Finite Group Databasebeta

← #16958769

Subgroups — #16958769

Order 4352.

2266 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×#10587569C211yesmaximal, characteristic
2C2×#11762702C211yesmaximal, characteristic, complemented
3C2×#11762688C211yesmaximal, characteristic
4C2×C4×#63227C211yesmaximal, characteristic, complemented
5#14527053C211yesmaximal, characteristic, complemented
6#14527031C211yesmaximal, characteristic, complemented
7#14527030C211yesmaximal, characteristic, complemented
8#14527023C211yesmaximal, characteristic
9#14527022C211yesmaximal, characteristic, complemented
10#14527019C211yesmaximal, characteristic, complemented
11#14527017C211yesmaximal, characteristic, complemented
12#14527014C211yesmaximal, characteristic, complemented
13#14527007C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C17C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C2×#10587569—24no—
19C2×#10587569—24no—
20C2×#10587569C418yescomplemented
21C22×C4⋊Dic17C2211yescharacteristic
22C22×C4⋊Dic17C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33#11762702—24no—
34#11762688—24no—
35C4×#63227—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×C22⋊C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C42×C17C2211yescharacteristic
54C22×C42×C17C2211yescharacteristic
55C4×C22⋊C4×C17—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—22no—
64C23×C4×C17—22no—
65C23×C4×C17—41no—
66C23×C4×C17—41no—
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C22×C22⋊D17—22no—
74C22×C22⋊D17—22no—
75C22×C22⋊D17—22no—
76C22×C22⋊D17—22no—
77C22×C22⋊D17—41no—
78C22×C22⋊D17—41no—
79C22×C22⋊D17C2×C414yes—
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C22×C4×D17—22no—
88C22×C4×D17—22no—
89C22×C4×D17—22no—
90C22×C4×D17—22no—
91C22×C4×D17—41no—
92C22×C4×D17—41no—
93C22×C4×D17C2×C414yescomplemented
94C2×C22⋊C4×C17—22no—
95C2×C22⋊C4×C17—22no—
96C2×C22⋊C4×C17—22no—
97C2×C22⋊C4×C17C2×C414yes—
98C2×C22⋊C4×C17D414yes—
99C2×C22⋊C4×C17D414yes—
100C2×C42×C17—22no—
101C2×C42×C17—22no—
102C2×C42×C17—22no—
103C2×C42×C17—22no—
104C2×C42×C17—41no—
105C2×C42×C17—41no—
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—22no—
124C2×#63227—22no—
125C2×#63227—22no—
126C2×#63227—41no—
127C2×#63227—41no—
128C2×#63227C2×C414yescomplemented
129C2×#63227D414yes—
130C2×C4⋊Dic17—22no—
131C2×C4⋊Dic17—22no—
132C2×C4⋊Dic17—22no—
133C2×C4⋊Dic17—22no—
134C2×C4⋊Dic17—41no—
135C2×C4⋊Dic17C2×C414yescomplemented
136C2×#63225—22no—
137C2×#63225—22no—
138C2×#63225C2×C414yescomplemented
139C2×C4×Dic17—22no—
140C2×C4×Dic17—22no—
141C2×C4×Dic17—41no—
142#10587569—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—22no—
153#10587502—22no—
154#10587502—22no—
155#10587502—41no—
156#10587502—41no—
157#10587502—41no—
158#10587502—41no—
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×D17C22×C412yes—
188C23×D17C2×D412yes—
189C23×D17#4112yes—
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—28no—
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—44no—
222C22×C4×C17—44no—
223C22×C4×C17—44no—
224C22×C4×C17—44no—
225C22×C4×C17—44no—
226C22×C4×C17—44no—
227C22×C4×C17C22×C412yes—
228C22×C4×C17C22×C412yes—
229C22×C4×C17C2×D412yes—
230C22×C4×C17C2×D412yes—
231C22×C4×C17C2×D412yes—
232C22×C4×C17C2×D412yes—
233C22×C4×C17C2×D412yes—
234C22×C4×C17#4112yes—
235C22×C4×C17#4112yes—
236C22×C4×C17#4112yes—
237C22×C4×C17#4112yes—
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×Dic17—21no—
289C22×Dic17—21no—
290C22×Dic17C22×C412yes—
291C22×Dic17C22×C412yes—
292C22×Dic17C22×C412yes—
293C22×Dic17C2×D412yes—
294C22×Dic17#4112yes—
295C2×C4×D17—28no—
296C2×C4×D17—28no—
297C2×C4×D17—44no—
298C2×C4×D17—44no—
299C2×C4×D17—44no—
300C2×C4×D17—44no—
301C2×C4×D17—44no—
302C22⋊C4×C17—28no—
303C22⋊C4×C17C22⋊C4116yescomplemented
304C42×C17—44no—
305C42×C17—44no—
306C22⋊Dic17—28no—
307C22⋊Dic17—44no—
308C22⋊Dic17—44no—
309#63227—28no—
310#63227—28no—
311#63227—28no—
312#63227—44no—
313#63227—44no—
314C4⋊Dic17—28no—
315C4⋊Dic17—44no—
316#63225—28no—
317C4×Dic17—44no—
318#14096—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×C17C2×#4111yescharacteristic
362C23×C17C2×#4111yescharacteristic
363C23×C17C2×#4111yescharacteristic
364C23×C17C2×#4111yescharacteristic
365C23×C17H(5,𝔽2)11yescharacteristic
366C23×C17H(5,𝔽2)11yescharacteristic
367C23×C17H(5,𝔽2)11yescharacteristic
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—22no—
377C22×D17—22no—
378C22×D17—22no—
379C22×D17—22no—
380C22×D17—22no—
381C22×D17—22no—
382C22×D17—22no—
383C22×D17—22no—
384C22×D17—22no—
385C22×D17—22no—
386C22×D17—22no—
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×D17C4×D414yes—
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—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—416no—
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×C17C2×C22⋊C414yes—
445C2×C4×C17C2×C22⋊C414yes—
446C2×C4×C17#12314yescomplemented
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—41no—
464C2×Dic17—41no—
465C2×Dic17—41no—
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×Dic17—41no—
497C4×D17—416no—
498C22×#123—171no—
499C2×#388—171no—
500C2×#386—171no—
501C2×C4×C22⋊C4—171no—
502C2×C4×C22⋊C4D1711yescharacteristic, complemented
503#1445—171no—
504#1440—171no—
505#1439—171no—
506#1438—171no—
507#1437—171no—
508#1436—171no—
509#1436—171no—
510C4⋊#95—171no—
511C22⋊#95—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×C17C4×#4111yescharacteristic
532C22×C17C4×#4111yescharacteristic
533C22×C17#51811yescharacteristic
534C22×C17#52011yescharacteristic
535C22×C17C2×#12311yescharacteristic
536C22×C17#52511yescharacteristic
537C22×C17#52511yescharacteristic
538C22×C17#52511yescharacteristic
539C22×C17#52911yescharacteristic
540C22×C17#52911yescharacteristic
541C22×C17#53211yescharacteristic
542C22×C17#53211yescharacteristic
543C22×C17#53811yescharacteristic
544C22×C17#53911yescharacteristic
545C22×C17#54011yescharacteristic
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#54711yescharacteristic
557C22×C17#55111yescharacteristic
558C22×C17#55111yescharacteristic
559C22×C17#55211yescharacteristic
560C22×C17#55311yescharacteristic
561C22×C17#55311yescharacteristic
562C22×C17#55911yescharacteristic
563C2×D17—24no—
564C2×D17—24no—
565C2×D17—24no—
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—
578C4×C17—24no—
579C4×C17—24no—
580C4×C17—24no—
581C4×C17—42no—
582C4×C17—42no—
583C4×C17—42no—
584Dic17—42no—
585Dic17—42no—
586Dic17—42no—
587Dic17—42no—
588Dic17—42no—
589Dic17—81no—
590Dic17—81no—
591C23×D4—171no—
592C24×C4—171no—
593C24×C4C2×D1711yescharacteristic
594C2×#123—178no—
595C2×#123—344no—
596C2×#123—344no—
597C22×C4⋊C4—171no—
598C22×C4⋊C4—171no—
599C22×C4⋊C4—171no—
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⋊C4C2×D1711yescharacteristic
609C22×C22⋊C4C2×D1711yescharacteristic
610C22×C42—171no—
611C22×C42C2×D1711yescharacteristic
612C22×C42C2×D1711yescharacteristic
613#388—344no—
614#386—344no—
615C4×C22⋊C4—24no—
616C4×C22⋊C4—344no—
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#229711yescharacteristic
635C2×C17C4×#12311yescharacteristic
636C2×C17#233511yescharacteristic
637C2×C17D4×C22⋊C411yescharacteristic
638C2×C17#233911yescharacteristic
639C2×C17#235911yescharacteristic
640C2×C17#237411yescharacteristic
641C2×C17#241811yescharacteristic
642C2×C17#242211yescharacteristic
643C2×C17#245511yescharacteristic
644C2×C17#245711yescharacteristic
645C2×C17#246411yescharacteristic
646C2×C17#247011yescharacteristic
647C2×C17#255311yescharacteristic
648C2×C17#255711yescharacteristic
649D17—44no—
650C25—171no—
651C25C22×D1711yescharacteristic
652C22×D4—174no—
653C22×D4—342no—
654C22×D4—342no—
655C22×D4—342no—
656C22×D4—342no—
657C22×D4—681no—
658C22×D4—681no—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—41no—
665C23×C4—41no—
666C23×C4—171no—
667C23×C4—171no—
668C23×C4—171no—
669C23×C4—171no—
670C23×C4—171no—
671C23×C4—174no—
672C23×C4—171no—
673C23×C4—171no—
674C23×C4—342no—
675C23×C4—342no—
676C23×C4—342no—
677C23×C4—342no—
678C23×C4—681no—
679C23×C4—681no—
680C23×C4C22×D1711yescharacteristic
681C23×C4C22×D1711yescharacteristic
682C23×C4C22×D1711yescharacteristic
683C23×C4C22×D1711yescharacteristic
684C23×C4C22×D1711yescharacteristic
685C23×C4C22×D1711yescharacteristic
686#123—3432no—
687C2×C4⋊C4—174no—
688C2×C4⋊C4—174no—
689C2×C4⋊C4—342no—
690C2×C4⋊C4—342no—
691C2×C4⋊C4—342no—
692C2×C4⋊C4—342no—
693C2×C4⋊C4—342no—
694C2×C4⋊C4—342no—
695C2×C4⋊C4—681no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
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—342no—
717C2×C22⋊C4—342no—
718C2×C22⋊C4—342no—
719C2×C22⋊C4—681no—
720C2×C22⋊C4—681no—
721C2×C22⋊C4—681no—
722C2×C22⋊C4—681no—
723C2×C22⋊C4C4×D1714yes—
724C2×C22⋊C4D6814yes—
725C2×C22⋊C4C22⋊D1714yes—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—41no—
731C2×C42—41no—
732C2×C42—342no—
733C2×C42—342no—
734C2×C42—681no—
735#95—22no—
736#95—22no—
737#95—342no—
738#95—342no—
739#95—342no—
740#95—342no—
741#95—342no—
742#95—342no—
743#95—342no—
744#95—342no—
745#95—342no—
746#95—342no—
747#95—681no—
748#95—681no—
749#95—681no—
750#95—681no—
751C17#1409611yescharacteristic, 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—172no—
766C24—172no—
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×D4—348no—
784C2×D4—348no—
785C2×D4—684no—
786C2×D4—684no—
787C2×D4—684no—
788C2×D4—684no—
789C2×D4—684no—
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—21no—
802C22×C4—28no—
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—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—172no—
828C22×C4—172no—
829C22×C4—172no—
830C22×C4—172no—
831C22×C4—172no—
832C22×C4—348no—
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×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—348no—
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—684no—
879C22×C4—684no—
880C22×C4—684no—
881C22×C4—684no—
882C22×C4—684no—
883C22×C4C2×C4×D1712yes—
884C22×C4C2×C4×D1712yes—
885C22×C4C2×D6812yes—
886C22×C4C2×D6812yes—
887C22×C4#6325212yes—
888C22×C4#6325212yes—
889C22×C4#6325212yes—
890C22×C4#6325212yes—
891C22×C4D4×D1712yes—
892C22×C4#6325412yes—
893C22×C4C2×C22⋊D1712yes—
894C22×C4C2×C22⋊D1712yes—
895C4⋊C4—348no—
896C4⋊C4—348no—
897C4⋊C4—684no—
898C22⋊C4—28no—
899C22⋊C4—348no—
900C22⋊C4—348no—
901C22⋊C4—348no—
902C22⋊C4—348no—
903C22⋊C4—684no—
904C22⋊C4—684no—
905C22⋊C4—684no—
906C22⋊C4—684no—
907C22⋊C4#63227116yescomplemented
908C42—44no—
909C42—44no—
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—174no—
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—342no—
960C23—342no—
961C23—342no—
962C23—342no—
963C23—342no—
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×#6325211yescharacteristic
984C23C2×#6325211yescharacteristic
985C23C2×#6325211yescharacteristic
986C23C2×#6325211yescharacteristic
987C23C2×D4×D1711yescharacteristic
988C23C2×#6325411yescharacteristic
989C23#1058769111yescharacteristic
990C23#1058769111yescharacteristic
991C23#41×D1711yescharacteristic
992C23#41×D1711yescharacteristic
993C23#1058769611yescharacteristic
994C23#1058769711yescharacteristic
995C23C22×C22⋊D1711yescharacteristic
996D4—6816no—
997C2×C4—22no—
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—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—416no—
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—342no—
1038C2×C4—342no—
1039C2×C4—342no—
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—6816no—
1053C2×C4—681no—
1054C2×C4—681no—
1055C2×C4—681no—
1056C2×C4—681no—
1057C2×C4—681no—
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#1058756914yescomplemented
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—344no—
1106C22—344no—
1107C22—344no—
1108C22—682no—
1109C22—682no—
1110C22—682no—
1111C22—682no—
1112C22—682no—
1113C22—682no—
1114C22—682no—
1115C22—682no—
1116C22—682no—
1117C22—682no—
1118C22—682no—
1119C22—682no—
1120C22C22×#6322711yescharacteristic
1121C22C4×D4×D1711yescharacteristic
1122C22C4×#6325411yescharacteristic
1123C22C4×#6325211yescharacteristic
1124C22C4×#6325211yescharacteristic
1125C22#1176328111yescharacteristic
1126C22#1176328811yescharacteristic
1127C22C2×#1058756911yescharacteristic
1128C22#1176331811yescharacteristic
1129C22#1176332011yescharacteristic
1130C22#1176332011yescharacteristic
1131C22#1176333711yescharacteristic
1132C22#1176334111yescharacteristic
1133C22#1176335911yescharacteristic
1134C22#1176335911yescharacteristic
1135C22#1176339711yescharacteristic
1136C22#1176340111yescharacteristic
1137C22#1176341011yescharacteristic
1138C22#1176343011yescharacteristic
1139C22D4×C22⋊D1711yescharacteristic
1140C22D4×D6811yescharacteristic
1141C22#1176344711yescharacteristic
1142C22#1176344911yescharacteristic
1143C22#1176345311yescharacteristic
1144C22#1176345411yescharacteristic
1145C22#1176345411yescharacteristic
1146C22#1176345811yescharacteristic
1147C22#1176346311yescharacteristic
1148C22#1176346411yescharacteristic
1149C22#1176348511yescharacteristic
1150C22#1176348811yescharacteristic
1151C22#1176349811yescharacteristic
1152C22#1176350311yescharacteristic
1153C22#1176350511yescharacteristic
1154C22#1176354211yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—682no—
1162C4—682no—
1163C4—682no—
1164C4—682no—
1165C4—682no—
1166C4—1361no—
1167C4—1361no—
1168C2—44no—
1169C2—684no—
1170C2#1453127411yescharacteristic
1171C2C4×#1058756911yescharacteristic
1172C2#1453157611yescharacteristic
1173C2D4×#6322711yescharacteristic
1174C2#1453160911yescharacteristic
1175C2#1453177711yescharacteristic
1176C2#1453191811yescharacteristic
1177C2#1453224611yescharacteristic
1178C2#1453229811yescharacteristic
1179C2#1453266111yescharacteristic
1180C2#1453268511yescharacteristic
1181C2#1453279011yescharacteristic
1182C2#1453287411yescharacteristic
1183C2#1453382311yescharacteristic
1184C2#1453387711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C4×C22⋊C4×C17C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×C4×C22⋊C4D17
hypocenterC17#14096
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11762702C2semidirect
4. C2×C4×#63227C2semidirect
5. #14527053C2semidirect
6. #14527031C2semidirect
7. #14527030C2semidirect
9. #14527022C2semidirect
10. #14527019C2semidirect
11. #14527017C2semidirect
12. #14527014C2semidirect
13. #14527007C2semidirect
14. #14527005C2semidirect
15. C2×C4×C22⋊C4×C17C2semidirect
20. C2×#10587569C4semidirect
93. C22×C4×D17C2×C4semidirect
128. C2×#63227C2×C4semidirect
135. C2×C4⋊Dic17C2×C4semidirect
138. C2×#63225C2×C4semidirect
303. C22⋊C4×C17C22⋊C4semidirect
446. C2×C4×C17#123semidirect
502. C2×C4×C22⋊C4D17semidirect
751. C17#14096semidirect
907. C22⋊C4#63227semidirect
1087. C2×C4#10587569semidirect

Maximal subgroups

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

subgroupindex
C22×#105875692
C2×#117627022
C2×#117626882
C2×C4×#632272
#145270532
#145270312
#145270302
#145270232
#145270222
#145270192
#145270172
#145270142
#145270072
#145270052
C2×C4×C22⋊C4×C172
#1409617