Finite Group Databasebeta

← #16961963

Subgroups — #16961963

Order 4352.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762708C211yesmaximal, characteristic, complemented
2C2×#11762702C211yesmaximal, characteristic
3C2×#11762672C211yesmaximal, characteristic
4C2×#11762669C211yesmaximal, characteristic
5#14527052C211yesmaximal, characteristic, complemented
6#14527041C211yesmaximal, characteristic, complemented
7#14527037C211yesmaximal, characteristic, complemented
8#14527037C211yesmaximal, characteristic, complemented
9#14527033C211yesmaximal, characteristic
10#14527029C211yesmaximal, characteristic
11#14527021C211yesmaximal, characteristic
12#14527018C211yesmaximal, characteristic, complemented
13#14527018C211yesmaximal, characteristic, complemented
14#14527009C211yesmaximal, characteristic, complemented
15C2×C17×#385C211yesmaximal, characteristic
16C22×C4⋊Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C4×Dic17C2211yescharacteristic
25C22×C4×Dic17C2211yescharacteristic
26#11762708—24no—
27#11762702—24no—
28#11762672—24no—
29#11762669—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
47C2×#10587502C2211yescharacteristic
48C24×C4×C17C2211yescharacteristic
49C22×C4⋊C4×C17C2211yescharacteristic
50C22×C4⋊C4×C17C2211yescharacteristic
51C22×C22⋊C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C17×#385C418yescomplemented
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C25×C17C2311yescharacteristic
57C23×C4×C17—22no—
58C23×C4×C17—22no—
59C23×C4×C17—22no—
60C23×C4×C17—22no—
61C23×C4×C17—41no—
62C23×C4×C17—41no—
63C23×C4×C17C2×C414yes—
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C2×C4⋊C4×C17—22no—
79C2×C4⋊C4×C17—22no—
80C2×C4⋊C4×C17—41no—
81C2×C4⋊C4×C17—41no—
82C2×C4⋊C4×C17C2×C414yes—
83C2×C4⋊C4×C17C2×C414yes—
84C2×C22⋊C4×C17—22no—
85C2×C22⋊C4×C17—22no—
86C2×C22⋊C4×C17—22no—
87C2×C22⋊C4×C17—22no—
88C2×C22⋊C4×C17C2×C414yes—
89C2×C22⋊C4×C17C2×C414yes—
90C2×C22⋊Dic17—22no—
91C2×C22⋊Dic17—22no—
92C2×C22⋊Dic17—22no—
93C2×C22⋊Dic17—22no—
94C2×C22⋊Dic17—22no—
95C2×C22⋊Dic17—41no—
96C2×C22⋊Dic17—41no—
97C2×C22⋊Dic17—41no—
98C2×C22⋊Dic17—41no—
99C2×C22⋊Dic17—41no—
100C2×C22⋊Dic17—41no—
101C2×C22⋊Dic17D414yes—
102C2×C4⋊Dic17—22no—
103C2×C4⋊Dic17—22no—
104C2×C4⋊Dic17—22no—
105C2×C4⋊Dic17—22no—
106C2×C4⋊Dic17—22no—
107C2×C4⋊Dic17—22no—
108C2×C4⋊Dic17—22no—
109C2×C4⋊Dic17—22no—
110C2×C4⋊Dic17—41no—
111C2×C4⋊Dic17—41no—
112C2×C4⋊Dic17—41no—
113C2×C4⋊Dic17—41no—
114C2×C4×Dic17—22no—
115C2×C4×Dic17—22no—
116C2×C4×Dic17—22no—
117C2×C4×Dic17—41no—
118C2×C4×Dic17—41no—
119C2×C4×Dic17—41no—
120C17×#95C2×C414yes—
121C17×#95C2×C414yes—
122#10587502—22no—
123#10587502—22no—
124#10587502—22no—
125#10587502—22no—
126#10587502—22no—
127#10587502—22no—
128#10587502—22no—
129#10587502—22no—
130#10587502—22no—
131#10587502—22no—
132#10587502—41no—
133#10587502—41no—
134#10587502—41no—
135#10587502—41no—
136#10587502—41no—
137#10587502—41no—
138#10587502—41no—
139#10587502D414yes—
140C24×C17—21no—
141C24×C17—21no—
142C24×C17—21no—
143C24×C17—21no—
144C24×C17—21no—
145C24×C17—21no—
146C24×C17—21no—
147C24×C17—21no—
148C24×C17—21no—
149C24×C17—21no—
150C24×C17—21no—
151C24×C17—21no—
152C24×C17C22×C412yes—
153C24×C17C2×D412yes—
154C24×C17#4112yes—
155C24×C17C2411yescharacteristic
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—28no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
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—28no—
190C22×C4×C17—44no—
191C22×C4×C17—44no—
192C22×C4×C17—44no—
193C22×C4×C17—44no—
194C22×C4×C17—44no—
195C22×C4×C17C22×C412yes—
196C22×C4×C17C22×C412yes—
197C22×C4×C17C22×C412yes—
198C22×C4×C17C22×C412yes—
199C22×C4×C17C22×C412yes—
200C22×C4×C17C22×C412yes—
201C22×C4×C17C2×D412yes—
202C22×C4×C17#4112yes—
203C22×C4×C17#4112yes—
204C22×C4×C17#4112yes—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—21no—
218C22×Dic17—21no—
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×Dic17C2×D412yes—
258C22×Dic17C2×D412yes—
259C22×Dic17C2×D412yes—
260C22×Dic17C2×D412yes—
261C4⋊C4×C17—28no—
262C4⋊C4×C17—44no—
263C22⋊C4×C17—28no—
264C22⋊C4×C17—28no—
265C22⋊Dic17—44no—
266C22⋊Dic17—44no—
267C22⋊Dic17—44no—
268C22⋊Dic17—44no—
269C4⋊Dic17—44no—
270C4⋊Dic17—44no—
271C4⋊Dic17—44no—
272C4⋊Dic17—44no—
273C4×Dic17—44no—
274C4×Dic17—44no—
275#14382—171nomaximal, Sylow
276C23×C17—22no—
277C23×C17—22no—
278C23×C17—22no—
279C23×C17—22no—
280C23×C17—22no—
281C23×C17—22no—
282C23×C17—22no—
283C23×C17—22no—
284C23×C17—22no—
285C23×C17—22no—
286C23×C17—22no—
287C23×C17—22no—
288C23×C17—22no—
289C23×C17—22no—
290C23×C17—22no—
291C23×C17—22no—
292C23×C17—22no—
293C23×C17—22no—
294C23×C17—41no—
295C23×C17—41no—
296C23×C17—41no—
297C23×C17—41no—
298C23×C17—41no—
299C23×C17—41no—
300C23×C17—41no—
301C23×C17—41no—
302C23×C17—41no—
303C23×C17—41no—
304C23×C17—41no—
305C23×C17—41no—
306C23×C17—41no—
307C23×C17—41no—
308C23×C17—41no—
309C23×C17—41no—
310C23×C17C4×D414yes—
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×C172−1+411yescharacteristic
323C23×C172−1+411yescharacteristic
324C23×C172−1+411yescharacteristic
325C23×C172−1+411yescharacteristic
326C2×C4×C17—22no—
327C2×C4×C17—22no—
328C2×C4×C17—22no—
329C2×C4×C17—22no—
330C2×C4×C17—22no—
331C2×C4×C17—22no—
332C2×C4×C17—22no—
333C2×C4×C17—22no—
334C2×C4×C17—22no—
335C2×C4×C17—22no—
336C2×C4×C17—22no—
337C2×C4×C17—22no—
338C2×C4×C17—22no—
339C2×C4×C17—22no—
340C2×C4×C17—22no—
341C2×C4×C17—22no—
342C2×C4×C17—22no—
343C2×C4×C17—22no—
344C2×C4×C17—22no—
345C2×C4×C17—22no—
346C2×C4×C17—22no—
347C2×C4×C17—22no—
348C2×C4×C17—22no—
349C2×C4×C17—22no—
350C2×C4×C17—416no—
351C2×C4×C17—41no—
352C2×C4×C17—41no—
353C2×C4×C17—41no—
354C2×C4×C17—41no—
355C2×C4×C17—41no—
356C2×C4×C17—41no—
357C2×C4×C17—41no—
358C2×C4×C17—41no—
359C2×C4×C17—41no—
360C2×C4×C17—41no—
361C2×C4×C17—41no—
362C2×C4×C17—41no—
363C2×C4×C17—41no—
364C2×C4×C17—41no—
365C2×C4×C17—41no—
366C2×C4×C17—41no—
367C2×C4×C17#11714yes—
368C2×C4×C17C4×D414yes—
369C2×Dic17—22no—
370C2×Dic17—22no—
371C2×Dic17—22no—
372C2×Dic17—22no—
373C2×Dic17—22no—
374C2×Dic17—22no—
375C2×Dic17—22no—
376C2×Dic17—22no—
377C2×Dic17—22no—
378C2×Dic17—22no—
379C2×Dic17—22no—
380C2×Dic17—22no—
381C2×Dic17—41no—
382C2×Dic17—41no—
383C2×Dic17—41no—
384C2×Dic17—41no—
385C2×Dic17—41no—
386C2×Dic17—41no—
387C2×Dic17—41no—
388C2×Dic17—41no—
389C2×Dic17—41no—
390C2×Dic17—41no—
391C2×Dic17—41no—
392C2×Dic17—41no—
393C2×Dic17—41no—
394C2×Dic17—41no—
395C2×Dic17—41no—
396C2×Dic17—41no—
397C2×Dic17—41no—
398C2×Dic17—41no—
399C2×Dic17—41no—
400C2×Dic17—41no—
401C2×Dic17—41no—
402C2×Dic17—41no—
403C2×Dic17—41no—
404C2×Dic17—41no—
405C2×Dic17—41no—
406C2×Dic17—41no—
407C2×Dic17—41no—
408C2×Dic17—41no—
409C2×Dic17—41no—
410C2×Dic17—41no—
411C2×Dic17—41no—
412C2×Dic17—41no—
413C2×Dic17—41no—
414C2×Dic17—41no—
415C2×Dic17—41no—
416C2×Dic17—41no—
417C2×Dic17—41no—
418C2×Dic17—41no—
419C2×Dic17—41no—
420C2×Dic17—41no—
421C2×Dic17—41no—
422C2×Dic17—41no—
423C2×Dic17—41no—
424C2×Dic17—41no—
425C2×#389—171no—
426C2×#388—171no—
427C2×#385D1711yescharacteristic
428C2×#381—171no—
429C2×#380—171no—
430#1445—171no—
431#1442—171no—
432#1441—171no—
433#1441—171no—
434#1440—171no—
435#1439—171no—
436#1437—171no—
437#1436—171no—
438#1436—171no—
439#1434—171no—
440C22×C17—24no—
441C22×C17—24no—
442C22×C17—24no—
443C22×C17—42no—
444C22×C17—42no—
445C22×C17—42no—
446C22×C17—42no—
447C22×C17—42no—
448C22×C17—42no—
449C22×C17—42no—
450C22×C17—42no—
451C22×C17—42no—
452C22×C17—42no—
453C22×C17—42no—
454C22×C17—42no—
455C22×C17C2×#11711yescharacteristic
456C22×C17C2×C4×D411yescharacteristic
457C22×C17C2×C4×D411yescharacteristic
458C22×C17#51811yescharacteristic
459C22×C17#51911yescharacteristic
460C22×C17#52011yescharacteristic
461C22×C17#52011yescharacteristic
462C22×C17#53411yescharacteristic
463C22×C17#53611yescharacteristic
464C22×C17#53611yescharacteristic
465C22×C17#53711yescharacteristic
466C22×C17#53911yescharacteristic
467C22×C17#53911yescharacteristic
468C22×C17#54011yescharacteristic
469C22×C17#54011yescharacteristic
470C22×C17#54111yescharacteristic
471C22×C17#54211yescharacteristic
472C22×C17#54211yescharacteristic
473C22×C17#54211yescharacteristic
474C22×C17D4211yescharacteristic
475C22×C17#54611yescharacteristic
476C22×C17#54611yescharacteristic
477C22×C17#54611yescharacteristic
478C22×C17#54711yescharacteristic
479C22×C17#54711yescharacteristic
480C22×C17#54811yescharacteristic
481C22×C17#55111yescharacteristic
482C22×C17#55211yescharacteristic
483C22×C17#55211yescharacteristic
484C22×C17#55211yescharacteristic
485C22×C17#55311yescharacteristic
486C22×C17#56211yescharacteristic
487C22×C17#56211yescharacteristic
488C22×C17#56311yescharacteristic
489C22×C17#56311yescharacteristic
490C4×C17—24no—
491C4×C17—24no—
492C4×C17—42no—
493C4×C17—42no—
494C4×C17—42no—
495C4×C17—42no—
496Dic17—42no—
497Dic17—42no—
498Dic17—42no—
499Dic17—42no—
500Dic17—81no—
501Dic17—81no—
502Dic17—81no—
503Dic17—81no—
504C24×C4C2×D1711yescharacteristic
505C22×C4⋊C4—171no—
506C22×C4⋊C4—171no—
507C22×C4⋊C4—171no—
508C22×C4⋊C4—171no—
509C22×C4⋊C4C2×D1711yescharacteristic
510C22×C4⋊C4C2×D1711yescharacteristic
511C22×C22⋊C4—171no—
512C22×C22⋊C4—171no—
513C22×C22⋊C4—171no—
514C22×C22⋊C4—171no—
515C22×C22⋊C4C2×D1711yescharacteristic
516C22×C22⋊C4C2×D1711yescharacteristic
517C22×C42—171no—
518C22×C42—171no—
519#389—344no—
520#388—344no—
521#385Dic1718yescomplemented
522#381—344no—
523#380—344no—
524C2×#95—171no—
525C2×#95—171no—
526C2×#95—171no—
527C2×#95—171no—
528C2×#95—171no—
529C2×#95—171no—
530C2×#95—171no—
531C2×#95—171no—
532C2×#95—171no—
533C2×#95—171no—
534C2×#95—171no—
535C2×#95—171no—
536C2×#95—171no—
537C2×#95—171no—
538C2×#95—171no—
539C2×#95—171no—
540C2×#95—171no—
541C2×#95—171no—
542C2×#95C2×D1711yescharacteristic
543C2×#95C2×D1711yescharacteristic
544C2×C17—44no—
545C2×C17#231911yescharacteristic
546C2×C17#232211yescharacteristic
547C2×C17#232311yescharacteristic
548C2×C17#234411yescharacteristic
549C2×C17#235211yescharacteristic
550C2×C17#235811yescharacteristic
551C2×C17#237811yescharacteristic
552C2×C17#267111yescharacteristic
553C2×C17#267411yescharacteristic
554C2×C17#268711yescharacteristic
555C2×C17#269811yescharacteristic
556C2×C17#270111yescharacteristic
557C2×C17#270711yescharacteristic
558C2×C17#273811yescharacteristic
559C2×C17#273911yescharacteristic
560C25C22×D1711yescharacteristic
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—41no—
566C23×C4—41no—
567C23×C4—171no—
568C23×C4—171no—
569C23×C4—171no—
570C23×C4—171no—
571C23×C4—171no—
572C23×C4—171no—
573C23×C4—171no—
574C23×C4—171no—
575C23×C4C2×Dic1714yes—
576C23×C4C22×D1711yescharacteristic
577C23×C4C22×D1711yescharacteristic
578C23×C4C22×D1711yescharacteristic
579C23×C4C22×D1711yescharacteristic
580C23×C4C22×D1711yescharacteristic
581C23×C4C22×D1711yescharacteristic
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—342no—
587C2×C4⋊C4—342no—
588C2×C4⋊C4—342no—
589C2×C4⋊C4—342no—
590C2×C4⋊C4—342no—
591C2×C4⋊C4—342no—
592C2×C4⋊C4—342no—
593C2×C4⋊C4—342no—
594C2×C4⋊C4—681no—
595C2×C4⋊C4—681no—
596C2×C4⋊C4—681no—
597C2×C4⋊C4—681no—
598C2×C4⋊C4C2×Dic1714yes—
599C2×C4⋊C4C2×Dic1714yes—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—174no—
605C2×C22⋊C4—342no—
606C2×C22⋊C4—342no—
607C2×C22⋊C4—342no—
608C2×C22⋊C4—342no—
609C2×C22⋊C4—342no—
610C2×C22⋊C4—681no—
611C2×C22⋊C4—681no—
612C2×C22⋊C4—681no—
613C2×C22⋊C4—681no—
614C2×C22⋊C4—681no—
615C2×C22⋊C4—681no—
616C2×C22⋊C4C2×Dic1714yes—
617C2×C22⋊C4C2×Dic1714yes—
618C2×C42—342no—
619C2×C42—342no—
620C2×C42—342no—
621C2×C42—681no—
622C2×C42—681no—
623C2×C42—681no—
624#95—174no—
625#95—342no—
626#95—342no—
627#95—342no—
628#95—342no—
629#95—342no—
630#95—342no—
631#95—342no—
632#95—342no—
633#95—342no—
634#95—342no—
635#95—681no—
636#95—681no—
637#95—681no—
638#95—681no—
639#95—681no—
640#95—681no—
641#95—681no—
642#95C2×Dic1714yes—
643#95C2×Dic1714yes—
644C17#1438211yescharacteristic, complemented, Sylow
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24D4×D1712yes—
658C24#6325412yes—
659C24C22×Dic1712yes—
660C24C23×D1711yescharacteristic
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—28no—
694C22×C4—28no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—172no—
701C22×C4—172no—
702C22×C4—172no—
703C22×C4—172no—
704C22×C4—341no—
705C22×C4—341no—
706C22×C4—341no—
707C22×C4—341no—
708C22×C4—341no—
709C22×C4—341no—
710C22×C4—341no—
711C22×C4—341no—
712C22×C4—341no—
713C22×C4—341no—
714C22×C4—341no—
715C22×C4—341no—
716C22×C4—341no—
717C22×C4—341no—
718C22×C4—341no—
719C22×C4—341no—
720C22×C4—341no—
721C22×C4—341no—
722C22×C4—341no—
723C22×C4—341no—
724C22×C4—341no—
725C22×C4—341no—
726C22×C4—341no—
727C22×C4—341no—
728C22×C4—341no—
729C22×C4—341no—
730C22×C4—341no—
731C22×C4—341no—
732C22×C4—341no—
733C22×C4—341no—
734C22×C4—341no—
735C22×C4—341no—
736C22×C4—341no—
737C22×C4—341no—
738C22×C4—341no—
739C22×C4—341no—
740C22×C4—341no—
741C22×C4—341no—
742C22×C4—341no—
743C22×C4—341no—
744C22×C4—341no—
745C22×C4—341no—
746C22×C4—341no—
747C22×C4—341no—
748C22×C4—341no—
749C22×C4—341no—
750C22×C4—341no—
751C22×C4—341no—
752C22×C4—341no—
753C22×C4—341no—
754C22×C4—341no—
755C22×C4—341no—
756C22×C4#6325212yes—
757C22×C4#6325212yes—
758C22×C4D4×D1712yes—
759C22×C4#6325412yes—
760C22×C4C22×Dic1712yes—
761C22×C4C22×Dic1712yes—
762C22×C4C22×Dic1712yes—
763C22×C4C22×Dic1712yes—
764C22×C4C22×Dic1712yes—
765C22×C4C22×Dic1712yes—
766C4⋊C4—28no—
767C4⋊C4—44no—
768C4⋊C4—684no—
769C4⋊C4—684no—
770C4⋊C4—684no—
771C4⋊C4—684no—
772C22⋊C4—28no—
773C22⋊C4—28no—
774C22⋊C4—684no—
775C22⋊C4—684no—
776C22⋊C4—684no—
777C22⋊C4—684no—
778C42—684no—
779C42—684no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23D4×Dic1714yes—
815C23C2×#6325211yescharacteristic
816C23C2×#6325211yescharacteristic
817C23C2×D4×D1711yescharacteristic
818C23C2×D4×D1711yescharacteristic
819C23C2×#6325411yescharacteristic
820C23C2×#6325411yescharacteristic
821C23#1058769111yescharacteristic
822C23#1058769111yescharacteristic
823C23#1058769411yescharacteristic
824C23#1058769411yescharacteristic
825C23#1058769611yescharacteristic
826C23#1058769611yescharacteristic
827C23#1058769711yescharacteristic
828C23#1058769711yescharacteristic
829C23C23×Dic1711yescharacteristic
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—416no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—342no—
872C2×C4—342no—
873C2×C4—342no—
874C2×C4—342no—
875C2×C4—342no—
876C2×C4—342no—
877C2×C4—342no—
878C2×C4—342no—
879C2×C4—342no—
880C2×C4—342no—
881C2×C4—342no—
882C2×C4—342no—
883C2×C4—681no—
884C2×C4—681no—
885C2×C4—681no—
886C2×C4—681no—
887C2×C4—681no—
888C2×C4—681no—
889C2×C4—681no—
890C2×C4—681no—
891C2×C4—681no—
892C2×C4—681no—
893C2×C4—681no—
894C2×C4—681no—
895C2×C4—681no—
896C2×C4—681no—
897C2×C4—681no—
898C2×C4—681no—
899C2×C4—681no—
900C2×C4—681no—
901C2×C4—681no—
902C2×C4—681no—
903C2×C4—681no—
904C2×C4—681no—
905C2×C4—681no—
906C2×C4—681no—
907C2×C4—681no—
908C2×C4—681no—
909C2×C4—681no—
910C2×C4—681no—
911C2×C4—681no—
912C2×C4—681no—
913C2×C4—681no—
914C2×C4—681no—
915C2×C4—681no—
916C2×C4—681no—
917C2×C4—681no—
918C2×C4—681no—
919C2×C4—681no—
920C2×C4—681no—
921C2×C4—681no—
922C2×C4—681no—
923C2×C4—681no—
924C2×C4—681no—
925C2×C4—681no—
926C2×C4—681no—
927C2×C4#1058761214yes—
928C2×C4D4×Dic1714yes—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22C2×#1058761211yescharacteristic
945C22C2×D4×Dic1711yescharacteristic
946C22C2×D4×Dic1711yescharacteristic
947C22#1176328411yescharacteristic
948C22#1176328711yescharacteristic
949C22#1176329211yescharacteristic
950C22#1176329211yescharacteristic
951C22#1176337011yescharacteristic
952C22#1176338111yescharacteristic
953C22#1176338211yescharacteristic
954C22#1176338911yescharacteristic
955C22#1176340311yescharacteristic
956C22#1176340311yescharacteristic
957C22#1176341011yescharacteristic
958C22#1176341011yescharacteristic
959C22#1176341911yescharacteristic
960C22#1176342411yescharacteristic
961C22#1176342411yescharacteristic
962C22#1176343211yescharacteristic
963C22#1176344111yescharacteristic
964C22#1176344611yescharacteristic
965C22#1176344611yescharacteristic
966C22#1176345511yescharacteristic
967C22#1176346011yescharacteristic
968C22#1176346011yescharacteristic
969C22#1176346811yescharacteristic
970C22#1176349011yescharacteristic
971C22#1176349411yescharacteristic
972C22#1176349411yescharacteristic
973C22#1176349911yescharacteristic
974C22#1176350511yescharacteristic
975C22#1176355511yescharacteristic
976C22#1176355511yescharacteristic
977C22#1176356011yescharacteristic
978C22#1176356011yescharacteristic
979C4—24no—
980C4—24no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—682no—
986C4—682no—
987C4—682no—
988C4—682no—
989C4—1361no—
990C4—1361no—
991C4—1361no—
992C4—1361no—
993C2—44no—
994C2#1453142711yescharacteristic
995C2#1453145611yescharacteristic
996C2#1453146811yescharacteristic
997C2#1453165311yescharacteristic
998C2#1453171311yescharacteristic
999C2#1453176811yescharacteristic
1000C2#1453195011yescharacteristic
1001C2#1453502411yescharacteristic
1002C2#1453506911yescharacteristic
1003C2#1453520811yescharacteristic
1004C2#1453536211yescharacteristic
1005C2#1453540111yescharacteristic
1006C2#1453549111yescharacteristic
1007C2#1453585811yescharacteristic
1008C2#1453587311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#385C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#385D17
hypocenterC17#14382
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#11762708C2semidirect
5. #14527052C2semidirect
6. #14527041C2semidirect
7. #14527037C2semidirect
8. #14527037C2semidirect
12. #14527018C2semidirect
13. #14527018C2semidirect
14. #14527009C2semidirect
53. C17×#385C4semidirect
521. #385Dic17semidirect
644. C17#14382semidirect

Maximal subgroups

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

subgroupindex
C2×#117627082
C2×#117627022
C2×#117626722
C2×#117626692
#145270522
#145270412
#145270372
#145270332
#145270292
#145270212
#145270182
#145270092
C2×C17×#3852
#1438217