Finite Group Databasebeta

← #16957506

Subgroups — #16957506

Order 4352.

1838 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762709C211yesmaximal, characteristic
2C2×#11762709C211yesmaximal, characteristic
3C2×#11762709C211yesmaximal, characteristic
4C2×#11762673C211yesmaximal, characteristic, complemented
5C2×#11762660C211yesmaximal, characteristic, complemented
6#14527032C211yesmaximal, characteristic, complemented
7#14527032C211yesmaximal, characteristic, complemented
8#14527031C211yesmaximal, characteristic, complemented
9#14527021C211yesmaximal, characteristic, complemented
10#14527021C211yesmaximal, characteristic, complemented
11#14527020C211yesmaximal, characteristic, complemented
12#14527020C211yesmaximal, characteristic, complemented
13#14527012C211yesmaximal, characteristic, complemented
14#95×Dic17C211yesmaximal, characteristic, complemented
15C17×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34#11762709—24no—
35#11762709—24no—
36#11762709C418yescomplemented
37#11762673—24no—
38#11762660—24no—
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C22×C22⋊C4×C17C2211yescharacteristic
50C22×C22⋊C4×C17C2211yescharacteristic
51C22×C22⋊C4×C17C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C25×C17C2311yescharacteristic
57C24×D17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C22×C22⋊D17—22no—
65C22×C22⋊D17—22no—
66C22×C22⋊D17—22no—
67C22×C22⋊D17—22no—
68C22×C22⋊D17—22no—
69C22×C22⋊D17—22no—
70C22×C22⋊D17C2×C414yes—
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C2×C22⋊C4×C17—22no—
79C2×C22⋊C4×C17—22no—
80C2×C22⋊C4×C17—22no—
81C2×C22⋊C4×C17—41no—
82C2×C22⋊C4×C17—41no—
83C2×C22⋊C4×C17—41no—
84C2×C22⋊C4×C17—41no—
85C2×C22⋊C4×C17—41no—
86C2×C22⋊C4×C17C2×C414yes—
87C2×C22⋊Dic17—22no—
88C2×C22⋊Dic17—22no—
89C2×C22⋊Dic17—22no—
90C2×C22⋊Dic17—22no—
91C2×C22⋊Dic17—22no—
92C2×C22⋊Dic17—41no—
93C2×C22⋊Dic17—41no—
94C2×C22⋊Dic17—41no—
95C2×C22⋊Dic17C2×C414yes—
96C2×#63227—22no—
97C2×#63227—22no—
98C2×#63227—22no—
99C2×#63227—22no—
100C2×#63227—22no—
101C2×#63227—22no—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227—41no—
105C2×#63227—41no—
106C2×#63227—41no—
107C2×#63227—41no—
108C2×#63227—41no—
109C2×#63227—41no—
110C2×#63227—41no—
111C2×#63227—41no—
112C2×#63227C2×C414yes—
113C2×#63227C2×C414yes—
114C2×#63225—22no—
115C2×#63225—22no—
116C2×#63225—22no—
117C2×#63225—22no—
118C2×#63225—22no—
119C2×#63225—22no—
120C2×#63225—22no—
121C2×#63225C2×C414yes—
122C2×#63225D414yes—
123C2×C4×Dic17—22no—
124C2×C4×Dic17—22no—
125C2×C4×Dic17—22no—
126C2×C4×Dic17—22no—
127C2×C4×Dic17—22no—
128C2×C4×Dic17—22no—
129C2×C4×Dic17—22no—
130C2×C4×Dic17—22no—
131C2×C4×Dic17—22no—
132C2×C4×Dic17—41no—
133C2×C4×Dic17—41no—
134C2×C4×Dic17—41no—
135C2×C4×Dic17—41no—
136C2×C4×Dic17C2×C414yes—
137C2×C4×Dic17D414yes—
138C17×#95—22no—
139C17×#95—22no—
140C17×#95—22no—
141C17×#95—41no—
142#10587502—22no—
143#10587502—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—22no—
148#10587502—22no—
149#10587502—41no—
150#10587502—41no—
151#10587502—41no—
152C24×C17—21no—
153C24×C17—21no—
154C24×C17—21no—
155C24×C17—21no—
156C24×C17—21no—
157C24×C17—21no—
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×C17C2411yescharacteristic
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×D17C22×C412yes—
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×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×C17C22×C412yes—
221C22×C4×C17C22×C412yes—
222C22×C4×C17C2×D412yes—
223C22×C4×C17C2×D412yes—
224C22×C4×C17#4112yes—
225C2×C22⋊D17—28no—
226C2×C22⋊D17—28no—
227C2×C22⋊D17—28no—
228C2×C22⋊D17—44no—
229C2×C22⋊D17—44no—
230C2×C22⋊D17—44no—
231C2×C22⋊D17—44no—
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×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17C22×C412yes—
268C22×Dic17C22×C412yes—
269C22×Dic17C22×C412yes—
270C22×Dic17C2×D412yes—
271C22×Dic17C2×D412yes—
272C22×Dic17C2×D412yes—
273C22×Dic17C2×D412yes—
274C22×Dic17#4112yes—
275C22×Dic17#4112yes—
276C22×Dic17#4112yes—
277C22×Dic17#4112yes—
278C22×Dic17#4112yes—
279C22×Dic17#4112yes—
280C22×Dic17#4112yes—
281C22⋊C4×C17—44no—
282C22⋊C4×C17—44no—
283C22⋊C4×C17—44no—
284C22⋊Dic17—44no—
285C22⋊Dic17—44no—
286C22⋊Dic17—44no—
287#63227—44no—
288#63227—44no—
289#63227—44no—
290#63227—44no—
291#63227—44no—
292#63227—44no—
293#63225—28no—
294#63225—28no—
295#63225—44no—
296C4×Dic17—28no—
297C4×Dic17—28no—
298C4×Dic17—44no—
299C4×Dic17—44no—
300C4×Dic17—44no—
301#14002—171nomaximal, Sylow
302C23×C17—22no—
303C23×C17—22no—
304C23×C17—22no—
305C23×C17—22no—
306C23×C17—22no—
307C23×C17—22no—
308C23×C17—22no—
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×C17—41no—
322C23×C17—41no—
323C23×C17—41no—
324C23×C17—41no—
325C23×C17—41no—
326C23×C17—41no—
327C23×C17—41no—
328C23×C17—41no—
329C23×C17—41no—
330C23×C17—41no—
331C23×C17—41no—
332C23×C17—41no—
333C23×C17—41no—
334C23×C17—41no—
335C23×C17—41no—
336C23×C17—41no—
337C23×C17C23×C411yescharacteristic
338C23×C17C22×D411yescharacteristic
339C23×C17C22×D411yescharacteristic
340C23×C17C2×#4111yescharacteristic
341C23×C17C2×#4111yescharacteristic
342C23×C17C2×#4111yescharacteristic
343C23×C17C2×#4111yescharacteristic
344C23×C17C2×#4111yescharacteristic
345C23×C17C2×#4111yescharacteristic
346C23×C17C2×#4111yescharacteristic
347C23×C17C2×#4111yescharacteristic
348C23×C17H(5,𝔽2)11yescharacteristic
349C23×C17H(5,𝔽2)11yescharacteristic
350C23×C17H(5,𝔽2)11yescharacteristic
351C23×C17H(5,𝔽2)11yescharacteristic
352C22×D17—22no—
353C22×D17—22no—
354C22×D17—22no—
355C22×D17—22no—
356C22×D17—22no—
357C22×D17—22no—
358C22×D17—22no—
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—
371C22×D17—41no—
372C22×D17—41no—
373C22×D17—41no—
374C22×D17—41no—
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—
387C2×C4×C17—22no—
388C2×C4×C17—22no—
389C2×C4×C17—22no—
390C2×C4×C17—22no—
391C2×C4×C17—22no—
392C2×C4×C17—22no—
393C2×C4×C17—22no—
394C2×C4×C17—22no—
395C2×C4×C17—22no—
396C2×C4×C17—22no—
397C2×C4×C17—22no—
398C2×C4×C17—22no—
399C2×C4×C17—22no—
400C2×C4×C17—22no—
401C2×C4×C17—22no—
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—
413C2×C4×C17—41no—
414C2×C4×C17—41no—
415C2×C4×C17—41no—
416C2×C4×C17—41no—
417C2×C4×C17—41no—
418C2×C4×C17—41no—
419C2×C4×C17—41no—
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—
429C22⋊D17—416no—
430C2×Dic17—22no—
431C2×Dic17—22no—
432C2×Dic17—22no—
433C2×Dic17—22no—
434C2×Dic17—22no—
435C2×Dic17—22no—
436C2×Dic17—22no—
437C2×Dic17—22no—
438C2×Dic17—22no—
439C2×Dic17—22no—
440C2×Dic17—22no—
441C2×Dic17—22no—
442C2×Dic17—22no—
443C2×Dic17—22no—
444C2×Dic17—22no—
445C2×Dic17—22no—
446C2×Dic17—22no—
447C2×Dic17—22no—
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—41no—
463C2×Dic17—41no—
464C2×Dic17—41no—
465C2×Dic17—41no—
466C2×Dic17—41no—
467C2×Dic17—41no—
468C2×Dic17—41no—
469C2×Dic17—41no—
470C2×Dic17—41no—
471C2×Dic17#11714yes—
472C2×Dic17C4×D414yes—
473C2×Dic17C4×D414yes—
474C2×Dic17#12114yes—
475C2×Dic17#12314yes—
476C2×Dic17#12414yes—
477C2×Dic17#12414yes—
478C2×Dic17#12614yes—
479C2×#390—171no—
480C2×#390—171no—
481C2×#390—171no—
482C2×#382—171no—
483C2×C4×C4⋊C4—171no—
484#1440—171no—
485#1440—171no—
486#1440—171no—
487#1440D1711yescharacteristic, complemented
488#1437—171no—
489#1437—171no—
490#1437—171no—
491#1437—171no—
492C4⋊#95—171no—
493C4×#95—171no—
494C22×C17—42no—
495C22×C17—42no—
496C22×C17—42no—
497C22×C17—42no—
498C22×C17—42no—
499C22×C17—42no—
500C22×C17—42no—
501C22×C17—81no—
502C22×C17—81no—
503C22×C17—81no—
504C22×C17—81no—
505C22×C17—81no—
506C22×C17—81no—
507C22×C17—81no—
508C22×C17—81no—
509C22×C17C2×#11711yescharacteristic
510C22×C17C2×C4×D411yescharacteristic
511C22×C17C2×C4×D411yescharacteristic
512C22×C17C4×#4111yescharacteristic
513C22×C17C4×#4111yescharacteristic
514C22×C17#51811yescharacteristic
515C22×C17#51811yescharacteristic
516C22×C17C2×#12111yescharacteristic
517C22×C17C2×#12311yescharacteristic
518C22×C17C2×#12411yescharacteristic
519C22×C17C2×#12411yescharacteristic
520C22×C17C2×#12611yescharacteristic
521C22×C17#52911yescharacteristic
522C22×C17#52911yescharacteristic
523C22×C17#53211yescharacteristic
524C22×C17#53511yescharacteristic
525C22×C17#53511yescharacteristic
526C22×C17#54011yescharacteristic
527C22×C17#54011yescharacteristic
528C22×C17#54611yescharacteristic
529C22×C17#54611yescharacteristic
530C22×C17#55011yescharacteristic
531C22×C17#55011yescharacteristic
532C22×C17#55311yescharacteristic
533C22×C17#55311yescharacteristic
534C22×C17#55311yescharacteristic
535C22×C17#55311yescharacteristic
536C22×C17#55311yescharacteristic
537C22×C17#55311yescharacteristic
538C22×C17#55511yescharacteristic
539C22×C17#55511yescharacteristic
540C22×C17#55911yescharacteristic
541C22×C17#55911yescharacteristic
542C22×C17#55911yescharacteristic
543C22×C17#55911yescharacteristic
544C2×D17—42no—
545C2×D17—42no—
546C2×D17—42no—
547C2×D17—42no—
548C2×D17—42no—
549C2×D17—42no—
550C2×D17—42no—
551C2×D17—81no—
552C2×D17—81no—
553C2×D17—81no—
554C2×D17—81no—
555C2×D17—81no—
556C2×D17—81no—
557C2×D17—81no—
558C2×D17—81no—
559C4×C17—42no—
560C4×C17—42no—
561C4×C17—42no—
562C4×C17—42no—
563C4×C17—42no—
564C4×C17—81no—
565Dic17—24no—
566Dic17—42no—
567Dic17—42no—
568Dic17—42no—
569Dic17—42no—
570Dic17—81no—
571Dic17#38818yes—
572C23×D4—171no—
573C22×C4⋊C4—171no—
574C22×C4⋊C4—171no—
575C22×C4⋊C4—171no—
576C22×C22⋊C4—171no—
577C22×C22⋊C4—171no—
578C22×C22⋊C4—171no—
579C22×C22⋊C4—171no—
580C22×C22⋊C4—171no—
581C22×C22⋊C4—171no—
582C22×C22⋊C4—171no—
583C22×C22⋊C4—171no—
584C22×C22⋊C4—171no—
585C22×C22⋊C4C2×D1711yescharacteristic
586C22×C22⋊C4C2×D1711yescharacteristic
587C22×C22⋊C4C2×D1711yescharacteristic
588C22×C42—171no—
589C22×C42—171no—
590C22×C42—171no—
591C22×C42—171no—
592C22×C42—171no—
593#390—178no—
594#390—344no—
595#390—344no—
596#382—344no—
597C4×C4⋊C4—344no—
598C2×#95—171no—
599C2×#95—171no—
600C2×#95—171no—
601C2×#95—171no—
602C2×#95—171no—
603C2×#95—171no—
604C2×#95—171no—
605C2×#95—171no—
606C2×#95—171no—
607C2×#95—171no—
608C2×#95C2×D1711yescharacteristic
609C2×#95C2×D1711yescharacteristic
610C2×#95C2×D1711yescharacteristic
611C2×#95C2×D1711yescharacteristic
612C2×C17—82no—
613C2×C17C2×#38811yescharacteristic
614C2×C17C4×#12411yescharacteristic
615C2×C17#232811yescharacteristic
616C2×C17#235711yescharacteristic
617C2×C17#235711yescharacteristic
618C2×C17#236311yescharacteristic
619C2×C17#236311yescharacteristic
620C2×C17#249011yescharacteristic
621C2×C17#249011yescharacteristic
622C2×C17#250011yescharacteristic
623C2×C17#250411yescharacteristic
624C2×C17#251311yescharacteristic
625C2×C17#251311yescharacteristic
626C2×C17#254411yescharacteristic
627C2×C17#254811yescharacteristic
628D17—82no—
629C25—171no—
630C25C22×D1711yescharacteristic
631C22×D4—174no—
632C22×D4—342no—
633C22×D4—342no—
634C22×D4—342no—
635C22×D4—342no—
636C22×D4—342no—
637C22×D4—342no—
638C23×C4—171no—
639C23×C4—171no—
640C23×C4—171no—
641C23×C4—171no—
642C23×C4—171no—
643C23×C4—171no—
644C23×C4—171no—
645C23×C4C22×D1711yescharacteristic
646C23×C4C22×D1711yescharacteristic
647C23×C4C22×D1711yescharacteristic
648C23×C4C22×D1711yescharacteristic
649C23×C4C22×D1711yescharacteristic
650C23×C4C22×D1711yescharacteristic
651C2×C4⋊C4—174no—
652C2×C4⋊C4—174no—
653C2×C4⋊C4—342no—
654C2×C4⋊C4—342no—
655C2×C4⋊C4—342no—
656C2×C4⋊C4—342no—
657C2×C4⋊C4—342no—
658C2×C4⋊C4—342no—
659C2×C4⋊C4—342no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—41no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—174no—
669C2×C22⋊C4—174no—
670C2×C22⋊C4—174no—
671C2×C22⋊C4—342no—
672C2×C22⋊C4—342no—
673C2×C22⋊C4—342no—
674C2×C22⋊C4—342no—
675C2×C22⋊C4—342no—
676C2×C22⋊C4—342no—
677C2×C22⋊C4—342no—
678C2×C22⋊C4—342no—
679C2×C22⋊C4—342no—
680C2×C22⋊C4—342no—
681C2×C22⋊C4—342no—
682C2×C22⋊C4—342no—
683C2×C22⋊C4—342no—
684C2×C22⋊C4—681no—
685C2×C22⋊C4—681no—
686C2×C22⋊C4—681no—
687C2×C22⋊C4—681no—
688C2×C22⋊C4—681no—
689C2×C22⋊C4—681no—
690C2×C22⋊C4—681no—
691C2×C22⋊C4—681no—
692C2×C22⋊C4—681no—
693C2×C22⋊C4—681no—
694C2×C22⋊C4—681no—
695C2×C22⋊C4C4×D1714yes—
696C2×C42—174no—
697C2×C42—174no—
698C2×C42—342no—
699C2×C42—342no—
700C2×C42—342no—
701C2×C42—342no—
702C2×C42—342no—
703C2×C42—342no—
704C2×C42—342no—
705C2×C42—342no—
706C2×C42—342no—
707C2×C42—681no—
708C2×C42—681no—
709C2×C42—681no—
710C2×C42—681no—
711#95—22no—
712#95—22no—
713#95—22no—
714#95—41no—
715#95—342no—
716#95—342no—
717#95—342no—
718#95—342no—
719#95—342no—
720#95—342no—
721#95—342no—
722#95—681no—
723#95—681no—
724#95—681no—
725C17#1400211yescharacteristic, complemented, Sylow
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—172no—
741C24—341no—
742C24—341no—
743C24—341no—
744C24—341no—
745C24—341no—
746C24—341no—
747C24—341no—
748C24—341no—
749C24—341no—
750C24—341no—
751C24—341no—
752C24—341no—
753C24—341no—
754C24—341no—
755C24C2×C4×D1712yes—
756C24C23×D1711yescharacteristic
757C2×D4—348no—
758C2×D4—348no—
759C2×D4—348no—
760C2×D4—684no—
761C2×D4—684no—
762C2×D4—684no—
763C2×D4—684no—
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—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—172no—
802C22×C4—172no—
803C22×C4—172no—
804C22×C4—172no—
805C22×C4—172no—
806C22×C4—172no—
807C22×C4—172no—
808C22×C4—172no—
809C22×C4—172no—
810C22×C4—172no—
811C22×C4—172no—
812C22×C4—172no—
813C22×C4—172no—
814C22×C4—172no—
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×C4—341no—
825C22×C4—341no—
826C22×C4—341no—
827C22×C4—341no—
828C22×C4—341no—
829C22×C4—341no—
830C22×C4—341no—
831C22×C4—341no—
832C22×C4—341no—
833C22×C4—341no—
834C22×C4—341no—
835C22×C4—341no—
836C22×C4—341no—
837C22×C4—341no—
838C22×C4—341no—
839C22×C4—341no—
840C22×C4—341no—
841C22×C4—341no—
842C22×C4—341no—
843C22×C4—341no—
844C22×C4—341no—
845C22×C4—341no—
846C22×C4—341no—
847C22×C4—341no—
848C22×C4—341no—
849C22×C4—341no—
850C22×C4C2×C4×D1712yes—
851C22×C4C2×C4×D1712yes—
852C22×C4D4×D1712yes—
853C22×C4D4×D1712yes—
854C22×C4#6325412yes—
855C4⋊C4—348no—
856C4⋊C4—348no—
857C4⋊C4—684no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—684no—
862C22⋊C4—684no—
863C22⋊C4—684no—
864C22⋊C4—684no—
865C22⋊C4—684no—
866C22⋊C4—684no—
867C22⋊C4—684no—
868C22⋊C4—684no—
869C22⋊C4—684no—
870C42—348no—
871C42—348no—
872C42—684no—
873C42—684no—
874C42—684no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—342no—
911C23—342no—
912C23—342no—
913C23—342no—
914C23—342no—
915C23—342no—
916C23—342no—
917C23—681no—
918C23—681no—
919C23—681no—
920C23—681no—
921C23—681no—
922C23—681no—
923C23—681no—
924C23—681no—
925C23—681no—
926C23—681no—
927C23—681no—
928C23—681no—
929C23—681no—
930C23—681no—
931C23—681no—
932C23—681no—
933C23—681no—
934C23—681no—
935C23—681no—
936C23—681no—
937C23—681no—
938C23—681no—
939C23—681no—
940C23—681no—
941C23—681no—
942C23—681no—
943C23—681no—
944C23—681no—
945C23C22×C4×D1711yescharacteristic
946C23C2×D4×D1711yescharacteristic
947C23C2×D4×D1711yescharacteristic
948C23C2×#6325411yescharacteristic
949C23#1058769111yescharacteristic
950C23#1058769111yescharacteristic
951C23#1058769111yescharacteristic
952C23#41×D1711yescharacteristic
953C23#41×D1711yescharacteristic
954C23#41×D1711yescharacteristic
955C23#41×D1711yescharacteristic
956C23#41×D1711yescharacteristic
957C23#41×D1711yescharacteristic
958C23#41×D1711yescharacteristic
959C23#1058769611yescharacteristic
960D4—6816no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—174no—
1004C2×C4—174no—
1005C2×C4—174no—
1006C2×C4—174no—
1007C2×C4—174no—
1008C2×C4—174no—
1009C2×C4—174no—
1010C2×C4—174no—
1011C2×C4—342no—
1012C2×C4—342no—
1013C2×C4—342no—
1014C2×C4—342no—
1015C2×C4—342no—
1016C2×C4—342no—
1017C2×C4—342no—
1018C2×C4—342no—
1019C2×C4—342no—
1020C2×C4—342no—
1021C2×C4—342no—
1022C2×C4—342no—
1023C2×C4—342no—
1024C2×C4—342no—
1025C2×C4—342no—
1026C2×C4—342no—
1027C2×C4—342no—
1028C2×C4—342no—
1029C2×C4—681no—
1030C2×C4—681no—
1031C2×C4—681no—
1032C2×C4—681no—
1033C2×C4—681no—
1034C2×C4—681no—
1035C2×C4—681no—
1036C2×C4—681no—
1037C2×C4—681no—
1038C2×C4—681no—
1039C2×C4—681no—
1040C2×C4—681no—
1041C2×C4—681no—
1042C2×C4—681no—
1043C2×C4—681no—
1044C2×C4—681no—
1045C2×C4—681no—
1046C2×C4—681no—
1047C2×C4—681no—
1048C2×C4—681no—
1049C2×C4—681no—
1050C2×C4—681no—
1051C2×C4—681no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—682no—
1068C22—682no—
1069C22—682no—
1070C22—682no—
1071C22—682no—
1072C22—682no—
1073C22—682no—
1074C22—1361no—
1075C22—1361no—
1076C22—1361no—
1077C22—1361no—
1078C22—1361no—
1079C22—1361no—
1080C22—1361no—
1081C22—1361no—
1082C22#117×D1711yescharacteristic
1083C22C4×D4×D1711yescharacteristic
1084C22C4×D4×D1711yescharacteristic
1085C22C4×#6325411yescharacteristic
1086C22#1176327711yescharacteristic
1087C22#1176328111yescharacteristic
1088C22#1176328211yescharacteristic
1089C22#121×D1711yescharacteristic
1090C22#123×D1711yescharacteristic
1091C22#124×D1711yescharacteristic
1092C22#124×D1711yescharacteristic
1093C22#126×D1711yescharacteristic
1094C22#1176333611yescharacteristic
1095C22#1176334211yescharacteristic
1096C22#1176335411yescharacteristic
1097C22#1176337411yescharacteristic
1098C22#1176337511yescharacteristic
1099C22#1176340911yescharacteristic
1100C22#1176341111yescharacteristic
1101C22#1176344611yescharacteristic
1102C22#1176345111yescharacteristic
1103C22#1176347711yescharacteristic
1104C22#1176347711yescharacteristic
1105C22#1176350211yescharacteristic
1106C22#1176350411yescharacteristic
1107C22#1176350411yescharacteristic
1108C22#1176350411yescharacteristic
1109C22#1176351011yescharacteristic
1110C22#1176351011yescharacteristic
1111C22#1176352111yescharacteristic
1112C22#1176352311yescharacteristic
1113C22#1176354111yescharacteristic
1114C22#1176354311yescharacteristic
1115C22#1176354311yescharacteristic
1116C22#1176354311yescharacteristic
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—81no—
1123C4—178no—
1124C4—344no—
1125C4—682no—
1126C4—682no—
1127C4—682no—
1128C4—682no—
1129C4—1361no—
1130C2—82no—
1131C2—1362no—
1132C2D17×#38811yescharacteristic
1133C2#1453132511yescharacteristic
1134C2#1453150511yescharacteristic
1135C2#1453175211yescharacteristic
1136C2#1453175411yescharacteristic
1137C2#1453181711yescharacteristic
1138C2#1453182511yescharacteristic
1139C2#1453312911yescharacteristic
1140C2#1453313111yescharacteristic
1141C2#1453324111yescharacteristic
1142C2#1453327111yescharacteristic
1143C2#1453337411yescharacteristic
1144C2#1453337611yescharacteristic
1145C2#1453375011yescharacteristic
1146C2#1453378211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1440C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1440D17
hypocenterC17#14002
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
4. C2×#11762673C2semidirect
5. C2×#11762660C2semidirect
6. #14527032C2semidirect
7. #14527032C2semidirect
8. #14527031C2semidirect
9. #14527021C2semidirect
10. #14527021C2semidirect
11. #14527020C2semidirect
12. #14527020C2semidirect
13. #14527012C2semidirect
14. #95×Dic17C2semidirect
15. C17×#1440C2semidirect
36. #11762709C4semidirect
487. #1440D17semidirect
725. C17#14002semidirect

Maximal subgroups

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

subgroupindex
C2×#117627092
C2×#117626732
C2×#117626602
#145270322
#145270312
#145270212
#145270202
#145270122
#95×Dic172
C17×#14402
#1400217