Finite Group Databasebeta

← #16961856

Subgroups — #16961856

Order 4352.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762686C211yesmaximal, characteristic
2C2×#11762685C211yesmaximal, characteristic
3C2×#11762670C211yesmaximal, characteristic, complemented
4#14527044C211yesmaximal, characteristic, complemented
5#14527044C211yesmaximal, characteristic, complemented
6#14527040C211yesmaximal, characteristic, complemented
7#14527030C211yesmaximal, characteristic, complemented
8#14527029C211yesmaximal, characteristic, complemented
9#14527023C211yesmaximal, characteristic
10#14527022C211yesmaximal, characteristic, complemented
11#14527011C211yesmaximal, characteristic, complemented
12#14527006C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27#11762686C418yescomplemented
28#11762685—24no—
29#11762670—24no—
30C2×#10587502C2211yescharacteristic
31C2×#10587502C2211yescharacteristic
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
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×C22⋊C4×C17C2211yescharacteristic
48C22×C22⋊C4×C17C2211yescharacteristic
49C22×C22⋊C4×C17C2211yescharacteristic
50C22×C42×C17C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C25×C17C2311yescharacteristic
55C24×D17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C22×C22⋊D17—22no—
63C22×C22⋊D17—22no—
64C22×C22⋊D17—22no—
65C22×C22⋊D17—22no—
66C22×C22⋊D17—41no—
67C22×C22⋊D17—41no—
68C22×C22⋊D17C2×C414yes—
69C23×Dic17—22no—
70C23×Dic17—22no—
71C23×Dic17—41no—
72C23×Dic17—41no—
73C23×Dic17—41no—
74C23×Dic17—41no—
75C23×Dic17C2×C414yescomplemented
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C22×C4×D17—22no—
84C22×C4×D17—22no—
85C22×C4×D17—22no—
86C22×C4×D17—41no—
87C22×C4×D17—41no—
88C22×C4×D17—41no—
89C22×C4×D17—41no—
90C2×C22⋊C4×C17—22no—
91C2×C22⋊C4×C17—22no—
92C2×C22⋊C4×C17—41no—
93C2×C22⋊C4×C17—41no—
94C2×C22⋊C4×C17—41no—
95C2×C22⋊C4×C17—41no—
96C2×C22⋊C4×C17—41no—
97C2×C22⋊C4×C17C2×C414yescomplemented
98C2×C22⋊C4×C17D414yes—
99C2×C42×C17—22no—
100C2×C42×C17—41no—
101C2×C42×C17—41no—
102C2×C22⋊Dic17—22no—
103C2×C22⋊Dic17—22no—
104C2×C22⋊Dic17—22no—
105C2×C22⋊Dic17—41no—
106C2×C22⋊Dic17—41no—
107C2×C22⋊Dic17—41no—
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×C4⋊Dic17—41no—
124C2×C4⋊Dic17—41no—
125C2×C4⋊Dic17—41no—
126C17×#95—41no—
127C17×#95—41no—
128C17×#95—41no—
129#10587502—22no—
130#10587502—22no—
131#10587502—22no—
132#10587502—22no—
133#10587502—22no—
134#10587502—22no—
135#10587502—22no—
136#10587502—41no—
137#10587502—41no—
138#10587502—41no—
139#10587502—41no—
140#10587502—41no—
141#10587502—41no—
142#10587502—41no—
143#10587502—41no—
144#10587502C2×C414yescomplemented
145#10587502C2×C414yescomplemented
146C24×C17—21no—
147C24×C17—21no—
148C24×C17—21no—
149C24×C17—21no—
150C24×C17—21no—
151C24×C17—21no—
152C24×C17—21no—
153C24×C17—21no—
154C24×C17—21no—
155C24×C17—21no—
156C24×C17—21no—
157C24×C17—21no—
158C24×C17C22×C412yes—
159C24×C17C2×D412yes—
160C24×C17#4112yes—
161C24×C17C2411yescharacteristic
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×D17C22×C412yes—
175C23×D17#4112yes—
176C23×D17#4112yes—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17C22×C412yes—
215C22×C4×C17C22×C412yes—
216C22×C4×C17C2×D412yes—
217C22×C4×C17C2×D412yes—
218C22×C4×C17#4112yes—
219C2×C22⋊D17—28no—
220C2×C22⋊D17—28no—
221C2×C22⋊D17—44no—
222C2×C22⋊D17—44no—
223C2×C22⋊D17—44no—
224C2×C22⋊D17—44no—
225C2×C22⋊D17—44no—
226C22×Dic17—28no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×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×Dic17—44no—
273C22×Dic17—44no—
274C22×Dic17—44no—
275C22×Dic17—44no—
276C22×Dic17—44no—
277C22×Dic17—44no—
278C22×Dic17C22×C412yes—
279C22×Dic17C22×C412yes—
280C22×Dic17C22×C412yes—
281C22×Dic17#4112yes—
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—
289C22⋊C4×C17—44no—
290C22⋊C4×C17—44no—
291C22⋊C4×C17—44no—
292C42×C17—44no—
293C22⋊Dic17—44no—
294C22⋊Dic17—44no—
295#63227—44no—
296#63227—44no—
297#63227—44no—
298#63227—44no—
299#63227—44no—
300C4⋊Dic17—44no—
301#14375—171nomaximal, Sylow
302C23×C17—22no—
303C23×C17—22no—
304C23×C17—22no—
305C23×C17—22no—
306C23×C17—22no—
307C23×C17—22no—
308C23×C17—22no—
309C23×C17—22no—
310C23×C17—22no—
311C23×C17—22no—
312C23×C17—22no—
313C23×C17—22no—
314C23×C17—22no—
315C23×C17—22no—
316C23×C17—22no—
317C23×C17—22no—
318C23×C17—22no—
319C23×C17—22no—
320C23×C17—41no—
321C23×C17—41no—
322C23×C17—41no—
323C23×C17—41no—
324C23×C17—41no—
325C23×C17—41no—
326C23×C17—41no—
327C23×C17—41no—
328C23×C17—41no—
329C23×C17—41no—
330C23×C17—41no—
331C23×C17—41no—
332C23×C17—41no—
333C23×C17—41no—
334C23×C17—41no—
335C23×C17—41no—
336C23×C17C4×D414yes—
337C23×C17C23×C411yescharacteristic
338C23×C17C22×D411yescharacteristic
339C23×C17C2×#4111yescharacteristic
340C23×C17C2×#4111yescharacteristic
341C23×C17C2×#4111yescharacteristic
342C23×C17C2×#4111yescharacteristic
343C23×C17C2×#4111yescharacteristic
344C23×C17H(5,𝔽2)11yescharacteristic
345C23×C17H(5,𝔽2)11yescharacteristic
346C23×C17H(5,𝔽2)11yescharacteristic
347C23×C17H(5,𝔽2)11yescharacteristic
348C23×C17H(5,𝔽2)11yescharacteristic
349C23×C17H(5,𝔽2)11yescharacteristic
350C23×C17H(5,𝔽2)11yescharacteristic
351C23×C172−1+411yescharacteristic
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—22no—
363C22×D17—22no—
364C22×D17—22no—
365C22×D17—22no—
366C22×D17—22no—
367C22×D17—22no—
368C22×D17—22no—
369C22×D17—22no—
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#11714yes—
387C2×C4×C17—22no—
388C2×C4×C17—22no—
389C2×C4×C17—22no—
390C2×C4×C17—22no—
391C2×C4×C17—22no—
392C2×C4×C17—22no—
393C2×C4×C17—22no—
394C2×C4×C17—22no—
395C2×C4×C17—22no—
396C2×C4×C17—22no—
397C2×C4×C17—22no—
398C2×C4×C17—22no—
399C2×C4×C17—22no—
400C2×C4×C17—22no—
401C2×C4×C17—22no—
402C2×C4×C17—41no—
403C2×C4×C17—41no—
404C2×C4×C17—41no—
405C2×C4×C17—41no—
406C2×C4×C17—41no—
407C2×C4×C17—41no—
408C2×C4×C17—41no—
409C2×C4×C17—41no—
410C2×C4×C17—41no—
411C2×C4×C17—41no—
412C2×C4×C17—41no—
413C2×C4×C17—41no—
414C2×C4×C17—41no—
415C2×C4×C17—41no—
416C2×C4×C17—41no—
417C2×C4×C17—41no—
418C2×C4×C17—41no—
419C2×C4×C17—41no—
420C2×C4×C17—41no—
421C2×C4×C17—41no—
422C2×C4×C17—41no—
423C2×C4×C17—41no—
424C2×C4×C17—41no—
425C2×C4×C17—41no—
426C2×C4×C17—41no—
427C2×C4×C17—41no—
428C2×C4×C17—41no—
429C22⋊D17—416no—
430C2×Dic17—22no—
431C2×Dic17—22no—
432C2×Dic17—22no—
433C2×Dic17—22no—
434C2×Dic17—22no—
435C2×Dic17—22no—
436C2×Dic17—22no—
437C2×Dic17—22no—
438C2×Dic17—22no—
439C2×Dic17—22no—
440C2×Dic17—22no—
441C2×Dic17—22no—
442C2×Dic17—416no—
443C2×Dic17—41no—
444C2×Dic17—41no—
445C2×Dic17—41no—
446C2×Dic17—41no—
447C2×Dic17—41no—
448C2×Dic17—41no—
449C2×Dic17—41no—
450C2×Dic17—41no—
451C2×Dic17—41no—
452C2×Dic17—41no—
453C2×Dic17—41no—
454C2×Dic17—41no—
455C2×Dic17—41no—
456C2×Dic17—41no—
457C2×Dic17—41no—
458C2×Dic17—41no—
459C2×Dic17—41no—
460C2×Dic17—41no—
461C2×Dic17—41no—
462C2×Dic17—41no—
463C2×Dic17—41no—
464C2×Dic17—41no—
465C2×Dic17—41no—
466C2×Dic17—41no—
467C2×Dic17—41no—
468C2×Dic17—41no—
469C2×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—
480C4×D17—416no—
481C2×#386—171no—
482C2×#386—171no—
483C2×#381—171no—
484#1443—171no—
485#1443—171no—
486#1442—171no—
487#1439—171no—
488#1439—171no—
489#1438—171no—
490#1437—171no—
491#1437D1711yescharacteristic, complemented
492#1434—171no—
493C22⋊#95—171no—
494C22⋊#95—171no—
495C22⋊#95—171no—
496C22×C17—24no—
497C22×C17—24no—
498C22×C17—24no—
499C22×C17—42no—
500C22×C17—42no—
501C22×C17—42no—
502C22×C17—42no—
503C22×C17—42no—
504C22×C17—42no—
505C22×C17—42no—
506C22×C17—42no—
507C22×C17—42no—
508C22×C17—42no—
509C22×C17—42no—
510C22×C17—42no—
511C22×C17C2×#11711yescharacteristic
512C22×C17C2×C4×D411yescharacteristic
513C22×C17C4×#4111yescharacteristic
514C22×C17#51811yescharacteristic
515C22×C17#51811yescharacteristic
516C22×C17#51811yescharacteristic
517C22×C17#52011yescharacteristic
518C22×C17#53411yescharacteristic
519C22×C17#53511yescharacteristic
520C22×C17#53811yescharacteristic
521C22×C17#53811yescharacteristic
522C22×C17#53811yescharacteristic
523C22×C17#53811yescharacteristic
524C22×C17#53811yescharacteristic
525C22×C17#53811yescharacteristic
526C22×C17#53911yescharacteristic
527C22×C17#53911yescharacteristic
528C22×C17#54011yescharacteristic
529C22×C17#54011yescharacteristic
530C22×C17#54611yescharacteristic
531C22×C17#54611yescharacteristic
532C22×C17#54611yescharacteristic
533C22×C17#54711yescharacteristic
534C22×C17#55111yescharacteristic
535C22×C17#55111yescharacteristic
536C22×C17#55111yescharacteristic
537C22×C17#55111yescharacteristic
538C22×C17#55111yescharacteristic
539C22×C17#55211yescharacteristic
540C22×C17#55311yescharacteristic
541C22×C17#55311yescharacteristic
542C22×C17#56011yescharacteristic
543C22×C17#56011yescharacteristic
544C22×C17#56211yescharacteristic
545C22×C17#56211yescharacteristic
546C2×D17—24no—
547C2×D17—24no—
548C2×D17—24no—
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—
561C4×C17—42no—
562C4×C17—42no—
563C4×C17—42no—
564C4×C17—42no—
565C4×C17—42no—
566C4×C17—81no—
567Dic17—42no—
568Dic17—42no—
569Dic17—42no—
570Dic17—42no—
571Dic17—81no—
572Dic17—81no—
573Dic17—81no—
574C23×D4—171no—
575C24×C4—171no—
576C24×C4—171no—
577C22×C4⋊C4—171no—
578C22×C22⋊C4—171no—
579C22×C22⋊C4—171no—
580C22×C22⋊C4—171no—
581C22×C22⋊C4—171no—
582C22×C22⋊C4—171no—
583C22×C22⋊C4—171no—
584C22×C22⋊C4—171no—
585C22×C22⋊C4C2×D1711yescharacteristic
586C22×C22⋊C4C2×D1711yescharacteristic
587C22×C22⋊C4C2×D1711yescharacteristic
588C22×C42C2×D1711yescharacteristic
589#386—178no—
590#386—344no—
591#381—344no—
592C2×#95—171no—
593C2×#95—171no—
594C2×#95—171no—
595C2×#95—171no—
596C2×#95—171no—
597C2×#95—171no—
598C2×#95—171no—
599C2×#95—171no—
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×#95C2×D1711yescharacteristic
610C2×#95C2×D1711yescharacteristic
611C2×#95C2×D1711yescharacteristic
612C2×C17—44no—
613C2×C17#231811yescharacteristic
614C2×C17#232111yescharacteristic
615C2×C17#233311yescharacteristic
616C2×C17#234211yescharacteristic
617C2×C17#235311yescharacteristic
618C2×C17#235911yescharacteristic
619C2×C17#237711yescharacteristic
620C2×C17#269711yescharacteristic
621C2×C17#270311yescharacteristic
622C2×C17#270611yescharacteristic
623C2×C17#270811yescharacteristic
624C2×C17#274311yescharacteristic
625C2×C17#274911yescharacteristic
626C2×C17#275011yescharacteristic
627C2×C17#276011yescharacteristic
628D17—44no—
629C25—171no—
630C25C22×D1711yescharacteristic
631C22×D4—174no—
632C22×D4—342no—
633C22×D4—342no—
634C22×D4—342no—
635C22×D4—342no—
636C22×D4—681no—
637C22×D4—681no—
638C23×C4—171no—
639C23×C4—171no—
640C23×C4—171no—
641C23×C4—171no—
642C23×C4—174no—
643C23×C4—171no—
644C23×C4—171no—
645C23×C4—171no—
646C23×C4—342no—
647C23×C4—342no—
648C23×C4—342no—
649C23×C4—342no—
650C23×C4—342no—
651C23×C4—681no—
652C23×C4—681no—
653C23×C4—681no—
654C23×C4—681no—
655C23×C4—681no—
656C23×C4—681no—
657C23×C4—681no—
658C23×C4—681no—
659C23×C4C22×D1711yescharacteristic
660C23×C4C22×D1711yescharacteristic
661C23×C4C22×D1711yescharacteristic
662C23×C4C22×D1711yescharacteristic
663C23×C4C22×D1711yescharacteristic
664C23×C4C22×D1711yescharacteristic
665C2×C4⋊C4—681no—
666C2×C4⋊C4—681no—
667C2×C4⋊C4—681no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—41no—
671C2×C22⋊C4—41no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4—174no—
676C2×C22⋊C4—174no—
677C2×C22⋊C4—342no—
678C2×C22⋊C4—342no—
679C2×C22⋊C4—342no—
680C2×C22⋊C4—342no—
681C2×C22⋊C4—342no—
682C2×C22⋊C4—342no—
683C2×C22⋊C4—342no—
684C2×C22⋊C4—342no—
685C2×C22⋊C4—681no—
686C2×C22⋊C4—681no—
687C2×C22⋊C4—681no—
688C2×C22⋊C4—681no—
689C2×C22⋊C4—681no—
690C2×C22⋊C4—681no—
691C2×C22⋊C4—681no—
692C2×C22⋊C4—681no—
693C2×C22⋊C4—681no—
694C2×C22⋊C4—681no—
695C2×C22⋊C4—681no—
696C2×C22⋊C4C4×D1714yescomplemented
697C2×C22⋊C4D6814yes—
698C2×C42—22no—
699C2×C42—41no—
700C2×C42—41no—
701#95—41no—
702#95—41no—
703#95—41no—
704#95—174no—
705#95—174no—
706#95—342no—
707#95—342no—
708#95—342no—
709#95—342no—
710#95—342no—
711#95—342no—
712#95—342no—
713#95—681no—
714#95—681no—
715#95—681no—
716#95—681no—
717#95—681no—
718#95—681no—
719#95—681no—
720#95—681no—
721C17#1437511yescharacteristic, complemented, Sylow
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
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—
749C24C2×C4×D1712yes—
750C24C2×D6812yes—
751C24#6325212yes—
752C24C23×D1711yescharacteristic
753C2×D4—348no—
754C2×D4—348no—
755C2×D4—684no—
756C2×D4—684no—
757C2×D4—684no—
758C2×D4—684no—
759C2×D4—684no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—172no—
798C22×C4—172no—
799C22×C4—172no—
800C22×C4—172no—
801C22×C4—341no—
802C22×C4—341no—
803C22×C4—341no—
804C22×C4—341no—
805C22×C4—341no—
806C22×C4—341no—
807C22×C4—341no—
808C22×C4—341no—
809C22×C4—341no—
810C22×C4—341no—
811C22×C4—341no—
812C22×C4—341no—
813C22×C4—341no—
814C22×C4—341no—
815C22×C4—341no—
816C22×C4—341no—
817C22×C4—341no—
818C22×C4—341no—
819C22×C4—341no—
820C22×C4—341no—
821C22×C4—341no—
822C22×C4—341no—
823C22×C4—341no—
824C22×C4—341no—
825C22×C4—348no—
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—684no—
848C22×C4—684no—
849C22×C4—684no—
850C22×C4—684no—
851C22×C4—684no—
852C22×C4—684no—
853C22×C4—684no—
854C22×C4—684no—
855C22×C4—684no—
856C22×C4—684no—
857C22×C4—684no—
858C22×C4—684no—
859C22×C4—684no—
860C22×C4C2×C4×D1712yes—
861C22×C4C2×C4×D1712yes—
862C22×C4C2×D6812yes—
863C22×C4C2×D6812yes—
864C22×C4#6325412yes—
865C4⋊C4—684no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—684no—
870C22⋊C4—684no—
871C22⋊C4—684no—
872C22⋊C4—684no—
873C22⋊C4—684no—
874C22⋊C4—684no—
875C22⋊C4—684no—
876C42—44no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—174no—
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—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—
946C23C4×D6814yes—
947C23C22×C4×D1711yescharacteristic
948C23C22×D6811yescharacteristic
949C23C2×#6325211yescharacteristic
950C23C2×#6325411yescharacteristic
951C23#1058769111yescharacteristic
952C23#1058769111yescharacteristic
953C23#1058769111yescharacteristic
954C23#1058769111yescharacteristic
955C23#1058769111yescharacteristic
956C23#41×D1711yescharacteristic
957C23#41×D1711yescharacteristic
958C23#41×D1711yescharacteristic
959C23#1058769611yescharacteristic
960C23#1058769611yescharacteristic
961C23#1058769711yescharacteristic
962D4—6816no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—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—342no—
1006C2×C4—342no—
1007C2×C4—342no—
1008C2×C4—342no—
1009C2×C4—342no—
1010C2×C4—342no—
1011C2×C4—342no—
1012C2×C4—342no—
1013C2×C4—342no—
1014C2×C4—342no—
1015C2×C4—342no—
1016C2×C4—342no—
1017C2×C4—6816no—
1018C2×C4—6816no—
1019C2×C4—681no—
1020C2×C4—681no—
1021C2×C4—681no—
1022C2×C4—681no—
1023C2×C4—681no—
1024C2×C4—681no—
1025C2×C4—681no—
1026C2×C4—681no—
1027C2×C4—681no—
1028C2×C4—681no—
1029C2×C4—681no—
1030C2×C4—681no—
1031C2×C4—681no—
1032C2×C4—681no—
1033C2×C4—681no—
1034C2×C4—681no—
1035C2×C4—681no—
1036C2×C4—681no—
1037C2×C4—681no—
1038C2×C4—681no—
1039C2×C4—681no—
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—
1056C22—24no—
1057C22—24no—
1058C22—24no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
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#117×D1711yescharacteristic
1087C22C2×C4×D6811yescharacteristic
1088C22C4×#6325411yescharacteristic
1089C22#1176328111yescharacteristic
1090C22#1176328111yescharacteristic
1091C22#1176328211yescharacteristic
1092C22#1176328811yescharacteristic
1093C22#1176337111yescharacteristic
1094C22#1176337811yescharacteristic
1095C22#1176339111yescharacteristic
1096C22#1176339111yescharacteristic
1097C22#1176339211yescharacteristic
1098C22#1176339211yescharacteristic
1099C22#1176339311yescharacteristic
1100C22#1176339411yescharacteristic
1101C22#1176340011yescharacteristic
1102C22#1176340211yescharacteristic
1103C22#1176341111yescharacteristic
1104C22#1176341211yescharacteristic
1105C22#1176345411yescharacteristic
1106C22#1176345411yescharacteristic
1107C22#1176345411yescharacteristic
1108C22#1176346311yescharacteristic
1109C22#1176348211yescharacteristic
1110C22#1176348511yescharacteristic
1111C22#1176348811yescharacteristic
1112C22#1176348811yescharacteristic
1113C22#1176348911yescharacteristic
1114C22#1176349211yescharacteristic
1115C22#1176350611yescharacteristic
1116C22#1176351011yescharacteristic
1117C22#1176354611yescharacteristic
1118C22#1176354711yescharacteristic
1119C22#1176355311yescharacteristic
1120C22#1176355411yescharacteristic
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—81no—
1127C4—682no—
1128C4—682no—
1129C4—682no—
1130C4—682no—
1131C4—1361no—
1132C4—1361no—
1133C4—1361no—
1134C2—44no—
1135C2—684no—
1136C2#1453141411yescharacteristic
1137C2#1453144411yescharacteristic
1138C2#1453155011yescharacteristic
1139C2#1453163611yescharacteristic
1140C2#1453171911yescharacteristic
1141C2#1453177811yescharacteristic
1142C2#1453193511yescharacteristic
1143C2#1453534611yescharacteristic
1144C2#1453542511yescharacteristic
1145C2#1453547011yescharacteristic
1146C2#1453550011yescharacteristic
1147C2#1453592411yescharacteristic
1148C2#1453600511yescharacteristic
1149C2#1453602011yescharacteristic
1150C2#1453616011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1437C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1437D17
hypocenterC17#14375
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
3. C2×#11762670C2semidirect
4. #14527044C2semidirect
5. #14527044C2semidirect
6. #14527040C2semidirect
7. #14527030C2semidirect
8. #14527029C2semidirect
10. #14527022C2semidirect
11. #14527011C2semidirect
12. #14527006C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1437C2semidirect
27. #11762686C4semidirect
75. C23×Dic17C2×C4semidirect
97. C2×C22⋊C4×C17C2×C4semidirect
144. #10587502C2×C4semidirect
145. #10587502C2×C4semidirect
491. #1437D17semidirect
696. C2×C22⋊C4C4×D17semidirect
721. C17#14375semidirect

Maximal subgroups

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

subgroupindex
C2×#117626862
C2×#117626852
C2×#117626702
#145270442
#145270402
#145270302
#145270292
#145270232
#145270222
#145270112
#145270062
#145270052
C17×#14372
#1437517