Finite Group Databasebeta

← #29646147

Subgroups — #29646147

Order 15616.

960 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840314C211yesmaximal, characteristic
2#21454448C211yesmaximal, characteristic
3C2×#16839816C211yesmaximal, characteristic
4#21444184C211yesmaximal, characteristic
5#21444183C211yesmaximal, characteristic
6#21444182C211yesmaximal, characteristic
7#21444173C214yesmaximal, complemented
8#21444161C214yesmaximal, complemented
9C61×#1472C211yesmaximal, characteristic
10#16840314—21no—
11#16840314—21no—
12#16840314—21no—
13#16840314—21no—
14#16840314—21no—
15#16840314—21no—
16#16840314—21no—
17#16840314—21no—
18C2×#14519776C411yescharacteristic
19C2×#14519775C411yescharacteristic
20C2×#14519767C2212yes—
21C2×#14519756C2211yescharacteristic
22C2×#14519754C412yes—
23C2×Q8×Dic61C411yescharacteristic
24C2×#14519742C411yescharacteristic
25C2×#14519742C2212yes—
26C2×#14519733C412yes—
27C22×C4×Dic61C2211yescharacteristic
28#16839816—21no—
29#16839816—21no—
30#16839816—21no—
31#16839816C2212yes—
32#16839816C2212yes—
33#16839816C2212yes—
34#16839812—21no—
35#16839812C2212yes—
36#16839785—21no—
37C2×#14519706—21no—
38#16839726C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40M16×Dic61—21no—
41C2×#14519687—21no—
42#16839488C2214yes—
43#16839487C2214yes—
44#16839487C2214yes—
45C2×C22⋊Q8×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C61×#324C2214yes—
49C22×Dic122C2×C411yescharacteristic
50C22×Dic122C2×C412yes—
51C23×Dic61C2×C411yescharacteristic
52C23×Dic61C2×C411yescharacteristic
53C2×#11758194—21no—
54C22×#92418—21no—
55#14519776—21no—
56#14519776—21no—
57#14519776—21no—
58#14519776—21no—
59#14519775—21no—
60#14519775—21no—
61#14519775—21no—
62#14519775—21no—
63#14519767—22no—
64#14519767—22no—
65#14519767—22no—
66#14519767—22no—
67#14519756—21no—
68#14519756—21no—
69#14519756—21no—
70#14519756—21no—
71#14519754—22no—
72#14519754—22no—
73#14519754—22no—
74#14519754—22no—
75Q8×Dic61—21no—
76Q8×Dic61—21no—
77Q8×Dic61—21no—
78Q8×Dic61—21no—
79#14519742—21no—
80#14519742—21no—
81#14519742—21no—
82#14519742—21no—
83#14519742—22no—
84#14519742—22no—
85#14519742—22no—
86#14519742—22no—
87#14519733—22no—
88#14519733—22no—
89#14519733—22no—
90#14519733—22no—
91C2×C4⋊Dic61C2×C412yes—
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×#11758196C2×C412yes—
94C2×#11758196C2×C412yes—
95C2×#11758196C2×C412yes—
96C2×#11758196C2×C412yes—
97C2×#11758196C2312yes—
98C2×C22⋊Dic61C2×C412yes—
99C2×C4×Dic61C2×C412yes—
100C2×C4×Dic61C2×C412yes—
101C2×C4×Dic61C2×C411yescharacteristic
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61D411yescharacteristic
104C2×C4×Dic61D411yescharacteristic
105C2×C4×Dic61D411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113#14519706—22no—
114#14519706—22no—
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418—21no—
118C22⋊#92418—21no—
119C22⋊#92418C2312yes—
120C22⋊#92418C2312yes—
121#14519687—22no—
122#14519687—22no—
123#14519687—22no—
124C8×Dic61—22no—
125C22×Q8×C61C2×C411yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C2×M16×C61—21no—
128C22×C8×C61—21no—
129C22⋊Q8×C61—21no—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C4⋊C4×C61C2312yes—
135C2×C22⋊C4×C61C2×C412yes—
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61C2312yes—
139C22⋊C8×C61C2312yes—
140C24×C61C22×C411yescharacteristic
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—42no—
144C22×C4×C61—42no—
145C22×C4×C61C22×C412yes—
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C412yes—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2411yescharacteristic
153C22×Dic61—24no—
154C22×Dic61—42no—
155C22×Dic61C22⋊C411yescharacteristic
156C22×Dic61C22⋊C411yescharacteristic
157C22×Dic61C22⋊C411yescharacteristic
158C22×Dic61C22⋊C411yescharacteristic
159C22×Dic61C22⋊C411yescharacteristic
160C22×Dic61C22⋊C411yescharacteristic
161C22×Dic61C22⋊C411yescharacteristic
162C22×Dic61C22⋊C411yescharacteristic
163C22×Dic61C22×C412yes—
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C412yes—
169C2×Dic122—21no—
170C2×Dic122—21no—
171C2×Dic122—22no—
172C2×Dic122—22no—
173C2×Dic122—44no—
174C2×Dic122—42no—
175M16×C61—42no—
176C2×C8×C61—22no—
177C2×C8×C61—22no—
178C2×C8×C61—42no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—22no—
183C22⋊C4×C61—22no—
184C22⋊C4×C61—22no—
185C22⋊Dic61—22no—
186C22⋊Dic61—22no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—22no—
190C4⋊Dic61—22no—
191#11758196—22no—
192#11758196—22no—
193#11758196—22no—
194#11758196—22no—
195#11758196—22no—
196#11758196—22no—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201C4×Dic61—22no—
202C4×Dic61—22no—
203C4×Dic61—22no—
204C4×Dic61—22no—
205C4×Dic61C22⋊C411yescharacteristic
206C4×Dic61C22⋊C411yescharacteristic
207C4×Dic61C22⋊C411yescharacteristic
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C2×D411yescharacteristic
214C4×Dic61C2×D411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221#11758194—42no—
222C2×#92418—22no—
223C2×#92418—22no—
224C2×#92418—42no—
225C23×C61—22no—
226C23×C61—22no—
227C23×C61—41no—
228C23×C61C2×C22⋊C411yescharacteristic
229C23×C61C2×C22⋊C411yescharacteristic
230C23×C61C23×C411yescharacteristic
231Q8×C61—42no—
232Q8×C61—42no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—24no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—42no—
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—24no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—42no—
262C2×Dic61#10114yes—
263C2×Dic61C2×C22⋊C411yescharacteristic
264C2×Dic61C2×C22⋊C411yescharacteristic
265C2×Dic61C2×C22⋊C411yescharacteristic
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271Dic122—44no—
272Dic122—44no—
273Dic122—42no—
274Dic122—42no—
275C8×C61—42no—
276C8×C61—42no—
277#92418—42no—
278#92418—42no—
279#17404—611nomaximal, Sylow
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—44no—
288C22×C61C2×#10112yes—
289C22×C61C22×C22⋊C411yescharacteristic
290C22×C61#56812yes—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—21no—
294C4×C61—42no—
295C4×C61—42no—
296C4×C61#41012yes—
297Dic61—21no—
298Dic61—21no—
299Dic61—21no—
300Dic61—21no—
301Dic61—21no—
302Dic61—21no—
303Dic61—42no—
304Dic61—42no—
305Dic61C2×#10112yes—
306Dic61C2×#10112yes—
307C2×#533—611no—
308#2920—611no—
309C2×#432—611no—
310#1472—611no—
311#1472—611no—
312#1472—611no—
313#1472D6111yescharacteristic
314#1470—614no—
315#1467—614no—
316C2×C61—22no—
317C2×C61—22no—
318C2×C61—41no—
319C2×C61#287911yescharacteristic
320C2×C61C2×#41011yescharacteristic
321C2×C61C22×#10111yescharacteristic
322#533—1221no—
323#533—1221no—
324#533—1221no—
325#533—1221no—
326#533—1221no—
327#533—1221no—
328#533—1221no—
329#533—1221no—
330C2×C4⋊Q8—611no—
331C2×C4⋊Q8—611no—
332C2×#125—612no—
333C2×C22⋊Q8—611no—
334C2×C22⋊Q8—612no—
335C2×C22⋊Q8C2×D6111yescharacteristic
336C2×C4×Q8—611no—
337C2×C4×Q8—611no—
338C2×C4×Q8—612no—
339C2×#117—612no—
340C22×C42—611no—
341#432—612no—
342#432—612no—
343#432—612no—
344#432—1221no—
345#432—1221no—
346#432—1221no—
347#431—612no—
348#431—1221no—
349#423—1221no—
350C2×C4⋊C8—1221no—
351#407—611no—
352#407C2×D6111yescharacteristic
353C2×C22⋊C8—611no—
354C2×C22⋊C8C2×D6111yescharacteristic
355C4×M16—1221no—
356C2×#97—1221no—
357#324—614no—
358#324—614no—
359#324—614no—
360#324C2×D6114yes—
361C61#1740411yescharacteristic, complemented, Sylow
362C22×Q8—612no—
363C22×Q8—611no—
364C22×Q8C4×D6111yescharacteristic
365C23×C4—611no—
366C23×C4—611no—
367C23×C4C22×D6111yescharacteristic
368C2×M16—21no—
369C2×M16—1221no—
370C22×C8—21no—
371C22×C8—1221no—
372C4⋊Q8—1221no—
373C4⋊Q8—1221no—
374C4⋊Q8—1221no—
375C4⋊Q8—1221no—
376C4⋊Q8—1221no—
377C4⋊Q8—1221no—
378C4⋊Q8—1221no—
379C4⋊Q8—1221no—
380#125—1222no—
381#125—1222no—
382#125—1222no—
383#125—1222no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—1222no—
389C22⋊Q8—1222no—
390C22⋊Q8—1222no—
391C22⋊Q8—1222no—
392C22⋊Q8—1221no—
393C22⋊Q8—1221no—
394C22⋊Q8—1221no—
395C22⋊Q8—1221no—
396C4×Q8—1222no—
397C4×Q8—1222no—
398C4×Q8—1222no—
399C4×Q8—1222no—
400C4×Q8—1221no—
401C4×Q8—1221no—
402C4×Q8—1221no—
403C4×Q8—1221no—
404C4×Q8—1221no—
405C4×Q8—1221no—
406C4×Q8—1221no—
407C4×Q8—1221no—
408#117—1222no—
409#117—1222no—
410#117—1222no—
411#117—1222no—
412C2×C4⋊C4—612no—
413C2×C4⋊C4—612no—
414C2×C4⋊C4—612no—
415C2×C4⋊C4—612no—
416C2×C4⋊C4—612no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—612no—
419C2×C4⋊C4C4×D6111yescharacteristic
420C2×C4⋊C4C22×D6112yes—
421C2×C22⋊C4—612no—
422C2×C22⋊C4C4×D6112yes—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—612no—
436C2×C42—612no—
437C4⋊C8—1222no—
438C4⋊C8—1222no—
439C4⋊C8—1222no—
440C4⋊C8—1222no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—612no—
444C22⋊C8—612no—
445C22⋊C8—1221no—
446C22⋊C8—1221no—
447C22⋊C8C22×D6112yes—
448C22⋊C8C22×D6112yes—
449#97—1222no—
450#97—1222no—
451#97—1222no—
452C4×C8—1222no—
453C24C2×C4×D6111yescharacteristic
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—42no—
457C2×Q8—1222no—
458C2×Q8—1222no—
459C2×Q8—1221no—
460C2×Q8—1221no—
461C2×Q8—2444no—
462C2×Q8—2442no—
463C22×C4—42no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—612no—
477C22×C4—612no—
478C22×C4—1224no—
479C22×C4—2442no—
480C22×C4C2×C4×D6112yes—
481C22×C4C2×C4×D6111yescharacteristic
482C22×C4C2×C4×D6112yes—
483C22×C4D4×D6111yescharacteristic
484C22×C4D4×D6111yescharacteristic
485C22×C4D4×D6111yescharacteristic
486C22×C4D4×D6111yescharacteristic
487C22×C4C23×D6111yescharacteristic
488M16—42no—
489M16—2442no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—42no—
493C2×C8—1222no—
494C2×C8—1222no—
495C2×C8—2442no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—1222no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—1222no—
517C22⋊C4—1222no—
518C42—611no—
519C42—611no—
520C42—611no—
521C42—611no—
522C42—611no—
523C42—611no—
524C42—611no—
525C42—611no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—1222no—
535C42—1222no—
536C42—1222no—
537C42—1222no—
538C23—22no—
539C23—22no—
540C23—41no—
541C23C22⋊C4×D6111yescharacteristic
542C23C22⋊C4×D6111yescharacteristic
543C23C22×C4×D6111yescharacteristic
544Q8—42no—
545Q8—42no—
546Q8—2442no—
547Q8—2444no—
548Q8—2444no—
549Q8—2442no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—611no—
561C2×C4—611no—
562C2×C4—614no—
563C2×C4—611no—
564C2×C4—611no—
565C2×C4—611no—
566C2×C4—611no—
567C2×C4—611no—
568C2×C4—611no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1224no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2442no—
584C2×C4C22⋊C4×D6111yescharacteristic
585C2×C4C22⋊C4×D6111yescharacteristic
586C2×C4C2×D4×D6111yescharacteristic
587C2×C4C2×D4×D6111yescharacteristic
588C8—42no—
589C8—42no—
590C8—2442no—
591C8—2442no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—44no—
600C22#101×D6112yes—
601C22C2×C22⋊C4×D6111yescharacteristic
602C22#1684052712yes—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—42no—
607C4—42no—
608C4—612no—
609C4—612no—
610C4—1221no—
611C4—1221no—
612C4—1221no—
613C4—1221no—
614C4—1221no—
615C4—1221no—
616C4—2442no—
617C4—2442no—
618C4#1683973412yes—
619C2—22no—
620C2—22no—
621C2—41no—
622C2#2145426111yescharacteristic
623C2C2×#1683973411yescharacteristic
624C2C2×#101×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1472C2
socleC22×C61C22×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC22×C4×C61C24
hypercenter#1472D61
hypocenterC61#17404
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
7. #21444173C2semidirect
8. #21444161C2semidirect
361. C61#17404semidirect

Maximal subgroups

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

subgroupindex
C2×#168403142
#214544482
C2×#168398162
#214441842
#214441832
#214441822
#214441732
#214441612
C61×#14722
#1740461