Finite Group Databasebeta

← #16957486

Subgroups — #16957486

Order 4352.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762698C211yesmaximal, characteristic, complemented
2C2×#11762688C211yesmaximal, characteristic
3C2×#11762686C211yesmaximal, characteristic
4C2×#11762686C211yesmaximal, characteristic
5C2×#11762667C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
7C22×#10587502C211yesmaximal, characteristic, complemented
8#14527045C211yesmaximal, characteristic, complemented
9#14527042C211yesmaximal, characteristic, complemented
10#14527032C211yesmaximal, characteristic, complemented
11#14527028C211yesmaximal, characteristic, complemented
12#14527020C211yesmaximal, characteristic, complemented
13#14527015C211yesmaximal, characteristic, complemented
14#14527009C211yesmaximal, characteristic, complemented
15C17×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C24×Dic17C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30#11762698—24no—
31#11762688—24no—
32#11762686—24no—
33#11762686C418yescomplemented
34#11762667—24no—
35C22⋊C4×Dic17—24no—
36C2×#10587502—24no—
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
50C2×#10587502C2211yescharacteristic
51C24×C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C24×D17C2311yescharacteristic
60C23×C4×C17—22no—
61C23×C4×C17—22no—
62C23×C4×C17—22no—
63C23×C4×C17—22no—
64C23×C4×C17—22no—
65C23×C4×C17—41no—
66C23×C4×C17—41no—
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C22×C22⋊D17—22no—
74C22×C22⋊D17—22no—
75C22×C22⋊D17—22no—
76C22×C22⋊D17—22no—
77C22×C22⋊D17—22no—
78C22×C22⋊D17—22no—
79C22×C22⋊D17C2×C414yes—
80C23×Dic17—22no—
81C23×Dic17—22no—
82C23×Dic17—22no—
83C23×Dic17—22no—
84C23×Dic17—22no—
85C23×Dic17—22no—
86C23×Dic17—22no—
87C23×Dic17—22no—
88C23×Dic17—41no—
89C23×Dic17—41no—
90C23×Dic17—41no—
91C23×Dic17—41no—
92C23×Dic17C2×C414yes—
93C23×Dic17D414yes—
94C23×Dic17C2311yescharacteristic
95C23×Dic17C2311yescharacteristic
96C23×Dic17C2311yescharacteristic
97C23×Dic17C2311yescharacteristic
98C23×Dic17C2311yescharacteristic
99C23×Dic17C2311yescharacteristic
100C23×Dic17C2311yescharacteristic
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×C17C2×C414yes—
107C2×C22⋊Dic17—22no—
108C2×C22⋊Dic17—22no—
109C2×C22⋊Dic17D414yes—
110C2×#63227—22no—
111C2×#63227—22no—
112C2×#63227—22no—
113C2×#63227—22no—
114C2×#63227—22no—
115C2×#63227—22no—
116C2×#63227—22no—
117C2×#63227—22no—
118C2×#63227—22no—
119C2×#63227—22no—
120C2×#63227—41no—
121C2×#63227—41no—
122C2×#63227—41no—
123C2×#63227—41no—
124C2×#63227—41no—
125C2×#63227—41no—
126C2×#63227C2×C414yescomplemented
127C2×#63227C2×C414yescomplemented
128C2×#63225—22no—
129C2×#63225—22no—
130C2×#63225—22no—
131C2×#63225—22no—
132C2×#63225—41no—
133C2×#63225—41no—
134C2×C4×Dic17—22no—
135C2×C4×Dic17—22no—
136C2×C4×Dic17—22no—
137C2×C4×Dic17—22no—
138C2×C4×Dic17—41no—
139C2×C4×Dic17—41no—
140C17×#95—22no—
141C17×#95—22no—
142C17×#95—41no—
143C17×#95—41no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—22no—
148#10587502—22no—
149#10587502—22no—
150#10587502—22no—
151#10587502—22no—
152#10587502—22no—
153#10587502—22no—
154#10587502—22no—
155#10587502C2×C414yescomplemented
156#10587502C2×C414yescomplemented
157#10587502D414yescomplemented
158C24×C17—21no—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17—21no—
164C24×C17—21no—
165C24×C17—21no—
166C24×C17C22×C412yes—
167C24×C17C2×D412yes—
168C24×C17C2×D412yes—
169C24×C17#4112yes—
170C24×C17#4112yes—
171C24×C17#4112yes—
172C24×C17#4112yes—
173C24×C17C2411yescharacteristic
174C23×D17—21no—
175C23×D17—21no—
176C23×D17—21no—
177C23×D17—21no—
178C23×D17—21no—
179C23×D17—21no—
180C23×D17—21no—
181C23×D17—21no—
182C23×D17—21no—
183C23×D17—21no—
184C23×D17—21no—
185C23×D17—21no—
186C23×D17—21no—
187C23×D17—21no—
188C23×D17C22×C412yes—
189C22×C4×C17—28no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
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—44no—
229C22×C4×C17—44no—
230C22×C4×C17—44no—
231C22×C4×C17—44no—
232C22×C4×C17—44no—
233C22×C4×C17—44no—
234C22×C4×C17C22×C412yes—
235C22×C4×C17C22×C412yes—
236C22×C4×C17C2×D412yes—
237C22×C4×C17#4112yes—
238C2×C22⋊D17—28no—
239C2×C22⋊D17—28no—
240C2×C22⋊D17—28no—
241C2×C22⋊D17—44no—
242C2×C22⋊D17—44no—
243C2×C22⋊D17—44no—
244C2×C22⋊D17—44no—
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—28no—
254C22×Dic17—28no—
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—28no—
286C22×Dic17—28no—
287C22×Dic17—44no—
288C22×Dic17—44no—
289C22×Dic17—44no—
290C22×Dic17—44no—
291C22×Dic17—44no—
292C22×Dic17—44no—
293C22×Dic17—44no—
294C22×Dic17—44no—
295C22×Dic17—44no—
296C22×Dic17—44no—
297C22×Dic17C22×C412yes—
298C22×Dic17C22×C412yes—
299C22×Dic17C22×C412yes—
300C22×Dic17C2×D412yes—
301C22×Dic17C2×D412yes—
302C22×Dic17C2×D412yes—
303C22×Dic17C2×D412yes—
304C22×Dic17C2×D412yes—
305C22×Dic17C2×D412yes—
306C22×Dic17#4112yes—
307C22×Dic17#4112yes—
308C22⋊C4×C17—28no—
309C22⋊C4×C17—44no—
310C22⋊Dic17—28no—
311#63227—28no—
312#63227—44no—
313#63227—44no—
314#63227—44no—
315#63227—44no—
316#63227—44no—
317#63225—44no—
318#63225—44no—
319C4×Dic17—44no—
320C4×Dic17—44no—
321#13999—171nomaximal, Sylow
322C23×C17—22no—
323C23×C17—22no—
324C23×C17—22no—
325C23×C17—22no—
326C23×C17—22no—
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#11714yes—
351C23×C17C4×D414yes—
352C23×C17C4×D414yes—
353C23×C17#12114yes—
354C23×C17#12314yes—
355C23×C17#12414yes—
356C23×C17#12614yes—
357C23×C17C23×C411yescharacteristic
358C23×C17C22×D411yescharacteristic
359C23×C17C22×D411yescharacteristic
360C23×C17C22×D411yescharacteristic
361C23×C17C2×#4111yescharacteristic
362C23×C17C2×#4111yescharacteristic
363C23×C17C2×#4111yescharacteristic
364C23×C17C2×#4111yescharacteristic
365C23×C17C2×#4111yescharacteristic
366C23×C17C2×#4111yescharacteristic
367C23×C17C2×#4111yescharacteristic
368C23×C17H(5,𝔽2)11yescharacteristic
369C23×C17H(5,𝔽2)11yescharacteristic
370C23×C17H(5,𝔽2)11yescharacteristic
371C23×C172−1+411yescharacteristic
372C22×D17—22no—
373C22×D17—22no—
374C22×D17—22no—
375C22×D17—22no—
376C22×D17—22no—
377C22×D17—22no—
378C22×D17—22no—
379C22×D17—41no—
380C22×D17—41no—
381C22×D17—41no—
382C22×D17—41no—
383C22×D17—41no—
384C22×D17—41no—
385C22×D17—41no—
386C22×D17—41no—
387C22×D17—41no—
388C22×D17—41no—
389C22×D17—41no—
390C22×D17—41no—
391C22×D17—41no—
392C22×D17—41no—
393C22×D17—41no—
394C22×D17—41no—
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—
407C2×C4×C17—22no—
408C2×C4×C17—22no—
409C2×C4×C17—22no—
410C2×C4×C17—22no—
411C2×C4×C17—22no—
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—416no—
420C2×C4×C17—41no—
421C2×C4×C17—41no—
422C2×C4×C17—41no—
423C2×C4×C17—41no—
424C2×C4×C17—41no—
425C2×C4×C17—41no—
426C2×C4×C17—41no—
427C2×C4×C17—41no—
428C2×C4×C17—41no—
429C2×C4×C17—41no—
430C2×C4×C17—41no—
431C2×C4×C17—41no—
432C2×C4×C17—41no—
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—
450C22⋊D17—416no—
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—22no—
472C2×Dic17—22no—
473C2×Dic17—22no—
474C2×Dic17—22no—
475C2×Dic17—22no—
476C2×Dic17—22no—
477C2×Dic17—22no—
478C2×Dic17—416no—
479C2×Dic17—416no—
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×Dic17C4×D414yes—
501C2×Dic17#12114yes—
502C2×#388—171no—
503C2×#386—171no—
504C2×#386—171no—
505C2×#386—171no—
506C2×#380—171no—
507C2×C4×C22⋊C4—171no—
508C22×#95—171no—
509#1443—171no—
510#1442—171no—
511#1440—171no—
512#1439—171no—
513#1437—171no—
514#1436—171no—
515#1434—171no—
516C22⋊#95D1711yescharacteristic, complemented
517C22×C17—24no—
518C22×C17—24no—
519C22×C17—24no—
520C22×C17—24no—
521C22×C17—24no—
522C22×C17—24no—
523C22×C17—24no—
524C22×C17—24no—
525C22×C17—24no—
526C22×C17—24no—
527C22×C17—24no—
528C22×C17—24no—
529C22×C17—24no—
530C22×C17—24no—
531C22×C17#38818yescomplemented
532C22×C17C2×#11711yescharacteristic
533C22×C17C2×C4×D411yescharacteristic
534C22×C17C2×C4×D411yescharacteristic
535C22×C17C2×C4×D411yescharacteristic
536C22×C17C4×#4111yescharacteristic
537C22×C17#51811yescharacteristic
538C22×C17#52011yescharacteristic
539C22×C17C2×#12111yescharacteristic
540C22×C17C2×#12111yescharacteristic
541C22×C17C2×#12311yescharacteristic
542C22×C17#52511yescharacteristic
543C22×C17C2×#12411yescharacteristic
544C22×C17C2×#12611yescharacteristic
545C22×C17#52911yescharacteristic
546C22×C17#53211yescharacteristic
547C22×C17#53411yescharacteristic
548C22×C17#53711yescharacteristic
549C22×C17#53811yescharacteristic
550C22×C17#53911yescharacteristic
551C22×C17D4211yescharacteristic
552C22×C17#54611yescharacteristic
553C22×C17#54611yescharacteristic
554C22×C17#54611yescharacteristic
555C22×C17#54611yescharacteristic
556C22×C17#54711yescharacteristic
557C22×C17#54811yescharacteristic
558C22×C17#55111yescharacteristic
559C22×C17#55111yescharacteristic
560C22×C17#55111yescharacteristic
561C22×C17#55111yescharacteristic
562C22×C17#55211yescharacteristic
563C22×C17#55211yescharacteristic
564C22×C17#55311yescharacteristic
565C22×C17#55311yescharacteristic
566C22×C17#55311yescharacteristic
567C2×D17—42no—
568C2×D17—42no—
569C2×D17—42no—
570C2×D17—42no—
571C2×D17—42no—
572C2×D17—42no—
573C2×D17—42no—
574C2×D17—81no—
575C2×D17—81no—
576C2×D17—81no—
577C2×D17—81no—
578C2×D17—81no—
579C2×D17—81no—
580C2×D17—81no—
581C2×D17—81no—
582C4×C17—42no—
583C4×C17—42no—
584C4×C17—42no—
585C4×C17—42no—
586C4×C17—81no—
587C4×C17—81no—
588Dic17—24no—
589Dic17—24no—
590Dic17—42no—
591Dic17—42no—
592Dic17—42no—
593Dic17—42no—
594Dic17—42no—
595C23×D4—171no—
596C24×C4—171no—
597C24×C4—171no—
598C24×C4C2×D1711yescharacteristic
599C22×C4⋊C4—171no—
600C22×C4⋊C4—171no—
601C22×C22⋊C4—171no—
602C22×C22⋊C4—171no—
603C22×C22⋊C4—171no—
604C22×C22⋊C4—171no—
605C22×C22⋊C4—171no—
606C22×C22⋊C4—171no—
607C22×C22⋊C4—171no—
608C22×C22⋊C4C2×D1711yescharacteristic
609C22×C22⋊C4C2×D1711yescharacteristic
610C22×C42—171no—
611C22×C42—171no—
612#388—344no—
613#386—178no—
614#386—344no—
615#386—344no—
616#380—344no—
617C4×C22⋊C4—344no—
618C2×#95—171no—
619C2×#95—171no—
620C2×#95—171no—
621C2×#95—171no—
622C2×#95—171no—
623C2×#95—171no—
624C2×#95—171no—
625C2×#95—171no—
626C2×#95—171no—
627C2×#95—171no—
628C2×#95—171no—
629C2×#95—171no—
630C2×#95—171no—
631C2×#95—171no—
632C2×#95—344no—
633C2×#95C2×D1711yescharacteristic
634C2×#95C2×D1711yescharacteristic
635C2×#95C2×D1711yescharacteristic
636C2×#95C2×D1711yescharacteristic
637C2×C17—28no—
638C2×C17C2×#38811yescharacteristic
639C2×C17C4×#12111yescharacteristic
640C2×C17#232511yescharacteristic
641C2×C17#235211yescharacteristic
642C2×C17#235311yescharacteristic
643C2×C17#235811yescharacteristic
644C2×C17#235911yescharacteristic
645C2×C17#241211yescharacteristic
646C2×C17#241611yescharacteristic
647C2×C17#247211yescharacteristic
648C2×C17#248111yescharacteristic
649C2×C17#248811yescharacteristic
650C2×C17#249811yescharacteristic
651C2×C17#251011yescharacteristic
652C2×C17#254311yescharacteristic
653D17—82no—
654C25—171no—
655C25C22×D1711yescharacteristic
656C22×D4—174no—
657C22×D4—342no—
658C22×D4—342no—
659C22×D4—342no—
660C22×D4—342no—
661C22×D4—342no—
662C22×D4—342no—
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—22no—
666C23×C4—22no—
667C23×C4—22no—
668C23×C4—41no—
669C23×C4—41no—
670C23×C4—171no—
671C23×C4—171no—
672C23×C4—171no—
673C23×C4—171no—
674C23×C4—171no—
675C23×C4—171no—
676C23×C4—171no—
677C23×C4—174no—
678C23×C4—174no—
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—681no—
688C23×C4—681no—
689C23×C4—681no—
690C23×C4—681no—
691C23×C4C22×D1711yescharacteristic
692C23×C4C22×D1711yescharacteristic
693C23×C4C22×D1711yescharacteristic
694C23×C4C22×D1711yescharacteristic
695C23×C4C22×D1711yescharacteristic
696C23×C4C22×D1711yescharacteristic
697C2×C4⋊C4—342no—
698C2×C4⋊C4—342no—
699C2×C4⋊C4—342no—
700C2×C4⋊C4—342no—
701C2×C4⋊C4—681no—
702C2×C4⋊C4—681no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—174no—
709C2×C22⋊C4—174no—
710C2×C22⋊C4—174no—
711C2×C22⋊C4—342no—
712C2×C22⋊C4—342no—
713C2×C22⋊C4—342no—
714C2×C22⋊C4—342no—
715C2×C22⋊C4—342no—
716C2×C22⋊C4—342no—
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—681no—
724C2×C22⋊C4—681no—
725C2×C22⋊C4—681no—
726C2×C22⋊C4—681no—
727C2×C22⋊C4—681no—
728C2×C22⋊C4—681no—
729C2×C22⋊C4C4×D1714yes—
730C2×C42—342no—
731C2×C42—342no—
732C2×C42—342no—
733C2×C42—342no—
734C2×C42—681no—
735C2×C42—681no—
736#95—22no—
737#95—22no—
738#95—41no—
739#95—41no—
740#95—174no—
741#95—174no—
742#95—174no—
743#95—342no—
744#95—342no—
745#95—342no—
746#95—342no—
747#95—342no—
748#95—342no—
749#95—342no—
750#95—342no—
751#95—342no—
752#95—342no—
753#95—342no—
754C17#1399911yescharacteristic, complemented, Sylow
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—172no—
764C24—341no—
765C24—341no—
766C24—341no—
767C24—341no—
768C24—341no—
769C24—341no—
770C24—341no—
771C24—341no—
772C24—341no—
773C24—341no—
774C24—341no—
775C24—341no—
776C24—341no—
777C24—341no—
778C24C2×C4×D1712yes—
779C24#6325212yes—
780C24#6325212yes—
781C24D4×D1712yes—
782C24D4×D1712yes—
783C24#6325412yes—
784C24#6325612yes—
785C24C23×D1711yescharacteristic
786C2×D4—348no—
787C2×D4—348no—
788C2×D4—348no—
789C2×D4—684no—
790C2×D4—684no—
791C2×D4—684no—
792C2×D4—684no—
793C22×C4—28no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
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—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
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—348no—
850C22×C4—348no—
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—348no—
890C22×C4—348no—
891C22×C4—684no—
892C22×C4—684no—
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×C4#6325412yes—
905C4⋊C4—684no—
906C4⋊C4—684no—
907C22⋊C4—28no—
908C22⋊C4—44no—
909C22⋊C4—348no—
910C22⋊C4—348no—
911C22⋊C4—684no—
912C22⋊C4—684no—
913C22⋊C4—684no—
914C22⋊C4—684no—
915C22⋊C4—684no—
916C42—684no—
917C42—684no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
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—342no—
947C23—342no—
948C23—342no—
949C23—342no—
950C23—342no—
951C23—342no—
952C23—342no—
953C23—681no—
954C23—681no—
955C23—681no—
956C23—681no—
957C23—681no—
958C23—681no—
959C23—681no—
960C23—681no—
961C23—681no—
962C23—681no—
963C23—681no—
964C23—681no—
965C23—681no—
966C23—681no—
967C23—681no—
968C23—681no—
969C23—681no—
970C23—681no—
971C23—681no—
972C23—681no—
973C23—681no—
974C23—681no—
975C23—681no—
976C23—681no—
977C23—681no—
978C23—681no—
979C23—681no—
980C23—681no—
981C23#1058755814yes—
982C23#1058756714yes—
983C23#1058757014yes—
984C23#1058757114yes—
985C23#1058757914yes—
986C23#1058758014yes—
987C23#1058758414yes—
988C23C22×C4×D1711yescharacteristic
989C23C2×#6325211yescharacteristic
990C23C2×#6325211yescharacteristic
991C23C2×D4×D1711yescharacteristic
992C23C2×D4×D1711yescharacteristic
993C23C2×D4×D1711yescharacteristic
994C23C2×#6325411yescharacteristic
995C23C2×#6325411yescharacteristic
996C23#1058769111yescharacteristic
997C23#1058769111yescharacteristic
998C23C2×#6325611yescharacteristic
999C23#41×D1711yescharacteristic
1000C23#41×D1711yescharacteristic
1001C23#1058769611yescharacteristic
1002C23#1058769711yescharacteristic
1003D4—6816no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—416no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
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—174no—
1048C2×C4—174no—
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—342no—
1070C2×C4—342no—
1071C2×C4—342no—
1072C2×C4—342no—
1073C2×C4—342no—
1074C2×C4—342no—
1075C2×C4—342no—
1076C2×C4—6816no—
1077C2×C4—6816no—
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—
1098C22—24no—
1099C22—24no—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—24no—
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—682no—
1113C22—682no—
1114C22—682no—
1115C22—682no—
1116C22—682no—
1117C22—682no—
1118C22—682no—
1119C22—1361no—
1120C22—1361no—
1121C22—1361no—
1122C22—1361no—
1123C22—1361no—
1124C22—1361no—
1125C22—1361no—
1126C22—1361no—
1127C22#1176269818yescomplemented
1128C22C2×#1058755811yescharacteristic
1129C22C4×D4×D1711yescharacteristic
1130C22C2×#1058756711yescharacteristic
1131C22C2×#1058757911yescharacteristic
1132C22C4×#6325411yescharacteristic
1133C22#1176328111yescharacteristic
1134C22#1176328811yescharacteristic
1135C22#121×D1711yescharacteristic
1136C22C2×#1058757011yescharacteristic
1137C22C2×#1058758011yescharacteristic
1138C22#1176331511yescharacteristic
1139C22C2×#1058757111yescharacteristic
1140C22C2×#1058758411yescharacteristic
1141C22#1176333611yescharacteristic
1142C22#1176335411yescharacteristic
1143C22#1176336711yescharacteristic
1144C22#1176338611yescharacteristic
1145C22#1176339411yescharacteristic
1146C22#1176340311yescharacteristic
1147C22#1176344111yescharacteristic
1148C22#1176344611yescharacteristic
1149C22#1176344911yescharacteristic
1150C22#1176345011yescharacteristic
1151C22#1176345111yescharacteristic
1152C22#1176345711yescharacteristic
1153C22#1176346811yescharacteristic
1154C22#1176348311yescharacteristic
1155C22#1176348511yescharacteristic
1156C22#1176348611yescharacteristic
1157C22#1176348611yescharacteristic
1158C22#1176349211yescharacteristic
1159C22#1176350111yescharacteristic
1160C22#1176350511yescharacteristic
1161C22#1176350811yescharacteristic
1162C22#1176350811yescharacteristic
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—42no—
1167C4—81no—
1168C4—81no—
1169C4—344no—
1170C4—344no—
1171C4—682no—
1172C4—682no—
1173C4—682no—
1174C4—682no—
1175C4—682no—
1176C2—28no—
1177C2—1362no—
1178C2C2×#1176269811yescharacteristic
1179C2#1453129411yescharacteristic
1180C2#1453148511yescharacteristic
1181C2#1453170711yescharacteristic
1182C2#1453171811yescharacteristic
1183C2#1453176011yescharacteristic
1184C2#1453177411yescharacteristic
1185C2#1453217711yescharacteristic
1186C2#1453222311yescharacteristic
1187C2#1453290711yescharacteristic
1188C2#1453304211yescharacteristic
1189C2#1453310611yescharacteristic
1190C2#1453322411yescharacteristic
1191C2#1453335011yescharacteristic
1192C2#1453374811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C22⋊#95C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC22⋊#95D17
hypocenterC17#13999
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#11762698C2semidirect
5. C2×#11762667C2semidirect
6. C2×C22⋊C4×Dic17C2semidirect
7. C22×#10587502C2semidirect
8. #14527045C2semidirect
9. #14527042C2semidirect
10. #14527032C2semidirect
11. #14527028C2semidirect
12. #14527020C2semidirect
13. #14527015C2semidirect
14. #14527009C2semidirect
15. C17×C22⋊#95C2semidirect
33. #11762686C4semidirect
126. C2×#63227C2×C4semidirect
127. C2×#63227C2×C4semidirect
155. #10587502C2×C4semidirect
156. #10587502C2×C4semidirect
157. #10587502D4semidirect
516. C22⋊#95D17semidirect
531. C22×C17#388semidirect
754. C17#13999semidirect
1127. C22#11762698semidirect

Maximal subgroups

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

subgroupindex
C2×#117626982
C2×#117626882
C2×#117626862
C2×#117626672
C2×C22⋊C4×Dic172
C22×#105875022
#145270452
#145270422
#145270322
#145270282
#145270202
#145270152
#145270092
C17×C22⋊#952
#1399917