Finite Group Databasebeta

← #29679938

Subgroups — #29679938

Order 15616.

1350 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840230C211yesmaximal, characteristic
2C2×#16839817C211yesmaximal, characteristic, complemented
3C2×#16839813C211yesmaximal, characteristic, complemented
4#21445889C212yesmaximal, complemented
5#21445798C212yesmaximal, complemented
6#21445797C212yesmaximal, complemented
7#21445730C212yesmaximal
8#21445588C211yesmaximal, characteristic, complemented
9#21445586C211yesmaximal, characteristic, complemented
10#21445585C211yesmaximal, characteristic, complemented
11C61×#1750C211yesmaximal, characteristic, complemented
12C22×#11758222C2211yescharacteristic
13#16840230—24no—
14#16840230—24no—
15C2×#14519742C411yescharacteristic
16C2×#14519742C411yescharacteristic
17C2×#14519739C411yescharacteristic
18C2×#14519739C411yescharacteristic
19C2×#14519737C411yescharacteristic
20C2×#14519737C411yescharacteristic
21C2×#14519737C411yescharacteristic
22C2×#14519737C411yescharacteristic
23C2×#14519734C2211yescharacteristic
24C2×#14519734C2211yescharacteristic
25C22×C4×Dic61C2211yescharacteristic
26C2×C42×D61C2211yescharacteristic
27C2×C42×D61C2211yescharacteristic
28#16839817—24no—
29#16839813—24no—
30C2×#14519706C2212yes—
31C2×#14519706C2212yes—
32C2×C22⋊#92418C2212yes—
33C2×#14519689C2212yes—
34C2×#14519689C2212yes—
35C2×#14519689C2212yes—
36C2×#14519689C2212yes—
37C2×#14519688C2211yescharacteristic
38C2×C4×#92418C2211yescharacteristic
39#16839517C2212yes—
40#16839516C2212yes—
41#16839516C2212yes—
42C2×#117×C61C2211yescharacteristic
43C2×C22⋊C8×C61C2212yes—
44C2×#97×C61C2211yescharacteristic
45C2×C4×C8×C61C2211yescharacteristic
46C61×#336C2212yes—
47C2×#11758222—24no—
48C2×#11758222—22no—
49C2×#11758222—22no—
50C2×#11758222—24no—
51C22×Dic122C2×C411yescharacteristic
52C22×D244C2×C411yescharacteristic
53C22×C22⋊D61C2×C411yescharacteristic
54C22×C22⋊D61C2×C411yescharacteristic
55C23×Dic61C2×C411yescharacteristic
56C23×Dic61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2311yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2312yes—
64C22×#92418C2312yes—
65#14519742—24no—
66#14519742—24no—
67#14519739—24no—
68#14519739—24no—
69#14519737—24no—
70#14519737—24no—
71#14519737—24no—
72#14519737—24no—
73#14519734—22no—
74#14519734—22no—
75#14519734—22no—
76#14519734—22no—
77C2×#11758196C2×C411yescharacteristic
78C2×#11758196C2×C411yescharacteristic
79C2×#11758196C2×C411yescharacteristic
80C2×#11758196C2×C411yescharacteristic
81C2×#11758198C2×C411yescharacteristic
82C2×#11758198C2×C411yescharacteristic
83C2×#11758198C2×C411yescharacteristic
84C2×#11758198C2×C411yescharacteristic
85C2×C4×Dic61—22no—
86C2×C4×Dic61—22no—
87C2×C4×Dic61C2×C411yescharacteristic
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2×C411yescharacteristic
91C2×C4×Dic61C2×C411yescharacteristic
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2311yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95C42×D61—22no—
96C42×D61—22no—
97C42×D61D414yes—
98C42×D61D414yes—
99#14519706—24no—
100#14519706—24no—
101C22⋊#92418—24no—
102#14519689—24no—
103#14519689—24no—
104#14519689—24no—
105#14519689—24no—
106#14519688—22no—
107C4×#92418—22no—
108C23×C4×C61C2311yescharacteristic
109C22×C8×C61C2312yes—
110C22×C8×C61C2312yes—
111#117×C61—22no—
112#117×C61—22no—
113C2×C4⋊C4×C61C2×C411yescharacteristic
114C2×C4⋊C4×C61C2×C411yescharacteristic
115C2×C22⋊C4×C61C2×C411yescharacteristic
116C2×C22⋊C4×C61C2×C411yescharacteristic
117C2×C42×C61C2311yescharacteristic
118C2×C42×C61C2311yescharacteristic
119C22⋊C8×C61—24no—
120#97×C61—22no—
121C4×C8×C61—22no—
122C24×C61C22×C411yescharacteristic
123C23×D61C22×C411yescharacteristic
124C23×D61C22×C411yescharacteristic
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—22no—
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61#4114yes—
134C22×C4×C61C2411yescharacteristic
135C2×C22⋊D61—22no—
136C2×C22⋊D61—22no—
137C2×C22⋊D61—22no—
138C2×C22⋊D61—22no—
139C2×C22⋊D61—22no—
140C2×C22⋊D61—22no—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—24no—
144C22×Dic61—42no—
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C22×C411yescharacteristic
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151#11758222—216no—
152#11758222—216no—
153C2×D244—22no—
154C2×D244—22no—
155C2×D244—22no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—22no—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—24no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—24no—
165C2×C4×D61—42no—
166C2×C4×D61—42no—
167C2×C4×D61C22⋊C414yes—
168C2×C4×D61C22⋊C414yes—
169C2×C4×D61C2×D412yes—
170C2×C4×D61C2×D412yes—
171C2×C4×D61#4114yes—
172C2×Dic122—22no—
173C2×Dic122—22no—
174C2×Dic122—22no—
175C2×C8×C61—22no—
176C2×C8×C61—22no—
177C2×C8×C61—22no—
178C2×C8×C61—22no—
179C2×C8×C61—22no—
180C2×C8×C61—22no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—22no—
183C22⋊C4×C61—22no—
184C22⋊C4×C61—22no—
185C42×C61—21no—
186C42×C61—21no—
187C42×C61C2×D412yes—
188C42×C61C2×D412yes—
189#11758198—22no—
190#11758198—22no—
191#11758198—22no—
192#11758198—22no—
193#11758196—22no—
194#11758196—22no—
195#11758196—22no—
196#11758196—22no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—22no—
200C4×Dic61—22no—
201C4×Dic61—22no—
202C4×Dic61—22no—
203C4×Dic61C22⋊C414yes—
204C4×Dic61C22⋊C414yes—
205C4×Dic61C2×D412yes—
206C4×Dic61C2×D412yes—
207C2×#92418—22no—
208C2×#92418—22no—
209C2×#92418—22no—
210C2×#92418—22no—
211C2×#92418—22no—
212C2×#92418—22no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—22no—
216C23×C61—22no—
217C23×C61#11712yes—
218C23×C61C23×C411yescharacteristic
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—22no—
224C22×D61—22no—
225C22×D61—22no—
226C22×D61—22no—
227C22×D61C2×C22⋊C412yes—
228C22×D61#11712yes—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—24no—
234C2×C4×C61—24no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61C2×C22⋊C412yes—
240C2×C4×C61C2×C22⋊C412yes—
241C2×C4×C61#11712yes—
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C2×#4112yes—
245C2×C4×C61C2×#4112yes—
246C22⋊D61—28no—
247C22⋊D61—28no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—22no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—44no—
258C2×Dic61—44no—
259C2×Dic61C2×C22⋊C412yes—
260C2×Dic61C2×C22⋊C412yes—
261C2×Dic61C2×C22⋊C412yes—
262C2×Dic61#11712yes—
263C2×Dic61#13114yes—
264D244—28no—
265C4×D61—24no—
266C4×D61—24no—
267C4×D61—24no—
268C4×D61—24no—
269C4×D61—28no—
270C4×D61—44no—
271C4×D61—44no—
272C4×D61—44no—
273Dic122—28no—
274C8×C61—42no—
275C8×C61—42no—
276#92418—42no—
277#92418—42no—
278#20721—611nomaximal, Sylow
279C22×C61—24no—
280C22×C61—22no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—42no—
284C22×C61C22×C22⋊C411yescharacteristic
285C22×C61C2×#11711yescharacteristic
286C22×C61C2×#11711yescharacteristic
287C22×C61C2×#13112yes—
288C22×C61#56812yes—
289C2×D61—22no—
290C2×D61—22no—
291C2×D61—24no—
292C2×D61—22no—
293C2×D61—22no—
294C2×D61—41no—
295C2×D61—41no—
296C2×D61—42no—
297C2×D61—42no—
298C2×D61—42no—
299C4×C61—22no—
300C4×C61—22no—
301C4×C61—22no—
302C4×C61—41no—
303C4×C61—41no—
304C4×C61#52512yes—
305C4×C61#52512yes—
306Dic61—22no—
307Dic61—22no—
308Dic61—22no—
309Dic61—41no—
310Dic61—41no—
311Dic61#40814yes—
312C2×C4×#41—611no—
313C2×#432—611no—
314C2×#431—611no—
315#1818—612no—
316#1797—612no—
317#1797—612no—
318#1780—612no—
319#1750—611no—
320#1750—611no—
321#1750—611no—
322#1750D6111yescharacteristic, complemented
323C2×C61—42no—
324C2×C61#228011yescharacteristic
325C2×C61C2×#40811yescharacteristic
326C2×C61#287911yescharacteristic
327C2×C61#292512yes—
328C2×C61#292512yes—
329D61—42no—
330D61—42no—
331C22×#41—611no—
332C4×#41—1224no—
333C4×#41—1224no—
334C2×C4×Q8—611no—
335C2×C4×Q8—611no—
336C2×C4×D4—611no—
337C2×C4×D4—611no—
338C2×C4×D4—611no—
339C2×C4×D4—611no—
340C2×C4×D4—611no—
341C2×C4×D4—611no—
342C2×#117—611no—
343C2×#117—611no—
344C2×#117C2×D6111yescharacteristic
345C22×C42—611no—
346C22×C42—611no—
347C22×C42—611no—
348#432—1224no—
349#431—1224no—
350C2×C4⋊C8—612no—
351C2×C4⋊C8—612no—
352C2×C22⋊C8—612no—
353C2×C22⋊C8—612no—
354C2×C22⋊C8—612no—
355C2×C22⋊C8—612no—
356C2×C22⋊C8—612no—
357C2×C22⋊C8C2×D6112yes—
358C2×#97—611no—
359C2×#97C2×D6111yescharacteristic
360C2×C4×C8—611no—
361C2×C4×C8C2×D6111yescharacteristic
362#336—612no—
363#336—612no—
364#336—612no—
365#336C2×D6112yes—
366C61#2072111yescharacteristic, complemented, Sylow
367C2×#41—1222no—
368C2×#41—1222no—
369C2×#41—1224no—
370C2×#41—1224no—
371C22×Q8—611no—
372C22×D4—611no—
373C22×D4—611no—
374C22×D4—611no—
375C23×C4—611no—
376C23×C4—611no—
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4C22×D6111yescharacteristic
384C22×C8—612no—
385C22×C8—612no—
386C22×C8C22×D6112yes—
387C22×C8C22×D6112yes—
388C4×Q8—1224no—
389C4×Q8—1224no—
390C4×D4—1224no—
391C4×D4—1224no—
392C4×D4—1224no—
393C4×D4—1224no—
394C4×D4—1224no—
395C4×D4—1224no—
396#117—22no—
397#117—22no—
398#117—1222no—
399#117—1222no—
400#117—1222no—
401#117—1222no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4C4×D6111yescharacteristic
407C2×C4⋊C4C4×D6111yescharacteristic
408C2×C22⋊C4—611no—
409C2×C22⋊C4—611no—
410C2×C22⋊C4—611no—
411C2×C22⋊C4—611no—
412C2×C22⋊C4C4×D6111yescharacteristic
413C2×C22⋊C4C4×D6111yescharacteristic
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—611no—
417C2×C42—614no—
418C2×C42—614no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—1222no—
425C2×C42—1222no—
426C2×C42—1222no—
427C2×C42—1222no—
428C2×C42C22×D6111yescharacteristic
429C2×C42C22×D6111yescharacteristic
430C4⋊C8—1224no—
431C4⋊C8—1224no—
432C22⋊C8—24no—
433C22⋊C8—1224no—
434C22⋊C8—1224no—
435C22⋊C8—1224no—
436C22⋊C8—1224no—
437C22⋊C8—1224no—
438#97—22no—
439#97—1222no—
440C4×C8—22no—
441C4×C8—1222no—
442C24—611no—
443C24—611no—
444C24C2×C4×D6111yescharacteristic
445#41—12216no—
446#41—12216no—
447C2×Q8—1222no—
448C2×Q8—1222no—
449C2×Q8—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—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—612no—
467C22×C4—612no—
468C22×C4—614no—
469C22×C4—614no—
470C22×C4—614no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—1224no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1224no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1224no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—2442no—
486C22×C4—2442no—
487C22×C4—2442no—
488C22×C4C2×C4×D6111yescharacteristic
489C22×C4C2×C4×D6111yescharacteristic
490C22×C4C2×C4×D6111yescharacteristic
491C22×C4C2×C4×D6111yescharacteristic
492C22×C4C2×C4×D6111yescharacteristic
493C22×C4#1175822214yes—
494C22×C4C23×D6111yescharacteristic
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—1222no—
502C2×C8—1222no—
503C2×C8—1222no—
504C2×C8—1222no—
505C2×C8—1222no—
506C2×C8—1222no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—1222no—
516C22⋊C4—1222no—
517C22⋊C4—1222no—
518C22⋊C4—1222no—
519C42—21no—
520C42—21no—
521C42—612no—
522C42—612no—
523C42—614no—
524C42—614no—
525C42—1222no—
526C42—1222no—
527C42—1222no—
528C42—1222no—
529C42—1221no—
530C42—1221no—
531C42D4×D6112yes—
532C42D4×D6112yes—
533C23—21no—
534C23—21no—
535C23—22no—
536C23—22no—
537C23—612no—
538C23—612no—
539C23—1221no—
540C23—1221no—
541C23—1221no—
542C23—1221no—
543C23—1222no—
544C23—1222no—
545C23—1222no—
546C23—1222no—
547C23#1451973412yes—
548C23C22×C4×D6111yescharacteristic
549Q8—1228no—
550D4—1228no—
551D4—1228no—
552D4—1228no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—612no—
564C2×C4—614no—
565C2×C4—612no—
566C2×C4—612no—
567C2×C4—612no—
568C2×C4—1228no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1222no—
574C2×C4—1224no—
575C2×C4—1224no—
576C2×C4—1224no—
577C2×C4—1224no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—2444no—
583C2×C4—2444no—
584C2×C4—2444no—
585C2×C4—2444no—
586C2×C4—2444no—
587C2×C4C22⋊C4×D6112yes—
588C2×C4C22⋊C4×D6112yes—
589C2×C4#1451973412yes—
590C2×C4C2×D4×D6111yescharacteristic
591C2×C4C2×D4×D6111yescharacteristic
592C2×C4#41×D6112yes—
593C2×C4C2×#1175822212yes—
594C8—42no—
595C8—42no—
596C8—2442no—
597C8—2442no—
598C22—22no—
599C22—24no—
600C22—42no—
601C22—41no—
602C22—41no—
603C22—1222no—
604C22—1222no—
605C22—1224no—
606C22—1222no—
607C22—1222no—
608C22—2442no—
609C22—2442no—
610C22—2442no—
611C22—2441no—
612C22—2441no—
613C22C2×C22⋊C4×D6111yescharacteristic
614C22#117×D6111yescharacteristic
615C22C2×#1451973411yescharacteristic
616C22#131×D6112yes—
617C22#1684052712yes—
618C4—22no—
619C4—22no—
620C4—22no—
621C4—41no—
622C4—41no—
623C4—614no—
624C4—1222no—
625C4—1222no—
626C4—1222no—
627C4—2441no—
628C4—2441no—
629C4#1684027112yes—
630C4#1684027112yes—
631C2—42no—
632C2—2442no—
633C2—2442no—
634C2#2144820011yescharacteristic
635C2#408×D6111yescharacteristic
636C2#2145426111yescharacteristic
637C2#2145448212yes—
638C2#2145448312yes—
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1750C2
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#1750D61
hypocenterC61#20721
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#16839817C2semidirect
3. C2×#16839813C2semidirect
4. #21445889C2semidirect
5. #21445798C2semidirect
6. #21445797C2semidirect
8. #21445588C2semidirect
9. #21445586C2semidirect
10. #21445585C2semidirect
11. C61×#1750C2semidirect
322. #1750D61semidirect
366. C61#20721semidirect

Maximal subgroups

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

subgroupindex
C2×#168402302
C2×#168398172
C2×#168398132
#214458892
#214457982
#214457972
#214457302
#214455882
#214455862
#214455852
C61×#17502
#2072161