Finite Group Databasebeta

← #29737499

Subgroups — #29737499

Order 15616.

928 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840055C211yesmaximal, characteristic, complemented
2#21449504C211yesmaximal, characteristic
3Q8×C22⋊Dic61C211yesmaximal, characteristic
4#21447365C211yesmaximal, characteristic, complemented
5#21447210C211yesmaximal, characteristic, complemented
6#21447198C211yesmaximal, characteristic, complemented
7#21446958C211yesmaximal, characteristic, complemented
8#21446089C211yesmaximal, characteristic, complemented
9#21446085C211yesmaximal, characteristic, complemented
10#21446018C211yesmaximal, characteristic
11#21446002C211yesmaximal, characteristic
12#21445852C211yesmaximal, characteristic
13#21445832C211yesmaximal, characteristic, complemented
14#21445754C211yesmaximal, characteristic
15C2×C61×#419C211yesmaximal, characteristic
16C2×#14519776C2211yescharacteristic
17C2×Q8×Dic61C2211yescharacteristic
18C2×Q8×Dic61C2211yescharacteristic
19#16840055—24no—
20C2×#14519711C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519709C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31#16839685—21no—
32#16839674—21no—
33#16839669—21no—
34#16839669—21no—
35#16839669C2211yescharacteristic
36#16839669C2211yescharacteristic
37#16839668—21no—
38#16839661C2211yescharacteristic
39#16839658C2211yescharacteristic
40#16839646—21no—
41#16839627C2211yescharacteristic
42#16839622—21no—
43#16839622C2211yescharacteristic
44#16839622C2211yescharacteristic
45C4×C22⋊Dic61—21no—
46C4×C22⋊Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C23×Q8×C61C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C2×#117×C61C2211yescharacteristic
56C61×#419—24no—
57C2×#103×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C22×Dic122—21no—
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64#14519776—22no—
65#14519776—41no—
66Q8×Dic61—22no—
67Q8×Dic61—22no—
68Q8×Dic61—41no—
69Q8×Dic61—41no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61D411yescharacteristic
82C2×C22⋊Dic61D411yescharacteristic
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61C2311yescharacteristic
86C2×C4×Dic61C2311yescharacteristic
87#14519711—22no—
88#14519710—22no—
89#14519709—41no—
90#14519708—41no—
91#14519706—22no—
92#14519706—41no—
93#14519701—22no—
94#14519701—22no—
95#14519701—41no—
96#14519701—41no—
97C22⋊#92418—22no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684D411yescharacteristic
109#14519684D411yescharacteristic
110C22×Q8×C61—21no—
111C22×Q8×C61—22no—
112C22×Q8×C61—22no—
113C22×Q8×C61—22no—
114C22×Q8×C61—41no—
115C22×Q8×C61—41no—
116C22×Q8×C61Q814yescomplemented
117C22×Q8×C61C2311yescharacteristic
118C22×Q8×C61C2311yescharacteristic
119C23×C4×C61—21no—
120C23×C4×C61C2311yescharacteristic
121C2×M16×C61—22no—
122C2×M16×C61—22no—
123C2×M16×C61—41no—
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126#117×C61—22no—
127#117×C61—41no—
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131C2×C42×C61—21no—
132#103×C61—22no—
133#103×C61—22no—
134#103×C61—22no—
135#103×C61D414yes—
136C24×C61C2×D411yescharacteristic
137C2×Q8×C61—24no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—28no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—42no—
148C2×Q8×C61—42no—
149C2×Q8×C61—44no—
150C2×Q8×C61—44no—
151C2×Q8×C61—44no—
152C2×Q8×C61C2×D412yes—
153C2×Q8×C61C2×Q812yes—
154C2×Q8×C61C2×Q812yes—
155C2×Q8×C61#4112yes—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—24no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—42no—
166C22×C4×C61—42no—
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×Q812yes—
169C22×C4×C61#4112yes—
170C22×C4×C61C2411yescharacteristic
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C2×Dic122—42no—
180C2×Dic122—42no—
181C2×Dic122—81no—
182M16×C61—44no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61C2×D412yes—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61C2×D412yes—
193C22⋊C4×C61—42no—
194C42×C61—42no—
195C22⋊Dic61—22no—
196C22⋊Dic61—41no—
197C22⋊Dic61—42no—
198C22⋊Dic61—81no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—42no—
208C4⋊Dic61—42no—
209C4⋊Dic61—81no—
210#11758196—42no—
211#11758196—42no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C4×Dic61—42no—
217C4×Dic61—42no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61C22⋊Q812yes—
231C23×C61C22×D411yescharacteristic
232Q8×C61—22no—
233Q8×C61—22no—
234Q8×C61—22no—
235Q8×C61—22no—
236Q8×C61—22no—
237Q8×C61—48no—
238Q8×C61—41no—
239Q8×C61—41no—
240Q8×C61C22⋊Q814yes—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—21no—
244C2×C4×C61—22no—
245C2×C4×C61—21no—
246C2×C4×C61—22no—
247C2×C4×C61—22no—
248C2×C4×C61—22no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—48no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61C22⋊Q812yes—
261C2×C4×C61C22×D411yescharacteristic
262C2×C4×C61C22×Q811yescharacteristic
263C2×C4×C61C2×#4111yescharacteristic
264C2×C4×C61C2×#4111yescharacteristic
265C2×C4×C61H(5,𝔽2)11yescharacteristic
266C2×C4×C61H(5,𝔽2)11yescharacteristic
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61#13712yes—
291Dic122—84no—
292C8×C61—22no—
293C8×C61—41no—
294#92418—41no—
295#92418—41no—
296#25979—611nomaximal, Sylow
297C22×C61—22no—
298C22×C61—22no—
299C22×C61—22no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61—41no—
303C22×C61—41no—
304C22×C61C2×C22⋊Q811yescharacteristic
305C22×C61D4211yescharacteristic
306C22×C61#54611yescharacteristic
307C22×C61C2×#13711yescharacteristic
308C22×C61#57511yescharacteristic
309C22×C61#57711yescharacteristic
310C22×C61#57811yescharacteristic
311C4×C61—22no—
312C4×C61—24no—
313C4×C61—42no—
314C4×C61—42no—
315C4×C61—81no—
316C4×C61C2×C22⋊Q811yescharacteristic
317C4×C61#54311yescharacteristic
318C4×C61#54611yescharacteristic
319C4×C61#55111yescharacteristic
320Dic61—22no—
321Dic61—41no—
322Dic61—41no—
323Dic61—41no—
324Dic61—81no—
325Dic61—81no—
326Dic61—81no—
327Dic61—81no—
328C2×#477—611no—
329C2×#419D6111yescharacteristic
330#2439—611no—
331Q8×C22⋊C4—611no—
332#2097—611no—
333#2068—611no—
334#2066—611no—
335#2024—611no—
336#1865—611no—
337#1865—611no—
338#1854—611no—
339#1851—611no—
340#1809—611no—
341#1805—611no—
342#1787—611no—
343C2×C61—42no—
344C2×C61#243711yescharacteristic
345C2×C61#307811yescharacteristic
346C2×C61#308211yescharacteristic
347C2×C61#327011yescharacteristic
348C2×C61#327511yescharacteristic
349C2×C61#331311yescharacteristic
350C2×C61#332911yescharacteristic
351C23×Q8C2×D6111yescharacteristic
352C22×M16C2×D6111yescharacteristic
353C2×C4⋊Q8—611no—
354C2×C4×Q8—611no—
355C2×C4×Q8—611no—
356C2×#117C2×D6111yescharacteristic
357#477—1224no—
358C2×#107—611no—
359C2×#107—611no—
360C2×#106—611no—
361C2×#106—611no—
362C2×C4⋊C8—611no—
363C2×C4⋊C8—611no—
364#419—24no—
365C2×#103—611no—
366C2×#103—611no—
367C2×#103—611no—
368C2×#103—611no—
369C2×#103C2×D6111yescharacteristic
370C2×#103C2×D6111yescharacteristic
371C2×#103C2×D6111yescharacteristic
372C2×#103C2×D6111yescharacteristic
373C2×C22⋊C8—611no—
374#396—1221no—
375#393—1221no—
376#391—611no—
377#391—611no—
378#391—1221no—
379#391—1221no—
380#391—1221no—
381#389—611no—
382#389—611no—
383#387—1221no—
384#382—611no—
385#380—611no—
386#380—611no—
387#380—1221no—
388C4×C22⋊C4—611no—
389C4×C22⋊C4—1221no—
390#340—611no—
391#340—611no—
392#340—611no—
393#340—611no—
394#336—611no—
395#336—611no—
396C61#2597911yescharacteristic, complemented, Sylow
397C22×Q8—21no—
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8—22no—
401C22×Q8—41no—
402C22×Q8—41no—
403C22×Q8—1221no—
404C22×Q8Dic12214yescomplemented
405C22×Q8C22×D6111yescharacteristic
406C22×Q8C22×D6111yescharacteristic
407C23×C4—21no—
408C23×C4C22×D6111yescharacteristic
409C2×M16—22no—
410C2×M16—22no—
411C2×M16—41no—
412C22×C8—611no—
413C22×C8—611no—
414C22×C8C22×D6111yescharacteristic
415C22×C8C22×D6111yescharacteristic
416C4⋊Q8—1222no—
417C4⋊Q8—2441no—
418C4×Q8—1222no—
419C4×Q8—1222no—
420C4×Q8—2441no—
421C4×Q8—2441no—
422#117—22no—
423#117—41no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—611no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4C22×D6111yescharacteristic
434C2×C4⋊C4C22×D6111yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—611no—
437C2×C22⋊C4—611no—
438C2×C22⋊C4—1221no—
439C2×C22⋊C4—1221no—
440C2×C42—21no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—1221no—
444C2×C42—1221no—
445#107—1222no—
446#107—1222no—
447#106—2441no—
448#106—2441no—
449C4⋊C8—1222no—
450C4⋊C8—2441no—
451#103—22no—
452#103—22no—
453#103—22no—
454#103—1222no—
455#103—1222no—
456#103—2441no—
457#103—2441no—
458#103C22⋊D6114yes—
459C22⋊C8—1222no—
460#95—611no—
461#95—611no—
462#95—1221no—
463#95—1221no—
464#95—1221no—
465#95—1221no—
466#95—1221no—
467#95—1221no—
468#95—1221no—
469#95—1221no—
470#95—1221no—
471#95—1221no—
472C24D4×D6111yescharacteristic
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—24no—
478C2×Q8—28no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—4881no—
489C2×Q8—2442no—
490C2×Q8—2442no—
491C2×Q8C2×Dic12212yes—
492C2×Q8C2×Dic12212yes—
493C2×Q8#1175822212yes—
494C2×Q8C2×C22⋊D6112yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—24no—
503C22×C4—21no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—1221no—
514C22×C4C2×Dic12212yes—
515C22×C4D4×D6111yescharacteristic
516C22×C4#1175822412yes—
517C22×C4C23×D6111yescharacteristic
518M16—44no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—1221no—
530C2×C8C2×C22⋊D6112yes—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—1221no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—1221no—
540C4⋊C4—1221no—
541C4⋊C4—1221no—
542C4⋊C4—4881no—
543C4⋊C4—2442no—
544C4⋊C4—2442no—
545C4⋊C4—2442no—
546C4⋊C4—2442no—
547C4⋊C4C2×C22⋊D6112yes—
548C22⋊C4—42no—
549C22⋊C4—1222no—
550C22⋊C4—4881no—
551C22⋊C4—2441no—
552C22⋊C4—2442no—
553C42—42no—
554C42—1221no—
555C42—1221no—
556C42—1221no—
557C42—1221no—
558C42—2442no—
559C42—2442no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23#1451975412yes—
567C23C2×D4×D6111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—22no—
571Q8—22no—
572Q8—22no—
573Q8—48no—
574Q8—41no—
575Q8—41no—
576Q8—4884no—
577Q8#1451975614yes—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—48no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—612no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
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#1451975412yes—
622C2×C4C22×C22⋊D6111yescharacteristic
623C2×C4C22×Dic12211yescharacteristic
624C2×C4C2×#1175822411yescharacteristic
625C2×C4C2×#1175822211yescharacteristic
626C2×C4#1451982211yescharacteristic
627C2×C4#1451982211yescharacteristic
628C8—22no—
629C8—41no—
630C8—2441no—
631C8—2441no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22C2×#1451975411yescharacteristic
640C22D4×C22⋊D6111yescharacteristic
641C22#1684040211yescharacteristic
642C22#137×D6111yescharacteristic
643C22#1684056111yescharacteristic
644C22#1684057111yescharacteristic
645C22#1684057811yescharacteristic
646C4—22no—
647C4—24no—
648C4—42no—
649C4—42no—
650C4—81no—
651C4—1222no—
652C4—4881no—
653C4—4881no—
654C4—4881no—
655C4—4881no—
656C4—2441no—
657C4—2441no—
658C4—2441no—
659C4C2×#1451975611yescharacteristic
660C4#1684038811yescharacteristic
661C4#1684040611yescharacteristic
662C4#1684043811yescharacteristic
663C2—42no—
664C2#2144948011yescharacteristic
665C2#2145562111yescharacteristic
666C2#2145566311yescharacteristic
667C2#2145738311yescharacteristic
668C2#2145744411yescharacteristic
669C2#2145788611yescharacteristic
670C2#2145810911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#419C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenterC2×#419D61
hypocenterC61#25979
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
1. C2×#16840055C2semidirect
4. #21447365C2semidirect
5. #21447210C2semidirect
6. #21447198C2semidirect
7. #21446958C2semidirect
8. #21446089C2semidirect
9. #21446085C2semidirect
13. #21445832C2semidirect
116. C22×Q8×C61Q8semidirect
396. C61#25979semidirect
404. C22×Q8Dic122semidirect

Maximal subgroups

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

subgroupindex
C2×#168400552
#214495042
Q8×C22⋊Dic612
#214473652
#214472102
#214471982
#214469582
#214460892
#214460852
#214460182
#214460022
#214458522
#214458322
#214457542
C2×C61×#4192
#2597961