Finite Group Databasebeta

← #16940492

Subgroups — #16940492

Order 4352.

958 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×#10587488C211yesmaximal, characteristic
2C2×C4×C4⋊Dic17C211yesmaximal, characteristic
3C2×#11762572C211yesmaximal, characteristic
4C2×#11762572C211yesmaximal, characteristic
5C2×#11762572C211yesmaximal, characteristic
6#14527014C211yesmaximal, characteristic
7C2×C17×#336C211yesmaximal, characteristic
8C22×C4⋊Dic17C2211yescharacteristic
9C22×C4⋊Dic17C2211yescharacteristic
10C22×C4⋊Dic17C2211yescharacteristic
11C22×C4⋊Dic17C2211yescharacteristic
12C22×C4×Dic17—21no—
13C2×#10587488—22no—
14C2×#10587488—22no—
15C2×#10587488C414yescomplemented
16C4×C4⋊Dic17—22no—
17C4×C4⋊Dic17—22no—
18C2×#10587502—21no—
19C2×#10587502—21no—
20C2×#10587502—21no—
21#11762572—22no—
22#11762572—22no—
23#11762572C414yescomplemented
24C23×C8×C17C2211yescharacteristic
25C23×C8×C17C2211yescharacteristic
26C22×C42×C17C2211yescharacteristic
27C17×#336C414yescomplemented
28C23×C4×C17D411yescharacteristic
29C23×C4×C17D411yescharacteristic
30C23×C4×C17C2311yescharacteristic
31C23×Dic17—21no—
32C23×Dic17—21no—
33C23×Dic17—21no—
34C23×Dic17—21no—
35C22×C8×C17—21no—
36C22×C8×C17—21no—
37C22×C8×C17—21no—
38C22×C8×C17—21no—
39C22×C8×C17—21no—
40C22×C8×C17—21no—
41C22×C8×C17—21no—
42C22×C8×C17—21no—
43C22×C8×C17—21no—
44C22×C8×C17—21no—
45C22×C8×C17C2×C412yes—
46C22×C8×C17C2×C412yes—
47C22×C8×C17C2×C412yes—
48C22×C8×C17C2×C412yes—
49C2×C42×C17—21no—
50C2×C42×C17—21no—
51C2×C42×C17—21no—
52C2×C42×C17—21no—
53C2×C42×C17C2×C412yes—
54C2×C42×C17Q812yes—
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⋊Dic17—21no—
63C2×C4⋊Dic17—21no—
64C2×C4⋊Dic17—21no—
65C2×C4⋊Dic17—21no—
66C2×C4⋊Dic17—21no—
67C2×C4⋊Dic17—21no—
68C2×C4⋊Dic17—21no—
69C2×C4⋊Dic17—21no—
70C2×C4⋊Dic17—21no—
71C2×C4⋊Dic17C2×C412yes—
72C2×C4⋊Dic17C2×C412yes—
73C2×C4⋊Dic17C2×C412yes—
74C2×C4⋊Dic17C2×C412yes—
75C2×C4⋊Dic17D412yes—
76C2×C4⋊Dic17D412yes—
77C2×C4⋊Dic17D412yes—
78C2×C4⋊Dic17Q812yes—
79C2×C4×Dic17—24no—
80C2×C4×Dic17—42no—
81C2×C4×Dic17—42no—
82#10587502—24no—
83#10587502—42no—
84#10587502—42no—
85#10587488—28no—
86C24×C17C2×D411yescharacteristic
87C22×C4×C17—21no—
88C22×C4×C17—21no—
89C22×C4×C17—21no—
90C22×C4×C17—21no—
91C22×C4×C17—21no—
92C22×C4×C17—21no—
93C22×C4×C17—21no—
94C22×C4×C17—21no—
95C22×C4×C17—21no—
96C22×C4×C17—21no—
97C22×C4×C17C4⋊C412yes—
98C22×C4×C17C4⋊C412yes—
99C22×C4×C17SD1612yes—
100C22×C4×C17SD1612yes—
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—22no—
116C22×Dic17—22no—
117C22×Dic17—22no—
118C22×Dic17—22no—
119C22×Dic17—22no—
120C22×Dic17—22no—
121C22×Dic17—22no—
122C22×Dic17—22no—
123C22×Dic17—41no—
124C22×Dic17—41no—
125C22×Dic17—41no—
126C22×Dic17—41no—
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×Dic17—41no—
138C22×Dic17—41no—
139C22×Dic17—41no—
140C22×Dic17—41no—
141C22×Dic17—41no—
142C22×Dic17—41no—
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×C17—22no—
150C2×C8×C17—22no—
151C2×C8×C17—22no—
152C2×C8×C17—41no—
153C2×C8×C17—41no—
154C2×C8×C17—41no—
155C2×C8×C17—41no—
156C2×C8×C17C4214yescomplemented
157C42×C17—22no—
158C42×C17—22no—
159C42×C17—22no—
160C42×C17—22no—
161C4⋊Dic17—22no—
162C4⋊Dic17—22no—
163C4⋊Dic17—22no—
164C4⋊Dic17—22no—
165C4⋊Dic17—22no—
166C4⋊Dic17—22no—
167C4⋊Dic17—22no—
168C4⋊Dic17—22no—
169C4⋊Dic17—22no—
170C4⋊Dic17—22no—
171C4⋊Dic17—41no—
172C4⋊Dic17—41no—
173C4⋊Dic17—41no—
174C4⋊Dic17—41no—
175C4⋊Dic17C22⋊C414yes—
176C4⋊Dic17C4⋊C414yes—
177C4×Dic17—48no—
178#10908—171nomaximal, Sylow
179C23×C17C2×C4⋊C411yescharacteristic
180C23×C17C4×D411yescharacteristic
181C23×C17C4×D411yescharacteristic
182C23×C17#12011yescharacteristic
183C23×C17#12111yescharacteristic
184C23×C17C22⋊Q811yescharacteristic
185C23×C17#12311yescharacteristic
186C23×C17C2×SD1611yescharacteristic
187C23×C17C2×SD1611yescharacteristic
188C23×C17#13511yescharacteristic
189C23×C17#13511yescharacteristic
190C23×C17AGL(1,ℤ/8)11yescharacteristic
191C23×C17AGL(1,ℤ/8)11yescharacteristic
192C23×C17#13711yescharacteristic
193C23×C17#13711yescharacteristic
194C2×C4×C17—22no—
195C2×C4×C17—22no—
196C2×C4×C17—22no—
197C2×C4×C17—22no—
198C2×C4×C17—22no—
199C2×C4×C17—22no—
200C2×C4×C17—22no—
201C2×C4×C17—22no—
202C2×C4×C17—22no—
203C2×C4×C17—41no—
204C2×C4×C17—41no—
205C2×C4×C17—41no—
206C2×C4×C17—41no—
207C2×C4×C17#10614yescomplemented
208C2×C4×C17C2×C4211yescharacteristic
209C2×C4×C17C2×C22⋊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#12111yescharacteristic
225C2×C4×C17C22⋊Q811yescharacteristic
226C2×C4×C17C22⋊Q811yescharacteristic
227C2×C4×C17C22⋊Q811yescharacteristic
228C2×C4×C17#12311yescharacteristic
229C2×C4×C17#12311yescharacteristic
230C2×C4×C17#12411yescharacteristic
231C2×C4×C17#12511yescharacteristic
232C2×C4×C17#12511yescharacteristic
233C2×C4×C17#12611yescharacteristic
234C2×C4×C17#12611yescharacteristic
235C2×C4×C17C4⋊Q811yescharacteristic
236C2×Dic17—24no—
237C2×Dic17—24no—
238C2×Dic17—42no—
239C2×Dic17—42no—
240C2×Dic17—42no—
241C2×Dic17—42no—
242C2×Dic17—42no—
243C2×Dic17—42no—
244C2×Dic17—42no—
245C2×Dic17—42no—
246C2×Dic17—42no—
247C2×Dic17—42no—
248C2×Dic17—42no—
249C2×Dic17—42no—
250C2×Dic17—42no—
251C2×Dic17—42no—
252C2×Dic17—42no—
253C2×Dic17—42no—
254C2×Dic17—42no—
255C2×Dic17—42no—
256C2×Dic17—81no—
257C2×Dic17—81no—
258C2×Dic17—81no—
259C2×Dic17—81no—
260C2×Dic17—81no—
261C2×Dic17—81no—
262C2×Dic17—81no—
263C2×Dic17—81no—
264C8×C17—24no—
265C8×C17—42no—
266C22×#106—171no—
267C2×C4×C4⋊C4—171no—
268C2×#340—171no—
269C2×#340—171no—
270C2×#340—171no—
271C2×#336D1711yescharacteristic
272C4⋊#95—171no—
273C22×C17C4×C4⋊C411yescharacteristic
274C22×C17#38511yescharacteristic
275C22×C17#38511yescharacteristic
276C22×C17#38611yescharacteristic
277C22×C17#38711yescharacteristic
278C22×C17#38811yescharacteristic
279C22×C17#38911yescharacteristic
280C22×C17C2×#10611yescharacteristic
281C22×C17#42711yescharacteristic
282C22×C17#42811yescharacteristic
283C22×C17#42811yescharacteristic
284C22×C17C4×SD1611yescharacteristic
285C22×C17C4×SD1611yescharacteristic
286C22×C17C4×SD1611yescharacteristic
287C22×C17C4×SD1611yescharacteristic
288C22×C17#44011yescharacteristic
289C22×C17#44011yescharacteristic
290C22×C17#44111yescharacteristic
291C22×C17#44211yescharacteristic
292C22×C17#44811yescharacteristic
293C22×C17#44911yescharacteristic
294C22×C17#45011yescharacteristic
295C22×C17#45211yescharacteristic
296C22×C17#46011yescharacteristic
297C22×C17#46111yescharacteristic
298C22×C17#46311yescharacteristic
299C22×C17#46411yescharacteristic
300C22×C17#47511yescharacteristic
301C22×C17#47611yescharacteristic
302C22×C17#47811yescharacteristic
303C22×C17#47911yescharacteristic
304C22×C17#48111yescharacteristic
305C22×C17#48211yescharacteristic
306C22×C17#48311yescharacteristic
307C22×C17#48511yescharacteristic
308C4×C17—24no—
309C4×C17—42no—
310C4×C17C4×C22⋊C411yescharacteristic
311C4×C17C4×C4⋊C411yescharacteristic
312C4×C17#38711yescharacteristic
313C4×C17#38711yescharacteristic
314C4×C17#38711yescharacteristic
315C4×C17#38811yescharacteristic
316C4×C17#38911yescharacteristic
317C4×C17#39111yescharacteristic
318Dic17—44no—
319Dic17—44no—
320Dic17—82no—
321Dic17—82no—
322C23×C8C2×D1711yescharacteristic
323C23×C8C2×D1711yescharacteristic
324C22×C4⋊C4—171no—
325C22×C4⋊C4—171no—
326C22×C4⋊C4—171no—
327C22×C4⋊C4—171no—
328C22×C42—341no—
329C22×C42C2×D1711yescharacteristic
330C2×#106—174no—
331C2×#106—342no—
332C2×#106—342no—
333C4×C4⋊C4—342no—
334C4×C4⋊C4—342no—
335C2×#95—341no—
336C2×#95—341no—
337C2×#95—341no—
338#340—174no—
339#340—342no—
340#340—342no—
341#336Dic1714yescomplemented
342C2×C17#143611yescharacteristic
343C2×C17C4×#10611yescharacteristic
344C2×C17#177611yescharacteristic
345C2×C17#185311yescharacteristic
346C2×C17#185411yescharacteristic
347C2×C17#186411yescharacteristic
348C2×C17#186511yescharacteristic
349C2×C17#187711yescharacteristic
350C2×C17#188011yescharacteristic
351C2×C17#191911yescharacteristic
352C2×C17#192011yescharacteristic
353C2×C17#192611yescharacteristic
354C2×C17#192711yescharacteristic
355C2×C17#194811yescharacteristic
356C2×C17#194911yescharacteristic
357C23×C4—341no—
358C23×C4—341no—
359C23×C4—341no—
360C23×C4—341no—
361C23×C4D6811yescharacteristic
362C23×C4D6811yescharacteristic
363C23×C4C22×D1711yescharacteristic
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8C4×D1712yes—
375C22×C8C4×D1712yes—
376C22×C8C2×Dic1712yes—
377C22×C8C2×Dic1712yes—
378C2×C4⋊C4—172no—
379C2×C4⋊C4—172no—
380C2×C4⋊C4—172no—
381C2×C4⋊C4—172no—
382C2×C4⋊C4—172no—
383C2×C4⋊C4—172no—
384C2×C4⋊C4—172no—
385C2×C4⋊C4—172no—
386C2×C4⋊C4—341no—
387C2×C4⋊C4—341no—
388C2×C4⋊C4—341no—
389C2×C4⋊C4—341no—
390C2×C4⋊C4—341no—
391C2×C4⋊C4—341no—
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—341no—
400C2×C4⋊C4—341no—
401C2×C4⋊C4—341no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—344no—
407C2×C42—682no—
408C2×C42—682no—
409C2×C42Dic3412yes—
410C2×C42C2×Dic1712yes—
411#106—348no—
412#95—344no—
413#95—682no—
414#95—682no—
415C17#1090811yescharacteristic, complemented, Sylow
416C24C2×D6811yescharacteristic
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—342no—
428C22×C4—342no—
429C22×C4—342no—
430C22×C4—342no—
431C22×C4—342no—
432C22×C4—342no—
433C22×C4—342no—
434C22×C4—342no—
435C22×C4—681no—
436C22×C4—681no—
437C22×C4—681no—
438C22×C4—681no—
439C22×C4—681no—
440C22×C4—681no—
441C22×C4—681no—
442C22×C4—681no—
443C22×C4—681no—
444C22×C4—681no—
445C22×C4—681no—
446C22×C4—681no—
447C22×C4—681no—
448C22×C4—681no—
449C22×C4—681no—
450C22×C4—681no—
451C22×C4—681no—
452C22×C4—681no—
453C22×C4—681no—
454C22×C4—681no—
455C22×C4#6321912yes—
456C22×C4#6321912yes—
457C22×C4C4⋊Dic1712yes—
458C22×C4C4⋊Dic1712yes—
459C22×C4C2×Dic3411yescharacteristic
460C22×C4C2×C4×D1711yescharacteristic
461C22×C4C2×C4×D1711yescharacteristic
462C22×C4#6325211yescharacteristic
463C22×C4#6325211yescharacteristic
464C22×C4D4×D1711yescharacteristic
465C22×C4D4×D1711yescharacteristic
466C22×C4D4×D1711yescharacteristic
467C22×C4#6325411yescharacteristic
468C22×C4#6325411yescharacteristic
469C22×C4#6325411yescharacteristic
470C22×C4Q8×D1711yescharacteristic
471C22×C4#6325611yescharacteristic
472C22×C4C22×Dic1711yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8C4×Dic1714yescomplemented
487C4⋊C4—174no—
488C4⋊C4—174no—
489C4⋊C4—342no—
490C4⋊C4—342no—
491C4⋊C4—342no—
492C4⋊C4—342no—
493C4⋊C4—342no—
494C4⋊C4—342no—
495C4⋊C4—342no—
496C4⋊C4—342no—
497C4⋊C4—342no—
498C4⋊C4—342no—
499C4⋊C4—681no—
500C4⋊C4—681no—
501C4⋊C4—681no—
502C4⋊C4—681no—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—688no—
508C23C4×D6811yescharacteristic
509C23C4×D6811yescharacteristic
510C23#1058756811yescharacteristic
511C23#1058757211yescharacteristic
512C23#1058758111yescharacteristic
513C23#1058758311yescharacteristic
514C23C2×#6321911yescharacteristic
515C23C2×#6321911yescharacteristic
516C23#1058759011yescharacteristic
517C23#1058759011yescharacteristic
518C23#1058759411yescharacteristic
519C23#1058759411yescharacteristic
520C23#1058759511yescharacteristic
521C23#1058759511yescharacteristic
522C23C2×C4⋊Dic1711yescharacteristic
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—344no—
537C2×C4—344no—
538C2×C4—682no—
539C2×C4—682no—
540C2×C4—682no—
541C2×C4—682no—
542C2×C4—682no—
543C2×C4—682no—
544C2×C4—682no—
545C2×C4—682no—
546C2×C4—682no—
547C2×C4—682no—
548C2×C4—682no—
549C2×C4—682no—
550C2×C4—682no—
551C2×C4—682no—
552C2×C4—682no—
553C2×C4—682no—
554C2×C4—682no—
555C2×C4—682no—
556C2×C4—1361no—
557C2×C4—1361no—
558C2×C4—1361no—
559C2×C4—1361no—
560C2×C4—1361no—
561C2×C4—1361no—
562C2×C4—1361no—
563C2×C4—1361no—
564C2×C4#1058748814yescomplemented
565C2×C4C4×Dic3411yescharacteristic
566C2×C4C4×Dic3411yescharacteristic
567C2×C4#1058756311yescharacteristic
568C2×C4#1058756411yescharacteristic
569C2×C4#1058756411yescharacteristic
570C2×C4#1058756511yescharacteristic
571C2×C4C22⋊C4×D1711yescharacteristic
572C2×C4#1058756711yescharacteristic
573C2×C4#1058756711yescharacteristic
574C2×C4#1058756911yescharacteristic
575C2×C4#1058757011yescharacteristic
576C2×C4#1058757111yescharacteristic
577C2×C4#1058757311yescharacteristic
578C2×C4#1058757411yescharacteristic
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×C4×Dic1711yescharacteristic
588C2×C4#1058761211yescharacteristic
589C2×C4D4×Dic1711yescharacteristic
590C2×C4D4×Dic1711yescharacteristic
591C2×C4D4×Dic1711yescharacteristic
592C2×C4Q8×Dic1711yescharacteristic
593C8—24no—
594C8—42no—
595C22C4×C4⋊Dic1711yescharacteristic
596C22#1176268311yescharacteristic
597C22#1176268411yescharacteristic
598C22#1176268711yescharacteristic
599C22#1176269411yescharacteristic
600C22#1176270111yescharacteristic
601C22#1176270811yescharacteristic
602C22C2×#1058748811yescharacteristic
603C22#1176284711yescharacteristic
604C22#1176285111yescharacteristic
605C22#1176285111yescharacteristic
606C22C4×#6321911yescharacteristic
607C22C4×#6321911yescharacteristic
608C22C4×#6321911yescharacteristic
609C22C4×#6321911yescharacteristic
610C22#1176291111yescharacteristic
611C22#1176291111yescharacteristic
612C22#1176291711yescharacteristic
613C22#1176292211yescharacteristic
614C22#1176295011yescharacteristic
615C22#1176295611yescharacteristic
616C22#1176296211yescharacteristic
617C22#1176297311yescharacteristic
618C22#1176301011yescharacteristic
619C22#1176301511yescharacteristic
620C22#1176302511yescharacteristic
621C22#1176303211yescharacteristic
622C22#1176309511yescharacteristic
623C22#1176310011yescharacteristic
624C22#1176311011yescharacteristic
625C22#1176311711yescharacteristic
626C22#1176312811yescharacteristic
627C22#1176313411yescharacteristic
628C22#1176314011yescharacteristic
629C22#1176315111yescharacteristic
630C4—24no—
631C4—42no—
632C4—684no—
633C4—684no—
634C4—1362no—
635C4—1362no—
636C4C22⋊C4×Dic1711yescharacteristic
637C4C4⋊C4×Dic1711yescharacteristic
638C4#1176269211yescharacteristic
639C4#1176269511yescharacteristic
640C4#1176269611yescharacteristic
641C4#1176270211yescharacteristic
642C4#1176270611yescharacteristic
643C4#1176271311yescharacteristic
644C2#1452701811yescharacteristic
645C2C4×#1058748811yescharacteristic
646C2#1452868111yescharacteristic
647C2#1452897911yescharacteristic
648C2#1452898511yescharacteristic
649C2#1452904811yescharacteristic
650C2#1452905511yescharacteristic
651C2#1452911711yescharacteristic
652C2#1452913811yescharacteristic
653C2#1452936311yescharacteristic
654C2#1452937011yescharacteristic
655C2#1452941211yescharacteristic
656C2#1452941911yescharacteristic
657C2#1452954811yescharacteristic
658C2#1452955411yescharacteristic
subgroupG/H
centerC24C2×D68
commutatorC2×C4×C17C2×C42
FrattiniC23×C4C22×D17
FittingC2×C17×#336C2
socle, prime radicalC24×C17C2×D4
cosocleC23×C4×C17C23
hypercenterC2×#336D17
hypocenterC17#10908
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
15. C2×#10587488C4semidirect
23. #11762572C4semidirect
27. C17×#336C4semidirect
156. C2×C8×C17C42semidirect
207. C2×C4×C17#106semidirect
341. #336Dic17semidirect
415. C17#10908semidirect
486. C2×C8C4×Dic17semidirect
564. C2×C4#10587488semidirect

Maximal subgroups

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

subgroupindex
C22×#105874882
C2×C4×C4⋊Dic172
C2×#117625722
#145270142
C2×C17×#3362
#1090817