Finite Group Databasebeta

← #29685387

Subgroups — #29685387

Order 15616.

1100 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840316C211yesmaximal, characteristic
2#21454450C211yesmaximal, characteristic
3C4×M16×D61C211yesmaximal, characteristic
4#21446806C212yesmaximal, complemented
5#21446661C212yesmaximal, complemented
6#21446286C212yesmaximal
7#21446284C212yesmaximal
8C4×#14519695C211yesmaximal, characteristic, complemented
9C4×#14519695C211yesmaximal, characteristic, complemented
10C4×#14519696C211yesmaximal, characteristic, complemented
11C4×#101×C61C211yesmaximal, characteristic, complemented
12C2×M16×D61C2212yes—
13#16840316—21no—
14#16840316—21no—
15#16840316—21no—
16#16840316—21no—
17#16840316—21no—
18#16840316—21no—
19#16840316—21no—
20#16840316—21no—
21C2×#14519776C2211yescharacteristic
22C2×#14519775C2211yescharacteristic
23C2×#14519767C412yes—
24C2×#14519757C2211yescharacteristic
25C2×#14519755C412yes—
26C2×#14519753C2211yescharacteristic
27C2×C4×Dic122C412yes—
28C2×C4×Dic122C2211yescharacteristic
29C2×#14519734C412yes—
30C2×C42×D61C2211yescharacteristic
31#16839817—21no—
32#16839817—21no—
33#16839813—21no—
34#16839813—21no—
35#16839785C2212yes—
36C2×#14519696C2212yes—
37C2×#14519695C2212yes—
38C2×#14519695C2212yes—
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×Dic122C2×C412yes—
56C22×Dic122C2311yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C2×#11758194C2312yes—
61C2×#11758194C2312yes—
62C2×#11758189—22no—
63M16×D61—24no—
64M16×D61—24no—
65C2×C8×D61—22no—
66#14519776—21no—
67#14519776—21no—
68#14519776—21no—
69#14519776—21no—
70#14519775—21no—
71#14519775—21no—
72#14519775—21no—
73#14519775—21no—
74#14519767—22no—
75#14519767—22no—
76#14519767—22no—
77#14519767—22no—
78#14519757—21no—
79#14519757—21no—
80#14519757—21no—
81#14519757—21no—
82#14519755—22no—
83#14519755—22no—
84#14519755—22no—
85#14519755—22no—
86#14519753—21no—
87#14519753—21no—
88#14519753—21no—
89#14519753—21no—
90C4×Dic122—21no—
91C4×Dic122—21no—
92C4×Dic122—21no—
93C4×Dic122—21no—
94C4×Dic122—22no—
95C4×Dic122—22no—
96C4×Dic122—22no—
97C4×Dic122—22no—
98#14519734—22no—
99#14519734—22no—
100#14519734—22no—
101#14519734—22no—
102C2×C4⋊Dic61C2×C412yes—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×#11758196C2×C412yes—
105C2×#11758196C2×C412yes—
106C2×#11758196C2×C412yes—
107C2×#11758196C2×C412yes—
108C2×#11758196C2×C412yes—
109C2×#11758198C2×C412yes—
110C2×#11758198C2×C412yes—
111C2×C4×Dic61C2×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#14519695—24no—
127#14519695—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
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—22no—
156C2×Q8×C61—22no—
157C22×C4×C61C22×C412yes—
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C412yes—
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C2411yescharacteristic
162C22×Dic61C22×C412yes—
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C412yes—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—24no—
170C2×C4×D61—42no—
171C2×C4×D61C22⋊C411yescharacteristic
172C2×C4×D61C22⋊C411yescharacteristic
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×D61C2×D411yescharacteristic
180C2×C4×D61C2×D411yescharacteristic
181C2×C4×D61C2×D411yescharacteristic
182C2×C4×D61C2×D411yescharacteristic
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—22no—
186C2×Dic122—22no—
187C2×Dic122—22no—
188C2×Dic122—22no—
189C2×Dic122—44no—
190M16×C61—22no—
191M16×C61—22no—
192M16×C61—22no—
193M16×C61#4114yes—
194C2×C8×C61—22no—
195C2×C8×C61—22no—
196C4⋊C4×C61—22no—
197C4⋊C4×C61—22no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C42×C61—22no—
201C42×C61—22no—
202C42×C61C2×D411yescharacteristic
203C42×C61C2×D411yescharacteristic
204C42×C61C2×D411yescharacteristic
205C42×C61C2×D411yescharacteristic
206#11758198—22no—
207#11758198—22no—
208#11758198—22no—
209#11758198—22no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—22no—
213C4⋊Dic61—22no—
214#11758196—22no—
215#11758196—22no—
216#11758196—22no—
217#11758196—22no—
218#11758196—22no—
219#11758196—22no—
220#11758196—22no—
221#11758196—22no—
222#11758196—22no—
223#11758196—22no—
224C4×Dic61—22no—
225C4×Dic61—22no—
226C4×Dic61C22⋊C411yescharacteristic
227C4×Dic61C22⋊C411yescharacteristic
228C4×Dic61C22⋊C411yescharacteristic
229C4×Dic61C22⋊C411yescharacteristic
230C4×Dic61C22⋊C411yescharacteristic
231C4×Dic61C22⋊C411yescharacteristic
232C4×Dic61C22⋊C411yescharacteristic
233C4×Dic61C22⋊C411yescharacteristic
234C4×Dic61C2×D411yescharacteristic
235C4×Dic61C2×D411yescharacteristic
236C4×Dic61C2×D411yescharacteristic
237C4×Dic61C2×D411yescharacteristic
238#11758194—22no—
239#11758194—22no—
240#11758194—22no—
241#11758194#4114yes—
242C2×#92418—22no—
243C2×#92418—22no—
244#11758189—28no—
245C8×D61—28no—
246C23×C61C23×C411yescharacteristic
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—22no—
250C22×D61—41no—
251C22×D61C2×C22⋊C411yescharacteristic
252C22×D61C2×C22⋊C411yescharacteristic
253Q8×C61—42no—
254Q8×C61—42no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—41no—
261C2×C4×C61—42no—
262C2×C4×C61C2×C22⋊C411yescharacteristic
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61C2×C22⋊C411yescharacteristic
265C2×C4×C61C2×C22⋊C411yescharacteristic
266C2×C4×C61C22×D411yescharacteristic
267C2×C4×C61C22×D411yescharacteristic
268C2×C4×C61C2×#4112yes—
269C2×C4×C61C2×#4112yes—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—22no—
278C2×Dic61—42no—
279C2×Dic61C2×C22⋊C411yescharacteristic
280C2×Dic61C2×C22⋊C411yescharacteristic
281C2×Dic61C2×C22⋊C411yescharacteristic
282C2×Dic61C2×C22⋊C411yescharacteristic
283C2×Dic61C2×C22⋊C411yescharacteristic
284C2×Dic61C2×C22⋊C411yescharacteristic
285C4×D61—22no—
286C4×D61—22no—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—22no—
290C4×D61—22no—
291C4×D61—22no—
292C4×D61—22no—
293C4×D61—22no—
294C4×D61—41no—
295C4×D61—41no—
296C4×D61#10114yescomplemented
297Dic122—44no—
298Dic122—42no—
299Dic122—42no—
300Dic122—44no—
301C8×C61—24no—
302C8×C61—42no—
303#92418—24no—
304#92418—42no—
305#21425—611nomaximal, Sylow
306C22×C61—21no—
307C22×C61—21no—
308C22×C61C22×C22⋊C411yescharacteristic
309C22×C61C4×#4111yescharacteristic
310C22×C61C4×#4111yescharacteristic
311C2×D61—21no—
312C2×D61—21no—
313C2×D61—21no—
314C2×D61—21no—
315C2×D61—21no—
316C2×D61—42no—
317C2×D61—42no—
318C2×D61C2×#10112yes—
319C4×C61—21no—
320C4×C61—21no—
321C4×C61—21no—
322C4×C61—42no—
323C4×C61—42no—
324C4×C61C2×#10112yes—
325C4×C61#52512yes—
326C4×C61#53212yes—
327Dic61—21no—
328Dic61—21no—
329Dic61—21no—
330Dic61—21no—
331Dic61—42no—
332Dic61—42no—
333Dic61C2×#10112yes—
334Dic61#41312yes—
335C2×#533—611no—
336#2920—611no—
337C2×C4×M16—611no—
338#1997—612no—
339#1966—612no—
340#1901—612no—
341#1901—612no—
342C4×#101—611no—
343C4×#101—611no—
344C4×#101—611no—
345C4×#101D6111yescharacteristic, complemented
346C2×C61—21no—
347C2×C61—21no—
348C2×C61#229711yescharacteristic
349C2×C61C22×#10111yescharacteristic
350C2×C61C2×#41311yescharacteristic
351D61—22no—
352D61—41no—
353C22×M16—612no—
354#533—1221no—
355#533—1221no—
356#533—1221no—
357#533—1221no—
358#533—1221no—
359#533—1221no—
360#533—1221no—
361#533—1221no—
362C2×C4⋊Q8—611no—
363C2×C4⋊Q8—611no—
364C2×#125—612no—
365C2×C22⋊Q8—611no—
366C2×C22⋊Q8—612no—
367C2×C22⋊Q8—611no—
368C2×C4×Q8—612no—
369C2×C4×Q8—611no—
370C2×C4×Q8C2×D6111yescharacteristic
371C2×#117—612no—
372C22×C42—611no—
373#432—1221no—
374#432—1221no—
375#431—1221no—
376#431—1221no—
377#423—612no—
378C2×#101—612no—
379C2×#101—612no—
380C2×#101—612no—
381C2×#101C2×D6112yes—
382#407—612no—
383C4×M16—612no—
384C4×M16—611no—
385C4×M16—611no—
386C4×M16—1221no—
387C4×M16—1221no—
388C4×M16C2×D6111yescharacteristic
389C4×M16C2×D6111yescharacteristic
390C2×#97—1221no—
391C2×C4×C8—1221no—
392#343—612no—
393#343—612no—
394#343—612no—
395#343C2×D6112yes—
396C61#2142511yescharacteristic, complemented, Sylow
397C22×Q8—612no—
398C22×Q8—611no—
399C22×Q8C22×D6111yescharacteristic
400C23×C4—611no—
401C23×C4—611no—
402C23×C4—611no—
403C2×M16—612no—
404C2×M16—612no—
405C2×M16—1222no—
406C2×M16—1224no—
407C2×M16—1224no—
408C2×M16C22×D6112yes—
409C2×M16C22×D6112yes—
410C22×C8—1222no—
411C4⋊Q8—1221no—
412C4⋊Q8—1221no—
413C4⋊Q8—1221no—
414C4⋊Q8—1221no—
415C4⋊Q8—1221no—
416C4⋊Q8—1221no—
417C4⋊Q8—1221no—
418C4⋊Q8—1221no—
419#125—1222no—
420#125—1222no—
421#125—1222no—
422#125—1222no—
423C22⋊Q8—1222no—
424C22⋊Q8—1222no—
425C22⋊Q8—1222no—
426C22⋊Q8—1222no—
427C22⋊Q8—1221no—
428C22⋊Q8—1221no—
429C22⋊Q8—1221no—
430C22⋊Q8—1221no—
431C22⋊Q8—1221no—
432C22⋊Q8—1221no—
433C22⋊Q8—1221no—
434C22⋊Q8—1221no—
435C4×Q8—21no—
436C4×Q8—21no—
437C4×Q8—21no—
438C4×Q8—21no—
439C4×Q8—1222no—
440C4×Q8—1222no—
441C4×Q8—1222no—
442C4×Q8—1222no—
443C4×Q8—1221no—
444C4×Q8—1221no—
445C4×Q8—1221no—
446C4×Q8—1221no—
447#117—1222no—
448#117—1222no—
449#117—1222no—
450#117—1222no—
451C2×C4⋊C4—612no—
452C2×C4⋊C4—612no—
453C2×C4⋊C4—612no—
454C2×C4⋊C4—612no—
455C2×C4⋊C4—612no—
456C2×C4⋊C4—612no—
457C2×C4⋊C4—611no—
458C2×C4⋊C4C4×D6112yes—
459C2×C4⋊C4C22×D6111yescharacteristic
460C2×C22⋊C4—612no—
461C2×C22⋊C4—612no—
462C2×C42—611no—
463C2×C42—611no—
464C2×C42—611no—
465C2×C42—611no—
466C2×C42—611no—
467C2×C42—611no—
468C2×C42—611no—
469C2×C42—611no—
470C2×C42—611no—
471C2×C42—611no—
472C2×C42—611no—
473C2×C42—612no—
474C2×C42C4×D6112yes—
475C2×C42C22×D6111yescharacteristic
476C4⋊C8—1222no—
477C4⋊C8—1222no—
478#101—24no—
479#101—1224no—
480#101—1224no—
481#101—1224no—
482C22⋊C8—1222no—
483C22⋊C8—1222no—
484#97—21no—
485#97—21no—
486#97—1222no—
487#97—1221no—
488#97—1221no—
489C4×C8—21no—
490C4×C8—21no—
491C4×C8—1222no—
492C4×C8—1221no—
493C4×C8—1221no—
494C24—611no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—1222no—
500C2×Q8—1222no—
501C2×Q8—1221no—
502C2×Q8—1221no—
503C2×Q8—1222no—
504C2×Q8—1222no—
505C2×Q8—2444no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—611no—
513C22×C4—611no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—612no—
522C22×C4—612no—
523C22×C4—1224no—
524C22×C4—1222no—
525C22×C4—1222no—
526C22×C4—2442no—
527C22×C4C2×C4×D6112yes—
528C22×C4C2×C4×D6111yescharacteristic
529C22×C4C2×C4×D6112yes—
530C22×C4C2×C4×D6111yescharacteristic
531C22×C4C23×D6111yescharacteristic
532M16—22no—
533M16—22no—
534M16—22no—
535M16—614no—
536M16—1228no—
537M16—1222no—
538M16—1222no—
539M16—1222no—
540M16#1175822214yes—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—1228no—
544C2×C8—1222no—
545C2×C8—1222no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—1222no—
551C4⋊C4—1222no—
552C4⋊C4—1222no—
553C4⋊C4—1222no—
554C4⋊C4—1222no—
555C4⋊C4—1222no—
556C4⋊C4—1222no—
557C4⋊C4—1222no—
558C4⋊C4—1222no—
559C4⋊C4—1222no—
560C4⋊C4—1221no—
561C4⋊C4—1221no—
562C4⋊C4—1222no—
563C4⋊C4—1222no—
564C22⋊C4—1222no—
565C22⋊C4—1222no—
566C22⋊C4—1222no—
567C22⋊C4—1222no—
568C42—22no—
569C42—22no—
570C42—611no—
571C42—611no—
572C42—611no—
573C42—611no—
574C42—611no—
575C42—611no—
576C42—611no—
577C42—611no—
578C42—611no—
579C42—611no—
580C42—611no—
581C42—611no—
582C42—1222no—
583C42—1222no—
584C42D4×D6111yescharacteristic
585C42D4×D6111yescharacteristic
586C42D4×D6111yescharacteristic
587C42D4×D6111yescharacteristic
588C23—611no—
589C23—611no—
590C23—1222no—
591C23—1221no—
592C23—1221no—
593C23—2441no—
594C23C22×C4×D6111yescharacteristic
595Q8—42no—
596Q8—42no—
597Q8—2444no—
598Q8—2444no—
599Q8—2442no—
600Q8—2442no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—611no—
609C2×C4—611no—
610C2×C4—614no—
611C2×C4—611no—
612C2×C4—611no—
613C2×C4—611no—
614C2×C4—611no—
615C2×C4—1222no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—1221no—
622C2×C4—1221no—
623C2×C4—1222no—
624C2×C4—1222no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—1222no—
628C2×C4—1222no—
629C2×C4—1222no—
630C2×C4—1222no—
631C2×C4—1222no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2442no—
635C2×C4C22⋊C4×D6111yescharacteristic
636C2×C4C22⋊C4×D6111yescharacteristic
637C2×C4C22⋊C4×D6111yescharacteristic
638C2×C4C22⋊C4×D6111yescharacteristic
639C2×C4C2×D4×D6111yescharacteristic
640C2×C4C2×D4×D6111yescharacteristic
641C2×C4#41×D6112yes—
642C2×C4C2×#1175822212yes—
643C8—24no—
644C8—42no—
645C8—1224no—
646C8—2442no—
647C22—21no—
648C22—21no—
649C22—612no—
650C22—1221no—
651C22—1221no—
652C22—1221no—
653C22—1221no—
654C22—1221no—
655C22—2442no—
656C22—2442no—
657C22C2×C22⋊C4×D6111yescharacteristic
658C22#1684023011yescharacteristic
659C22C4×#1175822211yescharacteristic
660C4—21no—
661C4—21no—
662C4—21no—
663C4—42no—
664C4—42no—
665C4—612no—
666C4—612no—
667C4—1221no—
668C4—1221no—
669C4—1221no—
670C4—1221no—
671C4—2442no—
672C4—2442no—
673C4#101×D6112yes—
674C4#1684027112yes—
675C4#1684030912yes—
676C2—21no—
677C2—21no—
678C2—1222no—
679C2—2441no—
680C2#2144830511yescharacteristic
681C2C2×#101×D6111yescharacteristic
682C2#413×D6111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#101×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenterC4×#101D61
hypocenterC61#21425
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
4. #21446806C2semidirect
5. #21446661C2semidirect
8. C4×#14519695C2semidirect
9. C4×#14519695C2semidirect
10. C4×#14519696C2semidirect
11. C4×#101×C61C2semidirect
296. C4×D61#101semidirect
345. C4×#101D61semidirect
396. C61#21425semidirect

Maximal subgroups

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

subgroupindex
C2×#168403162
#214544502
C4×M16×D612
#214468062
#214466612
#214462862
#214462842
C4×#145196952
C4×#145196962
C4×#101×C612
#2142561