Finite Group Databasebeta

← C2×#14533830 #17204376

Subgroups — C2×#14533830 #17204376

Order 4352.

2942 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587584C211yesmaximal, characteristic, complemented
2C22×#10587572C211yesmaximal, characteristic
3#14533830C2116yesmaximal, direct product factor
4C2×#11762741C211yesmaximal, characteristic, complemented
5C2×#11762735C211yesmaximal, characteristic, complemented
6C2×#11762725C211yesmaximal, characteristic
7C2×#11762708C211yesmaximal, characteristic, complemented
8C2×#11762703C211yesmaximal, characteristic, complemented
9C2×#11762695C211yesmaximal, characteristic, complemented
10C2×#11762685C211yesmaximal, characteristic
11C2×#11762684C211yesmaximal, characteristic, complemented
12C2×#11762674C211yesmaximal, characteristic, complemented
13C2×#11762666C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
15C2×#11762656C211yesmaximal, characteristic, complemented
16C2×C17×#399C211yesmaximal, characteristic, complemented
17C23×C22⋊D17C2211yescharacteristic
18C24×Dic17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C2×#10587584—28no—
21C2×#10587584C2218yescomplemented
22C2×#10587572—28no—
23C2×#10587572C2218yes—
24C22×C4⋊Dic17C2211yescharacteristic
25C22×C4⋊Dic17C2211yescharacteristic
26C22×C4⋊Dic17C2211yescharacteristic
27C22×C4⋊Dic17C2211yescharacteristic
28C22×C4⋊Dic17C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C22×C22⋊Dic17C2211yescharacteristic
31C22×C22⋊Dic17C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×#63227C2211yescharacteristic
36C22×#63227C2211yescharacteristic
37C22×C4×Dic17C2211yescharacteristic
38C22×C4×Dic17C2211yescharacteristic
39C22×C4×Dic17C2211yescharacteristic
40#11762741C2218yescomplemented
41#11762735C2218yescomplemented
42#11762725C2218yes—
43#11762708C2218yescomplemented
44#11762703C2218yescomplemented
45#11762695C2218yescomplemented
46#11762685C2218yes—
47#11762684C2218yescomplemented
48#11762674C2218yescomplemented
49#11762666C2218yescomplemented
50C22⋊C4×Dic17C2218yescomplemented
51#11762656C2218yescomplemented
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60C2×#10587502C2211yescharacteristic
61C22×C4⋊C4×C17C2211yescharacteristic
62C22×C4⋊C4×C17C2211yescharacteristic
63C22×C4⋊C4×C17C2211yescharacteristic
64C22×C22⋊C4×C17C2211yescharacteristic
65C22×C22⋊C4×C17C2211yescharacteristic
66C22×C22⋊C4×C17C2211yescharacteristic
67C17×#399C2218yescomplemented
68C2×C17×#95C2211yescharacteristic
69C25×C17C2311yescharacteristic
70C24×D17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C22×C22⋊D17—24no—
78C22×C22⋊D17—24no—
79C22×C22⋊D17—42no—
80C22×C22⋊D17C2314yes—
81C23×Dic17—24no—
82C23×Dic17—24no—
83C23×Dic17—42no—
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C23×Dic17C2314yes—
90C23×Dic17C2311yescharacteristic
91C23×Dic17C2311yescharacteristic
92C22×C4×D17—24no—
93C22×C4×D17—24no—
94C22×C4×D17—42no—
95C22×C4×D17C2314yes—
96C2×C4⋊C4×C17—24no—
97C2×C4⋊C4×C17—24no—
98C2×C4⋊C4×C17—24no—
99C2×C4⋊C4×C17C2314yes—
100C2×C4⋊C4×C17C2314yes—
101C2×C4⋊C4×C17C2314yes—
102C2×C22⋊C4×C17—24no—
103C2×C22⋊C4×C17—24no—
104C2×C22⋊C4×C17—24no—
105C2×C22⋊C4×C17C2314yes—
106C2×C22⋊C4×C17C2314yes—
107C2×C22⋊C4×C17C2314yes—
108C2×C22⋊Dic17—24no—
109C2×C22⋊Dic17—24no—
110C2×C22⋊Dic17C2314yes—
111C2×C22⋊Dic17C2314yes—
112C2×#63227—24no—
113C2×#63227—24no—
114C2×#63227—24no—
115C2×#63227—24no—
116C2×#63227D418yes—
117C2×#63227C2314yes—
118C2×#63227C2314yes—
119C2×#63227C2314yes—
120C2×#63227C2314yes—
121C2×#63227C2314yes—
122C2×C4⋊Dic17—24no—
123C2×C4⋊Dic17—24no—
124C2×C4⋊Dic17—24no—
125C2×C4⋊Dic17—42no—
126C2×C4⋊Dic17—42no—
127C2×C4⋊Dic17C2314yes—
128C2×C4⋊Dic17C2314yes—
129C2×C4⋊Dic17C2314yes—
130C2×C4⋊Dic17C2314yes—
131C2×C4⋊Dic17C2314yes—
132C2×#63225—24no—
133C2×#63225C2314yes—
134C2×C4×Dic17—24no—
135C2×C4×Dic17—24no—
136C2×C4×Dic17—42no—
137C2×C4×Dic17C2314yes—
138C2×C4×Dic17C2314yes—
139C2×C4×Dic17C2314yes—
140#10587584—232no—
141#10587572—232no—
142C17×#95C2314yes—
143#10587502C2314yes—
144#10587502C2314yes—
145#10587502C2314yes—
146#10587502C2314yes—
147#10587502C2314yes—
148#10587502C2314yes—
149#10587502C2314yes—
150#10587502C2314yes—
151#10587502C2314yes—
152C24×C17—22no—
153C24×C17—22no—
154C24×C17—22no—
155C24×C17—22no—
156C24×C17—22no—
157C24×C17—22no—
158C24×C17#4114yes—
159C24×C17C2412yes—
160C24×C17C2411yescharacteristic
161C23×D17—22no—
162C23×D17—22no—
163C23×D17—22no—
164C23×D17—22no—
165C23×D17—22no—
166C23×D17—22no—
167C23×D17C2×D414yes—
168C23×D17C2412yes—
169C22×C4×C17—22no—
170C22×C4×C17—22no—
171C22×C4×C17—22no—
172C22×C4×C17—22no—
173C22×C4×C17—22no—
174C22×C4×C17—22no—
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—22no—
183C22×C4×C17—22no—
184C22×C4×C17C2×D414yes—
185C22×C4×C17#4114yes—
186C22×C4×C17#4114yes—
187C22×C4×C17C2412yes—
188C22×C4×C17C2412yes—
189C22×C4×C17C2412yes—
190C22×C4×C17C2412yes—
191C22×C4×C17C2412yes—
192C22×C4×C17C2412yes—
193C2×C22⋊D17—28no—
194C2×C22⋊D17—28no—
195C2×C22⋊D17—44no—
196C2×C22⋊D17—416no—
197C22×Dic17—22no—
198C22×Dic17—22no—
199C22×Dic17—22no—
200C22×Dic17—22no—
201C22×Dic17—22no—
202C22×Dic17—22no—
203C22×Dic17—22no—
204C22×Dic17—22no—
205C22×Dic17—28no—
206C22×Dic17—22no—
207C22×Dic17—22no—
208C22×Dic17—22no—
209C22×Dic17—22no—
210C22×Dic17—22no—
211C22×Dic17—22no—
212C22×Dic17—22no—
213C22×Dic17—22no—
214C22×Dic17—22no—
215C22×Dic17—22no—
216C22×Dic17—22no—
217C22×Dic17—28no—
218C22×Dic17—44no—
219C22×Dic17—416no—
220C22×Dic17C2×D414yes—
221C22×Dic17#4114yes—
222C22×Dic17C2412yes—
223C22×Dic17C2412yes—
224C22×Dic17C2412yes—
225C22×Dic17C2412yes—
226C22×Dic17C2412yes—
227C22×Dic17C2412yes—
228C22×Dic17C2412yes—
229C2×C4×D17—28no—
230C2×C4×D17—28no—
231C2×C4×D17—44no—
232C2×C4×D17—416no—
233C4⋊C4×C17—28no—
234C4⋊C4×C17—28no—
235C4⋊C4×C17—28no—
236C22⋊C4×C17—28no—
237C22⋊C4×C17—28no—
238C22⋊C4×C17—28no—
239C22⋊Dic17—28no—
240C22⋊Dic17—28no—
241#63227—28no—
242#63227—28no—
243#63227—28no—
244#63227—28no—
245#63227C2×D4116yes—
246C4⋊Dic17—28no—
247C4⋊Dic17—28no—
248C4⋊Dic17—28no—
249C4⋊Dic17—44no—
250C4⋊Dic17—44no—
251#63225—28no—
252C4×Dic17—28no—
253C4×Dic17—28no—
254C4×Dic17—44no—
255C2×#2553—171nomaximal, Sylow
256C23×C17—28no—
257C23×C17—28no—
258C23×C17—28no—
259C23×C17—22no—
260C23×C17—22no—
261C23×C17—22no—
262C23×C17—22no—
263C23×C17—22no—
264C23×C17—22no—
265C23×C17—44no—
266C23×C17—44no—
267C23×C17—44no—
268C23×C17—44no—
269C23×C17C22×D412yes—
270C23×C17C2×#4112yes—
271C23×C17C2×#4112yes—
272C23×C17C2×#4114yes—
273C23×C17C2×#4112yes—
274C23×C17C2×#4112yes—
275C23×C17H(5,𝔽2)12yes—
276C23×C172−1+412yes—
277C23×C17C2511yescharacteristic
278C22×D17—28no—
279C22×D17—28no—
280C22×D17—28no—
281C22×D17—22no—
282C22×D17—22no—
283C22×D17—22no—
284C22×D17—22no—
285C22×D17—22no—
286C22×D17—22no—
287C22×D17—44no—
288C22×D17—44no—
289C22×D17—44no—
290C22×D17—44no—
291C22×D17C22×D414yes—
292C2×C4×C17—28no—
293C2×C4×C17—28no—
294C2×C4×C17—28no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—22no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—22no—
303C2×C4×C17—22no—
304C2×C4×C17—22no—
305C2×C4×C17—22no—
306C2×C4×C17—22no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—44no—
311C2×C4×C17—44no—
312C2×C4×C17—44no—
313C2×C4×C17C22×D414yes—
314C2×C4×C17C2×#4114yes—
315C2×C4×C17C2×#4114yes—
316C22⋊D17—416no—
317C2×Dic17—28no—
318C2×Dic17—28no—
319C2×Dic17—22no—
320C2×Dic17—22no—
321C2×Dic17—22no—
322C2×Dic17—22no—
323C2×Dic17—22no—
324C2×Dic17—22no—
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—22no—
329C2×Dic17—22no—
330C2×Dic17—22no—
331C2×Dic17—22no—
332C2×Dic17—22no—
333C2×Dic17—22no—
334C2×Dic17—22no—
335C2×Dic17—22no—
336C2×Dic17—22no—
337C2×Dic17—22no—
338C2×Dic17—416no—
339C2×Dic17—44no—
340C2×Dic17—44no—
341C2×Dic17—44no—
342C2×Dic17—44no—
343C2×Dic17—44no—
344C2×Dic17C22×D414yes—
345C2×Dic17C2×#4114yes—
346C4×D17—416no—
347C22×#126—171no—
348C22×#123—171no—
349#2553—1716no—
350C2×#399D1711yescharacteristic, complemented
351C2×#398—171no—
352C2×#397—171no—
353C2×#394—171no—
354C2×#389—171no—
355C2×#388—171no—
356C2×#387—171no—
357C2×#386—171no—
358C2×#385—171no—
359C2×#382—171no—
360C2×#380—171no—
361C2×C4×C22⋊C4—171no—
362C2×C4×C22⋊C4—171no—
363C22×C17—24no—
364C22×C17—24no—
365C22×C17—24no—
366C22×C17—42no—
367C22×C17—42no—
368C22×C17—42no—
369C22×C17—42no—
370C22×C17—416no—
371C22×C17#52914yes—
372C22×C17#53214yes—
373C22×C17#53914yes—
374C22×C17#54614yes—
375C22×C17#54714yes—
376C22×C17#55114yes—
377C22×C17#55214yes—
378C22×C17C23×D411yescharacteristic
379C22×C17C22×#4111yescharacteristic
380C22×C17C22×#4111yescharacteristic
381C22×C17C22×#4111yescharacteristic
382C22×C17C22×#4111yescharacteristic
383C22×C17C2×H(5,𝔽2)11yescharacteristic
384C22×C17C2×2−1+411yescharacteristic
385C2×D17—24no—
386C2×D17—24no—
387C2×D17—24no—
388C2×D17—42no—
389C2×D17—42no—
390C2×D17—42no—
391C2×D17—42no—
392C2×D17—416no—
393C4×C17—24no—
394C4×C17—24no—
395C4×C17—24no—
396C4×C17—42no—
397C4×C17—42no—
398C4×C17—42no—
399Dic17—24no—
400Dic17—24no—
401Dic17—42no—
402Dic17—42no—
403Dic17—42no—
404Dic17—42no—
405Dic17—42no—
406C23×D4—171no—
407C24×C4—171no—
408C24×C4—171no—
409C2×#126—178no—
410C2×#126—348no—
411C2×#123—178no—
412C2×#123—348no—
413C22×C4⋊C4—171no—
414C22×C4⋊C4—171no—
415C22×C4⋊C4—171no—
416C22×C4⋊C4—171no—
417C22×C4⋊C4—171no—
418C22×C4⋊C4—171no—
419C22×C4⋊C4C2×D1711yescharacteristic
420C22×C4⋊C4C2×D1711yescharacteristic
421C22×C4⋊C4C2×D1711yescharacteristic
422C22×C22⋊C4—171no—
423C22×C22⋊C4—171no—
424C22×C22⋊C4—171no—
425C22×C22⋊C4—171no—
426C22×C22⋊C4—171no—
427C22×C22⋊C4—171no—
428C22×C22⋊C4—171no—
429C22×C22⋊C4C2×D1711yescharacteristic
430C22×C22⋊C4C2×D1711yescharacteristic
431C22×C22⋊C4C2×D1711yescharacteristic
432C22×C42—171no—
433C22×C42—171no—
434C22×C42—171no—
435#399C2×D1718yescomplemented
436#398—178no—
437#397—178no—
438#394—178no—
439#389—178no—
440#388—178no—
441#387—178no—
442#386—178no—
443#385—178no—
444#382—178no—
445#380—178no—
446C4×C22⋊C4—178no—
447C4×C22⋊C4—178no—
448C2×#95—171no—
449C2×#95—171no—
450C2×#95—171no—
451C2×#95—171no—
452C2×#95—171no—
453C2×#95—171no—
454C2×#95—171no—
455C2×#95—171no—
456C2×#95—171no—
457C2×#95C2×D1711yescharacteristic
458C2×C17—44no—
459C2×C17#255318yescomplemented
460C2×C17C2×#52911yescharacteristic
461C2×C17C2×#53211yescharacteristic
462C2×C17C2×#53911yescharacteristic
463C2×C17C2×#54611yescharacteristic
464C2×C17C2×#54711yescharacteristic
465C2×C17C2×#55111yescharacteristic
466C2×C17C2×#55211yescharacteristic
467D17—44no—
468C25—171no—
469C25C22×D1711yescharacteristic
470C22×D4—174no—
471C22×D4—344no—
472C22×D4—344no—
473C22×D4—682no—
474C23×C4—171no—
475C23×C4—171no—
476C23×C4—171no—
477C23×C4—171no—
478C23×C4—171no—
479C23×C4—171no—
480C23×C4—171no—
481C23×C4—174no—
482C23×C4—174no—
483C23×C4—344no—
484C23×C4—344no—
485C23×C4—344no—
486C23×C4—344no—
487C23×C4—682no—
488C23×C4—682no—
489C23×C4C22×D1711yescharacteristic
490C23×C4C22×D1711yescharacteristic
491C23×C4C22×D1711yescharacteristic
492C23×C4C22×D1711yescharacteristic
493C23×C4C22×D1711yescharacteristic
494C23×C4C22×D1711yescharacteristic
495#126—3432no—
496#123—3432no—
497C2×C4⋊C4—24no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—174no—
501C2×C4⋊C4—174no—
502C2×C4⋊C4—174no—
503C2×C4⋊C4—174no—
504C2×C4⋊C4—174no—
505C2×C4⋊C4—174no—
506C2×C4⋊C4—344no—
507C2×C4⋊C4—344no—
508C2×C4⋊C4—344no—
509C2×C4⋊C4—344no—
510C2×C4⋊C4—682no—
511C2×C4⋊C4—682no—
512C2×C4⋊C4C22×D1714yes—
513C2×C4⋊C4C22×D1714yes—
514C2×C4⋊C4C22×D1714yes—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—178no—
519C2×C22⋊C4—174no—
520C2×C22⋊C4—174no—
521C2×C22⋊C4—174no—
522C2×C22⋊C4—174no—
523C2×C22⋊C4—174no—
524C2×C22⋊C4—174no—
525C2×C22⋊C4—174no—
526C2×C22⋊C4—344no—
527C2×C22⋊C4—344no—
528C2×C22⋊C4—344no—
529C2×C22⋊C4—344no—
530C2×C22⋊C4—344no—
531C2×C22⋊C4—344no—
532C2×C22⋊C4C22×D1714yes—
533C2×C22⋊C4C22×D1714yes—
534C2×C22⋊C4C22×D1714yes—
535C2×C42—174no—
536C2×C42—174no—
537C2×C42—174no—
538C2×C42—344no—
539C2×C42—344no—
540C2×C42—682no—
541#95—174no—
542#95—174no—
543#95—174no—
544#95—174no—
545#95—174no—
546#95—174no—
547#95—174no—
548#95—174no—
549#95—174no—
550#95C22×D1714yes—
551C17C2×#255311yescharacteristic, complemented, Sylow
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—174no—
559C24—172no—
560C24—342no—
561C24—342no—
562C24—342no—
563C24—342no—
564C24—342no—
565C24—342no—
566C24#6325614yes—
567C24C23×D1712yes—
568C24C23×D1711yescharacteristic
569C2×D4—348no—
570C2×D4—348no—
571C2×D4—684no—
572C2×D4—6816no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—174no—
589C22×C4—174no—
590C22×C4—172no—
591C22×C4—172no—
592C22×C4—172no—
593C22×C4—172no—
594C22×C4—172no—
595C22×C4—172no—
596C22×C4—172no—
597C22×C4—348no—
598C22×C4—348no—
599C22×C4—342no—
600C22×C4—342no—
601C22×C4—342no—
602C22×C4—342no—
603C22×C4—342no—
604C22×C4—342no—
605C22×C4—342no—
606C22×C4—342no—
607C22×C4—342no—
608C22×C4—342no—
609C22×C4—342no—
610C22×C4—348no—
611C22×C4—342no—
612C22×C4—342no—
613C22×C4—342no—
614C22×C4—342no—
615C22×C4—342no—
616C22×C4—342no—
617C22×C4—342no—
618C22×C4—342no—
619C22×C4—348no—
620C22×C4—684no—
621C22×C4—6816no—
622C22×C4—684no—
623C22×C4—6816no—
624C22×C4D4×D1714yes—
625C22×C4#6325414yes—
626C22×C4#6325414yes—
627C22×C4C23×D1712yes—
628C22×C4C23×D1712yes—
629C22×C4C23×D1712yes—
630C22×C4C23×D1712yes—
631C22×C4C23×D1712yes—
632C22×C4C23×D1712yes—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—28no—
636C4⋊C4—348no—
637C4⋊C4—348no—
638C4⋊C4—348no—
639C4⋊C4—348no—
640C4⋊C4—684no—
641C4⋊C4—684no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—28no—
645C22⋊C4—1716no—
646C22⋊C4—348no—
647C22⋊C4—348no—
648C22⋊C4—348no—
649C22⋊C4—348no—
650C22⋊C4—348no—
651C22⋊C4—348no—
652C42—348no—
653C42—348no—
654C42—684no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—28no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—174no—
669C23—348no—
670C23—348no—
671C23—342no—
672C23—342no—
673C23—342no—
674C23—342no—
675C23—342no—
676C23—342no—
677C23—348no—
678C23—684no—
679C23—684no—
680C23—684no—
681C23—684no—
682C23C2×D4×D1712yes—
683C23C2×#6325412yes—
684C23C2×#6325412yes—
685C23C2×#6325614yes—
686C23C2×#6325612yes—
687C23#41×D1712yes—
688C23#1058769612yes—
689C23#1058769712yes—
690C23C24×D1711yescharacteristic
691D4—6816no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—28no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—174no—
714C2×C4—174no—
715C2×C4—348no—
716C2×C4—342no—
717C2×C4—342no—
718C2×C4—342no—
719C2×C4—342no—
720C2×C4—348no—
721C2×C4—342no—
722C2×C4—342no—
723C2×C4—342no—
724C2×C4—342no—
725C2×C4—342no—
726C2×C4—342no—
727C2×C4—342no—
728C2×C4—342no—
729C2×C4—342no—
730C2×C4—342no—
731C2×C4—342no—
732C2×C4—342no—
733C2×C4—342no—
734C2×C4—342no—
735C2×C4—342no—
736C2×C4—6816no—
737C2×C4—6816no—
738C2×C4—684no—
739C2×C4—684no—
740C2×C4—684no—
741C2×C4—684no—
742C2×C4—684no—
743C2×C4C2×D4×D1714yes—
744C2×C4C2×#6325414yes—
745C2×C4C2×#6325414yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—416no—
752C22—42no—
753C22—42no—
754C22—344no—
755C22—344no—
756C22—344no—
757C22—682no—
758C22—6816no—
759C22—682no—
760C22—682no—
761C22—682no—
762C22#1176334514yes—
763C22#1176335714yes—
764C22#1176340314yes—
765C22#1176345014yes—
766C22#1176345714yes—
767C22#1176348214yes—
768C22#1176350114yes—
769C22C22×D4×D1711yescharacteristic
770C22C2×#41×D1711yescharacteristic
771C22C22×#6325411yescharacteristic
772C22C22×#6325411yescharacteristic
773C22C22×#6325611yescharacteristic
774C22C2×#1058769611yescharacteristic
775C22C2×#1058769711yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—344no—
783C4—344no—
784C4—682no—
785C4—682no—
786C4—682no—
787C4—682no—
788C4—682no—
789C2—44no—
790C2—684no—
791C2#1453383018yesdirect product factor
792C2C2×#1176334511yescharacteristic
793C2C2×#1176335711yescharacteristic
794C2C2×#1176340311yescharacteristic
795C2C2×#1176345011yescharacteristic
796C2C2×#1176345711yescharacteristic
797C2C2×#1176348211yescharacteristic
798C2C2×#1176350111yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#399C2
socleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×#399D17
hypocenterC17C2×#2553
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#10587584C2semidirect
3. #14533830C2direct (N × H)
4. C2×#11762741C2semidirect
5. C2×#11762735C2semidirect
7. C2×#11762708C2semidirect
8. C2×#11762703C2semidirect
9. C2×#11762695C2semidirect
11. C2×#11762684C2semidirect
12. C2×#11762674C2semidirect
13. C2×#11762666C2semidirect
14. C2×C22⋊C4×Dic17C2semidirect
15. C2×#11762656C2semidirect
16. C2×C17×#399C2semidirect
21. C2×#10587584C22semidirect
40. #11762741C22semidirect
41. #11762735C22semidirect
43. #11762708C22semidirect
44. #11762703C22semidirect
45. #11762695C22semidirect
47. #11762684C22semidirect
48. #11762674C22semidirect
49. #11762666C22semidirect
50. C22⋊C4×Dic17C22semidirect
51. #11762656C22semidirect
67. C17×#399C22semidirect
350. C2×#399D17semidirect
435. #399C2×D17semidirect
459. C2×C17#2553semidirect
551. C17C2×#2553semidirect
791. C2#14533830direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875842
C22×#105875722
#145338302
C2×#117627412
C2×#117627352
C2×#117627252
C2×#117627082
C2×#117627032
C2×#117626952
C2×#117626852
C2×#117626842
C2×#117626742
C2×#117626662
C2×C22⋊C4×Dic172
C2×#117626562
C2×C17×#3992
C2×#255317