Finite Group Databasebeta

← #16963505

Subgroups — #16963505

Order 4352.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587580C211yesmaximal, characteristic
2C2×#11762701C211yesmaximal, characteristic, complemented
3C2×#11762698C211yesmaximal, characteristic, complemented
4#14527050C211yesmaximal, characteristic, complemented
5#14527030C211yesmaximal, characteristic, complemented
6#14527028C211yesmaximal, characteristic, complemented
7#14527024C211yesmaximal, characteristic
8#14527024C211yesmaximal, characteristic
9#14527020C211yesmaximal, characteristic, complemented
10#14527020C211yesmaximal, characteristic, complemented
11#14527013C211yesmaximal, characteristic, complemented
12#14527012C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1445C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C2×#10587580—24no—
19C2×#10587580—24no—
20C2×#10587580C418yescomplemented
21C22×C4⋊Dic17C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36C22×C4×Dic17C2211yescharacteristic
37#11762701—24no—
38#11762698—24no—
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C22×C4⋊C4×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—41no—
74C22×D68—41no—
75C22×D68—41no—
76C22×D68—41no—
77C22×D68C2×C414yes—
78C22×C4×D17—22no—
79C22×C4×D17—22no—
80C22×C4×D17—41no—
81C22×C4×D17—41no—
82C22×C4×D17—41no—
83C22×C4×D17—41no—
84C22×C4×D17C2×C414yes—
85C2×C4⋊C4×C17—22no—
86C2×C4⋊C4×C17—22no—
87C2×C4⋊C4×C17C2×C414yes—
88C2×#63227—22no—
89C2×#63227—22no—
90C2×#63227—22no—
91C2×#63227—22no—
92C2×#63227—22no—
93C2×#63227—22no—
94C2×#63227—22no—
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—41no—
105C2×#63227—41no—
106C2×#63227—41no—
107C2×#63227—41no—
108C2×#63227—41no—
109C2×#63227—41no—
110C2×#63227—41no—
111C2×#63227—41no—
112C2×#63227—41no—
113C2×#63227—41no—
114C2×#63227—41no—
115C2×#63227—41no—
116C2×#63227C2×C414yes—
117C2×#63227C2×C414yes—
118C2×#63227C2×C414yes—
119C2×#63227D414yes—
120C2×#63227D414yes—
121C2×C4⋊Dic17—22no—
122C2×C4⋊Dic17—22no—
123C2×C4⋊Dic17—41no—
124C2×#63225—22no—
125C2×#63225—22no—
126C2×#63225—22no—
127C2×#63225—22no—
128C2×#63225—41no—
129C2×#63225C2×C414yes—
130C2×C4×Dic17—22no—
131C2×C4×Dic17—22no—
132C2×C4×Dic17—22no—
133C2×C4×Dic17—22no—
134C2×C4×Dic17—41no—
135C2×C4×Dic17—41no—
136#10587580—232no—
137C17×#95—22no—
138C17×#95—22no—
139C17×#95—41no—
140C17×#95—41no—
141C17×#95—41no—
142C17×#95—41no—
143#10587502—22no—
144#10587502—22no—
145#10587502—41no—
146#10587502—41no—
147#10587502—41no—
148#10587502—41no—
149#10587502—41no—
150#10587502—41no—
151#10587502—41no—
152#10587502—41no—
153C24×C17C2411yescharacteristic
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×D17—21no—
178C23×D17—21no—
179C23×D17—21no—
180C23×D17C22×C412yes—
181C23×D17C22×C412yes—
182C23×D17C2×D412yes—
183C23×D17C2×D412yes—
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×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17—21no—
226C22×C4×C17—21no—
227C22×C4×C17C22×C412yes—
228C22×C4×C17C22×C412yes—
229C22×C4×C17C22×C412yes—
230C22×C4×C17C2×D412yes—
231C22×C4×C17C2×D412yes—
232C22×C4×C17#4112yes—
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×Dic17C2×D412yes—
272C22×Dic17#4112yes—
273C22×Dic17#4112yes—
274C22×Dic17#4112yes—
275C2×D68—28no—
276C2×D68—44no—
277C2×D68—44no—
278C2×D68—44no—
279C2×D68—44no—
280C2×D68—44no—
281C2×D68—44no—
282C2×C4×D17—28no—
283C2×C4×D17—44no—
284C2×C4×D17—44no—
285C2×C4×D17—44no—
286C2×C4×D17—44no—
287C2×C4×D17—44no—
288C2×C4×D17—44no—
289C4⋊C4×C17—28no—
290#63227—28no—
291#63227—28no—
292#63227—44no—
293#63227—44no—
294#63227—44no—
295#63227—44no—
296#63227—44no—
297#63227—44no—
298#63227—44no—
299#63227—44no—
300#63227C22⋊C4116yescomplemented
301C4⋊Dic17—44no—
302#63225—28no—
303#63225—44no—
304C4×Dic17—44no—
305C4×Dic17—44no—
306#14506—171nomaximal, Sylow
307C23×C17C23×C411yescharacteristic
308C23×C17C22×D411yescharacteristic
309C23×C17C22×D411yescharacteristic
310C23×C17C2×#4111yescharacteristic
311C23×C17C2×#4111yescharacteristic
312C23×C17C2×#4111yescharacteristic
313C23×C17C2×#4111yescharacteristic
314C23×C17H(5,𝔽2)11yescharacteristic
315C23×C17H(5,𝔽2)11yescharacteristic
316C23×C17H(5,𝔽2)11yescharacteristic
317C23×C17H(5,𝔽2)11yescharacteristic
318C23×C17H(5,𝔽2)11yescharacteristic
319C23×C17H(5,𝔽2)11yescharacteristic
320C23×C172−1+411yescharacteristic
321C23×C172−1+411yescharacteristic
322C22×D17—22no—
323C22×D17—22no—
324C22×D17—22no—
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—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—
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×D17C2×C22⋊C414yes—
392C2×C4×C17—22no—
393C2×C4×C17—22no—
394C2×C4×C17—22no—
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—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×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×C17C2×C22⋊C414yes—
441C2×Dic17—22no—
442C2×Dic17—22no—
443C2×Dic17—22no—
444C2×Dic17—22no—
445C2×Dic17—22no—
446C2×Dic17—22no—
447C2×Dic17—22no—
448C2×Dic17—22no—
449C2×Dic17—22no—
450C2×Dic17—22no—
451C2×Dic17—22no—
452C2×Dic17—22no—
453C2×Dic17—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×Dic17C2×C22⋊C414yes—
483D68—416no—
484C4×D17—416no—
485C22×#123—171no—
486C2×#388—171no—
487C2×#388—171no—
488#1445—171no—
489#1445D1711yescharacteristic, complemented
490#1439—171no—
491#1439—171no—
492#1438—171no—
493#1438—171no—
494#1437—171no—
495#1437—171no—
496C4⋊#95—171no—
497C4⋊#95—171no—
498C22⋊#95—171no—
499C22⋊#95—171no—
500C22×C17C22×C22⋊C411yescharacteristic
501C22×C17C4×#4111yescharacteristic
502C22×C17C4×#4111yescharacteristic
503C22×C17#51811yescharacteristic
504C22×C17#51811yescharacteristic
505C22×C17#52011yescharacteristic
506C22×C17#52011yescharacteristic
507C22×C17#53511yescharacteristic
508C22×C17#53511yescharacteristic
509C22×C17#53511yescharacteristic
510C22×C17#53511yescharacteristic
511C22×C17#53811yescharacteristic
512C22×C17#53811yescharacteristic
513C22×C17#53911yescharacteristic
514C22×C17#53911yescharacteristic
515C22×C17#54011yescharacteristic
516C22×C17#54011yescharacteristic
517C22×C17#54211yescharacteristic
518C22×C17#54211yescharacteristic
519C22×C17#54611yescharacteristic
520C22×C17#54611yescharacteristic
521C22×C17#54611yescharacteristic
522C22×C17#54611yescharacteristic
523C22×C17#54711yescharacteristic
524C22×C17#54711yescharacteristic
525C22×C17#54711yescharacteristic
526C22×C17#54711yescharacteristic
527C22×C17#55111yescharacteristic
528C22×C17#55311yescharacteristic
529C22×C17#55311yescharacteristic
530C22×C17#55911yescharacteristic
531C22×C17#56011yescharacteristic
532C22×C17#56211yescharacteristic
533C22×C17#56211yescharacteristic
534C22×C17#56311yescharacteristic
535C2×D17—24no—
536C2×D17—24no—
537C2×D17—24no—
538C2×D17—42no—
539C2×D17—42no—
540C2×D17—42no—
541C2×D17—42no—
542C2×D17—42no—
543C2×D17—42no—
544C2×D17—42no—
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—81no—
558C2×D17—81no—
559C2×D17—81no—
560C2×D17—81no—
561C2×D17—81no—
562C2×D17—81no—
563C2×D17—81no—
564C2×D17—81no—
565C4×C17—24no—
566C4×C17—42no—
567C4×C17—42no—
568C4×C17—42no—
569C4×C17—81no—
570C4×C17—81no—
571C4×C17—81no—
572Dic17—24no—
573Dic17—42no—
574Dic17—42no—
575Dic17—42no—
576Dic17—42no—
577Dic17—81no—
578C23×D4—171no—
579C24×C4—171no—
580C2×#123—178no—
581C2×#123—344no—
582C2×#123—344no—
583C22×C4⋊C4—171no—
584C22×C4⋊C4—171no—
585C22×C4⋊C4—171no—
586C22×C4⋊C4C2×D1711yescharacteristic
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×C22⋊C4—171no—
597C22×C22⋊C4—171no—
598C22×C42—171no—
599C22×C42—171no—
600#388—344no—
601#388—344no—
602C2×#95—171no—
603C2×#95—171no—
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×#95C2×D1711yescharacteristic
613C2×#95C2×D1711yescharacteristic
614C2×#95C2×D1711yescharacteristic
615C2×#95C2×D1711yescharacteristic
616C2×#95C2×D1711yescharacteristic
617C2×#95C2×D1711yescharacteristic
618C2×C17#230911yescharacteristic
619C2×C17#233511yescharacteristic
620C2×C17#233511yescharacteristic
621C2×C17#233911yescharacteristic
622C2×C17#233911yescharacteristic
623C2×C17#237411yescharacteristic
624C2×C17#237611yescharacteristic
625C2×C17#270311yescharacteristic
626C2×C17#270311yescharacteristic
627C2×C17#270611yescharacteristic
628C2×C17#270611yescharacteristic
629C2×C17#271011yescharacteristic
630C2×C17#271011yescharacteristic
631C2×C17#271811yescharacteristic
632C2×C17#271811yescharacteristic
633D17—44no—
634D17—82no—
635C25—171no—
636C25—171no—
637C22×D4—174no—
638C22×D4—342no—
639C22×D4—342no—
640C22×D4—681no—
641C22×D4—681no—
642C22×D4—681no—
643C22×D4—681no—
644C23×C4—171no—
645C23×C4—171no—
646C23×C4—171no—
647C23×C4—171no—
648C23×C4—171no—
649C23×C4—174no—
650C23×C4—171no—
651C23×C4—342no—
652C23×C4—342no—
653C23×C4—681no—
654C23×C4—681no—
655C23×C4—681no—
656C23×C4—681no—
657C23×C4C22×D1711yescharacteristic
658C23×C4C22×D1711yescharacteristic
659C23×C4C22×D1711yescharacteristic
660C23×C4C22×D1711yescharacteristic
661C23×C4C22×D1711yescharacteristic
662C23×C4C22×D1711yescharacteristic
663C23×C4C22×D1711yescharacteristic
664#123—3432no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—174no—
668C2×C4⋊C4—342no—
669C2×C4⋊C4—342no—
670C2×C4⋊C4—342no—
671C2×C4⋊C4—342no—
672C2×C4⋊C4—342no—
673C2×C4⋊C4—342no—
674C2×C4⋊C4—681no—
675C2×C4⋊C4—681no—
676C2×C4⋊C4C4×D1714yes—
677C2×C22⋊C4—174no—
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—681no—
699C2×C22⋊C4—681no—
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×C22⋊C4—681no—
709C2×C22⋊C4—681no—
710C2×C42—342no—
711C2×C42—342no—
712C2×C42—342no—
713C2×C42—342no—
714C2×C42—681no—
715C2×C42—681no—
716#95—22no—
717#95—22no—
718#95—41no—
719#95—41no—
720#95—41no—
721#95—41no—
722#95—342no—
723#95—342no—
724#95—681no—
725#95—681no—
726#95—681no—
727#95—681no—
728#95—681no—
729#95—681no—
730#95—681no—
731#95—681no—
732C17#1450611yescharacteristic, complemented, Sylow
733C24—172no—
734C24—172no—
735C24—172no—
736C24—172no—
737C24—341no—
738C24—341no—
739C24—341no—
740C24—341no—
741C24—341no—
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—
763C24C23×D1711yescharacteristic
764C2×D4—348no—
765C2×D4—684no—
766C2×D4—684no—
767C2×D4—684no—
768C2×D4—684no—
769C2×D4—684no—
770C2×D4—684no—
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—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—172no—
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—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—684no—
858C22×C4—684no—
859C22×C4—684no—
860C22×C4—684no—
861C22×C4—684no—
862C22×C4—684no—
863C22×C4C2×C4×D1712yes—
864C22×C4C2×C4×D1712yes—
865C22×C4C2×C4×D1712yes—
866C22×C4D4×D1712yes—
867C22×C4D4×D1712yes—
868C22×C4#6325612yes—
869C4⋊C4—28no—
870C4⋊C4—348no—
871C4⋊C4—684no—
872C4⋊C4—684no—
873C22⋊C4—1716no—
874C22⋊C4—348no—
875C22⋊C4—348no—
876C22⋊C4—684no—
877C22⋊C4—684no—
878C22⋊C4—684no—
879C22⋊C4—684no—
880C22⋊C4—684no—
881C22⋊C4—684no—
882C22⋊C4—684no—
883C22⋊C4—684no—
884C42—684no—
885C42—684no—
886C23—174no—
887C23—342no—
888C23—342no—
889C23—342no—
890C23—342no—
891C23—342no—
892C23—342no—
893C23—342no—
894C23—342no—
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—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—
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—
956C23C22×C4×D1711yescharacteristic
957C23C2×D4×D1711yescharacteristic
958C23C2×D4×D1711yescharacteristic
959C23#1058769111yescharacteristic
960C23#1058769111yescharacteristic
961C23C2×#6325611yescharacteristic
962C23#1058769411yescharacteristic
963C23#41×D1711yescharacteristic
964C23#41×D1711yescharacteristic
965C23#41×D1711yescharacteristic
966C23#1058769611yescharacteristic
967C23#1058769611yescharacteristic
968C23#1058769611yescharacteristic
969C23#1058769611yescharacteristic
970C23#1058769711yescharacteristic
971D4—6816no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
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—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
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—174no—
1021C2×C4—342no—
1022C2×C4—342no—
1023C2×C4—342no—
1024C2×C4—342no—
1025C2×C4—342no—
1026C2×C4—342no—
1027C2×C4—342no—
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—6816no—
1040C2×C4—681no—
1041C2×C4—681no—
1042C2×C4—681no—
1043C2×C4—681no—
1044C2×C4—681no—
1045C2×C4—681no—
1046C2×C4—681no—
1047C2×C4—681no—
1048C2×C4—681no—
1049C2×C4—681no—
1050C2×C4—681no—
1051C2×C4—681no—
1052C2×C4—681no—
1053C2×C4—681no—
1054C2×C4—681no—
1055C2×C4—681no—
1056C2×C4—681no—
1057C2×C4—681no—
1058C2×C4—681no—
1059C2×C4—681no—
1060C2×C4—681no—
1061C2×C4—681no—
1062C2×C4—681no—
1063C2×C4C22⋊C4×D1714yes—
1064C22—344no—
1065C22—344no—
1066C22—344no—
1067C22—682no—
1068C22—682no—
1069C22—682no—
1070C22—682no—
1071C22—682no—
1072C22—682no—
1073C22—682no—
1074C22—682no—
1075C22—682no—
1076C22—682no—
1077C22—682no—
1078C22—682no—
1079C22—682no—
1080C22—682no—
1081C22—682no—
1082C22—682no—
1083C22—682no—
1084C22—682no—
1085C22—682no—
1086C22—1361no—
1087C22—1361no—
1088C22—1361no—
1089C22—1361no—
1090C22—1361no—
1091C22—1361no—
1092C22—1361no—
1093C22—1361no—
1094C22C2×C22⋊C4×D1711yescharacteristic
1095C22#1176327711yescharacteristic
1096C22C4×#6325611yescharacteristic
1097C22#1176328111yescharacteristic
1098C22#1176328111yescharacteristic
1099C22#1176328911yescharacteristic
1100C22#1176329111yescharacteristic
1101C22#1176337211yescharacteristic
1102C22#1176337511yescharacteristic
1103C22#1176337511yescharacteristic
1104C22#1176337711yescharacteristic
1105C22#1176339511yescharacteristic
1106C22#1176339811yescharacteristic
1107C22#1176340711yescharacteristic
1108C22#1176340811yescharacteristic
1109C22#1176341111yescharacteristic
1110C22#1176341511yescharacteristic
1111C22#1176342511yescharacteristic
1112C22#1176342911yescharacteristic
1113C22#1176345011yescharacteristic
1114C22#1176345111yescharacteristic
1115C22#1176345111yescharacteristic
1116C22#1176345211yescharacteristic
1117C22#1176345711yescharacteristic
1118C22#1176345711yescharacteristic
1119C22#1176346111yescharacteristic
1120C22#1176346211yescharacteristic
1121C22#1176348611yescharacteristic
1122C22#1176351011yescharacteristic
1123C22#1176351211yescharacteristic
1124C22#1176354311yescharacteristic
1125C22#1176355011yescharacteristic
1126C22#1176355511yescharacteristic
1127C22#1176355611yescharacteristic
1128C22#1176356311yescharacteristic
1129C4—24no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—81no—
1134C4—81no—
1135C4—81no—
1136C4—344no—
1137C4—682no—
1138C4—682no—
1139C4—682no—
1140C4—682no—
1141C4—1361no—
1142C2—684no—
1143C2—1362no—
1144C2#1453136311yescharacteristic
1145C2#1453157311yescharacteristic
1146C2#1453158011yescharacteristic
1147C2#1453160811yescharacteristic
1148C2#1453161311yescharacteristic
1149C2#1453191611yescharacteristic
1150C2#1453193111yescharacteristic
1151C2#1453542611yescharacteristic
1152C2#1453542911yescharacteristic
1153C2#1453547111yescharacteristic
1154C2#1453547411yescharacteristic
1155C2#1453552511yescharacteristic
1156C2#1453553111yescharacteristic
1157C2#1453563311yescharacteristic
1158C2#1453563911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1445C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1445D17
hypocenterC17#14506
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
2. C2×#11762701C2semidirect
3. C2×#11762698C2semidirect
4. #14527050C2semidirect
5. #14527030C2semidirect
6. #14527028C2semidirect
9. #14527020C2semidirect
10. #14527020C2semidirect
11. #14527013C2semidirect
12. #14527012C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1445C2semidirect
20. C2×#10587580C4semidirect
300. #63227C22⋊C4semidirect
489. #1445D17semidirect
732. C17#14506semidirect

Maximal subgroups

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

subgroupindex
C22×#105875802
C2×#117627012
C2×#117626982
#145270502
#145270302
#145270282
#145270242
#145270202
#145270132
#145270122
#145270052
C17×#14452
#1450617