Finite Group Databasebeta

← #16956275

Subgroups — #16956275

Order 4352.

1846 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×#11762702C212yesmaximal
2C2×#11762679C211yesmaximal, characteristic, complemented
3C2×#11762669C211yesmaximal, characteristic
4C2×#11762669C211yesmaximal, characteristic
5C2×C4×C4⋊Dic17C211yesmaximal, characteristic, complemented
6#14527041C212yesmaximal, complemented
7#14527029C212yesmaximal
8#14527018C212yesmaximal, complemented
9#14527014C211yesmaximal, characteristic, complemented
10#14527014C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C17C211yesmaximal, characteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C4⋊Dic17C2211yescharacteristic
14C22×C4⋊Dic17C2212yes—
15C22×C4⋊Dic17C2212yes—
16C22×C4⋊Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C22⋊Dic17C2212yes—
19C22×C22⋊Dic17C2212yes—
20C22×C4×Dic17C2212yes—
21#11762702—28no—
22#11762679—24no—
23#11762669—24no—
24#11762669—24no—
25C4×C4⋊Dic17—24no—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C24×C4×C17C2211yescharacteristic
34C22×C22⋊C4×C17C2211yescharacteristic
35C22×C22⋊C4×C17C2211yescharacteristic
36C22×C42×C17C2211yescharacteristic
37C22×C42×C17C2211yescharacteristic
38C4×C22⋊C4×C17C418yescomplemented
39C2×C17×#95C2211yescharacteristic
40C2×C17×#95C2211yescharacteristic
41C25×C17C2311yescharacteristic
42C23×C4×C17—22no—
43C23×C4×C17—22no—
44C23×C4×C17—22no—
45C23×C4×C17—22no—
46C23×C4×C17—22no—
47C23×C4×C17—22no—
48C23×C4×C17C2×C414yes—
49C23×C4×C17C2311yescharacteristic
50C23×C4×C17C2311yescharacteristic
51C23×C4×C17C2311yescharacteristic
52C23×C4×C17C2311yescharacteristic
53C23×C4×C17C2311yescharacteristic
54C23×C4×C17C2311yescharacteristic
55C23×Dic17C2312yes—
56C23×Dic17C2312yes—
57C23×Dic17C2312yes—
58C23×Dic17C2312yes—
59C2×C22⋊C4×C17—22no—
60C2×C22⋊C4×C17—22no—
61C2×C22⋊C4×C17C2×C414yes—
62C2×C22⋊C4×C17C2×C414yes—
63C2×C22⋊C4×C17D414yes—
64C2×C22⋊C4×C17Q814yes—
65C2×C42×C17—22no—
66C2×C42×C17—22no—
67C2×C42×C17—22no—
68C2×C42×C17—22no—
69C2×C42×C17C2×C414yes—
70C2×C42×C17C2×C414yes—
71C2×C22⋊Dic17—24no—
72C2×C22⋊Dic17—24no—
73C2×C22⋊Dic17—24no—
74C2×C22⋊Dic17—24no—
75C2×C22⋊Dic17—42no—
76C2×C22⋊Dic17—42no—
77C2×C4⋊Dic17—22no—
78C2×C4⋊Dic17—24no—
79C2×C4⋊Dic17—22no—
80C2×C4⋊Dic17—22no—
81C2×C4⋊Dic17—22no—
82C2×C4⋊Dic17—22no—
83C2×C4⋊Dic17—22no—
84C2×C4⋊Dic17—22no—
85C2×C4⋊Dic17—24no—
86C2×C4⋊Dic17—22no—
87C2×C4⋊Dic17—22no—
88C2×C4⋊Dic17—22no—
89C2×C4⋊Dic17—24no—
90C2×C4⋊Dic17—24no—
91C2×C4⋊Dic17—42no—
92C2×C4⋊Dic17—42no—
93C2×C4⋊Dic17D414yes—
94C2×C4⋊Dic17D414yes—
95C2×C4×Dic17—24no—
96C2×C4×Dic17—24no—
97C2×C4×Dic17—42no—
98C17×#95C2×C414yes—
99C17×#95C2×C414yes—
100#10587502—24no—
101#10587502—24no—
102#10587502—24no—
103#10587502—24no—
104#10587502—24no—
105#10587502—24no—
106#10587502—42no—
107C24×C17—21no—
108C24×C17—21no—
109C24×C17—21no—
110C24×C17—21no—
111C24×C17—21no—
112C24×C17—21no—
113C24×C17—21no—
114C24×C17—21no—
115C24×C17—21no—
116C24×C17—21no—
117C24×C17—21no—
118C24×C17—21no—
119C24×C17C22×C412yes—
120C24×C17C2×D412yes—
121C24×C17C2×Q812yes—
122C24×C17C2411yescharacteristic
123C22×C4×C17—21no—
124C22×C4×C17—21no—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17—21no—
128C22×C4×C17—21no—
129C22×C4×C17—21no—
130C22×C4×C17—21no—
131C22×C4×C17—21no—
132C22×C4×C17—21no—
133C22×C4×C17—21no—
134C22×C4×C17—21no—
135C22×C4×C17—21no—
136C22×C4×C17—21no—
137C22×C4×C17—21no—
138C22×C4×C17—21no—
139C22×C4×C17—21no—
140C22×C4×C17—21no—
141C22×C4×C17—21no—
142C22×C4×C17—21no—
143C22×C4×C17—21no—
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—28no—
148C22×C4×C17—28no—
149C22×C4×C17—28no—
150C22×C4×C17—44no—
151C22×C4×C17—44no—
152C22×C4×C17—44no—
153C22×C4×C17—44no—
154C22×C4×C17C22×C412yes—
155C22×C4×C17C22×C412yes—
156C22×C4×C17C22×C412yes—
157C22×C4×C17C22×C412yes—
158C22×C4×C17C22×C412yes—
159C22×C4×C17C22×C412yes—
160C22×C4×C17C2×D412yes—
161C22×C4×C17C2×D412yes—
162C22×C4×C17C2×D412yes—
163C22×C4×C17C2×D412yes—
164C22×C4×C17C2×Q812yes—
165C22×C4×C17C2×Q812yes—
166C22×C4×C17#4112yes—
167C22×C4×C17#4112yes—
168C22×C4×C17#4112yes—
169C22×C4×C17#4112yes—
170C22×C4×C17#4112yes—
171C22×C4×C17#4112yes—
172C22×Dic17—22no—
173C22×Dic17—22no—
174C22×Dic17—22no—
175C22×Dic17—22no—
176C22×Dic17—22no—
177C22×Dic17—22no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—22no—
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×Dic17C2×D414yes—
199C22×Dic17C2×D414yes—
200C22⋊C4×C17—28no—
201C22⋊C4×C17C4⋊C4116yescomplemented
202C42×C17—28no—
203C42×C17—28no—
204C22⋊Dic17—48no—
205C22⋊Dic17—48no—
206C4⋊Dic17—28no—
207C4⋊Dic17—28no—
208C4⋊Dic17—48no—
209C4⋊Dic17—48no—
210C4⋊Dic17—44no—
211C4⋊Dic17—44no—
212C4×Dic17—48no—
213#13876—171nomaximal, Sylow
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—22no—
226C23×C17—22no—
227C23×C17—22no—
228C23×C17—22no—
229C23×C17—22no—
230C23×C17—22no—
231C23×C17—22no—
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—41no—
242C23×C17—41no—
243C23×C17—41no—
244C23×C17—41no—
245C23×C17—41no—
246C23×C17—41no—
247C23×C17—41no—
248C23×C17C2×C4⋊C414yes—
249C23×C17C23×C411yescharacteristic
250C23×C17C22×D411yescharacteristic
251C23×C17C22×D411yescharacteristic
252C23×C17C22×D411yescharacteristic
253C23×C17C22×Q811yescharacteristic
254C23×C17C2×#4111yescharacteristic
255C23×C17C2×#4111yescharacteristic
256C23×C17C2×#4111yescharacteristic
257C23×C17C2×#4111yescharacteristic
258C23×C17C2×#4111yescharacteristic
259C23×C17C2×#4111yescharacteristic
260C23×C17H(5,𝔽2)11yescharacteristic
261C23×C17H(5,𝔽2)11yescharacteristic
262C23×C172−1+411yescharacteristic
263C23×C172−1+411yescharacteristic
264C2×C4×C17—22no—
265C2×C4×C17—22no—
266C2×C4×C17—22no—
267C2×C4×C17—22no—
268C2×C4×C17—22no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—41no—
289C2×C4×C17—41no—
290C2×C4×C17—41no—
291C2×C4×C17—41no—
292C2×C4×C17—41no—
293C2×C4×C17—41no—
294C2×C4×C17—41no—
295C2×C4×C17—41no—
296C2×C4×C17—416no—
297C2×C4×C17C2×C4⋊C414yes—
298C2×C4×C17C2×C4⋊C414yes—
299C2×C4×C17#11714yes—
300C2×C4×C17#11714yes—
301C2×C4×C17C4×D414yes—
302C2×C4×C17C4×D414yes—
303C2×C4×C17#12114yes—
304C2×C4×C17#12314yes—
305C2×C4×C17#12414yes—
306C2×C4×C17#12614yes—
307C2×Dic17—24no—
308C2×Dic17—24no—
309C2×Dic17—24no—
310C2×Dic17—24no—
311C2×Dic17—24no—
312C2×Dic17—24no—
313C2×Dic17—42no—
314C2×Dic17—42no—
315C2×Dic17—42no—
316C2×Dic17—42no—
317C2×Dic17—42no—
318C2×Dic17—42no—
319C2×Dic17—42no—
320C2×Dic17—42no—
321C2×Dic17—42no—
322C2×Dic17—42no—
323C2×Dic17—42no—
324C2×Dic17—42no—
325C2×Dic17—42no—
326C2×Dic17—42no—
327C2×Dic17—42no—
328C2×Dic17—42no—
329C2×Dic17—42no—
330C2×Dic17—42no—
331C2×Dic17—42no—
332C2×Dic17—42no—
333C2×Dic17—42no—
334C2×Dic17—42no—
335C2×#388—172no—
336C2×#384—171no—
337C2×#380—171no—
338C2×#380—171no—
339C2×C4×C4⋊C4—171no—
340C2×C4×C22⋊C4D1711yescharacteristic
341#1442—172no—
342#1439—172no—
343#1436—172no—
344C4⋊#95—171no—
345C4⋊#95—171no—
346C22×C17—24no—
347C22×C17—24no—
348C22×C17—24no—
349C22×C17—42no—
350C22×C17—42no—
351C22×C17—42no—
352C22×C17—42no—
353C22×C17—42no—
354C22×C17—42no—
355C22×C17—42no—
356C22×C17—42no—
357C22×C17—42no—
358C22×C17—42no—
359C22×C17—42no—
360C22×C17—42no—
361C22×C17C22×C4⋊C411yescharacteristic
362C22×C17C2×#11711yescharacteristic
363C22×C17C2×#11711yescharacteristic
364C22×C17C2×C4×D411yescharacteristic
365C22×C17C2×C4×D411yescharacteristic
366C22×C17#52011yescharacteristic
367C22×C17#52011yescharacteristic
368C22×C17C2×#12111yescharacteristic
369C22×C17C2×#12311yescharacteristic
370C22×C17C2×#12411yescharacteristic
371C22×C17C2×#12611yescharacteristic
372C22×C17#53211yescharacteristic
373C22×C17#53211yescharacteristic
374C22×C17#53311yescharacteristic
375C22×C17#53311yescharacteristic
376C22×C17#54011yescharacteristic
377C22×C17#54111yescharacteristic
378C22×C17#54211yescharacteristic
379C22×C17#54211yescharacteristic
380C22×C17D4211yescharacteristic
381C22×C17D4211yescharacteristic
382C22×C17#54611yescharacteristic
383C22×C17#54711yescharacteristic
384C22×C17#54711yescharacteristic
385C22×C17#54711yescharacteristic
386C22×C17#54811yescharacteristic
387C22×C17D4×Q811yescharacteristic
388C22×C17D4×Q811yescharacteristic
389C22×C17#55011yescharacteristic
390C22×C17#55211yescharacteristic
391C22×C17#55311yescharacteristic
392C22×C17#55411yescharacteristic
393C22×C17#55411yescharacteristic
394C22×C17#55511yescharacteristic
395C22×C17#55611yescharacteristic
396C4×C17—24no—
397C4×C17—24no—
398C4×C17—24no—
399C4×C17—42no—
400C4×C17—42no—
401C4×C17#38818yescomplemented
402Dic17—44no—
403Dic17—44no—
404Dic17—82no—
405Dic17—82no—
406C24×C4C2×D1711yescharacteristic
407C22×C4⋊C4—171no—
408C22×C4⋊C4—171no—
409C22×C4⋊C4—171no—
410C22×C4⋊C4—171no—
411C22×C4⋊C4—172no—
412C22×C4⋊C4—172no—
413C22×C22⋊C4—172no—
414C22×C22⋊C4—172no—
415C22×C22⋊C4C2×D1711yescharacteristic
416C22×C22⋊C4C2×D1711yescharacteristic
417C22×C42—172no—
418C22×C42C2×D1711yescharacteristic
419C22×C42C2×D1711yescharacteristic
420#388—348no—
421#384—344no—
422#380—344no—
423#380—344no—
424C4×C4⋊C4—344no—
425C4×C22⋊C4Dic1718yescomplemented
426C2×#95—172no—
427C2×#95—172no—
428C2×#95—172no—
429C2×#95—172no—
430C2×#95—172no—
431C2×#95—172no—
432C2×#95—172no—
433C2×#95C2×D1711yescharacteristic
434C2×#95C2×D1711yescharacteristic
435C2×C17—44no—
436C2×C17#228511yescharacteristic
437C2×C17C2×#38811yescharacteristic
438C2×C17#231411yescharacteristic
439C2×C17D4×C4⋊C411yescharacteristic
440C2×C17D4×C4⋊C411yescharacteristic
441C2×C17#235211yescharacteristic
442C2×C17#235411yescharacteristic
443C2×C17#242211yescharacteristic
444C2×C17#242311yescharacteristic
445C2×C17#242811yescharacteristic
446C2×C17#242911yescharacteristic
447C2×C17#249111yescharacteristic
448C2×C17#249211yescharacteristic
449C2×C17#249611yescharacteristic
450C2×C17#249711yescharacteristic
451C25C22×D1711yescharacteristic
452C23×C4—22no—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—172no—
459C23×C4—172no—
460C23×C4—172no—
461C23×C4—172no—
462C23×C4C2×Dic1714yes—
463C23×C4C22×D1711yescharacteristic
464C23×C4C22×D1711yescharacteristic
465C23×C4C22×D1711yescharacteristic
466C23×C4C22×D1711yescharacteristic
467C23×C4C22×D1711yescharacteristic
468C23×C4C22×D1711yescharacteristic
469C2×C4⋊C4—174no—
470C2×C4⋊C4—174no—
471C2×C4⋊C4—342no—
472C2×C4⋊C4—342no—
473C2×C4⋊C4—342no—
474C2×C4⋊C4—342no—
475C2×C4⋊C4—344no—
476C2×C4⋊C4—344no—
477C2×C4⋊C4—344no—
478C2×C4⋊C4—344no—
479C2×C4⋊C4—342no—
480C2×C4⋊C4—342no—
481C2×C4⋊C4—342no—
482C2×C4⋊C4—342no—
483C2×C4⋊C4—342no—
484C2×C4⋊C4—342no—
485C2×C4⋊C4—682no—
486C2×C4⋊C4—682no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—344no—
490C2×C22⋊C4—344no—
491C2×C22⋊C4—344no—
492C2×C22⋊C4—344no—
493C2×C22⋊C4—682no—
494C2×C22⋊C4—682no—
495C2×C22⋊C4Dic3414yes—
496C2×C22⋊C4D6814yes—
497C2×C22⋊C4C2×Dic1714yes—
498C2×C22⋊C4C2×Dic1714yes—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—344no—
504C2×C42—344no—
505C2×C42—682no—
506C2×C42C2×Dic1714yes—
507C2×C42C2×Dic1714yes—
508#95—344no—
509#95—344no—
510#95—344no—
511#95—344no—
512#95—344no—
513#95—344no—
514#95—682no—
515#95C2×Dic1714yes—
516#95C2×Dic1714yes—
517C17#1387611yescharacteristic, complemented, Sylow
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24C2×Dic3412yes—
531C24C2×D6812yes—
532C24C22×Dic1712yes—
533C24C23×D1711yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—174no—
566C22×C4—174no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4—342no—
570C22×C4—342no—
571C22×C4—342no—
572C22×C4—342no—
573C22×C4—342no—
574C22×C4—342no—
575C22×C4—342no—
576C22×C4—342no—
577C22×C4—342no—
578C22×C4—342no—
579C22×C4—342no—
580C22×C4—342no—
581C22×C4—342no—
582C22×C4—342no—
583C22×C4—342no—
584C22×C4—342no—
585C22×C4—342no—
586C22×C4—342no—
587C22×C4—342no—
588C22×C4—342no—
589C22×C4—342no—
590C22×C4—342no—
591C22×C4—342no—
592C22×C4—342no—
593C22×C4C2×Dic3412yes—
594C22×C4C2×Dic3412yes—
595C22×C4C2×D6812yes—
596C22×C4C2×D6812yes—
597C22×C4#6325212yes—
598C22×C4#6325212yes—
599C22×C4#6325212yes—
600C22×C4#6325212yes—
601C22×C4D4×D1712yes—
602C22×C4D4×D1712yes—
603C22×C4#6325412yes—
604C22×C4#6325412yes—
605C22×C4C22×Dic1712yes—
606C22×C4C22×Dic1712yes—
607C22×C4C22×Dic1712yes—
608C22×C4C22×Dic1712yes—
609C22×C4C22×Dic1712yes—
610C22×C4C22×Dic1712yes—
611C4⋊C4—348no—
612C4⋊C4—348no—
613C4⋊C4—688no—
614C4⋊C4—688no—
615C4⋊C4—684no—
616C4⋊C4—684no—
617C22⋊C4—28no—
618C22⋊C4—688no—
619C22⋊C4—688no—
620C22⋊C4C4⋊Dic17116yescomplemented
621C42—28no—
622C42—28no—
623C42—688no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23C2×C4⋊Dic1714yes—
659C23C22×Dic3411yescharacteristic
660C23C22×D6811yescharacteristic
661C23C2×#6325211yescharacteristic
662C23C2×#6325211yescharacteristic
663C23C2×#6325211yescharacteristic
664C23C2×#6325211yescharacteristic
665C23C2×D4×D1711yescharacteristic
666C23C2×D4×D1711yescharacteristic
667C23C2×#6325411yescharacteristic
668C23C2×#6325411yescharacteristic
669C23#1058769611yescharacteristic
670C23#1058769611yescharacteristic
671C23#1058769711yescharacteristic
672C23#1058769711yescharacteristic
673C23C23×Dic1711yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—416no—
707C2×C4—344no—
708C2×C4—344no—
709C2×C4—344no—
710C2×C4—344no—
711C2×C4—344no—
712C2×C4—344no—
713C2×C4—682no—
714C2×C4—682no—
715C2×C4—682no—
716C2×C4—682no—
717C2×C4—682no—
718C2×C4—682no—
719C2×C4—682no—
720C2×C4—682no—
721C2×C4—682no—
722C2×C4—682no—
723C2×C4—682no—
724C2×C4—682no—
725C2×C4—682no—
726C2×C4—682no—
727C2×C4—682no—
728C2×C4—682no—
729C2×C4—682no—
730C2×C4—682no—
731C2×C4—682no—
732C2×C4—682no—
733C2×C4—682no—
734C2×C4—682no—
735C2×C4#1058756514yes—
736C2×C4#1058756914yes—
737C2×C4#1058757014yes—
738C2×C4#1058757114yes—
739C2×C4C2×C4⋊Dic1714yes—
740C2×C4C2×C4⋊Dic1714yes—
741C2×C4#1058761214yes—
742C2×C4#1058761214yes—
743C2×C4D4×Dic1714yes—
744C2×C4D4×Dic1714yes—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22C22×C4⋊Dic1711yescharacteristic
761C22C2×#1058761211yescharacteristic
762C22C2×#1058761211yescharacteristic
763C22C2×D4×Dic1711yescharacteristic
764C22C2×D4×Dic1711yescharacteristic
765C22#1176329211yescharacteristic
766C22#1176329211yescharacteristic
767C22C2×#1058757011yescharacteristic
768C22C2×#1058756911yescharacteristic
769C22C2×#1058757111yescharacteristic
770C22C2×#1058756511yescharacteristic
771C22#1176335911yescharacteristic
772C22#1176335911yescharacteristic
773C22#1176336611yescharacteristic
774C22#1176336611yescharacteristic
775C22#1176341411yescharacteristic
776C22#1176342111yescharacteristic
777C22#1176343011yescharacteristic
778C22#1176343011yescharacteristic
779C22D4×D6811yescharacteristic
780C22D4×D6811yescharacteristic
781C22#1176345511yescharacteristic
782C22#1176346311yescharacteristic
783C22#1176346311yescharacteristic
784C22#1176346411yescharacteristic
785C22#1176346811yescharacteristic
786C22D4×Dic3411yescharacteristic
787C22D4×Dic3411yescharacteristic
788C22#1176348011yescharacteristic
789C22#1176349911yescharacteristic
790C22#1176350511yescharacteristic
791C22#1176351611yescharacteristic
792C22#1176351611yescharacteristic
793C22#1176352411yescharacteristic
794C22#1176352911yescharacteristic
795C4—24no—
796C4—24no—
797C4—24no—
798C4—42no—
799C4—42no—
800C4—684no—
801C4—684no—
802C4—1362no—
803C4—1362no—
804C4#1176270218yescomplemented
805C2—44no—
806C2#1453119111yescharacteristic
807C2C2×#1176270211yescharacteristic
808C2#1453139311yescharacteristic
809C2D4×C4⋊Dic1711yescharacteristic
810C2D4×C4⋊Dic1711yescharacteristic
811C2#1453171311yescharacteristic
812C2#1453173311yescharacteristic
813C2#1453229811yescharacteristic
814C2#1453230911yescharacteristic
815C2#1453237211yescharacteristic
816C2#1453238311yescharacteristic
817C2#1453314711yescharacteristic
818C2#1453315811yescharacteristic
819C2#1453320611yescharacteristic
820C2#1453321711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C4×C22⋊C4×C17C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×C4×C22⋊C4D17
hypocenterC17#13876
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11762679C2semidirect
5. C2×C4×C4⋊Dic17C2semidirect
6. #14527041C2semidirect
8. #14527018C2semidirect
9. #14527014C2semidirect
10. #14527014C2semidirect
38. C4×C22⋊C4×C17C4semidirect
201. C22⋊C4×C17C4⋊C4semidirect
401. C4×C17#388semidirect
425. C4×C22⋊C4Dic17semidirect
517. C17#13876semidirect
620. C22⋊C4C4⋊Dic17semidirect
804. C4#11762702semidirect

Maximal subgroups

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

subgroupindex
C2×#117627022
C2×#117626792
C2×#117626692
C2×C4×C4⋊Dic172
#145270412
#145270292
#145270182
#145270142
C2×C4×C22⋊C4×C172
#1387617