Finite Group Databasebeta

← #16959825

Subgroups — #16959825

Order 4352.

2746 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic17C211yesmaximal, characteristic, complemented
2C2×#11762712C211yesmaximal, characteristic, complemented
3C2×#11762702C211yesmaximal, characteristic, complemented
4C2×#11762689C211yesmaximal, characteristic, complemented
5C2×#11762689C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
7#14527029C211yesmaximal, characteristic, complemented
8#14527025C211yesmaximal, characteristic, complemented
9#14527025C211yesmaximal, characteristic, complemented
10#14527021C211yesmaximal, characteristic, complemented
11#14527021C211yesmaximal, characteristic, complemented
12#14527018C211yesmaximal, characteristic, complemented
13#14527018C211yesmaximal, characteristic, complemented
14#14527006C211yesmaximal, characteristic, complemented
15C2×C17×#392C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C2×D4×Dic17—24no—
19C2×D4×Dic17—24no—
20C2×D4×Dic17—24no—
21C22×C4⋊Dic17C2211yescharacteristic
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×C22⋊Dic17C2211yescharacteristic
30C22×C22⋊Dic17C2211yescharacteristic
31C22×C22⋊Dic17C2211yescharacteristic
32C22×C22⋊Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36#11762712—24no—
37#11762702—24no—
38#11762689—24no—
39#11762689—24no—
40C22⋊C4×Dic17—24no—
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C23×D4×C17C2211yescharacteristic
53C23×D4×C17C2211yescharacteristic
54C23×D4×C17C2211yescharacteristic
55C22×C22⋊C4×C17C2211yescharacteristic
56C22×C22⋊C4×C17C2211yescharacteristic
57C22×C22⋊C4×C17C2211yescharacteristic
58C17×#392C418yescomplemented
59C2×C17×#95C2211yescharacteristic
60C25×C17C2311yescharacteristic
61C25×C17C2311yescharacteristic
62C25×C17C2311yescharacteristic
63C22×D4×C17—22no—
64C22×D4×C17—22no—
65C22×D4×C17—22no—
66C22×D4×C17—22no—
67C22×D4×C17—22no—
68C22×D4×C17—22no—
69C22×D4×C17—22no—
70C22×D4×C17—22no—
71C22×D4×C17—22no—
72C22×D4×C17—22no—
73C22×D4×C17—22no—
74C22×D4×C17—22no—
75C22×D4×C17—41no—
76C22×D4×C17—41no—
77C22×D4×C17—41no—
78C22×D4×C17—41no—
79C22×D4×C17—41no—
80C22×D4×C17—41no—
81C22×D4×C17C2×C414yes—
82C22×D4×C17C2×C414yescomplemented
83C22×D4×C17C2×C414yescomplemented
84C23×C4×C17C2311yescharacteristic
85C23×C4×C17C2311yescharacteristic
86C23×C4×C17C2311yescharacteristic
87C23×C4×C17C2311yescharacteristic
88C23×Dic17—22no—
89C23×Dic17—22no—
90C23×Dic17—22no—
91C23×Dic17—22no—
92C23×Dic17—22no—
93C23×Dic17—22no—
94C23×Dic17—22no—
95C23×Dic17—22no—
96C23×Dic17—22no—
97C23×Dic17—41no—
98C23×Dic17—41no—
99C23×Dic17—41no—
100C23×Dic17—41no—
101C23×Dic17D414yescomplemented
102C23×Dic17C2311yescharacteristic
103C23×Dic17C2311yescharacteristic
104C23×Dic17C2311yescharacteristic
105C23×Dic17C2311yescharacteristic
106C23×Dic17C2311yescharacteristic
107C23×Dic17C2311yescharacteristic
108C23×Dic17C2311yescharacteristic
109C23×Dic17C2311yescharacteristic
110C2×C22⋊C4×C17—22no—
111C2×C22⋊C4×C17—22no—
112C2×C22⋊C4×C17—22no—
113C2×C22⋊C4×C17—22no—
114C2×C22⋊C4×C17—41no—
115C2×C22⋊C4×C17—41no—
116C2×C22⋊C4×C17C2×C414yescomplemented
117C2×C22⋊C4×C17C2×C414yescomplemented
118C2×C22⋊C4×C17C2×C414yescomplemented
119C2×C22⋊Dic17—22no—
120C2×C22⋊Dic17—22no—
121C2×C22⋊Dic17—22no—
122C2×C22⋊Dic17—22no—
123C2×C22⋊Dic17—22no—
124C2×C22⋊Dic17—22no—
125C2×C22⋊Dic17—22no—
126C2×C22⋊Dic17—22no—
127C2×C22⋊Dic17—22no—
128C2×C22⋊Dic17—22no—
129C2×C22⋊Dic17—22no—
130C2×C22⋊Dic17—22no—
131C2×C22⋊Dic17—22no—
132C2×C22⋊Dic17—22no—
133C2×C22⋊Dic17—22no—
134C2×C22⋊Dic17—22no—
135C2×C22⋊Dic17—22no—
136C2×C22⋊Dic17—22no—
137C2×C22⋊Dic17—22no—
138C2×C22⋊Dic17—22no—
139C2×C22⋊Dic17—22no—
140C2×C22⋊Dic17—22no—
141C2×C22⋊Dic17—22no—
142C2×C22⋊Dic17—41no—
143C2×C22⋊Dic17—41no—
144C2×C22⋊Dic17—41no—
145C2×C22⋊Dic17—41no—
146C2×C22⋊Dic17—41no—
147C2×C22⋊Dic17—41no—
148C2×C22⋊Dic17D414yescomplemented
149D4×Dic17—232no—
150C2×C4⋊Dic17—22no—
151C2×C4⋊Dic17—22no—
152C2×C4⋊Dic17—22no—
153C2×C4⋊Dic17—22no—
154C2×C4⋊Dic17—41no—
155C2×C4⋊Dic17D414yescomplemented
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×Dic17—22no—
163C2×C4×Dic17—41no—
164C2×C4×Dic17—41no—
165C17×#95C2×C414yescomplemented
166#10587502—22no—
167#10587502—22no—
168#10587502—22no—
169#10587502—22no—
170#10587502—22no—
171#10587502—22no—
172#10587502—22no—
173#10587502—41no—
174#10587502—41no—
175#10587502—41no—
176#10587502D414yescomplemented
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×C17—21no—
188C24×C17—21no—
189C24×C17—21no—
190C24×C17—21no—
191C24×C17—21no—
192C24×C17—21no—
193C24×C17—21no—
194C24×C17—21no—
195C24×C17—21no—
196C24×C17—21no—
197C24×C17—21no—
198C24×C17—21no—
199C24×C17—21no—
200C24×C17—21no—
201C24×C17—21no—
202C24×C17—21no—
203C24×C17—21no—
204C24×C17—21no—
205C24×C17—21no—
206C24×C17—21no—
207C24×C17—21no—
208C24×C17—21no—
209C24×C17—21no—
210C24×C17—21no—
211C24×C17—21no—
212C24×C17—21no—
213C24×C17—21no—
214C24×C17—21no—
215C24×C17C22×C412yes—
216C24×C17C22×C412yes—
217C24×C17C22×C412yes—
218C24×C17C2×D412yes—
219C24×C17C2×D412yes—
220C24×C17#4112yes—
221C24×C17#4112yes—
222C24×C17C2411yescharacteristic
223C2×D4×C17—28no—
224C2×D4×C17—28no—
225C2×D4×C17—28no—
226C2×D4×C17—28no—
227C2×D4×C17—28no—
228C2×D4×C17—28no—
229C2×D4×C17—28no—
230C2×D4×C17—28no—
231C2×D4×C17—28no—
232C2×D4×C17—28no—
233C2×D4×C17—44no—
234C2×D4×C17—44no—
235C2×D4×C17—44no—
236C2×D4×C17—44no—
237C2×D4×C17—44no—
238C2×D4×C17—44no—
239C2×D4×C17—44no—
240C2×D4×C17—44no—
241C2×D4×C17—44no—
242C2×D4×C17—44no—
243C2×D4×C17—44no—
244C22×C4×C17—21no—
245C22×C4×C17—21no—
246C22×C4×C17—21no—
247C22×C4×C17—21no—
248C22×C4×C17—21no—
249C22×C4×C17—21no—
250C22×C4×C17—21no—
251C22×C4×C17—21no—
252C22×C4×C17—21no—
253C22×C4×C17—21no—
254C22×C4×C17—21no—
255C22×C4×C17—21no—
256C22×C4×C17—21no—
257C22×C4×C17—21no—
258C22×C4×C17—21no—
259C22×C4×C17—21no—
260C22×C4×C17—21no—
261C22×C4×C17—21no—
262C22×C4×C17—21no—
263C22×C4×C17—21no—
264C22×C4×C17C22×C412yes—
265C22×C4×C17C22×C412yes—
266C22×C4×C17C22×C412yes—
267C22×C4×C17C22×C412yes—
268C22×C4×C17C2×D412yes—
269C22×C4×C17C2×D412yes—
270C22×C4×C17#4112yes—
271C22×C4×C17#4112yes—
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—28no—
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—21no—
290C22×Dic17—21no—
291C22×Dic17—21no—
292C22×Dic17—21no—
293C22×Dic17—21no—
294C22×Dic17—21no—
295C22×Dic17—21no—
296C22×Dic17—21no—
297C22×Dic17—21no—
298C22×Dic17—21no—
299C22×Dic17—21no—
300C22×Dic17—21no—
301C22×Dic17—21no—
302C22×Dic17—21no—
303C22×Dic17—21no—
304C22×Dic17—21no—
305C22×Dic17—28no—
306C22×Dic17—28no—
307C22×Dic17—21no—
308C22×Dic17—21no—
309C22×Dic17—21no—
310C22×Dic17—21no—
311C22×Dic17—21no—
312C22×Dic17—21no—
313C22×Dic17—21no—
314C22×Dic17—21no—
315C22×Dic17—21no—
316C22×Dic17—21no—
317C22×Dic17—21no—
318C22×Dic17—21no—
319C22×Dic17—21no—
320C22×Dic17—21no—
321C22×Dic17—44no—
322C22×Dic17—44no—
323C22×Dic17—44no—
324C22×Dic17—44no—
325C22×Dic17—44no—
326C22×Dic17—44no—
327C22×Dic17—44no—
328C22×Dic17—44no—
329C22×Dic17—44no—
330C22×Dic17—44no—
331C22×Dic17—44no—
332C22×Dic17C2×D412yes—
333C22×Dic17C2×D412yes—
334C22×Dic17C2×D412yes—
335C22×Dic17C2×D412yes—
336C22×Dic17C2×D412yes—
337C22×Dic17C2×D412yes—
338C22×Dic17C2×D412yes—
339C22×Dic17C2×D412yes—
340C22×Dic17#4112yes—
341C22×Dic17#4112yes—
342C22⋊C4×C17—28no—
343C22⋊C4×C17—28no—
344C22⋊C4×C17—44no—
345C22⋊Dic17—28no—
346C22⋊Dic17—28no—
347C22⋊Dic17—28no—
348C22⋊Dic17—44no—
349C22⋊Dic17—44no—
350C22⋊Dic17—44no—
351C22⋊Dic17—44no—
352C22⋊Dic17—44no—
353C22⋊Dic17—44no—
354C22⋊Dic17—44no—
355C4⋊Dic17—28no—
356C4⋊Dic17—44no—
357C4×Dic17—28no—
358C4×Dic17—44no—
359C4×Dic17—44no—
360#14187—171nomaximal, Sylow
361C23×C17—22no—
362C23×C17—22no—
363C23×C17—22no—
364C23×C17—22no—
365C23×C17—22no—
366C23×C17—22no—
367C23×C17—22no—
368C23×C17—22no—
369C23×C17—22no—
370C23×C17—22no—
371C23×C17—22no—
372C23×C17—22no—
373C23×C17—22no—
374C23×C17—22no—
375C23×C17—22no—
376C23×C17—22no—
377C23×C17—22no—
378C23×C17—22no—
379C23×C17—22no—
380C23×C17—22no—
381C23×C17—22no—
382C23×C17—22no—
383C23×C17—22no—
384C23×C17—22no—
385C23×C17—22no—
386C23×C17—22no—
387C23×C17—22no—
388C23×C17—22no—
389C23×C17—22no—
390C23×C17—22no—
391C23×C17—22no—
392C23×C17—22no—
393C23×C17—22no—
394C23×C17—22no—
395C23×C17—22no—
396C23×C17—22no—
397C23×C17—22no—
398C23×C17—22no—
399C23×C17—22no—
400C23×C17—22no—
401C23×C17—22no—
402C23×C17—22no—
403C23×C17—22no—
404C23×C17—41no—
405C23×C17—41no—
406C23×C17—41no—
407C23×C17—41no—
408C23×C17—41no—
409C23×C17—41no—
410C23×C17—41no—
411C23×C17—41no—
412C23×C17—41no—
413C23×C17—41no—
414C23×C17—41no—
415C23×C17—41no—
416C23×C17—41no—
417C23×C17—41no—
418C23×C17—41no—
419C23×C17—41no—
420C23×C17—41no—
421C23×C17—41no—
422C23×C17—41no—
423C23×C17—41no—
424C23×C17—41no—
425C23×C17—41no—
426C23×C17—41no—
427C23×C17—41no—
428C23×C17—41no—
429C23×C17—41no—
430C23×C17—41no—
431C23×C17—41no—
432C23×C17—41no—
433C23×C17—41no—
434C23×C17—41no—
435C23×C17—41no—
436C23×C17—41no—
437C23×C17—41no—
438C23×C17—41no—
439C23×C17—41no—
440C23×C17—41no—
441C23×C17—41no—
442C23×C17—41no—
443C23×C17—41no—
444C23×C17—41no—
445C23×C17—41no—
446C23×C17—41no—
447C23×C17—41no—
448C23×C17—41no—
449C23×C17—41no—
450C23×C17—41no—
451C23×C17—41no—
452C23×C17—41no—
453C23×C17—41no—
454C23×C17—41no—
455C23×C17—41no—
456C23×C17—41no—
457C23×C17—41no—
458C23×C17—41no—
459C23×C17—41no—
460C23×C17—41no—
461C23×C17—41no—
462C23×C17—41no—
463C23×C17—41no—
464C23×C17C4×D414yes—
465C23×C17C4×D414yes—
466C23×C17C23×C411yescharacteristic
467C23×C17C22×D411yescharacteristic
468C23×C17C22×D411yescharacteristic
469C23×C17C22×D411yescharacteristic
470C23×C17C22×D411yescharacteristic
471C23×C17C2×#4111yescharacteristic
472C23×C17C2×#4111yescharacteristic
473C23×C17C2×#4111yescharacteristic
474C23×C17C2×#4111yescharacteristic
475C23×C17C2×#4111yescharacteristic
476C23×C17C2×#4111yescharacteristic
477C23×C17H(5,𝔽2)11yescharacteristic
478C23×C17H(5,𝔽2)11yescharacteristic
479C23×C17H(5,𝔽2)11yescharacteristic
480C23×C17H(5,𝔽2)11yescharacteristic
481D4×C17—232no—
482D4×C17—416no—
483D4×C17—416no—
484C2×C4×C17—22no—
485C2×C4×C17—22no—
486C2×C4×C17—22no—
487C2×C4×C17—22no—
488C2×C4×C17—22no—
489C2×C4×C17—22no—
490C2×C4×C17—22no—
491C2×C4×C17—22no—
492C2×C4×C17—22no—
493C2×C4×C17—22no—
494C2×C4×C17—22no—
495C2×C4×C17—22no—
496C2×C4×C17—22no—
497C2×C4×C17—22no—
498C2×C4×C17—22no—
499C2×C4×C17—22no—
500C2×C4×C17—22no—
501C2×C4×C17—22no—
502C2×C4×C17—41no—
503C2×C4×C17—41no—
504C2×C4×C17—41no—
505C2×C4×C17—41no—
506C2×C4×C17—41no—
507C2×C4×C17—41no—
508C2×C4×C17—41no—
509C2×C4×C17—41no—
510C2×C4×C17C4×D414yes—
511C2×C4×C17C4×D414yescomplemented
512C2×Dic17—22no—
513C2×Dic17—22no—
514C2×Dic17—22no—
515C2×Dic17—22no—
516C2×Dic17—22no—
517C2×Dic17—22no—
518C2×Dic17—22no—
519C2×Dic17—22no—
520C2×Dic17—22no—
521C2×Dic17—22no—
522C2×Dic17—22no—
523C2×Dic17—22no—
524C2×Dic17—22no—
525C2×Dic17—22no—
526C2×Dic17—22no—
527C2×Dic17—22no—
528C2×Dic17—22no—
529C2×Dic17—22no—
530C2×Dic17—22no—
531C2×Dic17—22no—
532C2×Dic17—22no—
533C2×Dic17—22no—
534C2×Dic17—22no—
535C2×Dic17—22no—
536C2×Dic17—416no—
537C2×Dic17—416no—
538C2×Dic17—41no—
539C2×Dic17—41no—
540C2×Dic17—41no—
541C2×Dic17—41no—
542C2×Dic17—41no—
543C2×Dic17—41no—
544C2×Dic17—41no—
545C2×Dic17—41no—
546C2×Dic17—41no—
547C2×Dic17—41no—
548C2×Dic17—41no—
549C2×Dic17—41no—
550C2×Dic17—41no—
551C2×Dic17—41no—
552C2×Dic17—41no—
553C2×Dic17—41no—
554C2×Dic17—41no—
555C2×Dic17—41no—
556C2×Dic17—41no—
557C2×Dic17—41no—
558C2×Dic17—41no—
559C2×Dic17—41no—
560C2×Dic17—41no—
561C2×Dic17—41no—
562C2×Dic17—41no—
563C2×Dic17—41no—
564C2×Dic17—41no—
565C2×Dic17—41no—
566C2×Dic17—41no—
567C2×Dic17—41no—
568C2×Dic17#12014yes—
569C2×Dic17#12114yes—
570C22×C4×D4—171no—
571C2×#392D1711yescharacteristic
572C2×#390—171no—
573C2×#388—171no—
574C2×#386—171no—
575C2×#386—171no—
576C2×C4×C22⋊C4—171no—
577#1439—171no—
578#1438—171no—
579#1438—171no—
580#1437—171no—
581#1437—171no—
582#1436—171no—
583#1436—171no—
584C22⋊#95—171no—
585C22×C17—24no—
586C22×C17—24no—
587C22×C17—24no—
588C22×C17—24no—
589C22×C17—24no—
590C22×C17—24no—
591C22×C17—42no—
592C22×C17—42no—
593C22×C17—42no—
594C22×C17—42no—
595C22×C17—42no—
596C22×C17—42no—
597C22×C17—42no—
598C22×C17—42no—
599C22×C17—42no—
600C22×C17—42no—
601C22×C17—42no—
602C22×C17—42no—
603C22×C17—42no—
604C22×C17—42no—
605C22×C17—42no—
606C22×C17—42no—
607C22×C17—42no—
608C22×C17—42no—
609C22×C17—42no—
610C22×C17—42no—
611C22×C17—42no—
612C22×C17—42no—
613C22×C17—42no—
614C22×C17—42no—
615C22×C17—42no—
616C22×C17—42no—
617C22×C17—42no—
618C22×C17—42no—
619C22×C17—42no—
620C22×C17—42no—
621C22×C17—42no—
622C22×C17—81no—
623C22×C17—81no—
624C22×C17—81no—
625C22×C17—81no—
626C22×C17—81no—
627C22×C17—81no—
628C22×C17—81no—
629C22×C17—81no—
630C22×C17C2×C4×D411yescharacteristic
631C22×C17C2×C4×D411yescharacteristic
632C22×C17C2×C4×D411yescharacteristic
633C22×C17C2×C4×D411yescharacteristic
634C22×C17C4×#4111yescharacteristic
635C22×C17#51811yescharacteristic
636C22×C17#51811yescharacteristic
637C22×C17C2×#12011yescharacteristic
638C22×C17C2×#12111yescharacteristic
639C22×C17#52511yescharacteristic
640C22×C17#52511yescharacteristic
641C22×C17#52511yescharacteristic
642C22×C17#52511yescharacteristic
643C22×C17#52911yescharacteristic
644C22×C17#53211yescharacteristic
645C22×C17#53411yescharacteristic
646C22×C17#53511yescharacteristic
647C22×C17#53811yescharacteristic
648C22×C17#53811yescharacteristic
649C22×C17D4211yescharacteristic
650C22×C17D4211yescharacteristic
651C22×C17#54611yescharacteristic
652C22×C17#54611yescharacteristic
653C22×C17#54611yescharacteristic
654C22×C17#54611yescharacteristic
655C22×C17#54611yescharacteristic
656C22×C17#55011yescharacteristic
657C22×C17#55011yescharacteristic
658C22×C17#55011yescharacteristic
659C22×C17#55111yescharacteristic
660C22×C17#55311yescharacteristic
661C22×C17#55311yescharacteristic
662C22×C17#55311yescharacteristic
663C22×C17#55511yescharacteristic
664C22×C17#55911yescharacteristic
665C4×C17—24no—
666C4×C17—24no—
667C4×C17—42no—
668C4×C17—42no—
669Dic17—24no—
670Dic17—24no—
671Dic17—42no—
672Dic17—42no—
673Dic17—42no—
674Dic17—42no—
675Dic17—81no—
676Dic17—81no—
677C23×D4C2×D1711yescharacteristic
678C23×D4C2×D1711yescharacteristic
679C23×D4C2×D1711yescharacteristic
680C24×C4—171no—
681C24×C4—171no—
682C2×C4×D4—344no—
683C2×C4×D4—344no—
684C2×C4×D4—344no—
685C22×C4⋊C4—171no—
686C22×C4⋊C4—171no—
687C22×C22⋊C4—171no—
688C22×C22⋊C4—171no—
689C22×C22⋊C4—171no—
690C22×C22⋊C4—171no—
691C22×C22⋊C4—171no—
692C22×C22⋊C4—171no—
693C22×C22⋊C4—171no—
694C22×C22⋊C4—171no—
695C22×C22⋊C4—171no—
696C22×C22⋊C4—171no—
697C22×C22⋊C4C2×D1711yescharacteristic
698C22×C22⋊C4C2×D1711yescharacteristic
699C22×C22⋊C4C2×D1711yescharacteristic
700C22×C42—171no—
701C22×C42—171no—
702C22×C42—171no—
703#392Dic1718yescomplemented
704#390—344no—
705#388—344no—
706#386—344no—
707#386—344no—
708C4×C22⋊C4—344no—
709C2×#95—171no—
710C2×#95—171no—
711C2×#95—171no—
712C2×#95—171no—
713C2×#95—171no—
714C2×#95—171no—
715C2×#95—171no—
716C2×#95—171no—
717C2×#95—171no—
718C2×#95—171no—
719C2×#95—171no—
720C2×#95C2×D1711yescharacteristic
721C2×C17—44no—
722C2×C17—44no—
723C2×C17—82no—
724C2×C17C4×#12011yescharacteristic
725C2×C17C4×#12111yescharacteristic
726C2×C17#232111yescharacteristic
727C2×C17#235811yescharacteristic
728C2×C17#236311yescharacteristic
729C2×C17#236411yescharacteristic
730C2×C17#236611yescharacteristic
731C2×C17#241011yescharacteristic
732C2×C17#241411yescharacteristic
733C2×C17#243111yescharacteristic
734C2×C17#245611yescharacteristic
735C2×C17#245611yescharacteristic
736C2×C17#245911yescharacteristic
737C2×C17#246711yescharacteristic
738C2×C17#260211yescharacteristic
739C25C22×D1711yescharacteristic
740C25C22×D1711yescharacteristic
741C25C22×D1711yescharacteristic
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—41no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C22×D4—41no—
759C22×D4—41no—
760C22×D4C2×Dic1714yes—
761C22×D4C2×Dic1714yescomplemented
762C22×D4C2×Dic1714yescomplemented
763C23×C4—171no—
764C23×C4—171no—
765C23×C4—171no—
766C23×C4—171no—
767C23×C4—171no—
768C23×C4—171no—
769C23×C4—174no—
770C23×C4—171no—
771C23×C4—171no—
772C23×C4—342no—
773C23×C4—342no—
774C23×C4—342no—
775C23×C4—342no—
776C23×C4—342no—
777C23×C4—342no—
778C23×C4—342no—
779C23×C4—342no—
780C23×C4—342no—
781C23×C4—681no—
782C23×C4—681no—
783C23×C4—681no—
784C23×C4—681no—
785C23×C4C22×D1711yescharacteristic
786C23×C4C22×D1711yescharacteristic
787C23×C4C22×D1711yescharacteristic
788C23×C4C22×D1711yescharacteristic
789C4×D4—3432no—
790C2×C4⋊C4—174no—
791C2×C4⋊C4—342no—
792C2×C4⋊C4—342no—
793C2×C4⋊C4—342no—
794C2×C4⋊C4—342no—
795C2×C4⋊C4—681no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—174no—
803C2×C22⋊C4—342no—
804C2×C22⋊C4—342no—
805C2×C22⋊C4—342no—
806C2×C22⋊C4—342no—
807C2×C22⋊C4—342no—
808C2×C22⋊C4—342no—
809C2×C22⋊C4—342no—
810C2×C22⋊C4—342no—
811C2×C22⋊C4—342no—
812C2×C22⋊C4—342no—
813C2×C22⋊C4—342no—
814C2×C22⋊C4—342no—
815C2×C22⋊C4—342no—
816C2×C22⋊C4—342no—
817C2×C22⋊C4—342no—
818C2×C22⋊C4—342no—
819C2×C22⋊C4—342no—
820C2×C22⋊C4—342no—
821C2×C22⋊C4—342no—
822C2×C22⋊C4—342no—
823C2×C22⋊C4—342no—
824C2×C22⋊C4—342no—
825C2×C22⋊C4—342no—
826C2×C22⋊C4—681no—
827C2×C22⋊C4—681no—
828C2×C22⋊C4—681no—
829C2×C22⋊C4—681no—
830C2×C22⋊C4—681no—
831C2×C22⋊C4—681no—
832C2×C22⋊C4C2×Dic1714yescomplemented
833C2×C22⋊C4C2×Dic1714yescomplemented
834C2×C22⋊C4C2×Dic1714yescomplemented
835C2×C42—342no—
836C2×C42—342no—
837C2×C42—342no—
838C2×C42—342no—
839C2×C42—342no—
840C2×C42—342no—
841C2×C42—342no—
842C2×C42—681no—
843C2×C42—681no—
844#95—174no—
845#95—342no—
846#95—342no—
847#95—342no—
848#95—342no—
849#95—342no—
850#95—342no—
851#95—342no—
852#95—681no—
853#95—681no—
854#95—681no—
855#95C2×Dic1714yescomplemented
856C17#1418711yescharacteristic, complemented, Sylow
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24D4×D1712yes—
896C24D4×D1712yes—
897C24#6325412yes—
898C24#6325412yes—
899C24C22×Dic1712yes—
900C24C22×Dic1712yes—
901C24C22×Dic1712yes—
902C24C23×D1711yescharacteristic
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—172no—
945C22×C4—172no—
946C22×C4—172no—
947C22×C4—172no—
948C22×C4—172no—
949C22×C4—172no—
950C22×C4—172no—
951C22×C4—172no—
952C22×C4—172no—
953C22×C4—172no—
954C22×C4—348no—
955C22×C4—348no—
956C22×C4—341no—
957C22×C4—341no—
958C22×C4—341no—
959C22×C4—341no—
960C22×C4—341no—
961C22×C4—341no—
962C22×C4—341no—
963C22×C4—341no—
964C22×C4—348no—
965C22×C4—341no—
966C22×C4—341no—
967C22×C4—341no—
968C22×C4—341no—
969C22×C4—341no—
970C22×C4—341no—
971C22×C4—341no—
972C22×C4—341no—
973C22×C4—341no—
974C22×C4—341no—
975C22×C4—341no—
976C22×C4—341no—
977C22×C4—341no—
978C22×C4—341no—
979C22×C4—341no—
980C22×C4—341no—
981C22×C4—341no—
982C22×C4—341no—
983C22×C4—341no—
984C22×C4—341no—
985C22×C4—341no—
986C22×C4—341no—
987C22×C4—341no—
988C22×C4—341no—
989C22×C4—341no—
990C22×C4—341no—
991C22×C4—341no—
992C22×C4—341no—
993C22×C4—341no—
994C22×C4—341no—
995C22×C4—341no—
996C22×C4—341no—
997C22×C4—341no—
998C22×C4—341no—
999C22×C4—341no—
1000C22×C4—341no—
1001C22×C4—341no—
1002C22×C4—341no—
1003C22×C4—684no—
1004C22×C4—684no—
1005C22×C4—684no—
1006C22×C4—684no—
1007C22×C4—684no—
1008C22×C4—684no—
1009C22×C4—684no—
1010C22×C4—684no—
1011C22×C4—684no—
1012C22×C4—684no—
1013C22×C4—684no—
1014C22×C4D4×D1712yes—
1015C22×C4D4×D1712yes—
1016C22×C4#6325412yes—
1017C22×C4#6325412yes—
1018C22×C4C22×Dic1712yes—
1019C22×C4C22×Dic1712yes—
1020C22×C4C22×Dic1712yes—
1021C22×C4C22×Dic1712yes—
1022C4⋊C4—348no—
1023C4⋊C4—684no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—44no—
1027C22⋊C4—348no—
1028C22⋊C4—348no—
1029C22⋊C4—348no—
1030C22⋊C4—684no—
1031C22⋊C4—684no—
1032C22⋊C4—684no—
1033C22⋊C4—684no—
1034C22⋊C4—684no—
1035C22⋊C4—684no—
1036C22⋊C4—684no—
1037C42—348no—
1038C42—684no—
1039C42—684no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23D4×Dic1714yes—
1144C23D4×Dic1714yes—
1145C23C2×D4×D1711yescharacteristic
1146C23C2×D4×D1711yescharacteristic
1147C23C2×D4×D1711yescharacteristic
1148C23C2×D4×D1711yescharacteristic
1149C23C2×#6325411yescharacteristic
1150C23C2×#6325411yescharacteristic
1151C23C2×#6325411yescharacteristic
1152C23C2×#6325411yescharacteristic
1153C23#1058769111yescharacteristic
1154C23#1058769111yescharacteristic
1155C23#1058769111yescharacteristic
1156C23#1058769111yescharacteristic
1157C23#41×D1711yescharacteristic
1158C23#41×D1711yescharacteristic
1159C23C23×Dic1711yescharacteristic
1160D4—232no—
1161D4—416no—
1162D4—416no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—174no—
1190C2×C4—174no—
1191C2×C4—342no—
1192C2×C4—342no—
1193C2×C4—342no—
1194C2×C4—342no—
1195C2×C4—342no—
1196C2×C4—342no—
1197C2×C4—342no—
1198C2×C4—342no—
1199C2×C4—342no—
1200C2×C4—342no—
1201C2×C4—342no—
1202C2×C4—342no—
1203C2×C4—342no—
1204C2×C4—342no—
1205C2×C4—342no—
1206C2×C4—342no—
1207C2×C4—342no—
1208C2×C4—342no—
1209C2×C4—342no—
1210C2×C4—342no—
1211C2×C4—342no—
1212C2×C4—342no—
1213C2×C4—342no—
1214C2×C4—342no—
1215C2×C4—6816no—
1216C2×C4—6816no—
1217C2×C4—681no—
1218C2×C4—681no—
1219C2×C4—681no—
1220C2×C4—681no—
1221C2×C4—681no—
1222C2×C4—681no—
1223C2×C4—681no—
1224C2×C4—681no—
1225C2×C4—681no—
1226C2×C4—681no—
1227C2×C4—681no—
1228C2×C4—681no—
1229C2×C4—681no—
1230C2×C4—681no—
1231C2×C4—681no—
1232C2×C4—681no—
1233C2×C4—681no—
1234C2×C4—681no—
1235C2×C4—681no—
1236C2×C4—681no—
1237C2×C4—681no—
1238C2×C4—681no—
1239C2×C4—681no—
1240C2×C4—681no—
1241C2×C4—681no—
1242C2×C4—681no—
1243C2×C4—681no—
1244C2×C4—681no—
1245C2×C4—681no—
1246C2×C4—681no—
1247C2×C4D4×Dic1714yes—
1248C2×C4D4×Dic1714yescomplemented
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22C2×D4×Dic1711yescharacteristic
1295C22C2×D4×Dic1711yescharacteristic
1296C22C2×D4×Dic1711yescharacteristic
1297C22C2×D4×Dic1711yescharacteristic
1298C22#41×Dic1711yescharacteristic
1299C22#1176328411yescharacteristic
1300C22#1176328411yescharacteristic
1301C22#120×D1711yescharacteristic
1302C22#121×D1711yescharacteristic
1303C22#1176331511yescharacteristic
1304C22#1176331511yescharacteristic
1305C22#1176331511yescharacteristic
1306C22#1176331911yescharacteristic
1307C22#1176334011yescharacteristic
1308C22#1176335411yescharacteristic
1309C22#1176336911yescharacteristic
1310C22#1176337411yescharacteristic
1311C22#1176339411yescharacteristic
1312C22#1176339411yescharacteristic
1313C22#1176344111yescharacteristic
1314C22#1176344411yescharacteristic
1315C22#1176344611yescharacteristic
1316C22#1176344611yescharacteristic
1317C22#1176344811yescharacteristic
1318C22#1176344811yescharacteristic
1319C22#1176345611yescharacteristic
1320C22#1176347711yescharacteristic
1321C22#1176347911yescharacteristic
1322C22#1176347911yescharacteristic
1323C22#1176349011yescharacteristic
1324C22#1176350211yescharacteristic
1325C22#1176350211yescharacteristic
1326C22#1176350611yescharacteristic
1327C22#1176352311yescharacteristic
1328C22#1176354511yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—42no—
1332C4—42no—
1333C4—344no—
1334C4—344no—
1335C4—682no—
1336C4—682no—
1337C4—682no—
1338C4—682no—
1339C4—1361no—
1340C4—1361no—
1341C2—44no—
1342C2—44no—
1343C2—82no—
1344C2#120×Dic1711yescharacteristic
1345C2#121×Dic1711yescharacteristic
1346C2#1453144511yescharacteristic
1347C2#1453176811yescharacteristic
1348C2#1453182611yescharacteristic
1349C2#1453183611yescharacteristic
1350C2#1453184911yescharacteristic
1351C2#1453215111yescharacteristic
1352C2#1453219511yescharacteristic
1353C2#1453239811yescharacteristic
1354C2#1453267111yescharacteristic
1355C2#1453267711yescharacteristic
1356C2#1453271611yescharacteristic
1357C2#1453283011yescharacteristic
1358C2#1453438911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
Fitting, prime radicalC2×C17×#392C2
socle, cosocleC24×C17C24
hypercenterC2×#392D17
hypocenterC17#14187
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic17C2semidirect
2. C2×#11762712C2semidirect
3. C2×#11762702C2semidirect
4. C2×#11762689C2semidirect
5. C2×#11762689C2semidirect
6. C2×C22⋊C4×Dic17C2semidirect
7. #14527029C2semidirect
8. #14527025C2semidirect
9. #14527025C2semidirect
10. #14527021C2semidirect
11. #14527021C2semidirect
12. #14527018C2semidirect
13. #14527018C2semidirect
14. #14527006C2semidirect
58. C17×#392C4semidirect
82. C22×D4×C17C2×C4semidirect
83. C22×D4×C17C2×C4semidirect
101. C23×Dic17D4semidirect
116. C2×C22⋊C4×C17C2×C4semidirect
117. C2×C22⋊C4×C17C2×C4semidirect
118. C2×C22⋊C4×C17C2×C4semidirect
148. C2×C22⋊Dic17D4semidirect
155. C2×C4⋊Dic17D4semidirect
165. C17×#95C2×C4semidirect
176. #10587502D4semidirect
511. C2×C4×C17C4×D4semidirect
703. #392Dic17semidirect
761. C22×D4C2×Dic17semidirect
762. C22×D4C2×Dic17semidirect
832. C2×C22⋊C4C2×Dic17semidirect
833. C2×C22⋊C4C2×Dic17semidirect
834. C2×C22⋊C4C2×Dic17semidirect
855. #95C2×Dic17semidirect
856. C17#14187semidirect
1248. C2×C4D4×Dic17semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic172
C2×#117627122
C2×#117627022
C2×#117626892
C2×C22⋊C4×Dic172
#145270292
#145270252
#145270212
#145270182
#145270062
C2×C17×#3922
#1418717