Finite Group Databasebeta

← #29646457

Subgroups — #29646457

Order 15616.

1214 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D61C211yesmaximal, characteristic
2#21454447C211yesmaximal, characteristic
3#21454447C211yesmaximal, characteristic
4#21444264C214yesmaximal, complemented
5#21444246C214yesmaximal, complemented
6#21444215C211yesmaximal, characteristic, complemented
7#21444214C211yesmaximal, characteristic, complemented
8#21444213C211yesmaximal, characteristic, complemented
9C61×#1479C211yesmaximal, characteristic, complemented
10C22×Q8×D61C411yescharacteristic
11C2×Q8×Dic61C411yescharacteristic
12C2×C4×Dic122—21no—
13C2×C4×Dic122C2211yescharacteristic
14C2×#14519742—21no—
15C2×#14519742C411yescharacteristic
16C4×Q8×D61—21no—
17C4×Q8×D61—21no—
18C4×Q8×D61—21no—
19C4×Q8×D61—21no—
20C4×Q8×D61C412yes—
21C4×Q8×D61C412yes—
22C4×Q8×D61C2212yes—
23C4×Q8×D61C2212yes—
24C2×C4⋊C4×D61—21no—
25C2×C4⋊C4×D61C411yescharacteristic
26C2×C42×D61—21no—
27C2×C42×D61C2211yescharacteristic
28#16839818—21no—
29#16839818C2212yes—
30#16839816—21no—
31#16839816—21no—
32#16839815C2211yescharacteristic
33#16839815C2211yescharacteristic
34#16839813—21no—
35#16839813C2212yes—
36#16839784—21no—
37#16839784C2212yes—
38#16839724—21no—
39#16839724—21no—
40C4×#11758189—21no—
41C4×#11758189C2212yes—
42#16839494C2214yescomplemented
43Q8⋊#92418C2214yescomplemented
44#16839492C2214yescomplemented
45C2×C4×Q8×C61C2211yescharacteristic
46C61×#431C2211yescharacteristic
47C61×#431C2211yescharacteristic
48C61×Q8⋊C8C2214yescomplemented
49C22×Dic122—21no—
50C22×Dic122C2×C411yescharacteristic
51C2×Q8×D61—24no—
52C2×Q8×D61—21no—
53C2×Q8×D61—21no—
54C2×Q8×D61—24no—
55C2×Q8×D61C2×C412yes—
56C2×Q8×D61C2×C412yes—
57C22×C4×D61—21no—
58C22×C4×D61—21no—
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C2×#11758189—22no—
63C2×#11758189—22no—
64Q8×Dic61—21no—
65Q8×Dic61—21no—
66Q8×Dic61C2×C412yes—
67Q8×Dic61C2×C412yes—
68C4×Dic122—21no—
69C4×Dic122—21no—
70C4×Dic122—22no—
71C4×Dic122—22no—
72C4×Dic122—22no—
73C4×Dic122—22no—
74C4×Dic122C2×C412yes—
75C4×Dic122C2312yes—
76#14519742—21no—
77#14519742—21no—
78#14519742—22no—
79#14519742—22no—
80#14519742—22no—
81#14519742—22no—
82#14519742C2×C412yes—
83#14519742C2×C412yes—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61C2×C411yescharacteristic
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C4⋊C4×D61—22no—
90C4⋊C4×D61—22no—
91C4⋊C4×D61—21no—
92C4⋊C4×D61—21no—
93C4⋊C4×D61—22no—
94C4⋊C4×D61—22no—
95C4⋊C4×D61C2×C412yes—
96C4⋊C4×D61C2×C412yes—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61C2×C411yescharacteristic
101C2×C4×Dic61D411yescharacteristic
102C2×C4×Dic61D411yescharacteristic
103C42×D61—22no—
104C42×D61—22no—
105C42×D61—22no—
106C42×D61—22no—
107C42×D61C2×C411yescharacteristic
108C42×D61C2×C411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61C2311yescharacteristic
114C42×D61C2311yescharacteristic
115C4⋊#92418—21no—
116C4⋊#92418C2312yes—
117#14519706—22no—
118#14519706—22no—
119C22⋊#92418—21no—
120C22⋊#92418—21no—
121#14519689—22no—
122#14519689—22no—
123#14519687—22no—
124#14519687—22no—
125C4×#92418—21no—
126C4×#92418C2312yes—
127C22×Q8×C61C2×C411yescharacteristic
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C4×Q8×C61C2×C412yes—
131C4×Q8×C61C2312yes—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2312yes—
138C22⋊C8×C61—21no—
139C22⋊C8×C61—21no—
140C4×C8×C61—21no—
141C4×C8×C61C2312yes—
142C23×D61C22⋊C411yescharacteristic
143C2×Q8×C61—21no—
144C2×Q8×C61—22no—
145C2×Q8×C61M1614yescomplemented
146C2×Q8×C61C22×C412yes—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61C22⋊C411yescharacteristic
155C22×Dic61C22⋊C411yescharacteristic
156C22×Dic61C22⋊C411yescharacteristic
157Q8×D61—28no—
158Q8×D61—28no—
159Q8×D61—24no—
160Q8×D61—24no—
161Q8×D61—24no—
162Q8×D61—24no—
163C2×C4×D61—28no—
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—24no—
169C2×C4×D61—22no—
170C2×C4×D61—22no—
171C2×C4×D61—42no—
172C2×C4×D61—44no—
173C2×C4×D61C22⋊C411yescharacteristic
174C2×C4×D61C22⋊C411yescharacteristic
175C2×C4×D61C22⋊C411yescharacteristic
176C2×C4×D61C22⋊C411yescharacteristic
177C2×C4×D61C22⋊C411yescharacteristic
178C2×C4×D61C22⋊C411yescharacteristic
179C2×C4×D61C22×C411yescharacteristic
180C2×C4×D61C22×C411yescharacteristic
181C2×C4×D61C2×D411yescharacteristic
182C2×C4×D61C2×D411yescharacteristic
183C2×C4×D61C2×D411yescharacteristic
184C2×C4×D61C2×D411yescharacteristic
185C2×Dic122—28no—
186C2×Dic122—21no—
187C2×Dic122—22no—
188C2×Dic122—22no—
189C2×Dic122—22no—
190C2×Dic122M1614yescomplemented
191C2×Dic122C22×C412yes—
192C2×C8×C61—22no—
193C2×C8×C61—22no—
194C4⋊C4×C61—22no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—22no—
197C4⋊C4×C61C22×C412yes—
198C42×C61—22no—
199C42×C61—22no—
200C42×C61C22×C411yescharacteristic
201C42×C61C2×D411yescharacteristic
202C42×C61C2×D411yescharacteristic
203C42×C61C2411yescharacteristic
204C4⋊Dic61—21no—
205C4⋊Dic61—22no—
206C4⋊Dic61—22no—
207C4⋊Dic61C22×C412yes—
208#11758196—22no—
209#11758196—22no—
210#11758196—22no—
211#11758196—22no—
212#11758196—22no—
213#11758196—22no—
214C4×Dic61—22no—
215C4×Dic61—22no—
216C4×Dic61—22no—
217C4×Dic61—22no—
218C4×Dic61—22no—
219C4×Dic61—22no—
220C4×Dic61C22⋊C411yescharacteristic
221C4×Dic61C22⋊C411yescharacteristic
222C4×Dic61C22⋊C411yescharacteristic
223C4×Dic61C22⋊C411yescharacteristic
224C4×Dic61C22⋊C411yescharacteristic
225C4×Dic61C22⋊C411yescharacteristic
226C4×Dic61C22×C411yescharacteristic
227C4×Dic61C22×C411yescharacteristic
228C4×Dic61C2×D411yescharacteristic
229C4×Dic61C2×D411yescharacteristic
230C4×Dic61C2×D411yescharacteristic
231C4×Dic61C2×D411yescharacteristic
232C2×#92418—22no—
233C2×#92418—22no—
234#11758189—44no—
235#11758189—44no—
236C23×C61C2×C22⋊C411yescharacteristic
237C22×D61—22no—
238C22×D61—22no—
239C22×D61—22no—
240C22×D61C2×C22⋊C411yescharacteristic
241C22×D61C2×C22⋊C411yescharacteristic
242Q8×C61—22no—
243Q8×C61—24no—
244Q8×C61C2×M1614yes—
245C2×C4×C61—22no—
246C2×C4×C61—24no—
247C2×C4×C61—22no—
248C2×C4×C61—22no—
249C2×C4×C61—41no—
250C2×C4×C61—42no—
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C2×C22⋊C411yescharacteristic
254C2×C4×C61C2×M1612yes—
255C2×C4×C61C2×M1612yes—
256C2×C4×C61C23×C411yescharacteristic
257C2×C4×C61C22×D411yescharacteristic
258C2×C4×C61C22×D411yescharacteristic
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—24no—
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—41no—
265C2×Dic61—42no—
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C2×C22⋊C411yescharacteristic
272C4×D61—28no—
273C4×D61—28no—
274C4×D61—22no—
275C4×D61—22no—
276C4×D61—22no—
277C4×D61—21no—
278C4×D61—21no—
279C4×D61—21no—
280C4×D61—21no—
281C4×D61—22no—
282C4×D61—22no—
283C4×D61—22no—
284C4×D61—22no—
285C4×D61—41no—
286C4×D61—41no—
287C4×D61—44no—
288C4×D61—44no—
289C4×D61#13714yes—
290Dic122—28no—
291Dic122—28no—
292Dic122—22no—
293Dic122—24no—
294Dic122C2×M1614yes—
295C8×C61—42no—
296C8×C61—42no—
297#92418—42no—
298#92418—42no—
299#17449—611nomaximal, Sylow
300C22×C61—21no—
301C22×C61—21no—
302C22×C61#40712yes—
303C22×C61C22×C22⋊C411yescharacteristic
304C2×D61—28no—
305C2×D61—21no—
306C2×D61—21no—
307C2×D61—21no—
308C2×D61—21no—
309C2×D61#41912yes—
310C2×D61#42112yes—
311C4×C61—24no—
312C4×C61—21no—
313C4×C61—21no—
314C4×C61—21no—
315C4×C61—42no—
316C4×C61#40712yes—
317C4×C61C22×M1611yescharacteristic
318C4×C61C22×M1611yescharacteristic
319C4×C61C2×#13712yes—
320Dic61—21no—
321Dic61—21no—
322Dic61—24no—
323Dic61—21no—
324Dic61—21no—
325Dic61—21no—
326Dic61—42no—
327Dic61#41912yes—
328C22×C4×Q8—611no—
329#2920—611no—
330#2920—611no—
331#1491—614no—
332#1487—614no—
333#1479—611no—
334#1479—611no—
335#1479—611no—
336#1479D6111yescharacteristic, complemented
337C2×C61—22no—
338C2×C61C2×#40711yescharacteristic
339C2×C61C2×#41911yescharacteristic
340C2×C61C2×#42111yescharacteristic
341D61—22no—
342D61—22no—
343C23×Q8—611no—
344C2×C4×Q8—611no—
345C2×C4×Q8—612no—
346C2×C4×Q8—612no—
347C2×C4×Q8—612no—
348C2×C4×Q8—612no—
349C2×C4×Q8—611no—
350C2×C4×Q8—611no—
351C2×C4×Q8—1221no—
352C2×C4×Q8—1221no—
353C2×C4×Q8—1221no—
354C2×C4×Q8—1221no—
355C2×C4×Q8—1221no—
356C2×C4×Q8—1221no—
357C2×C4×Q8C2×D6111yescharacteristic
358C22×C4⋊C4—611no—
359C22×C4⋊C4—1221no—
360C22×C42—611no—
361C22×C42—1221no—
362#432—612no—
363#432—1221no—
364#432—1221no—
365#432—1221no—
366#431—611no—
367#431—612no—
368#431—611no—
369#431—1221no—
370#431C2×D6111yescharacteristic
371#431C2×D6111yescharacteristic
372#423—612no—
373#423—1221no—
374#407—1221no—
375#407—1221no—
376C4×M16—612no—
377C4×M16—1221no—
378Q8⋊C8—614no—
379Q8⋊C8—614no—
380Q8⋊C8—614no—
381Q8⋊C8C2×D6114yescomplemented
382C61#1744911yescharacteristic, complemented, Sylow
383C22×Q8—612no—
384C22×Q8—612no—
385C22×Q8—611no—
386C22×Q8—1221no—
387C22×Q8—1221no—
388C22×Q8—1221no—
389C22×Q8—1224no—
390C22×Q8—1224no—
391C22×Q8C4×D6111yescharacteristic
392C23×C4—611no—
393C23×C4—611no—
394C23×C4—611no—
395C23×C4—1221no—
396C23×C4—1221no—
397C2×M16—1222no—
398C2×M16—1222no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8—612no—
402C4×Q8—612no—
403C4×Q8—612no—
404C4×Q8—612no—
405C4×Q8—612no—
406C4×Q8—612no—
407C4×Q8—1222no—
408C4×Q8—1222no—
409C4×Q8—1222no—
410C4×Q8—1222no—
411C4×Q8—1222no—
412C4×Q8—1222no—
413C4×Q8—1222no—
414C4×Q8—1222no—
415C4×Q8—1221no—
416C4×Q8—1221no—
417C4×Q8—1221no—
418C4×Q8—1221no—
419C4×Q8—1221no—
420C4×Q8—1221no—
421C4×Q8C4×D6112yes—
422C4×Q8C22×D6112yes—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—612no—
426C2×C4⋊C4—612no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—1222no—
430C2×C4⋊C4—1222no—
431C2×C4⋊C4—1222no—
432C2×C4⋊C4—1222no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4—1221no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4C4×D6111yescharacteristic
438C2×C42—21no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—1222no—
451C2×C42—1222no—
452C2×C42—1222no—
453C2×C42—1222no—
454C2×C42—1221no—
455C2×C42—1221no—
456C2×C42—1221no—
457C2×C42C22×D6111yescharacteristic
458C4⋊C8—21no—
459C4⋊C8—612no—
460C4⋊C8—1222no—
461C4⋊C8—1222no—
462C4⋊C8—1221no—
463C4⋊C8C22×D6112yes—
464C22⋊C8—21no—
465C22⋊C8—21no—
466C22⋊C8—1222no—
467C22⋊C8—1222no—
468C22⋊C8—1221no—
469C22⋊C8—1221no—
470#97—1222no—
471#97—1222no—
472C4×C8—21no—
473C4×C8—612no—
474C4×C8—1221no—
475C4×C8C22×D6112yes—
476C24—611no—
477C2×Q8—21no—
478C2×Q8—22no—
479C2×Q8—612no—
480C2×Q8—614no—
481C2×Q8—1222no—
482C2×Q8—1222no—
483C2×Q8—1228no—
484C2×Q8—1224no—
485C2×Q8—1224no—
486C2×Q8—1228no—
487C2×Q8—1228no—
488C2×Q8—1224no—
489C2×Q8—1224no—
490C2×Q8—1221no—
491C2×Q8—1222no—
492C2×Q8#1175818914yescomplemented
493C2×Q8C2×C4×D6112yes—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—611no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—1224no—
512C22×C4—1222no—
513C22×C4—1222no—
514C22×C4—1228no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1221no—
518C22×C4—1222no—
519C22×C4—1222no—
520C22×C4—1221no—
521C22×C4—2442no—
522C22×C4—2444no—
523C22×C4C2×C4×D6111yescharacteristic
524C22×C4D4×D6111yescharacteristic
525C22×C4D4×D6111yescharacteristic
526M16—2444no—
527M16—2444no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—1222no—
531C2×C8—1222no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—21no—
535C4⋊C4—612no—
536C4⋊C4—1222no—
537C4⋊C4—1222no—
538C4⋊C4—1222no—
539C4⋊C4—1222no—
540C4⋊C4—1222no—
541C4⋊C4—1222no—
542C4⋊C4—1222no—
543C4⋊C4—1221no—
544C4⋊C4—1222no—
545C4⋊C4C2×C4×D6112yes—
546C42—22no—
547C42—22no—
548C42—611no—
549C42—611no—
550C42—611no—
551C42—611no—
552C42—611no—
553C42—611no—
554C42—611no—
555C42—611no—
556C42—611no—
557C42—611no—
558C42—611no—
559C42—611no—
560C42—1222no—
561C42—1222no—
562C42—1222no—
563C42—1222no—
564C42—1222no—
565C42—1222no—
566C42C2×C4×D6111yescharacteristic
567C42D4×D6111yescharacteristic
568C42D4×D6111yescharacteristic
569C42C23×D6111yescharacteristic
570C23—611no—
571C23—611no—
572C23—1222no—
573C23—1222no—
574C23—1222no—
575C23C22⋊C4×D6111yescharacteristic
576Q8—24no—
577Q8—22no—
578Q8—614no—
579Q8—1228no—
580Q8—1228no—
581Q8—1224no—
582Q8—1222no—
583Q8C2×#1175818914yes—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—611no—
591C2×C4—614no—
592C2×C4—611no—
593C2×C4—611no—
594C2×C4—611no—
595C2×C4—611no—
596C2×C4—611no—
597C2×C4—1222no—
598C2×C4—1222no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—1228no—
602C2×C4—1228no—
603C2×C4—1222no—
604C2×C4—1222no—
605C2×C4—1222no—
606C2×C4—1224no—
607C2×C4—1222no—
608C2×C4—1222no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—1221no—
613C2×C4—1222no—
614C2×C4—1222no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2444no—
618C2×C4—2444no—
619C2×C4—2441no—
620C2×C4—2442no—
621C2×C4C22⋊C4×D6111yescharacteristic
622C2×C4C22⋊C4×D6111yescharacteristic
623C2×C4C22⋊C4×D6111yescharacteristic
624C2×C4M16×D6112yes—
625C2×C4C2×#1175818912yes—
626C2×C4C22×C4×D6111yescharacteristic
627C2×C4C2×D4×D6111yescharacteristic
628C2×C4C2×D4×D6111yescharacteristic
629C8—42no—
630C8—42no—
631C8—2442no—
632C8—2442no—
633C22—21no—
634C22—21no—
635C22—612no—
636C22—612no—
637C22—1228no—
638C22—1221no—
639C22—1221no—
640C22—1221no—
641C22—1221no—
642C22#1683972412yes—
643C22C2×C22⋊C4×D6111yescharacteristic
644C4—21no—
645C4—21no—
646C4—24no—
647C4—21no—
648C4—42no—
649C4—612no—
650C4—1221no—
651C4—1221no—
652C4—1221no—
653C4—1221no—
654C4—1224no—
655C4—1221no—
656C4—2442no—
657C4#1683972412yes—
658C4C2×M16×D6111yescharacteristic
659C4C22×#1175818911yescharacteristic
660C4#137×D6112yes—
661C2—22no—
662C2—1222no—
663C2—1222no—
664C2C2×#1683972411yescharacteristic
665C2#419×D6111yescharacteristic
666C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1479C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC42×C61C24
hypercenter#1479D61
hypocenterC61#17449
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
4. #21444264C2semidirect
5. #21444246C2semidirect
6. #21444215C2semidirect
7. #21444214C2semidirect
8. #21444213C2semidirect
9. C61×#1479C2semidirect
42. #16839494C22semidirect
43. Q8⋊#92418C22semidirect
44. #16839492C22semidirect
48. C61×Q8⋊C8C22semidirect
145. C2×Q8×C61M16semidirect
190. C2×Dic122M16semidirect
336. #1479D61semidirect
381. Q8⋊C8C2×D61semidirect
382. C61#17449semidirect
492. C2×Q8#11758189semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D612
#214544472
#214442642
#214442462
#214442152
#214442142
#214442132
C61×#14792
#1744961