Finite Group Databasebeta

← #17044126

Subgroups — #17044126

Order 4352.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763320C211yesmaximal, characteristic
2C2×#11762669C211yesmaximal, characteristic, complemented
3#14529769C212yesmaximal, complemented
4#14529620C212yesmaximal, complemented
5#14529235C214yesmaximal, complemented
6#14528769C214yesmaximal, complemented
7C17×#2280C211yesmaximal, characteristic, complemented
8C22×#63252C411yescharacteristic, complemented
9#11763320—21no—
10#11763320—21no—
11#11763320—21no—
12#11763320—21no—
13#11763320—21no—
14#11763320—21no—
15#11763320—21no—
16#11763320—21no—
17C2×#10587615C412yescomplemented
18C2×#10587610C411yescharacteristic, complemented
19C2×#10587610C2211yescharacteristic
20C2×#10587616C411yescharacteristic, complemented
21C2×#10587616C2211yescharacteristic
22C2×#10587639C2212yes—
23C2×C4×C22⋊D17C412yescomplemented
24C2×C4×C22⋊D17C2212yes—
25C2×#10587612C411yescharacteristic, complemented
26C22×C4⋊Dic17—21no—
27C22×C22⋊Dic17C2212yes—
28C2×#10587477C2218yes—
29#11762669—21no—
30#11762669—21no—
31#11762669C2212yes—
32#11762669C2212yes—
33C2×#10587502—21no—
34#11762575C2218yes—
35C24×C4×C17C2211yescharacteristic
36C2×C17×#117—21no—
37C17×#381—21no—
38C17×#380—21no—
39C17×#380C2212yes—
40C17×#379C2212yes—
41C4×C22⋊C4×C17—21no—
42C4×C22⋊C4×C17C2212yes—
43C25×C17C2311yescharacteristic
44C23×C4×C17—44no—
45C23×C4×C17C2×C411yescharacteristic
46C23×C4×C17C2×C411yescharacteristic
47C23×C4×C17C2×C411yescharacteristic
48C23×C4×C17C2×C411yescharacteristic
49C23×C4×C17D411yescharacteristic
50C23×C4×C17D411yescharacteristic
51C23×C4×C17D411yescharacteristic
52C23×C4×C17D411yescharacteristic
53C23×C4×C17D411yescharacteristic
54C23×C4×C17D411yescharacteristic
55C23×C4×C17D411yescharacteristic
56C23×C4×C17D411yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C22×C22⋊D17C2×C412yes—
60C22×C22⋊D17C2×C412yes—
61C22×C22⋊D17C2312yes—
62C23×Dic17—22no—
63C2×#63252—21no—
64C2×#63252—21no—
65C2×#63252—21no—
66C2×#63252—21no—
67C2×#63252—44no—
68C22×D68C2×C411yescharacteristic, complemented
69C22×C4×D17C2×C412yescomplemented
70C22×Dic34C2×C411yescharacteristic, complemented
71C17×#117—44no—
72C2×C4⋊C4×C17—22no—
73C2×C22⋊C4×C17—22no—
74C2×C22⋊C4×C17—22no—
75C2×C22⋊C4×C17C2314yes—
76C2×C42×C17—22no—
77#10587639—22no—
78#10587639—22no—
79#10587639—22no—
80#10587639—22no—
81C2×C22⋊Dic17—22no—
82C2×C22⋊Dic17—44no—
83C2×C22⋊Dic17C2×C412yes—
84C2×C22⋊Dic17C2×C412yes—
85C2×C22⋊Dic17C2314yes—
86C2×C22⋊Dic17C2312yes—
87#10587616—21no—
88#10587616—21no—
89#10587616—21no—
90#10587616—21no—
91#10587616—21no—
92#10587616—21no—
93#10587616—21no—
94#10587616—21no—
95#10587615—22no—
96#10587615—22no—
97#10587615—22no—
98#10587615—22no—
99C4×C22⋊D17—22no—
100C4×C22⋊D17—22no—
101C4×C22⋊D17—22no—
102C4×C22⋊D17—22no—
103C4×C22⋊D17—22no—
104C4×C22⋊D17—22no—
105C4×C22⋊D17—22no—
106C4×C22⋊D17—22no—
107C2×#63227C2×C412yescomplemented
108C2×#63227C2×C412yescomplemented
109#10587612—21no—
110#10587612—21no—
111#10587612—21no—
112#10587612—21no—
113C2×C4⋊Dic17—22no—
114C2×C4⋊Dic17—22no—
115C2×C4⋊Dic17—44no—
116C2×C4⋊Dic17C2×C411yescharacteristic, complemented
117C2×C4⋊Dic17C2×C411yescharacteristic, complemented
118#10587610—21no—
119#10587610—21no—
120#10587610—21no—
121#10587610—21no—
122#10587610—21no—
123#10587610—21no—
124#10587610—21no—
125#10587610—21no—
126C2×#63225C2×C412yescomplemented
127C2×#63225C2×C412yescomplemented
128C2×C4×Dic17C2×C412yescomplemented
129C17×#95—22no—
130C17×#95—22no—
131#10587502—22no—
132#10587502—22no—
133#10587477—48no—
134C24×C17—22no—
135C24×C17—22no—
136C24×C17—42no—
137C24×C17—42no—
138C24×C17C22×C411yescharacteristic
139C24×C17C22×C411yescharacteristic
140C24×C17C2×D411yescharacteristic
141C24×C17C2×D411yescharacteristic
142C24×C17C2×D411yescharacteristic
143C24×C17C2×D411yescharacteristic
144C24×C17C2411yescharacteristic
145C23×D17C22×C412yes—
146C22×C4×C17—24no—
147C22×C4×C17—24no—
148C22×C4×C17—24no—
149C22×C4×C17—24no—
150C22×C4×C17—42no—
151C22×C4×C17—42no—
152C22×C4×C17—42no—
153C22×C4×C17—42no—
154C22×C4×C17—42no—
155C22×C4×C17—42no—
156C22×C4×C17—42no—
157C22×C4×C17—42no—
158C22×C4×C17—42no—
159C22×C4×C17—42no—
160C22×C4×C17—42no—
161C22×C4×C17C22⋊C411yescharacteristic
162C22×C4×C17C22⋊C411yescharacteristic
163C22×C4×C17C22⋊C411yescharacteristic
164C22×C4×C17C22⋊C411yescharacteristic
165C22×C4×C17C22⋊C411yescharacteristic
166C22×C4×C17C22⋊C411yescharacteristic
167C22×C4×C17C22⋊C411yescharacteristic
168C22×C4×C17C22⋊C411yescharacteristic
169C22×C4×C17C22⋊C411yescharacteristic
170C22×C4×C17C22⋊C411yescharacteristic
171C22×C4×C17C22⋊C411yescharacteristic
172C22×C4×C17C22⋊C411yescharacteristic
173C22×C4×C17C22⋊C411yescharacteristic
174C22×C4×C17C22⋊C411yescharacteristic
175C22×C4×C17C22⋊C411yescharacteristic
176C22×C4×C17C22⋊C411yescharacteristic
177C22×C4×C17C22×C411yescharacteristic
178C22×C4×C17C22×C411yescharacteristic
179C22×C4×C17C22×C411yescharacteristic
180C22×C4×C17C22×C411yescharacteristic
181C22×C4×C17C2×D411yescharacteristic
182C22×C4×C17C2×D411yescharacteristic
183C22×C4×C17C2×D411yescharacteristic
184C22×C4×C17C2×D411yescharacteristic
185C22×C4×C17C2×D411yescharacteristic
186C22×C4×C17C2×D411yescharacteristic
187C22×C4×C17C2×D411yescharacteristic
188C22×C4×C17C2×D411yescharacteristic
189C2×C22⋊D17—22no—
190C2×C22⋊D17—22no—
191C2×C22⋊D17—22no—
192C2×C22⋊D17—22no—
193C2×C22⋊D17—22no—
194C2×C22⋊D17—22no—
195C2×C22⋊D17—24no—
196C2×C22⋊D17—24no—
197C2×C22⋊D17—44no—
198C2×C22⋊D17—44no—
199C22×Dic17—24no—
200C22×Dic17—44no—
201C22×Dic17—44no—
202C22×Dic17—44no—
203C22×Dic17C22×C412yes—
204C22×Dic17C22×C412yes—
205C22×Dic17C22×C412yes—
206#63252—44no—
207#63252—44no—
208#63252—44no—
209#63252—44no—
210C2×D68—21no—
211C2×D68—21no—
212C2×D68—42no—
213C2×C4×D17—22no—
214C2×C4×D17—22no—
215C2×C4×D17—44no—
216C2×Dic34—21no—
217C2×Dic34—21no—
218C2×Dic34—42no—
219C4⋊C4×C17—44no—
220C22⋊C4×C17—24no—
221C22⋊C4×C17—24no—
222C22⋊C4×C17—44no—
223C22⋊C4×C17—44no—
224C42×C17—44no—
225C22⋊Dic17—22no—
226C22⋊Dic17—22no—
227C22⋊Dic17—22no—
228C22⋊Dic17—22no—
229C22⋊Dic17—22no—
230C22⋊Dic17—22no—
231C22⋊Dic17—28no—
232C22⋊Dic17—44no—
233#63227—22no—
234#63227—22no—
235#63227—22no—
236#63227—22no—
237C4⋊Dic17—21no—
238C4⋊Dic17—21no—
239C4⋊Dic17—21no—
240C4⋊Dic17—21no—
241C4⋊Dic17—44no—
242C4⋊Dic17—44no—
243#63225—22no—
244#63225—22no—
245#63225—22no—
246#63225—22no—
247C4×Dic17—22no—
248C4×Dic17—22no—
249#21874—171nomaximal, Sylow
250C23×C17—21no—
251C23×C17—21no—
252C23×C17—22no—
253C23×C17—22no—
254C23×C17—22no—
255C23×C17—22no—
256C23×C17—21no—
257C23×C17—21no—
258C23×C17—22no—
259C23×C17—22no—
260C23×C17—22no—
261C23×C17—22no—
262C23×C17—22no—
263C23×C17—22no—
264C23×C17—41no—
265C23×C17—41no—
266C23×C17—41no—
267C23×C17—41no—
268C23×C17—41no—
269C23×C17—41no—
270C23×C17—41no—
271C23×C17—41no—
272C23×C17—48no—
273C23×C17—48no—
274C23×C17C2×C22⋊C411yescharacteristic
275C23×C17C2×C22⋊C411yescharacteristic
276C23×C17C2×C22⋊C411yescharacteristic
277C23×C17C2×C22⋊C411yescharacteristic
278C23×C17C23×C411yescharacteristic
279C23×C17C22×D411yescharacteristic
280C23×C17C22×D411yescharacteristic
281C23×C17H(5,𝔽2)12yes—
282C23×C172−1+412yes—
283C22×D17—22no—
284C22×D17—24no—
285C22×D17—42no—
286C22×D17—42no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
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—22no—
302C2×C4×C17—41no—
303C2×C4×C17—41no—
304C2×C4×C17—41no—
305C2×C4×C17—41no—
306C2×C4×C17—41no—
307C2×C4×C17—41no—
308C2×C4×C17—41no—
309C2×C4×C17—41no—
310C2×C4×C17—41no—
311C2×C4×C17—41no—
312C2×C4×C17—41no—
313C2×C4×C17—41no—
314C2×C4×C17—44no—
315C2×C4×C17—44no—
316C2×C4×C17—44no—
317C2×C4×C17#9914yescomplemented
318C2×C4×C17C2×C22⋊C411yescharacteristic
319C2×C4×C17C2×C22⋊C411yescharacteristic
320C2×C4×C17C2×C22⋊C411yescharacteristic
321C2×C4×C17C2×C22⋊C411yescharacteristic
322C2×C4×C17C2×C22⋊C411yescharacteristic
323C2×C4×C17C2×C22⋊C411yescharacteristic
324C2×C4×C17C2×C22⋊C411yescharacteristic
325C2×C4×C17C2×C22⋊C411yescharacteristic
326C22⋊D17—44no—
327C22⋊D17—44no—
328C22⋊D17—42no—
329C22⋊D17—42no—
330C22⋊D17—44no—
331C22⋊D17—44no—
332C22⋊D17—44no—
333C2×Dic17—22no—
334C2×Dic17—22no—
335C2×Dic17—22no—
336C2×Dic17—24no—
337C2×Dic17—42no—
338C2×Dic17—42no—
339C2×Dic17—44no—
340C2×Dic17—44no—
341C2×Dic17—44no—
342C2×Dic17—88no—
343D68—42no—
344D68—42no—
345C4×D17—44no—
346C4×D17—44no—
347Dic34—42no—
348Dic34—42no—
349C2×#525—171no—
350#2280D1711yescharacteristic, complemented
351C2×#380—171no—
352#1996—172no—
353#1964—172no—
354#1898—174no—
355#1799—174no—
356C22×C17—24no—
357C22×C17—24no—
358C22×C17—21no—
359C22×C17—21no—
360C22×C17—21no—
361C22×C17—21no—
362C22×C17—21no—
363C22×C17—21no—
364C22×C17—21no—
365C22×C17—21no—
366C22×C17—21no—
367C22×C17—21no—
368C22×C17—21no—
369C22×C17—21no—
370C22×C17—21no—
371C22×C17—21no—
372C22×C17—21no—
373C22×C17—21no—
374C22×C17—42no—
375C22×C17—42no—
376C22×C17—44no—
377C22×C17—44no—
378C22×C17—44no—
379C22×C17—44no—
380C22×C17—42no—
381C22×C17—42no—
382C22×C17C2×#9912yes—
383C22×C17#41012yes—
384C22×C17C22×C22⋊C411yescharacteristic
385C22×C17#52012yes—
386C22×C17#53511yescharacteristic
387C22×C17#53611yescharacteristic
388C22×C17#53712yes—
389C2×D17—42no—
390C2×D17—42no—
391C2×D17—42no—
392C2×D17—84no—
393C4×C17—21no—
394C4×C17—21no—
395C4×C17—21no—
396C4×C17—21no—
397C4×C17—21no—
398C4×C17—21no—
399C4×C17—84no—
400C4×C17C2×#9912yes—
401C4×C17C2×#9912yes—
402Dic17—42no—
403Dic17—42no—
404Dic17—42no—
405Dic17—84no—
406C22×#41—171no—
407C24×C4C2×D1711yescharacteristic
408#525—341no—
409#525—341no—
410#525—341no—
411#525—341no—
412#525—341no—
413#525—341no—
414#525—341no—
415#525—341no—
416C2×#123—172no—
417C2×C22⋊Q8—171no—
418C2×C22⋊Q8—171no—
419C2×#121—171no—
420C2×#121—171no—
421C2×#120—172no—
422C2×C4×D4—172no—
423C2×C4×D4—172no—
424C2×#117—21no—
425C2×#117—171no—
426C22×C4⋊C4—341no—
427C22×C22⋊C4—172no—
428C2×#99—178no—
429#381—21no—
430#380—21no—
431#380—172no—
432#380—172no—
433#380—341no—
434#380—341no—
435#380C2×D1712yes—
436#379C2×D1712yes—
437C4×C22⋊C4—21no—
438C4×C22⋊C4C2×D1712yes—
439C2×#95—341no—
440#342—178no—
441C2×C17—21no—
442C2×C17—22no—
443C2×C17—22no—
444C2×C17—21no—
445C2×C17—22no—
446C2×C17—22no—
447C2×C17—41no—
448C2×C17—41no—
449C2×C17#231111yescharacteristic
450C2×C17C22×#9911yescharacteristic
451C2×C17C2×#41011yescharacteristic
452D17—82no—
453C25C22×D1711yescharacteristic
454C2×#41—341no—
455C2×#41—341no—
456C2×#41—341no—
457C2×#41—341no—
458C2×#41—684no—
459C22×Q8—171no—
460C22×D4—172no—
461C22×D4—172no—
462C22×D4—172no—
463C22×D4—171no—
464C23×C4—44no—
465C23×C4—172no—
466C23×C4—342no—
467C23×C4C4×D1711yescharacteristic
468C23×C4C4×D1711yescharacteristic
469C23×C4C4×D1711yescharacteristic
470C23×C4C4×D1711yescharacteristic
471C23×C4D6811yescharacteristic
472C23×C4D6811yescharacteristic
473C23×C4D6811yescharacteristic
474C23×C4D6811yescharacteristic
475C23×C4C22⋊D1711yescharacteristic
476C23×C4C22⋊D1711yescharacteristic
477C23×C4C22⋊D1711yescharacteristic
478C23×C4C22⋊D1711yescharacteristic
479C23×C4C22×D1711yescharacteristic
480C23×C4C22×D1711yescharacteristic
481#123—342no—
482#123—342no—
483#123—342no—
484#123—342no—
485C22⋊Q8—341no—
486C22⋊Q8—341no—
487C22⋊Q8—341no—
488C22⋊Q8—341no—
489C22⋊Q8—341no—
490C22⋊Q8—341no—
491C22⋊Q8—341no—
492C22⋊Q8—341no—
493#121—341no—
494#121—341no—
495#121—341no—
496#121—341no—
497#121—341no—
498#121—341no—
499#121—341no—
500#121—341no—
501#120—342no—
502#120—342no—
503#120—342no—
504#120—342no—
505C4×D4—342no—
506C4×D4—342no—
507C4×D4—342no—
508C4×D4—342no—
509C4×D4—342no—
510C4×D4—342no—
511C4×D4—342no—
512C4×D4—342no—
513#117—44no—
514#117—341no—
515#117—341no—
516#117—341no—
517#117—341no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—171no—
520C2×C4⋊C4—171no—
521C2×C4⋊C4—172no—
522C2×C4⋊C4—172no—
523C2×C4⋊C4—342no—
524C2×C4⋊C4—342no—
525C2×C4⋊C4—684no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—172no—
529C2×C22⋊C4—172no—
530C2×C22⋊C4—172no—
531C2×C22⋊C4—172no—
532C2×C22⋊C4—172no—
533C2×C22⋊C4—174no—
534C2×C22⋊C4—342no—
535C2×C22⋊C4—684no—
536C2×C22⋊C4C22×D1714yes—
537C2×C42—22no—
538C2×C42—172no—
539#99—688no—
540#95—22no—
541#95—22no—
542#95—342no—
543#95—342no—
544C17#2187411yescharacteristic, complemented, Sylow
545C24—22no—
546C24—22no—
547C24—42no—
548C24—42no—
549C24—172no—
550C24C2×C4×D1711yescharacteristic
551C24C2×C4×D1711yescharacteristic
552C24C2×D6811yescharacteristic
553C24C2×D6811yescharacteristic
554C24C2×C22⋊D1711yescharacteristic
555C24C2×C22⋊D1711yescharacteristic
556C24C23×D1711yescharacteristic
557#41—684no—
558#41—684no—
559#41—684no—
560#41—684no—
561C2×Q8—341no—
562C2×Q8—341no—
563C2×Q8—682no—
564C2×D4—342no—
565C2×D4—344no—
566C2×D4—344no—
567C2×D4—342no—
568C2×D4—342no—
569C2×D4—342no—
570C2×D4—342no—
571C2×D4—342no—
572C2×D4—341no—
573C2×D4—341no—
574C2×D4—682no—
575C2×D4—684no—
576C2×D4—684no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—172no—
593C22×C4—172no—
594C22×C4—172no—
595C22×C4—342no—
596C22×C4—342no—
597C22×C4—344no—
598C22×C4—684no—
599C22×C4—684no—
600C22×C4—684no—
601C22×C4—684no—
602C22×C4#6322711yescharacteristic
603C22×C4#6322711yescharacteristic
604C22×C4#6322711yescharacteristic
605C22×C4#6322711yescharacteristic
606C22×C4#6322711yescharacteristic
607C22×C4#6322711yescharacteristic
608C22×C4#6322711yescharacteristic
609C22×C4#6322711yescharacteristic
610C22×C4#6322711yescharacteristic
611C22×C4#6322711yescharacteristic
612C22×C4#6322711yescharacteristic
613C22×C4#6322711yescharacteristic
614C22×C4#6322711yescharacteristic
615C22×C4#6322711yescharacteristic
616C22×C4#6322711yescharacteristic
617C22×C4#6322711yescharacteristic
618C22×C4C2×C4×D1711yescharacteristic
619C22×C4C2×C4×D1711yescharacteristic
620C22×C4C2×C4×D1711yescharacteristic
621C22×C4C2×C4×D1711yescharacteristic
622C22×C4C2×D6811yescharacteristic
623C22×C4C2×D6811yescharacteristic
624C22×C4C2×D6811yescharacteristic
625C22×C4C2×D6811yescharacteristic
626C22×C4C2×C22⋊D1711yescharacteristic
627C22×C4C2×C22⋊D1711yescharacteristic
628C22×C4C2×C22⋊D1711yescharacteristic
629C22×C4C2×C22⋊D1711yescharacteristic
630C4⋊C4—44no—
631C4⋊C4—341no—
632C4⋊C4—341no—
633C4⋊C4—341no—
634C4⋊C4—341no—
635C4⋊C4—342no—
636C4⋊C4—342no—
637C4⋊C4—342no—
638C4⋊C4—342no—
639C4⋊C4—684no—
640C4⋊C4—684no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—342no—
646C22⋊C4—342no—
647C22⋊C4—342no—
648C22⋊C4—342no—
649C22⋊C4—342no—
650C22⋊C4—342no—
651C22⋊C4—342no—
652C22⋊C4—342no—
653C22⋊C4—342no—
654C22⋊C4—342no—
655C22⋊C4—348no—
656C22⋊C4—684no—
657C42—44no—
658C42—342no—
659C42—342no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—22no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—48no—
683C23—48no—
684C23—342no—
685C23—344no—
686C23—682no—
687C23—682no—
688C23C2×#6322711yescharacteristic
689C23C2×#6322711yescharacteristic
690C23C2×#6322711yescharacteristic
691C23C2×#6322711yescharacteristic
692C23C22×C4×D1711yescharacteristic
693C23C22×D6811yescharacteristic
694C23#1058769612yes—
695C23#1058769712yes—
696C23C22×C22⋊D1711yescharacteristic
697Q8—682no—
698Q8—682no—
699D4—682no—
700D4—684no—
701D4—684no—
702D4—684no—
703D4—684no—
704D4—682no—
705D4—682no—
706D4—684no—
707D4—682no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—342no—
739C2×C4—342no—
740C2×C4—342no—
741C2×C4—344no—
742C2×C4—684no—
743C2×C4—684no—
744C2×C4—682no—
745C2×C4—682no—
746C2×C4—684no—
747C2×C4—684no—
748C2×C4—684no—
749C2×C4—1368no—
750C2×C4#1058747714yescomplemented
751C2×C4C2×#6322711yescharacteristic
752C2×C4C2×#6322711yescharacteristic
753C2×C4C2×#6322711yescharacteristic
754C2×C4C2×#6322711yescharacteristic
755C2×C4C2×#6322711yescharacteristic
756C2×C4C2×#6322711yescharacteristic
757C2×C4C2×#6322711yescharacteristic
758C2×C4C2×#6322711yescharacteristic
759C22—24no—
760C22—24no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—682no—
786C22—682no—
787C22—682no—
788C22—1364no—
789C22C2×#1058747712yes—
790C22#1176278212yes—
791C22C22×#6322711yescharacteristic
792C22#1176328912yes—
793C22#1176337811yescharacteristic
794C22#1176338511yescharacteristic
795C22#1176338712yes—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—84no—
803C4—682no—
804C4—682no—
805C4—682no—
806C4—1364no—
807C4C2×#1058747712yes—
808C4C2×#1058747712yes—
809C2—22no—
810C2—21no—
811C2—22no—
812C2—22no—
813C2—21no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—1362no—
818C2#1453137211yescharacteristic
819C2C22×#1058747711yescharacteristic
820C2C2×#1176278211yescharacteristic
subgroupG/H
centerC22C22×#63227
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC17×#2280C2
socleC22×C17C22×C22⋊C4
prime radicalC2×#11763320C2
cosocleC24×C17C24
hypercenter#2280D17
hypocenterC17#21874
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×#11762669C2semidirect
3. #14529769C2semidirect
4. #14529620C2semidirect
5. #14529235C2semidirect
6. #14528769C2semidirect
7. C17×#2280C2semidirect
8. C22×#63252C4semidirect
17. C2×#10587615C4semidirect
18. C2×#10587610C4semidirect
20. C2×#10587616C4semidirect
23. C2×C4×C22⋊D17C4semidirect
25. C2×#10587612C4semidirect
68. C22×D68C2×C4semidirect
69. C22×C4×D17C2×C4semidirect
70. C22×Dic34C2×C4semidirect
107. C2×#63227C2×C4semidirect
108. C2×#63227C2×C4semidirect
116. C2×C4⋊Dic17C2×C4semidirect
117. C2×C4⋊Dic17C2×C4semidirect
126. C2×#63225C2×C4semidirect
127. C2×#63225C2×C4semidirect
128. C2×C4×Dic17C2×C4semidirect
317. C2×C4×C17#99semidirect
350. #2280D17semidirect
544. C17#21874semidirect
750. C2×C4#10587477semidirect

Maximal subgroups

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

subgroupindex
C2×#117633202
C2×#117626692
#145297692
#145296202
#145292352
#145287692
C17×#22802
#2187417