Finite Group Databasebeta

← #16957537

Subgroups — #16957537

Order 4352.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762705C211yesmaximal, characteristic, complemented
2C2×#11762684C211yesmaximal, characteristic
3C2×#11762682C211yesmaximal, characteristic
4C2×#11762667C211yesmaximal, characteristic
5C2×C22⋊C4×Dic17C211yesmaximal, characteristic
6C22×#10587502C211yesmaximal, characteristic
7#14527047C211yesmaximal, characteristic, complemented
8#14527043C211yesmaximal, characteristic, complemented
9#14527036C211yesmaximal, characteristic, complemented
10#14527036C211yesmaximal, characteristic, complemented
11#14527015C211yesmaximal, characteristic, complemented
12#14527015C211yesmaximal, characteristic, complemented
13#14527013C211yesmaximal, characteristic, complemented
14#14527006C211yesmaximal, characteristic
15C2×C17×#385C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28#11762705—24no—
29#11762684C418yescomplemented
30#11762682—24no—
31#11762667—24no—
32C22⋊C4×Dic17—24no—
33C2×#10587502—24no—
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
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C24×C4×C17C2211yescharacteristic
51C22×C4⋊C4×C17C2211yescharacteristic
52C22×C4⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C17×#385—24no—
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C23×C4×C17—22no—
60C23×C4×C17—22no—
61C23×C4×C17—22no—
62C23×C4×C17—22no—
63C23×C4×C17—22no—
64C23×C4×C17—41no—
65C23×C4×C17—41no—
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×Dic17—22no—
73C23×Dic17—22no—
74C23×Dic17—22no—
75C23×Dic17—22no—
76C23×Dic17—22no—
77C23×Dic17—22no—
78C23×Dic17—22no—
79C23×Dic17—22no—
80C23×Dic17—41no—
81C23×Dic17—41no—
82C23×Dic17—41no—
83C23×Dic17—41no—
84C23×Dic17C2×C414yes—
85C23×Dic17Q814yes—
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C23×Dic17C2311yescharacteristic
90C23×Dic17C2311yescharacteristic
91C23×Dic17C2311yescharacteristic
92C23×Dic17C2311yescharacteristic
93C23×Dic17C2311yescharacteristic
94C2×C4⋊C4×C17—22no—
95C2×C4⋊C4×C17—22no—
96C2×C4⋊C4×C17—22no—
97C2×C4⋊C4×C17—22no—
98C2×C4⋊C4×C17—41no—
99C2×C4⋊C4×C17—41no—
100C2×C22⋊C4×C17—22no—
101C2×C22⋊C4×C17—22no—
102C2×C22⋊C4×C17—22no—
103C2×C22⋊C4×C17C2×C414yes—
104C2×C22⋊C4×C17D414yes—
105C2×C22⋊C4×C17Q814yes—
106C2×C22⋊Dic17—22no—
107C2×C22⋊Dic17—22no—
108C2×C22⋊Dic17—22no—
109C2×C22⋊Dic17—22no—
110C2×C22⋊Dic17C2×C414yes—
111C2×C22⋊Dic17D414yes—
112C2×C4⋊Dic17—22no—
113C2×C4⋊Dic17—22no—
114C2×C4⋊Dic17—41no—
115C2×C4⋊Dic17—41no—
116C2×C4⋊Dic17C2×C414yescomplemented
117C2×C4⋊Dic17C2×C414yescomplemented
118C2×#63225—22no—
119C2×#63225—22no—
120C2×#63225—22no—
121C2×#63225—22no—
122C2×#63225—22no—
123C2×#63225—22no—
124C2×#63225—22no—
125C2×#63225—22no—
126C2×#63225—41no—
127C2×#63225—41no—
128C2×#63225—41no—
129C2×#63225—41no—
130C2×C4×Dic17—22no—
131C2×C4×Dic17—22no—
132C2×C4×Dic17—22no—
133C2×C4×Dic17—22no—
134C2×C4×Dic17—41no—
135C2×C4×Dic17—41no—
136C17×#95—22no—
137C17×#95—22no—
138#10587502—22no—
139#10587502—22no—
140#10587502—22no—
141#10587502—22no—
142#10587502—22no—
143#10587502—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—22no—
148#10587502—22no—
149#10587502—41no—
150#10587502—41no—
151#10587502C2×C414yescomplemented
152#10587502C2×C414yescomplemented
153#10587502D414yes—
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×C17C22×C412yes—
163C24×C17C2×D412yes—
164C24×C17C2×D412yes—
165C24×C17C2×Q812yes—
166C24×C17C2×Q812yes—
167C24×C17#4112yes—
168C24×C17#4112yes—
169C24×C17C2411yescharacteristic
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—28no—
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—44no—
206C22×C4×C17—44no—
207C22×C4×C17—44no—
208C22×C4×C17—44no—
209C22×C4×C17—44no—
210C22×C4×C17—44no—
211C22×C4×C17C22×C412yes—
212C22×C4×C17C22×C412yes—
213C22×C4×C17C2×D412yes—
214C22×C4×C17C2×D412yes—
215C22×C4×C17C2×D412yes—
216C22×C4×C17C2×Q812yes—
217C22×C4×C17C2×Q812yes—
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—28no—
228C22×Dic17—28no—
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—28no—
266C22×Dic17—28no—
267C22×Dic17—44no—
268C22×Dic17—44no—
269C22×Dic17—44no—
270C22×Dic17—44no—
271C22×Dic17—44no—
272C22×Dic17—44no—
273C22×Dic17—44no—
274C22×Dic17—44no—
275C22×Dic17—44no—
276C22×Dic17—44no—
277C22×Dic17C22×C412yes—
278C22×Dic17C22×C412yes—
279C22×Dic17C22×C412yes—
280C22×Dic17C22×C412yes—
281C22×Dic17C2×D412yes—
282C22×Dic17C2×D412yes—
283C22×Dic17C2×D412yes—
284C22×Dic17C2×D412yes—
285C22×Dic17C2×Q812yes—
286C22×Dic17C2×Q812yes—
287C22×Dic17#4112yes—
288C22×Dic17#4112yes—
289C4⋊C4×C17—44no—
290C4⋊C4×C17—44no—
291C22⋊C4×C17—44no—
292C22⋊C4×C17C4⋊C4116yescomplemented
293C22⋊Dic17—28no—
294C22⋊Dic17—28no—
295C4⋊Dic17—28no—
296C4⋊Dic17—44no—
297#63225—44no—
298#63225—44no—
299#63225—44no—
300#63225—44no—
301C4×Dic17—44no—
302C4×Dic17—44no—
303#14004—171nomaximal, Sylow
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—22no—
324C23×C17—22no—
325C23×C17—22no—
326C23×C17—22no—
327C23×C17—22no—
328C23×C17—22no—
329C23×C17—22no—
330C23×C17—22no—
331C23×C17—22no—
332C23×C17C2×C4⋊C414yes—
333C23×C17C4×D414yes—
334C23×C17C4×Q814yes—
335C23×C17#12114yes—
336C23×C17C22⋊Q814yes—
337C23×C17#12514yes—
338C23×C17C4⋊Q814yes—
339C23×C17C23×C411yescharacteristic
340C23×C17C22×D411yescharacteristic
341C23×C17C22×D411yescharacteristic
342C23×C17C22×D411yescharacteristic
343C23×C17C22×Q811yescharacteristic
344C23×C17C22×Q811yescharacteristic
345C23×C17C2×#4111yescharacteristic
346C23×C17C2×#4111yescharacteristic
347C23×C17C2×#4111yescharacteristic
348C23×C17C2×#4111yescharacteristic
349C23×C17C2×#4111yescharacteristic
350C23×C17H(5,𝔽2)11yescharacteristic
351C23×C17H(5,𝔽2)11yescharacteristic
352C23×C17H(5,𝔽2)11yescharacteristic
353C23×C172−1+411yescharacteristic
354C2×C4×C17—22no—
355C2×C4×C17—22no—
356C2×C4×C17—22no—
357C2×C4×C17—22no—
358C2×C4×C17—22no—
359C2×C4×C17—22no—
360C2×C4×C17—22no—
361C2×C4×C17—22no—
362C2×C4×C17—22no—
363C2×C4×C17—22no—
364C2×C4×C17—22no—
365C2×C4×C17—22no—
366C2×C4×C17—22no—
367C2×C4×C17—22no—
368C2×C4×C17—22no—
369C2×C4×C17—22no—
370C2×C4×C17—22no—
371C2×C4×C17—22no—
372C2×C4×C17—416no—
373C2×C4×C17—41no—
374C2×C4×C17—41no—
375C2×C4×C17—41no—
376C2×C4×C17—41no—
377C2×C4×C17—41no—
378C2×C4×C17—41no—
379C2×C4×C17—41no—
380C2×C4×C17—41no—
381C2×C4×C17—41no—
382C2×C4×C17—41no—
383C2×C4×C17—41no—
384C2×C4×C17—41no—
385C2×C4×C17—41no—
386C2×C4×C17—41no—
387C2×C4×C17—41no—
388C2×C4×C17—41no—
389C2×C4×C17—41no—
390C2×C4×C17—41no—
391C2×C4×C17—41no—
392C2×C4×C17—41no—
393C2×C4×C17—41no—
394C2×C4×C17—41no—
395C2×C4×C17C2×C4⋊C414yes—
396C2×C4×C17C2×C4⋊C414yes—
397C2×Dic17—22no—
398C2×Dic17—22no—
399C2×Dic17—22no—
400C2×Dic17—22no—
401C2×Dic17—22no—
402C2×Dic17—22no—
403C2×Dic17—22no—
404C2×Dic17—22no—
405C2×Dic17—22no—
406C2×Dic17—22no—
407C2×Dic17—22no—
408C2×Dic17—22no—
409C2×Dic17—22no—
410C2×Dic17—22no—
411C2×Dic17—22no—
412C2×Dic17—22no—
413C2×Dic17—22no—
414C2×Dic17—22no—
415C2×Dic17—22no—
416C2×Dic17—22no—
417C2×Dic17—22no—
418C2×Dic17—22no—
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—416no—
428C2×Dic17—416no—
429C2×Dic17—41no—
430C2×Dic17—41no—
431C2×Dic17—41no—
432C2×Dic17—41no—
433C2×Dic17—41no—
434C2×Dic17—41no—
435C2×Dic17—41no—
436C2×Dic17—41no—
437C2×Dic17—41no—
438C2×Dic17—41no—
439C2×Dic17—41no—
440C2×Dic17—41no—
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×Dic17C4×D414yes—
454C2×Dic17C22⋊Q814yes—
455C2×#389—171no—
456C2×#385—171no—
457C2×#385—171no—
458C2×#385D1711yescharacteristic
459C2×#380—171no—
460C2×C4×C22⋊C4—171no—
461C22×#95—171no—
462#1444—171no—
463#1442—171no—
464#1441—171no—
465#1441—171no—
466#1436—171no—
467#1436—171no—
468C4⋊#95—171no—
469C22⋊#95—171no—
470C22×C17—24no—
471C22×C17—24no—
472C22×C17—24no—
473C22×C17—24no—
474C22×C17—24no—
475C22×C17—24no—
476C22×C17—24no—
477C22×C17—24no—
478C22×C17—24no—
479C22×C17—24no—
480C22×C17—24no—
481C22×C17—24no—
482C22×C17—24no—
483C22×C17—24no—
484C22×C17#38918yescomplemented
485C22×C17C22×C4⋊C411yescharacteristic
486C22×C17C2×C4×D411yescharacteristic
487C22×C17C2×C4×D411yescharacteristic
488C22×C17C2×C4×Q811yescharacteristic
489C22×C17C4×#4111yescharacteristic
490C22×C17#51811yescharacteristic
491C22×C17#52011yescharacteristic
492C22×C17C2×#12111yescharacteristic
493C22×C17C2×C22⋊Q811yescharacteristic
494C22×C17C2×C22⋊Q811yescharacteristic
495C22×C17#52511yescharacteristic
496C22×C17C2×#12511yescharacteristic
497C22×C17#52911yescharacteristic
498C22×C17C2×C4⋊Q811yescharacteristic
499C22×C17#53311yescharacteristic
500C22×C17#53811yescharacteristic
501C22×C17#53911yescharacteristic
502C22×C17#54311yescharacteristic
503C22×C17#54411yescharacteristic
504C22×C17D4211yescharacteristic
505C22×C17D4211yescharacteristic
506C22×C17#54611yescharacteristic
507C22×C17#54611yescharacteristic
508C22×C17#54611yescharacteristic
509C22×C17#54611yescharacteristic
510C22×C17#54611yescharacteristic
511C22×C17#54711yescharacteristic
512C22×C17#54711yescharacteristic
513C22×C17D4×Q811yescharacteristic
514C22×C17#55111yescharacteristic
515C22×C17#55111yescharacteristic
516C22×C17#55211yescharacteristic
517C22×C17#55411yescharacteristic
518C22×C17#55411yescharacteristic
519C22×C17#55411yescharacteristic
520C4×C17—24no—
521C4×C17—24no—
522C4×C17—42no—
523C4×C17—42no—
524C4×C17—81no—
525C4×C17—81no—
526Dic17—24no—
527Dic17—24no—
528Dic17—42no—
529Dic17—42no—
530Dic17—42no—
531Dic17—42no—
532Dic17—42no—
533Dic17—42no—
534C24×C4—171no—
535C24×C4—171no—
536C24×C4C2×D1711yescharacteristic
537C22×C4⋊C4—171no—
538C22×C4⋊C4—171no—
539C22×C4⋊C4—171no—
540C22×C4⋊C4—171no—
541C22×C4⋊C4—171no—
542C22×C4⋊C4—171no—
543C22×C4⋊C4C2×D1711yescharacteristic
544C22×C4⋊C4C2×D1711yescharacteristic
545C22×C22⋊C4—171no—
546C22×C22⋊C4—171no—
547C22×C22⋊C4C2×D1711yescharacteristic
548C22×C22⋊C4C2×D1711yescharacteristic
549C22×C42—171no—
550C22×C42—171no—
551#389—344no—
552#385—24no—
553#385—178no—
554#385—344no—
555#380—344no—
556C4×C22⋊C4—344no—
557C2×#95—171no—
558C2×#95—171no—
559C2×#95—171no—
560C2×#95—171no—
561C2×#95—171no—
562C2×#95—171no—
563C2×#95—171no—
564C2×#95—171no—
565C2×#95—171no—
566C2×#95—171no—
567C2×#95—171no—
568C2×#95—171no—
569C2×#95—171no—
570C2×#95—171no—
571C2×#95—171no—
572C2×#95—171no—
573C2×#95—344no—
574C2×#95C2×D1711yescharacteristic
575C2×#95C2×D1711yescharacteristic
576C2×C17—28no—
577C2×C17C2×#38911yescharacteristic
578C2×C17C4×C22⋊Q811yescharacteristic
579C2×C17#232911yescharacteristic
580C2×C17D4×C4⋊C411yescharacteristic
581C2×C17#234911yescharacteristic
582C2×C17#235811yescharacteristic
583C2×C17#235911yescharacteristic
584C2×C17#242411yescharacteristic
585C2×C17#242511yescharacteristic
586C2×C17#243711yescharacteristic
587C2×C17#243811yescharacteristic
588C2×C17#244011yescharacteristic
589C2×C17#247311yescharacteristic
590C2×C17#250511yescharacteristic
591C2×C17#254911yescharacteristic
592C25C22×D1711yescharacteristic
593C23×C4—22no—
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—41no—
599C23×C4—41no—
600C23×C4—171no—
601C23×C4—171no—
602C23×C4—171no—
603C23×C4—171no—
604C23×C4—171no—
605C23×C4—171no—
606C23×C4—171no—
607C23×C4—171no—
608C23×C4—174no—
609C23×C4—174no—
610C23×C4—342no—
611C23×C4—342no—
612C23×C4—342no—
613C23×C4—342no—
614C23×C4—342no—
615C23×C4—342no—
616C23×C4—342no—
617C23×C4—342no—
618C23×C4—681no—
619C23×C4—681no—
620C23×C4—681no—
621C23×C4—681no—
622C23×C4C22×D1711yescharacteristic
623C23×C4C22×D1711yescharacteristic
624C23×C4C22×D1711yescharacteristic
625C23×C4C22×D1711yescharacteristic
626C23×C4C22×D1711yescharacteristic
627C23×C4C22×D1711yescharacteristic
628C2×C4⋊C4—22no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—174no—
635C2×C4⋊C4—174no—
636C2×C4⋊C4—342no—
637C2×C4⋊C4—342no—
638C2×C4⋊C4—342no—
639C2×C4⋊C4—342no—
640C2×C4⋊C4—342no—
641C2×C4⋊C4—342no—
642C2×C4⋊C4—342no—
643C2×C4⋊C4—342no—
644C2×C4⋊C4—342no—
645C2×C4⋊C4—342no—
646C2×C4⋊C4—681no—
647C2×C4⋊C4—681no—
648C2×C4⋊C4—681no—
649C2×C4⋊C4—681no—
650C2×C4⋊C4—681no—
651C2×C4⋊C4—681no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—174no—
656C2×C22⋊C4—174no—
657C2×C22⋊C4—342no—
658C2×C22⋊C4—342no—
659C2×C22⋊C4—342no—
660C2×C22⋊C4—342no—
661C2×C22⋊C4Dic3414yes—
662C2×C22⋊C4C4×D1714yes—
663C2×C22⋊C4C22⋊D1714yes—
664C2×C42—342no—
665C2×C42—342no—
666C2×C42—342no—
667C2×C42—342no—
668C2×C42—681no—
669C2×C42—681no—
670#95—22no—
671#95—22no—
672#95—174no—
673#95—174no—
674#95—174no—
675#95—342no—
676#95—342no—
677#95—342no—
678#95—342no—
679#95—342no—
680#95—342no—
681#95—342no—
682#95—342no—
683#95—342no—
684#95—342no—
685#95—342no—
686#95—681no—
687#95—681no—
688C17#1400411yescharacteristic, complemented, Sylow
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C2×Dic3412yes—
698C24C2×C4×D1712yes—
699C24D4×D1712yes—
700C24#6325412yes—
701C24Q8×D1712yes—
702C24#6325612yes—
703C24C2×C22⋊D1712yes—
704C24C23×D1711yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—28no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—172no—
747C22×C4—172no—
748C22×C4—172no—
749C22×C4—172no—
750C22×C4—172no—
751C22×C4—172no—
752C22×C4—172no—
753C22×C4—172no—
754C22×C4—172no—
755C22×C4—172no—
756C22×C4—172no—
757C22×C4—172no—
758C22×C4—348no—
759C22×C4—348no—
760C22×C4—341no—
761C22×C4—341no—
762C22×C4—341no—
763C22×C4—341no—
764C22×C4—341no—
765C22×C4—341no—
766C22×C4—341no—
767C22×C4—341no—
768C22×C4—341no—
769C22×C4—341no—
770C22×C4—341no—
771C22×C4—341no—
772C22×C4—341no—
773C22×C4—341no—
774C22×C4—341no—
775C22×C4—341no—
776C22×C4—341no—
777C22×C4—341no—
778C22×C4—341no—
779C22×C4—341no—
780C22×C4—341no—
781C22×C4—341no—
782C22×C4—341no—
783C22×C4—341no—
784C22×C4—341no—
785C22×C4—341no—
786C22×C4—341no—
787C22×C4—341no—
788C22×C4—341no—
789C22×C4—341no—
790C22×C4—341no—
791C22×C4—341no—
792C22×C4—341no—
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—348no—
805C22×C4—348no—
806C22×C4—684no—
807C22×C4—684no—
808C22×C4—684no—
809C22×C4—684no—
810C22×C4—684no—
811C22×C4—684no—
812C22×C4—684no—
813C22×C4—684no—
814C22×C4—684no—
815C22×C4—684no—
816C22×C4C2×Dic3412yes—
817C22×C4C2×Dic3412yes—
818C22×C4C2×C4×D1712yes—
819C22×C4C2×C4×D1712yes—
820C22×C4D4×D1712yes—
821C22×C4#6325412yes—
822C22×C4C2×C22⋊D1712yes—
823C22×C4C2×C22⋊D1712yes—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—348no—
827C4⋊C4—684no—
828C4⋊C4—684no—
829C4⋊C4—684no—
830C4⋊C4—684no—
831C4⋊C4—684no—
832C22⋊C4—44no—
833C22⋊C4—348no—
834C22⋊C4—348no—
835C22⋊C4#63225116yescomplemented
836C42—684no—
837C42—684no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23#1058757314yes—
867C23#1058757414yes—
868C23#1058757614yes—
869C23#1058757914yes—
870C23C2×#6322514yes—
871C23#1058762414yes—
872C23#1058763214yes—
873C23C22×Dic3411yescharacteristic
874C23C22×C4×D1711yescharacteristic
875C23C2×D4×D1711yescharacteristic
876C23C2×D4×D1711yescharacteristic
877C23C2×#6325411yescharacteristic
878C23C2×#6325411yescharacteristic
879C23#1058769111yescharacteristic
880C23#1058769111yescharacteristic
881C23C2×Q8×D1711yescharacteristic
882C23C2×#6325611yescharacteristic
883C23#41×D1711yescharacteristic
884C23#41×D1711yescharacteristic
885C23#1058769611yescharacteristic
886C23#1058769711yescharacteristic
887C23C22×C22⋊D1711yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—416no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—174no—
930C2×C4—174no—
931C2×C4—342no—
932C2×C4—342no—
933C2×C4—342no—
934C2×C4—342no—
935C2×C4—342no—
936C2×C4—342no—
937C2×C4—342no—
938C2×C4—342no—
939C2×C4—342no—
940C2×C4—342no—
941C2×C4—342no—
942C2×C4—342no—
943C2×C4—342no—
944C2×C4—342no—
945C2×C4—342no—
946C2×C4—342no—
947C2×C4—342no—
948C2×C4—342no—
949C2×C4—342no—
950C2×C4—342no—
951C2×C4—342no—
952C2×C4—342no—
953C2×C4—342no—
954C2×C4—342no—
955C2×C4—342no—
956C2×C4—342no—
957C2×C4—342no—
958C2×C4—342no—
959C2×C4—342no—
960C2×C4—342no—
961C2×C4—6816no—
962C2×C4—6816no—
963C2×C4—681no—
964C2×C4—681no—
965C2×C4—681no—
966C2×C4—681no—
967C2×C4—681no—
968C2×C4—681no—
969C2×C4—681no—
970C2×C4—681no—
971C2×C4—681no—
972C2×C4—681no—
973C2×C4—681no—
974C2×C4—681no—
975C2×C4—681no—
976C2×C4—681no—
977C2×C4—681no—
978C2×C4—681no—
979C2×C4—681no—
980C2×C4—681no—
981C2×C4—681no—
982C2×C4—681no—
983C2×C4—681no—
984C2×C4—681no—
985C2×C4—681no—
986C2×C4—681no—
987C2×C4C2×#6322514yes—
988C2×C4C2×#6322514yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22#1176270518yescomplemented
1004C22C22×#6322511yescharacteristic
1005C22C4×D4×D1711yescharacteristic
1006C22C2×#1058757911yescharacteristic
1007C22C2×#1058757311yescharacteristic
1008C22C4×#6325411yescharacteristic
1009C22#1176328111yescharacteristic
1010C22#1176328811yescharacteristic
1011C22C2×#1058762411yescharacteristic
1012C22C22⋊Q8×D1711yescharacteristic
1013C22C2×#1058763211yescharacteristic
1014C22#1176331511yescharacteristic
1015C22C2×#1058757611yescharacteristic
1016C22#1176333611yescharacteristic
1017C22C2×#1058757411yescharacteristic
1018C22#1176336111yescharacteristic
1019C22#1176339411yescharacteristic
1020C22#1176340311yescharacteristic
1021C22#1176343411yescharacteristic
1022C22#1176343811yescharacteristic
1023C22#1176344111yescharacteristic
1024C22D4×C22⋊D1711yescharacteristic
1025C22#1176344611yescharacteristic
1026C22#1176344711yescharacteristic
1027C22#1176345011yescharacteristic
1028C22#1176345111yescharacteristic
1029C22#1176345311yescharacteristic
1030C22#1176345711yescharacteristic
1031C22#1176345811yescharacteristic
1032C22D4×Dic3411yescharacteristic
1033C22#1176348611yescharacteristic
1034C22#1176348611yescharacteristic
1035C22#1176350111yescharacteristic
1036C22#1176351611yescharacteristic
1037C22#1176351811yescharacteristic
1038C22#1176351811yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—42no—
1042C4—42no—
1043C4—81no—
1044C4—81no—
1045C4—344no—
1046C4—344no—
1047C4—682no—
1048C4—682no—
1049C4—682no—
1050C4—682no—
1051C4—682no—
1052C4—682no—
1053C2—28no—
1054C2C2×#1176270511yescharacteristic
1055C2#1453131611yescharacteristic
1056C2#1453151511yescharacteristic
1057C2D4×#6322511yescharacteristic
1058C2#1453168911yescharacteristic
1059C2#1453176011yescharacteristic
1060C2#1453177411yescharacteristic
1061C2#1453231611yescharacteristic
1062C2#1453233111yescharacteristic
1063C2#1453244711yescharacteristic
1064C2#1453245611yescharacteristic
1065C2#1453248511yescharacteristic
1066C2#1453292411yescharacteristic
1067C2#1453329111yescharacteristic
1068C2#1453379711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#385C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#385D17
hypocenterC17#14004
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#11762705C2semidirect
7. #14527047C2semidirect
8. #14527043C2semidirect
9. #14527036C2semidirect
10. #14527036C2semidirect
11. #14527015C2semidirect
12. #14527015C2semidirect
13. #14527013C2semidirect
29. #11762684C4semidirect
116. C2×C4⋊Dic17C2×C4semidirect
117. C2×C4⋊Dic17C2×C4semidirect
151. #10587502C2×C4semidirect
152. #10587502C2×C4semidirect
292. C22⋊C4×C17C4⋊C4semidirect
484. C22×C17#389semidirect
688. C17#14004semidirect
835. C22⋊C4#63225semidirect
1003. C22#11762705semidirect

Maximal subgroups

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

subgroupindex
C2×#117627052
C2×#117626842
C2×#117626822
C2×#117626672
C2×C22⋊C4×Dic172
C22×#105875022
#145270472
#145270432
#145270362
#145270152
#145270132
#145270062
C2×C17×#3852
#1400417