Finite Group Databasebeta

← #16957684

Subgroups — #16957684

Order 4352.

2950 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D17C211yesmaximal, characteristic
2C22×C4⋊C4×D17C211yesmaximal, characteristic, complemented
3C2×#11762685C211yesmaximal, characteristic
4C2×#11762685C211yesmaximal, characteristic
5C2×#11762682C211yesmaximal, characteristic, complemented
6C2×#11762680C211yesmaximal, characteristic, complemented
7#14527048C211yesmaximal, characteristic, complemented
8#14527047C211yesmaximal, characteristic, complemented
9#14527029C211yesmaximal, characteristic, complemented
10#14527027C211yesmaximal, characteristic, complemented
11#14527019C211yesmaximal, characteristic, complemented
12#14527016C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C2×C17×#385C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C2×C4×C22⋊D17—24no—
21C2×C4×C22⋊D17—24no—
22C2×C4×C22⋊D17—24no—
23C22×C4⋊Dic17C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C2×C4⋊C4×D17—24no—
29C2×C4⋊C4×D17—24no—
30C2×C4⋊C4×D17—24no—
31C22×C22⋊Dic17C2211yescharacteristic
32C22×C22⋊Dic17C2211yescharacteristic
33C22×C22⋊Dic17C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×#63227C2211yescharacteristic
36C22×#63227C2211yescharacteristic
37C22×C4×Dic17C2211yescharacteristic
38#11762685—24no—
39#11762685C418yescomplemented
40#11762682—24no—
41#11762680—24no—
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C24×C4×C17C2211yescharacteristic
55C22×C4⋊C4×C17C2211yescharacteristic
56C22×C4⋊C4×C17C2211yescharacteristic
57C22×C22⋊C4×C17C2211yescharacteristic
58C22×C22⋊C4×C17C2211yescharacteristic
59C17×#385—24no—
60C2×C17×#95C2211yescharacteristic
61C2×C17×#95C2211yescharacteristic
62C25×C17C2311yescharacteristic
63C24×D17C2311yescharacteristic
64C23×C4×C17—22no—
65C23×C4×C17—22no—
66C23×C4×C17—22no—
67C23×C4×C17—22no—
68C23×C4×C17—22no—
69C23×C4×C17—41no—
70C23×C4×C17—41no—
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C22×C22⋊D17—22no—
78C22×C22⋊D17—22no—
79C22×C22⋊D17—22no—
80C22×C22⋊D17—22no—
81C22×C22⋊D17C2×C414yes—
82C22×C22⋊D17D414yes—
83C22×C22⋊D17Q814yes—
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—22no—
97C22×C4×D17—22no—
98C22×C4×D17—22no—
99C22×C4×D17—22no—
100C22×C4×D17—22no—
101C22×C4×D17—22no—
102C22×C4×D17—22no—
103C22×C4×D17—22no—
104C22×C4×D17—22no—
105C22×C4×D17—22no—
106C22×C4×D17—41no—
107C22×C4×D17—41no—
108C22×C4×D17—41no—
109C22×C4×D17—41no—
110C22×C4×D17C2×C414yescomplemented
111C22×C4×D17D414yes—
112C2×C4⋊C4×C17—22no—
113C2×C4⋊C4×C17—22no—
114C2×C4⋊C4×C17—22no—
115C2×C4⋊C4×C17—22no—
116C2×C4⋊C4×C17—41no—
117C2×C4⋊C4×C17D414yescomplemented
118C2×C22⋊C4×C17—22no—
119C2×C22⋊C4×C17—22no—
120C2×C22⋊C4×C17—22no—
121C2×C22⋊C4×C17—22no—
122C2×C22⋊C4×C17—41no—
123C2×C22⋊C4×C17C2×C414yescomplemented
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—41no—
132C2×C22⋊Dic17C2×C414yescomplemented
133C4×C22⋊D17—232no—
134C2×#63227—22no—
135C2×#63227—22no—
136C2×#63227—22no—
137C2×#63227—22no—
138C2×#63227—22no—
139C2×#63227—22no—
140C2×#63227—22no—
141C2×#63227C2×C414yescomplemented
142C2×#63227D414yes—
143C2×C4⋊Dic17—22no—
144C2×C4⋊Dic17—22no—
145C2×C4⋊Dic17—22no—
146C2×#63225—22no—
147C2×#63225—22no—
148C2×#63225—22no—
149C2×#63225—22no—
150C2×#63225—22no—
151C2×#63225—22no—
152C2×#63225—22no—
153C2×#63225—22no—
154C2×#63225—22no—
155C2×#63225—22no—
156C2×#63225—41no—
157C2×#63225D414yescomplemented
158C2×C4×Dic17—22no—
159C2×C4×Dic17—22no—
160C2×C4×Dic17—22no—
161C4⋊C4×D17—232no—
162C17×#95—22no—
163C17×#95—22no—
164#10587502—22no—
165#10587502—22no—
166#10587502—22no—
167#10587502—22no—
168#10587502—22no—
169#10587502—22no—
170#10587502—22no—
171#10587502—22no—
172#10587502—41no—
173#10587502—41no—
174#10587502C2×C414yescomplemented
175#10587502C2×C414yescomplemented
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×C17—21no—
188C24×C17C22×C412yes—
189C24×C17C2×D412yes—
190C24×C17C2×Q812yes—
191C24×C17C2411yescharacteristic
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×D17C22×C412yes—
201C23×D17C2×D412yes—
202C23×D17C2×D412yes—
203C23×D17C2×D412yes—
204C23×D17C2×Q812yes—
205C23×D17#4112yes—
206C23×D17#4112yes—
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—28no—
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×C17—44no—
242C22×C4×C17—44no—
243C22×C4×C17—44no—
244C22×C4×C17—44no—
245C22×C4×C17—44no—
246C22×C4×C17—44no—
247C22×C4×C17C22×C412yes—
248C22×C4×C17C22×C412yes—
249C22×C4×C17C2×D412yes—
250C22×C4×C17C2×D412yes—
251C22×C4×C17C2×D412yes—
252C22×C4×C17C2×D412yes—
253C22×C4×C17C2×D412yes—
254C22×C4×C17C2×D412yes—
255C22×C4×C17#4112yes—
256C2×C22⋊D17—28no—
257C2×C22⋊D17—28no—
258C2×C22⋊D17—28no—
259C2×C22⋊D17—28no—
260C2×C22⋊D17—28no—
261C2×C22⋊D17—28no—
262C2×C22⋊D17C4⋊C4116yescomplemented
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17—21no—
272C22×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17—21no—
278C22×Dic17—21no—
279C22×Dic17—21no—
280C22×Dic17—21no—
281C22×Dic17—21no—
282C22×Dic17—21no—
283C22×Dic17—21no—
284C22×Dic17—21no—
285C22×Dic17—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×Dic17C22×C412yes—
303C22×Dic17C22×C412yes—
304C22×Dic17C22×C412yes—
305C22×Dic17C2×D412yes—
306C22×Dic17C2×D412yes—
307C22×Dic17C2×D412yes—
308C22×Dic17C2×D412yes—
309C22×Dic17C2×D412yes—
310C22×Dic17C2×Q812yes—
311C22×Dic17#4112yes—
312C2×C4×D17—28no—
313C2×C4×D17—28no—
314C2×C4×D17—28no—
315C2×C4×D17—28no—
316C2×C4×D17—28no—
317C2×C4×D17—28no—
318C2×C4×D17—28no—
319C2×C4×D17—28no—
320C2×C4×D17—28no—
321C2×C4×D17—28no—
322C2×C4×D17—44no—
323C2×C4×D17—44no—
324C2×C4×D17—44no—
325C2×C4×D17—44no—
326C2×C4×D17—44no—
327C2×C4×D17—44no—
328C2×C4×D17—44no—
329C2×C4×D17—44no—
330C2×C4×D17—44no—
331C2×C4×D17—44no—
332C2×C4×D17—44no—
333C4⋊C4×C17—28no—
334C4⋊C4×C17—44no—
335C22⋊C4×C17—28no—
336C22⋊C4×C17—44no—
337C22⋊Dic17—28no—
338C22⋊Dic17—28no—
339C22⋊Dic17—44no—
340#63227—28no—
341#63227—28no—
342#63227—44no—
343C4⋊Dic17—28no—
344#63225—28no—
345#63225—28no—
346#63225—28no—
347#63225—44no—
348C4×Dic17—28no—
349#14015—171nomaximal, Sylow
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—41no—
369C23×C17—41no—
370C23×C17—41no—
371C23×C17—41no—
372C23×C17—41no—
373C23×C17—41no—
374C23×C17—41no—
375C23×C17—41no—
376C23×C17—41no—
377C23×C17—41no—
378C23×C17—41no—
379C23×C17—41no—
380C23×C17—41no—
381C23×C17—41no—
382C23×C17—41no—
383C23×C17—41no—
384C23×C17C2×C4⋊C414yescomplemented
385C23×C17C23×C411yescharacteristic
386C23×C17C22×D411yescharacteristic
387C23×C17C22×D411yescharacteristic
388C23×C17C22×D411yescharacteristic
389C23×C17C22×D411yescharacteristic
390C23×C17C22×D411yescharacteristic
391C23×C17C22×Q811yescharacteristic
392C23×C17C2×#4111yescharacteristic
393C23×C17C2×#4111yescharacteristic
394C23×C17C2×#4111yescharacteristic
395C23×C17C2×#4111yescharacteristic
396C23×C17H(5,𝔽2)11yescharacteristic
397C23×C17H(5,𝔽2)11yescharacteristic
398C23×C172−1+411yescharacteristic
399C23×C172−1+411yescharacteristic
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—22no—
410C22×D17—22no—
411C22×D17—22no—
412C22×D17—22no—
413C22×D17—22no—
414C22×D17—22no—
415C22×D17—22no—
416C22×D17—22no—
417C22×D17—22no—
418C22×D17—22no—
419C22×D17—22no—
420C22×D17—22no—
421C22×D17—22no—
422C22×D17—22no—
423C22×D17—22no—
424C22×D17—22no—
425C22×D17—22no—
426C22×D17—22no—
427C22×D17—22no—
428C22×D17C2×C4⋊C414yes—
429C22×D17C4×D414yes—
430C22×D17C4×D414yes—
431C22×D17#12014yes—
432C22×D17C22⋊Q814yes—
433C22×D17C22⋊Q814yes—
434C22×D17#12314yes—
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—22no—
454C2×C4×C17—22no—
455C2×C4×C17—22no—
456C2×C4×C17—416no—
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×C17—41no—
468C2×C4×C17—41no—
469C2×C4×C17—41no—
470C2×C4×C17—41no—
471C2×C4×C17—41no—
472C2×C4×C17—41no—
473C2×C4×C17—41no—
474C2×C4×C17—41no—
475C2×C4×C17—41no—
476C2×C4×C17C4×D414yescomplemented
477C2×C4×C17#12014yes—
478C22⋊D17—232no—
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—22no—
501C2×Dic17—22no—
502C2×Dic17—22no—
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×Dic17—41no—
519C2×Dic17—41no—
520C2×Dic17—41no—
521C2×Dic17—41no—
522C2×Dic17—41no—
523C2×Dic17—41no—
524C2×Dic17—41no—
525C2×Dic17—41no—
526C2×Dic17C2×C4⋊C414yescomplemented
527C2×Dic17C4×D414yescomplemented
528C4×D17—232no—
529C4×D17—416no—
530C4×D17—416no—
531C22×C4×D4—171no—
532C23×C4⋊C4—171no—
533C2×#386—171no—
534C2×#386—171no—
535C2×#385—171no—
536C2×#385—171no—
537C2×#385D1711yescharacteristic, complemented
538#1444—171no—
539#1444—171no—
540#1439—171no—
541#1439—171no—
542#1436—171no—
543#1436—171no—
544C22⋊#95—171no—
545C22⋊#95—171no—
546C22×C17—24no—
547C22×C17—24no—
548C22×C17—24no—
549C22×C17—42no—
550C22×C17—42no—
551C22×C17—42no—
552C22×C17—42no—
553C22×C17—42no—
554C22×C17—42no—
555C22×C17—42no—
556C22×C17—42no—
557C22×C17—42no—
558C22×C17—42no—
559C22×C17—42no—
560C22×C17—42no—
561C22×C17C22×C4⋊C411yescharacteristic
562C22×C17C2×C4×D411yescharacteristic
563C22×C17C2×C4×D411yescharacteristic
564C22×C17C2×C4×D411yescharacteristic
565C22×C17C2×C4×D411yescharacteristic
566C22×C17#52011yescharacteristic
567C22×C17#52011yescharacteristic
568C22×C17C2×#12011yescharacteristic
569C22×C17C2×#12011yescharacteristic
570C22×C17C2×C22⋊Q811yescharacteristic
571C22×C17C2×C22⋊Q811yescharacteristic
572C22×C17C2×#12311yescharacteristic
573C22×C17#52511yescharacteristic
574C22×C17#52511yescharacteristic
575C22×C17#52511yescharacteristic
576C22×C17#53411yescharacteristic
577C22×C17#53611yescharacteristic
578C22×C17#53911yescharacteristic
579C22×C17#53911yescharacteristic
580C22×C17D4211yescharacteristic
581C22×C17D4211yescharacteristic
582C22×C17D4211yescharacteristic
583C22×C17D4211yescharacteristic
584C22×C17#54711yescharacteristic
585C22×C17#54711yescharacteristic
586C22×C17#54711yescharacteristic
587C22×C17#54711yescharacteristic
588C22×C17#54811yescharacteristic
589C22×C17#54811yescharacteristic
590C22×C17D4×Q811yescharacteristic
591C22×C17D4×Q811yescharacteristic
592C22×C17#55311yescharacteristic
593C22×C17#55311yescharacteristic
594C22×C17#55411yescharacteristic
595C22×C17#55411yescharacteristic
596C2×D17—24no—
597C2×D17—24no—
598C2×D17—24no—
599C2×D17—24no—
600C2×D17—24no—
601C2×D17—24no—
602C2×D17—24no—
603C2×D17—24no—
604C2×D17—24no—
605C2×D17—24no—
606C2×D17—24no—
607C2×D17—24no—
608C2×D17—24no—
609C2×D17—24no—
610C2×D17#38518yescomplemented
611C4×C17—24no—
612C4×C17—24no—
613C4×C17—42no—
614C4×C17—42no—
615C4×C17—42no—
616C4×C17—81no—
617Dic17—24no—
618Dic17—24no—
619Dic17—42no—
620Dic17—42no—
621Dic17—42no—
622Dic17—42no—
623Dic17—81no—
624C23×D4—171no—
625C24×C4—171no—
626C24×C4—171no—
627C24×C4—171no—
628C24×C4C2×D1711yescharacteristic
629C2×C4×D4—344no—
630C2×C4×D4—344no—
631C2×C4×D4—344no—
632C22×C4⋊C4—171no—
633C22×C4⋊C4—171no—
634C22×C4⋊C4—171no—
635C22×C4⋊C4—171no—
636C22×C4⋊C4—171no—
637C22×C4⋊C4—344no—
638C22×C4⋊C4—344no—
639C22×C4⋊C4—344no—
640C22×C4⋊C4C2×D1711yescharacteristic
641C22×C4⋊C4C2×D1711yescharacteristic
642C22×C22⋊C4—171no—
643C22×C22⋊C4—171no—
644C22×C22⋊C4—171no—
645C22×C22⋊C4—171no—
646C22×C22⋊C4—171no—
647C22×C22⋊C4—171no—
648C22×C22⋊C4C2×D1711yescharacteristic
649C22×C22⋊C4C2×D1711yescharacteristic
650C22×C42—171no—
651#386—178no—
652#386—344no—
653#385—24no—
654#385—344no—
655#385—344no—
656C2×#95—171no—
657C2×#95—171no—
658C2×#95—171no—
659C2×#95—171no—
660C2×#95—171no—
661C2×#95—171no—
662C2×#95—171no—
663C2×#95—171no—
664C2×#95—171no—
665C2×#95—171no—
666C2×#95—171no—
667C2×#95—171no—
668C2×#95C2×D1711yescharacteristic
669C2×#95C2×D1711yescharacteristic
670C2×C17—44no—
671C2×C17C2×#38511yescharacteristic
672C2×C17C4×#12011yescharacteristic
673C2×C17#232211yescharacteristic
674C2×C17D4×C4⋊C411yescharacteristic
675C2×C17D4×C4⋊C411yescharacteristic
676C2×C17#236111yescharacteristic
677C2×C17#236111yescharacteristic
678C2×C17#240311yescharacteristic
679C2×C17#240611yescharacteristic
680C2×C17#240911yescharacteristic
681C2×C17#244311yescharacteristic
682C2×C17#244311yescharacteristic
683C2×C17#244911yescharacteristic
684C2×C17#244911yescharacteristic
685C2×C17#257911yescharacteristic
686D17—28no—
687C25—171no—
688C25C22×D1711yescharacteristic
689C22×D4—174no—
690C22×D4—174no—
691C22×D4—174no—
692C22×D4—342no—
693C22×D4—342no—
694C22×D4—342no—
695C22×D4—342no—
696C23×C4—22no—
697C23×C4—22no—
698C23×C4—22no—
699C23×C4—22no—
700C23×C4—22no—
701C23×C4—41no—
702C23×C4—41no—
703C23×C4—171no—
704C23×C4—171no—
705C23×C4—171no—
706C23×C4—171no—
707C23×C4—171no—
708C23×C4—171no—
709C23×C4—174no—
710C23×C4—174no—
711C23×C4—171no—
712C23×C4—342no—
713C23×C4—342no—
714C23×C4—342no—
715C23×C4—342no—
716C23×C4—342no—
717C23×C4—342no—
718C23×C4—342no—
719C23×C4—342no—
720C23×C4—342no—
721C23×C4—342no—
722C23×C4—342no—
723C23×C4—342no—
724C23×C4—342no—
725C23×C4—342no—
726C23×C4—342no—
727C23×C4—681no—
728C23×C4—681no—
729C23×C4—681no—
730C23×C4—681no—
731C23×C4C22×D1711yescharacteristic
732C23×C4C22×D1711yescharacteristic
733C23×C4C22×D1711yescharacteristic
734C23×C4C22×D1711yescharacteristic
735C23×C4C22×D1711yescharacteristic
736C23×C4C22×D1711yescharacteristic
737C4×D4—3432no—
738C2×C4⋊C4—22no—
739C2×C4⋊C4—22no—
740C2×C4⋊C4—22no—
741C2×C4⋊C4—22no—
742C2×C4⋊C4—41no—
743C2×C4⋊C4—174no—
744C2×C4⋊C4—3432no—
745C2×C4⋊C4—342no—
746C2×C4⋊C4—342no—
747C2×C4⋊C4—342no—
748C2×C4⋊C4—342no—
749C2×C4⋊C4—342no—
750C2×C4⋊C4—342no—
751C2×C4⋊C4—342no—
752C2×C4⋊C4—342no—
753C2×C4⋊C4—342no—
754C2×C4⋊C4—342no—
755C2×C4⋊C4—342no—
756C2×C4⋊C4—342no—
757C2×C4⋊C4—342no—
758C2×C4⋊C4—681no—
759C2×C4⋊C4C22⋊D1714yescomplemented
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—174no—
766C2×C22⋊C4—174no—
767C2×C22⋊C4—174no—
768C2×C22⋊C4—342no—
769C2×C22⋊C4—342no—
770C2×C22⋊C4—342no—
771C2×C22⋊C4—342no—
772C2×C22⋊C4—342no—
773C2×C22⋊C4—342no—
774C2×C22⋊C4—342no—
775C2×C22⋊C4—342no—
776C2×C22⋊C4—342no—
777C2×C22⋊C4—342no—
778C2×C22⋊C4—342no—
779C2×C22⋊C4—342no—
780C2×C22⋊C4—342no—
781C2×C22⋊C4—342no—
782C2×C22⋊C4—681no—
783C2×C22⋊C4C4×D1714yescomplemented
784C2×C42—342no—
785C2×C42—342no—
786C2×C42—342no—
787#95—22no—
788#95—22no—
789#95—174no—
790#95—174no—
791#95—342no—
792#95—342no—
793#95—342no—
794#95—342no—
795#95—342no—
796#95—342no—
797#95—342no—
798#95—342no—
799#95—681no—
800#95—681no—
801C17#1401511yescharacteristic, complemented, Sylow
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—172no—
815C24—172no—
816C24—172no—
817C24—172no—
818C24—172no—
819C24—172no—
820C24—172no—
821C24—341no—
822C24—341no—
823C24—341no—
824C24—341no—
825C24—341no—
826C24—341no—
827C24—341no—
828C24—341no—
829C24C2×C4×D1712yes—
830C24D4×D1712yes—
831C24Q8×D1712yes—
832C24C23×D1711yescharacteristic
833C2×D4—1716no—
834C2×D4—348no—
835C2×D4—348no—
836C2×D4—348no—
837C2×D4—348no—
838C2×D4—348no—
839C2×D4—348no—
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—28no—
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—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—172no—
881C22×C4—172no—
882C22×C4—172no—
883C22×C4—172no—
884C22×C4—172no—
885C22×C4—172no—
886C22×C4—172no—
887C22×C4—172no—
888C22×C4—172no—
889C22×C4—172no—
890C22×C4—348no—
891C22×C4—348no—
892C22×C4—348no—
893C22×C4—348no—
894C22×C4—348no—
895C22×C4—348no—
896C22×C4—348no—
897C22×C4—348no—
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—348no—
907C22×C4—341no—
908C22×C4—341no—
909C22×C4—341no—
910C22×C4—341no—
911C22×C4—341no—
912C22×C4—341no—
913C22×C4—341no—
914C22×C4—341no—
915C22×C4—341no—
916C22×C4—341no—
917C22×C4—341no—
918C22×C4—341no—
919C22×C4—341no—
920C22×C4—341no—
921C22×C4—341no—
922C22×C4—341no—
923C22×C4—341no—
924C22×C4—341no—
925C22×C4—341no—
926C22×C4—341no—
927C22×C4—341no—
928C22×C4—341no—
929C22×C4—341no—
930C22×C4—341no—
931C22×C4—348no—
932C22×C4—341no—
933C22×C4—341no—
934C22×C4—341no—
935C22×C4—341no—
936C22×C4—341no—
937C22×C4—341no—
938C22×C4—341no—
939C22×C4—684no—
940C22×C4—684no—
941C22×C4—684no—
942C22×C4—684no—
943C22×C4—684no—
944C22×C4—684no—
945C22×C4—684no—
946C22×C4—684no—
947C22×C4—684no—
948C22×C4—684no—
949C22×C4—684no—
950C22×C4C2×C4×D1712yes—
951C22×C4C2×C4×D1712yes—
952C22×C4#6325212yes—
953C22×C4D4×D1712yes—
954C22×C4D4×D1712yes—
955C22×C4D4×D1712yes—
956C22×C4C2×C22⋊D1712yes—
957C22×C4C2×C22⋊D1712yes—
958C22×C4C2×C22⋊D1712yes—
959C4⋊C4—28no—
960C4⋊C4—44no—
961C4⋊C4—348no—
962C4⋊C4—348no—
963C4⋊C4—348no—
964C4⋊C4—348no—
965C4⋊C4—684no—
966C22⋊C4—28no—
967C22⋊C4—44no—
968C22⋊C4—348no—
969C22⋊C4—348no—
970C22⋊C4—348no—
971C22⋊C4—348no—
972C22⋊C4—684no—
973C22⋊C4—684no—
974C42—348no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—174no—
1010C23—174no—
1011C23—174no—
1012C23—174no—
1013C23—174no—
1014C23—174no—
1015C23—174no—
1016C23—342no—
1017C23—342no—
1018C23—342no—
1019C23—342no—
1020C23—342no—
1021C23—342no—
1022C23—342no—
1023C23—342no—
1024C23—342no—
1025C23—342no—
1026C23—342no—
1027C23—342no—
1028C23—342no—
1029C23—342no—
1030C23—342no—
1031C23—342no—
1032C23—342no—
1033C23—342no—
1034C23—342no—
1035C23—342no—
1036C23—342no—
1037C23—342no—
1038C23—342no—
1039C23—342no—
1040C23—342no—
1041C23—342no—
1042C23—342no—
1043C23—342no—
1044C23C4⋊C4×D1714yescomplemented
1045C23C22×C4×D1711yescharacteristic
1046C23C2×#6325211yescharacteristic
1047C23C2×D4×D1711yescharacteristic
1048C23C2×D4×D1711yescharacteristic
1049C23C2×D4×D1711yescharacteristic
1050C23C2×D4×D1711yescharacteristic
1051C23#1058769111yescharacteristic
1052C23#1058769111yescharacteristic
1053C23C2×Q8×D1711yescharacteristic
1054C23#1058769411yescharacteristic
1055C23#41×D1711yescharacteristic
1056C23#41×D1711yescharacteristic
1057C23#41×D1711yescharacteristic
1058C23#1058769711yescharacteristic
1059C23C22×C22⋊D1711yescharacteristic
1060D4—3432no—
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—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—416no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—174no—
1103C2×C4—174no—
1104C2×C4—3432no—
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—342no—
1117C2×C4—342no—
1118C2×C4—342no—
1119C2×C4—342no—
1120C2×C4—342no—
1121C2×C4—342no—
1122C2×C4—342no—
1123C2×C4—342no—
1124C2×C4—342no—
1125C2×C4—342no—
1126C2×C4—342no—
1127C2×C4—342no—
1128C2×C4—342no—
1129C2×C4—6816no—
1130C2×C4—6816no—
1131C2×C4—681no—
1132C2×C4—681no—
1133C2×C4—681no—
1134C2×C4—681no—
1135C2×C4—681no—
1136C2×C4—681no—
1137C2×C4—681no—
1138C2×C4—681no—
1139C2×C4—681no—
1140C2×C4—681no—
1141C2×C4—681no—
1142C2×C4—681no—
1143C2×C4—681no—
1144C2×C4—681no—
1145C2×C4—681no—
1146C2×C4—681no—
1147C2×C4—681no—
1148C2×C4—681no—
1149C2×C4—681no—
1150C2×C4—681no—
1151C2×C4—681no—
1152C2×C4—681no—
1153C2×C4—681no—
1154C2×C4C4×C22⋊D1714yescomplemented
1155C2×C4#1058762314yes—
1156C22—24no—
1157C22—24no—
1158C22—24no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—178no—
1172C22—344no—
1173C22—344no—
1174C22—344no—
1175C22—344no—
1176C22—344no—
1177C22—344no—
1178C22—344no—
1179C22—344no—
1180C22—344no—
1181C22—344no—
1182C22—344no—
1183C22—344no—
1184C22—344no—
1185C22—344no—
1186C22C2×C4⋊C4×D1711yescharacteristic
1187C22C4×D4×D1711yescharacteristic
1188C22C4×D4×D1711yescharacteristic
1189C22C4×D4×D1711yescharacteristic
1190C22C2×C4×C22⋊D1711yescharacteristic
1191C22#1176328811yescharacteristic
1192C22#1176329011yescharacteristic
1193C22#120×D1711yescharacteristic
1194C22C2×#1058762311yescharacteristic
1195C22C22⋊Q8×D1711yescharacteristic
1196C22C22⋊Q8×D1711yescharacteristic
1197C22#123×D1711yescharacteristic
1198C22#1176331611yescharacteristic
1199C22#1176331811yescharacteristic
1200C22#1176331811yescharacteristic
1201C22#1176336911yescharacteristic
1202C22#1176338211yescharacteristic
1203C22#1176340211yescharacteristic
1204C22#1176340511yescharacteristic
1205C22#1176344111yescharacteristic
1206C22#1176344111yescharacteristic
1207C22D4×C22⋊D1711yescharacteristic
1208C22D4×C22⋊D1711yescharacteristic
1209C22#1176345711yescharacteristic
1210C22#1176346011yescharacteristic
1211C22#1176346111yescharacteristic
1212C22#1176346411yescharacteristic
1213C22#1176346611yescharacteristic
1214C22#1176346911yescharacteristic
1215C22#1176347211yescharacteristic
1216C22Q8×C22⋊D1711yescharacteristic
1217C22#1176350411yescharacteristic
1218C22#1176350911yescharacteristic
1219C22#1176351311yescharacteristic
1220C22#1176351411yescharacteristic
1221C4—24no—
1222C4—24no—
1223C4—42no—
1224C4—42no—
1225C4—42no—
1226C4—81no—
1227C4—344no—
1228C4—344no—
1229C4—682no—
1230C4—682no—
1231C4—682no—
1232C4—682no—
1233C4—1361no—
1234C2—44no—
1235C2—348no—
1236C2D17×#38511yescharacteristic
1237C2C4×#1058762311yescharacteristic
1238C2#1453145111yescharacteristic
1239C2#1453168211yescharacteristic
1240C2C4⋊C4×C22⋊D1711yescharacteristic
1241C2#1453179611yescharacteristic
1242C2#1453180311yescharacteristic
1243C2#1453209511yescharacteristic
1244C2#1453211711yescharacteristic
1245C2#1453214511yescharacteristic
1246C2#1453251611yescharacteristic
1247C2#1453251811yescharacteristic
1248C2#1453259011yescharacteristic
1249C2#1453259211yescharacteristic
1250C2#1453412911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#385C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×#385D17
hypocenterC17#14015
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D17C2semidirect
5. C2×#11762682C2semidirect
6. C2×#11762680C2semidirect
7. #14527048C2semidirect
8. #14527047C2semidirect
9. #14527029C2semidirect
10. #14527027C2semidirect
11. #14527019C2semidirect
12. #14527016C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C2×C17×#385C2semidirect
39. #11762685C4semidirect
110. C22×C4×D17C2×C4semidirect
117. C2×C4⋊C4×C17D4semidirect
123. C2×C22⋊C4×C17C2×C4semidirect
132. C2×C22⋊Dic17C2×C4semidirect
141. C2×#63227C2×C4semidirect
157. C2×#63225D4semidirect
174. #10587502C2×C4semidirect
175. #10587502C2×C4semidirect
262. C2×C22⋊D17C4⋊C4semidirect
384. C23×C17C2×C4⋊C4semidirect
476. C2×C4×C17C4×D4semidirect
526. C2×Dic17C2×C4⋊C4semidirect
527. C2×Dic17C4×D4semidirect
537. C2×#385D17semidirect
610. C2×D17#385semidirect
759. C2×C4⋊C4C22⋊D17semidirect
783. C2×C22⋊C4C4×D17semidirect
801. C17#14015semidirect
1044. C23C4⋊C4×D17semidirect
1154. C2×C4C4×C22⋊D17semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D172
C22×C4⋊C4×D172
C2×#117626852
C2×#117626822
C2×#117626802
#145270482
#145270472
#145270292
#145270272
#145270192
#145270162
#145270052
C2×C17×#3852
#1401517