Finite Group Databasebeta

← #29749898

Subgroups — #29749898

Order 15616.

868 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840123C211yesmaximal, characteristic, complemented
2#21449663C211yesmaximal, characteristic, complemented
3#21449611C211yesmaximal, characteristic, complemented
4#21447202C211yesmaximal, characteristic, complemented
5#21447145C211yesmaximal, characteristic, complemented
6#21447132C211yesmaximal, characteristic, complemented
7#21446893C211yesmaximal, characteristic
8#21446682C211yesmaximal, characteristic
9#21446516C211yesmaximal, characteristic, complemented
10#21446513C211yesmaximal, characteristic, complemented
11#21446497C211yesmaximal, characteristic, complemented
12#21446167C211yesmaximal, characteristic
13#21446073C211yesmaximal, characteristic, complemented
14#21445687C211yesmaximal, characteristic, complemented
15C2×C61×#440C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×#14519776C2211yescharacteristic
18C2×#14519766C2211yescharacteristic
19C2×#14519756—21no—
20#16840123—24no—
21C2×#14519710C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519701C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519687C2211yescharacteristic
30C2×C8×Dic61C2211yescharacteristic
31#16839697—21no—
32#16839688—21no—
33#16839685—21no—
34#16839674—21no—
35#16839669C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839665C2211yescharacteristic
38#16839664C2211yescharacteristic
39#16839663C2211yescharacteristic
40#16839661C2211yescharacteristic
41#16839660C2211yescharacteristic
42#16839658C2211yescharacteristic
43#16839653—21no—
44#16839653—21no—
45#16839635—21no—
46C4×#11758196C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839516C2211yescharacteristic
53C22×SD16×C61C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C61×#440—24no—
57C2×#107×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic
61C22×Dic122—21no—
62C22×D244C2311yescharacteristic
63C2×#11758199—22no—
64C2×#11758199—22no—
65C2×#11758199—41no—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519776—22no—
69#14519776—41no—
70#14519766—22no—
71#14519766—41no—
72#14519756—44no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196D411yescharacteristic
81C2×#11758196D411yescharacteristic
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×C4×Dic61C2311yescharacteristic
93C2×C4×Dic61C2311yescharacteristic
94#14519710—41no—
95#14519706—22no—
96#14519701—22no—
97#14519701—22no—
98#14519699—22no—
99#14519699—22no—
100#14519698—22no—
101#14519697—22no—
102#14519687—22no—
103C8×Dic61—22no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684D411yescharacteristic
110#14519684D411yescharacteristic
111C22×Q8×C61C2311yescharacteristic
112C22×D4×C61C2311yescharacteristic
113C23×C4×C61—21no—
114C2×SD16×C61—22no—
115C2×SD16×C61—22no—
116C2×SD16×C61—22no—
117C22×C8×C61C2311yescharacteristic
118C22×C8×C61C2311yescharacteristic
119C4×Q8×C61—22no—
120C4×Q8×C61—41no—
121C4×D4×C61—22no—
122C4×D4×C61—41no—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C22⋊C4×C61—21no—
127C2×C42×C61—21no—
128C2×C42×C61C2311yescharacteristic
129#107×C61—22no—
130#103×C61D414yes—
131#102×C61—22no—
132#97×C61—22no—
133C24×C61—21no—
134C23×D61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61C2×D412yes—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61#4112yes—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—42no—
151C22×C4×C61—42no—
152C22×C4×C61—81no—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2411yescharacteristic
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61C2×D411yescharacteristic
160C22×Dic61C2×D411yescharacteristic
161C22×Dic61C2×D411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163C2×D244—21no—
164C2×D244—21no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×Dic122—42no—
170C2×Dic122—42no—
171C2×Dic122—81no—
172SD16×C61—28no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61C2×D412yes—
178C2×C8×C61#4112yes—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—42no—
183C4⋊C4×C61C2×D412yes—
184C22⋊C4×C61—42no—
185C42×C61—21no—
186C42×C61—21no—
187C42×C61—42no—
188C22⋊Dic61—42no—
189C22⋊Dic61—42no—
190C22⋊Dic61—42no—
191C22⋊Dic61—81no—
192#11758199—44no—
193#11758198—42no—
194#11758198—42no—
195#11758198—42no—
196#11758198—42no—
197#11758198—81no—
198#11758198—81no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—42no—
206#11758196—22no—
207#11758196—41no—
208#11758196—42no—
209#11758196—42no—
210#11758196—81no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418#4112yes—
221C23×C61—22no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61C22×D411yescharacteristic
229C22×D61—41no—
230C22×D61—41no—
231C22×D61—41no—
232C22×D61—41no—
233C22×D61—41no—
234C22×D61—41no—
235C22×D61—41no—
236Q8×C61—22no—
237Q8×C61—22no—
238Q8×C61—41no—
239Q8×C61—41no—
240D4×C61—22no—
241D4×C61—22no—
242D4×C61—41no—
243D4×C61—41no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—41no—
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—84no—
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61C2×#4111yescharacteristic
264C2×C4×C61H(5,𝔽2)11yescharacteristic
265C2×C4×C612−1+411yescharacteristic
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×Dic61—21no—
277C2×Dic61—41no—
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×Dic61AGL(1,ℤ/8)12yes—
287D244—41no—
288D244—41no—
289D244—41no—
290D244—41no—
291Dic122—84no—
292C8×C61—22no—
293C8×C61—22no—
294#92418—22no—
295#92418—41no—
296#26844—611nomaximal, Sylow
297C22×C61—42no—
298C22×C61—42no—
299C22×C61—42no—
300C22×C61—81no—
301C22×C61—81no—
302C22×C61—81no—
303C22×C61—81no—
304C22×C61#53211yescharacteristic
305C22×C61D4211yescharacteristic
306C22×C61#54811yescharacteristic
307C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
308C22×C61#57511yescharacteristic
309C22×C61#57611yescharacteristic
310C22×C61#57811yescharacteristic
311C2×D61—81no—
312C2×D61—81no—
313C2×D61—81no—
314C2×D61—81no—
315C2×D61—81no—
316C2×D61—81no—
317C2×D61—81no—
318C4×C61—42no—
319C4×C61—42no—
320C4×C61—41no—
321C4×C61—41no—
322C4×C61—81no—
323C4×C61#52511yescharacteristic
324C4×C61#54211yescharacteristic
325C4×C61#54711yescharacteristic
326C4×C61#55111yescharacteristic
327Dic61—22no—
328Dic61—41no—
329Dic61—41no—
330Dic61—41no—
331Dic61—81no—
332Dic61—81no—
333Dic61—81no—
334C2×#489—611no—
335C2×#440D6111yescharacteristic, complemented
336#2452—611no—
337#2448—611no—
338#2067—611no—
339#2057—611no—
340#2055—611no—
341#2012—611no—
342#1970—611no—
343#1936—611no—
344#1936—611no—
345#1933—611no—
346#1879—611no—
347#1863—611no—
348#1770—611no—
349C2×C61—82no—
350C2×C61#246111yescharacteristic
351C2×C61#317511yescharacteristic
352C2×C61#318011yescharacteristic
353C2×C61#327411yescharacteristic
354C2×C61#327711yescharacteristic
355C2×C61#336711yescharacteristic
356C2×C61#337011yescharacteristic
357D61—161no—
358C22×SD16C2×D6111yescharacteristic
359C22×D8—611no—
360C2×C4⋊Q8—611no—
361C2×#124—611no—
362C2×C22⋊Q8—1221no—
363C2×C4×Q8C2×D6111yescharacteristic
364C2×C4×D4C2×D6111yescharacteristic
365#489—1224no—
366#440—24no—
367C2×#107—611no—
368C2×#107C2×D6111yescharacteristic
369C2×C4⋊C8—611no—
370C2×#103—611no—
371C2×#103—611no—
372C2×#103C2×D6111yescharacteristic
373C2×#102—611no—
374C2×#102—611no—
375C2×#102—611no—
376C2×#102—611no—
377C2×#102C2×D6111yescharacteristic
378C2×#97—611no—
379C2×#97C2×D6111yescharacteristic
380C2×C4×C8—611no—
381#399—1221no—
382#397—1221no—
383#396—1221no—
384#393—1221no—
385#391—611no—
386#390—611no—
387#390—611no—
388#390—611no—
389#390—611no—
390#389—611no—
391#389—611no—
392#389—611no—
393#388—1221no—
394#388—1221no—
395#385—1221no—
396C4×C4⋊C4—611no—
397#340—611no—
398#340—611no—
399#340—611no—
400#340—611no—
401#336—611no—
402#336—611no—
403C61#2684411yescharacteristic, complemented, Sylow
404C22×Q8—1221no—
405C22×Q8C22×D6111yescharacteristic
406C22×D4—611no—
407C22×D4C22×D6111yescharacteristic
408C23×C4—21no—
409C2×SD16—22no—
410C2×SD16—22no—
411C2×SD16—22no—
412C2×D8—1222no—
413C2×D8—1222no—
414C2×D8—2441no—
415C22×C8—611no—
416C22×C8—611no—
417C22×C8C22×D6111yescharacteristic
418C22×C8C22×D6111yescharacteristic
419C4⋊Q8—1222no—
420C4⋊Q8—2441no—
421#124—1222no—
422#124—2441no—
423C22⋊Q8—2444no—
424C4×Q8—22no—
425C4×Q8—41no—
426C4×D4—22no—
427C4×D4—41no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—611no—
434C2×C4⋊C4—1221no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4C22×D6111yescharacteristic
439C2×C4⋊C4C22×D6111yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—1221no—
442C2×C22⋊C4—1221no—
443C2×C22⋊C4—1221no—
444C2×C22⋊C4—1221no—
445C2×C22⋊C4—1221no—
446C2×C22⋊C4—1221no—
447C2×C22⋊C4—1221no—
448C2×C22⋊C4—1221no—
449C2×C22⋊C4—1221no—
450C2×C22⋊C4—1221no—
451C2×C42—21no—
452C2×C42—611no—
453C2×C42—611no—
454C2×C42C22×D6111yescharacteristic
455#107—22no—
456#107—2441no—
457C4⋊C8—1222no—
458#103—1222no—
459#103—1222no—
460#103C22⋊D6114yes—
461#102—22no—
462#102—1222no—
463#102—1222no—
464#102—1222no—
465#102—1222no—
466#97—22no—
467#97—1222no—
468C4×C8—1222no—
469#95—611no—
470#95—611no—
471#95—1221no—
472#95—1221no—
473#95—1221no—
474#95—1221no—
475#95—1221no—
476C24—21no—
477C24—1221no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—4881no—
484C2×Q8—2442no—
485C2×Q8—2442no—
486C2×Q8C2×C22⋊D6112yes—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—1221no—
493C2×D4—1221no—
494C2×D4—1221no—
495C2×D4—1221no—
496C2×D4—1221no—
497C2×D4—1221no—
498C2×D4#1175822212yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—1221no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4D4×D6111yescharacteristic
513C22×C4D4×D6111yescharacteristic
514C22×C4C23×D6111yescharacteristic
515SD16—28no—
516D8—2444no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—612no—
522C2×C8—1221no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8#1175822212yes—
528C2×C8C2×C22⋊D6112yes—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—1222no—
534C4⋊C4—1221no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—1221no—
540C4⋊C4—4881no—
541C4⋊C4—2441no—
542C4⋊C4—2442no—
543C4⋊C4—2442no—
544C4⋊C4—2442no—
545C4⋊C4C2×C22⋊D6112yes—
546C22⋊C4—42no—
547C22⋊C4—4881no—
548C22⋊C4—4881no—
549C22⋊C4—4881no—
550C22⋊C4—2442no—
551C22⋊C4—2442no—
552C22⋊C4—2442no—
553C22⋊C4—2442no—
554C22⋊C4—2442no—
555C22⋊C4—2442no—
556C22⋊C4—2442no—
557C42—21no—
558C42—21no—
559C42—42no—
560C42—1221no—
561C42—1221no—
562C42—1221no—
563C42—1221no—
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—2441no—
572C23—2441no—
573C23—2441no—
574C23—2441no—
575C23—2441no—
576C23—2441no—
577C23—2441no—
578C23C2×D4×D6111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—41no—
582Q8—41no—
583Q8—4884no—
584D4—22no—
585D4—22no—
586D4—41no—
587D4—41no—
588D4—2441no—
589D4—2441no—
590D4—2441no—
591D4—2441no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—84no—
608C2×C4—612no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—1221no—
613C2×C4—1221no—
614C2×C4—1221no—
615C2×C4—1221no—
616C2×C4—1221no—
617C2×C4—1221no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—2441no—
621C2×C4—2441no—
622C2×C4—2441no—
623C2×C4—2441no—
624C2×C4—2441no—
625C2×C4—2441no—
626C2×C4—2441no—
627C2×C4—2441no—
628C2×C4—2441no—
629C2×C4C22×C22⋊D6111yescharacteristic
630C2×C4#41×D6111yescharacteristic
631C2×C4C2×#1175822211yescharacteristic
632C2×C4C2×#1175822211yescharacteristic
633C2×C4#1451982211yescharacteristic
634C2×C4#1451982411yescharacteristic
635C8—22no—
636C8—22no—
637C8—1222no—
638C8—2441no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—4881no—
647C22—4881no—
648C22—4881no—
649C22—4881no—
650C22—4881no—
651C22—4881no—
652C22—4881no—
653C22#1684030911yescharacteristic
654C22D4×C22⋊D6111yescharacteristic
655C22#1684042111yescharacteristic
656C22AGL(1,ℤ/8)×D6111yescharacteristic
657C22#1684056111yescharacteristic
658C22#1684056611yescharacteristic
659C22#1684057811yescharacteristic
660C4—41no—
661C4—42no—
662C4—42no—
663C4—41no—
664C4—81no—
665C4—1222no—
666C4—4881no—
667C4—4881no—
668C4—4881no—
669C4—2441no—
670C4—2441no—
671C4—2441no—
672C4#1684027311yescharacteristic
673C4#1684037711yescharacteristic
674C4#1684041111yescharacteristic
675C4#1684044111yescharacteristic
676C2—82no—
677C2—9761no—
678C2#2144978011yescharacteristic
679C2#2145645611yescharacteristic
680C2#2145651311yescharacteristic
681C2#2145743311yescharacteristic
682C2#2145747011yescharacteristic
683C2#2145853811yescharacteristic
684C2#2145857311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenterC2×#440D61
hypocenterC61#26844
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16840123C2semidirect
2. #21449663C2semidirect
3. #21449611C2semidirect
4. #21447202C2semidirect
5. #21447145C2semidirect
6. #21447132C2semidirect
9. #21446516C2semidirect
10. #21446513C2semidirect
11. #21446497C2semidirect
13. #21446073C2semidirect
14. #21445687C2semidirect
15. C2×C61×#440C2semidirect
335. C2×#440D61semidirect
403. C61#26844semidirect

Maximal subgroups

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

subgroupindex
C2×#168401232
#214496632
#214496112
#214472022
#214471452
#214471322
#214468932
#214466822
#214465162
#214465132
#214464972
#214461672
#214460732
#214456872
C2×C61×#4402
#2684461