Finite Group Databasebeta

← #17054596

Subgroups — #17054596

Order 4352.

1170 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×#11762948C211yesmaximal, characteristic
2C2×#11762912C211yesmaximal, characteristic, complemented
3#14531800C211yesmaximal, characteristic
4Q8×C22⋊Dic17C211yesmaximal, characteristic, complemented
5#14529662C211yesmaximal, characteristic, complemented
6#14529471C211yesmaximal, characteristic, complemented
7#14529428C211yesmaximal, characteristic, complemented
8#14529212C211yesmaximal, characteristic
9#14529137C211yesmaximal, characteristic, complemented
10#14529115C211yesmaximal, characteristic, complemented
11#14529036C211yesmaximal, characteristic, complemented
12#14528972C211yesmaximal, characteristic, complemented
13#14528616C211yesmaximal, characteristic, complemented
14#14528560C211yesmaximal, characteristic, complemented
15C22×C17×#103C211yesmaximal, characteristic, complemented
16C22×#63230C2211yescharacteristic
17C22×#63230C2211yescharacteristic
18C2×#10587616C2211yescharacteristic
19C2×Q8×Dic17C2211yescharacteristic
20C2×Q8×Dic17C2211yescharacteristic
21C2×#10587579C2211yescharacteristic
22C2×C4×C22⋊D17—21no—
23#11762948C418yescomplemented
24#11762912—24no—
25C2×#10587478C2211yescharacteristic
26C2×#10587478C2211yescharacteristic
27C2×#10587506C2211yescharacteristic
28C2×#10587506C2211yescharacteristic
29C2×#10587492C2211yescharacteristic
30C2×#10587492C2211yescharacteristic
31C2×C22⋊#3622C2211yescharacteristic
32C2×#10587486C2211yescharacteristic
33C2×#10587486C2211yescharacteristic
34#11762716—21no—
35#11762716—21no—
36#11762716C2211yescharacteristic
37#11762716C2211yescharacteristic
38#11762710C2211yescharacteristic
39#11762705C2211yescharacteristic
40#11762699—21no—
41#11762688—21no—
42#11762680—21no—
43#11762669—21no—
44#11762669C2211yescharacteristic
45C4⋊C4×Dic17C2211yescharacteristic
46C4×C22⋊Dic17—21no—
47C4×C22⋊Dic17C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762571C2211yescharacteristic
52#11762563C2211yescharacteristic
53#11762563C2211yescharacteristic
54C23×Q8×C17C2211yescharacteristic
55C23×C8×C17C2211yescharacteristic
56C22×C4⋊C4×C17C2211yescharacteristic
57C2×C17×#103—24no—
58C2×C17×#103C2211yescharacteristic
59C2×C17×#103C2211yescharacteristic
60C2×C17×#103C2211yescharacteristic
61C2×C17×#103C2211yescharacteristic
62C22×Q8×C17—21no—
63C22×Q8×C17—22no—
64C22×Q8×C17—22no—
65C22×Q8×C17—22no—
66C22×Q8×C17—41no—
67C22×Q8×C17—41no—
68C22×Q8×C17C2×C414yescomplemented
69C22×Q8×C17C2311yescharacteristic
70C22×Q8×C17C2311yescharacteristic
71C23×C4×C17—21no—
72C23×C4×C17—21no—
73C23×C4×C17C2311yescharacteristic
74C22×C22⋊D17—21no—
75C22×D68C2311yescharacteristic
76C22×C4×D17—21no—
77C22×C8×C17—22no—
78C22×C8×C17—22no—
79C22×C8×C17—41no—
80C22×C8×C17C2311yescharacteristic
81C22×C8×C17C2311yescharacteristic
82C2×C4⋊C4×C17—22no—
83C2×C4⋊C4×C17—21no—
84C2×C4⋊C4×C17—41no—
85C2×C4⋊C4×C17C2311yescharacteristic
86C2×C4⋊C4×C17C2311yescharacteristic
87C2×C22⋊Dic17—21no—
88C2×C22⋊Dic17D411yescharacteristic
89C2×C22⋊Dic17D411yescharacteristic
90Q8×Dic17—22no—
91Q8×Dic17—22no—
92Q8×Dic17—41no—
93Q8×Dic17—41no—
94C2×#63230—22no—
95C2×#63230—22no—
96C2×#63230—41no—
97C2×#63230—41no—
98C2×#63230C2×C414yescomplemented
99C2×#63230C2×C414yescomplemented
100#10587616—22no—
101#10587616C2×C414yes—
102C4×C22⋊D17—44no—
103C2×#63227—21no—
104C2×#63227—21no—
105C2×#63227—21no—
106C2×#63227—21no—
107C2×C4⋊Dic17—21no—
108C2×C4⋊Dic17—21no—
109C2×C4⋊Dic17C2311yescharacteristic
110C2×C4⋊Dic17C2311yescharacteristic
111C2×C4⋊Dic17C2311yescharacteristic
112C2×#63225—21no—
113C2×C4×Dic17—21no—
114C2×C4×Dic17—21no—
115C2×C4×Dic17—21no—
116C2×C4×Dic17C2311yescharacteristic
117C2×C4×Dic17C2311yescharacteristic
118C22×#3622C2311yescharacteristic
119C22×#3622C2311yescharacteristic
120#10587579—22no—
121#10587579—41no—
122C17×#103—22no—
123C17×#103—22no—
124C17×#103—22no—
125C17×#103D414yescomplemented
126#10587506C2×C414yescomplemented
127#10587506C2×C414yescomplemented
128#10587502—21no—
129#10587502—21no—
130#10587502—21no—
131#10587502—21no—
132#10587502—21no—
133#10587502—21no—
134#10587502—21no—
135#10587502D411yescharacteristic
136#10587502D411yescharacteristic
137C22⋊#3622C2×C414yescomplemented
138#10587492—22no—
139#10587492—41no—
140#10587486—22no—
141#10587486—41no—
142#10587478—22no—
143#10587478—41no—
144C24×C17C2×D411yescharacteristic
145C23×D17—21no—
146C2×Q8×C17—24no—
147C2×Q8×C17—21no—
148C2×Q8×C17—21no—
149C2×Q8×C17—21no—
150C2×Q8×C17—21no—
151C2×Q8×C17—28no—
152C2×Q8×C17—21no—
153C2×Q8×C17—21no—
154C2×Q8×C17—21no—
155C2×Q8×C17—21no—
156C2×Q8×C17—42no—
157C2×Q8×C17—42no—
158C2×Q8×C17—44no—
159C2×Q8×C17—44no—
160C2×Q8×C17—44no—
161C2×Q8×C17C22×C412yes—
162C2×Q8×C17C22×C412yes—
163C2×Q8×C17C2×D412yes—
164C2×Q8×C17#4112yes—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—24no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—42no—
175C22×C4×C17—42no—
176C22×C4×C17—42no—
177C22×C4×C17—42no—
178C22×C4×C17—81no—
179C22×C4×C17C22×C412yes—
180C22×C4×C17C2×D411yescharacteristic
181C22×C4×C17#4112yes—
182C22×C4×C17C2411yescharacteristic
183C2×C22⋊D17—24no—
184C2×C22⋊D17—42no—
185C2×C22⋊D17—42no—
186C22×Dic17—21no—
187C22×Dic17—21no—
188C22×Dic17—21no—
189C22×Dic17C2×D411yescharacteristic
190C22×Dic17C2×D411yescharacteristic
191C22×Dic17C2×D411yescharacteristic
192C22×Dic17C2×D411yescharacteristic
193C2×D68—21no—
194C2×D68—21no—
195C2×D68—21no—
196C2×D68—21no—
197C2×D68—21no—
198C2×D68C22×C412yes—
199C2×C4×D17—42no—
200C2×C4×D17—42no—
201C2×C4×D17—81no—
202C2×C8×C17—21no—
203C2×C8×C17—21no—
204C2×C8×C17—21no—
205C2×C8×C17—21no—
206C2×C8×C17—21no—
207C2×C8×C17—44no—
208C2×C8×C17C2×D412yes—
209C4⋊C4×C17—21no—
210C4⋊C4×C17—21no—
211C4⋊C4×C17—21no—
212C4⋊C4×C17—42no—
213C4⋊C4×C17C2×D412yes—
214C22⋊Dic17—22no—
215C22⋊Dic17—22no—
216C22⋊Dic17—42no—
217#63230—28no—
218#63230—44no—
219#63227—24no—
220#63227—42no—
221#63227—42no—
222#63227—81no—
223C4⋊Dic17—21no—
224C4⋊Dic17—21no—
225C4⋊Dic17—21no—
226C4⋊Dic17—21no—
227C4⋊Dic17—21no—
228C4⋊Dic17—42no—
229C4⋊Dic17—42no—
230C4⋊Dic17C22×C412yes—
231#63225—42no—
232C4×Dic17—21no—
233C4×Dic17—21no—
234C4×Dic17—21no—
235C4×Dic17—21no—
236C4×Dic17—42no—
237C4×Dic17—42no—
238C4×Dic17—42no—
239C2×#3622—21no—
240C2×#3622—21no—
241C2×#3622—21no—
242C2×#3622—21no—
243C2×#3622C22×C412yes—
244C2×#3622C22×C412yes—
245#22855—171nomaximal, Sylow
246C23×C17—21no—
247C23×C17—21no—
248C23×C17—21no—
249C23×C17—21no—
250C23×C17C4×D412yes—
251C23×C17AGL(1,ℤ/8)12yes—
252C23×C17#13712yes—
253C23×C17C22×D411yescharacteristic
254C22×D17—22no—
255C22×D17—41no—
256C22×D17—41no—
257C22×D17—41no—
258C22×D17—41no—
259C22×D17—41no—
260C22×D17—41no—
261Q8×C17—22no—
262Q8×C17—22no—
263Q8×C17—22no—
264Q8×C17—22no—
265Q8×C17—22no—
266Q8×C17—48no—
267Q8×C17—41no—
268Q8×C17—41no—
269Q8×C17C4×D414yescomplemented
270C2×C4×C17—22no—
271C2×C4×C17—21no—
272C2×C4×C17—22no—
273C2×C4×C17—21no—
274C2×C4×C17—22no—
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—48no—
282C2×C4×C17—41no—
283C2×C4×C17—41no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—41no—
288C2×C4×C17—41no—
289C2×C4×C17—84no—
290C2×C4×C17C4×D412yes—
291C2×C4×C17C23×C411yescharacteristic
292C2×C4×C17C22×D411yescharacteristic
293C2×C4×C17C2×#4111yescharacteristic
294C2×C4×C17C2×#4111yescharacteristic
295C2×C4×C17H(5,𝔽2)11yescharacteristic
296C2×C4×C17H(5,𝔽2)11yescharacteristic
297C22⋊D17—48no—
298C2×Dic17—22no—
299C2×Dic17—21no—
300C2×Dic17—21no—
301C2×Dic17—21no—
302C2×Dic17—21no—
303C2×Dic17—21no—
304C2×Dic17—21no—
305C2×Dic17—21no—
306C2×Dic17—21no—
307C2×Dic17—21no—
308C2×Dic17—21no—
309C2×Dic17—21no—
310C2×Dic17—21no—
311C2×Dic17—41no—
312C2×Dic17—41no—
313C2×Dic17—41no—
314C2×Dic17—41no—
315C2×Dic17—41no—
316C2×Dic17—41no—
317C2×Dic17—41no—
318C2×Dic17—41no—
319D68—22no—
320D68—22no—
321D68—41no—
322D68—41no—
323C4×D17—84no—
324C8×C17—22no—
325C8×C17—41no—
326#3622—22no—
327#3622—22no—
328C2×#448—171no—
329C2×#440—171no—
330C22×#103D1711yescharacteristic, complemented
331#2361—171no—
332Q8×C22⋊C4—171no—
333#1973—171no—
334#1935—171no—
335#1928—171no—
336#1893—171no—
337#1880—171no—
338#1877—171no—
339#1863—171no—
340#1852—171no—
341#1763—171no—
342#1752—171no—
343C22×C17—22no—
344C22×C17—22no—
345C22×C17—22no—
346C22×C17—22no—
347C22×C17—22no—
348C22×C17—22no—
349C22×C17#44014yescomplemented
350C22×C17C2×C4×D411yescharacteristic
351C22×C17D4211yescharacteristic
352C22×C17#54611yescharacteristic
353C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C17C2×#13711yescharacteristic
355C22×C17#57711yescharacteristic
356C22×C17#57811yescharacteristic
357C2×D17—42no—
358C2×D17—42no—
359C2×D17—42no—
360C2×D17—81no—
361C2×D17—81no—
362C2×D17—81no—
363C2×D17—81no—
364C4×C17—22no—
365C4×C17—24no—
366C4×C17—42no—
367C4×C17—42no—
368C4×C17—81no—
369C4×C17C2×C4×D411yescharacteristic
370C4×C17#51811yescharacteristic
371C4×C17#54611yescharacteristic
372C4×C17#55111yescharacteristic
373Dic17—42no—
374Dic17—41no—
375Dic17—41no—
376Dic17—41no—
377Dic17—41no—
378Dic17—81no—
379Dic17—81no—
380C23×Q8C2×D1711yescharacteristic
381C22×SD16—171no—
382C22×SD16—171no—
383C23×C8C2×D1711yescharacteristic
384C2×#121—171no—
385C2×C4×Q8—171no—
386C2×C4×Q8—171no—
387C2×C4×D4—171no—
388C2×C4×D4—341no—
389C22×C4⋊C4C2×D1711yescharacteristic
390#448—178no—
391#440—344no—
392C2×#107—171no—
393C2×#107—171no—
394C2×#103—24no—
395C2×#103—171no—
396C2×#103—171no—
397C2×#103C2×D1711yescharacteristic
398C2×#103C2×D1711yescharacteristic
399C2×#103C2×D1711yescharacteristic
400C2×#103C2×D1711yescharacteristic
401C2×#102—171no—
402C2×#102—171no—
403C2×C22⋊C8—171no—
404C2×#97—171no—
405C2×#97—171no—
406#391—171no—
407#391—171no—
408#391—341no—
409#391—341no—
410#390—171no—
411#389—171no—
412#388—341no—
413#386—341no—
414#385—341no—
415#380—171no—
416#380—341no—
417C4×C4⋊C4—171no—
418C4×C22⋊C4—171no—
419C4×C22⋊C4—341no—
420#340—171no—
421#340—171no—
422#340—171no—
423#340—171no—
424#336—171no—
425#336—171no—
426C2×C17—24no—
427C2×C17#235811yescharacteristic
428C2×C17C2×#44011yescharacteristic
429C2×C17#294711yescharacteristic
430C2×C17#326511yescharacteristic
431C2×C17#327011yescharacteristic
432C2×C17#330811yescharacteristic
433C2×C17#332011yescharacteristic
434D17—82no—
435C22×Q8—21no—
436C22×Q8—22no—
437C22×Q8—22no—
438C22×Q8—22no—
439C22×Q8—41no—
440C22×Q8—41no—
441C22×Q8C4×D1714yescomplemented
442C22×Q8C22×D1711yescharacteristic
443C22×Q8C22×D1711yescharacteristic
444C22×D4—171no—
445C22×D4—341no—
446C23×C4—21no—
447C23×C4—21no—
448C23×C4—341no—
449C23×C4C22×D1711yescharacteristic
450C2×SD16—174no—
451C2×SD16—174no—
452C2×SD16—342no—
453C2×SD16—342no—
454C2×SD16—681no—
455C2×SD16—681no—
456C22×C8—22no—
457C22×C8—22no—
458C22×C8—41no—
459C22×C8—171no—
460C22×C8—171no—
461C22×C8C22×D1711yescharacteristic
462C22×C8C22×D1711yescharacteristic
463#121—174no—
464#121—342no—
465C4×Q8—342no—
466C4×Q8—342no—
467C4×Q8—681no—
468C4×Q8—681no—
469C4×D4—342no—
470C4×D4—681no—
471C4×D4—684no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4—171no—
476C2×C4⋊C4—171no—
477C2×C4⋊C4—171no—
478C2×C4⋊C4—341no—
479C2×C4⋊C4—341no—
480C2×C4⋊C4—341no—
481C2×C4⋊C4C22×D1711yescharacteristic
482C2×C4⋊C4C22×D1711yescharacteristic
483C2×C22⋊C4—171no—
484C2×C22⋊C4—171no—
485C2×C22⋊C4—341no—
486C2×C22⋊C4—341no—
487C2×C22⋊C4—341no—
488C2×C22⋊C4—341no—
489C2×C22⋊C4—341no—
490C2×C42—171no—
491C2×C42—171no—
492C2×C42—341no—
493C2×C42—341no—
494C2×C42—341no—
495#107—342no—
496#107—681no—
497#103—22no—
498#103—22no—
499#103—22no—
500#103—174no—
501#103—174no—
502#103C22⋊D1714yescomplemented
503#102—342no—
504#102—681no—
505C22⋊C8—174no—
506#97—342no—
507#97—681no—
508#95—171no—
509#95—171no—
510#95—341no—
511#95—341no—
512#95—341no—
513#95—341no—
514#95—341no—
515#95—341no—
516#95—341no—
517C17#2285511yescharacteristic, complemented, Sylow
518C24—341no—
519C24D4×D1711yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—24no—
525C2×Q8—28no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8—44no—
535C2×Q8C2×C4×D1712yes—
536C2×Q8C2×C4×D1712yes—
537C2×Q8#6325212yes—
538C2×Q8C2×C22⋊D1712yes—
539C2×D4—172no—
540C2×D4—344no—
541C2×D4—341no—
542C2×D4—341no—
543C2×D4—341no—
544C2×D4—341no—
545C2×D4—341no—
546C2×D4—682no—
547C2×D4—682no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—81no—
562C22×C4—171no—
563C22×C4—171no—
564C22×C4—171no—
565C22×C4—171no—
566C22×C4—341no—
567C22×C4—341no—
568C22×C4—341no—
569C22×C4—682no—
570C22×C4—682no—
571C22×C4—1361no—
572C22×C4C2×C4×D1712yes—
573C22×C4D4×D1711yescharacteristic
574C22×C4#6325412yes—
575C22×C4C23×D1711yescharacteristic
576SD16—348no—
577SD16—684no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—44no—
584C2×C8—172no—
585C2×C8—172no—
586C2×C8—341no—
587C2×C8—341no—
588C2×C8—341no—
589C2×C8—341no—
590C2×C8C2×C22⋊D1712yes—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—42no—
595C4⋊C4—172no—
596C4⋊C4—341no—
597C4⋊C4—341no—
598C4⋊C4—341no—
599C4⋊C4—341no—
600C4⋊C4—341no—
601C4⋊C4—682no—
602C4⋊C4—682no—
603C4⋊C4—682no—
604C4⋊C4C2×C22⋊D1712yes—
605C22⋊C4—342no—
606C22⋊C4—342no—
607C22⋊C4—344no—
608C22⋊C4—682no—
609C22⋊C4—682no—
610C22⋊C4—682no—
611C22⋊C4—1361no—
612C42—341no—
613C42—341no—
614C42—341no—
615C42—341no—
616C42—682no—
617C42—682no—
618C42—682no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—342no—
624C23—681no—
625C23—681no—
626C23—681no—
627C23—681no—
628C23—681no—
629C23—681no—
630C23#1058756712yes—
631C23#1058760012yes—
632C23#1058760412yes—
633C23C2×D4×D1711yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8C4×C22⋊D1714yescomplemented
643D4—342no—
644D4—342no—
645D4—688no—
646D4—681no—
647D4—681no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—48no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—342no—
669C2×C4—341no—
670C2×C4—341no—
671C2×C4—341no—
672C2×C4—341no—
673C2×C4—341no—
674C2×C4—341no—
675C2×C4—341no—
676C2×C4—341no—
677C2×C4—341no—
678C2×C4—341no—
679C2×C4—341no—
680C2×C4—341no—
681C2×C4—681no—
682C2×C4—681no—
683C2×C4—681no—
684C2×C4—681no—
685C2×C4—681no—
686C2×C4—681no—
687C2×C4—681no—
688C2×C4—681no—
689C2×C4—1364no—
690C2×C4#1058756712yes—
691C2×C4C22×C4×D1711yescharacteristic
692C2×C4C2×#6325211yescharacteristic
693C2×C4C2×#6325411yescharacteristic
694C2×C4#1058769111yescharacteristic
695C2×C4#1058769111yescharacteristic
696C2×C4C22×C22⋊D1711yescharacteristic
697C8—22no—
698C8—41no—
699C8—342no—
700C8—342no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—682no—
708C22—682no—
709C22—682no—
710C22—1361no—
711C22—1361no—
712C22—1361no—
713C22—1361no—
714C22#1176291214yescomplemented
715C22C2×#1058756711yescharacteristic
716C22D4×C22⋊D1711yescharacteristic
717C22#1176344911yescharacteristic
718C22C2×#1058760011yescharacteristic
719C22C2×#1058760411yescharacteristic
720C22#1176361511yescharacteristic
721C22#1176362211yescharacteristic
722C4—22no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—81no—
727C4—681no—
728C4—682no—
729C4—681no—
730C4—681no—
731C4—681no—
732C4—1361no—
733C4—1361no—
734C4C2×C4×C22⋊D1711yescharacteristic
735C4#1176328211yescharacteristic
736C4#1176345311yescharacteristic
737C4#1176348511yescharacteristic
738C2—24no—
739C2—1362no—
740C2#1453176311yescharacteristic
741C2C2×#1176291211yescharacteristic
742C2#1453762111yescharacteristic
743C2#1454027911yescharacteristic
744C2#1454035411yescharacteristic
745C2#1454077111yescharacteristic
746C2#1454095111yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC22×C17×#103C2
socleC23×C17C22×D4
prime radicalC2×#10587616C22
cosocleC22×C4×C17C24
hypercenterC22×#103D17
hypocenterC17#22855
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C2×#11762912C2semidirect
4. Q8×C22⋊Dic17C2semidirect
5. #14529662C2semidirect
6. #14529471C2semidirect
7. #14529428C2semidirect
9. #14529137C2semidirect
10. #14529115C2semidirect
11. #14529036C2semidirect
12. #14528972C2semidirect
13. #14528616C2semidirect
14. #14528560C2semidirect
15. C22×C17×#103C2semidirect
23. #11762948C4semidirect
68. C22×Q8×C17C2×C4semidirect
98. C2×#63230C2×C4semidirect
99. C2×#63230C2×C4semidirect
125. C17×#103D4semidirect
126. #10587506C2×C4semidirect
127. #10587506C2×C4semidirect
137. C22⋊#3622C2×C4semidirect
269. Q8×C17C4×D4semidirect
330. C22×#103D17semidirect
349. C22×C17#440semidirect
441. C22×Q8C4×D17semidirect
502. #103C22⋊D17semidirect
517. C17#22855semidirect
642. Q8C4×C22⋊D17semidirect
714. C22#11762912semidirect

Maximal subgroups

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

subgroupindex
C2×#117629482
C2×#117629122
#145318002
Q8×C22⋊Dic172
#145296622
#145294712
#145294282
#145292122
#145291372
#145291152
#145290362
#145289722
#145286162
#145285602
C22×C17×#1032
#2285517