Finite Group Databasebeta

← #16956977

Subgroups — #16956977

Order 4352.

2006 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587578C211yesmaximal, characteristic
2C2×#11762707C211yesmaximal, characteristic, complemented
3C2×#11762705C211yesmaximal, characteristic, complemented
4C2×#11762666C211yesmaximal, characteristic
5C2×C4×#63227C211yesmaximal, characteristic
6#14527028C212yesmaximal
7#14527028C212yesmaximal
8#14527013C211yesmaximal, characteristic, complemented
9#14527012C212yesmaximal, complemented
10#14527009C212yesmaximal, complemented
11C17×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D17C2211yescharacteristic
13C2×#10587578—24no—
14C2×#10587578—24no—
15C2×#10587578C418yescomplemented
16C22×C4⋊Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×#63225C2212yes—
19C22×#63225C2212yes—
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2212yes—
23C22×#63227C2212yes—
24C22×C4×Dic17C2211yescharacteristic
25C22×C4×Dic17C2212yes—
26#11762707—24no—
27#11762705—24no—
28#11762666—24no—
29C4×#63227—24no—
30C2×#10587502C2211yescharacteristic
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2212yes—
37C22×C4⋊C4×C17C2211yescharacteristic
38C22×C4⋊C4×C17C2211yescharacteristic
39C22×C42×C17C2211yescharacteristic
40C2×C17×#95C2212yes—
41C2×C17×#95C2212yes—
42C24×D17C2311yescharacteristic
43C23×C4×C17C2312yes—
44C23×C4×C17C2312yes—
45C23×C4×C17C2311yescharacteristic
46C23×C4×C17C2311yescharacteristic
47C23×C4×C17C2311yescharacteristic
48C23×Dic17C2312yes—
49C23×Dic17C2311yescharacteristic
50C23×Dic17C2311yescharacteristic
51C23×Dic17C2312yes—
52C23×Dic17C2311yescharacteristic
53C22×C4×D17—22no—
54C22×C4×D17—22no—
55C22×C4×D17—22no—
56C22×C4×D17—22no—
57C22×C4×D17C2×C414yes—
58C22×C4×D17D414yes—
59C22×C4×D17Q814yes—
60C2×C4⋊C4×C17—22no—
61C2×C4⋊C4×C17—22no—
62C2×C4⋊C4×C17—22no—
63C2×C4⋊C4×C17—22no—
64C2×C4⋊C4×C17—22no—
65C2×C4⋊C4×C17C2×C414yes—
66C2×C42×C17—22no—
67C2×C42×C17—22no—
68C2×C42×C17—22no—
69C2×#63227—22no—
70C2×#63227—22no—
71C2×#63227—24no—
72C2×#63227—22no—
73C2×#63227—22no—
74C2×#63227—24no—
75C2×#63227—24no—
76C2×#63227—22no—
77C2×#63227—22no—
78C2×#63227—42no—
79C2×#63227—42no—
80C2×#63227C2×C418yes—
81C2×C4⋊Dic17—22no—
82C2×C4⋊Dic17—22no—
83C2×C4⋊Dic17—22no—
84C2×C4⋊Dic17C2×C414yes—
85C2×C4⋊Dic17D414yes—
86C2×C4⋊Dic17D414yes—
87C2×#63225—24no—
88C2×#63225—24no—
89C2×#63225—24no—
90C2×#63225—24no—
91C2×#63225—42no—
92C2×#63225—42no—
93C2×C4×Dic17—22no—
94C2×C4×Dic17—22no—
95C2×C4×Dic17—22no—
96C2×C4×Dic17—24no—
97C2×C4×Dic17—24no—
98C2×C4×Dic17C2×C418yes—
99#10587578—232no—
100C17×#95—24no—
101C17×#95—42no—
102#10587502—24no—
103#10587502—24no—
104#10587502—22no—
105#10587502—22no—
106#10587502—24no—
107#10587502—24no—
108#10587502—42no—
109C24×C17C2411yescharacteristic
110C23×D17—21no—
111C23×D17—21no—
112C23×D17—21no—
113C23×D17—21no—
114C23×D17—21no—
115C23×D17—21no—
116C23×D17—21no—
117C23×D17—21no—
118C23×D17—21no—
119C23×D17—21no—
120C23×D17—21no—
121C23×D17—21no—
122C23×D17C22×C412yes—
123C23×D17C2×D412yes—
124C23×D17C2×Q812yes—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17—21no—
128C22×C4×C17—22no—
129C22×C4×C17—22no—
130C22×C4×C17—21no—
131C22×C4×C17—22no—
132C22×C4×C17—22no—
133C22×C4×C17—21no—
134C22×C4×C17—21no—
135C22×C4×C17—21no—
136C22×C4×C17—21no—
137C22×C4×C17—22no—
138C22×C4×C17—21no—
139C22×C4×C17—21no—
140C22×C4×C17—21no—
141C22×C4×C17—22no—
142C22×C4×C17—21no—
143C22×C4×C17—22no—
144C22×C4×C17—22no—
145C22×C4×C17—22no—
146C22×C4×C17—22no—
147C22×C4×C17—22no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17C22×C414yes—
151C22×C4×C17C22×C412yes—
152C22×C4×C17C2×D412yes—
153C22×C4×C17C2×D412yes—
154C22×C4×C17C2×D412yes—
155C22×C4×C17C2×Q812yes—
156C22×C4×C17#4112yes—
157C22×C4×C17#4112yes—
158C22×C4×C17#4112yes—
159C22×C4×C17#4112yes—
160C22×Dic17—21no—
161C22×Dic17—21no—
162C22×Dic17—21no—
163C22×Dic17—21no—
164C22×Dic17—22no—
165C22×Dic17—22no—
166C22×Dic17—22no—
167C22×Dic17—22no—
168C22×Dic17—21no—
169C22×Dic17—21no—
170C22×Dic17—21no—
171C22×Dic17—21no—
172C22×Dic17—21no—
173C22×Dic17—21no—
174C22×Dic17—21no—
175C22×Dic17—21no—
176C22×Dic17—21no—
177C22×Dic17—21no—
178C22×Dic17—21no—
179C22×Dic17—21no—
180C22×Dic17—22no—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17C22×C414yes—
188C22×Dic17C22×C412yes—
189C22×Dic17C2×D414yes—
190C22×Dic17C2×D414yes—
191C22×Dic17C2×D412yes—
192C22×Dic17C2×Q812yes—
193C22×Dic17#4112yes—
194C22×Dic17#4112yes—
195C2×C4×D17—28no—
196C2×C4×D17—28no—
197C2×C4×D17—28no—
198C2×C4×D17—28no—
199C2×C4×D17—28no—
200C2×C4×D17—28no—
201C2×C4×D17C4⋊C4116yescomplemented
202C4⋊C4×C17—28no—
203C4⋊C4×C17—44no—
204C42×C17—44no—
205#63227—28no—
206#63227—28no—
207#63227—216no—
208#63227—48no—
209C4⋊Dic17—44no—
210C4⋊Dic17C22⋊C4116yescomplemented
211#63225—48no—
212#63225—48no—
213C4×Dic17—216no—
214C4×Dic17—44no—
215#13951—171nomaximal, Sylow
216C23×C17C23×C411yescharacteristic
217C23×C17C22×D411yescharacteristic
218C23×C17C22×D411yescharacteristic
219C23×C17C22×D411yescharacteristic
220C23×C17C22×Q811yescharacteristic
221C23×C17C2×#4111yescharacteristic
222C23×C17C2×#4111yescharacteristic
223C23×C17C2×#4111yescharacteristic
224C23×C17C2×#4111yescharacteristic
225C23×C17C2×#4111yescharacteristic
226C23×C17C2×#4111yescharacteristic
227C23×C17H(5,𝔽2)11yescharacteristic
228C23×C17H(5,𝔽2)11yescharacteristic
229C23×C172−1+411yescharacteristic
230C23×C172−1+411yescharacteristic
231C22×D17—22no—
232C22×D17—22no—
233C22×D17—22no—
234C22×D17—22no—
235C22×D17—22no—
236C22×D17—22no—
237C22×D17—22no—
238C22×D17—22no—
239C22×D17—22no—
240C22×D17—22no—
241C22×D17—22no—
242C22×D17—22no—
243C22×D17—22no—
244C22×D17—22no—
245C22×D17—22no—
246C22×D17—22no—
247C22×D17—22no—
248C22×D17—22no—
249C22×D17—41no—
250C22×D17—41no—
251C22×D17—41no—
252C22×D17—41no—
253C22×D17—41no—
254C22×D17—41no—
255C22×D17—41no—
256C22×D17—41no—
257C22×D17—41no—
258C22×D17—41no—
259C22×D17—41no—
260C22×D17—41no—
261C22×D17—41no—
262C22×D17—41no—
263C22×D17—41no—
264C22×D17—41no—
265C22×D17C2×C4⋊C414yes—
266C2×C4×C17—24no—
267C2×C4×C17—24no—
268C2×C4×C17—24no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—41no—
276C2×C4×C17—41no—
277C2×C4×C17—41no—
278C2×C4×C17—41no—
279C2×C4×C17—41no—
280C2×C4×C17—42no—
281C2×C4×C17—42no—
282C2×C4×C17—42no—
283C2×C4×C17—41no—
284C2×C4×C17—42no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—42no—
288C2×C4×C17—42no—
289C2×C4×C17—42no—
290C2×C4×C17—42no—
291C2×C4×C17—42no—
292C2×C4×C17—42no—
293C2×C4×C17—42no—
294C2×C4×C17C2×C22⋊C414yes—
295C2×C4×C17C2×C4⋊C414yes—
296C2×C4×C17#11714yes—
297C2×C4×C17#12114yes—
298C2×C4×C17#12114yes—
299C2×C4×C17C22⋊Q814yes—
300C2×C4×C17C22⋊Q814yes—
301C2×Dic17—22no—
302C2×Dic17—22no—
303C2×Dic17—24no—
304C2×Dic17—24no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—24no—
310C2×Dic17—24no—
311C2×Dic17—24no—
312C2×Dic17—24no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—41no—
320C2×Dic17—41no—
321C2×Dic17—41no—
322C2×Dic17—41no—
323C2×Dic17—41no—
324C2×Dic17—41no—
325C2×Dic17—41no—
326C2×Dic17—41no—
327C2×Dic17—42no—
328C2×Dic17—42no—
329C2×Dic17—42no—
330C2×Dic17—42no—
331C2×Dic17—42no—
332C2×Dic17—42no—
333C2×Dic17—42no—
334C2×Dic17C2×C22⋊C418yes—
335C2×Dic17C2×C4⋊C414yes—
336C4×D17—232no—
337C22×#117—171no—
338C2×#389—171no—
339C2×#389—171no—
340C2×#380—171no—
341C2×C4×C22⋊C4—171no—
342#1439—172no—
343#1439—172no—
344C4⋊#95—172no—
345C4⋊#95—171no—
346C4⋊#95D1711yescharacteristic, complemented
347#1434—172no—
348C22×C17C22×C22⋊C411yescharacteristic
349C22×C17C22×C4⋊C411yescharacteristic
350C22×C17C2×#11711yescharacteristic
351C22×C17C4×#4111yescharacteristic
352C22×C17C4×#4111yescharacteristic
353C22×C17#52011yescharacteristic
354C22×C17#52011yescharacteristic
355C22×C17C2×#12111yescharacteristic
356C22×C17C2×#12111yescharacteristic
357C22×C17C2×C22⋊Q811yescharacteristic
358C22×C17C2×C22⋊Q811yescharacteristic
359C22×C17#52511yescharacteristic
360C22×C17#52511yescharacteristic
361C22×C17#53311yescharacteristic
362C22×C17#53311yescharacteristic
363C22×C17#53511yescharacteristic
364C22×C17#53611yescharacteristic
365C22×C17#54411yescharacteristic
366C22×C17#54411yescharacteristic
367C22×C17#54611yescharacteristic
368C22×C17#54611yescharacteristic
369C22×C17#54711yescharacteristic
370C22×C17#54711yescharacteristic
371C22×C17#54811yescharacteristic
372C22×C17#54811yescharacteristic
373C22×C17#55011yescharacteristic
374C22×C17#55011yescharacteristic
375C22×C17#55211yescharacteristic
376C22×C17#55211yescharacteristic
377C22×C17#55311yescharacteristic
378C22×C17#55311yescharacteristic
379C22×C17#55511yescharacteristic
380C22×C17#55511yescharacteristic
381C22×C17#55611yescharacteristic
382C22×C17#55611yescharacteristic
383C2×D17—24no—
384C2×D17—24no—
385C2×D17—24no—
386C2×D17—42no—
387C2×D17—42no—
388C2×D17—42no—
389C2×D17—42no—
390C2×D17—42no—
391C2×D17—42no—
392C2×D17—42no—
393C2×D17—42no—
394C2×D17—42no—
395C2×D17—42no—
396C2×D17—42no—
397C2×D17—42no—
398C4×C17—44no—
399C4×C17—42no—
400C4×C17—42no—
401C4×C17—82no—
402C4×C17#38018yes—
403Dic17—28no—
404Dic17—24no—
405Dic17—42no—
406Dic17—42no—
407Dic17—82no—
408C24×C4—171no—
409C2×#117—178no—
410C2×#117—344no—
411C2×#117—344no—
412C22×C4⋊C4—171no—
413C22×C4⋊C4—171no—
414C22×C4⋊C4—172no—
415C22×C4⋊C4—172no—
416C22×C4⋊C4C2×D1711yescharacteristic
417C22×C4⋊C4C2×D1711yescharacteristic
418C22×C22⋊C4—172no—
419C22×C22⋊C4—171no—
420C22×C22⋊C4—171no—
421C22×C22⋊C4—172no—
422C22×C42—172no—
423C22×C42—171no—
424C22×C42C2×D1711yescharacteristic
425#389—344no—
426#389—344no—
427#380—344no—
428C4×C22⋊C4—344no—
429C2×#95—171no—
430C2×#95—172no—
431C2×#95—172no—
432C2×#95—172no—
433C2×#95—172no—
434C2×#95—171no—
435C2×#95—172no—
436C2×#95C2×D1712yes—
437C2×#95C2×D1712yes—
438C2×C17C2×#38011yescharacteristic
439C2×C17#229611yescharacteristic
440C2×C17#231711yescharacteristic
441C2×C17#233911yescharacteristic
442C2×C17#234111yescharacteristic
443C2×C17#234611yescharacteristic
444C2×C17#234711yescharacteristic
445C2×C17#241411yescharacteristic
446C2×C17#241411yescharacteristic
447C2×C17#241511yescharacteristic
448C2×C17#241511yescharacteristic
449C2×C17#243911yescharacteristic
450C2×C17#243911yescharacteristic
451C2×C17#244111yescharacteristic
452C2×C17#244111yescharacteristic
453D17—44no—
454C25—171no—
455C23×C4—172no—
456C23×C4—171no—
457C23×C4—174no—
458C23×C4—174no—
459C23×C4—174no—
460C23×C4—171no—
461C23×C4—171no—
462C23×C4—172no—
463C23×C4—342no—
464C23×C4—342no—
465C23×C4—342no—
466C23×C4—342no—
467C23×C4C22×D1712yes—
468C23×C4C22×D1712yes—
469C23×C4C22×D1711yescharacteristic
470C23×C4C22×D1711yescharacteristic
471C23×C4C22×D1711yescharacteristic
472#117—3432no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—174no—
479C2×C4⋊C4—174no—
480C2×C4⋊C4—174no—
481C2×C4⋊C4—344no—
482C2×C4⋊C4—344no—
483C2×C4⋊C4—344no—
484C2×C4⋊C4—342no—
485C2×C4⋊C4—342no—
486C2×C4⋊C4—342no—
487C2×C4⋊C4—344no—
488C2×C4⋊C4—682no—
489C2×C4⋊C4—682no—
490C2×C4⋊C4C4×D1714yes—
491C2×C22⋊C4—178no—
492C2×C22⋊C4—344no—
493C2×C22⋊C4—344no—
494C2×C22⋊C4—342no—
495C2×C22⋊C4—342no—
496C2×C22⋊C4—342no—
497C2×C22⋊C4—342no—
498C2×C22⋊C4—342no—
499C2×C22⋊C4—342no—
500C2×C22⋊C4—344no—
501C2×C22⋊C4—682no—
502C2×C22⋊C4—682no—
503C2×C42—22no—
504C2×C42—22no—
505C2×C42—22no—
506C2×C42—178no—
507C2×C42—344no—
508C2×C42—344no—
509C2×C42—342no—
510C2×C42—342no—
511C2×C42—342no—
512#95—24no—
513#95—42no—
514#95—344no—
515#95—342no—
516#95—342no—
517#95—344no—
518#95—344no—
519#95—344no—
520#95—682no—
521C17#1395111yescharacteristic, complemented, Sylow
522C24—172no—
523C24—172no—
524C24—172no—
525C24—341no—
526C24—341no—
527C24—341no—
528C24—341no—
529C24—341no—
530C24—341no—
531C24—341no—
532C24—341no—
533C24—341no—
534C24—341no—
535C24—341no—
536C24—341no—
537C24C23×D1711yescharacteristic
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—172no—
564C22×C4—174no—
565C22×C4—172no—
566C22×C4—174no—
567C22×C4—174no—
568C22×C4—172no—
569C22×C4—1716no—
570C22×C4—172no—
571C22×C4—172no—
572C22×C4—341no—
573C22×C4—341no—
574C22×C4—341no—
575C22×C4—341no—
576C22×C4—342no—
577C22×C4—342no—
578C22×C4—342no—
579C22×C4—342no—
580C22×C4—348no—
581C22×C4—348no—
582C22×C4—348no—
583C22×C4—348no—
584C22×C4—348no—
585C22×C4—348no—
586C22×C4—341no—
587C22×C4—341no—
588C22×C4—341no—
589C22×C4—341no—
590C22×C4—341no—
591C22×C4—341no—
592C22×C4—341no—
593C22×C4—341no—
594C22×C4—341no—
595C22×C4—341no—
596C22×C4—341no—
597C22×C4—341no—
598C22×C4—342no—
599C22×C4—342no—
600C22×C4—342no—
601C22×C4—342no—
602C22×C4—342no—
603C22×C4—342no—
604C22×C4—342no—
605C22×C4C2×C4×D1714yes—
606C22×C4C2×C4×D1712yes—
607C22×C4#6325212yes—
608C22×C4#6325212yes—
609C22×C4D4×D1712yes—
610C22×C4D4×D1712yes—
611C22×C4D4×D1712yes—
612C22×C4#6325412yes—
613C22×C4Q8×D1712yes—
614C22×C4#6325612yes—
615C4⋊C4—28no—
616C4⋊C4—44no—
617C4⋊C4—1716no—
618C4⋊C4—688no—
619C4⋊C4—688no—
620C4⋊C4—684no—
621C22⋊C4—3416no—
622C22⋊C4—348no—
623C22⋊C4—348no—
624C22⋊C4—688no—
625C42—44no—
626C42—3416no—
627C42—684no—
628C23—174no—
629C23—342no—
630C23—342no—
631C23—342no—
632C23—342no—
633C23—342no—
634C23—342no—
635C23—342no—
636C23—342no—
637C23—342no—
638C23—342no—
639C23—342no—
640C23—342no—
641C23—342no—
642C23—342no—
643C23—342no—
644C23—342no—
645C23—342no—
646C23—342no—
647C23—681no—
648C23—681no—
649C23—681no—
650C23—681no—
651C23—681no—
652C23—681no—
653C23—681no—
654C23—681no—
655C23—681no—
656C23—681no—
657C23—681no—
658C23—681no—
659C23—681no—
660C23—681no—
661C23—681no—
662C23—681no—
663C23C22×C4×D1711yescharacteristic
664C23C2×#6325211yescharacteristic
665C23C2×#6325211yescharacteristic
666C23C2×D4×D1711yescharacteristic
667C23C2×D4×D1711yescharacteristic
668C23C2×D4×D1711yescharacteristic
669C23C2×#6325411yescharacteristic
670C23#1058769111yescharacteristic
671C23C2×Q8×D1711yescharacteristic
672C23C2×#6325611yescharacteristic
673C23#1058769411yescharacteristic
674C23#41×D1711yescharacteristic
675C23#41×D1711yescharacteristic
676C23#1058769611yescharacteristic
677C23#1058769711yescharacteristic
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—178no—
707C2×C4—174no—
708C2×C4—344no—
709C2×C4—344no—
710C2×C4—342no—
711C2×C4—342no—
712C2×C4—344no—
713C2×C4—344no—
714C2×C4—342no—
715C2×C4—342no—
716C2×C4—342no—
717C2×C4—342no—
718C2×C4—344no—
719C2×C4—344no—
720C2×C4—3432no—
721C2×C4—342no—
722C2×C4—342no—
723C2×C4—342no—
724C2×C4—342no—
725C2×C4—342no—
726C2×C4—342no—
727C2×C4—681no—
728C2×C4—681no—
729C2×C4—681no—
730C2×C4—681no—
731C2×C4—681no—
732C2×C4—681no—
733C2×C4—681no—
734C2×C4—681no—
735C2×C4—682no—
736C2×C4—682no—
737C2×C4—682no—
738C2×C4—682no—
739C2×C4—682no—
740C2×C4—682no—
741C2×C4—682no—
742C2×C4#1058755814yes—
743C2×C4C22⋊C4×D1714yes—
744C2×C4#1058757014yes—
745C2×C4#1058757014yes—
746C2×C4C4⋊C4×D1714yes—
747C2×C4#1058758214yes—
748C2×C4#1058758214yes—
749C22—344no—
750C22—344no—
751C22—344no—
752C22—682no—
753C22—682no—
754C22—682no—
755C22—682no—
756C22—682no—
757C22—682no—
758C22—682no—
759C22—682no—
760C22—682no—
761C22—682no—
762C22—682no—
763C22—682no—
764C22C2×C22⋊C4×D1711yescharacteristic
765C22C2×C4⋊C4×D1711yescharacteristic
766C22C2×#1058755811yescharacteristic
767C22C4×#6325411yescharacteristic
768C22C4×#6325611yescharacteristic
769C22#1176328811yescharacteristic
770C22#1176329111yescharacteristic
771C22C2×#1058757011yescharacteristic
772C22C2×#1058757011yescharacteristic
773C22C2×#1058758211yescharacteristic
774C22C2×#1058758211yescharacteristic
775C22#1176331911yescharacteristic
776C22#1176332211yescharacteristic
777C22#1176336411yescharacteristic
778C22#1176336511yescharacteristic
779C22#1176337511yescharacteristic
780C22#1176338211yescharacteristic
781C22#1176343611yescharacteristic
782C22#1176343911yescharacteristic
783C22#1176345011yescharacteristic
784C22#1176345211yescharacteristic
785C22#1176346111yescharacteristic
786C22#1176346211yescharacteristic
787C22#1176346511yescharacteristic
788C22#1176346711yescharacteristic
789C22#1176347711yescharacteristic
790C22#1176347911yescharacteristic
791C22#1176349411yescharacteristic
792C22#1176350011yescharacteristic
793C22#1176350711yescharacteristic
794C22#1176350911yescharacteristic
795C22#1176352211yescharacteristic
796C22#1176352411yescharacteristic
797C22#1176352711yescharacteristic
798C22#1176353211yescharacteristic
799C4—44no—
800C4—42no—
801C4—42no—
802C4—82no—
803C4—348no—
804C4—344no—
805C4—682no—
806C4—682no—
807C4—1362no—
808C4#1176266818yes—
809C2—684no—
810C2C2×#1176266811yescharacteristic
811C2#1453126511yescharacteristic
812C2#1453140611yescharacteristic
813C2#1453161311yescharacteristic
814C2#1453162311yescharacteristic
815C2#1453166511yescharacteristic
816C2#1453167311yescharacteristic
817C2#1453220411yescharacteristic
818C2#1453220511yescharacteristic
819C2#1453221511yescharacteristic
820C2#1453221611yescharacteristic
821C2#1453247711yescharacteristic
822C2#1453247811yescharacteristic
823C2#1453249911yescharacteristic
824C2#1453250011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C4⋊#95C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenterC4⋊#95D17
hypocenterC17#13951
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#11762707C2semidirect
3. C2×#11762705C2semidirect
8. #14527013C2semidirect
9. #14527012C2semidirect
10. #14527009C2semidirect
11. C17×C4⋊#95C2semidirect
15. C2×#10587578C4semidirect
201. C2×C4×D17C4⋊C4semidirect
210. C4⋊Dic17C22⋊C4semidirect
346. C4⋊#95D17semidirect
521. C17#13951semidirect

Maximal subgroups

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

subgroupindex
C22×#105875782
C2×#117627072
C2×#117627052
C2×#117626662
C2×C4×#632272
#145270282
#145270132
#145270122
#145270092
C17×C4⋊#952
#1395117