Finite Group Databasebeta

← #16963493

Subgroups — #16963493

Order 4352.

2070 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587580C211yesmaximal, characteristic
2C2×#11762711C211yesmaximal, characteristic
3C2×#11762687C211yesmaximal, characteristic
4#14527038C211yesmaximal, characteristic, complemented
5#14527037C211yesmaximal, characteristic, complemented
6#14527032C211yesmaximal, characteristic, complemented
7#14527032C211yesmaximal, characteristic, complemented
8#14527032C211yesmaximal, characteristic, complemented
9#14527032C211yesmaximal, characteristic, complemented
10#14527017C211yesmaximal, characteristic, complemented
11#14527005C211yesmaximal, characteristic, complemented
12#14527005C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1436C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C2×#10587580—24no—
20C2×#10587580—24no—
21C2×#10587580C418yescomplemented
22C22×C4⋊Dic17C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34#11762711—24no—
35#11762687—24no—
36C2×#10587502C2211yescharacteristic
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×C4⋊C4×C17C2211yescharacteristic
50C22×C42×C17C2211yescharacteristic
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—41no—
72C22×D68—41no—
73C22×D68—41no—
74C22×D68—41no—
75C22×D68C2×C414yes—
76C22×D68D414yes—
77C22×D68D414yes—
78C22×C4×D17—22no—
79C22×C4×D17—22no—
80C22×C4×D17—22no—
81C22×C4×D17—22no—
82C22×C4×D17—22no—
83C22×C4×D17—41no—
84C22×C4×D17—41no—
85C22×C4×D17—41no—
86C22×C4×D17—41no—
87C22×C4×D17—41no—
88C22×C4×D17—41no—
89C22×C4×D17—41no—
90C22×C4×D17—41no—
91C22×C4×D17C2×C414yescomplemented
92C2×C4⋊C4×C17—22no—
93C2×C4⋊C4×C17—22no—
94C2×C4⋊C4×C17C2×C414yescomplemented
95C2×C42×C17—22no—
96C2×C42×C17—41no—
97C2×C42×C17—41no—
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—41no—
118C2×#63227—41no—
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×C414yescomplemented
128C2×C4⋊Dic17—22no—
129C2×C4⋊Dic17—41no—
130C2×C4⋊Dic17—41no—
131C2×#63225—22no—
132C2×#63225—22no—
133C2×#63225C2×C414yescomplemented
134#10587580—232no—
135C17×#95—22no—
136C17×#95—22no—
137C17×#95—22no—
138C17×#95—41no—
139C17×#95—41no—
140#10587502—22no—
141#10587502—22no—
142#10587502—22no—
143#10587502—41no—
144#10587502—41no—
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×D17C22×C412yes—
179C23×D17C22×C412yes—
180C23×D17C2×D412yes—
181C23×D17C2×D412yes—
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×C17C22×C412yes—
226C22×C4×C17C22×C412yes—
227C22×C4×C17C22×C412yes—
228C22×C4×C17C2×D412yes—
229C22×C4×C17C2×D412yes—
230C22×C4×C17#4112yes—
231C22×C4×C17#4112yes—
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×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17—21no—
272C22×Dic17C22×C412yes—
273C22×Dic17C22×C412yes—
274C22×Dic17#4112yes—
275C2×D68—44no—
276C2×D68—44no—
277C2×D68—44no—
278C2×D68—44no—
279C2×D68—44no—
280C2×D68—44no—
281C2×D68C22⋊C4116yes—
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—
289C2×C4×D17—44no—
290C2×C4×D17—44no—
291C2×C4×D17—44no—
292C2×C4×D17—44no—
293C2×C4×D17—44no—
294C2×C4×D17—44no—
295C2×C4×D17—44no—
296C4⋊C4×C17—28no—
297C42×C17—44no—
298#63227—28no—
299#63227—28no—
300#63227—28no—
301#63227—44no—
302#63227—44no—
303#63227—44no—
304#63227—44no—
305#63227—44no—
306#63227—44no—
307#63227—44no—
308C4⋊Dic17—44no—
309#63225—28no—
310#14505—171nomaximal, Sylow
311C23×C17C23×C411yescharacteristic
312C23×C17C22×D411yescharacteristic
313C23×C17C22×D411yescharacteristic
314C23×C17C2×#4111yescharacteristic
315C23×C17C2×#4111yescharacteristic
316C23×C17C2×#4111yescharacteristic
317C23×C17C2×#4111yescharacteristic
318C23×C17H(5,𝔽2)11yescharacteristic
319C23×C17H(5,𝔽2)11yescharacteristic
320C23×C17H(5,𝔽2)11yescharacteristic
321C23×C17H(5,𝔽2)11yescharacteristic
322C23×C17H(5,𝔽2)11yescharacteristic
323C23×C17H(5,𝔽2)11yescharacteristic
324C23×C172−1+411yescharacteristic
325C23×C172−1+411yescharacteristic
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—22no—
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×D17C2×C22⋊C414yes—
395C22×D17C2×C22⋊C414yes—
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—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×C17—41no—
441C2×C4×C17—41no—
442C2×C4×C17—41no—
443C2×C4×C17—41no—
444C2×C4×C17C2×C22⋊C414yes—
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—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×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—
487D68—416no—
488C4×D17—416no—
489C4×D17—416no—
490C22×#123—171no—
491C2×#390—171no—
492C2×#386—171no—
493#1441—171no—
494#1441—171no—
495#1440—171no—
496#1440—171no—
497#1440—171no—
498#1440—171no—
499#1436—171no—
500#1436D1711yescharacteristic, complemented
501C22⋊#95—171no—
502C22⋊#95—171no—
503C22⋊#95—171no—
504C22⋊#95—171no—
505C22×C17C22×C22⋊C411yescharacteristic
506C22×C17C4×#4111yescharacteristic
507C22×C17C4×#4111yescharacteristic
508C22×C17#51811yescharacteristic
509C22×C17#51811yescharacteristic
510C22×C17#52011yescharacteristic
511C22×C17#52011yescharacteristic
512C22×C17#53411yescharacteristic
513C22×C17#53411yescharacteristic
514C22×C17#53411yescharacteristic
515C22×C17#53411yescharacteristic
516C22×C17#53811yescharacteristic
517C22×C17#53811yescharacteristic
518C22×C17#53911yescharacteristic
519C22×C17#53911yescharacteristic
520C22×C17#54011yescharacteristic
521C22×C17#54011yescharacteristic
522C22×C17#54211yescharacteristic
523C22×C17#54211yescharacteristic
524C22×C17#54611yescharacteristic
525C22×C17#54611yescharacteristic
526C22×C17#54611yescharacteristic
527C22×C17#54611yescharacteristic
528C22×C17#54711yescharacteristic
529C22×C17#54711yescharacteristic
530C22×C17#54711yescharacteristic
531C22×C17#54711yescharacteristic
532C22×C17#55111yescharacteristic
533C22×C17#55311yescharacteristic
534C22×C17#55311yescharacteristic
535C22×C17#55911yescharacteristic
536C22×C17#56011yescharacteristic
537C22×C17#56211yescharacteristic
538C22×C17#56211yescharacteristic
539C22×C17#56311yescharacteristic
540C2×D17—24no—
541C2×D17—24no—
542C2×D17—24no—
543C2×D17—24no—
544C2×D17—24no—
545C2×D17—24no—
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—
569C2×D17—42no—
570C4×C17—24no—
571C4×C17—42no—
572C4×C17—42no—
573C4×C17—42no—
574C4×C17—42no—
575C4×C17—42no—
576C4×C17—81no—
577Dic17—42no—
578Dic17—42no—
579Dic17—42no—
580Dic17—81no—
581Dic17—81no—
582Dic17—81no—
583C23×D4—171no—
584C24×C4—171no—
585C24×C4—171no—
586C2×#123—178no—
587C2×#123—344no—
588C2×#123—344no—
589C22×C4⋊C4—171no—
590C22×C4⋊C4—171no—
591C22×C4⋊C4C2×D1711yescharacteristic
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×C42C2×D1711yescharacteristic
603#390—344no—
604#386—344no—
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×#95—171no—
617C2×#95—171no—
618C2×#95C2×D1711yescharacteristic
619C2×#95C2×D1711yescharacteristic
620C2×#95C2×D1711yescharacteristic
621C2×#95C2×D1711yescharacteristic
622C2×#95C2×D1711yescharacteristic
623C2×C17#230811yescharacteristic
624C2×C17#233511yescharacteristic
625C2×C17#233511yescharacteristic
626C2×C17#233911yescharacteristic
627C2×C17#233911yescharacteristic
628C2×C17#237411yescharacteristic
629C2×C17#237611yescharacteristic
630C2×C17#269711yescharacteristic
631C2×C17#270111yescharacteristic
632C2×C17#270111yescharacteristic
633C2×C17#270811yescharacteristic
634C2×C17#270811yescharacteristic
635C2×C17#270911yescharacteristic
636C2×C17#271711yescharacteristic
637C2×C17#272411yescharacteristic
638D17—44no—
639D17—44no—
640C25—171no—
641C25—171no—
642C22×D4—174no—
643C22×D4—174no—
644C22×D4—174no—
645C22×D4—681no—
646C22×D4—681no—
647C22×D4—681no—
648C22×D4—681no—
649C23×C4—171no—
650C23×C4—171no—
651C23×C4—171no—
652C23×C4—174no—
653C23×C4—171no—
654C23×C4—171no—
655C23×C4—171no—
656C23×C4—342no—
657C23×C4—342no—
658C23×C4—342no—
659C23×C4—342no—
660C23×C4—342no—
661C23×C4—681no—
662C23×C4—681no—
663C23×C4—681no—
664C23×C4—681no—
665C23×C4—681no—
666C23×C4—681no—
667C23×C4—681no—
668C23×C4—681no—
669C23×C4C22×D1711yescharacteristic
670C23×C4C22×D1711yescharacteristic
671C23×C4C22×D1711yescharacteristic
672C23×C4C22×D1711yescharacteristic
673C23×C4C22×D1711yescharacteristic
674C23×C4C22×D1711yescharacteristic
675C23×C4C22×D1711yescharacteristic
676#123—3432no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—174no—
680C2×C4⋊C4—342no—
681C2×C4⋊C4—342no—
682C2×C4⋊C4—342no—
683C2×C4⋊C4—681no—
684C2×C4⋊C4—681no—
685C2×C4⋊C4C4×D1714yescomplemented
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—681no—
709C2×C22⋊C4—681no—
710C2×C22⋊C4—681no—
711C2×C22⋊C4—681no—
712C2×C22⋊C4—681no—
713C2×C22⋊C4—681no—
714C2×C22⋊C4—681no—
715C2×C22⋊C4—681no—
716C2×C42—22no—
717C2×C42—41no—
718C2×C42—41no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—41no—
723#95—41no—
724#95—342no—
725#95—342no—
726#95—342no—
727#95—681no—
728#95—681no—
729#95—681no—
730#95—681no—
731#95—681no—
732#95—681no—
733#95—681no—
734#95—681no—
735#95—681no—
736#95—681no—
737C17#1450511yescharacteristic, complemented, Sylow
738C24—172no—
739C24—172no—
740C24—172no—
741C24—172no—
742C24—172no—
743C24—172no—
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—
766C24—341no—
767C24—341no—
768C24C23×D1711yescharacteristic
769C2×D4—1716no—
770C2×D4—684no—
771C2×D4—684no—
772C2×D4—684no—
773C2×D4—684no—
774C2×D4—684no—
775C2×D4—684no—
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—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—172no—
818C22×C4—172no—
819C22×C4—172no—
820C22×C4—348no—
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×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—341no—
858C22×C4—341no—
859C22×C4—341no—
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×C4—684no—
871C22×C4—684no—
872C22×C4—684no—
873C22×C4C2×C4×D1712yes—
874C22×C4C2×C4×D1712yes—
875C22×C4C2×C4×D1712yes—
876C22×C4#6325212yes—
877C22×C4#6325212yes—
878C22×C4D4×D1712yes—
879C22×C4D4×D1712yes—
880C22×C4#6325612yes—
881C4⋊C4—28no—
882C4⋊C4—348no—
883C4⋊C4—684no—
884C22⋊C4—348no—
885C22⋊C4—348no—
886C22⋊C4—348no—
887C22⋊C4—684no—
888C22⋊C4—684no—
889C22⋊C4—684no—
890C22⋊C4—684no—
891C22⋊C4—684no—
892C22⋊C4—684no—
893C22⋊C4—684no—
894C42—44no—
895C23—174no—
896C23—174no—
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—342no—
932C23—342no—
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—
965C23C22×C4×D1711yescharacteristic
966C23C2×#6325211yescharacteristic
967C23C2×#6325211yescharacteristic
968C23C2×D4×D1711yescharacteristic
969C23C2×D4×D1711yescharacteristic
970C23#1058769111yescharacteristic
971C23#1058769111yescharacteristic
972C23C2×#6325611yescharacteristic
973C23#1058769411yescharacteristic
974C23#41×D1711yescharacteristic
975C23#1058769611yescharacteristic
976C23#1058769611yescharacteristic
977C23#1058769611yescharacteristic
978C23#1058769611yescharacteristic
979C23#1058769711yescharacteristic
980D4—6816no—
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—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—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—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—6816no—
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×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×C4C22⋊C4×D1714yes—
1074C22—344no—
1075C22—344no—
1076C22—344no—
1077C22—344no—
1078C22—344no—
1079C22—344no—
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—682no—
1103C22—682no—
1104C22C2×C22⋊C4×D1711yescharacteristic
1105C22C4×#6325211yescharacteristic
1106C22C4×#6325611yescharacteristic
1107C22#1176328111yescharacteristic
1108C22#1176328111yescharacteristic
1109C22#1176328911yescharacteristic
1110C22#1176329111yescharacteristic
1111C22#1176336711yescharacteristic
1112C22#1176336711yescharacteristic
1113C22#1176336911yescharacteristic
1114C22#1176337011yescharacteristic
1115C22#1176339211yescharacteristic
1116C22#1176339511yescharacteristic
1117C22#1176340611yescharacteristic
1118C22#1176340811yescharacteristic
1119C22#1176341411yescharacteristic
1120C22#1176341511yescharacteristic
1121C22#1176342511yescharacteristic
1122C22#1176343111yescharacteristic
1123C22#1176345011yescharacteristic
1124C22#1176345211yescharacteristic
1125C22#1176345511yescharacteristic
1126C22#1176345511yescharacteristic
1127C22#1176346111yescharacteristic
1128C22#1176346211yescharacteristic
1129C22#1176346411yescharacteristic
1130C22#1176346411yescharacteristic
1131C22#1176348311yescharacteristic
1132C22#1176350711yescharacteristic
1133C22#1176350811yescharacteristic
1134C22#1176354411yescharacteristic
1135C22#1176355011yescharacteristic
1136C22#1176355511yescharacteristic
1137C22#1176355611yescharacteristic
1138C22#1176356311yescharacteristic
1139C4—24no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—42no—
1145C4—81no—
1146C4—682no—
1147C4—682no—
1148C4—682no—
1149C4—1361no—
1150C4—1361no—
1151C4—1361no—
1152C2—684no—
1153C2—684no—
1154C2#1453135811yescharacteristic
1155C2#1453156811yescharacteristic
1156C2#1453157311yescharacteristic
1157C2#1453161311yescharacteristic
1158C2#1453161511yescharacteristic
1159C2#1453191311yescharacteristic
1160C2#1453193111yescharacteristic
1161C2#1453534411yescharacteristic
1162C2#1453539211yescharacteristic
1163C2#1453539411yescharacteristic
1164C2#1453550311yescharacteristic
1165C2#1453550511yescharacteristic
1166C2#1453551611yescharacteristic
1167C2#1453562411yescharacteristic
1168C2#1453571311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1436C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1436D17
hypocenterC17#14505
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. #14527038C2semidirect
5. #14527037C2semidirect
6. #14527032C2semidirect
7. #14527032C2semidirect
8. #14527032C2semidirect
9. #14527032C2semidirect
10. #14527017C2semidirect
11. #14527005C2semidirect
12. #14527005C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1436C2semidirect
21. C2×#10587580C4semidirect
91. C22×C4×D17C2×C4semidirect
94. C2×C4⋊C4×C17C2×C4semidirect
127. C2×#63227C2×C4semidirect
133. C2×#63225C2×C4semidirect
500. #1436D17semidirect
685. C2×C4⋊C4C4×D17semidirect
737. C17#14505semidirect

Maximal subgroups

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

subgroupindex
C22×#105875802
C2×#117627112
C2×#117626872
#145270382
#145270372
#145270322
#145270172
#145270052
C17×#14362
#1450517