Finite Group Databasebeta

← C2×#14534708 #17200733

Subgroups — C2×#14534708 #17200733

Order 4352.

2958 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587582C211yesmaximal, characteristic, complemented
2C22×C4×D68C211yesmaximal, characteristic
3#14534708C2116yesmaximal, direct product factor
4C2×#11762742C211yesmaximal, characteristic, complemented
5C2×#11762738C211yesmaximal, characteristic, complemented
6C2×#11762738C211yesmaximal, characteristic, complemented
7C2×#11762736C211yesmaximal, characteristic, complemented
8C2×#11762730C211yesmaximal, characteristic, complemented
9C2×#11762727C211yesmaximal, characteristic
10C2×#11762726C211yesmaximal, characteristic
11C2×#11762722C211yesmaximal, characteristic, complemented
12C2×#11762693C211yesmaximal, characteristic, complemented
13C2×#11762683C211yesmaximal, characteristic, complemented
14C2×#11762680C211yesmaximal, characteristic, complemented
15C2×#11762671C211yesmaximal, characteristic, complemented
16C2×C17×#387C211yesmaximal, characteristic, complemented
17C23×Dic34C2211yescharacteristic
18C23×D68C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C23×C4×D17C2211yescharacteristic
21C2×#10587582—28no—
22C2×#10587582C2218yescomplemented
23C2×C4×D68—28no—
24C2×C4×D68C2218yes—
25C22×C4⋊Dic17C2211yescharacteristic
26C22×C4⋊Dic17C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C22×#63225C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×#63227C2211yescharacteristic
36C22×#63227C2211yescharacteristic
37C22×#63227C2211yescharacteristic
38C22×#63227C2211yescharacteristic
39C22×#63227C2211yescharacteristic
40C22×#63227C2211yescharacteristic
41#11762742C2218yescomplemented
42#11762738C2218yescomplemented
43#11762738C2218yescomplemented
44#11762736C2218yescomplemented
45#11762730C2218yescomplemented
46#11762727C2218yes—
47#11762726C2218yes—
48#11762722C2218yescomplemented
49#11762693C2218yescomplemented
50#11762683C2218yescomplemented
51#11762680C2218yescomplemented
52#11762671C2218yescomplemented
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×C42×C17C2211yescharacteristic
64C17×#387C2218yescomplemented
65C2×C17×#95C2211yescharacteristic
66C2×C17×#95C2211yescharacteristic
67C2×C17×#95C2211yescharacteristic
68C2×C17×#95C2211yescharacteristic
69C24×D17C2311yescharacteristic
70C24×D17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C22×D68—24no—
85C22×D68—24no—
86C22×D68—24no—
87C22×D68C2314yes—
88C22×C4×D17—24no—
89C22×C4×D17—42no—
90C22×C4×D17—42no—
91C22×C4×D17—42no—
92C22×C4×D17—42no—
93C22×C4×D17D418yes—
94C22×C4×D17C2314yes—
95C22×C4×D17C2314yes—
96C22×Dic34—24no—
97C22×Dic34—42no—
98C22×Dic34—42no—
99C22×Dic34C2314yes—
100C2×C4⋊C4×C17—24no—
101C2×C4⋊C4×C17—24no—
102C2×C4⋊C4×C17C2314yes—
103C2×C4⋊C4×C17C2314yes—
104C2×C42×C17—24no—
105C2×C42×C17C2314yes—
106C2×#63227—24no—
107C2×#63227—24no—
108C2×#63227—24no—
109C2×#63227—24no—
110C2×#63227—24no—
111C2×#63227—24no—
112C2×#63227—42no—
113C2×#63227—42no—
114C2×#63227—42no—
115C2×#63227—42no—
116C2×#63227C2314yes—
117C2×#63227C2314yes—
118C2×#63227C2314yes—
119C2×#63227C2314yes—
120C2×#63227C2314yes—
121C2×#63227C2314yes—
122C2×#63227C2314yes—
123C2×#63227C2314yes—
124C2×#63227C2314yes—
125C2×#63227C2314yes—
126C2×C4⋊Dic17—24no—
127C2×C4⋊Dic17—42no—
128C2×C4⋊Dic17C2314yes—
129C2×C4⋊Dic17C2314yes—
130C2×#63225—24no—
131C2×#63225—24no—
132C2×#63225—24no—
133C2×#63225—42no—
134C2×#63225C2314yes—
135C2×#63225C2314yes—
136C2×#63225C2314yes—
137C2×#63225C2314yes—
138#10587582—232no—
139C4×D68—232no—
140C17×#95C2314yes—
141C17×#95C2314yes—
142C17×#95C2314yes—
143C17×#95C2314yes—
144#10587502C2314yes—
145#10587502C2314yes—
146#10587502C2314yes—
147#10587502C2314yes—
148#10587502C2314yes—
149#10587502C2314yes—
150#10587502C2314yes—
151#10587502C2314yes—
152C24×C17C2411yescharacteristic
153C23×D17—22no—
154C23×D17—22no—
155C23×D17—22no—
156C23×D17—22no—
157C23×D17—22no—
158C23×D17—22no—
159C23×D17—22no—
160C23×D17—22no—
161C23×D17—22no—
162C23×D17—22no—
163C23×D17—22no—
164C23×D17—22no—
165C23×D17C2×D414yes—
166C23×D17#4114yes—
167C23×D17C2412yes—
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×C17—22no—
185C22×C4×C17—22no—
186C22×C4×C17—22no—
187C22×C4×C17—22no—
188C22×C4×C17C2×D414yes—
189C22×C4×C17#4114yes—
190C22×C4×C17C2412yes—
191C22×C4×C17C2412yes—
192C22×C4×C17C2412yes—
193C22×C4×C17C2412yes—
194C22×C4×C17C2412yes—
195C22×C4×C17C2412yes—
196C22×C4×C17C2412yes—
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—22no—
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×Dic17C2×D414yes—
215C22×Dic17C2412yes—
216C22×Dic17C2412yes—
217C22×Dic17C2412yes—
218C22×Dic17C2412yes—
219C22×Dic17C2412yes—
220C22×Dic17C2412yes—
221C2×D68—232no—
222C2×D68—28no—
223C2×D68—28no—
224C2×D68—28no—
225C2×C4×D17—28no—
226C2×C4×D17—416no—
227C2×C4×D17—44no—
228C2×C4×D17—44no—
229C2×C4×D17—44no—
230C2×C4×D17—44no—
231C2×C4×D17—416no—
232C2×C4×D17C2×D4116yes—
233C2×Dic34—28no—
234C2×Dic34—44no—
235C2×Dic34—44no—
236C2×Dic34—416no—
237C4⋊C4×C17—28no—
238C4⋊C4×C17—28no—
239C42×C17—28no—
240#63227—28no—
241#63227—28no—
242#63227—28no—
243#63227—28no—
244#63227—28no—
245#63227—28no—
246#63227—44no—
247#63227—44no—
248#63227—44no—
249#63227—44no—
250C4⋊Dic17—28no—
251C4⋊Dic17—44no—
252#63225—28no—
253#63225—28no—
254#63225—28no—
255#63225—44no—
256C2×#2638—171nomaximal, Sylow
257C23×C17C22×D412yes—
258C23×C17C2×#4112yes—
259C23×C17C2×#4112yes—
260C23×C17H(5,𝔽2)12yes—
261C23×C17H(5,𝔽2)12yes—
262C23×C172−1+412yes—
263C23×C172−1+412yes—
264C23×C17C2511yescharacteristic
265C22×D17—28no—
266C22×D17—28no—
267C22×D17—28no—
268C22×D17—28no—
269C22×D17—28no—
270C22×D17—28no—
271C22×D17—22no—
272C22×D17—22no—
273C22×D17—22no—
274C22×D17—22no—
275C22×D17—22no—
276C22×D17—22no—
277C22×D17—22no—
278C22×D17—22no—
279C22×D17—22no—
280C22×D17—22no—
281C22×D17—22no—
282C22×D17—22no—
283C22×D17—44no—
284C22×D17—44no—
285C22×D17—44no—
286C22×D17—44no—
287C22×D17—44no—
288C22×D17—44no—
289C22×D17—44no—
290C22×D17—44no—
291C22×D17C22×D414yes—
292C22×D17C2×#4114yes—
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—22no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—44no—
315C2×C4×C17—44no—
316C2×C4×C17—44no—
317C2×C4×C17—44no—
318C2×C4×C17—44no—
319C2×C4×C17C22×D414yes—
320C2×C4×C17C2×#4114yes—
321C2×Dic17—28no—
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—22no—
339C2×Dic17—44no—
340C2×Dic17—44no—
341C2×Dic17—44no—
342C2×Dic17—44no—
343C2×Dic17—44no—
344C2×Dic17C22×D414yes—
345D68—232no—
346C4×D17—416no—
347C4×D17—416no—
348Dic34—416no—
349C22×C22⋊Q8—171no—
350C22×C4×D4—171no—
351#2638—1716no—
352C2×#398—171no—
353C2×#397—171no—
354C2×#397—171no—
355C2×#397—171no—
356C2×#395—171no—
357C2×#394—171no—
358C2×#394—171no—
359C2×#393—171no—
360C2×#387—171no—
361C2×#387D1711yescharacteristic, complemented
362C2×#385—171no—
363C2×#385—171no—
364C2×#381—171no—
365C22×C17#52514yes—
366C22×C17#53414yes—
367C22×C17#53614yes—
368C22×C17#53914yes—
369C22×C17#53914yes—
370C22×C17#54214yes—
371C22×C17#54214yes—
372C22×C17C23×D411yescharacteristic
373C22×C17C22×#4111yescharacteristic
374C22×C17C22×#4111yescharacteristic
375C22×C17C2×H(5,𝔽2)11yescharacteristic
376C22×C17C2×H(5,𝔽2)11yescharacteristic
377C22×C17C2×2−1+411yescharacteristic
378C22×C17C2×2−1+411yescharacteristic
379C2×D17—24no—
380C2×D17—24no—
381C2×D17—24no—
382C2×D17—24no—
383C2×D17—24no—
384C2×D17—24no—
385C2×D17—416no—
386C2×D17—416no—
387C2×D17—42no—
388C2×D17—42no—
389C2×D17—42no—
390C2×D17—42no—
391C2×D17—42no—
392C2×D17—42no—
393C2×D17—42no—
394C2×D17—42no—
395C4×C17—24no—
396C4×C17—24no—
397C4×C17—42no—
398C4×C17—42no—
399C4×C17—42no—
400C4×C17—42no—
401C4×C17—42no—
402Dic17—24no—
403Dic17—42no—
404Dic17—42no—
405Dic17—42no—
406Dic17—42no—
407Dic17—42no—
408C23×Q8—171no—
409C23×D4—171no—
410C24×C4—171no—
411C24×C4—171no—
412C2×C22⋊Q8—178no—
413C2×C22⋊Q8—348no—
414C2×C4×D4—178no—
415C2×C4×D4—348no—
416C22×C4⋊C4—171no—
417C22×C4⋊C4—171no—
418C22×C4⋊C4—171no—
419C22×C4⋊C4—171no—
420C22×C4⋊C4—171no—
421C22×C4⋊C4—171no—
422C22×C4⋊C4C2×D1711yescharacteristic
423C22×C4⋊C4C2×D1711yescharacteristic
424C22×C22⋊C4—171no—
425C22×C22⋊C4—171no—
426C22×C22⋊C4—171no—
427C22×C22⋊C4—171no—
428C22×C22⋊C4—171no—
429C22×C22⋊C4—171no—
430C22×C22⋊C4—171no—
431C22×C22⋊C4—171no—
432C22×C22⋊C4—171no—
433C22×C22⋊C4—171no—
434C22×C42C2×D1711yescharacteristic
435#398—178no—
436#397—178no—
437#397—178no—
438#397—178no—
439#395—178no—
440#394—178no—
441#394—178no—
442#393—178no—
443#387—178no—
444#387C2×D1718yescomplemented
445#385—178no—
446#385—178no—
447#381—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×#95C2×D1711yescharacteristic
457C2×#95C2×D1711yescharacteristic
458C2×#95C2×D1711yescharacteristic
459C2×#95C2×D1711yescharacteristic
460C2×C17#263818yescomplemented
461C2×C17C2×#52511yescharacteristic
462C2×C17C2×#53411yescharacteristic
463C2×C17C2×#53611yescharacteristic
464C2×C17C2×#53911yescharacteristic
465C2×C17C2×#53911yescharacteristic
466C2×C17C2×#54211yescharacteristic
467C2×C17C2×#54211yescharacteristic
468D17—44no—
469D17—44no—
470C25—171no—
471C25—171no—
472C22×Q8—174no—
473C22×Q8—344no—
474C22×Q8—682no—
475C22×Q8—682no—
476C22×D4—174no—
477C22×D4—344no—
478C22×D4—344no—
479C22×D4—344no—
480C23×C4—171no—
481C23×C4—178no—
482C23×C4—174no—
483C23×C4—171no—
484C23×C4—171no—
485C23×C4—171no—
486C23×C4—171no—
487C23×C4—171no—
488C23×C4—174no—
489C23×C4—344no—
490C23×C4—682no—
491C23×C4—682no—
492C23×C4—682no—
493C23×C4—682no—
494C23×C4C22×D1711yescharacteristic
495C23×C4C22×D1711yescharacteristic
496C23×C4C22×D1711yescharacteristic
497C23×C4C22×D1711yescharacteristic
498C23×C4C22×D1711yescharacteristic
499C23×C4C22×D1711yescharacteristic
500C23×C4C22×D1711yescharacteristic
501C22⋊Q8—3432no—
502C4×D4—3432no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—174no—
506C2×C4⋊C4—174no—
507C2×C4⋊C4—174no—
508C2×C4⋊C4—174no—
509C2×C4⋊C4—174no—
510C2×C4⋊C4—174no—
511C2×C4⋊C4—344no—
512C2×C4⋊C4—344no—
513C2×C4⋊C4—344no—
514C2×C4⋊C4—344no—
515C2×C4⋊C4—682no—
516C2×C4⋊C4—682no—
517C2×C4⋊C4C22×D1714yes—
518C2×C4⋊C4C22×D1714yes—
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—174no—
527C2×C22⋊C4—174no—
528C2×C22⋊C4—174no—
529C2×C22⋊C4—344no—
530C2×C22⋊C4—344no—
531C2×C22⋊C4—344no—
532C2×C22⋊C4—344no—
533C2×C22⋊C4—344no—
534C2×C22⋊C4—344no—
535C2×C22⋊C4—682no—
536C2×C22⋊C4—682no—
537C2×C22⋊C4—682no—
538C2×C22⋊C4—682no—
539C2×C42—24no—
540C2×C42C22×D1714yes—
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#95C22×D1714yes—
550#95C22×D1714yes—
551#95C22×D1714yes—
552#95C22×D1714yes—
553C17C2×#263811yescharacteristic, complemented, Sylow
554C24—174no—
555C24—174no—
556C24—172no—
557C24—172no—
558C24—342no—
559C24—342no—
560C24—342no—
561C24—342no—
562C24—342no—
563C24—342no—
564C24—342no—
565C24—342no—
566C24—342no—
567C24—342no—
568C24—342no—
569C24—342no—
570C24C23×D1711yescharacteristic
571C2×Q8—348no—
572C2×Q8—684no—
573C2×Q8—684no—
574C2×Q8—6816no—
575C2×D4—348no—
576C2×D4—348no—
577C2×D4—3432no—
578C2×D4—348no—
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—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
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—1716no—
601C22×C4—172no—
602C22×C4—172no—
603C22×C4—172no—
604C22×C4—172no—
605C22×C4—172no—
606C22×C4—342no—
607C22×C4—342no—
608C22×C4—342no—
609C22×C4—342no—
610C22×C4—342no—
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—342no—
620C22×C4—342no—
621C22×C4—342no—
622C22×C4—342no—
623C22×C4—348no—
624C22×C4—6816no—
625C22×C4—684no—
626C22×C4—684no—
627C22×C4—684no—
628C22×C4—684no—
629C22×C4—6816no—
630C22×C4#6325214yes—
631C22×C4D4×D1714yes—
632C22×C4C23×D1712yes—
633C22×C4C23×D1712yes—
634C22×C4C23×D1712yes—
635C22×C4C23×D1712yes—
636C22×C4C23×D1712yes—
637C22×C4C23×D1712yes—
638C22×C4C23×D1712yes—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—348no—
642C4⋊C4—348no—
643C4⋊C4—348no—
644C4⋊C4—348no—
645C4⋊C4—684no—
646C4⋊C4—684no—
647C22⋊C4—348no—
648C22⋊C4—348no—
649C22⋊C4—348no—
650C22⋊C4—348no—
651C22⋊C4—348no—
652C22⋊C4—348no—
653C22⋊C4—684no—
654C22⋊C4—684no—
655C22⋊C4—684no—
656C22⋊C4—684no—
657C42—28no—
658C23—174no—
659C23—174no—
660C23—348no—
661C23—348no—
662C23—348no—
663C23—342no—
664C23—342no—
665C23—342no—
666C23—342no—
667C23—348no—
668C23—342no—
669C23—342no—
670C23—342no—
671C23—342no—
672C23—342no—
673C23—342no—
674C23—342no—
675C23—342no—
676C23—348no—
677C23—348no—
678C23—684no—
679C23—684no—
680C23—684no—
681C23—684no—
682C23—684no—
683C23—684no—
684C23—684no—
685C23—684no—
686C23C2×#6325212yes—
687C23C2×D4×D1712yes—
688C23#1058769412yes—
689C23#41×D1712yes—
690C23#1058769612yes—
691C23#1058769612yes—
692C23#1058769712yes—
693C23C24×D1711yescharacteristic
694Q8—6816no—
695D4—3432no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
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—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—174no—
723C2×C4—348no—
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—342no—
737C2×C4—342no—
738C2×C4—342no—
739C2×C4—342no—
740C2×C4—342no—
741C2×C4—6816no—
742C2×C4—6816no—
743C2×C4—684no—
744C2×C4—684no—
745C2×C4—684no—
746C2×C4—684no—
747C2×C4—684no—
748C2×C4C2×#6325214yes—
749C2×C4C2×D4×D1714yes—
750C22—344no—
751C22—344no—
752C22—344no—
753C22—344no—
754C22—344no—
755C22—344no—
756C22—682no—
757C22—682no—
758C22—682no—
759C22—6816no—
760C22—6816no—
761C22—682no—
762C22—682no—
763C22—682no—
764C22—682no—
765C22—682no—
766C22#1176331814yes—
767C22#1176337014yes—
768C22#1176338214yes—
769C22#1176340014yes—
770C22#1176340714yes—
771C22#1176343014yes—
772C22#1176343114yes—
773C22C22×D4×D1711yescharacteristic
774C22C2×#41×D1711yescharacteristic
775C22C22×#6325211yescharacteristic
776C22C2×#1058769611yescharacteristic
777C22C2×#1058769611yescharacteristic
778C22C2×#1058769711yescharacteristic
779C22C2×#1058769411yescharacteristic
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—344no—
788C4—682no—
789C4—682no—
790C4—682no—
791C4—682no—
792C4—682no—
793C2—684no—
794C2—684no—
795C2#1453470818yesdirect product factor
796C2C2×#1176331811yescharacteristic
797C2C2×#1176337011yescharacteristic
798C2C2×#1176338211yescharacteristic
799C2C2×#1176340011yescharacteristic
800C2C2×#1176340711yescharacteristic
801C2C2×#1176343011yescharacteristic
802C2C2×#1176343111yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#387C2
socleC24×C17C24
prime radicalC23×D68C22
hypercenterC2×#387D17
hypocenterC17C2×#2638
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#10587582C2semidirect
3. #14534708C2direct (N × H)
4. C2×#11762742C2semidirect
5. C2×#11762738C2semidirect
6. C2×#11762738C2semidirect
7. C2×#11762736C2semidirect
8. C2×#11762730C2semidirect
11. C2×#11762722C2semidirect
12. C2×#11762693C2semidirect
13. C2×#11762683C2semidirect
14. C2×#11762680C2semidirect
15. C2×#11762671C2semidirect
16. C2×C17×#387C2semidirect
22. C2×#10587582C22semidirect
41. #11762742C22semidirect
42. #11762738C22semidirect
43. #11762738C22semidirect
44. #11762736C22semidirect
45. #11762730C22semidirect
48. #11762722C22semidirect
49. #11762693C22semidirect
50. #11762683C22semidirect
51. #11762680C22semidirect
52. #11762671C22semidirect
64. C17×#387C22semidirect
361. C2×#387D17semidirect
444. #387C2×D17semidirect
460. C2×C17#2638semidirect
553. C17C2×#2638semidirect
795. C2#14534708direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875822
C22×C4×D682
#145347082
C2×#117627422
C2×#117627382
C2×#117627362
C2×#117627302
C2×#117627272
C2×#117627262
C2×#117627222
C2×#117626932
C2×#117626832
C2×#117626802
C2×#117626712
C2×C17×#3872
C2×#263817