Finite Group Databasebeta

← #29699656

Subgroups — #29699656

Order 15616.

960 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839818C211yesmaximal, characteristic, complemented
2C2×#16839814C211yesmaximal, characteristic, complemented
3C42×D244C211yesmaximal, characteristic
4#21446616C212yesmaximal
5#21446431C212yesmaximal, complemented
6#21446424C212yesmaximal, complemented
7#21445796C211yesmaximal, characteristic, complemented
8#21445796C211yesmaximal, characteristic, complemented
9#21445696C212yesmaximal, complemented
10#21445672C211yesmaximal, characteristic, complemented
11C61×#1842C211yesmaximal, characteristic, complemented
12C2×C4×D244C411yescharacteristic
13C2×C4×D244C411yescharacteristic
14C2×C4×D244C2211yescharacteristic
15C2×C42×D61C2211yescharacteristic
16C2×C42×D61C2211yescharacteristic
17#16839818—24no—
18#16839814—24no—
19C2×C4⋊#92418C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519689C2212yes—
22C2×#14519689C2212yes—
23C2×#14519689C2212yes—
24C2×#14519689C2212yes—
25C2×#14519688C2212yes—
26C2×#14519687C2212yes—
27C2×C8×Dic61C2212yes—
28C4×C4⋊Dic61C411yescharacteristic
29C4×C4⋊Dic61C411yescharacteristic
30C4×C4⋊Dic61C2211yescharacteristic
31C4×#11758198C411yescharacteristic
32C4×#11758198C411yescharacteristic
33C4×#11758198C411yescharacteristic
34C4×#11758198C411yescharacteristic
35C4×#11758198C2211yescharacteristic
36C4×#11758198C2211yescharacteristic
37#16839517C2212yes—
38#16839516C2212yes—
39#16839516C2212yes—
40C2×C4⋊C8×C61C2212yes—
41C2×C4⋊C8×C61C2211yescharacteristic
42C2×C4⋊C8×C61C2211yescharacteristic
43C2×C4⋊C8×C61C2212yes—
44C43×C61C2211yescharacteristic
45C22×D244C2×C411yescharacteristic
46C22×C4×D61C2×C411yescharacteristic
47C22×C4×D61C2×C411yescharacteristic
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2311yescharacteristic
51C22×C4×D61C2311yescharacteristic
52C22×#92418C2312yes—
53C22×#92418C2312yes—
54C4×D244—24no—
55C4×D244—22no—
56C4×D244—22no—
57C4×D244—24no—
58C2×C4⋊Dic61C2×C411yescharacteristic
59C2×C4⋊Dic61C2×C411yescharacteristic
60C2×C4⋊Dic61C2×C411yescharacteristic
61C2×#11758198C2×C411yescharacteristic
62C2×#11758198C2×C411yescharacteristic
63C2×#11758198C2×C411yescharacteristic
64C2×#11758198C2×C411yescharacteristic
65C2×#11758198C2×C411yescharacteristic
66C2×#11758198C2×C411yescharacteristic
67C2×C4×Dic61C2×C411yescharacteristic
68C2×C4×Dic61C2×C411yescharacteristic
69C2×C4×Dic61C2×C411yescharacteristic
70C2×C4×Dic61C2×C411yescharacteristic
71C2×C4×Dic61C2311yescharacteristic
72C2×C4×Dic61C2311yescharacteristic
73C42×D61—22no—
74C42×D61—22no—
75C42×D61—22no—
76C42×D61—22no—
77C4⋊#92418—22no—
78C4⋊#92418D414yescomplemented
79#14519689—24no—
80#14519689—24no—
81#14519689—42no—
82#14519689—42no—
83#14519688—24no—
84#14519687—24no—
85C8×Dic61—24no—
86#14519684C2×C411yescharacteristic
87#14519684C2×C411yescharacteristic
88#14519684C2×C411yescharacteristic
89#14519684C2×C411yescharacteristic
90#14519684C2×C411yescharacteristic
91#14519684C2×C411yescharacteristic
92C22×C8×C61C2312yes—
93C22×C8×C61C2312yes—
94C2×C42×C61C2×C411yescharacteristic
95C2×C42×C61C2×C411yescharacteristic
96C2×C42×C61C2×C411yescharacteristic
97C2×C42×C61C2×C411yescharacteristic
98C2×C42×C61C2311yescharacteristic
99C2×C42×C61C2311yescharacteristic
100C2×C42×C61C2311yescharacteristic
101C4⋊C8×C61—22no—
102C4⋊C8×C61—22no—
103C4⋊C8×C61—24no—
104C4⋊C8×C61—42no—
105C23×D61C22×C411yescharacteristic
106C23×D61C22×C411yescharacteristic
107C22×C4×C61C22×C411yescharacteristic
108C22×C4×C61C22×C411yescharacteristic
109C22×C4×C61C22×C411yescharacteristic
110C22×C4×C61C22×C411yescharacteristic
111C22×C4×C61C22×C411yescharacteristic
112C22×C4×C61C22×C411yescharacteristic
113C22×C4×C61C2411yescharacteristic
114C22×Dic61C22×C411yescharacteristic
115C22×Dic61C22×C411yescharacteristic
116C22×Dic61C22×C411yescharacteristic
117C22×Dic61C22×C411yescharacteristic
118C22×Dic61C22×C411yescharacteristic
119C22×Dic61C22×C411yescharacteristic
120C2×D244—22no—
121C2×D244—22no—
122C2×D244—22no—
123C2×C4×D61—22no—
124C2×C4×D61—22no—
125C2×C4×D61—22no—
126C2×C4×D61—22no—
127C2×C4×D61—22no—
128C2×C4×D61—22no—
129C2×C4×D61—22no—
130C2×C4×D61—22no—
131C2×C4×D61—21no—
132C2×C4×D61—21no—
133C2×C4×D61—21no—
134C2×C4×D61—21no—
135C2×C4×D61—21no—
136C2×C4×D61—21no—
137C2×C4×D61—21no—
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61—22no—
144C2×C4×D61—41no—
145C2×C4×D61—41no—
146C2×C4×D61M1614yes—
147C2×C8×C61—22no—
148C2×C8×C61—22no—
149C2×C8×C61—22no—
150C2×C8×C61—22no—
151C2×C8×C61—22no—
152C2×C8×C61—22no—
153C42×C61—22no—
154C42×C61—22no—
155C42×C61—22no—
156C42×C61—21no—
157C42×C61—21no—
158C42×C61—41no—
159C42×C61C2×D412yes—
160C42×C61#4112yes—
161C42×C61#4112yes—
162C42×C61#4112yes—
163#11758198—22no—
164#11758198—22no—
165#11758198—22no—
166#11758198—22no—
167#11758198—22no—
168#11758198M1614yes—
169C4⋊Dic61—22no—
170C4⋊Dic61—22no—
171C4⋊Dic61—22no—
172C4×Dic61—22no—
173C4×Dic61—22no—
174C4×Dic61—22no—
175C4×Dic61—22no—
176C4×Dic61—21no—
177C4×Dic61—21no—
178C4×Dic61—21no—
179C4×Dic61—21no—
180C2×#92418—22no—
181C2×#92418—22no—
182C2×#92418—22no—
183C2×#92418—22no—
184C2×#92418—22no—
185C2×#92418C2×D414yes—
186C23×C61C23×C411yescharacteristic
187C22×D61—21no—
188C22×D61—21no—
189C22×D61—21no—
190C22×D61—21no—
191C22×D61—21no—
192C22×D61—21no—
193C22×D61—21no—
194C22×D61—21no—
195C22×D61—21no—
196C22×D61—21no—
197C22×D61—21no—
198C22×D61—21no—
199C22×D61C2×M1612yes—
200C22×D61C2×M1612yes—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61#11712yes—
213C2×C4×C61#11712yes—
214C2×C4×C61C4×D412yes—
215C2×C4×C61C4×D412yes—
216C2×C4×C61C2×M1612yes—
217C2×C4×C61C2×M1612yes—
218C2×C4×C61#13112yes—
219C2×C4×C61C22×D411yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C2×C4×C61C2×#4111yescharacteristic
222C2×C4×C61C2×#4111yescharacteristic
223C2×C4×C61H(5,𝔽2)11yescharacteristic
224C2×C4×C612−1+411yescharacteristic
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61C2×M1612yes—
242C2×Dic61C2×M1612yes—
243D244—28no—
244C4×D61—28no—
245C4×D61—44no—
246C4×D61—44no—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—41no—
252C4×D61—41no—
253C4×D61—41no—
254C4×D61—41no—
255C4×D61—44no—
256C8×C61—42no—
257C8×C61—42no—
258#92418—24no—
259#92418—42no—
260#22797—611nomaximal, Sylow
261C22×C61C2×#11711yescharacteristic
262C22×C61C2×C4×D411yescharacteristic
263C22×C61#52011yescharacteristic
264C22×C61C22×M1611yescharacteristic
265C22×C61C22×M1611yescharacteristic
266C22×C61C2×#13111yescharacteristic
267C22×C61#56811yescharacteristic
268C2×D61—22no—
269C2×D61—22no—
270C2×D61—22no—
271C2×D61—22no—
272C2×D61—22no—
273C2×D61—22no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C4×C61—22no—
283C4×C61—22no—
284C4×C61—22no—
285C4×C61—22no—
286C4×C61—41no—
287C4×C61#43514yes—
288C4×C61#54711yescharacteristic
289C4×C61#55011yescharacteristic
290C4×C61#55511yescharacteristic
291C4×C61#55611yescharacteristic
292Dic61—22no—
293Dic61—22no—
294Dic61—41no—
295Dic61—41no—
296Dic61—41no—
297Dic61—41no—
298C2×#432—611no—
299C2×#431—611no—
300C42×D4—611no—
301#1955—612no—
302#1924—612no—
303#1923—612no—
304#1842D6111yescharacteristic, complemented
305#1797—611no—
306#1797—611no—
307#1771—612no—
308#1767—611no—
309C2×C61#235411yescharacteristic
310C2×C61#292011yescharacteristic
311C2×C61#292511yescharacteristic
312C2×C61C2×#43511yescharacteristic
313C2×C61D4×M1611yescharacteristic
314C2×C61#298911yescharacteristic
315C2×C61#299011yescharacteristic
316D61—42no—
317D61—42no—
318C2×C4×D4—611no—
319C2×C4×D4—611no—
320C2×C4×D4—611no—
321C22×C42—611no—
322C22×C42—611no—
323#432—1224no—
324#431—1224no—
325C2×C4⋊C8—611no—
326C2×C4⋊C8—611no—
327C2×C4⋊C8C2×D6111yescharacteristic
328C2×C4⋊C8C2×D6111yescharacteristic
329C2×C4⋊C8C2×D6112yes—
330C2×C4⋊C8C2×D6112yes—
331C2×C22⋊C8—612no—
332C2×C22⋊C8—612no—
333C2×C22⋊C8—612no—
334C2×C22⋊C8—612no—
335C2×#97—612no—
336C2×#97—612no—
337C2×C4×C8—612no—
338C4×C4⋊C4—611no—
339C4×C4⋊C4—611no—
340C4×C4⋊C4—611no—
341C4×C22⋊C4—611no—
342C4×C22⋊C4—611no—
343C4×C22⋊C4—611no—
344C4×C22⋊C4—611no—
345C4×C22⋊C4—611no—
346C4×C22⋊C4—611no—
347C43C2×D6111yescharacteristic
348#336—612no—
349#336—612no—
350#336—612no—
351C61#2279711yescharacteristic, complemented, Sylow
352C22×D4—611no—
353C23×C4—611no—
354C23×C4—611no—
355C23×C4—611no—
356C23×C4—611no—
357C23×C4—611no—
358C23×C4—611no—
359C22×C8—612no—
360C22×C8—612no—
361C22×C8C22×D6112yes—
362C22×C8C22×D6112yes—
363C4×D4—1224no—
364C4×D4—1224no—
365C4×D4—1222no—
366C4×D4—1222no—
367C2×C4⋊C4—611no—
368C2×C4⋊C4—611no—
369C2×C4⋊C4—611no—
370C2×C22⋊C4—611no—
371C2×C22⋊C4—611no—
372C2×C22⋊C4—611no—
373C2×C22⋊C4—611no—
374C2×C22⋊C4—611no—
375C2×C22⋊C4—611no—
376C2×C42—611no—
377C2×C42—611no—
378C2×C42—611no—
379C2×C42—611no—
380C2×C42—611no—
381C2×C42—611no—
382C2×C42—1222no—
383C2×C42—1222no—
384C2×C42—1222no—
385C2×C42—1222no—
386C2×C42C4×D6111yescharacteristic
387C2×C42C4×D6111yescharacteristic
388C2×C42C4×D6111yescharacteristic
389C2×C42C4×D6111yescharacteristic
390C2×C42C22×D6111yescharacteristic
391C2×C42C22×D6111yescharacteristic
392C2×C42C22×D6111yescharacteristic
393C4⋊C8—22no—
394C4⋊C8—22no—
395C4⋊C8—24no—
396C4⋊C8—42no—
397C4⋊C8—614no—
398C4⋊C8—1222no—
399C22⋊C8—1224no—
400C22⋊C8—1224no—
401C22⋊C8—2442no—
402C22⋊C8—2442no—
403#97—1224no—
404#97—1224no—
405C4×C8—1224no—
406#95—611no—
407#95—611no—
408#95—611no—
409#95—611no—
410#95—611no—
411#95—611no—
412C24—611no—
413C24—611no—
414C2×D4—1222no—
415C2×D4—1222no—
416C2×D4—1222no—
417C22×C4—611no—
418C22×C4—611no—
419C22×C4—614no—
420C22×C4—611no—
421C22×C4—611no—
422C22×C4—611no—
423C22×C4—611no—
424C22×C4—1222no—
425C22×C4—1222no—
426C22×C4—1222no—
427C22×C4—1222no—
428C22×C4—1221no—
429C22×C4—1221no—
430C22×C4—1221no—
431C22×C4—1221no—
432C22×C4—1221no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1222no—
441C22×C4—1222no—
442C22×C4—1222no—
443C22×C4—1222no—
444C22×C4—1222no—
445C22×C4—2441no—
446C22×C4—2441no—
447C22×C4C2×C4×D6111yescharacteristic
448C22×C4C2×C4×D6111yescharacteristic
449C22×C4C2×C4×D6111yescharacteristic
450C22×C4C2×C4×D6111yescharacteristic
451C22×C4C2×C4×D6111yescharacteristic
452C22×C4C2×C4×D6111yescharacteristic
453C22×C4C23×D6111yescharacteristic
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—614no—
461C2×C8—1222no—
462C2×C8—1222no—
463C2×C8—1222no—
464C2×C8—1222no—
465C2×C8—1222no—
466C4⋊C4—1222no—
467C4⋊C4—1222no—
468C4⋊C4—1222no—
469C22⋊C4—614no—
470C22⋊C4—1222no—
471C22⋊C4—1222no—
472C22⋊C4—1222no—
473C22⋊C4—1222no—
474C22⋊C4—1222no—
475C42—21no—
476C42—21no—
477C42—22no—
478C42—22no—
479C42—22no—
480C42—41no—
481C42—1221no—
482C42—1221no—
483C42—1221no—
484C42—1221no—
485C42—1222no—
486C42—1222no—
487C42—1222no—
488C42—1222no—
489C42D4×D6112yes—
490C42#1175822412yes—
491C42#1175822612yes—
492C42#1175822612yes—
493C23—612no—
494C23—612no—
495C23—1221no—
496C23—1221no—
497C23—1221no—
498C23—1221no—
499C23—1221no—
500C23—1221no—
501C23—1221no—
502C23—1221no—
503C23—1221no—
504C23—1221no—
505C23—1221no—
506C23—1221no—
507C23C22×C4×D6111yescharacteristic
508D4—1228no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—612no—
521C2×C4—612no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1228no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—2444no—
540C2×C4—2444no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2444no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4#1451973512yes—
551C2×C4#1451973512yes—
552C2×C4#1451973912yes—
553C2×C4#1451973912yes—
554C2×C4M16×D6112yes—
555C2×C4M16×D6112yes—
556C2×C4#1451978312yes—
557C2×C4C2×D4×D6111yescharacteristic
558C2×C4C2×#1175822411yescharacteristic
559C2×C4C2×#1175822611yescharacteristic
560C2×C4C2×#1175822611yescharacteristic
561C2×C4#1451982211yescharacteristic
562C2×C4#1451982511yescharacteristic
563C8—42no—
564C8—42no—
565C8—1224no—
566C8—2442no—
567C22—1222no—
568C22—1222no—
569C22—1222no—
570C22—1222no—
571C22—1222no—
572C22—1222no—
573C22—2441no—
574C22—2441no—
575C22—2441no—
576C22—2441no—
577C22—2441no—
578C22—2441no—
579C22—2441no—
580C22—2441no—
581C22C2×#1451973511yescharacteristic
582C22C2×#1451973911yescharacteristic
583C22#1684024311yescharacteristic
584C22C2×M16×D6111yescharacteristic
585C22C2×M16×D6111yescharacteristic
586C22C2×#1451978311yescharacteristic
587C22#1684052811yescharacteristic
588C4—22no—
589C4—22no—
590C4—22no—
591C4—22no—
592C4—41no—
593C4—1222no—
594C4—1222no—
595C4—2441no—
596C4—2441no—
597C4—2441no—
598C4—2441no—
599C4#1683983214yes—
600C4#1684041511yescharacteristic
601C4#1684043211yescharacteristic
602C4#1684047811yescharacteristic
603C4#1684048611yescharacteristic
604C2—2442no—
605C2—2442no—
606C2#2144877011yescharacteristic
607C2#2145445111yescharacteristic
608C2#2145448411yescharacteristic
609C2C2×#1683983211yescharacteristic
610C2#2145455411yescharacteristic
611C2#2145493311yescharacteristic
612C2#2145494111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1842C2
prime radicalC22×D244C2×C4
cosocleC22×C4×C61C24
hypercenter#1842D61
hypocenterC61#22797
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1842

Complements

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

NH ≅ G/Ntype
1. C2×#16839818C2semidirect
2. C2×#16839814C2semidirect
5. #21446431C2semidirect
6. #21446424C2semidirect
7. #21445796C2semidirect
8. #21445796C2semidirect
9. #21445696C2semidirect
10. #21445672C2semidirect
11. C61×#1842C2semidirect
78. C4⋊#92418D4semidirect
304. #1842D61semidirect
351. C61#22797semidirect

Maximal subgroups

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

subgroupindex
C2×#168398182
C2×#168398142
C42×D2442
#214466162
#214464312
#214464242
#214457962
#214456962
#214456722
C61×#18422
#2279761