Finite Group Databasebeta

← #16957285

Subgroups — #16957285

Order 4352.

2070 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762687C211yesmaximal, characteristic
2C2×#11762687C211yesmaximal, characteristic
3C2×#11762671C211yesmaximal, characteristic, complemented
4C2×C4×#63227C211yesmaximal, characteristic, complemented
5C2×#11762656C211yesmaximal, characteristic, complemented
6#14527044C211yesmaximal, characteristic, complemented
7#14527030C211yesmaximal, characteristic, complemented
8#14527030C211yesmaximal, characteristic, complemented
9#14527024C211yesmaximal, characteristic
10#14527022C211yesmaximal, characteristic, complemented
11#14527020C211yesmaximal, characteristic, complemented
12#14527018C211yesmaximal, characteristic, complemented
13#14527008C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1434C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32#11762687—24no—
33#11762687C418yescomplemented
34#11762671—24no—
35C4×#63227—24no—
36#11762656—24no—
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C22×C42×C17C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C24×D17C2311yescharacteristic
57C24×D17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C22×D68—22no—
72C22×D68—22no—
73C22×D68—22no—
74C22×D68—22no—
75C22×D68—41no—
76C22×D68—41no—
77C22×D68C2×C414yes—
78C22×C4×D17—22no—
79C22×C4×D17—22no—
80C22×C4×D17—22no—
81C22×C4×D17—22no—
82C22×C4×D17—22no—
83C22×C4×D17—22no—
84C22×C4×D17—22no—
85C22×C4×D17—22no—
86C22×C4×D17—22no—
87C22×C4×D17—41no—
88C22×C4×D17—41no—
89C22×C4×D17—41no—
90C22×C4×D17—41no—
91C22×C4×D17C2×C414yescomplemented
92C2×C42×C17—22no—
93C2×C42×C17—22no—
94C2×C42×C17—41no—
95C2×#63227—22no—
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—41no—
114C2×#63227—41no—
115C2×#63227—41no—
116C2×#63227—41no—
117C2×#63227—41no—
118C2×#63227—41no—
119C2×#63227—41no—
120C2×#63227—41no—
121C2×#63227C2×C414yes—
122C2×#63227C2×C414yes—
123C2×#63227C2×C414yescomplemented
124C2×#63227D414yes—
125C2×C4⋊Dic17—22no—
126C2×C4⋊Dic17—41no—
127C2×C4⋊Dic17—41no—
128C2×C4×Dic17—22no—
129C2×C4×Dic17—22no—
130C2×C4×Dic17—22no—
131C2×C4×Dic17—22no—
132C2×C4×Dic17—41no—
133C2×C4×Dic17—41no—
134C17×#95—22no—
135C17×#95—41no—
136C17×#95—41no—
137C17×#95—41no—
138C17×#95C2×C414yescomplemented
139C17×#95D414yescomplemented
140#10587502—22no—
141#10587502—22no—
142#10587502—22no—
143#10587502—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—22no—
148#10587502—22no—
149#10587502—41no—
150#10587502—41no—
151#10587502C2×C414yescomplemented
152C24×C17C2411yescharacteristic
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×D17—21no—
176C23×D17—21no—
177C23×D17C22×C412yes—
178C23×D17C22×C412yes—
179C23×D17C2×D412yes—
180C23×D17#4112yes—
181C23×D17#4112yes—
182C23×D17#4112yes—
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×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17C22×C412yes—
224C22×C4×C17C22×C412yes—
225C22×C4×C17C22×C412yes—
226C22×C4×C17C2×D412yes—
227C22×C4×C17C2×D412yes—
228C22×C4×C17C2×D412yes—
229C22×C4×C17C2×D412yes—
230C22×C4×C17#4112yes—
231C22×C4×C17#4112yes—
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×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17—21no—
268C22×Dic17C22×C412yes—
269C22×Dic17C22×C412yes—
270C22×Dic17C2×D412yes—
271C22×Dic17#4112yes—
272C22×Dic17#4112yes—
273C22×Dic17#4112yes—
274C2×D68—28no—
275C2×D68—28no—
276C2×D68—44no—
277C2×D68—44no—
278C2×D68—44no—
279C2×D68—44no—
280C2×D68—44no—
281C2×C4×D17—28no—
282C2×C4×D17—28no—
283C2×C4×D17—28no—
284C2×C4×D17—44no—
285C2×C4×D17—44no—
286C2×C4×D17—44no—
287C2×C4×D17—44no—
288C2×C4×D17—44no—
289C2×C4×D17—44no—
290C2×C4×D17—44no—
291C2×C4×D17—44no—
292C2×C4×D17—44no—
293C2×C4×D17—44no—
294C2×C4×D17—44no—
295C42×C17—44no—
296#63227—28no—
297#63227—28no—
298#63227—28no—
299#63227—28no—
300#63227—44no—
301#63227—44no—
302#63227—44no—
303#63227—44no—
304#63227—44no—
305#63227—44no—
306C4⋊Dic17—44no—
307C4×Dic17—44no—
308C4×Dic17—44no—
309#13984—171nomaximal, Sylow
310C23×C17C23×C411yescharacteristic
311C23×C17C22×D411yescharacteristic
312C23×C17C22×D411yescharacteristic
313C23×C17C2×#4111yescharacteristic
314C23×C17C2×#4111yescharacteristic
315C23×C17C2×#4111yescharacteristic
316C23×C17C2×#4111yescharacteristic
317C23×C17C2×#4111yescharacteristic
318C23×C17C2×#4111yescharacteristic
319C23×C17C2×#4111yescharacteristic
320C23×C17C2×#4111yescharacteristic
321C23×C17H(5,𝔽2)11yescharacteristic
322C23×C17H(5,𝔽2)11yescharacteristic
323C23×C17H(5,𝔽2)11yescharacteristic
324C23×C17H(5,𝔽2)11yescharacteristic
325C22×D17—22no—
326C22×D17—22no—
327C22×D17—22no—
328C22×D17—22no—
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—22no—
355C22×D17—22no—
356C22×D17—22no—
357C22×D17—22no—
358C22×D17—22no—
359C22×D17—22no—
360C22×D17—22no—
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#11714yes—
394C22×D17C4×D414yes—
395C2×C4×C17—22no—
396C2×C4×C17—22no—
397C2×C4×C17—22no—
398C2×C4×C17—22no—
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—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×C4×C17—41no—
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×C17C4×D414yes—
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—22no—
454C2×Dic17—22no—
455C2×Dic17—22no—
456C2×Dic17—22no—
457C2×Dic17—22no—
458C2×Dic17—22no—
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#12314yes—
486D68—416no—
487C4×D17—416no—
488C4×D17—416no—
489C2×#386—171no—
490C2×#386—171no—
491C2×#381—171no—
492C2×C4×C22⋊C4—171no—
493C2×C4×C22⋊C4—171no—
494#1443—171no—
495#1439—171no—
496#1439—171no—
497#1438—171no—
498#1437—171no—
499#1437—171no—
500#1436—171no—
501#1434—171no—
502#1434D1711yescharacteristic, complemented
503C22⋊#95—171no—
504C22×C17C2×#11711yescharacteristic
505C22×C17C2×C4×D411yescharacteristic
506C22×C17C2×C4×D411yescharacteristic
507C22×C17C4×#4111yescharacteristic
508C22×C17C4×#4111yescharacteristic
509C22×C17#51811yescharacteristic
510C22×C17#51811yescharacteristic
511C22×C17C2×#12311yescharacteristic
512C22×C17#52511yescharacteristic
513C22×C17#52511yescharacteristic
514C22×C17#52511yescharacteristic
515C22×C17#52911yescharacteristic
516C22×C17#52911yescharacteristic
517C22×C17#52911yescharacteristic
518C22×C17#52911yescharacteristic
519C22×C17#53811yescharacteristic
520C22×C17#53811yescharacteristic
521C22×C17#54011yescharacteristic
522C22×C17#54011yescharacteristic
523C22×C17D4211yescharacteristic
524C22×C17#54611yescharacteristic
525C22×C17#54611yescharacteristic
526C22×C17#54611yescharacteristic
527C22×C17#54611yescharacteristic
528C22×C17#54611yescharacteristic
529C22×C17#55011yescharacteristic
530C22×C17#55111yescharacteristic
531C22×C17#55111yescharacteristic
532C22×C17#55111yescharacteristic
533C22×C17#55111yescharacteristic
534C22×C17#55111yescharacteristic
535C22×C17#55311yescharacteristic
536C22×C17#55311yescharacteristic
537C22×C17#55311yescharacteristic
538C22×C17#55511yescharacteristic
539C2×D17—24no—
540C2×D17—24no—
541C2×D17—24no—
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—42no—
565C2×D17—42no—
566C2×D17—42no—
567C2×D17—42no—
568C2×D17—42no—
569C4×C17—24no—
570C4×C17—42no—
571C4×C17—42no—
572C4×C17—42no—
573C4×C17—42no—
574C4×C17—42no—
575C4×C17—42no—
576Dic17—24no—
577Dic17—42no—
578Dic17—42no—
579Dic17—42no—
580Dic17—81no—
581Dic17—81no—
582C23×D4—171no—
583C24×C4—171no—
584C24×C4—171no—
585C22×C4⋊C4—171no—
586C22×C22⋊C4—171no—
587C22×C22⋊C4—171no—
588C22×C22⋊C4—171no—
589C22×C22⋊C4—171no—
590C22×C22⋊C4—171no—
591C22×C22⋊C4—171no—
592C22×C22⋊C4—171no—
593C22×C22⋊C4—171no—
594C22×C22⋊C4—171no—
595C22×C22⋊C4—171no—
596C22×C42—171no—
597C22×C42—171no—
598C22×C42C2×D1711yescharacteristic
599#386—178no—
600#386—344no—
601#381—344no—
602C4×C22⋊C4—344no—
603C4×C22⋊C4—344no—
604C2×#95—171no—
605C2×#95—171no—
606C2×#95—171no—
607C2×#95—171no—
608C2×#95—171no—
609C2×#95—171no—
610C2×#95—171no—
611C2×#95—171no—
612C2×#95—171no—
613C2×#95—171no—
614C2×#95—171no—
615C2×#95—171no—
616C2×#95C2×D1711yescharacteristic
617C2×#95C2×D1711yescharacteristic
618C2×#95C2×D1711yescharacteristic
619C2×#95C2×D1711yescharacteristic
620C2×#95C2×D1711yescharacteristic
621C2×#95C2×D1711yescharacteristic
622C2×C17#229011yescharacteristic
623C2×C17C4×#12311yescharacteristic
624C2×C17#233311yescharacteristic
625C2×C17#234211yescharacteristic
626C2×C17#235311yescharacteristic
627C2×C17#235811yescharacteristic
628C2×C17#236311yescharacteristic
629C2×C17#241811yescharacteristic
630C2×C17#242011yescharacteristic
631C2×C17#245611yescharacteristic
632C2×C17#245711yescharacteristic
633C2×C17#245711yescharacteristic
634C2×C17#247111yescharacteristic
635C2×C17#257211yescharacteristic
636C2×C17#257611yescharacteristic
637D17—44no—
638D17—44no—
639C25—171no—
640C25—171no—
641C22×D4—174no—
642C22×D4—342no—
643C22×D4—342no—
644C22×D4—342no—
645C22×D4—342no—
646C22×D4—681no—
647C22×D4—681no—
648C23×C4—171no—
649C23×C4—171no—
650C23×C4—171no—
651C23×C4—171no—
652C23×C4—174no—
653C23×C4—171no—
654C23×C4—171no—
655C23×C4—342no—
656C23×C4—342no—
657C23×C4—342no—
658C23×C4—342no—
659C23×C4—342no—
660C23×C4—342no—
661C23×C4—342no—
662C23×C4—342no—
663C23×C4—342no—
664C23×C4—681no—
665C23×C4—681no—
666C23×C4—681no—
667C23×C4—681no—
668C23×C4C22×D1711yescharacteristic
669C23×C4C22×D1711yescharacteristic
670C23×C4C22×D1711yescharacteristic
671C23×C4C22×D1711yescharacteristic
672C23×C4C22×D1711yescharacteristic
673C23×C4C22×D1711yescharacteristic
674C23×C4C22×D1711yescharacteristic
675C2×C4⋊C4—342no—
676C2×C4⋊C4—681no—
677C2×C4⋊C4—681no—
678C2×C22⋊C4—174no—
679C2×C22⋊C4—174no—
680C2×C22⋊C4—174no—
681C2×C22⋊C4—174no—
682C2×C22⋊C4—342no—
683C2×C22⋊C4—342no—
684C2×C22⋊C4—342no—
685C2×C22⋊C4—342no—
686C2×C22⋊C4—342no—
687C2×C22⋊C4—342no—
688C2×C22⋊C4—342no—
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—681no—
701C2×C22⋊C4—681no—
702C2×C22⋊C4—681no—
703C2×C22⋊C4—681no—
704C2×C22⋊C4—681no—
705C2×C22⋊C4—681no—
706C2×C22⋊C4—681no—
707C2×C22⋊C4—681no—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—41no—
711C2×C42—342no—
712C2×C42—342no—
713C2×C42—342no—
714C2×C42—342no—
715C2×C42—681no—
716C2×C42—681no—
717#95—22no—
718#95—41no—
719#95—41no—
720#95—41no—
721#95—174no—
722#95—342no—
723#95—342no—
724#95—342no—
725#95—342no—
726#95—342no—
727#95—342no—
728#95—342no—
729#95—342no—
730#95—342no—
731#95—681no—
732#95—681no—
733#95C4×D1714yescomplemented
734#95D6814yescomplemented
735C17#1398411yescharacteristic, complemented, Sylow
736C24—172no—
737C24—172no—
738C24—172no—
739C24—172no—
740C24—172no—
741C24—172no—
742C24—341no—
743C24—341no—
744C24—341no—
745C24—341no—
746C24—341no—
747C24—341no—
748C24—341no—
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—
766C24C23×D1711yescharacteristic
767C2×D4—348no—
768C2×D4—348no—
769C2×D4—684no—
770C2×D4—684no—
771C2×D4—684no—
772C2×D4—684no—
773C2×D4—684no—
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—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—172no—
815C22×C4—172no—
816C22×C4—172no—
817C22×C4—172no—
818C22×C4—172no—
819C22×C4—172no—
820C22×C4—348no—
821C22×C4—348no—
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×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—348no—
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—684no—
860C22×C4—684no—
861C22×C4—684no—
862C22×C4—684no—
863C22×C4—684no—
864C22×C4—684no—
865C22×C4—684no—
866C22×C4—684no—
867C22×C4—684no—
868C22×C4—684no—
869C22×C4—684no—
870C22×C4C2×C4×D1712yes—
871C22×C4C2×C4×D1712yes—
872C22×C4C2×C4×D1712yes—
873C22×C4C2×D6812yes—
874C22×C4C2×D6812yes—
875C22×C4C2×D6812yes—
876C22×C4#6325212yes—
877C22×C4D4×D1712yes—
878C22×C4#6325612yes—
879C4⋊C4—684no—
880C22⋊C4—348no—
881C22⋊C4—348no—
882C22⋊C4—348no—
883C22⋊C4—348no—
884C22⋊C4—684no—
885C22⋊C4—684no—
886C22⋊C4—684no—
887C22⋊C4—684no—
888C22⋊C4—684no—
889C22⋊C4—684no—
890C42—44no—
891C42—684no—
892C42—684no—
893C23—174no—
894C23—174no—
895C23—342no—
896C23—342no—
897C23—342no—
898C23—342no—
899C23—342no—
900C23—342no—
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—342no—
927C23—342no—
928C23—342no—
929C23—342no—
930C23—342no—
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—
963C23C22×C4×D1711yescharacteristic
964C23C22×D6811yescharacteristic
965C23C2×#6325211yescharacteristic
966C23C2×D4×D1711yescharacteristic
967C23#1058769111yescharacteristic
968C23#1058769111yescharacteristic
969C23C2×#6325611yescharacteristic
970C23#41×D1711yescharacteristic
971C23#41×D1711yescharacteristic
972C23#41×D1711yescharacteristic
973C23#41×D1711yescharacteristic
974C23#41×D1711yescharacteristic
975C23#41×D1711yescharacteristic
976C23#1058769611yescharacteristic
977C23#1058769611yescharacteristic
978D4—6816no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
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—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
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—174no—
1028C2×C4—342no—
1029C2×C4—342no—
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—342no—
1043C2×C4—6816no—
1044C2×C4—6816no—
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×C4C4×D6814yes—
1072C22—344no—
1073C22—344no—
1074C22—344no—
1075C22—344no—
1076C22—344no—
1077C22—344no—
1078C22—682no—
1079C22—682no—
1080C22—682no—
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—682no—
1101C22—682no—
1102C22#117×D1711yescharacteristic
1103C22C4×D4×D1711yescharacteristic
1104C22C2×C4×D6811yescharacteristic
1105C22#1176327711yescharacteristic
1106C22C4×#6325611yescharacteristic
1107C22#1176328111yescharacteristic
1108C22#1176328111yescharacteristic
1109C22#123×D1711yescharacteristic
1110C22#1176332111yescharacteristic
1111C22#1176332111yescharacteristic
1112C22#1176332211yescharacteristic
1113C22#1176333711yescharacteristic
1114C22#1176333711yescharacteristic
1115C22#1176334211yescharacteristic
1116C22#1176334411yescharacteristic
1117C22#1176339311yescharacteristic
1118C22#1176339811yescharacteristic
1119C22#1176340911yescharacteristic
1120C22#1176341111yescharacteristic
1121C22D4×D6811yescharacteristic
1122C22#1176344911yescharacteristic
1123C22#1176345111yescharacteristic
1124C22#1176345411yescharacteristic
1125C22#1176345411yescharacteristic
1126C22#1176345611yescharacteristic
1127C22#1176348111yescharacteristic
1128C22#1176348311yescharacteristic
1129C22#1176348411yescharacteristic
1130C22#1176348411yescharacteristic
1131C22#1176348611yescharacteristic
1132C22#1176348911yescharacteristic
1133C22#1176350411yescharacteristic
1134C22#1176350711yescharacteristic
1135C22#1176351211yescharacteristic
1136C22#1176352211yescharacteristic
1137C4—24no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—344no—
1145C4—682no—
1146C4—682no—
1147C4—682no—
1148C4—1361no—
1149C4—1361no—
1150C2—684no—
1151C2—684no—
1152C2#1453122811yescharacteristic
1153C2#1453130511yescharacteristic
1154C2#1453154711yescharacteristic
1155C2#1453162811yescharacteristic
1156C2#1453172311yescharacteristic
1157C2#1453176611yescharacteristic
1158C2#1453182411yescharacteristic
1159C2#1453225111yescharacteristic
1160C2#1453227511yescharacteristic
1161C2#1453267411yescharacteristic
1162C2#1453268911yescharacteristic
1163C2#1453269811yescharacteristic
1164C2#1453289311yescharacteristic
1165C2#1453403211yescharacteristic
1166C2#1453408611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1434C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1434D17
hypocenterC17#13984
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#11762671C2semidirect
4. C2×C4×#63227C2semidirect
5. C2×#11762656C2semidirect
6. #14527044C2semidirect
7. #14527030C2semidirect
8. #14527030C2semidirect
10. #14527022C2semidirect
11. #14527020C2semidirect
12. #14527018C2semidirect
13. #14527008C2semidirect
14. #14527005C2semidirect
15. C17×#1434C2semidirect
33. #11762687C4semidirect
91. C22×C4×D17C2×C4semidirect
123. C2×#63227C2×C4semidirect
138. C17×#95C2×C4semidirect
139. C17×#95D4semidirect
151. #10587502C2×C4semidirect
502. #1434D17semidirect
733. #95C4×D17semidirect
734. #95D68semidirect
735. C17#13984semidirect

Maximal subgroups

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

subgroupindex
C2×#117626872
C2×#117626712
C2×C4×#632272
C2×#117626562
#145270442
#145270302
#145270242
#145270222
#145270202
#145270182
#145270082
#145270052
C17×#14342
#1398417