Finite Group Databasebeta

← #16956266

Subgroups — #16956266

Order 4352.

1702 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762674C211yesmaximal, characteristic, complemented
2C2×#11762669C211yesmaximal, characteristic
3C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic17C211yesmaximal, characteristic
5#14527044C212yesmaximal, complemented
6#14527031C212yesmaximal
7#14527021C212yesmaximal
8#14527013C211yesmaximal, characteristic, complemented
9#14527013C211yesmaximal, characteristic, complemented
10#14527010C212yesmaximal, complemented
11C2×C17×#380C211yesmaximal, characteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C4⋊Dic17C2211yescharacteristic
14C22×C22⋊Dic17C2212yes—
15C22×C22⋊Dic17C2211yescharacteristic
16C22×C22⋊Dic17C2211yescharacteristic
17C22×C4×Dic17C2212yes—
18C22×C4×Dic17C2211yescharacteristic
19C22×C4×Dic17C2211yescharacteristic
20#11762674—24no—
21#11762669—24no—
22C4⋊C4×Dic17—24no—
23C4×C22⋊Dic17C418yescomplemented
24C2×#10587502C2212yes—
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2211yescharacteristic
34C24×C4×C17C2211yescharacteristic
35C22×C4⋊C4×C17C2211yescharacteristic
36C22×C4⋊C4×C17C2211yescharacteristic
37C22×C22⋊C4×C17C2212yes—
38C17×#380—24no—
39C2×C17×#95C2212yes—
40C25×C17C2311yescharacteristic
41C23×C4×C17—22no—
42C23×C4×C17—22no—
43C23×C4×C17—22no—
44C23×C4×C17—22no—
45C23×C4×C17—22no—
46C23×C4×C17—22no—
47C23×C4×C17C2×C414yes—
48C23×C4×C17C2312yes—
49C23×C4×C17C2311yescharacteristic
50C23×C4×C17C2312yes—
51C23×C4×C17C2311yescharacteristic
52C23×Dic17C2312yes—
53C23×Dic17C2311yescharacteristic
54C23×Dic17C2311yescharacteristic
55C23×Dic17C2311yescharacteristic
56C23×Dic17C2312yes—
57C23×Dic17C2311yescharacteristic
58C2×C4⋊C4×C17—22no—
59C2×C4⋊C4×C17—22no—
60C2×C4⋊C4×C17—22no—
61C2×C4⋊C4×C17—22no—
62C2×C4⋊C4×C17—22no—
63C2×C4⋊C4×C17D414yes—
64C2×C22⋊C4×C17—24no—
65C2×C22⋊C4×C17—24no—
66C2×C22⋊C4×C17—42no—
67C2×C22⋊Dic17—22no—
68C2×C22⋊Dic17—22no—
69C2×C22⋊Dic17—22no—
70C2×C22⋊Dic17—22no—
71C2×C22⋊Dic17—24no—
72C2×C22⋊Dic17—24no—
73C2×C22⋊Dic17—42no—
74C2×C22⋊Dic17C2×C414yes—
75C2×C22⋊Dic17C2×C414yes—
76C2×C4⋊Dic17—22no—
77C2×C4⋊Dic17—22no—
78C2×C4⋊Dic17—22no—
79C2×C4⋊Dic17—22no—
80C2×C4⋊Dic17—22no—
81C2×C4⋊Dic17D414yes—
82C2×C4×Dic17—22no—
83C2×C4×Dic17—22no—
84C2×C4×Dic17—22no—
85C2×C4×Dic17—22no—
86C2×C4×Dic17—24no—
87C2×C4×Dic17—24no—
88C2×C4×Dic17—42no—
89C2×C4×Dic17C2×C414yes—
90C2×C4×Dic17C2×C414yes—
91C17×#95—24no—
92#10587502—24no—
93#10587502—24no—
94#10587502—24no—
95#10587502—24no—
96#10587502—24no—
97#10587502—42no—
98#10587502—42no—
99#10587502—42no—
100#10587502C2×C414yes—
101#10587502C2×C414yes—
102C24×C17—21no—
103C24×C17—21no—
104C24×C17—21no—
105C24×C17—21no—
106C24×C17—21no—
107C24×C17—21no—
108C24×C17—21no—
109C24×C17—21no—
110C24×C17—21no—
111C24×C17—21no—
112C24×C17—21no—
113C24×C17—21no—
114C24×C17C22×C412yes—
115C24×C17#4112yes—
116C24×C17#4112yes—
117C24×C17C2411yescharacteristic
118C22×C4×C17—21no—
119C22×C4×C17—21no—
120C22×C4×C17—22no—
121C22×C4×C17—21no—
122C22×C4×C17—21no—
123C22×C4×C17—21no—
124C22×C4×C17—21no—
125C22×C4×C17—22no—
126C22×C4×C17—22no—
127C22×C4×C17—22no—
128C22×C4×C17—22no—
129C22×C4×C17—22no—
130C22×C4×C17—28no—
131C22×C4×C17—28no—
132C22×C4×C17—28no—
133C22×C4×C17—22no—
134C22×C4×C17—22no—
135C22×C4×C17—22no—
136C22×C4×C17—22no—
137C22×C4×C17—22no—
138C22×C4×C17—22no—
139C22×C4×C17—22no—
140C22×C4×C17—44no—
141C22×C4×C17—44no—
142C22×C4×C17—44no—
143C22×C4×C17—44no—
144C22×C4×C17C22×C412yes—
145C22×C4×C17C22×C412yes—
146C22×C4×C17C2×D412yes—
147C22×C4×C17C2×D414yes—
148C22×C4×C17C2×D412yes—
149C22×C4×C17#4112yes—
150C22×C4×C17#4112yes—
151C22×C4×C17#4112yes—
152C22×C4×C17#4112yes—
153C22×Dic17—21no—
154C22×Dic17—21no—
155C22×Dic17—21no—
156C22×Dic17—21no—
157C22×Dic17—21no—
158C22×Dic17—21no—
159C22×Dic17—21no—
160C22×Dic17—21no—
161C22×Dic17—21no—
162C22×Dic17—21no—
163C22×Dic17—22no—
164C22×Dic17—22no—
165C22×Dic17—22no—
166C22×Dic17—21no—
167C22×Dic17—21no—
168C22×Dic17—21no—
169C22×Dic17—21no—
170C22×Dic17—22no—
171C22×Dic17—21no—
172C22×Dic17—21no—
173C22×Dic17—21no—
174C22×Dic17—21no—
175C22×Dic17—21no—
176C22×Dic17—22no—
177C22×Dic17—22no—
178C22×Dic17—21no—
179C22×Dic17—21no—
180C22×Dic17—21no—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17C22×C412yes—
189C22×Dic17C22×C412yes—
190C22×Dic17C22×C412yes—
191C22×Dic17C22×C412yes—
192C22×Dic17C2×D414yes—
193C22×Dic17#4112yes—
194C22×Dic17#4112yes—
195C4⋊C4×C17—28no—
196C4⋊C4×C17—44no—
197C22⋊C4×C17—48no—
198C22⋊Dic17—28no—
199C22⋊Dic17—28no—
200C22⋊Dic17—48no—
201C4⋊Dic17—28no—
202C4⋊Dic17—44no—
203C4×Dic17—28no—
204C4×Dic17—28no—
205C4×Dic17—48no—
206#13875—171nomaximal, Sylow
207C23×C17—22no—
208C23×C17—22no—
209C23×C17—22no—
210C23×C17—22no—
211C23×C17—22no—
212C23×C17—22no—
213C23×C17—22no—
214C23×C17—22no—
215C23×C17—22no—
216C23×C17—22no—
217C23×C17—22no—
218C23×C17—22no—
219C23×C17—22no—
220C23×C17—22no—
221C23×C17—22no—
222C23×C17—22no—
223C23×C17—22no—
224C23×C17—22no—
225C23×C17—41no—
226C23×C17—41no—
227C23×C17—41no—
228C23×C17—41no—
229C23×C17—41no—
230C23×C17—41no—
231C23×C17—41no—
232C23×C17—41no—
233C23×C17—41no—
234C23×C17—41no—
235C23×C17—41no—
236C23×C17—41no—
237C23×C17—41no—
238C23×C17—41no—
239C23×C17—41no—
240C23×C17—41no—
241C23×C17#11714yes—
242C23×C17C23×C411yescharacteristic
243C23×C17C22×D411yescharacteristic
244C23×C17C22×D411yescharacteristic
245C23×C17C2×#4111yescharacteristic
246C23×C17C2×#4111yescharacteristic
247C23×C17C2×#4111yescharacteristic
248C23×C17C2×#4111yescharacteristic
249C23×C17C2×#4111yescharacteristic
250C23×C17C2×#4111yescharacteristic
251C23×C17C2×#4111yescharacteristic
252C23×C17C2×#4111yescharacteristic
253C23×C17H(5,𝔽2)11yescharacteristic
254C23×C17H(5,𝔽2)11yescharacteristic
255C23×C172−1+411yescharacteristic
256C23×C172−1+411yescharacteristic
257C2×C4×C17—22no—
258C2×C4×C17—22no—
259C2×C4×C17—22no—
260C2×C4×C17—24no—
261C2×C4×C17—24no—
262C2×C4×C17—24no—
263C2×C4×C17—41no—
264C2×C4×C17—41no—
265C2×C4×C17—41no—
266C2×C4×C17—41no—
267C2×C4×C17—42no—
268C2×C4×C17—42no—
269C2×C4×C17—42no—
270C2×C4×C17—42no—
271C2×C4×C17—416no—
272C2×C4×C17—42no—
273C2×C4×C17—42no—
274C2×C4×C17—42no—
275C2×C4×C17—42no—
276C2×C4×C17—42no—
277C2×C4×C17—42no—
278C2×C4×C17—42no—
279C2×C4×C17#11714yes—
280C2×C4×C17C4×D414yes—
281C2×C4×C17C4×D414yes—
282C2×C4×C17#12114yes—
283C2×C4×C17#12314yes—
284C2×C4×C17#12414yes—
285C2×C4×C17#12614yes—
286C2×Dic17—22no—
287C2×Dic17—22no—
288C2×Dic17—22no—
289C2×Dic17—22no—
290C2×Dic17—22no—
291C2×Dic17—22no—
292C2×Dic17—22no—
293C2×Dic17—22no—
294C2×Dic17—22no—
295C2×Dic17—22no—
296C2×Dic17—22no—
297C2×Dic17—22no—
298C2×Dic17—22no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—24no—
302C2×Dic17—24no—
303C2×Dic17—24no—
304C2×Dic17—42no—
305C2×Dic17—42no—
306C2×Dic17—41no—
307C2×Dic17—41no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—41no—
312C2×Dic17—41no—
313C2×Dic17—41no—
314C2×Dic17—41no—
315C2×Dic17—42no—
316C2×Dic17—41no—
317C2×Dic17—41no—
318C2×Dic17—42no—
319C2×Dic17—41no—
320C2×Dic17—42no—
321C2×Dic17—42no—
322C2×Dic17—42no—
323C2×Dic17—42no—
324C2×Dic17—42no—
325C2×Dic17—42no—
326C2×Dic17—42no—
327C2×Dic17#11714yes—
328C2×#382—171no—
329C2×#380—171no—
330C2×#380D1711yescharacteristic
331C2×C4×C4⋊C4—171no—
332C2×C4×C22⋊C4—171no—
333#1443—172no—
334#1440—172no—
335#1437—172no—
336C4⋊#95—171no—
337C4⋊#95—171no—
338#1434—172no—
339C22×C17—24no—
340C22×C17—24no—
341C22×C17—24no—
342C22×C17—42no—
343C22×C17—42no—
344C22×C17—42no—
345C22×C17—42no—
346C22×C17—42no—
347C22×C17—42no—
348C22×C17—42no—
349C22×C17—42no—
350C22×C17—42no—
351C22×C17—42no—
352C22×C17—42no—
353C22×C17—42no—
354C22×C17C2×#11711yescharacteristic
355C22×C17C2×#11711yescharacteristic
356C22×C17C2×#11711yescharacteristic
357C22×C17C2×C4×D411yescharacteristic
358C22×C17C2×C4×D411yescharacteristic
359C22×C17#52011yescharacteristic
360C22×C17#52011yescharacteristic
361C22×C17C2×#12111yescharacteristic
362C22×C17C2×#12311yescharacteristic
363C22×C17C2×#12411yescharacteristic
364C22×C17C2×#12611yescharacteristic
365C22×C17#52911yescharacteristic
366C22×C17#52911yescharacteristic
367C22×C17#52911yescharacteristic
368C22×C17#52911yescharacteristic
369C22×C17#54011yescharacteristic
370C22×C17#54111yescharacteristic
371C22×C17#54211yescharacteristic
372C22×C17#54211yescharacteristic
373C22×C17#54611yescharacteristic
374C22×C17#54611yescharacteristic
375C22×C17#54611yescharacteristic
376C22×C17#54711yescharacteristic
377C22×C17#54811yescharacteristic
378C22×C17#54811yescharacteristic
379C22×C17#54811yescharacteristic
380C22×C17#55011yescharacteristic
381C22×C17#55211yescharacteristic
382C22×C17#55211yescharacteristic
383C22×C17#55211yescharacteristic
384C22×C17#55311yescharacteristic
385C22×C17#55311yescharacteristic
386C22×C17#55311yescharacteristic
387C22×C17#55511yescharacteristic
388C22×C17#55611yescharacteristic
389C4×C17—44no—
390C4×C17—42no—
391C4×C17—82no—
392C4×C17#38818yes—
393Dic17—24no—
394Dic17—42no—
395Dic17—42no—
396Dic17—42no—
397Dic17—44no—
398Dic17—82no—
399C24×C4C2×D1711yescharacteristic
400C22×C4⋊C4—171no—
401C22×C4⋊C4—171no—
402C22×C4⋊C4C2×D1711yescharacteristic
403C22×C4⋊C4C2×D1711yescharacteristic
404C22×C22⋊C4—171no—
405C22×C22⋊C4—171no—
406C22×C22⋊C4—172no—
407C22×C22⋊C4C2×D1712yes—
408C22×C42—171no—
409C22×C42—171no—
410C22×C42—172no—
411#382—344no—
412#380—24no—
413#380—344no—
414C4×C4⋊C4—344no—
415C4×C22⋊C4—178no—
416C2×#95—171no—
417C2×#95—171no—
418C2×#95—172no—
419C2×#95—172no—
420C2×#95—172no—
421C2×#95—172no—
422C2×#95—172no—
423C2×#95—172no—
424C2×#95—172no—
425C2×#95—172no—
426C2×#95C2×D1712yes—
427C2×C17—44no—
428C2×C17#228311yescharacteristic
429C2×C17C2×#38811yescharacteristic
430C2×C17#231411yescharacteristic
431C2×C17#235211yescharacteristic
432C2×C17#235211yescharacteristic
433C2×C17#235211yescharacteristic
434C2×C17#235411yescharacteristic
435C2×C17#242011yescharacteristic
436C2×C17#242111yescharacteristic
437C2×C17#242611yescharacteristic
438C2×C17#242711yescharacteristic
439C2×C17#248911yescharacteristic
440C2×C17#249011yescharacteristic
441C2×C17#249411yescharacteristic
442C2×C17#249511yescharacteristic
443C25C22×D1711yescharacteristic
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—171no—
451C23×C4—172no—
452C23×C4—171no—
453C23×C4—171no—
454C23×C4—171no—
455C23×C4—172no—
456C23×C4C4×D1714yes—
457C23×C4C22×D1712yes—
458C23×C4C22×D1711yescharacteristic
459C23×C4C22×D1712yes—
460C23×C4C22×D1711yescharacteristic
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—174no—
467C2×C4⋊C4—342no—
468C2×C4⋊C4—342no—
469C2×C4⋊C4—342no—
470C2×C4⋊C4—342no—
471C2×C4⋊C4—342no—
472C2×C4⋊C4C22⋊D1714yes—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—174no—
477C2×C22⋊C4—174no—
478C2×C22⋊C4—342no—
479C2×C22⋊C4—342no—
480C2×C22⋊C4—342no—
481C2×C22⋊C4—342no—
482C2×C22⋊C4—344no—
483C2×C22⋊C4—344no—
484C2×C22⋊C4—682no—
485C2×C42—174no—
486C2×C42—174no—
487C2×C42—342no—
488C2×C42—342no—
489C2×C42—342no—
490C2×C42—342no—
491C2×C42—344no—
492C2×C42—344no—
493C2×C42—682no—
494#95—24no—
495#95—174no—
496#95—174no—
497#95—344no—
498#95—344no—
499#95—344no—
500#95—344no—
501#95—344no—
502#95—682no—
503#95—682no—
504#95—682no—
505C17#1387511yescharacteristic, complemented, Sylow
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24C2×C4×D1712yes—
519C24#6325412yes—
520C24#6325612yes—
521C24C23×D1711yescharacteristic
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—172no—
549C22×C4—172no—
550C22×C4—172no—
551C22×C4—172no—
552C22×C4—172no—
553C22×C4—172no—
554C22×C4—174no—
555C22×C4—341no—
556C22×C4—341no—
557C22×C4—341no—
558C22×C4—341no—
559C22×C4—341no—
560C22×C4—341no—
561C22×C4—342no—
562C22×C4—341no—
563C22×C4—341no—
564C22×C4—341no—
565C22×C4—341no—
566C22×C4—342no—
567C22×C4—341no—
568C22×C4—342no—
569C22×C4—341no—
570C22×C4—341no—
571C22×C4—342no—
572C22×C4—341no—
573C22×C4—342no—
574C22×C4—341no—
575C22×C4—341no—
576C22×C4—341no—
577C22×C4—341no—
578C22×C4—342no—
579C22×C4—341no—
580C22×C4—341no—
581C22×C4—341no—
582C22×C4—341no—
583C22×C4—342no—
584C22×C4—342no—
585C22×C4—342no—
586C22×C4—342no—
587C22×C4—342no—
588C22×C4—342no—
589C22×C4—342no—
590C22×C4C2×C4×D1712yes—
591C22×C4C2×C4×D1712yes—
592C22×C4#6325212yes—
593C22×C4D4×D1712yes—
594C22×C4#6325412yes—
595C22×C4#6325412yes—
596C22×C4#6325412yes—
597C22×C4C2×C22⋊D1714yes—
598C22×C4C2×C22⋊D1712yes—
599C4⋊C4—28no—
600C4⋊C4—44no—
601C4⋊C4—348no—
602C4⋊C4—684no—
603C22⋊C4—48no—
604C22⋊C4—348no—
605C22⋊C4—348no—
606C22⋊C4—688no—
607C42—348no—
608C42—348no—
609C42—688no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23#1058757814yes—
645C23C22×C4×D1711yescharacteristic
646C23C2×#6325211yescharacteristic
647C23C2×D4×D1711yescharacteristic
648C23C2×#6325411yescharacteristic
649C23C2×#6325411yescharacteristic
650C23C2×#6325411yescharacteristic
651C23C2×#6325411yescharacteristic
652C23#1058769111yescharacteristic
653C23C2×#6325611yescharacteristic
654C23#1058769411yescharacteristic
655C23#41×D1711yescharacteristic
656C23#41×D1711yescharacteristic
657C23#1058769611yescharacteristic
658C23#1058769711yescharacteristic
659C23C22×C22⋊D1711yescharacteristic
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—416no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—174no—
683C2×C4—342no—
684C2×C4—342no—
685C2×C4—342no—
686C2×C4—342no—
687C2×C4—342no—
688C2×C4—342no—
689C2×C4—344no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—342no—
693C2×C4—342no—
694C2×C4—342no—
695C2×C4—342no—
696C2×C4—342no—
697C2×C4—342no—
698C2×C4—342no—
699C2×C4—344no—
700C2×C4—344no—
701C2×C4—681no—
702C2×C4—681no—
703C2×C4—681no—
704C2×C4—681no—
705C2×C4—681no—
706C2×C4—681no—
707C2×C4—681no—
708C2×C4—682no—
709C2×C4—681no—
710C2×C4—681no—
711C2×C4—682no—
712C2×C4—681no—
713C2×C4—682no—
714C2×C4—682no—
715C2×C4—681no—
716C2×C4—681no—
717C2×C4—682no—
718C2×C4—682no—
719C2×C4—682no—
720C2×C4—682no—
721C2×C4—682no—
722C2×C4—682no—
723C2×C4—682no—
724C2×C4#1058756314yes—
725C2×C4#1058756514yes—
726C2×C4#1058756714yes—
727C2×C4#1058756914yes—
728C2×C4C4×C22⋊D1714yes—
729C2×C4#1058762214yes—
730C2×C4#1058762514yes—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22#117×D1711yescharacteristic
747C22C2×#1058756311yescharacteristic
748C22C2×#1058757811yescharacteristic
749C22C2×#1058756711yescharacteristic
750C22C2×C4×C22⋊D1711yescharacteristic
751C22#1176328911yescharacteristic
752C22#1176329011yescharacteristic
753C22C2×#1058762511yescharacteristic
754C22C2×#1058756911yescharacteristic
755C22C2×#1058762211yescharacteristic
756C22C2×#1058756511yescharacteristic
757C22#1176334011yescharacteristic
758C22#1176334011yescharacteristic
759C22#1176334511yescharacteristic
760C22#1176334511yescharacteristic
761C22#1176341211yescharacteristic
762C22#1176341911yescharacteristic
763C22#1176342611yescharacteristic
764C22#1176343211yescharacteristic
765C22#1176345011yescharacteristic
766C22#1176345311yescharacteristic
767C22#1176345611yescharacteristic
768C22#1176345811yescharacteristic
769C22#1176346511yescharacteristic
770C22#1176346911yescharacteristic
771C22#1176347011yescharacteristic
772C22#1176347811yescharacteristic
773C22#1176349311yescharacteristic
774C22#1176349411yescharacteristic
775C22#1176350111yescharacteristic
776C22#1176350611yescharacteristic
777C22#1176350711yescharacteristic
778C22#1176351111yescharacteristic
779C22#1176352211yescharacteristic
780C22#1176352711yescharacteristic
781C4—44no—
782C4—42no—
783C4—82no—
784C4—344no—
785C4—682no—
786C4—682no—
787C4—682no—
788C4—684no—
789C4—1362no—
790C4#1176270318yes—
791C2—44no—
792C2#1453117911yescharacteristic
793C2C2×#1176270311yescharacteristic
794C2#1453139111yescharacteristic
795C2#1453170611yescharacteristic
796C2#1453170911yescharacteristic
797C2#1453171511yescharacteristic
798C2#1453173411yescharacteristic
799C2#1453227811yescharacteristic
800C2#1453228911yescharacteristic
801C2#1453235211yescharacteristic
802C2#1453236311yescharacteristic
803C2#1453312711yescharacteristic
804C2#1453313811yescharacteristic
805C2#1453318611yescharacteristic
806C2#1453319711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#380C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#380D17
hypocenterC17#13875
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×#11762674C2semidirect
3. C2×C4⋊C4×Dic17C2semidirect
5. #14527044C2semidirect
8. #14527013C2semidirect
9. #14527013C2semidirect
10. #14527010C2semidirect
23. C4×C22⋊Dic17C4semidirect
505. C17#13875semidirect

Maximal subgroups

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

subgroupindex
C2×#117626742
C2×#117626692
C2×C4⋊C4×Dic172
C2×C4×C22⋊Dic172
#145270442
#145270312
#145270212
#145270132
#145270102
C2×C17×#3802
#1387517