Finite Group Databasebeta

← #16959622

Subgroups — #16959622

Order 4352.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic34C211yesmaximal, characteristic, complemented
2C2×#11762721C211yesmaximal, characteristic
3C2×#11762684C211yesmaximal, characteristic
4C2×#11762681C211yesmaximal, characteristic
5C2×C22⋊C4×Dic17C211yesmaximal, characteristic
6#14527054C211yesmaximal, characteristic, complemented
7#14527048C211yesmaximal, characteristic, complemented
8#14527027C211yesmaximal, characteristic
9#14527021C211yesmaximal, characteristic
10#14527018C211yesmaximal, characteristic, complemented
11#14527018C211yesmaximal, characteristic, complemented
12#14527017C211yesmaximal, characteristic, complemented
13#14527015C211yesmaximal, characteristic, complemented
14#14527010C211yesmaximal, characteristic, complemented
15C17×#1437C211yesmaximal, characteristic
16C23×Dic34C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C2×C4×Dic34—24no—
19C2×C4×Dic34—24no—
20C2×C4×Dic34—24no—
21C22×C4⋊Dic17C2211yescharacteristic
22C22×C4⋊Dic17C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32#11762721C418yescomplemented
33#11762684—24no—
34#11762681—24no—
35C22⋊C4×Dic17—24no—
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
50C2×#10587502C2211yescharacteristic
51C22×C22⋊C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C42×C17C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×Dic17—22no—
66C23×Dic17—22no—
67C23×Dic17—22no—
68C23×Dic17—22no—
69C23×Dic17—22no—
70C23×Dic17—41no—
71C23×Dic17—41no—
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C22×Dic34—22no—
81C22×Dic34—22no—
82C22×Dic34—22no—
83C22×Dic34—22no—
84C22×Dic34—22no—
85C22×Dic34—22no—
86C22×Dic34C2×C414yescomplemented
87C2×C22⋊C4×C17—22no—
88C2×C22⋊C4×C17—22no—
89C2×C22⋊C4×C17—22no—
90C2×C22⋊C4×C17—22no—
91C2×C22⋊C4×C17—22no—
92C2×C22⋊C4×C17—22no—
93C2×C22⋊C4×C17—41no—
94C2×C22⋊C4×C17C2×C414yes—
95C2×C22⋊C4×C17Q814yescomplemented
96C2×C42×C17—22no—
97C2×C42×C17—22no—
98C2×C42×C17—22no—
99C2×C22⋊Dic17—22no—
100C2×C22⋊Dic17—22no—
101C2×C22⋊Dic17—22no—
102C2×C22⋊Dic17—22no—
103C2×C22⋊Dic17—22no—
104C2×C22⋊Dic17—22no—
105C2×C22⋊Dic17—41no—
106C2×C22⋊Dic17C2×C414yes—
107C2×C22⋊Dic17C2×C414yes—
108C2×C4⋊Dic17—22no—
109C2×C4⋊Dic17—22no—
110C2×C4⋊Dic17—22no—
111C2×C4⋊Dic17—22no—
112C2×C4⋊Dic17—41no—
113C2×C4⋊Dic17D414yes—
114C2×#63225—22no—
115C2×#63225—22no—
116C2×#63225—22no—
117C2×#63225—22no—
118C2×#63225—22no—
119C2×#63225—22no—
120C2×#63225—22no—
121C2×#63225—41no—
122C2×#63225D414yes—
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×Dic17D414yes—
132C4×Dic34—232no—
133C17×#95—22no—
134C17×#95—22no—
135C17×#95—41no—
136#10587502—22no—
137#10587502—22no—
138#10587502—22no—
139#10587502—22no—
140#10587502—22no—
141#10587502—22no—
142#10587502—22no—
143#10587502—22no—
144#10587502—22no—
145#10587502—41no—
146#10587502—41no—
147#10587502—41no—
148#10587502C2×C414yescomplemented
149#10587502C2×C414yescomplemented
150#10587502C2×C414yescomplemented
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×C17C22×C412yes—
164C24×C17C2×Q812yes—
165C24×C17#4112yes—
166C24×C17C2411yescharacteristic
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—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×C17C22×C412yes—
201C22×C4×C17C22×C412yes—
202C22×C4×C17C2×D412yes—
203C22×C4×C17C2×D412yes—
204C22×C4×C17C2×D412yes—
205C22×C4×C17C2×Q812yes—
206C22×C4×C17C2×Q812yes—
207C22×C4×C17#4112yes—
208C22×C4×C17#4112yes—
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—28no—
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—44no—
254C22×Dic17—44no—
255C22×Dic17—44no—
256C22×Dic17—44no—
257C22×Dic17—44no—
258C22×Dic17—44no—
259C22×Dic17C22×C412yes—
260C22×Dic17C22×C412yes—
261C22×Dic17C22×C412yes—
262C22×Dic17C22×C412yes—
263C22×Dic17C2×D412yes—
264C22×Dic17C2×D412yes—
265C22×Dic17C2×D412yes—
266C22×Dic17C2×D412yes—
267C22×Dic17C2×D412yes—
268C22×Dic17C2×D412yes—
269C22×Dic17#4112yes—
270C22×Dic17#4112yes—
271C22×Dic17#4112yes—
272C2×Dic34—28no—
273C2×Dic34—28no—
274C2×Dic34—28no—
275C2×Dic34—28no—
276C2×Dic34—28no—
277C2×Dic34—28no—
278C2×Dic34—28no—
279C22⋊C4×C17—28no—
280C22⋊C4×C17—28no—
281C22⋊C4×C17—44no—
282C42×C17—28no—
283C22⋊Dic17—28no—
284C22⋊Dic17—28no—
285C22⋊Dic17—44no—
286C4⋊Dic17—28no—
287C4⋊Dic17—44no—
288#63225—28no—
289#63225—28no—
290#63225—44no—
291C4×Dic17—28no—
292C4×Dic17—28no—
293C4×Dic17—44no—
294#14172—171nomaximal, Sylow
295C23×C17—22no—
296C23×C17—22no—
297C23×C17—22no—
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—41no—
314C23×C17—41no—
315C23×C17—41no—
316C23×C17—41no—
317C23×C17—41no—
318C23×C17—41no—
319C23×C17—41no—
320C23×C17—41no—
321C23×C17—41no—
322C23×C17—41no—
323C23×C17—41no—
324C23×C17—41no—
325C23×C17—41no—
326C23×C17—41no—
327C23×C17—41no—
328C23×C17—41no—
329C23×C17C4×Q814yescomplemented
330C23×C17C23×C411yescharacteristic
331C23×C17C22×D411yescharacteristic
332C23×C17C22×D411yescharacteristic
333C23×C17C22×D411yescharacteristic
334C23×C17C22×Q811yescharacteristic
335C23×C17C2×#4111yescharacteristic
336C23×C17C2×#4111yescharacteristic
337C23×C17C2×#4111yescharacteristic
338C23×C17C2×#4111yescharacteristic
339C23×C17C2×#4111yescharacteristic
340C23×C17C2×#4111yescharacteristic
341C23×C17H(5,𝔽2)11yescharacteristic
342C23×C17H(5,𝔽2)11yescharacteristic
343C23×C172−1+411yescharacteristic
344C23×C172−1+411yescharacteristic
345C2×C4×C17—22no—
346C2×C4×C17—22no—
347C2×C4×C17—22no—
348C2×C4×C17—22no—
349C2×C4×C17—22no—
350C2×C4×C17—22no—
351C2×C4×C17—22no—
352C2×C4×C17—22no—
353C2×C4×C17—22no—
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—41no—
367C2×C4×C17—41no—
368C2×C4×C17—41no—
369C2×C4×C17—41no—
370C2×C4×C17—41no—
371C2×C4×C17—41no—
372C2×C4×C17—41no—
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×C17C4×D414yes—
386C2×C4×C17C22⋊Q814yes—
387C2×Dic17—22no—
388C2×Dic17—22no—
389C2×Dic17—22no—
390C2×Dic17—22no—
391C2×Dic17—22no—
392C2×Dic17—22no—
393C2×Dic17—22no—
394C2×Dic17—22no—
395C2×Dic17—22no—
396C2×Dic17—22no—
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—416no—
418C2×Dic17—41no—
419C2×Dic17—41no—
420C2×Dic17—41no—
421C2×Dic17—41no—
422C2×Dic17—41no—
423C2×Dic17—41no—
424C2×Dic17—41no—
425C2×Dic17—41no—
426C2×Dic17—41no—
427C2×Dic17—41no—
428C2×Dic17—41no—
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×Dic17C4×D414yes—
442C2×Dic17C4×D414yes—
443C2×Dic17#12014yes—
444Dic34—232no—
445C22×C4×Q8—171no—
446C2×#393—171no—
447C2×#385—171no—
448C2×#385—171no—
449C2×C4×C22⋊C4—171no—
450#1446—171no—
451#1444—171no—
452#1439—171no—
453#1437—171no—
454#1437D1711yescharacteristic
455#1436—171no—
456#1436—171no—
457#1436—171no—
458#1436—171no—
459#1434—171no—
460C22×C17—24no—
461C22×C17—24no—
462C22×C17—24no—
463C22×C17—42no—
464C22×C17—42no—
465C22×C17—42no—
466C22×C17—42no—
467C22×C17—42no—
468C22×C17—42no—
469C22×C17—42no—
470C22×C17—42no—
471C22×C17—42no—
472C22×C17—42no—
473C22×C17—42no—
474C22×C17—42no—
475C22×C17C2×C4×D411yescharacteristic
476C22×C17C2×C4×D411yescharacteristic
477C22×C17C2×C4×D411yescharacteristic
478C22×C17C2×C4×Q811yescharacteristic
479C22×C17C4×#4111yescharacteristic
480C22×C17#52011yescharacteristic
481C22×C17#52011yescharacteristic
482C22×C17C2×#12011yescharacteristic
483C22×C17C2×C22⋊Q811yescharacteristic
484C22×C17#52511yescharacteristic
485C22×C17#52511yescharacteristic
486C22×C17#52511yescharacteristic
487C22×C17#52511yescharacteristic
488C22×C17#52911yescharacteristic
489C22×C17#53311yescharacteristic
490C22×C17#53511yescharacteristic
491C22×C17#53611yescharacteristic
492C22×C17#54211yescharacteristic
493C22×C17#54211yescharacteristic
494C22×C17#54611yescharacteristic
495C22×C17#54611yescharacteristic
496C22×C17#54611yescharacteristic
497C22×C17#54611yescharacteristic
498C22×C17#54811yescharacteristic
499C22×C17#54811yescharacteristic
500C22×C17D4×Q811yescharacteristic
501C22×C17D4×Q811yescharacteristic
502C22×C17#55211yescharacteristic
503C22×C17#55211yescharacteristic
504C22×C17#55411yescharacteristic
505C22×C17#55411yescharacteristic
506C22×C17#55611yescharacteristic
507C22×C17#55611yescharacteristic
508C22×C17#55911yescharacteristic
509C22×C17#55911yescharacteristic
510C4×C17—24no—
511C4×C17—24no—
512C4×C17—42no—
513C4×C17—42no—
514C4×C17—42no—
515C4×C17—81no—
516Dic17—24no—
517Dic17—24no—
518Dic17—24no—
519Dic17—42no—
520Dic17—42no—
521Dic17—42no—
522Dic17—42no—
523Dic17—81no—
524C23×Q8—171no—
525C24×C4—171no—
526C2×C4×Q8—344no—
527C2×C4×Q8—344no—
528C2×C4×Q8—344no—
529C22×C4⋊C4—171no—
530C22×C4⋊C4—171no—
531C22×C4⋊C4—171no—
532C22×C4⋊C4—171no—
533C22×C4⋊C4—171no—
534C22×C22⋊C4—171no—
535C22×C22⋊C4—171no—
536C22×C22⋊C4—171no—
537C22×C22⋊C4C2×D1711yescharacteristic
538C22×C22⋊C4C2×D1711yescharacteristic
539C22×C22⋊C4C2×D1711yescharacteristic
540C22×C42—171no—
541C22×C42—171no—
542C22×C42—171no—
543C22×C42C2×D1711yescharacteristic
544#393—178no—
545#385—344no—
546#385—344no—
547C4×C22⋊C4—344no—
548C2×#95—171no—
549C2×#95—171no—
550C2×#95—171no—
551C2×#95—171no—
552C2×#95—171no—
553C2×#95—171no—
554C2×#95—171no—
555C2×#95—171no—
556C2×#95—171no—
557C2×#95—171no—
558C2×#95—171no—
559C2×#95—171no—
560C2×#95—171no—
561C2×#95—171no—
562C2×#95—171no—
563C2×#95C2×D1711yescharacteristic
564C2×#95C2×D1711yescharacteristic
565C2×#95C2×D1711yescharacteristic
566C2×C17—44no—
567C2×C17C4×#12011yescharacteristic
568C2×C17C4×C22⋊Q811yescharacteristic
569C2×C17#232611yescharacteristic
570C2×C17#236011yescharacteristic
571C2×C17#236011yescharacteristic
572C2×C17#236711yescharacteristic
573C2×C17#236711yescharacteristic
574C2×C17#240411yescharacteristic
575C2×C17#240911yescharacteristic
576C2×C17#245811yescharacteristic
577C2×C17#245811yescharacteristic
578C2×C17#246511yescharacteristic
579C2×C17#246511yescharacteristic
580C2×C17#258011yescharacteristic
581C2×C17#259911yescharacteristic
582C25C22×D1711yescharacteristic
583C22×Q8—174no—
584C22×Q8—342no—
585C22×Q8—342no—
586C22×Q8—342no—
587C22×Q8—342no—
588C22×Q8—342no—
589C22×Q8—342no—
590C23×C4—171no—
591C23×C4—171no—
592C23×C4—171no—
593C23×C4—171no—
594C23×C4—171no—
595C23×C4—171no—
596C23×C4—171no—
597C23×C4—171no—
598C23×C4—342no—
599C23×C4—342no—
600C23×C4—342no—
601C23×C4—342no—
602C23×C4—342no—
603C23×C4—681no—
604C23×C4—681no—
605C23×C4C22×D1711yescharacteristic
606C23×C4C22×D1711yescharacteristic
607C23×C4C22×D1711yescharacteristic
608C23×C4C22×D1711yescharacteristic
609C23×C4C22×D1711yescharacteristic
610C23×C4C22×D1711yescharacteristic
611C4×Q8—3432no—
612C2×C4⋊C4—174no—
613C2×C4⋊C4—174no—
614C2×C4⋊C4—342no—
615C2×C4⋊C4—342no—
616C2×C4⋊C4—342no—
617C2×C4⋊C4—342no—
618C2×C4⋊C4—342no—
619C2×C4⋊C4—342no—
620C2×C4⋊C4—342no—
621C2×C4⋊C4—342no—
622C2×C4⋊C4—342no—
623C2×C4⋊C4—342no—
624C2×C4⋊C4—342no—
625C2×C4⋊C4—681no—
626C2×C4⋊C4—681no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—41no—
634C2×C22⋊C4—174no—
635C2×C22⋊C4—174no—
636C2×C22⋊C4—342no—
637C2×C22⋊C4—342no—
638C2×C22⋊C4—342no—
639C2×C22⋊C4—342no—
640C2×C22⋊C4—342no—
641C2×C22⋊C4—342no—
642C2×C22⋊C4—681no—
643C2×C22⋊C4Dic3414yescomplemented
644C2×C22⋊C4C4×D1714yes—
645C2×C42—22no—
646C2×C42—22no—
647C2×C42—22no—
648C2×C42—174no—
649C2×C42—342no—
650C2×C42—342no—
651C2×C42—342no—
652C2×C42—342no—
653C2×C42—342no—
654C2×C42—342no—
655C2×C42—681no—
656C2×C42—681no—
657#95—22no—
658#95—22no—
659#95—41no—
660#95—174no—
661#95—174no—
662#95—174no—
663#95—342no—
664#95—342no—
665#95—342no—
666#95—342no—
667#95—342no—
668#95—342no—
669#95—342no—
670#95—342no—
671#95—342no—
672#95—681no—
673#95—681no—
674#95—681no—
675C17#1417211yescharacteristic, complemented, Sylow
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24C2×Dic3412yes—
689C24C2×C4×D1712yes—
690C24#6325212yes—
691C24C23×D1711yescharacteristic
692C2×Q8—348no—
693C2×Q8—348no—
694C2×Q8—348no—
695C2×Q8—348no—
696C2×Q8—348no—
697C2×Q8—348no—
698C2×Q8—348no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
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—172no—
733C22×C4—172no—
734C22×C4—172no—
735C22×C4—172no—
736C22×C4—172no—
737C22×C4—172no—
738C22×C4—172no—
739C22×C4—172no—
740C22×C4—172no—
741C22×C4—172no—
742C22×C4—172no—
743C22×C4—172no—
744C22×C4—172no—
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—341no—
757C22×C4—348no—
758C22×C4—341no—
759C22×C4—341no—
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—684no—
790C22×C4—684no—
791C22×C4—684no—
792C22×C4—684no—
793C22×C4—684no—
794C22×C4—684no—
795C22×C4C2×Dic3412yes—
796C22×C4C2×Dic3412yes—
797C22×C4C2×C4×D1712yes—
798C22×C4C2×C4×D1712yes—
799C22×C4D4×D1712yes—
800C22×C4D4×D1712yes—
801C22×C4D4×D1712yes—
802C22×C4#6325412yes—
803C22×C4#6325412yes—
804C4⋊C4—348no—
805C4⋊C4—348no—
806C4⋊C4—348no—
807C4⋊C4—684no—
808C4⋊C4—684no—
809C22⋊C4—28no—
810C22⋊C4—28no—
811C22⋊C4—44no—
812C22⋊C4—348no—
813C22⋊C4—348no—
814C22⋊C4—684no—
815C42—28no—
816C42—348no—
817C42—348no—
818C42—684no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23C4×Dic3414yescomplemented
854C23C22×Dic3411yescharacteristic
855C23C22×C4×D1711yescharacteristic
856C23C2×#6325211yescharacteristic
857C23C2×D4×D1711yescharacteristic
858C23C2×D4×D1711yescharacteristic
859C23C2×D4×D1711yescharacteristic
860C23C2×#6325411yescharacteristic
861C23C2×#6325411yescharacteristic
862C23#1058769111yescharacteristic
863C23#41×D1711yescharacteristic
864C23#41×D1711yescharacteristic
865C23#41×D1711yescharacteristic
866C23#1058769611yescharacteristic
867C23#1058769711yescharacteristic
868C23#1058769711yescharacteristic
869Q8—3432no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—174no—
911C2×C4—174no—
912C2×C4—174no—
913C2×C4—342no—
914C2×C4—342no—
915C2×C4—342no—
916C2×C4—342no—
917C2×C4—342no—
918C2×C4—342no—
919C2×C4—342no—
920C2×C4—342no—
921C2×C4—342no—
922C2×C4—342no—
923C2×C4—342no—
924C2×C4—342no—
925C2×C4—342no—
926C2×C4—342no—
927C2×C4—342no—
928C2×C4—342no—
929C2×C4—342no—
930C2×C4—342no—
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—6816no—
944C2×C4—681no—
945C2×C4—681no—
946C2×C4—681no—
947C2×C4—681no—
948C2×C4—681no—
949C2×C4—681no—
950C2×C4—681no—
951C2×C4—681no—
952C2×C4—681no—
953C2×C4—681no—
954C2×C4—681no—
955C2×C4—681no—
956C2×C4—681no—
957C2×C4—681no—
958C2×C4—681no—
959C2×C4—681no—
960C2×C4—681no—
961C2×C4—681no—
962C2×C4—681no—
963C2×C4—681no—
964C2×C4—681no—
965C2×C4—681no—
966C2×C4—681no—
967C2×C4#1058756414yes—
968C2×C4#1058756714yes—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22C4×D4×D1711yescharacteristic
985C22C4×D4×D1711yescharacteristic
986C22C2×#1058756711yescharacteristic
987C22C2×C4×Dic3411yescharacteristic
988C22C4×#6325411yescharacteristic
989C22#1176328811yescharacteristic
990C22#1176328911yescharacteristic
991C22#120×D1711yescharacteristic
992C22C2×#1058756411yescharacteristic
993C22#1176331711yescharacteristic
994C22#1176331811yescharacteristic
995C22#1176331911yescharacteristic
996C22#1176331911yescharacteristic
997C22#1176333911yescharacteristic
998C22#1176336211yescharacteristic
999C22#1176337511yescharacteristic
1000C22#1176338111yescharacteristic
1001C22#1176342311yescharacteristic
1002C22#1176342511yescharacteristic
1003C22#1176344911yescharacteristic
1004C22#1176345111yescharacteristic
1005C22#1176345511yescharacteristic
1006C22#1176345611yescharacteristic
1007C22#1176346511yescharacteristic
1008C22#1176346511yescharacteristic
1009C22D4×Dic3411yescharacteristic
1010C22D4×Dic3411yescharacteristic
1011C22#1176349211yescharacteristic
1012C22#1176349911yescharacteristic
1013C22#1176351611yescharacteristic
1014C22#1176351811yescharacteristic
1015C22#1176352611yescharacteristic
1016C22#1176352811yescharacteristic
1017C22#1176354111yescharacteristic
1018C22#1176354511yescharacteristic
1019C4—24no—
1020C4—24no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—81no—
1025C4—344no—
1026C4—344no—
1027C4—344no—
1028C4—682no—
1029C4—682no—
1030C4—682no—
1031C4—682no—
1032C4—1361no—
1033C2—44no—
1034C2#1453128911yescharacteristic
1035C2C4×#1058756411yescharacteristic
1036C2#1453149311yescharacteristic
1037C2#1453178711yescharacteristic
1038C2#1453179011yescharacteristic
1039C2#1453185411yescharacteristic
1040C2#1453185811yescharacteristic
1041C2#1453210111yescharacteristic
1042C2#1453214611yescharacteristic
1043C2#1453270311yescharacteristic
1044C2#1453271111yescharacteristic
1045C2#1453280211yescharacteristic
1046C2#1453281011yescharacteristic
1047C2#1453414011yescharacteristic
1048C2#1453435811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1437C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenter#1437D17
hypocenterC17#14172
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic34C2semidirect
6. #14527054C2semidirect
7. #14527048C2semidirect
10. #14527018C2semidirect
11. #14527018C2semidirect
12. #14527017C2semidirect
13. #14527015C2semidirect
14. #14527010C2semidirect
32. #11762721C4semidirect
86. C22×Dic34C2×C4semidirect
95. C2×C22⋊C4×C17Q8semidirect
148. #10587502C2×C4semidirect
149. #10587502C2×C4semidirect
150. #10587502C2×C4semidirect
329. C23×C17C4×Q8semidirect
643. C2×C22⋊C4Dic34semidirect
675. C17#14172semidirect
853. C23C4×Dic34semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic342
C2×#117627212
C2×#117626842
C2×#117626812
C2×C22⋊C4×Dic172
#145270542
#145270482
#145270272
#145270212
#145270182
#145270172
#145270152
#145270102
C17×#14372
#1417217