Finite Group Databasebeta

← #16956228

Subgroups — #16956228

Order 4352.

2950 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587579C211yesmaximal, characteristic
2C22×C4⋊C4×D17C211yesmaximal, characteristic, complemented
3C2×#11762687C212yesmaximal
4C2×#11762668C211yesmaximal, characteristic, complemented
5C2×#11762668C212yesmaximal, complemented
6#14527037C211yesmaximal, characteristic, complemented
7#14527030C211yesmaximal, characteristic, complemented
8#14527026C211yesmaximal, characteristic, complemented
9#14527012C212yesmaximal, complemented
10#14527005C212yesmaximal, complemented
11C17×#1441C211yesmaximal, characteristic, complemented
12C23×D68C2211yescharacteristic
13C23×C4×D17C2211yescharacteristic
14C23×C4×D17C2212yes—
15C23×C4×D17C2211yescharacteristic
16C2×#10587579—24no—
17C2×#10587579—24no—
18C2×#10587579C418yescomplemented
19C22×C4⋊Dic17C2211yescharacteristic
20C22×#63225C2212yes—
21C22×#63225C2212yes—
22C2×C4⋊C4×D17—28no—
23C2×C4⋊C4×D17—24no—
24C22×#63227C2212yes—
25C22×#63227C2212yes—
26C22×#63227C2212yes—
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30#11762687—28no—
31#11762668—28no—
32#11762668—24no—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2212yes—
37C2×#10587502C2212yes—
38C22×C4⋊C4×C17C2211yescharacteristic
39C22×C4⋊C4×C17C2211yescharacteristic
40C2×C17×#95C2212yes—
41C2×C17×#95C2212yes—
42C2×C17×#95C2211yescharacteristic
43C24×D17C2311yescharacteristic
44C24×D17C2311yescharacteristic
45C23×C4×C17C2312yes—
46C23×C4×C17C2311yescharacteristic
47C23×C4×C17C2312yes—
48C23×C4×C17C2311yescharacteristic
49C23×C4×C17C2311yescharacteristic
50C23×Dic17C2312yes—
51C23×Dic17C2311yescharacteristic
52C23×Dic17C2312yes—
53C23×Dic17C2311yescharacteristic
54C22×D68—22no—
55C22×D68—22no—
56C22×D68—22no—
57C22×D68—22no—
58C22×D68C2×C414yes—
59C22×D68D414yes—
60C22×D68Q814yes—
61C22×C4×D17—24no—
62C22×C4×D17—24no—
63C22×C4×D17—24no—
64C22×C4×D17—24no—
65C22×C4×D17—24no—
66C22×C4×D17—22no—
67C22×C4×D17—22no—
68C22×C4×D17—24no—
69C22×C4×D17—24no—
70C22×C4×D17—24no—
71C22×C4×D17—24no—
72C22×C4×D17—42no—
73C22×C4×D17—42no—
74C22×C4×D17C2×C414yes—
75C22×C4×D17C2×C414yescomplemented
76C22×C4×D17D414yes—
77C22×C4×D17D414yes—
78C2×C4⋊C4×C17—24no—
79C2×C4⋊C4×C17—22no—
80C2×C4⋊C4×C17—22no—
81C2×C4⋊C4×C17—22no—
82C2×C4⋊C4×C17C2×C414yescomplemented
83C2×#63227—22no—
84C2×#63227—22no—
85C2×#63227—24no—
86C2×#63227—24no—
87C2×#63227—24no—
88C2×#63227—24no—
89C2×#63227—24no—
90C2×#63227—22no—
91C2×#63227—22no—
92C2×#63227—24no—
93C2×#63227—24no—
94C2×#63227—42no—
95C2×#63227—42no—
96C2×#63227C2×C414yes—
97C2×#63227C2×C414yescomplemented
98C2×C4⋊Dic17—22no—
99C2×C4⋊Dic17—24no—
100C2×#63225—24no—
101C2×#63225—24no—
102C2×#63225—24no—
103C2×#63225—24no—
104C2×#63225—24no—
105C2×#63225D418yescomplemented
106C2×C4×Dic17—22no—
107C2×C4×Dic17—22no—
108C2×C4×Dic17C2×C414yescomplemented
109#10587579—232no—
110C4⋊C4×D17—232no—
111C17×#95—24no—
112C17×#95—22no—
113C17×#95—24no—
114#10587502—22no—
115#10587502—24no—
116#10587502—24no—
117#10587502—42no—
118#10587502—42no—
119C24×C17C2411yescharacteristic
120C23×D17—22no—
121C23×D17—22no—
122C23×D17—22no—
123C23×D17—22no—
124C23×D17—21no—
125C23×D17—21no—
126C23×D17—22no—
127C23×D17—22no—
128C23×D17—21no—
129C23×D17—21no—
130C23×D17—22no—
131C23×D17—22no—
132C23×D17C22×C412yes—
133C23×D17C22×C412yes—
134C23×D17C2×D412yes—
135C23×D17C2×D412yes—
136C23×D17C2×D412yes—
137C23×D17C2×D412yes—
138C23×D17C2×Q812yes—
139C23×D17C2×Q812yes—
140C23×D17#4112yes—
141C23×D17#4112yes—
142C22×C4×C17—22no—
143C22×C4×C17—21no—
144C22×C4×C17—21no—
145C22×C4×C17—22no—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17—22no—
151C22×C4×C17—22no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—22no—
155C22×C4×C17—22no—
156C22×C4×C17—22no—
157C22×C4×C17—22no—
158C22×C4×C17—22no—
159C22×C4×C17—22no—
160C22×C4×C17—22no—
161C22×C4×C17—22no—
162C22×C4×C17—22no—
163C22×C4×C17—22no—
164C22×C4×C17—22no—
165C22×C4×C17C22×C412yes—
166C22×C4×C17C22×C412yes—
167C22×C4×C17C22×C412yes—
168C22×C4×C17C2×D414yes—
169C22×C4×C17C2×D412yes—
170C22×C4×C17C2×D412yes—
171C22×C4×C17C2×D412yes—
172C22×C4×C17C2×Q812yes—
173C22×Dic17—22no—
174C22×Dic17—22no—
175C22×Dic17—22no—
176C22×Dic17—21no—
177C22×Dic17—21no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17C22×C412yes—
191C22×Dic17C22×C412yes—
192C22×Dic17C2×D414yes—
193C22×Dic17C2×D412yes—
194C22×Dic17C2×D412yes—
195C22×Dic17C2×D414yes—
196C22×Dic17#4114yes—
197C2×D68—28no—
198C2×D68—28no—
199C2×D68—28no—
200C2×D68—28no—
201C2×D68—28no—
202C2×D68—28no—
203C2×D68C4⋊C4116yescomplemented
204C2×C4×D17—216no—
205C2×C4×D17—28no—
206C2×C4×D17—216no—
207C2×C4×D17—28no—
208C2×C4×D17—216no—
209C2×C4×D17—28no—
210C2×C4×D17—216no—
211C2×C4×D17—48no—
212C2×C4×D17—48no—
213C2×C4×D17—48no—
214C2×C4×D17—48no—
215C2×C4×D17—48no—
216C2×C4×D17—48no—
217C2×C4×D17—44no—
218C2×C4×D17—48no—
219C2×C4×D17—44no—
220C2×C4×D17C22⋊C4116yescomplemented
221C4⋊C4×C17—28no—
222C4⋊C4×C17—28no—
223#63227—28no—
224#63227—28no—
225#63227—48no—
226#63227—48no—
227#63227—48no—
228C4⋊Dic17—28no—
229#63225—216no—
230#63225—48no—
231C4×Dic17—28no—
232#13872—171nomaximal, Sylow
233C23×C17C23×C411yescharacteristic
234C23×C17C22×D411yescharacteristic
235C23×C17C22×D411yescharacteristic
236C23×C17C22×D411yescharacteristic
237C23×C17C22×D412yes—
238C23×C17C22×Q811yescharacteristic
239C23×C17C2×#4111yescharacteristic
240C23×C17C2×#4111yescharacteristic
241C23×C17C2×#4112yes—
242C23×C17H(5,𝔽2)12yes—
243C23×C172−1+412yes—
244C22×D17—24no—
245C22×D17—24no—
246C22×D17—22no—
247C22×D17—24no—
248C22×D17—22no—
249C22×D17—22no—
250C22×D17—22no—
251C22×D17—24no—
252C22×D17—24no—
253C22×D17—24no—
254C22×D17—24no—
255C22×D17—24no—
256C22×D17—24no—
257C22×D17—24no—
258C22×D17—24no—
259C22×D17—24no—
260C22×D17—22no—
261C22×D17—22no—
262C22×D17—24no—
263C22×D17—24no—
264C22×D17—22no—
265C22×D17—22no—
266C22×D17—22no—
267C22×D17—22no—
268C22×D17—24no—
269C22×D17—24no—
270C22×D17—24no—
271C22×D17—24no—
272C22×D17—41no—
273C22×D17—42no—
274C22×D17—41no—
275C22×D17—41no—
276C22×D17—41no—
277C22×D17—42no—
278C22×D17—42no—
279C22×D17—42no—
280C22×D17—42no—
281C22×D17—42no—
282C22×D17C2×C22⋊C414yes—
283C22×D17C2×C4⋊C414yes—
284C22×D17C2×C4⋊C414yescomplemented
285C22×D17#11714yes—
286C22×D17#12114yes—
287C22×D17#12114yes—
288C22×D17C22⋊Q814yes—
289C22×D17C22⋊Q814yes—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—24no—
293C2×C4×C17—22no—
294C2×C4×C17—24no—
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—24no—
302C2×C4×C17—24no—
303C2×C4×C17—24no—
304C2×C4×C17—24no—
305C2×C4×C17—41no—
306C2×C4×C17—42no—
307C2×C4×C17—42no—
308C2×C4×C17—41no—
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×C17C2×C22⋊C414yes—
320C2×C4×C17C2×C4⋊C414yescomplemented
321C2×Dic17—22no—
322C2×Dic17—24no—
323C2×Dic17—24no—
324C2×Dic17—24no—
325C2×Dic17—24no—
326C2×Dic17—42no—
327C2×Dic17—42no—
328C2×Dic17—41no—
329C2×Dic17—41no—
330C2×Dic17—42no—
331C2×Dic17—42no—
332C2×Dic17—42no—
333C2×Dic17—42no—
334C2×Dic17—42no—
335C2×Dic17—42no—
336C2×Dic17—42no—
337C2×Dic17—42no—
338C2×Dic17—42no—
339C2×Dic17—42no—
340C2×Dic17C2×C22⋊C414yes—
341C2×Dic17C4×D418yes—
342C2×Dic17#12014yes—
343C2×Dic17#12118yes—
344C2×Dic17#12314yes—
345D68—232no—
346C4×D17—232no—
347C4×D17—432no—
348C4×D17—416no—
349C22×C4×D4—171no—
350C23×C4⋊C4—171no—
351C2×#386—172no—
352C2×#380—171no—
353C2×#380—172no—
354#1441—171no—
355#1441D1711yescharacteristic, complemented
356#1439—171no—
357#1439—171no—
358C4⋊#95—172no—
359C22⋊#95—172no—
360C22×C17C22×C22⋊C411yescharacteristic
361C22×C17C22×C4⋊C411yescharacteristic
362C22×C17C2×#11711yescharacteristic
363C22×C17C2×C4×D412yes—
364C22×C17#52012yes—
365C22×C17C2×#12011yescharacteristic
366C22×C17C2×#12111yescharacteristic
367C22×C17C2×#12111yescharacteristic
368C22×C17C2×#12112yes—
369C22×C17C2×C22⋊Q811yescharacteristic
370C22×C17C2×C22⋊Q811yescharacteristic
371C22×C17C2×#12311yescharacteristic
372C22×C17#53511yescharacteristic
373C22×C17#53611yescharacteristic
374C22×C17#53712yes—
375C22×C17D4212yes—
376C22×C17#54612yes—
377C22×C17#54712yes—
378C22×C17#54812yes—
379C22×C17D4×Q812yes—
380C22×C17#55212yes—
381C22×C17#55312yes—
382C22×C17#55412yes—
383C2×D17—24no—
384C2×D17—28no—
385C2×D17—28no—
386C2×D17—24no—
387C2×D17—24no—
388C2×D17—28no—
389C2×D17—28no—
390C2×D17—24no—
391C2×D17—24no—
392C2×D17—24no—
393C2×D17—28no—
394C2×D17—24no—
395C2×D17—42no—
396C2×D17—44no—
397C2×D17—42no—
398C2×D17—42no—
399C2×D17—44no—
400C2×D17—44no—
401C2×D17—42no—
402C2×D17—42no—
403C2×D17—42no—
404C2×D17#38018yescomplemented
405C4×C17—24no—
406C4×C17—24no—
407C4×C17—44no—
408C4×C17—42no—
409C4×C17—82no—
410Dic17—42no—
411Dic17—44no—
412Dic17—82no—
413Dic17#38618yescomplemented
414C23×D4—171no—
415C24×C4—171no—
416C24×C4—171no—
417C24×C4—172no—
418C2×C4×D4—178no—
419C2×C4×D4—344no—
420C2×C4×D4—344no—
421C22×C4⋊C4—172no—
422C22×C4⋊C4—172no—
423C22×C4⋊C4—171no—
424C22×C4⋊C4—348no—
425C22×C4⋊C4—344no—
426C22×C4⋊C4C2×D1711yescharacteristic
427C22×C4⋊C4C2×D1711yescharacteristic
428C22×C22⋊C4—171no—
429C22×C22⋊C4—171no—
430C22×C22⋊C4—172no—
431C22×C22⋊C4—172no—
432C22×C22⋊C4—172no—
433C22×C42—171no—
434#386—348no—
435#380—348no—
436#380—344no—
437C2×#95—172no—
438C2×#95—172no—
439C2×#95—171no—
440C2×#95—172no—
441C2×#95—172no—
442C2×#95C2×D1712yes—
443C2×#95C2×D1712yes—
444C2×#95C2×D1711yescharacteristic
445C2×C17C2×#38011yescharacteristic
446C2×C17C2×#38611yescharacteristic
447C2×C17#231111yescharacteristic
448C2×C17D4×C4⋊C412yes—
449C2×C17#235212yes—
450C2×C17#240811yescharacteristic
451C2×C17#240911yescharacteristic
452C2×C17#241612yes—
453C2×C17#241712yes—
454C2×C17#248611yescharacteristic
455C2×C17#248711yescharacteristic
456D17—28no—
457D17—44no—
458C25—171no—
459C25—171no—
460C22×D4—174no—
461C22×D4—174no—
462C22×D4—174no—
463C22×D4—342no—
464C22×D4—342no—
465C22×D4—342no—
466C22×D4—342no—
467C23×C4—171no—
468C23×C4—174no—
469C23×C4—174no—
470C23×C4—174no—
471C23×C4—171no—
472C23×C4—172no—
473C23×C4—174no—
474C23×C4—172no—
475C23×C4—344no—
476C23×C4—344no—
477C23×C4—344no—
478C23×C4—342no—
479C23×C4—342no—
480C23×C4—344no—
481C23×C4—344no—
482C23×C4—344no—
483C23×C4—344no—
484C23×C4—344no—
485C23×C4—344no—
486C23×C4—682no—
487C23×C4—682no—
488C23×C4C22×D1712yes—
489C23×C4C22×D1711yescharacteristic
490C23×C4C22×D1712yes—
491C23×C4C22×D1711yescharacteristic
492C23×C4C22×D1711yescharacteristic
493C4×D4—3432no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—178no—
499C2×C4⋊C4—3432no—
500C2×C4⋊C4—344no—
501C2×C4⋊C4—344no—
502C2×C4⋊C4—344no—
503C2×C4⋊C4—342no—
504C2×C4⋊C4—344no—
505C2×C4⋊C4—344no—
506C2×C4⋊C4—344no—
507C2×C4⋊C4C4×D1714yescomplemented
508C2×C22⋊C4—174no—
509C2×C22⋊C4—174no—
510C2×C22⋊C4—342no—
511C2×C22⋊C4—342no—
512C2×C22⋊C4—342no—
513C2×C22⋊C4—342no—
514C2×C22⋊C4—344no—
515C2×C22⋊C4—344no—
516C2×C22⋊C4—344no—
517C2×C22⋊C4—344no—
518C2×C22⋊C4—344no—
519C2×C22⋊C4—344no—
520C2×C22⋊C4—344no—
521C2×C22⋊C4—682no—
522C2×C22⋊C4—682no—
523C2×C42—174no—
524C2×C42—342no—
525C2×C42—342no—
526#95—24no—
527#95—22no—
528#95—24no—
529#95—344no—
530#95—342no—
531#95—344no—
532#95—682no—
533#95—682no—
534C17#1387211yescharacteristic, complemented, Sylow
535C24—172no—
536C24—172no—
537C24—172no—
538C24—172no—
539C24—172no—
540C24—172no—
541C24—172no—
542C24—172no—
543C24—172no—
544C24—172no—
545C24—342no—
546C24—342no—
547C24—342no—
548C24—342no—
549C24—342no—
550C24—341no—
551C24—341no—
552C24—342no—
553C24—342no—
554C24—341no—
555C24—341no—
556C24—342no—
557C24C23×D1711yescharacteristic
558C2×D4—1716no—
559C2×D4—348no—
560C2×D4—348no—
561C2×D4—348no—
562C2×D4—348no—
563C2×D4—348no—
564C2×D4—348no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
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—172no—
589C22×C4—172no—
590C22×C4—172no—
591C22×C4—174no—
592C22×C4—174no—
593C22×C4—1716no—
594C22×C4—172no—
595C22×C4—174no—
596C22×C4—348no—
597C22×C4—3416no—
598C22×C4—3416no—
599C22×C4—348no—
600C22×C4—348no—
601C22×C4—3416no—
602C22×C4—3416no—
603C22×C4—342no—
604C22×C4—341no—
605C22×C4—341no—
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—688no—
621C22×C4—688no—
622C22×C4—684no—
623C22×C4—688no—
624C22×C4—684no—
625C22×C4—688no—
626C22×C4—688no—
627C22×C4—688no—
628C22×C4—688no—
629C22×C4C2×C4×D1712yes—
630C22×C4C2×C4×D1712yes—
631C22×C4C2×C4×D1712yes—
632C22×C4D4×D1714yes—
633C22×C4D4×D1712yes—
634C22×C4D4×D1712yes—
635C22×C4D4×D1712yes—
636C22×C4Q8×D1712yes—
637C4⋊C4—28no—
638C4⋊C4—28no—
639C4⋊C4—3416no—
640C4⋊C4—348no—
641C4⋊C4—688no—
642C22⋊C4—348no—
643C22⋊C4—348no—
644C22⋊C4—688no—
645C22⋊C4—688no—
646C22⋊C4—688no—
647C42—348no—
648C23—174no—
649C23—174no—
650C23—174no—
651C23—174no—
652C23—174no—
653C23—174no—
654C23—174no—
655C23—174no—
656C23—344no—
657C23—344no—
658C23—344no—
659C23—344no—
660C23—344no—
661C23—344no—
662C23—344no—
663C23—344no—
664C23—342no—
665C23—344no—
666C23—342no—
667C23—342no—
668C23—342no—
669C23—344no—
670C23—344no—
671C23—344no—
672C23—344no—
673C23—344no—
674C23—342no—
675C23—344no—
676C23—342no—
677C23—344no—
678C23—344no—
679C23—342no—
680C23—342no—
681C23—342no—
682C23—342no—
683C23—344no—
684C23—682no—
685C23—682no—
686C23—682no—
687C23—681no—
688C23—682no—
689C23—681no—
690C23—681no—
691C23—681no—
692C23—682no—
693C23—682no—
694C23C22×C4×D1711yescharacteristic
695C23C2×D4×D1711yescharacteristic
696C23C2×D4×D1712yes—
697C23C2×D4×D1711yescharacteristic
698C23C2×D4×D1711yescharacteristic
699C23C2×Q8×D1711yescharacteristic
700C23#1058769412yes—
701C23#41×D1712yes—
702C23#41×D1711yescharacteristic
703C23#41×D1711yescharacteristic
704C23#1058769612yes—
705D4—3432no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—174no—
736C2×C4—178no—
737C2×C4—174no—
738C2×C4—178no—
739C2×C4—174no—
740C2×C4—3432no—
741C2×C4—342no—
742C2×C4—344no—
743C2×C4—344no—
744C2×C4—344no—
745C2×C4—344no—
746C2×C4—6816no—
747C2×C4—6832no—
748C2×C4—682no—
749C2×C4—682no—
750C2×C4—681no—
751C2×C4—681no—
752C2×C4—682no—
753C2×C4—682no—
754C2×C4—682no—
755C2×C4—682no—
756C2×C4—682no—
757C2×C4—682no—
758C2×C4—682no—
759C2×C4—682no—
760C2×C4—682no—
761C2×C4—682no—
762C2×C4C22⋊C4×D1714yes—
763C2×C4C4⋊C4×D1714yescomplemented
764C22—178no—
765C22—344no—
766C22—344no—
767C22—344no—
768C22—348no—
769C22—348no—
770C22—348no—
771C22—344no—
772C22—348no—
773C22—344no—
774C22—344no—
775C22—344no—
776C22—348no—
777C22—682no—
778C22—682no—
779C22—682no—
780C22—684no—
781C22—684no—
782C22—682no—
783C22—684no—
784C22—682no—
785C22—682no—
786C22C2×C22⋊C4×D1711yescharacteristic
787C22C2×C4⋊C4×D1711yescharacteristic
788C22#117×D1711yescharacteristic
789C22C4×D4×D1712yes—
790C22#1176329112yes—
791C22#120×D1711yescharacteristic
792C22#121×D1711yescharacteristic
793C22#121×D1711yescharacteristic
794C22#121×D1712yes—
795C22C22⋊Q8×D1711yescharacteristic
796C22C22⋊Q8×D1711yescharacteristic
797C22#123×D1711yescharacteristic
798C22#1176337711yescharacteristic
799C22#1176338411yescharacteristic
800C22#1176338912yes—
801C22#1176344312yes—
802C22#1176345112yes—
803C22#1176346112yes—
804C22#1176346912yes—
805C22#1176347412yes—
806C22#1176349112yes—
807C22#1176351012yes—
808C22#1176351512yes—
809C4—24no—
810C4—24no—
811C4—44no—
812C4—42no—
813C4—82no—
814C4—178no—
815C4—684no—
816C4—682no—
817C4—1362no—
818C2—348no—
819C2—684no—
820C2D17×#38011yescharacteristic
821C2D17×#38611yescharacteristic
822C2#1453137511yescharacteristic
823C2#1453168512yes—
824C2#1453170812yes—
825C2#1453213511yescharacteristic
826C2#1453214411yescharacteristic
827C2#1453221912yes—
828C2#1453223012yes—
829C2#1453308711yescharacteristic
830C2#1453309611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1441C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1441D17
hypocenterC17#13872
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D17C2semidirect
4. C2×#11762668C2semidirect
5. C2×#11762668C2semidirect
6. #14527037C2semidirect
7. #14527030C2semidirect
8. #14527026C2semidirect
9. #14527012C2semidirect
10. #14527005C2semidirect
11. C17×#1441C2semidirect
18. C2×#10587579C4semidirect
75. C22×C4×D17C2×C4semidirect
82. C2×C4⋊C4×C17C2×C4semidirect
97. C2×#63227C2×C4semidirect
105. C2×#63225D4semidirect
108. C2×C4×Dic17C2×C4semidirect
203. C2×D68C4⋊C4semidirect
220. C2×C4×D17C22⋊C4semidirect
284. C22×D17C2×C4⋊C4semidirect
320. C2×C4×C17C2×C4⋊C4semidirect
355. #1441D17semidirect
404. C2×D17#380semidirect
413. Dic17#386semidirect
507. C2×C4⋊C4C4×D17semidirect
534. C17#13872semidirect
763. C2×C4C4⋊C4×D17semidirect

Maximal subgroups

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

subgroupindex
C22×#105875792
C22×C4⋊C4×D172
C2×#117626872
C2×#117626682
#145270372
#145270302
#145270262
#145270122
#145270052
C17×#14412
#1387217