Finite Group Databasebeta

← #29739967

Subgroups — #29739967

Order 15616.

896 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840085C211yesmaximal, characteristic, complemented
2C2×#16839801C211yesmaximal, characteristic, complemented
3#21449240C211yesmaximal, characteristic
4#21448751C211yesmaximal, characteristic, complemented
5#21447340C211yesmaximal, characteristic, complemented
6#21447302C211yesmaximal, characteristic, complemented
7#21447257C211yesmaximal, characteristic, complemented
8#21447000C211yesmaximal, characteristic, complemented
9#21446390C211yesmaximal, characteristic, complemented
10#21446254C211yesmaximal, characteristic, complemented
11#21446133C211yesmaximal, characteristic, complemented
12#21446115C211yesmaximal, characteristic, complemented
13#21446019C211yesmaximal, characteristic, complemented
14#21446017C211yesmaximal, characteristic, complemented
15C61×#1926C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C2×#14519748C2211yescharacteristic
18C2×#14519748C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21C2×#14519735C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23#16840085—24no—
24#16839801—24no—
25C2×#14519711C2211yescharacteristic
26C2×#14519710C2211yescharacteristic
27C2×#14519710C2211yescharacteristic
28C2×#14519709C2211yescharacteristic
29C2×#14519708C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35#16839677—21no—
36#16839671—21no—
37#16839662—21no—
38#16839660C2211yescharacteristic
39#16839655—21no—
40#16839653—21no—
41#16839647—21no—
42#16839640—21no—
43#16839628C2211yescharacteristic
44#16839619C2211yescharacteristic
45#16839619C2211yescharacteristic
46#16839619C2211yescharacteristic
47C4×#11758198—21no—
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839517C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×D244D411yescharacteristic
62C22×C22⋊D61—21no—
63C22×C22⋊D61—21no—
64C22×C4×D61—21no—
65C22×C4×D61C2311yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×#11758189—22no—
68C2×#11758189—22no—
69C2×#11758189—22no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519748—22no—
73#14519748—22no—
74#14519748—22no—
75#14519748—41no—
76C4×D244—22no—
77C4×D244—22no—
78#14519735—22no—
79#14519735—22no—
80#14519735—41no—
81#14519735—41no—
82C2×C4⋊Dic61D411yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758196—21no—
88C2×#11758196—21no—
89C4⋊C4×D61—22no—
90C4⋊C4×D61—41no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198D411yescharacteristic
99C2×#11758198D411yescharacteristic
100C2×C4×Dic61—21no—
101C2×C4×Dic61—21no—
102#14519711—22no—
103#14519710—41no—
104#14519710D414yescomplemented
105#14519709—22no—
106#14519708—22no—
107#14519698—22no—
108#14519698—41no—
109#14519689—22no—
110#14519689—22no—
111#14519689—22no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118C22×D4×C61C2311yescharacteristic
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C42×C61—21no—
127C2×C42×C61C2311yescharacteristic
128#106×C61—22no—
129#102×C61—22no—
130#102×C61—22no—
131#95×C61—21no—
132C24×C61—21no—
133C23×D61C2×D411yescharacteristic
134C23×D61C2×D411yescharacteristic
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2411yescharacteristic
147C2×C22⋊D61—42no—
148C2×C22⋊D61—42no—
149C2×C22⋊D61—42no—
150C2×C22⋊D61—81no—
151C2×C22⋊D61—81no—
152C2×C22⋊D61—81no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159C2×D244—22no—
160C2×D244—41no—
161C2×D244—41no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—42no—
173C2×C4×D61—42no—
174C2×C4×D61—81no—
175C2×C4×D61#4112yes—
176C2×C4×D61#4112yes—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61#4112yes—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61C2×D412yes—
189C22⋊C4×C61—42no—
190C22⋊C4×C61—81no—
191C42×C61—21no—
192C42×C61—21no—
193C42×C61—81no—
194C22⋊Dic61—42no—
195C22⋊Dic61—42no—
196#11758198—22no—
197#11758198—22no—
198#11758198—42no—
199#11758198—42no—
200#11758198—42no—
201#11758198—81no—
202#11758198—81no—
203C4⋊Dic61—21no—
204C4⋊Dic61—22no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61C2×D412yes—
212#11758196—42no—
213#11758196—81no—
214C4×Dic61—42no—
215C4×Dic61—42no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418C2×D412yes—
222#11758189—28no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61C22×D411yescharacteristic
231C22×D61—21no—
232C22×D61—21no—
233C22×D61—21no—
234C22×D61—21no—
235C22×D61—21no—
236C22×D61—21no—
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61—21no—
241C22×D61—21no—
242C22×D61—21no—
243C22×D61—21no—
244C22×D61#12312yes—
245D4×C61—41no—
246D4×C61—41no—
247D4×C61—41no—
248D4×C61—41no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—22no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61C22×D411yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61C2×#4111yescharacteristic
267C2×C4×C61C2×#4111yescharacteristic
268C2×C4×C61H(5,𝔽2)11yescharacteristic
269C2×C4×C612−1+411yescharacteristic
270C22⋊D61—84no—
271C22⋊D61—84no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—22no—
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#12312yes—
290D244—44no—
291C4×D61—22no—
292C4×D61—22no—
293C4×D61—22no—
294C4×D61—22no—
295C4×D61—41no—
296C4×D61—41no—
297C4×D61—41no—
298C4×D61—41no—
299C4×D61—84no—
300C8×C61—22no—
301C8×C61—41no—
302#92418—22no—
303#92418—41no—
304#26156—611nomaximal, Sylow
305C22×C61—81no—
306C22×C61—81no—
307C22×C61—81no—
308C22×C61—81no—
309C22×C61—81no—
310C22×C61—81no—
311C22×C61—81no—
312C22×C61C2×#12311yescharacteristic
313C22×C61D4211yescharacteristic
314C22×C61#54711yescharacteristic
315C22×C61#57511yescharacteristic
316C22×C61#57511yescharacteristic
317C22×C61#57611yescharacteristic
318C22×C61#57711yescharacteristic
319C2×D61—22no—
320C2×D61—22no—
321C2×D61—22no—
322C2×D61—41no—
323C2×D61—41no—
324C2×D61—41no—
325C2×D61—41no—
326C2×D61—41no—
327C2×D61—41no—
328C2×D61—41no—
329C2×D61—41no—
330C2×D61—41no—
331C2×D61—41no—
332C2×D61—41no—
333C4×C61—41no—
334C4×C61—41no—
335C4×C61—42no—
336C4×C61—81no—
337C4×C61—81no—
338C4×C61#52511yescharacteristic
339C4×C61#53911yescharacteristic
340C4×C61#54811yescharacteristic
341C4×C61#55311yescharacteristic
342Dic61—22no—
343Dic61—41no—
344Dic61—42no—
345Dic61—81no—
346Dic61—81no—
347Dic61—81no—
348C2×#482—611no—
349C2×#428—611no—
350#2414—611no—
351#2352—611no—
352#2092—611no—
353#2085—611no—
354#2077—611no—
355#2033—611no—
356#1926D6111yescharacteristic, complemented
357#1918—611no—
358#1895—611no—
359#1874—611no—
360#1870—611no—
361#1854—611no—
362#1854—611no—
363C2×C61—161no—
364C2×C61#244311yescharacteristic
365C2×C61#309311yescharacteristic
366C2×C61#309611yescharacteristic
367C2×C61#327111yescharacteristic
368C2×C61#327311yescharacteristic
369C2×C61#334711yescharacteristic
370C2×C61#335111yescharacteristic
371D61—42no—
372D61—81no—
373C22×M16—611no—
374C2×#121—611no—
375C2×#121—611no—
376C2×C4×D4—611no—
377C2×#117—611no—
378C2×#117—611no—
379C22×C4⋊C4—611no—
380#482—1224no—
381#428—1224no—
382C2×#107—611no—
383C2×#107—611no—
384C2×#107—611no—
385C2×#106—611no—
386C2×#106—611no—
387C2×#106C2×D6111yescharacteristic
388C2×#102—611no—
389C2×#102—611no—
390C2×#102C2×D6111yescharacteristic
391C2×#102C2×D6111yescharacteristic
392C2×C22⋊C8—611no—
393C2×C22⋊C8—611no—
394C2×C22⋊C8—611no—
395#394—1221no—
396#392—1221no—
397#390—1221no—
398#390C2×D6111yescharacteristic
399#389—611no—
400#388—1221no—
401#388—1221no—
402#387—1221no—
403#386—1221no—
404#382—611no—
405#380—611no—
406#380—611no—
407#380—611no—
408C4×C4⋊C4C2×D6111yescharacteristic
409C4×C22⋊C4—1221no—
410#340—611no—
411#340—611no—
412#340—611no—
413#340—611no—
414#340—611no—
415#340C2×D6111yescharacteristic
416#336—611no—
417#336C2×D6111yescharacteristic
418C61#2615611yescharacteristic, complemented, Sylow
419C22×D4—611no—
420C22×D4—1221no—
421C22×D4—1221no—
422C22×D4C22×D6111yescharacteristic
423C23×C4—611no—
424C23×C4—611no—
425C23×C4—1221no—
426C2×M16—1222no—
427C2×M16—1222no—
428C2×M16—1222no—
429C22×C8—611no—
430C22×C8—611no—
431C22×C8C22×D6111yescharacteristic
432C22×C8C22×D6111yescharacteristic
433#121—1222no—
434#121—1222no—
435#121—1222no—
436#121—2441no—
437C4×D4—1222no—
438C4×D4—1222no—
439#117—1222no—
440#117—1222no—
441#117—2441no—
442#117—2441no—
443C2×C4⋊C4—611no—
444C2×C4⋊C4—611no—
445C2×C4⋊C4—611no—
446C2×C4⋊C4—611no—
447C2×C4⋊C4—611no—
448C2×C4⋊C4—1222no—
449C2×C4⋊C4—1221no—
450C2×C4⋊C4—1221no—
451C2×C4⋊C4—2441no—
452C2×C4⋊C4C22×D6111yescharacteristic
453C2×C4⋊C4C22×D6111yescharacteristic
454C2×C4⋊C4C22×D6111yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—611no—
458C2×C22⋊C4—611no—
459C2×C22⋊C4—1221no—
460C2×C22⋊C4—1221no—
461C2×C22⋊C4—1221no—
462C2×C22⋊C4—1221no—
463C2×C22⋊C4—1221no—
464C2×C22⋊C4—1221no—
465C2×C22⋊C4—1221no—
466C2×C42—21no—
467C2×C42—1221no—
468C2×C42—1221no—
469C2×C42C22×D6111yescharacteristic
470#107—614no—
471#107—1222no—
472#107—2441no—
473#106—22no—
474#106—1222no—
475#106—1222no—
476#102—22no—
477#102—22no—
478#102—1222no—
479#102—2441no—
480C22⋊C8—1222no—
481C22⋊C8—1222no—
482C22⋊C8—1222no—
483#95—21no—
484#95—1221no—
485#95—1221no—
486#95—1221no—
487#95—1221no—
488#95—1221no—
489#95—1221no—
490C24—21no—
491C24—611no—
492C24—611no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—1222no—
500C2×D4—4881no—
501C2×D4—4881no—
502C2×D4—4881no—
503C2×D4—2441no—
504C2×D4—2441no—
505C2×D4—2442no—
506C2×D4—2442no—
507C2×D4—2442no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—611no—
512C22×C4—612no—
513C22×C4—612no—
514C22×C4—611no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1221no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—1221no—
528C22×C4—1221no—
529C22×C4—4881no—
530C22×C4—2442no—
531C22×C4—2442no—
532C22×C4D4×D6111yescharacteristic
533C22×C4D4×D6111yescharacteristic
534C22×C4C23×D6111yescharacteristic
535M16—1228no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—612no—
542C2×C8—1221no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8—1221no—
546C2×C8—1221no—
547C2×C8#1175822212yes—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—612no—
554C4⋊C4—1222no—
555C4⋊C4—1221no—
556C4⋊C4—1221no—
557C4⋊C4—1221no—
558C4⋊C4—1221no—
559C4⋊C4—1221no—
560C4⋊C4—1221no—
561C4⋊C4—1221no—
562C4⋊C4—4881no—
563C4⋊C4—2442no—
564C4⋊C4D4×D6112yes—
565C22⋊C4—42no—
566C22⋊C4—81no—
567C22⋊C4—1222no—
568C22⋊C4—1222no—
569C22⋊C4—4881no—
570C22⋊C4—4881no—
571C22⋊C4—2442no—
572C22⋊C4—2442no—
573C22⋊C4—2442no—
574C22⋊C4—2442no—
575C22⋊C4—2442no—
576C42—21no—
577C42—21no—
578C42—81no—
579C42—2442no—
580C42—2442no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—612no—
589C23—1221no—
590C23—1221no—
591C23—1221no—
592C23—1221no—
593C23—1221no—
594C23—1221no—
595C23—1221no—
596C23—1221no—
597C23—1221no—
598C23—1221no—
599C23—1221no—
600C23—1221no—
601C23—1221no—
602C23C2×D4×D6111yescharacteristic
603D4—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—4884no—
608D4—4884no—
609D4—2444no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—612no—
626C2×C4—1221no—
627C2×C4—1221no—
628C2×C4—1222no—
629C2×C4—1222no—
630C2×C4—1222no—
631C2×C4—1222no—
632C2×C4—1221no—
633C2×C4—1221no—
634C2×C4—1222no—
635C2×C4—1221no—
636C2×C4—4884no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4—2441no—
652C2×C4C2×D4×D6111yescharacteristic
653C2×C4#41×D6111yescharacteristic
654C2×C4#41×D6111yescharacteristic
655C2×C4C2×#1175822211yescharacteristic
656C2×C4#1451982311yescharacteristic
657C2×C4#1451982411yescharacteristic
658C8—22no—
659C8—41no—
660C8—1222no—
661C8—2441no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—1222no—
670C22—1222no—
671C22—1222no—
672C22—2441no—
673C22—2441no—
674C22—2441no—
675C22—2441no—
676C22—2441no—
677C22—2441no—
678C22—2441no—
679C22—2441no—
680C22—2441no—
681C22—2441no—
682C22—2441no—
683C22#123×D6111yescharacteristic
684C22#1684039611yescharacteristic
685C22#1684041711yescharacteristic
686C22#1684055811yescharacteristic
687C22#1684055911yescharacteristic
688C22#1684056611yescharacteristic
689C22#1684056811yescharacteristic
690C4—42no—
691C4—41no—
692C4—41no—
693C4—81no—
694C4—81no—
695C4—1222no—
696C4—4881no—
697C4—4881no—
698C4—4881no—
699C4—2442no—
700C4—2441no—
701C4#1684027111yescharacteristic
702C4#1684035311yescharacteristic
703C4#1684042011yescharacteristic
704C4#1684045611yescharacteristic
705C2—161no—
706C2—4881no—
707C2—2442no—
708C2#2144956111yescharacteristic
709C2#2145574711yescharacteristic
710C2#2145577611yescharacteristic
711C2#2145739911yescharacteristic
712C2#2145742511yescharacteristic
713C2#2145832411yescharacteristic
714C2#2145838411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1926C2
socleC23×C61C22×D4
prime radical#21449240C2
hypercenter#1926D61
hypocenterC61#26156
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
1. C2×#16840085C2semidirect
2. C2×#16839801C2semidirect
4. #21448751C2semidirect
5. #21447340C2semidirect
6. #21447302C2semidirect
7. #21447257C2semidirect
8. #21447000C2semidirect
9. #21446390C2semidirect
10. #21446254C2semidirect
11. #21446133C2semidirect
12. #21446115C2semidirect
13. #21446019C2semidirect
14. #21446017C2semidirect
15. C61×#1926C2semidirect
104. #14519710D4semidirect
356. #1926D61semidirect
418. C61#26156semidirect

Maximal subgroups

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

subgroupindex
C2×#168400852
C2×#168398012
#214492402
#214487512
#214473402
#214473022
#214472572
#214470002
#214463902
#214462542
#214461332
#214461152
#214460192
#214460172
C61×#19262
#2615661