Finite Group Databasebeta

← #16957714

Subgroups — #16957714

Order 4352.

2474 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587567C211yesmaximal, characteristic
2C2×#11762709C211yesmaximal, characteristic
3C2×#11762709C211yesmaximal, characteristic
4C2×#11762706C211yesmaximal, characteristic, complemented
5C2×#11762684C211yesmaximal, characteristic, complemented
6C2×#11762683C211yesmaximal, characteristic, complemented
7C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
8#14527030C211yesmaximal, characteristic, complemented
9#14527027C211yesmaximal, characteristic, complemented
10#14527026C211yesmaximal, characteristic, complemented
11#14527012C211yesmaximal, characteristic, complemented
12#14527012C211yesmaximal, characteristic, complemented
13#14527006C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C2×#10587567—24no—
20C2×#10587567—24no—
21C2×#10587567—24no—
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C4⋊Dic17C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×C22⋊Dic17C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36C22×C4×Dic17C2211yescharacteristic
37C22×C4×Dic17C2211yescharacteristic
38#11762709—24no—
39#11762709C418yescomplemented
40#11762706—24no—
41#11762684—24no—
42#11762683—24no—
43C4⋊C4×Dic17—24no—
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C22×C4⋊C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C22×C22⋊C4×C17C2211yescharacteristic
56C22×C22⋊C4×C17C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C2×C17×#95C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C25×C17C2311yescharacteristic
61C24×D17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C22×C22⋊D17—22no—
69C22×C22⋊D17—22no—
70C22×C22⋊D17—22no—
71C22×C22⋊D17—22no—
72C22×C22⋊D17C2×C414yes—
73C22×C22⋊D17D414yes—
74C22×C22⋊D17Q814yes—
75C23×Dic17—22no—
76C23×Dic17—22no—
77C23×Dic17—22no—
78C23×Dic17—22no—
79C23×Dic17—22no—
80C23×Dic17—41no—
81C23×Dic17—41no—
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C22×C4×D17—22no—
90C22×C4×D17—22no—
91C22×C4×D17—22no—
92C22×C4×D17—22no—
93C22×C4×D17—22no—
94C22×C4×D17—41no—
95C22×C4×D17—41no—
96C2×C4⋊C4×C17—22no—
97C2×C4⋊C4×C17—22no—
98C2×C4⋊C4×C17—22no—
99C2×C22⋊C4×C17—22no—
100C2×C22⋊C4×C17—22no—
101C2×C22⋊C4×C17—22no—
102C2×C22⋊C4×C17—22no—
103C2×C22⋊C4×C17—22no—
104C2×C22⋊C4×C17—22no—
105C2×C22⋊C4×C17—22no—
106C2×C22⋊C4×C17—41no—
107C2×C22⋊C4×C17C2×C414yescomplemented
108C2×C22⋊Dic17—22no—
109C2×C22⋊Dic17—22no—
110C2×C22⋊Dic17—41no—
111C2×C22⋊Dic17—41no—
112C2×C22⋊Dic17—41no—
113C2×C22⋊Dic17C2×C414yescomplemented
114C2×#63227—22no—
115C2×#63227—22no—
116C2×#63227—22no—
117C2×#63227—22no—
118C2×#63227—22no—
119C2×#63227—22no—
120C2×#63227—22no—
121C2×#63227—22no—
122C2×#63227—22no—
123C2×#63227—41no—
124C2×#63227—41no—
125C2×#63227—41no—
126C2×#63227—41no—
127C2×#63227C2×C414yescomplemented
128C2×#63227C2×C414yescomplemented
129C2×C4⋊Dic17—22no—
130C2×C4⋊Dic17—22no—
131C2×C4⋊Dic17—22no—
132C2×C4⋊Dic17—22no—
133C2×C4⋊Dic17—41no—
134C2×C4⋊Dic17D414yescomplemented
135C2×#63225—22no—
136C2×#63225—22no—
137C2×#63225—22no—
138C2×#63225—22no—
139C2×#63225—22no—
140C2×#63225—22no—
141C2×#63225—22no—
142C2×#63225—22no—
143C2×#63225—22no—
144C2×#63225—41no—
145C2×#63225C2×C414yescomplemented
146C2×#63225D414yes—
147C2×C4×Dic17—22no—
148C2×C4×Dic17—22no—
149C2×C4×Dic17—22no—
150C2×C4×Dic17—22no—
151C2×C4×Dic17—22no—
152C2×C4×Dic17—22no—
153C2×C4×Dic17—22no—
154C2×C4×Dic17C2×C414yescomplemented
155C2×C4×Dic17D414yes—
156#10587567—232no—
157C17×#95—22no—
158C17×#95—22no—
159C17×#95—41no—
160#10587502—22no—
161#10587502—22no—
162#10587502—22no—
163#10587502—22no—
164#10587502—22no—
165#10587502—22no—
166#10587502—41no—
167#10587502—41no—
168#10587502—41no—
169C24×C17—21no—
170C24×C17—21no—
171C24×C17—21no—
172C24×C17—21no—
173C24×C17—21no—
174C24×C17—21no—
175C24×C17—21no—
176C24×C17—21no—
177C24×C17—21no—
178C24×C17—21no—
179C24×C17—21no—
180C24×C17—21no—
181C24×C17C22×C412yes—
182C24×C17C2×D412yes—
183C24×C17C2×Q812yes—
184C24×C17C2411yescharacteristic
185C23×D17—21no—
186C23×D17—21no—
187C23×D17—21no—
188C23×D17—21no—
189C23×D17—21no—
190C23×D17—21no—
191C23×D17—21no—
192C23×D17—21no—
193C23×D17—21no—
194C23×D17—21no—
195C23×D17—21no—
196C23×D17—21no—
197C23×D17C22×C412yes—
198C23×D17C2×D412yes—
199C23×D17C2×Q812yes—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17—21no—
226C22×C4×C17—21no—
227C22×C4×C17—21no—
228C22×C4×C17—21no—
229C22×C4×C17—21no—
230C22×C4×C17—21no—
231C22×C4×C17—21no—
232C22×C4×C17—21no—
233C22×C4×C17—21no—
234C22×C4×C17—21no—
235C22×C4×C17C22×C412yes—
236C22×C4×C17C22×C412yes—
237C22×C4×C17C2×D412yes—
238C22×C4×C17C2×D412yes—
239C22×C4×C17C2×D412yes—
240C22×C4×C17#4112yes—
241C22×C4×C17#4112yes—
242C2×C22⋊D17—28no—
243C2×C22⋊D17—28no—
244C2×C22⋊D17—28no—
245C2×C22⋊D17—28no—
246C2×C22⋊D17—28no—
247C2×C22⋊D17—28no—
248C2×C22⋊D17C4⋊C4116yescomplemented
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—28no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17—21no—
272C22×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17—21no—
278C22×Dic17—21no—
279C22×Dic17—21no—
280C22×Dic17—21no—
281C22×Dic17—21no—
282C22×Dic17—21no—
283C22×Dic17—21no—
284C22×Dic17—21no—
285C22×Dic17—44no—
286C22×Dic17—44no—
287C22×Dic17—44no—
288C22×Dic17—44no—
289C22×Dic17—44no—
290C22×Dic17—44no—
291C22×Dic17C22×C412yes—
292C22×Dic17C22×C412yes—
293C22×Dic17C22×C412yes—
294C22×Dic17C2×D412yes—
295C22×Dic17C2×D412yes—
296C22×Dic17C2×D412yes—
297C22×Dic17C2×D412yes—
298C22×Dic17C2×D412yes—
299C22×Dic17C2×D412yes—
300C22×Dic17C2×D412yes—
301C22×Dic17C2×Q812yes—
302C22×Dic17#4112yes—
303C22×Dic17#4112yes—
304C22×Dic17#4112yes—
305C2×C4×D17—28no—
306C2×C4×D17—44no—
307C2×C4×D17—44no—
308C2×C4×D17—44no—
309C2×C4×D17—44no—
310C2×C4×D17—44no—
311C2×C4×D17—44no—
312C4⋊C4×C17—28no—
313C22⋊C4×C17—28no—
314C22⋊C4×C17—28no—
315C22⋊C4×C17—44no—
316C22⋊Dic17—44no—
317C22⋊Dic17—44no—
318#63227—28no—
319#63227—28no—
320#63227—44no—
321#63227—44no—
322#63227—44no—
323C4⋊Dic17—28no—
324C4⋊Dic17—44no—
325#63225—28no—
326#63225—28no—
327#63225—44no—
328#63225—44no—
329C4×Dic17—28no—
330C4×Dic17—28no—
331C4×Dic17—44no—
332#14018—171nomaximal, Sylow
333C23×C17—22no—
334C23×C17—22no—
335C23×C17—22no—
336C23×C17—22no—
337C23×C17—22no—
338C23×C17—22no—
339C23×C17—22no—
340C23×C17—22no—
341C23×C17—22no—
342C23×C17—22no—
343C23×C17—22no—
344C23×C17—22no—
345C23×C17—22no—
346C23×C17—22no—
347C23×C17—22no—
348C23×C17—22no—
349C23×C17—22no—
350C23×C17—22no—
351C23×C17—41no—
352C23×C17—41no—
353C23×C17—41no—
354C23×C17—41no—
355C23×C17—41no—
356C23×C17—41no—
357C23×C17—41no—
358C23×C17—41no—
359C23×C17—41no—
360C23×C17—41no—
361C23×C17—41no—
362C23×C17—41no—
363C23×C17—41no—
364C23×C17—41no—
365C23×C17—41no—
366C23×C17—41no—
367C23×C17C2×C4⋊C414yes—
368C23×C17C23×C411yescharacteristic
369C23×C17C22×D411yescharacteristic
370C23×C17C22×D411yescharacteristic
371C23×C17C22×D411yescharacteristic
372C23×C17C22×D411yescharacteristic
373C23×C17C22×Q811yescharacteristic
374C23×C17C2×#4111yescharacteristic
375C23×C17C2×#4111yescharacteristic
376C23×C17C2×#4111yescharacteristic
377C23×C17C2×#4111yescharacteristic
378C23×C17C2×#4111yescharacteristic
379C23×C17H(5,𝔽2)11yescharacteristic
380C23×C17H(5,𝔽2)11yescharacteristic
381C23×C17H(5,𝔽2)11yescharacteristic
382C23×C172−1+411yescharacteristic
383C22×D17—22no—
384C22×D17—22no—
385C22×D17—22no—
386C22×D17—22no—
387C22×D17—22no—
388C22×D17—22no—
389C22×D17—22no—
390C22×D17—22no—
391C22×D17—22no—
392C22×D17—22no—
393C22×D17—22no—
394C22×D17—22no—
395C22×D17—22no—
396C22×D17—22no—
397C22×D17—22no—
398C22×D17—22no—
399C22×D17—22no—
400C22×D17—22no—
401C22×D17—41no—
402C22×D17—41no—
403C22×D17—41no—
404C22×D17—41no—
405C22×D17—41no—
406C22×D17—41no—
407C22×D17—41no—
408C22×D17—41no—
409C22×D17—41no—
410C22×D17—41no—
411C22×D17—41no—
412C22×D17—41no—
413C22×D17—41no—
414C22×D17—41no—
415C22×D17—41no—
416C22×D17—41no—
417C22×D17C2×C4⋊C414yes—
418C2×C4×C17—22no—
419C2×C4×C17—22no—
420C2×C4×C17—22no—
421C2×C4×C17—22no—
422C2×C4×C17—22no—
423C2×C4×C17—22no—
424C2×C4×C17—22no—
425C2×C4×C17—22no—
426C2×C4×C17—22no—
427C2×C4×C17—22no—
428C2×C4×C17—22no—
429C2×C4×C17—22no—
430C2×C4×C17—22no—
431C2×C4×C17—22no—
432C2×C4×C17—22no—
433C2×C4×C17—22no—
434C2×C4×C17—22no—
435C2×C4×C17—22no—
436C2×C4×C17—41no—
437C2×C4×C17—41no—
438C2×C4×C17—41no—
439C2×C4×C17—41no—
440C2×C4×C17—41no—
441C2×C4×C17—41no—
442C2×C4×C17—41no—
443C2×C4×C17—41no—
444C2×C4×C17—41no—
445C2×C4×C17—41no—
446C2×C4×C17—41no—
447C2×C4×C17—41no—
448C2×C4×C17—41no—
449C2×C4×C17—41no—
450C2×C4×C17—41no—
451C2×C4×C17—41no—
452C2×C4×C17—41no—
453C2×C4×C17—41no—
454C2×C4×C17—41no—
455C2×C4×C17—41no—
456C2×C4×C17—41no—
457C2×C4×C17—41no—
458C2×C4×C17—41no—
459C2×C4×C17C4×D414yescomplemented
460C22⋊D17—232no—
461C2×Dic17—22no—
462C2×Dic17—22no—
463C2×Dic17—22no—
464C2×Dic17—22no—
465C2×Dic17—22no—
466C2×Dic17—22no—
467C2×Dic17—22no—
468C2×Dic17—22no—
469C2×Dic17—22no—
470C2×Dic17—22no—
471C2×Dic17—22no—
472C2×Dic17—22no—
473C2×Dic17—22no—
474C2×Dic17—22no—
475C2×Dic17—22no—
476C2×Dic17—22no—
477C2×Dic17—22no—
478C2×Dic17—22no—
479C2×Dic17—416no—
480C2×Dic17—41no—
481C2×Dic17—41no—
482C2×Dic17—41no—
483C2×Dic17—41no—
484C2×Dic17—41no—
485C2×Dic17—41no—
486C2×Dic17—41no—
487C2×Dic17—41no—
488C2×Dic17—41no—
489C2×Dic17—41no—
490C2×Dic17—41no—
491C2×Dic17—41no—
492C2×Dic17—41no—
493C2×Dic17—41no—
494C2×Dic17—41no—
495C2×Dic17—41no—
496C2×Dic17—41no—
497C2×Dic17—41no—
498C2×Dic17—41no—
499C2×Dic17—41no—
500C2×Dic17—41no—
501C2×Dic17—41no—
502C2×Dic17—41no—
503C2×Dic17C2×C4⋊C414yes—
504C2×Dic17C4×D414yes—
505C2×Dic17C4×D414yes—
506C2×Dic17#12014yes—
507C2×Dic17#12114yes—
508C2×Dic17C22⋊Q814yes—
509C2×Dic17C22⋊Q814yes—
510C2×Dic17#12314yes—
511C4×D17—416no—
512C22×C4×D4—171no—
513C2×#390—171no—
514C2×#390—171no—
515C2×#389—171no—
516C2×#385—171no—
517C2×#385—171no—
518C2×C4×C4⋊C4—171no—
519#1439—171no—
520#1439—171no—
521#1439—171no—
522#1439D1711yescharacteristic, complemented
523C4⋊#95—171no—
524C4⋊#95—171no—
525C22⋊#95—171no—
526C22⋊#95—171no—
527C22×C17—24no—
528C22×C17—24no—
529C22×C17—24no—
530C22×C17—42no—
531C22×C17—42no—
532C22×C17—42no—
533C22×C17—42no—
534C22×C17—42no—
535C22×C17—42no—
536C22×C17—42no—
537C22×C17—42no—
538C22×C17—42no—
539C22×C17—42no—
540C22×C17—42no—
541C22×C17—42no—
542C22×C17C22×C4⋊C411yescharacteristic
543C22×C17C2×C4×D411yescharacteristic
544C22×C17C2×C4×D411yescharacteristic
545C22×C17C2×C4×D411yescharacteristic
546C22×C17C4×#4111yescharacteristic
547C22×C17#51811yescharacteristic
548C22×C17#52011yescharacteristic
549C22×C17C2×#12011yescharacteristic
550C22×C17C2×#12111yescharacteristic
551C22×C17C2×C22⋊Q811yescharacteristic
552C22×C17C2×C22⋊Q811yescharacteristic
553C22×C17C2×#12311yescharacteristic
554C22×C17#52511yescharacteristic
555C22×C17#52911yescharacteristic
556C22×C17#53211yescharacteristic
557C22×C17#53511yescharacteristic
558C22×C17#53711yescharacteristic
559C22×C17#54011yescharacteristic
560C22×C17#54211yescharacteristic
561C22×C17D4211yescharacteristic
562C22×C17D4211yescharacteristic
563C22×C17#54611yescharacteristic
564C22×C17#54611yescharacteristic
565C22×C17#54611yescharacteristic
566C22×C17#54711yescharacteristic
567C22×C17#54811yescharacteristic
568C22×C17D4×Q811yescharacteristic
569C22×C17#55011yescharacteristic
570C22×C17#55011yescharacteristic
571C22×C17#55411yescharacteristic
572C22×C17#55411yescharacteristic
573C22×C17#55411yescharacteristic
574C22×C17#55611yescharacteristic
575C22×C17#55911yescharacteristic
576C22×C17#55911yescharacteristic
577C2×D17—24no—
578C2×D17—24no—
579C2×D17—24no—
580C2×D17—42no—
581C2×D17—42no—
582C2×D17—42no—
583C2×D17—42no—
584C2×D17—42no—
585C2×D17—42no—
586C2×D17—42no—
587C2×D17—42no—
588C2×D17—42no—
589C2×D17—42no—
590C2×D17—42no—
591C2×D17—42no—
592C4×C17—24no—
593C4×C17—42no—
594C4×C17—42no—
595C4×C17—42no—
596C4×C17—42no—
597C4×C17—81no—
598Dic17—24no—
599Dic17—42no—
600Dic17—42no—
601Dic17—42no—
602Dic17—42no—
603Dic17—81no—
604Dic17#38518yescomplemented
605C23×D4—171no—
606C24×C4—171no—
607C24×C4—171no—
608C2×C4×D4—344no—
609C2×C4×D4—344no—
610C2×C4×D4—344no—
611C22×C4⋊C4—171no—
612C22×C4⋊C4—171no—
613C22×C4⋊C4—171no—
614C22×C4⋊C4—171no—
615C22×C4⋊C4—171no—
616C22×C4⋊C4—171no—
617C22×C4⋊C4C2×D1711yescharacteristic
618C22×C22⋊C4—171no—
619C22×C22⋊C4—171no—
620C22×C22⋊C4—171no—
621C22×C22⋊C4—171no—
622C22×C22⋊C4—171no—
623C22×C22⋊C4—171no—
624C22×C22⋊C4—171no—
625C22×C22⋊C4C2×D1711yescharacteristic
626C22×C22⋊C4C2×D1711yescharacteristic
627C22×C22⋊C4C2×D1711yescharacteristic
628C22×C42—171no—
629C22×C42—171no—
630C22×C42—171no—
631#390—178no—
632#390—344no—
633#389—344no—
634#385—344no—
635#385—344no—
636C4×C4⋊C4—344no—
637C2×#95—171no—
638C2×#95—171no—
639C2×#95—171no—
640C2×#95—171no—
641C2×#95—171no—
642C2×#95—171no—
643C2×#95—171no—
644C2×#95—171no—
645C2×#95—171no—
646C2×#95C2×D1711yescharacteristic
647C2×#95C2×D1711yescharacteristic
648C2×#95C2×D1711yescharacteristic
649C2×C17—44no—
650C2×C17C2×#38511yescharacteristic
651C2×C17C4×#12111yescharacteristic
652C2×C17#232411yescharacteristic
653C2×C17D4×C4⋊C411yescharacteristic
654C2×C17#234911yescharacteristic
655C2×C17#236611yescharacteristic
656C2×C17#236711yescharacteristic
657C2×C17#240711yescharacteristic
658C2×C17#240811yescharacteristic
659C2×C17#244511yescharacteristic
660C2×C17#244711yescharacteristic
661C2×C17#245211yescharacteristic
662C2×C17#245411yescharacteristic
663C2×C17#253811yescharacteristic
664C2×C17#258011yescharacteristic
665D17—44no—
666C25—171no—
667C25C22×D1711yescharacteristic
668C22×D4—174no—
669C22×D4—174no—
670C22×D4—174no—
671C22×D4—342no—
672C22×D4—342no—
673C22×D4—342no—
674C22×D4—342no—
675C23×C4—171no—
676C23×C4—171no—
677C23×C4—171no—
678C23×C4—171no—
679C23×C4—171no—
680C23×C4—171no—
681C23×C4—171no—
682C23×C4—342no—
683C23×C4—342no—
684C23×C4—342no—
685C23×C4—342no—
686C23×C4—342no—
687C23×C4—342no—
688C23×C4—342no—
689C23×C4—342no—
690C23×C4—342no—
691C23×C4—342no—
692C23×C4—681no—
693C23×C4—681no—
694C23×C4—681no—
695C23×C4—681no—
696C23×C4C22×D1711yescharacteristic
697C23×C4C22×D1711yescharacteristic
698C23×C4C22×D1711yescharacteristic
699C23×C4C22×D1711yescharacteristic
700C23×C4C22×D1711yescharacteristic
701C23×C4C22×D1711yescharacteristic
702C4×D4—3432no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4—174no—
707C2×C4⋊C4—174no—
708C2×C4⋊C4—174no—
709C2×C4⋊C4—342no—
710C2×C4⋊C4—342no—
711C2×C4⋊C4—342no—
712C2×C4⋊C4—342no—
713C2×C4⋊C4—342no—
714C2×C4⋊C4—342no—
715C2×C4⋊C4—342no—
716C2×C4⋊C4—342no—
717C2×C4⋊C4—342no—
718C2×C4⋊C4—342no—
719C2×C4⋊C4—342no—
720C2×C4⋊C4—342no—
721C2×C4⋊C4—342no—
722C2×C4⋊C4—681no—
723C2×C4⋊C4—681no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—41no—
732C2×C22⋊C4—174no—
733C2×C22⋊C4—174no—
734C2×C22⋊C4—174no—
735C2×C22⋊C4—342no—
736C2×C22⋊C4—342no—
737C2×C22⋊C4—342no—
738C2×C22⋊C4—342no—
739C2×C22⋊C4—342no—
740C2×C22⋊C4—342no—
741C2×C22⋊C4—342no—
742C2×C22⋊C4—342no—
743C2×C22⋊C4—342no—
744C2×C22⋊C4—342no—
745C2×C22⋊C4—342no—
746C2×C22⋊C4—681no—
747C2×C22⋊C4—681no—
748C2×C22⋊C4—681no—
749C2×C22⋊C4—681no—
750C2×C22⋊C4—681no—
751C2×C22⋊C4—681no—
752C2×C22⋊C4—681no—
753C2×C22⋊C4C4×D1714yescomplemented
754C2×C42—174no—
755C2×C42—174no—
756C2×C42—342no—
757C2×C42—342no—
758C2×C42—342no—
759C2×C42—342no—
760C2×C42—342no—
761C2×C42—342no—
762C2×C42—342no—
763#95—22no—
764#95—22no—
765#95—41no—
766#95—342no—
767#95—342no—
768#95—342no—
769#95—342no—
770#95—342no—
771#95—342no—
772#95—681no—
773#95—681no—
774#95—681no—
775C17#1401811yescharacteristic, complemented, Sylow
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—172no—
789C24—172no—
790C24—172no—
791C24—341no—
792C24—341no—
793C24—341no—
794C24—341no—
795C24—341no—
796C24—341no—
797C24—341no—
798C24—341no—
799C24—341no—
800C24—341no—
801C24—341no—
802C24—341no—
803C24C2×C4×D1712yes—
804C24D4×D1712yes—
805C24Q8×D1712yes—
806C24C23×D1711yescharacteristic
807C2×D4—1716no—
808C2×D4—348no—
809C2×D4—348no—
810C2×D4—348no—
811C2×D4—348no—
812C2×D4—348no—
813C2×D4—348no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—172no—
850C22×C4—172no—
851C22×C4—172no—
852C22×C4—172no—
853C22×C4—172no—
854C22×C4—172no—
855C22×C4—172no—
856C22×C4—172no—
857C22×C4—172no—
858C22×C4—172no—
859C22×C4—172no—
860C22×C4—172no—
861C22×C4—172no—
862C22×C4—172no—
863C22×C4—348no—
864C22×C4—341no—
865C22×C4—341no—
866C22×C4—341no—
867C22×C4—341no—
868C22×C4—348no—
869C22×C4—341no—
870C22×C4—341no—
871C22×C4—341no—
872C22×C4—341no—
873C22×C4—341no—
874C22×C4—341no—
875C22×C4—341no—
876C22×C4—341no—
877C22×C4—341no—
878C22×C4—341no—
879C22×C4—341no—
880C22×C4—341no—
881C22×C4—341no—
882C22×C4—341no—
883C22×C4—341no—
884C22×C4—341no—
885C22×C4—341no—
886C22×C4—341no—
887C22×C4—341no—
888C22×C4—341no—
889C22×C4—341no—
890C22×C4—341no—
891C22×C4—341no—
892C22×C4—341no—
893C22×C4—341no—
894C22×C4—341no—
895C22×C4—341no—
896C22×C4—341no—
897C22×C4—341no—
898C22×C4—341no—
899C22×C4—341no—
900C22×C4—684no—
901C22×C4—684no—
902C22×C4—684no—
903C22×C4—684no—
904C22×C4—684no—
905C22×C4—684no—
906C22×C4—684no—
907C22×C4—684no—
908C22×C4—684no—
909C22×C4—684no—
910C22×C4—684no—
911C22×C4—684no—
912C22×C4C2×C4×D1712yes—
913C22×C4C2×C4×D1712yes—
914C22×C4D4×D1712yes—
915C22×C4D4×D1712yes—
916C22×C4D4×D1712yes—
917C22×C4#6325412yes—
918C22×C4#6325412yes—
919C4⋊C4—28no—
920C4⋊C4—348no—
921C4⋊C4—348no—
922C4⋊C4—348no—
923C4⋊C4—684no—
924C4⋊C4—684no—
925C4⋊C4—684no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—44no—
929C22⋊C4—348no—
930C22⋊C4—348no—
931C22⋊C4—684no—
932C22⋊C4—684no—
933C22⋊C4—684no—
934C22⋊C4—684no—
935C22⋊C4—684no—
936C42—348no—
937C42—348no—
938C42—684no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—174no—
974C23—342no—
975C23—342no—
976C23—342no—
977C23—342no—
978C23—342no—
979C23—342no—
980C23—342no—
981C23—342no—
982C23—342no—
983C23—342no—
984C23—342no—
985C23—342no—
986C23—342no—
987C23—342no—
988C23—342no—
989C23—342no—
990C23—342no—
991C23—342no—
992C23—681no—
993C23—681no—
994C23—681no—
995C23—681no—
996C23—681no—
997C23—681no—
998C23—681no—
999C23—681no—
1000C23—681no—
1001C23—681no—
1002C23—681no—
1003C23—681no—
1004C23—681no—
1005C23—681no—
1006C23—681no—
1007C23—681no—
1008C23C4⋊C4×D1714yes—
1009C23C22×C4×D1711yescharacteristic
1010C23C2×D4×D1711yescharacteristic
1011C23C2×D4×D1711yescharacteristic
1012C23C2×D4×D1711yescharacteristic
1013C23C2×D4×D1711yescharacteristic
1014C23C2×#6325411yescharacteristic
1015C23C2×#6325411yescharacteristic
1016C23#1058769111yescharacteristic
1017C23C2×Q8×D1711yescharacteristic
1018C23#41×D1711yescharacteristic
1019C23#41×D1711yescharacteristic
1020C23#41×D1711yescharacteristic
1021C23#1058769611yescharacteristic
1022C23#1058769611yescharacteristic
1023C23#1058769711yescharacteristic
1024D4—3432no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—174no—
1067C2×C4—174no—
1068C2×C4—174no—
1069C2×C4—174no—
1070C2×C4—174no—
1071C2×C4—174no—
1072C2×C4—174no—
1073C2×C4—174no—
1074C2×C4—342no—
1075C2×C4—342no—
1076C2×C4—342no—
1077C2×C4—342no—
1078C2×C4—342no—
1079C2×C4—342no—
1080C2×C4—342no—
1081C2×C4—342no—
1082C2×C4—342no—
1083C2×C4—342no—
1084C2×C4—342no—
1085C2×C4—342no—
1086C2×C4—342no—
1087C2×C4—342no—
1088C2×C4—342no—
1089C2×C4—342no—
1090C2×C4—342no—
1091C2×C4—342no—
1092C2×C4—6816no—
1093C2×C4—6816no—
1094C2×C4—681no—
1095C2×C4—681no—
1096C2×C4—681no—
1097C2×C4—681no—
1098C2×C4—681no—
1099C2×C4—681no—
1100C2×C4—681no—
1101C2×C4—681no—
1102C2×C4—681no—
1103C2×C4—681no—
1104C2×C4—681no—
1105C2×C4—681no—
1106C2×C4—681no—
1107C2×C4—681no—
1108C2×C4—681no—
1109C2×C4—681no—
1110C2×C4—681no—
1111C2×C4—681no—
1112C2×C4—681no—
1113C2×C4—681no—
1114C2×C4—681no—
1115C2×C4—681no—
1116C2×C4—681no—
1117C2×C4#1058756714yescomplemented
1118C22—24no—
1119C22—24no—
1120C22—24no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—344no—
1134C22—344no—
1135C22—344no—
1136C22—682no—
1137C22—682no—
1138C22—682no—
1139C22—682no—
1140C22—682no—
1141C22—682no—
1142C22—682no—
1143C22—682no—
1144C22—682no—
1145C22—682no—
1146C22—682no—
1147C22—682no—
1148C22C2×C4⋊C4×D1711yescharacteristic
1149C22C4×D4×D1711yescharacteristic
1150C22C4×D4×D1711yescharacteristic
1151C22C2×#1058756711yescharacteristic
1152C22C4×#6325411yescharacteristic
1153C22#1176328111yescharacteristic
1154C22#1176328911yescharacteristic
1155C22#120×D1711yescharacteristic
1156C22#121×D1711yescharacteristic
1157C22C22⋊Q8×D1711yescharacteristic
1158C22C22⋊Q8×D1711yescharacteristic
1159C22#123×D1711yescharacteristic
1160C22#1176331511yescharacteristic
1161C22#1176333611yescharacteristic
1162C22#1176335411yescharacteristic
1163C22#1176337711yescharacteristic
1164C22#1176338611yescharacteristic
1165C22#1176341111yescharacteristic
1166C22#1176342511yescharacteristic
1167C22#1176344311yescharacteristic
1168C22#1176344311yescharacteristic
1169C22#1176344611yescharacteristic
1170C22#1176345111yescharacteristic
1171C22#1176345111yescharacteristic
1172C22#1176345911yescharacteristic
1173C22#1176346511yescharacteristic
1174C22#1176347211yescharacteristic
1175C22#1176347711yescharacteristic
1176C22#1176347911yescharacteristic
1177C22#1176351311yescharacteristic
1178C22#1176351711yescharacteristic
1179C22#1176351711yescharacteristic
1180C22#1176352611yescharacteristic
1181C22#1176354111yescharacteristic
1182C22#1176354111yescharacteristic
1183C4—24no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—81no—
1189C4—178no—
1190C4—344no—
1191C4—682no—
1192C4—682no—
1193C4—682no—
1194C4—682no—
1195C4—1361no—
1196C2—44no—
1197C2—684no—
1198C2D17×#38511yescharacteristic
1199C2#1453129411yescharacteristic
1200C2#1453147211yescharacteristic
1201C2#1453168011yescharacteristic
1202C2#1453169011yescharacteristic
1203C2#1453184511yescharacteristic
1204C2#1453185811yescharacteristic
1205C2#1453212211yescharacteristic
1206C2#1453213511yescharacteristic
1207C2#1453254211yescharacteristic
1208C2#1453256611yescharacteristic
1209C2#1453262711yescharacteristic
1210C2#1453265111yescharacteristic
1211C2#1453370111yescharacteristic
1212C2#1453413711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1439C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1439D17
hypocenterC17#14018
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
4. C2×#11762706C2semidirect
5. C2×#11762684C2semidirect
6. C2×#11762683C2semidirect
7. C2×C4⋊C4×Dic17C2semidirect
8. #14527030C2semidirect
9. #14527027C2semidirect
10. #14527026C2semidirect
11. #14527012C2semidirect
12. #14527012C2semidirect
13. #14527006C2semidirect
14. #14527005C2semidirect
15. C17×#1439C2semidirect
39. #11762709C4semidirect
107. C2×C22⋊C4×C17C2×C4semidirect
113. C2×C22⋊Dic17C2×C4semidirect
127. C2×#63227C2×C4semidirect
128. C2×#63227C2×C4semidirect
134. C2×C4⋊Dic17D4semidirect
145. C2×#63225C2×C4semidirect
154. C2×C4×Dic17C2×C4semidirect
248. C2×C22⋊D17C4⋊C4semidirect
459. C2×C4×C17C4×D4semidirect
522. #1439D17semidirect
604. Dic17#385semidirect
753. C2×C22⋊C4C4×D17semidirect
775. C17#14018semidirect
1117. C2×C4#10587567semidirect

Maximal subgroups

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

subgroupindex
C22×#105875672
C2×#117627092
C2×#117627062
C2×#117626842
C2×#117626832
C2×C4⋊C4×Dic172
#145270302
#145270272
#145270262
#145270122
#145270062
#145270052
C17×#14392
#1401817