Finite Group Databasebeta

← #103×C22⋊D17 #17049752

Subgroups — #103×C22⋊D17 #17049752

Order 4352.

1530 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
1C2×Q8×C22⋊D17C211yesmaximal, characteristic
2C2×C8×C22⋊D17C211yesmaximal, characteristic
3C2×#103×D17C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D17C211yesmaximal, characteristic
5#14529705C211yesmaximal, characteristic, complemented
6#14529584C211yesmaximal, characteristic, complemented
7#14529207C211yesmaximal, characteristic, complemented
8#14529204C211yesmaximal, characteristic, complemented
9#14529091C211yesmaximal, characteristic, complemented
10#14529088C211yesmaximal, characteristic, complemented
11#14528787C211yesmaximal, characteristic, complemented
12#14528719C211yesmaximal, characteristic, complemented
13#14528717C211yesmaximal, characteristic, complemented
14#103×Dic17C211yesmaximal, characteristic, complemented
15C22×C17×#103C211yesmaximal, characteristic, complemented
16C22×Q8×D17C2211yescharacteristic
17C22×C8×D17C2211yescharacteristic
18Q8×C22⋊D17—24no—
19Q8×C22⋊D17C418yescomplemented
20C2×#10587630—21no—
21C2×#10587630C2211yescharacteristic
22C2×#10587610—21no—
23C2×#10587610C2211yescharacteristic
24C2×#10587632—21no—
25C2×#10587632C2211yescharacteristic
26C2×Q8×Dic17C2211yescharacteristic
27C2×C4×C22⋊D17—21no—
28C2×C4×C22⋊D17—21no—
29C2×C4×C22⋊D17C2211yescharacteristic
30C2×C4⋊C4×D17C2211yescharacteristic
31C8×C22⋊D17—24no—
32C2×#10587485C2211yescharacteristic
33C2×#10587487C2211yescharacteristic
34C2×#10587487C2211yescharacteristic
35C2×#10587506C2211yescharacteristic
36C2×#10587506C2211yescharacteristic
37C2×#10587506C2211yescharacteristic
38C2×#10587506C2211yescharacteristic
39C2×#10587481C2211yescharacteristic
40C2×#10587481C2211yescharacteristic
41#103×D17—24no—
42C2×C22⋊#3622C2211yescharacteristic
43C2×#10587491C2211yescharacteristic
44C2×C8×Dic17C2211yescharacteristic
45#11762704—21no—
46#11762682—21no—
47#11762680—21no—
48#11762678C2211yescharacteristic
49#11762669C2211yescharacteristic
50#11762666C2211yescharacteristic
51C4⋊C4×Dic17C2211yescharacteristic
52#11762572C2211yescharacteristic
53#11762572C2211yescharacteristic
54#11762571C2211yescharacteristic
55#11762571C2211yescharacteristic
56C23×Q8×C17C2211yescharacteristic
57C23×C8×C17C2211yescharacteristic
58C22×C4⋊C4×C17C2211yescharacteristic
59C2×C17×#103—24no—
60C2×C17×#103C2211yescharacteristic
61C2×C17×#103C2211yescharacteristic
62C2×C17×#103C2211yescharacteristic
63C2×C17×#103C2211yescharacteristic
64C22×Q8×C17—22no—
65C22×Q8×C17—21no—
66C22×Q8×C17—22no—
67C22×Q8×C17—22no—
68C22×Q8×C17—41no—
69C22×Q8×C17—41no—
70C22×Q8×C17C2×C414yescomplemented
71C22×Q8×C17C2311yescharacteristic
72C22×Q8×C17C2311yescharacteristic
73C23×C4×C17—21no—
74C23×C4×C17—21no—
75C23×C4×C17C2311yescharacteristic
76C22×C22⋊D17D411yescharacteristic
77C2×Q8×D17—22no—
78C2×Q8×D17—22no—
79C2×Q8×D17—22no—
80C2×Q8×D17—41no—
81C2×Q8×D17—41no—
82C2×Q8×D17C2×C414yescomplemented
83C22×C4×D17—21no—
84C22×C4×D17—21no—
85C22×C4×D17C2311yescharacteristic
86C22×Dic34—21no—
87C22×Dic34C2311yescharacteristic
88C22×C8×C17—22no—
89C22×C8×C17—22no—
90C22×C8×C17—41no—
91C22×C8×C17C2311yescharacteristic
92C22×C8×C17C2311yescharacteristic
93C2×C4⋊C4×C17—22no—
94C2×C4⋊C4×C17—21no—
95C2×C4⋊C4×C17—41no—
96C2×C4⋊C4×C17C2311yescharacteristic
97C2×C4⋊C4×C17C2311yescharacteristic
98C2×C22⋊Dic17—21no—
99C2×C22⋊Dic17—21no—
100C2×C22⋊Dic17D411yescharacteristic
101#10587632—28no—
102#10587632—22no—
103#10587632C2×C414yescomplemented
104Q8×Dic17—22no—
105Q8×Dic17C2×C414yescomplemented
106#10587630—28no—
107#10587630—22no—
108#10587630C2×C414yescomplemented
109C4×C22⋊D17—28no—
110C4×C22⋊D17—44no—
111C4×C22⋊D17C2×C414yes—
112C4×C22⋊D17D414yes—
113C2×#63227—21no—
114C2×#63227—21no—
115C2×#63227D411yescharacteristic
116C2×C4⋊Dic17—21no—
117C2×C4⋊Dic17C2311yescharacteristic
118C2×C4⋊Dic17C2311yescharacteristic
119C2×C4⋊Dic17C2311yescharacteristic
120#10587610—22no—
121#10587610—28no—
122#10587610C2×C414yescomplemented
123C2×#63225—21no—
124C2×#63225—21no—
125C2×#63225—21no—
126C2×#63225—21no—
127C2×#63225—21no—
128C2×#63225—21no—
129C2×#63225—21no—
130C2×#63225D411yescharacteristic
131C2×C4×Dic17—21no—
132C2×C4×Dic17—21no—
133C2×C4×Dic17C2311yescharacteristic
134C22×#3622C2311yescharacteristic
135C22×#3622C2311yescharacteristic
136C2×C8×D17—22no—
137C2×C8×D17—22no—
138C2×C8×D17—41no—
139C4⋊C4×D17—22no—
140C4⋊C4×D17—41no—
141C17×#103—22no—
142C17×#103—22no—
143C17×#103—22no—
144C17×#103D414yescomplemented
145#10587506—22no—
146#10587506—22no—
147#10587506—41no—
148#10587506—41no—
149#10587502—21no—
150#10587502—21no—
151#10587502—21no—
152C22⋊#3622—22no—
153#10587491—22no—
154#10587487—22no—
155#10587487—41no—
156#10587485—22no—
157C8×Dic17—22no—
158#10587481—22no—
159#10587481—41no—
160C24×C17C2×D411yescharacteristic
161C23×D17C2×D411yescharacteristic
162C2×Q8×C17—24no—
163C2×Q8×C17—21no—
164C2×Q8×C17—21no—
165C2×Q8×C17—21no—
166C2×Q8×C17—21no—
167C2×Q8×C17—28no—
168C2×Q8×C17—21no—
169C2×Q8×C17—21no—
170C2×Q8×C17—21no—
171C2×Q8×C17—21no—
172C2×Q8×C17—42no—
173C2×Q8×C17—42no—
174C2×Q8×C17—44no—
175C2×Q8×C17—44no—
176C2×Q8×C17—44no—
177C2×Q8×C17C22×C412yes—
178C2×Q8×C17C22×C412yes—
179C2×Q8×C17C2×D412yes—
180C2×Q8×C17#4112yes—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—24no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—42no—
191C22×C4×C17—42no—
192C22×C4×C17—42no—
193C22×C4×C17—42no—
194C22×C4×C17—81no—
195C22×C4×C17C22×C412yes—
196C22×C4×C17C2×D411yescharacteristic
197C22×C4×C17C2×D412yes—
198C22×C4×C17C2411yescharacteristic
199C2×C22⋊D17C22⋊C414yes—
200C2×C22⋊D17SD1614yes—
201C2×C22⋊D17Q1614yes—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17C2×D411yescharacteristic
207C22×Dic17C2×D411yescharacteristic
208C22×Dic17C2×D411yescharacteristic
209Q8×D17—28no—
210Q8×D17—44no—
211Q8×D17—44no—
212Q8×D17—44no—
213C2×C4×D17—21no—
214C2×C4×D17—21no—
215C2×C4×D17—21no—
216C2×C4×D17—21no—
217C2×C4×D17—24no—
218C2×C4×D17—42no—
219C2×C4×D17—42no—
220C2×C4×D17—42no—
221C2×C4×D17—42no—
222C2×C4×D17—81no—
223C2×C4×D17C22×C412yes—
224C2×C4×D17C2×D412yes—
225C2×Dic34—21no—
226C2×Dic34—21no—
227C2×Dic34—21no—
228C2×Dic34—21no—
229C2×Dic34—21no—
230C2×Dic34—24no—
231C2×Dic34—42no—
232C2×Dic34—42no—
233C2×Dic34C22×C412yes—
234C2×C8×C17—21no—
235C2×C8×C17—21no—
236C2×C8×C17—21no—
237C2×C8×C17—21no—
238C2×C8×C17—21no—
239C2×C8×C17—44no—
240C2×C8×C17C2×D412yes—
241C4⋊C4×C17—21no—
242C4⋊C4×C17—21no—
243C4⋊C4×C17—21no—
244C4⋊C4×C17—42no—
245C4⋊C4×C17C2×D412yes—
246C22⋊Dic17—24no—
247C22⋊Dic17—42no—
248C22⋊Dic17C22⋊C414yes—
249#63227—24no—
250#63227—42no—
251#63227C22⋊C414yes—
252C4⋊Dic17—21no—
253C4⋊Dic17—24no—
254C4⋊Dic17—21no—
255C4⋊Dic17—21no—
256C4⋊Dic17—21no—
257C4⋊Dic17—21no—
258C4⋊Dic17C22×C412yes—
259#63225—24no—
260#63225—24no—
261#63225—24no—
262#63225—24no—
263#63225—42no—
264#63225—42no—
265#63225—81no—
266#63225C22⋊C414yes—
267C4×Dic17—24no—
268C4×Dic17—42no—
269C4×Dic17C22×C412yes—
270C4×Dic17C2×D412yes—
271C2×#3622—21no—
272C2×#3622—21no—
273C2×#3622—21no—
274C2×#3622—21no—
275C2×#3622—21no—
276C2×#3622—21no—
277C8×D17—44no—
278D4×#103—171nomaximal, Sylow
279C23×C17—21no—
280C23×C17—21no—
281C23×C17—21no—
282C23×C17—21no—
283C23×C17C2×C22⋊C412yes—
284C23×C17C2×SD1612yes—
285C23×C17C2×Q1612yes—
286C23×C17C22×D411yescharacteristic
287C22×D17—21no—
288C22×D17—21no—
289C22×D17—21no—
290C22×D17—21no—
291C22×D17C2×C22⋊C412yes—
292C22×D17C2×SD1612yes—
293C22×D17C2×Q1612yes—
294Q8×C17—22no—
295Q8×C17—22no—
296Q8×C17—22no—
297Q8×C17—22no—
298Q8×C17—22no—
299Q8×C17—48no—
300Q8×C17—41no—
301Q8×C17—41no—
302Q8×C17C4×D414yescomplemented
303C2×C4×C17—22no—
304C2×C4×C17—21no—
305C2×C4×C17—22no—
306C2×C4×C17—22no—
307C2×C4×C17—21no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—48no—
315C2×C4×C17—41no—
316C2×C4×C17—41no—
317C2×C4×C17—41no—
318C2×C4×C17—41no—
319C2×C4×C17—41no—
320C2×C4×C17—41no—
321C2×C4×C17—41no—
322C2×C4×C17—84no—
323C2×C4×C17C2×C22⋊C412yes—
324C2×C4×C17C23×C411yescharacteristic
325C2×C4×C17C22×D411yescharacteristic
326C2×C4×C17C22×D411yescharacteristic
327C2×C4×C17C2×#4111yescharacteristic
328C2×C4×C17H(5,𝔽2)11yescharacteristic
329C2×C4×C17H(5,𝔽2)11yescharacteristic
330C22⋊D17#103116yesdirect product factor
331C2×Dic17—21no—
332C2×Dic17—21no—
333C2×Dic17—21no—
334C2×Dic17—21no—
335C2×Dic17—22no—
336C2×Dic17—22no—
337C2×Dic17—41no—
338C2×Dic17—41no—
339C2×Dic17—41no—
340C2×Dic17—41no—
341C2×Dic17—41no—
342C2×Dic17—41no—
343C2×Dic17—41no—
344C2×Dic17—41no—
345C2×Dic17—41no—
346C2×Dic17—41no—
347C2×Dic17C2×C22⋊C412yes—
348C2×Dic17C2×C22⋊C412yes—
349C2×Dic17C2×C22⋊C412yes—
350C2×Dic17C2×SD1612yes—
351C2×Dic17C2×Q1612yes—
352C4×D17—22no—
353C4×D17—22no—
354C4×D17—22no—
355C4×D17—22no—
356C4×D17—48no—
357C4×D17—84no—
358Dic34—22no—
359Dic34—22no—
360Dic34—48no—
361Dic34—41no—
362Dic34—41no—
363C8×C17—22no—
364C8×C17—41no—
365#3622—41no—
366#3622—41no—
367C2×D4×Q8—171no—
368C2×C8×D4—171no—
369C22×#103—171no—
370C22×#103D1711yescharacteristic, complemented
371D4×C4⋊C4—171no—
372#1981—171no—
373#1956—171no—
374#1892—171no—
375#1892—171no—
376#1872—171no—
377#1872—171no—
378#1803—171no—
379#1787—171no—
380#1787—171no—
381C4×#103—171no—
382C22×C17—22no—
383C22×C17—22no—
384C22×C17—22no—
385C22×C17—22no—
386C22×C17—22no—
387C22×C17—22no—
388C22×C17C2×#10314yescomplemented
389C22×C17C22×C22⋊C411yescharacteristic
390C22×C17D4211yescharacteristic
391C22×C17#54611yescharacteristic
392C22×C17C22×SD1611yescharacteristic
393C22×C17C22×Q1611yescharacteristic
394C22×C17#57711yescharacteristic
395C22×C17#57811yescharacteristic
396C2×D17—22no—
397C2×D17—22no—
398C2×D17—22no—
399C2×D17—22no—
400C2×D17—22no—
401C2×D17—22no—
402C2×D17C2×#10314yescomplemented
403C4×C17—24no—
404C4×C17—22no—
405C4×C17—42no—
406C4×C17—42no—
407C4×C17—81no—
408C4×C17C2×C4×D411yescharacteristic
409C4×C17#51811yescharacteristic
410C4×C17D4211yescharacteristic
411C4×C17#54611yescharacteristic
412Dic17—22no—
413Dic17—22no—
414Dic17—42no—
415Dic17—42no—
416Dic17—81no—
417Dic17—81no—
418Dic17C2×#10314yescomplemented
419C23×Q8—171no—
420C23×Q8C2×D1711yescharacteristic
421C23×C8—171no—
422C23×C8C2×D1711yescharacteristic
423D4×Q8—178no—
424D4×Q8—344no—
425C2×C4⋊Q8—171no—
426C2×C4⋊Q8—341no—
427C2×C22⋊Q8—171no—
428C2×C22⋊Q8—171no—
429C2×C22⋊Q8—341no—
430C2×C22⋊Q8—341no—
431C2×C4×Q8—171no—
432C2×C4×D4—171no—
433C2×C4×D4—341no—
434C2×C4×D4—341no—
435C22×C4⋊C4—171no—
436C22×C4⋊C4C2×D1711yescharacteristic
437C8×D4—344no—
438C2×C4⋊C8—171no—
439C2×#103—24no—
440C2×#103—171no—
441C2×#103—171no—
442C2×#103—171no—
443C2×#103—171no—
444C2×#103—171no—
445C2×#103—171no—
446C2×#103—171no—
447C2×#103—171no—
448C2×#103—344no—
449C2×#103C2×D1711yescharacteristic
450C2×#103C2×D1711yescharacteristic
451C2×#103C2×D1711yescharacteristic
452C2×#103C2×D1711yescharacteristic
453C2×C22⋊C8—171no—
454C2×C22⋊C8—171no—
455C2×C4×C8—171no—
456#389—341no—
457#385—341no—
458#385—341no—
459#384—171no—
460#380—171no—
461#380—171no—
462C4×C4⋊C4—171no—
463#340—171no—
464#340—171no—
465#340—171no—
466#340—171no—
467C2×C17—24no—
468C2×C17D4×C22⋊C411yescharacteristic
469C2×C17C22×#10311yescharacteristic
470C2×C17#289811yescharacteristic
471C2×C17D4×SD1611yescharacteristic
472C2×C17D4×Q1611yescharacteristic
473C2×C17#329811yescharacteristic
474C2×C17#329911yescharacteristic
475D17—24no—
476C22×Q8—21no—
477C22×Q8—22no—
478C22×Q8—22no—
479C22×Q8—22no—
480C22×Q8—41no—
481C22×Q8—41no—
482C22×Q8—174no—
483C22×Q8—171no—
484C22×Q8—341no—
485C22×Q8—342no—
486C22×Q8—342no—
487C22×Q8—342no—
488C22×Q8—681no—
489C22×Q8—681no—
490C22×Q8C4×D1714yescomplemented
491C22×Q8C22×D1711yescharacteristic
492C22×Q8C22×D1711yescharacteristic
493C22×D4—171no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—171no—
497C23×C4—341no—
498C23×C4—341no—
499C23×C4C22×D1711yescharacteristic
500C22×C8—22no—
501C22×C8—22no—
502C22×C8—41no—
503C22×C8—171no—
504C22×C8—171no—
505C22×C8—342no—
506C22×C8—342no—
507C22×C8—681no—
508C22×C8C22×D1711yescharacteristic
509C22×C8C22×D1711yescharacteristic
510C4⋊Q8—174no—
511C4⋊Q8—342no—
512C4⋊Q8—348no—
513C22⋊Q8—174no—
514C22⋊Q8—174no—
515C22⋊Q8—348no—
516C22⋊Q8—348no—
517C22⋊Q8—342no—
518C22⋊Q8—342no—
519C4×Q8—174no—
520C4×Q8—342no—
521C4×D4—174no—
522C4×D4—174no—
523C4×D4—348no—
524C4×D4—684no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—41no—
528C2×C4⋊C4—171no—
529C2×C4⋊C4—171no—
530C2×C4⋊C4—171no—
531C2×C4⋊C4—171no—
532C2×C4⋊C4—341no—
533C2×C4⋊C4—341no—
534C2×C4⋊C4—341no—
535C2×C4⋊C4—341no—
536C2×C4⋊C4—341no—
537C2×C4⋊C4—342no—
538C2×C4⋊C4—341no—
539C2×C4⋊C4—341no—
540C2×C4⋊C4—341no—
541C2×C4⋊C4—681no—
542C2×C4⋊C4C22×D1711yescharacteristic
543C2×C4⋊C4C22×D1711yescharacteristic
544C2×C22⋊C4—171no—
545C2×C22⋊C4—171no—
546C2×C22⋊C4—341no—
547C2×C22⋊C4—341no—
548C2×C22⋊C4—341no—
549C2×C22⋊C4—341no—
550C2×C42—171no—
551C2×C42—341no—
552C2×C42—341no—
553C4⋊C8—342no—
554#103—22no—
555#103—22no—
556#103—22no—
557#103—342no—
558#103—342no—
559#103—342no—
560#103—342no—
561#103—681no—
562#103—681no—
563#103—681no—
564#103—681no—
565#103C22⋊D1714yesdirect product factor
566C22⋊C8—342no—
567C22⋊C8—342no—
568C4×C8—342no—
569#95—341no—
570#95—341no—
571#95—341no—
572C17D4×#10311yescharacteristic, complemented, Sylow
573C24—171no—
574C24D4×D1711yescharacteristic
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—24no—
580C2×Q8—28no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—42no—
586C2×Q8—42no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—44no—
590C2×Q8—172no—
591C2×Q8—344no—
592C2×Q8—341no—
593C2×Q8—348no—
594C2×Q8—341no—
595C2×Q8—341no—
596C2×Q8—341no—
597C2×Q8—341no—
598C2×Q8—682no—
599C2×Q8—682no—
600C2×Q8—684no—
601C2×Q8—684no—
602C2×Q8—684no—
603C2×Q8C2×C4×D1712yes—
604C2×Q8C2×C4×D1712yes—
605C2×Q8#6325212yes—
606C2×Q8C2×C22⋊D1712yes—
607C2×D4—174no—
608C2×D4—174no—
609C2×D4—174no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—24no—
618C22×C4—21no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—81no—
624C22×C4—171no—
625C22×C4—171no—
626C22×C4—171no—
627C22×C4—172no—
628C22×C4—172no—
629C22×C4—344no—
630C22×C4—341no—
631C22×C4—341no—
632C22×C4—341no—
633C22×C4—341no—
634C22×C4—341no—
635C22×C4—341no—
636C22×C4—341no—
637C22×C4—341no—
638C22×C4—682no—
639C22×C4—682no—
640C22×C4—682no—
641C22×C4—682no—
642C22×C4—1361no—
643C22×C4C2×C4×D1712yes—
644C22×C4D4×D1712yes—
645C22×C4D4×D1711yescharacteristic
646C22×C4C23×D1711yescharacteristic
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—44no—
653C2×C8—341no—
654C2×C8—341no—
655C2×C8—341no—
656C2×C8—341no—
657C2×C8—341no—
658C2×C8—341no—
659C2×C8—684no—
660C2×C8C2×C22⋊D1712yes—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—42no—
665C4⋊C4—174no—
666C4⋊C4—172no—
667C4⋊C4—344no—
668C4⋊C4—344no—
669C4⋊C4—344no—
670C4⋊C4—344no—
671C4⋊C4—341no—
672C4⋊C4—344no—
673C4⋊C4—341no—
674C4⋊C4—341no—
675C4⋊C4—341no—
676C4⋊C4—341no—
677C4⋊C4—682no—
678C4⋊C4—682no—
679C4⋊C4—1361no—
680C4⋊C4C2×C22⋊D1712yes—
681C22⋊C4—174no—
682C22⋊C4—174no—
683C22⋊C4—344no—
684C22⋊C4—344no—
685C22⋊C4—682no—
686C22⋊C4—682no—
687C42—172no—
688C42—172no—
689C42—344no—
690C42—682no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—172no—
696C23—172no—
697C23—172no—
698C23—341no—
699C23—341no—
700C23—341no—
701C23—341no—
702C23C22⋊C4×D1712yes—
703C23SD16×D1712yes—
704C23Q16×D1712yes—
705C23C2×D4×D1711yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—22no—
711Q8—48no—
712Q8—41no—
713Q8—41no—
714Q8—342no—
715Q8—342no—
716Q8—688no—
717Q8—681no—
718Q8—681no—
719Q8C4×C22⋊D1714yescomplemented
720D4—1716no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—48no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—84no—
741C2×C4—172no—
742C2×C4—172no—
743C2×C4—172no—
744C2×C4—172no—
745C2×C4—172no—
746C2×C4—341no—
747C2×C4—341no—
748C2×C4—341no—
749C2×C4—341no—
750C2×C4—342no—
751C2×C4—342no—
752C2×C4—342no—
753C2×C4—342no—
754C2×C4—342no—
755C2×C4—342no—
756C2×C4—688no—
757C2×C4—681no—
758C2×C4—681no—
759C2×C4—681no—
760C2×C4—681no—
761C2×C4—681no—
762C2×C4—681no—
763C2×C4—681no—
764C2×C4—681no—
765C2×C4—681no—
766C2×C4—681no—
767C2×C4—1364no—
768C2×C4C22⋊C4×D1712yes—
769C2×C4C22×C4×D1711yescharacteristic
770C2×C4C2×#6325211yescharacteristic
771C2×C4C2×D4×D1711yescharacteristic
772C2×C4#1058769111yescharacteristic
773C2×C4#1058769111yescharacteristic
774C2×C4C22×C22⋊D1711yescharacteristic
775C8—22no—
776C8—41no—
777C8—681no—
778C8—681no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—174no—
786C22—342no—
787C22—342no—
788C22—342no—
789C22—342no—
790C22—342no—
791C22—342no—
792C22#103×D1714yescomplemented
793C22C2×C22⋊C4×D1711yescharacteristic
794C22D4×C22⋊D1711yescharacteristic
795C22#1176344911yescharacteristic
796C22C2×SD16×D1711yescharacteristic
797C22C2×Q16×D1711yescharacteristic
798C22#1176361511yescharacteristic
799C22#1176362211yescharacteristic
800C4—22no—
801C4—24no—
802C4—42no—
803C4—42no—
804C4—81no—
805C4—174no—
806C4—342no—
807C4—342no—
808C4—682no—
809C4—682no—
810C4—1361no—
811C4—1361no—
812C4C2×C4×C22⋊D1711yescharacteristic
813C4#1176328211yescharacteristic
814C4D4×C22⋊D1711yescharacteristic
815C4#1176344911yescharacteristic
816C2—24no—
817C2—344no—
818C2C22⋊C4×C22⋊D1711yescharacteristic
819C2C2×#103×D1711yescharacteristic
820C2#1453731211yescharacteristic
821C2SD16×C22⋊D1711yescharacteristic
822C2Q16×C22⋊D1711yescharacteristic
823C2#1454064511yescharacteristic
824C2#1454065611yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC22×C17×#103C2
socleC23×C17C22×D4
prime radicalC22×C22⋊D17D4
cosocleC22×C4×C17C24
hypercenterC22×#103D17
hypocenterC17D4×#103
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
3. C2×#103×D17C2semidirect
5. #14529705C2semidirect
6. #14529584C2semidirect
7. #14529207C2semidirect
8. #14529204C2semidirect
9. #14529091C2semidirect
10. #14529088C2semidirect
11. #14528787C2semidirect
12. #14528719C2semidirect
13. #14528717C2semidirect
14. #103×Dic17C2semidirect
15. C22×C17×#103C2semidirect
19. Q8×C22⋊D17C4semidirect
70. C22×Q8×C17C2×C4semidirect
82. C2×Q8×D17C2×C4semidirect
103. #10587632C2×C4semidirect
105. Q8×Dic17C2×C4semidirect
108. #10587630C2×C4semidirect
122. #10587610C2×C4semidirect
144. C17×#103D4semidirect
302. Q8×C17C4×D4semidirect
330. C22⋊D17#103direct (N × H)
370. C22×#103D17semidirect
388. C22×C17C2×#103semidirect
402. C2×D17C2×#103semidirect
418. Dic17C2×#103semidirect
490. C22×Q8C4×D17semidirect
565. #103C22⋊D17direct (N × H)
572. C17D4×#103semidirect
719. Q8C4×C22⋊D17semidirect
792. C22#103×D17semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D172
C2×C8×C22⋊D172
C2×#103×D172
C4⋊C4×C22⋊D172
#145297052
#145295842
#145292072
#145292042
#145290912
#145290882
#145287872
#145287192
#145287172
#103×Dic172
C22×C17×#1032
D4×#10317