Finite Group Databasebeta

← #16961920

Subgroups — #16961920

Order 4352.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762712C211yesmaximal, characteristic
2C2×#11762689C211yesmaximal, characteristic
3C2×#11762676C211yesmaximal, characteristic, complemented
4#14527036C211yesmaximal, characteristic, complemented
5#14527031C211yesmaximal, characteristic, complemented
6#14527031C211yesmaximal, characteristic, complemented
7#14527027C211yesmaximal, characteristic, complemented
8#14527027C211yesmaximal, characteristic, complemented
9#14527021C211yesmaximal, characteristic, complemented
10#14527021C211yesmaximal, characteristic, complemented
11#14527018C211yesmaximal, characteristic, complemented
12#14527008C211yesmaximal, characteristic, complemented
13#14527006C211yesmaximal, characteristic, complemented
14#14527006C211yesmaximal, characteristic, complemented
15C17×#1438C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×C22⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28#11762712C418yescomplemented
29#11762689—24no—
30#11762676—24no—
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
47C23×D4×C17C2211yescharacteristic
48C22×C22⋊C4×C17C2211yescharacteristic
49C22×C22⋊C4×C17C2211yescharacteristic
50C22×C22⋊C4×C17C2211yescharacteristic
51C22×C22⋊C4×C17C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C25×C17C2311yescharacteristic
55C25×C17C2311yescharacteristic
56C22×D4×C17—22no—
57C22×D4×C17—22no—
58C22×D4×C17—22no—
59C22×D4×C17—22no—
60C22×D4×C17—41no—
61C22×D4×C17—41no—
62C22×D4×C17C2×C414yes—
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×Dic17—22no—
69C23×Dic17—22no—
70C23×Dic17—22no—
71C23×Dic17—41no—
72C23×Dic17—41no—
73C23×Dic17—41no—
74C23×Dic17—41no—
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C2×C22⋊C4×C17—22no—
84C2×C22⋊C4×C17—22no—
85C2×C22⋊C4×C17—22no—
86C2×C22⋊C4×C17—22no—
87C2×C22⋊C4×C17—41no—
88C2×C22⋊C4×C17—41no—
89C2×C22⋊C4×C17—41no—
90C2×C22⋊C4×C17—41no—
91C2×C22⋊C4×C17—41no—
92C2×C22⋊C4×C17—41no—
93C2×C22⋊C4×C17—41no—
94C2×C22⋊C4×C17—41no—
95C2×C22⋊Dic17—22no—
96C2×C22⋊Dic17—22no—
97C2×C22⋊Dic17—22no—
98C2×C22⋊Dic17—22no—
99C2×C22⋊Dic17—22no—
100C2×C22⋊Dic17—41no—
101C2×C22⋊Dic17—41no—
102C2×C22⋊Dic17—41no—
103C2×C22⋊Dic17—41no—
104C2×C22⋊Dic17—41no—
105C2×C22⋊Dic17—41no—
106C2×C22⋊Dic17—41no—
107C2×C22⋊Dic17—41no—
108C2×C22⋊Dic17—41no—
109C2×C22⋊Dic17—41no—
110C2×C22⋊Dic17—41no—
111C2×C22⋊Dic17—41no—
112C2×C22⋊Dic17C2×C414yes—
113C2×C22⋊Dic17C2×C414yes—
114C2×C22⋊Dic17C2×C414yescomplemented
115C2×C22⋊Dic17C2×C414yescomplemented
116C2×C4⋊Dic17—41no—
117C2×C4⋊Dic17—41no—
118C2×C4⋊Dic17C2×C414yescomplemented
119C2×#63225—41no—
120C2×#63225—41no—
121C2×#63225—41no—
122C2×C4×Dic17—22no—
123C2×C4×Dic17—22no—
124C2×C4×Dic17—41no—
125C2×C4×Dic17—41no—
126C2×C4×Dic17—41no—
127C2×C4×Dic17C2×C414yescomplemented
128C17×#95—22no—
129C17×#95—22no—
130#10587502—22no—
131#10587502—22no—
132#10587502—22no—
133#10587502—22no—
134#10587502—22no—
135#10587502—22no—
136#10587502—22no—
137#10587502—41no—
138#10587502—41no—
139#10587502—41no—
140#10587502—41no—
141#10587502—41no—
142#10587502—41no—
143#10587502—41no—
144#10587502—41no—
145#10587502D414yes—
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×C17—21no—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17—21no—
164C24×C17—21no—
165C24×C17—21no—
166C24×C17—21no—
167C24×C17—21no—
168C24×C17—21no—
169C24×C17—21no—
170C24×C17—21no—
171C24×C17—21no—
172C24×C17C22×C412yes—
173C24×C17C22×C412yes—
174C24×C17#4112yes—
175C24×C17#4112yes—
176C24×C17C2411yescharacteristic
177C2×D4×C17—28no—
178C2×D4×C17—28no—
179C2×D4×C17—44no—
180C2×D4×C17—44no—
181C2×D4×C17—44no—
182C2×D4×C17—44no—
183C2×D4×C17—44no—
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×C17C22×C412yes—
216C22×C4×C17C2×D412yes—
217C22×C4×C17#4112yes—
218C22×C4×C17#4112yes—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
226C22×Dic17—21no—
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—44no—
269C22×Dic17—44no—
270C22×Dic17—44no—
271C22×Dic17—44no—
272C22×Dic17—44no—
273C22×Dic17—44no—
274C22×Dic17—44no—
275C22×Dic17C22×C412yes—
276C22×Dic17C22×C412yes—
277C22×Dic17C22×C412yes—
278C22×Dic17C22×C412yes—
279C22×Dic17C2×D412yes—
280C22×Dic17C2×D412yes—
281C22×Dic17#4112yes—
282C22⋊C4×C17—44no—
283C22⋊C4×C17—44no—
284C22⋊C4×C17—44no—
285C22⋊C4×C17—44no—
286C22⋊Dic17—44no—
287C22⋊Dic17—44no—
288C22⋊Dic17—44no—
289C22⋊Dic17—44no—
290C22⋊Dic17—44no—
291C22⋊Dic17—44no—
292C22⋊Dic17—44no—
293C4⋊Dic17—44no—
294#63225—44no—
295C4×Dic17—28no—
296C4×Dic17—44no—
297#14379—171nomaximal, Sylow
298C23×C17—22no—
299C23×C17—22no—
300C23×C17—22no—
301C23×C17—22no—
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—22no—
321C23×C17—22no—
322C23×C17—22no—
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×C17—41no—
337C23×C17—41no—
338C23×C17—41no—
339C23×C17—41no—
340C23×C17—41no—
341C23×C17—41no—
342C23×C17—41no—
343C23×C17—41no—
344C23×C17—41no—
345C23×C17—41no—
346C23×C17—41no—
347C23×C17—41no—
348C23×C17—41no—
349C23×C17—41no—
350C23×C17—41no—
351C23×C17—41no—
352C23×C17—41no—
353C23×C17—41no—
354C23×C17—41no—
355C23×C17—41no—
356C23×C17—41no—
357C23×C17—41no—
358C23×C17—41no—
359C23×C17—41no—
360C23×C17—41no—
361C23×C17—41no—
362C23×C17—41no—
363C23×C17—41no—
364C23×C17—41no—
365C23×C17—41no—
366C23×C17—41no—
367C23×C17#11714yes—
368C23×C17C23×C411yescharacteristic
369C23×C17C22×D411yescharacteristic
370C23×C17C2×#4111yescharacteristic
371C23×C17C2×#4111yescharacteristic
372C23×C17C2×#4111yescharacteristic
373C23×C17C2×#4111yescharacteristic
374C23×C17C2×#4111yescharacteristic
375C23×C17H(5,𝔽2)11yescharacteristic
376C23×C17H(5,𝔽2)11yescharacteristic
377C23×C17H(5,𝔽2)11yescharacteristic
378C23×C17H(5,𝔽2)11yescharacteristic
379C23×C17H(5,𝔽2)11yescharacteristic
380C23×C17H(5,𝔽2)11yescharacteristic
381C23×C17H(5,𝔽2)11yescharacteristic
382C23×C172−1+411yescharacteristic
383D4×C17—416no—
384C2×C4×C17—22no—
385C2×C4×C17—22no—
386C2×C4×C17—22no—
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—41no—
394C2×C4×C17—41no—
395C2×C4×C17—41no—
396C2×C4×C17—41no—
397C2×C4×C17—41no—
398C2×C4×C17—41no—
399C2×C4×C17—41no—
400C2×C4×C17—41no—
401C2×C4×C17—41no—
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×C17C4×D414yes—
419C2×Dic17—22no—
420C2×Dic17—22no—
421C2×Dic17—22no—
422C2×Dic17—22no—
423C2×Dic17—22no—
424C2×Dic17—22no—
425C2×Dic17—22no—
426C2×Dic17—22no—
427C2×Dic17—22no—
428C2×Dic17—22no—
429C2×Dic17—22no—
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—416no—
441C2×Dic17—41no—
442C2×Dic17—41no—
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×#390—171no—
477C2×#386—171no—
478C2×#383—171no—
479#1441—171no—
480#1440—171no—
481#1440—171no—
482#1439—171no—
483#1439—171no—
484#1438D1711yescharacteristic
485#1437—171no—
486#1437—171no—
487#1436—171no—
488#1434—171no—
489C22⋊#95—171no—
490C22⋊#95—171no—
491C22×C17—24no—
492C22×C17—24no—
493C22×C17—24no—
494C22×C17—42no—
495C22×C17—42no—
496C22×C17—42no—
497C22×C17—42no—
498C22×C17—42no—
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×C17—42no—
512C22×C17—42no—
513C22×C17—81no—
514C22×C17—81no—
515C22×C17—81no—
516C22×C17—81no—
517C22×C17—81no—
518C22×C17—81no—
519C22×C17—81no—
520C22×C17—81no—
521C22×C17C2×#11711yescharacteristic
522C22×C17C2×C4×D411yescharacteristic
523C22×C17C4×#4111yescharacteristic
524C22×C17#51811yescharacteristic
525C22×C17#51811yescharacteristic
526C22×C17#51811yescharacteristic
527C22×C17#52011yescharacteristic
528C22×C17#53511yescharacteristic
529C22×C17#53711yescharacteristic
530C22×C17#53811yescharacteristic
531C22×C17#53811yescharacteristic
532C22×C17#53811yescharacteristic
533C22×C17#53811yescharacteristic
534C22×C17#53911yescharacteristic
535C22×C17#53911yescharacteristic
536C22×C17#54011yescharacteristic
537C22×C17#54211yescharacteristic
538C22×C17#54211yescharacteristic
539C22×C17#54211yescharacteristic
540C22×C17#54611yescharacteristic
541C22×C17#54611yescharacteristic
542C22×C17#54611yescharacteristic
543C22×C17#55011yescharacteristic
544C22×C17#55111yescharacteristic
545C22×C17#55111yescharacteristic
546C22×C17#55111yescharacteristic
547C22×C17#55111yescharacteristic
548C22×C17#55311yescharacteristic
549C22×C17#55311yescharacteristic
550C22×C17#55311yescharacteristic
551C22×C17#55511yescharacteristic
552C22×C17#56011yescharacteristic
553C22×C17#56011yescharacteristic
554C22×C17#56011yescharacteristic
555C22×C17#56011yescharacteristic
556C4×C17—24no—
557C4×C17—42no—
558C4×C17—81no—
559C4×C17—81no—
560C4×C17—81no—
561Dic17—42no—
562Dic17—42no—
563Dic17—42no—
564Dic17—42no—
565Dic17—42no—
566Dic17—42no—
567Dic17—42no—
568Dic17—81no—
569C23×D4C2×D1711yescharacteristic
570C24×C4—171no—
571C22×C4⋊C4—171no—
572C22×C4⋊C4—171no—
573C22×C22⋊C4—171no—
574C22×C22⋊C4—171no—
575C22×C22⋊C4—171no—
576C22×C22⋊C4—171no—
577C22×C22⋊C4—171no—
578C22×C22⋊C4—171no—
579C22×C22⋊C4—171no—
580C22×C22⋊C4C2×D1711yescharacteristic
581C22×C22⋊C4C2×D1711yescharacteristic
582C22×C22⋊C4C2×D1711yescharacteristic
583C22×C22⋊C4C2×D1711yescharacteristic
584C22×C42—171no—
585C22×C42—171no—
586#390—178no—
587#386—344no—
588#383—344no—
589C2×#95—171no—
590C2×#95—171no—
591C2×#95—171no—
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×#95C2×D1711yescharacteristic
606C2×#95C2×D1711yescharacteristic
607C2×C17—44no—
608C2×C17—82no—
609C2×C17#231811yescharacteristic
610C2×C17#232411yescharacteristic
611C2×C17#233711yescharacteristic
612C2×C17#234211yescharacteristic
613C2×C17#235311yescharacteristic
614C2×C17#236311yescharacteristic
615C2×C17#238011yescharacteristic
616C2×C17#268511yescharacteristic
617C2×C17#269111yescharacteristic
618C2×C17#270511yescharacteristic
619C2×C17#271411yescharacteristic
620C2×C17#273711yescharacteristic
621C2×C17#274911yescharacteristic
622C2×C17#275611yescharacteristic
623C2×C17#275711yescharacteristic
624C25C22×D1711yescharacteristic
625C25C22×D1711yescharacteristic
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—22no—
630C22×D4—41no—
631C22×D4—41no—
632C22×D4C4×D1714yes—
633C23×C4—171no—
634C23×C4—171no—
635C23×C4—171no—
636C23×C4—171no—
637C23×C4—171no—
638C23×C4—171no—
639C23×C4—171no—
640C23×C4—171no—
641C23×C4—342no—
642C23×C4—342no—
643C23×C4—342no—
644C23×C4—681no—
645C23×C4—681no—
646C23×C4—681no—
647C23×C4—681no—
648C23×C4C22×D1711yescharacteristic
649C23×C4C22×D1711yescharacteristic
650C23×C4C22×D1711yescharacteristic
651C23×C4C22×D1711yescharacteristic
652C23×C4C22×D1711yescharacteristic
653C2×C4⋊C4—174no—
654C2×C4⋊C4—681no—
655C2×C4⋊C4—681no—
656C2×C4⋊C4—681no—
657C2×C4⋊C4—681no—
658C2×C4⋊C4—681no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—41no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—41no—
669C2×C22⋊C4—41no—
670C2×C22⋊C4—41no—
671C2×C22⋊C4—174no—
672C2×C22⋊C4—174no—
673C2×C22⋊C4—174no—
674C2×C22⋊C4—174no—
675C2×C22⋊C4—342no—
676C2×C22⋊C4—342no—
677C2×C22⋊C4—342no—
678C2×C22⋊C4—342no—
679C2×C22⋊C4—342no—
680C2×C22⋊C4—681no—
681C2×C22⋊C4—681no—
682C2×C22⋊C4—681no—
683C2×C22⋊C4—681no—
684C2×C22⋊C4—681no—
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×C42—174no—
693C2×C42—342no—
694C2×C42—342no—
695C2×C42—681no—
696C2×C42—681no—
697C2×C42—681no—
698#95—22no—
699#95—22no—
700#95—174no—
701#95—342no—
702#95—342no—
703#95—342no—
704#95—342no—
705#95—342no—
706#95—342no—
707#95—342no—
708#95—681no—
709#95—681no—
710#95—681no—
711#95—681no—
712#95—681no—
713#95—681no—
714#95—681no—
715#95—681no—
716C17#1437911yescharacteristic, complemented, Sylow
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
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—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24C2×C4×D1712yes—
744C24C2×C4×D1712yes—
745C24#6325412yes—
746C24#6325412yes—
747C24C23×D1711yescharacteristic
748C2×D4—28no—
749C2×D4—28no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
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—172no—
787C22×C4—172no—
788C22×C4—172no—
789C22×C4—172no—
790C22×C4—172no—
791C22×C4—172no—
792C22×C4—172no—
793C22×C4—341no—
794C22×C4—341no—
795C22×C4—341no—
796C22×C4—341no—
797C22×C4—341no—
798C22×C4—341no—
799C22×C4—341no—
800C22×C4—341no—
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—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—684no—
843C22×C4—684no—
844C22×C4—684no—
845C22×C4—684no—
846C22×C4—684no—
847C22×C4—684no—
848C22×C4—684no—
849C22×C4C2×C4×D1712yes—
850C22×C4D4×D1712yes—
851C22×C4#6325412yes—
852C22×C4#6325412yes—
853C4⋊C4—684no—
854C4⋊C4—684no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—684no—
860C22⋊C4—684no—
861C22⋊C4—684no—
862C22⋊C4—684no—
863C22⋊C4—684no—
864C22⋊C4—684no—
865C22⋊C4—684no—
866C42—348no—
867C42—684no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
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—41no—
894C23—41no—
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—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23#1058756314yes—
938C23C22×C4×D1711yescharacteristic
939C23C2×D4×D1711yescharacteristic
940C23C2×#6325411yescharacteristic
941C23C2×#6325411yescharacteristic
942C23C2×#6325411yescharacteristic
943C23C2×#6325411yescharacteristic
944C23#1058769111yescharacteristic
945C23#1058769111yescharacteristic
946C23#1058769111yescharacteristic
947C23#1058769111yescharacteristic
948C23#1058769111yescharacteristic
949C23#41×D1711yescharacteristic
950C23#1058769611yescharacteristic
951C23#1058769611yescharacteristic
952C23#1058769711yescharacteristic
953D4—416no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
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—342no—
989C2×C4—342no—
990C2×C4—342no—
991C2×C4—342no—
992C2×C4—342no—
993C2×C4—342no—
994C2×C4—342no—
995C2×C4—342no—
996C2×C4—342no—
997C2×C4—342no—
998C2×C4—342no—
999C2×C4—342no—
1000C2×C4—342no—
1001C2×C4—342no—
1002C2×C4—342no—
1003C2×C4—342no—
1004C2×C4—342no—
1005C2×C4—342no—
1006C2×C4—342no—
1007C2×C4—342no—
1008C2×C4—342no—
1009C2×C4—6816no—
1010C2×C4—681no—
1011C2×C4—681no—
1012C2×C4—681no—
1013C2×C4—681no—
1014C2×C4—681no—
1015C2×C4—681no—
1016C2×C4—681no—
1017C2×C4—681no—
1018C2×C4—681no—
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#1058756714yes—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22C2×#1058756311yescharacteristic
1077C22C2×#1058756711yescharacteristic
1078C22C4×#6325411yescharacteristic
1079C22#1176328111yescharacteristic
1080C22#1176328111yescharacteristic
1081C22#1176328211yescharacteristic
1082C22#1176328811yescharacteristic
1083C22#1176337511yescharacteristic
1084C22#1176338811yescharacteristic
1085C22#1176339111yescharacteristic
1086C22#1176339411yescharacteristic
1087C22#1176339411yescharacteristic
1088C22#1176339611yescharacteristic
1089C22#1176340311yescharacteristic
1090C22#1176340411yescharacteristic
1091C22#1176341311yescharacteristic
1092C22#1176342611yescharacteristic
1093C22#1176342711yescharacteristic
1094C22#1176342811yescharacteristic
1095C22#1176344611yescharacteristic
1096C22#1176344611yescharacteristic
1097C22#1176345211yescharacteristic
1098C22#1176347911yescharacteristic
1099C22#1176348211yescharacteristic
1100C22#1176349011yescharacteristic
1101C22#1176349011yescharacteristic
1102C22#1176349011yescharacteristic
1103C22#1176350211yescharacteristic
1104C22#1176351111yescharacteristic
1105C22#1176351111yescharacteristic
1106C22#1176352311yescharacteristic
1107C22#1176354711yescharacteristic
1108C22#1176354711yescharacteristic
1109C22#1176354811yescharacteristic
1110C22#1176354911yescharacteristic
1111C4—24no—
1112C4—42no—
1113C4—81no—
1114C4—81no—
1115C4—81no—
1116C4—682no—
1117C4—682no—
1118C4—682no—
1119C4—682no—
1120C4—682no—
1121C4—682no—
1122C4—682no—
1123C4—1361no—
1124C2—44no—
1125C2—82no—
1126C2#1453141011yescharacteristic
1127C2#1453148011yescharacteristic
1128C2#1453159311yescharacteristic
1129C2#1453163511yescharacteristic
1130C2#1453172211yescharacteristic
1131C2#1453182711yescharacteristic
1132C2#1453195911yescharacteristic
1133C2#1453518011yescharacteristic
1134C2#1453527011yescharacteristic
1135C2#1453546411yescharacteristic
1136C2#1453558211yescharacteristic
1137C2#1453584111yescharacteristic
1138C2#1453600911yescharacteristic
1139C2#1453610811yescharacteristic
1140C2#1453612311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1438C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenter#1438D17
hypocenterC17#14379
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
3. C2×#11762676C2semidirect
4. #14527036C2semidirect
5. #14527031C2semidirect
6. #14527031C2semidirect
7. #14527027C2semidirect
8. #14527027C2semidirect
9. #14527021C2semidirect
10. #14527021C2semidirect
11. #14527018C2semidirect
12. #14527008C2semidirect
13. #14527006C2semidirect
14. #14527006C2semidirect
28. #11762712C4semidirect
114. C2×C22⋊Dic17C2×C4semidirect
115. C2×C22⋊Dic17C2×C4semidirect
118. C2×C4⋊Dic17C2×C4semidirect
127. C2×C4×Dic17C2×C4semidirect
716. C17#14379semidirect

Maximal subgroups

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

subgroupindex
C2×#117627122
C2×#117626892
C2×#117626762
#145270362
#145270312
#145270272
#145270212
#145270182
#145270082
#145270062
C17×#14382
#1437917