Finite Group Databasebeta

← #16957693

Subgroups — #16957693

Order 4352.

2590 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
1C2×#11762689C211yesmaximal, characteristic
2C2×#11762689C211yesmaximal, characteristic
3C2×#11762681C211yesmaximal, characteristic, complemented
4C22×#10587502C211yesmaximal, characteristic, complemented
5#14527043C212yesmaximal, complemented
6#14527027C212yesmaximal, complemented
7#14527017C212yesmaximal, complemented
8#14527007C211yesmaximal, characteristic, complemented
9#14527007C212yesmaximal, complemented
10#14527006C211yesmaximal, characteristic, complemented
11C22×C4×D4×C17C211yesmaximal, characteristic
12C24×Dic17C2211yescharacteristic
13C24×Dic17C2211yescharacteristic
14C22×#63225C2212yes—
15C22×C22⋊Dic17C2211yescharacteristic
16C22×C22⋊Dic17C2212yes—
17C22×C22⋊Dic17C2211yescharacteristic
18C22×C22⋊Dic17C2212yes—
19#11762689—24no—
20#11762689C418yescomplemented
21#11762681—24no—
22C2×#10587502—24no—
23C2×#10587502C2212yes—
24C2×#10587502C2212yes—
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C23×D4×C17C2211yescharacteristic
33C24×C4×C17C2211yescharacteristic
34C24×C4×C17C2211yescharacteristic
35C2×C4×D4×C17—24no—
36C2×C4×D4×C17—24no—
37C2×C4×D4×C17—24no—
38C22×C4⋊C4×C17C2211yescharacteristic
39C22×C22⋊C4×C17C2211yescharacteristic
40C22×C22⋊C4×C17C2211yescharacteristic
41C22×C42×C17C2211yescharacteristic
42C25×C17C2311yescharacteristic
43C25×C17C2311yescharacteristic
44C22×D4×C17—22no—
45C22×D4×C17—22no—
46C22×D4×C17—22no—
47C22×D4×C17—22no—
48C22×D4×C17C2×C414yes—
49C22×D4×C17D414yes—
50C22×D4×C17Q814yes—
51C23×C4×C17—22no—
52C23×C4×C17—22no—
53C23×C4×C17—22no—
54C23×C4×C17—22no—
55C23×C4×C17—22no—
56C23×C4×C17—24no—
57C23×C4×C17—24no—
58C23×C4×C17—42no—
59C23×C4×C17—42no—
60C23×C4×C17D414yes—
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×Dic17—22no—
67C23×Dic17—22no—
68C23×Dic17—22no—
69C23×Dic17—24no—
70C23×Dic17—22no—
71C23×Dic17—22no—
72C23×Dic17—42no—
73C23×Dic17—42no—
74C23×Dic17—42no—
75C23×Dic17C2×C414yescomplemented
76C23×Dic17C2312yes—
77C23×Dic17C2312yes—
78C23×Dic17C2312yes—
79C23×Dic17C2312yes—
80C4×D4×C17—232no—
81C2×C4⋊C4×C17—22no—
82C2×C4⋊C4×C17—22no—
83C2×C4⋊C4×C17—22no—
84C2×C22⋊C4×C17—22no—
85C2×C22⋊C4×C17—22no—
86C2×C22⋊C4×C17—22no—
87C2×C22⋊C4×C17—22no—
88C2×C22⋊C4×C17—22no—
89C2×C22⋊C4×C17D414yes—
90C2×C42×C17—22no—
91C2×C42×C17—22no—
92C2×C42×C17—22no—
93C2×C22⋊Dic17—22no—
94C2×C22⋊Dic17—22no—
95C2×C22⋊Dic17—24no—
96C2×C22⋊Dic17—22no—
97C2×C22⋊Dic17—22no—
98C2×C22⋊Dic17—22no—
99C2×C22⋊Dic17—24no—
100C2×C22⋊Dic17—42no—
101C2×C22⋊Dic17—42no—
102C2×C22⋊Dic17—42no—
103C2×C22⋊Dic17C2×C414yescomplemented
104C2×C22⋊Dic17C2×C418yescomplemented
105C2×#63225—24no—
106C2×#63225—24no—
107C2×#63225—42no—
108#10587502—24no—
109#10587502—24no—
110#10587502—24no—
111#10587502—24no—
112#10587502—24no—
113#10587502—42no—
114#10587502—42no—
115#10587502—42no—
116#10587502C2×C418yescomplemented
117C24×C17—22no—
118C24×C17—22no—
119C24×C17—22no—
120C24×C17—22no—
121C24×C17—21no—
122C24×C17—21no—
123C24×C17—22no—
124C24×C17—21no—
125C24×C17—21no—
126C24×C17—22no—
127C24×C17—22no—
128C24×C17—22no—
129C24×C17C22×C412yes—
130C24×C17C22×C412yes—
131C24×C17C2×D412yes—
132C24×C17C2×D412yes—
133C24×C17C2×D412yes—
134C24×C17C2×D412yes—
135C24×C17C2×Q812yes—
136C24×C17C2×Q812yes—
137C24×C17#4112yes—
138C24×C17#4112yes—
139C24×C17C2411yescharacteristic
140C2×D4×C17—28no—
141C2×D4×C17—28no—
142C2×D4×C17—28no—
143C2×D4×C17—28no—
144C2×D4×C17—28no—
145C2×D4×C17—28no—
146C2×D4×C17C4⋊C4116yescomplemented
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—22no—
154C22×C4×C17—28no—
155C22×C4×C17—28no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—22no—
163C22×C4×C17—22no—
164C22×C4×C17—22no—
165C22×C4×C17—22no—
166C22×C4×C17—22no—
167C22×C4×C17—22no—
168C22×C4×C17—28no—
169C22×C4×C17—44no—
170C22×C4×C17—48no—
171C22×C4×C17—48no—
172C22×C4×C17—48no—
173C22×C4×C17—48no—
174C22×C4×C17—44no—
175C22×C4×C17—44no—
176C22×C4×C17C22×C412yes—
177C22×C4×C17C2×D412yes—
178C22×C4×C17C2×D412yes—
179C22×C4×C17C2×D412yes—
180C22×C4×C17C2×D412yes—
181C22×C4×C17C2×D412yes—
182C22×C4×C17C2×Q812yes—
183C22×C4×C17#4114yes—
184C22×Dic17—28no—
185C22×Dic17—28no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17—22no—
191C22×Dic17—22no—
192C22×Dic17—22no—
193C22×Dic17—22no—
194C22×Dic17—22no—
195C22×Dic17—22no—
196C22×Dic17—22no—
197C22×Dic17—22no—
198C22×Dic17—22no—
199C22×Dic17—22no—
200C22×Dic17—22no—
201C22×Dic17—22no—
202C22×Dic17—22no—
203C22×Dic17—22no—
204C22×Dic17—22no—
205C22×Dic17—22no—
206C22×Dic17—22no—
207C22×Dic17—22no—
208C22×Dic17—22no—
209C22×Dic17—22no—
210C22×Dic17—22no—
211C22×Dic17—48no—
212C22×Dic17—48no—
213C22×Dic17—48no—
214C22×Dic17—44no—
215C22×Dic17—44no—
216C22×Dic17—44no—
217C22×Dic17—48no—
218C22×Dic17—44no—
219C22×Dic17C22×C414yes—
220C22×Dic17C22×C414yes—
221C22×Dic17#4114yes—
222C4⋊C4×C17—28no—
223C22⋊C4×C17—28no—
224C22⋊C4×C17—28no—
225C42×C17—28no—
226C22⋊Dic17—28no—
227C22⋊Dic17—48no—
228C22⋊Dic17—48no—
229C22⋊Dic17—44no—
230#63225—48no—
231#14016—171nomaximal, Sylow
232C23×C17—24no—
233C23×C17—24no—
234C23×C17—22no—
235C23×C17—22no—
236C23×C17—24no—
237C23×C17—22no—
238C23×C17—22no—
239C23×C17—24no—
240C23×C17—24no—
241C23×C17—24no—
242C23×C17—24no—
243C23×C17—24no—
244C23×C17—24no—
245C23×C17—24no—
246C23×C17—24no—
247C23×C17—24no—
248C23×C17—22no—
249C23×C17—22no—
250C23×C17—24no—
251C23×C17—24no—
252C23×C17—22no—
253C23×C17—22no—
254C23×C17—22no—
255C23×C17—22no—
256C23×C17—24no—
257C23×C17—24no—
258C23×C17—24no—
259C23×C17—24no—
260C23×C17—41no—
261C23×C17—41no—
262C23×C17—42no—
263C23×C17—41no—
264C23×C17—41no—
265C23×C17—42no—
266C23×C17—42no—
267C23×C17—42no—
268C23×C17—42no—
269C23×C17—42no—
270C23×C17C2×C4⋊C414yes—
271C23×C17C2×C4⋊C414yes—
272C23×C17C4×D414yes—
273C23×C17C4×D414yes—
274C23×C17#12014yes—
275C23×C17C22⋊Q814yes—
276C23×C17C22⋊Q814yes—
277C23×C17#12314yes—
278C23×C17C23×C411yescharacteristic
279C23×C17C22×D411yescharacteristic
280C23×C17C22×D411yescharacteristic
281C23×C17C22×D411yescharacteristic
282C23×C17C22×Q811yescharacteristic
283C23×C17C2×#4111yescharacteristic
284C23×C17C2×#4111yescharacteristic
285C23×C17C2×#4112yes—
286C23×C17C2×#4112yes—
287C23×C17H(5,𝔽2)12yes—
288C23×C17H(5,𝔽2)12yes—
289D4×C17—232no—
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—24no—
299C2×C4×C17—24no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—22no—
303C2×C4×C17—22no—
304C2×C4×C17—22no—
305C2×C4×C17—24no—
306C2×C4×C17—24no—
307C2×C4×C17—416no—
308C2×C4×C17—416no—
309C2×C4×C17—41no—
310C2×C4×C17—41no—
311C2×C4×C17—41no—
312C2×C4×C17—41no—
313C2×C4×C17—42no—
314C2×C4×C17—42no—
315C2×C4×C17—42no—
316C2×C4×C17—42no—
317C2×C4×C17C2×C4⋊C414yes—
318C2×C4×C17#12314yes—
319C2×Dic17—24no—
320C2×Dic17—24no—
321C2×Dic17—24no—
322C2×Dic17—24no—
323C2×Dic17—24no—
324C2×Dic17—24no—
325C2×Dic17—24no—
326C2×Dic17—24no—
327C2×Dic17—24no—
328C2×Dic17—416no—
329C2×Dic17—416no—
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×Dic17—42no—
341C2×Dic17—42no—
342C2×Dic17—42no—
343C2×Dic17—42no—
344C2×Dic17—42no—
345C2×Dic17—42no—
346C2×Dic17—42no—
347C2×Dic17—42no—
348C2×Dic17—42no—
349C22×C4×D4D1711yescharacteristic
350C2×#386—171no—
351C2×#386—171no—
352C2×#385—171no—
353C22×#95—171no—
354#1442—172no—
355#1439—172no—
356#1436—172no—
357C22⋊#95—171no—
358C22⋊#95—172no—
359C22⋊#95—171no—
360C22×C17—24no—
361C22×C17—24no—
362C22×C17—28no—
363C22×C17—28no—
364C22×C17—24no—
365C22×C17—24no—
366C22×C17—28no—
367C22×C17—28no—
368C22×C17—24no—
369C22×C17—24no—
370C22×C17—28no—
371C22×C17—24no—
372C22×C17—42no—
373C22×C17—42no—
374C22×C17—44no—
375C22×C17—42no—
376C22×C17—42no—
377C22×C17—44no—
378C22×C17—44no—
379C22×C17—42no—
380C22×C17—42no—
381C22×C17#38518yes—
382C22×C17C22×C4⋊C411yescharacteristic
383C22×C17C2×C4×D411yescharacteristic
384C22×C17C2×C4×D411yescharacteristic
385C22×C17C4×#4112yes—
386C22×C17#51812yes—
387C22×C17C2×#12011yescharacteristic
388C22×C17C2×C22⋊Q811yescharacteristic
389C22×C17C2×C22⋊Q811yescharacteristic
390C22×C17C2×#12311yescharacteristic
391C22×C17C2×#12311yescharacteristic
392C22×C17#52511yescharacteristic
393C22×C17#52912yes—
394C22×C17#53411yescharacteristic
395C22×C17#53511yescharacteristic
396C22×C17#53812yes—
397C22×C17#54612yes—
398C22×C17#54612yes—
399C22×C17#54612yes—
400C22×C17#54612yes—
401C22×C17#55312yes—
402C22×C17#55312yes—
403C22×C17#55412yes—
404C22×C17#55412yes—
405C4×C17—24no—
406C4×C17—24no—
407C4×C17—42no—
408C4×C17—42no—
409C4×C17—42no—
410Dic17—44no—
411Dic17—44no—
412Dic17—44no—
413Dic17—82no—
414C23×D4C2×D1711yescharacteristic
415C24×C4—171no—
416C24×C4—171no—
417C24×C4C2×D1711yescharacteristic
418C24×C4C2×D1711yescharacteristic
419C2×C4×D4—24no—
420C2×C4×D4—24no—
421C2×C4×D4—24no—
422C22×C4⋊C4—172no—
423C22×C4⋊C4C2×D1711yescharacteristic
424C22×C22⋊C4—171no—
425C22×C22⋊C4—172no—
426C22×C22⋊C4—171no—
427C22×C22⋊C4—172no—
428C22×C22⋊C4C2×D1711yescharacteristic
429C22×C22⋊C4C2×D1711yescharacteristic
430C22×C42C2×D1711yescharacteristic
431#386—178no—
432#386—344no—
433#385—344no—
434C2×#95—172no—
435C2×#95—172no—
436C2×#95—172no—
437C2×#95—172no—
438C2×#95—172no—
439C2×#95—172no—
440C2×#95—172no—
441C2×#95—172no—
442C2×#95—172no—
443C2×#95—344no—
444C2×C17—28no—
445C2×C17—44no—
446C2×C17C2×#38511yescharacteristic
447C2×C17C4×#12311yescharacteristic
448C2×C17#232111yescharacteristic
449C2×C17#234912yes—
450C2×C17#236412yes—
451C2×C17#240411yescharacteristic
452C2×C17#240511yescharacteristic
453C2×C17#244412yes—
454C2×C17#245012yes—
455C2×C17#248711yescharacteristic
456C2×C17#257911yescharacteristic
457C25C22×D1711yescharacteristic
458C25C22×D1711yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4Dic3414yes—
464C22×D4C4×D1714yes—
465C22×D4C22⋊D1714yes—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—24no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—24no—
473C23×C4—42no—
474C23×C4—42no—
475C23×C4—172no—
476C23×C4—172no—
477C23×C4—172no—
478C23×C4—174no—
479C23×C4—172no—
480C23×C4—344no—
481C23×C4—342no—
482C23×C4—342no—
483C23×C4—342no—
484C23×C4—342no—
485C23×C4—342no—
486C23×C4—682no—
487C23×C4—682no—
488C23×C4—682no—
489C23×C4C22⋊D1714yes—
490C23×C4C22×D1711yescharacteristic
491C23×C4C22×D1711yescharacteristic
492C23×C4C22×D1711yescharacteristic
493C23×C4C22×D1711yescharacteristic
494C23×C4C22×D1711yescharacteristic
495C4×D4—232no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—344no—
500C2×C4⋊C4—344no—
501C2×C4⋊C4—682no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—174no—
508C2×C22⋊C4—178no—
509C2×C22⋊C4—342no—
510C2×C22⋊C4—342no—
511C2×C22⋊C4—344no—
512C2×C22⋊C4—342no—
513C2×C22⋊C4—342no—
514C2×C22⋊C4—344no—
515C2×C22⋊C4—342no—
516C2×C22⋊C4—682no—
517C2×C22⋊C4—682no—
518C2×C22⋊C4—682no—
519C2×C22⋊C4C22⋊D1714yes—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523#95—178no—
524#95—344no—
525#95—344no—
526#95—344no—
527#95—344no—
528#95—344no—
529#95—682no—
530#95—682no—
531#95—682no—
532C17#1401611yescharacteristic, complemented, Sylow
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—21no—
538C24—21no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—21no—
544C24—21no—
545C24C2×Dic3412yes—
546C24C2×Dic3412yes—
547C24C2×C4×D1712yes—
548C24C2×C4×D1712yes—
549C24#6325212yes—
550C24#6325212yes—
551C24C2×C22⋊D1712yes—
552C24C2×C22⋊D1712yes—
553C24C2×C22⋊D1712yes—
554C24C2×C22⋊D1712yes—
555C24C23×D1711yescharacteristic
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4#63225116yescomplemented
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—28no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—44no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—174no—
593C22×C4—174no—
594C22×C4—174no—
595C22×C4—348no—
596C22×C4—342no—
597C22×C4—342no—
598C22×C4—342no—
599C22×C4—342no—
600C22×C4—342no—
601C22×C4—342no—
602C22×C4—342no—
603C22×C4—342no—
604C22×C4—342no—
605C22×C4—342no—
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—348no—
615C22×C4—342no—
616C22×C4—342no—
617C22×C4—342no—
618C22×C4—342no—
619C22×C4—342no—
620C22×C4—342no—
621C22×C4—342no—
622C22×C4—688no—
623C22×C4—688no—
624C22×C4—688no—
625C22×C4—684no—
626C22×C4—684no—
627C22×C4—684no—
628C22×C4—688no—
629C22×C4—684no—
630C22×C4C2×Dic3412yes—
631C22×C4C2×C4×D1712yes—
632C22×C4#6325414yes—
633C22×C4C2×C22⋊D1712yes—
634C22×C4C2×C22⋊D1712yes—
635C22×C4C2×C22⋊D1712yes—
636C22×C4C2×C22⋊D1712yes—
637C22×C4C2×C22⋊D1712yes—
638C4⋊C4—28no—
639C4⋊C4—688no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—348no—
643C22⋊C4—688no—
644C22⋊C4—688no—
645C22⋊C4—684no—
646C42—28no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—42no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—41no—
681C23—41no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23C2×#6322514yes—
686C23C2×#6322514yes—
687C23#1058761014yes—
688C23#1058761014yes—
689C23C4×C22⋊D1714yes—
690C23C4×C22⋊D1714yes—
691C23#1058761514yes—
692C23#1058763914yes—
693C23C22×Dic3411yescharacteristic
694C23C22×C4×D1711yescharacteristic
695C23C2×#6325211yescharacteristic
696C23C2×#6325211yescharacteristic
697C23C2×#6325412yes—
698C23#1058769112yes—
699C23#41×D1712yes—
700C23#1058769612yes—
701C23C22×C22⋊D1711yescharacteristic
702C23C22×C22⋊D1711yescharacteristic
703C23C22×C22⋊D1711yescharacteristic
704D4—232no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—416no—
723C2×C4—416no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—344no—
733C2×C4—344no—
734C2×C4—344no—
735C2×C4—344no—
736C2×C4—344no—
737C2×C4—344no—
738C2×C4—344no—
739C2×C4—344no—
740C2×C4—344no—
741C2×C4—6816no—
742C2×C4—6816no—
743C2×C4—682no—
744C2×C4—682no—
745C2×C4—682no—
746C2×C4—682no—
747C2×C4—682no—
748C2×C4—682no—
749C2×C4—682no—
750C2×C4—682no—
751C2×C4—682no—
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×C4C2×#6322514yes—
763C2×C4#1058762114yes—
764C22—24no—
765C22—24no—
766C22—28no—
767C22—24no—
768C22—28no—
769C22—24no—
770C22—24no—
771C22—24no—
772C22—28no—
773C22—28no—
774C22—28no—
775C22—24no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—44no—
784C22—44no—
785C22#1176268218yes—
786C22C22×#6322511yescharacteristic
787C22C2×C4×C22⋊D1711yescharacteristic
788C22C2×C4×C22⋊D1711yescharacteristic
789C22C4×#6325412yes—
790C22#1176328112yes—
791C22C2×#1058763911yescharacteristic
792C22C2×#1058761011yescharacteristic
793C22C2×#1058761011yescharacteristic
794C22C2×#1058762111yescharacteristic
795C22C2×#1058761511yescharacteristic
796C22#1176331611yescharacteristic
797C22#1176333912yes—
798C22#1176336811yescharacteristic
799C22#1176337311yescharacteristic
800C22#1176339212yes—
801C22#1176344712yes—
802C22#1176344712yes—
803C22#1176345312yes—
804C22#1176345312yes—
805C22#1176350512yes—
806C22#1176350812yes—
807C22#1176351612yes—
808C22#1176351812yes—
809C4—24no—
810C4—24no—
811C4—42no—
812C4—42no—
813C4—42no—
814C4—684no—
815C4—684no—
816C4—684no—
817C4—1362no—
818C2—28no—
819C2—44no—
820C2C2×#1176268211yescharacteristic
821C2C4×#1058762111yescharacteristic
822C2#1453143811yescharacteristic
823C2#1453168912yes—
824C2#1453182912yes—
825C2#1453209911yescharacteristic
826C2#1453210711yescharacteristic
827C2#1453252812yes—
828C2#1453260212yes—
829C2#1453310111yescharacteristic
830C2#1453412711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC22×C4×D4×C17C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC22×C4×D4D17
hypocenterC17#14016
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
3. C2×#11762681C2semidirect
4. C22×#10587502C2semidirect
5. #14527043C2semidirect
6. #14527027C2semidirect
7. #14527017C2semidirect
8. #14527007C2semidirect
9. #14527007C2semidirect
10. #14527006C2semidirect
20. #11762689C4semidirect
75. C23×Dic17C2×C4semidirect
103. C2×C22⋊Dic17C2×C4semidirect
104. C2×C22⋊Dic17C2×C4semidirect
116. #10587502C2×C4semidirect
146. C2×D4×C17C4⋊C4semidirect
532. C17#14016semidirect
562. C2×D4#63225semidirect

Maximal subgroups

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

subgroupindex
C2×#117626892
C2×#117626812
C22×#105875022
#145270432
#145270272
#145270172
#145270072
#145270062
C22×C4×D4×C172
#1401617