Finite Group Databasebeta

← #16957107

Subgroups — #16957107

Order 4352.

2742 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587572C211yesmaximal, characteristic
2C22×C4×C22⋊D17C211yesmaximal, characteristic
3C2×#11762686C211yesmaximal, characteristic
4C2×#11762670C211yesmaximal, characteristic, complemented
5C22×#10587502C211yesmaximal, characteristic, complemented
6#14527036C212yesmaximal, complemented
7#14527032C212yesmaximal, complemented
8#14527018C212yesmaximal, complemented
9#14527006C211yesmaximal, characteristic, complemented
10#14527005C212yesmaximal, complemented
11C17×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D17C2211yescharacteristic
13C24×Dic17C2211yescharacteristic
14C24×Dic17C2211yescharacteristic
15C23×C4×D17C2211yescharacteristic
16C2×#10587572—24no—
17C2×#10587572—24no—
18C2×#10587572C418yescomplemented
19C2×C4×C22⋊D17—24no—
20C2×C4×C22⋊D17—24no—
21C2×C4×C22⋊D17—24no—
22C22×C4⋊Dic17C2212yes—
23C22×#63225C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2212yes—
27C22×#63227C2212yes—
28C22×C4×Dic17C2211yescharacteristic
29#11762686—24no—
30#11762670—24no—
31C2×#10587502—24no—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2212yes—
36C2×#10587502C2212yes—
37C2×#10587502C2212yes—
38C2×#10587502C2212yes—
39C24×C4×C17C2211yescharacteristic
40C22×C22⋊C4×C17C2211yescharacteristic
41C22×C22⋊C4×C17C2211yescharacteristic
42C2×C17×#95C2212yes—
43C2×C17×#95C2212yes—
44C25×C17C2311yescharacteristic
45C24×D17C2311yescharacteristic
46C23×C4×C17—22no—
47C23×C4×C17—22no—
48C23×C4×C17—24no—
49C23×C4×C17—42no—
50C23×C4×C17D414yes—
51C23×C4×C17C2312yes—
52C23×C4×C17C2312yes—
53C23×C4×C17C2311yescharacteristic
54C23×C4×C17C2311yescharacteristic
55C22×C22⋊D17—22no—
56C22×C22⋊D17—22no—
57C22×C22⋊D17—22no—
58C22×C22⋊D17—22no—
59C22×C22⋊D17C2×C414yes—
60C22×C22⋊D17D414yes—
61C22×C22⋊D17D414yes—
62C23×Dic17—22no—
63C23×Dic17—22no—
64C23×Dic17—22no—
65C23×Dic17—22no—
66C23×Dic17—22no—
67C23×Dic17—22no—
68C23×Dic17—22no—
69C23×Dic17—24no—
70C23×Dic17—22no—
71C23×Dic17—22no—
72C23×Dic17—42no—
73C23×Dic17C2×C414yescomplemented
74C23×Dic17C2312yes—
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2312yes—
78C23×Dic17C2311yescharacteristic
79C22×C4×D17—22no—
80C22×C4×D17—22no—
81C22×C4×D17—22no—
82C22×C4×D17—24no—
83C22×C4×D17—42no—
84C2×C22⋊C4×C17—22no—
85C2×C22⋊C4×C17—22no—
86C2×C22⋊C4×C17—22no—
87C2×C22⋊C4×C17—22no—
88C2×C22⋊C4×C17—22no—
89C2×C22⋊C4×C17C2×C414yescomplemented
90C2×C22⋊Dic17—22no—
91C2×C22⋊Dic17—22no—
92C2×C22⋊Dic17D414yes—
93C4×C22⋊D17—232no—
94C2×#63227—22no—
95C2×#63227—24no—
96C2×#63227—24no—
97C2×#63227—24no—
98C2×#63227—22no—
99C2×#63227—22no—
100C2×#63227—24no—
101C2×#63227—42no—
102C2×#63227C2×C418yescomplemented
103C2×C4⋊Dic17—24no—
104C2×C4⋊Dic17—24no—
105C2×C4⋊Dic17C2×C418yescomplemented
106C2×#63225—22no—
107C2×#63225—22no—
108C2×#63225—22no—
109C2×C4×Dic17—22no—
110C2×C4×Dic17—22no—
111C2×C4×Dic17—22no—
112#10587572—232no—
113C17×#95—24no—
114C17×#95—42no—
115#10587502—24no—
116#10587502—24no—
117#10587502—24no—
118#10587502—24no—
119#10587502—24no—
120#10587502—24no—
121#10587502—42no—
122C24×C17—22no—
123C24×C17—22no—
124C24×C17—22no—
125C24×C17—22no—
126C24×C17C22×C412yes—
127C24×C17C2×D412yes—
128C24×C17C2×D412yes—
129C24×C17C2×D412yes—
130C24×C17C2×D412yes—
131C24×C17#4112yes—
132C24×C17#4112yes—
133C24×C17C2411yescharacteristic
134C23×D17—21no—
135C23×D17—21no—
136C23×D17—22no—
137C23×D17—21no—
138C23×D17—21no—
139C23×D17—22no—
140C23×D17—22no—
141C23×D17—22no—
142C23×D17C22×C412yes—
143C23×D17C2×D412yes—
144C23×D17C2×D412yes—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—22no—
148C22×C4×C17—28no—
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17—22no—
152C22×C4×C17—22no—
153C22×C4×C17—22no—
154C22×C4×C17—22no—
155C22×C4×C17—22no—
156C22×C4×C17—22no—
157C22×C4×C17—22no—
158C22×C4×C17—22no—
159C22×C4×C17—28no—
160C22×C4×C17—22no—
161C22×C4×C17—22no—
162C22×C4×C17—22no—
163C22×C4×C17—22no—
164C22×C4×C17—22no—
165C22×C4×C17—22no—
166C22×C4×C17—22no—
167C22×C4×C17—44no—
168C22×C4×C17—48no—
169C22×C4×C17—48no—
170C22×C4×C17C22×C414yes—
171C22×C4×C17C2×D412yes—
172C22×C4×C17C2×D412yes—
173C22×C4×C17#4114yes—
174C2×C22⋊D17—28no—
175C2×C22⋊D17—28no—
176C2×C22⋊D17—28no—
177C2×C22⋊D17—28no—
178C2×C22⋊D17—28no—
179C2×C22⋊D17—28no—
180C2×C22⋊D17C22⋊C4116yes—
181C22×Dic17—21no—
182C22×Dic17—21no—
183C22×Dic17—21no—
184C22×Dic17—21no—
185C22×Dic17—28no—
186C22×Dic17—28no—
187C22×Dic17—28no—
188C22×Dic17—28no—
189C22×Dic17—21no—
190C22×Dic17—21no—
191C22×Dic17—22no—
192C22×Dic17—22no—
193C22×Dic17—22no—
194C22×Dic17—22no—
195C22×Dic17—22no—
196C22×Dic17—22no—
197C22×Dic17—21no—
198C22×Dic17—21no—
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—48no—
210C22×Dic17—48no—
211C22×Dic17—44no—
212C22×Dic17—44no—
213C22×Dic17—44no—
214C22×Dic17—44no—
215C22×Dic17—44no—
216C22×Dic17—44no—
217C22×Dic17C22×C414yes—
218C22×Dic17C22×C412yes—
219C22×Dic17C2×D412yes—
220C22×Dic17C2×D412yes—
221C22×Dic17C2×D412yes—
222C22×Dic17C2×D412yes—
223C22×Dic17#4114yes—
224C2×C4×D17—28no—
225C2×C4×D17—48no—
226C2×C4×D17—48no—
227C2×C4×D17—44no—
228C2×C4×D17—44no—
229C22⋊C4×C17—28no—
230C22⋊C4×C17—44no—
231C22⋊Dic17—28no—
232#63227—28no—
233#63227—216no—
234#63227—48no—
235C4⋊Dic17—216no—
236#63225—28no—
237C4×Dic17—28no—
238#13968—171nomaximal, Sylow
239C23×C17—24no—
240C23×C17—24no—
241C23×C17—22no—
242C23×C17—22no—
243C23×C17—24no—
244C23×C17—22no—
245C23×C17—22no—
246C23×C17—24no—
247C23×C17—24no—
248C23×C17—24no—
249C23×C17—24no—
250C23×C17—24no—
251C23×C17—24no—
252C23×C17—24no—
253C23×C17—24no—
254C23×C17—24no—
255C23×C17C2×C22⋊C414yes—
256C23×C17C4×D414yes—
257C23×C17C4×D414yes—
258C23×C17#12014yes—
259C23×C17#12114yes—
260C23×C17#12114yes—
261C23×C17#12314yes—
262C23×C17C23×C411yescharacteristic
263C23×C17C22×D411yescharacteristic
264C23×C17C22×D411yescharacteristic
265C23×C17C22×D411yescharacteristic
266C23×C17C22×D411yescharacteristic
267C23×C17C2×#4111yescharacteristic
268C23×C17C2×#4112yes—
269C23×C17C2×#4111yescharacteristic
270C23×C17C2×#4112yes—
271C23×C17H(5,𝔽2)12yes—
272C23×C172−1+412yes—
273C22×D17—22no—
274C22×D17—22no—
275C22×D17—24no—
276C22×D17—24no—
277C22×D17—22no—
278C22×D17—22no—
279C22×D17—22no—
280C22×D17—22no—
281C22×D17—24no—
282C22×D17—24no—
283C22×D17—24no—
284C22×D17—24no—
285C22×D17—41no—
286C22×D17—41no—
287C22×D17—42no—
288C22×D17—41no—
289C22×D17—41no—
290C22×D17—42no—
291C22×D17—42no—
292C22×D17—42no—
293C22×D17—42no—
294C22×D17—42no—
295C22×D17C2×C22⋊C414yes—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—24no—
299C2×C4×C17—24no—
300C2×C4×C17—24no—
301C2×C4×C17—24no—
302C2×C4×C17—24no—
303C2×C4×C17—22no—
304C2×C4×C17—22no—
305C2×C4×C17—22no—
306C2×C4×C17—416no—
307C2×C4×C17—42no—
308C2×C4×C17—42no—
309C2×C4×C17—42no—
310C2×C4×C17—42no—
311C2×C4×C17—42no—
312C2×C4×C17—42no—
313C2×C4×C17—42no—
314C2×C4×C17—42no—
315C2×C4×C17—42no—
316C2×C4×C17—42no—
317C2×C4×C17—42no—
318C2×C4×C17—42no—
319C2×C4×C17—42no—
320C2×C4×C17#12314yescomplemented
321C22⋊D17—232no—
322C2×Dic17—22no—
323C2×Dic17—22no—
324C2×Dic17—22no—
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—24no—
329C2×Dic17—24no—
330C2×Dic17—24no—
331C2×Dic17—22no—
332C2×Dic17—22no—
333C2×Dic17—24no—
334C2×Dic17—24no—
335C2×Dic17—24no—
336C2×Dic17—24no—
337C2×Dic17—24no—
338C2×Dic17—416no—
339C2×Dic17—42no—
340C2×Dic17—42no—
341C2×Dic17—42no—
342C2×Dic17—42no—
343C2×Dic17—41no—
344C2×Dic17—42no—
345C2×Dic17—41no—
346C2×Dic17—41no—
347C2×Dic17—42no—
348C2×Dic17—41no—
349C2×Dic17—42no—
350C2×Dic17—42no—
351C2×Dic17—42no—
352C2×Dic17—42no—
353C2×Dic17—416no—
354C2×Dic17C2×C22⋊C414yes—
355C4×D17—416no—
356C22×#123—171no—
357C22×C4×D4—171no—
358C2×#386—171no—
359C2×#381—171no—
360C22×#95—171no—
361#1441—172no—
362#1440—172no—
363#1436—172no—
364C22⋊#95—172no—
365C22⋊#95—171no—
366C22⋊#95D1711yescharacteristic, complemented
367C22×C17—24no—
368C22×C17—28no—
369C22×C17—28no—
370C22×C17—24no—
371C22×C17—24no—
372C22×C17—28no—
373C22×C17—28no—
374C22×C17—24no—
375C22×C17—24no—
376C22×C17—24no—
377C22×C17#38618yes—
378C22×C17C22×C22⋊C411yescharacteristic
379C22×C17C2×C4×D411yescharacteristic
380C22×C17C2×C4×D411yescharacteristic
381C22×C17C4×#4112yes—
382C22×C17#52012yes—
383C22×C17C2×#12011yescharacteristic
384C22×C17C2×#12111yescharacteristic
385C22×C17C2×#12111yescharacteristic
386C22×C17C2×#12311yescharacteristic
387C22×C17C2×#12311yescharacteristic
388C22×C17#52511yescharacteristic
389C22×C17#52912yes—
390C22×C17#53411yescharacteristic
391C22×C17#53611yescharacteristic
392C22×C17#53912yes—
393C22×C17#54612yes—
394C22×C17#54612yes—
395C22×C17#54612yes—
396C22×C17#54712yes—
397C22×C17#54712yes—
398C22×C17#54712yes—
399C22×C17#55112yes—
400C22×C17#55212yes—
401C2×D17—28no—
402C2×D17—24no—
403C2×D17—42no—
404C2×D17—44no—
405C2×D17—42no—
406C2×D17—42no—
407C2×D17—44no—
408C2×D17—44no—
409C2×D17—42no—
410C2×D17—42no—
411C2×D17—42no—
412C4×C17—24no—
413C4×C17—44no—
414C4×C17—42no—
415C4×C17—82no—
416Dic17—24no—
417Dic17—42no—
418Dic17—42no—
419Dic17—44no—
420Dic17—44no—
421C23×D4—171no—
422C24×C4—171no—
423C24×C4—171no—
424C24×C4—171no—
425C24×C4C2×D1711yescharacteristic
426C2×#123—178no—
427C2×#123—344no—
428C2×#123—344no—
429C2×C4×D4—344no—
430C2×C4×D4—344no—
431C2×C4×D4—344no—
432C22×C4⋊C4—172no—
433C22×C4⋊C4—171no—
434C22×C22⋊C4—171no—
435C22×C22⋊C4—172no—
436C22×C22⋊C4—171no—
437C22×C22⋊C4—172no—
438C22×C22⋊C4C2×D1711yescharacteristic
439C22×C22⋊C4C2×D1711yescharacteristic
440C22×C42—171no—
441#386—344no—
442#381—344no—
443C2×#95—172no—
444C2×#95—172no—
445C2×#95—172no—
446C2×#95—172no—
447C2×#95—172no—
448C2×#95—172no—
449C2×#95—172no—
450C2×#95—344no—
451C2×#95C2×D1712yes—
452C2×#95C2×D1712yes—
453C2×C17—28no—
454C2×C17C2×#38611yescharacteristic
455C2×C17C4×#12311yescharacteristic
456C2×C17#232211yescharacteristic
457C2×C17#233912yes—
458C2×C17#235912yes—
459C2×C17#240511yescharacteristic
460C2×C17#240611yescharacteristic
461C2×C17#241912yes—
462C2×C17#242512yes—
463C2×C17#248611yescharacteristic
464C2×C17#253411yescharacteristic
465D17—44no—
466C25—171no—
467C25C22×D1711yescharacteristic
468C22×D4—174no—
469C22×D4—174no—
470C22×D4—174no—
471C22×D4—342no—
472C22×D4—342no—
473C22×D4—342no—
474C22×D4—342no—
475C23×C4—22no—
476C23×C4—22no—
477C23×C4—24no—
478C23×C4—42no—
479C23×C4—171no—
480C23×C4—174no—
481C23×C4—171no—
482C23×C4—172no—
483C23×C4—171no—
484C23×C4—172no—
485C23×C4—342no—
486C23×C4—342no—
487C23×C4—344no—
488C23×C4—342no—
489C23×C4—342no—
490C23×C4—342no—
491C23×C4—342no—
492C23×C4—342no—
493C23×C4—342no—
494C23×C4—342no—
495C23×C4—342no—
496C23×C4—342no—
497C23×C4—342no—
498C23×C4—344no—
499C23×C4—682no—
500C23×C4—682no—
501C23×C4D6814yes—
502C23×C4C22×D1712yes—
503C23×C4C22×D1712yes—
504C23×C4C22×D1711yescharacteristic
505C23×C4C22×D1711yescharacteristic
506#123—3432no—
507C4×D4—3432no—
508C2×C4⋊C4—178no—
509C2×C4⋊C4—342no—
510C2×C4⋊C4—342no—
511C2×C4⋊C4—344no—
512C2×C4⋊C4—344no—
513C2×C4⋊C4—342no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—174no—
520C2×C22⋊C4—178no—
521C2×C22⋊C4—342no—
522C2×C22⋊C4—342no—
523C2×C22⋊C4—344no—
524C2×C22⋊C4—344no—
525C2×C22⋊C4—342no—
526C2×C22⋊C4—342no—
527C2×C22⋊C4—342no—
528C2×C22⋊C4—344no—
529C2×C22⋊C4—344no—
530C2×C22⋊C4—682no—
531C2×C22⋊C4C4×D1714yescomplemented
532C2×C42—342no—
533C2×C42—342no—
534C2×C42—342no—
535#95—24no—
536#95—42no—
537#95—344no—
538#95—344no—
539#95—344no—
540#95—344no—
541#95—344no—
542#95—344no—
543#95—682no—
544C17#1396811yescharacteristic, complemented, Sylow
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—172no—
550C24—172no—
551C24—172no—
552C24—341no—
553C24—341no—
554C24—341no—
555C24—342no—
556C24—342no—
557C24—341no—
558C24—342no—
559C24—342no—
560C24C2×C4×D1712yes—
561C24C2×D6812yes—
562C24#6325212yes—
563C24D4×D1712yes—
564C24D4×D1712yes—
565C24D4×D1712yes—
566C24#6325612yes—
567C24C23×D1711yescharacteristic
568C2×D4—1716no—
569C2×D4—348no—
570C2×D4—348no—
571C2×D4—348no—
572C2×D4—348no—
573C2×D4—348no—
574C2×D4—348no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—28no—
589C22×C4—28no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—44no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—172no—
601C22×C4—172no—
602C22×C4—172no—
603C22×C4—174no—
604C22×C4—172no—
605C22×C4—172no—
606C22×C4—174no—
607C22×C4—348no—
608C22×C4—341no—
609C22×C4—341no—
610C22×C4—341no—
611C22×C4—341no—
612C22×C4—348no—
613C22×C4—342no—
614C22×C4—342no—
615C22×C4—341no—
616C22×C4—341no—
617C22×C4—342no—
618C22×C4—342no—
619C22×C4—342no—
620C22×C4—341no—
621C22×C4—342no—
622C22×C4—342no—
623C22×C4—341no—
624C22×C4—342no—
625C22×C4—342no—
626C22×C4—342no—
627C22×C4—342no—
628C22×C4—342no—
629C22×C4—342no—
630C22×C4—342no—
631C22×C4—342no—
632C22×C4—342no—
633C22×C4—348no—
634C22×C4—348no—
635C22×C4—348no—
636C22×C4—688no—
637C22×C4—688no—
638C22×C4—684no—
639C22×C4—688no—
640C22×C4—688no—
641C22×C4—684no—
642C22×C4—684no—
643C22×C4—684no—
644C22×C4—684no—
645C22×C4—684no—
646C22×C4—684no—
647C22×C4—684no—
648C22×C4C2×C4×D1714yes—
649C22×C4C2×D6812yes—
650C22×C4C2×D6812yes—
651C22×C4#6325414yes—
652C4⋊C4—3416no—
653C4⋊C4—348no—
654C22⋊C4—28no—
655C22⋊C4—44no—
656C22⋊C4—3416no—
657C22⋊C4—348no—
658C22⋊C4—348no—
659C22⋊C4—688no—
660C42—348no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—174no—
678C23—344no—
679C23—344no—
680C23—342no—
681C23—342no—
682C23—344no—
683C23—344no—
684C23—342no—
685C23—342no—
686C23—342no—
687C23—342no—
688C23—344no—
689C23—344no—
690C23—682no—
691C23—682no—
692C23—682no—
693C23—681no—
694C23—681no—
695C23—682no—
696C23—681no—
697C23—681no—
698C23—682no—
699C23—682no—
700C23C4×D6814yes—
701C23C22⋊C4×D1714yes—
702C23#1058756814yes—
703C23#1058757014yes—
704C23#1058757914yes—
705C23#1058758014yes—
706C23#1058758114yes—
707C23C22×C4×D1711yescharacteristic
708C23C22×D6811yescharacteristic
709C23C2×#6325211yescharacteristic
710C23C2×D4×D1711yescharacteristic
711C23C2×D4×D1711yescharacteristic
712C23C2×D4×D1711yescharacteristic
713C23C2×#6325412yes—
714C23#1058769112yes—
715C23C2×#6325611yescharacteristic
716C23#41×D1712yes—
717C23#1058769712yes—
718D4—3432no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—416no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—174no—
744C2×C4—342no—
745C2×C4—342no—
746C2×C4—342no—
747C2×C4—342no—
748C2×C4—342no—
749C2×C4—342no—
750C2×C4—344no—
751C2×C4—344no—
752C2×C4—344no—
753C2×C4—344no—
754C2×C4—344no—
755C2×C4—342no—
756C2×C4—342no—
757C2×C4—344no—
758C2×C4—344no—
759C2×C4—344no—
760C2×C4—6816no—
761C2×C4—6816no—
762C2×C4—682no—
763C2×C4—682no—
764C2×C4—682no—
765C2×C4—682no—
766C2×C4—682no—
767C2×C4—682no—
768C2×C4—681no—
769C2×C4—682no—
770C2×C4—681no—
771C2×C4—681no—
772C2×C4—682no—
773C2×C4—681no—
774C2×C4—682no—
775C2×C4—682no—
776C2×C4—6816no—
777C2×C4#1058757214yescomplemented
778C22—24no—
779C22—24no—
780C22—28no—
781C22—24no—
782C22—24no—
783C22—28no—
784C22—28no—
785C22—24no—
786C22—24no—
787C22—28no—
788C22—348no—
789C22—344no—
790C22—682no—
791C22—682no—
792C22—682no—
793C22—682no—
794C22—684no—
795C22—684no—
796C22—682no—
797C22—682no—
798C22—684no—
799C22#1176268718yes—
800C22C2×C22⋊C4×D1711yescharacteristic
801C22C2×#1058757911yescharacteristic
802C22C2×C4×D6811yescharacteristic
803C22C4×#6325412yes—
804C22#1176328812yes—
805C22C2×#1058756811yescharacteristic
806C22C2×#1058757011yescharacteristic
807C22C2×#1058758111yescharacteristic
808C22C2×#1058757211yescharacteristic
809C22C2×#1058758011yescharacteristic
810C22#1176332111yescharacteristic
811C22#1176333912yes—
812C22#1176337111yescharacteristic
813C22#1176338511yescharacteristic
814C22#1176340112yes—
815C22#1176344612yes—
816C22#1176344612yes—
817C22#1176344812yes—
818C22#1176345712yes—
819C22#1176345712yes—
820C22#1176345912yes—
821C22#1176348612yes—
822C22#1176350112yes—
823C4—24no—
824C4—42no—
825C4—44no—
826C4—82no—
827C4—344no—
828C4—682no—
829C4—682no—
830C4—684no—
831C4—684no—
832C2—28no—
833C2—684no—
834C2C2×#1176268711yescharacteristic
835C2C4×#1058757211yescharacteristic
836C2#1453145511yescharacteristic
837C2#1453161012yes—
838C2#1453177412yes—
839C2#1453211211yescharacteristic
840C2#1453212111yescharacteristic
841C2#1453226312yes—
842C2#1453233712yes—
843C2#1453309311yescharacteristic
844C2#1453367611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C22⋊#95C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC22⋊#95D17
hypocenterC17#13968
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#11762670C2semidirect
5. C22×#10587502C2semidirect
6. #14527036C2semidirect
7. #14527032C2semidirect
8. #14527018C2semidirect
9. #14527006C2semidirect
10. #14527005C2semidirect
11. C17×C22⋊#95C2semidirect
18. C2×#10587572C4semidirect
73. C23×Dic17C2×C4semidirect
89. C2×C22⋊C4×C17C2×C4semidirect
102. C2×#63227C2×C4semidirect
105. C2×C4⋊Dic17C2×C4semidirect
320. C2×C4×C17#123semidirect
366. C22⋊#95D17semidirect
531. C2×C22⋊C4C4×D17semidirect
544. C17#13968semidirect
777. C2×C4#10587572semidirect

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
C2×#117626862
C2×#117626702
C22×#105875022
#145270362
#145270322
#145270182
#145270062
#145270052
C17×C22⋊#952
#1396817