Finite Group Databasebeta

← #16955829

Subgroups — #16955829

Order 4352.

2298 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×#11762683C211yesmaximal, characteristic
2C2×#11762680C211yesmaximal, characteristic
3C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
4C2×C4×#63227C211yesmaximal, characteristic
5C2×#11762656C211yesmaximal, characteristic
6C2×#11762656C211yesmaximal, characteristic
7C2×#95×D17C211yesmaximal, characteristic
8#14527019C211yesmaximal, characteristic, complemented
9#14527018C211yesmaximal, characteristic, complemented
10#14527015C211yesmaximal, characteristic, complemented
11#14527012C211yesmaximal, characteristic, complemented
12#14527009C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic
14C4×#10587502C211yesmaximal, characteristic, complemented
15C17×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31#11762683C418yescomplemented
32#11762680C418yescomplemented
33C4⋊C4×Dic17—24no—
34C4×#63227—24no—
35#11762656—24no—
36#11762656C418yescomplemented
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
50#95×D17—24no—
51C22×C4⋊C4×C17C2211yescharacteristic
52C22×C42×C17C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C24×D17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C22×C4×D17—22no—
74C22×C4×D17—22no—
75C22×C4×D17—22no—
76C22×C4×D17—22no—
77C22×C4×D17—22no—
78C22×C4×D17—22no—
79C22×C4×D17—22no—
80C22×C4×D17—22no—
81C22×C4×D17—22no—
82C22×C4×D17—22no—
83C22×C4×D17—22no—
84C22×C4×D17—22no—
85C22×C4×D17—41no—
86C22×C4×D17—41no—
87C22×C4×D17—41no—
88C22×C4×D17—41no—
89C22×C4×D17—41no—
90C22×C4×D17—41no—
91C22×C4×D17C2×C414yes—
92C22×C4×D17C2×C414yes—
93C22×C4×D17C2×C414yes—
94C2×C4⋊C4×C17—22no—
95C2×C4⋊C4×C17—22no—
96C2×C4⋊C4×C17C2×C414yescomplemented
97C2×C42×C17—22no—
98C2×C42×C17—22no—
99C2×C42×C17—41no—
100C2×#63227—22no—
101C2×#63227—22no—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227C2×C414yes—
105C2×#63227C2×C414yes—
106C2×#63227C2×C414yes—
107C2×#63227C2×C414yes—
108C2×#63227C2×C414yes—
109C2×#63227C2×C414yes—
110C2×#63227D414yes—
111C2×#63227Q814yes—
112C2×C4⋊Dic17—22no—
113C2×C4⋊Dic17—22no—
114C2×C4⋊Dic17C2×C414yescomplemented
115C2×#63225—41no—
116C2×#63225—41no—
117C2×#63225—41no—
118C2×#63225—41no—
119C2×#63225C2×C414yescomplemented
120C2×#63225C2×C414yescomplemented
121C2×C4×Dic17—22no—
122C2×C4×Dic17—22no—
123C2×C4×Dic17—22no—
124C2×C4×Dic17—22no—
125C2×C4×Dic17—22no—
126C2×C4×Dic17—22no—
127C2×C4×Dic17—22no—
128C2×C4×Dic17—22no—
129C2×C4×Dic17—41no—
130C2×C4×Dic17—41no—
131C2×C4×Dic17—41no—
132C2×C4×Dic17—41no—
133C2×C4×Dic17—41no—
134C2×C4×Dic17C2×C414yescomplemented
135C2×C4×Dic17C2×C414yescomplemented
136C17×#95—22no—
137C17×#95—22no—
138C17×#95—41no—
139C17×#95C2×C414yescomplemented
140C17×#95C2×C414yescomplemented
141#10587502—22no—
142#10587502—22no—
143#10587502—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—22no—
148#10587502—41no—
149#10587502C2×C414yescomplemented
150#10587502C2×C414yescomplemented
151#10587502C2×C414yescomplemented
152#10587502C2×C414yescomplemented
153#10587502D414yes—
154C24×C17C2411yescharacteristic
155C23×D17—21no—
156C23×D17—21no—
157C23×D17—21no—
158C23×D17—21no—
159C23×D17—21no—
160C23×D17—21no—
161C23×D17—21no—
162C23×D17—21no—
163C23×D17C22×C412yes—
164C23×D17C22×C412yes—
165C23×D17C22×C412yes—
166C23×D17C2×D412yes—
167C23×D17C2×Q812yes—
168C23×D17#4112yes—
169C23×D17#4112yes—
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—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×C17C22×C412yes—
207C22×C4×C17C22×C412yes—
208C22×C4×C17C22×C412yes—
209C22×C4×C17C22×C412yes—
210C22×C4×C17C22×C412yes—
211C22×C4×C17C22×C412yes—
212C22×C4×C17C22×C412yes—
213C22×C4×C17C22×C412yes—
214C22×C4×C17C22×C412yes—
215C22×C4×C17C2×D412yes—
216C22×C4×C17C2×D412yes—
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—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×Dic17C22×C412yes—
254C22×Dic17C22×C412yes—
255C22×Dic17C22×C412yes—
256C22×Dic17C22×C412yes—
257C22×Dic17C22×C412yes—
258C22×Dic17C22×C412yes—
259C22×Dic17C22×C412yes—
260C22×Dic17C22×C412yes—
261C22×Dic17C22×C412yes—
262C22×Dic17C2×D412yes—
263C22×Dic17C2×D412yes—
264C22×Dic17C2×D412yes—
265C22×Dic17C2×Q812yes—
266C22×Dic17#4112yes—
267C22×Dic17#4112yes—
268C2×C4×D17—28no—
269C2×C4×D17—28no—
270C2×C4×D17—28no—
271C2×C4×D17—28no—
272C2×C4×D17—28no—
273C2×C4×D17—28no—
274C2×C4×D17—44no—
275C2×C4×D17—44no—
276C2×C4×D17—44no—
277C2×C4×D17—44no—
278C2×C4×D17—44no—
279C2×C4×D17—44no—
280C2×C4×D17—44no—
281C2×C4×D17—44no—
282C2×C4×D17—44no—
283C2×C4×D17—44no—
284C2×C4×D17—44no—
285C2×C4×D17—44no—
286C2×C4×D17—44no—
287C2×C4×D17—44no—
288C2×C4×D17—44no—
289C4⋊C4×C17—28no—
290C42×C17—44no—
291#63227—28no—
292#63227—28no—
293#63227C42116yescomplemented
294#63227C4⋊C4116yescomplemented
295C4⋊Dic17—28no—
296#63225—44no—
297#63225—44no—
298C4×Dic17—28no—
299C4×Dic17—44no—
300C4×Dic17—44no—
301C4×Dic17—44no—
302C4×Dic17—44no—
303#13814—171nomaximal, Sylow
304C23×C17C23×C411yescharacteristic
305C23×C17C23×C411yescharacteristic
306C23×C17C23×C411yescharacteristic
307C23×C17C22×D411yescharacteristic
308C23×C17C22×D411yescharacteristic
309C23×C17C22×Q811yescharacteristic
310C23×C17C2×#4111yescharacteristic
311C23×C17C2×#4111yescharacteristic
312C23×C17C2×#4111yescharacteristic
313C23×C17C2×#4111yescharacteristic
314C23×C17C2×#4111yescharacteristic
315C23×C17H(5,𝔽2)11yescharacteristic
316C23×C17H(5,𝔽2)11yescharacteristic
317C23×C17H(5,𝔽2)11yescharacteristic
318C23×C172−1+411yescharacteristic
319C22×D17—22no—
320C22×D17—22no—
321C22×D17—22no—
322C22×D17—22no—
323C22×D17—22no—
324C22×D17—22no—
325C22×D17—22no—
326C22×D17—22no—
327C22×D17—22no—
328C22×D17—22no—
329C22×D17—22no—
330C22×D17—22no—
331C22×D17—22no—
332C22×D17—22no—
333C22×D17—22no—
334C22×D17—22no—
335C22×D17—22no—
336C22×D17—22no—
337C22×D17—22no—
338C22×D17—22no—
339C22×D17—22no—
340C22×D17—22no—
341C22×D17—22no—
342C22×D17—22no—
343C22×D17—22no—
344C22×D17—22no—
345C22×D17—22no—
346C22×D17—22no—
347C22×D17C2×C4214yes—
348C22×D17C2×C4⋊C414yes—
349C22×D17#11714yes—
350C22×D17C4×D414yes—
351C22×D17C4×D414yes—
352C22×D17C4×Q814yes—
353C22×D17C4×Q814yes—
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—22no—
373C2×C4×C17—22no—
374C2×C4×C17—22no—
375C2×C4×C17—22no—
376C2×C4×C17—22no—
377C2×C4×C17—22no—
378C2×C4×C17—22no—
379C2×C4×C17—22no—
380C2×C4×C17—22no—
381C2×C4×C17—22no—
382C2×C4×C17—22no—
383C2×C4×C17—22no—
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×C17—41no—
396C2×C4×C17—41no—
397C2×C4×C17—41no—
398C2×C4×C17—41no—
399C2×C4×C17—41no—
400C2×C4×C17C2×C4214yes—
401C2×C4×C17C2×C4⋊C414yes—
402C2×C4×C17C4×D414yes—
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—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—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×Dic17C2×C4214yes—
449C2×Dic17C2×C4⋊C414yes—
450C2×Dic17C4×D414yes—
451C2×Dic17C4×D414yes—
452C4×D17—416no—
453C4×D17—416no—
454C4×D17—416no—
455C2×#385—171no—
456C2×#385—171no—
457C2×C4×C4⋊C4—171no—
458C2×C4×C22⋊C4—171no—
459C2×C4×C22⋊C4—171no—
460C2×C4×C22⋊C4—171no—
461C22×#95—171no—
462#1436—171no—
463#1436—171no—
464#1436—171no—
465#1436D1711yescharacteristic, complemented
466C4⋊#95—171no—
467#1434—171no—
468C22⋊#95—171no—
469C4×#95—171no—
470C22×C17C22×C4211yescharacteristic
471C22×C17C22×C4⋊C411yescharacteristic
472C22×C17C2×#11711yescharacteristic
473C22×C17C2×C4×D411yescharacteristic
474C22×C17C2×C4×D411yescharacteristic
475C22×C17C2×C4×D411yescharacteristic
476C22×C17C2×C4×D411yescharacteristic
477C22×C17C2×C4×D411yescharacteristic
478C22×C17C2×C4×Q811yescharacteristic
479C22×C17C2×C4×Q811yescharacteristic
480C22×C17C4×#4111yescharacteristic
481C22×C17C4×#4111yescharacteristic
482C22×C17C4×#4111yescharacteristic
483C22×C17#51811yescharacteristic
484C22×C17#51811yescharacteristic
485C22×C17#51811yescharacteristic
486C22×C17#52011yescharacteristic
487C22×C17#52011yescharacteristic
488C22×C17#52011yescharacteristic
489C22×C17D4211yescharacteristic
490C22×C17#54611yescharacteristic
491C22×C17#54611yescharacteristic
492C22×C17#54611yescharacteristic
493C22×C17#54611yescharacteristic
494C22×C17#54711yescharacteristic
495C22×C17D4×Q811yescharacteristic
496C22×C17#55111yescharacteristic
497C22×C17#55111yescharacteristic
498C22×C17#55111yescharacteristic
499C22×C17#55111yescharacteristic
500C22×C17#55211yescharacteristic
501C22×C17#55211yescharacteristic
502C22×C17#55411yescharacteristic
503C22×C17#55411yescharacteristic
504C22×C17#55411yescharacteristic
505C2×D17—24no—
506C2×D17—24no—
507C2×D17—24no—
508C2×D17—24no—
509C2×D17—24no—
510C2×D17—24no—
511C2×D17—24no—
512C2×D17—24no—
513C2×D17—24no—
514C2×D17—24no—
515C2×D17—24no—
516C2×D17—24no—
517C2×D17—24no—
518C2×D17—24no—
519C2×D17C4×C4⋊C418yescomplemented
520C4×C17—24no—
521C4×C17—24no—
522C4×C17—24no—
523C4×C17—42no—
524C4×C17—42no—
525C4×C17—42no—
526C4×C17—42no—
527Dic17—24no—
528Dic17—24no—
529Dic17—24no—
530Dic17—24no—
531Dic17—42no—
532Dic17—42no—
533Dic17—42no—
534C24×C4—171no—
535C24×C4—171no—
536C24×C4—171no—
537C22×C4⋊C4—171no—
538C22×C4⋊C4—171no—
539C22×C4⋊C4—171no—
540C22×C4⋊C4C2×D1711yescharacteristic
541C22×C22⋊C4—171no—
542C22×C22⋊C4—171no—
543C22×C22⋊C4—171no—
544C22×C22⋊C4—171no—
545C22×C42—171no—
546C22×C42—171no—
547C22×C42—171no—
548C22×C42—171no—
549C22×C42—171no—
550C22×C42C2×D1711yescharacteristic
551#385—178no—
552#385—178no—
553C4×C4⋊C4—344no—
554C4×C22⋊C4—178no—
555C4×C22⋊C4—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—344no—
571C2×#95C2×D1711yescharacteristic
572C2×#95C2×D1711yescharacteristic
573C2×#95C2×D1711yescharacteristic
574C2×#95C2×D1711yescharacteristic
575C2×#95C2×D1711yescharacteristic
576C2×C17C2×C4×C4⋊C411yescharacteristic
577C2×C17C42×D411yescharacteristic
578C2×C17#227511yescharacteristic
579C2×C17#234211yescharacteristic
580C2×C17#234311yescharacteristic
581C2×C17D4×C4⋊C411yescharacteristic
582C2×C17#234911yescharacteristic
583C2×C17#235811yescharacteristic
584C2×C17#235811yescharacteristic
585C2×C17#235911yescharacteristic
586C2×C17#235911yescharacteristic
587C2×C17#236011yescharacteristic
588C2×C17#236011yescharacteristic
589C2×C17#236811yescharacteristic
590C2×C17#236811yescharacteristic
591D17—28no—
592C25—171no—
593C23×C4—171no—
594C23×C4—171no—
595C23×C4—171no—
596C23×C4—171no—
597C23×C4—171no—
598C23×C4—171no—
599C23×C4—171no—
600C23×C4—174no—
601C23×C4—174no—
602C23×C4—174no—
603C23×C4—342no—
604C23×C4—342no—
605C23×C4—342no—
606C23×C4—342no—
607C23×C4—342no—
608C23×C4—342no—
609C23×C4—342no—
610C23×C4—342no—
611C23×C4—342no—
612C23×C4—342no—
613C23×C4—342no—
614C23×C4—342no—
615C23×C4—681no—
616C23×C4—681no—
617C23×C4—681no—
618C23×C4—681no—
619C23×C4—681no—
620C23×C4—681no—
621C23×C4C22×D1711yescharacteristic
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—174no—
631C2×C4⋊C4—174no—
632C2×C4⋊C4—174no—
633C2×C4⋊C4—342no—
634C2×C4⋊C4—342no—
635C2×C4⋊C4—681no—
636C2×C4⋊C4—681no—
637C2×C4⋊C4—681no—
638C2×C4⋊C4—681no—
639C2×C4⋊C4C4×D1714yescomplemented
640C2×C22⋊C4—174no—
641C2×C22⋊C4—174no—
642C2×C22⋊C4—174no—
643C2×C22⋊C4—174no—
644C2×C22⋊C4—174no—
645C2×C22⋊C4—174no—
646C2×C22⋊C4—174no—
647C2×C22⋊C4—174no—
648C2×C22⋊C4—342no—
649C2×C22⋊C4—342no—
650C2×C22⋊C4—342no—
651C2×C22⋊C4—342no—
652C2×C42—22no—
653C2×C42—22no—
654C2×C42—41no—
655C2×C42—174no—
656C2×C42—174no—
657C2×C42—342no—
658C2×C42—342no—
659C2×C42—342no—
660C2×C42—342no—
661C2×C42—342no—
662C2×C42—342no—
663C2×C42—342no—
664C2×C42—342no—
665C2×C42—681no—
666C2×C42—681no—
667C2×C42—681no—
668C2×C42—681no—
669C2×C42—681no—
670#95—22no—
671#95—22no—
672#95—41no—
673#95—174no—
674#95—174no—
675#95—174no—
676#95—174no—
677#95—174no—
678#95—342no—
679#95—342no—
680#95—342no—
681#95—342no—
682#95—342no—
683#95—342no—
684#95—342no—
685#95—681no—
686#95C4×D1714yescomplemented
687#95C4×D1714yescomplemented
688C17#1381411yescharacteristic, complemented, Sylow
689C24—172no—
690C24—172no—
691C24—172no—
692C24—172no—
693C24—172no—
694C24—172no—
695C24—172no—
696C24—341no—
697C24—341no—
698C24—341no—
699C24—341no—
700C24—341no—
701C24—341no—
702C24—341no—
703C24—341no—
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—21no—
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—21no—
741C22×C4—172no—
742C22×C4—172no—
743C22×C4—172no—
744C22×C4—172no—
745C22×C4—172no—
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—348no—
757C22×C4—348no—
758C22×C4—348no—
759C22×C4—348no—
760C22×C4—348no—
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—348no—
796C22×C4—684no—
797C22×C4—684no—
798C22×C4—684no—
799C22×C4—684no—
800C22×C4—684no—
801C22×C4—684no—
802C22×C4—684no—
803C22×C4—684no—
804C22×C4—684no—
805C22×C4—684no—
806C22×C4—684no—
807C22×C4—684no—
808C22×C4—684no—
809C22×C4—684no—
810C22×C4—684no—
811C22×C4C2×C4×D1712yes—
812C22×C4C2×C4×D1712yes—
813C22×C4C2×C4×D1712yes—
814C22×C4C2×C4×D1712yes—
815C22×C4C2×C4×D1712yes—
816C22×C4C2×C4×D1712yes—
817C22×C4C2×C4×D1712yes—
818C22×C4C2×C4×D1712yes—
819C22×C4C2×C4×D1712yes—
820C22×C4D4×D1712yes—
821C22×C4D4×D1712yes—
822C22×C4#6325412yes—
823C22×C4Q8×D1712yes—
824C4⋊C4—28no—
825C4⋊C4—348no—
826C4⋊C4—684no—
827C4⋊C4—684no—
828C22⋊C4—1716no—
829C22⋊C4—1716no—
830C22⋊C4—348no—
831C22⋊C4—348no—
832C42—44no—
833C42—348no—
834C42—684no—
835C42—684no—
836C42—684no—
837C42—684no—
838C23—174no—
839C23—174no—
840C23—174no—
841C23—174no—
842C23—174no—
843C23—174no—
844C23—174no—
845C23—342no—
846C23—342no—
847C23—342no—
848C23—342no—
849C23—342no—
850C23—342no—
851C23—342no—
852C23—342no—
853C23—342no—
854C23—342no—
855C23—342no—
856C23—342no—
857C23—342no—
858C23—342no—
859C23—342no—
860C23—342no—
861C23—342no—
862C23—342no—
863C23—342no—
864C23—342no—
865C23—342no—
866C23—342no—
867C23—342no—
868C23—342no—
869C23—342no—
870C23—342no—
871C23—342no—
872C23—342no—
873C23C22×C4×D1711yescharacteristic
874C23C22×C4×D1711yescharacteristic
875C23C22×C4×D1711yescharacteristic
876C23C2×D4×D1711yescharacteristic
877C23C2×D4×D1711yescharacteristic
878C23C2×#6325411yescharacteristic
879C23#1058769111yescharacteristic
880C23C2×Q8×D1711yescharacteristic
881C23#1058769411yescharacteristic
882C23#41×D1711yescharacteristic
883C23#41×D1711yescharacteristic
884C23#41×D1711yescharacteristic
885C23#41×D1711yescharacteristic
886C23#1058769611yescharacteristic
887C23#1058769611yescharacteristic
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—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
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—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—174no—
935C2×C4—174no—
936C2×C4—174no—
937C2×C4—174no—
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—342no—
962C2×C4—342no—
963C2×C4—342no—
964C2×C4—342no—
965C2×C4—342no—
966C2×C4—342no—
967C2×C4—342no—
968C2×C4—342no—
969C2×C4—342no—
970C2×C4—342no—
971C2×C4—6816no—
972C2×C4—6816no—
973C2×C4—6816no—
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×C4C42×D1714yes—
987C2×C4#1058756714yes—
988C2×C4C4⋊C4×D1714yes—
989C22—178no—
990C22—344no—
991C22—344no—
992C22—344no—
993C22—344no—
994C22—344no—
995C22—344no—
996C22—344no—
997C22—344no—
998C22—344no—
999C22—344no—
1000C22—344no—
1001C22—344no—
1002C22—344no—
1003C22—344no—
1004C22C2×C42×D1711yescharacteristic
1005C22C2×C4⋊C4×D1711yescharacteristic
1006C22#117×D1711yescharacteristic
1007C22C4×D4×D1711yescharacteristic
1008C22C4×D4×D1711yescharacteristic
1009C22C4×D4×D1711yescharacteristic
1010C22C4×D4×D1711yescharacteristic
1011C22C2×#1058756711yescharacteristic
1012C22C4×Q8×D1711yescharacteristic
1013C22C4×Q8×D1711yescharacteristic
1014C22C4×#6325411yescharacteristic
1015C22C4×#6325411yescharacteristic
1016C22#1176327711yescharacteristic
1017C22#1176328111yescharacteristic
1018C22#1176328111yescharacteristic
1019C22#1176328311yescharacteristic
1020C22#1176329011yescharacteristic
1021C22#1176329111yescharacteristic
1022C22#1176329111yescharacteristic
1023C22#1176344311yescharacteristic
1024C22#1176344611yescharacteristic
1025C22#1176344811yescharacteristic
1026C22#1176345111yescharacteristic
1027C22#1176345211yescharacteristic
1028C22#1176346111yescharacteristic
1029C22#1176347411yescharacteristic
1030C22#1176348211yescharacteristic
1031C22#1176348411yescharacteristic
1032C22#1176348411yescharacteristic
1033C22#1176348711yescharacteristic
1034C22#1176349111yescharacteristic
1035C22#1176349311yescharacteristic
1036C22#1176351311yescharacteristic
1037C22#1176351511yescharacteristic
1038C22#1176351711yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—344no—
1047C4—344no—
1048C4—344no—
1049C4—344no—
1050C4—682no—
1051C4—682no—
1052C4—682no—
1053C2—348no—
1054C2C4×C4⋊C4×D1711yescharacteristic
1055C2C4×#1058756711yescharacteristic
1056C2#1453114411yescharacteristic
1057C2#1453163211yescharacteristic
1058C2#1453163911yescharacteristic
1059C2#1453168511yescharacteristic
1060C2#1453169011yescharacteristic
1061C2#1453176211yescharacteristic
1062C2#1453176411yescharacteristic
1063C2#1453176911yescharacteristic
1064C2#1453177911yescharacteristic
1065C2#1453178611yescharacteristic
1066C2#1453179411yescharacteristic
1067C2#1453186111yescharacteristic
1068C2#1453186611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC17×#1436C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenter#1436D17
hypocenterC17#13814
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic17C2semidirect
8. #14527019C2semidirect
9. #14527018C2semidirect
10. #14527015C2semidirect
11. #14527012C2semidirect
12. #14527009C2semidirect
14. C4×#10587502C2semidirect
15. C17×#1436C2semidirect
31. #11762683C4semidirect
32. #11762680C4semidirect
36. #11762656C4semidirect
96. C2×C4⋊C4×C17C2×C4semidirect
114. C2×C4⋊Dic17C2×C4semidirect
119. C2×#63225C2×C4semidirect
120. C2×#63225C2×C4semidirect
134. C2×C4×Dic17C2×C4semidirect
135. C2×C4×Dic17C2×C4semidirect
139. C17×#95C2×C4semidirect
140. C17×#95C2×C4semidirect
149. #10587502C2×C4semidirect
150. #10587502C2×C4semidirect
151. #10587502C2×C4semidirect
152. #10587502C2×C4semidirect
293. #63227C42semidirect
294. #63227C4⋊C4semidirect
465. #1436D17semidirect
519. C2×D17C4×C4⋊C4semidirect
639. C2×C4⋊C4C4×D17semidirect
686. #95C4×D17semidirect
687. #95C4×D17semidirect
688. C17#13814semidirect

Maximal subgroups

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

subgroupindex
C2×#117626832
C2×#117626802
C2×C4⋊C4×Dic172
C2×C4×#632272
C2×#117626562
C2×#95×D172
#145270192
#145270182
#145270152
#145270122
#145270092
#145270052
C4×#105875022
C17×#14362
#1381417