Finite Group Databasebeta

← #16959792

Subgroups — #16959792

Order 4352.

2422 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
1C2×#11762723C211yesmaximal, characteristic
2C2×#11762704C211yesmaximal, characteristic, complemented
3C2×#11762703C211yesmaximal, characteristic, complemented
4C2×#11762682C211yesmaximal, characteristic, complemented
5C2×#11762682C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic17C211yesmaximal, characteristic, complemented
7#14527031C211yesmaximal, characteristic, complemented
8#14527027C211yesmaximal, characteristic, complemented
9#14527025C211yesmaximal, characteristic
10#14527021C211yesmaximal, characteristic, complemented
11#14527017C211yesmaximal, characteristic, complemented
12#14527017C211yesmaximal, characteristic, complemented
13#14527016C211yesmaximal, characteristic, complemented
14#14527007C211yesmaximal, characteristic, complemented
15C22×C4×D4×C17C211yesmaximal, characteristic
16C22×#63225C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30#11762723C418yescomplemented
31#11762704—24no—
32#11762703—24no—
33#11762682—24no—
34#11762682—24no—
35C4×C22⋊Dic17—24no—
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C23×D4×C17C2211yescharacteristic
51C24×C4×C17C2211yescharacteristic
52C24×C4×C17C2211yescharacteristic
53C2×C4×D4×C17—24no—
54C2×C4×D4×C17—24no—
55C2×C4×D4×C17—24no—
56C22×C4⋊C4×C17C2211yescharacteristic
57C22×C22⋊C4×C17C2211yescharacteristic
58C22×C22⋊C4×C17C2211yescharacteristic
59C22×C42×C17C2211yescharacteristic
60C25×C17C2311yescharacteristic
61C25×C17C2311yescharacteristic
62C22×D4×C17—22no—
63C22×D4×C17—22no—
64C22×D4×C17—22no—
65C22×D4×C17—22no—
66C22×D4×C17—22no—
67C22×D4×C17—22no—
68C22×D4×C17C2×C414yes—
69C23×C4×C17—22no—
70C23×C4×C17—22no—
71C23×C4×C17—22no—
72C23×C4×C17—22no—
73C23×C4×C17—22no—
74C23×C4×C17—22no—
75C23×C4×C17—22no—
76C23×C4×C17—22no—
77C23×C4×C17—22no—
78C23×C4×C17—41no—
79C23×C4×C17—41no—
80C23×C4×C17—41no—
81C23×C4×C17—41no—
82C23×C4×C17D414yes—
83C23×C4×C17C2311yescharacteristic
84C23×C4×C17C2311yescharacteristic
85C23×C4×C17C2311yescharacteristic
86C23×C4×C17C2311yescharacteristic
87C23×C4×C17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C23×Dic17C2311yescharacteristic
90C23×Dic17C2311yescharacteristic
91C23×Dic17C2311yescharacteristic
92C23×Dic17C2311yescharacteristic
93C23×Dic17C2311yescharacteristic
94C23×Dic17C2311yescharacteristic
95C23×Dic17C2311yescharacteristic
96C4×D4×C17—232no—
97C2×C4⋊C4×C17—22no—
98C2×C4⋊C4×C17—22no—
99C2×C4⋊C4×C17D414yes—
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×C17D414yes—
106C2×C42×C17—22no—
107C2×C42×C17—22no—
108C2×C42×C17—22no—
109C2×C22⋊Dic17—22no—
110C2×C22⋊Dic17—22no—
111C2×C22⋊Dic17—22no—
112C2×C22⋊Dic17—22no—
113C2×C22⋊Dic17—22no—
114C2×C22⋊Dic17—22no—
115C2×C22⋊Dic17—22no—
116C2×C22⋊Dic17—22no—
117C2×C22⋊Dic17—22no—
118C2×C22⋊Dic17—22no—
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—41no—
126C2×C22⋊Dic17—41no—
127C2×C22⋊Dic17—41no—
128C2×C22⋊Dic17—41no—
129C2×C22⋊Dic17C2×C414yescomplemented
130C2×C22⋊Dic17C2×C414yescomplemented
131C2×C22⋊Dic17C2×C414yescomplemented
132C2×C22⋊Dic17C2×C414yescomplemented
133C2×#63225—22no—
134C2×#63225—22no—
135C2×#63225—22no—
136C2×#63225—22no—
137C2×#63225—22no—
138C2×#63225—22no—
139C2×#63225—22no—
140C2×#63225—22no—
141C2×#63225—22no—
142C2×#63225—22no—
143C2×#63225—41no—
144C2×#63225C2×C414yescomplemented
145C2×C4×Dic17—22no—
146C2×C4×Dic17—22no—
147C2×C4×Dic17—22no—
148C2×C4×Dic17—22no—
149C2×C4×Dic17—41no—
150C2×C4×Dic17—41no—
151#10587502—22no—
152#10587502—22no—
153#10587502—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—41no—
163#10587502C2×C414yescomplemented
164#10587502D414yescomplemented
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×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×C17C22×C412yes—
190C24×C17C22×C412yes—
191C24×C17C2×D412yes—
192C24×C17C2×D412yes—
193C24×C17#4112yes—
194C24×C17#4112yes—
195C24×C17C2411yescharacteristic
196C2×D4×C17—28no—
197C2×D4×C17—28no—
198C2×D4×C17—28no—
199C2×D4×C17—28no—
200C2×D4×C17—28no—
201C2×D4×C17—28no—
202C2×D4×C17—28no—
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—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—28no—
229C22×C4×C17—28no—
230C22×C4×C17—44no—
231C22×C4×C17—44no—
232C22×C4×C17—44no—
233C22×C4×C17—44no—
234C22×C4×C17—44no—
235C22×C4×C17—44no—
236C22×C4×C17—44no—
237C22×C4×C17—44no—
238C22×C4×C17—44no—
239C22×C4×C17—44no—
240C22×C4×C17—44no—
241C22×C4×C17C22×C412yes—
242C22×C4×C17C2×D412yes—
243C22×C4×C17C2×D412yes—
244C22×C4×C17C2×D412yes—
245C22×C4×C17C2×D412yes—
246C22×C4×C17C2×D412yes—
247C22×C4×C17C2×D412yes—
248C22×C4×C17C2×D412yes—
249C22×C4×C17C2×D412yes—
250C22×C4×C17#4112yes—
251C22×C4×C17#4112yes—
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—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×Dic17C22×C412yes—
301C22×Dic17C22×C412yes—
302C22×Dic17C22×C412yes—
303C22×Dic17C22×C412yes—
304C22×Dic17C2×D412yes—
305C22×Dic17C2×D412yes—
306C22×Dic17#4112yes—
307C22×Dic17#4112yes—
308C4⋊C4×C17—28no—
309C22⋊C4×C17—28no—
310C22⋊C4×C17—28no—
311C42×C17—28no—
312C22⋊Dic17—28no—
313C22⋊Dic17—28no—
314C22⋊Dic17—28no—
315C22⋊Dic17—28no—
316C22⋊Dic17—28no—
317C22⋊Dic17—44no—
318C22⋊Dic17—44no—
319C22⋊Dic17—44no—
320#63225—28no—
321#63225—44no—
322#63225—44no—
323#63225—44no—
324C4×Dic17—44no—
325C4×Dic17—44no—
326#14185—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—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—41no—
364C23×C17—41no—
365C23×C17—41no—
366C23×C17—41no—
367C23×C17—41no—
368C23×C17—41no—
369C23×C17—41no—
370C23×C17—41no—
371C23×C17—41no—
372C23×C17—41no—
373C23×C17—41no—
374C23×C17—41no—
375C23×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×C17—41no—
385C23×C17—41no—
386C23×C17—41no—
387C23×C17—41no—
388C23×C17—41no—
389C23×C17—41no—
390C23×C17—41no—
391C23×C17—41no—
392C23×C17—41no—
393C23×C17—41no—
394C23×C17—41no—
395C23×C17C4×D414yes—
396C23×C17C4×D414yes—
397C23×C17C23×C411yescharacteristic
398C23×C17C22×D411yescharacteristic
399C23×C17C22×D411yescharacteristic
400C23×C17C22×D411yescharacteristic
401C23×C17C22×D411yescharacteristic
402C23×C17C2×#4111yescharacteristic
403C23×C17C2×#4111yescharacteristic
404C23×C17C2×#4111yescharacteristic
405C23×C17C2×#4111yescharacteristic
406C23×C17C2×#4111yescharacteristic
407C23×C17C2×#4111yescharacteristic
408C23×C17H(5,𝔽2)11yescharacteristic
409C23×C17H(5,𝔽2)11yescharacteristic
410C23×C172−1+411yescharacteristic
411C23×C172−1+411yescharacteristic
412D4×C17—232no—
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—22no—
434C2×C4×C17—22no—
435C2×C4×C17—22no—
436C2×C4×C17—22no—
437C2×C4×C17—416no—
438C2×C4×C17—416no—
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×C17C4×D414yes—
448C2×C4×C17#12014yes—
449C2×C4×C17#12114yes—
450C2×Dic17—22no—
451C2×Dic17—22no—
452C2×Dic17—22no—
453C2×Dic17—22no—
454C2×Dic17—22no—
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—41no—
472C2×Dic17—41no—
473C2×Dic17—41no—
474C2×Dic17—41no—
475C2×Dic17—41no—
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—41no—
497C2×Dic17—41no—
498C2×Dic17—41no—
499C2×Dic17—41no—
500C2×Dic17—41no—
501C2×Dic17—41no—
502C2×Dic17—41no—
503C2×Dic17—41no—
504C2×Dic17—41no—
505C2×Dic17C4×D414yescomplemented
506C22×C4×D4D1711yescharacteristic
507C2×#394—171no—
508C2×#389—171no—
509C2×#388—171no—
510C2×#385—171no—
511C2×#385—171no—
512C2×C4×C22⋊C4—171no—
513#1440—171no—
514#1439—171no—
515#1438—171no—
516#1437—171no—
517#1436—171no—
518#1436—171no—
519#1436—171no—
520C22⋊#95—171no—
521C22×C17—24no—
522C22×C17—24no—
523C22×C17—24no—
524C22×C17—24no—
525C22×C17—24no—
526C22×C17—24no—
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×C17—42no—
537C22×C17—42no—
538C22×C17—42no—
539C22×C17—42no—
540C22×C17—42no—
541C22×C17—42no—
542C22×C17—42no—
543C22×C17—42no—
544C22×C17—42no—
545C22×C17—42no—
546C22×C17—42no—
547C22×C17—42no—
548C22×C17—42no—
549C22×C17—42no—
550C22×C17—42no—
551C22×C17C2×C4×D411yescharacteristic
552C22×C17C2×C4×D411yescharacteristic
553C22×C17C2×C4×D411yescharacteristic
554C22×C17C2×C4×D411yescharacteristic
555C22×C17C4×#4111yescharacteristic
556C22×C17#52011yescharacteristic
557C22×C17#52011yescharacteristic
558C22×C17C2×#12011yescharacteristic
559C22×C17C2×#12111yescharacteristic
560C22×C17#52511yescharacteristic
561C22×C17#52511yescharacteristic
562C22×C17#52511yescharacteristic
563C22×C17#52511yescharacteristic
564C22×C17#52911yescharacteristic
565C22×C17#53211yescharacteristic
566C22×C17#53411yescharacteristic
567C22×C17#53611yescharacteristic
568C22×C17#53911yescharacteristic
569C22×C17#53911yescharacteristic
570C22×C17D4211yescharacteristic
571C22×C17D4211yescharacteristic
572C22×C17#54611yescharacteristic
573C22×C17#54611yescharacteristic
574C22×C17#54711yescharacteristic
575C22×C17#54711yescharacteristic
576C22×C17#54711yescharacteristic
577C22×C17#54811yescharacteristic
578C22×C17#54811yescharacteristic
579C22×C17#54811yescharacteristic
580C22×C17#55111yescharacteristic
581C22×C17#55211yescharacteristic
582C22×C17#55311yescharacteristic
583C22×C17#55311yescharacteristic
584C22×C17#55611yescharacteristic
585C22×C17#55911yescharacteristic
586C4×C17—24no—
587C4×C17—24no—
588C4×C17—24no—
589C4×C17—42no—
590C4×C17—42no—
591Dic17—24no—
592Dic17—42no—
593Dic17—42no—
594Dic17—42no—
595Dic17—42no—
596Dic17—42no—
597Dic17—81no—
598Dic17—81no—
599C23×D4C2×D1711yescharacteristic
600C24×C4C2×D1711yescharacteristic
601C24×C4C2×D1711yescharacteristic
602C2×C4×D4—24no—
603C2×C4×D4—24no—
604C2×C4×D4—24no—
605C22×C4⋊C4—171no—
606C22×C4⋊C4—171no—
607C22×C4⋊C4—171no—
608C22×C4⋊C4—171no—
609C22×C4⋊C4C2×D1711yescharacteristic
610C22×C22⋊C4—171no—
611C22×C22⋊C4—171no—
612C22×C22⋊C4—171no—
613C22×C22⋊C4—171no—
614C22×C22⋊C4—171no—
615C22×C22⋊C4—171no—
616C22×C22⋊C4—171no—
617C22×C22⋊C4—171no—
618C22×C22⋊C4C2×D1711yescharacteristic
619C22×C22⋊C4C2×D1711yescharacteristic
620C22×C42—171no—
621C22×C42—171no—
622C22×C42C2×D1711yescharacteristic
623#394—178no—
624#389—344no—
625#388—344no—
626#385—344no—
627#385—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×#95—171no—
641C2×#95—171no—
642C2×#95—171no—
643C2×C17—44no—
644C2×C17—44no—
645C2×C17C4×#12011yescharacteristic
646C2×C17C4×#12111yescharacteristic
647C2×C17#232211yescharacteristic
648C2×C17#235911yescharacteristic
649C2×C17#236111yescharacteristic
650C2×C17#236111yescharacteristic
651C2×C17#236711yescharacteristic
652C2×C17#241011yescharacteristic
653C2×C17#241511yescharacteristic
654C2×C17#243211yescharacteristic
655C2×C17#245511yescharacteristic
656C2×C17#246011yescharacteristic
657C2×C17#246311yescharacteristic
658C2×C17#246611yescharacteristic
659C2×C17#260211yescharacteristic
660C25C22×D1711yescharacteristic
661C25C22×D1711yescharacteristic
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—22no—
665C22×D4—22no—
666C22×D4—22no—
667C22×D4—22no—
668C22×D4C4×D1714yes—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—22no—
673C23×C4—22no—
674C23×C4—22no—
675C23×C4—22no—
676C23×C4—22no—
677C23×C4—22no—
678C23×C4—41no—
679C23×C4—41no—
680C23×C4—41no—
681C23×C4—41no—
682C23×C4—171no—
683C23×C4—171no—
684C23×C4—171no—
685C23×C4—171no—
686C23×C4—171no—
687C23×C4—171no—
688C23×C4—171no—
689C23×C4—171no—
690C23×C4C22⋊D1714yes—
691C23×C4C22×D1711yescharacteristic
692C23×C4C22×D1711yescharacteristic
693C23×C4C22×D1711yescharacteristic
694C23×C4C22×D1711yescharacteristic
695C23×C4C22×D1711yescharacteristic
696C4×D4—232no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—174no—
700C2×C4⋊C4—342no—
701C2×C4⋊C4—342no—
702C2×C4⋊C4—342no—
703C2×C4⋊C4—342no—
704C2×C4⋊C4—342no—
705C2×C4⋊C4—342no—
706C2×C4⋊C4—342no—
707C2×C4⋊C4—342no—
708C2×C4⋊C4—342no—
709C2×C4⋊C4—342no—
710C2×C4⋊C4—681no—
711C2×C4⋊C4C22⋊D1714yes—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—174no—
718C2×C22⋊C4—174no—
719C2×C22⋊C4—174no—
720C2×C22⋊C4—174no—
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⋊C4—342no—
736C2×C22⋊C4—342no—
737C2×C22⋊C4—681no—
738C2×C22⋊C4—681no—
739C2×C22⋊C4—681no—
740C2×C22⋊C4—681no—
741C2×C22⋊C4C22⋊D1714yes—
742C2×C42—22no—
743C2×C42—22no—
744C2×C42—22no—
745C2×C42—342no—
746C2×C42—342no—
747C2×C42—342no—
748C2×C42—342no—
749C2×C42—681no—
750C2×C42—681no—
751#95—174no—
752#95—174no—
753#95—342no—
754#95—342no—
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—681no—
765C17#1418511yescharacteristic, 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—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24C2×C4×D1712yes—
791C24C2×C4×D1712yes—
792C24#6325212yes—
793C24#6325212yes—
794C24C2×C22⋊D1712yes—
795C24C2×C22⋊D1712yes—
796C24C23×D1711yescharacteristic
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
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—28no—
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—28no—
830C22×C4—28no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
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—341no—
851C22×C4—341no—
852C22×C4—341no—
853C22×C4—341no—
854C22×C4—341no—
855C22×C4—341no—
856C22×C4—341no—
857C22×C4—341no—
858C22×C4—341no—
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—341no—
894C22×C4—341no—
895C22×C4—341no—
896C22×C4—341no—
897C22×C4—341no—
898C22×C4C2×C4×D1712yes—
899C22×C4#6325212yes—
900C22×C4D4×D1712yes—
901C22×C4#6325412yes—
902C22×C4C2×C22⋊D1712yes—
903C22×C4C2×C22⋊D1712yes—
904C22×C4C2×C22⋊D1712yes—
905C22×C4C2×C22⋊D1712yes—
906C22×C4C2×C22⋊D1712yes—
907C22×C4C2×C22⋊D1712yes—
908C22×C4C2×C22⋊D1712yes—
909C4⋊C4—28no—
910C4⋊C4—348no—
911C4⋊C4—684no—
912C4⋊C4—684no—
913C4⋊C4—684no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—348no—
917C22⋊C4—348no—
918C22⋊C4—348no—
919C22⋊C4—348no—
920C22⋊C4—348no—
921C22⋊C4—684no—
922C22⋊C4—684no—
923C22⋊C4—684no—
924C42—28no—
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—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23C4×C22⋊D1714yes—
996C23C4×C22⋊D1714yes—
997C23C22×C4×D1711yescharacteristic
998C23C2×#6325211yescharacteristic
999C23C2×#6325211yescharacteristic
1000C23C2×#6325211yescharacteristic
1001C23C2×D4×D1711yescharacteristic
1002C23C2×#6325411yescharacteristic
1003C23#1058769111yescharacteristic
1004C23#1058769111yescharacteristic
1005C23#41×D1711yescharacteristic
1006C23#41×D1711yescharacteristic
1007C23#1058769711yescharacteristic
1008C23#1058769711yescharacteristic
1009C23C22×C22⋊D1711yescharacteristic
1010C23C22×C22⋊D1711yescharacteristic
1011C23C22×C22⋊D1711yescharacteristic
1012D4—232no—
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—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—416no—
1038C2×C4—416no—
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—174no—
1048C2×C4—342no—
1049C2×C4—342no—
1050C2×C4—342no—
1051C2×C4—342no—
1052C2×C4—342no—
1053C2×C4—342no—
1054C2×C4—342no—
1055C2×C4—342no—
1056C2×C4—342no—
1057C2×C4—342no—
1058C2×C4—342no—
1059C2×C4—342no—
1060C2×C4—342no—
1061C2×C4—342no—
1062C2×C4—342no—
1063C2×C4—342no—
1064C2×C4—342no—
1065C2×C4—342no—
1066C2×C4—342no—
1067C2×C4—342no—
1068C2×C4—342no—
1069C2×C4—681no—
1070C2×C4—681no—
1071C2×C4—681no—
1072C2×C4—681no—
1073C2×C4—681no—
1074C2×C4—681no—
1075C2×C4—681no—
1076C2×C4—681no—
1077C2×C4—681no—
1078C2×C4—681no—
1079C2×C4—681no—
1080C2×C4—681no—
1081C2×C4—681no—
1082C2×C4—681no—
1083C2×C4—681no—
1084C2×C4—681no—
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×C4C4×C22⋊D1714yes—
1104C2×C4#1058762514yes—
1105C2×C4#1058763914yes—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22C4×D4×D1711yescharacteristic
1137C22C2×C4×C22⋊D1711yescharacteristic
1138C22C2×C4×C22⋊D1711yescharacteristic
1139C22C2×C4×C22⋊D1711yescharacteristic
1140C22C4×#6325411yescharacteristic
1141C22#1176328811yescharacteristic
1142C22#1176328811yescharacteristic
1143C22C2×#1058763911yescharacteristic
1144C22C2×#1058762511yescharacteristic
1145C22#1176331811yescharacteristic
1146C22#1176332011yescharacteristic
1147C22#1176332011yescharacteristic
1148C22#1176332011yescharacteristic
1149C22#1176333911yescharacteristic
1150C22#1176335511yescharacteristic
1151C22#1176336811yescharacteristic
1152C22#1176338011yescharacteristic
1153C22#1176340111yescharacteristic
1154C22#1176340111yescharacteristic
1155C22D4×C22⋊D1711yescharacteristic
1156C22D4×C22⋊D1711yescharacteristic
1157C22#1176345311yescharacteristic
1158C22#1176345311yescharacteristic
1159C22#1176345811yescharacteristic
1160C22#1176345811yescharacteristic
1161C22#1176346411yescharacteristic
1162C22#1176346611yescharacteristic
1163C22#1176346611yescharacteristic
1164C22#1176346811yescharacteristic
1165C22#1176348811yescharacteristic
1166C22#1176349911yescharacteristic
1167C22#1176350811yescharacteristic
1168C22#1176350911yescharacteristic
1169C22#1176352911yescharacteristic
1170C22#1176354211yescharacteristic
1171C4—24no—
1172C4—24no—
1173C4—24no—
1174C4—42no—
1175C4—42no—
1176C4—344no—
1177C4—682no—
1178C4—682no—
1179C4—682no—
1180C4—682no—
1181C4—682no—
1182C4—1361no—
1183C4—1361no—
1184C2—44no—
1185C2—44no—
1186C2C4×#1058763911yescharacteristic
1187C2C4×#1058762511yescharacteristic
1188C2#1453144911yescharacteristic
1189C2#1453177011yescharacteristic
1190C2#1453179611yescharacteristic
1191C2#1453180111yescharacteristic
1192C2#1453185711yescharacteristic
1193C2#1453215811yescharacteristic
1194C2#1453221311yescharacteristic
1195C2#1453240811yescharacteristic
1196C2#1453266111yescharacteristic
1197C2#1453273011yescharacteristic
1198C2#1453277511yescharacteristic
1199C2#1453281411yescharacteristic
1200C2#1453439611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC22×C4×D4×C17C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC22×C4×D4D17
hypocenterC17#14185
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#11762704C2semidirect
3. C2×#11762703C2semidirect
4. C2×#11762682C2semidirect
5. C2×#11762682C2semidirect
6. C2×C4×C22⋊Dic17C2semidirect
7. #14527031C2semidirect
8. #14527027C2semidirect
10. #14527021C2semidirect
11. #14527017C2semidirect
12. #14527017C2semidirect
13. #14527016C2semidirect
14. #14527007C2semidirect
30. #11762723C4semidirect
129. C2×C22⋊Dic17C2×C4semidirect
130. C2×C22⋊Dic17C2×C4semidirect
131. C2×C22⋊Dic17C2×C4semidirect
132. C2×C22⋊Dic17C2×C4semidirect
144. C2×#63225C2×C4semidirect
163. #10587502C2×C4semidirect
164. #10587502D4semidirect
505. C2×Dic17C4×D4semidirect
765. C17#14185semidirect

Maximal subgroups

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

subgroupindex
C2×#117627232
C2×#117627042
C2×#117627032
C2×#117626822
C2×C4×C22⋊Dic172
#145270312
#145270272
#145270252
#145270212
#145270172
#145270162
#145270072
C22×C4×D4×C172
#1418517