Finite Group Databasebeta

← #16958804

Subgroups — #16958804

Order 4352.

2206 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×#10587633C211yesmaximal, characteristic
2C2×#11762699C211yesmaximal, characteristic, complemented
3C2×#11762687C211yesmaximal, characteristic
4C2×C4×#63227C211yesmaximal, characteristic, complemented
5#14527055C211yesmaximal, characteristic, complemented
6#14527032C211yesmaximal, characteristic, complemented
7#14527026C211yesmaximal, characteristic, complemented
8#14527024C211yesmaximal, characteristic
9#14527022C211yesmaximal, characteristic, complemented
10#14527020C211yesmaximal, characteristic, complemented
11#14527020C211yesmaximal, characteristic, complemented
12#14527010C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#95×Dic17C211yesmaximal, characteristic, complemented
15C2×C17×#391C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C2×#10587633—24no—
19C2×#10587633—24no—
20C2×#10587633C418yescomplemented
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35#11762699—24no—
36#11762687—24no—
37C4×#63227—24no—
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C23×Q8×C17C2211yescharacteristic
51C22×C4⋊C4×C17C2211yescharacteristic
52C22×C42×C17C2211yescharacteristic
53C17×#391—24no—
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C24×D17C2311yescharacteristic
59C24×D17C2311yescharacteristic
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
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C22×D68—22no—
81C22×D68—22no—
82C22×D68—22no—
83C22×D68—22no—
84C22×D68—41no—
85C22×D68—41no—
86C22×D68C2×C414yes—
87C22×C4×D17—22no—
88C22×C4×D17—22no—
89C22×C4×D17—22no—
90C22×C4×D17—22no—
91C22×C4×D17—22no—
92C22×C4×D17—41no—
93C22×C4×D17—41no—
94C2×C4⋊C4×C17—22no—
95C2×C4⋊C4×C17—22no—
96C2×C4⋊C4×C17—41no—
97C2×C42×C17—22no—
98C2×C42×C17—22no—
99C2×C42×C17—41no—
100#10587633—232no—
101C2×#63227—22no—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227—22no—
105C2×#63227—22no—
106C2×#63227—22no—
107C2×#63227—22no—
108C2×#63227—22no—
109C2×#63227—22no—
110C2×#63227—22no—
111C2×#63227—22no—
112C2×#63227—22no—
113C2×#63227—22no—
114C2×#63227—22no—
115C2×#63227—22no—
116C2×#63227—22no—
117C2×#63227—22no—
118C2×#63227—22no—
119C2×#63227—22no—
120C2×#63227—22no—
121C2×#63227—22no—
122C2×#63227—41no—
123C2×#63227—41no—
124C2×#63227—41no—
125C2×#63227—41no—
126C2×#63227—41no—
127C2×#63227—41no—
128C2×#63227C2×C414yes—
129C2×#63227C2×C414yes—
130C2×#63227C2×C414yescomplemented
131C2×#63227C2×C414yescomplemented
132C2×#63227D414yes—
133C2×#63227D414yes—
134C2×C4×Dic17—22no—
135C2×C4×Dic17—22no—
136C2×C4×Dic17—22no—
137C2×C4×Dic17—22no—
138C2×C4×Dic17—22no—
139C2×C4×Dic17—22no—
140C2×C4×Dic17—41no—
141C2×C4×Dic17—41no—
142C2×C4×Dic17C2×C414yescomplemented
143C17×#95—22no—
144C17×#95—22no—
145C17×#95—22no—
146C17×#95D414yes—
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—22no—
156#10587502—22no—
157#10587502—41no—
158#10587502—41no—
159C24×C17C2411yescharacteristic
160C23×D17—21no—
161C23×D17—21no—
162C23×D17—21no—
163C23×D17—21no—
164C23×D17—21no—
165C23×D17—21no—
166C23×D17—21no—
167C23×D17—21no—
168C23×D17—21no—
169C23×D17—21no—
170C23×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×D17—21no—
183C23×D17—21no—
184C23×D17—21no—
185C23×D17—21no—
186C23×D17C22×C412yes—
187C23×D17C22×C412yes—
188C23×D17C2×D412yes—
189C23×D17C2×D412yes—
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—
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—21no—
225C22×C4×C17—21no—
226C22×C4×C17—21no—
227C22×C4×C17—21no—
228C22×C4×C17—21no—
229C22×C4×C17—21no—
230C22×C4×C17—21no—
231C22×C4×C17—21no—
232C22×C4×C17—21no—
233C22×C4×C17—21no—
234C22×C4×C17C22×C412yes—
235C22×C4×C17C22×C412yes—
236C22×C4×C17C22×C412yes—
237C22×C4×C17C2×D412yes—
238C22×C4×C17C2×D412yes—
239C22×C4×C17C2×D412yes—
240C22×C4×C17C2×D412yes—
241C22×C4×C17C2×D412yes—
242C22×C4×C17#4112yes—
243C22×C4×C17#4112yes—
244C22×C4×C17#4112yes—
245C22×C4×C17#4112yes—
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×Dic17C22×C412yes—
282C22×Dic17C22×C412yes—
283C22×Dic17C2×D412yes—
284C22×Dic17C2×D412yes—
285C22×Dic17#4112yes—
286C22×Dic17#4112yes—
287C22×Dic17#4112yes—
288C2×D68—28no—
289C2×D68—28no—
290C2×D68—44no—
291C2×D68—44no—
292C2×D68—44no—
293C2×D68—44no—
294C2×D68—44no—
295C2×C4×D17—28no—
296C2×C4×D17—44no—
297C2×C4×D17—44no—
298C2×C4×D17—44no—
299C2×C4×D17—44no—
300C2×C4×D17—44no—
301C2×C4×D17—44no—
302C4⋊C4×C17—44no—
303C42×C17—44no—
304#63227—28no—
305#63227—28no—
306#63227—28no—
307#63227—28no—
308#63227—44no—
309#63227—44no—
310#63227—44no—
311#63227—44no—
312#63227—44no—
313#63227—44no—
314#63227C22⋊C4116yescomplemented
315C4×Dic17—28no—
316C4×Dic17—44no—
317C4×Dic17—44no—
318#14098—171nomaximal, Sylow
319C23×C17C23×C411yescharacteristic
320C23×C17C22×D411yescharacteristic
321C23×C17C22×D411yescharacteristic
322C23×C17C22×D411yescharacteristic
323C23×C17C2×#4111yescharacteristic
324C23×C17C2×#4111yescharacteristic
325C23×C17C2×#4111yescharacteristic
326C23×C17C2×#4111yescharacteristic
327C23×C17C2×#4111yescharacteristic
328C23×C17C2×#4111yescharacteristic
329C23×C17C2×#4111yescharacteristic
330C23×C17H(5,𝔽2)11yescharacteristic
331C23×C17H(5,𝔽2)11yescharacteristic
332C23×C17H(5,𝔽2)11yescharacteristic
333C23×C172−1+411yescharacteristic
334C22×D17—22no—
335C22×D17—22no—
336C22×D17—22no—
337C22×D17—22no—
338C22×D17—22no—
339C22×D17—22no—
340C22×D17—22no—
341C22×D17—22no—
342C22×D17—22no—
343C22×D17—22no—
344C22×D17—22no—
345C22×D17—22no—
346C22×D17—22no—
347C22×D17—22no—
348C22×D17—22no—
349C22×D17—22no—
350C22×D17—22no—
351C22×D17—22no—
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—
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×D17C2×C22⋊C414yes—
404Q8×C17—416no—
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—22no—
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×C17—41no—
446C2×C4×C17—41no—
447C2×C4×C17—41no—
448C2×C4×C17—41no—
449C2×C4×C17—41no—
450C2×C4×C17—41no—
451C2×C4×C17C2×C22⋊C414yes—
452C2×C4×C17C4×D414yes—
453C2×C4×C17#12414yescomplemented
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—22no—
467C2×Dic17—22no—
468C2×Dic17—22no—
469C2×Dic17—22no—
470C2×Dic17—22no—
471C2×Dic17—22no—
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×Dic17C2×C22⋊C414yes—
496D68—416no—
497C4×D17—416no—
498C22×#124—171no—
499C2×#391D1711yescharacteristic, complemented
500C2×#388—171no—
501C2×#386—171no—
502C2×C4×C22⋊C4—171no—
503#1446—171no—
504#1440—171no—
505#1439—171no—
506#1438—171no—
507#1437—171no—
508#1437—171no—
509#1437—171no—
510#1434—171no—
511C22⋊#95—171no—
512C4×#95—171no—
513C22×C17C22×C22⋊C411yescharacteristic
514C22×C17C2×C4×D411yescharacteristic
515C22×C17C4×#4111yescharacteristic
516C22×C17C4×#4111yescharacteristic
517C22×C17C4×#4111yescharacteristic
518C22×C17#51811yescharacteristic
519C22×C17#52011yescharacteristic
520C22×C17#52511yescharacteristic
521C22×C17#52511yescharacteristic
522C22×C17C2×#12411yescharacteristic
523C22×C17#52911yescharacteristic
524C22×C17#52911yescharacteristic
525C22×C17#53211yescharacteristic
526C22×C17#53211yescharacteristic
527C22×C17#53211yescharacteristic
528C22×C17#53811yescharacteristic
529C22×C17#53811yescharacteristic
530C22×C17#54211yescharacteristic
531C22×C17#54211yescharacteristic
532C22×C17D4211yescharacteristic
533C22×C17D4211yescharacteristic
534C22×C17#54611yescharacteristic
535C22×C17#54611yescharacteristic
536C22×C17#54611yescharacteristic
537C22×C17#54611yescharacteristic
538C22×C17#54611yescharacteristic
539C22×C17#54711yescharacteristic
540C22×C17#54711yescharacteristic
541C22×C17#54811yescharacteristic
542C22×C17#55111yescharacteristic
543C22×C17#55111yescharacteristic
544C22×C17#55511yescharacteristic
545C22×C17#55511yescharacteristic
546C22×C17#55611yescharacteristic
547C22×C17#55911yescharacteristic
548C2×D17—24no—
549C2×D17—24no—
550C2×D17—24no—
551C2×D17—42no—
552C2×D17—42no—
553C2×D17—42no—
554C2×D17—42no—
555C2×D17—42no—
556C2×D17—42no—
557C2×D17—42no—
558C2×D17—42no—
559C2×D17—42no—
560C2×D17—42no—
561C2×D17—42no—
562C2×D17—42no—
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—24no—
581C4×C17—42no—
582C4×C17—42no—
583C4×C17—42no—
584C4×C17—81no—
585Dic17—24no—
586Dic17—42no—
587Dic17—42no—
588Dic17—42no—
589Dic17—42no—
590Dic17—81no—
591C23×Q8C2×D1711yescharacteristic
592C23×D4—171no—
593C24×C4—171no—
594C2×#124—178no—
595C2×#124—344no—
596C2×#124—344no—
597C22×C4⋊C4C2×D1711yescharacteristic
598C22×C22⋊C4—171no—
599C22×C22⋊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⋊C4—171no—
609C22×C42—171no—
610C22×C42—171no—
611C22×C42—171no—
612C22×C42C2×D1711yescharacteristic
613#391—24no—
614#388—344no—
615#386—344no—
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×#95C2×D1711yescharacteristic
630C2×#95C2×D1711yescharacteristic
631C2×#95C2×D1711yescharacteristic
632C2×#95C2×D1711yescharacteristic
633C2×C17#229711yescharacteristic
634C2×C17C4×#12411yescharacteristic
635C2×C17#233711yescharacteristic
636C2×C17D4×C22⋊C411yescharacteristic
637C2×C17#233911yescharacteristic
638C2×C17#236711yescharacteristic
639C2×C17#237211yescharacteristic
640C2×C17#245911yescharacteristic
641C2×C17#246111yescharacteristic
642C2×C17#247211yescharacteristic
643C2×C17#247411yescharacteristic
644C2×C17#249111yescharacteristic
645C2×C17#252111yescharacteristic
646C2×C17#255511yescharacteristic
647C2×C17#255711yescharacteristic
648D17—44no—
649D17—82no—
650C25—171no—
651C25—171no—
652C22×Q8—22no—
653C22×Q8—22no—
654C22×Q8—22no—
655C22×Q8—22no—
656C22×Q8—41no—
657C22×Q8—41no—
658C22×Q8C4×D1714yescomplemented
659C22×D4—174no—
660C22×D4—342no—
661C22×D4—342no—
662C22×D4—342no—
663C22×D4—342no—
664C22×D4—681no—
665C22×D4—681no—
666C23×C4—171no—
667C23×C4—171no—
668C23×C4—171no—
669C23×C4—171no—
670C23×C4—171no—
671C23×C4—171no—
672C23×C4—342no—
673C23×C4—342no—
674C23×C4—342no—
675C23×C4—342no—
676C23×C4—342no—
677C23×C4—681no—
678C23×C4—681no—
679C23×C4C22×D1711yescharacteristic
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—41no—
690C2×C22⋊C4—174no—
691C2×C22⋊C4—174no—
692C2×C22⋊C4—174no—
693C2×C22⋊C4—174no—
694C2×C22⋊C4—174no—
695C2×C22⋊C4—174no—
696C2×C22⋊C4—342no—
697C2×C22⋊C4—342no—
698C2×C22⋊C4—342no—
699C2×C22⋊C4—342no—
700C2×C22⋊C4—342no—
701C2×C22⋊C4—342no—
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—681no—
718C2×C22⋊C4—681no—
719C2×C22⋊C4—681no—
720C2×C22⋊C4—681no—
721C2×C22⋊C4—681no—
722C2×C22⋊C4—681no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—41no—
726C2×C42—174no—
727C2×C42—342no—
728C2×C42—342no—
729C2×C42—342no—
730C2×C42—342no—
731C2×C42—342no—
732C2×C42—342no—
733C2×C42—681no—
734C2×C42—681no—
735#95—22no—
736#95—22no—
737#95—22no—
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—342no—
748#95—681no—
749#95—681no—
750#95C22⋊D1714yes—
751C17#1409811yescharacteristic, complemented, Sylow
752C24—172no—
753C24—172no—
754C24—172no—
755C24—172no—
756C24—341no—
757C24—341no—
758C24—341no—
759C24—341no—
760C24—341no—
761C24—341no—
762C24—341no—
763C24—341no—
764C24—341no—
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—
779C24—341no—
780C24—341no—
781C24—341no—
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—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—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—172no—
835C22×C4—172no—
836C22×C4—172no—
837C22×C4—172no—
838C22×C4—172no—
839C22×C4—172no—
840C22×C4—172no—
841C22×C4—348no—
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×C4C2×C4×D1712yes—
884C22×C4C2×C4×D1712yes—
885C22×C4C2×C4×D1712yes—
886C22×C4#6325212yes—
887C22×C4D4×D1712yes—
888C22×C4D4×D1712yes—
889C22×C4#6325612yes—
890C22×C4#6325612yes—
891C22×C4#6325612yes—
892C22×C4C2×C22⋊D1712yes—
893C22×C4C2×C22⋊D1712yes—
894C22×C4C2×C22⋊D1712yes—
895C4⋊C4—44no—
896C22⋊C4—1716no—
897C22⋊C4—348no—
898C22⋊C4—348no—
899C22⋊C4—348no—
900C22⋊C4—348no—
901C22⋊C4—684no—
902C22⋊C4—684no—
903C22⋊C4—684no—
904C22⋊C4—684no—
905C22⋊C4—684no—
906C22⋊C4—684no—
907C42—44no—
908C42—348no—
909C42—684no—
910C42—684no—
911C23—174no—
912C23—342no—
913C23—342no—
914C23—342no—
915C23—342no—
916C23—342no—
917C23—342no—
918C23—342no—
919C23—342no—
920C23—342no—
921C23—342no—
922C23—342no—
923C23—342no—
924C23—342no—
925C23—342no—
926C23—342no—
927C23—342no—
928C23—342no—
929C23—342no—
930C23—342no—
931C23—342no—
932C23—342no—
933C23—342no—
934C23—342no—
935C23—342no—
936C23—342no—
937C23—681no—
938C23—681no—
939C23—681no—
940C23—681no—
941C23—681no—
942C23—681no—
943C23—681no—
944C23—681no—
945C23—681no—
946C23—681no—
947C23—681no—
948C23—681no—
949C23—681no—
950C23—681no—
951C23—681no—
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—
980C23—681no—
981C23C22×C4×D1711yescharacteristic
982C23C2×#6325211yescharacteristic
983C23C2×D4×D1711yescharacteristic
984C23C2×D4×D1711yescharacteristic
985C23#1058769111yescharacteristic
986C23#1058769111yescharacteristic
987C23C2×#6325611yescharacteristic
988C23C2×#6325611yescharacteristic
989C23C2×#6325611yescharacteristic
990C23#1058769411yescharacteristic
991C23#41×D1711yescharacteristic
992C23#41×D1711yescharacteristic
993C23#41×D1711yescharacteristic
994C23#1058769611yescharacteristic
995C23C22×C22⋊D1711yescharacteristic
996Q8—416no—
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—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
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—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—174no—
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—342no—
1059C2×C4—342no—
1060C2×C4—342no—
1061C2×C4—342no—
1062C2×C4—342no—
1063C2×C4—6816no—
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×C4C22⋊C4×D1714yes—
1088C2×C4C4×C22⋊D1714yes—
1089C2×C4#1058763314yescomplemented
1090C22—344no—
1091C22—344no—
1092C22—344no—
1093C22—682no—
1094C22—682no—
1095C22—682no—
1096C22—682no—
1097C22—682no—
1098C22—682no—
1099C22—682no—
1100C22—682no—
1101C22—682no—
1102C22—682no—
1103C22—682no—
1104C22—682no—
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—
1120C22C2×C22⋊C4×D1711yescharacteristic
1121C22C2×C4×C22⋊D1711yescharacteristic
1122C22C4×#6325611yescharacteristic
1123C22C4×#6325611yescharacteristic
1124C22C4×#6325611yescharacteristic
1125C22#1176328211yescharacteristic
1126C22#1176329111yescharacteristic
1127C22#1176332211yescharacteristic
1128C22#1176332211yescharacteristic
1129C22C2×#1058763311yescharacteristic
1130C22#1176334611yescharacteristic
1131C22#1176334611yescharacteristic
1132C22#1176335511yescharacteristic
1133C22#1176335811yescharacteristic
1134C22#1176336011yescharacteristic
1135C22#1176339311yescharacteristic
1136C22#1176339911yescharacteristic
1137C22#1176342911yescharacteristic
1138C22#1176343311yescharacteristic
1139C22D4×C22⋊D1711yescharacteristic
1140C22D4×C22⋊D1711yescharacteristic
1141C22#1176344711yescharacteristic
1142C22#1176344911yescharacteristic
1143C22#1176344911yescharacteristic
1144C22#1176345011yescharacteristic
1145C22#1176345211yescharacteristic
1146C22#1176346111yescharacteristic
1147C22#1176346211yescharacteristic
1148C22#1176347011yescharacteristic
1149C22#1176348611yescharacteristic
1150C22#1176348611yescharacteristic
1151C22#1176352111yescharacteristic
1152C22#1176352511yescharacteristic
1153C22#1176353111yescharacteristic
1154C22#1176354411yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—81no—
1162C4—344no—
1163C4—682no—
1164C4—682no—
1165C4—682no—
1166C4—682no—
1167C4—1361no—
1168C2—684no—
1169C2—1362no—
1170C2#1453127311yescharacteristic
1171C2C4×#1058763311yescharacteristic
1172C2#1453159611yescharacteristic
1173C2C22⋊C4×C22⋊D1711yescharacteristic
1174C2#1453161311yescharacteristic
1175C2#1453185111yescharacteristic
1176C2#1453189511yescharacteristic
1177C2#1453272811yescharacteristic
1178C2#1453275811yescharacteristic
1179C2#1453291711yescharacteristic
1180C2#1453294711yescharacteristic
1181C2#1453315011yescharacteristic
1182C2#1453349311yescharacteristic
1183C2#1453385511yescharacteristic
1184C2#1453389011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#391C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenterC2×#391D17
hypocenterC17#14098
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×#11762699C2semidirect
4. C2×C4×#63227C2semidirect
5. #14527055C2semidirect
6. #14527032C2semidirect
7. #14527026C2semidirect
9. #14527022C2semidirect
10. #14527020C2semidirect
11. #14527020C2semidirect
12. #14527010C2semidirect
13. #14527005C2semidirect
14. #95×Dic17C2semidirect
15. C2×C17×#391C2semidirect
20. C2×#10587633C4semidirect
66. C22×Q8×C17C2×C4semidirect
130. C2×#63227C2×C4semidirect
131. C2×#63227C2×C4semidirect
142. C2×C4×Dic17C2×C4semidirect
314. #63227C22⋊C4semidirect
453. C2×C4×C17#124semidirect
499. C2×#391D17semidirect
658. C22×Q8C4×D17semidirect
751. C17#14098semidirect
1089. C2×C4#10587633semidirect

Maximal subgroups

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

subgroupindex
C22×#105876332
C2×#117626992
C2×#117626872
C2×C4×#632272
#145270552
#145270322
#145270262
#145270242
#145270222
#145270202
#145270102
#145270052
#95×Dic172
C2×C17×#3912
#1409817