Finite Group Databasebeta

← #29687891

Subgroups — #29687891

Order 15616.

884 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839891C211yesmaximal, characteristic, complemented
2C2×#16839832C211yesmaximal, characteristic
3C4×#14519765C211yesmaximal, characteristic
4#21446758C211yesmaximal, characteristic, complemented
5#21446616C211yesmaximal, characteristic
6#21446430C211yesmaximal, characteristic, complemented
7#21446430C211yesmaximal, characteristic, complemented
8#21446423C211yesmaximal, characteristic, complemented
9#21446423C211yesmaximal, characteristic, complemented
10#21445601C211yesmaximal, characteristic, complemented
11#21445599C211yesmaximal, characteristic, complemented
12#21445594C211yesmaximal, characteristic, complemented
13#21445589C211yesmaximal, characteristic, complemented
14C4×#14519688C211yesmaximal, characteristic, complemented
15C61×#1831C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×#14519765C411yescharacteristic
19C2×C4×Dic122C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21#16839891—24no—
22#16839832—24no—
23C2×#14519706C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519689C2211yescharacteristic
26C2×#14519689C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519688C2211yescharacteristic
32C2×#14519688C2211yescharacteristic
33C2×#14519688C2211yescharacteristic
34C2×#14519688C2211yescharacteristic
35C2×#14519687C2211yescharacteristic
36C2×C4×#92418C2211yescharacteristic
37C2×C4×#92418C2211yescharacteristic
38C2×C8×Dic61C2211yescharacteristic
39#16839668C411yescharacteristic
40#16839664C411yescharacteristic
41#16839653C411yescharacteristic
42#16839653C411yescharacteristic
43#16839653C411yescharacteristic
44#16839653C411yescharacteristic
45#16839628C411yescharacteristic
46C4×#11758198C2211yescharacteristic
47C4×#11758198C2211yescharacteristic
48C4×#11758198C2211yescharacteristic
49C4×#11758198C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×C4⋊C8×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C43×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Dic122C2×C411yescharacteristic
62C22×D244C2×C411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C2×#11758189—22no—
66C2×#11758189—22no—
67C2×#11758189—22no—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C2×C8×D61—22no—
73C2×C8×D61—22no—
74C2×C8×D61—22no—
75#14519765—24no—
76C4×Dic122—22no—
77C4×Dic122—22no—
78C4×D244—22no—
79C4×D244—22no—
80C2×C4⋊Dic61C2×C411yescharacteristic
81C2×C4⋊Dic61C2×C411yescharacteristic
82C2×#11758196C2×C411yescharacteristic
83C2×#11758196C2×C411yescharacteristic
84C2×#11758198C2×C411yescharacteristic
85C2×#11758198C2×C411yescharacteristic
86C2×#11758198C2×C411yescharacteristic
87C2×#11758198C2×C411yescharacteristic
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×#11758198C2×C411yescharacteristic
93C2×#11758198C2×C411yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95C2×C4×Dic61C2311yescharacteristic
96#14519706—22no—
97#14519706—22no—
98#14519689—22no—
99#14519689—22no—
100#14519689—22no—
101#14519689—22no—
102#14519689—22no—
103#14519689—22no—
104#14519688—22no—
105#14519688—22no—
106#14519688—22no—
107#14519688D414yes—
108#14519687—22no—
109C4×#92418—22no—
110C4×#92418—22no—
111C8×Dic61—22no—
112#14519684C2×C411yescharacteristic
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124C2×C42×C61C2×C411yescharacteristic
125C2×C42×C61C2×C411yescharacteristic
126C2×C42×C61C2×C411yescharacteristic
127C2×C42×C61C2×C411yescharacteristic
128C2×C42×C61C2311yescharacteristic
129C2×C42×C61C2311yescharacteristic
130C2×C42×C61C2311yescharacteristic
131C4⋊C8×C61—22no—
132C4⋊C8×C61—22no—
133C23×D61C22×C411yescharacteristic
134C23×D61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C2411yescharacteristic
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148C2×D244—22no—
149C2×D244—22no—
150C2×D244—41no—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×Dic122—22no—
164C2×Dic122—22no—
165C2×Dic122—41no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C42×C61—22no—
179C42×C61—22no—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61—21no—
183C42×C61—21no—
184C42×C61—41no—
185C42×C61—41no—
186C42×C61C2×D412yes—
187C42×C61#4112yes—
188#11758198—22no—
189#11758198—22no—
190#11758198—22no—
191#11758198—22no—
192#11758198—22no—
193#11758198—22no—
194#11758198—22no—
195#11758198—41no—
196#11758198—41no—
197#11758198M1614yescomplemented
198C4⋊Dic61—22no—
199C4⋊Dic61—22no—
200#11758196—22no—
201#11758196—22no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418C2×D412yes—
213C2×#92418C2×D412yes—
214C2×#92418#4112yes—
215C2×#92418#4112yes—
216C2×#92418#4112yes—
217C2×#92418#4112yes—
218#11758189—44no—
219C8×D61—44no—
220C23×C61C23×C411yescharacteristic
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61—21no—
226C22×D61—21no—
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—21no—
232C22×D61—21no—
233C22×D61—21no—
234C22×D61C2×M1612yes—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61C4×D412yes—
250C2×C4×C61C4×D412yes—
251C2×C4×C61C2×M1612yes—
252C2×C4×C61#13112yes—
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C2×#4111yescharacteristic
255C2×C4×C61C2×#4111yescharacteristic
256C2×C4×C61C2×#4111yescharacteristic
257C2×C4×C61C2×#4111yescharacteristic
258C2×C4×C61C2×#4111yescharacteristic
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
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×Dic61C2×M1612yes—
277D244—44no—
278C4×D61—41no—
279C4×D61—41no—
280C4×D61—41no—
281C4×D61—41no—
282C4×D61—41no—
283C4×D61—41no—
284C4×D61—41no—
285C4×D61—41no—
286Dic122—44no—
287C8×C61—41no—
288C8×C61—41no—
289C8×C61—41no—
290C8×C61—41no—
291#92418—22no—
292#92418—22no—
293#92418—22no—
294#92418#12414yescomplemented
295#21632—611nomaximal, Sylow
296C22×C61C2×C4×D411yescharacteristic
297C22×C61C4×#4111yescharacteristic
298C22×C61C4×#4111yescharacteristic
299C22×C61C22×M1611yescharacteristic
300C22×C61C2×#13111yescharacteristic
301C22×C61#56811yescharacteristic
302C22×C61#56811yescharacteristic
303C2×D61—22no—
304C2×D61—22no—
305C2×D61—22no—
306C2×D61—41no—
307C2×D61—41no—
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C2×D61—41no—
312C2×D61—41no—
313C2×D61—41no—
314C2×D61—41no—
315C2×D61—41no—
316C2×D61—41no—
317C4×C61—22no—
318C4×C61—22no—
319C4×C61—22no—
320C4×C61—22no—
321C4×C61—41no—
322C4×C61—41no—
323C4×C61C2×#12411yescharacteristic
324C4×C61#52911yescharacteristic
325C4×C61#52911yescharacteristic
326C4×C61#53211yescharacteristic
327Dic61—22no—
328Dic61—41no—
329Dic61—41no—
330Dic61—41no—
331Dic61—41no—
332Dic61—41no—
333C2×#446—611no—
334C2×#435—611no—
335C4×#124—611no—
336#1985—611no—
337#1955—611no—
338#1924—611no—
339#1924—611no—
340#1923—611no—
341#1923—611no—
342#1831D6111yescharacteristic, complemented
343#1753—611no—
344#1753—611no—
345#1752—611no—
346C8×C22⋊C4—611no—
347C4×#97—611no—
348C2×C61C4×#12411yescharacteristic
349C2×C61D4×M1611yescharacteristic
350C2×C61#293511yescharacteristic
351C2×C61#296511yescharacteristic
352C2×C61#296711yescharacteristic
353C2×C61#296811yescharacteristic
354C2×C61#297011yescharacteristic
355D61—42no—
356D61—81no—
357C22×M16—611no—
358C23×C8—611no—
359C2×#124—611no—
360C2×C4×Q8—611no—
361C2×C4×D4—611no—
362#446—1224no—
363#435—1224no—
364C2×C4⋊C8—611no—
365C2×C4⋊C8—611no—
366C2×C4⋊C8C2×D6111yescharacteristic
367C2×C4⋊C8C2×D6111yescharacteristic
368C2×C22⋊C8—611no—
369C2×C22⋊C8—611no—
370C2×C22⋊C8—611no—
371C2×C22⋊C8—611no—
372C2×C22⋊C8—611no—
373C2×C22⋊C8—611no—
374C2×#97—611no—
375C2×#97—611no—
376C2×#97—611no—
377C2×#97—611no—
378C2×#97—611no—
379C2×C4×C8—611no—
380C2×C4×C8—611no—
381C2×C4×C8—611no—
382#391—611no—
383#390—611no—
384#388—611no—
385#388—611no—
386#388—611no—
387#388—611no—
388#382—611no—
389C4×C22⋊C4—611no—
390C4×C22⋊C4—611no—
391C4×C22⋊C4—611no—
392C4×C22⋊C4—611no—
393C43C2×D6111yescharacteristic
394#336—611no—
395#336—611no—
396#336—611no—
397#336—611no—
398#336C2×D6111yescharacteristic
399#336C2×D6111yescharacteristic
400#336C2×D6111yescharacteristic
401#336C2×D6111yescharacteristic
402C61#2163211yescharacteristic, complemented, Sylow
403C22×Q8—611no—
404C22×D4—611no—
405C23×C4—611no—
406C23×C4—611no—
407C2×M16—1222no—
408C2×M16—1222no—
409C2×M16—1222no—
410C22×C8—611no—
411C22×C8—611no—
412C22×C8—611no—
413C22×C8—611no—
414C22×C8—1222no—
415C22×C8—1222no—
416C22×C8—1222no—
417C22×C8C22×D6111yescharacteristic
418C22×C8C22×D6111yescharacteristic
419C22×C8C22×D6111yescharacteristic
420C22×C8C22×D6111yescharacteristic
421#124—1224no—
422C4×Q8—1222no—
423C4×Q8—1222no—
424C4×D4—1222no—
425C4×D4—1222no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—611no—
430C2×C22⋊C4—611no—
431C2×C22⋊C4—611no—
432C2×C22⋊C4—611no—
433C2×C22⋊C4—611no—
434C2×C22⋊C4—611no—
435C2×C22⋊C4—611no—
436C2×C22⋊C4—611no—
437C2×C22⋊C4—611no—
438C2×C22⋊C4—611no—
439C2×C22⋊C4—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42C4×D6111yescharacteristic
443C2×C42C4×D6111yescharacteristic
444C2×C42C4×D6111yescharacteristic
445C2×C42C4×D6111yescharacteristic
446C2×C42C22×D6111yescharacteristic
447C2×C42C22×D6111yescharacteristic
448C2×C42C22×D6111yescharacteristic
449C4⋊C8—22no—
450C4⋊C8—22no—
451C4⋊C8—1222no—
452C4⋊C8—1222no—
453C22⋊C8—1222no—
454C22⋊C8—1222no—
455C22⋊C8—1222no—
456C22⋊C8—1222no—
457C22⋊C8—1222no—
458C22⋊C8—1222no—
459#97—614no—
460#97—1222no—
461#97—1222no—
462#97—1222no—
463#97—1222no—
464C4×C8—1222no—
465C4×C8—1222no—
466C4×C8—1222no—
467#95—611no—
468#95—611no—
469#95—611no—
470#95—611no—
471#95—611no—
472#95—611no—
473#95—611no—
474#95—611no—
475C24—611no—
476C24—611no—
477C2×Q8—1222no—
478C2×Q8—1222no—
479C2×Q8—2441no—
480C2×D4—1222no—
481C2×D4—1222no—
482C2×D4—2441no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4—1221no—
501C22×C4C2×C4×D6111yescharacteristic
502C22×C4C2×C4×D6111yescharacteristic
503C22×C4C2×C4×D6111yescharacteristic
504C22×C4C2×C4×D6111yescharacteristic
505C22×C4C2×C4×D6111yescharacteristic
506C22×C4C2×C4×D6111yescharacteristic
507C22×C4C23×D6111yescharacteristic
508M16—2444no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—612no—
522C2×C8—612no—
523C2×C8—612no—
524C2×C8—612no—
525C2×C8—612no—
526C2×C8—612no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—1221no—
530C2×C8—1221no—
531C2×C8—1221no—
532C2×C8—1221no—
533C2×C8—2444no—
534C4⋊C4—1222no—
535C4⋊C4—1222no—
536C4⋊C4—1222no—
537C4⋊C4—1222no—
538C22⋊C4—614no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C22⋊C4—1222no—
542C22⋊C4—1222no—
543C22⋊C4—1222no—
544C22⋊C4—1222no—
545C22⋊C4—1222no—
546C22⋊C4—2441no—
547C22⋊C4—2441no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—22no—
553C42—22no—
554C42—41no—
555C42—41no—
556C42—1221no—
557C42—1221no—
558C42—1221no—
559C42—1221no—
560C42D4×D6112yes—
561C42#1175822612yes—
562C23—612no—
563C23—1221no—
564C23—1221no—
565C23—1221no—
566C23—1221no—
567C23—1221no—
568C23—1221no—
569C23—1221no—
570C23—1221no—
571C23—1221no—
572C23—1221no—
573C23—1221no—
574C23—1221no—
575C23—1221no—
576C23C22×C4×D6111yescharacteristic
577Q8—2444no—
578D4—2444no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—612no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—1221no—
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—1221no—
610C2×C4—1221no—
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#1451973912yes—
620C2×C4#1451973912yes—
621C2×C4M16×D6112yes—
622C2×C4#1451978312yes—
623C2×C4C2×D4×D6111yescharacteristic
624C2×C4#41×D6111yescharacteristic
625C2×C4#41×D6111yescharacteristic
626C2×C4#41×D6111yescharacteristic
627C2×C4#41×D6111yescharacteristic
628C2×C4C2×#1175822611yescharacteristic
629C8—41no—
630C8—41no—
631C8—41no—
632C8—41no—
633C8—614no—
634C8—1222no—
635C8—1222no—
636C8—1222no—
637C22—1222no—
638C22—1222no—
639C22—1222no—
640C22—2441no—
641C22—2441no—
642C22—2441no—
643C22—2441no—
644C22—2441no—
645C22—2441no—
646C22—2441no—
647C22—2441no—
648C22—2441no—
649C22—2441no—
650C22—2441no—
651C22C2×#1451973911yescharacteristic
652C22#1684023011yescharacteristic
653C22#1684023011yescharacteristic
654C22C2×M16×D6111yescharacteristic
655C22C2×#1451978311yescharacteristic
656C22#1684052811yescharacteristic
657C22#1684052811yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—41no—
663C4—41no—
664C4—1222no—
665C4—2441no—
666C4—2441no—
667C4—2441no—
668C4—2441no—
669C4—2441no—
670C4#124×D6111yescharacteristic
671C4#1684029711yescharacteristic
672C4#1684029711yescharacteristic
673C4#1684031111yescharacteristic
674C2—4881no—
675C2—2442no—
676C2#2144835811yescharacteristic
677C2#2145455411yescharacteristic
678C2#2145456211yescharacteristic
679C2#2145478311yescharacteristic
680C2#2145479911yescharacteristic
681C2#2145480811yescharacteristic
682C2#2145482811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1831C2
prime radicalC22×D244C2×C4
cosocleC22×C4×C61C24
hypercenter#1831D61
hypocenterC61#21632
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1831

Complements

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

NH ≅ G/Ntype
1. C2×#16839891C2semidirect
4. #21446758C2semidirect
6. #21446430C2semidirect
7. #21446430C2semidirect
8. #21446423C2semidirect
9. #21446423C2semidirect
10. #21445601C2semidirect
11. #21445599C2semidirect
12. #21445594C2semidirect
13. #21445589C2semidirect
14. C4×#14519688C2semidirect
15. C61×#1831C2semidirect
197. #11758198M16semidirect
294. #92418#124semidirect
342. #1831D61semidirect
402. C61#21632semidirect

Maximal subgroups

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

subgroupindex
C2×#168398912
C2×#168398322
C4×#145197652
#214467582
#214466162
#214464302
#214464232
#214456012
#214455992
#214455942
#214455892
C4×#145196882
C61×#18312
#2163261