Finite Group Databasebeta

← #29690567

Subgroups — #29690567

Order 15616.

858 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839818C211yesmaximal, characteristic
2#21448223C211yesmaximal, characteristic
3#382×D61C211yesmaximal, characteristic
4#21446589C211yesmaximal, characteristic, complemented
5#21446587C211yesmaximal, characteristic, complemented
6#21446585C211yesmaximal, characteristic, complemented
7#21446013C211yesmaximal, characteristic
8#21446010C211yesmaximal, characteristic
9#21446008C211yesmaximal, characteristic
10#21446005C211yesmaximal, characteristic
11#21445986C211yesmaximal, characteristic, complemented
12#21445984C211yesmaximal, characteristic, complemented
13#21445951C211yesmaximal, characteristic, complemented
14#21445951C211yesmaximal, characteristic, complemented
15C61×#1949C211yesmaximal, characteristic, complemented
16C2×#14519734—21no—
17C2×C4⋊C4×D61C2211yescharacteristic
18C2×C4⋊C4×D61C2211yescharacteristic
19C2×C42×D61C2211yescharacteristic
20#16839818C418yescomplemented
21C2×#14519711C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519709C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519687C2211yescharacteristic
31C2×#14519687C2211yescharacteristic
32#16839631C2211yescharacteristic
33#16839631C2211yescharacteristic
34#16839628C2211yescharacteristic
35#16839627C2211yescharacteristic
36#16839627C2211yescharacteristic
37#16839626—21no—
38#16839626—21no—
39#16839626—21no—
40#16839621—21no—
41#16839619C2211yescharacteristic
42#16839619C2211yescharacteristic
43C4×#11758196—21no—
44C4×C4⋊Dic61C2211yescharacteristic
45#95×D61—21no—
46#95×D61—21no—
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C61×#382C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×C4×D61—21no—
61C22×C4×D61—21no—
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519734—44no—
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C4⋊C4×D61—41no—
79C4⋊C4×D61—41no—
80C4⋊C4×D61—41no—
81C4⋊C4×D61—41no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61D411yescharacteristic
86C2×C4×Dic61D411yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88C42×D61C2×C414yes—
89C42×D61Q814yes—
90#14519711—41no—
91#14519710—41no—
92#14519710—41no—
93#14519709—41no—
94#14519708—41no—
95#14519708—41no—
96C4⋊#92418C2×C414yescomplemented
97#14519689C2×C414yes—
98#14519689C2×C414yes—
99#14519687C2×C414yescomplemented
100#14519687C2×C414yescomplemented
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110C22×C8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C42×C61—21no—
117C2×C42×C61C2311yescharacteristic
118#107×C61—41no—
119#106×C61—41no—
120C4⋊C8×C61C2×C414yescomplemented
121#95×C61—21no—
122#95×C61—21no—
123#95×C61—21no—
124C23×D61C2×D411yescharacteristic
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2411yescharacteristic
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61C2×D411yescharacteristic
137C22×Dic61C2×D411yescharacteristic
138C22×Dic61C2×D411yescharacteristic
139C2×C4×D61—22no—
140C2×C4×D61—22no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61—21no—
144C2×C4×D61—21no—
145C2×C4×D61—41no—
146C2×C4×D61—41no—
147C2×C4×D61—42no—
148C2×C4×D61—42no—
149C2×C4×D61—42no—
150C2×C4×D61—42no—
151C2×C4×D61—42no—
152C2×C4×D61—42no—
153C2×C4×D61C4⋊C414yes—
154C2×C4×D61C4⋊C414yes—
155C2×C4×D61C22×C412yes—
156C2×C4×D61C2×Q812yes—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61C22×C412yes—
162C2×C8×C61C22×C412yes—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C42×C61—42no—
172C42×C61C22×C412yes—
173C42×C61C2×Q812yes—
174#11758198—42no—
175#11758198—42no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184#11758196—42no—
185#11758196—42no—
186#11758196—42no—
187#11758196—42no—
188#11758196—42no—
189#11758196—42no—
190C4×Dic61—42no—
191C4×Dic61C4⋊C414yes—
192C4×Dic61C4⋊C414yes—
193C4×Dic61C22×C412yes—
194C4×Dic61C2×Q812yes—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418C22×C412yes—
200C2×#92418C22×C412yes—
201C23×C61C22×D411yescharacteristic
202C22×D61—21no—
203C22×D61—21no—
204C22×D61—21no—
205C22×D61—21no—
206C22×D61C2×C4⋊C412yes—
207C22×D61AGL(1,ℤ/8)12yes—
208C22×D61#13712yes—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61C2×C4⋊C412yes—
226C2×C4×C61C2×C4⋊C412yes—
227C2×C4×C61C23×C411yescharacteristic
228C2×C4×C61C22×Q811yescharacteristic
229C2×C4×C61H(5,𝔽2)11yescharacteristic
230C2×C4×C61H(5,𝔽2)11yescharacteristic
231C2×C4×C612−1+411yescharacteristic
232C2×C4×C612−1+411yescharacteristic
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61C2×C4⋊C412yes—
252C2×Dic61C2×C4⋊C412yes—
253C2×Dic61C2×C4⋊C412yes—
254C4×D61—28no—
255C4×D61—22no—
256C4×D61—22no—
257C4×D61—22no—
258C4×D61—22no—
259C4×D61—44no—
260C4×D61—84no—
261C4×D61—84no—
262C8×C61—22no—
263C8×C61—22no—
264#92418—22no—
265#92418—22no—
266#21986—611nomaximal, Sylow
267C22×C61C22×C4⋊C411yescharacteristic
268C22×C61#53511yescharacteristic
269C22×C61#53611yescharacteristic
270C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C61C2×#13711yescharacteristic
272C22×C61#57511yescharacteristic
273C22×C61#57511yescharacteristic
274C2×D61—22no—
275C2×D61—22no—
276C2×D61—22no—
277C2×D61—22no—
278C2×D61—22no—
279C2×D61—22no—
280C2×D61#42814yes—
281C4×C61—22no—
282C4×C61—22no—
283C4×C61—81no—
284C4×C61—81no—
285C4×C61—81no—
286C4×C61—81no—
287C4×C61#52011yescharacteristic
288C4×C61#52011yescharacteristic
289C4×C61#54411yescharacteristic
290C4×C61#54411yescharacteristic
291Dic61—22no—
292Dic61—22no—
293Dic61—22no—
294Dic61—81no—
295Dic61—81no—
296Dic61—81no—
297Dic61—81no—
298C2×#432—611no—
299#2285—611no—
300C2×#382—611no—
301#1949—611no—
302#1949—611no—
303#1949—611no—
304#1949D6111yescharacteristic, complemented
305#1853—611no—
306#1853—611no—
307#1852—611no—
308#1852—611no—
309#1847—611no—
310#1847—611no—
311#1836—611no—
312#1836—611no—
313C2×C61#231711yescharacteristic
314C2×C61C2×#42811yescharacteristic
315C2×C61#291111yescharacteristic
316C2×C61#321311yescharacteristic
317C2×C61#321511yescharacteristic
318C2×C61#323411yescharacteristic
319C2×C61#323611yescharacteristic
320D61—24no—
321C2×#117—1221no—
322C22×C4⋊C4—611no—
323C22×C4⋊C4—611no—
324C22×C42—611no—
325#432—618no—
326C2×#107—611no—
327C2×#107—611no—
328C2×#107—611no—
329C2×#107C2×D6111yescharacteristic
330C2×#106—611no—
331C2×#106—611no—
332C2×#106—611no—
333C2×#106C2×D6111yescharacteristic
334C2×C4⋊C8—611no—
335C2×C4⋊C8C2×D6111yescharacteristic
336C2×C22⋊C8—611no—
337C2×C22⋊C8—611no—
338C2×#97—611no—
339C2×#97—611no—
340#384—611no—
341#384—611no—
342#382—611no—
343#382—611no—
344#382—611no—
345#382—1221no—
346#382—1221no—
347#382—1221no—
348#382C2×D6111yescharacteristic
349#380—611no—
350#380—611no—
351#380—1221no—
352C4×C4⋊C4—611no—
353C4×C4⋊C4—1221no—
354C4×C4⋊C4C2×D6111yescharacteristic
355C2×#95—1221no—
356C2×#95—1221no—
357#340—611no—
358#340—611no—
359#340—611no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340C2×D6111yescharacteristic
364#340C2×D6111yescharacteristic
365C61#2198611yescharacteristic, complemented, Sylow
366C23×C4—611no—
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—1221no—
370C23×C4—1221no—
371C22×C8—611no—
372C22×C8—611no—
373C22×C8C22×D6111yescharacteristic
374C22×C8C22×D6111yescharacteristic
375#117—2444no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4—611no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4—1221no—
385C2×C4⋊C4—1221no—
386C2×C4⋊C4—2441no—
387C2×C4⋊C4—2441no—
388C2×C4⋊C4—2441no—
389C2×C4⋊C4—2441no—
390C2×C4⋊C4C22×D6111yescharacteristic
391C2×C4⋊C4C22×D6111yescharacteristic
392C2×C4⋊C4C22×D6111yescharacteristic
393C2×C4⋊C4C22×D6111yescharacteristic
394C2×C22⋊C4—1221no—
395C2×C22⋊C4—1221no—
396C2×C42—21no—
397C2×C42—611no—
398C2×C42—611no—
399C2×C42—611no—
400C2×C42—614no—
401C2×C42—614no—
402C2×C42—1221no—
403C2×C42C22×D6111yescharacteristic
404#107—41no—
405#107—2441no—
406#107—2441no—
407#107—2441no—
408#106—41no—
409#106—2441no—
410#106—2441no—
411#106—2441no—
412C4⋊C8—614no—
413C4⋊C8C4×D6114yescomplemented
414C22⋊C8—614no—
415C22⋊C8—614no—
416#97—614no—
417#97—614no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—1221no—
422#95—1221no—
423#95—1221no—
424#95—1221no—
425#95—1221no—
426#95—1221no—
427#95—1221no—
428#95—1221no—
429#95—1221no—
430C24—611no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—612no—
439C22×C4—612no—
440C22×C4—614no—
441C22×C4—614no—
442C22×C4—1222no—
443C22×C4—1222no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—2441no—
453C22×C4—2441no—
454C22×C4—2442no—
455C22×C4—2442no—
456C22×C4—2442no—
457C22×C4—2442no—
458C22×C4—2442no—
459C22×C4—2442no—
460C22×C4D4×D6111yescharacteristic
461C22×C4D4×D6111yescharacteristic
462C22×C4C23×D6111yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—612no—
468C2×C8—612no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8C2×C4×D6112yes—
474C2×C8C2×C4×D6112yes—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—2442no—
492C4⋊C4—2442no—
493C4⋊C4—2442no—
494C4⋊C4—2442no—
495C4⋊C4—2442no—
496C4⋊C4—2442no—
497C22⋊C4—2442no—
498C22⋊C4—2442no—
499C42—42no—
500C42—612no—
501C42—612no—
502C42—614no—
503C42—614no—
504C42—2442no—
505C42C2×C4×D6112yes—
506C42Q8×D6112yes—
507C23—612no—
508C23—612no—
509C23—612no—
510C23—1221no—
511C23—1221no—
512C23—1221no—
513C23—1221no—
514C23C2×D4×D6111yescharacteristic
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—612no—
532C2×C4—612no—
533C2×C4—612no—
534C2×C4—1228no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1222no—
542C2×C4—1222no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—4884no—
546C2×C4—4884no—
547C2×C4—2444no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4C4⋊C4×D6112yes—
561C2×C4C4⋊C4×D6112yes—
562C2×C4C22×C4×D6111yescharacteristic
563C2×C4C2×Q8×D6111yescharacteristic
564C2×C4#1451982211yescharacteristic
565C2×C4#1451982311yescharacteristic
566C2×C4#1451982411yescharacteristic
567C2×C4#1451982511yescharacteristic
568C8—22no—
569C8—22no—
570C8—1222no—
571C8—1222no—
572C22—614no—
573C22—1222no—
574C22—1222no—
575C22—1222no—
576C22—1222no—
577C22—1222no—
578C22—1222no—
579C22C2×C4⋊C4×D6111yescharacteristic
580C22#1684032811yescharacteristic
581C22#1684033511yescharacteristic
582C22AGL(1,ℤ/8)×D6111yescharacteristic
583C22#137×D6111yescharacteristic
584C22#1684055911yescharacteristic
585C22#1684055911yescharacteristic
586C4—22no—
587C4—22no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—1222no—
593C4—1222no—
594C4—1222no—
595C4—4881no—
596C4—4881no—
597C4—4881no—
598C4—4881no—
599C4#1684024111yescharacteristic
600C4#1684024411yescharacteristic
601C4#1684038911yescharacteristic
602C4#1684039211yescharacteristic
603C2—1224no—
604C2#2144844111yescharacteristic
605C2#428×D6111yescharacteristic
606C2#2145440711yescharacteristic
607C2#2145680411yescharacteristic
608C2#2145682011yescharacteristic
609C2#2145700711yescharacteristic
610C2#2145702311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1949C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1949D61
hypocenterC61#21986
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #21446589C2semidirect
5. #21446587C2semidirect
6. #21446585C2semidirect
11. #21445986C2semidirect
12. #21445984C2semidirect
13. #21445951C2semidirect
14. #21445951C2semidirect
15. C61×#1949C2semidirect
20. #16839818C4semidirect
96. C4⋊#92418C2×C4semidirect
99. #14519687C2×C4semidirect
100. #14519687C2×C4semidirect
120. C4⋊C8×C61C2×C4semidirect
304. #1949D61semidirect
365. C61#21986semidirect
413. C4⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398182
#214482232
#382×D612
#214465892
#214465872
#214465852
#214460132
#214460102
#214460082
#214460052
#214459862
#214459842
#214459512
C61×#19492
#2198661