Finite Group Databasebeta

← #17033906

Subgroups — #17033906

Order 4352.

1590 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D17C211yesmaximal, characteristic
2C2×#11762850C211yesmaximal, characteristic, complemented
3C2×#11762848C211yesmaximal, characteristic, complemented
4#14531166C211yesmaximal, characteristic
5D17×#380C211yesmaximal, characteristic
6#14528817C211yesmaximal, characteristic, complemented
7#14528815C211yesmaximal, characteristic, complemented
8#14528815C211yesmaximal, characteristic, complemented
9#14528812C211yesmaximal, characteristic, complemented
10#14528810C211yesmaximal, characteristic, complemented
11#14528808C211yesmaximal, characteristic, complemented
12#14528806C211yesmaximal, characteristic, complemented
13#14528502C211yesmaximal, characteristic, complemented
14#14528502C211yesmaximal, characteristic, complemented
15C17×#1809C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C22×#63223C2211yescharacteristic
18C22×#63218C2211yescharacteristic
19C22×#63218C2211yescharacteristic
20C2×M16×D17—24no—
21C2×M16×D17—24no—
22C2×M16×D17C418yescomplemented
23C22×C8×D17C2211yescharacteristic
24C22×C8×D17C2211yescharacteristic
25C2×#10587578C2211yescharacteristic
26C2×#10587578C2211yescharacteristic
27C2×C4⋊C4×D17C2211yescharacteristic
28C2×C4⋊C4×D17C2211yescharacteristic
29C2×C22⋊C4×D17—21no—
30#11762850—24no—
31#11762848—24no—
32C2×#10587489C2211yescharacteristic, complemented
33C2×#10587478C2211yescharacteristic, complemented
34C2×#10587478C2211yescharacteristic, complemented
35C2×#10587488C2211yescharacteristic, complemented
36C2×#10587479C2211yescharacteristic, complemented
37C2×#10587479C2211yescharacteristic, complemented
38#11762671—21no—
39#11762669C2211yescharacteristic
40#11762669C2211yescharacteristic
41#11762668—21no—
42#11762667—21no—
43#11762666C2211yescharacteristic
44#11762666C2211yescharacteristic
45#11762666C2211yescharacteristic
46#11762666C2211yescharacteristic
47#11762664—21no—
48C22⋊C4×Dic17—21no—
49#11762656—21no—
50#95×D17—21no—
51#11762572C2211yescharacteristic, complemented
52#11762572C2211yescharacteristic, complemented
53#11762571C2211yescharacteristic, complemented
54#11762571C2211yescharacteristic, complemented
55#11762571C2211yescharacteristic, complemented
56#11762571C2211yescharacteristic, complemented
57C22×M16×C17C2211yescharacteristic
58C2×C17×#107C2211yescharacteristic, complemented
59C2×C17×#106C2211yescharacteristic, complemented
60C17×#380C2211yescharacteristic
61C17×#380C2211yescharacteristic
62C17×#340C2211yescharacteristic, complemented
63C17×#340C2211yescharacteristic, complemented
64C24×D17D411yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×Dic17D411yescharacteristic
67C22×C4×D17—22no—
68C22×C4×D17—22no—
69C22×C4×D17—22no—
70C22×C4×D17—22no—
71C22×C4×D17—21no—
72C22×C4×D17—21no—
73C22×C4×D17C2×C414yes—
74C22×C4×D17D411yescharacteristic
75C22×C4×D17D411yescharacteristic
76C22×C4×D17Q814yes—
77C22×C4×D17C2311yescharacteristic
78C22×C4×D17C2311yescharacteristic
79C2×M16×C17—22no—
80C2×M16×C17—22no—
81C2×M16×C17C2×C414yescomplemented
82C22×C8×C17C2311yescharacteristic
83C22×C8×C17C2311yescharacteristic
84C2×C4⋊C4×C17C2311yescharacteristic
85C2×C4⋊C4×C17C2311yescharacteristic
86C2×C4⋊C4×C17C2311yescharacteristic
87C2×C4⋊C4×C17C2311yescharacteristic
88C2×C22⋊C4×C17—21no—
89C2×C22⋊C4×C17—21no—
90C2×C22⋊Dic17—21no—
91C2×C22⋊Dic17—21no—
92C2×#63227—21no—
93C2×#63227—21no—
94C2×#63227—21no—
95C2×#63227—21no—
96C2×#63227—21no—
97C2×#63227—21no—
98C2×C4⋊Dic17C2311yescharacteristic
99C2×C4⋊Dic17C2311yescharacteristic
100C2×C4⋊Dic17C2311yescharacteristic
101C2×C4⋊Dic17C2311yescharacteristic
102C2×#63225—21no—
103C2×#63225—21no—
104C2×C4×Dic17—21no—
105C2×C4×Dic17—21no—
106C2×#63223—22no—
107C2×#63223—22no—
108C2×#63223C2×C414yescomplemented
109C22×#3622C2311yescharacteristic
110C22×#3622C2311yescharacteristic
111M16×D17—232no—
112C2×#63218—22no—
113C2×#63218—22no—
114C2×#63218C2×C414yes—
115C2×#63218C2×C414yes—
116C2×#63218D414yes—
117C2×#63218D414yes—
118C2×C8×D17—22no—
119C2×C8×D17—22no—
120C2×C8×D17—22no—
121C2×C8×D17—22no—
122C2×C8×D17C2×C414yescomplemented
123C2×C8×D17C2×C414yescomplemented
124#10587578—22no—
125#10587578—22no—
126#10587578—22no—
127#10587578—22no—
128C4⋊C4×D17—22no—
129C4⋊C4×D17—22no—
130C4⋊C4×D17—22no—
131C4⋊C4×D17—22no—
132C22⋊C4×D17—44no—
133C17×#107—22no—
134C17×#106—22no—
135C17×#95—21no—
136C17×#95—21no—
137#10587502—21no—
138#10587502—21no—
139#10587502—21no—
140#10587502—21no—
141#10587502—21no—
142#10587502—21no—
143#10587489—22no—
144#10587488—22no—
145#10587479—22no—
146#10587479—22no—
147#10587478—22no—
148#10587478—22no—
149C24×C17C2×D411yescharacteristic
150C23×D17—22no—
151C23×D17—22no—
152C23×D17—22no—
153C23×D17—22no—
154C23×D17—41no—
155C23×D17—41no—
156C23×D17C4⋊C414yes—
157C23×D17C2×D411yescharacteristic
158C23×D17C2×D411yescharacteristic
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17C22×C412yes—
168C22×C4×C17C2×D411yescharacteristic
169C22×C4×C17C2×Q812yes—
170C22×C4×C17C2411yescharacteristic
171C22×Dic17—22no—
172C22×Dic17—22no—
173C22×Dic17—21no—
174C22×Dic17—21no—
175C22×Dic17—21no—
176C22×Dic17—21no—
177C22×Dic17C4⋊C414yes—
178C22×Dic17C2×D411yescharacteristic
179C22×Dic17C2×D411yescharacteristic
180C2×C4×D17—22no—
181C2×C4×D17—22no—
182C2×C4×D17—21no—
183C2×C4×D17—21no—
184C2×C4×D17—21no—
185C2×C4×D17—21no—
186C2×C4×D17—22no—
187C2×C4×D17—22no—
188C2×C4×D17—28no—
189C2×C4×D17—28no—
190C2×C4×D17—28no—
191C2×C4×D17—28no—
192C2×C4×D17—42no—
193C2×C4×D17—42no—
194C2×C4×D17—42no—
195C2×C4×D17—42no—
196C2×C4×D17—42no—
197C2×C4×D17—42no—
198C2×C4×D17C4⋊C414yes—
199C2×C4×D17C4⋊C414yes—
200C2×C4×D17C22×C412yes—
201C2×C4×D17C22×C412yes—
202C2×C4×D17C2×D412yes—
203C2×C4×D17C2×D412yes—
204C2×C4×D17C2×Q812yes—
205C2×C4×D17C2×Q812yes—
206C2×C4×D17#4112yes—
207C2×C4×D17#4112yes—
208M16×C17—28no—
209C2×C8×C17—21no—
210C2×C8×C17—21no—
211C2×C8×C17C22×C412yes—
212C2×C8×C17C22×C412yes—
213C2×C8×C17C2×D412yes—
214C2×C8×C17C2×D412yes—
215C4⋊C4×C17—21no—
216C4⋊C4×C17—21no—
217C4⋊C4×C17—21no—
218C4⋊C4×C17—21no—
219C4⋊C4×C17—21no—
220C4⋊C4×C17—21no—
221C4⋊C4×C17—21no—
222C4⋊C4×C17—21no—
223C22⋊C4×C17—42no—
224C22⋊C4×C17—42no—
225C22⋊Dic17—42no—
226C22⋊Dic17—42no—
227#63227—42no—
228#63227—42no—
229#63227—42no—
230#63227—42no—
231#63227—42no—
232#63227—42no—
233C4⋊Dic17—21no—
234C4⋊Dic17—21no—
235C4⋊Dic17—21no—
236C4⋊Dic17—21no—
237C4⋊Dic17—21no—
238C4⋊Dic17—21no—
239C4⋊Dic17—21no—
240C4⋊Dic17—21no—
241#63225—42no—
242#63225—42no—
243C4×Dic17—42no—
244C4×Dic17—42no—
245#63223—28no—
246C2×#3622—21no—
247C2×#3622—21no—
248C2×#3622C22×C412yes—
249C2×#3622C22×C412yes—
250C2×#3622C2×D412yes—
251C2×#3622C2×D412yes—
252#63218—28no—
253#63218C22⋊C4116yescomplemented
254C8×D17—28no—
255C8×D17—28no—
256#20661—171nomaximal, Sylow
257C23×C17—21no—
258C23×C17—21no—
259C23×C17—21no—
260C23×C17—21no—
261C23×C17—21no—
262C23×C17—21no—
263C23×C17C2×C4⋊C412yes—
264C23×C17C22×D411yescharacteristic
265C22×D17—21no—
266C22×D17—21no—
267C22×D17—21no—
268C22×D17—21no—
269C22×D17—21no—
270C22×D17—21no—
271C22×D17—21no—
272C22×D17—21no—
273C22×D17—28no—
274C22×D17—28no—
275C22×D17—44no—
276C22×D17—44no—
277C22×D17—44no—
278C22×D17—44no—
279C22×D17—44no—
280C22×D17C2×C4⋊C412yes—
281C22×D17C2×C4⋊C412yes—
282C22×D17#12112yes—
283C22×D17#12112yes—
284C22×D17AGL(1,ℤ/8)12yes—
285C22×D17#13712yes—
286C2×C4×C17—21no—
287C2×C4×C17—21no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—41no—
293C2×C4×C17—41no—
294C2×C4×C17—41no—
295C2×C4×C17—41no—
296C2×C4×C17—41no—
297C2×C4×C17—41no—
298C2×C4×C17—41no—
299C2×C4×C17—41no—
300C2×C4×C17—41no—
301C2×C4×C17—41no—
302C2×C4×C17—41no—
303C2×C4×C17—41no—
304C2×C4×C17C2×C4⋊C412yes—
305C2×C4×C17C23×C411yescharacteristic
306C2×C4×C17C22×D411yescharacteristic
307C2×C4×C17C22×D411yescharacteristic
308C2×C4×C17C22×Q811yescharacteristic
309C2×C4×C17C2×#4111yescharacteristic
310C2×C4×C17C2×#4111yescharacteristic
311C2×Dic17—21no—
312C2×Dic17—21no—
313C2×Dic17—28no—
314C2×Dic17—41no—
315C2×Dic17—41no—
316C2×Dic17—41no—
317C2×Dic17—41no—
318C2×Dic17—41no—
319C2×Dic17—41no—
320C2×Dic17—41no—
321C2×Dic17—41no—
322C2×Dic17—41no—
323C2×Dic17—41no—
324C2×Dic17—41no—
325C2×Dic17—41no—
326C2×Dic17C2×C4⋊C412yes—
327C2×Dic17C2×C4⋊C412yes—
328C2×Dic17#12112yes—
329C2×Dic17#12112yes—
330C4×D17—28no—
331C4×D17—22no—
332C4×D17—22no—
333C4×D17—22no—
334C4×D17—22no—
335C4×D17—28no—
336C4×D17—84no—
337C4×D17—84no—
338C4×D17C2×C22⋊C414yes—
339C4×D17#11714yes—
340C4×D17C22⋊Q814yes—
341C4×D17C22⋊Q814yes—
342C8×C17—22no—
343C8×C17C2×C22⋊C414yescomplemented
344#3622—22no—
345#3622C2×C22⋊C414yescomplemented
346C23×M16—171no—
347C2×#428—171no—
348C2×#428—171no—
349#2280—171no—
350C2×#380—171no—
351#1809—171no—
352#1809—171no—
353#1809—171no—
354#1809D1711yescharacteristic, complemented
355#1808—171no—
356#1808—171no—
357#1807—171no—
358#1807—171no—
359#1736—171no—
360#1736—171no—
361C22×C17—22no—
362C22×C17—22no—
363C22×C17—22no—
364C22×C17—41no—
365C22×C17—41no—
366C22×C17—41no—
367C22×C17—41no—
368C22×C17C22×C4⋊C411yescharacteristic
369C22×C17C2×#12111yescharacteristic
370C22×C17C2×#12111yescharacteristic
371C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C17C2×#13711yescharacteristic
373C22×C17#57511yescharacteristic
374C22×C17#57511yescharacteristic
375C2×D17—22no—
376C2×D17—22no—
377C2×D17—22no—
378C2×D17—22no—
379C2×D17—22no—
380C2×D17—22no—
381C2×D17—22no—
382C2×D17—22no—
383C2×D17—22no—
384C2×D17—22no—
385C2×D17—22no—
386C2×D17—22no—
387C2×D17—416no—
388C2×D17#38014yes—
389C2×D17#42814yescomplemented
390C4×C17—22no—
391C4×C17—81no—
392C4×C17—81no—
393C4×C17—81no—
394C4×C17—81no—
395C4×C17C22×C22⋊C411yescharacteristic
396C4×C17C2×#11711yescharacteristic
397C4×C17C2×C22⋊Q811yescharacteristic
398C4×C17C2×C22⋊Q811yescharacteristic
399Dic17—22no—
400Dic17—81no—
401Dic17—81no—
402Dic17—81no—
403Dic17—81no—
404Dic17#38014yes—
405C24×C4—171no—
406C22×M16—171no—
407C22×M16—178no—
408C22×M16—171no—
409C22×M16—171no—
410C22×M16—344no—
411C22×M16—344no—
412C22×M16C2×D1711yescharacteristic
413C23×C8—171no—
414C23×C8—171no—
415C2×#117—171no—
416C2×#117—171no—
417C22×C4⋊C4—171no—
418C22×C4⋊C4—171no—
419C22×C22⋊C4—341no—
420#428—344no—
421#428—344no—
422C2×#107—171no—
423C2×#107—171no—
424C2×#107—171no—
425C2×#107C2×D1711yescharacteristic, complemented
426C2×#106—171no—
427C2×#106—171no—
428C2×#106—171no—
429C2×#106C2×D1711yescharacteristic, complemented
430#381—341no—
431#380—171no—
432#380—171no—
433#380—171no—
434#380—171no—
435#380—171no—
436#380—171no—
437#380—341no—
438#380—341no—
439#380C2×D1711yescharacteristic
440#380C2×D1711yescharacteristic
441#379—341no—
442C4×C22⋊C4—341no—
443C4×C22⋊C4—341no—
444C2×#95—341no—
445#340—171no—
446#340—171no—
447#340—171no—
448#340—171no—
449#340—171no—
450#340—171no—
451#340C2×D1711yescharacteristic, complemented
452#340C2×D1711yescharacteristic, complemented
453C2×C17—42no—
454C2×C17C2×#38011yescharacteristic
455C2×C17C2×#42811yescharacteristic
456C2×C17#291111yescharacteristic
457C2×C17#305511yescharacteristic
458C2×C17#305511yescharacteristic
459C2×C17#305611yescharacteristic
460C2×C17#305611yescharacteristic
461D17—24no—
462D17—24no—
463C25—171no—
464C23×C4—171no—
465C23×C4—171no—
466C23×C4—174no—
467C23×C4—171no—
468C23×C4—171no—
469C23×C4—174no—
470C23×C4—171no—
471C23×C4—342no—
472C23×C4—342no—
473C23×C4—342no—
474C23×C4—342no—
475C23×C4—341no—
476C23×C4—341no—
477C23×C4C22×D1711yescharacteristic
478C2×M16—22no—
479C2×M16—22no—
480C2×M16—174no—
481C2×M16—174no—
482C2×M16—174no—
483C2×M16—174no—
484C2×M16—174no—
485C2×M16—342no—
486C2×M16—342no—
487C2×M16—342no—
488C2×M16—342no—
489C2×M16—3432no—
490C2×M16C4×D1714yescomplemented
491C22×C8—171no—
492C22×C8—171no—
493C22×C8—174no—
494C22×C8—174no—
495C22×C8—342no—
496C22×C8—342no—
497C22×C8—342no—
498C22×C8—342no—
499C22×C8C22×D1711yescharacteristic
500C22×C8C22×D1711yescharacteristic
501#117—342no—
502#117—342no—
503#117—342no—
504#117—342no—
505C2×C4⋊C4—171no—
506C2×C4⋊C4—171no—
507C2×C4⋊C4—171no—
508C2×C4⋊C4—171no—
509C2×C4⋊C4—342no—
510C2×C4⋊C4—342no—
511C2×C4⋊C4—342no—
512C2×C4⋊C4—342no—
513C2×C4⋊C4—341no—
514C2×C4⋊C4—341no—
515C2×C4⋊C4C22×D1711yescharacteristic
516C2×C4⋊C4C22×D1711yescharacteristic
517C2×C4⋊C4C22×D1711yescharacteristic
518C2×C4⋊C4C22×D1711yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—341no—
522C2×C22⋊C4—341no—
523C2×C22⋊C4—341no—
524C2×C22⋊C4—341no—
525C2×C22⋊C4—341no—
526C2×C22⋊C4—341no—
527C2×C22⋊C4—341no—
528C2×C22⋊C4—341no—
529C2×C22⋊C4—684no—
530C2×C42—341no—
531C2×C42—341no—
532#107—22no—
533#107—342no—
534#107—342no—
535#107—342no—
536#106—22no—
537#106—342no—
538#106—342no—
539#106—342no—
540#95—21no—
541#95—21no—
542#95—341no—
543#95—341no—
544#95—341no—
545#95—341no—
546#95—341no—
547#95—341no—
548C17#2066111yescharacteristic, complemented, Sylow
549C24—171no—
550C24—171no—
551C24—174no—
552C24—342no—
553C24—342no—
554C24—342no—
555C24—342no—
556C24—681no—
557C24—681no—
558C24D4×D1711yescharacteristic
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—171no—
568C22×C4—172no—
569C22×C4—172no—
570C22×C4—172no—
571C22×C4—172no—
572C22×C4—172no—
573C22×C4—172no—
574C22×C4—171no—
575C22×C4—174no—
576C22×C4—172no—
577C22×C4—172no—
578C22×C4—174no—
579C22×C4—174no—
580C22×C4—348no—
581C22×C4—342no—
582C22×C4—342no—
583C22×C4—348no—
584C22×C4—348no—
585C22×C4—348no—
586C22×C4—342no—
587C22×C4—342no—
588C22×C4—342no—
589C22×C4—342no—
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—682no—
599C22×C4—682no—
600C22×C4—682no—
601C22×C4—682no—
602C22×C4—682no—
603C22×C4—682no—
604C22×C4C2×C4×D1712yes—
605C22×C4D4×D1711yescharacteristic
606C22×C4Q8×D1712yes—
607C22×C4C23×D1711yescharacteristic
608M16—28no—
609M16—1716no—
610M16—348no—
611M16—348no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—172no—
615C2×C8—172no—
616C2×C8—172no—
617C2×C8—172no—
618C2×C8—348no—
619C2×C8—341no—
620C2×C8—341no—
621C2×C8—348no—
622C2×C8C2×C4×D1712yes—
623C2×C8C2×C4×D1712yes—
624C2×C8D4×D1712yes—
625C2×C8D4×D1712yes—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—341no—
635C4⋊C4—341no—
636C4⋊C4—341no—
637C4⋊C4—341no—
638C4⋊C4—341no—
639C4⋊C4—341no—
640C4⋊C4—341no—
641C4⋊C4—341no—
642C4⋊C4—682no—
643C4⋊C4—682no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—682no—
647C22⋊C4—682no—
648C22⋊C4—682no—
649C22⋊C4—682no—
650C22⋊C4—682no—
651C22⋊C4—682no—
652C22⋊C4—682no—
653C22⋊C4—682no—
654C42—682no—
655C42—682no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—172no—
663C23—172no—
664C23—172no—
665C23—172no—
666C23—172no—
667C23—172no—
668C23—348no—
669C23—348no—
670C23—341no—
671C23—341no—
672C23—341no—
673C23—341no—
674C23—341no—
675C23—341no—
676C23—341no—
677C23—341no—
678C23—684no—
679C23—684no—
680C23—684no—
681C23—684no—
682C23—684no—
683C23C4⋊C4×D1712yes—
684C23C2×D4×D1711yescharacteristic
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—172no—
704C2×C4—172no—
705C2×C4—172no—
706C2×C4—174no—
707C2×C4—174no—
708C2×C4—174no—
709C2×C4—174no—
710C2×C4—172no—
711C2×C4—348no—
712C2×C4—348no—
713C2×C4—348no—
714C2×C4—341no—
715C2×C4—341no—
716C2×C4—342no—
717C2×C4—342no—
718C2×C4—342no—
719C2×C4—342no—
720C2×C4—681no—
721C2×C4—681no—
722C2×C4—681no—
723C2×C4—681no—
724C2×C4—681no—
725C2×C4—681no—
726C2×C4—681no—
727C2×C4—681no—
728C2×C4—681no—
729C2×C4—681no—
730C2×C4—681no—
731C2×C4—681no—
732C2×C4—1364no—
733C2×C4—1364no—
734C2×C4C4⋊C4×D1712yes—
735C2×C4C22×C4×D1711yescharacteristic
736C2×C4C2×D4×D1711yescharacteristic
737C2×C4C2×D4×D1711yescharacteristic
738C2×C4C2×Q8×D1711yescharacteristic
739C2×C4#41×D1711yescharacteristic
740C2×C4#41×D1711yescharacteristic
741C8—22no—
742C8—174no—
743C8—342no—
744C8C22⋊C4×D1714yescomplemented
745C22—22no—
746C22—22no—
747C22—22no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—174no—
753C22—174no—
754C22—342no—
755C22—342no—
756C22—342no—
757C22—342no—
758C22—342no—
759C22—342no—
760C22—342no—
761C22—342no—
762C22—342no—
763C22—342no—
764C22—342no—
765C22—342no—
766C22—6816no—
767C22C2×C4⋊C4×D1711yescharacteristic
768C22#121×D1711yescharacteristic
769C22#121×D1711yescharacteristic
770C22AGL(1,ℤ/8)×D1711yescharacteristic
771C22#137×D1711yescharacteristic
772C22#1176360511yescharacteristic
773C22#1176360811yescharacteristic
774C4—22no—
775C4—81no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4—174no—
780C4—342no—
781C4—1361no—
782C4—1361no—
783C4—1361no—
784C4—1361no—
785C4C2×C22⋊C4×D1711yescharacteristic
786C4#117×D1711yescharacteristic
787C4C22⋊Q8×D1711yescharacteristic
788C4C22⋊Q8×D1711yescharacteristic
789C2—42no—
790C2—344no—
791C2—344no—
792C2D17×#38011yescharacteristic
793C2D17×#42811yescharacteristic
794C2#1453737111yescharacteristic
795C2#1453839811yescharacteristic
796C2#1453840211yescharacteristic
797C2#1453840911yescharacteristic
798C2#1453841311yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1809C2
socleC23×C17C22×D4
prime radicalC24×D17D4
cosocleC22×C4×C17C24
hypercenter#1809D17
hypocenterC17#20661
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#11762850C2semidirect
3. C2×#11762848C2semidirect
6. #14528817C2semidirect
7. #14528815C2semidirect
8. #14528815C2semidirect
9. #14528812C2semidirect
10. #14528810C2semidirect
11. #14528808C2semidirect
12. #14528806C2semidirect
13. #14528502C2semidirect
14. #14528502C2semidirect
15. C17×#1809C2semidirect
22. C2×M16×D17C4semidirect
32. C2×#10587489C22semidirect
33. C2×#10587478C22semidirect
34. C2×#10587478C22semidirect
35. C2×#10587488C22semidirect
36. C2×#10587479C22semidirect
37. C2×#10587479C22semidirect
51. #11762572C22semidirect
52. #11762572C22semidirect
53. #11762571C22semidirect
54. #11762571C22semidirect
55. #11762571C22semidirect
56. #11762571C22semidirect
58. C2×C17×#107C22semidirect
59. C2×C17×#106C22semidirect
62. C17×#340C22semidirect
63. C17×#340C22semidirect
81. C2×M16×C17C2×C4semidirect
108. C2×#63223C2×C4semidirect
122. C2×C8×D17C2×C4semidirect
123. C2×C8×D17C2×C4semidirect
253. #63218C22⋊C4semidirect
343. C8×C17C2×C22⋊C4semidirect
345. #3622C2×C22⋊C4semidirect
354. #1809D17semidirect
389. C2×D17#428semidirect
425. C2×#107C2×D17semidirect
429. C2×#106C2×D17semidirect
451. #340C2×D17semidirect
452. #340C2×D17semidirect
490. C2×M16C4×D17semidirect
548. C17#20661semidirect
744. C8C22⋊C4×D17semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D172
C2×#117628502
C2×#117628482
#145311662
D17×#3802
#145288172
#145288152
#145288122
#145288102
#145288082
#145288062
#145285022
C17×#18092
#2066117