Finite Group Databasebeta

← #16958287

Subgroups — #16958287

Order 4352.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587578C211yesmaximal, characteristic
2C2×#11762701C211yesmaximal, characteristic
3C2×#11762690C211yesmaximal, characteristic, complemented
4C2×#11762683C211yesmaximal, characteristic
5C2×C4×C4⋊Dic17C211yesmaximal, characteristic, complemented
6#14527049C211yesmaximal, characteristic, complemented
7#14527038C211yesmaximal, characteristic, complemented
8#14527032C211yesmaximal, characteristic
9#14527030C211yesmaximal, characteristic
10#14527022C211yesmaximal, characteristic
11#14527018C211yesmaximal, characteristic, complemented
12#14527018C211yesmaximal, characteristic, complemented
13#14527008C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic
15C17×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C2×#10587578—24no—
18C2×#10587578—24no—
19C2×#10587578—24no—
20C22×C4⋊Dic17C2211yescharacteristic
21C22×C4⋊Dic17C2211yescharacteristic
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C4⋊Dic17C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34#11762701—24no—
35#11762690—24no—
36#11762683C418yescomplemented
37C4×C4⋊Dic17—24no—
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C22×C4⋊C4×C17C2211yescharacteristic
52C22×C42×C17C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C24×D17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C22×C4×D17—22no—
74C22×C4×D17—22no—
75C22×C4×D17—22no—
76C22×C4×D17—22no—
77C22×C4×D17—22no—
78C22×C4×D17—22no—
79C22×C4×D17C2×C414yes—
80C2×C4⋊C4×C17—22no—
81C2×C4⋊C4×C17—22no—
82C2×C4⋊C4×C17D414yes—
83C2×C42×C17—22no—
84C2×C42×C17—22no—
85C2×C42×C17—22no—
86C2×#63227—22no—
87C2×#63227—22no—
88C2×#63227—22no—
89C2×#63227—22no—
90C2×#63227—22no—
91C2×#63227—22no—
92C2×#63227—22no—
93C2×#63227—22no—
94C2×#63227—22no—
95C2×#63227—22no—
96C2×#63227—22no—
97C2×#63227—22no—
98C2×#63227—22no—
99C2×#63227—41no—
100C2×#63227—41no—
101C2×#63227C2×C414yes—
102C2×#63227C2×C414yes—
103C2×#63227D414yes—
104C2×C4⋊Dic17—22no—
105C2×C4⋊Dic17—22no—
106C2×C4⋊Dic17—22no—
107C2×C4⋊Dic17—22no—
108C2×C4⋊Dic17—22no—
109C2×C4⋊Dic17—22no—
110C2×C4⋊Dic17—22no—
111C2×C4⋊Dic17—22no—
112C2×C4⋊Dic17—22no—
113C2×C4⋊Dic17—22no—
114C2×C4⋊Dic17—41no—
115C2×C4⋊Dic17C2×C414yes—
116C2×#63225—22no—
117C2×#63225—22no—
118C2×#63225C2×C414yes—
119C2×C4×Dic17—22no—
120C2×C4×Dic17—22no—
121C2×C4×Dic17—22no—
122C2×C4×Dic17—22no—
123C2×C4×Dic17—22no—
124C2×C4×Dic17—22no—
125C2×C4×Dic17—22no—
126C2×C4×Dic17—22no—
127C2×C4×Dic17D414yes—
128#10587578—232no—
129C17×#95—22no—
130C17×#95—22no—
131C17×#95—22no—
132C17×#95—22no—
133C17×#95C2×C414yes—
134#10587502—22no—
135#10587502—22no—
136#10587502—22no—
137#10587502—22no—
138#10587502—22no—
139#10587502—22no—
140#10587502—22no—
141#10587502—22no—
142#10587502—22no—
143#10587502—41no—
144#10587502—41no—
145#10587502—41no—
146#10587502C2×C414yes—
147C24×C17C2411yescharacteristic
148C23×D17—21no—
149C23×D17—21no—
150C23×D17—21no—
151C23×D17—21no—
152C23×D17—21no—
153C23×D17—21no—
154C23×D17—21no—
155C23×D17—21no—
156C23×D17—21no—
157C23×D17—21no—
158C23×D17—21no—
159C23×D17—21no—
160C23×D17C22×C412yes—
161C23×D17C2×D412yes—
162C23×D17#4112yes—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17C22×C412yes—
201C22×C4×C17C22×C412yes—
202C22×C4×C17C22×C412yes—
203C22×C4×C17C2×D412yes—
204C22×C4×C17C2×D412yes—
205C22×C4×C17C2×D412yes—
206C22×C4×C17C2×D412yes—
207C22×C4×C17C2×D412yes—
208C22×C4×C17#4112yes—
209C22×C4×C17#4112yes—
210C22×C4×C17#4112yes—
211C22×C4×C17#4112yes—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—21no—
218C22×Dic17—21no—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17C22×C412yes—
254C22×Dic17C22×C412yes—
255C22×Dic17C22×C412yes—
256C22×Dic17C2×D412yes—
257C22×Dic17C2×D412yes—
258C22×Dic17C2×D412yes—
259C22×Dic17#4112yes—
260C22×Dic17#4112yes—
261C2×C4×D17—28no—
262C2×C4×D17—28no—
263C2×C4×D17—28no—
264C2×C4×D17—28no—
265C2×C4×D17—28no—
266C2×C4×D17—28no—
267C2×C4×D17—28no—
268C4⋊C4×C17—28no—
269C42×C17—28no—
270#63227—28no—
271#63227—28no—
272#63227—28no—
273#63227—28no—
274#63227—44no—
275#63227—44no—
276C4⋊Dic17—28no—
277C4⋊Dic17—28no—
278C4⋊Dic17—28no—
279C4⋊Dic17—44no—
280#63225—28no—
281C4×Dic17—28no—
282C4×Dic17—28no—
283C4×Dic17—44no—
284#14063—171nomaximal, Sylow
285C23×C17C23×C411yescharacteristic
286C23×C17C22×D411yescharacteristic
287C23×C17C22×D411yescharacteristic
288C23×C17C22×D411yescharacteristic
289C23×C17C2×#4111yescharacteristic
290C23×C17C2×#4111yescharacteristic
291C23×C17C2×#4111yescharacteristic
292C23×C17C2×#4111yescharacteristic
293C23×C17C2×#4111yescharacteristic
294C23×C17C2×#4111yescharacteristic
295C23×C17C2×#4111yescharacteristic
296C23×C17H(5,𝔽2)11yescharacteristic
297C23×C172−1+411yescharacteristic
298C23×C172−1+411yescharacteristic
299C23×C172−1+411yescharacteristic
300C22×D17—22no—
301C22×D17—22no—
302C22×D17—22no—
303C22×D17—22no—
304C22×D17—22no—
305C22×D17—22no—
306C22×D17—22no—
307C22×D17—22no—
308C22×D17—22no—
309C22×D17—22no—
310C22×D17—22no—
311C22×D17—22no—
312C22×D17—22no—
313C22×D17—22no—
314C22×D17—22no—
315C22×D17—22no—
316C22×D17—22no—
317C22×D17—22no—
318C22×D17—41no—
319C22×D17—41no—
320C22×D17—41no—
321C22×D17—41no—
322C22×D17—41no—
323C22×D17—41no—
324C22×D17—41no—
325C22×D17—41no—
326C22×D17—41no—
327C22×D17—41no—
328C22×D17—41no—
329C22×D17—41no—
330C22×D17—41no—
331C22×D17—41no—
332C22×D17—41no—
333C22×D17—41no—
334C22×D17C4×D414yes—
335C2×C4×C17—22no—
336C2×C4×C17—22no—
337C2×C4×C17—22no—
338C2×C4×C17—22no—
339C2×C4×C17—22no—
340C2×C4×C17—22no—
341C2×C4×C17—22no—
342C2×C4×C17—22no—
343C2×C4×C17—22no—
344C2×C4×C17—22no—
345C2×C4×C17—22no—
346C2×C4×C17—22no—
347C2×C4×C17—22no—
348C2×C4×C17—22no—
349C2×C4×C17—22no—
350C2×C4×C17—22no—
351C2×C4×C17—22no—
352C2×C4×C17—22no—
353C2×C4×C17—22no—
354C2×C4×C17—22no—
355C2×C4×C17—22no—
356C2×C4×C17—22no—
357C2×C4×C17—22no—
358C2×C4×C17—22no—
359C2×C4×C17—22no—
360C2×C4×C17—22no—
361C2×C4×C17—22no—
362C2×C4×C17—41no—
363C2×C4×C17—41no—
364C2×C4×C17—41no—
365C2×C4×C17—41no—
366C2×C4×C17—41no—
367C2×C4×C17—41no—
368C2×C4×C17—41no—
369C2×C4×C17—41no—
370C2×C4×C17—41no—
371C2×C4×C17—41no—
372C2×C4×C17—41no—
373C2×C4×C17—41no—
374C2×C4×C17—41no—
375C2×C4×C17—41no—
376C2×C4×C17—41no—
377C2×C4×C17—41no—
378C2×C4×C17—41no—
379C2×C4×C17—41no—
380C2×C4×C17—41no—
381C2×C4×C17#11714yescomplemented
382C2×C4×C17C4×D414yes—
383C2×C4×C17#12014yes—
384C2×Dic17—22no—
385C2×Dic17—22no—
386C2×Dic17—22no—
387C2×Dic17—22no—
388C2×Dic17—22no—
389C2×Dic17—22no—
390C2×Dic17—22no—
391C2×Dic17—22no—
392C2×Dic17—22no—
393C2×Dic17—22no—
394C2×Dic17—22no—
395C2×Dic17—22no—
396C2×Dic17—22no—
397C2×Dic17—22no—
398C2×Dic17—22no—
399C2×Dic17—22no—
400C2×Dic17—22no—
401C2×Dic17—22no—
402C2×Dic17—22no—
403C2×Dic17—22no—
404C2×Dic17—22no—
405C2×Dic17—41no—
406C2×Dic17—41no—
407C2×Dic17—41no—
408C2×Dic17—41no—
409C2×Dic17—41no—
410C2×Dic17—41no—
411C2×Dic17—41no—
412C2×Dic17—41no—
413C2×Dic17—41no—
414C2×Dic17—41no—
415C2×Dic17—41no—
416C2×Dic17—41no—
417C2×Dic17—41no—
418C2×Dic17—41no—
419C2×Dic17—41no—
420C2×Dic17—41no—
421C2×Dic17—41no—
422C2×Dic17—41no—
423C2×Dic17—41no—
424C2×Dic17—41no—
425C2×Dic17—41no—
426C2×Dic17—41no—
427C2×Dic17—41no—
428C2×Dic17—41no—
429C2×Dic17—41no—
430C2×Dic17—41no—
431C2×Dic17—41no—
432C2×Dic17C4×D414yes—
433C4×D17—232no—
434C22×#117—171no—
435C2×#388—171no—
436C2×#387—171no—
437C2×#385—171no—
438C2×C4×C4⋊C4—171no—
439#1444—171no—
440#1441—171no—
441#1440—171no—
442#1439—171no—
443#1437—171no—
444#1436—171no—
445#1436—171no—
446#1436D1711yescharacteristic, complemented
447#1434—171no—
448C22⋊#95—171no—
449C22×C17C2×#11711yescharacteristic
450C22×C17C2×C4×D411yescharacteristic
451C22×C17C2×C4×D411yescharacteristic
452C22×C17C2×C4×D411yescharacteristic
453C22×C17C4×#4111yescharacteristic
454C22×C17#51911yescharacteristic
455C22×C17#52011yescharacteristic
456C22×C17C2×#12011yescharacteristic
457C22×C17#52511yescharacteristic
458C22×C17#52511yescharacteristic
459C22×C17#52511yescharacteristic
460C22×C17#52511yescharacteristic
461C22×C17#52511yescharacteristic
462C22×C17#52911yescharacteristic
463C22×C17#52911yescharacteristic
464C22×C17#53611yescharacteristic
465C22×C17#53711yescharacteristic
466C22×C17#54111yescharacteristic
467C22×C17#54211yescharacteristic
468C22×C17#54611yescharacteristic
469C22×C17#54711yescharacteristic
470C22×C17#54711yescharacteristic
471C22×C17#54711yescharacteristic
472C22×C17#54711yescharacteristic
473C22×C17#54711yescharacteristic
474C22×C17#54811yescharacteristic
475C22×C17#55011yescharacteristic
476C22×C17#55111yescharacteristic
477C22×C17#55211yescharacteristic
478C22×C17#55211yescharacteristic
479C22×C17#55211yescharacteristic
480C22×C17#55211yescharacteristic
481C22×C17#55511yescharacteristic
482C22×C17#55611yescharacteristic
483C22×C17#55611yescharacteristic
484C2×D17—24no—
485C2×D17—24no—
486C2×D17—24no—
487C2×D17—42no—
488C2×D17—42no—
489C2×D17—42no—
490C2×D17—42no—
491C2×D17—42no—
492C2×D17—42no—
493C2×D17—42no—
494C2×D17—42no—
495C2×D17—42no—
496C2×D17—42no—
497C2×D17—42no—
498C2×D17—42no—
499C4×C17—24no—
500C4×C17—24no—
501C4×C17—24no—
502C4×C17—42no—
503C4×C17—42no—
504C4×C17—42no—
505C4×C17—81no—
506Dic17—24no—
507Dic17—42no—
508Dic17—42no—
509Dic17—42no—
510Dic17—42no—
511Dic17—42no—
512Dic17—81no—
513C24×C4—171no—
514C2×#117—344no—
515C2×#117—344no—
516C2×#117—344no—
517C22×C4⋊C4—171no—
518C22×C4⋊C4—171no—
519C22×C4⋊C4—171no—
520C22×C4⋊C4—171no—
521C22×C4⋊C4—171no—
522C22×C4⋊C4C2×D1711yescharacteristic
523C22×C22⋊C4—171no—
524C22×C22⋊C4—171no—
525C22×C22⋊C4—171no—
526C22×C22⋊C4—171no—
527C22×C22⋊C4—171no—
528C22×C22⋊C4—171no—
529C22×C42—171no—
530C22×C42—171no—
531C22×C42—171no—
532C22×C42C2×D1711yescharacteristic
533#388—344no—
534#387—344no—
535#385—178no—
536C4×C4⋊C4—344no—
537C2×#95—171no—
538C2×#95—171no—
539C2×#95—171no—
540C2×#95—171no—
541C2×#95—171no—
542C2×#95—171no—
543C2×#95—171no—
544C2×#95—171no—
545C2×#95—171no—
546C2×#95—171no—
547C2×#95—171no—
548C2×#95—171no—
549C2×#95—171no—
550C2×#95C2×D1711yescharacteristic
551C2×#95C2×D1711yescharacteristic
552C2×#95C2×D1711yescharacteristic
553C2×#95C2×D1711yescharacteristic
554C2×#95C2×D1711yescharacteristic
555C2×C17#229011yescharacteristic
556C2×C17C4×#12011yescharacteristic
557C2×C17#232311yescharacteristic
558C2×C17#234411yescharacteristic
559C2×C17#235411yescharacteristic
560C2×C17#235911yescharacteristic
561C2×C17#236211yescharacteristic
562C2×C17#240611yescharacteristic
563C2×C17#240711yescharacteristic
564C2×C17#247411yescharacteristic
565C2×C17#247511yescharacteristic
566C2×C17#247811yescharacteristic
567C2×C17#247911yescharacteristic
568C2×C17#259911yescharacteristic
569C2×C17#260911yescharacteristic
570D17—44no—
571C25—171no—
572C23×C4—171no—
573C23×C4—171no—
574C23×C4—171no—
575C23×C4—171no—
576C23×C4—171no—
577C23×C4—171no—
578C23×C4—174no—
579C23×C4—171no—
580C23×C4—342no—
581C23×C4—342no—
582C23×C4—342no—
583C23×C4—342no—
584C23×C4—342no—
585C23×C4—342no—
586C23×C4C22×D1711yescharacteristic
587C23×C4C22×D1711yescharacteristic
588C23×C4C22×D1711yescharacteristic
589C23×C4C22×D1711yescharacteristic
590C23×C4C22×D1711yescharacteristic
591C23×C4C22×D1711yescharacteristic
592C23×C4C22×D1711yescharacteristic
593#117—3432no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—174no—
597C2×C4⋊C4—174no—
598C2×C4⋊C4—342no—
599C2×C4⋊C4—342no—
600C2×C4⋊C4—342no—
601C2×C4⋊C4—342no—
602C2×C4⋊C4—342no—
603C2×C4⋊C4—342no—
604C2×C4⋊C4—342no—
605C2×C4⋊C4—342no—
606C2×C4⋊C4—342no—
607C2×C4⋊C4—342no—
608C2×C4⋊C4—342no—
609C2×C4⋊C4—342no—
610C2×C4⋊C4—681no—
611C2×C4⋊C4D6814yes—
612C2×C22⋊C4—174no—
613C2×C22⋊C4—174no—
614C2×C22⋊C4—174no—
615C2×C22⋊C4—342no—
616C2×C22⋊C4—342no—
617C2×C22⋊C4—342no—
618C2×C22⋊C4—342no—
619C2×C22⋊C4—342no—
620C2×C22⋊C4—342no—
621C2×C22⋊C4—342no—
622C2×C22⋊C4—342no—
623C2×C22⋊C4—342no—
624C2×C22⋊C4—342no—
625C2×C22⋊C4—342no—
626C2×C22⋊C4—342no—
627C2×C22⋊C4—342no—
628C2×C22⋊C4—681no—
629C2×C22⋊C4—681no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—174no—
634C2×C42—342no—
635C2×C42—342no—
636C2×C42—342no—
637C2×C42—342no—
638C2×C42—342no—
639C2×C42—342no—
640C2×C42—342no—
641C2×C42—342no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—174no—
647#95—342no—
648#95—342no—
649#95—342no—
650#95—342no—
651#95—342no—
652#95—342no—
653#95—342no—
654#95—342no—
655#95—342no—
656#95—681no—
657#95—681no—
658#95—681no—
659#95C4×D1714yes—
660C17#1406311yescharacteristic, complemented, Sylow
661C24—172no—
662C24—172no—
663C24—172no—
664C24—341no—
665C24—341no—
666C24—341no—
667C24—341no—
668C24—341no—
669C24—341no—
670C24—341no—
671C24—341no—
672C24—341no—
673C24—341no—
674C24—341no—
675C24—341no—
676C24C23×D1711yescharacteristic
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—172no—
715C22×C4—172no—
716C22×C4—172no—
717C22×C4—172no—
718C22×C4—172no—
719C22×C4—172no—
720C22×C4—172no—
721C22×C4—172no—
722C22×C4—348no—
723C22×C4—348no—
724C22×C4—348no—
725C22×C4—348no—
726C22×C4—348no—
727C22×C4—348no—
728C22×C4—341no—
729C22×C4—341no—
730C22×C4—341no—
731C22×C4—341no—
732C22×C4—348no—
733C22×C4—341no—
734C22×C4—341no—
735C22×C4—341no—
736C22×C4—341no—
737C22×C4—341no—
738C22×C4—341no—
739C22×C4—341no—
740C22×C4—341no—
741C22×C4—341no—
742C22×C4—341no—
743C22×C4—341no—
744C22×C4—341no—
745C22×C4—341no—
746C22×C4—341no—
747C22×C4—341no—
748C22×C4—341no—
749C22×C4—341no—
750C22×C4—341no—
751C22×C4—341no—
752C22×C4—341no—
753C22×C4—341no—
754C22×C4—341no—
755C22×C4—341no—
756C22×C4—341no—
757C22×C4—341no—
758C22×C4—341no—
759C22×C4—341no—
760C22×C4—341no—
761C22×C4—341no—
762C22×C4—341no—
763C22×C4—341no—
764C22×C4—341no—
765C22×C4—341no—
766C22×C4—341no—
767C22×C4—341no—
768C22×C4—341no—
769C22×C4—341no—
770C22×C4C2×C4×D1712yes—
771C22×C4C2×C4×D1712yes—
772C22×C4C2×C4×D1712yes—
773C22×C4C2×D6812yes—
774C22×C4C2×D6812yes—
775C22×C4C2×D6812yes—
776C22×C4#6325212yes—
777C22×C4D4×D1712yes—
778C22×C4D4×D1712yes—
779C22×C4#6325412yes—
780C22×C4#6325412yes—
781C22×C4#6325612yes—
782C4⋊C4—28no—
783C4⋊C4—348no—
784C4⋊C4—348no—
785C4⋊C4—348no—
786C4⋊C4—348no—
787C4⋊C4—684no—
788C22⋊C4—348no—
789C22⋊C4—348no—
790C22⋊C4—348no—
791C22⋊C4—348no—
792C22⋊C4—684no—
793C22⋊C4—684no—
794C42—28no—
795C42—348no—
796C42—348no—
797C42—684no—
798C23—174no—
799C23—342no—
800C23—342no—
801C23—342no—
802C23—342no—
803C23—342no—
804C23—342no—
805C23—342no—
806C23—342no—
807C23—342no—
808C23—342no—
809C23—342no—
810C23—342no—
811C23—342no—
812C23—342no—
813C23—342no—
814C23—342no—
815C23—342no—
816C23—342no—
817C23—681no—
818C23—681no—
819C23—681no—
820C23—681no—
821C23—681no—
822C23—681no—
823C23—681no—
824C23—681no—
825C23—681no—
826C23—681no—
827C23—681no—
828C23—681no—
829C23—681no—
830C23—681no—
831C23—681no—
832C23—681no—
833C23C22×C4×D1711yescharacteristic
834C23C22×D6811yescharacteristic
835C23C2×#6325211yescharacteristic
836C23C2×D4×D1711yescharacteristic
837C23C2×D4×D1711yescharacteristic
838C23C2×#6325411yescharacteristic
839C23C2×#6325411yescharacteristic
840C23C2×#6325611yescharacteristic
841C23#1058769411yescharacteristic
842C23#41×D1711yescharacteristic
843C23#41×D1711yescharacteristic
844C23#41×D1711yescharacteristic
845C23#1058769611yescharacteristic
846C23#1058769711yescharacteristic
847C23#1058769711yescharacteristic
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—174no—
895C2×C4—3432no—
896C2×C4—342no—
897C2×C4—342no—
898C2×C4—342no—
899C2×C4—342no—
900C2×C4—342no—
901C2×C4—342no—
902C2×C4—342no—
903C2×C4—342no—
904C2×C4—342no—
905C2×C4—342no—
906C2×C4—342no—
907C2×C4—342no—
908C2×C4—342no—
909C2×C4—342no—
910C2×C4—342no—
911C2×C4—342no—
912C2×C4—342no—
913C2×C4—342no—
914C2×C4—342no—
915C2×C4—342no—
916C2×C4—342no—
917C2×C4—681no—
918C2×C4—681no—
919C2×C4—681no—
920C2×C4—681no—
921C2×C4—681no—
922C2×C4—681no—
923C2×C4—681no—
924C2×C4—681no—
925C2×C4—681no—
926C2×C4—681no—
927C2×C4—681no—
928C2×C4—681no—
929C2×C4—681no—
930C2×C4—681no—
931C2×C4—681no—
932C2×C4—681no—
933C2×C4—681no—
934C2×C4—681no—
935C2×C4—681no—
936C2×C4—681no—
937C2×C4—681no—
938C2×C4—681no—
939C2×C4—681no—
940C2×C4—681no—
941C2×C4—681no—
942C2×C4—681no—
943C2×C4—681no—
944C2×C4C4×D6814yes—
945C2×C4#1058756814yes—
946C2×C4#1058757814yescomplemented
947C22—344no—
948C22—344no—
949C22—344no—
950C22—682no—
951C22—682no—
952C22—682no—
953C22—682no—
954C22—682no—
955C22—682no—
956C22—682no—
957C22—682no—
958C22—682no—
959C22—682no—
960C22—682no—
961C22—682no—
962C22C2×#1058757811yescharacteristic
963C22C4×D4×D1711yescharacteristic
964C22C4×D4×D1711yescharacteristic
965C22C2×C4×D6811yescharacteristic
966C22C4×#6325411yescharacteristic
967C22#1176328511yescharacteristic
968C22#1176328911yescharacteristic
969C22C2×#1058756811yescharacteristic
970C22#1176331511yescharacteristic
971C22#1176331811yescharacteristic
972C22#1176331811yescharacteristic
973C22#1176332111yescharacteristic
974C22#1176332211yescharacteristic
975C22#1176333611yescharacteristic
976C22#1176334511yescharacteristic
977C22#1176338111yescharacteristic
978C22#1176338911yescharacteristic
979C22#1176341811yescharacteristic
980C22#1176342511yescharacteristic
981C22#1176345211yescharacteristic
982C22#1176345911yescharacteristic
983C22#1176345911yescharacteristic
984C22#1176346211yescharacteristic
985C22#1176346311yescharacteristic
986C22#1176346311yescharacteristic
987C22#1176347111yescharacteristic
988C22#1176348111yescharacteristic
989C22#1176348211yescharacteristic
990C22#1176349311yescharacteristic
991C22#1176349411yescharacteristic
992C22#1176349511yescharacteristic
993C22#1176349711yescharacteristic
994C22#1176352411yescharacteristic
995C22#1176352711yescharacteristic
996C22#1176353211yescharacteristic
997C4—24no—
998C4—24no—
999C4—24no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—81no—
1004C4—344no—
1005C4—682no—
1006C4—682no—
1007C4—682no—
1008C4—682no—
1009C4—682no—
1010C4—1361no—
1011C2—684no—
1012C2#1453122011yescharacteristic
1013C2C4×#1058756811yescharacteristic
1014C2#1453146511yescharacteristic
1015C2#1453165211yescharacteristic
1016C2#1453173111yescharacteristic
1017C2#1453177511yescharacteristic
1018C2#1453181311yescharacteristic
1019C2#1453211811yescharacteristic
1020C2#1453213211yescharacteristic
1021C2#1453294611yescharacteristic
1022C2#1453295311yescharacteristic
1023C2#1453300611yescharacteristic
1024C2#1453301311yescharacteristic
1025C2#1453436011yescharacteristic
1026C2#1453446011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1436C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenter#1436D17
hypocenterC17#14063
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×#11762690C2semidirect
5. C2×C4×C4⋊Dic17C2semidirect
6. #14527049C2semidirect
7. #14527038C2semidirect
11. #14527018C2semidirect
12. #14527018C2semidirect
13. #14527008C2semidirect
15. C17×#1436C2semidirect
36. #11762683C4semidirect
381. C2×C4×C17#117semidirect
446. #1436D17semidirect
660. C17#14063semidirect
946. C2×C4#10587578semidirect

Maximal subgroups

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

subgroupindex
C22×#105875782
C2×#117627012
C2×#117626902
C2×#117626832
C2×C4×C4⋊Dic172
#145270492
#145270382
#145270322
#145270302
#145270222
#145270182
#145270082
#145270052
C17×#14362
#1406317