Finite Group Databasebeta

← #16962497

Subgroups — #16962497

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
1C2×#11762716C211yesmaximal, characteristic, complemented
2C2×#11762702C211yesmaximal, characteristic, complemented
3C2×#11762689C211yesmaximal, characteristic
4C2×#11762684C211yesmaximal, characteristic, complemented
5#14527055C211yesmaximal, characteristic, complemented
6#14527033C211yesmaximal, characteristic, complemented
7#14527029C211yesmaximal, characteristic, complemented
8#14527029C211yesmaximal, characteristic, complemented
9#14527029C211yesmaximal, characteristic, complemented
10#14527025C211yesmaximal, characteristic
11#14527021C211yesmaximal, characteristic, complemented
12#14527014C211yesmaximal, characteristic, complemented
13#14527011C211yesmaximal, characteristic, complemented
14#14527006C211yesmaximal, characteristic, complemented
15C22×C17×#124C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28#11762716—24no—
29#11762702—24no—
30#11762689—24no—
31#11762684—24no—
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
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C23×Q8×C17C2211yescharacteristic
49C23×D4×C17C2211yescharacteristic
50C2×C17×#124—24no—
51C2×C17×#124—24no—
52C2×C17×#124C418yescomplemented
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C22×C22⋊C4×C17C2211yescharacteristic
56C22×C22⋊C4×C17C2211yescharacteristic
57C22×C42×C17C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C25×C17C2311yescharacteristic
60C22×Q8×C17—22no—
61C22×Q8×C17—22no—
62C22×Q8×C17—22no—
63C22×Q8×C17—22no—
64C22×Q8×C17—41no—
65C22×Q8×C17—41no—
66C22×Q8×C17C2×C414yescomplemented
67C22×D4×C17—22no—
68C22×D4×C17—22no—
69C22×D4×C17—22no—
70C22×D4×C17—22no—
71C22×D4×C17—41no—
72C22×D4×C17—41no—
73C22×D4×C17C2×C414yes—
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C23×Dic17—22no—
80C23×Dic17—22no—
81C23×Dic17—22no—
82C23×Dic17—41no—
83C23×Dic17—41no—
84C23×Dic17—41no—
85C23×Dic17—41no—
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C23×Dic17C2311yescharacteristic
90C23×Dic17C2311yescharacteristic
91C23×Dic17C2311yescharacteristic
92C23×Dic17C2311yescharacteristic
93C23×Dic17C2311yescharacteristic
94C17×#124—232no—
95C2×C22⋊C4×C17—22no—
96C2×C22⋊C4×C17—22no—
97C2×C22⋊C4×C17—22no—
98C2×C22⋊C4×C17—22no—
99C2×C22⋊C4×C17—22no—
100C2×C22⋊C4×C17—22no—
101C2×C22⋊C4×C17C2×C414yes—
102C2×C22⋊C4×C17C2×C414yes—
103C2×C22⋊C4×C17C2×C414yescomplemented
104C2×C22⋊C4×C17C2×C414yescomplemented
105C2×C22⋊C4×C17D414yes—
106C2×C22⋊C4×C17D414yes—
107C2×C42×C17—22no—
108C2×C42×C17—22no—
109C2×C42×C17C2×C414yescomplemented
110C2×C22⋊Dic17—22no—
111C2×C22⋊Dic17—22no—
112C2×C22⋊Dic17—22no—
113C2×C22⋊Dic17—22no—
114C2×C22⋊Dic17—22no—
115C2×C22⋊Dic17—22no—
116C2×C22⋊Dic17—22no—
117C2×C22⋊Dic17—22no—
118C2×C22⋊Dic17—22no—
119C2×C22⋊Dic17—41no—
120C2×C22⋊Dic17—41no—
121C2×C22⋊Dic17—41no—
122C2×C22⋊Dic17—41no—
123C2×C22⋊Dic17—41no—
124C2×C22⋊Dic17—41no—
125C2×C22⋊Dic17—41no—
126C2×C22⋊Dic17—41no—
127C2×C22⋊Dic17—41no—
128C2×C22⋊Dic17—41no—
129C2×C22⋊Dic17—41no—
130C2×C22⋊Dic17—41no—
131C2×C4⋊Dic17—22no—
132C2×C4⋊Dic17—22no—
133C2×C4⋊Dic17—22no—
134C2×C4⋊Dic17—22no—
135C2×C4⋊Dic17—22no—
136C2×C4⋊Dic17—22no—
137C2×C4⋊Dic17—41no—
138C2×C4⋊Dic17—41no—
139C2×C4⋊Dic17—41no—
140C2×C4×Dic17—22no—
141C2×C4×Dic17—22no—
142C2×C4×Dic17—41no—
143#10587502—22no—
144#10587502—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×C17—21no—
172C24×C17—21no—
173C24×C17—21no—
174C24×C17—21no—
175C24×C17—21no—
176C24×C17—21no—
177C24×C17—21no—
178C24×C17—21no—
179C24×C17—21no—
180C24×C17—21no—
181C24×C17—21no—
182C24×C17—21no—
183C24×C17—21no—
184C24×C17—21no—
185C24×C17C22×C412yes—
186C24×C17C22×C412yes—
187C24×C17C2×D412yes—
188C24×C17C2×D412yes—
189C24×C17C2411yescharacteristic
190C2×Q8×C17—28no—
191C2×Q8×C17—28no—
192C2×Q8×C17—44no—
193C2×Q8×C17—44no—
194C2×Q8×C17—44no—
195C2×Q8×C17—44no—
196C2×Q8×C17—44no—
197C2×D4×C17—28no—
198C2×D4×C17—28no—
199C2×D4×C17—44no—
200C2×D4×C17—44no—
201C2×D4×C17—44no—
202C2×D4×C17—44no—
203C2×D4×C17—44no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17—21no—
226C22×C4×C17—21no—
227C22×C4×C17—21no—
228C22×C4×C17C22×C412yes—
229C22×C4×C17C22×C412yes—
230C22×C4×C17C22×C412yes—
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—
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×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×Dic17—21no—
291C22×Dic17—44no—
292C22×Dic17—44no—
293C22×Dic17—44no—
294C22×Dic17—44no—
295C22×Dic17—44no—
296C22×Dic17—44no—
297C22×Dic17—44no—
298C22×Dic17C2×D412yes—
299C22×Dic17C2×D412yes—
300C22×Dic17#4112yes—
301C22×Dic17#4112yes—
302C22⋊C4×C17—28no—
303C22⋊C4×C17—28no—
304C22⋊C4×C17—28no—
305C22⋊C4×C17C22⋊C4116yescomplemented
306C42×C17—28no—
307C22⋊Dic17—44no—
308C22⋊Dic17—44no—
309C22⋊Dic17—44no—
310C22⋊Dic17—44no—
311C22⋊Dic17—44no—
312C22⋊Dic17—44no—
313C22⋊Dic17—44no—
314C4⋊Dic17—44no—
315C4⋊Dic17—44no—
316C4⋊Dic17—44no—
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—22no—
338C23×C17—22no—
339C23×C17—22no—
340C23×C17—22no—
341C23×C17—22no—
342C23×C17—22no—
343C23×C17—22no—
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×C17—41no—
354C23×C17—41no—
355C23×C17—41no—
356C23×C17—41no—
357C23×C17—41no—
358C23×C17—41no—
359C23×C17—41no—
360C23×C17—41no—
361C23×C17—41no—
362C23×C17—41no—
363C23×C17—41no—
364C23×C17—41no—
365C23×C17—41no—
366C23×C17—41no—
367C23×C17—41no—
368C23×C17—41no—
369C23×C17—41no—
370C23×C17—41no—
371C23×C17—41no—
372C23×C17—41no—
373C23×C17—41no—
374C23×C17—41no—
375C23×C17—41no—
376C23×C17—41no—
377C23×C17—41no—
378C23×C17—41no—
379C23×C17—41no—
380C23×C17—41no—
381C23×C17—41no—
382C23×C17—41no—
383C23×C17—41no—
384C23×C17—41no—
385C23×C17—41no—
386C23×C17—41no—
387C23×C17—41no—
388C23×C17C2×C22⋊C414yes—
389C23×C17C23×C411yescharacteristic
390C23×C17C22×D411yescharacteristic
391C23×C17C22×D411yescharacteristic
392C23×C17C22×D411yescharacteristic
393C23×C17C2×#4111yescharacteristic
394C23×C17C2×#4111yescharacteristic
395C23×C17C2×#4111yescharacteristic
396C23×C17H(5,𝔽2)11yescharacteristic
397C23×C17H(5,𝔽2)11yescharacteristic
398C23×C17H(5,𝔽2)11yescharacteristic
399C23×C17H(5,𝔽2)11yescharacteristic
400C23×C17H(5,𝔽2)11yescharacteristic
401C23×C172−1+411yescharacteristic
402C23×C172−1+411yescharacteristic
403C23×C172−1+411yescharacteristic
404Q8×C17—416no—
405D4×C17—416no—
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—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×C17C2×C22⋊C414yes—
439C2×C4×C17C2×C22⋊C414yes—
440C2×C4×C17C4×D414yes—
441C2×Dic17—22no—
442C2×Dic17—22no—
443C2×Dic17—22no—
444C2×Dic17—22no—
445C2×Dic17—22no—
446C2×Dic17—22no—
447C2×Dic17—22no—
448C2×Dic17—22no—
449C2×Dic17—22no—
450C2×Dic17—22no—
451C2×Dic17—22no—
452C2×Dic17—22no—
453C2×Dic17—416no—
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—41no—
472C2×Dic17—41no—
473C2×Dic17—41no—
474C2×Dic17—41no—
475C2×Dic17—41no—
476C2×Dic17—41no—
477C2×Dic17—41no—
478C2×Dic17—41no—
479C2×Dic17—41no—
480C2×Dic17—41no—
481C2×Dic17—41no—
482C2×Dic17—41no—
483C2×Dic17—41no—
484C2×Dic17—41no—
485C2×Dic17—41no—
486C2×Dic17—41no—
487C2×Dic17—41no—
488C2×Dic17—41no—
489C2×Dic17—41no—
490C2×Dic17—41no—
491C2×Dic17—41no—
492C2×Dic17—41no—
493C2×Dic17—41no—
494C2×Dic17—41no—
495C2×Dic17—41no—
496C2×Dic17—41no—
497C2×Dic17—41no—
498C22×#124D1711yescharacteristic
499C2×#391—171no—
500C2×#388—171no—
501C2×#386—171no—
502C2×#385—171no—
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×C17—42no—
529C22×C17—42no—
530C22×C17—42no—
531C22×C17—42no—
532C22×C17—42no—
533C22×C17—42no—
534C22×C17—42no—
535C22×C17—81no—
536C22×C17—81no—
537C22×C17—81no—
538C22×C17—81no—
539C22×C17—81no—
540C22×C17—81no—
541C22×C17—81no—
542C22×C17—81no—
543C22×C17C22×C22⋊C411yescharacteristic
544C22×C17C2×C4×D411yescharacteristic
545C22×C17C4×#4111yescharacteristic
546C22×C17#51811yescharacteristic
547C22×C17#52011yescharacteristic
548C22×C17#52011yescharacteristic
549C22×C17#52011yescharacteristic
550C22×C17#53511yescharacteristic
551C22×C17#53511yescharacteristic
552C22×C17#53611yescharacteristic
553C22×C17#53611yescharacteristic
554C22×C17#53711yescharacteristic
555C22×C17#53711yescharacteristic
556C22×C17#53811yescharacteristic
557C22×C17#53811yescharacteristic
558C22×C17#54211yescharacteristic
559C22×C17#54211yescharacteristic
560C22×C17#54211yescharacteristic
561C22×C17#54211yescharacteristic
562C22×C17D4211yescharacteristic
563C22×C17D4211yescharacteristic
564C22×C17#54611yescharacteristic
565C22×C17#54611yescharacteristic
566C22×C17#54611yescharacteristic
567C22×C17#54611yescharacteristic
568C22×C17#54611yescharacteristic
569C22×C17#54711yescharacteristic
570C22×C17#54711yescharacteristic
571C22×C17#54811yescharacteristic
572C22×C17#55611yescharacteristic
573C22×C17#55911yescharacteristic
574C22×C17H(3,𝔽4)11yescharacteristic
575C22×C17#56211yescharacteristic
576C22×C17#56211yescharacteristic
577C22×C17#56311yescharacteristic
578C4×C17—24no—
579C4×C17—24no—
580C4×C17—24no—
581C4×C17—42no—
582C4×C17—42no—
583Dic17—42no—
584Dic17—42no—
585Dic17—42no—
586Dic17—42no—
587Dic17—81no—
588Dic17—81no—
589Dic17—81no—
590Dic17—81no—
591C23×Q8C2×D1711yescharacteristic
592C23×D4C2×D1711yescharacteristic
593C24×C4—171no—
594C2×#124—24no—
595C2×#124—24no—
596C2×#124Dic1718yescomplemented
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⋊C4C2×D1711yescharacteristic
608C22×C22⋊C4C2×D1711yescharacteristic
609C22×C22⋊C4C2×D1711yescharacteristic
610C22×C22⋊C4C2×D1711yescharacteristic
611C22×C42—171no—
612C22×C42C2×D1711yescharacteristic
613#391—344no—
614#388—344no—
615#386—344no—
616#385—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×#95—171no—
632C2×#95—171no—
633C2×C17—44no—
634C2×C17—82no—
635C2×C17#231111yescharacteristic
636C2×C17#232611yescharacteristic
637C2×C17#233711yescharacteristic
638C2×C17D4×C22⋊C411yescharacteristic
639C2×C17#233911yescharacteristic
640C2×C17#236711yescharacteristic
641C2×C17#237911yescharacteristic
642C2×C17#267011yescharacteristic
643C2×C17#267211yescharacteristic
644C2×C17#267411yescharacteristic
645C2×C17#267611yescharacteristic
646C2×C17#270011yescharacteristic
647C2×C17#271011yescharacteristic
648C2×C17#271211yescharacteristic
649C2×C17#271511yescharacteristic
650C25C22×D1711yescharacteristic
651C25C22×D1711yescharacteristic
652C22×Q8—22no—
653C22×Q8—22no—
654C22×Q8—22no—
655C22×Q8—22no—
656C22×Q8—41no—
657C22×Q8—41no—
658C22×Q8C2×Dic1714yescomplemented
659C22×D4—22no—
660C22×D4—22no—
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—41no—
664C22×D4—41no—
665C22×D4C2×Dic1714yes—
666C23×C4—171no—
667C23×C4—171no—
668C23×C4—171no—
669C23×C4—171no—
670C23×C4—171no—
671C23×C4—171no—
672C23×C4—171no—
673C23×C4—171no—
674C23×C4—342no—
675C23×C4—342no—
676C23×C4—342no—
677C23×C4—681no—
678C23×C4—681no—
679C23×C4—681no—
680C23×C4—681no—
681C23×C4C22×D1711yescharacteristic
682C23×C4C22×D1711yescharacteristic
683C23×C4C22×D1711yescharacteristic
684C23×C4C22×D1711yescharacteristic
685C23×C4C22×D1711yescharacteristic
686#124—232no—
687C2×C4⋊C4—342no—
688C2×C4⋊C4—342no—
689C2×C4⋊C4—342no—
690C2×C4⋊C4—342no—
691C2×C4⋊C4—342no—
692C2×C4⋊C4—342no—
693C2×C4⋊C4—681no—
694C2×C4⋊C4—681no—
695C2×C4⋊C4—681no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
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—681no—
712C2×C22⋊C4—681no—
713C2×C22⋊C4—681no—
714C2×C22⋊C4—681no—
715C2×C22⋊C4—681no—
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⋊C4C2×Dic1714yes—
724C2×C22⋊C4C2×Dic1714yes—
725C2×C22⋊C4C2×Dic1714yescomplemented
726C2×C22⋊C4C2×Dic1714yescomplemented
727C2×C22⋊C4C22⋊D1714yes—
728C2×C22⋊C4C22⋊D1714yes—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—342no—
732C2×C42—342no—
733C2×C42—681no—
734C2×C42C2×Dic1714yescomplemented
735#95—174no—
736#95—342no—
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—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—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24C22×Dic1712yes—
779C24C22×Dic1712yes—
780C24C2×C22⋊D1712yes—
781C24C2×C22⋊D1712yes—
782C24C23×D1711yescharacteristic
783C2×Q8—28no—
784C2×Q8—28no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×D4—28no—
791C2×D4—28no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
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—172no—
822C22×C4—172no—
823C22×C4—172no—
824C22×C4—172no—
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×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—684no—
878C22×C4—684no—
879C22×C4—684no—
880C22×C4—684no—
881C22×C4—684no—
882C22×C4—684no—
883C22×C4—684no—
884C22×C4D4×D1712yes—
885C22×C4#6325412yes—
886C22×C4C22×Dic1712yes—
887C22×C4C22×Dic1712yes—
888C22×C4C22×Dic1712yes—
889C22×C4C22×Dic1712yes—
890C22×C4C22×Dic1712yes—
891C22×C4C2×C22⋊D1712yes—
892C22×C4C2×C22⋊D1712yes—
893C22×C4C2×C22⋊D1712yes—
894C22×C4C2×C22⋊D1712yes—
895C4⋊C4—684no—
896C4⋊C4—684no—
897C4⋊C4—684no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—684no—
902C22⋊C4—684no—
903C22⋊C4—684no—
904C22⋊C4—684no—
905C22⋊C4—684no—
906C22⋊C4—684no—
907C22⋊C4—684no—
908C22⋊C4C22⋊Dic17116yescomplemented
909C42—28no—
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—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23C2×C22⋊Dic1714yes—
981C23C2×D4×D1711yescharacteristic
982C23C2×#6325411yescharacteristic
983C23#1058769111yescharacteristic
984C23#1058769111yescharacteristic
985C23#41×D1711yescharacteristic
986C23#41×D1711yescharacteristic
987C23#1058769611yescharacteristic
988C23#1058769611yescharacteristic
989C23#1058769611yescharacteristic
990C23#1058769711yescharacteristic
991C23#1058769711yescharacteristic
992C23#1058769711yescharacteristic
993C23C23×Dic1711yescharacteristic
994C23C22×C22⋊D1711yescharacteristic
995C23C22×C22⋊D1711yescharacteristic
996Q8—416no—
997D4—416no—
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—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—342no—
1031C2×C4—342no—
1032C2×C4—342no—
1033C2×C4—342no—
1034C2×C4—342no—
1035C2×C4—342no—
1036C2×C4—342no—
1037C2×C4—342no—
1038C2×C4—342no—
1039C2×C4—342no—
1040C2×C4—342no—
1041C2×C4—342no—
1042C2×C4—6816no—
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—
1052C2×C4—681no—
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×C4D4×Dic1714yes—
1088C2×C4C2×C22⋊Dic1714yes—
1089C2×C4C2×C22⋊Dic1714yes—
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—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22C22×C22⋊Dic1711yescharacteristic
1121C22C2×D4×Dic1711yescharacteristic
1122C22#41×Dic1711yescharacteristic
1123C22#1176328411yescharacteristic
1124C22#1176329211yescharacteristic
1125C22#1176329211yescharacteristic
1126C22#1176329211yescharacteristic
1127C22#1176337311yescharacteristic
1128C22#1176337711yescharacteristic
1129C22#1176337911yescharacteristic
1130C22#1176338011yescharacteristic
1131C22#1176338711yescharacteristic
1132C22#1176338711yescharacteristic
1133C22#1176339311yescharacteristic
1134C22#1176339311yescharacteristic
1135C22#1176342311yescharacteristic
1136C22#1176342311yescharacteristic
1137C22#1176342811yescharacteristic
1138C22#1176342811yescharacteristic
1139C22D4×C22⋊D1711yescharacteristic
1140C22D4×C22⋊D1711yescharacteristic
1141C22#1176344711yescharacteristic
1142C22#1176344711yescharacteristic
1143C22#1176345211yescharacteristic
1144C22#1176345311yescharacteristic
1145C22#1176345311yescharacteristic
1146C22#1176345811yescharacteristic
1147C22#1176345811yescharacteristic
1148C22#1176346711yescharacteristic
1149C22#1176352811yescharacteristic
1150C22#1176354111yescharacteristic
1151C22#1176355111yescharacteristic
1152C22#1176355311yescharacteristic
1153C22#1176355311yescharacteristic
1154C22#1176355911yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—682no—
1161C4—682no—
1162C4—682no—
1163C4—682no—
1164C4—1361no—
1165C4—1361no—
1166C4—1361no—
1167C4—1361no—
1168C2—44no—
1169C2—82no—
1170C2#1453137611yescharacteristic
1171C2#1453149711yescharacteristic
1172C2#1453159911yescharacteristic
1173C2D4×C22⋊Dic1711yescharacteristic
1174C2#1453161411yescharacteristic
1175C2#1453185911yescharacteristic
1176C2#1453195811yescharacteristic
1177C2#1453500511yescharacteristic
1178C2#1453503011yescharacteristic
1179C2#1453505911yescharacteristic
1180C2#1453508011yescharacteristic
1181C2#1453537611yescharacteristic
1182C2#1453552011yescharacteristic
1183C2#1453555011yescharacteristic
1184C2#1453558911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC22×C17×#124C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC22×#124D17
hypocenterC17#14421
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C2×#11762716C2semidirect
2. C2×#11762702C2semidirect
4. C2×#11762684C2semidirect
5. #14527055C2semidirect
6. #14527033C2semidirect
7. #14527029C2semidirect
8. #14527029C2semidirect
9. #14527029C2semidirect
11. #14527021C2semidirect
12. #14527014C2semidirect
13. #14527011C2semidirect
14. #14527006C2semidirect
52. C2×C17×#124C4semidirect
66. C22×Q8×C17C2×C4semidirect
103. C2×C22⋊C4×C17C2×C4semidirect
104. C2×C22⋊C4×C17C2×C4semidirect
109. C2×C42×C17C2×C4semidirect
305. C22⋊C4×C17C22⋊C4semidirect
596. C2×#124Dic17semidirect
658. C22×Q8C2×Dic17semidirect
725. C2×C22⋊C4C2×Dic17semidirect
726. C2×C22⋊C4C2×Dic17semidirect
734. C2×C42C2×Dic17semidirect
751. C17#14421semidirect
908. C22⋊C4C22⋊Dic17semidirect

Maximal subgroups

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

subgroupindex
C2×#117627162
C2×#117627022
C2×#117626892
C2×#117626842
#145270552
#145270332
#145270292
#145270252
#145270212
#145270142
#145270112
#145270062
C22×C17×#1242
#1442117