Finite Group Databasebeta

← #29716152

Subgroups — #29716152

Order 15616.

1066 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840318C211yesmaximal, characteristic
2C2×#16840069C211yesmaximal, characteristic, complemented
3C4×#14519753C211yesmaximal, characteristic
4#21447150C211yesmaximal, characteristic, complemented
5#21447145C211yesmaximal, characteristic, complemented
6#21446958C211yesmaximal, characteristic, complemented
7#21446958C211yesmaximal, characteristic, complemented
8#21446777C211yesmaximal, characteristic, complemented
9#21446774C211yesmaximal, characteristic, complemented
10#21446128C211yesmaximal, characteristic
11#21446128C211yesmaximal, characteristic
12#21446017C211yesmaximal, characteristic
13#21446015C211yesmaximal, characteristic
14#21445796C211yesmaximal, characteristic
15C2×C61×#479C211yesmaximal, characteristic, complemented
16#16840318—24no—
17#16840318—24no—
18C2×#14519776C2211yescharacteristic
19C2×#14519776C2211yescharacteristic
20C2×#14519769C2211yescharacteristic
21C2×#14519755—21no—
22C2×#14519755—21no—
23C2×#14519753C2211yescharacteristic
24C2×#14519742—21no—
25C2×#14519742—21no—
26C2×#14519735C2211yescharacteristic
27C2×#14519735C2211yescharacteristic
28C2×C42×D61C2211yescharacteristic
29#16840069—24no—
30C2×#14519710C2211yescharacteristic
31C2×#14519708C2211yescharacteristic
32C2×C4⋊#92418C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37#16839669C2211yescharacteristic
38#16839658C2211yescharacteristic
39#16839643—21no—
40#16839633—21no—
41#16839619C2211yescharacteristic
42C4×#11758196—21no—
43C4×C4⋊Dic61C2211yescharacteristic
44C4×#11758198—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C2×#125×C61C2211yescharacteristic
56C2×C4×Q8×C61C2211yescharacteristic
57C61×#479—24no—
58C2×#107×C61C2211yescharacteristic
59C2×#106×C61C2211yescharacteristic
60C2×C4⋊C8×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#103×C61C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122—21no—
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70#14519776—22no—
71#14519776—22no—
72#14519776—22no—
73#14519776—22no—
74#14519769—22no—
75#14519769D414yes—
76#14519755—28no—
77#14519755—28no—
78#14519753—22no—
79#14519753Q814yescomplemented
80#14519742—28no—
81#14519742—28no—
82#14519735—22no—
83#14519735—22no—
84#14519735—22no—
85#14519735—22no—
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61D411yescharacteristic
104C2×C4×Dic61D411yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106C42×D61—22no—
107C42×D61—22no—
108#14519710—22no—
109#14519708—22no—
110C4⋊#92418—22no—
111#14519701—22no—
112#14519701—22no—
113#14519689—22no—
114#14519689—22no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120C22×Q8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123#125×C61—22no—
124#125×C61D414yes—
125C4×Q8×C61—22no—
126C4×Q8×C61—22no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C42×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#107×C61—22no—
136#106×C61—22no—
137C4⋊C8×C61—22no—
138#103×C61—22no—
139#103×C61—22no—
140C23×D61C2×D411yescharacteristic
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×Q812yes—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2411yescharacteristic
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61C2×D411yescharacteristic
159C22×Dic61C2×D411yescharacteristic
160C22×Dic61C2×D411yescharacteristic
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—22no—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—41no—
170C2×C4×D61—41no—
171C2×C4×D61C2×Q812yes—
172C2×C4×D61#4112yes—
173C2×Dic122—24no—
174C2×Dic122—24no—
175C2×Dic122—42no—
176C2×Dic122—42no—
177C2×Dic122—42no—
178C2×Dic122—42no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C4⋊C4×C61—24no—
186C4⋊C4×C61—24no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—42no—
192C4⋊C4×C61C2×D412yes—
193C4⋊C4×C61C2×D412yes—
194C42×C61—42no—
195C42×C61C2×D412yes—
196C42×C61C2×D412yes—
197#11758198—24no—
198#11758198—24no—
199#11758198—24no—
200#11758198—42no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61C2×D412yes—
207C4⋊Dic61C2×D412yes—
208C4⋊Dic61C2×Q812yes—
209#11758196—24no—
210#11758196—24no—
211#11758196—24no—
212#11758196—24no—
213#11758196—24no—
214#11758196—42no—
215C4×Dic61—24no—
216C4×Dic61—24no—
217C4×Dic61—22no—
218C4×Dic61—22no—
219C4×Dic61—21no—
220C4×Dic61—21no—
221C4×Dic61—42no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C23×C61C22×D411yescharacteristic
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—21no—
232C22×D61—21no—
233C22×D61—21no—
234C22×D61—21no—
235C22×D61C22⋊Q812yes—
236Q8×C61—22no—
237Q8×C61—22no—
238Q8×C61—41no—
239Q8×C61—41no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61#12012yes—
257C2×C4×C61#12012yes—
258C2×C4×C61C22×D411yescharacteristic
259C2×C4×C61C22×D411yescharacteristic
260C2×C4×C61C22×Q811yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C612−1+411yescharacteristic
263C2×C4×C612−1+411yescharacteristic
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61C22⋊Q812yes—
283C2×Dic61#13512yes—
284C2×Dic61#13712yes—
285C4×D61—22no—
286C4×D61—22no—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—44no—
290C4×D61—44no—
291Dic122—48no—
292Dic122—48no—
293C8×C61—41no—
294C8×C61—41no—
295#92418—41no—
296#92418—41no—
297#24306—611nomaximal, Sylow
298C22×C61C2×#12011yescharacteristic
299C22×C61C2×C22⋊Q811yescharacteristic
300C22×C61#53611yescharacteristic
301C22×C61C2×#13511yescharacteristic
302C22×C61C2×#13711yescharacteristic
303C22×C61#57511yescharacteristic
304C22×C61#57511yescharacteristic
305C2×D61—22no—
306C2×D61—22no—
307C2×D61—22no—
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C2×D61—41no—
312C4×C61—22no—
313C4×C61—22no—
314C4×C61—42no—
315C4×C61—42no—
316C4×C61—42no—
317C4×C61—81no—
318C4×C61#54811yescharacteristic
319C4×C61#54811yescharacteristic
320C4×C61D4×Q811yescharacteristic
321C4×C61D4×Q811yescharacteristic
322Dic61—22no—
323Dic61—22no—
324Dic61—22no—
325Dic61—42no—
326Dic61—42no—
327Dic61—42no—
328Dic61—81no—
329C2×#533—611no—
330C2×#479—611no—
331C2×#479D6111yescharacteristic, complemented
332C4×C22⋊Q8—611no—
333#2058—611no—
334#2057—611no—
335#2024—611no—
336#2024—611no—
337#1989—611no—
338#1989—611no—
339#1873—611no—
340#1873—611no—
341#1854—611no—
342#1854—611no—
343#1797—611no—
344C2×C61#240911yescharacteristic
345C2×C61#300211yescharacteristic
346C2×C61#300711yescharacteristic
347C2×C61#307611yescharacteristic
348C2×C61#307811yescharacteristic
349C2×C61#323111yescharacteristic
350C2×C61#324011yescharacteristic
351D61—42no—
352#533—1224no—
353#533—1224no—
354C2×C4⋊Q8—611no—
355C2×C4⋊Q8—611no—
356C2×#125—611no—
357C2×#125C2×D6111yescharacteristic
358C2×C22⋊Q8—611no—
359C2×C22⋊Q8—1221no—
360C2×C22⋊Q8—1221no—
361C2×C4×Q8—1221no—
362C2×C4×Q8—1221no—
363C2×C4×Q8C2×D6111yescharacteristic
364C2×#117—611no—
365C2×#117—611no—
366C22×C42—611no—
367#479—24no—
368#479—1224no—
369C2×#107—611no—
370C2×#107C2×D6111yescharacteristic
371C2×#106—611no—
372C2×#106C2×D6111yescharacteristic
373C2×C4⋊C8—611no—
374C2×C4⋊C8C2×D6111yescharacteristic
375C2×#103—611no—
376C2×#103—611no—
377C2×#103C2×D6111yescharacteristic
378C2×#103C2×D6111yescharacteristic
379C2×C22⋊C8—611no—
380C2×C22⋊C8—611no—
381#391—611no—
382#389—611no—
383#387—1221no—
384#385—1221no—
385#380—611no—
386C4×C4⋊C4—611no—
387C4×C4⋊C4—1221no—
388C4×C22⋊C4—1221no—
389#340—611no—
390#340—611no—
391#340—611no—
392#340—611no—
393#340—611no—
394#340—611no—
395#340—611no—
396#340—611no—
397#336—611no—
398#336—611no—
399C61#2430611yescharacteristic, complemented, Sylow
400C22×Q8—1221no—
401C22×Q8—1221no—
402C22×Q8C22×D6111yescharacteristic
403C23×C4—611no—
404C23×C4—611no—
405C23×C4—611no—
406C22×C8—611no—
407C22×C8—611no—
408C22×C8C22×D6111yescharacteristic
409C22×C8C22×D6111yescharacteristic
410C4⋊Q8—1222no—
411C4⋊Q8—1222no—
412C4⋊Q8—1222no—
413C4⋊Q8—1222no—
414#125—22no—
415#125—614no—
416#125—1222no—
417#125C22⋊D6114yes—
418C22⋊Q8—614no—
419C22⋊Q8—1228no—
420C22⋊Q8—1228no—
421C22⋊Q8—1222no—
422C4×Q8—22no—
423C4×Q8—22no—
424C4×Q8—1228no—
425C4×Q8—1228no—
426#117—1222no—
427#117—1222no—
428#117—1222no—
429#117—1222no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—611no—
434C2×C4⋊C4—611no—
435C2×C4⋊C4—611no—
436C2×C4⋊C4—611no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4—1221no—
439C2×C4⋊C4—1221no—
440C2×C4⋊C4—1221no—
441C2×C4⋊C4—1221no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4C22×D6111yescharacteristic
444C2×C4⋊C4C22×D6111yescharacteristic
445C2×C4⋊C4C22×D6111yescharacteristic
446C2×C22⋊C4—1221no—
447C2×C22⋊C4—1221no—
448C2×C22⋊C4—1221no—
449C2×C22⋊C4—1221no—
450C2×C42—21no—
451C2×C42—611no—
452C2×C42—611no—
453C2×C42—611no—
454C2×C42—1221no—
455C2×C42—1221no—
456C2×C42—1222no—
457C2×C42—1222no—
458C2×C42—1221no—
459C2×C42C22×D6111yescharacteristic
460#107—22no—
461#107—1222no—
462#106—22no—
463#106—1222no—
464C4⋊C8—22no—
465C4⋊C8—1222no—
466#103—22no—
467#103—22no—
468#103—1222no—
469#103—1222no—
470C22⋊C8—1222no—
471C22⋊C8—1222no—
472#95—1221no—
473#95—1221no—
474#95—1221no—
475#95—1221no—
476#95—1221no—
477C24—611no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—1224no—
484C2×Q8—1224no—
485C2×Q8—2442no—
486C2×Q8—2442no—
487C2×Q8—2442no—
488C2×Q8—2442no—
489C2×Q8Q8×D6112yes—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—612no—
498C22×C4—612no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—1221no—
502C22×C4—1221no—
503C22×C4—1221no—
504C22×C4—1221no—
505C22×C4—1221no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4—1222no—
509C22×C4—1222no—
510C22×C4—1221no—
511C22×C4—2441no—
512C22×C4—2441no—
513C22×C4D4×D6111yescharacteristic
514C22×C4D4×D6111yescharacteristic
515C22×C4C23×D6111yescharacteristic
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—1221no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—1221no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—612no—
536C4⋊C4—612no—
537C4⋊C4—612no—
538C4⋊C4—1224no—
539C4⋊C4—1224no—
540C4⋊C4—1224no—
541C4⋊C4—1221no—
542C4⋊C4—1221no—
543C4⋊C4—1221no—
544C4⋊C4—1224no—
545C4⋊C4—1224no—
546C4⋊C4—1221no—
547C4⋊C4—1221no—
548C4⋊C4—2442no—
549C4⋊C4C2×C22⋊D6112yes—
550C4⋊C4C2×C22⋊D6112yes—
551C22⋊C4—1224no—
552C22⋊C4—1224no—
553C22⋊C4—1224no—
554C22⋊C4—2442no—
555C42—42no—
556C42—1224no—
557C42—1224no—
558C42—1221no—
559C42—1221no—
560C42—1222no—
561C42—1222no—
562C42—2442no—
563C42D4×D6112yes—
564C42C2×C22⋊D6112yes—
565C23—612no—
566C23—1221no—
567C23—1221no—
568C23—1221no—
569C23—1221no—
570C23—1221no—
571C23—1221no—
572C23C2×D4×D6111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577Q8—2448no—
578Q8—2448no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—612no—
596C2×C4—612no—
597C2×C4—612no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1222no—
605C2×C4—1222no—
606C2×C4—1222no—
607C2×C4—1222no—
608C2×C4—1222no—
609C2×C4—1222no—
610C2×C4—1222no—
611C2×C4—2444no—
612C2×C4—2444no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4—2441no—
622C2×C4#1451974512yes—
623C2×C4#1451974512yes—
624C2×C4C2×D4×D6111yescharacteristic
625C2×C4C22×C22⋊D6111yescharacteristic
626C2×C4C2×Q8×D6111yescharacteristic
627C2×C4#41×D6111yescharacteristic
628C2×C4#1451982411yescharacteristic
629C2×C4#1451982511yescharacteristic
630C8—41no—
631C8—41no—
632C8—2441no—
633C8—2441no—
634C22—1222no—
635C22—1222no—
636C22—1222no—
637C22—2441no—
638C22—2441no—
639C22—2441no—
640C22—2441no—
641C22C2×#1451974511yescharacteristic
642C22C22⋊Q8×D6111yescharacteristic
643C22#1684033511yescharacteristic
644C22#135×D6111yescharacteristic
645C22#137×D6111yescharacteristic
646C22#1684055911yescharacteristic
647C22#1684056111yescharacteristic
648C4—22no—
649C4—22no—
650C4—42no—
651C4—42no—
652C4—42no—
653C4—81no—
654C4—1222no—
655C4—1222no—
656C4—1222no—
657C4—4881no—
658C4—2442no—
659C4—2442no—
660C4—2442no—
661C4#1684041911yescharacteristic
662C4#1684042211yescharacteristic
663C4#1684042511yescharacteristic
664C4Q8×C22⋊D6111yescharacteristic
665C2—2442no—
666C2#2144918011yescharacteristic
667C2#2145503311yescharacteristic
668C2#2145507511yescharacteristic
669C2#2145560611yescharacteristic
670C2#2145562211yescharacteristic
671C2#2145697711yescharacteristic
672C2#2145706411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#479C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenterC2×#479D61
hypocenterC61#24306
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
2. C2×#16840069C2semidirect
4. #21447150C2semidirect
5. #21447145C2semidirect
6. #21446958C2semidirect
7. #21446958C2semidirect
8. #21446777C2semidirect
9. #21446774C2semidirect
15. C2×C61×#479C2semidirect
79. #14519753Q8semidirect
331. C2×#479D61semidirect
399. C61#24306semidirect

Maximal subgroups

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

subgroupindex
C2×#168403182
C2×#168400692
C4×#145197532
#214471502
#214471452
#214469582
#214467772
#214467742
#214461282
#214460172
#214460152
#214457962
C2×C61×#4792
#2430661