Finite Group Databasebeta

← #29585377

Subgroups — #29585377

Order 15616.

1562 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840236C211yesmaximal, characteristic
2C22×#14519693C211yesmaximal, characteristic
3C2×#16839664C211yesmaximal, characteristic
4#21445540C211yesmaximal, characteristic, complemented
5#21445539C211yesmaximal, characteristic, complemented
6C2×#16839522C211yesmaximal, characteristic, complemented
7C2×C61×#339C211yesmaximal, characteristic, complemented
8C23×D244C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10#16840236—22no—
11#16840236—22no—
12#16840236—22no—
13#16840236C414yescomplemented
14C2×C4×D244—22no—
15C2×#14519739—22no—
16C2×#14519736C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×#11758198—22no—
19C2×C22⋊C4×D61—22no—
20C2×#14519693—22no—
21C2×#14519693—22no—
22C2×#14519693C414yescomplemented
23#16839664—22no—
24#16839664C414yescomplemented
25#16839525—22no—
26#16839524—22no—
27#16839522—22no—
28C22×M16×C61C2211yescharacteristic
29C2×#117×C61C2211yescharacteristic
30C22×C42×C61C2211yescharacteristic
31C61×#339—22no—
32C24×D61D412yes—
33C22×D244—21no—
34C22×D244—21no—
35C22×D244—21no—
36C22×D244—21no—
37C22×D244—21no—
38C22×D244—21no—
39C22×D244—21no—
40C22×D244—21no—
41C22×D244C2×C412yes—
42C22×D244C2×C412yes—
43C22×D244C2×C412yes—
44C22×D244D412yes—
45C22×D244D412yes—
46C22×D244Q812yes—
47C23×Dic61—21no—
48C22×C4×D61—24no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194C2×C412yescomplemented
55C22×#92418—21no—
56C4×D244—28no—
57C4×D244—28no—
58#14519739—28no—
59#14519739—28no—
60#14519736—21no—
61#14519736—21no—
62#14519736C2×C412yes—
63#14519736D412yes—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61C2×C412yescomplemented
70C2×C4⋊Dic61D412yes—
71C2×C22⋊Dic61—21no—
72C2×#11758198—24no—
73C2×#11758198—28no—
74C2×#11758198—48no—
75C22⋊C4×D61—28no—
76C22⋊C4×D61—28no—
77C2×C4×Dic61—21no—
78#14519693—28no—
79C23×C4×C61—21no—
80C23×C4×C61C2311yescharacteristic
81C2×M16×C61—21no—
82C2×M16×C61—21no—
83C2×M16×C61—21no—
84C2×M16×C61—21no—
85C2×M16×C61—21no—
86C2×M16×C61C2×C412yescomplemented
87C22×C8×C61—21no—
88#117×C61—21no—
89#117×C61—21no—
90#117×C61C2×C412yes—
91#117×C61D412yes—
92C2×C4⋊C4×C61D412yes—
93C2×C22⋊C4×C61—21no—
94C2×C42×C61—21no—
95C2×C42×C61—21no—
96C2×C42×C61—21no—
97C2×C42×C61—21no—
98C2×C42×C61—21no—
99C2×C42×C61—21no—
100C2×C42×C61C2×C412yescomplemented
101C24×C61C2×D411yescharacteristic
102C23×D61—22no—
103C23×D61—22no—
104C23×D61—22no—
105C23×D61—22no—
106C23×D61—44no—
107C23×D61—44no—
108C23×D61C22⋊C414yes—
109C23×D61C22⋊C414yes—
110C23×D61C4⋊C414yes—
111C22×C4×C61—24no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—42no—
115C22×C4×C61—41no—
116C22×C4×C61—41no—
117C22×C4×C61C22×C411yescharacteristic
118C22×C4×C61C22×C411yescharacteristic
119C22×C4×C61C22×C411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×Q811yescharacteristic
127C22×C4×C61#4111yescharacteristic
128C22×C4×C61#4111yescharacteristic
129C22×C4×C61#4111yescharacteristic
130C22×C4×C61#4111yescharacteristic
131C22×Dic61—22no—
132C22×Dic61—22no—
133C22×Dic61—44no—
134C22×Dic61—41no—
135C22×Dic61—41no—
136C2×D244—22no—
137C2×D244—22no—
138C2×D244—22no—
139C2×D244—22no—
140C2×D244—22no—
141C2×D244—22no—
142C2×D244—22no—
143C2×D244—22no—
144C2×D244—22no—
145C2×D244—22no—
146C2×D244—22no—
147C2×D244—22no—
148C2×D244—22no—
149C2×D244—22no—
150C2×D244—22no—
151C2×D244—22no—
152C2×D244—22no—
153C2×D244—22no—
154C2×D244—22no—
155C2×D244—22no—
156C2×D244—22no—
157C2×D244—22no—
158C2×D244—22no—
159C2×D244—22no—
160C2×D244C4214yes—
161C2×D244C22⋊C414yes—
162C2×D244C4⋊C414yes—
163C2×D244C4⋊C414yes—
164C2×C4×D61—216no—
165C2×C4×D61—84no—
166C2×C4×D61—84no—
167M16×C61—22no—
168M16×C61—22no—
169M16×C61—41no—
170M16×C61—41no—
171C2×C8×C61—22no—
172C2×C8×C61—41no—
173C2×C8×C61—41no—
174C4⋊C4×C61—22no—
175C4⋊C4×C61C22⋊C414yescomplemented
176C22⋊C4×C61—22no—
177C22⋊C4×C61—22no—
178C42×C61—22no—
179C42×C61—22no—
180C42×C61—22no—
181C42×C61—22no—
182C42×C61—41no—
183C42×C61—41no—
184C22⋊Dic61—22no—
185C22⋊Dic61—22no—
186#11758198—216no—
187#11758198—416no—
188C4⋊Dic61—22no—
189C4⋊Dic61—22no—
190C4⋊Dic61—22no—
191C4⋊Dic61—41no—
192C4⋊Dic61—41no—
193C4⋊Dic61C22⋊C414yescomplemented
194C4×Dic61—22no—
195C4×Dic61—22no—
196#11758194—22no—
197#11758194—22no—
198#11758194—41no—
199#11758194—41no—
200C2×#92418—22no—
201C2×#92418—41no—
202C2×#92418—41no—
203C23×C61—22no—
204C23×C61—22no—
205C23×C61C2×C22⋊C411yescharacteristic
206C23×C61C2×C22⋊C411yescharacteristic
207C23×C61C2×C4⋊C411yescharacteristic
208C23×C61#12011yescharacteristic
209C23×C61#12011yescharacteristic
210C23×C61#12311yescharacteristic
211C23×C61#12311yescharacteristic
212C22×D61—24no—
213C22×D61—24no—
214C22×D61—24no—
215C22×D61—24no—
216C22×D61—24no—
217C22×D61—24no—
218C22×D61—44no—
219C22×D61—44no—
220C22×D61—44no—
221C22×D61—48no—
222C22×D61—44no—
223C22×D61—48no—
224C22×D61—84no—
225C22×D61—84no—
226C22×D61—82no—
227C22×D61—82no—
228C22×D61#9518yes—
229C2×C4×C61—24no—
230C2×C4×C61—24no—
231C2×C4×C61—44no—
232C2×C4×C61—44no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61C2×C4211yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C2×C4⋊C411yescharacteristic
242C2×C4×C61C2×C4⋊C411yescharacteristic
243C2×C4×C61#11711yescharacteristic
244C2×C4×C61#11711yescharacteristic
245C2×C4×C61C4×D411yescharacteristic
246C2×C4×C61C4×D411yescharacteristic
247C2×C4×C61C4×D411yescharacteristic
248C2×C4×C61C4×D411yescharacteristic
249C2×C4×C61C4×D411yescharacteristic
250C2×C4×C61C4×D411yescharacteristic
251C2×C4×C61C4×D411yescharacteristic
252C2×C4×C61C4×D411yescharacteristic
253C2×C4×C61#12011yescharacteristic
254C2×C4×C61#12011yescharacteristic
255C2×C4×C61#12111yescharacteristic
256C2×C4×C61#12111yescharacteristic
257C2×C4×C61#12111yescharacteristic
258C2×C4×C61#12111yescharacteristic
259C2×C4×C61C22⋊Q811yescharacteristic
260C2×C4×C61C22⋊Q811yescharacteristic
261C2×C4×C61C22⋊Q811yescharacteristic
262C2×C4×C61C22⋊Q811yescharacteristic
263C2×C4×C61#12311yescharacteristic
264C2×C4×C61#12311yescharacteristic
265C2×Dic61—24no—
266C2×Dic61—42no—
267C2×Dic61—42no—
268C2×Dic61—44no—
269C2×Dic61—42no—
270C2×Dic61—82no—
271C2×Dic61—82no—
272D244—24no—
273D244—24no—
274D244—24no—
275D244—24no—
276D244—24no—
277D244—24no—
278D244—24no—
279D244—24no—
280C4×D61—816no—
281C8×C61—42no—
282#92418—42no—
283#10749—611nomaximal, Sylow
284C22×C61—22no—
285C22×C61—22no—
286C22×C61—22no—
287C22×C61—22no—
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—21no—
291C22×C61—21no—
292C22×C61C2×#9511yescharacteristic
293C22×C61#37911yescharacteristic
294C22×C61#38111yescharacteristic
295C22×C61#38511yescharacteristic
296C22×C61#38511yescharacteristic
297C22×C61#38611yescharacteristic
298C22×C61#38611yescharacteristic
299C22×C61#45312yes—
300C22×C61#45512yes—
301C2×D61—28no—
302C2×D61—48no—
303C2×D61—48no—
304C2×D61—44no—
305C2×D61—44no—
306C2×D61—48no—
307C2×D61—84no—
308C2×D61—84no—
309C2×D61—84no—
310C4×C61—44no—
311C4×C61—44no—
312C4×C61C4×C22⋊C411yescharacteristic
313C4×C61C4×C22⋊C411yescharacteristic
314C4×C61#38011yescharacteristic
315C4×C61#38011yescharacteristic
316C4×C61#38511yescharacteristic
317C4×C61#38511yescharacteristic
318C4×C61#38611yescharacteristic
319C4×C61#38611yescharacteristic
320Dic61—44no—
321Dic61—82no—
322C2×#518—611no—
323C22×#100—611no—
324C2×#390—611no—
325#1736—611no—
326#1736—611no—
327C2×#339—611no—
328C2×#339D6111yescharacteristic, complemented
329C2×C61—21no—
330C2×C61—21no—
331C2×C61—21no—
332C2×C61—21no—
333C2×C61C22⋊#9511yescharacteristic
334C2×C61#179212yes—
335C2×C61#185612yes—
336C2×C61#188511yescharacteristic
337C2×C61#188711yescharacteristic
338D61—48no—
339C23×D4—611no—
340C22×M16—611no—
341C22×M16C2×D6111yescharacteristic
342#518—614no—
343#518—1222no—
344#518—1222no—
345#518—1222no—
346C2×C4×D4—1222no—
347C2×C4×D4—1222no—
348C2×#117—611no—
349C2×#117C2×D6111yescharacteristic
350C22×C4⋊C4—611no—
351C22×C22⋊C4—1222no—
352C22×C22⋊C4—1222no—
353C22×C42C2×D6111yescharacteristic
354C2×#100—614no—
355C2×#100—1222no—
356C2×#100—1222no—
357#390—614no—
358#390—1222no—
359#340—1222no—
360#340—1222no—
361#339—22no—
362#339—1222no—
363C61#1074911yescharacteristic, complemented, Sylow
364C25—612no—
365C22×D4—612no—
366C22×D4—612no—
367C22×D4—612no—
368C22×D4—612no—
369C22×D4—612no—
370C22×D4—612no—
371C22×D4—1221no—
372C22×D4—1221no—
373C22×D4—1221no—
374C22×D4—1221no—
375C22×D4—1221no—
376C22×D4—1221no—
377C22×D4—1221no—
378C22×D4—1221no—
379C23×C4—21no—
380C23×C4—1224no—
381C23×C4—1221no—
382C23×C4C22×D6111yescharacteristic
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—612no—
389C2×M16—1221no—
390C2×M16—1221no—
391C2×M16—1221no—
392C2×M16—1221no—
393C2×M16—1221no—
394C2×M16C4×D6112yescomplemented
395C22×C8—21no—
396C22×C8—1221no—
397C4×D4—1228no—
398C4×D4—1228no—
399C4×D4—1228no—
400C4×D4—1228no—
401#117—21no—
402#117—21no—
403#117—612no—
404#117—612no—
405#117—1221no—
406#117—1221no—
407#117C4×D6112yes—
408#117C22⋊D6112yes—
409C2×C4⋊C4—612no—
410C2×C4⋊C4—612no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4D24412yes—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—1228no—
419C2×C22⋊C4—1228no—
420C2×C22⋊C4—1224no—
421C2×C22⋊C4—1221no—
422C2×C22⋊C4—1228no—
423C2×C22⋊C4—2448no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—1221no—
431C2×C42C4×D6112yescomplemented
432#100—1228no—
433C24—614no—
434C24—614no—
435C24—614no—
436C24—1222no—
437C24—1222no—
438C24—1222no—
439C24—1222no—
440C24—2444no—
441C24—2444no—
442C24D4×D6111yescharacteristic
443C2×D4—614no—
444C2×D4—614no—
445C2×D4—614no—
446C2×D4—614no—
447C2×D4—1222no—
448C2×D4—1222no—
449C2×D4—1222no—
450C2×D4—1222no—
451C2×D4—1222no—
452C2×D4—1222no—
453C2×D4—1222no—
454C2×D4—1222no—
455C2×D4—1222no—
456C2×D4—1222no—
457C2×D4—1222no—
458C2×D4—1222no—
459C2×D4—1222no—
460C2×D4—1222no—
461C2×D4—1222no—
462C2×D4—1222no—
463C2×D4—1222no—
464C2×D4—1222no—
465C2×D4—1222no—
466C2×D4—1222no—
467C2×D4—1222no—
468C2×D4—1222no—
469C2×D4—1222no—
470C2×D4—1222no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—42no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—12216no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—4884no—
481C22×C4—4884no—
482C22×C4—2444no—
483C22×C4—2441no—
484C22×C4—2441no—
485C22×C4C2×C4×D6111yescharacteristic
486C22×C4C2×C4×D6111yescharacteristic
487C22×C4C2×C4×D6111yescharacteristic
488C22×C4C2×D24411yescharacteristic
489C22×C4#1175822211yescharacteristic
490C22×C4#1175822211yescharacteristic
491C22×C4D4×D6111yescharacteristic
492C22×C4D4×D6111yescharacteristic
493C22×C4D4×D6111yescharacteristic
494C22×C4D4×D6111yescharacteristic
495C22×C4#1175822411yescharacteristic
496C22×C4Q8×D6111yescharacteristic
497C22×C4#1175822611yescharacteristic
498C22×C4C2×C22⋊D6111yescharacteristic
499M16—22no—
500M16—22no—
501M16—41no—
502M16—41no—
503M16—1222no—
504M16—1222no—
505M16—2441no—
506M16—2441no—
507C2×C8—22no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—1222no—
511C2×C8—2441no—
512C2×C8—2441no—
513C4⋊C4—22no—
514C4⋊C4—614no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—2441no—
519C4⋊C4—2441no—
520C4⋊C4#1175819814yescomplemented
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—12216no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C22⋊C4—24416no—
527C42—22no—
528C42—22no—
529C42—22no—
530C42—22no—
531C42—41no—
532C42—41no—
533C42—1222no—
534C42—1222no—
535C23—22no—
536C23—22no—
537C23—618no—
538C23—1224no—
539C23—1224no—
540C23—1224no—
541C23—1224no—
542C23—1224no—
543C23—1224no—
544C23—4882no—
545C23—4882no—
546C23—4884no—
547C23—4884no—
548C23—2444no—
549C23—2444no—
550C23—2448no—
551C23—2448no—
552C23—2444no—
553C23—2444no—
554C23C22⋊C4×D6111yescharacteristic
555C23C22⋊C4×D6111yescharacteristic
556C23C4⋊C4×D6111yescharacteristic
557C23#1451974511yescharacteristic
558C23#1451974711yescharacteristic
559C23#1451975911yescharacteristic
560C23#1451976211yescharacteristic
561D4—1224no—
562D4—1224no—
563D4—1224no—
564D4—1224no—
565D4—1224no—
566D4—1224no—
567D4—1224no—
568D4—1224no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—42no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—1224no—
578C2×C4—48816no—
579C2×C4—4882no—
580C2×C4—4882no—
581C2×C4—2444no—
582C2×C4—2442no—
583C2×C4—2442no—
584C2×C4—2442no—
585C2×C4C42×D6111yescharacteristic
586C2×C4C22⋊C4×D6111yescharacteristic
587C2×C4C22⋊C4×D6111yescharacteristic
588C2×C4C2×#1175819811yescharacteristic
589C2×C4C4⋊C4×D6111yescharacteristic
590C2×C4C4⋊C4×D6111yescharacteristic
591C2×C4#1451973411yescharacteristic
592C2×C4#1451973511yescharacteristic
593C2×C4#1451973711yescharacteristic
594C2×C4#1451973711yescharacteristic
595C2×C4C4×C22⋊D6111yescharacteristic
596C2×C4C4×C22⋊D6111yescharacteristic
597C2×C4#1451973911yescharacteristic
598C2×C4#1451973911yescharacteristic
599C2×C4C4×D24411yescharacteristic
600C2×C4C4×D24411yescharacteristic
601C2×C4#1451974511yescharacteristic
602C2×C4#1451974711yescharacteristic
603C2×C4#1451974811yescharacteristic
604C2×C4#1451975011yescharacteristic
605C2×C4#1451975011yescharacteristic
606C2×C4#1451975211yescharacteristic
607C2×C4#1451975311yescharacteristic
608C2×C4#1451975511yescharacteristic
609C2×C4#1451975511yescharacteristic
610C2×C4#1451975711yescharacteristic
611C2×C4#1451975911yescharacteristic
612C2×C4#1451976211yescharacteristic
613C8—42no—
614C8—2442no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—1228no—
624C22—4884no—
625C22—4884no—
626C22—4884no—
627C22—2448no—
628C22—2444no—
629C22—2444no—
630C22—2448no—
631C22—2448no—
632C22#95×D6111yescharacteristic
633C22#1683961711yescharacteristic
634C22#1683962411yescharacteristic
635C22#1683963311yescharacteristic
636C22#1683963611yescharacteristic
637C22#1683963811yescharacteristic
638C22#1683964011yescharacteristic
639C22#1683993112yes—
640C22#1683994112yes—
641C4—44no—
642C4—44no—
643C4—4882no—
644C4—2444no—
645C4#1683960911yescharacteristic
646C4C4×#1175819811yescharacteristic
647C4#1683961911yescharacteristic
648C4#1683962111yescharacteristic
649C4#1683963311yescharacteristic
650C4#1683963611yescharacteristic
651C4#1683963811yescharacteristic
652C4#1683964011yescharacteristic
653C2—21no—
654C2—21no—
655C2—21no—
656C2—21no—
657C2—2448no—
658C2#2144404011yescharacteristic
659C2#2144577412yes—
660C2#2144603012yes—
661C2#2144620611yescharacteristic
662C2#2144621611yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#339C2
socleC23×C61#120
prime radicalC23×D244C22
cosocleC23×C4×C61C23
hypercenterC2×#339D61
hypocenterC61#10749
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. #21445540C2semidirect
5. #21445539C2semidirect
6. C2×#16839522C2semidirect
7. C2×C61×#339C2semidirect
13. #16840236C4semidirect
22. C2×#14519693C4semidirect
24. #16839664C4semidirect
54. C2×#11758194C2×C4semidirect
69. C2×C4⋊Dic61C2×C4semidirect
86. C2×M16×C61C2×C4semidirect
100. C2×C42×C61C2×C4semidirect
175. C4⋊C4×C61C22⋊C4semidirect
193. C4⋊Dic61C22⋊C4semidirect
328. C2×#339D61semidirect
363. C61#10749semidirect
394. C2×M16C4×D61semidirect
431. C2×C42C4×D61semidirect
520. C4⋊C4#11758198semidirect

Maximal subgroups

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

subgroupindex
C2×#168402362
C22×#145196932
C2×#168396642
#214455402
#214455392
C2×#168395222
C2×C61×#3392
#1074961