Finite Group Databasebeta

← #16955822

Subgroups — #16955822

Order 4352.

2882 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587567C211yesmaximal, characteristic
2C2×#11762688C211yesmaximal, characteristic
3C2×#11762686C211yesmaximal, characteristic
4C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
5C2×C4×#63227C211yesmaximal, characteristic, complemented
6C22×#10587502C211yesmaximal, characteristic, complemented
7#14527022C211yesmaximal, characteristic, complemented
8#14527020C211yesmaximal, characteristic, complemented
9#14527019C211yesmaximal, characteristic, complemented
10#14527017C211yesmaximal, characteristic, complemented
11#14527008C211yesmaximal, characteristic, complemented
12#14527006C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14C4×#10587502C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C17C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C24×Dic17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C2×#10587567—24no—
21C2×#10587567—24no—
22C2×#10587567C418yescomplemented
23C22×#63225C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33#11762688C418yescomplemented
34#11762686C418yescomplemented
35C22⋊C4×Dic17—24no—
36C4×#63227—24no—
37C2×#10587502—24no—
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C24×C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C22×C42×C17C2211yescharacteristic
56C22×C42×C17C2211yescharacteristic
57C4×C22⋊C4×C17—24no—
58C2×C17×#95C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C25×C17C2311yescharacteristic
61C24×D17C2311yescharacteristic
62C23×C4×C17—22no—
63C23×C4×C17—22no—
64C23×C4×C17—22no—
65C23×C4×C17—22no—
66C23×C4×C17—41no—
67C23×C4×C17—41no—
68C23×C4×C17C2×C414yescomplemented
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C22×C22⋊D17—22no—
76C22×C22⋊D17—22no—
77C22×C22⋊D17—22no—
78C22×C22⋊D17—22no—
79C22×C22⋊D17C2×C414yes—
80C22×C22⋊D17C2×C414yes—
81C22×C22⋊D17C2×C414yes—
82C23×Dic17—22no—
83C23×Dic17—22no—
84C23×Dic17—22no—
85C23×Dic17—22no—
86C23×Dic17—22no—
87C23×Dic17—22no—
88C23×Dic17—22no—
89C23×Dic17—22no—
90C23×Dic17—41no—
91C23×Dic17—41no—
92C23×Dic17—41no—
93C23×Dic17—41no—
94C23×Dic17C2×C414yes—
95C23×Dic17C2×C414yescomplemented
96C23×Dic17C2311yescharacteristic
97C23×Dic17C2311yescharacteristic
98C23×Dic17C2311yescharacteristic
99C23×Dic17C2311yescharacteristic
100C23×Dic17C2311yescharacteristic
101C23×Dic17C2311yescharacteristic
102C23×Dic17C2311yescharacteristic
103C22×C4×D17—22no—
104C22×C4×D17—22no—
105C22×C4×D17—22no—
106C22×C4×D17—22no—
107C22×C4×D17—41no—
108C22×C4×D17—41no—
109C22×C4×D17C2×C414yescomplemented
110C2×C22⋊C4×C17—22no—
111C2×C22⋊C4×C17—22no—
112C2×C22⋊C4×C17C2×C414yes—
113C2×C22⋊C4×C17C2×C414yescomplemented
114C2×C22⋊C4×C17D414yes—
115C2×C22⋊C4×C17D414yes—
116C2×C42×C17—22no—
117C2×C42×C17—22no—
118C2×C42×C17—22no—
119C2×C42×C17—22no—
120C2×C42×C17—41no—
121C2×C42×C17—41no—
122C2×C22⋊Dic17—22no—
123C2×C22⋊Dic17—22no—
124C2×C22⋊Dic17C2×C414yescomplemented
125C2×#63227—22no—
126C2×#63227—22no—
127C2×#63227—22no—
128C2×#63227—22no—
129C2×#63227—22no—
130C2×#63227—22no—
131C2×#63227—41no—
132C2×#63227—41no—
133C2×#63227—41no—
134C2×#63227—41no—
135C2×#63227C2×C414yescomplemented
136C2×#63227C2×C414yescomplemented
137C2×#63227C2×C414yescomplemented
138C2×#63227C2×C414yescomplemented
139C2×#63227C2×C414yescomplemented
140C2×#63225—22no—
141C2×#63225—22no—
142C2×#63225C2×C414yescomplemented
143C2×C4×Dic17—22no—
144C2×C4×Dic17—22no—
145C2×C4×Dic17—22no—
146C2×C4×Dic17—22no—
147C2×C4×Dic17—22no—
148C2×C4×Dic17—22no—
149C2×C4×Dic17—41no—
150C2×C4×Dic17—41no—
151C2×C4×Dic17C2×C414yescomplemented
152#10587567—232no—
153C17×#95—22no—
154C17×#95—22no—
155#10587502—22no—
156#10587502—22no—
157#10587502—22no—
158#10587502—22no—
159#10587502—22no—
160#10587502—22no—
161#10587502—22no—
162#10587502—41no—
163#10587502—41no—
164#10587502C2×C414yescomplemented
165#10587502C2×C414yescomplemented
166#10587502C2×C414yescomplemented
167#10587502C2×C414yescomplemented
168#10587502D414yescomplemented
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×C17C22×C412yes—
179C24×C17C22×C412yes—
180C24×C17C2×D412yes—
181C24×C17C2×D412yes—
182C24×C17#4112yes—
183C24×C17#4112yes—
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×D17C22×C412yes—
199C23×D17C22×C412yes—
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—28no—
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—28no—
232C22×C4×C17—44no—
233C22×C4×C17—44no—
234C22×C4×C17—44no—
235C22×C4×C17—44no—
236C22×C4×C17—44no—
237C22×C4×C17C22×C412yes—
238C22×C4×C17C22×C412yes—
239C22×C4×C17C22×C412yes—
240C22×C4×C17C22×C412yes—
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×C17C2×D412yes—
248C22×C4×C17#4112yes—
249C2×C22⋊D17—28no—
250C2×C22⋊D17—28no—
251C2×C22⋊D17—28no—
252C2×C22⋊D17—28no—
253C2×C22⋊D17—28no—
254C2×C22⋊D17—28no—
255C2×C22⋊D17C42116yescomplemented
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—28no—
269C22×Dic17—28no—
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—21no—
290C22×Dic17—21no—
291C22×Dic17—21no—
292C22×Dic17—21no—
293C22×Dic17—21no—
294C22×Dic17—28no—
295C22×Dic17—28no—
296C22×Dic17—44no—
297C22×Dic17—44no—
298C22×Dic17—44no—
299C22×Dic17—44no—
300C22×Dic17—44no—
301C22×Dic17—44no—
302C22×Dic17—44no—
303C22×Dic17—44no—
304C22×Dic17—44no—
305C22×Dic17—44no—
306C22×Dic17C22×C412yes—
307C22×Dic17C22×C412yes—
308C22×Dic17C22×C412yes—
309C22×Dic17C22×C412yes—
310C22×Dic17C22×C412yes—
311C22×Dic17C22×C412yes—
312C22×Dic17C22×C412yes—
313C22×Dic17C22×C412yes—
314C22×Dic17C22×C412yes—
315C22×Dic17C2×D412yes—
316C22×Dic17C2×D412yes—
317C22×Dic17#4112yes—
318C22×Dic17#4112yes—
319C2×C4×D17—28no—
320C2×C4×D17—28no—
321C2×C4×D17—44no—
322C2×C4×D17—44no—
323C2×C4×D17—44no—
324C2×C4×D17—44no—
325C2×C4×D17—44no—
326C22⋊C4×C17—28no—
327C22⋊C4×C17C22⋊C4116yescomplemented
328C42×C17—44no—
329C42×C17—44no—
330C22⋊Dic17—28no—
331#63227—28no—
332#63227—28no—
333#63227—28no—
334#63227—44no—
335#63227—44no—
336#63225—28no—
337C4×Dic17—28no—
338C4×Dic17—44no—
339C4×Dic17—44no—
340#13813—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—22no—
360C23×C17—22no—
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×C17C2×C4214yes—
370C23×C17C2×C22⋊C414yes—
371C23×C17#11714yes—
372C23×C17C4×D414yes—
373C23×C17C4×D414yes—
374C23×C17C4×D414yes—
375C23×C17C4×D414yes—
376C23×C17C23×C411yescharacteristic
377C23×C17C23×C411yescharacteristic
378C23×C17C23×C411yescharacteristic
379C23×C17C22×D411yescharacteristic
380C23×C17C22×D411yescharacteristic
381C23×C17C22×D411yescharacteristic
382C23×C17C2×#4111yescharacteristic
383C23×C17C2×#4111yescharacteristic
384C23×C17C2×#4111yescharacteristic
385C23×C17C2×#4111yescharacteristic
386C23×C17C2×#4111yescharacteristic
387C23×C17H(5,𝔽2)11yescharacteristic
388C23×C17H(5,𝔽2)11yescharacteristic
389C23×C17H(5,𝔽2)11yescharacteristic
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×C4214yes—
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—22no—
445C2×C4×C17—22no—
446C2×C4×C17—22no—
447C2×C4×C17—22no—
448C2×C4×C17—22no—
449C2×C4×C17—22no—
450C2×C4×C17—22no—
451C2×C4×C17—22no—
452C2×C4×C17—22no—
453C2×C4×C17—416no—
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×C17C2×C22⋊C414yes—
467C2×C4×C17C2×C22⋊C414yes—
468C2×C4×C17C4×D414yescomplemented
469C22⋊D17—232no—
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—22no—
491C2×Dic17—22no—
492C2×Dic17—22no—
493C2×Dic17—22no—
494C2×Dic17—22no—
495C2×Dic17—22no—
496C2×Dic17—22no—
497C2×Dic17—22no—
498C2×Dic17—22no—
499C2×Dic17—22no—
500C2×Dic17—416no—
501C2×Dic17—416no—
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×Dic17—41no—
511C2×Dic17—41no—
512C2×Dic17—41no—
513C2×Dic17—41no—
514C2×Dic17—41no—
515C2×Dic17—41no—
516C2×Dic17—41no—
517C2×Dic17—41no—
518C2×Dic17C2×C4214yes—
519C2×Dic17C4×D414yes—
520C2×Dic17C4×D414yescomplemented
521C4×D17—416no—
522C22×C4×D4—171no—
523C2×#386—171no—
524C2×#386—171no—
525C2×C4×C22⋊C4—171no—
526C2×C4×C22⋊C4—171no—
527C2×C4×C22⋊C4D1711yescharacteristic, complemented
528C22×#95—171no—
529#1437—171no—
530#1437—171no—
531#1436—171no—
532#1436—171no—
533#1434—171no—
534C22⋊#95—171no—
535C22⋊#95—171no—
536C4×#95—171no—
537C22×C17—24no—
538C22×C17—24no—
539C22×C17—24no—
540C22×C17—24no—
541C22×C17—24no—
542C22×C17—24no—
543C22×C17—24no—
544C22×C17—24no—
545C22×C17—24no—
546C22×C17—24no—
547C22×C17—24no—
548C22×C17—24no—
549C22×C17—24no—
550C22×C17—24no—
551C22×C17C4×C22⋊C418yescomplemented
552C22×C17C22×C4211yescharacteristic
553C22×C17C22×C22⋊C411yescharacteristic
554C22×C17C2×#11711yescharacteristic
555C22×C17C2×C4×D411yescharacteristic
556C22×C17C2×C4×D411yescharacteristic
557C22×C17C2×C4×D411yescharacteristic
558C22×C17C2×C4×D411yescharacteristic
559C22×C17C2×C4×D411yescharacteristic
560C22×C17C2×C4×D411yescharacteristic
561C22×C17C2×C4×D411yescharacteristic
562C22×C17C4×#4111yescharacteristic
563C22×C17C4×#4111yescharacteristic
564C22×C17C4×#4111yescharacteristic
565C22×C17#51811yescharacteristic
566C22×C17#51811yescharacteristic
567C22×C17#51811yescharacteristic
568C22×C17#52011yescharacteristic
569C22×C17#52011yescharacteristic
570C22×C17#52011yescharacteristic
571C22×C17D4211yescharacteristic
572C22×C17D4211yescharacteristic
573C22×C17#54611yescharacteristic
574C22×C17#54611yescharacteristic
575C22×C17#54611yescharacteristic
576C22×C17#54611yescharacteristic
577C22×C17#54611yescharacteristic
578C22×C17#54711yescharacteristic
579C22×C17#54711yescharacteristic
580C22×C17#54811yescharacteristic
581C22×C17#55111yescharacteristic
582C22×C17#55111yescharacteristic
583C22×C17#55211yescharacteristic
584C22×C17#55311yescharacteristic
585C22×C17#55311yescharacteristic
586C22×C17#55311yescharacteristic
587C2×D17—24no—
588C2×D17—24no—
589C2×D17—24no—
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—
600C2×D17—42no—
601C2×D17—42no—
602C4×C17—24no—
603C4×C17—24no—
604C4×C17—24no—
605C4×C17—42no—
606C4×C17—42no—
607C4×C17—42no—
608Dic17—24no—
609Dic17—24no—
610Dic17—24no—
611Dic17—42no—
612Dic17—42no—
613Dic17—42no—
614Dic17—42no—
615C23×D4—171no—
616C24×C4—171no—
617C24×C4—171no—
618C24×C4—171no—
619C24×C4C2×D1711yescharacteristic
620C2×C4×D4—178no—
621C2×C4×D4—344no—
622C2×C4×D4—344no—
623C22×C4⋊C4—171no—
624C22×C22⋊C4—171no—
625C22×C22⋊C4—171no—
626C22×C22⋊C4—171no—
627C22×C22⋊C4—171no—
628C22×C22⋊C4—171no—
629C22×C22⋊C4—171no—
630C22×C22⋊C4C2×D1711yescharacteristic
631C22×C22⋊C4C2×D1711yescharacteristic
632C22×C42—171no—
633C22×C42—171no—
634C22×C42—171no—
635C22×C42C2×D1711yescharacteristic
636C22×C42C2×D1711yescharacteristic
637#386—178no—
638#386—178no—
639C4×C22⋊C4—24no—
640C4×C22⋊C4—344no—
641C4×C22⋊C4—344no—
642C2×#95—171no—
643C2×#95—171no—
644C2×#95—171no—
645C2×#95—171no—
646C2×#95—171no—
647C2×#95—171no—
648C2×#95—171no—
649C2×#95—171no—
650C2×#95—171no—
651C2×#95—171no—
652C2×#95—171no—
653C2×#95—171no—
654C2×#95—171no—
655C2×#95—171no—
656C2×#95—344no—
657C2×#95C2×D1711yescharacteristic
658C2×#95C2×D1711yescharacteristic
659C2×C17—28no—
660C2×C17C2×C4×C22⋊C411yescharacteristic
661C2×C17C42×D411yescharacteristic
662C2×C17#227511yescharacteristic
663C2×C17D4×C22⋊C411yescharacteristic
664C2×C17#233911yescharacteristic
665C2×C17#235211yescharacteristic
666C2×C17#235311yescharacteristic
667C2×C17#235811yescharacteristic
668C2×C17#235811yescharacteristic
669C2×C17#235911yescharacteristic
670C2×C17#235911yescharacteristic
671C2×C17#236111yescharacteristic
672C2×C17#236111yescharacteristic
673C2×C17#236411yescharacteristic
674C2×C17#236411yescharacteristic
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—22no—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—41no—
690C23×C4—41no—
691C23×C4—171no—
692C23×C4—171no—
693C23×C4—171no—
694C23×C4—171no—
695C23×C4—171no—
696C23×C4—171no—
697C23×C4—171no—
698C23×C4—174no—
699C23×C4—174no—
700C23×C4—174no—
701C23×C4—342no—
702C23×C4—342no—
703C23×C4—342no—
704C23×C4—342no—
705C23×C4—342no—
706C23×C4—342no—
707C23×C4—342no—
708C23×C4—342no—
709C23×C4—342no—
710C23×C4—342no—
711C23×C4—342no—
712C23×C4—342no—
713C23×C4—681no—
714C23×C4—681no—
715C23×C4—681no—
716C23×C4—681no—
717C23×C4—681no—
718C23×C4—681no—
719C23×C4C4×D1714yescomplemented
720C23×C4C22×D1711yescharacteristic
721C23×C4C22×D1711yescharacteristic
722C23×C4C22×D1711yescharacteristic
723C23×C4C22×D1711yescharacteristic
724C23×C4C22×D1711yescharacteristic
725C23×C4C22×D1711yescharacteristic
726C4×D4—3432no—
727C2×C4⋊C4—174no—
728C2×C4⋊C4—342no—
729C2×C4⋊C4—342no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—174no—
733C2×C22⋊C4—174no—
734C2×C22⋊C4—174no—
735C2×C22⋊C4—174no—
736C2×C22⋊C4—174no—
737C2×C22⋊C4—174no—
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⋊C4C4×D1714yes—
751C2×C22⋊C4C4×D1714yescomplemented
752C2×C22⋊C4D6814yes—
753C2×C22⋊C4C22⋊D1714yes—
754C2×C42—22no—
755C2×C42—22no—
756C2×C42—22no—
757C2×C42—22no—
758C2×C42—41no—
759C2×C42—41no—
760C2×C42—174no—
761C2×C42—342no—
762C2×C42—342no—
763C2×C42—342no—
764C2×C42—342no—
765C2×C42—342no—
766C2×C42—342no—
767C2×C42—681no—
768C2×C42—681no—
769#95—22no—
770#95—22no—
771#95—174no—
772#95—174no—
773#95—174no—
774#95—174no—
775#95—174no—
776#95—342no—
777#95—342no—
778#95—342no—
779#95—342no—
780#95—342no—
781#95—342no—
782#95—342no—
783#95—681no—
784#95—681no—
785C17#1381311yescharacteristic, complemented, Sylow
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—172no—
795C24—172no—
796C24—172no—
797C24—341no—
798C24—341no—
799C24—341no—
800C24—341no—
801C24—341no—
802C24—341no—
803C24—341no—
804C24—341no—
805C24—341no—
806C24—341no—
807C24—341no—
808C24—341no—
809C24C2×C4×D1712yes—
810C24C2×C4×D1712yes—
811C24C2×C4×D1712yes—
812C24C2×D6812yes—
813C24#6325212yes—
814C24#6325212yes—
815C24C2×C22⋊D1712yes—
816C24C23×D1711yescharacteristic
817C2×D4—1716no—
818C2×D4—348no—
819C2×D4—348no—
820C2×D4—348no—
821C2×D4—348no—
822C2×D4—348no—
823C2×D4—348no—
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—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—28no—
855C22×C4—28no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—172no—
862C22×C4—172no—
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—348no—
875C22×C4—348no—
876C22×C4—348no—
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—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—348no—
914C22×C4—348no—
915C22×C4—348no—
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×C4—684no—
927C22×C4—684no—
928C22×C4—684no—
929C22×C4—684no—
930C22×C4—684no—
931C22×C4C2×C4×D1712yes—
932C22×C4C2×C4×D1712yes—
933C22×C4C2×C4×D1712yes—
934C22×C4C2×C4×D1712yes—
935C22×C4C2×C4×D1712yes—
936C22×C4C2×C4×D1712yes—
937C22×C4C2×D6812yes—
938C22×C4C2×D6812yes—
939C22×C4D4×D1712yes—
940C22×C4#6325412yes—
941C22×C4C2×C22⋊D1712yes—
942C22×C4C2×C22⋊D1712yes—
943C4⋊C4—348no—
944C22⋊C4—28no—
945C22⋊C4—348no—
946C22⋊C4—348no—
947C22⋊C4—348no—
948C22⋊C4—348no—
949C22⋊C4—684no—
950C22⋊C4—684no—
951C22⋊C4#63227116yescomplemented
952C42—44no—
953C42—44no—
954C42—348no—
955C42—684no—
956C42—684no—
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—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—174no—
986C23—342no—
987C23—342no—
988C23—342no—
989C23—342no—
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—681no—
1005C23—681no—
1006C23—681no—
1007C23—681no—
1008C23—681no—
1009C23—681no—
1010C23—681no—
1011C23—681no—
1012C23—681no—
1013C23—681no—
1014C23—681no—
1015C23—681no—
1016C23—681no—
1017C23—681no—
1018C23—681no—
1019C23—681no—
1020C23C42×D1714yes—
1021C23#1058755814yes—
1022C23C4×D6814yes—
1023C23C4×D6814yes—
1024C23C2×#6322714yes—
1025C23C4×C22⋊D1714yes—
1026C23C4×C22⋊D1714yes—
1027C23C22×C4×D1711yescharacteristic
1028C23C22×C4×D1711yescharacteristic
1029C23C22×C4×D1711yescharacteristic
1030C23C22×D6811yescharacteristic
1031C23C2×#6325211yescharacteristic
1032C23C2×#6325211yescharacteristic
1033C23C2×D4×D1711yescharacteristic
1034C23C2×#6325411yescharacteristic
1035C23#1058769111yescharacteristic
1036C23#1058769111yescharacteristic
1037C23#41×D1711yescharacteristic
1038C23#41×D1711yescharacteristic
1039C23#1058769611yescharacteristic
1040C23#1058769711yescharacteristic
1041C23C22×C22⋊D1711yescharacteristic
1042D4—3432no—
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—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—416no—
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—41no—
1083C2×C4—174no—
1084C2×C4—174no—
1085C2×C4—174no—
1086C2×C4—342no—
1087C2×C4—342no—
1088C2×C4—342no—
1089C2×C4—342no—
1090C2×C4—342no—
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—342no—
1113C2×C4—342no—
1114C2×C4—342no—
1115C2×C4—342no—
1116C2×C4—6816no—
1117C2×C4—6816no—
1118C2×C4—6816no—
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—681no—
1134C2×C4—681no—
1135C2×C4#1058756714yescomplemented
1136C2×C4C2×#6322714yes—
1137C2×C4C2×#6322714yes—
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—344no—
1153C22—344no—
1154C22—344no—
1155C22—682no—
1156C22—682no—
1157C22—682no—
1158C22—682no—
1159C22—682no—
1160C22—682no—
1161C22—682no—
1162C22—682no—
1163C22—682no—
1164C22—682no—
1165C22—682no—
1166C22—682no—
1167C22C4×#6322718yescomplemented
1168C22C2×C42×D1711yescharacteristic
1169C22C22×#6322711yescharacteristic
1170C22C2×#1058755811yescharacteristic
1171C22C4×D4×D1711yescharacteristic
1172C22C4×D4×D1711yescharacteristic
1173C22C2×#1058756711yescharacteristic
1174C22C2×C4×C22⋊D1711yescharacteristic
1175C22C2×C4×C22⋊D1711yescharacteristic
1176C22C2×C4×D6811yescharacteristic
1177C22C2×C4×D6811yescharacteristic
1178C22C4×#6325411yescharacteristic
1179C22C4×#6325411yescharacteristic
1180C22#1176327711yescharacteristic
1181C22#1176328111yescharacteristic
1182C22#1176328111yescharacteristic
1183C22#1176328211yescharacteristic
1184C22#1176328811yescharacteristic
1185C22#1176328811yescharacteristic
1186C22#1176328911yescharacteristic
1187C22D4×C22⋊D1711yescharacteristic
1188C22D4×D6811yescharacteristic
1189C22#1176344711yescharacteristic
1190C22#1176344911yescharacteristic
1191C22#1176345311yescharacteristic
1192C22#1176345411yescharacteristic
1193C22#1176345411yescharacteristic
1194C22#1176345811yescharacteristic
1195C22#1176346311yescharacteristic
1196C22#1176346811yescharacteristic
1197C22#1176348311yescharacteristic
1198C22#1176348511yescharacteristic
1199C22#1176349211yescharacteristic
1200C22#1176350511yescharacteristic
1201C22#1176350811yescharacteristic
1202C22#1176350811yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—24no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—344no—
1210C4—344no—
1211C4—344no—
1212C4—682no—
1213C4—682no—
1214C4—682no—
1215C4—682no—
1216C2—28no—
1217C2—684no—
1218C2C2×C4×#6322711yescharacteristic
1219C2C4×#1058756711yescharacteristic
1220C2#1453114311yescharacteristic
1221C2D4×#6322711yescharacteristic
1222C2#1453160911yescharacteristic
1223C2#1453170711yescharacteristic
1224C2#1453171811yescharacteristic
1225C2#1453176311yescharacteristic
1226C2#1453176611yescharacteristic
1227C2#1453177611yescharacteristic
1228C2#1453177811yescharacteristic
1229C2#1453179811yescharacteristic
1230C2#1453180111yescharacteristic
1231C2#1453182911yescharacteristic
1232C2#1453183411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC2×C4×C22⋊C4×C17C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×C4×C22⋊C4D17
hypocenterC17#13813
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic17C2semidirect
5. C2×C4×#63227C2semidirect
6. C22×#10587502C2semidirect
7. #14527022C2semidirect
8. #14527020C2semidirect
9. #14527019C2semidirect
10. #14527017C2semidirect
11. #14527008C2semidirect
12. #14527006C2semidirect
13. #14527005C2semidirect
14. C4×#10587502C2semidirect
15. C2×C4×C22⋊C4×C17C2semidirect
22. C2×#10587567C4semidirect
33. #11762688C4semidirect
34. #11762686C4semidirect
68. C23×C4×C17C2×C4semidirect
95. C23×Dic17C2×C4semidirect
109. C22×C4×D17C2×C4semidirect
113. C2×C22⋊C4×C17C2×C4semidirect
124. C2×C22⋊Dic17C2×C4semidirect
135. C2×#63227C2×C4semidirect
136. C2×#63227C2×C4semidirect
137. C2×#63227C2×C4semidirect
138. C2×#63227C2×C4semidirect
139. C2×#63227C2×C4semidirect
142. C2×#63225C2×C4semidirect
151. C2×C4×Dic17C2×C4semidirect
164. #10587502C2×C4semidirect
165. #10587502C2×C4semidirect
166. #10587502C2×C4semidirect
167. #10587502C2×C4semidirect
168. #10587502D4semidirect
255. C2×C22⋊D17C42semidirect
327. C22⋊C4×C17C22⋊C4semidirect
468. C2×C4×C17C4×D4semidirect
520. C2×Dic17C4×D4semidirect
527. C2×C4×C22⋊C4D17semidirect
551. C22×C17C4×C22⋊C4semidirect
719. C23×C4C4×D17semidirect
751. C2×C22⋊C4C4×D17semidirect
785. C17#13813semidirect
951. C22⋊C4#63227semidirect
1135. C2×C4#10587567semidirect
1167. C22C4×#63227semidirect

Maximal subgroups

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

subgroupindex
C22×#105875672
C2×#117626882
C2×#117626862
C2×C22⋊C4×Dic172
C2×C4×#632272
C22×#105875022
#145270222
#145270202
#145270192
#145270172
#145270082
#145270062
#145270052
C4×#105875022
C2×C4×C22⋊C4×C172
#1381317