Finite Group Databasebeta

← #16956116

Subgroups — #16956116

Order 4352.

2550 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587567C211yesmaximal, characteristic
2C2×#11762725C211yesmaximal, characteristic
3C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
6C2×#11762656C211yesmaximal, characteristic, complemented
7C2×#11762656C211yesmaximal, characteristic, complemented
8#14527042C211yesmaximal, characteristic, complemented
9#14527036C211yesmaximal, characteristic, complemented
10#14527032C211yesmaximal, characteristic, complemented
11#14527031C211yesmaximal, characteristic, complemented
12#14527026C211yesmaximal, characteristic, complemented
13#14527023C211yesmaximal, characteristic
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×#63225C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36#11762725C418yescomplemented
37C4⋊C4×Dic17—24no—
38C22⋊C4×Dic17—24no—
39C22⋊C4×Dic17—24no—
40#11762656—24no—
41#11762656—24no—
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
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⋊D17—22no—
73C22×C22⋊D17—22no—
74C22×C22⋊D17C2×C414yes—
75C23×Dic17—22no—
76C23×Dic17—22no—
77C23×Dic17—22no—
78C23×Dic17—22no—
79C23×Dic17—22no—
80C23×Dic17—22no—
81C23×Dic17D414yes—
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—22no—
95C22×C4×D17D414yes—
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—22no—
107C2×C22⋊C4×C17C2×C414yescomplemented
108C2×C22⋊Dic17—22no—
109C2×C22⋊Dic17—22no—
110C2×C22⋊Dic17—22no—
111C2×C22⋊Dic17—22no—
112C2×C22⋊Dic17—22no—
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—22no—
124C2×#63227—22no—
125C2×#63227—22no—
126C2×#63227—22no—
127C2×#63227C2×C414yescomplemented
128C2×#63227C2×C414yescomplemented
129C2×C4⋊Dic17—22no—
130C2×C4⋊Dic17—22no—
131C2×C4⋊Dic17C2×C414yescomplemented
132C2×#63225—22no—
133C2×#63225—22no—
134C2×#63225—22no—
135C2×C4×Dic17—22no—
136C2×C4×Dic17—22no—
137C2×C4×Dic17—22no—
138C2×C4×Dic17—22no—
139C2×C4×Dic17—22no—
140C2×C4×Dic17—22no—
141C2×C4×Dic17—22no—
142C2×C4×Dic17—22no—
143C2×C4×Dic17—22no—
144C2×C4×Dic17—22no—
145C2×C4×Dic17—22no—
146C2×C4×Dic17—22no—
147C2×C4×Dic17—22no—
148C2×C4×Dic17D414yes—
149C2×C4×Dic17D414yescomplemented
150#10587567—232no—
151C17×#95—22no—
152C17×#95—22no—
153C17×#95—22no—
154#10587502—22no—
155#10587502—22no—
156#10587502—22no—
157#10587502—22no—
158#10587502—22no—
159#10587502—22no—
160#10587502—22no—
161#10587502—22no—
162#10587502—22no—
163#10587502—22no—
164#10587502C2×C414yescomplemented
165C24×C17—21no—
166C24×C17—21no—
167C24×C17—21no—
168C24×C17—21no—
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×C17C22×C412yes—
178C24×C17C2×D412yes—
179C24×C17#4112yes—
180C24×C17C2411yescharacteristic
181C23×D17—21no—
182C23×D17—21no—
183C23×D17—21no—
184C23×D17—21no—
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×D17C22×C412yes—
194C23×D17C2×D412yes—
195C23×D17#4112yes—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
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×C17C22×C412yes—
231C22×C4×C17C22×C412yes—
232C22×C4×C17C2×D412yes—
233C22×C4×C17C2×D412yes—
234C22×C4×C17C2×D412yes—
235C22×C4×C17#4112yes—
236C22×C4×C17#4112yes—
237C22×C4×C17#4112yes—
238C2×C22⋊D17—28no—
239C2×C22⋊D17—28no—
240C2×C22⋊D17—28no—
241C2×C22⋊D17—28no—
242C2×C22⋊D17—28no—
243C2×C22⋊D17—28no—
244C2×C22⋊D17—28no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
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—28no—
280C22×Dic17—28no—
281C22×Dic17—28no—
282C22×Dic17—44no—
283C22×Dic17—44no—
284C22×Dic17—44no—
285C22×Dic17—44no—
286C22×Dic17C22×C412yes—
287C22×Dic17C22×C412yes—
288C22×Dic17C22×C412yes—
289C22×Dic17C2×D412yes—
290C22×Dic17C2×D412yes—
291C22×Dic17C2×D412yes—
292C22×Dic17C2×D412yes—
293C22×Dic17C2×D412yes—
294C22×Dic17C2×D412yes—
295C22×Dic17C2×D412yes—
296C22×Dic17#4112yes—
297C22×Dic17#4112yes—
298C22×Dic17#4112yes—
299C22×Dic17#4112yes—
300C22×Dic17#4112yes—
301C2×C4×D17—28no—
302C2×C4×D17—28no—
303C2×C4×D17—28no—
304C2×C4×D17—44no—
305C2×C4×D17—44no—
306C2×C4×D17—44no—
307C2×C4×D17—44no—
308C4⋊C4×C17—28no—
309C22⋊C4×C17—28no—
310C22⋊C4×C17—28no—
311C22⋊C4×C17—28no—
312C22⋊Dic17—28no—
313C22⋊Dic17—28no—
314#63227—28no—
315#63227—28no—
316#63227—28no—
317#63227—28no—
318#63227—28no—
319C4⋊Dic17—28no—
320#63225—28no—
321C4×Dic17—28no—
322C4×Dic17—28no—
323C4×Dic17—44no—
324C4×Dic17—44no—
325C4×Dic17—44no—
326C4×#394—171nomaximal, Sylow
327C23×C17—22no—
328C23×C17—22no—
329C23×C17—22no—
330C23×C17—22no—
331C23×C17—22no—
332C23×C17—22no—
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—41no—
346C23×C17—41no—
347C23×C17—41no—
348C23×C17—41no—
349C23×C17—41no—
350C23×C17—41no—
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×C17C4×D414yes—
362C23×C17C23×C411yescharacteristic
363C23×C17C22×D411yescharacteristic
364C23×C17C22×D411yescharacteristic
365C23×C17C22×D411yescharacteristic
366C23×C17C22×D411yescharacteristic
367C23×C17C2×#4111yescharacteristic
368C23×C17C2×#4111yescharacteristic
369C23×C17C2×#4111yescharacteristic
370C23×C17C2×#4111yescharacteristic
371C23×C17C2×#4111yescharacteristic
372C23×C17C2×#4111yescharacteristic
373C23×C17C2×#4111yescharacteristic
374C23×C17C2×#4111yescharacteristic
375C23×C17C2×#4111yescharacteristic
376C23×C17C2×#4111yescharacteristic
377C22×D17—22no—
378C22×D17—22no—
379C22×D17—22no—
380C22×D17—22no—
381C22×D17—22no—
382C22×D17—22no—
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—41no—
396C22×D17—41no—
397C22×D17—41no—
398C22×D17—41no—
399C22×D17—41no—
400C22×D17—41no—
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×D17C4×D414yes—
412C2×C4×C17—22no—
413C2×C4×C17—22no—
414C2×C4×C17—22no—
415C2×C4×C17—22no—
416C2×C4×C17—22no—
417C2×C4×C17—22no—
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—41no—
434C2×C4×C17—41no—
435C2×C4×C17—41no—
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×C17C4×D414yescomplemented
454C22⋊D17—232no—
455C2×Dic17—22no—
456C2×Dic17—22no—
457C2×Dic17—22no—
458C2×Dic17—22no—
459C2×Dic17—22no—
460C2×Dic17—22no—
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—41no—
477C2×Dic17—41no—
478C2×Dic17—41no—
479C2×Dic17—41no—
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—416no—
497C2×Dic17C4×D414yes—
498C2×Dic17#12014yes—
499C2×Dic17#12114yes—
500C2×Dic17#12114yes—
501C2×Dic17#12114yes—
502C2×Dic17#12314yes—
503C2×Dic17#12314yes—
504C2×Dic17#12414yes—
505C4×D17—416no—
506C22×C4×D4—171no—
507C2×#394—171no—
508C2×C4×C4⋊C4—171no—
509C2×C4×C22⋊C4—171no—
510C2×C4×C22⋊C4—171no—
511C2×C4×C22⋊C4—171no—
512C2×C4×C22⋊C4—171no—
513#1442—171no—
514#1441—171no—
515#1440—171no—
516#1440—171no—
517#1439—171no—
518#1439D1711yescharacteristic, complemented
519#1438—171no—
520C4×#95—171no—
521C22×C17—24no—
522C22×C17—24no—
523C22×C17—24no—
524C22×C17—42no—
525C22×C17—42no—
526C22×C17—42no—
527C22×C17—42no—
528C22×C17—42no—
529C22×C17—42no—
530C22×C17—42no—
531C22×C17—42no—
532C22×C17—42no—
533C22×C17—42no—
534C22×C17—42no—
535C22×C17—42no—
536C22×C17C2×C4×D411yescharacteristic
537C22×C17C2×C4×D411yescharacteristic
538C22×C17C2×C4×D411yescharacteristic
539C22×C17C2×C4×D411yescharacteristic
540C22×C17C4×#4111yescharacteristic
541C22×C17C4×#4111yescharacteristic
542C22×C17C4×#4111yescharacteristic
543C22×C17C2×#12011yescharacteristic
544C22×C17C2×#12111yescharacteristic
545C22×C17C2×#12111yescharacteristic
546C22×C17C2×#12111yescharacteristic
547C22×C17C2×#12311yescharacteristic
548C22×C17C2×#12311yescharacteristic
549C22×C17#52511yescharacteristic
550C22×C17#52511yescharacteristic
551C22×C17#52511yescharacteristic
552C22×C17#52511yescharacteristic
553C22×C17#52511yescharacteristic
554C22×C17#52511yescharacteristic
555C22×C17#52511yescharacteristic
556C22×C17#52511yescharacteristic
557C22×C17C2×#12411yescharacteristic
558C22×C17#52911yescharacteristic
559C22×C17#52911yescharacteristic
560C22×C17#52911yescharacteristic
561C22×C17#52911yescharacteristic
562C22×C17#52911yescharacteristic
563C22×C17#52911yescharacteristic
564C22×C17#52911yescharacteristic
565C22×C17#52911yescharacteristic
566C22×C17#52911yescharacteristic
567C22×C17#53211yescharacteristic
568C22×C17#53211yescharacteristic
569C22×C17#53211yescharacteristic
570C22×C17#53211yescharacteristic
571C2×D17—24no—
572C2×D17—24no—
573C2×D17—24no—
574C2×D17—42no—
575C2×D17—42no—
576C2×D17—42no—
577C2×D17—42no—
578C2×D17—42no—
579C2×D17—42no—
580C2×D17—42no—
581C2×D17—42no—
582C2×D17—42no—
583C2×D17—42no—
584C2×D17—42no—
585C2×D17—42no—
586C4×C17—24no—
587C4×C17—42no—
588C4×C17—42no—
589C4×C17—42no—
590C4×C17—42no—
591C4×C17—42no—
592Dic17—24no—
593Dic17—42no—
594Dic17—42no—
595Dic17—42no—
596Dic17—42no—
597Dic17—42no—
598Dic17#39418yescomplemented
599C23×D4—171no—
600C24×C4—171no—
601C24×C4—171no—
602C2×C4×D4—344no—
603C2×C4×D4—344no—
604C2×C4×D4—344no—
605C22×C4⋊C4—171no—
606C22×C4⋊C4—171no—
607C22×C4⋊C4C2×D1711yescharacteristic
608C22×C22⋊C4—171no—
609C22×C22⋊C4—171no—
610C22×C22⋊C4—171no—
611C22×C22⋊C4—171no—
612C22×C22⋊C4—171no—
613C22×C22⋊C4—171no—
614C22×C22⋊C4—171no—
615C22×C22⋊C4C2×D1711yescharacteristic
616C22×C22⋊C4C2×D1711yescharacteristic
617C22×C22⋊C4C2×D1711yescharacteristic
618C22×C42—171no—
619C22×C42—171no—
620C22×C42—171no—
621C22×C42—171no—
622C22×C42—171no—
623#394—178no—
624C4×C4⋊C4—344no—
625C4×C22⋊C4—344no—
626C4×C22⋊C4—344no—
627C4×C22⋊C4—344no—
628C4×C22⋊C4—344no—
629C2×#95—171no—
630C2×#95—171no—
631C2×#95—171no—
632C2×#95—171no—
633C2×#95—171no—
634C2×#95—171no—
635C2×#95—171no—
636C2×#95—171no—
637C2×#95—171no—
638C2×#95—171no—
639C2×#95—171no—
640C2×#95C2×D1711yescharacteristic
641C2×#95C2×D1711yescharacteristic
642C2×#95C2×D1711yescharacteristic
643C2×C17—44no—
644C2×C17C4×#12011yescharacteristic
645C2×C17C4×#12111yescharacteristic
646C2×C17C4×#12111yescharacteristic
647C2×C17C4×#12111yescharacteristic
648C2×C17C4×#12311yescharacteristic
649C2×C17C4×#12311yescharacteristic
650C2×C17C4×#12411yescharacteristic
651C2×C17C2×#39411yescharacteristic
652C2×C17#238811yescharacteristic
653C2×C17#239211yescharacteristic
654C2×C17#239211yescharacteristic
655C2×C17#239211yescharacteristic
656C2×C17#239511yescharacteristic
657C2×C17#239511yescharacteristic
658C2×C17#239811yescharacteristic
659D17—44no—
660C25—171no—
661C25C22×D1711yescharacteristic
662C22×D4—174no—
663C22×D4—342no—
664C22×D4—342no—
665C22×D4—342no—
666C22×D4—342no—
667C22×D4—342no—
668C22×D4—342no—
669C23×C4—171no—
670C23×C4—171no—
671C23×C4—174no—
672C23×C4—171no—
673C23×C4—171no—
674C23×C4—171no—
675C23×C4—171no—
676C23×C4—171no—
677C23×C4—174no—
678C23×C4—342no—
679C23×C4—342no—
680C23×C4—342no—
681C23×C4—342no—
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×C4C22×D1711yescharacteristic
691C23×C4C22×D1711yescharacteristic
692C23×C4C22×D1711yescharacteristic
693C23×C4C22×D1711yescharacteristic
694C23×C4C22×D1711yescharacteristic
695C23×C4C22×D1711yescharacteristic
696C4×D4—3432no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—174no—
701C2×C4⋊C4—342no—
702C2×C4⋊C4—342no—
703C2×C4⋊C4—342no—
704C2×C4⋊C4—342no—
705C2×C4⋊C4—342no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—174no—
715C2×C22⋊C4—174no—
716C2×C22⋊C4—174no—
717C2×C22⋊C4—342no—
718C2×C22⋊C4—342no—
719C2×C22⋊C4—342no—
720C2×C22⋊C4—342no—
721C2×C22⋊C4—342no—
722C2×C22⋊C4—342no—
723C2×C22⋊C4—342no—
724C2×C22⋊C4—342no—
725C2×C22⋊C4—342no—
726C2×C22⋊C4—342no—
727C2×C22⋊C4—342no—
728C2×C22⋊C4—342no—
729C2×C22⋊C4—342no—
730C2×C22⋊C4—342no—
731C2×C22⋊C4—342no—
732C2×C22⋊C4—342no—
733C2×C22⋊C4—342no—
734C2×C22⋊C4—342no—
735C2×C22⋊C4C4×D1714yescomplemented
736C2×C42—174no—
737C2×C42—174no—
738C2×C42—342no—
739C2×C42—342no—
740C2×C42—342no—
741C2×C42—342no—
742C2×C42—342no—
743C2×C42—342no—
744C2×C42—342no—
745C2×C42—342no—
746C2×C42—342no—
747C2×C42—342no—
748C2×C42—342no—
749C2×C42—342no—
750C2×C42—342no—
751#95—22no—
752#95—22no—
753#95—22no—
754#95—174no—
755#95—342no—
756#95—342no—
757#95—342no—
758#95—342no—
759#95—342no—
760#95—342no—
761#95—342no—
762#95—342no—
763#95—342no—
764#95—342no—
765C17C4×#39411yescharacteristic, complemented, Sylow
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—172no—
779C24—172no—
780C24—172no—
781C24—341no—
782C24—341no—
783C24—341no—
784C24—341no—
785C24—341no—
786C24—341no—
787C24—341no—
788C24—341no—
789C24—341no—
790C24—341no—
791C24—341no—
792C24—341no—
793C24C2×C4×D1712yes—
794C24D4×D1712yes—
795C24#6325612yes—
796C24C23×D1711yescharacteristic
797C2×D4—348no—
798C2×D4—348no—
799C2×D4—348no—
800C2×D4—348no—
801C2×D4—348no—
802C2×D4—348no—
803C2×D4—348no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
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—172no—
839C22×C4—172no—
840C22×C4—172no—
841C22×C4—172no—
842C22×C4—172no—
843C22×C4—172no—
844C22×C4—172no—
845C22×C4—172no—
846C22×C4—172no—
847C22×C4—172no—
848C22×C4—172no—
849C22×C4—172no—
850C22×C4—172no—
851C22×C4—172no—
852C22×C4—172no—
853C22×C4—348no—
854C22×C4—348no—
855C22×C4—348no—
856C22×C4—348no—
857C22×C4—348no—
858C22×C4—348no—
859C22×C4—341no—
860C22×C4—341no—
861C22×C4—341no—
862C22×C4—341no—
863C22×C4—341no—
864C22×C4—341no—
865C22×C4—341no—
866C22×C4—341no—
867C22×C4—341no—
868C22×C4—341no—
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—684no—
894C22×C4—684no—
895C22×C4—684no—
896C22×C4—684no—
897C22×C4—684no—
898C22×C4—684no—
899C22×C4—684no—
900C22×C4—684no—
901C22×C4C2×C4×D1712yes—
902C22×C4C2×C4×D1712yes—
903C22×C4D4×D1712yes—
904C22×C4D4×D1712yes—
905C22×C4D4×D1712yes—
906C22×C4#6325412yes—
907C22×C4#6325412yes—
908C22×C4#6325412yes—
909C4⋊C4—28no—
910C4⋊C4—348no—
911C4⋊C4—348no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—348no—
916C22⋊C4—348no—
917C22⋊C4—348no—
918C22⋊C4—348no—
919C22⋊C4—348no—
920C22⋊C4—348no—
921C22⋊C4—348no—
922C42—348no—
923C42—348no—
924C42—684no—
925C42—684no—
926C42—684no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—174no—
962C23—342no—
963C23—342no—
964C23—342no—
965C23—342no—
966C23—342no—
967C23—342no—
968C23—342no—
969C23—342no—
970C23—342no—
971C23—342no—
972C23—342no—
973C23—342no—
974C23—342no—
975C23—342no—
976C23—342no—
977C23—342no—
978C23—342no—
979C23—342no—
980C23—681no—
981C23—681no—
982C23—681no—
983C23—681no—
984C23—681no—
985C23—681no—
986C23—681no—
987C23—681no—
988C23—681no—
989C23—681no—
990C23—681no—
991C23—681no—
992C23—681no—
993C23—681no—
994C23—681no—
995C23—681no—
996C23#1058757914yes—
997C23C22×C4×D1711yescharacteristic
998C23C2×D4×D1711yescharacteristic
999C23C2×D4×D1711yescharacteristic
1000C23C2×D4×D1711yescharacteristic
1001C23C2×D4×D1711yescharacteristic
1002C23C2×#6325411yescharacteristic
1003C23C2×#6325411yescharacteristic
1004C23C2×#6325411yescharacteristic
1005C23C2×#6325611yescharacteristic
1006C23#41×D1711yescharacteristic
1007C23#41×D1711yescharacteristic
1008C23#41×D1711yescharacteristic
1009C23#41×D1711yescharacteristic
1010C23#41×D1711yescharacteristic
1011C23#41×D1711yescharacteristic
1012D4—3432no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
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—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
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—174no—
1055C2×C4—174no—
1056C2×C4—174no—
1057C2×C4—174no—
1058C2×C4—174no—
1059C2×C4—174no—
1060C2×C4—174no—
1061C2×C4—174no—
1062C2×C4—342no—
1063C2×C4—342no—
1064C2×C4—342no—
1065C2×C4—342no—
1066C2×C4—342no—
1067C2×C4—342no—
1068C2×C4—342no—
1069C2×C4—342no—
1070C2×C4—342no—
1071C2×C4—342no—
1072C2×C4—342no—
1073C2×C4—342no—
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—6816no—
1084C2×C4—6816no—
1085C2×C4—681no—
1086C2×C4—681no—
1087C2×C4—681no—
1088C2×C4—681no—
1089C2×C4—681no—
1090C2×C4—681no—
1091C2×C4—681no—
1092C2×C4—681no—
1093C2×C4—681no—
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#1058756714yescomplemented
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—344no—
1122C22—344no—
1123C22—344no—
1124C22—682no—
1125C22—682no—
1126C22—682no—
1127C22—682no—
1128C22—682no—
1129C22—682no—
1130C22—682no—
1131C22—682no—
1132C22—682no—
1133C22—682no—
1134C22—682no—
1135C22—682no—
1136C22C4×D4×D1711yescharacteristic
1137C22C4×D4×D1711yescharacteristic
1138C22C2×#1058756711yescharacteristic
1139C22C2×#1058757911yescharacteristic
1140C22C4×#6325411yescharacteristic
1141C22C4×#6325411yescharacteristic
1142C22#1176327711yescharacteristic
1143C22#120×D1711yescharacteristic
1144C22#121×D1711yescharacteristic
1145C22#121×D1711yescharacteristic
1146C22#121×D1711yescharacteristic
1147C22#123×D1711yescharacteristic
1148C22#123×D1711yescharacteristic
1149C22#1176331511yescharacteristic
1150C22#1176331511yescharacteristic
1151C22#1176331711yescharacteristic
1152C22#1176331911yescharacteristic
1153C22#1176331911yescharacteristic
1154C22#1176332211yescharacteristic
1155C22#1176332211yescharacteristic
1156C22#1176332211yescharacteristic
1157C22#124×D1711yescharacteristic
1158C22#1176333611yescharacteristic
1159C22#1176333611yescharacteristic
1160C22#1176333811yescharacteristic
1161C22#1176333811yescharacteristic
1162C22#1176334211yescharacteristic
1163C22#1176334211yescharacteristic
1164C22#1176334511yescharacteristic
1165C22#1176334511yescharacteristic
1166C22#1176334511yescharacteristic
1167C22#1176335411yescharacteristic
1168C22#1176335411yescharacteristic
1169C22#1176335411yescharacteristic
1170C22#1176335711yescharacteristic
1171C4—24no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—178no—
1178C4—344no—
1179C4—682no—
1180C4—682no—
1181C4—682no—
1182C4—682no—
1183C4—682no—
1184C2—44no—
1185C2—684no—
1186C2#1453128511yescharacteristic
1187C2#1453129011yescharacteristic
1188C2#1453129411yescharacteristic
1189C2#1453130011yescharacteristic
1190C2#1453130311yescharacteristic
1191C2#1453131111yescharacteristic
1192C2#1453132511yescharacteristic
1193C2D17×#39411yescharacteristic
1194C2#1453199611yescharacteristic
1195C2#1453202711yescharacteristic
1196C2#1453202911yescharacteristic
1197C2#1453202911yescharacteristic
1198C2#1453204211yescharacteristic
1199C2#1453204911yescharacteristic
1200C2#1453206611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1439C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1439D17
hypocenterC17C4×#394
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic17C2semidirect
4. C2×C22⋊C4×Dic17C2semidirect
5. C2×C22⋊C4×Dic17C2semidirect
6. C2×#11762656C2semidirect
7. C2×#11762656C2semidirect
8. #14527042C2semidirect
9. #14527036C2semidirect
10. #14527032C2semidirect
11. #14527031C2semidirect
12. #14527026C2semidirect
14. #95×Dic17C2semidirect
15. C17×#1439C2semidirect
36. #11762725C4semidirect
107. C2×C22⋊C4×C17C2×C4semidirect
113. C2×C22⋊Dic17C2×C4semidirect
127. C2×#63227C2×C4semidirect
128. C2×#63227C2×C4semidirect
131. C2×C4⋊Dic17C2×C4semidirect
149. C2×C4×Dic17D4semidirect
164. #10587502C2×C4semidirect
453. C2×C4×C17C4×D4semidirect
518. #1439D17semidirect
598. Dic17#394semidirect
735. C2×C22⋊C4C4×D17semidirect
765. C17C4×#394semidirect
1105. 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×#117627252
C2×C4⋊C4×Dic172
C2×C22⋊C4×Dic172
C2×#117626562
#145270422
#145270362
#145270322
#145270312
#145270262
#145270232
#95×Dic172
C17×#14392
C4×#39417