Finite Group Databasebeta

← C2×#14531774 #17193825

Subgroups — C2×#14531774 #17193825

Order 4352.

3830 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587572C211yesmaximal, characteristic
2C22×C4×C22⋊D17C211yesmaximal, characteristic
3C22×#10587563C211yesmaximal, characteristic, complemented
4#14531774C2116yesmaximal, direct product factor
5C2×#11762705C211yesmaximal, characteristic, complemented
6C2×#11762699C211yesmaximal, characteristic, complemented
7C2×#11762698C211yesmaximal, characteristic, complemented
8C2×#11762692C211yesmaximal, characteristic, complemented
9C2×#11762692C211yesmaximal, characteristic, complemented
10C2×#11762686C211yesmaximal, characteristic
11C2×#11762680C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
14C2×#11762656C211yesmaximal, characteristic, complemented
15C22×#10587502C211yesmaximal, characteristic, complemented
16C2×C17×#385C211yesmaximal, characteristic, complemented
17C23×C22⋊D17C2211yescharacteristic
18C24×Dic17C2211yescharacteristic
19C24×Dic17C2211yescharacteristic
20C23×C4×D17C2211yescharacteristic
21C2×#10587572C4116yescomplemented
22C2×#10587572C2218yes—
23C2×C4×C22⋊D17—28no—
24C2×C4×C22⋊D17C2218yes—
25C2×#10587563—28no—
26C2×#10587563C2218yescomplemented
27C22×C4⋊Dic17C2211yescharacteristic
28C22×C4⋊Dic17C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C22×#63225C2211yescharacteristic
31C22×#63225C2211yescharacteristic
32C22×C22⋊Dic17C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×#63227C2211yescharacteristic
36C22×#63227C2211yescharacteristic
37C22×#63227C2211yescharacteristic
38C22×C4×Dic17C2211yescharacteristic
39C22×C4×Dic17C2211yescharacteristic
40C22×C4×Dic17C2211yescharacteristic
41C22×C4×Dic17C2211yescharacteristic
42C22×C4×Dic17C2211yescharacteristic
43#11762705C2218yescomplemented
44#11762699C2218yescomplemented
45#11762698C2218yescomplemented
46#11762692C2218yescomplemented
47#11762692C2218yescomplemented
48#11762686C2218yes—
49#11762680C2218yescomplemented
50C4⋊C4×Dic17C2218yescomplemented
51C22⋊C4×Dic17C2218yescomplemented
52#11762656C2218yescomplemented
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60C2×#10587502C2211yescharacteristic
61C2×#10587502C2218yescomplemented
62C24×C4×C17C2211yescharacteristic
63C22×C4⋊C4×C17C2211yescharacteristic
64C22×C4⋊C4×C17C2211yescharacteristic
65C22×C22⋊C4×C17C2211yescharacteristic
66C22×C22⋊C4×C17C2211yescharacteristic
67C17×#385C2218yescomplemented
68C2×C17×#95C2211yescharacteristic
69C2×C17×#95C2211yescharacteristic
70C25×C17C2311yescharacteristic
71C24×D17C2311yescharacteristic
72C23×C4×C17—24no—
73C23×C4×C17—24no—
74C23×C4×C17—42no—
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×C4×C17C2314yes—
79C23×C4×C17C2311yescharacteristic
80C23×C4×C17C2311yescharacteristic
81C23×C4×C17C2311yescharacteristic
82C22×C22⋊D17—24no—
83C22×C22⋊D17—24no—
84C22×C22⋊D17C2×C418yes—
85C22×C22⋊D17C2314yes—
86C23×Dic17—24no—
87C23×Dic17—24no—
88C23×Dic17—24no—
89C23×Dic17—24no—
90C23×Dic17—42no—
91C23×Dic17C2×C418yescomplemented
92C23×Dic17C2311yescharacteristic
93C23×Dic17C2314yes—
94C23×Dic17C2311yescharacteristic
95C23×Dic17C2311yescharacteristic
96C23×Dic17C2311yescharacteristic
97C23×Dic17C2314yes—
98C23×Dic17C2311yescharacteristic
99C23×Dic17C2311yescharacteristic
100C23×Dic17C2311yescharacteristic
101C22×C4×D17—24no—
102C22×C4×D17—24no—
103C22×C4×D17—42no—
104C22×C4×D17C2314yes—
105C2×C4⋊C4×C17—24no—
106C2×C4⋊C4×C17—42no—
107C2×C4⋊C4×C17C2314yes—
108C2×C4⋊C4×C17C2314yes—
109C2×C22⋊C4×C17—24no—
110C2×C22⋊C4×C17C2×C418yescomplemented
111C2×C22⋊C4×C17C2314yes—
112C2×C22⋊C4×C17C2314yes—
113C2×C22⋊Dic17D418yes—
114C2×C22⋊Dic17C2314yes—
115C4×C22⋊D17—232no—
116C2×#63227—24no—
117C2×#63227—24no—
118C2×#63227—42no—
119C2×#63227C2×C418yescomplemented
120C2×#63227C2×C418yescomplemented
121C2×#63227C2314yes—
122C2×#63227C2314yes—
123C2×#63227C2314yes—
124C2×#63227C2314yes—
125C2×#63227C2314yes—
126C2×C4⋊Dic17C2×C418yescomplemented
127C2×C4⋊Dic17C2×C418yescomplemented
128C2×C4⋊Dic17C2314yes—
129C2×C4⋊Dic17C2314yes—
130C2×#63225—24no—
131C2×#63225—24no—
132C2×#63225—24no—
133C2×#63225C2314yes—
134C2×#63225C2314yes—
135C2×#63225C2314yes—
136C2×C4×Dic17—24no—
137C2×C4×Dic17—24no—
138C2×C4×Dic17—24no—
139C2×C4×Dic17—24no—
140C2×C4×Dic17—42no—
141C2×C4×Dic17C2314yes—
142C2×C4×Dic17C2314yes—
143C2×C4×Dic17C2314yes—
144C2×C4×Dic17C2314yes—
145C2×C4×Dic17C2314yes—
146#10587572C2×C4164yescomplemented
147#10587563—232no—
148C17×#95C2314yes—
149C17×#95C2314yes—
150#10587502C2314yes—
151#10587502C2314yes—
152#10587502C2314yes—
153#10587502C2314yes—
154#10587502C2314yes—
155#10587502C2314yes—
156#10587502C2314yes—
157#10587502C2314yes—
158C24×C17—22no—
159C24×C17—22no—
160C24×C17—22no—
161C24×C17—22no—
162C24×C17C22×C414yes—
163C24×C17C2×D414yes—
164C24×C17#4114yes—
165C24×C17C2412yes—
166C24×C17C2411yescharacteristic
167C23×D17—22no—
168C23×D17—22no—
169C23×D17—22no—
170C23×D17—22no—
171C23×D17—22no—
172C23×D17—22no—
173C23×D17C22×C414yes—
174C23×D17C2412yes—
175C22×C4×C17—22no—
176C22×C4×C17—22no—
177C22×C4×C17—22no—
178C22×C4×C17—22no—
179C22×C4×C17—22no—
180C22×C4×C17—22no—
181C22×C4×C17—22no—
182C22×C4×C17—28no—
183C22×C4×C17—22no—
184C22×C4×C17—22no—
185C22×C4×C17—22no—
186C22×C4×C17—22no—
187C22×C4×C17—22no—
188C22×C4×C17—22no—
189C22×C4×C17—22no—
190C22×C4×C17—22no—
191C22×C4×C17—28no—
192C22×C4×C17—44no—
193C22×C4×C17—416no—
194C22×C4×C17C22×C414yes—
195C22×C4×C17C22×C414yes—
196C22×C4×C17#4114yes—
197C22×C4×C17C2412yes—
198C22×C4×C17C2412yes—
199C22×C4×C17C2412yes—
200C22×C4×C17C2412yes—
201C22×C4×C17C2412yes—
202C22×C4×C17C2412yes—
203C2×C22⋊D17—232no—
204C2×C22⋊D17—28no—
205C2×C22⋊D17—28no—
206C2×C22⋊D17C22×C4116yes—
207C22×Dic17—232no—
208C22×Dic17—28no—
209C22×Dic17—22no—
210C22×Dic17—22no—
211C22×Dic17—22no—
212C22×Dic17—22no—
213C22×Dic17—22no—
214C22×Dic17—22no—
215C22×Dic17—28no—
216C22×Dic17—22no—
217C22×Dic17—22no—
218C22×Dic17—22no—
219C22×Dic17—22no—
220C22×Dic17—22no—
221C22×Dic17—22no—
222C22×Dic17—28no—
223C22×Dic17—22no—
224C22×Dic17—22no—
225C22×Dic17—22no—
226C22×Dic17—28no—
227C22×Dic17—44no—
228C22×Dic17—416no—
229C22×Dic17C22×C414yes—
230C22×Dic17C22×C414yes—
231C22×Dic17C22×C414yes—
232C22×Dic17C22×C4116yescomplemented
233C22×Dic17C2×D414yes—
234C22×Dic17C2×D414yes—
235C22×Dic17#4114yes—
236C22×Dic17C2412yes—
237C22×Dic17C2412yes—
238C22×Dic17C2412yes—
239C22×Dic17C2412yes—
240C22×Dic17C2412yes—
241C22×Dic17C2412yes—
242C22×Dic17C2412yes—
243C2×C4×D17—28no—
244C2×C4×D17—28no—
245C2×C4×D17—44no—
246C2×C4×D17—416no—
247C4⋊C4×C17—28no—
248C4⋊C4×C17—44no—
249C22⋊C4×C17—28no—
250C22⋊C4×C17C22×C4116yescomplemented
251C22⋊Dic17C2×D4116yes—
252#63227—28no—
253#63227—28no—
254#63227—44no—
255#63227C22×C4116yescomplemented
256#63227C22×C4116yescomplemented
257C4⋊Dic17C22×C4116yescomplemented
258C4⋊Dic17C22×C4116yescomplemented
259#63225—28no—
260#63225—28no—
261#63225—28no—
262C4×Dic17—28no—
263C4×Dic17—28no—
264C4×Dic17—28no—
265C4×Dic17—28no—
266C4×Dic17—44no—
267C2×#2359—171nomaximal, Sylow
268C23×C17—28no—
269C23×C17—28no—
270C23×C17—28no—
271C23×C17—28no—
272C23×C17—28no—
273C23×C17—28no—
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—22no—
277C23×C17—22no—
278C23×C17C4×D4116yes—
279C23×C17C23×C414yes—
280C23×C17C23×C412yes—
281C23×C17C22×D414yes—
282C23×C17C22×D412yes—
283C23×C17C2×#4112yes—
284C23×C17C2×#4114yes—
285C23×C17C2×#4112yes—
286C23×C17C2×#4112yes—
287C23×C17H(5,𝔽2)12yes—
288C23×C172−1+412yes—
289C23×C17C2511yescharacteristic
290C22×D17—28no—
291C22×D17—28no—
292C22×D17—28no—
293C22×D17—22no—
294C22×D17—22no—
295C22×D17—22no—
296C22×D17—22no—
297C22×D17—22no—
298C22×D17—22no—
299C22×D17—44no—
300C22×D17—44no—
301C22×D17—44no—
302C22×D17—44no—
303C22×D17C23×C414yes—
304C2×C4×C17—28no—
305C2×C4×C17—28no—
306C2×C4×C17—28no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
316C2×C4×C17—22no—
317C2×C4×C17—22no—
318C2×C4×C17—22no—
319C2×C4×C17—22no—
320C2×C4×C17—22no—
321C2×C4×C17—22no—
322C2×C4×C17—416no—
323C2×C4×C17—44no—
324C2×C4×C17—44no—
325C2×C4×C17—44no—
326C2×C4×C17C23×C414yes—
327C2×C4×C17C23×C414yes—
328C2×C4×C17C2×#4114yes—
329C22⋊D17—232no—
330C2×Dic17—28no—
331C2×Dic17—28no—
332C2×Dic17—232no—
333C2×Dic17—28no—
334C2×Dic17—28no—
335C2×Dic17—28no—
336C2×Dic17—28no—
337C2×Dic17—22no—
338C2×Dic17—22no—
339C2×Dic17—22no—
340C2×Dic17—22no—
341C2×Dic17—22no—
342C2×Dic17—22no—
343C2×Dic17—22no—
344C2×Dic17—22no—
345C2×Dic17—22no—
346C2×Dic17—22no—
347C2×Dic17—22no—
348C2×Dic17—22no—
349C2×Dic17—22no—
350C2×Dic17—22no—
351C2×Dic17—22no—
352C2×Dic17—416no—
353C2×Dic17—44no—
354C2×Dic17C23×C414yes—
355C2×Dic17C23×C414yes—
356C2×Dic17C23×C414yes—
357C2×Dic17C22×D414yes—
358C2×Dic17C22×D414yes—
359C2×Dic17C2×#4114yes—
360C4×D17—416no—
361C22×#123—171no—
362C22×C4×D4—171no—
363C22×#117—171no—
364#2359—1716no—
365C2×#389—171no—
366C2×#388—171no—
367C2×#388—171no—
368C2×#387—171no—
369C2×#387—171no—
370C2×#386—171no—
371C2×#385—171no—
372C2×#385D1711yescharacteristic, complemented
373C2×C4×C4⋊C4—171no—
374C2×C4×C22⋊C4—171no—
375C2×C4×C22⋊C4—171no—
376C22×#95—171no—
377C22×C17—232no—
378C22×C17—24no—
379C22×C17—24no—
380C22×C17—24no—
381C22×C17—24no—
382C22×C17—24no—
383C22×C17—24no—
384C22×C17C2×C4×D418yes—
385C22×C17C2×C4×D414yes—
386C22×C17C4×#4114yes—
387C22×C17#52014yes—
388C22×C17#54614yes—
389C22×C17#54714yes—
390C22×C17#55114yes—
391C22×C17#55214yes—
392C22×C17C24×C411yescharacteristic
393C22×C17C23×D411yescharacteristic
394C22×C17C22×#4111yescharacteristic
395C22×C17C22×#4111yescharacteristic
396C22×C17C22×#4111yescharacteristic
397C22×C17C2×H(5,𝔽2)11yescharacteristic
398C22×C17C2×2−1+411yescharacteristic
399C2×D17—24no—
400C2×D17—24no—
401C2×D17—24no—
402C2×D17—416no—
403C2×D17—42no—
404C2×D17—42no—
405C2×D17—42no—
406C2×D17—42no—
407C4×C17—24no—
408C4×C17—24no—
409C4×C17—24no—
410C4×C17—42no—
411C4×C17—42no—
412C4×C17—42no—
413Dic17—24no—
414Dic17—24no—
415Dic17—24no—
416Dic17—24no—
417Dic17—24no—
418Dic17—24no—
419Dic17—42no—
420C23×D4—171no—
421C24×C4—171no—
422C24×C4—171no—
423C24×C4—171no—
424C24×C4C2×D1711yescharacteristic
425C2×#123—1716no—
426C2×#123—178no—
427C2×C4×D4—178no—
428C2×C4×D4—348no—
429C2×#117—178no—
430C2×#117—348no—
431C22×C4⋊C4—171no—
432C22×C4⋊C4—171no—
433C22×C4⋊C4—171no—
434C22×C4⋊C4—171no—
435C22×C4⋊C4—171no—
436C22×C4⋊C4C2×D1711yescharacteristic
437C22×C4⋊C4C2×D1711yescharacteristic
438C22×C22⋊C4—171no—
439C22×C22⋊C4—171no—
440C22×C22⋊C4—171no—
441C22×C22⋊C4—171no—
442C22×C22⋊C4—171no—
443C22×C22⋊C4—171no—
444C22×C22⋊C4C2×D1711yescharacteristic
445C22×C22⋊C4C2×D1711yescharacteristic
446C22×C42—171no—
447C22×C42—171no—
448C22×C42—171no—
449C22×C42—171no—
450C22×C42—171no—
451#389—178no—
452#388—178no—
453#388—178no—
454#387—178no—
455#387—178no—
456#386—178no—
457#385—178no—
458#385C2×D1718yescomplemented
459C4×C4⋊C4—178no—
460C4×C22⋊C4—178no—
461C4×C22⋊C4—178no—
462C2×#95—178no—
463C2×#95—171no—
464C2×#95—171no—
465C2×#95—171no—
466C2×#95—171no—
467C2×#95—171no—
468C2×#95—171no—
469C2×#95—171no—
470C2×#95—171no—
471C2×#95C2×D1711yescharacteristic
472C2×#95C2×D1711yescharacteristic
473C2×C17—28no—
474C2×C17#235918yescomplemented
475C2×C17C22×C4×D411yescharacteristic
476C2×C17C2×C4×#4111yescharacteristic
477C2×C17C2×#52011yescharacteristic
478C2×C17C2×#54611yescharacteristic
479C2×C17C2×#54711yescharacteristic
480C2×C17C2×#55111yescharacteristic
481C2×C17C2×#55211yescharacteristic
482D17—44no—
483C25—171no—
484C25C22×D1711yescharacteristic
485C22×D4—178no—
486C22×D4—174no—
487C22×D4—344no—
488C22×D4—344no—
489C23×C4—24no—
490C23×C4—24no—
491C23×C4—42no—
492C23×C4—178no—
493C23×C4—174no—
494C23×C4—171no—
495C23×C4—171no—
496C23×C4—171no—
497C23×C4—171no—
498C23×C4—171no—
499C23×C4—171no—
500C23×C4—171no—
501C23×C4—174no—
502C23×C4—174no—
503C23×C4—344no—
504C23×C4—344no—
505C23×C4—344no—
506C23×C4—344no—
507C23×C4—344no—
508C23×C4—344no—
509C23×C4—682no—
510C23×C4—682no—
511C23×C4C22×D1711yescharacteristic
512C23×C4C22×D1711yescharacteristic
513C23×C4C22×D1711yescharacteristic
514C23×C4C22×D1714yes—
515C23×C4C22×D1711yescharacteristic
516C23×C4C22×D1711yescharacteristic
517C23×C4C22×D1711yescharacteristic
518#123—1764no—
519C4×D4—3432no—
520#117—3432no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—42no—
523C2×C4⋊C4—178no—
524C2×C4⋊C4—178no—
525C2×C4⋊C4—174no—
526C2×C4⋊C4—174no—
527C2×C4⋊C4—174no—
528C2×C4⋊C4—174no—
529C2×C4⋊C4—174no—
530C2×C4⋊C4—344no—
531C2×C4⋊C4—344no—
532C2×C4⋊C4—344no—
533C2×C4⋊C4C22×D1714yes—
534C2×C4⋊C4C22×D1714yes—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—178no—
537C2×C22⋊C4—174no—
538C2×C22⋊C4—178no—
539C2×C22⋊C4—178no—
540C2×C22⋊C4—174no—
541C2×C22⋊C4—174no—
542C2×C22⋊C4—174no—
543C2×C22⋊C4—174no—
544C2×C22⋊C4—174no—
545C2×C22⋊C4—344no—
546C2×C22⋊C4—344no—
547C2×C22⋊C4—682no—
548C2×C22⋊C4C4×D1718yescomplemented
549C2×C22⋊C4C22×D1714yes—
550C2×C22⋊C4C22×D1714yes—
551C2×C42—174no—
552C2×C42—174no—
553C2×C42—174no—
554C2×C42—174no—
555C2×C42—174no—
556C2×C42—344no—
557C2×C42—344no—
558C2×C42—344no—
559C2×C42—344no—
560C2×C42—682no—
561#95—174no—
562#95—174no—
563#95—174no—
564#95—174no—
565#95—174no—
566#95—174no—
567#95—174no—
568#95—174no—
569#95C22×D1714yes—
570#95C22×D1714yes—
571C17C2×#235911yescharacteristic, complemented, Sylow
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—174no—
577C24—172no—
578C24—342no—
579C24—342no—
580C24—342no—
581C24—342no—
582C24—342no—
583C24—342no—
584C24C2×C4×D1714yes—
585C24D4×D1714yes—
586C24#6325614yes—
587C24C23×D1712yes—
588C24C23×D1711yescharacteristic
589C2×D4—1716no—
590C2×D4—348no—
591C2×D4—348no—
592C2×D4—3432no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—28no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—28no—
610C22×C4—44no—
611C22×C4—416no—
612C22×C4—174no—
613C22×C4—174no—
614C22×C4—174no—
615C22×C4—1716no—
616C22×C4—174no—
617C22×C4—174no—
618C22×C4—174no—
619C22×C4—172no—
620C22×C4—172no—
621C22×C4—172no—
622C22×C4—172no—
623C22×C4—172no—
624C22×C4—172no—
625C22×C4—172no—
626C22×C4—348no—
627C22×C4—348no—
628C22×C4—342no—
629C22×C4—342no—
630C22×C4—342no—
631C22×C4—348no—
632C22×C4—342no—
633C22×C4—342no—
634C22×C4—342no—
635C22×C4—342no—
636C22×C4—348no—
637C22×C4—342no—
638C22×C4—342no—
639C22×C4—342no—
640C22×C4—342no—
641C22×C4—342no—
642C22×C4—3432no—
643C22×C4—342no—
644C22×C4—348no—
645C22×C4—342no—
646C22×C4—342no—
647C22×C4—348no—
648C22×C4—684no—
649C22×C4—6816no—
650C22×C4—684no—
651C22×C4—6816no—
652C22×C4C2×C4×D1714yes—
653C22×C4C2×C4×D1714yes—
654C22×C4#6325414yes—
655C22×C4C23×D1712yes—
656C22×C4C23×D1712yes—
657C22×C4C23×D1712yes—
658C22×C4C23×D1712yes—
659C22×C4C23×D1712yes—
660C22×C4C23×D1712yes—
661C4⋊C4—28no—
662C4⋊C4—44no—
663C4⋊C4—1716no—
664C4⋊C4—1716no—
665C4⋊C4—348no—
666C4⋊C4—348no—
667C4⋊C4—348no—
668C22⋊C4—28no—
669C22⋊C4—1716no—
670C22⋊C4—1716no—
671C22⋊C4—1716no—
672C22⋊C4—348no—
673C22⋊C4—348no—
674C22⋊C4—684no—
675C22⋊C4C2×C4×D17116yescomplemented
676C42—348no—
677C42—348no—
678C42—348no—
679C42—348no—
680C42—684no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—28no—
691C23—174no—
692C23—348no—
693C23—348no—
694C23—348no—
695C23—342no—
696C23—342no—
697C23—342no—
698C23—342no—
699C23—342no—
700C23—342no—
701C23—684no—
702C23—684no—
703C23—684no—
704C23—684no—
705C23#10587579116yes—
706C23C22×C4×D1714yes—
707C23C22×C4×D1712yes—
708C23C2×D4×D1714yes—
709C23C2×D4×D1712yes—
710C23C2×#6325412yes—
711C23#1058769112yes—
712C23C2×#6325614yes—
713C23C2×#6325612yes—
714C23#41×D1712yes—
715C23#1058769712yes—
716C23C24×D1711yescharacteristic
717D4—3432no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—28no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—174no—
741C2×C4—174no—
742C2×C4—174no—
743C2×C4—174no—
744C2×C4—174no—
745C2×C4—174no—
746C2×C4—348no—
747C2×C4—348no—
748C2×C4—3432no—
749C2×C4—348no—
750C2×C4—348no—
751C2×C4—348no—
752C2×C4—342no—
753C2×C4—342no—
754C2×C4—342no—
755C2×C4—342no—
756C2×C4—342no—
757C2×C4—342no—
758C2×C4—342no—
759C2×C4—342no—
760C2×C4—342no—
761C2×C4—342no—
762C2×C4—342no—
763C2×C4—342no—
764C2×C4—348no—
765C2×C4—342no—
766C2×C4—342no—
767C2×C4—342no—
768C2×C4—6816no—
769C2×C4—6816no—
770C2×C4—684no—
771C2×C4C22×C4×D1714yes—
772C2×C4C22×C4×D1714yes—
773C2×C4C2×#6325414yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—232no—
779C22—24no—
780C22—24no—
781C22—344no—
782C22—344no—
783C22—344no—
784C22—682no—
785C22—682no—
786C22—6816no—
787C22—682no—
788C22—682no—
789C22C2×#1058757918yes—
790C22C2×#1058757914yes—
791C22C4×#6325414yes—
792C22#1176328814yes—
793C22#1176344614yes—
794C22#1176345714yes—
795C22#1176348614yes—
796C22#1176350114yes—
797C22C23×C4×D1711yescharacteristic
798C22C22×D4×D1711yescharacteristic
799C22C2×#41×D1711yescharacteristic
800C22C22×#6325411yescharacteristic
801C22C22×#6325611yescharacteristic
802C22C2×#1058769111yescharacteristic
803C22C2×#1058769711yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—344no—
811C4—344no—
812C4—344no—
813C4—344no—
814C4—344no—
815C4—344no—
816C4—682no—
817C2—28no—
818C2—684no—
819C2#1453177418yesdirect product factor
820C2C22×#1058757911yescharacteristic
821C2C2×C4×#6325411yescharacteristic
822C2C2×#1176328811yescharacteristic
823C2C2×#1176344611yescharacteristic
824C2C2×#1176345711yescharacteristic
825C2C2×#1176348611yescharacteristic
826C2C2×#1176350111yescharacteristic
subgroupG/H
centerC24C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC2×C17×#385C2
socleC24×C17C24
prime radicalC23×C22⋊D17C22
cosocleC23×C17C25
hypercenterC2×#385D17
hypocenterC17C2×#2359
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C22×#10587563C2semidirect
4. #14531774C2direct (N × H)
5. C2×#11762705C2semidirect
6. C2×#11762699C2semidirect
7. C2×#11762698C2semidirect
8. C2×#11762692C2semidirect
9. C2×#11762692C2semidirect
11. C2×#11762680C2semidirect
12. C2×C4⋊C4×Dic17C2semidirect
13. C2×C22⋊C4×Dic17C2semidirect
14. C2×#11762656C2semidirect
15. C22×#10587502C2semidirect
16. C2×C17×#385C2semidirect
21. C2×#10587572C4semidirect
26. C2×#10587563C22semidirect
43. #11762705C22semidirect
44. #11762699C22semidirect
45. #11762698C22semidirect
46. #11762692C22semidirect
47. #11762692C22semidirect
49. #11762680C22semidirect
50. C4⋊C4×Dic17C22semidirect
51. C22⋊C4×Dic17C22semidirect
52. #11762656C22semidirect
61. C2×#10587502C22semidirect
67. C17×#385C22semidirect
91. C23×Dic17C2×C4semidirect
110. C2×C22⋊C4×C17C2×C4semidirect
119. C2×#63227C2×C4semidirect
120. C2×#63227C2×C4semidirect
126. C2×C4⋊Dic17C2×C4semidirect
127. C2×C4⋊Dic17C2×C4semidirect
146. #10587572C2×C4semidirect
232. C22×Dic17C22×C4semidirect
250. C22⋊C4×C17C22×C4semidirect
255. #63227C22×C4semidirect
256. #63227C22×C4semidirect
257. C4⋊Dic17C22×C4semidirect
258. C4⋊Dic17C22×C4semidirect
372. C2×#385D17semidirect
458. #385C2×D17semidirect
474. C2×C17#2359semidirect
548. C2×C22⋊C4C4×D17semidirect
571. C17C2×#2359semidirect
675. C22⋊C4C2×C4×D17semidirect
819. C2#14531774direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875722
C22×C4×C22⋊D172
C22×#105875632
#145317742
C2×#117627052
C2×#117626992
C2×#117626982
C2×#117626922
C2×#117626862
C2×#117626802
C2×C4⋊C4×Dic172
C2×C22⋊C4×Dic172
C2×#117626562
C22×#105875022
C2×C17×#3852
C2×#235917