Finite Group Databasebeta

← #17035957

Subgroups — #17035957

Order 4352.

2126 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763368C211yesmaximal, characteristic
2C22×#10587505C211yesmaximal, characteristic, complemented
3#14531359C212yesmaximal, complemented
4#14529197C214yesmaximal, complemented
5#14529192C214yesmaximal, complemented
6C2×#11762576C212yesmaximal, complemented
7C2×C17×#518C211yesmaximal, characteristic, complemented
8C23×C22⋊D17C2211yescharacteristic
9#11763368—24no—
10#11763368C418yescomplemented
11C2×#10587615—21no—
12C2×#10587621C2212yes—
13C2×#10587625—22no—
14C2×#10587639—21no—
15C2×#10587623C2212yes—
16C22×C22⋊Dic17C2212yes—
17C22×C22⋊Dic17C2211yescharacteristic
18C2×#10587505—24no—
19C2×#10587505C2214yes—
20#11762688—24no—
21#11762686—24no—
22#11762670C2214yescomplemented
23#11762664C2214yescomplemented
24#11762576C2218yescomplemented
25C23×D4×C17C2211yescharacteristic
26C17×#518—24no—
27C17×#518—22no—
28C17×#518C2214yes—
29C2×C4×D4×C17—24no—
30C2×C17×#117—21no—
31C22×C22⋊C4×C17—21no—
32C22×C22⋊C4×C17C2212yes—
33C25×C17D411yescharacteristic
34C25×C17C2311yescharacteristic
35C24×D17C2311yescharacteristic
36C22×D4×C17—22no—
37C22×D4×C17—22no—
38C22×D4×C17—24no—
39C22×D4×C17C2×C414yes—
40C22×D4×C17D414yes—
41C22×D4×C17D412yes—
42C22×D4×C17C2312yes—
43C23×C4×C17—22no—
44C23×C4×C17D411yescharacteristic
45C23×C4×C17D414yescomplemented
46C22×C22⋊D17—22no—
47C22×C22⋊D17—21no—
48C22×C22⋊D17—21no—
49C22×C22⋊D17—22no—
50C22×C22⋊D17—22no—
51C22×C22⋊D17—24no—
52C22×C22⋊D17—22no—
53C22×C22⋊D17C2×C414yescomplemented
54C23×Dic17—21no—
55C23×Dic17—22no—
56C23×Dic17C2311yescharacteristic
57C4×D4×C17—216no—
58C4×D4×C17—216no—
59C17×#117—24no—
60C17×#117—24no—
61C2×C4⋊C4×C17—22no—
62C2×C22⋊C4×C17—22no—
63C2×C22⋊C4×C17—24no—
64C2×C22⋊C4×C17—22no—
65C2×C22⋊C4×C17—24no—
66C2×C22⋊C4×C17—22no—
67C2×C22⋊C4×C17—22no—
68C2×C22⋊C4×C17—22no—
69C2×C22⋊C4×C17D414yescomplemented
70C2×C22⋊C4×C17C2314yes—
71C2×C42×C17—22no—
72#10587639—28no—
73C2×C22⋊Dic17—21no—
74C2×C22⋊Dic17—22no—
75C2×C22⋊Dic17—22no—
76C2×C22⋊Dic17—24no—
77C2×C22⋊Dic17—24no—
78C2×C22⋊Dic17—22no—
79C2×C22⋊Dic17C2×C414yescomplemented
80C2×C22⋊Dic17C2314yes—
81C2×C22⋊Dic17C2312yes—
82#10587625—216no—
83#10587623—24no—
84#10587623C2×C418yescomplemented
85#10587621—24no—
86#10587621C2×C418yescomplemented
87#10587615—28no—
88C2×#63227—22no—
89C2×#63227—28no—
90C2×#63225—22no—
91#10587505—28no—
92#10587502—28no—
93C24×C17—21no—
94C24×C17—21no—
95C24×C17—22no—
96C24×C17—82no—
97C24×C17—82no—
98C24×C17C22⋊C414yescomplemented
99C24×C17C22×C412yes—
100C24×C17C2×D412yes—
101C24×C17C2×D412yes—
102C24×C17C2×D411yescharacteristic
103C24×C17C2×D411yescharacteristic
104C24×C17C2×D412yes—
105C24×C17C2×D412yes—
106C24×C17#4114yes—
107C24×C17C2411yescharacteristic
108C23×D17—21no—
109C23×D17—22no—
110C23×D17—21no—
111C23×D17—22no—
112C23×D17—82no—
113C23×D17C22×C412yescomplemented
114C2×D4×C17—28no—
115C2×D4×C17—28no—
116C2×D4×C17—24no—
117C2×D4×C17—28no—
118C2×D4×C17—28no—
119C2×D4×C17—24no—
120C2×D4×C17—24no—
121C2×D4×C17—24no—
122C2×D4×C17C22⋊C418yescomplemented
123C2×D4×C17C22×C414yes—
124C2×D4×C17C2×D414yes—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17—22no—
128C22×C4×C17—24no—
129C22×C4×C17—28no—
130C22×C4×C17—24no—
131C22×C4×C17—84no—
132C22×C4×C17—84no—
133C22×C4×C17C22⋊C414yescomplemented
134C22×C4×C17C2×D412yes—
135C22×C4×C17C2×D418yes—
136C2×C22⋊D17—24no—
137C2×C22⋊D17—24no—
138C2×C22⋊D17—28no—
139C2×C22⋊D17—28no—
140C2×C22⋊D17—28no—
141C2×C22⋊D17—41no—
142C2×C22⋊D17—42no—
143C2×C22⋊D17—41no—
144C2×C22⋊D17—44no—
145C2×C22⋊D17—44no—
146C2×C22⋊D17—42no—
147C2×C22⋊D17—42no—
148C2×C22⋊D17—84no—
149C22×Dic17—22no—
150C22×Dic17—22no—
151C22×Dic17—21no—
152C22×Dic17—21no—
153C22×Dic17—22no—
154C22×Dic17—24no—
155C22×Dic17—24no—
156C22×Dic17—44no—
157C22×Dic17—82no—
158C22×Dic17—84no—
159C22×Dic17C22×C412yescomplemented
160C4⋊C4×C17—28no—
161C22⋊C4×C17—28no—
162C22⋊C4×C17—24no—
163C22⋊C4×C17—24no—
164C22⋊C4×C17—24no—
165C22⋊C4×C17—24no—
166C42×C17—28no—
167C22⋊Dic17—24no—
168C22⋊Dic17—28no—
169C22⋊Dic17—22no—
170C22⋊Dic17—24no—
171C22⋊Dic17—24no—
172C22⋊Dic17—44no—
173C22⋊Dic17C22×C414yescomplemented
174#63227—28no—
175#63227—88no—
176#63225—28no—
177#20960—171nomaximal, Sylow
178C23×C17—22no—
179C23×C17—24no—
180C23×C17—22no—
181C23×C17—24no—
182C23×C17—44no—
183C23×C17—42no—
184C23×C17—44no—
185C23×C17—42no—
186C23×C17—42no—
187C23×C17—44no—
188C23×C17—44no—
189C23×C17—82no—
190C23×C17—82no—
191C23×C17—82no—
192C23×C17—84no—
193C23×C17—84no—
194C23×C17—84no—
195C23×C17C2×C22⋊C414yes—
196C23×C17C2×C22⋊C412yes—
197C23×C17C2×C22⋊C412yes—
198C23×C17C4×D414yes—
199C23×C17C4×D414yes—
200C23×C17#12011yescharacteristic
201C23×C17#12012yes—
202C23×C17#12011yescharacteristic
203C23×C17#12114yes—
204C23×C17#12114yes—
205C23×C17#12312yes—
206C23×C17#12312yes—
207C23×C17C23×C411yescharacteristic
208C23×C17C22×D411yescharacteristic
209C23×C17C22×D411yescharacteristic
210C23×C17C22×D412yes—
211C23×C17C2×#4112yes—
212C22×D17—22no—
213C22×D17—24no—
214C22×D17—44no—
215C22×D17—48no—
216C22×D17—41no—
217C22×D17—42no—
218C22×D17—41no—
219C22×D17—82no—
220C22×D17—82no—
221C22×D17—84no—
222D4×C17—28no—
223D4×C17—28no—
224D4×C17—216no—
225C2×C4×C17—22no—
226C2×C4×C17—22no—
227C2×C4×C17—24no—
228C2×C4×C17—24no—
229C2×C4×C17—28no—
230C2×C4×C17—48no—
231C2×C4×C17—48no—
232C2×C4×C17—84no—
233C2×C4×C17—88no—
234C2×C4×C17C2×C22⋊C414yes—
235C22⋊D17—44no—
236C22⋊D17—44no—
237C22⋊D17—48no—
238C22⋊D17—88no—
239C2×Dic17—24no—
240C2×Dic17—22no—
241C2×Dic17—24no—
242C2×Dic17—44no—
243C2×Dic17—41no—
244C2×Dic17—42no—
245C2×Dic17—41no—
246C2×Dic17—48no—
247C2×Dic17—44no—
248C2×Dic17—84no—
249C2×Dic17—88no—
250C2×#534—171no—
251C2×#518D1711yescharacteristic, complemented
252C22×#99—171no—
253#2308—172no—
254#1890—174no—
255#1889—174no—
256C2×#342—172no—
257C22×C17—24no—
258C22×C17—22no—
259C22×C17—22no—
260C22×C17—24no—
261C22×C17—22no—
262C22×C17—24no—
263C22×C17—42no—
264C22×C17—44no—
265C22×C17—41no—
266C22×C17—41no—
267C22×C17—42no—
268C22×C17—42no—
269C22×C17—42no—
270C22×C17—44no—
271C22×C17—44no—
272C22×C17—44no—
273C22×C17—42no—
274C22×C17—44no—
275C22×C17—48no—
276C22×C17—44no—
277C22×C17—82no—
278C22×C17—84no—
279C22×C17#38612yes—
280C22×C17#38612yes—
281C22×C17#38614yes—
282C22×C17C22×C22⋊C411yescharacteristic
283C22×C17C2×C4×D412yes—
284C22×C17C2×#12011yescharacteristic
285C22×C17C2×#12112yes—
286C22×C17C2×#12311yescharacteristic
287C2×D17—44no—
288C2×D17—48no—
289C2×D17—42no—
290C2×D17—84no—
291C2×D17—82no—
292C2×D17—82no—
293C4×C17—24no—
294C4×C17—48no—
295Dic17—44no—
296Dic17—42no—
297Dic17—84no—
298C23×D4—171no—
299C23×D4C2×D1711yescharacteristic
300#534—178no—
301#534—344no—
302C2×#123—172no—
303C2×#123—341no—
304C2×#121—342no—
305C2×#120—172no—
306C2×#120—341no—
307#518—22no—
308#518—24no—
309#518C2×D1714yes—
310C2×C4×D4—24no—
311C2×#117—21no—
312C22×C22⋊C4—21no—
313C22×C22⋊C4—171no—
314C22×C22⋊C4—172no—
315C22×C22⋊C4C2×D1712yes—
316C2×#99—174no—
317C2×#99—344no—
318#386—344no—
319#386—344no—
320#381—174no—
321#379—174no—
322#342—178no—
323C2×C17—21no—
324C2×C17—22no—
325C2×C17—22no—
326C2×C17—21no—
327C2×C17—22no—
328C2×C17—22no—
329C2×C17—24no—
330C2×C17—44no—
331C2×C17C2×#38611yescharacteristic
332C2×C17#302612yes—
333D17—82no—
334C25—171no—
335C25C22⋊D1711yescharacteristic
336C25C22×D1711yescharacteristic
337C22×D4—24no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—174no—
341C22×D4—342no—
342C22×D4—344no—
343C22×D4—341no—
344C22×D4—341no—
345C22×D4—342no—
346C22×D4—342no—
347C22×D4—342no—
348C22×D4C4×D1714yes—
349C22×D4D6814yes—
350C22×D4C22⋊D1712yes—
351C22×D4C22×D1712yes—
352C23×C4—22no—
353C23×C4—171no—
354C23×C4—341no—
355C23×C4—342no—
356C23×C4C22⋊D1711yescharacteristic
357C23×C4C22⋊D1714yescomplemented
358#123—178no—
359#123—344no—
360#123—348no—
361#121—3416no—
362#120—178no—
363#120—348no—
364#120—344no—
365C4×D4—216no—
366C4×D4—216no—
367#117—24no—
368#117—24no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—342no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—174no—
379C2×C22⋊C4—172no—
380C2×C22⋊C4—174no—
381C2×C22⋊C4—342no—
382C2×C22⋊C4—341no—
383C2×C22⋊C4—342no—
384C2×C22⋊C4—342no—
385C2×C22⋊C4—344no—
386C2×C22⋊C4—344no—
387C2×C22⋊C4—342no—
388C2×C22⋊C4—348no—
389C2×C22⋊C4C22⋊D1714yescomplemented
390C2×C22⋊C4C22×D1714yes—
391C2×C42—22no—
392#99—348no—
393#95—348no—
394C17#2096011yescharacteristic, complemented, Sylow
395C24—21no—
396C24—22no—
397C24—21no—
398C24—82no—
399C24—82no—
400C24—172no—
401C24—342no—
402C24—341no—
403C24—341no—
404C24—342no—
405C24—1362no—
406C24#6322714yescomplemented
407C24C2×C4×D1712yes—
408C24C2×D6812yes—
409C24#6325214yes—
410C24C2×C22⋊D1712yes—
411C24C2×C22⋊D1711yescharacteristic
412C24C2×C22⋊D1711yescharacteristic
413C24C2×C22⋊D1712yes—
414C24C2×C22⋊D1712yes—
415C24C23×D1711yescharacteristic
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—24no—
421C2×D4—28no—
422C2×D4—28no—
423C2×D4—24no—
424C2×D4—344no—
425C2×D4—344no—
426C2×D4—348no—
427C2×D4—348no—
428C2×D4—348no—
429C2×D4—682no—
430C2×D4—682no—
431C2×D4—684no—
432C2×D4—684no—
433C2×D4—681no—
434C2×D4—682no—
435C2×D4—681no—
436C2×D4—1364no—
437C2×D4#6322718yescomplemented
438C2×D4C2×C4×D1714yes—
439C2×D4C2×D6814yes—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—24no—
444C22×C4—28no—
445C22×C4—24no—
446C22×C4—84no—
447C22×C4—84no—
448C22×C4—172no—
449C22×C4—341no—
450C22×C4—342no—
451C22×C4—342no—
452C22×C4—342no—
453C22×C4—341no—
454C22×C4—344no—
455C22×C4—344no—
456C22×C4—684no—
457C22×C4—1362no—
458C22×C4—1364no—
459C22×C4#6322714yescomplemented
460C22×C4C2×C22⋊D1712yes—
461C22×C4C2×C22⋊D1718yes—
462C4⋊C4—28no—
463C4⋊C4—348no—
464C22⋊C4—28no—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4—174no—
470C22⋊C4—342no—
471C22⋊C4—344no—
472C22⋊C4—348no—
473C22⋊C4—348no—
474C22⋊C4—344no—
475C22⋊C4—344no—
476C22⋊C4—684no—
477C22⋊C4—1368no—
478C42—28no—
479C23—24no—
480C23—22no—
481C23—24no—
482C23—22no—
483C23—44no—
484C23—44no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—44no—
489C23—44no—
490C23—82no—
491C23—82no—
492C23—82no—
493C23—84no—
494C23—84no—
495C23—84no—
496C23—342no—
497C23—344no—
498C23—688no—
499C23—684no—
500C23—681no—
501C23—682no—
502C23—681no—
503C23—1362no—
504C23—1362no—
505C23—1364no—
506C23C2×#6322714yes—
507C23C2×#6322712yes—
508C23C2×#6322712yes—
509C23C4×C22⋊D1714yes—
510C23C4×C22⋊D1714yes—
511C23#1058761512yes—
512C23#1058761512yes—
513C23#1058761614yes—
514C23#1058761614yes—
515C23#1058763911yescharacteristic
516C23#1058763912yes—
517C23#1058763911yescharacteristic
518C23C22×C4×D1711yescharacteristic
519C23C22×D6811yescharacteristic
520C23C2×#6325212yes—
521C23C22×C22⋊D1711yescharacteristic
522C23C22×C22⋊D1712yes—
523D4—216no—
524D4—28no—
525D4—28no—
526D4—684no—
527D4—684no—
528D4—688no—
529D4—1368no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—28no—
535C2×C4—48no—
536C2×C4—48no—
537C2×C4—84no—
538C2×C4—88no—
539C2×C4—344no—
540C2×C4—342no—
541C2×C4—344no—
542C2×C4—684no—
543C2×C4—681no—
544C2×C4—682no—
545C2×C4—681no—
546C2×C4—688no—
547C2×C4—684no—
548C2×C4—1364no—
549C2×C4—1368no—
550C2×C4C2×#6322714yes—
551C22—22no—
552C22—24no—
553C22—24no—
554C22—22no—
555C22—22no—
556C22—24no—
557C22—42no—
558C22—44no—
559C22—42no—
560C22—42no—
561C22—41no—
562C22—41no—
563C22—42no—
564C22—44no—
565C22—44no—
566C22—42no—
567C22—44no—
568C22—44no—
569C22—48no—
570C22—44no—
571C22—82no—
572C22—84no—
573C22—684no—
574C22—688no—
575C22—682no—
576C22—1364no—
577C22—1362no—
578C22—1362no—
579C22#1176268812yes—
580C22#1176268812yes—
581C22#1176268814yes—
582C22C22×#6322711yescharacteristic
583C22C2×C4×C22⋊D1712yes—
584C22C2×#1058763911yescharacteristic
585C22C2×#1058761612yes—
586C22C2×#1058761511yescharacteristic
587C4—24no—
588C4—48no—
589C4—684no—
590C4—682no—
591C4—1364no—
592C2—21no—
593C2—22no—
594C2—22no—
595C2—21no—
596C2—22no—
597C2—22no—
598C2—24no—
599C2—44no—
600C2—1362no—
601C2C2×#1176268811yescharacteristic
602C2#1453818112yes—
subgroupG/H
centerC22C2×#10587639
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC2×C17×#518C2
socleC22×C17C2×#120
prime radicalC2×#11763368C2
cosocleC24×C17C24
hypercenterC2×#518D17
hypocenterC17#20960
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C25 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
2. C22×#10587505C2semidirect
3. #14531359C2semidirect
4. #14529197C2semidirect
5. #14529192C2semidirect
6. C2×#11762576C2semidirect
7. C2×C17×#518C2semidirect
10. #11763368C4semidirect
22. #11762670C22semidirect
23. #11762664C22semidirect
24. #11762576C22semidirect
45. C23×C4×C17D4semidirect
53. C22×C22⋊D17C2×C4semidirect
69. C2×C22⋊C4×C17D4semidirect
79. C2×C22⋊Dic17C2×C4semidirect
84. #10587623C2×C4semidirect
86. #10587621C2×C4semidirect
98. C24×C17C22⋊C4semidirect
113. C23×D17C22×C4semidirect
122. C2×D4×C17C22⋊C4semidirect
133. C22×C4×C17C22⋊C4semidirect
159. C22×Dic17C22×C4semidirect
173. C22⋊Dic17C22×C4semidirect
251. C2×#518D17semidirect
357. C23×C4C22⋊D17semidirect
389. C2×C22⋊C4C22⋊D17semidirect
394. C17#20960semidirect
406. C24#63227semidirect
437. C2×D4#63227semidirect
459. C22×C4#63227semidirect

Maximal subgroups

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

subgroupindex
C2×#117633682
C22×#105875052
#145313592
#145291972
#145291922
C2×#117625762
C2×C17×#5182
#2096017