Finite Group Databasebeta

← #16957201

Subgroups — #16957201

Order 4352.

2558 conjugacy classes of subgroups.

The subgroup lattice has 1230 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×#11762681C211yesmaximal, characteristic, complemented
8C2×#11762680C211yesmaximal, characteristic, complemented
9C2×#11762678C211yesmaximal, characteristic, complemented
10#14527030C211yesmaximal, characteristic, complemented
11#14527028C211yesmaximal, characteristic, complemented
12#14527027C211yesmaximal, characteristic, complemented
13#14527012C211yesmaximal, characteristic, complemented
14#95×Dic17C211yesmaximal, 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×#63225C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C22×C22⋊Dic17C2211yescharacteristic
31C22×C22⋊Dic17C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×#63227C2211yescharacteristic
36C22×#63227C2211yescharacteristic
37C22×C4×Dic17C2211yescharacteristic
38C22×C4×Dic17C2211yescharacteristic
39C22×C4×Dic17C2211yescharacteristic
40#11762709—24no—
41#11762709C418yescomplemented
42#11762706—24no—
43#11762684—24no—
44#11762683—24no—
45#11762681—24no—
46#11762680—24no—
47#11762678—24no—
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C22×C4⋊C4×C17C2211yescharacteristic
56C22×C22⋊C4×C17C2211yescharacteristic
57C22×C22⋊C4×C17C2211yescharacteristic
58C22×C22⋊C4×C17C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C2×C17×#95C2211yescharacteristic
61C2×C17×#95C2211yescharacteristic
62C25×C17C2311yescharacteristic
63C24×D17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C22×C22⋊D17—22no—
71C22×C22⋊D17—22no—
72C22×C22⋊D17—22no—
73C22×C22⋊D17—22no—
74C22×C22⋊D17C2×C414yes—
75C22×C22⋊D17D414yes—
76C22×C22⋊D17Q814yes—
77C23×Dic17—22no—
78C23×Dic17—22no—
79C23×Dic17—22no—
80C23×Dic17—22no—
81C23×Dic17—22no—
82C23×Dic17—41no—
83C23×Dic17—41no—
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C23×Dic17C2311yescharacteristic
90C23×Dic17C2311yescharacteristic
91C22×C4×D17—22no—
92C22×C4×D17—22no—
93C22×C4×D17—22no—
94C22×C4×D17—22no—
95C22×C4×D17—22no—
96C22×C4×D17—41no—
97C22×C4×D17—41no—
98C2×C4⋊C4×C17—22no—
99C2×C4⋊C4×C17—22no—
100C2×C4⋊C4×C17—41no—
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—22no—
107C2×C22⋊C4×C17—22no—
108C2×C22⋊C4×C17—41no—
109C2×C22⋊C4×C17C2×C414yescomplemented
110C2×C22⋊Dic17—22no—
111C2×C22⋊Dic17—22no—
112C2×C22⋊Dic17—22no—
113C2×C22⋊Dic17—22no—
114C2×C22⋊Dic17—41no—
115C2×C22⋊Dic17C2×C414yescomplemented
116C2×#63227—22no—
117C2×#63227—22no—
118C2×#63227—22no—
119C2×#63227—22no—
120C2×#63227—22no—
121C2×#63227—22no—
122C2×#63227—22no—
123C2×#63227—22no—
124C2×#63227—22no—
125C2×#63227—22no—
126C2×#63227—22no—
127C2×#63227—41no—
128C2×#63227—41no—
129C2×#63227C2×C414yescomplemented
130C2×#63227C2×C414yescomplemented
131C2×C4⋊Dic17—22no—
132C2×C4⋊Dic17—22no—
133C2×C4⋊Dic17—22no—
134C2×C4⋊Dic17—22no—
135C2×C4⋊Dic17—22no—
136C2×C4⋊Dic17—41no—
137C2×#63225—22no—
138C2×#63225—22no—
139C2×#63225—22no—
140C2×#63225—22no—
141C2×#63225—22no—
142C2×#63225—22no—
143C2×#63225—22no—
144C2×#63225—22no—
145C2×#63225—22no—
146C2×#63225—22no—
147C2×#63225—22no—
148C2×#63225—22no—
149C2×#63225—22no—
150C2×#63225—22no—
151C2×#63225—41no—
152C2×#63225—41no—
153C2×#63225C2×C414yescomplemented
154C2×#63225D414yes—
155C2×C4×Dic17—22no—
156C2×C4×Dic17—22no—
157C2×C4×Dic17—22no—
158C2×C4×Dic17—22no—
159C2×C4×Dic17—22no—
160C2×C4×Dic17—22no—
161C2×C4×Dic17—22no—
162C2×C4×Dic17C2×C414yescomplemented
163C2×C4×Dic17D414yes—
164#10587567—232no—
165C17×#95—22no—
166C17×#95—22no—
167C17×#95—22no—
168#10587502—22no—
169#10587502—22no—
170#10587502—22no—
171#10587502—22no—
172#10587502—22no—
173#10587502D414yescomplemented
174#10587502D414yescomplemented
175C24×C17—21no—
176C24×C17—21no—
177C24×C17—21no—
178C24×C17—21no—
179C24×C17—21no—
180C24×C17—21no—
181C24×C17—21no—
182C24×C17—21no—
183C24×C17—21no—
184C24×C17—21no—
185C24×C17—21no—
186C24×C17—21no—
187C24×C17C22×C412yes—
188C24×C17C2×D412yes—
189C24×C17C2×Q812yes—
190C24×C17C2411yescharacteristic
191C23×D17—21no—
192C23×D17—21no—
193C23×D17—21no—
194C23×D17—21no—
195C23×D17—21no—
196C23×D17—21no—
197C23×D17—21no—
198C23×D17—21no—
199C23×D17—21no—
200C23×D17—21no—
201C23×D17—21no—
202C23×D17—21no—
203C23×D17C22×C412yes—
204C23×D17C2×D412yes—
205C23×D17C2×Q812yes—
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×C17—21no—
236C22×C4×C17—21no—
237C22×C4×C17—21no—
238C22×C4×C17—21no—
239C22×C4×C17—21no—
240C22×C4×C17—21no—
241C22×C4×C17C22×C412yes—
242C22×C4×C17C22×C412yes—
243C22×C4×C17C2×D412yes—
244C22×C4×C17C2×D412yes—
245C22×C4×C17C2×D412yes—
246C22×C4×C17C2×D412yes—
247C22×C4×C17#4112yes—
248C2×C22⋊D17—28no—
249C2×C22⋊D17—28no—
250C2×C22⋊D17—28no—
251C2×C22⋊D17—28no—
252C2×C22⋊D17—28no—
253C2×C22⋊D17—28no—
254C2×C22⋊D17C4⋊C4116yescomplemented
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—28no—
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—21no—
286C22×Dic17—21no—
287C22×Dic17—21no—
288C22×Dic17—21no—
289C22×Dic17—44no—
290C22×Dic17—44no—
291C22×Dic17—44no—
292C22×Dic17—44no—
293C22×Dic17—44no—
294C22×Dic17—44no—
295C22×Dic17C22×C412yes—
296C22×Dic17C22×C412yes—
297C22×Dic17C22×C412yes—
298C22×Dic17C2×D412yes—
299C22×Dic17C2×D412yes—
300C22×Dic17C2×D412yes—
301C22×Dic17C2×D412yes—
302C22×Dic17C2×D412yes—
303C22×Dic17C2×D412yes—
304C22×Dic17C2×D412yes—
305C22×Dic17C2×D412yes—
306C22×Dic17C2×D412yes—
307C22×Dic17C2×Q812yes—
308C22×Dic17#4112yes—
309C22×Dic17#4112yes—
310C22×Dic17#4112yes—
311C2×C4×D17—28no—
312C2×C4×D17—44no—
313C2×C4×D17—44no—
314C2×C4×D17—44no—
315C2×C4×D17—44no—
316C2×C4×D17—44no—
317C2×C4×D17—44no—
318C4⋊C4×C17—44no—
319C22⋊C4×C17—28no—
320C22⋊C4×C17—28no—
321C22⋊C4×C17—44no—
322C22⋊Dic17—28no—
323C22⋊Dic17—44no—
324#63227—28no—
325#63227—28no—
326#63227—28no—
327#63227—44no—
328#63227—44no—
329C4⋊Dic17—44no—
330C4⋊Dic17—44no—
331#63225—28no—
332#63225—28no—
333#63225—44no—
334#63225—44no—
335#63225—44no—
336#63225—44no—
337C4×Dic17—28no—
338C4×Dic17—28no—
339C4×Dic17—44no—
340#13977—171nomaximal, Sylow
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—22no—
352C23×C17—22no—
353C23×C17—22no—
354C23×C17—22no—
355C23×C17—22no—
356C23×C17—22no—
357C23×C17—22no—
358C23×C17—22no—
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×C17—41no—
368C23×C17—41no—
369C23×C17—41no—
370C23×C17—41no—
371C23×C17—41no—
372C23×C17—41no—
373C23×C17—41no—
374C23×C17—41no—
375C23×C17C2×C4⋊C414yes—
376C23×C17C23×C411yescharacteristic
377C23×C17C22×D411yescharacteristic
378C23×C17C22×D411yescharacteristic
379C23×C17C22×D411yescharacteristic
380C23×C17C22×D411yescharacteristic
381C23×C17C22×D411yescharacteristic
382C23×C17C22×Q811yescharacteristic
383C23×C17C2×#4111yescharacteristic
384C23×C17C2×#4111yescharacteristic
385C23×C17C2×#4111yescharacteristic
386C23×C17C2×#4111yescharacteristic
387C23×C17H(5,𝔽2)11yescharacteristic
388C23×C17H(5,𝔽2)11yescharacteristic
389C23×C172−1+411yescharacteristic
390C23×C172−1+411yescharacteristic
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—22no—
402C22×D17—22no—
403C22×D17—22no—
404C22×D17—22no—
405C22×D17—22no—
406C22×D17—22no—
407C22×D17—22no—
408C22×D17—22no—
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×D17—41no—
418C22×D17—41no—
419C22×D17—41no—
420C22×D17—41no—
421C22×D17—41no—
422C22×D17—41no—
423C22×D17—41no—
424C22×D17—41no—
425C22×D17C2×C4⋊C414yes—
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—22no—
437C2×C4×C17—22no—
438C2×C4×C17—22no—
439C2×C4×C17—22no—
440C2×C4×C17—22no—
441C2×C4×C17—22no—
442C2×C4×C17—22no—
443C2×C4×C17—22no—
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×C17—41no—
460C2×C4×C17—41no—
461C2×C4×C17—41no—
462C2×C4×C17—41no—
463C2×C4×C17—41no—
464C2×C4×C17—41no—
465C2×C4×C17—41no—
466C2×C4×C17—41no—
467C2×C4×C17C4×D414yescomplemented
468C22⋊D17—232no—
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—22no—
480C2×Dic17—22no—
481C2×Dic17—22no—
482C2×Dic17—22no—
483C2×Dic17—22no—
484C2×Dic17—22no—
485C2×Dic17—22no—
486C2×Dic17—22no—
487C2×Dic17—22no—
488C2×Dic17—22no—
489C2×Dic17—22no—
490C2×Dic17—416no—
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×Dic17—41no—
504C2×Dic17—41no—
505C2×Dic17—41no—
506C2×Dic17—41no—
507C2×Dic17—41no—
508C2×Dic17—41no—
509C2×Dic17—41no—
510C2×Dic17C2×C4⋊C414yes—
511C2×Dic17C4×D414yes—
512C2×Dic17C4×D414yes—
513C2×Dic17C4×D414yescomplemented
514C2×Dic17#12014yes—
515C2×Dic17C22⋊Q814yes—
516C2×Dic17C22⋊Q814yes—
517C2×Dic17#12314yes—
518C2×Dic17#12714yes—
519C4×D17—416no—
520C22×C4×D4—171no—
521C2×#390—171no—
522C2×#390—171no—
523C2×#389—171no—
524C2×#385—171no—
525C2×#385—171no—
526C2×#385—171no—
527C2×#385—171no—
528C2×#384—171no—
529#1439—171no—
530#1439—171no—
531#1439—171no—
532#1439D1711yescharacteristic, complemented
533C4⋊#95—171no—
534C4×#95—171no—
535C22×C17—24no—
536C22×C17—24no—
537C22×C17—24no—
538C22×C17—42no—
539C22×C17—42no—
540C22×C17—42no—
541C22×C17—42no—
542C22×C17—42no—
543C22×C17—42no—
544C22×C17—42no—
545C22×C17—42no—
546C22×C17—42no—
547C22×C17—42no—
548C22×C17—42no—
549C22×C17—42no—
550C22×C17C22×C4⋊C411yescharacteristic
551C22×C17C2×C4×D411yescharacteristic
552C22×C17C2×C4×D411yescharacteristic
553C22×C17C2×C4×D411yescharacteristic
554C22×C17C2×C4×D411yescharacteristic
555C22×C17#52011yescharacteristic
556C22×C17#52011yescharacteristic
557C22×C17C2×#12011yescharacteristic
558C22×C17C2×C22⋊Q811yescharacteristic
559C22×C17C2×C22⋊Q811yescharacteristic
560C22×C17C2×#12311yescharacteristic
561C22×C17C2×#12711yescharacteristic
562C22×C17#53211yescharacteristic
563C22×C17#53211yescharacteristic
564C22×C17#53211yescharacteristic
565C22×C17#53511yescharacteristic
566C22×C17#53611yescharacteristic
567C22×C17#54211yescharacteristic
568C22×C17#54211yescharacteristic
569C22×C17D4211yescharacteristic
570C22×C17D4211yescharacteristic
571C22×C17D4211yescharacteristic
572C22×C17D4211yescharacteristic
573C22×C17#54711yescharacteristic
574C22×C17#54711yescharacteristic
575C22×C17#54711yescharacteristic
576C22×C17#54711yescharacteristic
577C22×C17#54811yescharacteristic
578C22×C17#54811yescharacteristic
579C22×C17D4×Q811yescharacteristic
580C22×C17D4×Q811yescharacteristic
581C22×C17#55311yescharacteristic
582C22×C17#55311yescharacteristic
583C22×C17#55411yescharacteristic
584C22×C17#55411yescharacteristic
585C2×D17—24no—
586C2×D17—24no—
587C2×D17—24no—
588C2×D17—42no—
589C2×D17—42no—
590C2×D17—42no—
591C2×D17—42no—
592C2×D17—42no—
593C2×D17—42no—
594C2×D17—42no—
595C2×D17—42no—
596C2×D17—42no—
597C2×D17—42no—
598C2×D17—42no—
599C2×D17—42no—
600C4×C17—24no—
601C4×C17—42no—
602C4×C17—42no—
603C4×C17—42no—
604C4×C17—42no—
605C4×C17—81no—
606Dic17—24no—
607Dic17—24no—
608Dic17—42no—
609Dic17—42no—
610Dic17—42no—
611Dic17—81no—
612Dic17#38518yescomplemented
613C23×D4—171no—
614C24×C4—171no—
615C24×C4—171no—
616C2×C4×D4—344no—
617C2×C4×D4—344no—
618C2×C4×D4—344no—
619C22×C4⋊C4—171no—
620C22×C4⋊C4—171no—
621C22×C4⋊C4—171no—
622C22×C4⋊C4—171no—
623C22×C4⋊C4—171no—
624C22×C4⋊C4—171no—
625C22×C4⋊C4—171no—
626C22×C4⋊C4—171no—
627C22×C4⋊C4C2×D1711yescharacteristic
628C22×C22⋊C4—171no—
629C22×C22⋊C4—171no—
630C22×C22⋊C4—171no—
631C22×C22⋊C4—171no—
632C22×C22⋊C4—171no—
633C22×C22⋊C4—171no—
634C22×C22⋊C4—171no—
635C22×C22⋊C4C2×D1711yescharacteristic
636C22×C22⋊C4C2×D1711yescharacteristic
637C22×C22⋊C4C2×D1711yescharacteristic
638C22×C42—171no—
639C22×C42—171no—
640C22×C42—171no—
641#390—178no—
642#390—344no—
643#389—344no—
644#385—344no—
645#385—344no—
646#385—344no—
647#385—344no—
648#384—344no—
649C2×#95—171no—
650C2×#95—171no—
651C2×#95—171no—
652C2×#95—171no—
653C2×#95—171no—
654C2×#95—171no—
655C2×#95—171no—
656C2×#95C2×D1711yescharacteristic
657C2×#95C2×D1711yescharacteristic
658C2×#95C2×D1711yescharacteristic
659C2×C17—44no—
660C2×C17C2×#38511yescharacteristic
661C2×C17C4×#12711yescharacteristic
662C2×C17#232611yescharacteristic
663C2×C17D4×C4⋊C411yescharacteristic
664C2×C17D4×C4⋊C411yescharacteristic
665C2×C17#236111yescharacteristic
666C2×C17#236111yescharacteristic
667C2×C17#242211yescharacteristic
668C2×C17#242211yescharacteristic
669C2×C17#243211yescharacteristic
670C2×C17#243311yescharacteristic
671C2×C17#245211yescharacteristic
672C2×C17#245211yescharacteristic
673C2×C17#254211yescharacteristic
674C2×C17#256611yescharacteristic
675D17—44no—
676C25—171no—
677C25C22×D1711yescharacteristic
678C22×D4—174no—
679C22×D4—174no—
680C22×D4—174no—
681C22×D4—342no—
682C22×D4—342no—
683C22×D4—342no—
684C22×D4—342no—
685C23×C4—171no—
686C23×C4—171no—
687C23×C4—171no—
688C23×C4—171no—
689C23×C4—171no—
690C23×C4—171no—
691C23×C4—171no—
692C23×C4—342no—
693C23×C4—342no—
694C23×C4—342no—
695C23×C4—342no—
696C23×C4—342no—
697C23×C4—342no—
698C23×C4—342no—
699C23×C4—342no—
700C23×C4—342no—
701C23×C4—342no—
702C23×C4—681no—
703C23×C4—681no—
704C23×C4—681no—
705C23×C4—681no—
706C23×C4C22×D1711yescharacteristic
707C23×C4C22×D1711yescharacteristic
708C23×C4C22×D1711yescharacteristic
709C23×C4C22×D1711yescharacteristic
710C23×C4C22×D1711yescharacteristic
711C23×C4C22×D1711yescharacteristic
712C4×D4—3432no—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—41no—
716C2×C4⋊C4—174no—
717C2×C4⋊C4—174no—
718C2×C4⋊C4—342no—
719C2×C4⋊C4—342no—
720C2×C4⋊C4—342no—
721C2×C4⋊C4—342no—
722C2×C4⋊C4—342no—
723C2×C4⋊C4—342no—
724C2×C4⋊C4—342no—
725C2×C4⋊C4—342no—
726C2×C4⋊C4—342no—
727C2×C4⋊C4—342no—
728C2×C4⋊C4—342no—
729C2×C4⋊C4—342no—
730C2×C4⋊C4—342no—
731C2×C4⋊C4—342no—
732C2×C4⋊C4—342no—
733C2×C4⋊C4—342no—
734C2×C4⋊C4—342no—
735C2×C4⋊C4—342no—
736C2×C4⋊C4—342no—
737C2×C4⋊C4—681no—
738C2×C4⋊C4—681no—
739C2×C4⋊C4—681no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—41no—
748C2×C22⋊C4—174no—
749C2×C22⋊C4—174no—
750C2×C22⋊C4—174no—
751C2×C22⋊C4—342no—
752C2×C22⋊C4—342no—
753C2×C22⋊C4—342no—
754C2×C22⋊C4—342no—
755C2×C22⋊C4—342no—
756C2×C22⋊C4—342no—
757C2×C22⋊C4—342no—
758C2×C22⋊C4—342no—
759C2×C22⋊C4—342no—
760C2×C22⋊C4—342no—
761C2×C22⋊C4—342no—
762C2×C22⋊C4—342no—
763C2×C22⋊C4—342no—
764C2×C22⋊C4—342no—
765C2×C22⋊C4—342no—
766C2×C22⋊C4—681no—
767C2×C22⋊C4—681no—
768C2×C22⋊C4—681no—
769C2×C22⋊C4C4×D1714yescomplemented
770C2×C42—174no—
771C2×C42—174no—
772C2×C42—342no—
773C2×C42—342no—
774C2×C42—342no—
775C2×C42—342no—
776C2×C42—342no—
777C2×C42—342no—
778C2×C42—342no—
779#95—22no—
780#95—22no—
781#95—22no—
782#95—174no—
783#95—174no—
784#95—342no—
785#95—342no—
786#95—342no—
787#95—342no—
788#95—342no—
789C17#1397711yescharacteristic, complemented, Sylow
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—172no—
803C24—172no—
804C24—172no—
805C24—341no—
806C24—341no—
807C24—341no—
808C24—341no—
809C24—341no—
810C24—341no—
811C24—341no—
812C24—341no—
813C24—341no—
814C24—341no—
815C24—341no—
816C24—341no—
817C24C2×C4×D1712yes—
818C24D4×D1712yes—
819C24Q8×D1712yes—
820C24C23×D1711yescharacteristic
821C2×D4—1716no—
822C2×D4—348no—
823C2×D4—348no—
824C2×D4—348no—
825C2×D4—348no—
826C2×D4—348no—
827C2×D4—348no—
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—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—172no—
864C22×C4—172no—
865C22×C4—172no—
866C22×C4—172no—
867C22×C4—172no—
868C22×C4—172no—
869C22×C4—172no—
870C22×C4—172no—
871C22×C4—172no—
872C22×C4—172no—
873C22×C4—172no—
874C22×C4—172no—
875C22×C4—172no—
876C22×C4—172no—
877C22×C4—172no—
878C22×C4—172no—
879C22×C4—348no—
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—348no—
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—341no—
901C22×C4—341no—
902C22×C4—341no—
903C22×C4—341no—
904C22×C4—341no—
905C22×C4—341no—
906C22×C4—341no—
907C22×C4—341no—
908C22×C4—341no—
909C22×C4—341no—
910C22×C4—341no—
911C22×C4—341no—
912C22×C4—341no—
913C22×C4—341no—
914C22×C4—684no—
915C22×C4—684no—
916C22×C4—684no—
917C22×C4—684no—
918C22×C4—684no—
919C22×C4—684no—
920C22×C4—684no—
921C22×C4—684no—
922C22×C4—684no—
923C22×C4—684no—
924C22×C4—684no—
925C22×C4—684no—
926C22×C4C2×C4×D1712yes—
927C22×C4C2×C4×D1712yes—
928C22×C4D4×D1712yes—
929C22×C4D4×D1712yes—
930C22×C4D4×D1712yes—
931C22×C4D4×D1712yes—
932C22×C4#6325412yes—
933C4⋊C4—44no—
934C4⋊C4—348no—
935C4⋊C4—348no—
936C4⋊C4—684no—
937C4⋊C4—684no—
938C4⋊C4—684no—
939C4⋊C4—684no—
940C4⋊C4—684no—
941C4⋊C4—684no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—44no—
945C22⋊C4—348no—
946C22⋊C4—348no—
947C22⋊C4—348no—
948C22⋊C4—348no—
949C22⋊C4—684no—
950C22⋊C4—684no—
951C22⋊C4—684no—
952C42—348no—
953C42—348no—
954C42—684no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—174no—
990C23—342no—
991C23—342no—
992C23—342no—
993C23—342no—
994C23—342no—
995C23—342no—
996C23—342no—
997C23—342no—
998C23—342no—
999C23—342no—
1000C23—342no—
1001C23—342no—
1002C23—342no—
1003C23—342no—
1004C23—342no—
1005C23—342no—
1006C23—342no—
1007C23—342no—
1008C23—681no—
1009C23—681no—
1010C23—681no—
1011C23—681no—
1012C23—681no—
1013C23—681no—
1014C23—681no—
1015C23—681no—
1016C23—681no—
1017C23—681no—
1018C23—681no—
1019C23—681no—
1020C23—681no—
1021C23—681no—
1022C23—681no—
1023C23—681no—
1024C23C4⋊C4×D1714yes—
1025C23C22×C4×D1711yescharacteristic
1026C23C2×D4×D1711yescharacteristic
1027C23C2×D4×D1711yescharacteristic
1028C23C2×D4×D1711yescharacteristic
1029C23C2×D4×D1711yescharacteristic
1030C23C2×D4×D1711yescharacteristic
1031C23C2×#6325411yescharacteristic
1032C23#1058769111yescharacteristic
1033C23C2×Q8×D1711yescharacteristic
1034C23#41×D1711yescharacteristic
1035C23#41×D1711yescharacteristic
1036C23#41×D1711yescharacteristic
1037C23#1058769611yescharacteristic
1038C23#1058769711yescharacteristic
1039C23#1058769711yescharacteristic
1040D4—3432no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—174no—
1083C2×C4—174no—
1084C2×C4—174no—
1085C2×C4—174no—
1086C2×C4—174no—
1087C2×C4—174no—
1088C2×C4—174no—
1089C2×C4—174no—
1090C2×C4—174no—
1091C2×C4—342no—
1092C2×C4—342no—
1093C2×C4—342no—
1094C2×C4—342no—
1095C2×C4—342no—
1096C2×C4—342no—
1097C2×C4—342no—
1098C2×C4—342no—
1099C2×C4—342no—
1100C2×C4—342no—
1101C2×C4—342no—
1102C2×C4—342no—
1103C2×C4—342no—
1104C2×C4—342no—
1105C2×C4—342no—
1106C2×C4—342no—
1107C2×C4—342no—
1108C2×C4—342no—
1109C2×C4—342no—
1110C2×C4—342no—
1111C2×C4—342no—
1112C2×C4—6816no—
1113C2×C4—6816no—
1114C2×C4—681no—
1115C2×C4—681no—
1116C2×C4—681no—
1117C2×C4—681no—
1118C2×C4—681no—
1119C2×C4—681no—
1120C2×C4—681no—
1121C2×C4—681no—
1122C2×C4—681no—
1123C2×C4—681no—
1124C2×C4—681no—
1125C2×C4—681no—
1126C2×C4—681no—
1127C2×C4—681no—
1128C2×C4—681no—
1129C2×C4—681no—
1130C2×C4—681no—
1131C2×C4—681no—
1132C2×C4—681no—
1133C2×C4#1058756714yescomplemented
1134C22—24no—
1135C22—24no—
1136C22—24no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—344no—
1150C22—344no—
1151C22—344no—
1152C22—682no—
1153C22—682no—
1154C22—682no—
1155C22—682no—
1156C22—682no—
1157C22—682no—
1158C22—682no—
1159C22—682no—
1160C22—682no—
1161C22—682no—
1162C22—682no—
1163C22—682no—
1164C22C2×C4⋊C4×D1711yescharacteristic
1165C22C4×D4×D1711yescharacteristic
1166C22C4×D4×D1711yescharacteristic
1167C22C4×D4×D1711yescharacteristic
1168C22C2×#1058756711yescharacteristic
1169C22#1176328811yescharacteristic
1170C22#1176328911yescharacteristic
1171C22#120×D1711yescharacteristic
1172C22C22⋊Q8×D1711yescharacteristic
1173C22C22⋊Q8×D1711yescharacteristic
1174C22#123×D1711yescharacteristic
1175C22#127×D1711yescharacteristic
1176C22#1176335411yescharacteristic
1177C22#1176335411yescharacteristic
1178C22#1176335811yescharacteristic
1179C22#1176337511yescharacteristic
1180C22#1176338111yescharacteristic
1181C22#1176342311yescharacteristic
1182C22#1176342511yescharacteristic
1183C22#1176344111yescharacteristic
1184C22#1176344111yescharacteristic
1185C22#1176344311yescharacteristic
1186C22#1176344311yescharacteristic
1187C22#1176345711yescharacteristic
1188C22#1176345711yescharacteristic
1189C22#1176345711yescharacteristic
1190C22#1176345911yescharacteristic
1191C22#1176346511yescharacteristic
1192C22#1176346711yescharacteristic
1193C22#1176347211yescharacteristic
1194C22#1176347211yescharacteristic
1195C22#1176350211yescharacteristic
1196C22#1176351011yescharacteristic
1197C22#1176351311yescharacteristic
1198C22#1176351711yescharacteristic
1199C4—24no—
1200C4—42no—
1201C4—42no—
1202C4—42no—
1203C4—42no—
1204C4—81no—
1205C4—178no—
1206C4—344no—
1207C4—344no—
1208C4—682no—
1209C4—682no—
1210C4—682no—
1211C4—1361no—
1212C2—44no—
1213C2—684no—
1214C2D17×#38511yescharacteristic
1215C2#1453134811yescharacteristic
1216C2#1453149311yescharacteristic
1217C2#1453168011yescharacteristic
1218C2#1453168211yescharacteristic
1219C2#1453179511yescharacteristic
1220C2#1453179711yescharacteristic
1221C2#1453229111yescharacteristic
1222C2#1453229311yescharacteristic
1223C2#1453240711yescharacteristic
1224C2#1453241611yescharacteristic
1225C2#1453262711yescharacteristic
1226C2#1453262911yescharacteristic
1227C2#1453373211yescharacteristic
1228C2#1453397911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1439C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1439D17
hypocenterC17#13977
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×#11762681C2semidirect
8. C2×#11762680C2semidirect
9. C2×#11762678C2semidirect
10. #14527030C2semidirect
11. #14527028C2semidirect
12. #14527027C2semidirect
13. #14527012C2semidirect
14. #95×Dic17C2semidirect
15. C17×#1439C2semidirect
41. #11762709C4semidirect
109. C2×C22⋊C4×C17C2×C4semidirect
115. C2×C22⋊Dic17C2×C4semidirect
129. C2×#63227C2×C4semidirect
130. C2×#63227C2×C4semidirect
153. C2×#63225C2×C4semidirect
162. C2×C4×Dic17C2×C4semidirect
173. #10587502D4semidirect
174. #10587502D4semidirect
254. C2×C22⋊D17C4⋊C4semidirect
467. C2×C4×C17C4×D4semidirect
513. C2×Dic17C4×D4semidirect
532. #1439D17semidirect
612. Dic17#385semidirect
769. C2×C22⋊C4C4×D17semidirect
789. C17#13977semidirect
1133. 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×#117626812
C2×#117626802
C2×#117626782
#145270302
#145270282
#145270272
#145270122
#95×Dic172
C17×#14392
#1397717