Finite Group Databasebeta

← #16956949

Subgroups — #16956949

Order 4352.

1630 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762697C212yesmaximal
2C2×C4×C22⋊Dic17C211yesmaximal, characteristic
3#14527042C212yesmaximal, complemented
4#14527027C212yesmaximal
5#14527019C212yesmaximal, complemented
6#14527012C211yesmaximal, characteristic, complemented
7#14527012C211yesmaximal, characteristic, complemented
8#14527009C211yesmaximal, characteristic, complemented
9#14527007C211yesmaximal, characteristic
10#95×Dic17C211yesmaximal, characteristic, complemented
11C17×C22⋊#95C211yesmaximal, characteristic
12C22×#63225C2212yes—
13C22×#63225C2212yes—
14C22×C22⋊Dic17C2212yes—
15C22×C22⋊Dic17C2211yescharacteristic
16C22×C22⋊Dic17C2211yescharacteristic
17C22×C4×Dic17C2212yes—
18C22×C4×Dic17C2211yescharacteristic
19C22×C4×Dic17C2211yescharacteristic
20#11762697—28no—
21C4×C22⋊Dic17C418yescomplemented
22C2×#10587502C2211yescharacteristic
23C2×#10587502C2212yes—
24C2×#10587502C2211yescharacteristic
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2211yescharacteristic
31C2×#10587502C2211yescharacteristic
32C24×C4×C17C2211yescharacteristic
33C22×C22⋊C4×C17C2212yes—
34C2×C17×#95C2211yescharacteristic
35C2×C17×#95C2211yescharacteristic
36C2×C17×#95C2212yes—
37C25×C17C2311yescharacteristic
38C23×C4×C17—22no—
39C23×C4×C17—22no—
40C23×C4×C17—42no—
41C23×C4×C17—42no—
42C23×C4×C17C2×C414yes—
43C23×C4×C17C2312yes—
44C23×C4×C17C2311yescharacteristic
45C23×C4×C17C2312yes—
46C23×C4×C17C2311yescharacteristic
47C23×Dic17C2312yes—
48C23×Dic17C2311yescharacteristic
49C23×Dic17C2312yes—
50C23×Dic17C2311yescharacteristic
51C23×Dic17C2311yescharacteristic
52C23×Dic17C2311yescharacteristic
53C2×C22⋊C4×C17—24no—
54C2×C22⋊C4×C17—24no—
55C2×C22⋊C4×C17—42no—
56C2×C22⋊Dic17—22no—
57C2×C22⋊Dic17—22no—
58C2×C22⋊Dic17—24no—
59C2×C22⋊Dic17—24no—
60C2×C22⋊Dic17—42no—
61C2×C22⋊Dic17C2×C414yes—
62C2×C22⋊Dic17C2×C414yes—
63C2×C22⋊Dic17D414yes—
64C2×C22⋊Dic17Q814yes—
65C2×#63225—24no—
66C2×#63225—24no—
67C2×#63225—24no—
68C2×#63225—24no—
69C2×#63225—42no—
70C2×#63225—42no—
71C2×C4×Dic17—24no—
72C2×C4×Dic17—24no—
73C2×C4×Dic17—42no—
74C2×C4×Dic17—42no—
75C2×C4×Dic17—42no—
76C2×C4×Dic17C2×C414yes—
77C2×C4×Dic17C2×C414yes—
78C17×#95—22no—
79C17×#95—22no—
80C17×#95—42no—
81#10587502—22no—
82#10587502—22no—
83#10587502—24no—
84#10587502—24no—
85#10587502—24no—
86#10587502—24no—
87#10587502—42no—
88#10587502—42no—
89#10587502C2×C414yes—
90#10587502C2×C414yes—
91C24×C17—21no—
92C24×C17—21no—
93C24×C17—21no—
94C24×C17—21no—
95C24×C17—22no—
96C24×C17—22no—
97C24×C17—22no—
98C24×C17—22no—
99C24×C17C22×C412yes—
100C24×C17C2×D412yes—
101C24×C17C2×Q812yes—
102C24×C17C2411yescharacteristic
103C22×C4×C17—22no—
104C22×C4×C17—22no—
105C22×C4×C17—22no—
106C22×C4×C17—21no—
107C22×C4×C17—21no—
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—28no—
116C22×C4×C17—22no—
117C22×C4×C17—22no—
118C22×C4×C17—22no—
119C22×C4×C17—22no—
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17—22no—
123C22×C4×C17—44no—
124C22×C4×C17—44no—
125C22×C4×C17—48no—
126C22×C4×C17—48no—
127C22×C4×C17C22×C412yes—
128C22×C4×C17C22×C412yes—
129C22×C4×C17#4114yes—
130C22×C4×C17#4112yes—
131C22×C4×C17#4112yes—
132C22×Dic17—22no—
133C22×Dic17—22no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—22no—
137C22×Dic17—22no—
138C22×Dic17—22no—
139C22×Dic17—22no—
140C22×Dic17—22no—
141C22×Dic17—22no—
142C22×Dic17—22no—
143C22×Dic17—21no—
144C22×Dic17—21no—
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×Dic17—22no—
155C22×Dic17C22×C412yes—
156C22×Dic17C22×C412yes—
157C22×Dic17C22×C412yes—
158C22×Dic17C22×C412yes—
159C22×Dic17C2×D412yes—
160C22×Dic17C2×D412yes—
161C22×Dic17C2×Q812yes—
162C22×Dic17C2×Q812yes—
163C22×Dic17#4114yes—
164C22×Dic17#4112yes—
165C22×Dic17#4112yes—
166C22⋊C4×C17—48no—
167C22⋊Dic17—28no—
168C22⋊Dic17—48no—
169C22⋊Dic17C4⋊C4116yescomplemented
170#63225—48no—
171#63225—48no—
172C4×Dic17—44no—
173C4×Dic17—44no—
174C4×Dic17—48no—
175#13948—171nomaximal, Sylow
176C23×C17—22no—
177C23×C17—22no—
178C23×C17—22no—
179C23×C17—22no—
180C23×C17—22no—
181C23×C17—22no—
182C23×C17—22no—
183C23×C17—22no—
184C23×C17—22no—
185C23×C17—22no—
186C23×C17—24no—
187C23×C17—24no—
188C23×C17—24no—
189C23×C17—24no—
190C23×C17—42no—
191C23×C17—42no—
192C23×C17—42no—
193C23×C17—42no—
194C23×C17—42no—
195C23×C17—42no—
196C23×C17—42no—
197C23×C17—42no—
198C23×C17C2×C4⋊C414yes—
199C23×C17C23×C411yescharacteristic
200C23×C17C22×D411yescharacteristic
201C23×C17C22×Q811yescharacteristic
202C23×C17C2×#4112yes—
203C23×C17C2×#4111yescharacteristic
204C23×C17C2×#4111yescharacteristic
205C23×C17C2×#4111yescharacteristic
206C23×C17C2×#4111yescharacteristic
207C23×C17C2×#4112yes—
208C23×C17H(5,𝔽2)12yes—
209C23×C17H(5,𝔽2)12yes—
210C2×C4×C17—22no—
211C2×C4×C17—22no—
212C2×C4×C17—24no—
213C2×C4×C17—24no—
214C2×C4×C17—22no—
215C2×C4×C17—22no—
216C2×C4×C17—22no—
217C2×C4×C17—24no—
218C2×C4×C17—24no—
219C2×C4×C17—24no—
220C2×C4×C17—416no—
221C2×C4×C17—42no—
222C2×C4×C17—42no—
223C2×C4×C17—42no—
224C2×C4×C17—42no—
225C2×C4×C17—42no—
226C2×C4×C17—42no—
227C2×C4×C17—42no—
228C2×C4×C17—42no—
229C2×C4×C17—42no—
230C2×C4×C17—42no—
231C2×C4×C17—42no—
232C2×C4×C17—42no—
233C2×C4×C17—42no—
234C2×C4×C17#11714yes—
235C2×Dic17—22no—
236C2×Dic17—22no—
237C2×Dic17—22no—
238C2×Dic17—22no—
239C2×Dic17—22no—
240C2×Dic17—22no—
241C2×Dic17—24no—
242C2×Dic17—24no—
243C2×Dic17—24no—
244C2×Dic17—24no—
245C2×Dic17—24no—
246C2×Dic17—24no—
247C2×Dic17—22no—
248C2×Dic17—22no—
249C2×Dic17—22no—
250C2×Dic17—24no—
251C2×Dic17—24no—
252C2×Dic17—24no—
253C2×Dic17—42no—
254C2×Dic17—42no—
255C2×Dic17—42no—
256C2×Dic17—42no—
257C2×Dic17—42no—
258C2×Dic17—42no—
259C2×Dic17—42no—
260C2×Dic17—42no—
261C2×Dic17—42no—
262C2×Dic17—42no—
263C2×Dic17—42no—
264C2×Dic17—42no—
265C2×Dic17—42no—
266C2×Dic17C2×C4⋊C414yes—
267C2×Dic17C2×C4⋊C414yes—
268C2×Dic17#11714yes—
269C2×#388—172no—
270C2×C4×C22⋊C4—171no—
271#1442—172no—
272#1439—172no—
273#1436—172no—
274C4⋊#95—171no—
275C4⋊#95—171no—
276#1434—171no—
277C22⋊#95—171no—
278C22⋊#95D1711yescharacteristic
279C4×#95—171no—
280C22×C17—24no—
281C22×C17—24no—
282C22×C17—24no—
283C22×C17—42no—
284C22×C17—44no—
285C22×C17—44no—
286C22×C17—42no—
287C22×C17—42no—
288C22×C17—42no—
289C22×C17—44no—
290C22×C17—44no—
291C22×C17C22×C4⋊C411yescharacteristic
292C22×C17C2×#11711yescharacteristic
293C22×C17C2×#11711yescharacteristic
294C22×C17C4×#4111yescharacteristic
295C22×C17C4×#4111yescharacteristic
296C22×C17#51811yescharacteristic
297C22×C17#51811yescharacteristic
298C22×C17#52912yes—
299C22×C17#52912yes—
300C22×C17#53211yescharacteristic
301C22×C17#53211yescharacteristic
302C22×C17#53311yescharacteristic
303C22×C17#53311yescharacteristic
304C22×C17#53812yes—
305C22×C17#53812yes—
306C22×C17#54612yes—
307C22×C17#54612yes—
308C22×C17#55112yes—
309C22×C17#55312yes—
310C22×C17#55312yes—
311C22×C17#55412yes—
312C22×C17#55412yes—
313C22×C17#55912yes—
314C4×C17—24no—
315C4×C17—42no—
316C4×C17—44no—
317C4×C17—82no—
318Dic17—24no—
319Dic17—24no—
320Dic17—24no—
321Dic17—42no—
322Dic17—44no—
323Dic17—82no—
324C24×C4C2×D1711yescharacteristic
325C22×C4⋊C4—172no—
326C22×C4⋊C4—172no—
327C22×C22⋊C4—171no—
328C22×C22⋊C4—171no—
329C22×C22⋊C4—172no—
330C22×C22⋊C4C2×D1712yes—
331C22×C42—171no—
332C22×C42—171no—
333C22×C42—172no—
334#388—348no—
335C4×C22⋊C4—178no—
336C2×#95—171no—
337C2×#95—171no—
338C2×#95—171no—
339C2×#95—172no—
340C2×#95—171no—
341C2×#95—172no—
342C2×#95—172no—
343C2×#95—172no—
344C2×#95—172no—
345C2×#95—172no—
346C2×#95C2×D1711yescharacteristic
347C2×#95C2×D1711yescharacteristic
348C2×#95C2×D1712yes—
349C2×C17—44no—
350C2×C17#228511yescharacteristic
351C2×C17#229811yescharacteristic
352C2×C17#231211yescharacteristic
353C2×C17#234911yescharacteristic
354C2×C17#234911yescharacteristic
355C2×C17#235311yescharacteristic
356C2×C17#235711yescharacteristic
357C2×C17#255712yes—
358C2×C17#255912yes—
359C2×C17#258712yes—
360C2×C17#258912yes—
361C25C22×D1711yescharacteristic
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—42no—
365C23×C4—42no—
366C23×C4—171no—
367C23×C4—171no—
368C23×C4—171no—
369C23×C4—172no—
370C23×C4—171no—
371C23×C4—172no—
372C23×C4C4×D1714yes—
373C23×C4C22×D1712yes—
374C23×C4C22×D1711yescharacteristic
375C23×C4C22×D1712yes—
376C23×C4C22×D1711yescharacteristic
377C2×C4⋊C4—344no—
378C2×C4⋊C4—344no—
379C2×C4⋊C4—344no—
380C2×C4⋊C4—344no—
381C2×C4⋊C4—682no—
382C2×C4⋊C4—682no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—174no—
387C2×C22⋊C4—174no—
388C2×C22⋊C4—174no—
389C2×C22⋊C4—174no—
390C2×C22⋊C4—342no—
391C2×C22⋊C4—342no—
392C2×C22⋊C4—344no—
393C2×C22⋊C4—344no—
394C2×C22⋊C4—682no—
395C2×C42—174no—
396C2×C42—174no—
397C2×C42—344no—
398C2×C42—344no—
399C2×C42—682no—
400C2×C42—682no—
401C2×C42—682no—
402#95—22no—
403#95—22no—
404#95—42no—
405#95—174no—
406#95—174no—
407#95—344no—
408#95—344no—
409#95—344no—
410#95—344no—
411#95—342no—
412#95—342no—
413#95—682no—
414#95—682no—
415C17#1394811yescharacteristic, complemented, Sylow
416C24—22no—
417C24—21no—
418C24—21no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—21no—
423C24—21no—
424C24C2×C4×D1712yes—
425C24D4×D1712yes—
426C24Q8×D1712yes—
427C24C23×D1711yescharacteristic
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—28no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—48no—
451C22×C4—48no—
452C22×C4—172no—
453C22×C4—172no—
454C22×C4—172no—
455C22×C4—172no—
456C22×C4—172no—
457C22×C4—172no—
458C22×C4—172no—
459C22×C4—172no—
460C22×C4—172no—
461C22×C4—172no—
462C22×C4—174no—
463C22×C4—342no—
464C22×C4—342no—
465C22×C4—342no—
466C22×C4—342no—
467C22×C4—342no—
468C22×C4—342no—
469C22×C4—342no—
470C22×C4—342no—
471C22×C4—342no—
472C22×C4—342no—
473C22×C4—342no—
474C22×C4—342no—
475C22×C4—342no—
476C22×C4—342no—
477C22×C4—341no—
478C22×C4—341no—
479C22×C4—342no—
480C22×C4—342no—
481C22×C4—342no—
482C22×C4—342no—
483C22×C4—342no—
484C22×C4—342no—
485C22×C4—342no—
486C22×C4C2×C4×D1712yes—
487C22×C4C2×C4×D1712yes—
488C22×C4#6325214yes—
489C22×C4#6325412yes—
490C22×C4#6325412yes—
491C4⋊C4—688no—
492C4⋊C4—688no—
493C22⋊C4—48no—
494C22⋊C4—1716no—
495C22⋊C4—348no—
496C22⋊C4—688no—
497C42—684no—
498C42—684no—
499C42—688no—
500C23—24no—
501C23—24no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—24no—
513C23—24no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23C4⋊C4×D1714yes—
523C23C22×C4×D1711yescharacteristic
524C23C2×#6325212yes—
525C23C2×D4×D1711yescharacteristic
526C23C2×#6325411yescharacteristic
527C23C2×#6325411yescharacteristic
528C23#1058769112yes—
529C23#1058769112yes—
530C23C2×Q8×D1711yescharacteristic
531C23#41×D1711yescharacteristic
532C23#41×D1711yescharacteristic
533C23#41×D1712yes—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—416no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—174no—
559C2×C4—174no—
560C2×C4—174no—
561C2×C4—344no—
562C2×C4—344no—
563C2×C4—344no—
564C2×C4—344no—
565C2×C4—342no—
566C2×C4—342no—
567C2×C4—342no—
568C2×C4—342no—
569C2×C4—342no—
570C2×C4—342no—
571C2×C4—344no—
572C2×C4—344no—
573C2×C4—344no—
574C2×C4—342no—
575C2×C4—342no—
576C2×C4—342no—
577C2×C4—344no—
578C2×C4—344no—
579C2×C4—682no—
580C2×C4—682no—
581C2×C4—682no—
582C2×C4—682no—
583C2×C4—682no—
584C2×C4—682no—
585C2×C4—682no—
586C2×C4—682no—
587C2×C4—682no—
588C2×C4—682no—
589C2×C4—682no—
590C2×C4—682no—
591C2×C4—682no—
592C2×C4#1058756314yes—
593C22—24no—
594C22—24no—
595C22—24no—
596C22—44no—
597C22—42no—
598C22—44no—
599C22—44no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—44no—
604C22C2×C4⋊C4×D1711yescharacteristic
605C22#117×D1711yescharacteristic
606C22C2×#1058756311yescharacteristic
607C22#1176327711yescharacteristic
608C22C4×#6325211yescharacteristic
609C22#1176328211yescharacteristic
610C22#1176328211yescharacteristic
611C22#1176333912yes—
612C22#1176334112yes—
613C22#1176335411yescharacteristic
614C22#1176335411yescharacteristic
615C22#1176336111yescharacteristic
616C22#1176336111yescharacteristic
617C22#1176339412yes—
618C22#1176339412yes—
619C22#1176344812yes—
620C22#1176344912yes—
621C22#1176348812yes—
622C22#1176350412yes—
623C22#1176350912yes—
624C22#1176351312yes—
625C22#1176351412yes—
626C22#1176354312yes—
627C4—24no—
628C4—42no—
629C4—44no—
630C4—82no—
631C4—344no—
632C4—344no—
633C4—344no—
634C4—684no—
635C4—682no—
636C4—1362no—
637C2—44no—
638C2#1453118611yescharacteristic
639C2#1453128011yescharacteristic
640C2#1453138011yescharacteristic
641C2#1453168811yescharacteristic
642C2#1453169111yescharacteristic
643C2#1453172711yescharacteristic
644C2#1453175211yescharacteristic
645C2#1453388012yes—
646C2#1453391212yes—
647C2#1453420212yes—
648C2#1453423412yes—
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C22⋊#95C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC22⋊#95D17
hypocenterC17#13948
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. #14527042C2semidirect
5. #14527019C2semidirect
6. #14527012C2semidirect
7. #14527012C2semidirect
8. #14527009C2semidirect
10. #95×Dic17C2semidirect
21. C4×C22⋊Dic17C4semidirect
169. C22⋊Dic17C4⋊C4semidirect
415. C17#13948semidirect

Maximal subgroups

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

subgroupindex
C2×#117626972
C2×C4×C22⋊Dic172
#145270422
#145270272
#145270192
#145270122
#145270092
#145270072
#95×Dic172
C17×C22⋊#952
#1394817