Finite Group Databasebeta

← D17×#2077 #17063148

Subgroups — D17×#2077 #17063148

Order 4352.

1270 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#106×D17C211yesmaximal, characteristic, complemented
2C2×C22⋊C8×D17C211yesmaximal, characteristic
3D17×#380C211yesmaximal, characteristic
4D17×#380C211yesmaximal, characteristic
5#14530223C211yesmaximal, characteristic, complemented
6#14530222C211yesmaximal, characteristic, complemented
7#14530221C211yesmaximal, characteristic, complemented
8#14530220C211yesmaximal, characteristic, complemented
9#14530219C211yesmaximal, characteristic, complemented
10#14530218C211yesmaximal, characteristic, complemented
11#14530217C211yesmaximal, characteristic, complemented
12D17×#340C211yesmaximal, characteristic, complemented
13D17×#340C211yesmaximal, characteristic, complemented
14D17×#340C211yesmaximal, characteristic, complemented
15C17×#2077C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C22×C8×D17C2211yescharacteristic
18C22×C8×D17C2211yescharacteristic
19C2×C4⋊C4×D17C2211yescharacteristic
20C2×C4⋊C4×D17C2211yescharacteristic
21C2×C4⋊C4×D17C2211yescharacteristic
22C2×C4⋊C4×D17C2211yescharacteristic
23C2×C22⋊C4×D17—21no—
24C2×C22⋊C4×D17—21no—
25C2×#10587488C2211yescharacteristic, complemented
26C2×#10587479C2211yescharacteristic, complemented
27C2×#10587479C2211yescharacteristic, complemented
28#106×D17—24no—
29C2×C22⋊#3622C2211yescharacteristic
30C2×#10587491C2211yescharacteristic
31C2×#10587491C2211yescharacteristic
32C22⋊C8×D17—24no—
33#11762669C2211yescharacteristic
34#11762669C2211yescharacteristic
35#11762668—21no—
36#11762668—21no—
37#11762667—21no—
38#11762667—21no—
39#11762666C2211yescharacteristic
40#11762666C2211yescharacteristic
41#11762666C2211yescharacteristic
42#11762666C2211yescharacteristic
43#95×D17—21no—
44#95×D17—21no—
45#11762572C2211yescharacteristic, complemented
46#11762572C2211yescharacteristic, complemented
47#11762572C2211yescharacteristic, complemented
48#11762571C2211yescharacteristic, complemented
49#11762571C2211yescharacteristic, complemented
50#11762571C2211yescharacteristic, complemented
51#11762571C2211yescharacteristic, complemented
52#11762571C2211yescharacteristic, complemented
53#11762571C2211yescharacteristic, complemented
54C2×C17×#106C2211yescharacteristic, complemented
55C2×C17×C22⋊C8C2211yescharacteristic
56C17×#380C2211yescharacteristic
57C17×#380C2211yescharacteristic
58C17×#340C2211yescharacteristic, complemented
59C17×#340C2211yescharacteristic, complemented
60C17×#340C2211yescharacteristic, complemented
61C24×D17D411yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×Dic17D411yescharacteristic
64C22×C4×D17—22no—
65C22×C4×D17—22no—
66C22×C4×D17—22no—
67C22×C4×D17—22no—
68C22×C4×D17—22no—
69C22×C4×D17—22no—
70C22×C4×D17—21no—
71C22×C4×D17—21no—
72C22×C4×D17—21no—
73C22×C4×D17—21no—
74C22×C4×D17D411yescharacteristic
75C22×C4×D17D411yescharacteristic
76C22×C4×D17C2311yescharacteristic
77C22×C4×D17C2311yescharacteristic
78C22×C8×C17C2311yescharacteristic
79C22×C8×C17C2311yescharacteristic
80C2×C4⋊C4×C17C2311yescharacteristic
81C2×C4⋊C4×C17C2311yescharacteristic
82C2×C4⋊C4×C17C2311yescharacteristic
83C2×C4⋊C4×C17C2311yescharacteristic
84C2×C22⋊C4×C17—21no—
85C2×C22⋊C4×C17—21no—
86C2×C22⋊Dic17—21no—
87C2×C22⋊Dic17—21no—
88C2×#63227—21no—
89C2×#63227—21no—
90C2×#63227—21no—
91C2×#63227—21no—
92C2×C4⋊Dic17C2311yescharacteristic
93C2×C4⋊Dic17C2311yescharacteristic
94C2×C4⋊Dic17C2311yescharacteristic
95C2×C4⋊Dic17C2311yescharacteristic
96C2×#63225—21no—
97C2×#63225—21no—
98C2×#63225—21no—
99C2×#63225—21no—
100C22×#3622C2311yescharacteristic
101C22×#3622C2311yescharacteristic
102C2×C8×D17—22no—
103C2×C8×D17—22no—
104C2×C8×D17—22no—
105C2×C8×D17—22no—
106C2×C8×D17—22no—
107C2×C8×D17D414yes—
108C4⋊C4×D17—22no—
109C4⋊C4×D17—22no—
110C4⋊C4×D17—22no—
111C4⋊C4×D17—22no—
112C4⋊C4×D17—22no—
113C4⋊C4×D17—22no—
114C4⋊C4×D17—22no—
115C4⋊C4×D17—22no—
116C22⋊C4×D17—44no—
117C22⋊C4×D17—44no—
118C17×#106—22no—
119C17×C22⋊C8—22no—
120C17×#95—21no—
121C17×#95—21no—
122#10587502—21no—
123#10587502—21no—
124#10587502—21no—
125#10587502—21no—
126#10587502—21no—
127#10587502—21no—
128C22⋊#3622—22no—
129#10587491—22no—
130#10587491—22no—
131#10587488—22no—
132#10587479—22no—
133#10587479—22no—
134C24×C17C2×D411yescharacteristic
135C23×D17—22no—
136C23×D17—22no—
137C23×D17—22no—
138C23×D17—22no—
139C23×D17—22no—
140C23×D17—22no—
141C23×D17SD1614yes—
142C23×D17C2×D411yescharacteristic
143C23×D17C2×D411yescharacteristic
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
148C22×C4×C17—21no—
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17C2×D411yescharacteristic
155C22×C4×C17C2411yescharacteristic
156C22×Dic17—22no—
157C22×Dic17—22no—
158C22×Dic17—22no—
159C22×Dic17—21no—
160C22×Dic17—21no—
161C22×Dic17—21no—
162C22×Dic17—21no—
163C22×Dic17C2×D411yescharacteristic
164C22×Dic17C2×D411yescharacteristic
165C2×C4×D17—22no—
166C2×C4×D17—22no—
167C2×C4×D17—22no—
168C2×C4×D17—21no—
169C2×C4×D17—21no—
170C2×C4×D17—21no—
171C2×C4×D17—21no—
172C2×C4×D17—21no—
173C2×C4×D17—21no—
174C2×C4×D17—22no—
175C2×C4×D17—22no—
176C2×C4×D17—22no—
177C2×C4×D17—44no—
178C2×C4×D17—44no—
179C2×C4×D17—44no—
180C2×C4×D17—44no—
181C2×C4×D17—42no—
182C2×C4×D17—42no—
183C2×C4×D17—42no—
184C2×C4×D17—42no—
185C2×C4×D17—42no—
186C2×C4×D17—42no—
187C2×C4×D17—42no—
188C2×C4×D17—42no—
189C2×C4×D17—42no—
190C2×C4×D17—42no—
191C2×C4×D17—42no—
192C2×C4×D17—42no—
193C2×C4×D17C2×D412yes—
194C2×C4×D17#4112yes—
195C2×C4×D17#4112yes—
196C2×C4×D17#4112yes—
197C2×C4×D17#4112yes—
198C2×C4×D17#4112yes—
199C2×C8×C17—21no—
200C2×C8×C17—21no—
201C2×C8×C17—21no—
202C2×C8×C17—21no—
203C2×C8×C17—21no—
204C2×C8×C17C2×D412yes—
205C4⋊C4×C17—21no—
206C4⋊C4×C17—21no—
207C4⋊C4×C17—21no—
208C4⋊C4×C17—21no—
209C4⋊C4×C17—21no—
210C4⋊C4×C17—21no—
211C4⋊C4×C17—21no—
212C4⋊C4×C17—21no—
213C22⋊C4×C17—42no—
214C22⋊C4×C17—42no—
215C22⋊Dic17—42no—
216C22⋊Dic17—42no—
217#63227—42no—
218#63227—42no—
219#63227—42no—
220#63227—42no—
221C4⋊Dic17—21no—
222C4⋊Dic17—21no—
223C4⋊Dic17—21no—
224C4⋊Dic17—21no—
225C4⋊Dic17—21no—
226C4⋊Dic17—21no—
227C4⋊Dic17—21no—
228C4⋊Dic17—21no—
229#63225—42no—
230#63225—42no—
231#63225—42no—
232#63225—42no—
233C2×#3622—21no—
234C2×#3622—21no—
235C2×#3622—21no—
236C2×#3622—21no—
237C2×#3622—21no—
238C2×#3622C2×D412yes—
239C8×D17—28no—
240C8×D17—44no—
241C2×#2077—171nomaximal, Sylow
242C23×C17—21no—
243C23×C17—21no—
244C23×C17—21no—
245C23×C17—21no—
246C23×C17—21no—
247C23×C17—21no—
248C23×C17C2×SD1612yes—
249C23×C17C22×D411yescharacteristic
250C22×D17—21no—
251C22×D17—21no—
252C22×D17—21no—
253C22×D17—21no—
254C22×D17—21no—
255C22×D17—21no—
256C22×D17—28no—
257C22×D17—28no—
258C22×D17—28no—
259C22×D17—44no—
260C22×D17—44no—
261C22×D17—44no—
262C22×D17—44no—
263C22×D17#12112yes—
264C22×D17#12312yes—
265C22×D17#12312yes—
266C22×D17C2×SD1612yes—
267C22×D17C2×SD1612yes—
268C22×D17#13512yes—
269C22×D17AGL(1,ℤ/8)12yes—
270C22×D17#13712yes—
271C2×C4×C17—21no—
272C2×C4×C17—21no—
273C2×C4×C17—21no—
274C2×C4×C17—41no—
275C2×C4×C17—41no—
276C2×C4×C17—41no—
277C2×C4×C17—41no—
278C2×C4×C17—41no—
279C2×C4×C17—41no—
280C2×C4×C17—41no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—41no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—41no—
288C2×C4×C17—41no—
289C2×C4×C17—41no—
290C2×C4×C17C22×D411yescharacteristic
291C2×C4×C17C2×#4111yescharacteristic
292C2×C4×C17C2×#4111yescharacteristic
293C2×C4×C17C2×#4111yescharacteristic
294C2×C4×C17C2×#4111yescharacteristic
295C2×C4×C17C2×#4111yescharacteristic
296C2×Dic17—21no—
297C2×Dic17—21no—
298C2×Dic17—21no—
299C2×Dic17—44no—
300C2×Dic17—41no—
301C2×Dic17—41no—
302C2×Dic17—41no—
303C2×Dic17—41no—
304C2×Dic17—41no—
305C2×Dic17—41no—
306C2×Dic17—41no—
307C2×Dic17—41no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—41no—
312C2×Dic17#12112yes—
313C2×Dic17#12312yes—
314C2×Dic17#12312yes—
315C4×D17—44no—
316C4×D17—41no—
317C4×D17—41no—
318C4×D17—41no—
319C4×D17—41no—
320C4×D17—44no—
321C4×D17—84no—
322C4×D17—84no—
323C4×D17—84no—
324C4×D17—84no—
325C4×D17#12314yes—
326C4×D17#12414yes—
327C4×D17#12614yes—
328C4×D17#12614yes—
329C8×C17—22no—
330C8×C17—41no—
331#3622—22no—
332#3622—41no—
333C22×#106—171no—
334C22×C22⋊C8—171no—
335C2×#380—171no—
336C2×#380—171no—
337#2077—171no—
338#2077—171no—
339#2077—171no—
340#2077—171no—
341#2077—171no—
342#2077—171no—
343#2077—171no—
344#2077D1711yescharacteristic, direct product factor
345C2×#340—171no—
346C2×#340—171no—
347C2×#340—171no—
348C22×C17—22no—
349C22×C17—22no—
350C22×C17—22no—
351C22×C17—41no—
352C22×C17—41no—
353C22×C17—41no—
354C22×C17—41no—
355C22×C17C2×#12111yescharacteristic
356C22×C17C2×#12311yescharacteristic
357C22×C17C2×#12311yescharacteristic
358C22×C17C22×SD1611yescharacteristic
359C22×C17C2×#13511yescharacteristic
360C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
361C22×C17C2×#13711yescharacteristic
362C2×D17—22no—
363C2×D17—22no—
364C2×D17—22no—
365C2×D17—41no—
366C2×D17—41no—
367C2×D17—41no—
368C2×D17—41no—
369C2×D17—416no—
370C2×D17#39714yes—
371C2×D17#46514yes—
372C2×D17#46814yes—
373C2×D17#48114yes—
374C2×D17#48214yes—
375C2×D17#48314yes—
376C2×D17#48514yes—
377C4×C17—41no—
378C4×C17—81no—
379C4×C17—81no—
380C4×C17—81no—
381C4×C17—81no—
382C4×C17C2×#12311yescharacteristic
383C4×C17C2×#12411yescharacteristic
384C4×C17C2×#12611yescharacteristic
385C4×C17C2×#12611yescharacteristic
386Dic17—41no—
387Dic17—81no—
388Dic17—81no—
389Dic17—81no—
390Dic17—81no—
391Dic17#39714yes—
392C24×C4—171no—
393C23×C8—171no—
394C23×C8—171no—
395C22×C4⋊C4—171no—
396C22×C4⋊C4—171no—
397C22×C4⋊C4—171no—
398C22×C4⋊C4—171no—
399C22×C22⋊C4—341no—
400C22×C22⋊C4—341no—
401C2×#106—171no—
402C2×#106—171no—
403C2×#106—171no—
404C2×#106—344no—
405C2×#106C2×D1711yescharacteristic, complemented
406C2×C22⋊C8—171no—
407C2×C22⋊C8—171no—
408C2×C22⋊C8—171no—
409C2×C22⋊C8—344no—
410C2×C22⋊C8C2×D1711yescharacteristic
411#380—171no—
412#380—171no—
413#380—171no—
414#380—171no—
415#380—171no—
416#380—171no—
417#380—341no—
418#380—341no—
419#380—341no—
420#380—341no—
421#380C2×D1711yescharacteristic
422#380C2×D1711yescharacteristic
423C2×#95—341no—
424C2×#95—341no—
425#340—171no—
426#340—171no—
427#340—171no—
428#340—171no—
429#340—171no—
430#340—171no—
431#340—171no—
432#340—171no—
433#340—171no—
434#340C2×D1711yescharacteristic, complemented
435#340C2×D1711yescharacteristic, complemented
436#340C2×D1711yescharacteristic, complemented
437C2×C17—42no—
438C2×C17C2×#39711yescharacteristic
439C2×C17C2×#46511yescharacteristic
440C2×C17C2×#46811yescharacteristic
441C2×C17C2×#48311yescharacteristic
442C2×C17C2×#48211yescharacteristic
443C2×C17C2×#48511yescharacteristic
444C2×C17C2×#48111yescharacteristic
445D17—42no—
446D17#207718yesdirect product factor
447C25—171no—
448C23×C4—171no—
449C23×C4—171no—
450C23×C4—171no—
451C23×C4—171no—
452C23×C4—171no—
453C23×C4—342no—
454C23×C4—342no—
455C23×C4—342no—
456C23×C4—342no—
457C23×C4—342no—
458C23×C4—342no—
459C23×C4—341no—
460C23×C4—341no—
461C23×C4—341no—
462C23×C4—341no—
463C23×C4C22×D1711yescharacteristic
464C22×C8—171no—
465C22×C8—174no—
466C22×C8—171no—
467C22×C8—342no—
468C22×C8—342no—
469C22×C8—342no—
470C22×C8—342no—
471C22×C8—342no—
472C22×C8C22×D1711yescharacteristic
473C22×C8C22×D1711yescharacteristic
474C2×C4⋊C4—171no—
475C2×C4⋊C4—171no—
476C2×C4⋊C4—171no—
477C2×C4⋊C4—171no—
478C2×C4⋊C4—342no—
479C2×C4⋊C4—342no—
480C2×C4⋊C4—342no—
481C2×C4⋊C4—342no—
482C2×C4⋊C4—342no—
483C2×C4⋊C4—342no—
484C2×C4⋊C4—342no—
485C2×C4⋊C4—342no—
486C2×C4⋊C4—341no—
487C2×C4⋊C4—341no—
488C2×C4⋊C4—341no—
489C2×C4⋊C4—341no—
490C2×C4⋊C4C22×D1711yescharacteristic
491C2×C4⋊C4C22×D1711yescharacteristic
492C2×C4⋊C4C22×D1711yescharacteristic
493C2×C4⋊C4C22×D1711yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—341no—
497C2×C22⋊C4—341no—
498C2×C22⋊C4—341no—
499C2×C22⋊C4—341no—
500C2×C22⋊C4—341no—
501C2×C22⋊C4—341no—
502C2×C22⋊C4—684no—
503C2×C22⋊C4—684no—
504#106—22no—
505#106—342no—
506#106—342no—
507#106—342no—
508C22⋊C8—22no—
509C22⋊C8—342no—
510C22⋊C8—342no—
511C22⋊C8—342no—
512#95—21no—
513#95—21no—
514#95—341no—
515#95—341no—
516#95—341no—
517#95—341no—
518#95—341no—
519#95—341no—
520C17C2×#207711yescharacteristic, complemented, Sylow
521C24—171no—
522C24—171no—
523C24—174no—
524C24—342no—
525C24—342no—
526C24—342no—
527C24—342no—
528C24—342no—
529C24—342no—
530C24D4×D1711yescharacteristic
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—171no—
542C22×C4—172no—
543C22×C4—172no—
544C22×C4—172no—
545C22×C4—172no—
546C22×C4—172no—
547C22×C4—172no—
548C22×C4—171no—
549C22×C4—342no—
550C22×C4—342no—
551C22×C4—342no—
552C22×C4—342no—
553C22×C4—342no—
554C22×C4—342no—
555C22×C4—342no—
556C22×C4—342no—
557C22×C4—342no—
558C22×C4—341no—
559C22×C4—341no—
560C22×C4—341no—
561C22×C4—341no—
562C22×C4—341no—
563C22×C4—341no—
564C22×C4—341no—
565C22×C4—341no—
566C22×C4—341no—
567C22×C4—341no—
568C22×C4—684no—
569C22×C4—684no—
570C22×C4—684no—
571C22×C4—684no—
572C22×C4—682no—
573C22×C4—682no—
574C22×C4—682no—
575C22×C4—682no—
576C22×C4—682no—
577C22×C4—682no—
578C22×C4—682no—
579C22×C4—682no—
580C22×C4—682no—
581C22×C4—682no—
582C22×C4—682no—
583C22×C4—682no—
584C22×C4D4×D1711yescharacteristic
585C22×C4C23×D1711yescharacteristic
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—172no—
592C2×C8—348no—
593C2×C8—341no—
594C2×C8—341no—
595C2×C8—341no—
596C2×C8—341no—
597C2×C8—341no—
598C2×C8—684no—
599C2×C8D4×D1712yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—341no—
609C4⋊C4—341no—
610C4⋊C4—341no—
611C4⋊C4—341no—
612C4⋊C4—341no—
613C4⋊C4—341no—
614C4⋊C4—341no—
615C4⋊C4—341no—
616C4⋊C4—682no—
617C4⋊C4—682no—
618C4⋊C4—682no—
619C4⋊C4—682no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—682no—
623C22⋊C4—682no—
624C22⋊C4—682no—
625C22⋊C4—682no—
626C22⋊C4—682no—
627C22⋊C4—682no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—172no—
635C23—172no—
636C23—172no—
637C23—172no—
638C23—172no—
639C23—172no—
640C23—172no—
641C23—172no—
642C23—348no—
643C23—348no—
644C23—348no—
645C23—341no—
646C23—341no—
647C23—341no—
648C23—341no—
649C23—341no—
650C23—341no—
651C23—684no—
652C23—684no—
653C23—684no—
654C23—684no—
655C23SD16×D1712yes—
656C23C2×D4×D1711yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—172no—
677C2×C4—172no—
678C2×C4—172no—
679C2×C4—174no—
680C2×C4—174no—
681C2×C4—174no—
682C2×C4—174no—
683C2×C4—341no—
684C2×C4—341no—
685C2×C4—341no—
686C2×C4—684no—
687C2×C4—684no—
688C2×C4—684no—
689C2×C4—681no—
690C2×C4—681no—
691C2×C4—681no—
692C2×C4—681no—
693C2×C4—681no—
694C2×C4—681no—
695C2×C4—681no—
696C2×C4—681no—
697C2×C4—681no—
698C2×C4—681no—
699C2×C4—681no—
700C2×C4—681no—
701C2×C4—681no—
702C2×C4—681no—
703C2×C4—681no—
704C2×C4—681no—
705C2×C4—1364no—
706C2×C4—1364no—
707C2×C4—1364no—
708C2×C4—1364no—
709C2×C4C2×D4×D1711yescharacteristic
710C2×C4#41×D1711yescharacteristic
711C2×C4#41×D1711yescharacteristic
712C2×C4#41×D1711yescharacteristic
713C2×C4#41×D1711yescharacteristic
714C2×C4#41×D1711yescharacteristic
715C8—22no—
716C8—41no—
717C8—342no—
718C8—681no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—174no—
727C22—174no—
728C22—174no—
729C22—174no—
730C22—174no—
731C22—174no—
732C22—174no—
733C22—342no—
734C22—342no—
735C22—342no—
736C22—6816no—
737C22—681no—
738C22—681no—
739C22—681no—
740C22—681no—
741C22#121×D1711yescharacteristic
742C22#123×D1711yescharacteristic
743C22#123×D1711yescharacteristic
744C22C2×SD16×D1711yescharacteristic
745C22#135×D1711yescharacteristic
746C22AGL(1,ℤ/8)×D1711yescharacteristic
747C22#137×D1711yescharacteristic
748C4—41no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4—81no—
753C4—174no—
754C4—681no—
755C4—1361no—
756C4—1361no—
757C4—1361no—
758C4—1361no—
759C4#123×D1711yescharacteristic
760C4#124×D1711yescharacteristic
761C4#126×D1711yescharacteristic
762C4#126×D1711yescharacteristic
763C2—42no—
764C2—178no—
765C2—682no—
766C2D17×#39711yescharacteristic
767C2D17×#46511yescharacteristic
768C2D17×#46811yescharacteristic
769C2D17×#48311yescharacteristic
770C2D17×#48211yescharacteristic
771C2D17×#48511yescharacteristic
772C2D17×#48111yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2077C2
socleC23×C17C22×D4
prime radicalC24×D17D4
hypercenter#2077D17
hypocenterC17C2×#2077
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2077

Complements

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

NH ≅ G/Ntype
1. C2×#106×D17C2semidirect
5. #14530223C2semidirect
6. #14530222C2semidirect
7. #14530221C2semidirect
8. #14530220C2semidirect
9. #14530219C2semidirect
10. #14530218C2semidirect
11. #14530217C2semidirect
12. D17×#340C2semidirect
13. D17×#340C2semidirect
14. D17×#340C2semidirect
15. C17×#2077C2semidirect
25. C2×#10587488C22semidirect
26. C2×#10587479C22semidirect
27. C2×#10587479C22semidirect
45. #11762572C22semidirect
46. #11762572C22semidirect
47. #11762572C22semidirect
48. #11762571C22semidirect
49. #11762571C22semidirect
50. #11762571C22semidirect
51. #11762571C22semidirect
52. #11762571C22semidirect
53. #11762571C22semidirect
54. C2×C17×#106C22semidirect
58. C17×#340C22semidirect
59. C17×#340C22semidirect
60. C17×#340C22semidirect
344. #2077D17direct (N × H)
405. C2×#106C2×D17semidirect
434. #340C2×D17semidirect
435. #340C2×D17semidirect
436. #340C2×D17semidirect
446. D17#2077direct (N × H)
520. C17C2×#2077semidirect

Maximal subgroups

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

subgroupindex
C2×#106×D172
C2×C22⋊C8×D172
D17×#3802
#145302232
#145302222
#145302212
#145302202
#145302192
#145302182
#145302172
D17×#3402
C17×#20772
C2×#207717