Finite Group Databasebeta

← #17193767

Subgroups — #17193767

Order 4352.

3142 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D17C211yesmaximal, characteristic
2#14531759C211yesmaximal, characteristic, complemented
3#14531755C211yesmaximal, characteristic, complemented
4#14531726C212yesmaximal, complemented
5#14531720C212yesmaximal, complemented
6#14531694C211yesmaximal, characteristic, complemented
7#14531660C212yesmaximal, complemented
8#14531631C214yesmaximal, complemented
9D4×#63227C212yesmaximal
10#14531242C212yesmaximal, complemented
11#14531220C214yesmaximal, complemented
12#14531177C211yesmaximal, characteristic, complemented
13#14531166C212yesmaximal, complemented
14C4×D4×Dic17C212yesmaximal, complemented
15C4×#10587578C211yesmaximal, characteristic, complemented
16C2×#11762656C212yesmaximal, complemented
17C17×#2349C211yesmaximal, characteristic, complemented
18C22×D4×D17C2211yescharacteristic
19C23×C4×D17C2212yes—
20C2×C4×D68C2211yescharacteristic
21C2×D4×Dic17C2212yes—
22C2×D4×Dic17C2211yescharacteristic
23C2×#10587579C2211yescharacteristic
24C2×C4×C22⋊D17C2212yes—
25C2×#10587567C2212yes—
26C4×D4×D17C4116yescomplemented
27C2×#10587578C2212yes—
28C2×#10587578C2214yescomplemented
29C2×C4⋊C4×D17C2211yescharacteristic
30C22×#63227C2214yes—
31C2×C22⋊C4×D17C2212yes—
32C22×C4×Dic17C2214yescomplemented
33C2×C42×D17C2211yescharacteristic
34#11762711C2212yes—
35#11762710C2212yes—
36#11762708C2212yescomplemented
37#11762701C2214yescomplemented
38#11762701C2214yescomplemented
39#11762699C2214yescomplemented
40#11762699C2214yescomplemented
41#11762696C2214yescomplemented
42#11762690C2214yescomplemented
43#11762688C2214yes—
44#11762686C2214yes—
45#11762684C2214yescomplemented
46#11762676C2212yescomplemented
47#11762675C2211yescharacteristic, complemented
48#11762671C2212yes—
49#11762671C2212yescomplemented
50#11762671C2212yescomplemented
51#11762669C2212yescomplemented
52#11762666C2212yes—
53#11762666C2214yes—
54#11762664C2214yes—
55C4⋊C4×Dic17C2212yescomplemented
56C4⋊C4×Dic17C2212yescomplemented
57C4⋊C4×Dic17C2212yescomplemented
58C4×C4⋊Dic17C2211yescharacteristic, complemented
59C4×C4⋊Dic17C2212yescomplemented
60C22⋊C4×Dic17C2214yescomplemented
61C22⋊C4×Dic17C2214yescomplemented
62C4×#63227C2212yes—
63C4×C22⋊Dic17C2214yescomplemented
64#11762656C2211yescharacteristic
65#11762656C2214yes—
66#11762656C2212yes—
67#11762656C2211yescharacteristic
68#11762656C2212yescomplemented
69#11762656C2212yescomplemented
70#11762656C2214yescomplemented
71#11762654C2211yescharacteristic, complemented
72#11762654C2211yescharacteristic, complemented
73#11762654C2212yescomplemented
74C2×#10587502C2212yescomplemented
75C42×Dic17C2212yescomplemented
76C2×C4×D4×C17C2212yes—
77C2×C4×D4×C17C2211yescharacteristic
78C17×#389C2212yescomplemented
79C17×#385C2214yescomplemented
80C17×#382C2211yescharacteristic, complemented
81C17×#380C2212yescomplemented
82C4×C4⋊C4×C17C2211yescharacteristic, complemented
83C2×C17×#95C2212yescomplemented
84C24×D17C2312yes—
85C22×D4×C17C2311yescharacteristic
86C23×C4×C17C2314yes—
87C23×C4×C17C2312yes—
88C22×C22⋊D17C2312yes—
89C23×Dic17C2314yes—
90C23×Dic17C2312yes—
91C2×D4×D17—24no—
92C2×D4×D17—24no—
93C2×D4×D17C2×C418yes—
94C22×D68C2311yescharacteristic
95C22×C4×D17—48no—
96C22×C4×D17C2×C4116yescomplemented
97C22×C4×D17C2311yescharacteristic
98C22×C4×D17C2311yescharacteristic
99C22×C4×D17C2311yescharacteristic
100C22×C4×D17C2312yes—
101C22×C4×D17C2312yes—
102C22×C4×D17C2312yes—
103C4×D4×C17—28no—
104C4×D4×C17C2×C418yes—
105C2×C4⋊C4×C17C2312yes—
106C2×C4⋊C4×C17C2312yes—
107C2×C4⋊C4×C17C2314yes—
108C2×C4⋊C4×C17C2311yescharacteristic
109C2×C22⋊C4×C17C2314yes—
110C2×C22⋊C4×C17C2312yes—
111C2×C42×C17C2312yes—
112C2×C42×C17C2311yescharacteristic
113C2×C22⋊Dic17C2314yes—
114C2×C22⋊Dic17C2312yes—
115D4×Dic17—28no—
116D4×Dic17C2×C418yes—
117C4×C22⋊D17C2×C4116yescomplemented
118C2×#63227—216no—
119C2×#63227C2314yes—
120C2×#63227C2314yes—
121C2×#63227C2314yes—
122C2×#63227C2312yes—
123C2×#63227C2314yes—
124C2×#63227C2314yes—
125C2×#63227C2312yes—
126C2×#63227C2312yes—
127C2×#63227C2312yes—
128C2×C4⋊Dic17C2312yes—
129C2×C4⋊Dic17C2312yes—
130C2×C4⋊Dic17C2314yes—
131C2×C4⋊Dic17C2311yescharacteristic
132C2×#63225C2312yes—
133C2×C4×Dic17—48no—
134C2×C4×Dic17C2312yes—
135C2×C4×Dic17C2312yes—
136C2×C4×Dic17C2312yes—
137C2×C4×Dic17C2312yes—
138C2×C4×Dic17C2314yes—
139C2×C4×Dic17C2312yes—
140C2×C4×Dic17C2314yes—
141C2×C4×Dic17C2314yes—
142C2×C4×Dic17C2311yescharacteristic
143C2×C4×Dic17C2311yescharacteristic
144C2×C4×Dic17C2311yescharacteristic
145#10587579C2×C418yescomplemented
146#10587578—28no—
147#10587578—48no—
148C4⋊C4×D17C2×C418yescomplemented
149#10587567C2×C4116yescomplemented
150C22⋊C4×D17C2×C4116yescomplemented
151C4×D68C2×C418yescomplemented
152C42×D17C2×C418yescomplemented
153C17×#95C2314yes—
154C17×#95C2312yes—
155C17×#95C2311yescharacteristic
156C17×#95C2312yes—
157C17×#95C2311yescharacteristic
158#10587502C2312yes—
159#10587502C2314yes—
160#10587502C2312yes—
161#10587502C2314yes—
162#10587502C2314yes—
163#10587502C2314yes—
164#10587502C2312yes—
165#10587502C2314yes—
166#10587502C2311yescharacteristic
167#10587502C2312yes—
168#10587502C2311yescharacteristic
169C24×C17C2412yes—
170C23×D17—24no—
171C23×D17—24no—
172C23×D17—28no—
173C23×D17—44no—
174C23×D17C22×C418yes—
175C23×D17C2412yes—
176C23×D17C2411yescharacteristic
177C2×D4×C17C22×C414yes—
178C2×D4×C17#4114yes—
179C2×D4×C17#4114yes—
180C22×C4×C17—28no—
181C22×C4×C17—28no—
182C22×C4×C17—44no—
183C22×C4×C17—44no—
184C22×C4×C17C22×C418yes—
185C22×C4×C17C2414yes—
186C22×C4×C17C2412yes—
187C22×C4×C17C2411yescharacteristic
188C22×C4×C17C2412yes—
189C22×C4×C17C2411yescharacteristic
190C22×C4×C17C2412yes—
191C22×C4×C17C2411yescharacteristic
192C2×C22⋊D17—24no—
193C2×C22⋊D17—24no—
194C2×C22⋊D17C22×C418yes—
195C22×Dic17—28no—
196C22×Dic17—28no—
197C22×Dic17—28no—
198C22×Dic17—44no—
199C22×Dic17C22×C418yes—
200C22×Dic17C2414yes—
201C22×Dic17C2412yes—
202C22×Dic17C2412yes—
203C22×Dic17C2411yescharacteristic
204C22×Dic17C2411yescharacteristic
205C22×Dic17C2412yes—
206C22×Dic17C2411yescharacteristic
207D4×D17—232no—
208C2×D68—22no—
209C2×D68—22no—
210C2×D68C22×C414yes—
211C2×C4×D17—24no—
212C2×C4×D17—22no—
213C2×C4×D17—22no—
214C2×C4×D17—24no—
215C2×C4×D17—28no—
216C2×C4×D17—432no—
217C2×C4×D17—44no—
218C2×C4×D17—44no—
219C2×C4×D17C22×C414yes—
220C2×C4×D17C22×C418yes—
221C2×C4×D17C22×C414yes—
222C2×C4×D17C22×C414yes—
223C2×C4×D17C22×C418yes—
224C2×C4×D17C22×C418yes—
225C4⋊C4×C17—24no—
226C4⋊C4×C17—24no—
227C4⋊C4×C17—44no—
228C4⋊C4×C17C22×C414yes—
229C22⋊C4×C17—28no—
230C22⋊C4×C17C22×C418yes—
231C42×C17—24no—
232C42×C17C22×C414yes—
233C22⋊Dic17—28no—
234C22⋊Dic17C22×C418yes—
235#63227—24no—
236#63227—28no—
237#63227—28no—
238#63227—28no—
239#63227—44no—
240#63227—44no—
241#63227C22×C418yes—
242#63227C22×C418yes—
243#63227#4118yes—
244C4⋊Dic17—24no—
245C4⋊Dic17—24no—
246C4⋊Dic17—44no—
247C4⋊Dic17C22×C414yes—
248#63225C22×C418yes—
249C4×Dic17—24no—
250C4×Dic17—24no—
251C4×Dic17—24no—
252C4×Dic17—24no—
253C4×Dic17—28no—
254C4×Dic17—24no—
255C4×Dic17—44no—
256C4×Dic17—44no—
257C4×Dic17C22×C414yes—
258C4×Dic17C22×C414yes—
259C4×Dic17C22×C414yes—
260#34126—171nomaximal, Sylow
261C23×C17—24no—
262C23×C17—24no—
263C23×C17C23×C414yes—
264C23×C17C2×#4114yes—
265C23×C17C2×#4114yes—
266C23×C17C2511yescharacteristic
267C22×D17—21no—
268C22×D17—21no—
269C22×D17—22no—
270C22×D17—216no—
271C22×D17—22no—
272C22×D17—22no—
273C22×D17—24no—
274C22×D17—24no—
275C22×D17—216no—
276C22×D17—48no—
277C22×D17—416no—
278C22×D17—416no—
279C22×D17C23×C414yes—
280C22×D17C23×C412yes—
281C22×D17C2×#4114yes—
282D4×C17#117116yescomplemented
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—24no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—24no—
290C2×C4×C17—22no—
291C2×C4×C17—24no—
292C2×C4×C17—22no—
293C2×C4×C17—24no—
294C2×C4×C17—48no—
295C2×C4×C17—416no—
296C2×C4×C17C23×C412yes—
297C2×C4×C17C23×C412yes—
298C2×C4×C17C23×C414yes—
299C2×C4×C17C23×C412yes—
300C2×C4×C17C2×#4112yes—
301C2×C4×C17C2×#4112yes—
302C2×C4×C17C2×#4114yes—
303C22⋊D17—216no—
304C2×Dic17—21no—
305C2×Dic17—21no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—24no—
309C2×Dic17—22no—
310C2×Dic17—216no—
311C2×Dic17—22no—
312C2×Dic17—24no—
313C2×Dic17—24no—
314C2×Dic17—22no—
315C2×Dic17—24no—
316C2×Dic17—22no—
317C2×Dic17—416no—
318C2×Dic17C23×C412yes—
319C2×Dic17C23×C414yes—
320C2×Dic17C23×C412yes—
321C2×Dic17C23×C412yes—
322C2×Dic17C2×#4114yes—
323C2×Dic17H(5,𝔽2)14yes—
324D68—28no—
325C4×D17—28no—
326C4×D17—28no—
327C4×D17—28no—
328C4×D17—216no—
329C4×D17—48no—
330C4×D17—48no—
331C22×C4×D4—171no—
332#2357—171no—
333#2357—171no—
334#2353—172no—
335#2353—172no—
336#2349—171no—
337#2349D1711yescharacteristic, complemented
338#2345—172no—
339#2342—174no—
340D4×C22⋊C4—172no—
341#2293—172no—
342#2290—174no—
343#2283—171no—
344#2280—172no—
345C42×D4—172no—
346C4×#117—171no—
347C2×C4×C22⋊C4—172no—
348C22×C17—24no—
349C22×C17—24no—
350C22×C17—28no—
351C22×C17—28no—
352C22×C17C2×#11718yes—
353C22×C17C24×C411yescharacteristic
354C22×C17C22×#4112yes—
355C22×C17C22×#4111yescharacteristic
356C22×C17C22×#4111yescharacteristic
357C22×C17C2×H(5,𝔽2)12yes—
358C2×D17—22no—
359C2×D17—22no—
360C2×D17—24no—
361C2×D17—24no—
362C2×D17—24no—
363C2×D17—24no—
364C2×D17—24no—
365C2×D17—432no—
366C2×D17—44no—
367C2×D17—44no—
368C2×D17C4×#4114yes—
369C4×C17—22no—
370C4×C17—22no—
371C4×C17—24no—
372C4×C17—24no—
373C4×C17—42no—
374C4×C17—44no—
375C4×C17C2×#11714yes—
376Dic17—22no—
377Dic17—22no—
378Dic17—24no—
379Dic17—24no—
380Dic17—42no—
381Dic17—44no—
382Dic17#51814yes—
383C23×D4—171no—
384C24×C4—172no—
385C2×C4×D4—171no—
386C2×C4×D4—172no—
387C2×C4×D4—1716no—
388C2×C4×D4—172no—
389C2×C4×D4—171no—
390C2×C4×D4—172no—
391C2×C4×D4—171no—
392C2×C4×D4C2×D1712yes—
393C2×C4×D4C2×D1711yescharacteristic
394C2×#117—172no—
395C2×#117—174no—
396C22×C4⋊C4—171no—
397C22×C22⋊C4—172no—
398C22×C22⋊C4—174no—
399C22×C42—171no—
400C22×C42—174no—
401#390—172no—
402#390—172no—
403#389—172no—
404#389C2×D1712yescomplemented
405#388—174no—
406#388—174no—
407#388—174no—
408#388—174no—
409#387—174no—
410#387—174no—
411#386—174no—
412#386—174no—
413#385—174no—
414#385C2×D1714yescomplemented
415#383—172no—
416#382—171no—
417#382C2×D1711yescharacteristic, complemented
418#381—172no—
419#381—172no—
420#381—172no—
421#380—172no—
422#380—172no—
423#380—174no—
424#380C2×D1712yescomplemented
425#379—174no—
426C4×C4⋊C4—172no—
427C4×C4⋊C4—172no—
428C4×C4⋊C4—172no—
429C4×C4⋊C4—172no—
430C4×C4⋊C4—171no—
431C4×C4⋊C4C2×D1711yescharacteristic, complemented
432C4×C22⋊C4—174no—
433C4×C22⋊C4—174no—
434C4×C22⋊C4—174no—
435C4×C22⋊C4—172no—
436C4×C22⋊C4—174no—
437C4×C22⋊C4—172no—
438C4×C22⋊C4—172no—
439C4×C22⋊C4—171no—
440C4×C22⋊C4—172no—
441C4×C22⋊C4—174no—
442C4×C22⋊C4—171no—
443#376—171no—
444#376—171no—
445#376—172no—
446C2×#95—172no—
447C2×#95C2×D1712yescomplemented
448C43—172no—
449C2×C17—28no—
450C2×C17C22×#11711yescharacteristic
451C2×C17C2×C4×#4111yescharacteristic
452C2×C17C2×#51811yescharacteristic
453C2×C17#348112yes—
454C2×C17#348112yes—
455D17—24no—
456D17—44no—
457C25—172no—
458C22×D4—172no—
459C22×D4—178no—
460C22×D4—171no—
461C22×D4—344no—
462C22×D4—344no—
463C22×D4C22×D1711yescharacteristic
464C23×C4—172no—
465C23×C4—171no—
466C23×C4—171no—
467C23×C4—172no—
468C23×C4—171no—
469C23×C4—1716no—
470C23×C4—172no—
471C23×C4—172no—
472C23×C4—174no—
473C23×C4—688no—
474C23×C4C22×D1714yes—
475C23×C4C22×D1712yes—
476C4×D4—28no—
477C4×D4—178no—
478C4×D4—1716no—
479C4×D4—178no—
480C4×D4—1716no—
481C4×D4—178no—
482C4×D4—348no—
483C4×D4C4×D1718yes—
484#117—348no—
485#117—688no—
486C2×C4⋊C4—171no—
487C2×C4⋊C4—172no—
488C2×C4⋊C4—178no—
489C2×C4⋊C4—172no—
490C2×C4⋊C4—172no—
491C2×C4⋊C4—174no—
492C2×C4⋊C4C22×D1712yes—
493C2×C4⋊C4C22×D1712yes—
494C2×C4⋊C4C22×D1714yes—
495C2×C4⋊C4C22×D1711yescharacteristic
496C2×C22⋊C4—172no—
497C2×C22⋊C4—172no—
498C2×C22⋊C4—172no—
499C2×C22⋊C4—172no—
500C2×C22⋊C4—1716no—
501C2×C22⋊C4—174no—
502C2×C22⋊C4—174no—
503C2×C22⋊C4—174no—
504C2×C22⋊C4—174no—
505C2×C22⋊C4—172no—
506C2×C22⋊C4—174no—
507C2×C22⋊C4—174no—
508C2×C22⋊C4—3416no—
509C2×C22⋊C4C22×D1714yes—
510C2×C22⋊C4C22×D1712yes—
511C2×C42—171no—
512C2×C42—171no—
513C2×C42—171no—
514C2×C42—178no—
515C2×C42—172no—
516C2×C42—172no—
517C2×C42—172no—
518C2×C42—174no—
519C2×C42—172no—
520C2×C42—172no—
521C2×C42—174no—
522C2×C42—174no—
523C2×C42—688no—
524C2×C42C22×D1712yes—
525C2×C42C22×D1711yescharacteristic
526#95—171no—
527#95—172no—
528#95—174no—
529#95—171no—
530#95—172no—
531#95—172no—
532#95—174no—
533#95—172no—
534#95—174no—
535#95—174no—
536#95—174no—
537#95C22×D1711yescharacteristic
538#95C22×D1712yes—
539#95C22×D1714yes—
540#95C22×D1711yescharacteristic
541#95C22×D1712yes—
542C17#3412611yescharacteristic, complemented, Sylow
543C24—171no—
544C24—172no—
545C24—178no—
546C24—348no—
547C24—344no—
548C24—344no—
549C24—684no—
550C24C23×D1712yes—
551C2×D4—178no—
552C2×D4—174no—
553C2×D4—344no—
554C2×D4—344no—
555C2×D4—3432no—
556C2×D4—342no—
557C2×D4—342no—
558C2×D4C2×C4×D1714yes—
559C2×D4#6325414yes—
560C2×D4#6325614yes—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—171no—
566C22×C4—178no—
567C22×C4—171no—
568C22×C4—171no—
569C22×C4—172no—
570C22×C4—172no—
571C22×C4—174no—
572C22×C4—174no—
573C22×C4—174no—
574C22×C4—178no—
575C22×C4—178no—
576C22×C4—178no—
577C22×C4—174no—
578C22×C4—172no—
579C22×C4—348no—
580C22×C4—344no—
581C22×C4—344no—
582C22×C4—348no—
583C22×C4—348no—
584C22×C4—342no—
585C22×C4—342no—
586C22×C4—348no—
587C22×C4—684no—
588C22×C4—684no—
589C22×C4—6832no—
590C22×C4—684no—
591C22×C4C2×C4×D1718yes—
592C22×C4C23×D1714yes—
593C22×C4C23×D1712yes—
594C22×C4C23×D1711yescharacteristic
595C22×C4C23×D1711yescharacteristic
596C22×C4C23×D1712yes—
597C22×C4C23×D1712yes—
598C22×C4C23×D1711yescharacteristic
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—44no—
602C4⋊C4—178no—
603C4⋊C4—174no—
604C4⋊C4—344no—
605C4⋊C4—344no—
606C4⋊C4—684no—
607C4⋊C4C2×C4×D1714yes—
608C22⋊C4—28no—
609C22⋊C4—178no—
610C22⋊C4—178no—
611C22⋊C4—178no—
612C22⋊C4—178no—
613C22⋊C4—348no—
614C22⋊C4—348no—
615C22⋊C4—344no—
616C22⋊C4—348no—
617C22⋊C4—348no—
618C22⋊C4—684no—
619C22⋊C4—684no—
620C22⋊C4C2×C4×D1718yes—
621C42—24no—
622C42—174no—
623C42—174no—
624C42—174no—
625C42—344no—
626C42—348no—
627C42—344no—
628C42—344no—
629C42—344no—
630C42—344no—
631C42—684no—
632C42—684no—
633C42C2×C4×D1714yes—
634C23—24no—
635C23—24no—
636C23—172no—
637C23—174no—
638C23—174no—
639C23—3416no—
640C23—341no—
641C23—341no—
642C23—342no—
643C23—3416no—
644C23—344no—
645C23—342no—
646C23—342no—
647C23—344no—
648C23—688no—
649C23—6816no—
650C23—6816no—
651C23C22×C4×D1714yes—
652C23C2×#6325414yes—
653C23C2×#6325614yes—
654C23C24×D1711yescharacteristic
655D4—3416no—
656D4—348no—
657D4#10587578116yescomplemented
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—48no—
670C2×C4—416no—
671C2×C4—172no—
672C2×C4—174no—
673C2×C4—172no—
674C2×C4—172no—
675C2×C4—174no—
676C2×C4—174no—
677C2×C4—348no—
678C2×C4—3416no—
679C2×C4—348no—
680C2×C4—3416no—
681C2×C4—342no—
682C2×C4—341no—
683C2×C4—342no—
684C2×C4—341no—
685C2×C4—342no—
686C2×C4—344no—
687C2×C4—348no—
688C2×C4—342no—
689C2×C4—344no—
690C2×C4—342no—
691C2×C4—344no—
692C2×C4—344no—
693C2×C4—342no—
694C2×C4—688no—
695C2×C4—688no—
696C2×C4—6816no—
697C2×C4C22×C4×D1712yes—
698C2×C4C22×C4×D1712yes—
699C2×C4C22×C4×D1714yes—
700C2×C4C22×C4×D1712yes—
701C2×C4C2×#6325412yes—
702C2×C4C2×#6325612yes—
703C2×C4#41×D1714yes—
704C22—28no—
705C22—28no—
706C22—24no—
707C22—24no—
708C22—174no—
709C22—344no—
710C22—344no—
711C22—342no—
712C22—342no—
713C22—344no—
714C22—344no—
715C22—344no—
716C22—6832no—
717C22—684no—
718C22—684no—
719C22C2×#1058757818yes—
720C22C23×C4×D1711yescharacteristic
721C22C2×#41×D1712yes—
722C22C22×#6325411yescharacteristic
723C22C22×#6325611yescharacteristic
724C22H(5,𝔽2)×D1712yes—
725C4—24no—
726C4—22no—
727C4—22no—
728C4—24no—
729C4—44no—
730C4—42no—
731C4—174no—
732C4—344no—
733C4—342no—
734C4—342no—
735C4—344no—
736C4—684no—
737C4—682no—
738C4C2×#1058757814yes—
739C2—28no—
740C2—344no—
741C2—684no—
742C2C22×#1058757811yescharacteristic
743C2C4×#41×D1711yescharacteristic
744C2D17×#51811yescharacteristic
745C2#1454238912yes—
746C2#1454239512yes—
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2349C2
socle, cosocleC23×C17C25
prime radicalC22×D4×D17C22
hypercenter#2349D17
hypocenterC17#34126
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2349

Complements

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

NH ≅ G/Ntype
2. #14531759C2semidirect
3. #14531755C2semidirect
4. #14531726C2semidirect
5. #14531720C2semidirect
6. #14531694C2semidirect
7. #14531660C2semidirect
8. #14531631C2semidirect
10. #14531242C2semidirect
11. #14531220C2semidirect
12. #14531177C2semidirect
13. #14531166C2semidirect
14. C4×D4×Dic17C2semidirect
15. C4×#10587578C2semidirect
16. C2×#11762656C2semidirect
17. C17×#2349C2semidirect
26. C4×D4×D17C4semidirect
28. C2×#10587578C22semidirect
32. C22×C4×Dic17C22semidirect
36. #11762708C22semidirect
37. #11762701C22semidirect
38. #11762701C22semidirect
39. #11762699C22semidirect
40. #11762699C22semidirect
41. #11762696C22semidirect
42. #11762690C22semidirect
45. #11762684C22semidirect
46. #11762676C22semidirect
47. #11762675C22semidirect
49. #11762671C22semidirect
50. #11762671C22semidirect
51. #11762669C22semidirect
55. C4⋊C4×Dic17C22semidirect
56. C4⋊C4×Dic17C22semidirect
57. C4⋊C4×Dic17C22semidirect
58. C4×C4⋊Dic17C22semidirect
59. C4×C4⋊Dic17C22semidirect
60. C22⋊C4×Dic17C22semidirect
61. C22⋊C4×Dic17C22semidirect
63. C4×C22⋊Dic17C22semidirect
68. #11762656C22semidirect
69. #11762656C22semidirect
70. #11762656C22semidirect
71. #11762654C22semidirect
72. #11762654C22semidirect
73. #11762654C22semidirect
74. C2×#10587502C22semidirect
75. C42×Dic17C22semidirect
78. C17×#389C22semidirect
79. C17×#385C22semidirect
80. C17×#382C22semidirect
81. C17×#380C22semidirect
82. C4×C4⋊C4×C17C22semidirect
83. C2×C17×#95C22semidirect
96. C22×C4×D17C2×C4semidirect
117. C4×C22⋊D17C2×C4semidirect
145. #10587579C2×C4semidirect
148. C4⋊C4×D17C2×C4semidirect
149. #10587567C2×C4semidirect
150. C22⋊C4×D17C2×C4semidirect
151. C4×D68C2×C4semidirect
152. C42×D17C2×C4semidirect
282. D4×C17#117semidirect
337. #2349D17semidirect
404. #389C2×D17semidirect
414. #385C2×D17semidirect
417. #382C2×D17semidirect
424. #380C2×D17semidirect
431. C4×C4⋊C4C2×D17semidirect
447. C2×#95C2×D17semidirect
542. C17#34126semidirect
657. D4#10587578semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D172
#145317592
#145317552
#145317262
#145317202
#145316942
#145316602
#145316312
D4×#632272
#145312422
#145312202
#145311772
#145311662
C4×D4×Dic172
C4×#105875782
C2×#117626562
C17×#23492
#3412617