Finite Group Databasebeta

← #16940310

Subgroups — #16940310

Order 4352.

966 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C8×Dic17C211yesmaximal, characteristic
2C2×#11762705C211yesmaximal, characteristic
3C2×#11762572C211yesmaximal, characteristic
4C2×#11762571C211yesmaximal, characteristic
5C2×#11762571C211yesmaximal, characteristic
6#14527013C211yesmaximal, characteristic
7C2×C17×#340C211yesmaximal, characteristic
8C23×#3622C2211yescharacteristic
9C22×C4⋊Dic17C2211yescharacteristic
10C22×C4⋊Dic17C2211yescharacteristic
11C22×#63225—21no—
12C22×C4×Dic17C2211yescharacteristic
13C2×C8×Dic17—22no—
14C2×C8×Dic17—22no—
15C2×C8×Dic17—22no—
16#11762705—22no—
17#11762705C414yescomplemented
18C2×#10587502—21no—
19C2×#10587502—21no—
20C2×#10587502—21no—
21#11762572C414yescomplemented
22#11762571—22no—
23#11762571C414yescomplemented
24C23×C8×C17C2211yescharacteristic
25C22×C4⋊C4×C17C2211yescharacteristic
26C22×C4⋊C4×C17C2211yescharacteristic
27C17×#340—22no—
28C23×C4×C17—21no—
29C23×C4×C17—21no—
30C23×C4×C17C2311yescharacteristic
31C23×Dic17—21no—
32C23×Dic17—21no—
33C23×Dic17D411yescharacteristic
34C23×Dic17D411yescharacteristic
35C22×C8×C17—21no—
36C22×C8×C17—21no—
37C22×C8×C17—21no—
38C22×C8×C17—21no—
39C22×C8×C17C2×C412yes—
40C22×C8×C17D412yes—
41C22×C8×C17Q812yes—
42C2×C4⋊C4×C17—21no—
43C2×C4⋊C4×C17—21no—
44C2×C4⋊C4×C17—21no—
45C2×C4⋊C4×C17—21no—
46C2×C4⋊C4×C17—21no—
47C2×C4⋊C4×C17—21no—
48C2×C4⋊C4×C17—21no—
49C2×C4⋊C4×C17—21no—
50C2×C4⋊C4×C17—21no—
51C2×C4⋊C4×C17—21no—
52C2×C4⋊C4×C17C2×C412yes—
53C2×C4⋊C4×C17C2×C412yes—
54C2×C4⋊Dic17—21no—
55C2×C4⋊Dic17—21no—
56C2×C4⋊Dic17—21no—
57C2×C4⋊Dic17—21no—
58C2×C4⋊Dic17—21no—
59C2×C4⋊Dic17—21no—
60C2×C4⋊Dic17—21no—
61C2×C4⋊Dic17—21no—
62C2×C4⋊Dic17C2×C412yes—
63C2×C4⋊Dic17C2×C412yes—
64C2×C4⋊Dic17C2×C412yes—
65C2×C4⋊Dic17C2×C412yes—
66C2×#63225—24no—
67C2×#63225—42no—
68C2×#63225—42no—
69C2×C4×Dic17—21no—
70C2×C4×Dic17—21no—
71C2×C4×Dic17—21no—
72C2×C4×Dic17—21no—
73C2×C4×Dic17C2×C412yes—
74C2×C4×Dic17D412yes—
75C22×#3622—21no—
76C22×#3622—21no—
77C22×#3622—21no—
78C22×#3622—21no—
79C22×#3622C2×C412yes—
80C22×#3622D412yes—
81C22×#3622Q812yes—
82#10587502—24no—
83#10587502—42no—
84#10587502—42no—
85C8×Dic17—28no—
86C24×C17C2×D411yescharacteristic
87C22×C4×C17—22no—
88C22×C4×C17—22no—
89C22×C4×C17—41no—
90C22×C4×C17—41no—
91C22×C4×C17—41no—
92C22×C4×C17—41no—
93C22×C4×C17—41no—
94C22×C4×C17—41no—
95C22×C4×C17—41no—
96C22×C4×C17—41no—
97C22×C4×C17—41no—
98C22×C4×C17—41no—
99C22×C4×C17—41no—
100C22×C4×C17—41no—
101C22×C4×C17C22×C411yescharacteristic
102C22×C4×C17C22×C411yescharacteristic
103C22×C4×C17C22×C411yescharacteristic
104C22×C4×C17C2×D411yescharacteristic
105C22×C4×C17C2×D411yescharacteristic
106C22×C4×C17C2×D411yescharacteristic
107C22×C4×C17C2×Q811yescharacteristic
108C22×C4×C17C2×Q811yescharacteristic
109C22×C4×C17#4111yescharacteristic
110C22×C4×C17#4111yescharacteristic
111C22×C4×C17#4111yescharacteristic
112C22×C4×C17#4111yescharacteristic
113C22×C4×C17#4111yescharacteristic
114C22×C4×C17#4111yescharacteristic
115C22×Dic17—21no—
116C22×Dic17—21no—
117C22×Dic17—21no—
118C22×Dic17—21no—
119C22×Dic17—21no—
120C22×Dic17—21no—
121C22×Dic17—21no—
122C22×Dic17—21no—
123C22×Dic17—22no—
124C22×Dic17—22no—
125C22×Dic17—22no—
126C22×Dic17—22no—
127C22×Dic17—41no—
128C22×Dic17—41no—
129C22×Dic17—41no—
130C22×Dic17—41no—
131C22×Dic17—41no—
132C22×Dic17—41no—
133C22×Dic17—41no—
134C22×Dic17—41no—
135C22×Dic17—41no—
136C22×Dic17—41no—
137C22×Dic17C22⋊C412yes—
138C22×Dic17C22⋊C412yes—
139C22×Dic17D812yes—
140C22×Dic17SD1612yes—
141C22×Dic17SD1612yes—
142C22×Dic17Q1612yes—
143C2×C8×C17—22no—
144C2×C8×C17—22no—
145C2×C8×C17—22no—
146C2×C8×C17—22no—
147C2×C8×C17—22no—
148C2×C8×C17—22no—
149C2×C8×C17C4⋊C414yescomplemented
150C4⋊C4×C17—22no—
151C4⋊C4×C17—22no—
152C4⋊C4×C17—22no—
153C4⋊C4×C17—22no—
154C4⋊C4×C17—41no—
155C4⋊C4×C17—41no—
156C4⋊C4×C17—41no—
157C4⋊C4×C17—41no—
158C4⋊Dic17—22no—
159C4⋊Dic17—22no—
160C4⋊Dic17—22no—
161C4⋊Dic17—22no—
162C4⋊Dic17—22no—
163C4⋊Dic17—41no—
164C4⋊Dic17—41no—
165C4⋊Dic17C4214yes—
166#63225—48no—
167C4×Dic17—22no—
168C4×Dic17—22no—
169C4×Dic17—22no—
170C4×Dic17—22no—
171C2×#3622—22no—
172C2×#3622—22no—
173C2×#3622—22no—
174C2×#3622—22no—
175C2×#3622—22no—
176C2×#3622—22no—
177C2×#3622C4⋊C414yescomplemented
178#10880—171nomaximal, Sylow
179C23×C17C2×C22⋊C411yescharacteristic
180C23×C17C4×D411yescharacteristic
181C23×C17C4×D411yescharacteristic
182C23×C17#12111yescharacteristic
183C23×C17#12111yescharacteristic
184C23×C17#12411yescharacteristic
185C23×C17C4⋊Q811yescharacteristic
186C23×C17C2×D811yescharacteristic
187C23×C17C2×SD1611yescharacteristic
188C23×C17C2×SD1611yescharacteristic
189C23×C17C2×Q1611yescharacteristic
190C23×C17#13511yescharacteristic
191C23×C17#13511yescharacteristic
192C23×C17#13511yescharacteristic
193C23×C17#13511yescharacteristic
194C2×C4×C17—42no—
195C2×C4×C17—42no—
196C2×C4×C17—42no—
197C2×C4×C17—42no—
198C2×C4×C17—42no—
199C2×C4×C17—42no—
200C2×C4×C17—81no—
201C2×C4×C17—81no—
202C2×C4×C17—81no—
203C2×C4×C17—81no—
204C2×C4×C17—81no—
205C2×C4×C17—81no—
206C2×C4×C17—81no—
207C2×C4×C17—81no—
208C2×C4×C17C2×C4211yescharacteristic
209C2×C4×C17C2×C4⋊C411yescharacteristic
210C2×C4×C17C2×C4⋊C411yescharacteristic
211C2×C4×C17#11711yescharacteristic
212C2×C4×C17#11711yescharacteristic
213C2×C4×C17#11711yescharacteristic
214C2×C4×C17C4×D411yescharacteristic
215C2×C4×C17C4×D411yescharacteristic
216C2×C4×C17C4×D411yescharacteristic
217C2×C4×C17C4×D411yescharacteristic
218C2×C4×C17C4×D411yescharacteristic
219C2×C4×C17C4×D411yescharacteristic
220C2×C4×C17C4×Q811yescharacteristic
221C2×C4×C17C4×Q811yescharacteristic
222C2×C4×C17C4×Q811yescharacteristic
223C2×C4×C17C4×Q811yescharacteristic
224C2×C4×C17#12011yescharacteristic
225C2×C4×C17C22⋊Q811yescharacteristic
226C2×C4×C17C22⋊Q811yescharacteristic
227C2×C4×C17C22⋊Q811yescharacteristic
228C2×C4×C17C22⋊Q811yescharacteristic
229C2×C4×C17#12311yescharacteristic
230C2×C4×C17#12311yescharacteristic
231C2×C4×C17#12311yescharacteristic
232C2×C4×C17#12511yescharacteristic
233C2×C4×C17#12511yescharacteristic
234C2×C4×C17#12611yescharacteristic
235C2×C4×C17#12611yescharacteristic
236C2×Dic17—22no—
237C2×Dic17—22no—
238C2×Dic17—22no—
239C2×Dic17—22no—
240C2×Dic17—22no—
241C2×Dic17—22no—
242C2×Dic17—22no—
243C2×Dic17—22no—
244C2×Dic17—22no—
245C2×Dic17—22no—
246C2×Dic17—22no—
247C2×Dic17—22no—
248C2×Dic17—24no—
249C2×Dic17—42no—
250C2×Dic17—42no—
251C2×Dic17—42no—
252C2×Dic17—42no—
253C2×Dic17—42no—
254C2×Dic17—42no—
255C2×Dic17—42no—
256C2×Dic17—42no—
257C2×Dic17—42no—
258C2×Dic17—81no—
259C2×Dic17—81no—
260C2×Dic17—81no—
261C2×Dic17—81no—
262C2×Dic17#10214yes—
263C2×Dic17#10314yes—
264C8×C17—24no—
265#3622—24no—
266C22×C4×C8—171no—
267C2×#389—171no—
268C2×#340—171no—
269C2×#340—171no—
270C2×#340—171no—
271C2×#340D1711yescharacteristic
272C4⋊#95—171no—
273C22×C17C4×C22⋊C411yescharacteristic
274C22×C17#38611yescharacteristic
275C22×C17#38811yescharacteristic
276C22×C17#38811yescharacteristic
277C22×C17#38911yescharacteristic
278C22×C17#38911yescharacteristic
279C22×C17#39111yescharacteristic
280C22×C17C2×#10211yescharacteristic
281C22×C17C2×#10311yescharacteristic
282C22×C17#41611yescharacteristic
283C22×C17#41611yescharacteristic
284C22×C17C4×D811yescharacteristic
285C22×C17C4×D811yescharacteristic
286C22×C17C4×SD1611yescharacteristic
287C22×C17C4×SD1611yescharacteristic
288C22×C17C4×SD1611yescharacteristic
289C22×C17C4×SD1611yescharacteristic
290C22×C17C4×Q1611yescharacteristic
291C22×C17C4×Q1611yescharacteristic
292C22×C17#46511yescharacteristic
293C22×C17#46511yescharacteristic
294C22×C17#46511yescharacteristic
295C22×C17#46511yescharacteristic
296C22×C17#46611yescharacteristic
297C22×C17#46611yescharacteristic
298C22×C17#46711yescharacteristic
299C22×C17#46711yescharacteristic
300C22×C17#48611yescharacteristic
301C22×C17#48711yescharacteristic
302C22×C17#48811yescharacteristic
303C22×C17#48811yescharacteristic
304C22×C17#49811yescharacteristic
305C22×C17#49911yescharacteristic
306C22×C17#49911yescharacteristic
307C22×C17#50011yescharacteristic
308C4×C17—82no—
309C4×C17—82no—
310C4×C17C4×C4⋊C411yescharacteristic
311C4×C17C4×C4⋊C411yescharacteristic
312C4×C17#38511yescharacteristic
313C4×C17#38511yescharacteristic
314C4×C17#38711yescharacteristic
315C4×C17#38711yescharacteristic
316C4×C17#38711yescharacteristic
317C4×C17#38711yescharacteristic
318Dic17—24no—
319Dic17—24no—
320Dic17—44no—
321Dic17—82no—
322C23×C8—171no—
323C23×C8C2×D1711yescharacteristic
324C22×C4⋊C4—171no—
325C22×C4⋊C4—171no—
326C22×C4⋊C4—341no—
327C22×C4⋊C4C2×D1711yescharacteristic
328C22×C4⋊C4C2×D1711yescharacteristic
329C22×C42—171no—
330C2×C4×C8—342no—
331C2×C4×C8—342no—
332C2×C4×C8—342no—
333#389—174no—
334#389—342no—
335C2×#95—341no—
336C2×#95—341no—
337C2×#95—341no—
338#340—22no—
339#340—174no—
340#340—174no—
341#340—342no—
342C2×C17#143611yescharacteristic
343C2×C17C4×#10211yescharacteristic
344C2×C17C4×#10311yescharacteristic
345C2×C17#189211yescharacteristic
346C2×C17#189311yescharacteristic
347C2×C17#193311yescharacteristic
348C2×C17#193311yescharacteristic
349C2×C17#193411yescharacteristic
350C2×C17#193411yescharacteristic
351C2×C17#194111yescharacteristic
352C2×C17#194111yescharacteristic
353C2×C17#194211yescharacteristic
354C2×C17#194211yescharacteristic
355C2×C17#199011yescharacteristic
356C2×C17#199111yescharacteristic
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—171no—
360C23×C4—171no—
361C23×C4—341no—
362C23×C4—341no—
363C23×C4C22×D1711yescharacteristic
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—172no—
369C22×C8—172no—
370C22×C8—172no—
371C22×C8—341no—
372C22×C8—341no—
373C22×C8—341no—
374C22×C8—341no—
375C22×C8Dic3412yes—
376C22×C8C4×D1712yes—
377C22×C8C22⋊D1712yes—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—172no—
389C2×C4⋊C4—172no—
390C2×C4⋊C4—172no—
391C2×C4⋊C4—172no—
392C2×C4⋊C4—341no—
393C2×C4⋊C4—341no—
394C2×C4⋊C4—341no—
395C2×C4⋊C4—341no—
396C2×C4⋊C4—341no—
397C2×C4⋊C4—341no—
398C2×C4⋊C4—341no—
399C2×C4⋊C4—344no—
400C2×C4⋊C4—341no—
401C2×C4⋊C4—682no—
402C2×C4⋊C4—682no—
403C2×C4⋊C4C4×D1712yes—
404C2×C4⋊C4C4×D1712yes—
405C2×C42—172no—
406C2×C42—172no—
407C2×C42—341no—
408C2×C42—341no—
409C2×C42—341no—
410C2×C42—341no—
411C4×C8—348no—
412#95—344no—
413#95—682no—
414#95—682no—
415C17#1088011yescharacteristic, complemented, Sylow
416C24D4×D1711yescharacteristic
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—172no—
432C22×C4—172no—
433C22×C4—172no—
434C22×C4—172no—
435C22×C4—172no—
436C22×C4—172no—
437C22×C4—341no—
438C22×C4—341no—
439C22×C4—341no—
440C22×C4—341no—
441C22×C4—341no—
442C22×C4—341no—
443C22×C4—341no—
444C22×C4—341no—
445C22×C4—342no—
446C22×C4—342no—
447C22×C4—342no—
448C22×C4—342no—
449C22×C4—681no—
450C22×C4—681no—
451C22×C4—681no—
452C22×C4—681no—
453C22×C4—681no—
454C22×C4—681no—
455C22×C4—681no—
456C22×C4—681no—
457C22×C4—681no—
458C22×C4—681no—
459C22×C4C2×Dic3411yescharacteristic
460C22×C4C2×C4×D1711yescharacteristic
461C22×C4C2×C4×D1711yescharacteristic
462C22×C4C2×C4×D1711yescharacteristic
463C22×C4#6325211yescharacteristic
464C22×C4#6325211yescharacteristic
465C22×C4D4×D1711yescharacteristic
466C22×C4D4×D1711yescharacteristic
467C22×C4#6325411yescharacteristic
468C22×C4#6325411yescharacteristic
469C22×C4#6325411yescharacteristic
470C22×C4Q8×D1711yescharacteristic
471C22×C4#6325611yescharacteristic
472C22×C4C2×C22⋊D1711yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—174no—
480C2×C8—342no—
481C2×C8—342no—
482C2×C8—342no—
483C2×C8—342no—
484C2×C8—342no—
485C2×C8—342no—
486C2×C8#6322514yescomplemented
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—174no—
496C4⋊C4—342no—
497C4⋊C4—342no—
498C4⋊C4—342no—
499C4⋊C4—342no—
500C4⋊C4—342no—
501C4⋊C4—688no—
502C4⋊C4—681no—
503C4⋊C4—681no—
504C42—342no—
505C42—342no—
506C42—342no—
507C42—342no—
508C23C22⋊C4×D1711yescharacteristic
509C23#1058756711yescharacteristic
510C23#1058757011yescharacteristic
511C23#1058757111yescharacteristic
512C23#1058757411yescharacteristic
513C23#1058757911yescharacteristic
514C23D8×D1711yescharacteristic
515C23#1058759811yescharacteristic
516C23SD16×D1711yescharacteristic
517C23SD16×D1711yescharacteristic
518C23#1058760211yescharacteristic
519C23#1058760211yescharacteristic
520C23Q16×D1711yescharacteristic
521C23#1058760511yescharacteristic
522C23#1058762411yescharacteristic
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—174no—
538C2×C4—174no—
539C2×C4—342no—
540C2×C4—342no—
541C2×C4—342no—
542C2×C4—342no—
543C2×C4—342no—
544C2×C4—342no—
545C2×C4—342no—
546C2×C4—342no—
547C2×C4—342no—
548C2×C4—342no—
549C2×C4—342no—
550C2×C4—342no—
551C2×C4—344no—
552C2×C4—682no—
553C2×C4—682no—
554C2×C4—682no—
555C2×C4—682no—
556C2×C4—682no—
557C2×C4—682no—
558C2×C4—682no—
559C2×C4—682no—
560C2×C4—682no—
561C2×C4—1361no—
562C2×C4—1361no—
563C2×C4—1361no—
564C2×C4—1361no—
565C2×C4C4×Dic3411yescharacteristic
566C2×C4C4×Dic3411yescharacteristic
567C2×C4C42×D1711yescharacteristic
568C2×C4#1058755811yescharacteristic
569C2×C4#1058756311yescharacteristic
570C2×C4#1058756411yescharacteristic
571C2×C4#1058756411yescharacteristic
572C2×C4#1058756511yescharacteristic
573C2×C4#1058756711yescharacteristic
574C2×C4#1058756711yescharacteristic
575C2×C4#1058756711yescharacteristic
576C2×C4#1058756911yescharacteristic
577C2×C4#1058757311yescharacteristic
578C2×C4#1058757311yescharacteristic
579C2×C4#1058757511yescharacteristic
580C2×C4#1058757611yescharacteristic
581C2×C4C4⋊C4×D1711yescharacteristic
582C2×C4#1058757811yescharacteristic
583C2×C4#1058757911yescharacteristic
584C2×C4#1058758011yescharacteristic
585C2×C4#1058758211yescharacteristic
586C2×C4#1058758411yescharacteristic
587C2×C4C2×#6322511yescharacteristic
588C2×C4C4×C22⋊D1711yescharacteristic
589C2×C4C4×C22⋊D1711yescharacteristic
590C2×C4#1058762111yescharacteristic
591C2×C4#1058762311yescharacteristic
592C2×C4#1058763211yescharacteristic
593C8—24no—
594C8—344no—
595C22#1176265611yescharacteristic
596C22#1176268511yescharacteristic
597C22#1176269711yescharacteristic
598C22#1176269811yescharacteristic
599C22#1176270511yescharacteristic
600C22#1176270611yescharacteristic
601C22#1176271311yescharacteristic
602C22#102×D1711yescharacteristic
603C22#103×D1711yescharacteristic
604C22#1176280211yescharacteristic
605C22#1176280411yescharacteristic
606C22#1176288911yescharacteristic
607C22#1176289111yescharacteristic
608C22#1176289411yescharacteristic
609C22#1176289611yescharacteristic
610C22#1176289611yescharacteristic
611C22#1176290011yescharacteristic
612C22#1176290111yescharacteristic
613C22#1176290311yescharacteristic
614C22#1176303511yescharacteristic
615C22#1176303511yescharacteristic
616C22#1176303711yescharacteristic
617C22#1176304111yescharacteristic
618C22#1176304211yescharacteristic
619C22#1176304411yescharacteristic
620C22#1176304711yescharacteristic
621C22#1176304911yescharacteristic
622C22#1176315411yescharacteristic
623C22#1176315811yescharacteristic
624C22#1176316211yescharacteristic
625C22#1176316511yescharacteristic
626C22#1176320611yescharacteristic
627C22#1176320911yescharacteristic
628C22#1176321011yescharacteristic
629C22#1176321311yescharacteristic
630C4—82no—
631C4—82no—
632C4—344no—
633C4—344no—
634C4—684no—
635C4—1362no—
636C4#1176266011yescharacteristic
637C4C4×#6322511yescharacteristic
638C4#1176268011yescharacteristic
639C4#1176268111yescharacteristic
640C4#1176269011yescharacteristic
641C4#1176269111yescharacteristic
642C4#1176269211yescharacteristic
643C4#1176269611yescharacteristic
644C2#1452701511yescharacteristic
645C2#1452859811yescharacteristic
646C2#1452860311yescharacteristic
647C2#1452920411yescharacteristic
648C2#1452920911yescharacteristic
649C2#1452945711yescharacteristic
650C2#1452945811yescharacteristic
651C2#1452946411yescharacteristic
652C2#1452946511yescharacteristic
653C2#1452951011yescharacteristic
654C2#1452951111yescharacteristic
655C2#1452951511yescharacteristic
656C2#1452951611yescharacteristic
657C2#1452974311yescharacteristic
658C2#1452974711yescharacteristic
subgroupG/H
centerC24D4×D17
commutatorC2×C4×C17C2×C42
FrattiniC23×C4C22×D17
FittingC2×C17×#340C2
socle, prime radicalC24×C17C2×D4
cosocleC23×C4×C17C23
hypercenterC2×#340D17
hypocenterC17#10880
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
17. #11762705C4semidirect
21. #11762572C4semidirect
23. #11762571C4semidirect
149. C2×C8×C17C4⋊C4semidirect
177. C2×#3622C4⋊C4semidirect
415. C17#10880semidirect
486. C2×C8#63225semidirect

Maximal subgroups

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

subgroupindex
C22×C8×Dic172
C2×#117627052
C2×#117625722
C2×#117625712
#145270132
C2×C17×#3402
#1088017