Finite Group Databasebeta

← #16964601

Subgroups — #16964601

Order 4352.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762727C211yesmaximal, characteristic
2C2×#11762700C211yesmaximal, characteristic, complemented
3C2×#11762698C211yesmaximal, characteristic, complemented
4#14527035C211yesmaximal, characteristic, complemented
5#14527028C211yesmaximal, characteristic, complemented
6#14527028C211yesmaximal, characteristic, complemented
7#14527024C211yesmaximal, characteristic
8#14527024C211yesmaximal, characteristic
9#14527022C211yesmaximal, characteristic, complemented
10#14527020C211yesmaximal, characteristic, complemented
11#14527020C211yesmaximal, characteristic, complemented
12#14527020C211yesmaximal, characteristic, complemented
13#14527012C211yesmaximal, characteristic, complemented
14#14527009C211yesmaximal, characteristic, complemented
15C17×#1434C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63227C2211yescharacteristic
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
34#11762727C418yescomplemented
35#11762700—24no—
36#11762698—24no—
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C22×C42×C17C2211yescharacteristic
48C2×C17×#95C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C24×D17C2311yescharacteristic
55C24×D17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×Dic17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C22×D68—41no—
70C22×D68—41no—
71C22×D68—41no—
72C22×D68—41no—
73C22×D68—41no—
74C22×D68—41no—
75C22×D68C2×C414yes—
76C2×C42×C17—22no—
77C2×C42×C17—22no—
78C2×C42×C17—41no—
79C2×#63227—22no—
80C2×#63227—22no—
81C2×#63227—22no—
82C2×#63227—22no—
83C2×#63227—22no—
84C2×#63227—22no—
85C2×#63227—22no—
86C2×#63227—22no—
87C2×#63227—22no—
88C2×#63227—22no—
89C2×#63227—22no—
90C2×#63227—22no—
91C2×#63227—22no—
92C2×#63227—22no—
93C2×#63227—22no—
94C2×#63227—22no—
95C2×#63227—41no—
96C2×#63227—41no—
97C2×#63227—41no—
98C2×#63227—41no—
99C2×#63227—41no—
100C2×#63227—41no—
101C2×#63227—41no—
102C2×#63227—41no—
103C2×#63227—41no—
104C2×#63227—41no—
105C2×#63227—41no—
106C2×#63227—41no—
107C2×#63227—41no—
108C2×#63227—41no—
109C2×#63227—41no—
110C2×#63227—41no—
111C2×#63227C2×C414yes—
112C2×#63227C2×C414yes—
113C2×#63227C2×C414yes—
114C2×#63227C2×C414yes—
115C2×#63225—41no—
116C2×#63225—41no—
117C2×#63225—41no—
118C2×#63225—41no—
119C2×#63225—41no—
120C2×#63225—41no—
121C2×#63225—41no—
122C2×#63225C2×C414yes—
123C2×#63225D414yescomplemented
124C2×C4×Dic17—22no—
125C2×C4×Dic17—22no—
126C2×C4×Dic17—22no—
127C2×C4×Dic17—41no—
128C2×C4×Dic17—41no—
129C2×C4×Dic17—41no—
130C17×#95—22no—
131C17×#95—22no—
132C17×#95—41no—
133C17×#95—41no—
134C17×#95—41no—
135C17×#95C2×C414yes—
136#10587502—22no—
137#10587502—22no—
138#10587502—22no—
139#10587502—22no—
140#10587502—41no—
141#10587502—41no—
142#10587502—41no—
143#10587502—41no—
144#10587502—41no—
145#10587502—41no—
146C24×C17C2411yescharacteristic
147C23×D17—21no—
148C23×D17—21no—
149C23×D17—21no—
150C23×D17—21no—
151C23×D17—21no—
152C23×D17—21no—
153C23×D17—21no—
154C23×D17—21no—
155C23×D17—21no—
156C23×D17—21no—
157C23×D17—21no—
158C23×D17—21no—
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×D17C22×C412yes—
176C23×D17C22×C412yes—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
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×C17C22×C412yes—
221C22×C4×C17C22×C412yes—
222C22×C4×C17C22×C412yes—
223C22×C4×C17C2×D412yes—
224C22×C4×C17#4112yes—
225C22×C4×C17#4112yes—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
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×Dic17C22×C412yes—
262C22×Dic17C22×C412yes—
263C22×Dic17C2×D412yes—
264C22×Dic17C2×D412yes—
265C22×Dic17#4112yes—
266C22×Dic17#4112yes—
267C22×Dic17#4112yes—
268C2×D68—44no—
269C2×D68—44no—
270C2×D68—44no—
271C2×D68—44no—
272C2×D68—44no—
273C2×D68—44no—
274C2×D68—44no—
275C42×C17—44no—
276#63227—28no—
277#63227—28no—
278#63227—44no—
279#63227—44no—
280#63227—44no—
281#63227—44no—
282#63227—44no—
283#63227—44no—
284#63227—44no—
285#63227—44no—
286#63227—44no—
287#63227—44no—
288#63225—44no—
289#63225—44no—
290#63225—44no—
291C4×Dic17—44no—
292C4×Dic17—44no—
293#14589—171nomaximal, Sylow
294C23×C17C23×C411yescharacteristic
295C23×C17C22×D411yescharacteristic
296C23×C17C2×#4111yescharacteristic
297C23×C17C2×#4111yescharacteristic
298C23×C17C2×#4111yescharacteristic
299C23×C17C2×#4111yescharacteristic
300C23×C17C2×#4111yescharacteristic
301C23×C17H(5,𝔽2)11yescharacteristic
302C23×C17H(5,𝔽2)11yescharacteristic
303C23×C17H(5,𝔽2)11yescharacteristic
304C23×C17H(5,𝔽2)11yescharacteristic
305C23×C17H(5,𝔽2)11yescharacteristic
306C23×C17H(5,𝔽2)11yescharacteristic
307C23×C17H(5,𝔽2)11yescharacteristic
308C23×C172−1+411yescharacteristic
309C22×D17—22no—
310C22×D17—22no—
311C22×D17—22no—
312C22×D17—22no—
313C22×D17—22no—
314C22×D17—22no—
315C22×D17—22no—
316C22×D17—22no—
317C22×D17—22no—
318C22×D17—22no—
319C22×D17—22no—
320C22×D17—22no—
321C22×D17—22no—
322C22×D17—22no—
323C22×D17—41no—
324C22×D17—41no—
325C22×D17—41no—
326C22×D17—41no—
327C22×D17—41no—
328C22×D17—41no—
329C22×D17—41no—
330C22×D17—41no—
331C22×D17—41no—
332C22×D17—41no—
333C22×D17—41no—
334C22×D17—41no—
335C22×D17—41no—
336C22×D17—41no—
337C22×D17—41no—
338C22×D17—41no—
339C22×D17—41no—
340C22×D17—41no—
341C22×D17—41no—
342C22×D17—41no—
343C22×D17—41no—
344C22×D17—41no—
345C22×D17—41no—
346C22×D17—41no—
347C22×D17—41no—
348C22×D17—41no—
349C22×D17—41no—
350C22×D17—41no—
351C22×D17—41no—
352C22×D17—41no—
353C22×D17—41no—
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—
379C2×C4×C17—22no—
380C2×C4×C17—22no—
381C2×C4×C17—22no—
382C2×C4×C17—22no—
383C2×C4×C17—22no—
384C2×C4×C17—22no—
385C2×C4×C17—22no—
386C2×C4×C17—22no—
387C2×C4×C17—22no—
388C2×C4×C17—22no—
389C2×C4×C17—22no—
390C2×C4×C17—22no—
391C2×C4×C17—22no—
392C2×C4×C17—22no—
393C2×C4×C17—22no—
394C2×C4×C17—22no—
395C2×C4×C17—22no—
396C2×C4×C17—22no—
397C2×C4×C17—41no—
398C2×C4×C17—41no—
399C2×C4×C17—41no—
400C2×C4×C17—41no—
401C2×C4×C17—41no—
402C2×C4×C17—41no—
403C2×C4×C17—41no—
404C2×C4×C17—41no—
405C2×C4×C17—41no—
406C2×C4×C17—41no—
407C2×C4×C17—41no—
408C2×C4×C17—41no—
409C2×C4×C17—41no—
410C2×C4×C17—41no—
411C2×C4×C17—41no—
412C2×C4×C17—41no—
413C2×C4×C17—41no—
414C2×C4×C17—41no—
415C2×C4×C17—41no—
416C2×C4×C17—41no—
417C2×C4×C17—41no—
418C2×C4×C17—41no—
419C2×C4×C17—41no—
420C2×C4×C17—41no—
421C2×C4×C17—41no—
422C2×C4×C17—41no—
423C2×C4×C17—41no—
424C2×C4×C17—41no—
425C2×C4×C17—41no—
426C2×C4×C17—41no—
427C2×C4×C17—41no—
428C2×Dic17—22no—
429C2×Dic17—22no—
430C2×Dic17—22no—
431C2×Dic17—22no—
432C2×Dic17—22no—
433C2×Dic17—22no—
434C2×Dic17—22no—
435C2×Dic17—22no—
436C2×Dic17—22no—
437C2×Dic17—22no—
438C2×Dic17—22no—
439C2×Dic17—22no—
440C2×Dic17—22no—
441C2×Dic17—22no—
442C2×Dic17—22no—
443C2×Dic17—22no—
444C2×Dic17—22no—
445C2×Dic17—22no—
446C2×Dic17—41no—
447C2×Dic17—41no—
448C2×Dic17—41no—
449C2×Dic17—41no—
450C2×Dic17—41no—
451C2×Dic17—41no—
452C2×Dic17—41no—
453C2×Dic17—41no—
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×Dic17C4×D414yes—
470D68—416no—
471C2×#394—171no—
472C2×#388—171no—
473C2×#388—171no—
474#1441—171no—
475#1439—171no—
476#1439—171no—
477#1438—171no—
478#1438—171no—
479#1437—171no—
480#1437—171no—
481#1437—171no—
482#1437—171no—
483C4⋊#95—171no—
484#1434—171no—
485#1434D1711yescharacteristic, complemented
486C22×C17C2×C4×D411yescharacteristic
487C22×C17C4×#4111yescharacteristic
488C22×C17C4×#4111yescharacteristic
489C22×C17#51811yescharacteristic
490C22×C17#51811yescharacteristic
491C22×C17#51811yescharacteristic
492C22×C17#52011yescharacteristic
493C22×C17#53411yescharacteristic
494C22×C17#53711yescharacteristic
495C22×C17#53811yescharacteristic
496C22×C17#53811yescharacteristic
497C22×C17#53811yescharacteristic
498C22×C17#53911yescharacteristic
499C22×C17#53911yescharacteristic
500C22×C17#53911yescharacteristic
501C22×C17#54011yescharacteristic
502C22×C17#54011yescharacteristic
503C22×C17#54211yescharacteristic
504C22×C17#54211yescharacteristic
505C22×C17#54611yescharacteristic
506C22×C17#54611yescharacteristic
507C22×C17#55011yescharacteristic
508C22×C17#55011yescharacteristic
509C22×C17#55111yescharacteristic
510C22×C17#55111yescharacteristic
511C22×C17#55311yescharacteristic
512C22×C17#55311yescharacteristic
513C22×C17#55511yescharacteristic
514C22×C17#55511yescharacteristic
515C22×C17#55511yescharacteristic
516C22×C17#55511yescharacteristic
517C22×C17#56011yescharacteristic
518C22×C17#56011yescharacteristic
519C22×C17#56011yescharacteristic
520C22×C17H(3,𝔽4)11yescharacteristic
521C2×D17—42no—
522C2×D17—42no—
523C2×D17—42no—
524C2×D17—42no—
525C2×D17—42no—
526C2×D17—42no—
527C2×D17—42no—
528C2×D17—42no—
529C2×D17—42no—
530C2×D17—42no—
531C2×D17—42no—
532C2×D17—42no—
533C2×D17—42no—
534C2×D17—42no—
535C2×D17—81no—
536C2×D17—81no—
537C2×D17—81no—
538C2×D17—81no—
539C2×D17—81no—
540C2×D17—81no—
541C2×D17—81no—
542C2×D17—81no—
543C2×D17—81no—
544C2×D17—81no—
545C2×D17—81no—
546C2×D17—81no—
547C2×D17—81no—
548C2×D17—81no—
549C2×D17—81no—
550C2×D17—81no—
551C4×C17—42no—
552C4×C17—42no—
553C4×C17—42no—
554C4×C17—42no—
555C4×C17—42no—
556C4×C17—42no—
557C4×C17—81no—
558Dic17—24no—
559Dic17—42no—
560Dic17—42no—
561Dic17—42no—
562Dic17—42no—
563Dic17—81no—
564C23×D4—171no—
565C22×C4⋊C4—171no—
566C22×C4⋊C4—171no—
567C22×C4⋊C4—171no—
568C22×C22⋊C4—171no—
569C22×C22⋊C4—171no—
570C22×C22⋊C4—171no—
571C22×C22⋊C4—171no—
572C22×C22⋊C4—171no—
573C22×C22⋊C4—171no—
574C22×C22⋊C4—171no—
575C22×C22⋊C4—171no—
576C22×C22⋊C4—171no—
577C22×C22⋊C4—171no—
578C22×C22⋊C4—171no—
579C22×C22⋊C4—171no—
580C22×C42—171no—
581C22×C42—171no—
582C22×C42C2×D1711yescharacteristic
583#394—178no—
584#388—344no—
585#388—344no—
586C2×#95—171no—
587C2×#95—171no—
588C2×#95—171no—
589C2×#95—171no—
590C2×#95—171no—
591C2×#95—171no—
592C2×#95—171no—
593C2×#95—171no—
594C2×#95—171no—
595C2×#95—171no—
596C2×#95C2×D1711yescharacteristic
597C2×#95C2×D1711yescharacteristic
598C2×#95C2×D1711yescharacteristic
599C2×#95C2×D1711yescharacteristic
600C2×#95C2×D1711yescharacteristic
601C2×#95C2×D1711yescharacteristic
602C2×C17#232511yescharacteristic
603C2×C17#233511yescharacteristic
604C2×C17#233511yescharacteristic
605C2×C17#236311yescharacteristic
606C2×C17#236311yescharacteristic
607C2×C17#237211yescharacteristic
608C2×C17#237511yescharacteristic
609C2×C17#269911yescharacteristic
610C2×C17#270511yescharacteristic
611C2×C17#270511yescharacteristic
612C2×C17#273311yescharacteristic
613C2×C17#275611yescharacteristic
614C2×C17#275611yescharacteristic
615C2×C17#278511yescharacteristic
616C2×C17#279511yescharacteristic
617D17—82no—
618D17—82no—
619C25—171no—
620C25—171no—
621C22×D4—174no—
622C22×D4—681no—
623C22×D4—681no—
624C22×D4—681no—
625C22×D4—681no—
626C22×D4—681no—
627C22×D4—681no—
628C23×C4—171no—
629C23×C4—171no—
630C23×C4—171no—
631C23×C4—171no—
632C23×C4—171no—
633C23×C4—171no—
634C23×C4C22×D1711yescharacteristic
635C23×C4C22×D1711yescharacteristic
636C23×C4C22×D1711yescharacteristic
637C23×C4C22×D1711yescharacteristic
638C23×C4C22×D1711yescharacteristic
639C23×C4C22×D1711yescharacteristic
640C23×C4C22×D1711yescharacteristic
641C2×C4⋊C4—174no—
642C2×C4⋊C4—174no—
643C2×C4⋊C4—681no—
644C2×C4⋊C4—681no—
645C2×C4⋊C4—681no—
646C2×C4⋊C4—681no—
647C2×C4⋊C4—681no—
648C2×C4⋊C4—681no—
649C2×C4⋊C4—681no—
650C2×C22⋊C4—174no—
651C2×C22⋊C4—174no—
652C2×C22⋊C4—174no—
653C2×C22⋊C4—174no—
654C2×C22⋊C4—342no—
655C2×C22⋊C4—342no—
656C2×C22⋊C4—342no—
657C2×C22⋊C4—342no—
658C2×C22⋊C4—342no—
659C2×C22⋊C4—342no—
660C2×C22⋊C4—342no—
661C2×C22⋊C4—342no—
662C2×C22⋊C4—342no—
663C2×C22⋊C4—342no—
664C2×C22⋊C4—342no—
665C2×C22⋊C4—342no—
666C2×C22⋊C4—342no—
667C2×C22⋊C4—342no—
668C2×C22⋊C4—342no—
669C2×C22⋊C4—342no—
670C2×C22⋊C4—681no—
671C2×C22⋊C4—681no—
672C2×C22⋊C4—681no—
673C2×C22⋊C4—681no—
674C2×C22⋊C4—681no—
675C2×C22⋊C4—681no—
676C2×C22⋊C4—681no—
677C2×C22⋊C4—681no—
678C2×C22⋊C4—681no—
679C2×C22⋊C4—681no—
680C2×C22⋊C4—681no—
681C2×C22⋊C4—681no—
682C2×C22⋊C4—681no—
683C2×C22⋊C4—681no—
684C2×C22⋊C4—681no—
685C2×C22⋊C4—681no—
686C2×C42—22no—
687C2×C42—22no—
688C2×C42—41no—
689C2×C42—342no—
690C2×C42—342no—
691C2×C42—342no—
692C2×C42—681no—
693C2×C42—681no—
694C2×C42—681no—
695#95—22no—
696#95—22no—
697#95—41no—
698#95—41no—
699#95—41no—
700#95—342no—
701#95—342no—
702#95—342no—
703#95—342no—
704#95—681no—
705#95—681no—
706#95—681no—
707#95—681no—
708#95—681no—
709#95—681no—
710#95C4×D1714yes—
711C17#1458911yescharacteristic, complemented, Sylow
712C24—172no—
713C24—172no—
714C24—341no—
715C24—341no—
716C24—341no—
717C24—341no—
718C24—341no—
719C24—341no—
720C24—341no—
721C24—341no—
722C24—341no—
723C24—341no—
724C24—341no—
725C24—341no—
726C24—341no—
727C24—341no—
728C24—341no—
729C24—341no—
730C24—341no—
731C24—341no—
732C24—341no—
733C24—341no—
734C24—341no—
735C24—341no—
736C24—341no—
737C24—341no—
738C24—341no—
739C24—341no—
740C24—341no—
741C24—341no—
742C24C23×D1711yescharacteristic
743C2×D4—684no—
744C2×D4—684no—
745C2×D4—684no—
746C2×D4—684no—
747C2×D4—684no—
748C2×D4—684no—
749C2×D4—684no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
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—172no—
794C22×C4—172no—
795C22×C4—172no—
796C22×C4—172no—
797C22×C4—172no—
798C22×C4—172no—
799C22×C4—172no—
800C22×C4—341no—
801C22×C4—341no—
802C22×C4—341no—
803C22×C4—341no—
804C22×C4—341no—
805C22×C4—341no—
806C22×C4—341no—
807C22×C4—341no—
808C22×C4—341no—
809C22×C4—341no—
810C22×C4—341no—
811C22×C4—341no—
812C22×C4—341no—
813C22×C4—341no—
814C22×C4—341no—
815C22×C4—341no—
816C22×C4—341no—
817C22×C4—341no—
818C22×C4—341no—
819C22×C4—341no—
820C22×C4—341no—
821C22×C4—341no—
822C22×C4—341no—
823C22×C4—341no—
824C22×C4—341no—
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×C4C2×C4×D1712yes—
836C22×C4C2×C4×D1712yes—
837C22×C4C2×C4×D1712yes—
838C22×C4#6325212yes—
839C22×C4#6325212yes—
840C22×C4D4×D1712yes—
841C4⋊C4—684no—
842C4⋊C4—684no—
843C4⋊C4—684no—
844C22⋊C4—348no—
845C22⋊C4—348no—
846C22⋊C4—684no—
847C22⋊C4—684no—
848C22⋊C4—684no—
849C22⋊C4—684no—
850C22⋊C4—684no—
851C22⋊C4—684no—
852C22⋊C4—684no—
853C22⋊C4—684no—
854C22⋊C4—684no—
855C22⋊C4—684no—
856C42—44no—
857C42—684no—
858C42—684no—
859C23—342no—
860C23—342no—
861C23—342no—
862C23—342no—
863C23—342no—
864C23—342no—
865C23—342no—
866C23—342no—
867C23—342no—
868C23—342no—
869C23—342no—
870C23—342no—
871C23—342no—
872C23—342no—
873C23—681no—
874C23—681no—
875C23—681no—
876C23—681no—
877C23—681no—
878C23—681no—
879C23—681no—
880C23—681no—
881C23—681no—
882C23—681no—
883C23—681no—
884C23—681no—
885C23—681no—
886C23—681no—
887C23—681no—
888C23—681no—
889C23—681no—
890C23—681no—
891C23—681no—
892C23—681no—
893C23—681no—
894C23—681no—
895C23—681no—
896C23—681no—
897C23—681no—
898C23—681no—
899C23—681no—
900C23—681no—
901C23—681no—
902C23—681no—
903C23—681no—
904C23—681no—
905C23—681no—
906C23—681no—
907C23—681no—
908C23—681no—
909C23—681no—
910C23—681no—
911C23—681no—
912C23—681no—
913C23—681no—
914C23—681no—
915C23—681no—
916C23—681no—
917C23—681no—
918C23—681no—
919C23—681no—
920C23—681no—
921C23—681no—
922C23—681no—
923C23—681no—
924C23—681no—
925C23—681no—
926C23—681no—
927C23—681no—
928C23—681no—
929C23C22×C4×D1711yescharacteristic
930C23C2×#6325211yescharacteristic
931C23C2×#6325211yescharacteristic
932C23C2×D4×D1711yescharacteristic
933C23#1058769111yescharacteristic
934C23#1058769111yescharacteristic
935C23#1058769411yescharacteristic
936C23#41×D1711yescharacteristic
937C23#41×D1711yescharacteristic
938C23#41×D1711yescharacteristic
939C23#1058769611yescharacteristic
940C23#1058769611yescharacteristic
941C23#1058769611yescharacteristic
942C23#1058769611yescharacteristic
943C23#1058769611yescharacteristic
944D4—6816no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—174no—
995C2×C4—342no—
996C2×C4—342no—
997C2×C4—342no—
998C2×C4—342no—
999C2×C4—342no—
1000C2×C4—342no—
1001C2×C4—342no—
1002C2×C4—342no—
1003C2×C4—342no—
1004C2×C4—342no—
1005C2×C4—342no—
1006C2×C4—342no—
1007C2×C4—342no—
1008C2×C4—342no—
1009C2×C4—342no—
1010C2×C4—342no—
1011C2×C4—342no—
1012C2×C4—342no—
1013C2×C4—681no—
1014C2×C4—681no—
1015C2×C4—681no—
1016C2×C4—681no—
1017C2×C4—681no—
1018C2×C4—681no—
1019C2×C4—681no—
1020C2×C4—681no—
1021C2×C4—681no—
1022C2×C4—681no—
1023C2×C4—681no—
1024C2×C4—681no—
1025C2×C4—681no—
1026C2×C4—681no—
1027C2×C4—681no—
1028C2×C4—681no—
1029C2×C4—681no—
1030C2×C4—681no—
1031C2×C4—681no—
1032C2×C4—681no—
1033C2×C4—681no—
1034C2×C4—681no—
1035C2×C4—681no—
1036C22—682no—
1037C22—682no—
1038C22—682no—
1039C22—682no—
1040C22—682no—
1041C22—682no—
1042C22—682no—
1043C22—682no—
1044C22—682no—
1045C22—682no—
1046C22—682no—
1047C22—682no—
1048C22—682no—
1049C22—682no—
1050C22—1361no—
1051C22—1361no—
1052C22—1361no—
1053C22—1361no—
1054C22—1361no—
1055C22—1361no—
1056C22—1361no—
1057C22—1361no—
1058C22—1361no—
1059C22—1361no—
1060C22—1361no—
1061C22—1361no—
1062C22—1361no—
1063C22—1361no—
1064C22—1361no—
1065C22—1361no—
1066C22C4×D4×D1711yescharacteristic
1067C22#1176327711yescharacteristic
1068C22C4×#6325211yescharacteristic
1069C22#1176328111yescharacteristic
1070C22#1176328111yescharacteristic
1071C22#1176328311yescharacteristic
1072C22#1176329111yescharacteristic
1073C22#1176337011yescharacteristic
1074C22#1176338911yescharacteristic
1075C22#1176339211yescharacteristic
1076C22#1176339811yescharacteristic
1077C22#1176339811yescharacteristic
1078C22#1176340611yescharacteristic
1079C22#1176340711yescharacteristic
1080C22#1176340711yescharacteristic
1081C22#1176341111yescharacteristic
1082C22#1176341411yescharacteristic
1083C22#1176342911yescharacteristic
1084C22#1176343111yescharacteristic
1085C22#1176344911yescharacteristic
1086C22#1176345111yescharacteristic
1087C22#1176347711yescharacteristic
1088C22#1176348011yescharacteristic
1089C22#1176348311yescharacteristic
1090C22#1176348311yescharacteristic
1091C22#1176350811yescharacteristic
1092C22#1176351011yescharacteristic
1093C22#1176352111yescharacteristic
1094C22#1176352211yescharacteristic
1095C22#1176352211yescharacteristic
1096C22#1176352211yescharacteristic
1097C22#1176354711yescharacteristic
1098C22#1176354911yescharacteristic
1099C22#1176355011yescharacteristic
1100C22#1176355111yescharacteristic
1101C4—42no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4—81no—
1108C4—344no—
1109C4—682no—
1110C4—682no—
1111C4—682no—
1112C4—682no—
1113C4—1361no—
1114C2—1362no—
1115C2—1362no—
1116C2#1453148311yescharacteristic
1117C2#1453156811yescharacteristic
1118C2#1453158011yescharacteristic
1119C2#1453181711yescharacteristic
1120C2#1453182311yescharacteristic
1121C2#1453189411yescharacteristic
1122C2#1453192411yescharacteristic
1123C2#1453537111yescharacteristic
1124C2#1453545711yescharacteristic
1125C2#1453545811yescharacteristic
1126C2#1453581111yescharacteristic
1127C2#1453610111yescharacteristic
1128C2#1453610211yescharacteristic
1129C2#1453649011yescharacteristic
1130C2#1453661211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1434C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1434D17
hypocenterC17#14589
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#11762700C2semidirect
3. C2×#11762698C2semidirect
4. #14527035C2semidirect
5. #14527028C2semidirect
6. #14527028C2semidirect
9. #14527022C2semidirect
10. #14527020C2semidirect
11. #14527020C2semidirect
12. #14527020C2semidirect
13. #14527012C2semidirect
14. #14527009C2semidirect
15. C17×#1434C2semidirect
34. #11762727C4semidirect
123. C2×#63225D4semidirect
485. #1434D17semidirect
711. C17#14589semidirect

Maximal subgroups

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

subgroupindex
C2×#117627272
C2×#117627002
C2×#117626982
#145270352
#145270282
#145270242
#145270222
#145270202
#145270122
#145270092
C17×#14342
#1458917