Finite Group Databasebeta

← #16957637

Subgroups — #16957637

Order 4352.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762711C211yesmaximal, characteristic
2C2×#11762700C211yesmaximal, characteristic, complemented
3C2×#11762700C211yesmaximal, characteristic, complemented
4C2×#11762698C211yesmaximal, characteristic, complemented
5C2×#11762687C211yesmaximal, characteristic
6C2×#11762668C211yesmaximal, characteristic, complemented
7C2×C4×#63227C211yesmaximal, characteristic, complemented
8#14527048C211yesmaximal, characteristic, complemented
9#14527032C211yesmaximal, characteristic, complemented
10#14527028C211yesmaximal, characteristic, complemented
11#14527024C211yesmaximal, characteristic
12#14527022C211yesmaximal, characteristic, complemented
13#14527018C211yesmaximal, characteristic, complemented
14#14527017C211yesmaximal, characteristic, complemented
15C4×C17×#95C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34#11762711—24no—
35#11762700—24no—
36#11762700—24no—
37#11762698—24no—
38#11762687C418yescomplemented
39#11762668—24no—
40C4×#63227—24no—
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C22×C42×C17C2211yescharacteristic
52C22×C42×C17C2211yescharacteristic
53C22×C42×C17C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C24×D17C2311yescharacteristic
59C24×D17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C22×D68—22no—
74C22×D68—22no—
75C22×D68—22no—
76C22×D68—22no—
77C22×D68—41no—
78C22×D68—41no—
79C22×D68C2×C414yes—
80C22×C4×D17—22no—
81C22×C4×D17—22no—
82C22×C4×D17—22no—
83C22×C4×D17—22no—
84C22×C4×D17—41no—
85C22×C4×D17—41no—
86C22×C4×D17C2×C414yes—
87C2×C42×C17—22no—
88C2×C42×C17—22no—
89C2×C42×C17—22no—
90C2×C42×C17—22no—
91C2×C42×C17—22no—
92C2×C42×C17—22no—
93C2×C42×C17—22no—
94C2×C42×C17—41no—
95C2×C42×C17—41no—
96C2×#63227—22no—
97C2×#63227—22no—
98C2×#63227—22no—
99C2×#63227—22no—
100C2×#63227—22no—
101C2×#63227—22no—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227—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—41no—
120C2×#63227—41no—
121C2×#63227—41no—
122C2×#63227—41no—
123C2×#63227—41no—
124C2×#63227—41no—
125C2×#63227C2×C414yes—
126C2×#63227C2×C414yes—
127C2×#63227C2×C414yes—
128C2×#63227D414yes—
129C2×C4⋊Dic17—22no—
130C2×C4⋊Dic17—22no—
131C2×C4⋊Dic17—41no—
132C2×#63225—22no—
133C2×#63225—22no—
134C2×#63225—22no—
135C2×#63225—22no—
136C2×#63225—22no—
137C2×#63225—22no—
138C2×#63225—41no—
139C2×#63225—41no—
140C2×#63225—41no—
141C2×C4×Dic17—22no—
142C2×C4×Dic17—22no—
143C2×C4×Dic17—41no—
144C17×#95—22no—
145C17×#95—22no—
146C17×#95C2×C414yes—
147C17×#95D414yescomplemented
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#10587502C2×C414yes—
157#10587502D414yescomplemented
158C24×C17C2411yescharacteristic
159C23×D17—21no—
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×D17C22×C412yes—
186C23×D17C22×C412yes—
187C23×D17C2×D412yes—
188C23×D17#4112yes—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17C22×C412yes—
226C22×C4×C17C22×C412yes—
227C22×C4×C17C22×C412yes—
228C22×C4×C17C2×D412yes—
229C22×C4×C17C2×D412yes—
230C22×C4×C17C2×D412yes—
231C22×C4×C17C2×D412yes—
232C22×C4×C17C2×D412yes—
233C22×C4×C17#4112yes—
234C22×C4×C17#4112yes—
235C22×C4×C17#4112yes—
236C22×C4×C17#4112yes—
237C22×C4×C17#4112yes—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17—21no—
272C22×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17C22×C412yes—
275C22×Dic17C22×C412yes—
276C22×Dic17C2×D412yes—
277C22×Dic17C2×D412yes—
278C22×Dic17C2×D412yes—
279C22×Dic17#4112yes—
280C2×D68—28no—
281C2×D68—28no—
282C2×D68—44no—
283C2×D68—44no—
284C2×D68—44no—
285C2×D68—44no—
286C2×D68—44no—
287C2×C4×D17—28no—
288C2×C4×D17—28no—
289C2×C4×D17—44no—
290C2×C4×D17—44no—
291C2×C4×D17—44no—
292C2×C4×D17—44no—
293C2×C4×D17—44no—
294C42×C17—44no—
295C42×C17—44no—
296C42×C17—44no—
297#63227—28no—
298#63227—28no—
299#63227—28no—
300#63227—28no—
301#63227—28no—
302#63227—44no—
303#63227—44no—
304#63227—44no—
305#63227—44no—
306#63227—44no—
307#63227—44no—
308C4⋊Dic17—44no—
309#63225—44no—
310#63225—44no—
311#63225—44no—
312C4×Dic17—44no—
313#14012—171nomaximal, Sylow
314C23×C17C23×C411yescharacteristic
315C23×C17C22×D411yescharacteristic
316C23×C17C22×D411yescharacteristic
317C23×C17C22×D411yescharacteristic
318C23×C17C2×#4111yescharacteristic
319C23×C17C2×#4111yescharacteristic
320C23×C17C2×#4111yescharacteristic
321C23×C17C2×#4111yescharacteristic
322C23×C17C2×#4111yescharacteristic
323C23×C17C2×#4111yescharacteristic
324C23×C17C2×#4111yescharacteristic
325C23×C17H(5,𝔽2)11yescharacteristic
326C23×C17H(5,𝔽2)11yescharacteristic
327C23×C17H(5,𝔽2)11yescharacteristic
328C23×C172−1+411yescharacteristic
329C22×D17—22no—
330C22×D17—22no—
331C22×D17—22no—
332C22×D17—22no—
333C22×D17—22no—
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—41no—
355C22×D17—41no—
356C22×D17—41no—
357C22×D17—41no—
358C22×D17—41no—
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×D17C4×D414yes—
399C2×C4×C17—22no—
400C2×C4×C17—22no—
401C2×C4×C17—22no—
402C2×C4×C17—22no—
403C2×C4×C17—22no—
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—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×C17#11714yes—
446C2×C4×C17C4×D414yes—
447C2×C4×C17#12114yes—
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×Dic17C4×D414yes—
490D68—416no—
491C4×D17—416no—
492C2×#390—171no—
493C2×#388—171no—
494C2×#388—171no—
495C2×#388—171no—
496C2×#386—171no—
497C2×#380—171no—
498C2×C4×C22⋊C4—171no—
499#1444—171no—
500#1440—171no—
501#1439—171no—
502#1438—171no—
503#1437—171no—
504#1436—171no—
505#1436—171no—
506C4×#95D1711yescharacteristic, complemented
507C22×C17C2×#11711yescharacteristic
508C22×C17C2×C4×D411yescharacteristic
509C22×C17C2×C4×D411yescharacteristic
510C22×C17C2×C4×D411yescharacteristic
511C22×C17C4×#4111yescharacteristic
512C22×C17#51811yescharacteristic
513C22×C17#52011yescharacteristic
514C22×C17C2×#12111yescharacteristic
515C22×C17#52511yescharacteristic
516C22×C17#52911yescharacteristic
517C22×C17#52911yescharacteristic
518C22×C17#52911yescharacteristic
519C22×C17#53211yescharacteristic
520C22×C17#53211yescharacteristic
521C22×C17#53211yescharacteristic
522C22×C17#53811yescharacteristic
523C22×C17#53911yescharacteristic
524C22×C17#54011yescharacteristic
525C22×C17#54211yescharacteristic
526C22×C17D4211yescharacteristic
527C22×C17D4211yescharacteristic
528C22×C17#54611yescharacteristic
529C22×C17#54611yescharacteristic
530C22×C17#54611yescharacteristic
531C22×C17#54611yescharacteristic
532C22×C17#54711yescharacteristic
533C22×C17#54711yescharacteristic
534C22×C17#54811yescharacteristic
535C22×C17#55011yescharacteristic
536C22×C17#55111yescharacteristic
537C22×C17#55111yescharacteristic
538C22×C17#55111yescharacteristic
539C22×C17#55311yescharacteristic
540C22×C17#55511yescharacteristic
541C22×C17#55611yescharacteristic
542C2×D17—24no—
543C2×D17—24no—
544C2×D17—24no—
545C2×D17—42no—
546C2×D17—42no—
547C2×D17—42no—
548C2×D17—42no—
549C2×D17—42no—
550C2×D17—42no—
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—81no—
565C2×D17—81no—
566C2×D17—81no—
567C2×D17—81no—
568C2×D17—81no—
569C2×D17—81no—
570C2×D17—81no—
571C2×D17—81no—
572C4×C17—24no—
573C4×C17—24no—
574C4×C17—24no—
575C4×C17—42no—
576C4×C17—42no—
577C4×C17—42no—
578C4×C17—42no—
579Dic17—24no—
580Dic17—42no—
581Dic17—42no—
582Dic17—42no—
583Dic17—81no—
584Dic17—81no—
585C23×D4—171no—
586C24×C4—171no—
587C22×C4⋊C4—171no—
588C22×C4⋊C4—171no—
589C22×C4⋊C4—171no—
590C22×C4⋊C4—171no—
591C22×C22⋊C4—171no—
592C22×C22⋊C4—171no—
593C22×C22⋊C4—171no—
594C22×C22⋊C4—171no—
595C22×C22⋊C4—171no—
596C22×C22⋊C4—171no—
597C22×C22⋊C4—171no—
598C22×C22⋊C4—171no—
599C22×C22⋊C4—171no—
600C22×C22⋊C4—171no—
601C22×C22⋊C4—171no—
602C22×C42—171no—
603C22×C42C2×D1711yescharacteristic
604C22×C42C2×D1711yescharacteristic
605C22×C42C2×D1711yescharacteristic
606#390—344no—
607#388—344no—
608#388—344no—
609#388—344no—
610#386—178no—
611#380—344no—
612C4×C22⋊C4—344no—
613C2×#95—171no—
614C2×#95—171no—
615C2×#95—171no—
616C2×#95—171no—
617C2×#95—171no—
618C2×#95—171no—
619C2×#95—171no—
620C2×#95—171no—
621C2×#95—171no—
622C2×#95—171no—
623C2×#95C2×D1711yescharacteristic
624C2×#95C2×D1711yescharacteristic
625C2×#95C2×D1711yescharacteristic
626C2×#95C2×D1711yescharacteristic
627C2×C17#229311yescharacteristic
628C2×C17C4×#12111yescharacteristic
629C2×C17#233511yescharacteristic
630C2×C17#234211yescharacteristic
631C2×C17#235411yescharacteristic
632C2×C17#235811yescharacteristic
633C2×C17#236111yescharacteristic
634C2×C17#242511yescharacteristic
635C2×C17#242811yescharacteristic
636C2×C17#246111yescharacteristic
637C2×C17#246711yescharacteristic
638C2×C17#252111yescharacteristic
639C2×C17#253111yescharacteristic
640C2×C17#255511yescharacteristic
641C2×C17#256011yescharacteristic
642D17—44no—
643D17—82no—
644C25—171no—
645C25—171no—
646C22×D4—174no—
647C22×D4—342no—
648C22×D4—342no—
649C22×D4—342no—
650C22×D4—342no—
651C22×D4—681no—
652C22×D4—681no—
653C23×C4—171no—
654C23×C4—171no—
655C23×C4—171no—
656C23×C4—171no—
657C23×C4—174no—
658C23×C4—171no—
659C23×C4—171no—
660C23×C4—342no—
661C23×C4—342no—
662C23×C4—342no—
663C23×C4—342no—
664C23×C4—681no—
665C23×C4—681no—
666C23×C4C22×D1711yescharacteristic
667C23×C4C22×D1711yescharacteristic
668C23×C4C22×D1711yescharacteristic
669C23×C4C22×D1711yescharacteristic
670C23×C4C22×D1711yescharacteristic
671C23×C4C22×D1711yescharacteristic
672C23×C4C22×D1711yescharacteristic
673C2×C4⋊C4—342no—
674C2×C4⋊C4—342no—
675C2×C4⋊C4—342no—
676C2×C4⋊C4—342no—
677C2×C4⋊C4—342no—
678C2×C4⋊C4—342no—
679C2×C4⋊C4—342no—
680C2×C4⋊C4—342no—
681C2×C4⋊C4—681no—
682C2×C4⋊C4—681no—
683C2×C4⋊C4—681no—
684C2×C4⋊C4—681no—
685C2×C22⋊C4—174no—
686C2×C22⋊C4—174no—
687C2×C22⋊C4—174no—
688C2×C22⋊C4—174no—
689C2×C22⋊C4—342no—
690C2×C22⋊C4—342no—
691C2×C22⋊C4—342no—
692C2×C22⋊C4—342no—
693C2×C22⋊C4—342no—
694C2×C22⋊C4—342no—
695C2×C22⋊C4—342no—
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—681no—
713C2×C22⋊C4—681no—
714C2×C22⋊C4—681no—
715C2×C22⋊C4—681no—
716C2×C22⋊C4—681no—
717C2×C22⋊C4—681no—
718C2×C42—22no—
719C2×C42—22no—
720C2×C42—22no—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—41no—
726C2×C42—41no—
727C2×C42—342no—
728C2×C42—342no—
729C2×C42—681no—
730#95—22no—
731#95—22no—
732#95—174no—
733#95—174no—
734#95—342no—
735#95—342no—
736#95—342no—
737#95—342no—
738#95—342no—
739#95—342no—
740#95—342no—
741#95—681no—
742#95C4×D1714yes—
743#95D6814yescomplemented
744C17#1401211yescharacteristic, complemented, Sylow
745C24—172no—
746C24—172no—
747C24—172no—
748C24—172no—
749C24—341no—
750C24—341no—
751C24—341no—
752C24—341no—
753C24—341no—
754C24—341no—
755C24—341no—
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—
775C24C23×D1711yescharacteristic
776C2×D4—348no—
777C2×D4—348no—
778C2×D4—684no—
779C2×D4—684no—
780C2×D4—684no—
781C2×D4—684no—
782C2×D4—684no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—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—172no—
820C22×C4—172no—
821C22×C4—172no—
822C22×C4—172no—
823C22×C4—172no—
824C22×C4—172no—
825C22×C4—348no—
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—348no—
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—684no—
864C22×C4—684no—
865C22×C4—684no—
866C22×C4—684no—
867C22×C4—684no—
868C22×C4C2×C4×D1712yes—
869C22×C4C2×C4×D1712yes—
870C22×C4C2×C4×D1712yes—
871C22×C4C2×D6812yes—
872C22×C4C2×D6812yes—
873C22×C4C2×D6812yes—
874C22×C4#6325212yes—
875C22×C4#6325212yes—
876C22×C4#6325212yes—
877C22×C4#6325212yes—
878C22×C4#6325212yes—
879C22×C4D4×D1712yes—
880C22×C4D4×D1712yes—
881C4⋊C4—684no—
882C4⋊C4—684no—
883C4⋊C4—684no—
884C4⋊C4—684no—
885C22⋊C4—348no—
886C22⋊C4—348no—
887C22⋊C4—348no—
888C22⋊C4—348no—
889C22⋊C4—348no—
890C22⋊C4—684no—
891C22⋊C4—684no—
892C22⋊C4—684no—
893C22⋊C4—684no—
894C22⋊C4—684no—
895C22⋊C4—684no—
896C42—44no—
897C42—44no—
898C42—44no—
899C42—684no—
900C23—174no—
901C23—342no—
902C23—342no—
903C23—342no—
904C23—342no—
905C23—342no—
906C23—342no—
907C23—342no—
908C23—342no—
909C23—342no—
910C23—342no—
911C23—342no—
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—681no—
927C23—681no—
928C23—681no—
929C23—681no—
930C23—681no—
931C23—681no—
932C23—681no—
933C23—681no—
934C23—681no—
935C23—681no—
936C23—681no—
937C23—681no—
938C23—681no—
939C23—681no—
940C23—681no—
941C23—681no—
942C23—681no—
943C23—681no—
944C23—681no—
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—
970C23C22×C4×D1711yescharacteristic
971C23C22×D6811yescharacteristic
972C23C2×#6325211yescharacteristic
973C23C2×#6325211yescharacteristic
974C23C2×#6325211yescharacteristic
975C23C2×#6325211yescharacteristic
976C23C2×#6325211yescharacteristic
977C23C2×D4×D1711yescharacteristic
978C23C2×D4×D1711yescharacteristic
979C23#1058769111yescharacteristic
980C23#1058769411yescharacteristic
981C23#41×D1711yescharacteristic
982C23#41×D1711yescharacteristic
983C23#1058769611yescharacteristic
984C23#1058769611yescharacteristic
985D4—6816no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
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—41no—
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—174no—
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—342no—
1043C2×C4—342no—
1044C2×C4—342no—
1045C2×C4—342no—
1046C2×C4—342no—
1047C2×C4—342no—
1048C2×C4—6816no—
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#1058755814yes—
1076C2×C4C4×D6814yes—
1077C2×C4#1058757014yes—
1078C22—344no—
1079C22—344no—
1080C22—344no—
1081C22—682no—
1082C22—682no—
1083C22—682no—
1084C22—682no—
1085C22—682no—
1086C22—682no—
1087C22—682no—
1088C22—682no—
1089C22—682no—
1090C22—682no—
1091C22—682no—
1092C22—682no—
1093C22—682no—
1094C22—682no—
1095C22—682no—
1096C22—682no—
1097C22—682no—
1098C22—682no—
1099C22—682no—
1100C22—1361no—
1101C22—1361no—
1102C22—1361no—
1103C22—1361no—
1104C22—1361no—
1105C22—1361no—
1106C22—1361no—
1107C22—1361no—
1108C22C2×#1058755811yescharacteristic
1109C22C4×D4×D1711yescharacteristic
1110C22C4×D4×D1711yescharacteristic
1111C22C2×C4×D6811yescharacteristic
1112C22C4×#6325211yescharacteristic
1113C22#1176328111yescharacteristic
1114C22#1176329111yescharacteristic
1115C22C2×#1058757011yescharacteristic
1116C22#1176331811yescharacteristic
1117C22#1176333711yescharacteristic
1118C22#1176334311yescharacteristic
1119C22#1176334311yescharacteristic
1120C22#1176335611yescharacteristic
1121C22#1176335911yescharacteristic
1122C22#1176335911yescharacteristic
1123C22#1176339211yescharacteristic
1124C22#1176340611yescharacteristic
1125C22#1176341411yescharacteristic
1126C22#1176343111yescharacteristic
1127C22D4×D6811yescharacteristic
1128C22D4×D6811yescharacteristic
1129C22#1176344911yescharacteristic
1130C22#1176344911yescharacteristic
1131C22#1176345411yescharacteristic
1132C22#1176345511yescharacteristic
1133C22#1176346011yescharacteristic
1134C22#1176346011yescharacteristic
1135C22#1176347111yescharacteristic
1136C22#1176348011yescharacteristic
1137C22#1176348311yescharacteristic
1138C22#1176348311yescharacteristic
1139C22#1176348811yescharacteristic
1140C22#1176350311yescharacteristic
1141C22#1176352211yescharacteristic
1142C22#1176353111yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—24no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—344no—
1151C4—682no—
1152C4—682no—
1153C4—682no—
1154C4—1361no—
1155C4—1361no—
1156C2—684no—
1157C2—1362no—
1158C2#1453124811yescharacteristic
1159C2C4×#1058757011yescharacteristic
1160C2#1453156811yescharacteristic
1161C2#1453162711yescharacteristic
1162C2#1453172911yescharacteristic
1163C2#1453176611yescharacteristic
1164C2#1453180211yescharacteristic
1165C2#1453233511yescharacteristic
1166C2#1453237211yescharacteristic
1167C2#1453275111yescharacteristic
1168C2#1453283511yescharacteristic
1169C2#1453348111yescharacteristic
1170C2#1453362511yescharacteristic
1171C2#1453385311yescharacteristic
1172C2#1453392211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC4×C17×#95C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenterC4×#95D17
hypocenterC17#14012
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×#11762700C2semidirect
3. C2×#11762700C2semidirect
4. C2×#11762698C2semidirect
6. C2×#11762668C2semidirect
7. C2×C4×#63227C2semidirect
8. #14527048C2semidirect
9. #14527032C2semidirect
10. #14527028C2semidirect
12. #14527022C2semidirect
13. #14527018C2semidirect
14. #14527017C2semidirect
15. C4×C17×#95C2semidirect
38. #11762687C4semidirect
147. C17×#95D4semidirect
157. #10587502D4semidirect
506. C4×#95D17semidirect
743. #95D68semidirect
744. C17#14012semidirect

Maximal subgroups

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

subgroupindex
C2×#117627112
C2×#117627002
C2×#117626982
C2×#117626872
C2×#117626682
C2×C4×#632272
#145270482
#145270322
#145270282
#145270242
#145270222
#145270182
#145270172
C4×C17×#952
#1401217