Finite Group Databasebeta

← #17045599

Subgroups — #17045599

Order 4352.

1080 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762959C211yesmaximal, characteristic
2#14531364C211yesmaximal, characteristic
3#14529668C211yesmaximal, characteristic, complemented
4#14529641C211yesmaximal, characteristic, complemented
5#14529480C211yesmaximal, characteristic, complemented
6#14529466C211yesmaximal, characteristic, complemented
7#14529411C211yesmaximal, characteristic, complemented
8#14529404C211yesmaximal, characteristic, complemented
9#14529139C211yesmaximal, characteristic, complemented
10#14529139C211yesmaximal, characteristic, complemented
11#14529097C211yesmaximal, characteristic, complemented
12#14528981C211yesmaximal, characteristic, complemented
13#14528714C211yesmaximal, characteristic
14#14528550C211yesmaximal, characteristic, complemented
15C17×#2323C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C22×#63230C2211yescharacteristic
18C22×#63230C2211yescharacteristic
19C2×#10587612C2211yescharacteristic
20#11762959C418yescomplemented
21C2×#10587478C2211yescharacteristic, complemented
22C2×#10587479C2211yescharacteristic, complemented
23C2×#10587506C2211yescharacteristic, complemented
24C2×#10587506C2211yescharacteristic, complemented
25C2×#10587480C2211yescharacteristic
26C2×#10587480C2211yescharacteristic
27C2×#10587480C2211yescharacteristic
28C2×#10587480C2211yescharacteristic
29C2×#10587480C2211yescharacteristic
30C2×#10587480C2211yescharacteristic
31C2×C22⋊#3622C2211yescharacteristic
32C2×C22⋊#3622C2211yescharacteristic
33C2×#10587474C2211yescharacteristic, complemented
34C2×C4×#3622C2211yescharacteristic, complemented
35#11762711C2211yescharacteristic
36#11762711C2211yescharacteristic
37#11762711C2211yescharacteristic
38#11762711C2211yescharacteristic
39#11762710—21no—
40#11762710—21no—
41#11762664—21no—
42#11762664—21no—
43#11762571C2211yescharacteristic, complemented
44#11762571C2211yescharacteristic, complemented
45#11762571C2211yescharacteristic, complemented
46#11762571C2211yescharacteristic, complemented
47#11762564C2211yescharacteristic, complemented
48#11762564C2211yescharacteristic, complemented
49C2×C17×C22⋊Q8C2211yescharacteristic
50C2×C4×Q8×C17C2211yescharacteristic, complemented
51C2×C17×#117C2211yescharacteristic
52C17×#391C2211yescharacteristic, complemented
53C17×#389—21no—
54C17×#389C2211yescharacteristic, complemented
55C17×#388—21no—
56C17×#388—21no—
57C17×#387—21no—
58C17×#380C2211yescharacteristic
59C4×C4⋊C4×C17C2211yescharacteristic, complemented
60C24×D17—21no—
61C22×Q8×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C22×D68—21no—
64C22×D68—22no—
65C22×D68—41no—
66C22×D68—41no—
67C22×D68—41no—
68C22×D68—41no—
69C22×D68C2×C414yes—
70C22×D68C2311yescharacteristic
71C22×D68C2311yescharacteristic
72C17×C22⋊Q8—22no—
73C17×C22⋊Q8C2×C414yes—
74C4×Q8×C17—41no—
75C4×Q8×C17—41no—
76C17×#117—41no—
77C17×#117—41no—
78C2×C4⋊C4×C17—21no—
79C2×C4⋊C4×C17—21no—
80C2×C4⋊C4×C17—21no—
81C2×C4⋊C4×C17D411yescharacteristic
82C2×C4⋊C4×C17D411yescharacteristic
83C2×C4⋊C4×C17C2311yescharacteristic
84C2×C4⋊C4×C17C2311yescharacteristic
85C2×C4⋊C4×C17C2311yescharacteristic
86C2×C22⋊C4×C17—21no—
87C2×C22⋊C4×C17—21no—
88C2×C22⋊C4×C17D411yescharacteristic
89C2×C22⋊C4×C17D411yescharacteristic
90C2×C42×C17—21no—
91C2×C42×C17—21no—
92C2×C42×C17C2311yescharacteristic
93C2×C42×C17C2311yescharacteristic
94C2×C22⋊Dic17—21no—
95C2×#63230—41no—
96C2×#63230—41no—
97C2×#63230—41no—
98C2×#63230—41no—
99C2×#63230C2×C414yes—
100C2×#63230C2×C414yes—
101C2×#63227—21no—
102C2×#63227—21no—
103C2×#63227—21no—
104C2×#63227—21no—
105C2×#63227—21no—
106C2×#63227—21no—
107C2×#63227—21no—
108C2×#63227—21no—
109#10587612—41no—
110#10587612—41no—
111C2×C4⋊Dic17C2311yescharacteristic
112C2×C4⋊Dic17C2311yescharacteristic
113C2×C4×Dic17—21no—
114C22×#3622C2311yescharacteristic
115C22×#3622C2311yescharacteristic
116C22×#3622C2311yescharacteristic
117C22×#3622C2311yescharacteristic
118C17×#95—21no—
119C17×#95—21no—
120C17×#95—21no—
121C17×#95—21no—
122C17×#95—21no—
123#10587506—41no—
124#10587506—41no—
125C22⋊#3622—22no—
126C22⋊#3622C2×C414yes—
127#10587480—41no—
128#10587480—41no—
129#10587480—41no—
130#10587480—41no—
131#10587480C2×C414yes—
132#10587480C2×C414yes—
133#10587479—41no—
134#10587478—41no—
135#10587474—41no—
136C4×#3622—41no—
137C24×C17C2×D411yescharacteristic
138C23×D17—21no—
139C23×D17—21no—
140C23×D17—24no—
141C23×D17—42no—
142C23×D17—42no—
143C23×D17—81no—
144C23×D17—81no—
145C23×D17—81no—
146C23×D17—81no—
147C2×Q8×C17—21no—
148C2×Q8×C17—21no—
149C2×Q8×C17—21no—
150C2×Q8×C17—21no—
151C2×Q8×C17—21no—
152C2×Q8×C17C22×C412yes—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17C22×C412yes—
162C22×C4×C17C2×D411yescharacteristic
163C22×C4×C17C2×D411yescharacteristic
164C22×C4×C17C2×D411yescharacteristic
165C22×C4×C17C2×D411yescharacteristic
166C22×C4×C17C2×D411yescharacteristic
167C22×C4×C17#4112yes—
168C22×C4×C17C2411yescharacteristic
169C22×Dic17—21no—
170C22×Dic17—21no—
171C2×D68—21no—
172C2×D68—21no—
173C2×D68—21no—
174C2×D68—21no—
175C2×D68—21no—
176C2×D68—21no—
177C2×D68—21no—
178C2×D68—21no—
179C2×D68—24no—
180C2×D68—21no—
181C2×D68—21no—
182C2×D68—44no—
183C2×D68—44no—
184C2×D68—42no—
185C2×D68—42no—
186C2×D68—44no—
187C2×D68—44no—
188C2×D68C22×C412yes—
189C2×D68C22×C412yes—
190C4⋊C4×C17—24no—
191C4⋊C4×C17—21no—
192C4⋊C4×C17—21no—
193C4⋊C4×C17—21no—
194C4⋊C4×C17—21no—
195C4⋊C4×C17—21no—
196C4⋊C4×C17—41no—
197C4⋊C4×C17—41no—
198C4⋊C4×C17—42no—
199C4⋊C4×C17—81no—
200C4⋊C4×C17C22×C412yes—
201C22⋊C4×C17—24no—
202C22⋊C4×C17—41no—
203C22⋊C4×C17—41no—
204C22⋊C4×C17—81no—
205C42×C17—21no—
206C42×C17—21no—
207C42×C17—21no—
208C42×C17—21no—
209C42×C17—42no—
210C42×C17—81no—
211C22⋊Dic17—42no—
212#63230—44no—
213#63230—44no—
214#63227—81no—
215#63227—81no—
216#63227—81no—
217#63227—81no—
218#63227—81no—
219#63227—81no—
220#63227—81no—
221#63227—81no—
222C4⋊Dic17—21no—
223C4⋊Dic17—21no—
224C4⋊Dic17—21no—
225C4⋊Dic17—21no—
226C4×Dic17—42no—
227C2×#3622—21no—
228C2×#3622—21no—
229C2×#3622—21no—
230C2×#3622—21no—
231C2×#3622—21no—
232C2×#3622—21no—
233C2×#3622—21no—
234C2×#3622—21no—
235C2×#3622—21no—
236C2×#3622—21no—
237C2×#3622C22×C412yes—
238C2×#3622C22×C412yes—
239#22052—171nomaximal, Sylow
240C23×C17—21no—
241C23×C17—21no—
242C23×C17—21no—
243C23×C17—21no—
244C23×C17—21no—
245C23×C17—21no—
246C23×C17C4×D412yes—
247C23×C17C22×D411yescharacteristic
248C22×D17—22no—
249C22×D17—22no—
250C22×D17—48no—
251C22×D17—41no—
252C22×D17—41no—
253C22×D17—41no—
254C22×D17—41no—
255C22×D17—41no—
256C22×D17—41no—
257C22×D17—41no—
258C22×D17—41no—
259C22×D17—41no—
260C22×D17—41no—
261C22×D17—41no—
262C22×D17—41no—
263C22×D17—84no—
264C22×D17—84no—
265C22×D17—84no—
266C22×D17—84no—
267C22×D17—84no—
268C22×D17—84no—
269Q8×C17—22no—
270Q8×C17—22no—
271Q8×C17—41no—
272Q8×C17—41no—
273C2×C4×C17—21no—
274C2×C4×C17—21no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—21no—
282C2×C4×C17—21no—
283C2×C4×C17—21no—
284C2×C4×C17—21no—
285C2×C4×C17—21no—
286C2×C4×C17—21no—
287C2×C4×C17—21no—
288C2×C4×C17—21no—
289C2×C4×C17—21no—
290C2×C4×C17—21no—
291C2×C4×C17—21no—
292C2×C4×C17—21no—
293C2×C4×C17—41no—
294C2×C4×C17—41no—
295C2×C4×C17—41no—
296C2×C4×C17—41no—
297C2×C4×C17—41no—
298C2×C4×C17—41no—
299C2×C4×C17—41no—
300C2×C4×C17—41no—
301C2×C4×C17—41no—
302C2×C4×C17—41no—
303C2×C4×C17C4×D412yes—
304C2×C4×C17C23×C411yescharacteristic
305C2×C4×C17C2×#4111yescharacteristic
306C2×C4×C17H(5,𝔽2)11yescharacteristic
307C2×C4×C17H(5,𝔽2)11yescharacteristic
308C2×C4×C17H(5,𝔽2)11yescharacteristic
309C2×C4×C17H(5,𝔽2)11yescharacteristic
310C2×Dic17—41no—
311C2×Dic17—41no—
312C2×Dic17—41no—
313C2×Dic17—41no—
314C2×Dic17—41no—
315C2×Dic17—41no—
316D68—22no—
317D68—22no—
318D68—22no—
319D68—22no—
320D68—48no—
321D68—41no—
322D68—41no—
323D68—41no—
324D68—41no—
325#3622—22no—
326#3622—22no—
327#3622—41no—
328#3622—41no—
329C2×#450—171no—
330#2323D1711yescharacteristic, complemented
331#2309—171no—
332#1973—171no—
333#1968—171no—
334#1936—171no—
335#1934—171no—
336#1926—171no—
337#1925—171no—
338#1880—171no—
339#1880—171no—
340#1873—171no—
341#1854—171no—
342#1786—171no—
343#1750—171no—
344C22×C17—22no—
345C22×C17—22no—
346C22×C17—22no—
347C22×C17—41no—
348C22×C17—41no—
349C22×C17—41no—
350C22×C17—41no—
351C22×C17C2×C4×D411yescharacteristic
352C22×C17#53411yescharacteristic
353C22×C17#53511yescharacteristic
354C22×C17#57611yescharacteristic
355C22×C17#57711yescharacteristic
356C22×C17#57711yescharacteristic
357C22×C17#57711yescharacteristic
358C2×D17—42no—
359C2×D17—42no—
360C2×D17—42no—
361C2×D17—42no—
362C2×D17—42no—
363C2×D17—42no—
364C2×D17—816no—
365C2×D17—81no—
366C2×D17—81no—
367C2×D17—81no—
368C2×D17—81no—
369C2×D17—81no—
370C2×D17—81no—
371C2×D17—81no—
372C2×D17—81no—
373C4×C17—22no—
374C4×C17—42no—
375C4×C17—41no—
376C4×C17—41no—
377C4×C17—41no—
378C4×C17—41no—
379C4×C17—42no—
380C4×C17—81no—
381C4×C17—81no—
382C4×C17#51811yescharacteristic
383C4×C17#51811yescharacteristic
384C4×C17#53811yescharacteristic
385C4×C17#53811yescharacteristic
386Dic17—81no—
387Dic17—81no—
388C23×D4—171no—
389C22×SD16—171no—
390C22×SD16—171no—
391C2×C22⋊Q8C2×D1711yescharacteristic
392C2×C4×Q8C2×D1711yescharacteristic, complemented
393C2×#117—171no—
394C2×#117C2×D1711yescharacteristic
395#450—178no—
396C2×#107—171no—
397C2×#106—171no—
398C2×#103—171no—
399C2×#103—171no—
400C2×#102—171no—
401C2×#102—171no—
402C2×#102—171no—
403C2×#102—171no—
404C2×#102—171no—
405C2×#102—171no—
406C2×C22⋊C8—171no—
407C2×C22⋊C8—171no—
408C2×#97—171no—
409C2×C4×C8—171no—
410#391C2×D1711yescharacteristic, complemented
411#390—171no—
412#390—171no—
413#390—171no—
414#390—171no—
415#390—341no—
416#390—341no—
417#389—21no—
418#389C2×D1711yescharacteristic, complemented
419#388—21no—
420#388—21no—
421#387—21no—
422#380C2×D1711yescharacteristic
423#379—341no—
424#379—341no—
425C4×C4⋊C4C2×D1711yescharacteristic, complemented
426#340—171no—
427#340—171no—
428#340—171no—
429#340—171no—
430#336—171no—
431#336—171no—
432C2×C17—42no—
433C2×C17#232111yescharacteristic
434C2×C17#294611yescharacteristic
435C2×C17#294911yescharacteristic
436C2×C17#319811yescharacteristic
437C2×C17#320011yescharacteristic
438C2×C17#322211yescharacteristic
439C2×C17#322411yescharacteristic
440D17—82no—
441D17—82no—
442C25—341no—
443C22×Q8C22×D1711yescharacteristic
444C22×D4—174no—
445C22×D4—171no—
446C22×D4—171no—
447C22×D4—342no—
448C22×D4—341no—
449C22×D4—681no—
450C22×D4—681no—
451C22×D4—681no—
452C22×D4—681no—
453C23×C4C22×D1711yescharacteristic
454C2×SD16—174no—
455C2×SD16—174no—
456C2×SD16—681no—
457C2×SD16—681no—
458C2×SD16—681no—
459C2×SD16—681no—
460C22×C8—171no—
461C22×C8—171no—
462C22×C8—171no—
463C22×C8—171no—
464C22⋊Q8—22no—
465C22⋊Q8C4×D1714yes—
466C4×Q8—41no—
467C4×Q8—41no—
468#117—41no—
469#117—41no—
470#117—681no—
471#117—681no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—171no—
476C2×C4⋊C4—171no—
477C2×C4⋊C4C22⋊D1711yescharacteristic
478C2×C4⋊C4C22⋊D1711yescharacteristic
479C2×C4⋊C4C22×D1711yescharacteristic
480C2×C4⋊C4C22×D1711yescharacteristic
481C2×C4⋊C4C22×D1711yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—341no—
485C2×C22⋊C4—341no—
486C2×C22⋊C4—341no—
487C2×C22⋊C4—341no—
488C2×C22⋊C4—341no—
489C2×C22⋊C4—341no—
490C2×C22⋊C4—341no—
491C2×C22⋊C4—341no—
492C2×C22⋊C4—341no—
493C2×C22⋊C4C22⋊D1711yescharacteristic
494C2×C22⋊C4C22⋊D1711yescharacteristic
495C2×C42—21no—
496C2×C42—21no—
497C2×C42—341no—
498C2×C42C22×D1711yescharacteristic
499C2×C42C22×D1711yescharacteristic
500#107—681no—
501#106—681no—
502#103—681no—
503#103—681no—
504#102—174no—
505#102—174no—
506#102—681no—
507#102—681no—
508#102—681no—
509#102—681no—
510C22⋊C8—174no—
511C22⋊C8—342no—
512#97—681no—
513C4×C8—681no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519C17#2205211yescharacteristic, complemented, Sylow
520C24—341no—
521C24—341no—
522C24—344no—
523C24—682no—
524C24—682no—
525C24—1361no—
526C24—1361no—
527C24—1361no—
528C24—1361no—
529C24C2×C22⋊D1711yescharacteristic
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8C2×C4×D1712yes—
536C2×D4—172no—
537C2×D4—172no—
538C2×D4—341no—
539C2×D4—341no—
540C2×D4—341no—
541C2×D4—341no—
542C2×D4—341no—
543C2×D4—341no—
544C2×D4—341no—
545C2×D4—341no—
546C2×D4—341no—
547C2×D4—341no—
548C2×D4—344no—
549C2×D4—684no—
550C2×D4—684no—
551C2×D4—682no—
552C2×D4—682no—
553C2×D4—684no—
554C2×D4—684no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—341no—
564C22×C4—341no—
565C22×C4C2×C4×D1712yes—
566C22×C4#6325212yes—
567C22×C4C2×C22⋊D1711yescharacteristic
568C22×C4C2×C22⋊D1711yescharacteristic
569C22×C4C2×C22⋊D1711yescharacteristic
570C22×C4C2×C22⋊D1711yescharacteristic
571C22×C4C2×C22⋊D1711yescharacteristic
572C22×C4C23×D1711yescharacteristic
573SD16—684no—
574SD16—684no—
575C2×C8—172no—
576C2×C8—172no—
577C2×C8—341no—
578C2×C8—341no—
579C2×C8—341no—
580C2×C8—341no—
581C2×C8—341no—
582C2×C8—341no—
583C2×C8—341no—
584C2×C8—341no—
585C2×C8—341no—
586C2×C8—341no—
587C4⋊C4—21no—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—42no—
596C4⋊C4—81no—
597C4⋊C4—341no—
598C4⋊C4—341no—
599C4⋊C4—341no—
600C4⋊C4—341no—
601C4⋊C4C2×C4×D1712yes—
602C22⋊C4—24no—
603C22⋊C4—41no—
604C22⋊C4—41no—
605C22⋊C4—81no—
606C22⋊C4—682no—
607C22⋊C4—1361no—
608C22⋊C4—1361no—
609C22⋊C4—1361no—
610C22⋊C4—1361no—
611C22⋊C4—1361no—
612C22⋊C4—1361no—
613C22⋊C4—1361no—
614C22⋊C4—1361no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—42no—
620C42—81no—
621C42—682no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—342no—
629C23—342no—
630C23—688no—
631C23—681no—
632C23—681no—
633C23—681no—
634C23—681no—
635C23—681no—
636C23—681no—
637C23—681no—
638C23—681no—
639C23—681no—
640C23—681no—
641C23—681no—
642C23—681no—
643C23—1364no—
644C23—1364no—
645C23—1364no—
646C23—1364no—
647C23—1364no—
648C23—1364no—
649C23C4×C22⋊D1712yes—
650C23C22×C22⋊D1711yescharacteristic
651Q8—22no—
652Q8—22no—
653Q8—41no—
654Q8—41no—
655D4—342no—
656D4—342no—
657D4—342no—
658D4—342no—
659D4—688no—
660D4—681no—
661D4—681no—
662D4—681no—
663D4—681no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—681no—
695C2×C4—681no—
696C2×C4—681no—
697C2×C4—681no—
698C2×C4—681no—
699C2×C4—681no—
700C2×C4C4×C22⋊D1712yes—
701C2×C4C22×C4×D1711yescharacteristic
702C2×C4C2×#6325211yescharacteristic
703C2×C4#1058769111yescharacteristic
704C2×C4#1058769111yescharacteristic
705C2×C4#1058769611yescharacteristic
706C2×C4#1058769611yescharacteristic
707C8—342no—
708C8—342no—
709C8—681no—
710C8—681no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—682no—
719C22—682no—
720C22—682no—
721C22—682no—
722C22—682no—
723C22—682no—
724C22—13616no—
725C22—1361no—
726C22—1361no—
727C22—1361no—
728C22—1361no—
729C22—1361no—
730C22—1361no—
731C22—1361no—
732C22—1361no—
733C22C2×C4×C22⋊D1711yescharacteristic
734C22#1176336811yescharacteristic
735C22#1176337311yescharacteristic
736C22#1176361211yescharacteristic
737C22#1176361711yescharacteristic
738C22#1176361711yescharacteristic
739C22#1176361711yescharacteristic
740C4—22no—
741C4—42no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—42no—
747C4—81no—
748C4—81no—
749C4—1361no—
750C4—1361no—
751C4#1176328111yescharacteristic
752C4#1176328111yescharacteristic
753C4#1176339211yescharacteristic
754C4#1176339211yescharacteristic
755C2—42no—
756C2—1362no—
757C2—1362no—
758C2#1453143811yescharacteristic
759C2#1453761211yescharacteristic
760C2#1453764311yescharacteristic
761C2#1453963011yescharacteristic
762C2#1453965111yescharacteristic
763C2#1453985011yescharacteristic
764C2#1453987211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2323C2
socleC23×C17C22×D4
prime radicalC23×D68C22
cosocleC22×C4×C17C24
hypercenter#2323D17
hypocenterC17#22052
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
3. #14529668C2semidirect
4. #14529641C2semidirect
5. #14529480C2semidirect
6. #14529466C2semidirect
7. #14529411C2semidirect
8. #14529404C2semidirect
9. #14529139C2semidirect
10. #14529139C2semidirect
11. #14529097C2semidirect
12. #14528981C2semidirect
14. #14528550C2semidirect
15. C17×#2323C2semidirect
20. #11762959C4semidirect
21. C2×#10587478C22semidirect
22. C2×#10587479C22semidirect
23. C2×#10587506C22semidirect
24. C2×#10587506C22semidirect
33. C2×#10587474C22semidirect
34. C2×C4×#3622C22semidirect
43. #11762571C22semidirect
44. #11762571C22semidirect
45. #11762571C22semidirect
46. #11762571C22semidirect
47. #11762564C22semidirect
48. #11762564C22semidirect
50. C2×C4×Q8×C17C22semidirect
52. C17×#391C22semidirect
54. C17×#389C22semidirect
59. C4×C4⋊C4×C17C22semidirect
330. #2323D17semidirect
392. C2×C4×Q8C2×D17semidirect
410. #391C2×D17semidirect
418. #389C2×D17semidirect
425. C4×C4⋊C4C2×D17semidirect
519. C17#22052semidirect

Maximal subgroups

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

subgroupindex
C2×#117629592
#145313642
#145296682
#145296412
#145294802
#145294662
#145294112
#145294042
#145291392
#145290972
#145289812
#145287142
#145285502
C17×#23232
#2205217