Finite Group Databasebeta

← #16963593

Subgroups — #16963593

Order 4352.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762710C211yesmaximal, characteristic
2C2×#11762687C211yesmaximal, characteristic
3C2×#11762687C211yesmaximal, characteristic
4#14527043C211yesmaximal, characteristic, complemented
5#14527030C211yesmaximal, characteristic, complemented
6#14527030C211yesmaximal, characteristic, complemented
7#14527028C211yesmaximal, characteristic, complemented
8#14527028C211yesmaximal, characteristic, complemented
9#14527018C211yesmaximal, characteristic, complemented
10#14527015C211yesmaximal, characteristic, complemented
11#14527005C211yesmaximal, characteristic, complemented
12#14527005C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1442C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32#11762710—24no—
33#11762687—24no—
34#11762687C418yescomplemented
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C22×C4⋊C4×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×D68C2×C414yes—
74C22×D68D414yes—
75C22×D68Q814yes—
76C22×C4×D17—22no—
77C22×C4×D17—22no—
78C22×C4×D17—22no—
79C22×C4×D17—41no—
80C22×C4×D17—41no—
81C22×C4×D17—41no—
82C22×C4×D17—41no—
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×D17C2×C414yescomplemented
90C2×C4⋊C4×C17—22no—
91C2×C4⋊C4×C17—41no—
92C2×C4⋊C4×C17—41no—
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—22no—
105C2×#63227—22no—
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×#63227—41no—
117C2×#63227—41no—
118C2×#63227—41no—
119C2×#63227—41no—
120C2×#63227C2×C414yes—
121C2×#63227C2×C414yes—
122C2×#63227C2×C414yescomplemented
123C2×C4⋊Dic17—22no—
124C2×C4⋊Dic17—41no—
125C2×C4⋊Dic17—41no—
126C2×#63225—22no—
127C2×#63225—41no—
128C2×#63225—41no—
129C2×C4×Dic17—22no—
130C2×C4×Dic17—41no—
131C2×C4×Dic17—41no—
132C17×#95—22no—
133C17×#95—41no—
134C17×#95—41no—
135C17×#95—41no—
136C17×#95—41no—
137C17×#95C2×C414yescomplemented
138#10587502—22no—
139#10587502—22no—
140#10587502—22no—
141#10587502—41no—
142#10587502—41no—
143#10587502—41no—
144#10587502—41no—
145#10587502—41no—
146#10587502—41no—
147#10587502—41no—
148#10587502—41no—
149#10587502C2×C414yescomplemented
150C24×C17C2411yescharacteristic
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—
177C23×D17C2×D412yes—
178C23×D17C2×D412yes—
179C23×D17C2×Q812yes—
180C23×D17C2×Q812yes—
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×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17C22×C412yes—
225C22×C4×C17C22×C412yes—
226C22×C4×C17C22×C412yes—
227C22×C4×C17C2×D412yes—
228C22×C4×C17C2×Q812yes—
229C22×C4×C17#4112yes—
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×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17C22×C412yes—
268C22×Dic17C22×C412yes—
269C22×Dic17#4112yes—
270C22×Dic17#4112yes—
271C22×Dic17#4112yes—
272C2×D68—44no—
273C2×D68—44no—
274C2×D68—44no—
275C2×D68—44no—
276C2×D68—44no—
277C2×D68—44no—
278C2×D68C4⋊C4116yescomplemented
279C2×C4×D17—44no—
280C2×C4×D17—44no—
281C2×C4×D17—44no—
282C2×C4×D17—44no—
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—
293C4⋊C4×C17—44no—
294#63227—44no—
295#63227—44no—
296#63227—44no—
297#63227—44no—
298#63227—44no—
299#63227—44no—
300#63227—44no—
301#63227—44no—
302#63227—44no—
303#63227—44no—
304C4⋊Dic17—44no—
305#63225—44no—
306C4×Dic17—44no—
307#14513—171nomaximal, Sylow
308C23×C17C23×C411yescharacteristic
309C23×C17C22×D411yescharacteristic
310C23×C17C22×Q811yescharacteristic
311C23×C17C2×#4111yescharacteristic
312C23×C17C2×#4111yescharacteristic
313C23×C17C2×#4111yescharacteristic
314C23×C17C2×#4111yescharacteristic
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×C17H(5,𝔽2)11yescharacteristic
321C23×C17H(5,𝔽2)11yescharacteristic
322C23×C17H(5,𝔽2)11yescharacteristic
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—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—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×C4⋊C414yes—
392C22×D17C2×C4⋊C414yes—
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—22no—
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×C17—41no—
441C2×C4×C17C2×C4⋊C414yes—
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—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—
484D68—416no—
485C4×D17—416no—
486C4×D17—416no—
487C2×#390—171no—
488C2×#386—171no—
489C2×#386—171no—
490#1442—171no—
491#1442D1711yescharacteristic, complemented
492#1439—171no—
493#1439—171no—
494#1439—171no—
495#1439—171no—
496#1436—171no—
497#1436—171no—
498C22⋊#95—171no—
499C22⋊#95—171no—
500C22⋊#95—171no—
501C22⋊#95—171no—
502C22×C17C22×C4⋊C411yescharacteristic
503C22×C17C4×#4111yescharacteristic
504C22×C17C4×#4111yescharacteristic
505C22×C17#51811yescharacteristic
506C22×C17#51811yescharacteristic
507C22×C17#51811yescharacteristic
508C22×C17#51811yescharacteristic
509C22×C17#53411yescharacteristic
510C22×C17#53411yescharacteristic
511C22×C17#53811yescharacteristic
512C22×C17#53811yescharacteristic
513C22×C17#53811yescharacteristic
514C22×C17#53811yescharacteristic
515C22×C17#54011yescharacteristic
516C22×C17#54011yescharacteristic
517C22×C17#54011yescharacteristic
518C22×C17#54011yescharacteristic
519C22×C17#54311yescharacteristic
520C22×C17#54311yescharacteristic
521C22×C17#54611yescharacteristic
522C22×C17#54611yescharacteristic
523C22×C17#54611yescharacteristic
524C22×C17#54611yescharacteristic
525C22×C17#55111yescharacteristic
526C22×C17#55311yescharacteristic
527C22×C17#55311yescharacteristic
528C22×C17#55411yescharacteristic
529C22×C17#55411yescharacteristic
530C22×C17#55411yescharacteristic
531C22×C17#55411yescharacteristic
532C22×C17#55911yescharacteristic
533C22×C17#56011yescharacteristic
534C22×C17#56011yescharacteristic
535C22×C17#56011yescharacteristic
536C22×C17H(3,𝔽4)11yescharacteristic
537C2×D17—24no—
538C2×D17—24no—
539C2×D17—24no—
540C2×D17—24no—
541C2×D17—24no—
542C2×D17—24no—
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—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—
567C4×C17—24no—
568C4×C17—42no—
569C4×C17—42no—
570C4×C17—42no—
571C4×C17—81no—
572C4×C17—81no—
573C4×C17—81no—
574Dic17—42no—
575Dic17—42no—
576Dic17—42no—
577Dic17—42no—
578Dic17—42no—
579Dic17—81no—
580C23×D4—171no—
581C24×C4—171no—
582C24×C4—171no—
583C22×C4⋊C4—171no—
584C22×C4⋊C4—171no—
585C22×C4⋊C4C2×D1711yescharacteristic
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—
597#390—344no—
598#386—178no—
599#386—344no—
600C2×#95—171no—
601C2×#95—171no—
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#231511yescharacteristic
619C2×C17#233311yescharacteristic
620C2×C17#233311yescharacteristic
621C2×C17#234911yescharacteristic
622C2×C17#234911yescharacteristic
623C2×C17#237411yescharacteristic
624C2×C17#237511yescharacteristic
625C2×C17#268411yescharacteristic
626C2×C17#268811yescharacteristic
627C2×C17#268811yescharacteristic
628C2×C17#270911yescharacteristic
629C2×C17#274811yescharacteristic
630C2×C17#278011yescharacteristic
631C2×C17#278011yescharacteristic
632C2×C17#280411yescharacteristic
633D17—44no—
634D17—44no—
635C25—171no—
636C25—171no—
637C22×D4—174no—
638C22×D4—174no—
639C22×D4—174no—
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—342no—
654C23×C4—681no—
655C23×C4—681no—
656C23×C4—681no—
657C23×C4—681no—
658C23×C4—681no—
659C23×C4—681no—
660C23×C4—681no—
661C23×C4—681no—
662C23×C4—681no—
663C23×C4—681no—
664C23×C4C22×D1711yescharacteristic
665C23×C4C22×D1711yescharacteristic
666C23×C4C22×D1711yescharacteristic
667C23×C4C22×D1711yescharacteristic
668C23×C4C22×D1711yescharacteristic
669C23×C4C22×D1711yescharacteristic
670C23×C4C22×D1711yescharacteristic
671C2×C4⋊C4—22no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4—342no—
675C2×C4⋊C4—342no—
676C2×C4⋊C4—681no—
677C2×C4⋊C4—681no—
678C2×C4⋊C4—681no—
679C2×C4⋊C4—681no—
680C2×C22⋊C4—174no—
681C2×C22⋊C4—174no—
682C2×C22⋊C4—174no—
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—681no—
697C2×C22⋊C4—681no—
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—681no—
712C2×C42—681no—
713#95—22no—
714#95—41no—
715#95—41no—
716#95—41no—
717#95—41no—
718#95—174no—
719#95—342no—
720#95—342no—
721#95—342no—
722#95—681no—
723#95—681no—
724#95—681no—
725#95—681no—
726#95—681no—
727#95—681no—
728#95—681no—
729#95—681no—
730#95C4×D1714yescomplemented
731C17#1451311yescharacteristic, complemented, Sylow
732C24—172no—
733C24—172no—
734C24—172no—
735C24—172no—
736C24—172no—
737C24—172no—
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—
762C24C23×D1711yescharacteristic
763C2×D4—1716no—
764C2×D4—684no—
765C2×D4—684no—
766C2×D4—684no—
767C2×D4—684no—
768C2×D4—684no—
769C2×D4—684no—
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—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—172no—
814C22×C4—172no—
815C22×C4—172no—
816C22×C4—172no—
817C22×C4—172no—
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×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—684no—
856C22×C4—684no—
857C22×C4—684no—
858C22×C4—684no—
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×C4C2×C4×D1712yes—
870C22×C4C2×C4×D1712yes—
871C22×C4C2×C4×D1712yes—
872C22×C4D4×D1712yes—
873C22×C4Q8×D1712yes—
874C22×C4#6325612yes—
875C4⋊C4—44no—
876C4⋊C4—684no—
877C4⋊C4—684no—
878C22⋊C4—684no—
879C22⋊C4—684no—
880C22⋊C4—684no—
881C22⋊C4—684no—
882C22⋊C4—684no—
883C22⋊C4—684no—
884C22⋊C4—684no—
885C22⋊C4—684no—
886C22⋊C4—684no—
887C22⋊C4—684no—
888C42—684no—
889C23—174no—
890C23—174no—
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—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—681no—
928C23—681no—
929C23—681no—
930C23—681no—
931C23—681no—
932C23—681no—
933C23—681no—
934C23—681no—
935C23—681no—
936C23—681no—
937C23—681no—
938C23—681no—
939C23—681no—
940C23—681no—
941C23—681no—
942C23—681no—
943C23—681no—
944C23—681no—
945C23—681no—
946C23—681no—
947C23—681no—
948C23—681no—
949C23—681no—
950C23—681no—
951C23—681no—
952C23—681no—
953C23—681no—
954C23—681no—
955C23—681no—
956C23—681no—
957C23—681no—
958C23—681no—
959C23C22×C4×D1711yescharacteristic
960C23C2×D4×D1711yescharacteristic
961C23#1058769111yescharacteristic
962C23#1058769111yescharacteristic
963C23#1058769111yescharacteristic
964C23C2×Q8×D1711yescharacteristic
965C23C2×#6325611yescharacteristic
966C23#41×D1711yescharacteristic
967C23#41×D1711yescharacteristic
968C23#41×D1711yescharacteristic
969C23#1058769611yescharacteristic
970C23#1058769611yescharacteristic
971C23#1058769611yescharacteristic
972C23#1058769611yescharacteristic
973C23#1058769611yescharacteristic
974D4—6816no—
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—22no—
988C2×C4—22no—
989C2×C4—22no—
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—41no—
1021C2×C4—41no—
1022C2×C4—41no—
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—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×C4C4⋊C4×D1714yes—
1068C22—344no—
1069C22—344no—
1070C22—344no—
1071C22—344no—
1072C22—344no—
1073C22—344no—
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—682no—
1087C22—682no—
1088C22—682no—
1089C22—682no—
1090C22—682no—
1091C22—682no—
1092C22—682no—
1093C22—682no—
1094C22—682no—
1095C22—682no—
1096C22—682no—
1097C22—682no—
1098C22C2×C4⋊C4×D1711yescharacteristic
1099C22#1176327711yescharacteristic
1100C22C4×#6325611yescharacteristic
1101C22#1176328111yescharacteristic
1102C22#1176328111yescharacteristic
1103C22#1176328111yescharacteristic
1104C22#1176328311yescharacteristic
1105C22#1176336911yescharacteristic
1106C22#1176337011yescharacteristic
1107C22#1176339311yescharacteristic
1108C22#1176339811yescharacteristic
1109C22#1176339811yescharacteristic
1110C22#1176339911yescharacteristic
1111C22#1176340911yescharacteristic
1112C22#1176341111yescharacteristic
1113C22#1176341111yescharacteristic
1114C22#1176341511yescharacteristic
1115C22#1176343411yescharacteristic
1116C22#1176343411yescharacteristic
1117C22#1176345011yescharacteristic
1118C22#1176345211yescharacteristic
1119C22#1176345211yescharacteristic
1120C22#1176345611yescharacteristic
1121C22#1176348611yescharacteristic
1122C22#1176351011yescharacteristic
1123C22#1176351211yescharacteristic
1124C22#1176351511yescharacteristic
1125C22#1176351511yescharacteristic
1126C22#1176351511yescharacteristic
1127C22#1176352011yescharacteristic
1128C22#1176354311yescharacteristic
1129C22#1176354711yescharacteristic
1130C22#1176354911yescharacteristic
1131C22#1176355011yescharacteristic
1132C22#1176355111yescharacteristic
1133C4—24no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—682no—
1141C4—682no—
1142C4—682no—
1143C4—682no—
1144C4—682no—
1145C4—1361no—
1146C2—684no—
1147C2—684no—
1148C2#1453139511yescharacteristic
1149C2#1453154711yescharacteristic
1150C2#1453154811yescharacteristic
1151C2#1453169211yescharacteristic
1152C2#1453169311yescharacteristic
1153C2#1453191611yescharacteristic
1154C2#1453192411yescharacteristic
1155C2#1453516711yescharacteristic
1156C2#1453522511yescharacteristic
1157C2#1453522711yescharacteristic
1158C2#1453551811yescharacteristic
1159C2#1453599611yescharacteristic
1160C2#1453643111yescharacteristic
1161C2#1453643811yescharacteristic
1162C2#1453672911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1442C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1442D17
hypocenterC17#14513
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
4. #14527043C2semidirect
5. #14527030C2semidirect
6. #14527030C2semidirect
7. #14527028C2semidirect
8. #14527028C2semidirect
9. #14527018C2semidirect
10. #14527015C2semidirect
11. #14527005C2semidirect
12. #14527005C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1442C2semidirect
34. #11762687C4semidirect
89. C22×C4×D17C2×C4semidirect
122. C2×#63227C2×C4semidirect
137. C17×#95C2×C4semidirect
149. #10587502C2×C4semidirect
278. C2×D68C4⋊C4semidirect
491. #1442D17semidirect
730. #95C4×D17semidirect
731. C17#14513semidirect

Maximal subgroups

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

subgroupindex
C2×#117627102
C2×#117626872
#145270432
#145270302
#145270282
#145270182
#145270152
#145270052
C17×#14422
#1451317