Finite Group Databasebeta

← #14532155

Subgroups — #14532155

Order 2176.

1246 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D17C211yesmaximal, characteristic, complemented
2C2×#10587625C211yesmaximal, characteristic, complemented
3C2×#10587623C211yesmaximal, characteristic, complemented
4C2×#10587623C211yesmaximal, characteristic, complemented
5C22×#63227C211yesmaximal, characteristic, complemented
6#11762726C211yesmaximal, characteristic, complemented
7#11762724C211yesmaximal, characteristic, complemented
8#11762718C211yesmaximal, characteristic, complemented
9#11762717C211yesmaximal, characteristic, complemented
10#11762689C211yesmaximal, characteristic, complemented
11#11762688C211yesmaximal, characteristic, complemented
12#11762685C211yesmaximal, characteristic, complemented
13#11762680C211yesmaximal, characteristic, complemented
14#11762664C211yesmaximal, characteristic, complemented
15C2×C17×#121C211yesmaximal, characteristic, complemented
16C24×D17C2211yescharacteristic
17C24×D17C2211yescharacteristic
18C22×D4×C17C2211yescharacteristic
19C22×D4×C17C2211yescharacteristic, complemented
20C22×D4×C17C2211yescharacteristic, complemented
21C23×C4×C17C2211yescharacteristic, complemented
22C22×C22⋊D17C2211yescharacteristic
23C22×C22⋊D17C2211yescharacteristic
24C22×C22⋊D17C2211yescharacteristic
25C22×C22⋊D17C2211yescharacteristic, complemented
26C22×C22⋊D17C2211yescharacteristic, complemented
27C23×Dic17C2211yescharacteristic, complemented
28C2×D4×D17—24no—
29C2×D4×D17—24no—
30C2×D4×D17—24no—
31C22×D68C2211yescharacteristic
32C22×C4×D17C2211yescharacteristic
33C17×#121—24no—
34C2×C4⋊C4×C17C2211yescharacteristic, complemented
35C2×C22⋊C4×C17C2211yescharacteristic, complemented
36C2×C22⋊C4×C17C2211yescharacteristic, complemented
37C2×C22⋊Dic17C2211yescharacteristic, complemented
38C2×C22⋊Dic17C2211yescharacteristic, complemented
39C2×C22⋊Dic17C2211yescharacteristic, complemented
40C2×C22⋊Dic17C2211yescharacteristic, complemented
41#10587625—24no—
42#10587623—24no—
43#10587623—24no—
44C2×#63227—24no—
45C2×#63227C2211yescharacteristic
46C2×#63227C2211yescharacteristic
47C2×#63227C2211yescharacteristic
48C2×#63227C2211yescharacteristic, complemented
49C2×#63227C2211yescharacteristic, complemented
50C2×#63227C2211yescharacteristic, complemented
51C2×#63227C2211yescharacteristic, complemented
52C2×#63227C2211yescharacteristic, complemented
53C2×#63227C2211yescharacteristic, complemented
54C2×#63225C2211yescharacteristic, complemented
55#10587502C2211yescharacteristic, complemented
56#10587502C2211yescharacteristic, complemented
57#10587502C2211yescharacteristic, complemented
58#10587502C2211yescharacteristic, complemented
59C24×C17C2311yescharacteristic
60C24×C17C2311yescharacteristic
61C24×C17C2311yescharacteristic
62C23×D17—22no—
63C23×D17—22no—
64C23×D17—22no—
65C23×D17—22no—
66C23×D17—22no—
67C23×D17—22no—
68C23×D17—22no—
69C23×D17—22no—
70C23×D17—22no—
71C23×D17—41no—
72C23×D17—41no—
73C23×D17—41no—
74C23×D17—41no—
75C23×D17D414yescomplemented
76C23×D17C2311yescharacteristic
77C23×D17C2311yescharacteristic
78C23×D17C2311yescharacteristic
79C2×D4×C17—22no—
80C2×D4×C17—22no—
81C2×D4×C17—22no—
82C2×D4×C17—22no—
83C2×D4×C17—22no—
84C2×D4×C17—22no—
85C2×D4×C17—22no—
86C2×D4×C17—41no—
87C2×D4×C17D414yescomplemented
88C22×C4×C17—22no—
89C22×C4×C17—22no—
90C22×C4×C17—41no—
91C22×C4×C17C2311yescharacteristic
92C22×C4×C17C2311yescharacteristic
93C22×C4×C17C2311yescharacteristic
94C22×C4×C17C2311yescharacteristic
95C2×C22⋊D17—22no—
96C2×C22⋊D17—22no—
97C2×C22⋊D17—22no—
98C2×C22⋊D17—22no—
99C2×C22⋊D17—22no—
100C2×C22⋊D17—22no—
101C2×C22⋊D17—22no—
102C2×C22⋊D17—22no—
103C2×C22⋊D17—22no—
104C2×C22⋊D17—22no—
105C2×C22⋊D17—22no—
106C2×C22⋊D17—41no—
107C2×C22⋊D17—41no—
108C2×C22⋊D17—41no—
109C2×C22⋊D17D414yescomplemented
110C22×Dic17—22no—
111C22×Dic17—22no—
112C22×Dic17—41no—
113C22×Dic17C2311yescharacteristic
114C22×Dic17C2311yescharacteristic
115C22×Dic17C2311yescharacteristic
116C22×Dic17C2311yescharacteristic
117C22×Dic17C2311yescharacteristic
118D4×D17—232no—
119C2×D68—22no—
120C2×D68—22no—
121C2×D68—22no—
122C2×C4×D17—22no—
123C2×C4×D17—22no—
124C2×C4×D17—22no—
125C4⋊C4×C17—22no—
126C22⋊C4×C17—22no—
127C22⋊C4×C17—22no—
128C22⋊Dic17—22no—
129C22⋊Dic17—22no—
130C22⋊Dic17—22no—
131C22⋊Dic17—41no—
132#63227—22no—
133#63227—22no—
134#63227—22no—
135#63227—22no—
136#63227—22no—
137#63227—22no—
138#63227—22no—
139#63227—41no—
140#63227D414yescomplemented
141#63225—22no—
142C23×C17—21no—
143C23×C17—21no—
144C23×C17—21no—
145C23×C17—21no—
146C23×C17—21no—
147C23×C17—21no—
148C23×C17—21no—
149C23×C17—21no—
150C23×C17—21no—
151C23×C17—21no—
152C23×C17—21no—
153C23×C17—21no—
154C23×C17—21no—
155C23×C17—21no—
156C23×C17—21no—
157C23×C17—21no—
158C23×C17—21no—
159C23×C17C2×D412yes—
160C23×C17C2×D412yes—
161C23×C17C2×D412yes—
162C23×C17C2×D412yes—
163C23×C17C2411yescharacteristic
164C22×D17—21no—
165C22×D17—21no—
166C22×D17—21no—
167C22×D17—21no—
168C22×D17—28no—
169C22×D17—28no—
170C22×D17—21no—
171C22×D17—21no—
172C22×D17—21no—
173C22×D17—21no—
174C22×D17—21no—
175C22×D17—21no—
176C22×D17—21no—
177C22×D17—21no—
178C22×D17—21no—
179C22×D17—21no—
180C22×D17—21no—
181C22×D17—21no—
182C22×D17—28no—
183C22×D17—44no—
184C22×D17—44no—
185C22×D17—44no—
186C22×D17—44no—
187C22×D17—44no—
188C22×D17—44no—
189C22×D17—44no—
190C22×D17—44no—
191C22×D17—44no—
192C22×D17—44no—
193C22×D17—44no—
194C22×D17C2×D412yes—
195C22×D17C2×D412yes—
196C22×D17C2×D412yes—
197C22×D17C2×D412yes—
198C22×D17#4112yes—
199D4×C17—28no—
200D4×C17—44no—
201D4×C17—44no—
202C2×C4×C17—21no—
203C2×C4×C17—21no—
204C2×C4×C17—21no—
205C2×C4×C17—21no—
206C2×C4×C17—21no—
207C2×C4×C17—21no—
208C2×C4×C17—21no—
209C2×C4×C17—21no—
210C2×C4×C17—21no—
211C2×C4×C17—21no—
212C2×C4×C17—44no—
213C2×C4×C17C2×D412yes—
214C2×C4×C17C2×D412yescomplemented
215C22⋊D17—28no—
216C22⋊D17—28no—
217C22⋊D17—44no—
218C22⋊D17—44no—
219C22⋊D17—44no—
220C2×Dic17—21no—
221C2×Dic17—21no—
222C2×Dic17—21no—
223C2×Dic17—21no—
224C2×Dic17—21no—
225C2×Dic17—21no—
226C2×Dic17—21no—
227C2×Dic17—21no—
228C2×Dic17—21no—
229C2×Dic17—21no—
230C2×Dic17—21no—
231C2×Dic17—21no—
232C2×Dic17—21no—
233C2×Dic17—44no—
234C2×Dic17C2×D412yes—
235C2×Dic17C2×D412yescomplemented
236D68—28no—
237C4×D17—28no—
238#2410—171nomaximal, Sylow
239C22×C17—22no—
240C22×C17—22no—
241C22×C17—22no—
242C22×C17—22no—
243C22×C17—22no—
244C22×C17—22no—
245C22×C17—22no—
246C22×C17—22no—
247C22×C17—22no—
248C22×C17—41no—
249C22×C17—41no—
250C22×C17—41no—
251C22×C17—41no—
252C22×C17—41no—
253C22×C17—41no—
254C22×C17—41no—
255C22×C17—41no—
256C22×C17—41no—
257C22×C17—41no—
258C22×C17—41no—
259C22×C17#12014yescomplemented
260C22×C17C22×D411yescharacteristic
261C22×C17C22×D411yescharacteristic
262C22×C17C22×D411yescharacteristic
263C22×C17C22×D411yescharacteristic
264C22×C17C2×#4111yescharacteristic
265C22×C17H(5,𝔽2)11yescharacteristic
266C22×C17H(5,𝔽2)11yescharacteristic
267C2×D17—22no—
268C2×D17—22no—
269C2×D17—22no—
270C2×D17—22no—
271C2×D17—22no—
272C2×D17—22no—
273C2×D17—22no—
274C2×D17—22no—
275C2×D17—22no—
276C2×D17—22no—
277C2×D17—22no—
278C2×D17—22no—
279C2×D17—416no—
280C2×D17—416no—
281C2×D17—41no—
282C2×D17—41no—
283C2×D17—41no—
284C2×D17—41no—
285C2×D17—41no—
286C2×D17—41no—
287C2×D17—41no—
288C2×D17—41no—
289C2×D17#12114yescomplemented
290C4×C17—22no—
291C4×C17—22no—
292C4×C17—41no—
293C4×C17—41no—
294Dic17—22no—
295Dic17—22no—
296Dic17—41no—
297Dic17—41no—
298Dic17—41no—
299C23×D4—171no—
300C2×#121—171no—
301C2×#121D1711yescharacteristic, complemented
302C2×#120—171no—
303C2×#120—171no—
304C22×C22⋊C4—171no—
305#394—171no—
306#394—171no—
307#392—171no—
308#392—171no—
309#386—171no—
310#386—171no—
311#386—171no—
312#385—171no—
313#379—171no—
314C2×C17—24no—
315C2×C17—42no—
316C2×C17—81no—
317C2×C17C2×#12011yescharacteristic
318C2×C17C2×#12111yescharacteristic
319C2×C17#53411yescharacteristic
320C2×C17D4211yescharacteristic
321C2×C17D4211yescharacteristic
322C2×C17#54611yescharacteristic
323C2×C17#54611yescharacteristic
324D17—24no—
325D17—42no—
326D17—42no—
327C25—171no—
328C25—171no—
329C22×D4—171no—
330C22×D4—171no—
331C22×D4—171no—
332C22×D4—171no—
333C22×D4—171no—
334C22×D4—171no—
335C22×D4—344no—
336C22×D4—344no—
337C22×D4—344no—
338C22×D4C2×D1711yescharacteristic
339C22×D4C2×D1711yescharacteristic, complemented
340C22×D4C2×D1711yescharacteristic, complemented
341C23×C4—171no—
342C23×C4—171no—
343C23×C4C2×D1711yescharacteristic, complemented
344#121—24no—
345#121—344no—
346#120—344no—
347#120—344no—
348C2×C4⋊C4—171no—
349C2×C4⋊C4C2×D1711yescharacteristic, complemented
350C2×C22⋊C4—171no—
351C2×C22⋊C4—171no—
352C2×C22⋊C4—171no—
353C2×C22⋊C4—171no—
354C2×C22⋊C4—171no—
355C2×C22⋊C4—171no—
356C2×C22⋊C4—171no—
357C2×C22⋊C4—171no—
358C2×C22⋊C4—171no—
359C2×C22⋊C4—171no—
360C2×C22⋊C4—171no—
361C2×C22⋊C4—171no—
362C2×C22⋊C4—171no—
363C2×C22⋊C4—344no—
364C2×C22⋊C4C2×D1711yescharacteristic, complemented
365C2×C22⋊C4C2×D1711yescharacteristic, complemented
366#95—171no—
367#95—171no—
368#95—171no—
369#95—171no—
370C17#241011yescharacteristic, complemented, Sylow
371C24—171no—
372C24—171no—
373C24—171no—
374C24—174no—
375C24—342no—
376C24—342no—
377C24—342no—
378C24—342no—
379C24—342no—
380C24—342no—
381C24—342no—
382C24—342no—
383C24—342no—
384C24—681no—
385C24—681no—
386C24—681no—
387C24—681no—
388C24C22×D1711yescharacteristic
389C24C22×D1711yescharacteristic
390C24C22×D1711yescharacteristic
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—41no—
399C2×D4—174no—
400C2×D4—342no—
401C2×D4—342no—
402C2×D4—342no—
403C2×D4—342no—
404C2×D4—3432no—
405C2×D4—342no—
406C2×D4—342no—
407C2×D4—342no—
408C2×D4—342no—
409C2×D4—342no—
410C2×D4—342no—
411C2×D4—342no—
412C2×D4—342no—
413C2×D4—342no—
414C2×D4—342no—
415C2×D4—681no—
416C2×D4—681no—
417C2×D4—681no—
418C2×D4C22⋊D1714yescomplemented
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—41no—
422C22×C4—171no—
423C22×C4—171no—
424C22×C4—171no—
425C22×C4—171no—
426C22×C4—171no—
427C22×C4—342no—
428C22×C4—342no—
429C22×C4—342no—
430C22×C4—342no—
431C22×C4—342no—
432C22×C4—681no—
433C22×C4C22×D1711yescharacteristic
434C22×C4C22×D1711yescharacteristic
435C22×C4C22×D1711yescharacteristic
436C22×C4C22×D1711yescharacteristic
437C4⋊C4—22no—
438C4⋊C4—342no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—174no—
442C22⋊C4—342no—
443C22⋊C4—342no—
444C22⋊C4—342no—
445C22⋊C4—342no—
446C22⋊C4—342no—
447C22⋊C4—342no—
448C22⋊C4—342no—
449C22⋊C4—342no—
450C22⋊C4—342no—
451C22⋊C4—342no—
452C22⋊C4—681no—
453C22⋊C4—681no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—172no—
472C23—172no—
473C23—172no—
474C23—172no—
475C23—172no—
476C23—348no—
477C23—348no—
478C23—341no—
479C23—341no—
480C23—341no—
481C23—341no—
482C23—341no—
483C23—341no—
484C23—341no—
485C23—341no—
486C23—341no—
487C23—341no—
488C23—341no—
489C23—341no—
490C23—341no—
491C23—341no—
492C23—341no—
493C23—341no—
494C23—348no—
495C23—684no—
496C23—684no—
497C23—684no—
498C23—684no—
499C23—684no—
500C23—684no—
501C23—684no—
502C23—684no—
503C23—684no—
504C23—684no—
505C23—684no—
506C23D4×D1712yes—
507C23D4×D1712yes—
508C23C2×C22⋊D1712yes—
509C23C2×C22⋊D1712yes—
510C23C23×D1711yescharacteristic
511D4—28no—
512D4—44no—
513D4—44no—
514D4—348no—
515D4—348no—
516D4—348no—
517D4—684no—
518D4—684no—
519D4—684no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—44no—
531C2×C4—172no—
532C2×C4—172no—
533C2×C4—348no—
534C2×C4—341no—
535C2×C4—341no—
536C2×C4—341no—
537C2×C4—341no—
538C2×C4—341no—
539C2×C4—341no—
540C2×C4—341no—
541C2×C4—341no—
542C2×C4—341no—
543C2×C4—341no—
544C2×C4—341no—
545C2×C4—341no—
546C2×C4—341no—
547C2×C4—684no—
548C2×C4D4×D1712yescomplemented
549C2×C4C2×C22⋊D1712yes—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—174no—
571C22—342no—
572C22—342no—
573C22—342no—
574C22—342no—
575C22—342no—
576C22—342no—
577C22—342no—
578C22—342no—
579C22—342no—
580C22—342no—
581C22—342no—
582C22—342no—
583C22—6816no—
584C22—6816no—
585C22—681no—
586C22—681no—
587C22—681no—
588C22—681no—
589C22—681no—
590C22—681no—
591C22—681no—
592C22—681no—
593C22#1058762314yescomplemented
594C22C2×D4×D1711yescharacteristic
595C22C2×D4×D1711yescharacteristic
596C22C2×D4×D1711yescharacteristic
597C22#1058769111yescharacteristic
598C22#41×D1711yescharacteristic
599C22#1058769611yescharacteristic
600C22C22×C22⋊D1711yescharacteristic
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—342no—
606C4—342no—
607C4—681no—
608C4—681no—
609C4—681no—
610C2—24no—
611C2—42no—
612C2—81no—
613C2—344no—
614C2—682no—
615C2—682no—
616C2C2×#1058762311yescharacteristic
617C2#121×D1711yescharacteristic
618C2#1176336711yescharacteristic
619C2D4×C22⋊D1711yescharacteristic
620C2#1176344311yescharacteristic
621C2#1176344711yescharacteristic
622C2#1176344811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, cosocleC23×C17C24
FittingC2×C17×#121C2
hypercenterC2×#121D17
hypocenterC17#2410
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×D4×D17C2semidirect
2. C2×#10587625C2semidirect
3. C2×#10587623C2semidirect
4. C2×#10587623C2semidirect
5. C22×#63227C2semidirect
6. #11762726C2semidirect
7. #11762724C2semidirect
8. #11762718C2semidirect
9. #11762717C2semidirect
10. #11762689C2semidirect
11. #11762688C2semidirect
12. #11762685C2semidirect
13. #11762680C2semidirect
14. #11762664C2semidirect
15. C2×C17×#121C2semidirect
19. C22×D4×C17C22semidirect
20. C22×D4×C17C22semidirect
21. C23×C4×C17C22semidirect
25. C22×C22⋊D17C22semidirect
26. C22×C22⋊D17C22semidirect
27. C23×Dic17C22semidirect
34. C2×C4⋊C4×C17C22semidirect
35. C2×C22⋊C4×C17C22semidirect
36. C2×C22⋊C4×C17C22semidirect
37. C2×C22⋊Dic17C22semidirect
38. C2×C22⋊Dic17C22semidirect
39. C2×C22⋊Dic17C22semidirect
40. C2×C22⋊Dic17C22semidirect
48. C2×#63227C22semidirect
49. C2×#63227C22semidirect
50. C2×#63227C22semidirect
51. C2×#63227C22semidirect
52. C2×#63227C22semidirect
53. C2×#63227C22semidirect
54. C2×#63225C22semidirect
55. #10587502C22semidirect
56. #10587502C22semidirect
57. #10587502C22semidirect
58. #10587502C22semidirect
75. C23×D17D4semidirect
87. C2×D4×C17D4semidirect
109. C2×C22⋊D17D4semidirect
140. #63227D4semidirect
214. C2×C4×C17C2×D4semidirect
235. C2×Dic17C2×D4semidirect
259. C22×C17#120semidirect
289. C2×D17#121semidirect
301. C2×#121D17semidirect
339. C22×D4C2×D17semidirect
340. C22×D4C2×D17semidirect
343. C23×C4C2×D17semidirect
349. C2×C4⋊C4C2×D17semidirect
364. C2×C22⋊C4C2×D17semidirect
365. C2×C22⋊C4C2×D17semidirect
370. C17#2410semidirect
418. C2×D4C22⋊D17semidirect
548. C2×C4D4×D17semidirect
593. C22#10587623semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D172
C2×#105876252
C2×#105876232
C22×#632272
#117627262
#117627242
#117627182
#117627172
#117626892
#117626882
#117626852
#117626802
#117626642
C2×C17×#1212
#241017