Finite Group Databasebeta

← #16956704

Subgroups — #16956704

Order 4352.

1282 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762676C212yesmaximal
2C2×C4⋊C4×Dic17C211yesmaximal, characteristic
3#14527045C212yesmaximal
4#14527044C212yesmaximal
5#14527014C211yesmaximal, characteristic
6#14527013C211yesmaximal, characteristic
7#14527013C211yesmaximal, characteristic
8#14527013C211yesmaximal, characteristic
9#14527010C212yesmaximal
10C4×#10587502C211yesmaximal, characteristic
11C17×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C4⋊Dic17C2211yescharacteristic
14C22×C4×Dic17C2211yescharacteristic
15C22×C4×Dic17C2211yescharacteristic
16C22×C4×Dic17C2212yes—
17#11762676—28no—
18C4⋊C4×Dic17C418yescomplemented
19C2×#10587502C2211yescharacteristic
20C2×#10587502C2211yescharacteristic
21C2×#10587502C2211yescharacteristic
22C2×#10587502C2212yes—
23C2×#10587502C2212yes—
24C2×#10587502C2212yes—
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2211yescharacteristic
32C22×C4⋊C4×C17C2211yescharacteristic
33C22×C4⋊C4×C17C2211yescharacteristic
34C22×C42×C17C2211yescharacteristic
35C2×C17×#95C2212yes—
36C2×C17×#95C2212yes—
37C23×C4×C17C2312yes—
38C23×C4×C17C2312yes—
39C23×C4×C17C2311yescharacteristic
40C23×C4×C17C2311yescharacteristic
41C23×C4×C17C2311yescharacteristic
42C23×Dic17C2312yes—
43C23×Dic17C2312yes—
44C23×Dic17C2311yescharacteristic
45C23×Dic17C2311yescharacteristic
46C23×Dic17C2311yescharacteristic
47C23×Dic17C2311yescharacteristic
48C2×C4⋊C4×C17—22no—
49C2×C4⋊C4×C17—22no—
50C2×C4⋊C4×C17—22no—
51C2×C4⋊C4×C17—22no—
52C2×C4⋊C4×C17—22no—
53C2×C4⋊C4×C17C2×C414yes—
54C2×C42×C17—22no—
55C2×C42×C17—22no—
56C2×C42×C17—22no—
57C2×C4⋊Dic17—22no—
58C2×C4⋊Dic17—22no—
59C2×C4⋊Dic17—22no—
60C2×C4⋊Dic17—22no—
61C2×C4⋊Dic17—22no—
62C2×C4⋊Dic17C2×C414yes—
63C2×C4×Dic17—22no—
64C2×C4×Dic17—22no—
65C2×C4×Dic17—22no—
66C2×C4×Dic17—22no—
67C2×C4×Dic17—22no—
68C2×C4×Dic17—24no—
69C2×C4×Dic17—24no—
70C2×C4×Dic17C2×C414yes—
71C2×C4×Dic17C2×C418yes—
72C17×#95—24no—
73C17×#95—42no—
74#10587502—24no—
75#10587502—22no—
76#10587502—24no—
77#10587502—24no—
78#10587502—24no—
79#10587502—24no—
80#10587502—22no—
81#10587502—24no—
82#10587502—22no—
83#10587502—42no—
84#10587502—42no—
85#10587502C2×C418yes—
86#10587502D414yes—
87C24×C17C2411yescharacteristic
88C22×C4×C17—22no—
89C22×C4×C17—21no—
90C22×C4×C17—21no—
91C22×C4×C17—22no—
92C22×C4×C17—21no—
93C22×C4×C17—21no—
94C22×C4×C17—21no—
95C22×C4×C17—21no—
96C22×C4×C17—21no—
97C22×C4×C17—21no—
98C22×C4×C17—22no—
99C22×C4×C17—22no—
100C22×C4×C17—22no—
101C22×C4×C17—21no—
102C22×C4×C17—21no—
103C22×C4×C17—22no—
104C22×C4×C17—21no—
105C22×C4×C17—21no—
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×C17C22×C414yes—
114C22×C4×C17C22×C412yes—
115C22×C4×C17C2×D412yes—
116C22×C4×C17#4112yes—
117C22×C4×C17#4112yes—
118C22×C4×C17#4112yes—
119C22×C4×C17#4112yes—
120C22×C4×C17#4112yes—
121C22×C4×C17#4112yes—
122C22×C4×C17#4112yes—
123C22×Dic17—21no—
124C22×Dic17—21no—
125C22×Dic17—21no—
126C22×Dic17—21no—
127C22×Dic17—22no—
128C22×Dic17—22no—
129C22×Dic17—21no—
130C22×Dic17—21no—
131C22×Dic17—22no—
132C22×Dic17—21no—
133C22×Dic17—21no—
134C22×Dic17—21no—
135C22×Dic17—21no—
136C22×Dic17—21no—
137C22×Dic17—21no—
138C22×Dic17—21no—
139C22×Dic17—21no—
140C22×Dic17—21no—
141C22×Dic17—21no—
142C22×Dic17—22no—
143C22×Dic17—22no—
144C22×Dic17—22no—
145C22×Dic17—21no—
146C22×Dic17—21no—
147C22×Dic17—21no—
148C22×Dic17—21no—
149C22×Dic17—21no—
150C22×Dic17—21no—
151C22×Dic17—22no—
152C22×Dic17—22no—
153C22×Dic17—22no—
154C22×Dic17—22no—
155C22×Dic17—22no—
156C22×Dic17—22no—
157C22×Dic17—22no—
158C22×Dic17C22×C412yes—
159C22×Dic17C22×C414yes—
160C22×Dic17C22×C412yes—
161C22×Dic17C2×D412yes—
162C22×Dic17C2×D412yes—
163C22×Dic17#4112yes—
164C22×Dic17#4112yes—
165C4⋊C4×C17—28no—
166C4⋊C4×C17—44no—
167C42×C17—44no—
168C4⋊Dic17—28no—
169C4⋊Dic17—44no—
170C4×Dic17—28no—
171C4×Dic17—216no—
172C4×Dic17—44no—
173#13921—171nomaximal, Sylow
174C23×C17C23×C411yescharacteristic
175C23×C17C22×D411yescharacteristic
176C23×C17C2×#4111yescharacteristic
177C23×C17C2×#4111yescharacteristic
178C23×C17C2×#4111yescharacteristic
179C23×C17C2×#4111yescharacteristic
180C23×C17C2×#4111yescharacteristic
181C23×C17C2×#4111yescharacteristic
182C23×C17C2×#4111yescharacteristic
183C23×C17C2×#4111yescharacteristic
184C23×C17C2×#4111yescharacteristic
185C23×C17H(5,𝔽2)11yescharacteristic
186C23×C172−1+411yescharacteristic
187C23×C172−1+411yescharacteristic
188C23×C172−1+411yescharacteristic
189C2×C4×C17—24no—
190C2×C4×C17—24no—
191C2×C4×C17—24no—
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—41no—
199C2×C4×C17—41no—
200C2×C4×C17—41no—
201C2×C4×C17—41no—
202C2×C4×C17—42no—
203C2×C4×C17—42no—
204C2×C4×C17—41no—
205C2×C4×C17—41no—
206C2×C4×C17—42no—
207C2×C4×C17—41no—
208C2×C4×C17—41no—
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#11714yes—
218C2×C4×C17#11714yes—
219C2×C4×C17#11714yes—
220C2×C4×C17#12614yes—
221C2×C4×C17#12614yes—
222C2×C4×C17#12614yes—
223C2×C4×C17#12614yes—
224C2×Dic17—22no—
225C2×Dic17—22no—
226C2×Dic17—22no—
227C2×Dic17—22no—
228C2×Dic17—22no—
229C2×Dic17—22no—
230C2×Dic17—22no—
231C2×Dic17—24no—
232C2×Dic17—24no—
233C2×Dic17—22no—
234C2×Dic17—24no—
235C2×Dic17—22no—
236C2×Dic17—22no—
237C2×Dic17—22no—
238C2×Dic17—22no—
239C2×Dic17—22no—
240C2×Dic17—22no—
241C2×Dic17—22no—
242C2×Dic17—41no—
243C2×Dic17—41no—
244C2×Dic17—42no—
245C2×Dic17—42no—
246C2×Dic17—42no—
247C2×Dic17—42no—
248C2×Dic17—41no—
249C2×Dic17—41no—
250C2×Dic17—41no—
251C2×Dic17—41no—
252C2×Dic17—41no—
253C2×Dic17—41no—
254C2×Dic17—41no—
255C2×Dic17—41no—
256C2×Dic17—41no—
257C2×Dic17—41no—
258C2×Dic17—42no—
259C2×Dic17—42no—
260C2×Dic17—42no—
261C2×Dic17—42no—
262C2×Dic17—42no—
263C2×Dic17—42no—
264C2×Dic17—42no—
265C2×Dic17C4×D414yes—
266C2×#383—172no—
267C2×C4×C4⋊C4—171no—
268#1443—172no—
269#1443—172no—
270C4⋊#95—171no—
271C4⋊#95—171no—
272C4⋊#95—171no—
273C4⋊#95—171no—
274C4⋊#95D1711yescharacteristic
275#1434—172no—
276C4×#95—171no—
277C22×C17C2×#11711yescharacteristic
278C22×C17C2×#11711yescharacteristic
279C22×C17C2×#11711yescharacteristic
280C22×C17C2×C4×D411yescharacteristic
281C22×C17C4×#4111yescharacteristic
282C22×C17#51911yescharacteristic
283C22×C17#52011yescharacteristic
284C22×C17C2×#12611yescharacteristic
285C22×C17C2×#12611yescharacteristic
286C22×C17C2×#12611yescharacteristic
287C22×C17C2×#12611yescharacteristic
288C22×C17#52911yescharacteristic
289C22×C17#52911yescharacteristic
290C22×C17#53211yescharacteristic
291C22×C17#53211yescharacteristic
292C22×C17#54111yescharacteristic
293C22×C17#54111yescharacteristic
294C22×C17#54211yescharacteristic
295C22×C17#54211yescharacteristic
296C22×C17#54711yescharacteristic
297C22×C17#54711yescharacteristic
298C22×C17#54711yescharacteristic
299C22×C17#55011yescharacteristic
300C22×C17#55211yescharacteristic
301C22×C17#55211yescharacteristic
302C22×C17#55211yescharacteristic
303C22×C17#55211yescharacteristic
304C22×C17#55311yescharacteristic
305C22×C17#55311yescharacteristic
306C22×C17#55511yescharacteristic
307C22×C17#55611yescharacteristic
308C22×C17#55611yescharacteristic
309C22×C17#55611yescharacteristic
310C22×C17#55611yescharacteristic
311C22×C17#55611yescharacteristic
312C4×C17—44no—
313C4×C17—42no—
314C4×C17—42no—
315C4×C17—82no—
316C4×C17#38318yescomplemented
317Dic17—24no—
318Dic17—42no—
319Dic17—42no—
320Dic17—42no—
321Dic17—44no—
322Dic17—82no—
323C22×C4⋊C4—171no—
324C22×C4⋊C4—171no—
325C22×C4⋊C4C2×D1711yescharacteristic
326C22×C4⋊C4C2×D1711yescharacteristic
327C22×C42—171no—
328C22×C42—172no—
329C22×C42—171no—
330C22×C42C2×D1711yescharacteristic
331#383—348no—
332C4×C4⋊C4—178no—
333C2×#95—171no—
334C2×#95—172no—
335C2×#95—171no—
336C2×#95—171no—
337C2×#95—171no—
338C2×#95—172no—
339C2×#95—172no—
340C2×#95—172no—
341C2×#95—172no—
342C2×#95—172no—
343C2×#95—172no—
344C2×#95—172no—
345C2×#95—172no—
346C2×#95C2×D1712yes—
347C2×#95C2×D1712yes—
348C2×C17C2×#38311yescharacteristic
349C2×C17#229311yescharacteristic
350C2×C17#232011yescharacteristic
351C2×C17#234411yescharacteristic
352C2×C17#234711yescharacteristic
353C2×C17#235411yescharacteristic
354C2×C17#235611yescharacteristic
355C2×C17#249511yescharacteristic
356C2×C17#249511yescharacteristic
357C2×C17#249611yescharacteristic
358C2×C17#249611yescharacteristic
359C2×C17#251211yescharacteristic
360C2×C17#251211yescharacteristic
361C2×C17#251411yescharacteristic
362C2×C17#251411yescharacteristic
363C23×C4—171no—
364C23×C4—172no—
365C23×C4—171no—
366C23×C4—171no—
367C23×C4—171no—
368C23×C4—172no—
369C23×C4C22×D1712yes—
370C23×C4C22×D1712yes—
371C23×C4C22×D1711yescharacteristic
372C23×C4C22×D1711yescharacteristic
373C23×C4C22×D1711yescharacteristic
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—174no—
380C2×C4⋊C4—342no—
381C2×C4⋊C4—342no—
382C2×C4⋊C4—342no—
383C2×C4⋊C4—342no—
384C2×C4⋊C4—342no—
385C2×C4⋊C4C4×D1714yes—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—178no—
390C2×C42—174no—
391C2×C42—344no—
392C2×C42—344no—
393C2×C42—342no—
394C2×C42—342no—
395C2×C42—342no—
396C2×C42—342no—
397C2×C42—342no—
398#95—24no—
399#95—42no—
400#95—178no—
401#95—174no—
402#95—342no—
403#95—342no—
404#95—344no—
405#95—344no—
406#95—344no—
407#95—344no—
408#95—344no—
409#95—342no—
410#95—344no—
411#95—682no—
412#95—682no—
413C17#1392111yescharacteristic, complemented, Sylow
414C24C23×D1711yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—172no—
441C22×C4—172no—
442C22×C4—172no—
443C22×C4—172no—
444C22×C4—174no—
445C22×C4—172no—
446C22×C4—172no—
447C22×C4—341no—
448C22×C4—341no—
449C22×C4—341no—
450C22×C4—341no—
451C22×C4—341no—
452C22×C4—341no—
453C22×C4—341no—
454C22×C4—341no—
455C22×C4—342no—
456C22×C4—341no—
457C22×C4—341no—
458C22×C4—342no—
459C22×C4—341no—
460C22×C4—341no—
461C22×C4—341no—
462C22×C4—342no—
463C22×C4—341no—
464C22×C4—341no—
465C22×C4—341no—
466C22×C4—342no—
467C22×C4—341no—
468C22×C4—341no—
469C22×C4—342no—
470C22×C4—341no—
471C22×C4—342no—
472C22×C4—341no—
473C22×C4—341no—
474C22×C4—341no—
475C22×C4—342no—
476C22×C4—342no—
477C22×C4—342no—
478C22×C4—342no—
479C22×C4—342no—
480C22×C4—342no—
481C22×C4—342no—
482C22×C4C2×C4×D1714yes—
483C22×C4C2×C4×D1712yes—
484C22×C4#6325212yes—
485C22×C4#6325212yes—
486C22×C4D4×D1712yes—
487C22×C4#6325412yes—
488C22×C4#6325412yes—
489C22×C4#6325412yes—
490C22×C4#6325612yes—
491C22×C4#6325612yes—
492C4⋊C4—28no—
493C4⋊C4—44no—
494C4⋊C4—348no—
495C4⋊C4—684no—
496C42—44no—
497C42—3416no—
498C42—348no—
499C42—684no—
500C23C22×C4×D1711yescharacteristic
501C23C2×#6325211yescharacteristic
502C23C2×#6325211yescharacteristic
503C23C2×D4×D1711yescharacteristic
504C23C2×#6325411yescharacteristic
505C23C2×#6325411yescharacteristic
506C23C2×#6325411yescharacteristic
507C23#1058769111yescharacteristic
508C23C2×#6325611yescharacteristic
509C23C2×#6325611yescharacteristic
510C23#1058769411yescharacteristic
511C23#41×D1711yescharacteristic
512C23#41×D1711yescharacteristic
513C23#1058769711yescharacteristic
514C23#1058769711yescharacteristic
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—174no—
544C2×C4—342no—
545C2×C4—342no—
546C2×C4—342no—
547C2×C4—342no—
548C2×C4—342no—
549C2×C4—342no—
550C2×C4—342no—
551C2×C4—342no—
552C2×C4—342no—
553C2×C4—342no—
554C2×C4—342no—
555C2×C4—344no—
556C2×C4—344no—
557C2×C4—342no—
558C2×C4—344no—
559C2×C4—342no—
560C2×C4—342no—
561C2×C4—342no—
562C2×C4—681no—
563C2×C4—681no—
564C2×C4—681no—
565C2×C4—681no—
566C2×C4—681no—
567C2×C4—681no—
568C2×C4—681no—
569C2×C4—681no—
570C2×C4—681no—
571C2×C4—681no—
572C2×C4—682no—
573C2×C4—682no—
574C2×C4—682no—
575C2×C4—682no—
576C2×C4—681no—
577C2×C4—681no—
578C2×C4—682no—
579C2×C4—682no—
580C2×C4—682no—
581C2×C4—682no—
582C2×C4—682no—
583C2×C4—682no—
584C2×C4—682no—
585C2×C4#1058755814yes—
586C2×C4#1058756314yes—
587C2×C4#1058756514yes—
588C2×C4#1058756514yes—
589C2×C4#1058757814yes—
590C2×C4#1058758414yes—
591C2×C4#1058758414yes—
592C22C2×#1058756311yescharacteristic
593C22C2×#1058755811yescharacteristic
594C22C2×#1058757811yescharacteristic
595C22C4×D4×D1711yescharacteristic
596C22C4×#6325611yescharacteristic
597C22#1176328511yescharacteristic
598C22#1176328811yescharacteristic
599C22C2×#1058756511yescharacteristic
600C22C2×#1058756511yescharacteristic
601C22C2×#1058758411yescharacteristic
602C22C2×#1058758411yescharacteristic
603C22#1176334411yescharacteristic
604C22#1176334511yescharacteristic
605C22#1176335411yescharacteristic
606C22#1176336011yescharacteristic
607C22#1176341911yescharacteristic
608C22#1176342211yescharacteristic
609C22#1176342611yescharacteristic
610C22#1176343311yescharacteristic
611C22#1176345911yescharacteristic
612C22#1176346011yescharacteristic
613C22#1176346411yescharacteristic
614C22#1176347911yescharacteristic
615C22#1176349311yescharacteristic
616C22#1176349811yescharacteristic
617C22#1176350011yescharacteristic
618C22#1176350111yescharacteristic
619C22#1176350711yescharacteristic
620C22#1176350911yescharacteristic
621C22#1176352311yescharacteristic
622C22#1176352711yescharacteristic
623C22#1176352811yescharacteristic
624C22#1176352811yescharacteristic
625C22#1176353211yescharacteristic
626C22#1176353311yescharacteristic
627C4—42no—
628C4—42no—
629C4—44no—
630C4—82no—
631C4—344no—
632C4—682no—
633C4—682no—
634C4—682no—
635C4—684no—
636C4—1362no—
637C4#1176267618yescomplemented
638C2C2×#1176267611yescharacteristic
639C2#1453124211yescharacteristic
640C2#1453143111yescharacteristic
641C2#1453164911yescharacteristic
642C2#1453167311yescharacteristic
643C2#1453173211yescharacteristic
644C2#1453174811yescharacteristic
645C2#1453319111yescharacteristic
646C2#1453319311yescharacteristic
647C2#1453320211yescharacteristic
648C2#1453320411yescharacteristic
649C2#1453336611yescharacteristic
650C2#1453336811yescharacteristic
651C2#1453338811yescharacteristic
652C2#1453339011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C4⋊#95C2
socle, prime radical, cosocleC24×C17C24
hypercenterC4⋊#95D17
hypocenterC17#13921
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
18. C4⋊C4×Dic17C4semidirect
316. C4×C17#383semidirect
413. C17#13921semidirect
637. C4#11762676semidirect

Maximal subgroups

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

subgroupindex
C2×#117626762
C2×C4⋊C4×Dic172
#145270452
#145270442
#145270142
#145270132
#145270102
C4×#105875022
C17×C4⋊#952
#1392117