Finite Group Databasebeta

← #29685398

Subgroups — #29685398

Order 15616.

1132 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840299C211yesmaximal, characteristic
2#21454450C211yesmaximal, characteristic, complemented
3C4×M16×D61C211yesmaximal, characteristic, complemented
4#21446810C212yesmaximal, complemented
5#21446667C212yesmaximal, complemented
6#21446284C212yesmaximal, complemented
7#21446281C212yesmaximal
8C4×#14519696C211yesmaximal, characteristic, complemented
9C4×#14519693C211yesmaximal, characteristic, complemented
10C4×#14519693C211yesmaximal, characteristic, complemented
11C4×#101×C61C211yesmaximal, characteristic, complemented
12C2×M16×D61C2212yes—
13#16840299—21no—
14#16840299—21no—
15#16840299—21no—
16#16840299—21no—
17#16840299—21no—
18#16840299—21no—
19#16840299—21no—
20#16840299—21no—
21C2×#14519772C412yes—
22C2×#14519768C2211yescharacteristic
23C2×#14519766C2211yescharacteristic
24C2×#14519762C412yes—
25C2×#14519753C2211yescharacteristic
26C2×#14519752C2211yescharacteristic
27C2×C4×D244C412yes—
28C2×C4×D244C2211yescharacteristic
29C2×#14519734C412yes—
30C2×C42×D61C2211yescharacteristic
31#16839817—21no—
32#16839817—21no—
33#16839813—21no—
34#16839813—21no—
35#16839785C2212yes—
36C2×#14519696C2212yes—
37C2×#14519693C2212yes—
38C2×#14519693C2212yes—
39#16839725C2212yes—
40C4×#11758194C2211yescharacteristic
41C4×#11758194C2211yescharacteristic
42#16839714—21no—
43M16×Dic61C2212yes—
44C4×#11758189—21no—
45#97×D61—21no—
46C4×C8×D61—21no—
47#16839531C2212yes—
48#16839530C2212yes—
49#16839530C2212yes—
50C2×C4×Q8×C61C2211yescharacteristic
51C2×#101×C61C2212yes—
52C4×M16×C61C2211yescharacteristic
53C4×M16×C61C2211yescharacteristic
54C61×#343C2212yes—
55C22×D244C2×C412yes—
56C22×D244C2311yescharacteristic
57C22×C4×D61C2×C412yes—
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2311yescharacteristic
61C2×#11758194C2312yes—
62C2×#11758194C2312yes—
63C2×#11758189—22no—
64M16×D61—24no—
65M16×D61—24no—
66C2×C8×D61—22no—
67#14519772—22no—
68#14519772—22no—
69#14519772—22no—
70#14519772—22no—
71#14519768—21no—
72#14519768—21no—
73#14519768—21no—
74#14519768—21no—
75#14519766—21no—
76#14519766—21no—
77#14519766—21no—
78#14519766—21no—
79#14519762—22no—
80#14519762—22no—
81#14519762—22no—
82#14519762—22no—
83#14519753—21no—
84#14519753—21no—
85#14519753—21no—
86#14519753—21no—
87#14519752—21no—
88#14519752—21no—
89#14519752—21no—
90#14519752—21no—
91C4×D244—22no—
92C4×D244—22no—
93C4×D244—22no—
94C4×D244—22no—
95C4×D244—21no—
96C4×D244—21no—
97C4×D244—21no—
98C4×D244—21no—
99#14519734—22no—
100#14519734—22no—
101#14519734—22no—
102#14519734—22no—
103C2×C4⋊Dic61C2×C412yes—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196C2×C412yes—
106C2×#11758196C2×C412yes—
107C2×#11758198C2×C412yes—
108C2×#11758198C2×C412yes—
109C2×#11758198C2×C412yes—
110C2×#11758198C2×C412yes—
111C2×#11758198C2×C412yes—
112C2×C4×Dic61C2×C411yescharacteristic
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61D411yescharacteristic
120C42×D61D411yescharacteristic
121C42×D61D411yescharacteristic
122C42×D61D411yescharacteristic
123#14519706—22no—
124#14519706—22no—
125#14519696—24no—
126#14519693—24no—
127#14519693—24no—
128#14519689—22no—
129#14519689—22no—
130#14519688—21no—
131#14519688—21no—
132#14519687—22no—
133C4×#92418—21no—
134C4×#92418—21no—
135C8×Dic61—22no—
136C22×Q8×C61C2311yescharacteristic
137C2×M16×C61C2312yes—
138C2×M16×C61C2312yes—
139C4×Q8×C61—21no—
140C4×Q8×C61—21no—
141C4×Q8×C61—21no—
142C4×Q8×C61—21no—
143C2×C4⋊C4×C61C2×C412yes—
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C42×C61C2×C412yes—
146C2×C42×C61C2311yescharacteristic
147#101×C61—24no—
148#97×C61—21no—
149#97×C61—21no—
150C4×C8×C61—21no—
151C4×C8×C61—21no—
152C23×D61C22×C411yescharacteristic
153C23×D61C22×C412yes—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—22no—
157C2×Q8×C61—22no—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C412yes—
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C2411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C412yes—
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C2×D244—22no—
168C2×D244—22no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—22no—
172C2×D244—22no—
173C2×D244—44no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—42no—
179C2×C4×D61—42no—
180C2×C4×D61—44no—
181C2×C4×D61C22⋊C411yescharacteristic
182C2×C4×D61C22⋊C411yescharacteristic
183C2×C4×D61C22⋊C411yescharacteristic
184C2×C4×D61C22⋊C411yescharacteristic
185C2×C4×D61C22⋊C411yescharacteristic
186C2×C4×D61C22⋊C411yescharacteristic
187C2×C4×D61C22⋊C411yescharacteristic
188C2×C4×D61C22⋊C411yescharacteristic
189C2×C4×D61C2×D411yescharacteristic
190C2×C4×D61C2×D411yescharacteristic
191C2×C4×D61C2×D411yescharacteristic
192C2×C4×D61C2×D411yescharacteristic
193M16×C61—22no—
194M16×C61—22no—
195M16×C61—22no—
196M16×C61#4114yes—
197C2×C8×C61—22no—
198C2×C8×C61—22no—
199C4⋊C4×C61—22no—
200C4⋊C4×C61—22no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C42×C61—22no—
204C42×C61—22no—
205C42×C61C2×D411yescharacteristic
206C42×C61C2×D411yescharacteristic
207C42×C61C2×D411yescharacteristic
208C42×C61C2×D411yescharacteristic
209#11758198—22no—
210#11758198—22no—
211#11758198—22no—
212#11758198—22no—
213#11758198—22no—
214#11758198—22no—
215#11758198—22no—
216#11758198—22no—
217#11758198—22no—
218#11758198—22no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—22no—
222C4⋊Dic61—22no—
223#11758196—22no—
224#11758196—22no—
225#11758196—22no—
226#11758196—22no—
227C4×Dic61C22⋊C411yescharacteristic
228C4×Dic61C22⋊C411yescharacteristic
229C4×Dic61C22⋊C411yescharacteristic
230C4×Dic61C22⋊C411yescharacteristic
231C4×Dic61C22⋊C411yescharacteristic
232C4×Dic61C22⋊C411yescharacteristic
233C4×Dic61C22⋊C411yescharacteristic
234C4×Dic61C22⋊C411yescharacteristic
235C4×Dic61C2×D411yescharacteristic
236C4×Dic61C2×D411yescharacteristic
237C4×Dic61C2×D411yescharacteristic
238C4×Dic61C2×D411yescharacteristic
239#11758194—22no—
240#11758194—22no—
241#11758194—22no—
242#11758194#4114yes—
243C2×#92418—22no—
244C2×#92418—22no—
245#11758189—28no—
246C8×D61—28no—
247C23×C61C23×C411yescharacteristic
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—41no—
255C22×D61—42no—
256C22×D61—42no—
257C22×D61C2×C22⋊C411yescharacteristic
258C22×D61C2×C22⋊C411yescharacteristic
259Q8×C61—42no—
260Q8×C61—42no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—41no—
267C2×C4×C61—42no—
268C2×C4×C61C2×C22⋊C411yescharacteristic
269C2×C4×C61C2×C22⋊C411yescharacteristic
270C2×C4×C61C2×C22⋊C411yescharacteristic
271C2×C4×C61C2×C22⋊C411yescharacteristic
272C2×C4×C61C22×D411yescharacteristic
273C2×C4×C61C22×D411yescharacteristic
274C2×C4×C61C2×#4112yes—
275C2×C4×C61C2×#4112yes—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—22no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—42no—
282C2×Dic61C2×C22⋊C411yescharacteristic
283C2×Dic61C2×C22⋊C411yescharacteristic
284C2×Dic61C2×C22⋊C411yescharacteristic
285C2×Dic61C2×C22⋊C411yescharacteristic
286C2×Dic61C2×C22⋊C411yescharacteristic
287C2×Dic61C2×C22⋊C411yescharacteristic
288D244—44no—
289D244—44no—
290D244—42no—
291D244—42no—
292C4×D61—22no—
293C4×D61—22no—
294C4×D61—22no—
295C4×D61—22no—
296C4×D61—22no—
297C4×D61—22no—
298C4×D61—22no—
299C4×D61—22no—
300C4×D61—41no—
301C4×D61—41no—
302C4×D61—41no—
303C4×D61—41no—
304C4×D61—44no—
305C4×D61—44no—
306C8×C61—24no—
307C8×C61—42no—
308#92418—24no—
309#92418—42no—
310#21426—611nomaximal, Sylow
311C22×C61—21no—
312C22×C61—21no—
313C22×C61C22×C22⋊C411yescharacteristic
314C22×C61C4×#4111yescharacteristic
315C22×C61C4×#4111yescharacteristic
316C2×D61—21no—
317C2×D61—21no—
318C2×D61—21no—
319C2×D61—21no—
320C2×D61—21no—
321C2×D61—42no—
322C2×D61—42no—
323C2×D61—42no—
324C2×D61—42no—
325C2×D61—42no—
326C2×D61—82no—
327C2×D61—82no—
328C2×D61#41312yes—
329C4×C61—21no—
330C4×C61—21no—
331C4×C61—21no—
332C4×C61—42no—
333C4×C61—42no—
334C4×C61#41312yes—
335C4×C61#52512yes—
336C4×C61#53212yes—
337Dic61—21no—
338Dic61—21no—
339Dic61—21no—
340Dic61—21no—
341Dic61—21no—
342Dic61—21no—
343Dic61—42no—
344C2×#529—611no—
345#2920—611no—
346C2×C4×M16—611no—
347#1998—612no—
348#1967—612no—
349#1901—612no—
350#1900—612no—
351C4×#101—611no—
352C4×#101D6111yescharacteristic, complemented
353C4×#100—611no—
354C4×#100—611no—
355C2×C61—21no—
356C2×C61—21no—
357C2×C61#229711yescharacteristic
358C2×C61C2×#41311yescharacteristic
359C2×C61C2×#41311yescharacteristic
360D61—22no—
361D61—41no—
362D61—82no—
363C22×M16—612no—
364#529—1221no—
365#529—1221no—
366#529—1221no—
367#529—1221no—
368#529—1221no—
369#529—1221no—
370#529—1221no—
371#529—1221no—
372C2×#126—612no—
373C2×#125—611no—
374C2×#124—611no—
375C2×#123—612no—
376C2×C22⋊Q8—611no—
377C2×#121—611no—
378C2×C4×Q8C2×D6111yescharacteristic
379C2×C4×D4—612no—
380C2×C4×D4—611no—
381C2×#117—612no—
382C22×C42—611no—
383#432—1221no—
384#432—1221no—
385#431—1221no—
386#431—1221no—
387#423—612no—
388C2×#101—612no—
389C2×#101C2×D6112yes—
390C2×#100—612no—
391C2×#100—612no—
392#407—612no—
393C4×M16—612no—
394C4×M16—611no—
395C4×M16—611no—
396C4×M16—1221no—
397C4×M16—1221no—
398C4×M16C2×D6111yescharacteristic
399C4×M16C2×D6111yescharacteristic
400C2×#97—1221no—
401C2×C4×C8—1221no—
402#343—612no—
403#343—612no—
404#343—612no—
405#343C2×D6112yes—
406C61#2142611yescharacteristic, complemented, Sylow
407C22×Q8C22×D6111yescharacteristic
408C22×D4—612no—
409C22×D4—611no—
410C23×C4—611no—
411C23×C4—611no—
412C23×C4—611no—
413C23×C4—612no—
414C2×M16—612no—
415C2×M16—612no—
416C2×M16—1222no—
417C2×M16—1224no—
418C2×M16—1224no—
419C2×M16C22×D6112yes—
420C2×M16C22×D6112yes—
421C22×C8—1222no—
422#126—1222no—
423#126—1222no—
424#126—1222no—
425#126—1222no—
426#125—1221no—
427#125—1221no—
428#125—1221no—
429#125—1221no—
430#124—1221no—
431#124—1221no—
432#124—1221no—
433#124—1221no—
434#123—1222no—
435#123—1222no—
436#123—1222no—
437#123—1222no—
438C22⋊Q8—1221no—
439C22⋊Q8—1221no—
440C22⋊Q8—1221no—
441C22⋊Q8—1221no—
442#121—1221no—
443#121—1221no—
444#121—1221no—
445#121—1221no—
446C4×Q8—21no—
447C4×Q8—21no—
448C4×Q8—21no—
449C4×Q8—21no—
450C4×D4—1222no—
451C4×D4—1222no—
452C4×D4—1222no—
453C4×D4—1222no—
454C4×D4—1221no—
455C4×D4—1221no—
456C4×D4—1221no—
457C4×D4—1221no—
458#117—1222no—
459#117—1222no—
460#117—1222no—
461#117—1222no—
462C2×C4⋊C4—612no—
463C2×C4⋊C4—612no—
464C2×C4⋊C4—612no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4C4×D6112yes—
467C2×C4⋊C4C22×D6111yescharacteristic
468C2×C22⋊C4—612no—
469C2×C22⋊C4—612no—
470C2×C22⋊C4—612no—
471C2×C22⋊C4—612no—
472C2×C22⋊C4—612no—
473C2×C42—611no—
474C2×C42—611no—
475C2×C42—611no—
476C2×C42—611no—
477C2×C42—611no—
478C2×C42—611no—
479C2×C42—611no—
480C2×C42—611no—
481C2×C42—611no—
482C2×C42—611no—
483C2×C42—611no—
484C2×C42C4×D6112yes—
485C2×C42C22×D6111yescharacteristic
486C4⋊C8—1222no—
487C4⋊C8—1222no—
488#101—24no—
489#101—1224no—
490#100—1224no—
491#100—1224no—
492C22⋊C8—1222no—
493C22⋊C8—1222no—
494#97—21no—
495#97—21no—
496#97—1222no—
497#97—1221no—
498#97—1221no—
499C4×C8—21no—
500C4×C8—21no—
501C4×C8—1222no—
502C4×C8—1221no—
503C4×C8—1221no—
504C24—611no—
505C24—612no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×D4—1222no—
511C2×D4—1222no—
512C2×D4—1221no—
513C2×D4—1221no—
514C2×D4—1222no—
515C2×D4—1222no—
516C2×D4—2444no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—612no—
533C22×C4—1222no—
534C22×C4—1222no—
535C22×C4—1222no—
536C22×C4—1222no—
537C22×C4—2442no—
538C22×C4—2444no—
539C22×C4—2442no—
540C22×C4C2×C4×D6112yes—
541C22×C4C2×C4×D6111yescharacteristic
542C22×C4C2×C4×D6112yes—
543C22×C4C2×C4×D6111yescharacteristic
544C22×C4C23×D6111yescharacteristic
545M16—22no—
546M16—22no—
547M16—22no—
548M16—614no—
549M16—1228no—
550M16—1222no—
551M16—1222no—
552M16—1222no—
553M16#1175822214yes—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—1228no—
557C2×C8—1222no—
558C2×C8—1222no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—1222no—
564C4⋊C4—1222no—
565C4⋊C4—1222no—
566C4⋊C4—1222no—
567C4⋊C4—1222no—
568C4⋊C4—1222no—
569C4⋊C4—1221no—
570C4⋊C4—1221no—
571C22⋊C4—1222no—
572C22⋊C4—1222no—
573C22⋊C4—1222no—
574C22⋊C4—1222no—
575C22⋊C4—1222no—
576C22⋊C4—1222no—
577C22⋊C4—1222no—
578C22⋊C4—1222no—
579C22⋊C4—1222no—
580C22⋊C4—1222no—
581C42—22no—
582C42—22no—
583C42—611no—
584C42—611no—
585C42—611no—
586C42—611no—
587C42—611no—
588C42—611no—
589C42—611no—
590C42—611no—
591C42—611no—
592C42—611no—
593C42—611no—
594C42—611no—
595C42D4×D6111yescharacteristic
596C42D4×D6111yescharacteristic
597C42D4×D6111yescharacteristic
598C42D4×D6111yescharacteristic
599C23—611no—
600C23—611no—
601C23—1222no—
602C23—1221no—
603C23—1221no—
604C23—1222no—
605C23—1222no—
606C23—1222no—
607C23—2441no—
608C23—2442no—
609C23—2442no—
610C23C22×C4×D6111yescharacteristic
611Q8—42no—
612Q8—42no—
613D4—2444no—
614D4—2444no—
615D4—2442no—
616D4—2442no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—611no—
625C2×C4—611no—
626C2×C4—611no—
627C2×C4—611no—
628C2×C4—611no—
629C2×C4—611no—
630C2×C4—1222no—
631C2×C4—1222no—
632C2×C4—1221no—
633C2×C4—1221no—
634C2×C4—1222no—
635C2×C4—1222no—
636C2×C4—1222no—
637C2×C4—1222no—
638C2×C4—1222no—
639C2×C4—1222no—
640C2×C4—1222no—
641C2×C4—2441no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4—2444no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4—2444no—
649C2×C4—2442no—
650C2×C4C22⋊C4×D6111yescharacteristic
651C2×C4C22⋊C4×D6111yescharacteristic
652C2×C4C22⋊C4×D6111yescharacteristic
653C2×C4C22⋊C4×D6111yescharacteristic
654C2×C4C2×D4×D6111yescharacteristic
655C2×C4C2×D4×D6111yescharacteristic
656C2×C4#41×D6112yes—
657C2×C4C2×#1175822212yes—
658C8—24no—
659C8—42no—
660C8—1224no—
661C8—2442no—
662C22—21no—
663C22—21no—
664C22—612no—
665C22—1221no—
666C22—1221no—
667C22—1221no—
668C22—1221no—
669C22—1221no—
670C22—4882no—
671C22—4882no—
672C22—2442no—
673C22—2442no—
674C22—2442no—
675C22—2442no—
676C22—2442no—
677C22C2×C22⋊C4×D6111yescharacteristic
678C22#1684023011yescharacteristic
679C22C4×#1175822211yescharacteristic
680C4—21no—
681C4—21no—
682C4—21no—
683C4—42no—
684C4—42no—
685C4—1221no—
686C4—1221no—
687C4—1221no—
688C4—1221no—
689C4—1221no—
690C4—1221no—
691C4—2442no—
692C4#1683974512yes—
693C4#1684027112yes—
694C4#1684030912yes—
695C2—21no—
696C2—21no—
697C2—1222no—
698C2—4882no—
699C2—2441no—
700C2#2144830511yescharacteristic
701C2#413×D6111yescharacteristic
702C2C2×#1683974511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#101×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519752C22
cosocleC22×C4×C61C24
hypercenterC4×#101D61
hypocenterC61#21426
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
2. #21454450C2semidirect
3. C4×M16×D61C2semidirect
4. #21446810C2semidirect
5. #21446667C2semidirect
6. #21446284C2semidirect
8. C4×#14519696C2semidirect
9. C4×#14519693C2semidirect
10. C4×#14519693C2semidirect
11. C4×#101×C61C2semidirect
352. C4×#101D61semidirect
406. C61#21426semidirect

Maximal subgroups

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

subgroupindex
C2×#168402992
#214544502
C4×M16×D612
#214468102
#214466672
#214462842
#214462812
C4×#145196962
C4×#145196932
C4×#101×C612
#2142661