611no—
509C42—611no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42—611no—
515C42—611no—
516C42—611no—
517C42—611no—
518C42—611no—
519C42—611no—
520C42—1228no—
521C42—2444no—
522C42—2444no—
523C42C22⋊#692311yescharacteristic
524C42C22⋊#692311yescharacteristic
525C42C22×#692311yescharacteristic
526C42C22×#692311yescharacteristic
527C23—611no—
528C23—611no—
529C23—1222no—
530C23—1222no—
531C23—1222no—
532C23—2441no—
533C23—2442no—
534C23—2442no—
535C23—2442no—
536C23C2×C22⋊#692311yescharacteristic
537Q8—42no—
538Q8—42no—
539D4—2442no—
540D4—2444no—
541D4—2444no—
542D4—2442no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
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—1222no—
564C2×C4—1228no—
565C2×C4—1222no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2444no—
573C2×C4—2444no—
574C2×C4—2442no—
575C2×C4—2444no—
576C2×C4—2444no—
577C2×C4#1451984214yes—
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—612no—
588C22—1221no—
589C22—1221no—
590C22—1221no—
591C22—1221no—
592C22—1221no—
593C22—4884no—
594C22—2444no—
595C22—2442no—
596C22—2442no—
597C22—2442no—
598C22C2×#1451984212yes—
599C22C22×C22⋊#692311yescharacteristic
600C4—21no—
601C4—21no—
602C4—21no—
603C4—42no—
604C4—42no—
605C4—1221no—
606C4—1221no—
607C4—1221no—
608C4—1221no—
609C4—1221no—
610C4—1221no—
611C4—2448no—
612C4—2442no—
613C4#1684074112yes—
614C4C2×#1451984212yes—
615C4C2×#1451984212yes—
616C2—22no—
617C2—1222no—
618C2—4882no—
619C2—2441no—
620C2C2×#1684074111yescharacteristic
621C2#2146243911yescharacteristic
622C2C22×#1451984211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519752C22
cosocleC2×C4×D61C24
hypercenterC2×C4×Q8#6923
hypocenterC61#17537
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #21462496C2semidirect
2. C4×#14519856C2semidirect
3. #21461223C2semidirect
4. #21461219C2semidirect
6. #21461192C2semidirect
9. #16840784C22semidirect
11. #16840781C22semidirect
17. C4×C4⋊#6923C22semidirect
20. #16840698C22semidirect
22. #16840616C22semidirect
28. #16840299C4semidirect
29. #16840299C4semidirect
33. C2×#14519768C4semidirect
34. C2×#14519766C4semidirect
39. C2×C4×D244C4semidirect
42. C2×C4×Q8×C61C4semidirect
333. C2×C4×Q8#6923semidirect
354. C61#17537semidirect

Maximal subgroups

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

subgroupindex
#214624962
C4×#145198562
#214612232
#214612192
#214612162
#214611922
C2×#168402992
#1753761