Finite Group Databasebeta

← #16957689

Subgroups — #16957689

Order 4352.

2950 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic17C211yesmaximal, characteristic
2C23×C4⋊Dic17C211yesmaximal, characteristic, complemented
3C2×#11762689C211yesmaximal, characteristic
4C2×#11762684C211yesmaximal, characteristic, complemented
5C2×#11762684C212yesmaximal, complemented
6#14527049C212yesmaximal, complemented
7#14527029C212yesmaximal, complemented
8#14527018C212yesmaximal, complemented
9#14527007C211yesmaximal, characteristic, complemented
10#14527006C211yesmaximal, characteristic, complemented
11C2×C17×#386C211yesmaximal, characteristic
12C24×Dic17C2211yescharacteristic
13C24×Dic17C2211yescharacteristic
14C24×Dic17C2211yescharacteristic
15C2×D4×Dic17—24no—
16C2×D4×Dic17—24no—
17C2×D4×Dic17—24no—
18C22×C4⋊Dic17—28no—
19C22×C4⋊Dic17—24no—
20C22×C4⋊Dic17C2212yes—
21C22×C4⋊Dic17C2211yescharacteristic
22C22×C4⋊Dic17C2212yes—
23C22×C4⋊Dic17C2212yes—
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2212yes—
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29#11762689—24no—
30#11762684—24no—
31#11762684—28no—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2212yes—
36C2×#10587502C2212yes—
37C2×#10587502C2212yes—
38C23×D4×C17C2211yescharacteristic
39C24×C4×C17C2211yescharacteristic
40C22×C22⋊C4×C17C2211yescharacteristic
41C22×C22⋊C4×C17C2212yes—
42C17×#386C418yescomplemented
43C2×C17×#95C2212yes—
44C25×C17C2311yescharacteristic
45C25×C17C2311yescharacteristic
46C22×D4×C17—22no—
47C22×D4×C17—22no—
48C22×D4×C17—22no—
49C22×D4×C17—22no—
50C22×D4×C17C2×C414yes—
51C22×D4×C17D414yes—
52C22×D4×C17Q814yes—
53C23×C4×C17—22no—
54C23×C4×C17—22no—
55C23×C4×C17—24no—
56C23×C4×C17—24no—
57C23×C4×C17C2×C414yescomplemented
58C23×C4×C17C2312yes—
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2312yes—
61C23×Dic17—22no—
62C23×Dic17—22no—
63C23×Dic17—22no—
64C23×Dic17—22no—
65C23×Dic17—24no—
66C23×Dic17—24no—
67C23×Dic17—22no—
68C23×Dic17—22no—
69C23×Dic17—22no—
70C23×Dic17—22no—
71C23×Dic17—24no—
72C23×Dic17—42no—
73C23×Dic17—42no—
74C23×Dic17—42no—
75C23×Dic17D414yes—
76C23×Dic17C2312yes—
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2312yes—
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C2×C22⋊C4×C17—22no—
83C2×C22⋊C4×C17—22no—
84C2×C22⋊C4×C17—24no—
85C2×C22⋊C4×C17—24no—
86C2×C22⋊C4×C17C2×C414yescomplemented
87C2×C22⋊C4×C17C2×C418yescomplemented
88C2×C22⋊Dic17—22no—
89C2×C22⋊Dic17—22no—
90C2×C22⋊Dic17—22no—
91C2×C22⋊Dic17—22no—
92C2×C22⋊Dic17—22no—
93C2×C22⋊Dic17—24no—
94C2×C22⋊Dic17—22no—
95C2×C22⋊Dic17—22no—
96C2×C22⋊Dic17—22no—
97C2×C22⋊Dic17—24no—
98C2×C22⋊Dic17—42no—
99C2×C22⋊Dic17D414yes—
100D4×Dic17—232no—
101C2×C4⋊Dic17—232no—
102C2×C4⋊Dic17—24no—
103C2×C4⋊Dic17—22no—
104C2×C4⋊Dic17—24no—
105C2×C4⋊Dic17—24no—
106C2×C4⋊Dic17—24no—
107C2×C4⋊Dic17—24no—
108C2×C4⋊Dic17—22no—
109C2×C4⋊Dic17—22no—
110C2×C4⋊Dic17—24no—
111C2×C4⋊Dic17—24no—
112C2×C4⋊Dic17—42no—
113C2×C4⋊Dic17D418yescomplemented
114C2×C4×Dic17—22no—
115C2×C4×Dic17—22no—
116C2×C4×Dic17—22no—
117C17×#95C2×C418yescomplemented
118#10587502—24no—
119#10587502—24no—
120#10587502—24no—
121#10587502—24no—
122#10587502—24no—
123#10587502—42no—
124C24×C17—22no—
125C24×C17—22no—
126C24×C17—22no—
127C24×C17—22no—
128C24×C17—21no—
129C24×C17—21no—
130C24×C17—22no—
131C24×C17—21no—
132C24×C17—21no—
133C24×C17—22no—
134C24×C17—22no—
135C24×C17—22no—
136C24×C17C22×C412yes—
137C24×C17C22×C412yes—
138C24×C17C2×D412yes—
139C24×C17C2×D412yes—
140C24×C17C2×D412yes—
141C24×C17C2×D412yes—
142C24×C17C2×Q812yes—
143C24×C17C2×Q812yes—
144C24×C17#4112yes—
145C24×C17#4112yes—
146C24×C17C2411yescharacteristic
147C2×D4×C17—28no—
148C2×D4×C17—28no—
149C2×D4×C17—28no—
150C2×D4×C17—28no—
151C2×D4×C17—28no—
152C2×D4×C17—28no—
153C2×D4×C17C4⋊C4116yescomplemented
154C22×C4×C17—216no—
155C22×C4×C17—28no—
156C22×C4×C17—28no—
157C22×C4×C17—28no—
158C22×C4×C17—22no—
159C22×C4×C17—22no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—22no—
163C22×C4×C17—22no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—216no—
167C22×C4×C17—22no—
168C22×C4×C17—22no—
169C22×C4×C17—22no—
170C22×C4×C17—22no—
171C22×C4×C17—22no—
172C22×C4×C17—22no—
173C22×C4×C17C22×C414yes—
174C22×C4×C17C22×C412yes—
175C22×C4×C17C22×C414yes—
176C22×C4×C17C2×D412yes—
177C22×C4×C17C2×D414yes—
178C22×C4×C17C2×Q812yes—
179C22×C4×C17#4114yes—
180C22×Dic17—21no—
181C22×Dic17—21no—
182C22×Dic17—22no—
183C22×Dic17—28no—
184C22×Dic17—28no—
185C22×Dic17—28no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17—22no—
191C22×Dic17—22no—
192C22×Dic17—21no—
193C22×Dic17—21no—
194C22×Dic17—21no—
195C22×Dic17—21no—
196C22×Dic17—21no—
197C22×Dic17—21no—
198C22×Dic17—22no—
199C22×Dic17—22no—
200C22×Dic17—22no—
201C22×Dic17—22no—
202C22×Dic17—22no—
203C22×Dic17—22no—
204C22×Dic17—28no—
205C22×Dic17—22no—
206C22×Dic17—22no—
207C22×Dic17—22no—
208C22×Dic17—22no—
209C22×Dic17—22no—
210C22×Dic17—22no—
211C22×Dic17—22no—
212C22×Dic17—44no—
213C22×Dic17—48no—
214C22×Dic17—48no—
215C22×Dic17—48no—
216C22×Dic17—48no—
217C22×Dic17—48no—
218C22×Dic17—48no—
219C22×Dic17—44no—
220C22×Dic17—44no—
221C22×Dic17—44no—
222C22×Dic17—44no—
223C22×Dic17C2×D412yes—
224C22×Dic17C2×D414yes—
225C22×Dic17C2×D412yes—
226C22×Dic17C2×D412yes—
227C22×Dic17C2×D414yes—
228C22×Dic17C2×D412yes—
229C22⋊C4×C17—28no—
230C22⋊C4×C17—216no—
231C22⋊Dic17—28no—
232C22⋊Dic17—28no—
233C22⋊Dic17—48no—
234C22⋊Dic17—44no—
235C4⋊Dic17—216no—
236C4⋊Dic17—28no—
237C4⋊Dic17—216no—
238C4⋊Dic17—48no—
239C4×Dic17—28no—
240#14015—171nomaximal, Sylow
241C23×C17—24no—
242C23×C17—24no—
243C23×C17—22no—
244C23×C17—22no—
245C23×C17—24no—
246C23×C17—22no—
247C23×C17—22no—
248C23×C17—24no—
249C23×C17—24no—
250C23×C17—24no—
251C23×C17—24no—
252C23×C17—24no—
253C23×C17—24no—
254C23×C17—24no—
255C23×C17—24no—
256C23×C17—24no—
257C23×C17—24no—
258C23×C17—22no—
259C23×C17—22no—
260C23×C17—24no—
261C23×C17—22no—
262C23×C17—22no—
263C23×C17—22no—
264C23×C17—22no—
265C23×C17—24no—
266C23×C17—24no—
267C23×C17—24no—
268C23×C17—24no—
269C23×C17—41no—
270C23×C17—41no—
271C23×C17—42no—
272C23×C17—41no—
273C23×C17—41no—
274C23×C17—42no—
275C23×C17—42no—
276C23×C17—42no—
277C23×C17—42no—
278C23×C17—42no—
279C23×C17C2×C4⋊C414yes—
280C23×C17C2×C4⋊C414yescomplemented
281C23×C17C4×D414yes—
282C23×C17C4×D414yes—
283C23×C17#12014yes—
284C23×C17C22⋊Q814yes—
285C23×C17C22⋊Q814yes—
286C23×C17#12314yes—
287C23×C17C23×C411yescharacteristic
288C23×C17C22×D411yescharacteristic
289C23×C17C22×D411yescharacteristic
290C23×C17C22×D411yescharacteristic
291C23×C17C22×D412yes—
292C23×C17C22×Q811yescharacteristic
293C23×C17C2×#4111yescharacteristic
294C23×C17C2×#4111yescharacteristic
295C23×C17C2×#4112yes—
296C23×C17H(5,𝔽2)12yes—
297C23×C172−1+412yes—
298D4×C17—232no—
299C2×C4×C17—232no—
300C2×C4×C17—24no—
301C2×C4×C17—24no—
302C2×C4×C17—22no—
303C2×C4×C17—22no—
304C2×C4×C17—24no—
305C2×C4×C17—22no—
306C2×C4×C17—22no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—24no—
310C2×C4×C17—24no—
311C2×C4×C17—24no—
312C2×C4×C17—24no—
313C2×C4×C17—24no—
314C2×C4×C17—24no—
315C2×C4×C17—42no—
316C2×C4×C17—42no—
317C2×C4×C17—42no—
318C2×C4×C17—42no—
319C2×C4×C17C2×C4⋊C414yescomplemented
320C2×C4×C17C4×D418yescomplemented
321C2×Dic17—22no—
322C2×Dic17—22no—
323C2×Dic17—24no—
324C2×Dic17—24no—
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—24no—
329C2×Dic17—22no—
330C2×Dic17—22no—
331C2×Dic17—24no—
332C2×Dic17—24no—
333C2×Dic17—24no—
334C2×Dic17—24no—
335C2×Dic17—416no—
336C2×Dic17—416no—
337C2×Dic17—416no—
338C2×Dic17—41no—
339C2×Dic17—42no—
340C2×Dic17—41no—
341C2×Dic17—42no—
342C2×Dic17—41no—
343C2×Dic17—41no—
344C2×Dic17—42no—
345C2×Dic17—42no—
346C2×Dic17—42no—
347C2×Dic17—42no—
348C2×Dic17—42no—
349C2×Dic17—42no—
350C2×Dic17—42no—
351C2×Dic17—42no—
352C2×Dic17—42no—
353C2×Dic17—42no—
354C2×Dic17—42no—
355C2×Dic17—42no—
356C2×Dic17—42no—
357C2×Dic17#12014yes—
358C22×C4×D4—171no—
359C23×C4⋊C4—171no—
360C2×#386—171no—
361C2×#386D1711yescharacteristic
362C2×#385—171no—
363C2×#385—172no—
364#1444—172no—
365#1439—172no—
366#1436—172no—
367C22⋊#95—171no—
368C22⋊#95—171no—
369C22×C17—24no—
370C22×C17—24no—
371C22×C17—28no—
372C22×C17—28no—
373C22×C17—24no—
374C22×C17—24no—
375C22×C17—24no—
376C22×C17—28no—
377C22×C17—28no—
378C22×C17—24no—
379C22×C17—28no—
380C22×C17—24no—
381C22×C17—42no—
382C22×C17—42no—
383C22×C17—44no—
384C22×C17—42no—
385C22×C17—42no—
386C22×C17—42no—
387C22×C17—44no—
388C22×C17—44no—
389C22×C17—42no—
390C22×C17#38518yescomplemented
391C22×C17C22×C4⋊C411yescharacteristic
392C22×C17C2×C4×D411yescharacteristic
393C22×C17C2×C4×D412yes—
394C22×C17C2×C4×D411yescharacteristic
395C22×C17#52012yes—
396C22×C17C2×#12011yescharacteristic
397C22×C17C2×#12011yescharacteristic
398C22×C17C2×C22⋊Q811yescharacteristic
399C22×C17C2×C22⋊Q811yescharacteristic
400C22×C17C2×#12311yescharacteristic
401C22×C17#52511yescharacteristic
402C22×C17#52512yes—
403C22×C17#53411yescharacteristic
404C22×C17#53611yescharacteristic
405C22×C17#53912yes—
406C22×C17D4212yes—
407C22×C17D4212yes—
408C22×C17#54712yes—
409C22×C17#54712yes—
410C22×C17#54812yes—
411C22×C17D4×Q812yes—
412C22×C17#55312yes—
413C22×C17#55412yes—
414C4×C17—24no—
415C4×C17—28no—
416C4×C17—44no—
417Dic17—24no—
418Dic17—42no—
419Dic17—42no—
420Dic17—44no—
421Dic17—42no—
422Dic17—82no—
423C23×D4C2×D1711yescharacteristic
424C24×C4—171no—
425C24×C4—171no—
426C24×C4—171no—
427C24×C4C2×D1711yescharacteristic
428C2×C4×D4—344no—
429C2×C4×D4—344no—
430C2×C4×D4—344no—
431C22×C4⋊C4—172no—
432C22×C4⋊C4—172no—
433C22×C4⋊C4—171no—
434C22×C4⋊C4—172no—
435C22×C4⋊C4—348no—
436C22×C4⋊C4—344no—
437C22×C22⋊C4—171no—
438C22×C22⋊C4—171no—
439C22×C22⋊C4—171no—
440C22×C22⋊C4—172no—
441C22×C22⋊C4C2×D1711yescharacteristic
442C22×C22⋊C4C2×D1712yes—
443C22×C42—171no—
444#386—344no—
445#386Dic1718yescomplemented
446#385—344no—
447#385—348no—
448C2×#95—172no—
449C2×#95—172no—
450C2×#95—172no—
451C2×#95—172no—
452C2×#95—172no—
453C2×#95—172no—
454C2×#95C2×D1712yes—
455C2×C17—28no—
456C2×C17—44no—
457C2×C17C2×#38511yescharacteristic
458C2×C17C4×#12011yescharacteristic
459C2×C17#232211yescharacteristic
460C2×C17D4×C4⋊C412yes—
461C2×C17#236112yes—
462C2×C17#240311yescharacteristic
463C2×C17#240611yescharacteristic
464C2×C17#240911yescharacteristic
465C2×C17#244312yes—
466C2×C17#244912yes—
467C2×C17#257911yescharacteristic
468C25C22×D1711yescharacteristic
469C25C22×D1711yescharacteristic
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4Dic3414yes—
475C22×D4D6814yes—
476C22×D4C2×Dic1714yes—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—171no—
482C23×C4—171no—
483C23×C4—171no—
484C23×C4—172no—
485C23×C4—171no—
486C23×C4—174no—
487C23×C4—172no—
488C23×C4—344no—
489C23×C4—344no—
490C23×C4—342no—
491C23×C4—342no—
492C23×C4—344no—
493C23×C4—342no—
494C23×C4—342no—
495C23×C4—342no—
496C23×C4—342no—
497C23×C4—342no—
498C23×C4—342no—
499C23×C4—682no—
500C23×C4—682no—
501C23×C4—682no—
502C23×C4C2×Dic1714yescomplemented
503C23×C4C22×D1712yes—
504C23×C4C22×D1711yescharacteristic
505C23×C4C22×D1712yes—
506C4×D4—3432no—
507C2×C4⋊C4—178no—
508C2×C4⋊C4—344no—
509C2×C4⋊C4—344no—
510C2×C4⋊C4—344no—
511C2×C4⋊C4—344no—
512C2×C4⋊C4—342no—
513C2×C4⋊C4—342no—
514C2×C4⋊C4—3432no—
515C2×C4⋊C4—342no—
516C2×C4⋊C4—344no—
517C2×C4⋊C4—344no—
518C2×C4⋊C4—344no—
519C2×C4⋊C4—682no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—174no—
525C2×C22⋊C4—342no—
526C2×C22⋊C4—342no—
527C2×C22⋊C4—342no—
528C2×C22⋊C4—342no—
529C2×C22⋊C4—342no—
530C2×C22⋊C4—344no—
531C2×C22⋊C4—344no—
532C2×C22⋊C4—342no—
533C2×C22⋊C4—342no—
534C2×C22⋊C4—342no—
535C2×C22⋊C4—682no—
536C2×C22⋊C4C2×Dic1714yescomplemented
537C2×C22⋊C4C2×Dic1718yescomplemented
538C2×C42—342no—
539C2×C42—342no—
540C2×C42—342no—
541#95—344no—
542#95—344no—
543#95—344no—
544#95—344no—
545#95—344no—
546#95—682no—
547#95C2×Dic1718yescomplemented
548C17#1401511yescharacteristic, complemented, Sylow
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—21no—
555C24—21no—
556C24—22no—
557C24—21no—
558C24—21no—
559C24—22no—
560C24—22no—
561C24C2×Dic3412yes—
562C24C2×Dic3412yes—
563C24C2×D6812yes—
564C24C2×D6812yes—
565C24D4×D1712yes—
566C24D4×D1712yes—
567C24#6325412yes—
568C24#6325412yes—
569C24C22×Dic1712yes—
570C24C22×Dic1712yes—
571C24C23×D1711yescharacteristic
572C2×D4—28no—
573C2×D4—28no—
574C2×D4—28no—
575C2×D4—28no—
576C2×D4—28no—
577C2×D4—28no—
578C2×D4C4⋊Dic17116yescomplemented
579C22×C4—28no—
580C22×C4—216no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—28no—
591C22×C4—216no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—174no—
599C22×C4—172no—
600C22×C4—172no—
601C22×C4—172no—
602C22×C4—174no—
603C22×C4—172no—
604C22×C4—348no—
605C22×C4—341no—
606C22×C4—341no—
607C22×C4—342no—
608C22×C4—348no—
609C22×C4—348no—
610C22×C4—342no—
611C22×C4—341no—
612C22×C4—341no—
613C22×C4—341no—
614C22×C4—342no—
615C22×C4—342no—
616C22×C4—341no—
617C22×C4—341no—
618C22×C4—341no—
619C22×C4—342no—
620C22×C4—342no—
621C22×C4—342no—
622C22×C4—342no—
623C22×C4—342no—
624C22×C4—342no—
625C22×C4—342no—
626C22×C4—342no—
627C22×C4—342no—
628C22×C4—348no—
629C22×C4—342no—
630C22×C4—342no—
631C22×C4—342no—
632C22×C4—342no—
633C22×C4—342no—
634C22×C4—342no—
635C22×C4—342no—
636C22×C4—684no—
637C22×C4—684no—
638C22×C4—688no—
639C22×C4—688no—
640C22×C4—688no—
641C22×C4—688no—
642C22×C4—688no—
643C22×C4—688no—
644C22×C4—684no—
645C22×C4—684no—
646C22×C4—684no—
647C22×C4C2×Dic3412yes—
648C22×C4C2×D6812yes—
649C22×C4D4×D1714yes—
650C22×C4#6325414yes—
651C22×C4C22×Dic1714yes—
652C22×C4C22×Dic1712yes—
653C22×C4C22×Dic1714yes—
654C4⋊C4—3416no—
655C4⋊C4—3416no—
656C4⋊C4—348no—
657C4⋊C4—688no—
658C22⋊C4—28no—
659C22⋊C4—216no—
660C22⋊C4—348no—
661C22⋊C4—348no—
662C22⋊C4—688no—
663C22⋊C4—684no—
664C42—348no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—22no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—22no—
686C23—22no—
687C23—24no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—24no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—41no—
697C23—41no—
698C23—42no—
699C23—41no—
700C23—41no—
701C23—42no—
702C23—42no—
703C23#1058756414yes—
704C23#1058756414yes—
705C23#1058756814yes—
706C23#1058757214yes—
707C23C2×C4⋊Dic1714yes—
708C23C2×C4⋊Dic1714yescomplemented
709C23D4×Dic1714yes—
710C23D4×Dic1714yes—
711C23C22×Dic3411yescharacteristic
712C23C22×D6811yescharacteristic
713C23C2×D4×D1711yescharacteristic
714C23C2×D4×D1712yes—
715C23C2×D4×D1711yescharacteristic
716C23C2×#6325412yes—
717C23C2×#6325411yescharacteristic
718C23C2×#6325411yescharacteristic
719C23#1058769612yes—
720C23#1058769712yes—
721C23C23×Dic1711yescharacteristic
722D4—232no—
723C2×C4—232no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—174no—
744C2×C4—342no—
745C2×C4—342no—
746C2×C4—344no—
747C2×C4—344no—
748C2×C4—344no—
749C2×C4—344no—
750C2×C4—342no—
751C2×C4—342no—
752C2×C4—342no—
753C2×C4—342no—
754C2×C4—342no—
755C2×C4—344no—
756C2×C4—344no—
757C2×C4—344no—
758C2×C4—6816no—
759C2×C4—6816no—
760C2×C4—6816no—
761C2×C4—682no—
762C2×C4—681no—
763C2×C4—682no—
764C2×C4—681no—
765C2×C4—681no—
766C2×C4—682no—
767C2×C4—681no—
768C2×C4—682no—
769C2×C4—682no—
770C2×C4—682no—
771C2×C4—682no—
772C2×C4—682no—
773C2×C4—682no—
774C2×C4—682no—
775C2×C4—682no—
776C2×C4—682no—
777C2×C4—682no—
778C2×C4—682no—
779C2×C4—682no—
780C2×C4C2×C4⋊Dic1714yescomplemented
781C2×C4D4×Dic1718yescomplemented
782C22—24no—
783C22—24no—
784C22—24no—
785C22—28no—
786C22—24no—
787C22—28no—
788C22—24no—
789C22—28no—
790C22—24no—
791C22—28no—
792C22—28no—
793C22—24no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—44no—
801C22—42no—
802C22—44no—
803C22#1176268418yescomplemented
804C22C22×C4⋊Dic1711yescharacteristic
805C22C2×D4×Dic1712yes—
806C22C2×D4×Dic1711yescharacteristic
807C22C2×D4×Dic1711yescharacteristic
808C22#1176329212yes—
809C22#120×D1711yescharacteristic
810C22C2×#1058756811yescharacteristic
811C22C2×#1058756411yescharacteristic
812C22C2×#1058756411yescharacteristic
813C22C2×#1058757211yescharacteristic
814C22#1176331511yescharacteristic
815C22#1176331512yes—
816C22#1176337011yescharacteristic
817C22#1176338111yescharacteristic
818C22#1176340312yes—
819C22#1176344312yes—
820C22D4×D6812yes—
821C22#1176345912yes—
822C22#1176346312yes—
823C22#1176346512yes—
824C22D4×Dic3412yes—
825C22#1176351112yes—
826C22#1176351612yes—
827C4—24no—
828C4—28no—
829C4—44no—
830C4—344no—
831C4—682no—
832C4—684no—
833C4—682no—
834C4—682no—
835C4—1362no—
836C2—28no—
837C2—44no—
838C2C2×#1176268411yescharacteristic
839C2#120×Dic1711yescharacteristic
840C2#1453145611yescharacteristic
841C2D4×C4⋊Dic1712yes—
842C2#1453180412yes—
843C2#1453209611yescharacteristic
844C2#1453211811yescharacteristic
845C2#1453214611yescharacteristic
846C2#1453251712yes—
847C2#1453259912yes—
848C2#1453412811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#386C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC2×#386D17
hypocenterC17#14015
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C23×C4⋊Dic17C2semidirect
4. C2×#11762684C2semidirect
5. C2×#11762684C2semidirect
6. #14527049C2semidirect
7. #14527029C2semidirect
8. #14527018C2semidirect
9. #14527007C2semidirect
10. #14527006C2semidirect
42. C17×#386C4semidirect
57. C23×C4×C17C2×C4semidirect
86. C2×C22⋊C4×C17C2×C4semidirect
87. C2×C22⋊C4×C17C2×C4semidirect
113. C2×C4⋊Dic17D4semidirect
117. C17×#95C2×C4semidirect
153. C2×D4×C17C4⋊C4semidirect
280. C23×C17C2×C4⋊C4semidirect
319. C2×C4×C17C2×C4⋊C4semidirect
320. C2×C4×C17C4×D4semidirect
390. C22×C17#385semidirect
445. #386Dic17semidirect
502. C23×C4C2×Dic17semidirect
536. C2×C22⋊C4C2×Dic17semidirect
537. C2×C22⋊C4C2×Dic17semidirect
547. #95C2×Dic17semidirect
548. C17#14015semidirect
578. C2×D4C4⋊Dic17semidirect
708. C23C2×C4⋊Dic17semidirect
780. C2×C4C2×C4⋊Dic17semidirect
781. C2×C4D4×Dic17semidirect
803. C22#11762684semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic172
C23×C4⋊Dic172
C2×#117626892
C2×#117626842
#145270492
#145270292
#145270182
#145270072
#145270062
C2×C17×#3862
#1401517