Finite Group Databasebeta

← #17070385

Subgroups — #17070385

Order 4352.

1378 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D17C211yesmaximal, characteristic, complemented
2C2×#11763090C211yesmaximal, characteristic, complemented
3C2×#11763086C211yesmaximal, characteristic, complemented
4C4×#10587581C211yesmaximal, characteristic
5#14530111C212yesmaximal, complemented
6#14529919C212yesmaximal, complemented
7#14529736C211yesmaximal, characteristic, complemented
8#14529100C212yesmaximal
9#14528973C212yesmaximal, complemented
10#14528761C211yesmaximal, characteristic, complemented
11C17×#1988C211yesmaximal, characteristic, complemented
12C22×Q8×D17—21no—
13C2×#10587555C2211yescharacteristic
14C2×#10587574—21no—
15C2×#10587574C2212yes—
16C2×#10587630—21no—
17C4⋊Q8×D17—24no—
18C4⋊Q8×D17—24no—
19C2×#10587581C2211yescharacteristic
20C2×C4×D68—21no—
21C2×C4×D68C2211yescharacteristic
22C2×C4⋊C4×D17—21no—
23C2×C4⋊C4×D17C2212yes—
24C2×C42×D17C2211yescharacteristic
25#11763090—24no—
26#11763086—24no—
27C2×#10587489C2212yes—
28C2×#10587478C2212yes—
29C2×C4⋊#3622C2211yescharacteristic
30C2×#10587492C2212yes—
31C2×#10587480C2212yes—
32C2×#10587491C2212yes—
33#11762710C2211yescharacteristic
34#11762708C2211yescharacteristic
35#11762701—21no—
36#11762687—21no—
37#11762666C2211yescharacteristic
38C4×#63227—21no—
39#11762571C2212yes—
40#11762571C2212yes—
41#11762563C2212yes—
42C2×C17×C4⋊Q8C2211yescharacteristic
43C2×C17×C4⋊C8C2211yescharacteristic
44C4×C4⋊C4×C17C2211yescharacteristic
45C17×#340C2212yes—
46C17×#340C2212yes—
47C22×Q8×C17—21no—
48C2×Q8×D17—28no—
49C2×Q8×D17—44no—
50C2×Q8×D17—44no—
51C22×D68—21no—
52C22×D68C2311yescharacteristic
53C22×C4×D17—22no—
54C22×C4×D17—21no—
55C22×C4×D17D411yescharacteristic
56C22×C4×D17D411yescharacteristic
57C22×C4×D17C2311yescharacteristic
58C22×Dic34—21no—
59C22×Dic34—22no—
60C22×C8×C17C2312yes—
61C17×C4⋊Q8—22no—
62C17×C4⋊Q8D414yescomplemented
63C2×C4⋊C4×C17—21no—
64C2×C4⋊C4×C17C2311yescharacteristic
65C2×C4⋊C4×C17C2312yes—
66C2×C4⋊C4×C17C2311yescharacteristic
67C2×C42×C17—21no—
68C2×C42×C17C2311yescharacteristic
69#10587630—28no—
70C2×#63227—21no—
71C2×#63227—21no—
72C2×#63227—21no—
73C2×#63227—21no—
74C2×#63227—21no—
75C2×C4⋊Dic17—21no—
76C2×C4⋊Dic17—21no—
77C2×C4⋊Dic17C2311yescharacteristic
78C2×C4⋊Dic17C2312yes—
79C2×#63225—22no—
80C2×#63225—22no—
81C2×C4×Dic17D411yescharacteristic
82C2×C4×Dic17D411yescharacteristic
83C2×C4×Dic17C2311yescharacteristic
84C22×#3622C2312yes—
85#10587581—22no—
86#10587581Q814yescomplemented
87C4⋊C4×D17—28no—
88C4⋊C4×D17—24no—
89C4⋊C4×D17—24no—
90#10587574—28no—
91#10587574—24no—
92#10587574—24no—
93C4×D68—22no—
94C4×D68—22no—
95C4×D68—44no—
96C42×D17—22no—
97C42×D17—22no—
98#10587555—22no—
99#10587555D414yescomplemented
100C17×C4⋊C8—22no—
101C17×#95—21no—
102#10587502—21no—
103#10587502—21no—
104#10587492—24no—
105#10587491—24no—
106#10587489—24no—
107#10587480—24no—
108#10587478—24no—
109C4⋊#3622—22no—
110C23×D17—21no—
111C23×D17C2×D411yescharacteristic
112C2×Q8×C17—24no—
113C2×Q8×C17—42no—
114C2×Q8×C17—42no—
115C22×C4×C17—22no—
116C22×C4×C17—21no—
117C22×C4×C17—21no—
118C22×C4×C17C2×D411yescharacteristic
119C22×C4×C17C2×D411yescharacteristic
120C22×C4×C17C2411yescharacteristic
121C22×Dic17—22no—
122C22×Dic17—21no—
123C22×Dic17C2×D411yescharacteristic
124C22×Dic17C2×D411yescharacteristic
125C22×Dic17C2×D411yescharacteristic
126Q8×D17—432no—
127C2×D68—21no—
128C2×D68—21no—
129C2×D68—21no—
130C2×D68—21no—
131C2×D68—24no—
132C2×D68—21no—
133C2×D68—42no—
134C2×D68—42no—
135C2×D68C2×Q812yescomplemented
136C2×C4×D17—22no—
137C2×C4×D17—22no—
138C2×C4×D17—22no—
139C2×C4×D17—22no—
140C2×C4×D17—21no—
141C2×C4×D17—21no—
142C2×C4×D17—21no—
143C2×C4×D17—21no—
144C2×C4×D17—22no—
145C2×C4×D17—28no—
146C2×C4×D17—44no—
147C2×C4×D17—44no—
148C2×C4×D17—42no—
149C2×C4×D17—42no—
150C2×C4×D17—42no—
151C2×C4×D17D814yes—
152C2×C4×D17C2×Q812yes—
153C2×C4×D17#4112yes—
154C2×Dic34—28no—
155C2×Dic34—24no—
156C2×Dic34—44no—
157C2×Dic34—42no—
158C2×Dic34—42no—
159C2×Dic34—44no—
160C2×C8×C17—22no—
161C2×C8×C17—22no—
162C2×C8×C17—22no—
163C4⋊C4×C17—24no—
164C4⋊C4×C17—22no—
165C4⋊C4×C17—21no—
166C4⋊C4×C17—21no—
167C4⋊C4×C17—21no—
168C4⋊C4×C17C2×D414yes—
169C4⋊C4×C17C2×Q812yescomplemented
170C42×C17—42no—
171C42×C17C2×D412yes—
172C42×C17C2×D412yes—
173#63227—24no—
174#63227—42no—
175#63227—42no—
176#63227—42no—
177#63227—42no—
178C4⋊Dic17—24no—
179C4⋊Dic17—22no—
180C4⋊Dic17—21no—
181C4⋊Dic17—21no—
182C4⋊Dic17—42no—
183C4⋊Dic17C2×D414yes—
184#63225—28no—
185#63225—28no—
186C4×Dic17—22no—
187C4×Dic17—22no—
188C4×Dic17—21no—
189C4×Dic17—21no—
190C2×#3622—22no—
191C2×#3622—22no—
192C2×#3622—22no—
193#24298—171nomaximal, Sylow
194C23×C17C22×D411yescharacteristic
195C22×D17—21no—
196C22×D17—21no—
197C22×D17—21no—
198C22×D17—21no—
199C22×D17—22no—
200C22×D17—41no—
201C22×D17—41no—
202C22×D17—41no—
203C22×D17—41no—
204C22×D17—41no—
205C22×D17—41no—
206C22×D17C22⋊Q812yes—
207C22×D17C2×D812yes—
208C22×D17#13712yes—
209Q8×C17—48no—
210C2×C4×C17—21no—
211C2×C4×C17—21no—
212C2×C4×C17—24no—
213C2×C4×C17—22no—
214C2×C4×C17—41no—
215C2×C4×C17—42no—
216C2×C4×C17—42no—
217C2×C4×C17—41no—
218C2×C4×C17—41no—
219C2×C4×C17—41no—
220C2×C4×C17—41no—
221C2×C4×C17#12012yes—
222C2×C4×C17#12012yes—
223C2×C4×C17C2×D812yes—
224C2×C4×C17AGL(1,ℤ/8)12yes—
225C2×C4×C17C22×D411yescharacteristic
226C2×C4×C17C22×D411yescharacteristic
227C2×C4×C17C22×Q811yescharacteristic
228C2×C4×C17C2×#4111yescharacteristic
229C2×C4×C172−1+411yescharacteristic
230C2×C4×C172−1+411yescharacteristic
231C2×Dic17—21no—
232C2×Dic17—21no—
233C2×Dic17—21no—
234C2×Dic17—21no—
235C2×Dic17—21no—
236C2×Dic17—21no—
237C2×Dic17—24no—
238C2×Dic17—42no—
239C2×Dic17—42no—
240C2×Dic17—41no—
241C2×Dic17—41no—
242C2×Dic17—41no—
243C2×Dic17C22⋊Q812yes—
244C2×Dic17C2×D812yes—
245C2×Dic17#13712yes—
246D68—22no—
247D68—22no—
248D68—48no—
249D68—41no—
250D68—41no—
251C4×D17—28no—
252C4×D17—22no—
253C4×D17—22no—
254C4×D17—22no—
255C4×D17—22no—
256C4×D17—28no—
257C4×D17—416no—
258C4×D17—84no—
259Dic34—416no—
260Dic34—48no—
261C8×C17—42no—
262#3622—42no—
263C22×C4⋊Q8—171no—
264C2×#474—171no—
265C2×#474—171no—
266C4×#121—171no—
267#2057—172no—
268#2023—172no—
269#1988—171no—
270#1988D1711yescharacteristic, complemented
271#1874—172no—
272#1852—172no—
273#1797—171no—
274C22×C17C2×#12011yescharacteristic
275C22×C17C2×C22⋊Q811yescharacteristic
276C22×C17#53611yescharacteristic
277C22×C17C22×D811yescharacteristic
278C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C17C2×#13711yescharacteristic
280C22×C17C2×#13711yescharacteristic
281C2×D17—22no—
282C2×D17—22no—
283C2×D17—22no—
284C2×D17—22no—
285C2×D17—22no—
286C2×D17—22no—
287C2×D17—42no—
288C2×D17—42no—
289C2×D17—42no—
290C2×D17—81no—
291C2×D17—81no—
292C2×D17—81no—
293C2×D17—81no—
294C2×D17#47414yescomplemented
295C4×C17—22no—
296C4×C17—44no—
297C4×C17—42no—
298C4×C17—81no—
299C4×C17#44714yes—
300C4×C17#54811yescharacteristic
301C4×C17#54811yescharacteristic
302C4×C17D4×Q811yescharacteristic
303C4×C17D4×Q811yescharacteristic
304Dic17—22no—
305Dic17—22no—
306Dic17—22no—
307Dic17—44no—
308Dic17—81no—
309C23×Q8—341no—
310C2×C4⋊Q8—172no—
311C2×C4⋊Q8—171no—
312C2×C4⋊Q8—341no—
313C2×C4⋊Q8—341no—
314C2×C4⋊Q8—344no—
315C2×C4⋊Q8—344no—
316C2×C4⋊Q8C2×D1711yescharacteristic
317C2×#121—171no—
318C2×C4×D4—171no—
319C2×C4×D4—341no—
320C22×C4⋊C4—172no—
321C22×C4⋊C4—341no—
322C22×C42—171no—
323#474—344no—
324#474—344no—
325C2×#107—172no—
326C2×#107—172no—
327C2×C4⋊C8—171no—
328C2×C4⋊C8C2×D1711yescharacteristic
329C2×#102—172no—
330C2×#102—172no—
331C2×C22⋊C8—172no—
332#390—171no—
333#389—171no—
334#388—341no—
335#386—341no—
336#380—171no—
337C4×C4⋊C4C2×D1711yescharacteristic
338C4×C22⋊C4—341no—
339#340—172no—
340#340—172no—
341#340C2×D1712yes—
342#340C2×D1712yes—
343#336—172no—
344C2×C17#240911yescharacteristic
345C2×C17C2×#44711yescharacteristic
346C2×C17#300411yescharacteristic
347C2×C17C2×#47411yescharacteristic
348C2×C17#307911yescharacteristic
349C2×C17#322611yescharacteristic
350C2×C17#323911yescharacteristic
351D17—24no—
352D17—82no—
353C22×Q8—21no—
354C22×Q8—342no—
355C22×Q8—348no—
356C22×Q8—341no—
357C22×Q8—684no—
358C22×Q8—684no—
359C22×D4—171no—
360C22×D4—341no—
361C23×C4—171no—
362C23×C4—171no—
363C23×C4—171no—
364C23×C4—342no—
365C23×C4—341no—
366C22×C8—172no—
367C22×C8C22×D1712yes—
368C4⋊Q8—22no—
369C4⋊Q8—174no—
370C4⋊Q8—344no—
371C4⋊Q8—348no—
372C4⋊Q8—348no—
373C4⋊Q8—344no—
374C4⋊Q8—342no—
375C4⋊Q8D6814yescomplemented
376#121—174no—
377#121—342no—
378C4×D4—342no—
379C4×D4—342no—
380C4×D4—684no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—172no—
383C2×C4⋊C4—171no—
384C2×C4⋊C4—344no—
385C2×C4⋊C4—348no—
386C2×C4⋊C4—342no—
387C2×C4⋊C4—342no—
388C2×C4⋊C4—341no—
389C2×C4⋊C4—344no—
390C2×C4⋊C4—341no—
391C2×C4⋊C4C22×D1711yescharacteristic
392C2×C4⋊C4C22×D1712yes—
393C2×C4⋊C4C22×D1711yescharacteristic
394C2×C22⋊C4—341no—
395C2×C22⋊C4—341no—
396C2×C22⋊C4—341no—
397C2×C22⋊C4—341no—
398C2×C22⋊C4—341no—
399C2×C42—21no—
400C2×C42—171no—
401C2×C42—171no—
402C2×C42—171no—
403C2×C42—342no—
404C2×C42—342no—
405C2×C42C22×D1711yescharacteristic
406#107—344no—
407#107—344no—
408C4⋊C8—22no—
409C4⋊C8—342no—
410#102—344no—
411#102—344no—
412C22⋊C8—344no—
413#95—21no—
414#95—341no—
415#95—341no—
416C17#2429811yescharacteristic, complemented, Sylow
417C24—171no—
418C24—341no—
419C2×Q8—24no—
420C2×Q8—42no—
421C2×Q8—42no—
422C2×Q8—348no—
423C2×Q8—344no—
424C2×Q8—684no—
425C2×Q8—684no—
426C2×Q8—6832no—
427C2×Q8—682no—
428C2×Q8—682no—
429C2×D4—172no—
430C2×D4—344no—
431C2×D4—341no—
432C2×D4—341no—
433C2×D4—341no—
434C2×D4—341no—
435C2×D4—341no—
436C2×D4—682no—
437C2×D4—682no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—171no—
442C22×C4—171no—
443C22×C4—171no—
444C22×C4—172no—
445C22×C4—172no—
446C22×C4—174no—
447C22×C4—342no—
448C22×C4—342no—
449C22×C4—348no—
450C22×C4—341no—
451C22×C4—341no—
452C22×C4—341no—
453C22×C4—341no—
454C22×C4—342no—
455C22×C4—342no—
456C22×C4—342no—
457C22×C4—342no—
458C22×C4—341no—
459C22×C4—684no—
460C22×C4—684no—
461C22×C4—682no—
462C22×C4—682no—
463C22×C4—682no—
464C22×C4D4×D1711yescharacteristic
465C22×C4D4×D1711yescharacteristic
466C22×C4C23×D1711yescharacteristic
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—342no—
471C2×C8—342no—
472C2×C8—342no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—24no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—174no—
479C4⋊C4—348no—
480C4⋊C4—348no—
481C4⋊C4—342no—
482C4⋊C4—344no—
483C4⋊C4—341no—
484C4⋊C4—341no—
485C4⋊C4—682no—
486C4⋊C4C2×D6814yes—
487C4⋊C4Q8×D1712yescomplemented
488C22⋊C4—344no—
489C22⋊C4—682no—
490C22⋊C4—682no—
491C22⋊C4—682no—
492C22⋊C4—682no—
493C42—42no—
494C42—341no—
495C42—341no—
496C42—342no—
497C42—342no—
498C42C2×D6812yes—
499C42D4×D1712yes—
500C23—172no—
501C23—172no—
502C23—172no—
503C23—341no—
504C23—341no—
505C23—341no—
506C23—341no—
507C23—342no—
508C23—681no—
509C23—681no—
510C23—681no—
511C23—681no—
512C23—681no—
513C23—681no—
514C23C2×D4×D1711yescharacteristic
515Q8—48no—
516Q8—6816no—
517Q8—688no—
518D4—342no—
519D4—342no—
520D4—688no—
521D4—681no—
522D4—681no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—172no—
535C2×C4—172no—
536C2×C4—172no—
537C2×C4—348no—
538C2×C4—341no—
539C2×C4—341no—
540C2×C4—341no—
541C2×C4—341no—
542C2×C4—341no—
543C2×C4—341no—
544C2×C4—348no—
545C2×C4—342no—
546C2×C4—342no—
547C2×C4—342no—
548C2×C4—342no—
549C2×C4—344no—
550C2×C4—6816no—
551C2×C4—682no—
552C2×C4—682no—
553C2×C4—681no—
554C2×C4—681no—
555C2×C4—681no—
556C2×C4—1364no—
557C2×C4#1058756812yes—
558C2×C4#1058756812yes—
559C2×C4D8×D1712yes—
560C2×C4#1058760012yes—
561C2×C4C22×D6811yescharacteristic
562C2×C4C2×D4×D1711yescharacteristic
563C2×C4C2×Q8×D1711yescharacteristic
564C2×C4#1058769411yescharacteristic
565C2×C4#41×D1711yescharacteristic
566C2×C4#1058769711yescharacteristic
567C8—42no—
568C8—682no—
569C22—174no—
570C22—342no—
571C22—342no—
572C22—342no—
573C22—342no—
574C22—342no—
575C22—342no—
576C22—682no—
577C22—682no—
578C22—682no—
579C22—1361no—
580C22—1361no—
581C22—1361no—
582C22—1361no—
583C22C2×#1058756811yescharacteristic
584C22C22⋊Q8×D1711yescharacteristic
585C22#1176338211yescharacteristic
586C22C2×D8×D1711yescharacteristic
587C22C2×#1058760011yescharacteristic
588C22#137×D1711yescharacteristic
589C22#137×D1711yescharacteristic
590C4—22no—
591C4—42no—
592C4—44no—
593C4—81no—
594C4—342no—
595C4—342no—
596C4—342no—
597C4—684no—
598C4—1361no—
599C4#1176294414yes—
600C4#1176346711yescharacteristic
601C4#1176347111yescharacteristic
602C4#1176347411yescharacteristic
603C4Q8×D6811yescharacteristic
604C2—344no—
605C2—1362no—
606C2#1453214711yescharacteristic
607C2C2×#1176294411yescharacteristic
608C2#1453802011yescharacteristic
609C2D17×#47411yescharacteristic
610C2#1453859411yescharacteristic
611C2#1453990411yescharacteristic
612C2#1454001811yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#1988C2
socleC23×C17C22×D4
prime radicalC2×#10587581C22
hypercenter#1988D17
hypocenterC17#24298
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×D17C2semidirect
2. C2×#11763090C2semidirect
3. C2×#11763086C2semidirect
5. #14530111C2semidirect
6. #14529919C2semidirect
7. #14529736C2semidirect
9. #14528973C2semidirect
10. #14528761C2semidirect
11. C17×#1988C2semidirect
62. C17×C4⋊Q8D4semidirect
86. #10587581Q8semidirect
99. #10587555D4semidirect
135. C2×D68C2×Q8semidirect
169. C4⋊C4×C17C2×Q8semidirect
270. #1988D17semidirect
294. C2×D17#474semidirect
375. C4⋊Q8D68semidirect
416. C17#24298semidirect
487. C4⋊C4Q8×D17semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D172
C2×#117630902
C2×#117630862
C4×#105875812
#145301112
#145299192
#145297362
#145291002
#145289732
#145287612
C17×#19882
#2429817