Finite Group Databasebeta

← #16956269

Subgroups — #16956269

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×#11762700C212yesmaximal
2C2×#11762678C211yesmaximal, characteristic, complemented
3C2×#11762666C211yesmaximal, characteristic
4C2×#11762666C211yesmaximal, characteristic
5C2×C4×#63227C211yesmaximal, characteristic
6#14527039C212yesmaximal, complemented
7#14527028C212yesmaximal
8#14527017C212yesmaximal, complemented
9#14527014C211yesmaximal, characteristic, complemented
10#14527013C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊C4×C17C211yesmaximal, characteristic, complemented
12C23×C4×D17C2211yescharacteristic
13C22×C4⋊Dic17C2211yescharacteristic
14C22×C4⋊Dic17C2211yescharacteristic
15C22×#63225C2212yes—
16C22×#63225C2212yes—
17C22×#63227C2212yes—
18C22×#63227C2212yes—
19C22×#63227C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×C4×Dic17C2211yescharacteristic
22#11762700—28no—
23#11762678—24no—
24#11762666—24no—
25#11762666—24no—
26C4×#63227C418yescomplemented
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C22×C4⋊C4×C17C2211yescharacteristic
36C22×C4⋊C4×C17C2211yescharacteristic
37C22×C42×C17C2212yes—
38C22×C42×C17C2211yescharacteristic
39C4×C4⋊C4×C17—24no—
40C2×C17×#95C2212yes—
41C24×D17C2311yescharacteristic
42C23×C4×C17C2311yescharacteristic
43C23×C4×C17C2312yes—
44C23×C4×C17C2312yes—
45C23×C4×C17C2311yescharacteristic
46C23×C4×C17C2311yescharacteristic
47C23×Dic17C2312yes—
48C23×Dic17C2312yes—
49C23×Dic17C2311yescharacteristic
50C23×Dic17C2311yescharacteristic
51C23×Dic17C2311yescharacteristic
52C22×C4×D17—22no—
53C22×C4×D17—22no—
54C22×C4×D17—22no—
55C22×C4×D17—22no—
56C22×C4×D17—22no—
57C22×C4×D17—22no—
58C22×C4×D17C2×C414yes—
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×C4⋊C4×C17D414yes—
65C2×C42×C17—22no—
66C2×C42×C17—22no—
67C2×C42×C17—24no—
68C2×C42×C17—24no—
69C2×C42×C17—42no—
70C2×C42×C17C2×C414yes—
71C2×#63227—24no—
72C2×#63227—24no—
73C2×#63227—24no—
74C2×#63227—24no—
75C2×#63227—22no—
76C2×#63227—22no—
77C2×#63227—42no—
78C2×#63227—42no—
79C2×#63227C2×C414yes—
80C2×#63227C2×C414yes—
81C2×#63227D414yes—
82C2×#63227Q814yes—
83C2×C4⋊Dic17—22no—
84C2×C4⋊Dic17—22no—
85C2×C4⋊Dic17—22no—
86C2×C4⋊Dic17—22no—
87C2×C4⋊Dic17—22no—
88C2×C4⋊Dic17—22no—
89C2×#63225—24no—
90C2×#63225—24no—
91C2×#63225—24no—
92C2×#63225—24no—
93C2×#63225—42no—
94C2×#63225—42no—
95C2×C4×Dic17—22no—
96C2×C4×Dic17—22no—
97C2×C4×Dic17C2×C414yes—
98C17×#95—24no—
99#10587502—24no—
100#10587502—24no—
101#10587502—24no—
102#10587502—24no—
103#10587502—24no—
104#10587502—42no—
105#10587502C2×C414yes—
106#10587502C2×C414yes—
107C24×C17C2411yescharacteristic
108C23×D17—21no—
109C23×D17—21no—
110C23×D17—21no—
111C23×D17—21no—
112C23×D17—21no—
113C23×D17—21no—
114C23×D17—21no—
115C23×D17—21no—
116C23×D17—21no—
117C23×D17—21no—
118C23×D17—21no—
119C23×D17—21no—
120C23×D17C22×C412yes—
121C23×D17C2×D412yes—
122C23×D17C2×Q812yes—
123C22×C4×C17—21no—
124C22×C4×C17—21no—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17—22no—
128C22×C4×C17—21no—
129C22×C4×C17—22no—
130C22×C4×C17—22no—
131C22×C4×C17—22no—
132C22×C4×C17—22no—
133C22×C4×C17—21no—
134C22×C4×C17—21no—
135C22×C4×C17—21no—
136C22×C4×C17—22no—
137C22×C4×C17—22no—
138C22×C4×C17—22no—
139C22×C4×C17—21no—
140C22×C4×C17—22no—
141C22×C4×C17—22no—
142C22×C4×C17—22no—
143C22×C4×C17—21no—
144C22×C4×C17—22no—
145C22×C4×C17C22×C412yes—
146C22×C4×C17C22×C412yes—
147C22×C4×C17C22×C412yes—
148C22×C4×C17C2×D414yes—
149C22×C4×C17C2×D412yes—
150C22×C4×C17C2×D412yes—
151C22×C4×C17C2×D414yes—
152C22×C4×C17C2×D412yes—
153C22×C4×C17C2×Q812yes—
154C22×C4×C17#4112yes—
155C22×C4×C17#4112yes—
156C22×C4×C17#4112yes—
157C22×C4×C17#4112yes—
158C22×Dic17—21no—
159C22×Dic17—21no—
160C22×Dic17—21no—
161C22×Dic17—21no—
162C22×Dic17—21no—
163C22×Dic17—21no—
164C22×Dic17—21no—
165C22×Dic17—21no—
166C22×Dic17—21no—
167C22×Dic17—21no—
168C22×Dic17—21no—
169C22×Dic17—21no—
170C22×Dic17—21no—
171C22×Dic17—21no—
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×Dic17C22×C412yes—
187C22×Dic17C22×C412yes—
188C22×Dic17C22×C412yes—
189C22×Dic17C2×D412yes—
190C22×Dic17C2×Q812yes—
191C22×Dic17#4112yes—
192C22×Dic17#4112yes—
193C2×C4×D17—28no—
194C2×C4×D17—28no—
195C2×C4×D17—28no—
196C2×C4×D17—44no—
197C2×C4×D17—44no—
198C2×C4×D17—44no—
199C2×C4×D17—44no—
200C4⋊C4×C17—28no—
201C4⋊C4×C17—28no—
202C42×C17—28no—
203C42×C17—48no—
204#63227—28no—
205#63227—48no—
206#63227—48no—
207#63227C4⋊C4116yescomplemented
208C4⋊Dic17—44no—
209C4⋊Dic17—44no—
210#63225—48no—
211#63225—48no—
212C4×Dic17—28no—
213#13876—171nomaximal, Sylow
214C23×C17C23×C411yescharacteristic
215C23×C17C22×D411yescharacteristic
216C23×C17C22×D411yescharacteristic
217C23×C17C22×D411yescharacteristic
218C23×C17C22×Q811yescharacteristic
219C23×C17C2×#4111yescharacteristic
220C23×C17C2×#4111yescharacteristic
221C23×C17C2×#4111yescharacteristic
222C23×C17C2×#4111yescharacteristic
223C23×C17C2×#4111yescharacteristic
224C23×C17C2×#4111yescharacteristic
225C23×C17H(5,𝔽2)11yescharacteristic
226C23×C17H(5,𝔽2)11yescharacteristic
227C23×C172−1+411yescharacteristic
228C23×C172−1+411yescharacteristic
229C22×D17—22no—
230C22×D17—22no—
231C22×D17—22no—
232C22×D17—22no—
233C22×D17—22no—
234C22×D17—22no—
235C22×D17—22no—
236C22×D17—22no—
237C22×D17—22no—
238C22×D17—22no—
239C22×D17—22no—
240C22×D17—22no—
241C22×D17—22no—
242C22×D17—22no—
243C22×D17—22no—
244C22×D17—22no—
245C22×D17—22no—
246C22×D17—22no—
247C22×D17—41no—
248C22×D17—41no—
249C22×D17—41no—
250C22×D17—41no—
251C22×D17—41no—
252C22×D17—41no—
253C22×D17—41no—
254C22×D17—41no—
255C22×D17—41no—
256C22×D17—41no—
257C22×D17—41no—
258C22×D17—41no—
259C22×D17—41no—
260C22×D17—41no—
261C22×D17—41no—
262C22×D17—41no—
263C22×D17C2×C4⋊C414yes—
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—24no—
274C2×C4×C17—24no—
275C2×C4×C17—24no—
276C2×C4×C17—24no—
277C2×C4×C17—24no—
278C2×C4×C17—24no—
279C2×C4×C17—42no—
280C2×C4×C17—42no—
281C2×C4×C17—42no—
282C2×C4×C17—42no—
283C2×C4×C17—42no—
284C2×C4×C17—41no—
285C2×C4×C17—42no—
286C2×C4×C17—41no—
287C2×C4×C17—42no—
288C2×C4×C17—42no—
289C2×C4×C17—41no—
290C2×C4×C17—41no—
291C2×C4×C17C2×C4⋊C414yes—
292C2×C4×C17#11714yes—
293C2×C4×C17C4×D414yes—
294C2×C4×C17C4×D414yes—
295C2×C4×C17#12114yes—
296C2×C4×C17#12314yes—
297C2×C4×C17#12414yes—
298C2×C4×C17#12614yes—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—22no—
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—41no—
315C2×Dic17—41no—
316C2×Dic17—41no—
317C2×Dic17—41no—
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×Dic17C2×C4⋊C414yes—
333C2×Dic17#11714yes—
334C4×D17—416no—
335C2×#388—172no—
336C2×#384—171no—
337C2×#380—171no—
338C2×#380—171no—
339C2×C4×C4⋊C4D1711yescharacteristic, complemented
340C2×C4×C22⋊C4—171no—
341#1442—172no—
342#1439—172no—
343#1436—172no—
344C4⋊#95—171no—
345C4⋊#95—171no—
346C22×C17C22×C4⋊C411yescharacteristic
347C22×C17C2×#11711yescharacteristic
348C22×C17C2×#11711yescharacteristic
349C22×C17C2×C4×D411yescharacteristic
350C22×C17C2×C4×D411yescharacteristic
351C22×C17#52011yescharacteristic
352C22×C17#52011yescharacteristic
353C22×C17C2×#12111yescharacteristic
354C22×C17C2×#12311yescharacteristic
355C22×C17C2×#12411yescharacteristic
356C22×C17C2×#12611yescharacteristic
357C22×C17#53211yescharacteristic
358C22×C17#53211yescharacteristic
359C22×C17#53311yescharacteristic
360C22×C17#53311yescharacteristic
361C22×C17#54011yescharacteristic
362C22×C17#54111yescharacteristic
363C22×C17#54211yescharacteristic
364C22×C17#54211yescharacteristic
365C22×C17D4211yescharacteristic
366C22×C17D4211yescharacteristic
367C22×C17#54611yescharacteristic
368C22×C17#54711yescharacteristic
369C22×C17#54711yescharacteristic
370C22×C17#54711yescharacteristic
371C22×C17#54811yescharacteristic
372C22×C17D4×Q811yescharacteristic
373C22×C17D4×Q811yescharacteristic
374C22×C17#55011yescharacteristic
375C22×C17#55211yescharacteristic
376C22×C17#55311yescharacteristic
377C22×C17#55411yescharacteristic
378C22×C17#55411yescharacteristic
379C22×C17#55511yescharacteristic
380C22×C17#55611yescharacteristic
381C2×D17—24no—
382C2×D17—24no—
383C2×D17—24no—
384C2×D17—42no—
385C2×D17—42no—
386C2×D17—42no—
387C2×D17—42no—
388C2×D17—42no—
389C2×D17—42no—
390C2×D17—42no—
391C2×D17—42no—
392C2×D17—42no—
393C2×D17—42no—
394C2×D17—42no—
395C2×D17—42no—
396C4×C17—24no—
397C4×C17—42no—
398C4×C17—44no—
399C4×C17—44no—
400C4×C17#38818yescomplemented
401Dic17—24no—
402Dic17—24no—
403Dic17—42no—
404Dic17—82no—
405Dic17—82no—
406C24×C4—171no—
407C22×C4⋊C4—171no—
408C22×C4⋊C4—171no—
409C22×C4⋊C4—172no—
410C22×C4⋊C4—172no—
411C22×C4⋊C4C2×D1711yescharacteristic
412C22×C4⋊C4C2×D1711yescharacteristic
413C22×C22⋊C4—171no—
414C22×C22⋊C4—171no—
415C22×C22⋊C4—172no—
416C22×C22⋊C4—172no—
417C22×C42—171no—
418C22×C42C2×D1712yes—
419C22×C42C2×D1711yescharacteristic
420#388—348no—
421#384—344no—
422#380—344no—
423#380—344no—
424C4×C4⋊C4—24no—
425C4×C22⋊C4—178no—
426C2×#95—171no—
427C2×#95—171no—
428C2×#95—172no—
429C2×#95—172no—
430C2×#95—172no—
431C2×#95—172no—
432C2×#95—172no—
433C2×#95—172no—
434C2×#95C2×D1712yes—
435C2×C17#228511yescharacteristic
436C2×C17C2×#38811yescharacteristic
437C2×C17#231411yescharacteristic
438C2×C17D4×C4⋊C411yescharacteristic
439C2×C17D4×C4⋊C411yescharacteristic
440C2×C17#235211yescharacteristic
441C2×C17#235411yescharacteristic
442C2×C17#242211yescharacteristic
443C2×C17#242311yescharacteristic
444C2×C17#242811yescharacteristic
445C2×C17#242911yescharacteristic
446C2×C17#249111yescharacteristic
447C2×C17#249211yescharacteristic
448C2×C17#249611yescharacteristic
449C2×C17#249711yescharacteristic
450D17—44no—
451C25—171no—
452C23×C4—171no—
453C23×C4—171no—
454C23×C4—171no—
455C23×C4—174no—
456C23×C4—172no—
457C23×C4—172no—
458C23×C4—342no—
459C23×C4—342no—
460C23×C4—342no—
461C23×C4—342no—
462C23×C4—342no—
463C23×C4—342no—
464C23×C4C22×D1711yescharacteristic
465C23×C4C22×D1712yes—
466C23×C4C22×D1712yes—
467C23×C4C22×D1711yescharacteristic
468C23×C4C22×D1711yescharacteristic
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—344no—
474C2×C4⋊C4—344no—
475C2×C4⋊C4—342no—
476C2×C4⋊C4—344no—
477C2×C4⋊C4—344no—
478C2×C4⋊C4—342no—
479C2×C4⋊C4—342no—
480C2×C4⋊C4—342no—
481C2×C4⋊C4—342no—
482C2×C4⋊C4—342no—
483C2×C4⋊C4—682no—
484C2×C4⋊C4—682no—
485C2×C4⋊C4D6814yes—
486C2×C4⋊C4C22⋊D1714yes—
487C2×C22⋊C4—174no—
488C2×C22⋊C4—174no—
489C2×C22⋊C4—174no—
490C2×C22⋊C4—174no—
491C2×C22⋊C4—342no—
492C2×C22⋊C4—342no—
493C2×C22⋊C4—344no—
494C2×C22⋊C4—344no—
495C2×C22⋊C4—344no—
496C2×C22⋊C4—344no—
497C2×C22⋊C4—682no—
498C2×C22⋊C4—682no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—24no—
502C2×C42—24no—
503C2×C42—42no—
504C2×C42—174no—
505C2×C42—342no—
506C2×C42—342no—
507C2×C42C4×D1714yes—
508#95—24no—
509#95—174no—
510#95—174no—
511#95—344no—
512#95—344no—
513#95—344no—
514#95—344no—
515#95—344no—
516#95—682no—
517C17#1387611yescharacteristic, complemented, Sylow
518C24—172no—
519C24—172no—
520C24—172no—
521C24—341no—
522C24—341no—
523C24—341no—
524C24—341no—
525C24—341no—
526C24—341no—
527C24—341no—
528C24—341no—
529C24—341no—
530C24—341no—
531C24—341no—
532C24—341no—
533C24C23×D1711yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—172no—
557C22×C4—172no—
558C22×C4—172no—
559C22×C4—172no—
560C22×C4—172no—
561C22×C4—172no—
562C22×C4—172no—
563C22×C4—341no—
564C22×C4—341no—
565C22×C4—341no—
566C22×C4—341no—
567C22×C4—341no—
568C22×C4—341no—
569C22×C4—341no—
570C22×C4—341no—
571C22×C4—341no—
572C22×C4—341no—
573C22×C4—341no—
574C22×C4—341no—
575C22×C4—341no—
576C22×C4—341no—
577C22×C4—348no—
578C22×C4—348no—
579C22×C4—348no—
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×C4—342no—
594C22×C4—684no—
595C22×C4—684no—
596C22×C4—684no—
597C22×C4—684no—
598C22×C4C2×C4×D1712yes—
599C22×C4C2×C4×D1712yes—
600C22×C4C2×C4×D1712yes—
601C22×C4C2×D6814yes—
602C22×C4C2×D6812yes—
603C22×C4#6325212yes—
604C22×C4#6325212yes—
605C22×C4#6325212yes—
606C22×C4#6325212yes—
607C22×C4D4×D1712yes—
608C22×C4Q8×D1712yes—
609C22×C4C2×C22⋊D1714yes—
610C22×C4C2×C22⋊D1712yes—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—688no—
614C4⋊C4—688no—
615C4⋊C4—684no—
616C4⋊C4—684no—
617C22⋊C4—1716no—
618C22⋊C4—348no—
619C22⋊C4—688no—
620C22⋊C4—688no—
621C42—28no—
622C42—48no—
623C42—348no—
624C23—174no—
625C23—342no—
626C23—342no—
627C23—342no—
628C23—342no—
629C23—342no—
630C23—342no—
631C23—342no—
632C23—342no—
633C23—342no—
634C23—342no—
635C23—342no—
636C23—342no—
637C23—342no—
638C23—342no—
639C23—342no—
640C23—342no—
641C23—342no—
642C23—342no—
643C23—681no—
644C23—681no—
645C23—681no—
646C23—681no—
647C23—681no—
648C23—681no—
649C23—681no—
650C23—681no—
651C23—681no—
652C23—681no—
653C23—681no—
654C23—681no—
655C23—681no—
656C23—681no—
657C23—681no—
658C23—681no—
659C23C22×C4×D1711yescharacteristic
660C23C22×D6811yescharacteristic
661C23C2×#6325211yescharacteristic
662C23C2×#6325211yescharacteristic
663C23C2×#6325211yescharacteristic
664C23C2×#6325211yescharacteristic
665C23C2×D4×D1711yescharacteristic
666C23#1058769111yescharacteristic
667C23C2×Q8×D1711yescharacteristic
668C23#1058769411yescharacteristic
669C23#41×D1711yescharacteristic
670C23#41×D1711yescharacteristic
671C23#1058769611yescharacteristic
672C23#1058769711yescharacteristic
673C23C22×C22⋊D1711yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—174no—
702C2×C4—174no—
703C2×C4—342no—
704C2×C4—342no—
705C2×C4—342no—
706C2×C4—342no—
707C2×C4—342no—
708C2×C4—342no—
709C2×C4—342no—
710C2×C4—342no—
711C2×C4—342no—
712C2×C4—342no—
713C2×C4—342no—
714C2×C4—342no—
715C2×C4—342no—
716C2×C4—342no—
717C2×C4—342no—
718C2×C4—681no—
719C2×C4—681no—
720C2×C4—681no—
721C2×C4—681no—
722C2×C4—6816no—
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—682no—
736C2×C4—682no—
737C2×C4#1058755814yes—
738C2×C4C4×D6814yes—
739C2×C4#1058756114yes—
740C2×C4#1058756214yes—
741C2×C4C4⋊C4×D1714yes—
742C2×C4C4×C22⋊D1714yes—
743C2×C4#1058761514yes—
744C2×C4#1058761614yes—
745C22—344no—
746C22—344no—
747C22—344no—
748C22—682no—
749C22—682no—
750C22—682no—
751C22—682no—
752C22—682no—
753C22—682no—
754C22—682no—
755C22—682no—
756C22—682no—
757C22—682no—
758C22—682no—
759C22—682no—
760C22C2×C4⋊C4×D1711yescharacteristic
761C22#117×D1711yescharacteristic
762C22C2×#1058755811yescharacteristic
763C22C2×C4×C22⋊D1711yescharacteristic
764C22C2×C4×D6811yescharacteristic
765C22#1176328911yescharacteristic
766C22#1176329011yescharacteristic
767C22C2×#1058761611yescharacteristic
768C22C2×#1058761511yescharacteristic
769C22C2×#1058756111yescharacteristic
770C22C2×#1058756211yescharacteristic
771C22#1176335611yescharacteristic
772C22#1176335611yescharacteristic
773C22#1176336311yescharacteristic
774C22#1176336311yescharacteristic
775C22#1176341011yescharacteristic
776C22#1176341711yescharacteristic
777C22#1176342411yescharacteristic
778C22#1176343111yescharacteristic
779C22D4×C22⋊D1711yescharacteristic
780C22D4×D6811yescharacteristic
781C22#1176345411yescharacteristic
782C22#1176345811yescharacteristic
783C22#1176346011yescharacteristic
784C22#1176346411yescharacteristic
785C22#1176347111yescharacteristic
786C22Q8×C22⋊D1711yescharacteristic
787C22Q8×D6811yescharacteristic
788C22#1176347811yescharacteristic
789C22#1176350011yescharacteristic
790C22#1176350911yescharacteristic
791C22#1176351411yescharacteristic
792C22#1176351911yescharacteristic
793C22#1176352211yescharacteristic
794C22#1176352711yescharacteristic
795C4—24no—
796C4—44no—
797C4—42no—
798C4—44no—
799C4—344no—
800C4—344no—
801C4—682no—
802C4—1362no—
803C4—1362no—
804C4#1176270018yescomplemented
805C2—684no—
806C2#1453118811yescharacteristic
807C2C2×#1176270011yescharacteristic
808C2#1453138911yescharacteristic
809C2C4⋊C4×C22⋊D1711yescharacteristic
810C2C4⋊C4×D6811yescharacteristic
811C2#1453171611yescharacteristic
812C2#1453173411yescharacteristic
813C2#1453229211yescharacteristic
814C2#1453230311yescharacteristic
815C2#1453236611yescharacteristic
816C2#1453237711yescharacteristic
817C2#1453314111yescharacteristic
818C2#1453315211yescharacteristic
819C2#1453320011yescharacteristic
820C2#1453321111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C4×C4⋊C4×C17C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenterC2×C4×C4⋊C4D17
hypocenterC17#13876
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11762678C2semidirect
6. #14527039C2semidirect
8. #14527017C2semidirect
9. #14527014C2semidirect
10. #14527013C2semidirect
11. C2×C4×C4⋊C4×C17C2semidirect
26. C4×#63227C4semidirect
207. #63227C4⋊C4semidirect
339. C2×C4×C4⋊C4D17semidirect
400. C4×C17#388semidirect
517. C17#13876semidirect
804. C4#11762700semidirect

Maximal subgroups

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

subgroupindex
C2×#117627002
C2×#117626782
C2×#117626662
C2×C4×#632272
#145270392
#145270282
#145270172
#145270142
#145270132
C2×C4×C4⋊C4×C172
#1387617