Finite Group Databasebeta

← #16963468

Subgroups — #16963468

Order 4352.

1558 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762709C211yesmaximal, characteristic
2#14527032C211yesmaximal, characteristic, complemented
3#14527032C211yesmaximal, characteristic, complemented
4#14527031C211yesmaximal, characteristic, complemented
5#14527023C211yesmaximal, characteristic
6#14527023C211yesmaximal, characteristic
7#14527021C211yesmaximal, characteristic, complemented
8#14527021C211yesmaximal, characteristic, complemented
9#14527020C211yesmaximal, characteristic, complemented
10#14527020C211yesmaximal, characteristic, complemented
11#14527019C211yesmaximal, characteristic, complemented
12#14527015C211yesmaximal, characteristic, complemented
13#14527009C211yesmaximal, characteristic, complemented
14#14527008C211yesmaximal, characteristic, complemented
15C17×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×C22⋊Dic17C2211yescharacteristic
19C22×C22⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30#11762709C418yescomplemented
31C2×#10587502C2211yescharacteristic
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C22×C22⋊C4×C17C2211yescharacteristic
46C22×C22⋊C4×C17C2211yescharacteristic
47C22×C22⋊C4×C17C2211yescharacteristic
48C2×C17×#95C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C25×C17C2311yescharacteristic
53C24×D17C2311yescharacteristic
54C23×C4×C17C2311yescharacteristic
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C22×C22⋊D17—22no—
61C22×C22⋊D17—22no—
62C22×C22⋊D17—41no—
63C22×C22⋊D17—41no—
64C22×C22⋊D17—41no—
65C22×C22⋊D17—41no—
66C22×C22⋊D17C2×C414yes—
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C2×C22⋊C4×C17—22no—
75C2×C22⋊C4×C17—41no—
76C2×C22⋊C4×C17—41no—
77C2×C22⋊C4×C17—41no—
78C2×C22⋊C4×C17—41no—
79C2×C22⋊C4×C17—41no—
80C2×C22⋊C4×C17—41no—
81C2×C22⋊C4×C17—41no—
82C2×C22⋊C4×C17C2×C414yes—
83C2×C22⋊Dic17—22no—
84C2×C22⋊Dic17—22no—
85C2×C22⋊Dic17—22no—
86C2×C22⋊Dic17—41no—
87C2×C22⋊Dic17—41no—
88C2×C22⋊Dic17—41no—
89C2×C22⋊Dic17—41no—
90C2×C22⋊Dic17—41no—
91C2×C22⋊Dic17C2×C414yes—
92C2×#63227—22no—
93C2×#63227—22no—
94C2×#63227—22no—
95C2×#63227—22no—
96C2×#63227—41no—
97C2×#63227—41no—
98C2×#63227—41no—
99C2×#63227—41no—
100C2×#63227—41no—
101C2×#63227—41no—
102C2×#63227—41no—
103C2×#63227—41no—
104C2×#63227—41no—
105C2×#63227—41no—
106C2×#63227—41no—
107C2×#63227—41no—
108C2×#63227C2×C414yes—
109C2×#63227C2×C414yes—
110C2×#63225—41no—
111C2×#63225—41no—
112C2×#63225C2×C414yes—
113C2×C4×Dic17—41no—
114C2×C4×Dic17—41no—
115C2×C4×Dic17—41no—
116C2×C4×Dic17—41no—
117C2×C4×Dic17—41no—
118C2×C4×Dic17—41no—
119C2×C4×Dic17—41no—
120C2×C4×Dic17—41no—
121C2×C4×Dic17C2×C414yes—
122C17×#95—22no—
123C17×#95—41no—
124C17×#95—41no—
125C17×#95—41no—
126#10587502—22no—
127#10587502—22no—
128#10587502—22no—
129#10587502—22no—
130#10587502—22no—
131#10587502—22no—
132#10587502—22no—
133#10587502—41no—
134#10587502—41no—
135#10587502—41no—
136#10587502—41no—
137#10587502—41no—
138#10587502—41no—
139#10587502—41no—
140C24×C17—21no—
141C24×C17—21no—
142C24×C17—21no—
143C24×C17—21no—
144C24×C17—21no—
145C24×C17—21no—
146C24×C17—21no—
147C24×C17—21no—
148C24×C17—21no—
149C24×C17—21no—
150C24×C17—21no—
151C24×C17—21no—
152C24×C17—21no—
153C24×C17—21no—
154C24×C17C22×C412yes—
155C24×C17C2411yescharacteristic
156C23×D17—21no—
157C23×D17—21no—
158C23×D17—21no—
159C23×D17—21no—
160C23×D17—21no—
161C23×D17—21no—
162C23×D17—21no—
163C23×D17—21no—
164C23×D17—21no—
165C23×D17—21no—
166C23×D17—21no—
167C23×D17—21no—
168C23×D17—21no—
169C23×D17—21no—
170C23×D17C22×C412yes—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
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×C17C22×C412yes—
211C22×C4×C17C22×C412yes—
212C22×C4×C17#4112yes—
213C2×C22⋊D17—28no—
214C2×C22⋊D17—44no—
215C2×C22⋊D17—44no—
216C2×C22⋊D17—44no—
217C2×C22⋊D17—44no—
218C2×C22⋊D17—44no—
219C2×C22⋊D17—44no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
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×Dic17C22×C412yes—
262C22×Dic17C22×C412yes—
263C22×Dic17C22×C412yes—
264C22×Dic17#4112yes—
265C22×Dic17#4112yes—
266C22×Dic17#4112yes—
267C22×Dic17#4112yes—
268C22×Dic17#4112yes—
269C22⋊C4×C17—44no—
270C22⋊C4×C17—44no—
271C22⋊C4×C17—44no—
272C22⋊Dic17—44no—
273C22⋊Dic17—44no—
274C22⋊Dic17—44no—
275#63227—44no—
276#63227—44no—
277#63227—44no—
278#63227—44no—
279#63227—44no—
280#63227—44no—
281#63225—44no—
282C4×Dic17—44no—
283C4×Dic17—44no—
284C4×Dic17—44no—
285#14503—171nomaximal, Sylow
286C23×C17—22no—
287C23×C17—22no—
288C23×C17—22no—
289C23×C17—22no—
290C23×C17—22no—
291C23×C17—22no—
292C23×C17—22no—
293C23×C17—41no—
294C23×C17—41no—
295C23×C17—41no—
296C23×C17—41no—
297C23×C17—41no—
298C23×C17—41no—
299C23×C17—41no—
300C23×C17—41no—
301C23×C17—41no—
302C23×C17—41no—
303C23×C17—41no—
304C23×C17—41no—
305C23×C17—41no—
306C23×C17—41no—
307C23×C17—41no—
308C23×C17—41no—
309C23×C17—41no—
310C23×C17—41no—
311C23×C17—41no—
312C23×C17—41no—
313C23×C17—41no—
314C23×C17—41no—
315C23×C17—41no—
316C23×C17—41no—
317C23×C17—41no—
318C23×C17—41no—
319C23×C17—41no—
320C23×C17—41no—
321C23×C17C23×C411yescharacteristic
322C23×C17C2×#4111yescharacteristic
323C23×C17C2×#4111yescharacteristic
324C23×C17C2×#4111yescharacteristic
325C23×C17C2×#4111yescharacteristic
326C23×C17C2×#4111yescharacteristic
327C23×C17C2×#4111yescharacteristic
328C23×C17H(5,𝔽2)11yescharacteristic
329C23×C17H(5,𝔽2)11yescharacteristic
330C23×C17H(5,𝔽2)11yescharacteristic
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
336C22×D17—22no—
337C22×D17—22no—
338C22×D17—22no—
339C22×D17—22no—
340C22×D17—22no—
341C22×D17—22no—
342C22×D17—22no—
343C22×D17—41no—
344C22×D17—41no—
345C22×D17—41no—
346C22×D17—41no—
347C22×D17—41no—
348C22×D17—41no—
349C22×D17—41no—
350C22×D17—41no—
351C22×D17—41no—
352C22×D17—41no—
353C22×D17—41no—
354C22×D17—41no—
355C22×D17—41no—
356C22×D17—41no—
357C22×D17—41no—
358C22×D17—41no—
359C22×D17—41no—
360C22×D17—41no—
361C22×D17—41no—
362C22×D17—41no—
363C22×D17—41no—
364C22×D17—41no—
365C22×D17—41no—
366C22×D17—41no—
367C22×D17—41no—
368C22×D17—41no—
369C22×D17—41no—
370C22×D17—41no—
371C2×C4×C17—22no—
372C2×C4×C17—22no—
373C2×C4×C17—22no—
374C2×C4×C17—22no—
375C2×C4×C17—22no—
376C2×C4×C17—22no—
377C2×C4×C17—22no—
378C2×C4×C17—22no—
379C2×C4×C17—22no—
380C2×C4×C17—41no—
381C2×C4×C17—41no—
382C2×C4×C17—41no—
383C2×C4×C17—41no—
384C2×C4×C17—41no—
385C2×C4×C17—41no—
386C2×C4×C17—41no—
387C2×C4×C17—41no—
388C2×C4×C17—41no—
389C2×C4×C17—41no—
390C2×C4×C17—41no—
391C2×C4×C17—41no—
392C2×C4×C17—41no—
393C2×C4×C17—41no—
394C2×C4×C17—41no—
395C2×C4×C17—41no—
396C2×C4×C17—41no—
397C2×C4×C17—41no—
398C2×C4×C17—41no—
399C2×C4×C17—41no—
400C2×C4×C17—41no—
401C2×C4×C17—41no—
402C2×C4×C17—41no—
403C2×C4×C17—41no—
404C2×C4×C17—41no—
405C2×C4×C17—41no—
406C2×C4×C17—41no—
407C2×C4×C17—41no—
408C2×C4×C17—41no—
409C2×C4×C17—41no—
410C2×C4×C17—41no—
411C2×C4×C17—41no—
412C2×C4×C17—41no—
413C22⋊D17—416no—
414C2×Dic17—22no—
415C2×Dic17—22no—
416C2×Dic17—22no—
417C2×Dic17—22no—
418C2×Dic17—22no—
419C2×Dic17—22no—
420C2×Dic17—22no—
421C2×Dic17—22no—
422C2×Dic17—22no—
423C2×Dic17—22no—
424C2×Dic17—22no—
425C2×Dic17—22no—
426C2×Dic17—22no—
427C2×Dic17—22no—
428C2×Dic17—22no—
429C2×Dic17—22no—
430C2×Dic17—22no—
431C2×Dic17—22no—
432C2×Dic17—22no—
433C2×Dic17—22no—
434C2×Dic17—22no—
435C2×Dic17—41no—
436C2×Dic17—41no—
437C2×Dic17—41no—
438C2×Dic17—41no—
439C2×Dic17—41no—
440C2×Dic17—41no—
441C2×Dic17—41no—
442C2×Dic17—41no—
443C2×Dic17—41no—
444C2×Dic17—41no—
445C2×Dic17—41no—
446C2×Dic17—41no—
447C2×Dic17—41no—
448C2×Dic17—41no—
449C2×Dic17—41no—
450C2×Dic17—41no—
451C2×Dic17—41no—
452C2×Dic17—41no—
453C2×Dic17—41no—
454C2×Dic17—41no—
455C2×Dic17—41no—
456C2×Dic17—41no—
457C2×Dic17—41no—
458C2×Dic17—41no—
459C2×Dic17—41no—
460C2×Dic17—41no—
461C2×Dic17—41no—
462C2×Dic17#11714yes—
463C2×#390—171no—
464#1440—171no—
465#1440—171no—
466#1440—171no—
467#1440D1711yescharacteristic, complemented
468#1438—171no—
469#1438—171no—
470#1437—171no—
471#1437—171no—
472#1437—171no—
473#1437—171no—
474#1436—171no—
475#1436—171no—
476#1434—171no—
477#1434—171no—
478C22×C17—42no—
479C22×C17—42no—
480C22×C17—42no—
481C22×C17—42no—
482C22×C17—42no—
483C22×C17—42no—
484C22×C17—42no—
485C22×C17—81no—
486C22×C17—81no—
487C22×C17—81no—
488C22×C17—81no—
489C22×C17—81no—
490C22×C17—81no—
491C22×C17—81no—
492C22×C17—81no—
493C22×C17C2×#11711yescharacteristic
494C22×C17C4×#4111yescharacteristic
495C22×C17C4×#4111yescharacteristic
496C22×C17#51811yescharacteristic
497C22×C17#51811yescharacteristic
498C22×C17#51811yescharacteristic
499C22×C17#51811yescharacteristic
500C22×C17#53811yescharacteristic
501C22×C17#53811yescharacteristic
502C22×C17#53811yescharacteristic
503C22×C17#53811yescharacteristic
504C22×C17#53811yescharacteristic
505C22×C17#53811yescharacteristic
506C22×C17#53811yescharacteristic
507C22×C17#53811yescharacteristic
508C22×C17#54011yescharacteristic
509C22×C17#54011yescharacteristic
510C22×C17#54011yescharacteristic
511C22×C17#54011yescharacteristic
512C22×C17#55111yescharacteristic
513C22×C17#55111yescharacteristic
514C22×C17#55311yescharacteristic
515C22×C17#55311yescharacteristic
516C22×C17#55311yescharacteristic
517C22×C17#55311yescharacteristic
518C22×C17#55511yescharacteristic
519C22×C17#55511yescharacteristic
520C22×C17#55911yescharacteristic
521C22×C17#55911yescharacteristic
522C22×C17#55911yescharacteristic
523C22×C17#55911yescharacteristic
524C22×C17#56011yescharacteristic
525C22×C17#56011yescharacteristic
526C22×C17#56011yescharacteristic
527C22×C17#56011yescharacteristic
528C2×D17—42no—
529C2×D17—42no—
530C2×D17—42no—
531C2×D17—42no—
532C2×D17—42no—
533C2×D17—42no—
534C2×D17—42no—
535C2×D17—81no—
536C2×D17—81no—
537C2×D17—81no—
538C2×D17—81no—
539C2×D17—81no—
540C2×D17—81no—
541C2×D17—81no—
542C2×D17—81no—
543C4×C17—42no—
544C4×C17—42no—
545C4×C17—42no—
546C4×C17—81no—
547C4×C17—81no—
548C4×C17—81no—
549Dic17—24no—
550Dic17—42no—
551Dic17—42no—
552Dic17—42no—
553Dic17—42no—
554Dic17—42no—
555Dic17—81no—
556C23×D4—171no—
557C22×C4⋊C4—171no—
558C22×C22⋊C4—171no—
559C22×C22⋊C4—171no—
560C22×C22⋊C4—171no—
561C22×C22⋊C4—171no—
562C22×C22⋊C4—171no—
563C22×C22⋊C4—171no—
564C22×C22⋊C4—171no—
565C22×C22⋊C4—171no—
566C22×C22⋊C4—171no—
567C22×C22⋊C4C2×D1711yescharacteristic
568C22×C22⋊C4C2×D1711yescharacteristic
569C22×C22⋊C4C2×D1711yescharacteristic
570C22×C42—171no—
571C22×C42—171no—
572C22×C42—171no—
573#390—178no—
574C2×#95—171no—
575C2×#95—171no—
576C2×#95—171no—
577C2×#95—171no—
578C2×#95—171no—
579C2×#95—171no—
580C2×#95—171no—
581C2×#95—171no—
582C2×#95—171no—
583C2×#95—171no—
584C2×#95—171no—
585C2×#95—171no—
586C2×#95—171no—
587C2×#95—171no—
588C2×#95C2×D1711yescharacteristic
589C2×#95C2×D1711yescharacteristic
590C2×#95C2×D1711yescharacteristic
591C2×#95C2×D1711yescharacteristic
592C2×C17—82no—
593C2×C17#231211yescharacteristic
594C2×C17#233311yescharacteristic
595C2×C17#233311yescharacteristic
596C2×C17#235711yescharacteristic
597C2×C17#235711yescharacteristic
598C2×C17#237211yescharacteristic
599C2×C17#238011yescharacteristic
600C2×C17#279711yescharacteristic
601C2×C17#279711yescharacteristic
602C2×C17#279711yescharacteristic
603C2×C17#279711yescharacteristic
604C2×C17#280311yescharacteristic
605C2×C17#280311yescharacteristic
606C2×C17#280311yescharacteristic
607C2×C17#280311yescharacteristic
608D17—82no—
609C25—171no—
610C25C22×D1711yescharacteristic
611C22×D4—174no—
612C22×D4—342no—
613C22×D4—342no—
614C22×D4—681no—
615C22×D4—681no—
616C22×D4—681no—
617C22×D4—681no—
618C23×C4—171no—
619C23×C4—171no—
620C23×C4—171no—
621C23×C4—171no—
622C23×C4—171no—
623C23×C4—171no—
624C23×C4—171no—
625C23×C4C22×D1711yescharacteristic
626C23×C4C22×D1711yescharacteristic
627C23×C4C22×D1711yescharacteristic
628C23×C4C22×D1711yescharacteristic
629C23×C4C22×D1711yescharacteristic
630C23×C4C22×D1711yescharacteristic
631C2×C4⋊C4—174no—
632C2×C4⋊C4—681no—
633C2×C4⋊C4—681no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—41no—
636C2×C22⋊C4—41no—
637C2×C22⋊C4—41no—
638C2×C22⋊C4—41no—
639C2×C22⋊C4—41no—
640C2×C22⋊C4—41no—
641C2×C22⋊C4—41no—
642C2×C22⋊C4—174no—
643C2×C22⋊C4—174no—
644C2×C22⋊C4—174no—
645C2×C22⋊C4—342no—
646C2×C22⋊C4—342no—
647C2×C22⋊C4—342no—
648C2×C22⋊C4—342no—
649C2×C22⋊C4—342no—
650C2×C22⋊C4—342no—
651C2×C22⋊C4—342no—
652C2×C22⋊C4—681no—
653C2×C22⋊C4—681no—
654C2×C22⋊C4—681no—
655C2×C22⋊C4—681no—
656C2×C22⋊C4—681no—
657C2×C22⋊C4—681no—
658C2×C22⋊C4—681no—
659C2×C22⋊C4—681no—
660C2×C22⋊C4—681no—
661C2×C22⋊C4—681no—
662C2×C22⋊C4—681no—
663C2×C22⋊C4—681no—
664C2×C22⋊C4—681no—
665C2×C22⋊C4—681no—
666C2×C22⋊C4—681no—
667C2×C22⋊C4—681no—
668C2×C22⋊C4—681no—
669C2×C22⋊C4C4×D1714yes—
670C2×C42—174no—
671C2×C42—681no—
672C2×C42—681no—
673C2×C42—681no—
674C2×C42—681no—
675C2×C42—681no—
676C2×C42—681no—
677C2×C42—681no—
678C2×C42—681no—
679#95—22no—
680#95—41no—
681#95—41no—
682#95—41no—
683#95—342no—
684#95—342no—
685#95—342no—
686#95—342no—
687#95—342no—
688#95—342no—
689#95—342no—
690#95—681no—
691#95—681no—
692#95—681no—
693#95—681no—
694#95—681no—
695#95—681no—
696#95—681no—
697C17#1450311yescharacteristic, complemented, Sylow
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—172no—
713C24—341no—
714C24—341no—
715C24—341no—
716C24—341no—
717C24—341no—
718C24—341no—
719C24—341no—
720C24—341no—
721C24—341no—
722C24—341no—
723C24—341no—
724C24—341no—
725C24—341no—
726C24—341no—
727C24C2×C4×D1712yes—
728C24C23×D1711yescharacteristic
729C2×D4—348no—
730C2×D4—684no—
731C2×D4—684no—
732C2×D4—684no—
733C2×D4—684no—
734C2×D4—684no—
735C2×D4—684no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—172no—
776C22×C4—172no—
777C22×C4—172no—
778C22×C4—172no—
779C22×C4—172no—
780C22×C4—172no—
781C22×C4—172no—
782C22×C4—172no—
783C22×C4—341no—
784C22×C4—341no—
785C22×C4—341no—
786C22×C4—341no—
787C22×C4—341no—
788C22×C4—341no—
789C22×C4—341no—
790C22×C4—341no—
791C22×C4—341no—
792C22×C4—341no—
793C22×C4—341no—
794C22×C4—341no—
795C22×C4—341no—
796C22×C4—341no—
797C22×C4—341no—
798C22×C4—341no—
799C22×C4—341no—
800C22×C4—341no—
801C22×C4—341no—
802C22×C4—341no—
803C22×C4—341no—
804C22×C4—341no—
805C22×C4—341no—
806C22×C4—341no—
807C22×C4—341no—
808C22×C4—341no—
809C22×C4—341no—
810C22×C4—341no—
811C22×C4—341no—
812C22×C4—341no—
813C22×C4—341no—
814C22×C4—341no—
815C22×C4—341no—
816C22×C4—341no—
817C22×C4—341no—
818C22×C4—341no—
819C22×C4—341no—
820C22×C4—341no—
821C22×C4—341no—
822C22×C4—341no—
823C22×C4—341no—
824C22×C4C2×C4×D1712yes—
825C22×C4C2×C4×D1712yes—
826C22×C4#6325412yes—
827C4⋊C4—684no—
828C22⋊C4—44no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—684no—
832C22⋊C4—684no—
833C22⋊C4—684no—
834C22⋊C4—684no—
835C22⋊C4—684no—
836C22⋊C4—684no—
837C22⋊C4—684no—
838C22⋊C4—684no—
839C22⋊C4—684no—
840C42—684no—
841C42—684no—
842C42—684no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—342no—
879C23—342no—
880C23—342no—
881C23—342no—
882C23—342no—
883C23—342no—
884C23—342no—
885C23—681no—
886C23—681no—
887C23—681no—
888C23—681no—
889C23—681no—
890C23—681no—
891C23—681no—
892C23—681no—
893C23—681no—
894C23—681no—
895C23—681no—
896C23—681no—
897C23—681no—
898C23—681no—
899C23—681no—
900C23—681no—
901C23—681no—
902C23—681no—
903C23—681no—
904C23—681no—
905C23—681no—
906C23—681no—
907C23—681no—
908C23—681no—
909C23—681no—
910C23—681no—
911C23—681no—
912C23—681no—
913C23C22×C4×D1711yescharacteristic
914C23C2×#6325411yescharacteristic
915C23#1058769111yescharacteristic
916C23#1058769111yescharacteristic
917C23#1058769111yescharacteristic
918C23#1058769111yescharacteristic
919C23#1058769111yescharacteristic
920C23#41×D1711yescharacteristic
921C23#41×D1711yescharacteristic
922C23#41×D1711yescharacteristic
923C23#41×D1711yescharacteristic
924C23#41×D1711yescharacteristic
925C23#1058769611yescharacteristic
926C23#1058769611yescharacteristic
927C23#1058769611yescharacteristic
928D4—6816no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—174no—
972C2×C4—342no—
973C2×C4—342no—
974C2×C4—342no—
975C2×C4—342no—
976C2×C4—342no—
977C2×C4—342no—
978C2×C4—342no—
979C2×C4—342no—
980C2×C4—342no—
981C2×C4—342no—
982C2×C4—342no—
983C2×C4—342no—
984C2×C4—342no—
985C2×C4—342no—
986C2×C4—342no—
987C2×C4—342no—
988C2×C4—342no—
989C2×C4—342no—
990C2×C4—342no—
991C2×C4—342no—
992C2×C4—342no—
993C2×C4—681no—
994C2×C4—681no—
995C2×C4—681no—
996C2×C4—681no—
997C2×C4—681no—
998C2×C4—681no—
999C2×C4—681no—
1000C2×C4—681no—
1001C2×C4—681no—
1002C2×C4—681no—
1003C2×C4—681no—
1004C2×C4—681no—
1005C2×C4—681no—
1006C2×C4—681no—
1007C2×C4—681no—
1008C2×C4—681no—
1009C2×C4—681no—
1010C2×C4—681no—
1011C2×C4—681no—
1012C2×C4—681no—
1013C2×C4—681no—
1014C2×C4—681no—
1015C2×C4—681no—
1016C2×C4—681no—
1017C2×C4—681no—
1018C2×C4—681no—
1019C2×C4—681no—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—81no—
1031C22—81no—
1032C22—81no—
1033C22—81no—
1034C22—81no—
1035C22—682no—
1036C22—682no—
1037C22—682no—
1038C22—682no—
1039C22—682no—
1040C22—682no—
1041C22—682no—
1042C22—1361no—
1043C22—1361no—
1044C22—1361no—
1045C22—1361no—
1046C22—1361no—
1047C22—1361no—
1048C22—1361no—
1049C22—1361no—
1050C22#117×D1711yescharacteristic
1051C22C4×#6325411yescharacteristic
1052C22#1176327711yescharacteristic
1053C22#1176328111yescharacteristic
1054C22#1176328111yescharacteristic
1055C22#1176328111yescharacteristic
1056C22#1176328211yescharacteristic
1057C22#1176339111yescharacteristic
1058C22#1176339111yescharacteristic
1059C22#1176339311yescharacteristic
1060C22#1176339311yescharacteristic
1061C22#1176339411yescharacteristic
1062C22#1176339511yescharacteristic
1063C22#1176339811yescharacteristic
1064C22#1176339811yescharacteristic
1065C22#1176340911yescharacteristic
1066C22#1176341111yescharacteristic
1067C22#1176341111yescharacteristic
1068C22#1176341211yescharacteristic
1069C22#1176348211yescharacteristic
1070C22#1176348411yescharacteristic
1071C22#1176350211yescharacteristic
1072C22#1176350411yescharacteristic
1073C22#1176350411yescharacteristic
1074C22#1176351011yescharacteristic
1075C22#1176352111yescharacteristic
1076C22#1176352311yescharacteristic
1077C22#1176354111yescharacteristic
1078C22#1176354311yescharacteristic
1079C22#1176354311yescharacteristic
1080C22#1176354311yescharacteristic
1081C22#1176354711yescharacteristic
1082C22#1176354711yescharacteristic
1083C22#1176354811yescharacteristic
1084C22#1176354911yescharacteristic
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—81no—
1089C4—81no—
1090C4—81no—
1091C4—344no—
1092C4—682no—
1093C4—682no—
1094C4—682no—
1095C4—682no—
1096C4—682no—
1097C4—1361no—
1098C2—82no—
1099C2—1362no—
1100C2#1453137811yescharacteristic
1101C2#1453154711yescharacteristic
1102C2#1453155011yescharacteristic
1103C2#1453175211yescharacteristic
1104C2#1453175411yescharacteristic
1105C2#1453189111yescharacteristic
1106C2#1453195911yescharacteristic
1107C2#1453663411yescharacteristic
1108C2#1453664011yescharacteristic
1109C2#1453664611yescharacteristic
1110C2#1453664711yescharacteristic
1111C2#1453671011yescharacteristic
1112C2#1453671611yescharacteristic
1113C2#1453672211yescharacteristic
1114C2#1453672411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1440C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1440D17
hypocenterC17#14503
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. #14527032C2semidirect
3. #14527032C2semidirect
4. #14527031C2semidirect
7. #14527021C2semidirect
8. #14527021C2semidirect
9. #14527020C2semidirect
10. #14527020C2semidirect
11. #14527019C2semidirect
12. #14527015C2semidirect
13. #14527009C2semidirect
14. #14527008C2semidirect
15. C17×#1440C2semidirect
30. #11762709C4semidirect
467. #1440D17semidirect
697. C17#14503semidirect

Maximal subgroups

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

subgroupindex
C2×#117627092
#145270322
#145270312
#145270232
#145270212
#145270202
#145270192
#145270152
#145270092
#145270082
C17×#14402
#1450317