Finite Group Databasebeta

← #16957262

Subgroups — #16957262

Order 4352.

1326 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762708C211yesmaximal, characteristic
2C2×#11762674C211yesmaximal, characteristic
3C2×C4×C4⋊Dic17C211yesmaximal, characteristic
4#14527053C212yesmaximal
5#14527045C212yesmaximal
6#14527018C212yesmaximal
7#14527013C211yesmaximal, characteristic
8#14527013C211yesmaximal, characteristic
9#14527010C212yesmaximal
10C4×#10587502C211yesmaximal, characteristic
11C17×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C4⋊Dic17C2211yescharacteristic
14C22×C4⋊Dic17C2212yes—
15C22×C4×Dic17C2211yescharacteristic
16C22×C4×Dic17C2212yes—
17C22×C4×Dic17C2211yescharacteristic
18#11762708C418yescomplemented
19#11762674—24no—
20C4×C4⋊Dic17—24no—
21C2×#10587502C2211yescharacteristic
22C2×#10587502C2211yescharacteristic
23C2×#10587502C2211yescharacteristic
24C2×#10587502C2211yescharacteristic
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C22×C4⋊C4×C17C2211yescharacteristic
34C22×C4⋊C4×C17C2211yescharacteristic
35C22×C42×C17C2211yescharacteristic
36C2×C17×#95C2212yes—
37C2×C17×#95C2212yes—
38C23×C4×C17C2312yes—
39C23×C4×C17C2312yes—
40C23×C4×C17C2311yescharacteristic
41C23×C4×C17C2311yescharacteristic
42C23×C4×C17C2311yescharacteristic
43C23×Dic17C2311yescharacteristic
44C23×Dic17C2312yes—
45C23×Dic17C2311yescharacteristic
46C23×Dic17C2312yes—
47C23×Dic17C2311yescharacteristic
48C23×Dic17C2311yescharacteristic
49C2×C4⋊C4×C17—22no—
50C2×C4⋊C4×C17—22no—
51C2×C4⋊C4×C17—22no—
52C2×C4⋊C4×C17—22no—
53C2×C4⋊C4×C17—22no—
54C2×C4⋊C4×C17C2×C414yes—
55C2×C42×C17—22no—
56C2×C42×C17—22no—
57C2×C42×C17Q814yes—
58C2×C4⋊Dic17—22no—
59C2×C4⋊Dic17—22no—
60C2×C4⋊Dic17—22no—
61C2×C4⋊Dic17—22no—
62C2×C4⋊Dic17—42no—
63C2×C4⋊Dic17—42no—
64C2×C4⋊Dic17C2×C414yes—
65C2×C4⋊Dic17C2×C418yes—
66C2×C4⋊Dic17D414yes—
67C2×C4×Dic17—22no—
68C2×C4×Dic17—22no—
69C2×C4×Dic17—22no—
70C2×C4×Dic17—22no—
71C2×C4×Dic17—24no—
72C2×C4×Dic17—22no—
73C2×C4×Dic17—24no—
74C2×C4×Dic17—42no—
75C2×C4×Dic17C2×C414yes—
76C17×#95—24no—
77C17×#95—42no—
78#10587502—22no—
79#10587502—22no—
80#10587502—24no—
81#10587502—24no—
82#10587502—24no—
83#10587502—22no—
84#10587502—22no—
85#10587502—24no—
86#10587502—24no—
87#10587502—42no—
88#10587502—42no—
89#10587502C2×C418yes—
90C24×C17C2411yescharacteristic
91C22×C4×C17—21no—
92C22×C4×C17—21no—
93C22×C4×C17—21no—
94C22×C4×C17—21no—
95C22×C4×C17—21no—
96C22×C4×C17—22no—
97C22×C4×C17—21no—
98C22×C4×C17—21no—
99C22×C4×C17—22no—
100C22×C4×C17—21no—
101C22×C4×C17—22no—
102C22×C4×C17—22no—
103C22×C4×C17—22no—
104C22×C4×C17—21no—
105C22×C4×C17—22no—
106C22×C4×C17—21no—
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×C17C22×C414yes—
115C22×C4×C17C22×C412yes—
116C22×C4×C17C2×D412yes—
117C22×C4×C17C2×Q812yes—
118C22×C4×C17C2×Q812yes—
119C22×C4×C17C2×Q812yes—
120C22×C4×C17#4112yes—
121C22×C4×C17#4112yes—
122C22×C4×C17#4112yes—
123C22×C4×C17#4112yes—
124C22×C4×C17#4112yes—
125C22×C4×C17#4112yes—
126C22×Dic17—21no—
127C22×Dic17—21no—
128C22×Dic17—22no—
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—21no—
138C22×Dic17—21no—
139C22×Dic17—21no—
140C22×Dic17—21no—
141C22×Dic17—21no—
142C22×Dic17—21no—
143C22×Dic17—22no—
144C22×Dic17—22no—
145C22×Dic17—21no—
146C22×Dic17—21no—
147C22×Dic17—22no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—21no—
151C22×Dic17—21no—
152C22×Dic17—22no—
153C22×Dic17—22no—
154C22×Dic17—22no—
155C22×Dic17—21no—
156C22×Dic17—21no—
157C22×Dic17—21no—
158C22×Dic17—22no—
159C22×Dic17—21no—
160C22×Dic17—21no—
161C22×Dic17—21no—
162C22×Dic17C22×C412yes—
163C22×Dic17C22×C414yes—
164C22×Dic17C22×C412yes—
165C22×Dic17C2×D414yes—
166C22×Dic17#4112yes—
167C22×Dic17#4112yes—
168C4⋊C4×C17—28no—
169C4⋊C4×C17—44no—
170C42×C17—28no—
171C4⋊Dic17—28no—
172C4⋊Dic17—28no—
173C4⋊Dic17—48no—
174C4×Dic17—28no—
175C4×Dic17—48no—
176C4×Dic17—44no—
177#13982—171nomaximal, Sylow
178C23×C17C23×C411yescharacteristic
179C23×C17C22×D411yescharacteristic
180C23×C17C22×Q811yescharacteristic
181C23×C17C2×#4111yescharacteristic
182C23×C17C2×#4111yescharacteristic
183C23×C17C2×#4111yescharacteristic
184C23×C17C2×#4111yescharacteristic
185C23×C17C2×#4111yescharacteristic
186C23×C17C2×#4111yescharacteristic
187C23×C17C2×#4111yescharacteristic
188C23×C17C2×#4111yescharacteristic
189C23×C17H(5,𝔽2)11yescharacteristic
190C23×C17H(5,𝔽2)11yescharacteristic
191C23×C172−1+411yescharacteristic
192C23×C172−1+411yescharacteristic
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—24no—
202C2×C4×C17—22no—
203C2×C4×C17—22no—
204C2×C4×C17—22no—
205C2×C4×C17—41no—
206C2×C4×C17—41no—
207C2×C4×C17—41no—
208C2×C4×C17—42no—
209C2×C4×C17—41no—
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×C17#11714yes—
221C2×C4×C17C4×D414yes—
222C2×C4×C17C4×Q814yes—
223C2×C4×C17C22⋊Q814yes—
224C2×C4×C17#12314yes—
225C2×C4×C17#12514yes—
226C2×C4×C17#12514yes—
227C2×C4×C17#12614yes—
228C2×Dic17—22no—
229C2×Dic17—22no—
230C2×Dic17—24no—
231C2×Dic17—22no—
232C2×Dic17—22no—
233C2×Dic17—24no—
234C2×Dic17—24no—
235C2×Dic17—22no—
236C2×Dic17—22no—
237C2×Dic17—24no—
238C2×Dic17—22no—
239C2×Dic17—22no—
240C2×Dic17—24no—
241C2×Dic17—24no—
242C2×Dic17—22no—
243C2×Dic17—22no—
244C2×Dic17—22no—
245C2×Dic17—22no—
246C2×Dic17—41no—
247C2×Dic17—41no—
248C2×Dic17—42no—
249C2×Dic17—41no—
250C2×Dic17—42no—
251C2×Dic17—41no—
252C2×Dic17—41no—
253C2×Dic17—42no—
254C2×Dic17—41no—
255C2×Dic17—41no—
256C2×Dic17—41no—
257C2×Dic17—42no—
258C2×Dic17—41no—
259C2×Dic17—41no—
260C2×Dic17—41no—
261C2×Dic17—41no—
262C2×Dic17—42no—
263C2×Dic17—41no—
264C2×Dic17—42no—
265C2×Dic17—41no—
266C2×Dic17—41no—
267C2×Dic17—42no—
268C2×Dic17—41no—
269C2×Dic17—42no—
270C2×#389—171no—
271C2×#382—171no—
272C2×C4×C4⋊C4—171no—
273#1445—172no—
274#1443—172no—
275#1436—172no—
276C4⋊#95—171no—
277C4⋊#95—171no—
278C4⋊#95D1711yescharacteristic
279#1434—172no—
280C4×#95—171no—
281C22×C17C2×#11711yescharacteristic
282C22×C17C2×C4×D411yescharacteristic
283C22×C17C2×C4×Q811yescharacteristic
284C22×C17C4×#4111yescharacteristic
285C22×C17C4×#4111yescharacteristic
286C22×C17#51811yescharacteristic
287C22×C17#51911yescharacteristic
288C22×C17C2×C22⋊Q811yescharacteristic
289C22×C17C2×#12311yescharacteristic
290C22×C17C2×#12511yescharacteristic
291C22×C17C2×#12511yescharacteristic
292C22×C17C2×#12611yescharacteristic
293C22×C17#52911yescharacteristic
294C22×C17#52911yescharacteristic
295C22×C17#53311yescharacteristic
296C22×C17#54211yescharacteristic
297C22×C17#54211yescharacteristic
298C22×C17#54411yescharacteristic
299C22×C17#54411yescharacteristic
300C22×C17#54611yescharacteristic
301C22×C17#54711yescharacteristic
302C22×C17#54811yescharacteristic
303C22×C17#55011yescharacteristic
304C22×C17#55211yescharacteristic
305C22×C17#55211yescharacteristic
306C22×C17#55211yescharacteristic
307C22×C17#55311yescharacteristic
308C22×C17#55311yescharacteristic
309C22×C17#55311yescharacteristic
310C22×C17#55511yescharacteristic
311C22×C17#55611yescharacteristic
312C22×C17#55611yescharacteristic
313C22×C17#55611yescharacteristic
314C22×C17#55911yescharacteristic
315C22×C17#55911yescharacteristic
316C4×C17—24no—
317C4×C17—44no—
318C4×C17—42no—
319C4×C17—82no—
320C4×C17#38718yes—
321Dic17—42no—
322Dic17—42no—
323Dic17—44no—
324Dic17—44no—
325Dic17—42no—
326Dic17—42no—
327C22×C4⋊C4—171no—
328C22×C4⋊C4—171no—
329C22×C4⋊C4—172no—
330C22×C4⋊C4C2×D1711yescharacteristic
331C22×C4⋊C4C2×D1711yescharacteristic
332C22×C42—171no—
333C22×C42—171no—
334C22×C42—172no—
335C22×C42C2×D1711yescharacteristic
336#389—178no—
337#382—344no—
338C4×C4⋊C4—344no—
339C2×#95—172no—
340C2×#95—171no—
341C2×#95—171no—
342C2×#95—171no—
343C2×#95—171no—
344C2×#95—172no—
345C2×#95—172no—
346C2×#95—172no—
347C2×#95—172no—
348C2×#95—172no—
349C2×#95—172no—
350C2×#95—172no—
351C2×#95C2×D1712yes—
352C2×#95C2×D1712yes—
353C2×C17C2×#38711yescharacteristic
354C2×C17C4×#12511yescharacteristic
355C2×C17#233111yescharacteristic
356C2×C17#235611yescharacteristic
357C2×C17#235711yescharacteristic
358C2×C17#236211yescharacteristic
359C2×C17#236311yescharacteristic
360C2×C17#244111yescharacteristic
361C2×C17#244211yescharacteristic
362C2×C17#244711yescharacteristic
363C2×C17#244811yescharacteristic
364C2×C17#249411yescharacteristic
365C2×C17#249511yescharacteristic
366C2×C17#257011yescharacteristic
367C2×C17#257111yescharacteristic
368C23×C4—172no—
369C23×C4—171no—
370C23×C4—172no—
371C23×C4—171no—
372C23×C4—171no—
373C23×C4—171no—
374C23×C4C22×D1712yes—
375C23×C4C22×D1711yescharacteristic
376C23×C4C22×D1712yes—
377C23×C4C22×D1711yescharacteristic
378C23×C4C22×D1711yescharacteristic
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—174no—
385C2×C4⋊C4—174no—
386C2×C4⋊C4—178no—
387C2×C4⋊C4—342no—
388C2×C4⋊C4—342no—
389C2×C4⋊C4—342no—
390C2×C4⋊C4—342no—
391C2×C4⋊C4—682no—
392C2×C4⋊C4—682no—
393C2×C4⋊C4C4×D1714yes—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—174no—
397C2×C42—342no—
398C2×C42—342no—
399C2×C42—344no—
400C2×C42—342no—
401C2×C42—342no—
402C2×C42—344no—
403C2×C42—342no—
404C2×C42—682no—
405C2×C42Dic3414yes—
406#95—24no—
407#95—42no—
408#95—178no—
409#95—342no—
410#95—342no—
411#95—344no—
412#95—344no—
413#95—344no—
414#95—344no—
415#95—344no—
416#95—342no—
417#95—342no—
418#95—682no—
419#95—682no—
420C17#1398211yescharacteristic, complemented, Sylow
421C24C23×D1711yescharacteristic
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—172no—
446C22×C4—174no—
447C22×C4—172no—
448C22×C4—174no—
449C22×C4—172no—
450C22×C4—172no—
451C22×C4—341no—
452C22×C4—341no—
453C22×C4—342no—
454C22×C4—341no—
455C22×C4—341no—
456C22×C4—342no—
457C22×C4—341no—
458C22×C4—341no—
459C22×C4—341no—
460C22×C4—341no—
461C22×C4—342no—
462C22×C4—341no—
463C22×C4—342no—
464C22×C4—341no—
465C22×C4—341no—
466C22×C4—341no—
467C22×C4—341no—
468C22×C4—341no—
469C22×C4—341no—
470C22×C4—341no—
471C22×C4—342no—
472C22×C4—342no—
473C22×C4—342no—
474C22×C4—342no—
475C22×C4—341no—
476C22×C4—341no—
477C22×C4—342no—
478C22×C4—341no—
479C22×C4—342no—
480C22×C4—341no—
481C22×C4—341no—
482C22×C4—342no—
483C22×C4—342no—
484C22×C4—341no—
485C22×C4—341no—
486C22×C4—341no—
487C22×C4C2×Dic3412yes—
488C22×C4C2×Dic3412yes—
489C22×C4C2×Dic3412yes—
490C22×C4C2×C4×D1714yes—
491C22×C4C2×C4×D1712yes—
492C22×C4#6325212yes—
493C22×C4D4×D1712yes—
494C22×C4#6325412yes—
495C22×C4#6325412yes—
496C22×C4#6325412yes—
497C22×C4#6325612yes—
498C22×C4#6325612yes—
499C4⋊C4—28no—
500C4⋊C4—44no—
501C4⋊C4—348no—
502C4⋊C4—348no—
503C4⋊C4—688no—
504C42—28no—
505C42—348no—
506C42—688no—
507C42—684no—
508C23C22×Dic3411yescharacteristic
509C23C22×C4×D1711yescharacteristic
510C23C2×#6325211yescharacteristic
511C23C2×D4×D1711yescharacteristic
512C23C2×#6325411yescharacteristic
513C23C2×#6325411yescharacteristic
514C23C2×#6325411yescharacteristic
515C23#1058769111yescharacteristic
516C23C2×#6325611yescharacteristic
517C23C2×#6325611yescharacteristic
518C23#1058769411yescharacteristic
519C23#41×D1711yescharacteristic
520C23#41×D1711yescharacteristic
521C23#1058769611yescharacteristic
522C23#1058769711yescharacteristic
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—344no—
551C2×C4—342no—
552C2×C4—342no—
553C2×C4—342no—
554C2×C4—342no—
555C2×C4—342no—
556C2×C4—342no—
557C2×C4—344no—
558C2×C4—342no—
559C2×C4—344no—
560C2×C4—342no—
561C2×C4—342no—
562C2×C4—344no—
563C2×C4—342no—
564C2×C4—344no—
565C2×C4—342no—
566C2×C4—342no—
567C2×C4—344no—
568C2×C4—681no—
569C2×C4—681no—
570C2×C4—681no—
571C2×C4—682no—
572C2×C4—681no—
573C2×C4—681no—
574C2×C4—681no—
575C2×C4—681no—
576C2×C4—682no—
577C2×C4—681no—
578C2×C4—682no—
579C2×C4—681no—
580C2×C4—681no—
581C2×C4—682no—
582C2×C4—681no—
583C2×C4—682no—
584C2×C4—681no—
585C2×C4—681no—
586C2×C4—682no—
587C2×C4—681no—
588C2×C4—681no—
589C2×C4—682no—
590C2×C4—682no—
591C2×C4—681no—
592C2×C4C4×Dic3414yes—
593C2×C4#1058756314yes—
594C2×C4#1058756414yes—
595C2×C4#1058756914yes—
596C2×C4#1058757614yes—
597C2×C4#1058757614yes—
598C2×C4#1058757914yes—
599C2×C4#1058758414yes—
600C22C2×#1058756311yescharacteristic
601C22C2×#1058757911yescharacteristic
602C22C2×C4×Dic3411yescharacteristic
603C22C4×#6325411yescharacteristic
604C22C4×#6325611yescharacteristic
605C22#1176328111yescharacteristic
606C22#1176328511yescharacteristic
607C22C2×#1058756411yescharacteristic
608C22C2×#1058756911yescharacteristic
609C22C2×#1058757611yescharacteristic
610C22C2×#1058757611yescharacteristic
611C22C2×#1058758411yescharacteristic
612C22#1176334111yescharacteristic
613C22#1176334611yescharacteristic
614C22#1176336211yescharacteristic
615C22#1176342411yescharacteristic
616C22#1176343111yescharacteristic
617C22#1176343711yescharacteristic
618C22#1176344011yescharacteristic
619C22#1176345011yescharacteristic
620C22#1176346111yescharacteristic
621C22#1176346511yescharacteristic
622C22#1176347711yescharacteristic
623C22#1176349311yescharacteristic
624C22#1176349711yescharacteristic
625C22#1176350111yescharacteristic
626C22#1176350611yescharacteristic
627C22#1176351111yescharacteristic
628C22#1176351211yescharacteristic
629C22#1176352511yescharacteristic
630C22#1176352811yescharacteristic
631C22#1176353311yescharacteristic
632C22#1176353311yescharacteristic
633C22#1176354111yescharacteristic
634C22#1176354511yescharacteristic
635C4—24no—
636C4—42no—
637C4—44no—
638C4—82no—
639C4—682no—
640C4—682no—
641C4—684no—
642C4—682no—
643C4—682no—
644C4—684no—
645C4#1176269218yes—
646C2C2×#1176269211yescharacteristic
647C2C4×#1058757611yescharacteristic
648C2#1453152811yescharacteristic
649C2#1453174811yescharacteristic
650C2#1453175611yescharacteristic
651C2#1453181011yescharacteristic
652C2#1453182111yescharacteristic
653C2#1453249811yescharacteristic
654C2#1453250911yescharacteristic
655C2#1453257211yescharacteristic
656C2#1453258311yescharacteristic
657C2#1453318511yescharacteristic
658C2#1453319611yescharacteristic
659C2#1453401911yescharacteristic
660C2#1453402611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C4⋊#95C2
socle, prime radical, cosocleC24×C17C24
hypercenterC4⋊#95D17
hypocenterC17#13982
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
18. #11762708C4semidirect
420. C17#13982semidirect

Maximal subgroups

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

subgroupindex
C2×#117627082
C2×#117626742
C2×C4×C4⋊Dic172
#145270532
#145270452
#145270182
#145270132
#145270102
C4×#105875022
C17×C4⋊#952
#1398217