Finite Group Databasebeta

← #16957050

Subgroups — #16957050

Order 4352.

1622 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic34C211yesmaximal, characteristic
2C2×#11762676C211yesmaximal, characteristic
3C2×#11762654C211yesmaximal, characteristic
4#14527054C212yesmaximal
5#14527050C212yesmaximal
6#14527018C212yesmaximal
7#14527015C212yesmaximal
8#14527011C211yesmaximal, characteristic
9#14527008C211yesmaximal, characteristic
10#14527008C211yesmaximal, characteristic
11C17×#1434C211yesmaximal, characteristic
12C23×Dic34C2211yescharacteristic
13C2×C4×Dic34—24no—
14C2×C4×Dic34—24no—
15C2×C4×Dic34C418yescomplemented
16C22×C4⋊Dic17C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×C4×Dic17C2212yes—
20C22×C4×Dic17C2211yescharacteristic
21C22×C4×Dic17C2211yescharacteristic
22#11762676—24no—
23#11762654—24no—
24C2×#10587502C2211yescharacteristic
25C2×#10587502C2211yescharacteristic
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C22×C42×C17C2211yescharacteristic
36C2×C17×#95C2211yescharacteristic
37C2×C17×#95C2211yescharacteristic
38C2×C17×#95C2212yes—
39C2×C17×#95C2212yes—
40C23×C4×C17C2312yes—
41C23×C4×C17C2311yescharacteristic
42C23×C4×C17C2312yes—
43C23×C4×C17C2311yescharacteristic
44C23×C4×C17C2311yescharacteristic
45C23×Dic17C2312yes—
46C23×Dic17C2311yescharacteristic
47C23×Dic17C2312yes—
48C23×Dic17C2311yescharacteristic
49C23×Dic17C2311yescharacteristic
50C23×Dic17C2311yescharacteristic
51C22×Dic34—22no—
52C22×Dic34—22no—
53C22×Dic34—22no—
54C22×Dic34—22no—
55C22×Dic34—22no—
56C22×Dic34—22no—
57C22×Dic34C2×C414yes—
58C2×C42×C17—22no—
59C2×C42×C17—22no—
60C2×C42×C17C2×C414yes—
61C2×C4⋊Dic17—22no—
62C2×C4⋊Dic17—22no—
63C2×C4⋊Dic17C2×C414yes—
64C2×#63225—22no—
65C2×#63225—22no—
66C2×#63225—22no—
67C2×#63225—22no—
68C2×#63225C2×C414yes—
69C2×#63225C2×C414yes—
70C2×C4×Dic17—22no—
71C2×C4×Dic17—22no—
72C2×C4×Dic17—24no—
73C2×C4×Dic17—24no—
74C2×C4×Dic17—24no—
75C2×C4×Dic17C2×C414yes—
76C2×C4×Dic17C2×C414yes—
77C2×C4×Dic17D414yes—
78C2×C4×Dic17D414yes—
79C4×Dic34—232no—
80C17×#95—22no—
81C17×#95—22no—
82C17×#95—24no—
83C17×#95—24no—
84#10587502—22no—
85#10587502—22no—
86#10587502—24no—
87#10587502—24no—
88#10587502—24no—
89#10587502—24no—
90#10587502—24no—
91#10587502—24no—
92#10587502—24no—
93#10587502—24no—
94#10587502—24no—
95C24×C17C2411yescharacteristic
96C22×C4×C17—21no—
97C22×C4×C17—21no—
98C22×C4×C17—21no—
99C22×C4×C17—21no—
100C22×C4×C17—22no—
101C22×C4×C17—22no—
102C22×C4×C17—22no—
103C22×C4×C17—21no—
104C22×C4×C17—21no—
105C22×C4×C17—22no—
106C22×C4×C17—22no—
107C22×C4×C17—22no—
108C22×C4×C17—22no—
109C22×C4×C17—22no—
110C22×C4×C17—22no—
111C22×C4×C17—22no—
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—22no—
115C22×C4×C17—22no—
116C22×C4×C17—22no—
117C22×C4×C17—22no—
118C22×C4×C17—22no—
119C22×C4×C17C22×C412yes—
120C22×C4×C17C22×C412yes—
121C22×C4×C17C22×C412yes—
122C22×C4×C17C2×D412yes—
123C22×C4×C17C2×D412yes—
124C22×C4×C17#4114yes—
125C22×C4×C17#4112yes—
126C22×C4×C17#4112yes—
127C22×Dic17—21no—
128C22×Dic17—21no—
129C22×Dic17—21no—
130C22×Dic17—21no—
131C22×Dic17—21no—
132C22×Dic17—21no—
133C22×Dic17—21no—
134C22×Dic17—21no—
135C22×Dic17—22no—
136C22×Dic17—22no—
137C22×Dic17—22no—
138C22×Dic17—21no—
139C22×Dic17—21no—
140C22×Dic17—22no—
141C22×Dic17—22no—
142C22×Dic17—22no—
143C22×Dic17—22no—
144C22×Dic17—22no—
145C22×Dic17—22no—
146C22×Dic17—22no—
147C22×Dic17—22no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—22no—
151C22×Dic17—22no—
152C22×Dic17—22no—
153C22×Dic17—22no—
154C22×Dic17C22×C412yes—
155C22×Dic17C22×C412yes—
156C22×Dic17C22×C412yes—
157C22×Dic17C22×C412yes—
158C22×Dic17C2×D412yes—
159C22×Dic17C2×D412yes—
160C22×Dic17C2×D412yes—
161C22×Dic17C2×D412yes—
162C22×Dic17#4114yes—
163C22×Dic17#4112yes—
164C22×Dic17#4112yes—
165C2×Dic34—28no—
166C2×Dic34—28no—
167C2×Dic34—28no—
168C2×Dic34—28no—
169C2×Dic34—28no—
170C2×Dic34—28no—
171C2×Dic34—28no—
172C42×C17—28no—
173C4⋊Dic17—28no—
174#63225—28no—
175#63225—28no—
176C4×Dic17—216no—
177C4×Dic17—28no—
178C4×Dic17C22⋊C4116yes—
179#13961—171nomaximal, Sylow
180C23×C17C23×C411yescharacteristic
181C23×C17C22×D411yescharacteristic
182C23×C17C22×D411yescharacteristic
183C23×C17C2×#4112yes—
184C23×C17C2×#4111yescharacteristic
185C23×C17C2×#4111yescharacteristic
186C23×C17C2×#4111yescharacteristic
187C23×C17C2×#4111yescharacteristic
188C23×C17C2×#4112yes—
189C23×C172−1+412yes—
190C23×C172−1+412yes—
191C2×C4×C17—22no—
192C2×C4×C17—22no—
193C2×C4×C17—22no—
194C2×C4×C17—22no—
195C2×C4×C17—22no—
196C2×C4×C17—22no—
197C2×C4×C17—22no—
198C2×C4×C17—22no—
199C2×C4×C17—24no—
200C2×C4×C17—24no—
201C2×C4×C17—22no—
202C2×C4×C17—22no—
203C2×C4×C17—22no—
204C2×C4×C17—24no—
205C2×C4×C17—24no—
206C2×C4×C17—24no—
207C2×C4×C17—42no—
208C2×C4×C17—42no—
209C2×C4×C17—42no—
210C2×C4×C17—42no—
211C2×C4×C17—42no—
212C2×C4×C17—42no—
213C2×C4×C17—42no—
214C2×C4×C17—42no—
215C2×C4×C17—42no—
216C2×C4×C17—42no—
217C2×C4×C17—42no—
218C2×C4×C17—42no—
219C2×C4×C17—42no—
220C2×C4×C17C2×C22⋊C414yes—
221C2×C4×C17#11714yes—
222C2×Dic17—22no—
223C2×Dic17—22no—
224C2×Dic17—22no—
225C2×Dic17—22no—
226C2×Dic17—22no—
227C2×Dic17—22no—
228C2×Dic17—22no—
229C2×Dic17—22no—
230C2×Dic17—22no—
231C2×Dic17—22no—
232C2×Dic17—22no—
233C2×Dic17—22no—
234C2×Dic17—22no—
235C2×Dic17—22no—
236C2×Dic17—24no—
237C2×Dic17—24no—
238C2×Dic17—22no—
239C2×Dic17—22no—
240C2×Dic17—22no—
241C2×Dic17—24no—
242C2×Dic17—24no—
243C2×Dic17—24no—
244C2×Dic17—42no—
245C2×Dic17—42no—
246C2×Dic17—42no—
247C2×Dic17—42no—
248C2×Dic17—42no—
249C2×Dic17—42no—
250C2×Dic17—42no—
251C2×Dic17—42no—
252C2×Dic17—42no—
253C2×Dic17—42no—
254C2×Dic17—42no—
255C2×Dic17—42no—
256C2×Dic17—42no—
257C2×Dic17C2×C22⋊C414yes—
258C2×Dic17C2×C22⋊C414yes—
259C2×Dic17#11714yes—
260Dic34—232no—
261C22×C4×Q8—171no—
262C2×#383—171no—
263C2×#376—171no—
264#1446—172no—
265#1445—172no—
266#1436—172no—
267#1436—172no—
268#1434—171no—
269#1434—171no—
270#1434—171no—
271#1434D1711yescharacteristic
272C22×C17C22×C22⋊C411yescharacteristic
273C22×C17C2×#11711yescharacteristic
274C22×C17C2×#11711yescharacteristic
275C22×C17C4×#4111yescharacteristic
276C22×C17C4×#4111yescharacteristic
277C22×C17#51911yescharacteristic
278C22×C17#51911yescharacteristic
279C22×C17#52512yes—
280C22×C17#52511yescharacteristic
281C22×C17#52511yescharacteristic
282C22×C17#52511yescharacteristic
283C22×C17#52511yescharacteristic
284C22×C17#53212yes—
285C22×C17#53612yes—
286C22×C17#53612yes—
287C22×C17#55212yes—
288C22×C17#55212yes—
289C22×C17#55212yes—
290C22×C17#55212yes—
291C22×C17#55612yes—
292C22×C17#55612yes—
293C22×C17#55612yes—
294C22×C17#55612yes—
295C4×C17—24no—
296C4×C17—24no—
297C4×C17—44no—
298C4×C17—42no—
299C4×C17—82no—
300Dic17—24no—
301Dic17—24no—
302Dic17—24no—
303Dic17—44no—
304Dic17—42no—
305Dic17—82no—
306C23×Q8—171no—
307C2×C4×Q8—178no—
308C2×C4×Q8—344no—
309C2×C4×Q8—344no—
310C22×C4⋊C4—171no—
311C22×C4⋊C4—171no—
312C22×C4⋊C4—171no—
313C22×C42—171no—
314C22×C42—171no—
315C22×C42—172no—
316C22×C42C2×D1711yescharacteristic
317#383—344no—
318#376—344no—
319C2×#95—171no—
320C2×#95—171no—
321C2×#95—172no—
322C2×#95—172no—
323C2×#95—172no—
324C2×#95—172no—
325C2×#95—172no—
326C2×#95—172no—
327C2×#95—172no—
328C2×#95—172no—
329C2×#95—172no—
330C2×#95C2×D1711yescharacteristic
331C2×#95C2×D1711yescharacteristic
332C2×#95C2×D1712yes—
333C2×#95C2×D1712yes—
334C2×C17#228011yescharacteristic
335C2×C17#229711yescharacteristic
336C2×C17#231011yescharacteristic
337C2×C17#235611yescharacteristic
338C2×C17#235611yescharacteristic
339C2×C17#235611yescharacteristic
340C2×C17#235611yescharacteristic
341C2×C17#259912yes—
342C2×C17#259912yes—
343C2×C17#260412yes—
344C2×C17#260412yes—
345C22×Q8—174no—
346C22×Q8—342no—
347C22×Q8—342no—
348C22×Q8—342no—
349C22×Q8—342no—
350C22×Q8—342no—
351C22×Q8—342no—
352C23×C4—171no—
353C23×C4—171no—
354C23×C4—171no—
355C23×C4—171no—
356C23×C4—172no—
357C23×C4—172no—
358C23×C4C22×D1712yes—
359C23×C4C22×D1711yescharacteristic
360C23×C4C22×D1712yes—
361C23×C4C22×D1711yescharacteristic
362C23×C4C22×D1711yescharacteristic
363C4×Q8—3432no—
364C2×C4⋊C4—174no—
365C2×C4⋊C4—174no—
366C2×C4⋊C4—174no—
367C2×C4⋊C4—342no—
368C2×C4⋊C4—342no—
369C2×C4⋊C4—342no—
370C2×C4⋊C4—342no—
371C2×C4⋊C4—342no—
372C2×C4⋊C4—342no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—174no—
376C2×C42—174no—
377C2×C42—174no—
378C2×C42—174no—
379C2×C42—344no—
380C2×C42—344no—
381C2×C42—344no—
382C2×C42—342no—
383C2×C42—342no—
384C2×C42C4×D1714yes—
385#95—24no—
386#95—22no—
387#95—22no—
388#95—24no—
389#95—344no—
390#95—344no—
391#95—344no—
392#95—344no—
393#95—344no—
394#95—344no—
395#95—344no—
396#95—344no—
397#95—342no—
398#95—342no—
399#95—344no—
400C17#1396111yescharacteristic, complemented, Sylow
401C24C23×D1711yescharacteristic
402C2×Q8—348no—
403C2×Q8—348no—
404C2×Q8—348no—
405C2×Q8—348no—
406C2×Q8—348no—
407C2×Q8—348no—
408C2×Q8—348no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—172no—
433C22×C4—172no—
434C22×C4—172no—
435C22×C4—172no—
436C22×C4—172no—
437C22×C4—172no—
438C22×C4—172no—
439C22×C4—172no—
440C22×C4—172no—
441C22×C4—172no—
442C22×C4—174no—
443C22×C4—342no—
444C22×C4—341no—
445C22×C4—341no—
446C22×C4—341no—
447C22×C4—341no—
448C22×C4—341no—
449C22×C4—341no—
450C22×C4—342no—
451C22×C4—341no—
452C22×C4—341no—
453C22×C4—342no—
454C22×C4—342no—
455C22×C4—342no—
456C22×C4—341no—
457C22×C4—341no—
458C22×C4—342no—
459C22×C4—342no—
460C22×C4—342no—
461C22×C4—342no—
462C22×C4—342no—
463C22×C4—342no—
464C22×C4—342no—
465C22×C4—342no—
466C22×C4—342no—
467C22×C4—342no—
468C22×C4—342no—
469C22×C4—342no—
470C22×C4C2×C4×D1712yes—
471C22×C4C2×C4×D1712yes—
472C22×C4C2×C4×D1712yes—
473C22×C4#6325214yes—
474C22×C4D4×D1712yes—
475C22×C4D4×D1712yes—
476C22×C4#6325412yes—
477C22×C4#6325612yes—
478C4⋊C4—348no—
479C4⋊C4—348no—
480C4⋊C4—348no—
481C42—28no—
482C42—1716no—
483C42—3416no—
484C42—348no—
485C23C22×C4×D1711yescharacteristic
486C23C2×#6325212yes—
487C23C2×D4×D1711yescharacteristic
488C23C2×D4×D1711yescharacteristic
489C23C2×#6325411yescharacteristic
490C23C2×#6325611yescharacteristic
491C23#41×D1711yescharacteristic
492C23#41×D1711yescharacteristic
493C23#41×D1712yes—
494C23#1058769712yes—
495C23#1058769712yes—
496Q8—3432no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—174no—
527C2×C4—174no—
528C2×C4—174no—
529C2×C4—342no—
530C2×C4—342no—
531C2×C4—342no—
532C2×C4—342no—
533C2×C4—342no—
534C2×C4—342no—
535C2×C4—344no—
536C2×C4—342no—
537C2×C4—342no—
538C2×C4—342no—
539C2×C4—342no—
540C2×C4—342no—
541C2×C4—342no—
542C2×C4—342no—
543C2×C4—342no—
544C2×C4—344no—
545C2×C4—344no—
546C2×C4—344no—
547C2×C4—342no—
548C2×C4—342no—
549C2×C4—342no—
550C2×C4—344no—
551C2×C4—682no—
552C2×C4—682no—
553C2×C4—682no—
554C2×C4—682no—
555C2×C4—682no—
556C2×C4—682no—
557C2×C4—682no—
558C2×C4—682no—
559C2×C4—682no—
560C2×C4—682no—
561C2×C4—682no—
562C2×C4—682no—
563C2×C4—682no—
564C2×C4C22⋊C4×D1714yes—
565C2×C4#1058757814yes—
566C22C2×C22⋊C4×D1711yescharacteristic
567C22#117×D1711yescharacteristic
568C22C2×#1058757811yescharacteristic
569C22#1176327711yescharacteristic
570C22C4×#6325211yescharacteristic
571C22#1176328611yescharacteristic
572C22#1176328611yescharacteristic
573C22#1176331812yes—
574C22#1176331911yescharacteristic
575C22#1176331911yescharacteristic
576C22#1176332211yescharacteristic
577C22#1176332211yescharacteristic
578C22#1176335612yes—
579C22#1176338112yes—
580C22#1176338112yes—
581C22#1176349212yes—
582C22#1176349512yes—
583C22#1176349712yes—
584C22#1176349912yes—
585C22#1176352612yes—
586C22#1176352712yes—
587C22#1176352812yes—
588C22#1176353212yes—
589C4—24no—
590C4—24no—
591C4—42no—
592C4—44no—
593C4—82no—
594C4—344no—
595C4—344no—
596C4—344no—
597C4—682no—
598C4—684no—
599C4—1362no—
600C2#1453116611yescharacteristic
601C2#1453127011yescharacteristic
602C2#1453136911yescharacteristic
603C2#1453174411yescharacteristic
604C2#1453174711yescharacteristic
605C2#1453175011yescharacteristic
606C2#1453175111yescharacteristic
607C2#1453435812yes—
608C2#1453436012yes—
609C2#1453441912yes—
610C2#1453442112yes—
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1434C2
socle, prime radical, cosocleC24×C17C24
hypercenter#1434D17
hypocenterC17#13961
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
15. C2×C4×Dic34C4semidirect
400. C17#13961semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic342
C2×#117626762
C2×#117626542
#145270542
#145270502
#145270182
#145270152
#145270112
#145270082
C17×#14342
#1396117