Finite Group Databasebeta

← #16962245

Subgroups — #16962245

Order 4352.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762711C211yesmaximal, characteristic
2C2×#11762687C211yesmaximal, characteristic
3C2×#11762687C211yesmaximal, characteristic
4C2×#11762683C211yesmaximal, characteristic, complemented
5C2×#11762683C211yesmaximal, characteristic, complemented
6C2×#11762668C211yesmaximal, characteristic, complemented
7C2×#11762666C211yesmaximal, characteristic, complemented
8#14527049C211yesmaximal, characteristic, complemented
9#14527048C211yesmaximal, characteristic, complemented
10#14527030C211yesmaximal, characteristic, complemented
11#14527028C211yesmaximal, characteristic, complemented
12#14527028C211yesmaximal, characteristic, complemented
13#14527026C211yesmaximal, characteristic, complemented
14#14527017C211yesmaximal, characteristic, complemented
15C17×#1436C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic
21C22×C4⋊Dic17C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35#11762711—24no—
36#11762687—24no—
37#11762687C418yescomplemented
38#11762683—24no—
39#11762683—24no—
40#11762668—24no—
41#11762666—24no—
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C22×C4⋊C4×C17C2211yescharacteristic
52C22×C42×C17C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C24×D17C2311yescharacteristic
59C24×D17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C22×D68—41no—
74C22×D68—41no—
75C22×D68—41no—
76C22×D68—41no—
77C22×D68C2×C414yes—
78C22×D68D414yes—
79C22×D68Q814yes—
80C22×C4×D17—22no—
81C22×C4×D17—22no—
82C22×C4×D17—22no—
83C22×C4×D17—22no—
84C22×C4×D17—22no—
85C22×C4×D17—22no—
86C22×C4×D17—22no—
87C22×C4×D17—41no—
88C22×C4×D17—41no—
89C22×C4×D17—41no—
90C22×C4×D17—41no—
91C22×C4×D17—41no—
92C22×C4×D17—41no—
93C22×C4×D17C2×C414yescomplemented
94C2×C4⋊C4×C17—22no—
95C2×C4⋊C4×C17—22no—
96C2×C4⋊C4×C17—41no—
97C2×C42×C17—22no—
98C2×C42×C17—41no—
99C2×C42×C17—41no—
100C2×#63227—22no—
101C2×#63227—22no—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227—22no—
105C2×#63227—22no—
106C2×#63227—22no—
107C2×#63227—22no—
108C2×#63227—22no—
109C2×#63227—22no—
110C2×#63227—22no—
111C2×#63227—22no—
112C2×#63227—22no—
113C2×#63227—22no—
114C2×#63227—22no—
115C2×#63227—22no—
116C2×#63227—22no—
117C2×#63227—41no—
118C2×#63227—41no—
119C2×#63227—41no—
120C2×#63227—41no—
121C2×#63227—41no—
122C2×#63227—41no—
123C2×#63227—41no—
124C2×#63227—41no—
125C2×#63227—41no—
126C2×#63227—41no—
127C2×#63227C2×C414yes—
128C2×#63227C2×C414yes—
129C2×#63227C2×C414yescomplemented
130C2×C4⋊Dic17—22no—
131C2×C4⋊Dic17—22no—
132C2×C4⋊Dic17—22no—
133C2×C4⋊Dic17—22no—
134C2×C4⋊Dic17—41no—
135C2×C4⋊Dic17—41no—
136C2×C4⋊Dic17—41no—
137C2×C4⋊Dic17—41no—
138C2×C4⋊Dic17—41no—
139C2×#63225—22no—
140C2×#63225—22no—
141C2×#63225—22no—
142C2×#63225—22no—
143C2×#63225—22no—
144C2×#63225—41no—
145C2×#63225—41no—
146C2×#63225—41no—
147C2×#63225—41no—
148C17×#95—22no—
149C17×#95—22no—
150C17×#95—41no—
151C17×#95C2×C414yescomplemented
152C17×#95D414yescomplemented
153#10587502—22no—
154#10587502—22no—
155#10587502—22no—
156#10587502—22no—
157#10587502—41no—
158#10587502—41no—
159#10587502—41no—
160#10587502C2×C414yescomplemented
161#10587502D414yescomplemented
162C24×C17C2411yescharacteristic
163C23×D17—21no—
164C23×D17—21no—
165C23×D17—21no—
166C23×D17—21no—
167C23×D17—21no—
168C23×D17—21no—
169C23×D17—21no—
170C23×D17—21no—
171C23×D17—21no—
172C23×D17—21no—
173C23×D17—21no—
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×D17C22×C412yes—
188C23×D17C22×C412yes—
189C23×D17C2×D412yes—
190C23×D17C2×D412yes—
191C23×D17C2×Q812yes—
192C23×D17C2×Q812yes—
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—21no—
229C22×C4×C17—21no—
230C22×C4×C17—21no—
231C22×C4×C17—21no—
232C22×C4×C17C22×C412yes—
233C22×C4×C17C22×C412yes—
234C22×C4×C17C22×C412yes—
235C22×C4×C17C2×D412yes—
236C22×C4×C17C2×D412yes—
237C22×C4×C17C2×D412yes—
238C22×C4×C17C2×D412yes—
239C22×C4×C17C2×D412yes—
240C22×C4×C17C2×Q812yes—
241C22×C4×C17#4112yes—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17—21no—
272C22×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17—21no—
278C22×Dic17—21no—
279C22×Dic17C22×C412yes—
280C22×Dic17C22×C412yes—
281C22×Dic17C2×D412yes—
282C22×Dic17C2×D412yes—
283C22×Dic17#4112yes—
284C2×D68—44no—
285C2×D68—44no—
286C2×D68—44no—
287C2×D68—44no—
288C2×D68—44no—
289C2×D68—44no—
290C2×D68C4⋊C4116yescomplemented
291C2×C4×D17—28no—
292C2×C4×D17—28no—
293C2×C4×D17—44no—
294C2×C4×D17—44no—
295C2×C4×D17—44no—
296C2×C4×D17—44no—
297C2×C4×D17—44no—
298C2×C4×D17—44no—
299C2×C4×D17—44no—
300C2×C4×D17—44no—
301C2×C4×D17—44no—
302C2×C4×D17—44no—
303C2×C4×D17—44no—
304C2×C4×D17—44no—
305C4⋊C4×C17—44no—
306C42×C17—44no—
307#63227—28no—
308#63227—28no—
309#63227—44no—
310#63227—44no—
311#63227—44no—
312#63227—44no—
313#63227—44no—
314#63227—44no—
315#63227—44no—
316#63227—44no—
317C4⋊Dic17—44no—
318C4⋊Dic17—44no—
319C4⋊Dic17—44no—
320#63225—44no—
321#63225—44no—
322#63225—44no—
323#14401—171nomaximal, Sylow
324C23×C17C23×C411yescharacteristic
325C23×C17C22×D411yescharacteristic
326C23×C17C22×D411yescharacteristic
327C23×C17C22×D411yescharacteristic
328C23×C17C22×Q811yescharacteristic
329C23×C17C2×#4111yescharacteristic
330C23×C17C2×#4111yescharacteristic
331C23×C17H(5,𝔽2)11yescharacteristic
332C23×C17H(5,𝔽2)11yescharacteristic
333C23×C17H(5,𝔽2)11yescharacteristic
334C23×C17H(5,𝔽2)11yescharacteristic
335C23×C17H(5,𝔽2)11yescharacteristic
336C23×C17H(5,𝔽2)11yescharacteristic
337C23×C172−1+411yescharacteristic
338C23×C172−1+411yescharacteristic
339C22×D17—22no—
340C22×D17—22no—
341C22×D17—22no—
342C22×D17—22no—
343C22×D17—22no—
344C22×D17—22no—
345C22×D17—22no—
346C22×D17—22no—
347C22×D17—22no—
348C22×D17—22no—
349C22×D17—22no—
350C22×D17—22no—
351C22×D17—22no—
352C22×D17—22no—
353C22×D17—22no—
354C22×D17—22no—
355C22×D17—22no—
356C22×D17—22no—
357C22×D17—22no—
358C22×D17—22no—
359C22×D17—22no—
360C22×D17—22no—
361C22×D17—22no—
362C22×D17—22no—
363C22×D17—22no—
364C22×D17—22no—
365C22×D17—22no—
366C22×D17—22no—
367C22×D17—22no—
368C22×D17—22no—
369C22×D17—22no—
370C22×D17—22no—
371C22×D17—22no—
372C22×D17—22no—
373C22×D17—22no—
374C22×D17—22no—
375C22×D17—41no—
376C22×D17—41no—
377C22×D17—41no—
378C22×D17—41no—
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—
407C22×D17C2×C4⋊C414yes—
408C22×D17C2×C4⋊C414yes—
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—22no—
420C2×C4×C17—22no—
421C2×C4×C17—22no—
422C2×C4×C17—22no—
423C2×C4×C17—22no—
424C2×C4×C17—22no—
425C2×C4×C17—22no—
426C2×C4×C17—22no—
427C2×C4×C17—22no—
428C2×C4×C17—22no—
429C2×C4×C17—22no—
430C2×C4×C17—22no—
431C2×C4×C17—22no—
432C2×C4×C17—22no—
433C2×C4×C17—41no—
434C2×C4×C17—41no—
435C2×C4×C17—41no—
436C2×C4×C17—41no—
437C2×C4×C17—41no—
438C2×C4×C17—41no—
439C2×C4×C17—41no—
440C2×C4×C17—41no—
441C2×C4×C17—41no—
442C2×C4×C17—41no—
443C2×C4×C17—41no—
444C2×C4×C17—41no—
445C2×C4×C17—41no—
446C2×C4×C17—41no—
447C2×C4×C17—41no—
448C2×C4×C17—41no—
449C2×C4×C17—41no—
450C2×C4×C17—41no—
451C2×C4×C17—41no—
452C2×C4×C17—41no—
453C2×C4×C17—41no—
454C2×C4×C17—41no—
455C2×C4×C17—41no—
456C2×C4×C17C2×C4⋊C414yes—
457C2×C4×C17C4×D414yes—
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—41no—
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×Dic17C4×D414yes—
500D68—416no—
501C4×D17—416no—
502C4×D17—416no—
503C2×#390—171no—
504C2×#386—171no—
505C2×#386—171no—
506C2×#385—171no—
507C2×#385—171no—
508C2×#380—171no—
509C2×#380—171no—
510#1444—171no—
511#1444—171no—
512#1439—171no—
513#1439—171no—
514#1439—171no—
515#1439—171no—
516#1436—171no—
517#1436D1711yescharacteristic, complemented
518C22×C17C22×C4⋊C411yescharacteristic
519C22×C17C2×C4×D411yescharacteristic
520C22×C17C2×C4×D411yescharacteristic
521C22×C17#51811yescharacteristic
522C22×C17#51811yescharacteristic
523C22×C17#52011yescharacteristic
524C22×C17#52011yescharacteristic
525C22×C17#53411yescharacteristic
526C22×C17#53411yescharacteristic
527C22×C17#53511yescharacteristic
528C22×C17#53511yescharacteristic
529C22×C17#53711yescharacteristic
530C22×C17#53711yescharacteristic
531C22×C17#54011yescharacteristic
532C22×C17#54011yescharacteristic
533C22×C17#54211yescharacteristic
534C22×C17#54211yescharacteristic
535C22×C17#54311yescharacteristic
536C22×C17#54311yescharacteristic
537C22×C17D4211yescharacteristic
538C22×C17D4211yescharacteristic
539C22×C17D4211yescharacteristic
540C22×C17#54611yescharacteristic
541C22×C17#54611yescharacteristic
542C22×C17#54711yescharacteristic
543C22×C17#54711yescharacteristic
544C22×C17D4×Q811yescharacteristic
545C22×C17D4×Q811yescharacteristic
546C22×C17#55111yescharacteristic
547C22×C17#55411yescharacteristic
548C22×C17#55411yescharacteristic
549C22×C17#56011yescharacteristic
550C22×C17#56211yescharacteristic
551C22×C17#56211yescharacteristic
552C22×C17#56311yescharacteristic
553C2×D17—24no—
554C2×D17—24no—
555C2×D17—24no—
556C2×D17—24no—
557C2×D17—24no—
558C2×D17—24no—
559C2×D17—42no—
560C2×D17—42no—
561C2×D17—42no—
562C2×D17—42no—
563C2×D17—42no—
564C2×D17—42no—
565C2×D17—42no—
566C2×D17—42no—
567C2×D17—42no—
568C2×D17—42no—
569C2×D17—42no—
570C2×D17—42no—
571C2×D17—42no—
572C2×D17—42no—
573C2×D17—42no—
574C2×D17—42no—
575C2×D17—42no—
576C2×D17—42no—
577C2×D17—42no—
578C2×D17—42no—
579C2×D17—42no—
580C2×D17—42no—
581C2×D17—42no—
582C2×D17—42no—
583C4×C17—24no—
584C4×C17—24no—
585C4×C17—42no—
586C4×C17—42no—
587C4×C17—42no—
588C4×C17—42no—
589C4×C17—81no—
590Dic17—24no—
591Dic17—42no—
592Dic17—42no—
593Dic17—81no—
594Dic17—81no—
595Dic17—81no—
596C23×D4—171no—
597C24×C4—171no—
598C24×C4—171no—
599C22×C4⋊C4—171no—
600C22×C4⋊C4—171no—
601C22×C4⋊C4—171no—
602C22×C4⋊C4—171no—
603C22×C4⋊C4—171no—
604C22×C4⋊C4—171no—
605C22×C4⋊C4C2×D1711yescharacteristic
606C22×C22⋊C4—171no—
607C22×C22⋊C4—171no—
608C22×C22⋊C4—171no—
609C22×C22⋊C4—171no—
610C22×C22⋊C4—171no—
611C22×C22⋊C4—171no—
612C22×C22⋊C4—171no—
613C22×C22⋊C4—171no—
614C22×C22⋊C4—171no—
615C22×C22⋊C4—171no—
616C22×C42C2×D1711yescharacteristic
617#390—344no—
618#386—178no—
619#386—344no—
620#385—344no—
621#385—344no—
622#380—344no—
623#380—344no—
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—171no—
633C2×#95C2×D1711yescharacteristic
634C2×#95C2×D1711yescharacteristic
635C2×#95C2×D1711yescharacteristic
636C2×#95C2×D1711yescharacteristic
637C2×#95C2×D1711yescharacteristic
638C2×C17#231511yescharacteristic
639C2×C17#232411yescharacteristic
640C2×C17#232411yescharacteristic
641C2×C17D4×C4⋊C411yescharacteristic
642C2×C17D4×C4⋊C411yescharacteristic
643C2×C17#235811yescharacteristic
644C2×C17#237611yescharacteristic
645C2×C17#266911yescharacteristic
646C2×C17#267111yescharacteristic
647C2×C17#267111yescharacteristic
648C2×C17#268311yescharacteristic
649C2×C17#269211yescharacteristic
650C2×C17#269211yescharacteristic
651C2×C17#271711yescharacteristic
652C2×C17#274811yescharacteristic
653D17—44no—
654D17—44no—
655C25—171no—
656C25—171no—
657C22×D4—174no—
658C22×D4—174no—
659C22×D4—174no—
660C22×D4—681no—
661C22×D4—681no—
662C22×D4—681no—
663C22×D4—681no—
664C23×C4—171no—
665C23×C4—171no—
666C23×C4—171no—
667C23×C4—174no—
668C23×C4—171no—
669C23×C4—171no—
670C23×C4—171no—
671C23×C4—342no—
672C23×C4—342no—
673C23×C4—342no—
674C23×C4—342no—
675C23×C4—342no—
676C23×C4—342no—
677C23×C4—342no—
678C23×C4—681no—
679C23×C4—681no—
680C23×C4—681no—
681C23×C4—681no—
682C23×C4—681no—
683C23×C4—681no—
684C23×C4C22×D1711yescharacteristic
685C23×C4C22×D1711yescharacteristic
686C23×C4C22×D1711yescharacteristic
687C23×C4C22×D1711yescharacteristic
688C23×C4C22×D1711yescharacteristic
689C23×C4C22×D1711yescharacteristic
690C23×C4C22×D1711yescharacteristic
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—41no—
694C2×C4⋊C4—342no—
695C2×C4⋊C4—342no—
696C2×C4⋊C4—342no—
697C2×C4⋊C4—342no—
698C2×C4⋊C4—342no—
699C2×C4⋊C4—342no—
700C2×C4⋊C4—342no—
701C2×C4⋊C4—342no—
702C2×C4⋊C4—342no—
703C2×C4⋊C4—681no—
704C2×C4⋊C4—681no—
705C2×C4⋊C4—681no—
706C2×C4⋊C4—681no—
707C2×C4⋊C4—681no—
708C2×C4⋊C4—681no—
709C2×C4⋊C4—681no—
710C2×C4⋊C4—681no—
711C2×C4⋊C4—681no—
712C2×C22⋊C4—174no—
713C2×C22⋊C4—174no—
714C2×C22⋊C4—174no—
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—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—681no—
733C2×C22⋊C4—681no—
734C2×C22⋊C4—681no—
735C2×C22⋊C4—681no—
736C2×C22⋊C4—681no—
737C2×C22⋊C4—681no—
738C2×C22⋊C4—681no—
739C2×C22⋊C4—681no—
740C2×C22⋊C4—681no—
741C2×C22⋊C4—681no—
742C2×C42—22no—
743C2×C42—41no—
744C2×C42—41no—
745#95—22no—
746#95—22no—
747#95—41no—
748#95—174no—
749#95—174no—
750#95—342no—
751#95—342no—
752#95—342no—
753#95—342no—
754#95—681no—
755#95—681no—
756#95—681no—
757#95C4×D1714yescomplemented
758#95D6814yescomplemented
759C17#1440111yescharacteristic, complemented, Sylow
760C24—172no—
761C24—172no—
762C24—172no—
763C24—172no—
764C24—172no—
765C24—172no—
766C24—341no—
767C24—341no—
768C24—341no—
769C24—341no—
770C24—341no—
771C24—341no—
772C24—341no—
773C24—341no—
774C24—341no—
775C24—341no—
776C24—341no—
777C24—341no—
778C24—341no—
779C24—341no—
780C24—341no—
781C24—341no—
782C24—341no—
783C24—341no—
784C24—341no—
785C24—341no—
786C24—341no—
787C24—341no—
788C24—341no—
789C24—341no—
790C24C23×D1711yescharacteristic
791C2×D4—1716no—
792C2×D4—684no—
793C2×D4—684no—
794C2×D4—684no—
795C2×D4—684no—
796C2×D4—684no—
797C2×D4—684no—
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—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—172no—
838C22×C4—172no—
839C22×C4—172no—
840C22×C4—172no—
841C22×C4—172no—
842C22×C4—348no—
843C22×C4—341no—
844C22×C4—341no—
845C22×C4—341no—
846C22×C4—341no—
847C22×C4—341no—
848C22×C4—341no—
849C22×C4—341no—
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—348no—
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—684no—
882C22×C4—684no—
883C22×C4—684no—
884C22×C4—684no—
885C22×C4—684no—
886C22×C4—684no—
887C22×C4—684no—
888C22×C4—684no—
889C22×C4—684no—
890C22×C4—684no—
891C22×C4—684no—
892C22×C4—684no—
893C22×C4C2×C4×D1712yes—
894C22×C4C2×C4×D1712yes—
895C22×C4C2×C4×D1712yes—
896C22×C4C2×D6812yes—
897C22×C4C2×D6812yes—
898C22×C4C2×D6812yes—
899C22×C4#6325212yes—
900C22×C4D4×D1712yes—
901C22×C4D4×D1712yes—
902C22×C4Q8×D1712yes—
903C4⋊C4—44no—
904C4⋊C4—684no—
905C4⋊C4—684no—
906C4⋊C4—684no—
907C4⋊C4—684no—
908C4⋊C4—684no—
909C4⋊C4—684no—
910C22⋊C4—348no—
911C22⋊C4—348no—
912C22⋊C4—684no—
913C22⋊C4—684no—
914C22⋊C4—684no—
915C22⋊C4—684no—
916C22⋊C4—684no—
917C22⋊C4—684no—
918C22⋊C4—684no—
919C22⋊C4—684no—
920C42—44no—
921C23—174no—
922C23—174no—
923C23—342no—
924C23—342no—
925C23—342no—
926C23—342no—
927C23—342no—
928C23—342no—
929C23—342no—
930C23—342no—
931C23—342no—
932C23—342no—
933C23—342no—
934C23—342no—
935C23—342no—
936C23—342no—
937C23—342no—
938C23—342no—
939C23—342no—
940C23—342no—
941C23—342no—
942C23—342no—
943C23—342no—
944C23—342no—
945C23—342no—
946C23—342no—
947C23—342no—
948C23—342no—
949C23—342no—
950C23—342no—
951C23—342no—
952C23—342no—
953C23—342no—
954C23—342no—
955C23—342no—
956C23—342no—
957C23—342no—
958C23—342no—
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—681no—
982C23—681no—
983C23—681no—
984C23—681no—
985C23—681no—
986C23—681no—
987C23—681no—
988C23—681no—
989C23—681no—
990C23—681no—
991C23C22×C4×D1711yescharacteristic
992C23C22×D6811yescharacteristic
993C23C2×#6325211yescharacteristic
994C23C2×D4×D1711yescharacteristic
995C23C2×D4×D1711yescharacteristic
996C23#1058769111yescharacteristic
997C23#1058769111yescharacteristic
998C23C2×Q8×D1711yescharacteristic
999C23#1058769411yescharacteristic
1000C23#41×D1711yescharacteristic
1001C23#1058769611yescharacteristic
1002C23#1058769611yescharacteristic
1003C23#1058769611yescharacteristic
1004C23#1058769611yescharacteristic
1005C23#1058769711yescharacteristic
1006D4—6816no—
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—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—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—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—174no—
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—6816no—
1068C2×C4—6816no—
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×C4C4×D6814yes—
1099C2×C4C4⋊C4×D1714yes—
1100C22—344no—
1101C22—344no—
1102C22—344no—
1103C22—344no—
1104C22—344no—
1105C22—344no—
1106C22—682no—
1107C22—682no—
1108C22—682no—
1109C22—682no—
1110C22—682no—
1111C22—682no—
1112C22—682no—
1113C22—682no—
1114C22—682no—
1115C22—682no—
1116C22—682no—
1117C22—682no—
1118C22—682no—
1119C22—682no—
1120C22—682no—
1121C22—682no—
1122C22—682no—
1123C22—682no—
1124C22—682no—
1125C22—682no—
1126C22—682no—
1127C22—682no—
1128C22—682no—
1129C22—682no—
1130C22C2×C4⋊C4×D1711yescharacteristic
1131C22C4×D4×D1711yescharacteristic
1132C22C2×C4×D6811yescharacteristic
1133C22#1176328111yescharacteristic
1134C22#1176328111yescharacteristic
1135C22#1176328911yescharacteristic
1136C22#1176329111yescharacteristic
1137C22#1176336911yescharacteristic
1138C22#1176337011yescharacteristic
1139C22#1176337711yescharacteristic
1140C22#1176337811yescharacteristic
1141C22#1176338611yescharacteristic
1142C22#1176339011yescharacteristic
1143C22#1176341011yescharacteristic
1144C22#1176341111yescharacteristic
1145C22#1176342511yescharacteristic
1146C22#1176343111yescharacteristic
1147C22#1176343411yescharacteristic
1148C22#1176343411yescharacteristic
1149C22#1176344311yescharacteristic
1150C22D4×D6811yescharacteristic
1151C22D4×D6811yescharacteristic
1152C22#1176344911yescharacteristic
1153C22#1176345411yescharacteristic
1154C22#1176346111yescharacteristic
1155C22#1176346411yescharacteristic
1156C22#1176347411yescharacteristic
1157C22Q8×D6811yescharacteristic
1158C22#1176348311yescharacteristic
1159C22#1176351511yescharacteristic
1160C22#1176351911yescharacteristic
1161C22#1176355011yescharacteristic
1162C22#1176355511yescharacteristic
1163C22#1176355611yescharacteristic
1164C22#1176356311yescharacteristic
1165C4—24no—
1166C4—24no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—81no—
1172C4—344no—
1173C4—682no—
1174C4—682no—
1175C4—1361no—
1176C4—1361no—
1177C4—1361no—
1178C2—684no—
1179C2—684no—
1180C2#1453139511yescharacteristic
1181C2#1453147211yescharacteristic
1182C2#1453147811yescharacteristic
1183C2#1453168511yescharacteristic
1184C2C4⋊C4×D6811yescharacteristic
1185C2#1453176611yescharacteristic
1186C2#1453193111yescharacteristic
1187C2#1453499911yescharacteristic
1188C2#1453502111yescharacteristic
1189C2#1453502311yescharacteristic
1190C2#1453515511yescharacteristic
1191C2#1453527511yescharacteristic
1192C2#1453527811yescharacteristic
1193C2#1453562411yescharacteristic
1194C2#1453599211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1436C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1436D17
hypocenterC17#14401
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C2×#11762683C2semidirect
5. C2×#11762683C2semidirect
6. C2×#11762668C2semidirect
7. C2×#11762666C2semidirect
8. #14527049C2semidirect
9. #14527048C2semidirect
10. #14527030C2semidirect
11. #14527028C2semidirect
12. #14527028C2semidirect
13. #14527026C2semidirect
14. #14527017C2semidirect
15. C17×#1436C2semidirect
37. #11762687C4semidirect
93. C22×C4×D17C2×C4semidirect
129. C2×#63227C2×C4semidirect
151. C17×#95C2×C4semidirect
152. C17×#95D4semidirect
160. #10587502C2×C4semidirect
161. #10587502D4semidirect
290. C2×D68C4⋊C4semidirect
517. #1436D17semidirect
757. #95C4×D17semidirect
758. #95D68semidirect
759. C17#14401semidirect

Maximal subgroups

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

subgroupindex
C2×#117627112
C2×#117626872
C2×#117626832
C2×#117626682
C2×#117626662
#145270492
#145270482
#145270302
#145270282
#145270262
#145270172
C17×#14362
#1440117