Finite Group Databasebeta

← #16962500

Subgroups — #16962500

Order 4352.

2126 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587571C211yesmaximal, characteristic
2C2×#11762714C211yesmaximal, characteristic, complemented
3C2×#11762702C211yesmaximal, characteristic, complemented
4C2×#11762688C211yesmaximal, characteristic
5#14527054C211yesmaximal, characteristic, complemented
6#14527031C211yesmaximal, characteristic, complemented
7#14527030C211yesmaximal, characteristic, complemented
8#14527026C211yesmaximal, characteristic, complemented
9#14527026C211yesmaximal, characteristic, complemented
10#14527023C211yesmaximal, characteristic
11#14527020C211yesmaximal, characteristic, complemented
12#14527013C211yesmaximal, characteristic, complemented
13#14527008C211yesmaximal, characteristic, complemented
14#14527007C211yesmaximal, characteristic, complemented
15C2×C17×#385C211yesmaximal, characteristic, complemented
16C23×Dic34C2211yescharacteristic
17C23×C22⋊D17C2211yescharacteristic
18C2×#10587571—24no—
19C2×#10587571—24no—
20C2×#10587571C418yescomplemented
21C22×C4⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33#11762714—24no—
34#11762702—24no—
35#11762688—24no—
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C24×C4×C17C2211yescharacteristic
51C22×C4⋊C4×C17C2211yescharacteristic
52C22×C4⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C17×#385—24no—
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—41no—
64C23×C4×C17—41no—
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—41no—
78C22×C22⋊D17—41no—
79C22×C22⋊D17C2×C414yes—
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C22×Dic34—22no—
88C22×Dic34—22no—
89C22×Dic34—22no—
90C22×Dic34—22no—
91C22×Dic34—41no—
92C22×Dic34—41no—
93C22×Dic34C2×C414yescomplemented
94C2×C4⋊C4×C17—22no—
95C2×C4⋊C4×C17—22no—
96C2×C4⋊C4×C17—22no—
97C2×C4⋊C4×C17—22no—
98C2×C4⋊C4×C17—41no—
99C2×C4⋊C4×C17—41no—
100C2×C22⋊C4×C17—22no—
101C2×C22⋊C4×C17—41no—
102C2×C22⋊C4×C17—41no—
103C2×C22⋊C4×C17C2×C414yes—
104C2×C22⋊C4×C17D414yes—
105C2×C22⋊C4×C17D414yes—
106C2×C22⋊Dic17—22no—
107C2×C22⋊Dic17—22no—
108C2×C22⋊Dic17—22no—
109C2×C22⋊Dic17—22no—
110C2×C22⋊Dic17—22no—
111C2×C22⋊Dic17—22no—
112C2×C22⋊Dic17—41no—
113C2×C22⋊Dic17—41no—
114C2×C22⋊Dic17C2×C414yes—
115C2×#63227—22no—
116C2×#63227—22no—
117C2×#63227—22no—
118C2×#63227—22no—
119C2×#63227—22no—
120C2×#63227—22no—
121C2×#63227—22no—
122C2×#63227—22no—
123C2×#63227—41no—
124C2×#63227—41no—
125C2×#63227—41no—
126C2×#63227—41no—
127C2×#63227—41no—
128C2×#63227—41no—
129C2×#63227—41no—
130C2×#63227—41no—
131C2×#63227C2×C414yescomplemented
132C2×#63227C2×C414yescomplemented
133C2×C4⋊Dic17—22no—
134C2×C4⋊Dic17—22no—
135C2×C4⋊Dic17—41no—
136C2×C4×Dic17—22no—
137C2×C4×Dic17—22no—
138C2×C4×Dic17—22no—
139C2×C4×Dic17—22no—
140C2×C4×Dic17—41no—
141C2×C4×Dic17C2×C414yescomplemented
142#10587571—232no—
143C17×#95—22no—
144C17×#95—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—22no—
148#10587502—22no—
149#10587502—22no—
150#10587502—22no—
151#10587502—22no—
152#10587502—41no—
153#10587502—41no—
154#10587502—41no—
155#10587502—41no—
156#10587502—41no—
157#10587502—41no—
158#10587502D414yes—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17—21no—
164C24×C17—21no—
165C24×C17—21no—
166C24×C17—21no—
167C24×C17—21no—
168C24×C17—21no—
169C24×C17—21no—
170C24×C17—21no—
171C24×C17C22×C412yes—
172C24×C17C2×D412yes—
173C24×C17C2×D412yes—
174C24×C17C2411yescharacteristic
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×D17—21no—
189C23×D17C22×C412yes—
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—44no—
225C22×C4×C17—44no—
226C22×C4×C17—44no—
227C22×C4×C17—44no—
228C22×C4×C17—44no—
229C22×C4×C17—44no—
230C22×C4×C17—44no—
231C22×C4×C17C22×C412yes—
232C22×C4×C17C22×C412yes—
233C22×C4×C17C2×D412yes—
234C22×C4×C17C2×D412yes—
235C22×C4×C17C2×D412yes—
236C22×C4×C17C2×D412yes—
237C22×C4×C17C2×D412yes—
238C22×C4×C17#4112yes—
239C2×C22⋊D17—28no—
240C2×C22⋊D17—28no—
241C2×C22⋊D17—44no—
242C2×C22⋊D17—44no—
243C2×C22⋊D17—44no—
244C2×C22⋊D17—44no—
245C2×C22⋊D17—44no—
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×Dic17—21no—
280C22×Dic17—21no—
281C22×Dic17—21no—
282C22×Dic17—21no—
283C22×Dic17—21no—
284C22×Dic17—21no—
285C22×Dic17—21no—
286C22×Dic17—21no—
287C22×Dic17—21no—
288C22×Dic17C22×C412yes—
289C22×Dic17C22×C412yes—
290C22×Dic17C22×C412yes—
291C22×Dic17C2×D412yes—
292C22×Dic17C2×D412yes—
293C22×Dic17#4112yes—
294C22×Dic17#4112yes—
295C2×Dic34—28no—
296C2×Dic34—28no—
297C2×Dic34—44no—
298C2×Dic34—44no—
299C2×Dic34—44no—
300C2×Dic34—44no—
301C2×Dic34—44no—
302C4⋊C4×C17—44no—
303C4⋊C4×C17—44no—
304C22⋊C4×C17—44no—
305C22⋊C4×C17C22⋊C4116yescomplemented
306C22⋊Dic17—28no—
307C22⋊Dic17—44no—
308C22⋊Dic17—44no—
309#63227—28no—
310#63227—28no—
311#63227—44no—
312#63227—44no—
313#63227—44no—
314#63227—44no—
315C4⋊Dic17—44no—
316C4×Dic17—28no—
317C4×Dic17—44no—
318#14421—171nomaximal, Sylow
319C23×C17—22no—
320C23×C17—22no—
321C23×C17—22no—
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—41no—
338C23×C17—41no—
339C23×C17—41no—
340C23×C17—41no—
341C23×C17—41no—
342C23×C17—41no—
343C23×C17—41no—
344C23×C17—41no—
345C23×C17—41no—
346C23×C17—41no—
347C23×C17—41no—
348C23×C17—41no—
349C23×C17—41no—
350C23×C17—41no—
351C23×C17—41no—
352C23×C17—41no—
353C23×C17C2×C22⋊C414yes—
354C23×C17C23×C411yescharacteristic
355C23×C17C22×D411yescharacteristic
356C23×C17C22×D411yescharacteristic
357C23×C17C22×D411yescharacteristic
358C23×C17C2×#4111yescharacteristic
359C23×C17C2×#4111yescharacteristic
360C23×C17C2×#4111yescharacteristic
361C23×C17H(5,𝔽2)11yescharacteristic
362C23×C17H(5,𝔽2)11yescharacteristic
363C23×C17H(5,𝔽2)11yescharacteristic
364C23×C17H(5,𝔽2)11yescharacteristic
365C23×C17H(5,𝔽2)11yescharacteristic
366C23×C172−1+411yescharacteristic
367C23×C172−1+411yescharacteristic
368C23×C172−1+411yescharacteristic
369C22×D17—22no—
370C22×D17—22no—
371C22×D17—22no—
372C22×D17—22no—
373C22×D17—22no—
374C22×D17—22no—
375C22×D17—22no—
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—
404C2×C4×C17—22no—
405C2×C4×C17—22no—
406C2×C4×C17—22no—
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—22no—
420C2×C4×C17—22no—
421C2×C4×C17—22no—
422C2×C4×C17—416no—
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×C17C2×C22⋊C414yes—
446C2×C4×C17C2×C22⋊C414yes—
447C22⋊D17—416no—
448C2×Dic17—22no—
449C2×Dic17—22no—
450C2×Dic17—22no—
451C2×Dic17—22no—
452C2×Dic17—22no—
453C2×Dic17—22no—
454C2×Dic17—22no—
455C2×Dic17—22no—
456C2×Dic17—22no—
457C2×Dic17—22no—
458C2×Dic17—22no—
459C2×Dic17—22no—
460C2×Dic17—22no—
461C2×Dic17—22no—
462C2×Dic17—22no—
463C2×Dic17—22no—
464C2×Dic17—22no—
465C2×Dic17—22no—
466C2×Dic17—41no—
467C2×Dic17—41no—
468C2×Dic17—41no—
469C2×Dic17—41no—
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×Dic17C4×D414yes—
497Dic34—416no—
498C22×#124—171no—
499C2×#391—171no—
500C2×#388—171no—
501C2×#386—171no—
502C2×#385D1711yescharacteristic, complemented
503#1446—171no—
504#1440—171no—
505#1439—171no—
506#1439—171no—
507#1439—171no—
508#1438—171no—
509#1437—171no—
510C4⋊#95—171no—
511#1434—171no—
512C22⋊#95—171no—
513C22×C17—24no—
514C22×C17—24no—
515C22×C17—24no—
516C22×C17—42no—
517C22×C17—42no—
518C22×C17—42no—
519C22×C17—42no—
520C22×C17—42no—
521C22×C17—42no—
522C22×C17—42no—
523C22×C17—42no—
524C22×C17—42no—
525C22×C17—42no—
526C22×C17—42no—
527C22×C17—42no—
528C22×C17C22×C22⋊C411yescharacteristic
529C22×C17C2×C4×D411yescharacteristic
530C22×C17C4×#4111yescharacteristic
531C22×C17#51811yescharacteristic
532C22×C17#52011yescharacteristic
533C22×C17#52011yescharacteristic
534C22×C17#52011yescharacteristic
535C22×C17#53511yescharacteristic
536C22×C17#53511yescharacteristic
537C22×C17#53611yescharacteristic
538C22×C17#53611yescharacteristic
539C22×C17#53711yescharacteristic
540C22×C17#53711yescharacteristic
541C22×C17#53811yescharacteristic
542C22×C17#53811yescharacteristic
543C22×C17#54211yescharacteristic
544C22×C17#54211yescharacteristic
545C22×C17#54211yescharacteristic
546C22×C17#54211yescharacteristic
547C22×C17D4211yescharacteristic
548C22×C17D4211yescharacteristic
549C22×C17#54611yescharacteristic
550C22×C17#54611yescharacteristic
551C22×C17#54611yescharacteristic
552C22×C17#54611yescharacteristic
553C22×C17#54611yescharacteristic
554C22×C17#54711yescharacteristic
555C22×C17#54711yescharacteristic
556C22×C17#54811yescharacteristic
557C22×C17#55611yescharacteristic
558C22×C17#55911yescharacteristic
559C22×C17H(3,𝔽4)11yescharacteristic
560C22×C17#56211yescharacteristic
561C22×C17#56211yescharacteristic
562C22×C17#56311yescharacteristic
563C2×D17—42no—
564C2×D17—42no—
565C2×D17—42no—
566C2×D17—42no—
567C2×D17—42no—
568C2×D17—42no—
569C2×D17—42no—
570C2×D17—81no—
571C2×D17—81no—
572C2×D17—81no—
573C2×D17—81no—
574C2×D17—81no—
575C2×D17—81no—
576C2×D17—81no—
577C2×D17—81no—
578C4×C17—24no—
579C4×C17—24no—
580C4×C17—42no—
581C4×C17—42no—
582C4×C17—81no—
583C4×C17—81no—
584Dic17—24no—
585Dic17—42no—
586Dic17—42no—
587Dic17—42no—
588Dic17—42no—
589Dic17—81no—
590Dic17—81no—
591C23×Q8—171no—
592C23×D4—171no—
593C24×C4C2×D1711yescharacteristic
594C2×#124—178no—
595C2×#124—344no—
596C2×#124—344no—
597C22×C4⋊C4—171no—
598C22×C4⋊C4C2×D1711yescharacteristic
599C22×C4⋊C4C2×D1711yescharacteristic
600C22×C22⋊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⋊C4—171no—
609C22×C22⋊C4C2×D1711yescharacteristic
610C22×C22⋊C4C2×D1711yescharacteristic
611C22×C42—171no—
612C22×C42—171no—
613#391—344no—
614#388—344no—
615#386—344no—
616#385—24no—
617C2×#95—171no—
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×#95C2×D1711yescharacteristic
632C2×#95C2×D1711yescharacteristic
633C2×C17—44no—
634C2×C17#231111yescharacteristic
635C2×C17#232611yescharacteristic
636C2×C17#233711yescharacteristic
637C2×C17D4×C22⋊C411yescharacteristic
638C2×C17#233911yescharacteristic
639C2×C17#236711yescharacteristic
640C2×C17#237911yescharacteristic
641C2×C17#267011yescharacteristic
642C2×C17#267211yescharacteristic
643C2×C17#267411yescharacteristic
644C2×C17#267611yescharacteristic
645C2×C17#270011yescharacteristic
646C2×C17#271011yescharacteristic
647C2×C17#271211yescharacteristic
648C2×C17#271511yescharacteristic
649D17—82no—
650C25—171no—
651C25C22×D1711yescharacteristic
652C22×Q8—174no—
653C22×Q8—342no—
654C22×Q8—342no—
655C22×Q8—342no—
656C22×Q8—342no—
657C22×Q8—681no—
658C22×Q8—681no—
659C22×D4—174no—
660C22×D4—342no—
661C22×D4—342no—
662C22×D4—342no—
663C22×D4—342no—
664C22×D4—681no—
665C22×D4—681no—
666C23×C4—22no—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—41no—
670C23×C4—41no—
671C23×C4—41no—
672C23×C4—41no—
673C23×C4—171no—
674C23×C4—171no—
675C23×C4—171no—
676C23×C4—171no—
677C23×C4—171no—
678C23×C4—171no—
679C23×C4—171no—
680C23×C4C22×D1711yescharacteristic
681C23×C4C22×D1711yescharacteristic
682C23×C4C22×D1711yescharacteristic
683C23×C4C22×D1711yescharacteristic
684C23×C4C22×D1711yescharacteristic
685C23×C4C22×D1711yescharacteristic
686#124—3432no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—41no—
692C2×C4⋊C4—41no—
693C2×C4⋊C4—342no—
694C2×C4⋊C4—342no—
695C2×C4⋊C4—681no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—174no—
700C2×C22⋊C4—174no—
701C2×C22⋊C4—174no—
702C2×C22⋊C4—342no—
703C2×C22⋊C4—342no—
704C2×C22⋊C4—342no—
705C2×C22⋊C4—342no—
706C2×C22⋊C4—342no—
707C2×C22⋊C4—342no—
708C2×C22⋊C4—342no—
709C2×C22⋊C4—342no—
710C2×C22⋊C4—342no—
711C2×C22⋊C4—342no—
712C2×C22⋊C4—342no—
713C2×C22⋊C4—342no—
714C2×C22⋊C4—342no—
715C2×C22⋊C4—342no—
716C2×C22⋊C4—681no—
717C2×C22⋊C4—681no—
718C2×C22⋊C4—681no—
719C2×C22⋊C4—681no—
720C2×C22⋊C4—681no—
721C2×C22⋊C4—681no—
722C2×C22⋊C4—681no—
723C2×C22⋊C4—681no—
724C2×C22⋊C4—681no—
725C2×C22⋊C4—681no—
726C2×C22⋊C4C4×D1714yes—
727C2×C22⋊C4D6814yes—
728C2×C22⋊C4C22⋊D1714yes—
729C2×C42—174no—
730C2×C42—342no—
731C2×C42—342no—
732C2×C42—342no—
733C2×C42—342no—
734C2×C42—681no—
735#95—22no—
736#95—22no—
737#95—174no—
738#95—342no—
739#95—342no—
740#95—342no—
741#95—342no—
742#95—342no—
743#95—342no—
744#95—342no—
745#95—681no—
746#95—681no—
747#95—681no—
748#95—681no—
749#95—681no—
750#95—681no—
751C17#1442111yescharacteristic, complemented, Sylow
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—172no—
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—
778C24—341no—
779C24C2×C4×D1712yes—
780C24C2×D6812yes—
781C24C2×C22⋊D1712yes—
782C24C23×D1711yescharacteristic
783C2×Q8—348no—
784C2×Q8—348no—
785C2×Q8—684no—
786C2×Q8—684no—
787C2×Q8—684no—
788C2×Q8—684no—
789C2×Q8—684no—
790C2×D4—348no—
791C2×D4—348no—
792C2×D4—684no—
793C2×D4—684no—
794C2×D4—684no—
795C2×D4—684no—
796C2×D4—684no—
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—44no—
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—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—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×C4C2×C4×D1712yes—
888C22×C4C2×C4×D1712yes—
889C22×C4C2×D6812yes—
890C22×C4C2×D6812yes—
891C22×C4D4×D1712yes—
892C22×C4#6325412yes—
893C22×C4C2×C22⋊D1712yes—
894C22×C4C2×C22⋊D1712yes—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—684no—
898C22⋊C4—44no—
899C22⋊C4—348no—
900C22⋊C4—348no—
901C22⋊C4—348no—
902C22⋊C4—684no—
903C22⋊C4—684no—
904C22⋊C4—684no—
905C22⋊C4—684no—
906C22⋊C4—684no—
907C22⋊C4—684no—
908C22⋊C4#63227116yescomplemented
909C42—348no—
910C42—684no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—342no—
946C23—342no—
947C23—342no—
948C23—342no—
949C23—342no—
950C23—342no—
951C23—342no—
952C23—681no—
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—
980C23C2×#6322714yes—
981C23C22×C4×D1711yescharacteristic
982C23C22×D6811yescharacteristic
983C23C2×D4×D1711yescharacteristic
984C23C2×#6325411yescharacteristic
985C23#1058769111yescharacteristic
986C23#1058769111yescharacteristic
987C23#1058769111yescharacteristic
988C23#1058769111yescharacteristic
989C23#1058769411yescharacteristic
990C23#1058769411yescharacteristic
991C23#41×D1711yescharacteristic
992C23#41×D1711yescharacteristic
993C23#1058769611yescharacteristic
994C23#1058769711yescharacteristic
995C23C22×C22⋊D1711yescharacteristic
996Q8—6816no—
997D4—6816no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
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—174no—
1040C2×C4—342no—
1041C2×C4—342no—
1042C2×C4—342no—
1043C2×C4—342no—
1044C2×C4—342no—
1045C2×C4—342no—
1046C2×C4—342no—
1047C2×C4—342no—
1048C2×C4—342no—
1049C2×C4—342no—
1050C2×C4—342no—
1051C2×C4—342no—
1052C2×C4—342no—
1053C2×C4—342no—
1054C2×C4—342no—
1055C2×C4—342no—
1056C2×C4—342no—
1057C2×C4—342no—
1058C2×C4—681no—
1059C2×C4—681no—
1060C2×C4—681no—
1061C2×C4—681no—
1062C2×C4—681no—
1063C2×C4—681no—
1064C2×C4—681no—
1065C2×C4—681no—
1066C2×C4—681no—
1067C2×C4—681no—
1068C2×C4—681no—
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×C4C2×#6322714yes—
1089C2×C4C2×#6322714yes—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—682no—
1106C22—682no—
1107C22—682no—
1108C22—682no—
1109C22—682no—
1110C22—682no—
1111C22—682no—
1112C22—1361no—
1113C22—1361no—
1114C22—1361no—
1115C22—1361no—
1116C22—1361no—
1117C22—1361no—
1118C22—1361no—
1119C22—1361no—
1120C22C22×#6322711yescharacteristic
1121C22C4×D4×D1711yescharacteristic
1122C22C4×#6325411yescharacteristic
1123C22#1176328111yescharacteristic
1124C22#1176328811yescharacteristic
1125C22#1176329011yescharacteristic
1126C22#1176329011yescharacteristic
1127C22#1176337411yescharacteristic
1128C22#1176337611yescharacteristic
1129C22#1176338211yescharacteristic
1130C22#1176338311yescharacteristic
1131C22#1176339011yescharacteristic
1132C22#1176339011yescharacteristic
1133C22#1176339411yescharacteristic
1134C22#1176339511yescharacteristic
1135C22#1176342711yescharacteristic
1136C22#1176342911yescharacteristic
1137C22#1176342911yescharacteristic
1138C22#1176343211yescharacteristic
1139C22D4×C22⋊D1711yescharacteristic
1140C22D4×D6811yescharacteristic
1141C22#1176344611yescharacteristic
1142C22#1176344711yescharacteristic
1143C22#1176345311yescharacteristic
1144C22#1176345411yescharacteristic
1145C22#1176345411yescharacteristic
1146C22#1176345811yescharacteristic
1147C22#1176346311yescharacteristic
1148C22#1176346911yescharacteristic
1149C22#1176353011yescharacteristic
1150C22#1176354311yescharacteristic
1151C22#1176355211yescharacteristic
1152C22#1176355511yescharacteristic
1153C22#1176355611yescharacteristic
1154C22#1176356011yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—81no—
1161C4—344no—
1162C4—682no—
1163C4—682no—
1164C4—682no—
1165C4—682no—
1166C4—1361no—
1167C4—1361no—
1168C2—44no—
1169C2—1362no—
1170C2#1453137711yescharacteristic
1171C2#1453149011yescharacteristic
1172C2#1453159811yescharacteristic
1173C2D4×#6322711yescharacteristic
1174C2#1453160911yescharacteristic
1175C2#1453185211yescharacteristic
1176C2#1453195711yescharacteristic
1177C2#1453500611yescharacteristic
1178C2#1453503811yescharacteristic
1179C2#1453506111yescharacteristic
1180C2#1453508811yescharacteristic
1181C2#1453537811yescharacteristic
1182C2#1453552211yescharacteristic
1183C2#1453555211yescharacteristic
1184C2#1453559311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#385C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×#385D17
hypocenterC17#14421
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#11762714C2semidirect
3. C2×#11762702C2semidirect
5. #14527054C2semidirect
6. #14527031C2semidirect
7. #14527030C2semidirect
8. #14527026C2semidirect
9. #14527026C2semidirect
11. #14527020C2semidirect
12. #14527013C2semidirect
13. #14527008C2semidirect
14. #14527007C2semidirect
15. C2×C17×#385C2semidirect
20. C2×#10587571C4semidirect
93. C22×Dic34C2×C4semidirect
131. C2×#63227C2×C4semidirect
132. C2×#63227C2×C4semidirect
141. C2×C4×Dic17C2×C4semidirect
305. C22⋊C4×C17C22⋊C4semidirect
502. C2×#385D17semidirect
751. C17#14421semidirect
908. C22⋊C4#63227semidirect

Maximal subgroups

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

subgroupindex
C22×#105875712
C2×#117627142
C2×#117627022
C2×#117626882
#145270542
#145270312
#145270302
#145270262
#145270232
#145270202
#145270132
#145270082
#145270072
C2×C17×#3852
#1442117